Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(271,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bz (of order \(6\), 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: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.4 | ||
Character | \(\chi\) | \(=\) | 1120.271 |
Dual form | 1120.2.bz.f.591.4 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.90624 | + | 1.10057i | −1.10057 | + | 0.635414i | −0.936370 | − | 0.351014i | \(-0.885837\pi\) |
−0.164198 | + | 0.986427i | \(0.552504\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.584379 | − | 2.58041i | −0.220874 | − | 0.975302i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.922503 | − | 1.59782i | 0.307501 | − | 0.532608i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.90486 | + | 5.03137i | 0.875849 | + | 1.51701i | 0.855856 | + | 0.517214i | \(0.173031\pi\) |
0.0199929 | + | 0.999800i | \(0.493636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.83332 | −1.34052 | −0.670260 | − | 0.742126i | \(-0.733818\pi\) | ||||
−0.670260 | + | 0.742126i | \(0.733818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.20114i | 0.568331i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.78236 | − | 2.18375i | 0.917357 | − | 0.529636i | 0.0345662 | − | 0.999402i | \(-0.488995\pi\) |
0.882791 | + | 0.469766i | \(0.155662\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.63783 | − | 0.945600i | −0.375743 | − | 0.216936i | 0.300221 | − | 0.953870i | \(-0.402939\pi\) |
−0.675965 | + | 0.736934i | \(0.736273\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.95388 | + | 4.27573i | 0.862808 | + | 0.933041i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.157820 | + | 0.0911173i | 0.0329077 | + | 0.0189993i | 0.516364 | − | 0.856369i | \(-0.327285\pi\) |
−0.483456 | + | 0.875369i | \(0.660619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.54230i | − | 0.489266i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.38898i | − | 0.815013i | −0.913202 | − | 0.407506i | \(-0.866398\pi\) | ||
0.913202 | − | 0.407506i | \(-0.133602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.03983 | − | 3.53308i | −0.366364 | − | 0.634560i | 0.622630 | − | 0.782516i | \(-0.286064\pi\) |
−0.988994 | + | 0.147956i | \(0.952731\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.0747 | − | 6.39400i | −1.92786 | − | 1.11305i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.52689 | − | 0.784117i | −0.427122 | − | 0.132540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.69132 | − | 2.13119i | −0.606849 | − | 0.350365i | 0.164882 | − | 0.986313i | \(-0.447276\pi\) |
−0.771731 | + | 0.635949i | \(0.780609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.21347 | − | 5.31940i | 1.47534 | − | 0.851785i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.44314i | 0.537729i | 0.963178 | + | 0.268864i | \(0.0866483\pi\) | ||||
−0.963178 | + | 0.268864i | \(0.913352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.10796 | 0.321461 | 0.160731 | − | 0.986998i | \(-0.448615\pi\) | ||||
0.160731 | + | 0.986998i | \(0.448615\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.922503 | − | 1.59782i | −0.137519 | − | 0.238189i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.946816 | − | 1.63993i | 0.138107 | − | 0.239209i | −0.788673 | − | 0.614813i | \(-0.789231\pi\) |
0.926780 | + | 0.375604i | \(0.122565\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.31700 | + | 3.01587i | −0.902429 | + | 0.430839i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.80673 | + | 8.32550i | −0.673076 | + | 1.16580i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.54212 | − | 4.93180i | 1.17335 | − | 0.677434i | 0.218884 | − | 0.975751i | \(-0.429758\pi\) |
0.954467 | + | 0.298317i | \(0.0964252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.80972 | 0.783383 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.16279 | 0.551375 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.35546 | − | 3.66932i | 0.827410 | − | 0.477705i | −0.0255550 | − | 0.999673i | \(-0.508135\pi\) |
0.852965 | + | 0.521968i | \(0.174802\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.89522 | − | 8.47877i | 0.626769 | − | 1.08560i | −0.361427 | − | 0.932400i | \(-0.617710\pi\) |
0.988196 | − | 0.153195i | \(-0.0489562\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.66212 | − | 1.44670i | −0.587373 | − | 0.182267i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.41666 | + | 4.18577i | −0.299750 | + | 0.519181i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.04954 | − | 10.4781i | −0.739069 | − | 1.28011i | −0.952915 | − | 0.303238i | \(-0.901932\pi\) |
0.213845 | − | 0.976868i | \(-0.431401\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.401124 | −0.0482896 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.80669i | − | 1.04516i | −0.852590 | − | 0.522581i | \(-0.824969\pi\) | ||
