Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(127,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.x (of order \(4\), degree \(2\), 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 463.8 | ||
Character | \(\chi\) | \(=\) | 560.463 |
Dual form | 560.2.x.b.127.8 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0.333196 | − | 0.333196i | 0.192371 | − | 0.192371i | −0.604349 | − | 0.796720i | \(-0.706567\pi\) |
0.796720 | + | 0.604349i | \(0.206567\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.17403 | − | 0.523047i | −0.972257 | − | 0.233914i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.77796i | 0.925987i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.81740i | 1.15099i | 0.817806 | + | 0.575494i | \(0.195190\pi\) | ||||
−0.817806 | + | 0.575494i | \(0.804810\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82628 | + | 2.82628i | 0.783870 | + | 0.783870i | 0.980481 | − | 0.196612i | \(-0.0629938\pi\) |
−0.196612 | + | 0.980481i | \(0.562994\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.898656 | + | 0.550102i | −0.232032 | + | 0.142036i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.97020 | + | 2.97020i | −0.720379 | + | 0.720379i | −0.968682 | − | 0.248303i | \(-0.920127\pi\) |
0.248303 | + | 0.968682i | \(0.420127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.82967 | 1.33742 | 0.668709 | − | 0.743525i | \(-0.266847\pi\) | ||||
0.668709 | + | 0.743525i | \(0.266847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.471210 | −0.102826 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.07917 | − | 6.07917i | 1.26759 | − | 1.26759i | 0.320266 | − | 0.947328i | \(-0.396228\pi\) |
0.947328 | − | 0.320266i | \(-0.103772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.45284 | + | 2.27424i | 0.890569 | + | 0.454849i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.92519 | + | 1.92519i | 0.370503 | + | 0.370503i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.62607i | 1.78752i | 0.448550 | + | 0.893758i | \(0.351941\pi\) | ||||
−0.448550 | + | 0.893758i | \(0.648059\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.98706i | − | 0.716097i | −0.933703 | − | 0.358049i | \(-0.883442\pi\) | ||
0.933703 | − | 0.358049i | \(-0.116558\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.27194 | + | 1.27194i | 0.221416 | + | 0.221416i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.16742 | + | 1.90712i | 0.197331 | + | 0.322363i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50707 | − | 1.50707i | 0.247761 | − | 0.247761i | −0.572290 | − | 0.820051i | \(-0.693945\pi\) |
0.820051 | + | 0.572290i | \(0.193945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.88341 | 0.301587 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.04673 | −1.41286 | −0.706431 | − | 0.707782i | \(-0.749696\pi\) | ||||
−0.706431 | + | 0.707782i | \(0.749696\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.59941 | + | 7.59941i | −1.15890 | + | 1.15890i | −0.174187 | + | 0.984713i | \(0.555730\pi\) |
−0.984713 | + | 0.174187i | \(0.944270\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.45301 | − | 6.03938i | 0.216601 | − | 0.900298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.02037 | − | 4.02037i | −0.586432 | − | 0.586432i | 0.350231 | − | 0.936663i | \(-0.386103\pi\) |
−0.936663 | + | 0.350231i | \(0.886103\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.97932i | 0.277160i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.08195 | + | 2.08195i | 0.285978 | + | 0.285978i | 0.835488 | − | 0.549509i | \(-0.185185\pi\) |
−0.549509 | + | 0.835488i | \(0.685185\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.99668 | − | 8.29915i | 0.269232 | − | 1.11906i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.94242 | − | 1.94242i | 0.257280 | − | 0.257280i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.30659 | 0.170103 | 0.0850517 | − | 0.996377i | \(-0.472894\pi\) | ||||
0.0850517 | + | 0.996377i | \(0.472894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.60862 | −0.846147 | −0.423074 | − | 0.906095i | \(-0.639049\pi\) | ||||
−0.423074 | + | 0.906095i | \(0.639049\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.96432 | − | 1.96432i | 0.247480 | − | 0.247480i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.66615 | − | 7.62271i | −0.578765 | − | 0.945481i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.76751 | − | 1.76751i | −0.215936 | − | 0.215936i | 0.590848 | − | 0.806783i | \(-0.298793\pi\) |
−0.806783 | + | 0.590848i | \(0.798793\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4.05110i | − | 0.487696i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3833i | 1.94434i | 0.234273 | + | 0.972171i | \(0.424729\pi\) | ||||
−0.234273 | + | 0.972171i | \(0.575271\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.53966 | + | 7.53966i | 0.882450 | + | 0.882450i | 0.993783 | − | 0.111333i | \(-0.0355120\pi\) |
−0.111333 | + | 0.993783i | \(0.535512\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.24144 | − | 0.725900i | 0.258819 | − | 0.0838197i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.69931 | − | 2.69931i | 0.307615 | − | 0.307615i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.84221 | −0.544792 | −0.272396 | − | 0.962185i | \(-0.587816\pi\) | ||||
−0.272396 | + | 0.962185i | \(0.587816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.05095 | −0.783439 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.140128 | − | 0.140128i | 0.0153810 | − | 0.0153810i | −0.699374 | − | 0.714755i | \(-0.746538\pi\) |
0.714755 | + | 0.699374i | \(0.246538\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.01087 | − | 4.90376i | 0.868901 | − | 0.531887i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.20736 | + | 3.20736i | 0.343866 | + | 0.343866i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.64739i | − | 0.916621i | −0.888792 | − | 0.458310i | \(-0.848455\pi\) | ||
0.888792 | − | 0.458310i | \(-0.151545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.99697i | − | 0.418996i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.32847 | − | 1.32847i | −0.137756 | − | 0.137756i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.6739 | − | 3.04919i | −1.30031 | − | 0.312840i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.77699 | − | 7.77699i | 0.789634 | − | 0.789634i | −0.191800 | − | 0.981434i | \(-0.561433\pi\) |
0.981434 | + | 0.191800i | \(0.0614326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.6046 | −1.06580 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.137557 | 0.0136875 | 0.00684374 | − | 0.999977i | \(-0.497822\pi\) | ||||
0.00684374 | + | 0.999977i | \(0.497822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1193 | − | 11.1193i | 1.09562 | − | 1.09562i | 0.100701 | − | 0.994917i | \(-0.467892\pi\) |
0.994917 | − | 0.100701i | \(-0.0321084\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.02443 | + | 0.246465i | 0.0999738 | + | 0.0240525i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.72055 | + | 1.72055i | 0.166332 | + | 0.166332i | 0.785365 | − | 0.619033i | \(-0.212475\pi\) |
−0.619033 | + | 0.785365i | \(0.712475\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.60302i | 0.249324i | 0.992199 | + | 0.124662i | \(0.0397846\pi\) | ||||
−0.992199 | + | 0.124662i | \(0.960215\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.00430i | − | 0.0953238i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.64057 | + | 4.64057i | 0.436549 | + | 0.436549i | 0.890849 | − | 0.454300i | \(-0.150111\pi\) |
