Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.3 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.e.3599.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.51504 | − | 2.51504i | −1.12476 | − | 1.12476i | −0.991016 | − | 0.133742i | \(-0.957301\pi\) |
−0.133742 | − | 0.991016i | \(-0.542699\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.984548 | − | 0.984548i | 0.296852 | − | 0.296852i | −0.542927 | − | 0.839780i | \(-0.682684\pi\) |
0.839780 | + | 0.542927i | \(0.182684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.26086 | − | 3.26086i | −0.904399 | − | 0.904399i | 0.0914142 | − | 0.995813i | \(-0.470861\pi\) |
−0.995813 | + | 0.0914142i | \(0.970861\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.50927i | 1.33619i | 0.744074 | + | 0.668097i | \(0.232891\pi\) | ||||
−0.744074 | + | 0.668097i | \(0.767109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.21444 | − | 1.21444i | 0.278613 | − | 0.278613i | −0.553942 | − | 0.832555i | \(-0.686877\pi\) |
0.832555 | + | 0.553942i | \(0.186877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.62021i | 1.79744i | 0.438526 | + | 0.898719i | \(0.355501\pi\) | ||||
−0.438526 | + | 0.898719i | \(0.644499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.65081i | 1.53016i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.04663 | + | 2.04663i | −0.380050 | + | 0.380050i | −0.871120 | − | 0.491070i | \(-0.836606\pi\) |
0.491070 | + | 0.871120i | \(0.336606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.164437i | − | 0.0295337i | −0.999891 | − | 0.0147669i | \(-0.995299\pi\) | ||
0.999891 | − | 0.0147669i | \(-0.00470061\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.51504 | + | 2.51504i | 0.425119 | + | 0.425119i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.31105 | + | 8.31105i | −1.36633 | + | 1.36633i | −0.500717 | + | 0.865611i | \(0.666930\pi\) |
−0.865611 | + | 0.500717i | \(0.833070\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.56578 | 1.49392 | 0.746962 | − | 0.664867i | \(-0.231512\pi\) | ||||
0.746962 | + | 0.664867i | \(0.231512\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.01867 | − | 5.01867i | −0.765340 | − | 0.765340i | 0.211942 | − | 0.977282i | \(-0.432021\pi\) |
−0.977282 | + | 0.211942i | \(0.932021\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.37837 | −0.492786 | −0.246393 | − | 0.969170i | \(-0.579245\pi\) | ||||
−0.246393 | + | 0.969170i | \(0.579245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.72717 | + | 3.72717i | 0.511966 | + | 0.511966i | 0.915129 | − | 0.403162i | \(-0.132089\pi\) |
−0.403162 | + | 0.915129i | \(0.632089\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.95235 | −0.667774 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0781 | − | 10.0781i | 1.31206 | − | 1.31206i | 0.392162 | − | 0.919896i | \(-0.371727\pi\) |
0.919896 | − | 0.392162i | \(-0.128273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.07042 | − | 1.07042i | −0.137054 | − | 0.137054i | 0.635252 | − | 0.772305i | \(-0.280896\pi\) |
−0.772305 | + | 0.635252i | \(0.780896\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.4023i | 2.03446i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.12073 | − | 3.12073i | 0.381258 | − | 0.381258i | −0.490297 | − | 0.871555i | \(-0.663112\pi\) |
0.871555 | + | 0.490297i | \(0.163112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.66257i | − | 0.909380i | −0.890650 | − | 0.454690i | \(-0.849750\pi\) | ||
0.890650 | − | 0.454690i | \(-0.150250\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.40588i | − | 0.983834i | −0.870642 | − | 0.491917i | \(-0.836296\pi\) | ||
0.870642 | − | 0.491917i | \(-0.163704\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.984548 | + | 0.984548i | −0.112200 | + | 0.112200i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.8712i | − | 1.56063i | −0.625387 | − | 0.780315i | \(-0.715059\pi\) | ||
0.625387 | − | 0.780315i | \(-0.284941\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.31214 | + | 7.31214i | 0.802611 | + | 0.802611i | 0.983503 | − | 0.180892i | \(-0.0578984\pi\) |
−0.180892 | + | 0.983503i | \(0.557898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8560 | − | 13.8560i | 1.50290 | − | 1.50290i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.49158 | 0.794106 | 0.397053 | − | 0.917796i | \(-0.370033\pi\) | ||||
0.397053 | + | 0.917796i | \(0.370033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.26086 | + | 3.26086i | 0.341831 | + | 0.341831i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.10874 | −0.626744 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.84085 | −0.796118 | −0.398059 | − | 0.917360i | \(-0.630316\pi\) | ||||
−0.398059 | + | 0.917360i | \(0.630316\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.748257 | + | 0.748257i | 0.0744543 | + | 0.0744543i | 0.743353 | − | 0.668899i | \(-0.233234\pi\) |
−0.668899 | + | 0.743353i | \(0.733234\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8161 | 1.16428 | 0.582140 | − | 0.813089i | \(-0.302216\pi\) | ||||
0.582140 | + | 0.813089i | \(0.302216\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.41189 | − | 4.41189i | 0.426514 | − | 0.426514i | −0.460925 | − | 0.887439i | \(-0.652482\pi\) |
0.887439 | + | 0.460925i | \(0.152482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.128743 | − | 0.128743i | −0.0123314 | − | 0.0123314i | 0.700914 | − | 0.713246i | \(-0.252776\pi\) |
−0.713246 | + | 0.700914i | \(0.752776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3042i | 1.34563i | 0.739811 | + | 0.672815i | \(0.234915\pi\) | ||||