0.852590 | − | 0.522581i | \(-0.175031\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34998 | − | 4.24351i | 0.860250 | − | 0.496666i | −0.00384586 | − | 0.999993i | \(-0.501224\pi\) |
0.864096 | + | 0.503327i | \(0.167891\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.90624 | + | 1.10057i | 0.220114 | + | 0.127083i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.2854 | − | 10.4360i | 1.28610 | − | 1.18929i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5541 | + | 6.09342i | 1.18743 | + | 0.685563i | 0.957722 | − | 0.287696i | \(-0.0928894\pi\) |
0.229708 | + | 0.973259i | \(0.426223\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.56549 | + | 9.63970i | 0.618387 | + | 1.07108i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 16.9697i | − | 1.86267i | −0.364163 | − | 0.931335i | \(-0.618645\pi\) | ||
0.364163 | − | 0.931335i | \(-0.381355\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.36749i | − | 0.473721i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.83037 | + | 8.36645i | 0.517870 | + | 0.896977i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.11692 | − | 2.95425i | −0.542392 | − | 0.313150i | 0.203656 | − | 0.979043i | \(-0.434718\pi\) |
−0.746048 | + | 0.665892i | \(0.768051\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82449 | + | 12.4719i | 0.296087 | + | 1.30741i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.77680 | + | 4.48994i | 0.806417 | + | 0.465585i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.63783 | + | 0.945600i | −0.168038 | + | 0.0970165i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.2388i | − | 1.34420i | −0.740461 | − | 0.672100i | \(-0.765393\pi\) | ||
0.740461 | − | 0.672100i | \(-0.234607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.7190 | 1.07730 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.23442 | + | 2.13807i | 0.122829 | + | 0.212746i | 0.920882 | − | 0.389841i | \(-0.127470\pi\) |
−0.798053 | + | 0.602587i | \(0.794137\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.920346 | − | 1.59409i | 0.0906844 | − | 0.157070i | −0.817115 | − | 0.576475i | \(-0.804428\pi\) |
0.907799 | + | 0.419405i | \(0.137761\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.67983 | − | 1.28630i | 0.554295 | − | 0.125530i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.08674 | + | 15.7387i | −0.878448 | + | 1.52152i | −0.0254044 | + | 0.999677i | \(0.508087\pi\) |
−0.853044 | + | 0.521839i | \(0.825246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.40525 | + | 1.96602i | −0.326164 | + | 0.188311i | −0.654137 | − | 0.756376i | \(-0.726968\pi\) |
0.327973 | + | 0.944687i | \(0.393635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.38206 | 0.890506 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.16641 | 0.674159 | 0.337079 | − | 0.941476i | \(-0.390561\pi\) | ||||
0.337079 | + | 0.941476i | \(0.390561\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.157820 | − | 0.0911173i | 0.0147168 | − | 0.00849673i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.45875 | + | 7.72278i | −0.412212 | + | 0.713972i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.84529 | − | 8.48390i | −0.719176 | − | 0.777717i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.3764 | + | 19.7046i | −1.03422 | + | 1.79133i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.78942 | − | 6.56346i | −0.341680 | − | 0.591808i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.88206i | − | 0.255742i | −0.991791 | − | 0.127871i | \(-0.959186\pi\) | ||
0.991791 | − | 0.127871i | \(-0.0408143\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.01829 | + | 2.31996i | −0.353790 | + | 0.204261i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.92953 | − | 4.00076i | −0.605436 | − | 0.349548i | 0.165741 | − | 0.986169i | \(-0.446998\pi\) |
−0.771177 | + | 0.636621i | \(0.780332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.48292 | + | 4.77885i | −0.128586 | + | 0.414379i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.20170 | − | 1.27115i | −0.189492 | − | 0.109403i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.09925 | + | 8.83216i | 0.435658 | + | 0.754582i | 0.997349 | − | 0.0727651i | \(-0.0231823\pi\) |
−0.561691 | + | 0.827347i | \(0.689849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.93769i | − | 0.842904i | −0.906851 | − | 0.421452i | \(-0.861521\pi\) | ||
0.906851 | − | 0.421452i | \(-0.138479\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.16814i | 0.351021i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.0401 | − | 24.3182i | −1.17409 | − | 2.03359i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.80097 | − | 2.19449i | −0.315653 | − | 0.182242i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.72256 | − | 12.7013i | 0.719424 | − | 1.04758i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.6559 | − | 7.88422i | −1.11873 | − | 0.645900i | −0.177655 | − | 0.984093i | \(-0.556851\pi\) |