−0.454300 | + | 0.890849i | \(0.650111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.3960 | + | 10.0366i | −1.52893 | + | 0.935919i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.85130 | + | 7.85130i | −0.725853 | + | 0.725853i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.20050 | 0.385059 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.57253 | −0.324775 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.01433 | + | 3.01433i | −0.271793 | + | 0.271793i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.49109 | − | 7.27333i | −0.759466 | − | 0.650547i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.73689 | − | 9.73689i | −0.864009 | − | 0.864009i | 0.127792 | − | 0.991801i | \(-0.459211\pi\) |
−0.991801 | + | 0.127792i | \(0.959211\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.06418i | 0.445876i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.27741i | 0.461089i | 0.973062 | + | 0.230545i | \(0.0740508\pi\) | ||||
−0.973062 | + | 0.230545i | \(0.925949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.12220 | − | 4.12220i | −0.357440 | − | 0.357440i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.17847 | − | 5.19240i | −0.273559 | − | 0.446891i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4098 | − | 10.4098i | 0.889370 | − | 0.889370i | −0.105093 | − | 0.994462i | \(-0.533514\pi\) |
0.994462 | + | 0.105093i | \(0.0335139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.5519 | 1.82801 | 0.914004 | − | 0.405705i | \(-0.132974\pi\) | ||||
0.914004 | + | 0.405705i | \(0.132974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.67914 | −0.225625 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.7890 | + | 10.7890i | −0.902226 | + | 0.902226i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.03489 | − | 20.9274i | 0.418125 | − | 1.73793i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.333196 | + | 0.333196i | 0.0274815 | + | 0.0274815i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.55520i | − | 0.209330i | −0.994508 | − | 0.104665i | \(-0.966623\pi\) | ||
0.994508 | − | 0.104665i | \(-0.0333770\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.09193i | − | 0.414376i | −0.978301 | − | 0.207188i | \(-0.933569\pi\) | ||
0.978301 | − | 0.207188i | \(-0.0664311\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.25110 | − | 8.25110i | −0.667062 | − | 0.667062i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.08542 | + | 8.66800i | −0.167505 | + | 0.696231i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4072 | − | 11.4072i | 0.910396 | − | 0.910396i | −0.0859073 | − | 0.996303i | \(-0.527379\pi\) |
0.996303 | + | 0.0859073i | \(0.0273789\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.38740 | 0.110028 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.59724 | −0.677557 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.35866 | − | 8.35866i | 0.654701 | − | 0.654701i | −0.299420 | − | 0.954121i | \(-0.596793\pi\) |
0.954121 | + | 0.299420i | \(0.0967933\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.09996 | − | 3.43053i | −0.163481 | − | 0.267066i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.72096 | − | 7.72096i | −0.597466 | − | 0.597466i | 0.342172 | − | 0.939637i | \(-0.388837\pi\) |
−0.939637 | + | 0.342172i | \(0.888837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.97575i | 0.228904i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.1946i | 1.23843i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.11677 | − | 4.11677i | −0.312992 | − | 0.312992i | 0.533075 | − | 0.846068i | \(-0.321036\pi\) |
−0.846068 | + | 0.533075i | \(0.821036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.54050 | − | 4.75677i | −0.116451 | − | 0.359578i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.435350 | − | 0.435350i | 0.0327229 | − | 0.0327229i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.11797 | −0.0835612 | −0.0417806 | − | 0.999127i | \(-0.513303\pi\) | ||||
−0.0417806 | + | 0.999127i | \(0.513303\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.22127 | 0.239435 | 0.119718 | − | 0.992808i | \(-0.461801\pi\) | ||||
0.119718 | + | 0.992808i | \(0.461801\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.20196 | + | 2.20196i | −0.162774 | + | 0.162774i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.06469 | + | 2.48815i | −0.298842 | + | 0.182933i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3384 | − | 11.3384i | −0.829148 | − | 0.829148i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 2.72263i | − | 0.198042i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.68124i | − | 0.628152i | −0.949398 | − | 0.314076i | \(-0.898305\pi\) | ||
0.949398 | − | 0.314076i | \(-0.101695\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.69834 | + | 4.69834i | 0.338194 | + | 0.338194i | 0.855687 | − | 0.517493i | \(-0.173135\pi\) |
−0.517493 | + | 0.855687i | \(0.673135\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.09460 | − | 0.985113i | −0.293220 | − | 0.0705454i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.367432 | − | 0.367432i | 0.0261784 | − | 0.0261784i | −0.693896 | − | 0.720075i | \(-0.744107\pi\) |
0.720075 | + | 0.693896i | \(0.244107\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0339 | −0.994836 | −0.497418 | − | 0.867511i | \(-0.665718\pi\) | ||||
−0.497418 | + | 0.867511i | \(0.665718\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.17785 | −0.0830794 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.80666 | − | 6.80666i | 0.477734 | − | 0.477734i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.6679 | + | 4.73187i | 1.37366 | + | 0.330488i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.8877 | + | 16.8877i | 1.17378 | + | 1.17378i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.2542i | 1.53935i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.2984i | 1.05319i | 0.850117 | + | 0.526594i | \(0.176531\pi\) | ||||
−0.850117 | + | 0.526594i | \(0.823469\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.45885 | + | 5.45885i | 0.374034 | + | 0.374034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.4962 | − | 12.5465i | 1.39783 | − | 0.855666i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.81928 | + | 2.81928i | −0.191385 | + | 0.191385i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.02436 | 0.339515 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.7892 | −1.12937 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.89248 | − | 9.89248i | 0.662449 | − | 0.662449i | −0.293508 | − | 0.955957i | \(-0.594823\pi\) |
0.955957 | + | 0.293508i | \(0.0948226\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.31776 | + | 12.3698i | −0.421184 | + | 0.824655i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.567441 | − | 0.567441i | −0.0376624 | − | 0.0376624i | 0.688025 | − | 0.725687i | \(-0.258478\pi\) |
−0.725687 | + | 0.688025i | \(0.758478\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.7682i | 0.777665i | 0.921308 | + | 0.388833i | \(0.127122\pi\) | ||||
−0.921308 | + | 0.388833i | \(0.872878\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.79880i | − | 0.118352i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.92993 | + | 1.92993i | 0.126434 | + | 0.126434i | 0.767492 | − | 0.641058i | \(-0.221504\pi\) |
−0.641058 | + | 0.767492i | \(0.721504\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.63758 | + | 10.8433i | 0.432988 | + | 0.707337i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.61341 | + | 1.61341i | −0.104802 | + | 0.104802i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.8823 | −0.768599 | −0.384300 | − | 0.923208i | \(-0.625557\pi\) | ||||