−0.739811 | + | 0.672815i | \(0.765085\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.6801 | − | 21.6801i | 2.02168 | − | 2.02168i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.50927i | − | 0.505034i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.06133i | 0.823757i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.66689 | − | 6.66689i | 0.596304 | − | 0.596304i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.31914i | − | 0.117055i | −0.998286 | − | 0.0585274i | \(-0.981359\pi\) | ||
0.998286 | − | 0.0585274i | \(-0.0186405\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.84141 | + | 3.84141i | 0.335626 | + | 0.335626i | 0.854718 | − | 0.519093i | \(-0.173730\pi\) |
−0.519093 | + | 0.854718i | \(0.673730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.21444 | + | 1.21444i | −0.105306 | + | 0.105306i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.8262 | −1.01038 | −0.505191 | − | 0.863008i | \(-0.668578\pi\) | ||||
−0.505191 | + | 0.863008i | \(0.668578\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6322 | + | 10.6322i | 0.901814 | + | 0.901814i | 0.995593 | − | 0.0937788i | \(-0.0298947\pi\) |
−0.0937788 | + | 0.995593i | \(0.529895\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.42094 | −0.536946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.2947 | 0.854930 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.66703 | + | 9.66703i | 0.791954 | + | 0.791954i | 0.981812 | − | 0.189858i | \(-0.0608027\pi\) |
−0.189858 | + | 0.981812i | \(0.560803\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.05132 | 0.411070 | 0.205535 | − | 0.978650i | \(-0.434107\pi\) | ||||
0.205535 | + | 0.978650i | \(0.434107\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.413565 | + | 0.413565i | −0.0332183 | + | 0.0332183i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.1102 | + | 11.1102i | 0.886692 | + | 0.886692i | 0.994204 | − | 0.107512i | \(-0.0342884\pi\) |
−0.107512 | + | 0.994204i | \(0.534288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 8.62021i | − | 0.679367i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.936756 | + | 0.936756i | −0.0733724 | + | 0.0733724i | −0.742841 | − | 0.669468i | \(-0.766522\pi\) |
0.669468 | + | 0.742841i | \(0.266522\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.9147i | 1.38628i | 0.720804 | + | 0.693139i | \(0.243773\pi\) | ||||
−0.720804 | + | 0.693139i | \(0.756227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.26636i | 0.635874i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.95689 | + | 1.95689i | −0.148780 | + | 0.148780i | −0.777573 | − | 0.628793i | \(-0.783549\pi\) |
0.628793 | + | 0.777573i | \(0.283549\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.65081i | − | 0.578347i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.4536 | − | 16.4536i | −1.22980 | − | 1.22980i | −0.964039 | − | 0.265760i | \(-0.914377\pi\) |
−0.265760 | − | 0.964039i | \(-0.585623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.01639 | − | 2.01639i | 0.149877 | − | 0.149877i | −0.628186 | − | 0.778063i | \(-0.716202\pi\) |
0.778063 | + | 0.628186i | \(0.216202\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 41.8052 | 3.07358 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.42414 | + | 5.42414i | 0.396653 | + | 0.396653i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.72330 | 0.486481 | 0.243240 | − | 0.969966i | \(-0.421790\pi\) | ||||
0.243240 | + | 0.969966i | \(0.421790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.37543 | 0.0990058 | 0.0495029 | − | 0.998774i | \(-0.484236\pi\) | ||||
0.0495029 | + | 0.998774i | \(0.484236\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.2035 | − | 10.2035i | −0.726967 | − | 0.726967i | 0.243048 | − | 0.970014i | \(-0.421853\pi\) |
−0.970014 | + | 0.243048i | \(0.921853\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.9391 | 1.05900 | 0.529501 | − | 0.848309i | \(-0.322379\pi\) | ||||
0.529501 | + | 0.848309i | \(0.322379\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.04663 | − | 2.04663i | 0.143646 | − | 0.143646i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.0583 | − | 24.0583i | −1.68030 | − | 1.68030i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.39136i | − | 0.165414i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.93531 | + | 4.93531i | −0.339761 | + | 0.339761i | −0.856277 | − | 0.516516i | \(-0.827228\pi\) |
0.516516 | + | 0.856277i | \(0.327228\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.2443i | 1.72164i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.164437i | 0.0111627i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.9649 | − | 17.9649i | 1.20845 | − | 1.20845i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.25747i | 0.352066i | 0.984384 | + | 0.176033i | \(0.0563266\pi\) | ||||
−0.984384 | + | 0.176033i | \(0.943673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.30931 | + | 6.30931i | 0.418763 | + | 0.418763i | 0.884777 | − | 0.466014i | \(-0.154310\pi\) |
−0.466014 | + | 0.884777i | \(0.654310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.1785 | − | 19.1785i | 1.26735 | − | 1.26735i | 0.319899 | − | 0.947452i | \(-0.396351\pi\) |
0.947452 | − | 0.319899i | \(-0.103649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.555029 | −0.0363611 | −0.0181806 | − | 0.999835i | \(-0.505787\pi\) | ||||
−0.0181806 | + | 0.999835i | \(0.505787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.49672 | + | 8.49672i | 0.554265 | + | 0.554265i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.0408 | 1.49039 | 0.745194 | − | 0.666848i | \(-0.232357\pi\) | ||||
