Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.78695 | 1.03170 | 0.515849 | − | 0.856680i | \(-0.327477\pi\) | ||||
0.515849 | + | 0.856680i | \(0.327477\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.35040 | −1.26633 | −0.633166 | − | 0.774016i | \(-0.718245\pi\) | ||||
−0.633166 | + | 0.774016i | \(0.718245\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.193201 | 0.0644003 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.67045 | 1.10668 | 0.553341 | − | 0.832955i | \(-0.313353\pi\) | ||||
0.553341 | + | 0.832955i | \(0.313353\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.18268 | −0.605366 | −0.302683 | − | 0.953091i | \(-0.597882\pi\) | ||||
−0.302683 | + | 0.953091i | \(0.597882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.78695 | −0.461389 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.43273 | 0.590023 | 0.295011 | − | 0.955494i | \(-0.404677\pi\) | ||||
0.295011 | + | 0.955494i | \(0.404677\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.922582 | 0.211655 | 0.105827 | − | 0.994385i | \(-0.466251\pi\) | ||||
0.105827 | + | 0.994385i | \(0.466251\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.98700 | −1.30647 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.388193 | −0.0809438 | −0.0404719 | − | 0.999181i | \(-0.512886\pi\) | ||||
−0.0404719 | + | 0.999181i | \(0.512886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.01562 | −0.965256 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.57159 | −0.663228 | −0.331614 | − | 0.943415i | \(-0.607593\pi\) | ||||
−0.331614 | + | 0.943415i | \(0.607593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.21772 | 0.757525 | 0.378762 | − | 0.925494i | \(-0.376350\pi\) | ||||
0.378762 | + | 0.925494i | \(0.376350\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.55892 | 1.14176 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.35040 | 0.566321 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.05508 | −1.15985 | −0.579924 | − | 0.814671i | \(-0.696918\pi\) | ||||
−0.579924 | + | 0.814671i | \(0.696918\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.90034 | −0.624555 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.95489 | 1.24234 | 0.621172 | − | 0.783674i | \(-0.286657\pi\) | ||||
0.621172 | + | 0.783674i | \(0.286657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.97665 | 1.36893 | 0.684463 | − | 0.729047i | \(-0.260037\pi\) | ||||
0.684463 | + | 0.729047i | \(0.260037\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.193201 | −0.0288007 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.141117 | 0.0205840 | 0.0102920 | − | 0.999947i | \(-0.496724\pi\) | ||||
0.0102920 | + | 0.999947i | \(0.496724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.22517 | 0.603595 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.34717 | 0.608725 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4249 | 1.84405 | 0.922025 | − | 0.387130i | \(-0.126533\pi\) | ||||
0.922025 | + | 0.387130i | \(0.126533\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.67045 | −0.494923 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.64861 | 0.218364 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.54689 | −1.11271 | −0.556355 | − | 0.830944i | \(-0.687801\pi\) | ||||
−0.556355 | + | 0.830944i | \(0.687801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.52029 | −0.706801 | −0.353400 | − | 0.935472i | \(-0.614975\pi\) | ||||
−0.353400 | + | 0.935472i | \(0.614975\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.647300 | −0.0815521 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.18268 | 0.270728 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.45721 | −0.178027 | −0.0890133 | − | 0.996030i | \(-0.528371\pi\) | ||||
−0.0890133 | + | 0.996030i | \(0.528371\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.693682 | −0.0835095 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.463799 | −0.0550428 | −0.0275214 | − | 0.999621i | \(-0.508761\pi\) | ||||
−0.0275214 | + | 0.999621i | \(0.508761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.01284 | −0.703750 | −0.351875 | − | 0.936047i | \(-0.614456\pi\) | ||||
−0.351875 | + | 0.936047i | \(0.614456\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.78695 | 0.206340 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.2975 | −1.40143 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.8055 | −1.89076 | −0.945382 | − | 0.325963i | \(-0.894311\pi\) | ||||
−0.945382 | + | 0.325963i | \(0.894311\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.54228 | −1.06025 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.6170 | −1.49466 | −0.747331 | − | 0.664452i | \(-0.768665\pi\) | ||||
−0.747331 | + | 0.664452i | \(0.768665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.43273 | −0.263866 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.38227 | −0.684251 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.56062 | −0.377425 | −0.188713 | − | 0.982032i | \(-0.560431\pi\) | ||||
−0.188713 | + | 0.982032i | \(0.560431\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.31284 | 0.766594 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.53687 | 0.781537 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.922582 | −0.0946549 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.44507 | −0.451328 | −0.225664 | − | 0.974205i | \(-0.572455\pi\) | ||||
−0.225664 | + | 0.974205i | \(0.572455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.709134 | 0.0712706 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.90925 | −0.587992 | −0.293996 | − | 0.955807i | \(-0.594985\pi\) | ||||
−0.293996 | + | 0.955807i | \(0.594985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.2801 | −1.40706 | −0.703532 | − | 0.710664i | \(-0.748395\pi\) | ||||
−0.703532 | + | 0.710664i | \(0.748395\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.98700 | 0.584272 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2869 | 0.994468 | 0.497234 | − | 0.867616i | \(-0.334349\pi\) | ||||
0.497234 | + | 0.867616i | \(0.334349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.1935 | −1.07214 | −0.536071 | − | 0.844173i | \(-0.680092\pi\) | ||||
−0.536071 | + | 0.844173i | \(0.680092\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.6071 | −1.19661 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.94884 | 0.183332 | 0.0916659 | − | 0.995790i | \(-0.470781\pi\) | ||||