−0.384300 | + | 0.923208i | \(0.625557\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0826315 | −0.00532276 | −0.00266138 | − | 0.999996i | \(-0.500847\pi\) | ||||
−0.00266138 | + | 0.999996i | \(0.500847\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.12492 | + | 8.12492i | −0.521214 | + | 0.521214i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.523047 | − | 2.17403i | 0.0334163 | − | 0.138894i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4763 | + | 16.4763i | 1.04836 | + | 1.04836i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 0.0933799i | − | 0.00591771i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.5411i | − | 1.35966i | −0.733370 | − | 0.679830i | \(-0.762054\pi\) | ||
0.733370 | − | 0.679830i | \(-0.237946\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.2066 | + | 23.2066i | 1.45899 | + | 1.45899i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.03528 | − | 4.30310i | 0.0648315 | − | 0.269471i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.29985 | − | 2.29985i | 0.143461 | − | 0.143461i | −0.631729 | − | 0.775189i | \(-0.717654\pi\) |
0.775189 | + | 0.631729i | \(0.217654\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.13132 | −0.132434 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.7408 | −1.65522 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.06625 | − | 7.06625i | 0.435724 | − | 0.435724i | −0.454846 | − | 0.890570i | \(-0.650306\pi\) |
0.890570 | + | 0.454846i | \(0.150306\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.43728 | − | 5.61520i | −0.211150 | − | 0.344939i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.88127 | − | 2.88127i | −0.176331 | − | 0.176331i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.9551i | 1.15571i | 0.816138 | + | 0.577857i | \(0.196111\pi\) | ||||
−0.816138 | + | 0.577857i | \(0.803889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.29238i | 0.382235i | 0.981567 | + | 0.191117i | \(0.0612111\pi\) | ||||
−0.981567 | + | 0.191117i | \(0.938789\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.33177 | − | 1.33177i | −0.0806026 | − | 0.0806026i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.68170 | + | 16.9983i | −0.523526 | + | 1.02503i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.90581 | + | 9.90581i | −0.595183 | + | 0.595183i | −0.939027 | − | 0.343844i | \(-0.888271\pi\) |
0.343844 | + | 0.939027i | \(0.388271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.0759 | 0.663097 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0267 | 0.956073 | 0.478037 | − | 0.878340i | \(-0.341349\pi\) | ||||
0.478037 | + | 0.878340i | \(0.341349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2462 | − | 11.2462i | 0.668519 | − | 0.668519i | −0.288854 | − | 0.957373i | \(-0.593274\pi\) |
0.957373 | + | 0.288854i | \(0.0932744\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.23886 | + | 3.20691i | −0.310323 | + | 0.189961i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.39700 | + | 6.39700i | 0.377603 | + | 0.377603i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 0.644170i | − | 0.0378924i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 5.18252i | − | 0.303805i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.0612109 | − | 0.0612109i | −0.00357598 | − | 0.00357598i | 0.705317 | − | 0.708893i | \(-0.250805\pi\) |
−0.708893 | + | 0.705317i | \(0.750805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.84057 | − | 0.683408i | −0.165384 | − | 0.0397896i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.34923 | + | 7.34923i | −0.426445 | + | 0.426445i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 34.3629 | 1.98726 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.7472 | 0.619458 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.0458336 | − | 0.0458336i | 0.00263307 | − | 0.00263307i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.3674 | + | 3.45662i | 0.822673 | + | 0.197926i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.06970 | − | 2.06970i | −0.118124 | − | 0.118124i | 0.645574 | − | 0.763698i | \(-0.276618\pi\) |
−0.763698 | + | 0.645574i | \(0.776618\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 7.40981i | − | 0.421529i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.71330i | 0.323971i | 0.986793 | + | 0.161986i | \(0.0517899\pi\) | ||||
−0.986793 | + | 0.161986i | \(0.948210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9453 | + | 12.9453i | 0.731710 | + | 0.731710i | 0.970958 | − | 0.239248i | \(-0.0769010\pi\) |
−0.239248 | + | 0.970958i | \(0.576901\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.29792 | + | 3.24306i | −0.298504 | + | 0.182726i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.42299 | + | 2.42299i | −0.136089 | + | 0.136089i | −0.771870 | − | 0.635781i | \(-0.780678\pi\) |
0.635781 | + | 0.771870i | \(0.280678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.7465 | −2.05741 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.14656 | 0.0639947 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.3153 | + | 17.3153i | −0.963447 | + | 0.963447i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.15734 | + | 19.0127i | 0.341548 | + | 1.05463i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.867315 | + | 0.867315i | 0.0479626 | + | 0.0479626i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.68567i | 0.313461i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 19.4379i | − | 1.06840i | −0.845357 | − | 0.534201i | \(-0.820613\pi\) | ||
0.845357 | − | 0.534201i | \(-0.179387\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.18658 | + | 4.18658i | 0.229423 | + | 0.229423i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.91813 | + | 4.76712i | 0.159435 | + | 0.260455i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.92413 | + | 9.92413i | −0.540602 | + | 0.540602i | −0.923705 | − | 0.383103i | \(-0.874855\pi\) |
0.383103 | + | 0.923705i | \(0.374855\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.09244 | 0.167958 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.2202 | 0.824220 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.11892 | + | 8.80724i | −0.114079 | + | 0.474166i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.03794 | + | 3.03794i | 0.163085 | + | 0.163085i | 0.783932 | − | 0.620847i | \(-0.213211\pi\) |
−0.620847 | + | 0.783932i | \(0.713211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 34.2112i | − | 1.83128i | −0.401995 | − | 0.915642i | \(-0.631683\pi\) | ||
0.401995 | − | 0.915642i | \(-0.368317\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.8823i | 0.580853i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.7240 | − | 17.7240i | −0.943353 | − | 0.943353i | 0.0551265 | − | 0.998479i | \(-0.482444\pi\) |
−0.998479 | + | 0.0551265i | \(0.982444\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.56925 | − | 35.6179i | 0.454808 | − | 1.89040i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.39959 | − | 1.39959i | 0.0740740 | − | 0.0740740i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1630 | 0.853053 | 0.426527 | − | 0.904475i | \(-0.359737\pi\) | ||||
0.426527 | + | 0.904475i | \(0.359737\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.9850 | 0.788684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.19035 | + | 1.19035i | −0.0624773 | + | 0.0624773i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.4479 | − | 20.3351i | −0.651551 | − | 1.06439i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.88533 | + | 4.88533i | 0.255012 | + | 0.255012i | 0.823022 | − | 0.568010i | \(-0.192286\pi\) |