0.745194 | + | 0.666848i | \(0.232357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.47827 | −0.481718 | −0.240859 | − | 0.970560i | \(-0.577429\pi\) | ||||
−0.240859 | + | 0.970560i | \(0.577429\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.51504 | − | 2.51504i | −0.160680 | − | 0.160680i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.92026 | −0.503954 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7049 | + | 18.7049i | −1.18064 | + | 1.18064i | −0.201066 | + | 0.979578i | \(0.564441\pi\) |
−0.979578 | + | 0.201066i | \(0.935559\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.48701 | + | 8.48701i | 0.533574 | + | 0.533574i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 18.3076i | − | 1.14200i | −0.820951 | − | 0.570998i | \(-0.806556\pi\) | ||
0.820951 | − | 0.570998i | \(-0.193444\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.31105 | − | 8.31105i | 0.516423 | − | 0.516423i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.1306i | 1.24130i | 0.784086 | + | 0.620652i | \(0.213132\pi\) | ||||
−0.784086 | + | 0.620652i | \(0.786868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 18.7479i | − | 1.15168i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.69779 | + | 8.69779i | −0.530313 | + | 0.530313i | −0.920666 | − | 0.390352i | \(-0.872353\pi\) |
0.390352 | + | 0.920666i | \(0.372353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.6299i | − | 0.706466i | −0.935535 | − | 0.353233i | \(-0.885082\pi\) | ||
0.935535 | − | 0.353233i | \(-0.114918\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.53259 | + | 7.53259i | 0.454232 | + | 0.454232i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.9876 | − | 22.9876i | 1.38119 | − | 1.38119i | 0.538679 | − | 0.842511i | \(-0.318923\pi\) |
0.842511 | − | 0.538679i | \(-0.181077\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.5187 | 0.687148 | 0.343574 | − | 0.939126i | \(-0.388362\pi\) | ||||
0.343574 | + | 0.939126i | \(0.388362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6255 | + | 15.6255i | 0.928839 | + | 0.928839i | 0.997631 | − | 0.0687924i | \(-0.0219146\pi\) |
−0.0687924 | + | 0.997631i | \(0.521915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.56578 | −0.564650 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3521 | −0.785417 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.77816 | − | 3.77816i | −0.220722 | − | 0.220722i | 0.588080 | − | 0.808803i | \(-0.299884\pi\) |
−0.808803 | + | 0.588080i | \(0.799884\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −50.6936 | −2.95150 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.1093 | − | 28.1093i | 1.62560 | − | 1.62560i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.01867 | + | 5.01867i | 0.289271 | + | 0.289271i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.38430i | 0.308304i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.708546 | + | 0.708546i | −0.0404389 | + | 0.0404389i | −0.727037 | − | 0.686598i | \(-0.759103\pi\) |
0.686598 | + | 0.727037i | \(0.259103\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 21.6074i | − | 1.22525i | −0.790376 | − | 0.612623i | \(-0.790115\pi\) | ||
0.790376 | − | 0.612623i | \(-0.209885\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.11637i | 0.289194i | 0.989491 | + | 0.144597i | \(0.0461886\pi\) | ||||
−0.989491 | + | 0.144597i | \(0.953811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.88622 | + | 7.88622i | −0.442934 | + | 0.442934i | −0.892997 | − | 0.450063i | \(-0.851402\pi\) |
0.450063 | + | 0.892997i | \(0.351402\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.03002i | 0.225638i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.69070 | + | 6.69070i | 0.372281 | + | 0.372281i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.9482 | − | 24.9482i | 1.38388 | − | 1.38388i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.37837 | 0.186256 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.144453 | − | 0.144453i | −0.00793985 | − | 0.00793985i | 0.703126 | − | 0.711066i | \(-0.251787\pi\) |
−0.711066 | + | 0.703126i | \(0.751787\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.6975 | −0.857646 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.3255 | −0.998256 | −0.499128 | − | 0.866528i | \(-0.666346\pi\) | ||||
−0.499128 | + | 0.866528i | \(0.666346\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.161896 | − | 0.161896i | −0.00876716 | − | 0.00876716i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.70010 | − | 7.70010i | 0.413363 | − | 0.413363i | −0.469545 | − | 0.882908i | \(-0.655582\pi\) |
0.882908 | + | 0.469545i | \(0.155582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.23902 | + | 9.23902i | 0.494553 | + | 0.494553i | 0.909737 | − | 0.415184i | \(-0.136283\pi\) |
−0.415184 | + | 0.909737i | \(0.636283\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9051i | 0.740092i | 0.929013 | + | 0.370046i | \(0.120658\pi\) | ||||
−0.929013 | + | 0.370046i | \(0.879342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.2716 | + | 19.2716i | −1.02283 | + | 1.02283i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.3979i | 1.07656i | 0.842766 | + | 0.538281i | \(0.180926\pi\) | ||||
−0.842766 | + | 0.538281i | \(0.819074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0503i | 0.844750i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.1411 | + | 21.1411i | −1.10658 | + | 1.10658i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 21.2755i | − | 1.11057i | −0.831660 | − | 0.555285i | \(-0.812609\pi\) | ||