−0.941077 | + | 0.338192i | \(0.890185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.24155 | + | 3.02621i | −0.426552 | + | 0.246270i | −0.697877 | − | 0.716218i | \(-0.745872\pi\) |
0.271325 | + | 0.962488i | \(0.412538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 8.05806i | − | 0.651455i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.07965 | −0.327686 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2074 | + | 17.6798i | 0.814641 | + | 1.41100i | 0.909585 | + | 0.415518i | \(0.136400\pi\) |
−0.0949439 | + | 0.995483i | \(0.530267\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.8556 | + | 18.8024i | −0.860902 | + | 1.49113i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.142893 | − | 0.460486i | 0.0112616 | − | 0.0362914i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.91267 | + | 3.31285i | −0.149812 | + | 0.259482i | −0.931158 | − | 0.364616i | \(-0.881200\pi\) |
0.781346 | + | 0.624098i | \(0.214534\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.0747 | + | 6.39400i | −0.862167 | + | 0.497772i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.6531 | −1.67556 | −0.837782 | − | 0.546005i | \(-0.816148\pi\) | ||||
−0.837782 | + | 0.546005i | \(0.816148\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3609 | 0.796996 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.02180 | + | 1.74464i | −0.231083 | + | 0.133416i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.20160 | + | 9.00944i | −0.395470 | + | 0.684975i | −0.993161 | − | 0.116752i | \(-0.962752\pi\) |
0.597691 | + | 0.801727i | \(0.296085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.94251 | + | 1.79629i | −0.146840 | + | 0.135787i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.07669 | + | 13.9892i | −0.607081 | + | 1.05150i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.80514 | − | 6.59069i | −0.284409 | − | 0.492611i | 0.688056 | − | 0.725657i | \(-0.258464\pi\) |
−0.972466 | + | 0.233046i | \(0.925131\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2225 | 0.834160 | 0.417080 | − | 0.908870i | \(-0.363054\pi\) | ||||
0.417080 | + | 0.908870i | \(0.363054\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.5501i | 1.59303i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.69132 | + | 2.13119i | −0.271391 | + | 0.156688i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.9745 | + | 12.6870i | 1.60693 | + | 0.927763i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.56017 | + | 1.48567i | −0.477182 | + | 0.108066i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.68571 | + | 3.86000i | 0.483761 | + | 0.279300i | 0.721983 | − | 0.691911i | \(-0.243231\pi\) |
−0.238222 | + | 0.971211i | \(0.576564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7011 | − | 20.2669i | −0.842265 | − | 1.45885i | −0.887975 | − | 0.459892i | \(-0.847888\pi\) |
0.0457097 | − | 0.998955i | \(-0.485445\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 10.6388i | − | 0.761860i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.4272i | − | 1.45538i | −0.685907 | − | 0.727689i | \(-0.740594\pi\) | ||
0.685907 | − | 0.727689i | \(-0.259406\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.10091 | + | 1.90683i | 0.0780413 | + | 0.135172i | 0.902405 | − | 0.430889i | \(-0.141800\pi\) |
−0.824363 | + | 0.566061i | \(0.808467\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.0638 | + | 13.3159i | 1.62679 | + | 0.939230i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.3253 | + | 2.56482i | −0.794884 | + | 0.180015i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.98185 | + | 1.72157i | 0.208261 | + | 0.120240i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.291179 | − | 0.168112i | 0.0202383 | − | 0.0116846i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.9874i | − | 0.760011i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.9363 | 1.99206 | 0.996028 | − | 0.0890425i | \(-0.0283807\pi\) | ||||
0.996028 | + | 0.0890425i | \(0.0283807\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.69236 | + | 16.7877i | 0.664110 | + | 1.15027i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.05398 | − | 1.82555i | 0.0718810 | − | 0.124501i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.92476 | + | 7.32824i | −0.537968 | + | 0.497473i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.34056 | + | 16.1783i | −0.631176 | + | 1.09323i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.2813 | + | 10.5547i | −1.22974 | + | 0.709989i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0535 | −0.740200 | −0.370100 | − | 0.928992i | \(-0.620677\pi\) | ||||