−0.568010 | + | 0.823022i | \(0.692286\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 25.1315i | − | 1.30829i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.94433i | − | 0.152862i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.1847 | − | 20.1847i | −1.04512 | − | 1.04512i | −0.998933 | − | 0.0461909i | \(-0.985292\pi\) |
−0.0461909 | − | 0.998933i | \(-0.514708\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.25264 | + | 0.405753i | −0.271245 | + | 0.0209530i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.2060 | + | 27.2060i | −1.40118 | + | 1.40118i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.3515 | 1.55905 | 0.779525 | − | 0.626371i | \(-0.215460\pi\) | ||||
0.779525 | + | 0.626371i | \(0.215460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.48858 | −0.332420 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.7350 | + | 11.7350i | −0.599632 | + | 0.599632i | −0.940215 | − | 0.340583i | \(-0.889376\pi\) |
0.340583 | + | 0.940215i | \(0.389376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.28025 | + | 4.45652i | −0.371036 | + | 0.227125i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.1109 | − | 21.1109i | −1.07313 | − | 1.07313i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.1406i | 1.07187i | 0.844260 | + | 0.535934i | \(0.180041\pi\) | ||||
−0.844260 | + | 0.535934i | \(0.819959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.1127i | 1.82630i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.75841 | + | 1.75841i | 0.0887000 | + | 0.0887000i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.5271 | + | 2.53271i | 0.529678 | + | 0.127434i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.7106 | + | 13.7106i | −0.688116 | + | 0.688116i | −0.961815 | − | 0.273699i | \(-0.911753\pi\) |
0.273699 | + | 0.961815i | \(0.411753\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.74700 | −0.137522 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.204376 | 0.0102061 | 0.00510303 | − | 0.999987i | \(-0.498376\pi\) | ||||
0.00510303 | + | 0.999987i | \(0.498376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.2686 | − | 11.2686i | 0.561327 | − | 0.561327i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.3290 | + | 3.68798i | 0.761704 | + | 0.183257i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.75309 | + | 5.75309i | 0.285170 | + | 0.285170i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.828467i | − | 0.0409650i | −0.999790 | − | 0.0204825i | \(-0.993480\pi\) | ||
0.999790 | − | 0.0204825i | \(-0.00652024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.93701i | − | 0.342177i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.923898 | − | 0.923898i | −0.0454621 | − | 0.0454621i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.377936 | + | 0.231349i | −0.0185521 | + | 0.0113565i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.18100 | − | 7.18100i | 0.351655 | − | 0.351655i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.4341 | −0.802858 | −0.401429 | − | 0.915890i | \(-0.631486\pi\) | ||||
−0.401429 | + | 0.915890i | \(0.631486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3657 | 1.23625 | 0.618125 | − | 0.786080i | \(-0.287893\pi\) | ||||
0.618125 | + | 0.786080i | \(0.287893\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.1684 | − | 11.1684i | 0.543028 | − | 0.543028i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.9808 | + | 6.47087i | −0.969211 | + | 0.313883i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.67300 | + | 4.67300i | 0.226142 | + | 0.226142i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.18973i | 0.347123i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.01988i | 0.241799i | 0.992665 | + | 0.120899i | \(0.0385779\pi\) | ||||
−0.992665 | + | 0.120899i | \(0.961422\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.5692 | + | 10.5692i | 0.507922 | + | 0.507922i | 0.913888 | − | 0.405966i | \(-0.133065\pi\) |
−0.405966 | + | 0.913888i | \(0.633065\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.29532 | − | 8.65052i | −0.253891 | − | 0.414761i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 35.4395 | − | 35.4395i | 1.69530 | − | 1.69530i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0536 | −1.05256 | −0.526281 | − | 0.850311i | \(-0.676414\pi\) | ||||
−0.526281 | + | 0.850311i | \(0.676414\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.77796 | −0.132284 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.29114 | + | 3.29114i | −0.156367 | + | 0.156367i | −0.780955 | − | 0.624588i | \(-0.785267\pi\) |
0.624588 | + | 0.780955i | \(0.285267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.52299 | + | 18.7997i | −0.214410 | + | 0.891191i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.851380 | − | 0.851380i | −0.0402689 | − | 0.0402689i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.98319i | 0.235171i | 0.993063 | + | 0.117586i | \(0.0375154\pi\) | ||||
−0.993063 | + | 0.117586i | \(0.962485\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 34.5350i | − | 1.62619i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.69661 | − | 1.69661i | −0.0797137 | − | 0.0797137i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.09060 | + | 8.68954i | −0.0980090 | + | 0.407372i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.5710 | − | 25.5710i | 1.19616 | − | 1.19616i | 0.220852 | − | 0.975307i | \(-0.429116\pi\) |
0.975307 | − | 0.220852i | \(-0.0708839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.4364 | −0.533806 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.0776 | 1.07483 | 0.537415 | − | 0.843318i | \(-0.319401\pi\) | ||||
0.537415 | + | 0.843318i | \(0.319401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.9238 | + | 16.9238i | −0.786515 | + | 0.786515i | −0.980921 | − | 0.194406i | \(-0.937722\pi\) |
0.194406 | + | 0.980921i | \(0.437722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.19329 | + | 3.58299i | 0.101711 | + | 0.166157i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.7840 | − | 22.7840i | −1.05432 | − | 1.05432i | −0.998437 | − | 0.0558816i | \(-0.982203\pi\) |
−0.0558816 | − | 0.998437i | \(-0.517797\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.49964i | 0.115423i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.60168i | − | 0.350267i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −29.0100 | − | 29.0100i | −1.33388 | − | 1.33388i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.9586 | + | 13.2581i | 1.19106 | + | 0.608323i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.78359 | + | 5.78359i | −0.264812 | + | 0.264812i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.95663 | −0.226474 | −0.113237 | − | 0.993568i | \(-0.536122\pi\) | ||||
−0.113237 | + | 0.993568i | \(0.536122\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.51881 | 0.388424 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.86456 | + | 2.86456i | −0.130342 | + | 0.130342i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.9752 | + | 12.8397i | −0.952433 | + | 0.583021i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.2990 | + | 17.2990i | 0.783890 | + | 0.783890i | 0.980485 | − | 0.196594i | \(-0.0629882\pi\) |
−0.196594 | + | 0.980485i | \(0.562988\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.57014i | − | 0.251890i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 33.3763i | − | 1.50625i | −0.657875 | − | 0.753127i | \(-0.728545\pi\) | ||