0.831660 | − | 0.555285i | \(-0.187391\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.72717 | − | 3.72717i | −0.193505 | − | 0.193505i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6527 | − | 14.6527i | 0.758688 | − | 0.758688i | −0.217396 | − | 0.976084i | \(-0.569756\pi\) |
0.976084 | + | 0.217396i | \(0.0697562\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.3476 | 0.687434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.85565 | + | 8.85565i | 0.454884 | + | 0.454884i | 0.896972 | − | 0.442088i | \(-0.145762\pi\) |
−0.442088 | + | 0.896972i | \(0.645762\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.3573 | 1.70448 | 0.852238 | − | 0.523154i | \(-0.175245\pi\) | ||||
0.852238 | + | 0.523154i | \(0.175245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.95235 | 0.252395 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.00738 | + | 2.00738i | 0.101778 | + | 0.101778i | 0.756162 | − | 0.654384i | \(-0.227072\pi\) |
−0.654384 | + | 0.756162i | \(0.727072\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −47.4911 | −2.40173 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −34.8865 | + | 34.8865i | −1.75533 | + | 1.75533i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.43985 | − | 2.43985i | −0.122453 | − | 0.122453i | 0.643225 | − | 0.765677i | \(-0.277596\pi\) |
−0.765677 | + | 0.643225i | \(0.777596\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6798i | 0.583263i | 0.956531 | + | 0.291632i | \(0.0941981\pi\) | ||||
−0.956531 | + | 0.291632i | \(0.905802\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.536205 | + | 0.536205i | −0.0267103 | + | 0.0267103i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.3653i | 0.811195i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.2951i | 0.756292i | 0.925746 | + | 0.378146i | \(0.123438\pi\) | ||||
−0.925746 | + | 0.378146i | \(0.876562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.0781 | + | 10.0781i | −0.495911 | + | 0.495911i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 36.7806i | − | 1.80549i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.1833 | − | 13.1833i | −0.644045 | − | 0.644045i | 0.307502 | − | 0.951547i | \(-0.400507\pi\) |
−0.951547 | + | 0.307502i | \(0.900507\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.2574 | + | 22.2574i | −1.08476 | + | 1.08476i | −0.0887017 | + | 0.996058i | \(0.528272\pi\) |
−0.996058 | + | 0.0887017i | \(0.971728\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −42.1504 | −2.04459 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.07042 | + | 1.07042i | 0.0518014 | + | 0.0518014i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.0326 | 0.916769 | 0.458385 | − | 0.888754i | \(-0.348428\pi\) | ||||
0.458385 | + | 0.888754i | \(0.348428\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.7120 | −1.52398 | −0.761992 | − | 0.647587i | \(-0.775778\pi\) | ||||
−0.761992 | + | 0.647587i | \(0.775778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.4688 | + | 10.4688i | 0.500789 | + | 0.500789i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.9521 | −1.57272 | −0.786359 | − | 0.617770i | \(-0.788036\pi\) | ||||
−0.786359 | + | 0.617770i | \(0.788036\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.94776 | − | 4.94776i | 0.235075 | − | 0.235075i | −0.579732 | − | 0.814807i | \(-0.696843\pi\) |
0.814807 | + | 0.579732i | \(0.196843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.8416 | − | 18.8416i | −0.893177 | − | 0.893177i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.5258i | − | 1.48779i | −0.668294 | − | 0.743897i | \(-0.732975\pi\) | ||
0.668294 | − | 0.743897i | \(-0.267025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.41796 | − | 9.41796i | 0.443475 | − | 0.443475i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 16.4023i | − | 0.768954i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.2517i | 1.64901i | 0.565857 | + | 0.824503i | \(0.308545\pi\) | ||||
−0.565857 | + | 0.824503i | \(0.691455\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.8769 | + | 15.8769i | −0.739462 | + | 0.739462i | −0.972474 | − | 0.233012i | \(-0.925142\pi\) |
0.233012 | + | 0.972474i | \(0.425142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.9217i | 0.739946i | 0.929043 | + | 0.369973i | \(0.120633\pi\) | ||||
−0.929043 | + | 0.369973i | \(0.879367\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.52420 | + | 6.52420i | 0.301904 | + | 0.301904i | 0.841758 | − | 0.539854i | \(-0.181521\pi\) |
−0.539854 | + | 0.841758i | \(0.681521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.12073 | + | 3.12073i | −0.144102 | + | 0.144102i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.88224 | −0.454386 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.29148 | + | 9.29148i | 0.426323 | + | 0.426323i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.5891 | 1.44334 | 0.721671 | − | 0.692237i | \(-0.243375\pi\) | ||||
0.721671 | + | 0.692237i | \(0.243375\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 54.2023 | 2.47141 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.7200 | + | 19.7200i | 0.895440 | + | 0.895440i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.4810 | 1.33591 | 0.667955 | − | 0.744202i | \(-0.267170\pi\) | ||||
0.667955 | + | 0.744202i | \(0.267170\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.06862 | − | 6.06862i | 0.273873 | − | 0.273873i | −0.556784 | − | 0.830657i | \(-0.687965\pi\) |