0.0916659 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.388193 | 0.0361992 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.421696 | −0.0389858 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.15060 | −0.747164 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.47218 | 0.224744 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.2150 | 1.28172 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.92151 | −0.259242 | −0.129621 | − | 0.991564i | \(-0.541376\pi\) | ||||
−0.129621 | + | 0.991564i | \(0.541376\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.0409 | 1.41232 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.29337 | −0.200373 | −0.100187 | − | 0.994969i | \(-0.531944\pi\) | ||||
−0.100187 | + | 0.994969i | \(0.531944\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.09102 | −0.268025 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.01562 | 0.431676 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.09705 | −0.350035 | −0.175017 | − | 0.984565i | \(-0.555998\pi\) | ||||
−0.175017 | + | 0.984565i | \(0.555998\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7915 | −1.16978 | −0.584891 | − | 0.811112i | \(-0.698863\pi\) | ||||
−0.584891 | + | 0.811112i | \(0.698863\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.252169 | 0.0212364 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.01141 | −0.669948 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.57159 | 0.296605 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.55018 | 0.622728 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.864421 | −0.0708161 | −0.0354081 | − | 0.999373i | \(-0.511273\pi\) | ||||
−0.0354081 | + | 0.999373i | \(0.511273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7319 | −1.28025 | −0.640123 | − | 0.768273i | \(-0.721116\pi\) | ||||
−0.640123 | + | 0.768273i | \(0.721116\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.470005 | 0.0379976 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.21772 | −0.338775 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.6334 | 1.48711 | 0.743554 | − | 0.668675i | \(-0.233138\pi\) | ||||
0.743554 | + | 0.668675i | \(0.233138\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.9896 | 1.90250 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.30060 | 0.102502 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.97284 | 0.467829 | 0.233914 | − | 0.972257i | \(-0.424846\pi\) | ||||
0.233914 | + | 0.972257i | \(0.424846\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.55892 | −0.510611 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.8344 | 1.76698 | 0.883490 | − | 0.468450i | \(-0.155187\pi\) | ||||
0.883490 | + | 0.468450i | \(0.155187\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.23591 | −0.633532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.178244 | 0.0136306 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.7784 | −1.12358 | −0.561789 | − | 0.827280i | \(-0.689887\pi\) | ||||
−0.561789 | + | 0.827280i | \(0.689887\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.35040 | −0.253266 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.2729 | −1.14798 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.50945 | −0.187565 | −0.0937825 | − | 0.995593i | \(-0.529896\pi\) | ||||
−0.0937825 | + | 0.995593i | \(0.529896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6277 | 0.789948 | 0.394974 | − | 0.918692i | \(-0.370754\pi\) | ||||
0.394974 | + | 0.918692i | \(0.370754\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.86450 | −0.729205 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.05508 | 0.518700 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.92919 | 0.652967 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.8043 | 1.22233 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.925727 | −0.0669833 | −0.0334916 | − | 0.999439i | \(-0.510663\pi\) | ||||
−0.0334916 | + | 0.999439i | \(0.510663\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.29130 | 0.164931 | 0.0824656 | − | 0.996594i | \(-0.473721\pi\) | ||||
0.0824656 | + | 0.996594i | \(0.473721\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.90034 | 0.279309 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.9368 | −1.70542 | −0.852712 | − | 0.522382i | \(-0.825044\pi\) | ||||
−0.852712 | + | 0.522382i | \(0.825044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.4764 | −1.59331 | −0.796655 | − | 0.604434i | \(-0.793399\pi\) | ||||
−0.796655 | + | 0.604434i | \(0.793399\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.60397 | −0.183670 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.9663 | 0.839867 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.95489 | −0.555593 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0749992 | −0.00521281 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.38629 | 0.234235 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0752 | −1.72625 | −0.863125 | − | 0.504990i | \(-0.831496\pi\) | ||||
−0.863125 | + | 0.504990i | \(0.831496\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.828787 | −0.0567876 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.97665 | −0.612203 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.1310 | −0.959277 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.7447 | −0.726057 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.30986 | −0.357180 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.30732 | −0.0875446 | −0.0437723 | − | 0.999042i | \(-0.513938\pi\) | ||||
−0.0437723 | + | 0.999042i | \(0.513938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.193201 | 0.0128801 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.0007 | 1.06200 | 0.531001 | − | 0.847371i | \(-0.321816\pi\) | ||||
0.531001 | + | 0.847371i | \(0.321816\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.775853 | 0.0512698 | 0.0256349 | − | 0.999671i | \(-0.491839\pi\) | ||||
0.0256349 | + | 0.999671i | \(0.491839\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.9750 | −1.44585 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.5965 | 1.28381 | 0.641904 | − | 0.766785i | \(-0.278145\pi\) | ||||