0.657875 | − | 0.753127i | \(-0.271455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.5913 | − | 28.5913i | −1.28769 | − | 1.28769i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.0547 | + | 5.54670i | 1.03623 | + | 0.249306i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.5848 | − | 11.5848i | 0.519647 | − | 0.519647i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.33451 | 0.0597409 | 0.0298704 | − | 0.999554i | \(-0.490491\pi\) | ||||
0.0298704 | + | 0.999554i | \(0.490491\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.14518 | −0.229870 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.91743 | + | 6.91743i | −0.308433 | + | 0.308433i | −0.844301 | − | 0.535868i | \(-0.819984\pi\) |
0.535868 | + | 0.844301i | \(0.319984\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.299054 | − | 0.0719490i | −0.0133077 | − | 0.00320169i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.991508 | + | 0.991508i | 0.0440344 | + | 0.0440344i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17.9574i | − | 0.795948i | −0.917397 | − | 0.397974i | \(-0.869713\pi\) | ||
0.917397 | − | 0.397974i | \(-0.130287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.6627i | − | 0.471689i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.2232 | + | 11.2232i | 0.495518 | + | 0.495518i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.9897 | + | 18.3578i | −1.32150 | + | 0.808942i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.3474 | − | 15.3474i | 0.674977 | − | 0.674977i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.74338 | −0.120421 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.98311 | −0.218314 | −0.109157 | − | 0.994025i | \(-0.534815\pi\) | ||||
−0.109157 | + | 0.994025i | \(0.534815\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.4478 | + | 25.4478i | −1.11275 | + | 1.11275i | −0.119978 | + | 0.992777i | \(0.538283\pi\) |
−0.992777 | + | 0.119978i | \(0.961717\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.09822 | − | 1.07165i | −0.0915740 | − | 0.0467705i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.8424 | + | 11.8424i | 0.515861 | + | 0.515861i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 50.9125i | − | 2.21359i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.62966i | 0.157514i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.5686 | − | 25.5686i | −1.10750 | − | 1.10750i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.84060 | − | 4.64046i | −0.122810 | − | 0.200625i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.372504 | + | 0.372504i | −0.0160747 | + | 0.0160747i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.81740 | −0.164427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.6523 | 1.10288 | 0.551439 | − | 0.834215i | \(-0.314079\pi\) | ||||
0.551439 | + | 0.834215i | \(0.314079\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.07331 | − | 1.07331i | 0.0460603 | − | 0.0460603i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.36150 | − | 5.65905i | 0.0583203 | − | 0.242407i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0308 | − | 16.0308i | −0.685427 | − | 0.685427i | 0.275791 | − | 0.961218i | \(-0.411060\pi\) |
−0.961218 | + | 0.275791i | \(0.911060\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 18.3585i | − | 0.783521i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 56.1168i | 2.39065i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.42396 | + | 3.42396i | 0.145602 | + | 0.145602i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.525296 | + | 2.18338i | −0.0222976 | + | 0.0926793i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.1371 | + | 21.1371i | −0.895609 | + | 0.895609i | −0.995044 | − | 0.0994352i | \(-0.968296\pi\) |
0.0994352 | + | 0.995044i | \(0.468296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.9562 | −1.81685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.55584 | −0.319008 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6782 | + | 15.6782i | −0.660756 | + | 0.660756i | −0.955558 | − | 0.294802i | \(-0.904746\pi\) |
0.294802 | + | 0.955558i | \(0.404746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.66152 | − | 12.5160i | −0.322323 | − | 0.526552i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.98578 | + | 4.98578i | 0.209383 | + | 0.209383i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 18.9016i | − | 0.792398i | −0.918165 | − | 0.396199i | \(-0.870329\pi\) | ||
0.918165 | − | 0.396199i | \(-0.129671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 31.8188i | − | 1.33158i | −0.746141 | − | 0.665788i | \(-0.768096\pi\) | ||
0.746141 | − | 0.665788i | \(-0.231904\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.89255 | − | 2.89255i | −0.120838 | − | 0.120838i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.8951 | − | 13.2441i | 1.70544 | − | 0.552315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.9993 | + | 25.9993i | −1.08236 | + | 1.08236i | −0.0860749 | + | 0.996289i | \(0.527432\pi\) |
−0.996289 | + | 0.0860749i | \(0.972568\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.13093 | 0.130117 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.198171 | −0.00822150 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.94765 | + | 7.94765i | −0.329158 | + | 0.329158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.1756 | − | 12.9624i | 0.875503 | − | 0.535929i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.1808 | − | 23.1808i | −0.956773 | − | 0.956773i | 0.0423309 | − | 0.999104i | \(-0.486522\pi\) |
−0.999104 | + | 0.0423309i | \(0.986522\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 23.2432i | − | 0.957720i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 0.244853i | − | 0.0100719i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.87270 | + | 2.87270i | 0.117968 | + | 0.117968i | 0.763626 | − | 0.645659i | \(-0.223417\pi\) |
−0.645659 | + | 0.763626i | \(0.723417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.13202 | − | 2.19706i | −0.374376 | − | 0.0900706i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.67603 | + | 4.67603i | −0.191377 | + | 0.191377i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3151 | 0.625757 | 0.312878 | − | 0.949793i | \(-0.398707\pi\) | ||||
0.312878 | + | 0.949793i | \(0.398707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.00274728 | 0.000112064 | 5.60320e−5 | − | 1.00000i | \(-0.499982\pi\) | ||||
5.60320e−5 | 1.00000i | \(0.499982\pi\) | ||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.91007 | − | 4.91007i | 0.199954 | − | 0.199954i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.76680 | + | 1.86860i | 0.315765 | + | 0.0759695i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.7364 | − | 34.7364i | −1.40991 | − | 1.40991i | −0.760091 | − | 0.649817i | \(-0.774845\pi\) |
−0.649817 | − | 0.760091i | \(-0.725155\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 4.53590i | − | 0.183804i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 22.7254i | − | 0.919373i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.06336 | + | 3.06336i | 0.123728 | + | 0.123728i | 0.766259 | − | 0.642531i | \(-0.222116\pi\) |
−0.642531 | + | 0.766259i | \(0.722116\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.12990 | − | 4.97662i | 0.327829 | − | 0.200677i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.24856 | + | 9.24856i | −0.372333 | + | 0.372333i | −0.868326 | − | 0.495993i | \(-0.834804\pi\) |