−0.370100 | + | 0.928992i | \(0.620677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.84501 | −0.123000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.11916 | + | 4.11025i | −0.472515 | + | 0.272807i | −0.717292 | − | 0.696773i | \(-0.754619\pi\) |
0.244777 | + | 0.969579i | \(0.421285\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.03725 | + | 8.72478i | −0.332871 | + | 0.576549i | −0.983074 | − | 0.183211i | \(-0.941351\pi\) |
0.650203 | + | 0.759761i | \(0.274684\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0273 | + | 32.3138i | −0.659747 | + | 2.12609i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.68557 | − | 6.38359i | 0.241450 | − | 0.418203i | −0.719678 | − | 0.694308i | \(-0.755711\pi\) |
0.961127 | + | 0.276105i | \(0.0890438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.946816 | − | 1.63993i | −0.0617634 | − | 0.106977i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.8249 | −1.74246 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.9534i | 1.35536i | 0.735355 | + | 0.677682i | \(0.237016\pi\) | ||||
−0.735355 | + | 0.677682i | \(0.762984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.42132 | + | 1.39795i | −0.155971 | + | 0.0900498i | −0.575954 | − | 0.817482i | \(-0.695369\pi\) |
0.419983 | + | 0.907532i | \(0.362036\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6132 | − | 8.43695i | −0.937439 | − | 0.541231i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.546681 | + | 6.97862i | −0.0349262 | + | 0.445848i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.91614 | + | 4.57039i | 0.503692 | + | 0.290807i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.6764 | + | 32.3484i | 1.18357 | + | 2.05000i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7656i | 1.18448i | 0.805763 | + | 0.592238i | \(0.201756\pi\) | ||||
−0.805763 | + | 0.592238i | \(0.798244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.05873i | 0.0665620i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.80673 | + | 8.32550i | 0.301009 | + | 0.521363i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.76564 | − | 3.90615i | −0.422029 | − | 0.243659i | 0.273916 | − | 0.961754i | \(-0.411681\pi\) |
−0.695945 | + | 0.718095i | \(0.745014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.34220 | + | 10.7705i | −0.207674 | + | 0.669248i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.01281 | − | 4.04885i | −0.434082 | − | 0.250617i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.03985 | − | 2.90976i | 0.310770 | − | 0.179423i | −0.336501 | − | 0.941683i | \(-0.609243\pi\) |
0.647271 | + | 0.762260i | \(0.275910\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.86359i | − | 0.605916i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.0054 | 0.795920 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0950 | − | 20.9492i | −0.737445 | − | 1.27729i | −0.953642 | − | 0.300943i | \(-0.902699\pi\) |
0.216197 | − | 0.976350i | \(-0.430635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.83742 | − | 13.5748i | 0.476089 | − | 0.824611i | −0.523536 | − | 0.852004i | \(-0.675387\pi\) |
0.999625 | + | 0.0273932i | \(0.00872061\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.1104 | − | 20.6660i | −1.15661 | − | 1.25076i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.90486 | − | 5.03137i | 0.175170 | − | 0.303403i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6984 | + | 7.33142i | −0.762972 | + | 0.440502i | −0.830362 | − | 0.557225i | \(-0.811866\pi\) |
0.0673898 | + | 0.997727i | \(0.478533\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.52699 | −0.450629 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0418 | 0.897320 | 0.448660 | − | 0.893703i | \(-0.351901\pi\) | ||||
0.448660 | + | 0.893703i | \(0.351901\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.29409 | + | 2.47919i | −0.255257 | + | 0.147373i | −0.622169 | − | 0.782883i | \(-0.713748\pi\) |
0.366912 | + | 0.930256i | \(0.380415\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.08140 | − | 3.60508i | 0.123291 | − | 0.213547i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.88471 | − | 2.01210i | 0.524448 | − | 0.118771i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.03750 | − | 1.79700i | 0.0610294 | − | 0.105706i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.5702 | + | 25.2364i | 0.854123 | + | 1.47938i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.56812 | −0.150031 | −0.0750156 | − | 0.997182i | \(-0.523901\pi\) | ||||
−0.0750156 | + | 0.997182i | \(0.523901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.33865i | − | 0.427273i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.7912 | − | 7.38503i | 0.742223 | − | 0.428523i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.762793 | − | 0.440399i | −0.0441135 | − | 0.0254689i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.23185 | − | 5.43941i | −0.0710026 | − | 0.313522i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.70619 | − | 2.71712i | −0.270363 | − | 0.156094i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.89522 | − | 8.47877i | −0.280299 | − | 0.485493i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.4425i | 0.824280i | 0.911121 | + | 0.412140i | \(0.135219\pi\) | ||||