0.641904 | + | 0.766785i | \(0.278145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.141117 | −0.00920543 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.0306 | −1.95070 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.7558 | −0.889791 | −0.444895 | − | 0.895583i | \(-0.646759\pi\) | ||||
−0.444895 | + | 0.895583i | \(0.646759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.269687 | 0.0173721 | 0.00868604 | − | 0.999962i | \(-0.497235\pi\) | ||||
0.00868604 | + | 0.999962i | \(0.497235\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.00475 | −0.128604 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.22517 | −0.269936 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.01370 | −0.128129 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.3330 | −1.54204 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.93704 | −0.500982 | −0.250491 | − | 0.968119i | \(-0.580592\pi\) | ||||
−0.250491 | + | 0.968119i | \(0.580592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.42484 | −0.0895790 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.34717 | −0.272230 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.58454 | −0.473111 | −0.236555 | − | 0.971618i | \(-0.576018\pi\) | ||||
−0.236555 | + | 0.971618i | \(0.576018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.6373 | 1.46875 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.690035 | −0.0427121 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.9321 | −0.859088 | −0.429544 | − | 0.903046i | \(-0.641326\pi\) | ||||
−0.429544 | + | 0.903046i | \(0.641326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.4249 | −0.824685 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.36266 | −0.389389 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7172 | −0.775382 | −0.387691 | − | 0.921789i | \(-0.626727\pi\) | ||||
−0.387691 | + | 0.921789i | \(0.626727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.586141 | −0.0356055 | −0.0178028 | − | 0.999842i | \(-0.505667\pi\) | ||||
−0.0178028 | + | 0.999842i | \(0.505667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.0677 | 0.790894 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.67045 | 0.221336 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.2552 | 1.21702 | 0.608509 | − | 0.793547i | \(-0.291768\pi\) | ||||
0.608509 | + | 0.793547i | \(0.291768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.814867 | 0.0487848 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.1365 | 1.85745 | 0.928725 | − | 0.370769i | \(-0.120906\pi\) | ||||
0.928725 | + | 0.370769i | \(0.120906\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.7551 | 0.936543 | 0.468272 | − | 0.883585i | \(-0.344877\pi\) | ||||
0.468272 | + | 0.883585i | \(0.344877\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.64861 | −0.0976553 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.6520 | −1.57322 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0818 | −0.651873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.94313 | −0.465634 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.8065 | −1.15711 | −0.578554 | − | 0.815644i | \(-0.696383\pi\) | ||||
−0.578554 | + | 0.815644i | \(0.696383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.54689 | 0.497619 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.4096 | −1.06823 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.847300 | 0.0490006 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.0754 | −1.73352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.5595 | −0.606630 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.52029 | 0.316091 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.8761 | 1.24853 | 0.624266 | − | 0.781212i | \(-0.285398\pi\) | ||||
0.624266 | + | 0.781212i | \(0.285398\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.5179 | −1.45166 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4538 | 0.876306 | 0.438153 | − | 0.898900i | \(-0.355633\pi\) | ||||
0.438153 | + | 0.898900i | \(0.355633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4191 | −0.815016 | −0.407508 | − | 0.913202i | \(-0.633602\pi\) | ||||
−0.407508 | + | 0.913202i | \(0.633602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.647300 | 0.0364712 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.0743 | 1.80147 | 0.900737 | − | 0.434366i | \(-0.143027\pi\) | ||||
0.900737 | + | 0.434366i | \(0.143027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.1093 | −0.733982 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.3821 | 1.02599 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.24439 | 0.124881 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.18268 | −0.121073 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.0022 | −1.10613 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.472797 | −0.0260661 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.40996 | −0.187428 | −0.0937142 | − | 0.995599i | \(-0.529874\pi\) | ||||
−0.0937142 | + | 0.995599i | \(0.529874\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.36305 | −0.0746945 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.45721 | 0.0796159 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5511 | −0.792650 | −0.396325 | − | 0.918110i | \(-0.629715\pi\) | ||||
−0.396325 | + | 0.918110i | \(0.629715\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.48249 | 0.189143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.4809 | 0.838339 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.29679 | 0.501980 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.693682 | 0.0373466 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.9684 | −0.696179 | −0.348089 | − | 0.937461i | \(-0.613169\pi\) | ||||
−0.348089 | + | 0.937461i | \(0.613169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.67490 | −0.196713 | −0.0983563 | − | 0.995151i | \(-0.531358\pi\) | ||||
−0.0983563 | + | 0.995151i | \(0.531358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.9475 | 0.584333 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.31330 | −0.176349 | −0.0881747 | − | 0.996105i | \(-0.528103\pi\) | ||||
−0.0881747 | + | 0.996105i | \(0.528103\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.463799 | 0.0246159 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.5647 | −0.770848 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.94756 | −0.419456 | −0.209728 | − | 0.977760i | \(-0.567258\pi\) | ||||