0.830657 | + | 0.556784i | \(0.187965\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.2755 | − | 11.2755i | −0.507821 | − | 0.507821i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.66257i | 0.343713i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.8968 | + | 15.8968i | −0.711638 | + | 0.711638i | −0.966878 | − | 0.255240i | \(-0.917846\pi\) |
0.255240 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 17.1978i | − | 0.766813i | −0.923580 | − | 0.383406i | \(-0.874751\pi\) | ||
0.923580 | − | 0.383406i | \(-0.125249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.76379i | − | 0.167486i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.959431 | − | 0.959431i | 0.0425260 | − | 0.0425260i | −0.685524 | − | 0.728050i | \(-0.740427\pi\) |
0.728050 | + | 0.685524i | \(0.240427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.40588i | 0.371854i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.7180 | − | 29.7180i | −1.30953 | − | 1.30953i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.32617 | + | 3.32617i | −0.146285 | + | 0.146285i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.04026 | −0.396061 | −0.198030 | − | 0.980196i | \(-0.563454\pi\) | ||||
−0.198030 | + | 0.980196i | \(0.563454\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.32615 | + | 5.32615i | 0.232896 | + | 0.232896i | 0.813901 | − | 0.581004i | \(-0.197340\pi\) |
−0.581004 | + | 0.813901i | \(0.697340\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.905927 | 0.0394628 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −51.3080 | −2.23078 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.1926 | − | 31.1926i | −1.35110 | − | 1.35110i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.1921 | −0.959449 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.984548 | − | 0.984548i | 0.0424075 | − | 0.0424075i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7082 | + | 12.7082i | 0.546367 | + | 0.546367i | 0.925388 | − | 0.379021i | \(-0.123739\pi\) |
−0.379021 | + | 0.925388i | \(0.623739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.647588i | 0.0277396i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.7217 | + | 19.7217i | −0.843239 | + | 0.843239i | −0.989279 | − | 0.146040i | \(-0.953347\pi\) |
0.146040 | + | 0.989279i | \(0.453347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.97105i | 0.211774i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8712i | 0.589863i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.2571 | − | 32.2571i | 1.36678 | − | 1.36678i | 0.501789 | − | 0.864990i | \(-0.332675\pi\) |
0.864990 | − | 0.501789i | \(-0.167325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.7303i | 1.38434i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.0814 | + | 27.0814i | 1.14134 | + | 1.14134i | 0.988205 | + | 0.153138i | \(0.0489380\pi\) |
0.153138 | + | 0.988205i | \(0.451062\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.9757 | − | 35.9757i | 1.51351 | − | 1.51351i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.4823 | 1.19404 | 0.597020 | − | 0.802226i | \(-0.296351\pi\) | ||||
0.597020 | + | 0.802226i | \(0.296351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8844 | − | 15.8844i | −0.664743 | − | 0.664743i | 0.291751 | − | 0.956494i | \(-0.405762\pi\) |
−0.956494 | + | 0.291751i | \(0.905762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −65.9516 | −2.75037 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.65713 | 0.193879 | 0.0969395 | − | 0.995290i | \(-0.469095\pi\) | ||||
0.0969395 | + | 0.995290i | \(0.469095\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.31214 | − | 7.31214i | −0.303359 | − | 0.303359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.33916 | 0.303957 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.2034 | − | 13.2034i | 0.544963 | − | 0.544963i | −0.380017 | − | 0.924980i | \(-0.624082\pi\) |
0.924980 | + | 0.380017i | \(0.124082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.199699 | − | 0.199699i | −0.00822847 | − | 0.00822847i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.00745i | 0.328827i | 0.986392 | + | 0.164413i | \(0.0525731\pi\) | ||||
−0.986392 | + | 0.164413i | \(0.947427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.8560 | + | 13.8560i | −0.568041 | + | 0.568041i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.8782i | 1.22079i | 0.792096 | + | 0.610396i | \(0.208990\pi\) | ||||
−0.792096 | + | 0.610396i | \(0.791010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.4594i | − | 1.16088i | −0.814302 | − | 0.580441i | \(-0.802880\pi\) | ||
0.814302 | − | 0.580441i | \(-0.197120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.7896 | − | 22.7896i | 0.926528 | − | 0.926528i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.1606i | − | 1.10242i | −0.834368 | − | 0.551208i | \(-0.814167\pi\) | ||
0.834368 | − | 0.551208i | \(-0.185833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0164 | + | 11.0164i | 0.445675 | + | 0.445675i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.1239 | + | 25.1239i | −1.01474 | + | 1.01474i | −0.0148539 | + | 0.999890i | \(0.504728\pi\) |
−0.999890 | + | 0.0148539i | \(0.995272\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.2712 | −0.816089 | −0.408044 | − | 0.912962i | \(-0.633789\pi\) | ||||
−0.408044 | + | 0.912962i | \(0.633789\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2344 | + | 13.2344i | 0.531937 | + | 0.531937i | 0.921148 | − | 0.389211i | \(-0.127252\pi\) |