0.495993 | + | 0.868326i | \(0.334804\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.4110 | −0.458647 | −0.229323 | − | 0.973350i | \(-0.573651\pi\) | ||||
−0.229323 | + | 0.973350i | \(0.573651\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.4071 | 0.939296 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.11462 | + | 6.11462i | −0.244977 | + | 0.244977i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.6556 | + | 20.2537i | 0.586225 | + | 0.810148i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.41499 | + | 7.41499i | 0.296126 | + | 0.296126i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.95260i | 0.356963i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.5223i | − | 0.458694i | −0.973345 | − | 0.229347i | \(-0.926341\pi\) | ||
0.973345 | − | 0.229347i | \(-0.0736591\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.09737 | + | 5.09737i | 0.202602 | + | 0.202602i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0755 | + | 26.2612i | 0.637935 | + | 1.04214i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.82628 | + | 2.82628i | −0.111981 | + | 0.111981i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.5122 | −1.80044 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.4926 | 1.63886 | 0.819429 | − | 0.573180i | \(-0.194291\pi\) | ||||
0.819429 | + | 0.573180i | \(0.194291\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.262424 | + | 0.262424i | −0.0103490 | + | 0.0103490i | −0.712262 | − | 0.701913i | \(-0.752329\pi\) |
0.701913 | + | 0.712262i | \(0.252329\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.64881 | − | 11.0097i | 0.104297 | − | 0.433507i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.3573 | + | 16.3573i | 0.643072 | + | 0.643072i | 0.951309 | − | 0.308237i | \(-0.0997391\pi\) |
−0.308237 | + | 0.951309i | \(0.599739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.98777i | 0.195787i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.87874i | 0.0736337i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.04424 | + | 5.04424i | 0.197397 | + | 0.197397i | 0.798883 | − | 0.601486i | \(-0.205425\pi\) |
−0.601486 | + | 0.798883i | \(0.705425\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.76033 | − | 11.4733i | 0.107855 | − | 0.448297i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.9449 | + | 20.9449i | −0.817137 | + | 0.817137i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.0645 | 0.976374 | 0.488187 | − | 0.872739i | \(-0.337658\pi\) | ||||
0.488187 | + | 0.872739i | \(0.337658\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.39811 | 0.0932757 | 0.0466378 | − | 0.998912i | \(-0.485149\pi\) | ||||
0.0466378 | + | 0.998912i | \(0.485149\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.59411 | + | 5.59411i | −0.217257 | + | 0.217257i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.80569 | + | 11.1179i | 0.263913 | + | 0.431134i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 58.5185 | + | 58.5185i | 2.26584 | + | 2.26584i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 6.59226i | − | 0.254872i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 25.2277i | − | 0.973906i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.7100 | − | 28.7100i | −1.10669 | − | 1.10669i | −0.993583 | − | 0.113105i | \(-0.963920\pi\) |
−0.113105 | − | 0.993583i | \(-0.536080\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.19422 | + | 12.9509i | 0.161436 | + | 0.498482i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.1474 | + | 20.1474i | −0.774328 | + | 0.774328i | −0.978860 | − | 0.204532i | \(-0.934433\pi\) |
0.204532 | + | 0.978860i | \(0.434433\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9983 | −0.422077 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.378138 | −0.0144903 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.9562 | − | 28.9562i | 1.10798 | − | 1.10798i | 0.114562 | − | 0.993416i | \(-0.463453\pi\) |
0.993416 | − | 0.114562i | \(-0.0365466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.0761 | + | 17.1864i | −1.07273 | + | 0.656660i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.92112 | + | 3.92112i | 0.149600 | + | 0.149600i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.7684i | 0.448340i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.1260i | 1.37430i | 0.726517 | + | 0.687149i | \(0.241138\pi\) | ||||
−0.726517 | + | 0.687149i | \(0.758862\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.49857 | + | 7.49857i | 0.284847 | + | 0.284847i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46.8546 | − | 11.2727i | −1.77729 | − | 0.427597i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.8706 | − | 26.8706i | 1.01780 | − | 1.01780i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.28609 | 0.0486444 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.3685 | 0.693768 | 0.346884 | − | 0.937908i | \(-0.387240\pi\) | ||||
0.346884 | + | 0.937908i | \(0.387240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.78571 | − | 8.78571i | 0.331359 | − | 0.331359i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.82455 | + | 1.40132i | 0.219365 | + | 0.0527767i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0972678 | − | 0.0972678i | −0.00365813 | − | 0.00365813i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.15273i | 0.231071i | 0.993303 | + | 0.115535i | \(0.0368583\pi\) | ||||
−0.993303 | + | 0.115535i | \(0.963142\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 13.4515i | − | 0.504470i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.2380 | − | 24.2380i | −0.907720 | − | 0.907720i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.0989 | − | 17.8126i | 1.08824 | − | 0.666152i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.95912 | + | 3.95912i | −0.147856 | + | 0.147856i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.8753 | 0.778516 | 0.389258 | − | 0.921129i | \(-0.372731\pi\) | ||||
0.389258 | + | 0.921129i | \(0.372731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7251 | −0.585632 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.0275325 | + | 0.0275325i | −0.00102394 | + | 0.00102394i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.8920 | + | 42.8634i | −0.813050 | + | 1.59191i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.4058 | + | 11.4058i | 0.423018 | + | 0.423018i | 0.886241 | − | 0.463224i | \(-0.153307\pi\) |
−0.463224 | + | 0.886241i | \(0.653307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 15.7385i | − | 0.582906i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 45.1435i | − | 1.66969i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.7765 | + | 15.7765i | 0.582720 | + | 0.582720i | 0.935650 | − | 0.352930i | \(-0.114815\pi\) |
−0.352930 | + | 0.935650i | \(0.614815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.550102 | − | 0.898656i | −0.0202908 | − | 0.0331474i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.74729 | − | 6.74729i | 0.248540 | − | 0.248540i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4438 | 0.788821 | 0.394411 | − | 0.918934i | \(-0.370949\pi\) | ||||
0.394411 | + | 0.918934i | \(0.370949\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.9797 | 0.403348 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.7547 | − | 36.7547i | 1.34840 | − | 1.34840i | 0.460999 | − | 0.887401i | \(-0.347491\pi\) |