−0.209728 | + | 0.977760i | \(0.567258\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1488 | −0.955202 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.41768 | 0.231868 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.01284 | 0.314727 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4816 | −0.703731 | −0.351866 | − | 0.936050i | \(-0.614453\pi\) | ||||
−0.351866 | + | 0.936050i | \(0.614453\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.53689 | 0.0800074 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −44.9787 | −2.33518 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.24708 | 0.116349 | 0.0581746 | − | 0.998306i | \(-0.481472\pi\) | ||||
0.0581746 | + | 0.998306i | \(0.481472\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.78695 | −0.0922779 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.79564 | 0.401496 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1523 | 0.675586 | 0.337793 | − | 0.941220i | \(-0.390320\pi\) | ||||
0.337793 | + | 0.941220i | \(0.390320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.22060 | −0.267459 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.6831 | 1.77222 | 0.886111 | − | 0.463473i | \(-0.153397\pi\) | ||||
0.886111 | + | 0.463473i | \(0.153397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.2975 | 0.626737 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.73430 | 0.0881593 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.8872 | −0.856214 | −0.428107 | − | 0.903728i | \(-0.640819\pi\) | ||||
−0.428107 | + | 0.903728i | \(0.640819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.944367 | −0.0477587 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.09815 | −0.206724 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.8055 | 0.845576 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.1796 | −0.761841 | −0.380921 | − | 0.924608i | \(-0.624393\pi\) | ||||
−0.380921 | + | 0.924608i | \(0.624393\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.52350 | −0.276521 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.20593 | −0.458580 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.54228 | 0.474160 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.8953 | −1.28358 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.58297 | −0.374954 | −0.187477 | − | 0.982269i | \(-0.560031\pi\) | ||||
−0.187477 | + | 0.982269i | \(0.560031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.32124 | −0.361130 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.6355 | 1.40906 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.6170 | 0.668433 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.6448 | −1.20686 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.3497 | 1.18956 | 0.594781 | − | 0.803888i | \(-0.297239\pi\) | ||||
0.594781 | + | 0.803888i | \(0.297239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.2232 | −1.57046 | −0.785231 | − | 0.619203i | \(-0.787456\pi\) | ||||
−0.785231 | + | 0.619203i | \(0.787456\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.0272639 | 0.00132561 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.43273 | 0.118005 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.4952 | 0.895044 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.3160 | −0.691183 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.85869 | −0.378540 | −0.189270 | − | 0.981925i | \(-0.560612\pi\) | ||||
−0.189270 | + | 0.981925i | \(0.560612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.3280 | 1.55358 | 0.776792 | − | 0.629757i | \(-0.216846\pi\) | ||||
0.776792 | + | 0.629757i | \(0.216846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.38227 | 0.306006 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.358140 | −0.0171321 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.65347 | 0.269825 | 0.134913 | − | 0.990857i | \(-0.456925\pi\) | ||||
0.134913 | + | 0.990857i | \(0.456925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.816306 | 0.0388717 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.9347 | −1.37473 | −0.687364 | − | 0.726313i | \(-0.741232\pi\) | ||||
−0.687364 | + | 0.726313i | \(0.741232\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.56062 | 0.168790 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.54468 | −0.0730609 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.1416 | −1.28089 | −0.640445 | − | 0.768004i | \(-0.721250\pi\) | ||||
−0.640445 | + | 0.768004i | \(0.721250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.1980 | 1.37488 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28.1122 | −1.32083 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.31284 | −0.342831 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.87447 | −0.461908 | −0.230954 | − | 0.972965i | \(-0.574185\pi\) | ||||
−0.230954 | + | 0.972965i | \(0.574185\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.2016 | −0.569523 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.6815 | 0.730361 | 0.365181 | − | 0.930937i | \(-0.381007\pi\) | ||||
0.365181 | + | 0.930937i | \(0.381007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6644 | 0.774459 | 0.387229 | − | 0.921983i | \(-0.373432\pi\) | ||||
0.387229 | + | 0.921983i | \(0.373432\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.53687 | −0.349514 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.82136 | −0.361929 | −0.180965 | − | 0.983490i | \(-0.557922\pi\) | ||||
−0.180965 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.88223 | 0.225441 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.2970 | 1.53425 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.9483 | 1.51497 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.922582 | 0.0423310 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.59370 | 0.118757 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2431 | −0.468021 | −0.234010 | − | 0.972234i | \(-0.575185\pi\) | ||||
−0.234010 | + | 0.972234i | \(0.575185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.3990 | 0.702132 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.32411 | 0.105751 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.44507 | 0.201840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.8658 | −1.53460 | −0.767302 | − | 0.641286i | \(-0.778401\pi\) | ||||