−0.389211 | + | 0.921148i | \(0.627252\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.49158 | −0.300144 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.71914 | 0.188766 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.7878 | − | 45.7878i | −1.82568 | − | 1.82568i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.8911 | 1.90651 | 0.953257 | − | 0.302161i | \(-0.0977080\pi\) | ||||
0.953257 | + | 0.302161i | \(0.0977080\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.31769 | + | 3.31769i | −0.131658 | + | 0.131658i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.26086 | − | 3.26086i | −0.129200 | − | 0.129200i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.5861i | 0.931595i | 0.884891 | + | 0.465797i | \(0.154232\pi\) | ||||
−0.884891 | + | 0.465797i | \(0.845768\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.9073 | − | 29.9073i | 1.17943 | − | 1.17943i | 0.199537 | − | 0.979890i | \(-0.436056\pi\) |
0.979890 | − | 0.199537i | \(-0.0639437\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.8559i | 1.40964i | 0.709385 | + | 0.704821i | \(0.248973\pi\) | ||||
−0.709385 | + | 0.704821i | \(0.751027\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 19.8448i | − | 0.778975i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.7966 | + | 26.7966i | −1.04863 | + | 1.04863i | −0.0498765 | + | 0.998755i | \(0.515883\pi\) |
−0.998755 | + | 0.0498765i | \(0.984117\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 19.3226i | − | 0.754995i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.9220 | + | 19.9220i | 0.776050 | + | 0.776050i | 0.979157 | − | 0.203107i | \(-0.0651038\pi\) |
−0.203107 | + | 0.979157i | \(0.565104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.02969 | − | 3.02969i | 0.117841 | − | 0.117841i | −0.645727 | − | 0.763568i | \(-0.723446\pi\) |
0.763568 | + | 0.645727i | \(0.223446\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.10874 | 0.236887 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.6424 | − | 17.6424i | −0.683117 | − | 0.683117i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.10776 | −0.0813693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.8102 | 1.61166 | 0.805832 | − | 0.592144i | \(-0.201718\pi\) | ||||
0.805832 | + | 0.592144i | \(0.201718\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.0622 | − | 11.0622i | −0.425154 | − | 0.425154i | 0.461820 | − | 0.886974i | \(-0.347197\pi\) |
−0.886974 | + | 0.461820i | \(0.847197\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.84085 | 0.300904 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.6844 | − | 25.6844i | 0.982786 | − | 0.982786i | −0.0170687 | − | 0.999854i | \(-0.505433\pi\) |
0.999854 | + | 0.0170687i | \(0.00543339\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.7434 | + | 29.7434i | 1.13644 | + | 1.13644i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 24.3075i | − | 0.926044i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.7276 | + | 15.7276i | −0.598306 | + | 0.598306i | −0.939862 | − | 0.341556i | \(-0.889046\pi\) |
0.341556 | + | 0.939862i | \(0.389046\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 53.4809i | − | 2.02865i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.7005i | 1.99617i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.35804 | + | 4.35804i | −0.164601 | + | 0.164601i | −0.784601 | − | 0.620000i | \(-0.787132\pi\) |
0.620000 | + | 0.784601i | \(0.287132\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.1866i | 0.761352i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.748257 | − | 0.748257i | −0.0281411 | − | 0.0281411i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.68056 | + | 2.68056i | −0.100670 | + | 0.100670i | −0.755648 | − | 0.654978i | \(-0.772678\pi\) |
0.654978 | + | 0.755648i | \(0.272678\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.41748 | 0.0530850 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.1489 | + | 16.1489i | 0.603934 | + | 0.603934i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.9117 | −0.742581 | −0.371290 | − | 0.928517i | \(-0.621085\pi\) | ||||
−0.371290 | + | 0.928517i | \(0.621085\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.8161 | −0.440056 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.6584 | − | 15.6584i | −0.581539 | − | 0.581539i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0642 | −0.892491 | −0.446246 | − | 0.894911i | \(-0.647239\pi\) | ||||
−0.446246 | + | 0.894911i | \(0.647239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.6492 | − | 27.6492i | 1.02264 | − | 1.02264i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.18890 | − | 3.18890i | −0.117785 | − | 0.117785i | 0.645758 | − | 0.763542i | \(-0.276542\pi\) |
−0.763542 | + | 0.645758i | \(0.776542\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.14502i | − | 0.226355i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.8311 | + | 20.8311i | −0.766285 | + | 0.766285i | −0.977450 | − | 0.211165i | \(-0.932274\pi\) |
0.211165 | + | 0.977450i | \(0.432274\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.6291i | − | 1.05030i | −0.851010 | − | 0.525150i | \(-0.824009\pi\) | ||
0.851010 | − | 0.525150i | \(-0.175991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 48.6258i | − | 1.78151i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.41189 | + | 4.41189i | −0.161207 | + | 0.161207i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.1706i | 1.02796i | 0.857802 | + | 0.513980i | \(0.171830\pi\) | ||||
−0.857802 | + | 0.513980i | \(0.828170\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.7042 | − | 12.7042i | −0.462355 | − | 0.462355i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.64056 | + | 4.64056i | −0.168664 | + | 0.168664i | −0.786392 | − | 0.617728i | \(-0.788053\pi\) |