−0.911121 | + | 0.412140i | \(0.864781\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.05162i | 0.230488i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.26712 | − | 14.3191i | −0.468785 | − | 0.811960i | 0.530578 | − | 0.847636i | \(-0.321975\pi\) |
−0.999363 | + | 0.0356762i | \(0.988641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.19818 | + | 1.26912i | 0.124248 | + | 0.0717348i | 0.560836 | − | 0.827927i | \(-0.310480\pi\) |
−0.436588 | + | 0.899662i | \(0.643813\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.58394 | + | 3.31417i | −0.201932 | + | 0.186732i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.8432 | + | 8.56971i | 0.833676 | + | 0.481323i | 0.855109 | − | 0.518447i | \(-0.173490\pi\) |
−0.0214339 | + | 0.999770i | \(0.506823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.0826 | − | 12.7494i | 1.23639 | − | 0.713828i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 40.0023i | − | 2.23271i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.25981 | −0.459588 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41666 | + | 4.18577i | 0.134052 | + | 0.232185i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.32749 | − | 7.49543i | 0.239311 | − | 0.414498i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.78499 | − | 1.48483i | −0.263805 | − | 0.0818612i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9027 | − | 20.6161i | 0.654233 | − | 1.13317i | −0.327852 | − | 0.944729i | \(-0.606325\pi\) |
0.982085 | − | 0.188436i | \(-0.0603418\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.81051 | + | 3.93205i | −0.373214 | + | 0.215475i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0991 | −0.661044 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.22715 | 0.0668470 | 0.0334235 | − | 0.999441i | \(-0.489359\pi\) | ||||
0.0334235 | + | 0.999441i | \(0.489359\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.6609 | + | 7.88712i | −0.741958 | + | 0.428370i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.8508 | − | 20.5262i | 0.641758 | − | 1.11156i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4737 | + | 14.5380i | 0.619521 | + | 0.784980i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.200562 | + | 0.347383i | −0.0107979 | + | 0.0187025i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4834 | + | 26.8181i | 0.831194 | + | 1.43967i | 0.897092 | + | 0.441844i | \(0.145675\pi\) |
−0.0658983 | + | 0.997826i | \(0.520991\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6776 | 1.42802 | 0.714010 | − | 0.700136i | \(-0.246877\pi\) | ||||
0.714010 | + | 0.700136i | \(0.246877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.2877i | 0.655871i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.1501 | + | 7.01487i | −0.646685 | + | 0.373364i | −0.787185 | − | 0.616717i | \(-0.788462\pi\) |
0.140500 | + | 0.990081i | \(0.455129\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.62681 | − | 4.40334i | −0.404789 | − | 0.233705i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.2921 | + | 7.53807i | 1.28568 | + | 0.398957i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.5164 | + | 6.07165i | 0.555035 | + | 0.320450i | 0.751150 | − | 0.660131i | \(-0.229499\pi\) |
−0.196115 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.71168 | − | 13.3570i | −0.405878 | − | 0.703001i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 50.0822i | − | 2.62864i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 8.48703i | − | 0.444231i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.75583 | + | 9.96939i | 0.300452 | + | 0.520398i | 0.976238 | − | 0.216700i | \(-0.0695292\pi\) |
−0.675787 | + | 0.737097i | \(0.736196\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.50153 | + | 3.17631i | 0.286398 | + | 0.165352i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.7179 | − | 19.1601i | −0.919866 | − | 0.994744i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3241 | − | 11.7341i | −1.05234 | − | 0.607570i | −0.129037 | − | 0.991640i | \(-0.541189\pi\) |
−0.923304 | + | 0.384070i | \(0.874522\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.90624 | − | 1.10057i | 0.0984379 | − | 0.0568331i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.2133i | 1.09254i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.5653 | 0.799536 | 0.399768 | − | 0.916616i | \(-0.369091\pi\) | ||||