−0.767302 | + | 0.641286i | \(0.778401\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.6732 | 0.482658 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.9507 | 1.48704 | 0.743521 | − | 0.668712i | \(-0.233154\pi\) | ||||
0.743521 | + | 0.668712i | \(0.233154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.68871 | −0.391320 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.709134 | −0.0318732 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.55391 | 0.0697025 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9132 | −0.667608 | −0.333804 | − | 0.942643i | \(-0.608332\pi\) | ||||
−0.333804 | + | 0.942643i | \(0.608332\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 40.8040 | 1.82299 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.5064 | −1.36021 | −0.680106 | − | 0.733114i | \(-0.738066\pi\) | ||||
−0.680106 | + | 0.733114i | \(0.738066\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.90925 | 0.262958 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.7172 | −0.653613 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.33146 | −0.147664 | −0.0738321 | − | 0.997271i | \(-0.523523\pi\) | ||||
−0.0738321 | + | 0.997271i | \(0.523523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.1454 | 0.891181 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.62732 | −0.204301 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2801 | 0.629258 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.517961 | 0.0227799 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.4082 | −1.15919 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.6262 | 1.03508 | 0.517541 | − | 0.855658i | \(-0.326847\pi\) | ||||
0.517541 | + | 0.855658i | \(0.326847\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9782 | 0.567498 | 0.283749 | − | 0.958899i | \(-0.408422\pi\) | ||||
0.283749 | + | 0.958899i | \(0.408422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.98700 | −0.261294 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2606 | 0.446957 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8493 | −0.993448 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.65127 | −0.0716589 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.3630 | −0.752073 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2869 | −0.444740 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.48427 | −0.193510 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5083 | 0.667988 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.7194 | 0.589841 | 0.294921 | − | 0.955522i | \(-0.404707\pi\) | ||||
0.294921 | + | 0.955522i | \(0.404707\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.9911 | 0.814988 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.1935 | 0.479476 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4791 | −0.704597 | −0.352299 | − | 0.935888i | \(-0.614600\pi\) | ||||
−0.352299 | + | 0.935888i | \(0.614600\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.06653 | −0.0455182 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.29509 | −0.140375 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 56.3051 | 2.39433 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.6071 | 0.535141 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.9333 | −1.43780 | −0.718901 | − | 0.695113i | \(-0.755354\pi\) | ||||
−0.718901 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.5932 | −0.828702 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.9560 | 0.673665 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.00240 | 0.126536 | 0.0632680 | − | 0.997997i | \(-0.479848\pi\) | ||||
0.0632680 | + | 0.997997i | \(0.479848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.94884 | −0.0819885 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.9704 | 1.34263 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.42927 | 0.101840 | 0.0509201 | − | 0.998703i | \(-0.483785\pi\) | ||||
0.0509201 | + | 0.998703i | \(0.483785\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.2844 | −1.47661 | −0.738303 | − | 0.674469i | \(-0.764373\pi\) | ||||
−0.738303 | + | 0.674469i | \(0.764373\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.65423 | −0.0691065 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.388193 | −0.0161888 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.24045 | 0.218163 | 0.109081 | − | 0.994033i | \(-0.465209\pi\) | ||||
0.109081 | + | 0.994033i | \(0.465209\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.09444 | 0.170159 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.6224 | 1.89274 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 49.2754 | 2.04078 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.421696 | 0.0174350 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.2392 | −0.422616 | −0.211308 | − | 0.977419i | \(-0.567772\pi\) | ||||
−0.211308 | + | 0.977419i | \(0.567772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.89119 | 0.160334 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −42.7739 | −1.75948 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.5841 | 1.66659 | 0.833295 | − | 0.552829i | \(-0.186452\pi\) | ||||
0.833295 | + | 0.552829i | \(0.186452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.15060 | 0.334142 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −40.1643 | −1.64381 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0021 | 0.694687 | 0.347344 | − | 0.937738i | \(-0.387084\pi\) | ||||
0.347344 | + | 0.937738i | \(0.387084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.7608 | −1.29555 | −0.647774 | − | 0.761832i | \(-0.724300\pi\) | ||||
−0.647774 | + | 0.761832i | \(0.724300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.281534 | −0.0114650 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.47218 | −0.100509 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.2822 | −1.06676 | −0.533382 | − | 0.845875i | \(-0.679079\pi\) | ||||
−0.533382 | + | 0.845875i | \(0.679079\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.3831 | 0.866489 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.308012 | −0.0124608 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.7765 | 1.97007 | 0.985033 | − | 0.172367i | \(-0.0551415\pi\) | ||||