0.617728 | + | 0.786392i | \(0.288053\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.29768 | 0.228291 | 0.114145 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114145 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.128743 | + | 0.128743i | 0.00466082 | + | 0.00466082i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −65.7265 | −2.37325 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.73382 | 0.170706 | 0.0853529 | − | 0.996351i | \(-0.472798\pi\) | ||||
0.0853529 | + | 0.996351i | \(0.472798\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.44275 | − | 5.44275i | −0.195762 | − | 0.195762i | 0.602418 | − | 0.798180i | \(-0.294204\pi\) |
−0.798180 | + | 0.602418i | \(0.794204\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.25808 | 0.0451914 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.6171 | − | 11.6171i | 0.416226 | − | 0.416226i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.54417 | − | 7.54417i | −0.269952 | − | 0.269952i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 55.8852i | − | 1.99463i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.1082 | − | 27.1082i | 0.966302 | − | 0.966302i | −0.0331485 | − | 0.999450i | \(-0.510553\pi\) |
0.999450 | + | 0.0331485i | \(0.0105534\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 14.3042i | − | 0.508600i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.98099i | 0.247902i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.7301 | − | 11.7301i | 0.415501 | − | 0.415501i | −0.468149 | − | 0.883650i | \(-0.655079\pi\) |
0.883650 | + | 0.468149i | \(0.155079\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18.6124i | − | 0.658458i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.27599 | − | 8.27599i | −0.292053 | − | 0.292053i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.6801 | + | 21.6801i | −0.764124 | + | 0.764124i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.7126 | −0.482111 | −0.241055 | − | 0.970511i | \(-0.577494\pi\) | ||||
−0.241055 | + | 0.970511i | \(0.577494\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.2730 | − | 22.2730i | −0.782111 | − | 0.782111i | 0.198076 | − | 0.980187i | \(-0.436531\pi\) |
−0.980187 | + | 0.198076i | \(0.936531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.71195 | 0.165052 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.1898 | −0.426467 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.690329 | − | 0.690329i | −0.0240926 | − | 0.0240926i | 0.694958 | − | 0.719050i | \(-0.255423\pi\) |
−0.719050 | + | 0.694958i | \(0.755423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.43063 | 0.0498688 | 0.0249344 | − | 0.999689i | \(-0.492062\pi\) | ||||
0.0249344 | + | 0.999689i | \(0.492062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.59770 | − | 9.59770i | 0.333745 | − | 0.333745i | −0.520262 | − | 0.854007i | \(-0.674166\pi\) |
0.854007 | + | 0.520262i | \(0.174166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.0260 | + | 17.0260i | 0.591337 | + | 0.591337i | 0.937992 | − | 0.346656i | \(-0.112683\pi\) |
−0.346656 | + | 0.937992i | \(0.612683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.50927i | 0.190885i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.0560 | − | 45.0560i | 1.55923 | − | 1.55923i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 29.0214i | − | 1.00193i | −0.865467 | − | 0.500965i | \(-0.832978\pi\) | ||
0.865467 | − | 0.500965i | \(-0.167022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.6226i | 0.711123i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.7902 | − | 20.7902i | 0.715205 | − | 0.715205i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.06133i | − | 0.311351i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −71.6430 | − | 71.6430i | −2.45589 | − | 2.45589i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.4096 | − | 17.4096i | 0.596092 | − | 0.596092i | −0.343178 | − | 0.939270i | \(-0.611503\pi\) |
0.939270 | + | 0.343178i | \(0.111503\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.6637 | 0.603379 | 0.301690 | − | 0.953406i | \(-0.402449\pi\) | ||||
0.301690 | + | 0.953406i | \(0.402449\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.79823 | − | 5.79823i | −0.197833 | − | 0.197833i | 0.601237 | − | 0.799070i | \(-0.294675\pi\) |
−0.799070 | + | 0.601237i | \(0.794675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.0789 | −1.33026 | −0.665131 | − | 0.746727i | \(-0.731624\pi\) | ||||
−0.665131 | + | 0.746727i | \(0.731624\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.84331 | 0.334683 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.6568 | − | 13.6568i | −0.463277 | − | 0.463277i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.3525 | −0.689618 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.66689 | + | 6.66689i | −0.225382 | + | 0.225382i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.28950 | + | 6.28950i | 0.212381 | + | 0.212381i | 0.805278 | − | 0.592897i | \(-0.202016\pi\) |
−0.592897 | + | 0.805278i | \(0.702016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.5545i | 0.726190i | 0.931752 | + | 0.363095i | \(0.118280\pi\) | ||||
−0.931752 | + | 0.363095i | \(0.881720\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.85864 | + | 5.85864i | −0.197159 | + | 0.197159i | −0.798781 | − | 0.601622i | \(-0.794521\pi\) |
0.601622 | + | 0.798781i | \(0.294521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.0138i | 0.940613i | 0.882503 | + | 0.470306i | \(0.155857\pi\) | ||||