0.887401 | − | 0.460999i | \(-0.152509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.33649 | + | 5.55508i | −0.0489651 | + | 0.203522i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.389269 | + | 0.389269i | 0.0142426 | + | 0.0142426i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.43323i | − | 0.0889081i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.0404i | 1.64355i | 0.569814 | + | 0.821773i | \(0.307015\pi\) | ||||
−0.569814 | + | 0.821773i | \(0.692985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.17739 | − | 7.17739i | −0.261559 | − | 0.261559i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.66332 | + | 11.0700i | −0.0969282 | + | 0.402880i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.5287 | + | 15.5287i | −0.564402 | + | 0.564402i | −0.930555 | − | 0.366153i | \(-0.880675\pi\) |
0.366153 | + | 0.930555i | \(0.380675\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.4647 | 0.561332 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.8503 | 1.77082 | 0.885410 | − | 0.464810i | \(-0.153877\pi\) | ||||
0.885410 | + | 0.464810i | \(0.153877\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.84061 | − | 1.84061i | 0.0666346 | − | 0.0666346i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.6225 | + | 22.2539i | 0.492521 | + | 0.804591i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.69279 | + | 3.69279i | 0.133339 | + | 0.133339i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.0179i | 1.51520i | 0.652717 | + | 0.757602i | \(0.273629\pi\) | ||||
−0.652717 | + | 0.757602i | \(0.726371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.53260i | − | 0.0551952i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.2873 | + | 22.2873i | 0.801617 | + | 0.801617i | 0.983348 | − | 0.181731i | \(-0.0581700\pi\) |
−0.181731 | + | 0.983348i | \(0.558170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.06755 | − | 17.7538i | 0.325716 | − | 0.637734i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.710146 | + | 0.710146i | −0.0254764 | + | 0.0254764i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52.7394 | −1.88959 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62.5416 | −2.23792 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.5320 | + | 18.5320i | −0.662281 | + | 0.662281i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.7662 | + | 18.8332i | −1.09809 | + | 0.672185i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.02249 | − | 7.02249i | −0.250325 | − | 0.250325i | 0.570779 | − | 0.821104i | \(-0.306641\pi\) |
−0.821104 | + | 0.570779i | \(0.806641\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 4.70889i | − | 0.167641i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.56276i | − | 0.233345i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.6778 | − | 18.6778i | −0.663269 | − | 0.663269i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.01625 | − | 0.725674i | −0.106975 | − | 0.0257370i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.5655 | − | 32.5655i | 1.15353 | − | 1.15353i | 0.167689 | − | 0.985840i | \(-0.446370\pi\) |
0.985840 | − | 0.167689i | \(-0.0536305\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.8826 | 0.844907 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0221 | 0.848779 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.7819 | + | 28.7819i | −1.01569 | + | 1.01569i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.6907 | + | 4.49676i | 0.658760 | + | 0.158490i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.31577 | + | 6.31577i | 0.222326 | + | 0.222326i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.1322i | 1.30550i | 0.757574 | + | 0.652749i | \(0.226385\pi\) | ||||
−0.757574 | + | 0.652749i | \(0.773615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.6853i | 1.35842i | 0.733942 | + | 0.679212i | \(0.237678\pi\) | ||||
−0.733942 | + | 0.679212i | \(0.762322\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.09660 | + | 2.09660i | 0.0735308 | + | 0.0735308i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.5440 | + | 13.8000i | −0.789681 | + | 0.483394i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44.3020 | + | 44.3020i | −1.54993 | + | 1.54993i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.1034 | 0.387985 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.64526 | 0.162121 | 0.0810604 | − | 0.996709i | \(-0.474169\pi\) | ||||
0.0810604 | + | 0.996709i | \(0.474169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.06410 | + | 1.06410i | −0.0370922 | + | 0.0370922i | −0.725410 | − | 0.688317i | \(-0.758350\pi\) |
0.688317 | + | 0.725410i | \(0.258350\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.77105 | + | 8.55646i | 0.0964755 | + | 0.297898i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.7207 | − | 23.7207i | −0.824848 | − | 0.824848i | 0.161951 | − | 0.986799i | \(-0.448221\pi\) |
−0.986799 | + | 0.161951i | \(0.948221\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.1640i | − | 0.908712i | −0.890820 | − | 0.454356i | \(-0.849869\pi\) | ||
0.890820 | − | 0.454356i | \(-0.150131\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.60115i | 0.228991i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.97020 | − | 2.97020i | −0.102911 | − | 0.102911i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.7472 | + | 20.8240i | 0.441135 | + | 0.720646i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.67586 | − | 7.67586i | 0.265316 | − | 0.265316i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.6861 | 0.472497 | 0.236248 | − | 0.971693i | \(-0.424082\pi\) | ||||
0.236248 | + | 0.971693i | \(0.424082\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −63.6612 | −2.19521 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.34003 | − | 5.34003i | 0.183920 | − | 0.183920i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.55646 | − | 6.46939i | 0.0535438 | − | 0.222554i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.52616 | + | 2.52616i | 0.0867999 | + | 0.0867999i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 7.49439i | − | 0.257207i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 18.3235i | − | 0.628120i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.6605 | + | 27.6605i | 0.947078 | + | 0.947078i | 0.998668 | − | 0.0515899i | \(-0.0164289\pi\) |
−0.0515899 | + | 0.998668i | \(0.516429\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.47053 | − | 35.2076i | 0.289686 | − | 1.20407i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.1713 | − | 13.1713i | 0.449924 | − | 0.449924i | −0.445405 | − | 0.895329i | \(-0.646940\pi\) |
0.895329 | + | 0.445405i | \(0.146940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.4624 | −0.356972 | −0.178486 | − | 0.983942i | \(-0.557120\pi\) | ||||
−0.178486 | + | 0.983942i | \(0.557120\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.26291 | 0.145280 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.3600 | − | 21.3600i | 0.727104 | − | 0.727104i | −0.242938 | − | 0.970042i | \(-0.578111\pi\) |
0.970042 | + | 0.242938i | \(0.0781110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.79673 | + | 11.1033i | 0.231096 | + | 0.377522i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.214635 | − | 0.214635i | −0.00728938 | − | 0.00728938i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 18.4847i | − | 0.627049i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9.99097i | − | 0.338531i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.6042 | + | 21.6042i | 0.731191 | + | 0.731191i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.861087 | + | 11.1471i | 0.0291100 | + | 0.376842i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.4351 | + | 10.4351i | −0.352367 | + | 0.352367i | −0.860990 | − | 0.508623i | \(-0.830155\pi\) |