0.985033 | + | 0.172367i | \(0.0551415\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.2150 | −0.573204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.6957 | 1.63835 | 0.819173 | − | 0.573546i | \(-0.194433\pi\) | ||||
0.819173 | + | 0.573546i | \(0.194433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.3689 | 0.899082 | 0.449541 | − | 0.893260i | \(-0.351588\pi\) | ||||
0.449541 | + | 0.893260i | \(0.351588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.94703 | 0.0781315 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.9295 | 0.477945 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.05114 | 0.241659 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.1631 | −0.684336 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.40314 | 0.294714 | 0.147357 | − | 0.989083i | \(-0.452923\pi\) | ||||
0.147357 | + | 0.989083i | \(0.452923\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −44.8083 | −1.78097 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.92151 | 0.115936 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.22218 | −0.365396 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0896064 | −0.00354478 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.92817 | 0.194651 | 0.0973255 | − | 0.995253i | \(-0.468971\pi\) | ||||
0.0973255 | + | 0.995253i | \(0.468971\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.4930 | −0.532113 | −0.266057 | − | 0.963957i | \(-0.585721\pi\) | ||||
−0.266057 | + | 0.963957i | \(0.585721\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.0409 | −0.631608 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.0533 | 1.69260 | 0.846301 | − | 0.532706i | \(-0.178825\pi\) | ||||
0.846301 | + | 0.532706i | \(0.178825\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.3709 | −1.23142 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.2515 | −0.989684 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.13210 | −0.279101 | −0.139550 | − | 0.990215i | \(-0.544566\pi\) | ||||
−0.139550 | + | 0.990215i | \(0.544566\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.29337 | 0.0896096 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.16169 | −0.0453217 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.68310 | 0.0655642 | 0.0327821 | − | 0.999463i | \(-0.489563\pi\) | ||||
0.0327821 | + | 0.999463i | \(0.489563\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7950 | −0.419878 | −0.209939 | − | 0.977714i | \(-0.567327\pi\) | ||||
−0.209939 | + | 0.977714i | \(0.567327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.48847 | −0.368502 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.09102 | 0.119865 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.38647 | 0.0536842 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.33612 | −0.0903196 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.2619 | −0.782204 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.5476 | 1.37026 | 0.685129 | − | 0.728422i | \(-0.259746\pi\) | ||||
0.685129 | + | 0.728422i | \(0.259746\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.01562 | −0.193051 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.1798 | −1.54423 | −0.772117 | − | 0.635480i | \(-0.780802\pi\) | ||||
−0.772117 | + | 0.635480i | \(0.780802\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.8927 | 0.571531 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.5924 | 1.09566 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.7900 | 0.910298 | 0.455149 | − | 0.890415i | \(-0.349586\pi\) | ||||
0.455149 | + | 0.890415i | \(0.349586\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.09705 | 0.156540 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.38641 | 0.0528950 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.3022 | −1.11633 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.2862 | −0.467388 | −0.233694 | − | 0.972310i | \(-0.575081\pi\) | ||||
−0.233694 | + | 0.972310i | \(0.575081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.37588 | −0.0902523 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.7915 | 0.523142 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.3521 | 0.733012 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.0180 | 1.32450 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.649217 | −0.0245206 | −0.0122603 | − | 0.999925i | \(-0.503903\pi\) | ||||
−0.0122603 | + | 0.999925i | \(0.503903\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.50889 | −0.245487 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.252169 | −0.00949723 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.7983 | 0.744593 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0672 | 0.528303 | 0.264152 | − | 0.964481i | \(-0.414908\pi\) | ||||
0.264152 | + | 0.964481i | \(0.414908\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.24684 | −0.121766 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.63729 | −0.0613169 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.01141 | 0.299610 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.5810 | −0.917995 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.0719 | 1.12149 | 0.560747 | − | 0.827987i | \(-0.310514\pi\) | ||||
0.560747 | + | 0.827987i | \(0.310514\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.8441 | 1.78181 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.481919 | 0.0179227 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.57159 | −0.132646 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.13470 | 0.264611 | 0.132306 | − | 0.991209i | \(-0.457762\pi\) | ||||
0.132306 | + | 0.991209i | \(0.457762\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.0444 | 0.927572 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.8377 | 0.807698 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.14338 | −0.226911 | −0.113455 | − | 0.993543i | \(-0.536192\pi\) | ||||
−0.113455 | + | 0.993543i | \(0.536192\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.55018 | −0.278492 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.34861 | −0.197019 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.9056 | −0.805811 | −0.402906 | − | 0.915242i | \(-0.632000\pi\) | ||||
−0.402906 | + | 0.915242i | \(0.632000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.59839 | −0.132190 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.3938 | −0.417999 | −0.209000 | − | 0.977916i | \(-0.567021\pi\) | ||||