−0.882503 | + | 0.470306i | \(0.844143\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.31914i | 0.0442426i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.10284 | + | 4.10284i | −0.137296 | + | 0.137296i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 82.7628i | 2.76645i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.336542 | + | 0.336542i | 0.0112243 | + | 0.0112243i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.5340 | + | 20.5340i | −0.684087 | + | 0.684087i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.1426 | −0.337151 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.74119 | − | 3.74119i | −0.124224 | − | 0.124224i | 0.642262 | − | 0.766486i | \(-0.277996\pi\) |
−0.766486 | + | 0.642262i | \(0.777996\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.9910 | −1.55688 | −0.778441 | − | 0.627718i | \(-0.783989\pi\) | ||||
−0.778441 | + | 0.627718i | \(0.783989\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.3983 | 0.476514 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.84141 | − | 3.84141i | −0.126855 | − | 0.126855i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.7166 | 0.947272 | 0.473636 | − | 0.880721i | \(-0.342941\pi\) | ||||
0.473636 | + | 0.880721i | \(0.342941\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.9866 | + | 24.9866i | −0.822442 | + | 0.822442i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −63.5863 | − | 63.5863i | −2.09070 | − | 2.09070i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.0905i | 1.28252i | 0.767325 | + | 0.641259i | \(0.221587\pi\) | ||||
−0.767325 | + | 0.641259i | \(0.778413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.21444 | − | 1.21444i | 0.0398018 | − | 0.0398018i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 27.2838i | − | 0.892277i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0325i | 0.719770i | 0.932997 | + | 0.359885i | \(0.117184\pi\) | ||||
−0.932997 | + | 0.359885i | \(0.882816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.7845 | + | 28.7845i | −0.938349 | + | 0.938349i | −0.998207 | − | 0.0598579i | \(-0.980935\pi\) |
0.0598579 | + | 0.998207i | \(0.480935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 82.4590i | 2.68523i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.81984 | + | 8.81984i | 0.286606 | + | 0.286606i | 0.835737 | − | 0.549130i | \(-0.185041\pi\) |
−0.549130 | + | 0.835737i | \(0.685041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.4104 | + | 27.4104i | −0.889778 | + | 0.889778i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.32312 | 0.0428599 | 0.0214300 | − | 0.999770i | \(-0.493178\pi\) | ||||
0.0214300 | + | 0.999770i | \(0.493178\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.9093 | − | 16.9093i | −0.547173 | − | 0.547173i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.8262 | 0.381889 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9730 | 0.999128 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.45926 | − | 3.45926i | −0.111358 | − | 0.111358i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.3028 | −0.524263 | −0.262132 | − | 0.965032i | \(-0.584425\pi\) | ||||
−0.262132 | + | 0.965032i | \(0.584425\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.8788 | + | 16.8788i | −0.541666 | + | 0.541666i | −0.924017 | − | 0.382351i | \(-0.875114\pi\) |
0.382351 | + | 0.924017i | \(0.375114\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.6322 | − | 10.6322i | −0.340854 | − | 0.340854i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.46807i | 0.0469676i | 0.999724 | + | 0.0234838i | \(0.00747581\pi\) | ||||
−0.999724 | + | 0.0234838i | \(0.992524\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.37582 | − | 7.37582i | 0.235732 | − | 0.235732i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.4565i | 1.09899i | 0.835496 | + | 0.549496i | \(0.185180\pi\) | ||||
−0.835496 | + | 0.549496i | \(0.814820\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 51.3241i | 1.63532i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.2620 | − | 43.2620i | 1.37565 | − | 1.37565i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.4789i | 0.459937i | 0.973198 | + | 0.229969i | \(0.0738624\pi\) | ||||
−0.973198 | + | 0.229969i | \(0.926138\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −37.5723 | − | 37.5723i | −1.19112 | − | 1.19112i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.5498 | + | 32.5498i | −1.03086 | + | 1.03086i | −0.0313557 | + | 0.999508i | \(0.509982\pi\) |
−0.999508 | + | 0.0313557i | \(0.990018\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 4032.2.v.e.1583.3 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.1583.18 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.323.2 | ✓ | 40 | ||
12.11 | even | 2 | 1008.2.v.e.323.19 | yes | 40 | ||
16.5 | even | 4 | 1008.2.v.e.827.19 | yes | 40 | ||
16.11 | odd | 4 | inner | 4032.2.v.e.3599.18 | 40 | ||
48.5 | odd | 4 | 1008.2.v.e.827.2 | yes | 40 | ||
48.11 | even | 4 | inner | 4032.2.v.e.3599.3 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.2 | ✓ | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.323.19 | yes | 40 | 12.11 | even | 2 | ||
1008.2.v.e.827.2 | yes | 40 | 48.5 | odd | 4 | ||
1008.2.v.e.827.19 | yes | 40 | 16.5 | even | 4 | ||
4032.2.v.e.1583.3 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.1583.18 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.3599.3 | 40 | 48.11 | even | 4 | inner | ||
4032.2.v.e.3599.18 | 40 | 16.11 | odd | 4 | inner |