0.399768 | + | 0.916616i | \(0.369091\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.17191 | + | 5.49391i | 0.162502 | + | 0.281462i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.45943 | + | 12.9201i | −0.381159 | + | 0.660187i | −0.991228 | − | 0.132161i | \(-0.957808\pi\) |
0.610069 | + | 0.792348i | \(0.291142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.39508 | − | 14.9915i | −0.173029 | − | 0.764035i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.94460 | − | 3.36815i | 0.0988498 | − | 0.171213i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.9524 | − | 6.32338i | 0.555310 | − | 0.320608i | −0.195951 | − | 0.980614i | \(-0.562779\pi\) |
0.751261 | + | 0.660006i | \(0.229446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.795909 | 0.0402508 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.6125 | 0.888431 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.5541 | − | 6.09342i | 0.531035 | − | 0.306593i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.61650 | + | 13.1922i | −0.382261 | + | 0.662095i | −0.991385 | − | 0.130979i | \(-0.958188\pi\) |
0.609124 | + | 0.793075i | \(0.291521\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.43265 | − | 10.7417i | −0.121785 | − | 0.537758i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.73594 | + | 13.3990i | −0.386315 | + | 0.669117i | −0.991951 | − | 0.126625i | \(-0.959585\pi\) |
0.605636 | + | 0.795742i | \(0.292919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.85913 | + | 17.0765i | 0.491118 | + | 0.850641i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.1310 | 0.553102 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 24.7632i | − | 1.22747i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.47055 | + | 4.31313i | −0.369395 | + | 0.213270i | −0.673194 | − | 0.739466i | \(-0.735078\pi\) |
0.303799 | + | 0.952736i | \(0.401745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.4408 | − | 11.2241i | −0.958944 | − | 0.553646i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.1823 | − | 14.2554i | −0.648661 | − | 0.701462i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.6962 | − | 8.48487i | −0.721409 | − | 0.416506i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9371 | + | 18.9436i | 0.535592 | + | 0.927673i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.6898i | 0.522230i | 0.965308 | + | 0.261115i | \(0.0840902\pi\) | ||||
−0.965308 | + | 0.261115i | \(0.915910\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.4941i | 0.998823i | 0.866365 | + | 0.499412i | \(0.166450\pi\) | ||||
−0.866365 | + | 0.499412i | \(0.833550\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.74688 | − | 3.02569i | −0.0849363 | − | 0.147114i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.78236 | − | 2.18375i | −0.183471 | − | 0.105927i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.7393 | − | 7.67685i | −1.19722 | − | 0.371509i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 53.5277 | + | 30.9042i | 2.58434 | + | 1.49207i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.9544 | − | 12.0980i | 1.00934 | − | 0.582740i | 0.0983389 | − | 0.995153i | \(-0.468647\pi\) |
0.910997 | + | 0.412412i | \(0.135314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2949i | 0.975311i | 0.873036 | + | 0.487655i | \(0.162148\pi\) | ||||
−0.873036 | + | 0.487655i | \(0.837852\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.66074 | 0.463197 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.172321 | − | 0.298469i | −0.00824324 | − | 0.0142777i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.52231 | + | 4.36878i | −0.120384 | + | 0.208510i | −0.919919 | − | 0.392109i | \(-0.871746\pi\) |
0.799535 | + | 0.600619i | \(0.205079\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00863 | + | 12.8756i | −0.0480300 | + | 0.613124i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.04696 | − | 7.00955i | 0.192277 | − | 0.333034i | −0.753727 | − | 0.657187i | \(-0.771746\pi\) |
0.946005 | + | 0.324153i | \(0.105079\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.11692 | + | 2.95425i | −0.242565 | + | 0.140045i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.7085 | 1.64166 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.05786 | −0.191502 | −0.0957511 | − | 0.995405i | \(-0.530525\pi\) | ||||
−0.0957511 | + | 0.995405i | \(0.530525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.3237 | + | 10.0019i | −0.815742 | + | 0.470969i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.66111 | − | 11.5374i | 0.312966 | − | 0.542074i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.2132 | + | 3.78988i | 0.572566 | + | 0.177673i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.70734 | + | 4.68925i | −0.126644 | + | 0.219354i | −0.922374 | − | 0.386297i | \(-0.873754\pi\) |