−0.209000 | + | 0.977916i | \(0.567021\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.864421 | 0.0316699 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.63082 | −0.0962567 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.4651 | −1.25933 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5295 | 0.566679 | 0.283339 | − | 0.959020i | \(-0.408558\pi\) | ||||
0.283339 | + | 0.959020i | \(0.408558\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.1831 | −0.516862 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.7319 | 0.572543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.3814 | 0.813466 | 0.406733 | − | 0.913547i | \(-0.366668\pi\) | ||||
0.406733 | + | 0.913547i | \(0.366668\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.54612 | −0.0924185 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.29721 | 0.337024 | 0.168512 | − | 0.985700i | \(-0.446104\pi\) | ||||
0.168512 | + | 0.985700i | \(0.446104\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.5026 | 1.35769 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.470005 | −0.0169931 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.6551 | 0.673598 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.4922 | 1.09958 | 0.549789 | − | 0.835304i | \(-0.314708\pi\) | ||||
0.549789 | + | 0.835304i | \(0.314708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.5532 | −0.488107 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.7976 | −1.35948 | −0.679742 | − | 0.733451i | \(-0.737908\pi\) | ||||
−0.679742 | + | 0.733451i | \(0.737908\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.21772 | 0.151505 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 42.2388 | 1.51531 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.33904 | 0.262948 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.70235 | −0.0609149 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.9137 | 0.640185 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.6334 | −0.665055 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0189 | 0.535366 | 0.267683 | − | 0.963507i | \(-0.413742\pi\) | ||||
0.267683 | + | 0.963507i | \(0.413742\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.8959 | −0.886319 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.52940 | −0.232159 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0490 | 0.427873 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.9896 | −0.850825 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.9916 | −0.885249 | −0.442624 | − | 0.896707i | \(-0.645953\pi\) | ||||
−0.442624 | + | 0.896707i | \(0.645953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.343298 | 0.0121450 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.687915 | −0.0243063 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.0698 | −0.778827 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.30060 | −0.0458401 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.7251 | −0.799960 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4758 | −0.579258 | −0.289629 | − | 0.957139i | \(-0.593532\pi\) | ||||
−0.289629 | + | 0.957139i | \(0.593532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.5489 | −0.897142 | −0.448571 | − | 0.893747i | \(-0.648067\pi\) | ||||
−0.448571 | + | 0.893747i | \(0.648067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.04741 | −0.0367342 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.97284 | −0.209219 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.28170 | 0.289740 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.41285 | 0.0493689 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.7596 | 1.03862 | 0.519308 | − | 0.854587i | \(-0.326190\pi\) | ||||
0.519308 | + | 0.854587i | \(0.326190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.1579 | −1.05124 | −0.525619 | − | 0.850720i | \(-0.676166\pi\) | ||||
−0.525619 | + | 0.850720i | \(0.676166\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.55892 | 0.228352 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.0353484 | 0.00122918 | 0.000614592 | − | 1.00000i | \(-0.499804\pi\) | ||||
0.000614592 | 1.00000i | \(0.499804\pi\) | ||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.9544 | 1.24875 | 0.624374 | − | 0.781125i | \(-0.285354\pi\) | ||||
0.624374 | + | 0.781125i | \(0.285354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.1951 | 1.25559 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.2787 | 0.356135 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.8344 | −0.790218 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.1545 | −0.731205 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.74075 | 0.198193 | 0.0990964 | − | 0.995078i | \(-0.468405\pi\) | ||||
0.0990964 | + | 0.995078i | \(0.468405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.2437 | −0.560128 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55.6395 | 1.91633 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.23591 | 0.283324 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.28280 | −0.284600 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.1536 | 0.966230 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.73873 | 0.0938824 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.8946 | −1.12629 | −0.563145 | − | 0.826358i | \(-0.690409\pi\) | ||||
−0.563145 | + | 0.826358i | \(0.690409\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.178244 | −0.00609581 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.92868 | −0.236679 | −0.118340 | − | 0.992973i | \(-0.537757\pi\) | ||||
−0.118340 | + | 0.992973i | \(0.537757\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.4826 | 1.24477 | 0.622385 | − | 0.782711i | \(-0.286164\pi\) | ||||
0.622385 | + | 0.782711i | \(0.286164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −47.6259 | −1.62309 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.6369 | 0.940772 | 0.470386 | − | 0.882461i | \(-0.344115\pi\) | ||||
0.470386 | + | 0.882461i | \(0.344115\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7784 | 0.502480 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.8027 | −0.672536 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −61.6836 | −2.09247 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.18062 | 0.107771 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.858791 | −0.0290657 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.35040 | 0.113264 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.0675 | −0.508794 | −0.254397 | − | 0.967100i | \(-0.581877\pi\) | ||||