0.508623 | + | 0.860990i | \(0.330155\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.0407904 | −0.00137583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.8293 | 1.34188 | 0.670941 | − | 0.741511i | \(-0.265890\pi\) | ||||
0.670941 | + | 0.741511i | \(0.265890\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.3264 | − | 29.3264i | 0.986911 | − | 0.986911i | −0.0130045 | − | 0.999915i | \(-0.504140\pi\) |
0.999915 | + | 0.0130045i | \(0.00413956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.17417 | + | 0.718757i | −0.0394694 | + | 0.0241608i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.8366 | − | 20.8366i | −0.699626 | − | 0.699626i | 0.264704 | − | 0.964330i | \(-0.414726\pi\) |
−0.964330 | + | 0.264704i | \(0.914726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7700i | 0.461832i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 26.9163i | − | 0.901730i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.4374 | − | 23.4374i | −0.784304 | − | 0.784304i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.43051 | + | 0.584753i | 0.0812430 | + | 0.0195461i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.4496 | − | 11.4496i | 0.382290 | − | 0.382290i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.3797 | 1.28003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.3676 | −0.412026 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.58092 | − | 3.58092i | 0.119165 | − | 0.119165i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.00315 | − | 1.68488i | −0.232792 | − | 0.0560072i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.86316 | + | 7.86316i | 0.261092 | + | 0.261092i | 0.825498 | − | 0.564406i | \(-0.190895\pi\) |
−0.564406 | + | 0.825498i | \(0.690895\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.382129i | 0.0126744i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6.94201i | − | 0.229999i | −0.993366 | − | 0.115000i | \(-0.963313\pi\) | ||
0.993366 | − | 0.115000i | \(-0.0366867\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.534923 | + | 0.534923i | 0.0177034 | + | 0.0177034i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.93888 | − | 3.63541i | 0.196333 | − | 0.120183i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.73169 | − | 3.73169i | 0.123231 | − | 0.123231i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.93888 | 0.294867 | 0.147433 | − | 0.989072i | \(-0.452899\pi\) | ||||
0.147433 | + | 0.989072i | \(0.452899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.37923 | −0.0454471 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −46.3039 | + | 46.3039i | −1.52411 | + | 1.52411i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1382 | − | 3.28330i | 0.333342 | − | 0.107954i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.8890 | + | 30.8890i | 1.01453 | + | 1.01453i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.13928i | 0.299850i | 0.988697 | + | 0.149925i | \(0.0479032\pi\) | ||||
−0.988697 | + | 0.149925i | \(0.952097\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.82967i | 0.191060i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.90365 | + | 1.90365i | 0.0623226 | + | 0.0623226i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.7196 | + | 30.5807i | 0.612196 | + | 1.00009i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.7955 | + | 17.7955i | −0.581354 | + | 0.581354i | −0.935275 | − | 0.353921i | \(-0.884848\pi\) |
0.353921 | + | 0.935275i | \(0.384848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.62662 | 0.281519 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.510241 | 0.0166334 | 0.00831668 | − | 0.999965i | \(-0.497353\pi\) | ||||
0.00831668 | + | 0.999965i | \(0.497353\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −54.9966 | + | 54.9966i | −1.79093 | + | 1.79093i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.42407 | + | 5.91910i | −0.0463249 | + | 0.192548i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.77672 | − | 8.77672i | −0.285205 | − | 0.285205i | 0.549976 | − | 0.835181i | \(-0.314637\pi\) |
−0.835181 | + | 0.549976i | \(0.814637\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.6184i | 1.38345i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.61466i | 0.0523590i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.7810 | + | 33.7810i | 1.09427 | + | 1.09427i | 0.995067 | + | 0.0992066i | \(0.0316305\pi\) |
0.0992066 | + | 0.995067i | \(0.468370\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.54070 | + | 18.8733i | −0.146934 | + | 0.610726i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.2438 | + | 12.2438i | −0.395785 | + | 0.395785i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.7217 | −0.475388 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1034 | 0.487205 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.77962 | + | 4.77962i | −0.154021 | + | 0.154021i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.75689 | − | 12.6718i | −0.249703 | − | 0.407919i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0215 | + | 11.0215i | 0.354428 | + | 0.354428i | 0.861754 | − | 0.507326i | \(-0.169366\pi\) |
−0.507326 | + | 0.861754i | \(0.669366\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.5387i | 0.370678i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.58041i | 0.114901i | 0.998348 | + | 0.0574504i | \(0.0182971\pi\) | ||||
−0.998348 | + | 0.0574504i | \(0.981703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.2395 | − | 15.2395i | −0.488556 | − | 0.488556i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.38653 | + | 4.28334i | 0.268584 | + | 0.137177i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.4459 | − | 42.4459i | 1.35796 | − | 1.35796i | 0.481540 | − | 0.876424i | \(-0.340078\pi\) |
0.876424 | − | 0.481540i | \(-0.159922\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.0105 | 1.05502 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.23108 | −0.230871 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.9216 | − | 41.9216i | 1.33709 | − | 1.33709i | 0.438228 | − | 0.898864i | \(-0.355606\pi\) |
0.898864 | − | 0.438228i | \(-0.144394\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.990993 | + | 0.606624i | −0.0315756 | + | 0.0193287i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.89444 | + | 1.89444i | 0.0603007 | + | 0.0603007i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 92.3961i | 2.93803i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 61.0367i | − | 1.93889i | −0.245300 | − | 0.969447i | \(-0.578887\pi\) | ||
0.245300 | − | 0.969447i | \(-0.421113\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.47662 | − | 6.47662i | −0.205529 | − | 0.205529i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.5101 | + | 7.34039i | 0.967237 | + | 0.232706i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.2374 | + | 30.2374i | −0.957629 | + | 0.957629i | −0.999138 | − | 0.0415091i | \(-0.986783\pi\) |
0.0415091 | + | 0.999138i | \(0.486783\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.80280 | 0.183592 |
(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 | 560.2.x.b.463.8 | yes | 24 | |
4.3 | odd | 2 | inner | 560.2.x.b.463.5 | yes | 24 | |
5.2 | odd | 4 | inner | 560.2.x.b.127.5 | ✓ | 24 | |
20.7 | even | 4 | inner | 560.2.x.b.127.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.x.b.127.5 | ✓ | 24 | 5.2 | odd | 4 | inner | |
560.2.x.b.127.8 | yes | 24 | 20.7 | even | 4 | inner | |
560.2.x.b.463.5 | yes | 24 | 4.3 | odd | 2 | inner | |
560.2.x.b.463.8 | yes | 24 | 1.1 | even | 1 | trivial |