−0.254397 | + | 0.967100i | \(0.581877\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −35.3933 | −1.19379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.22760 | 0.310886 | 0.155443 | − | 0.987845i | \(-0.450320\pi\) | ||||
0.155443 | + | 0.987845i | \(0.450320\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.7426 | −1.37110 | −0.685549 | − | 0.728026i | \(-0.740438\pi\) | ||||
−0.685549 | + | 0.728026i | \(0.740438\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.2729 | 0.513393 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.9799 | 1.00663 | 0.503313 | − | 0.864104i | \(-0.332114\pi\) | ||||
0.503313 | + | 0.864104i | \(0.332114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.78821 | 0.328286 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.0244 | −1.17336 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.130192 | 0.00435670 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.50945 | 0.0838816 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.51409 | 0.0505538 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.0640 | −0.502412 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.6591 | 1.08803 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −53.7433 | −1.78846 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.6277 | −0.353276 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07576 | 0.0357200 | 0.0178600 | − | 0.999840i | \(-0.494315\pi\) | ||||
0.0178600 | + | 0.999840i | \(0.494315\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.14167 | −0.0378669 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.536627 | −0.0177792 | −0.00888962 | − | 0.999960i | \(-0.502830\pi\) | ||||
−0.00888962 | + | 0.999960i | \(0.502830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.9806 | −1.65412 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.86450 | 0.326110 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.68372 | 0.253739 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.3306 | 1.23142 | 0.615711 | − | 0.787972i | \(-0.288869\pi\) | ||||
0.615711 | + | 0.787972i | \(0.288869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.0915 | 1.28811 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.01232 | 0.0333211 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.05508 | −0.231969 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.75894 | −0.0906154 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.9873 | 1.08228 | 0.541139 | − | 0.840933i | \(-0.317993\pi\) | ||||
0.541139 | + | 0.840933i | \(0.317993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.89806 | 0.127754 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.6152 | 0.904083 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.92919 | −0.292016 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.4870 | −1.58400 | −0.792000 | − | 0.610521i | \(-0.790960\pi\) | ||||
−0.792000 | + | 0.610521i | \(0.790960\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.7663 | −0.840850 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.2876 | −0.693956 | −0.346978 | − | 0.937873i | \(-0.612792\pi\) | ||||
−0.346978 | + | 0.937873i | \(0.612792\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.08803 | −0.100560 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.8043 | −0.546644 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.3715 | 0.694481 | 0.347241 | − | 0.937776i | \(-0.387119\pi\) | ||||
0.347241 | + | 0.937776i | \(0.387119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.1241 | 0.426026 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.3153 | 1.85858 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.9098 | −1.71391 | −0.856957 | − | 0.515387i | \(-0.827648\pi\) | ||||
−0.856957 | + | 0.515387i | \(0.827648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.925727 | 0.0299558 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.4258 | −0.757248 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.7268 | 0.443260 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.2108 | −0.426156 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.98743 | 0.0640441 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.29130 | −0.0737594 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.65921 | 0.117672 | 0.0588362 | − | 0.998268i | \(-0.481261\pi\) | ||||
0.0588362 | + | 0.998268i | \(0.481261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.01062 | 0.128840 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.03188 | −0.257755 | −0.128878 | − | 0.991661i | \(-0.541137\pi\) | ||||
−0.128878 | + | 0.991661i | \(0.541137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46.2071 | 1.48133 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.90034 | −0.124911 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0646 | −0.673916 | −0.336958 | − | 0.941520i | \(-0.609398\pi\) | ||||
−0.336958 | + | 0.941520i | \(0.609398\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.0691 | −0.417689 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.16259 | −0.0690463 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.1729 | −0.866680 | −0.433340 | − | 0.901231i | \(-0.642665\pi\) | ||||
−0.433340 | + | 0.901231i | \(0.642665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.9368 | 0.762688 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.844866 | −0.0268924 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.48467 | −0.110806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.70561 | 0.0541805 | 0.0270902 | − | 0.999633i | \(-0.491376\pi\) | ||||
0.0270902 | + | 0.999633i | \(0.491376\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.09344 | −0.193369 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.4764 | 0.712550 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.1166 | 1.84057 | 0.920285 | − | 0.391248i | \(-0.127956\pi\) | ||||
0.920285 | + | 0.391248i | \(0.127956\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.3856 | 1.11955 |
(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 | 8020.2.a.c.1.21 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.21 | ✓ | 28 | 1.1 | even | 1 | trivial |