0.795730 | + | 0.605651i | \(0.207087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.55174 | − | 9.61589i | −0.259133 | − | 0.448831i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.9095 | −0.880702 | −0.440351 | − | 0.897826i | \(-0.645146\pi\) | ||||
−0.440351 | + | 0.897826i | \(0.645146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.304782i | 0.0141644i | 0.999975 | + | 0.00708220i | \(0.00225435\pi\) | ||||
−0.999975 | + | 0.00708220i | \(0.997746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.77680 | − | 4.48994i | 0.360641 | − | 0.208216i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.35368 | + | 1.93625i | 0.155190 | + | 0.0895989i | 0.575584 | − | 0.817743i | \(-0.304775\pi\) |
−0.420394 | + | 0.907342i | \(0.638108\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.5026 | + | 21.7335i | −1.08525 | + | 1.00356i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −38.9156 | − | 22.4680i | −1.79314 | − | 1.03527i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.12334 | + | 10.6059i | 0.281552 | + | 0.487662i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.89120i | 0.0867742i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 18.1984i | − | 0.833247i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.4744 | − | 28.5344i | −0.752732 | − | 1.30377i | −0.946494 | − | 0.322722i | \(-0.895402\pi\) |
0.193761 | − | 0.981049i | \(-0.437931\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.8413 | + | 10.3007i | 0.813494 | + | 0.469671i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.234408 | + | 1.03506i | 0.0106659 | + | 0.0470970i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.4652 | − | 6.61941i | −0.520606 | − | 0.300572i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.8923 | + | 20.7224i | −1.62643 | + | 0.939022i | −0.641289 | + | 0.767300i | \(0.721600\pi\) |
−0.985145 | + | 0.171722i | \(0.945067\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8.42012i | − | 0.380771i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.4339 | 1.14782 | 0.573908 | − | 0.818920i | \(-0.305427\pi\) | ||||
0.573908 | + | 0.818920i | \(0.305427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.58441 | − | 16.6007i | −0.431660 | − | 0.747658i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.35949 | − | 9.28291i | 0.240891 | − | 0.417236i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.7248 | + | 5.14644i | −1.01935 | + | 0.230849i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.25059 | + | 5.63019i | −0.145516 | + | 0.252042i | −0.929565 | − | 0.368657i | \(-0.879818\pi\) |
0.784049 | + | 0.620699i | \(0.213151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.2759 | − | 23.8307i | 1.84407 | − | 1.06468i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.4094 | 1.04378 | 0.521888 | − | 0.853014i | \(-0.325228\pi\) | ||||
0.521888 | + | 0.853014i | \(0.325228\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.46883 | 0.109862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.7505 | + | 11.4029i | −0.877149 | + | 0.506422i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.44031 | − | 14.6190i | 0.374110 | − | 0.647978i | −0.616083 | − | 0.787681i | \(-0.711281\pi\) |
0.990193 | + | 0.139703i | \(0.0446148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.2452 | − | 16.4861i | −0.674406 | − | 0.729303i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.40400 | + | 4.16385i | −0.106139 | + | 0.183838i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.920346 | − | 1.59409i | −0.0405553 | − | 0.0702438i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0015 | 0.483844 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 22.8989i | − | 1.00515i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.2245 | − | 12.2540i | 0.929864 | − | 0.536857i | 0.0430955 | − | 0.999071i | \(-0.486278\pi\) |
0.886769 | + | 0.462214i | \(0.152945\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.2087 | + | 14.5543i | 1.10230 | + | 0.636414i | 0.936824 | − | 0.349800i | \(-0.113751\pi\) |
0.165476 | + | 0.986214i | \(0.447084\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.72595 | − | 5.56203i | 0.0753266 | − | 0.242747i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.4307 | − | 8.90893i | −0.672173 | − | 0.388079i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4834 | − | 19.8898i | −0.499278 | − | 0.864775i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 13.5399i | − | 0.587580i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 16.6418i | − | 0.720837i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.08674 | + | 15.7387i | 0.392854 | + | 0.680443i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.5070 | + | 8.37563i | 0.626024 | + | 0.361435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.5240 | − | 23.0225i | −1.44398 | − | 0.991649i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.98939 | − | 2.30327i | −0.171517 | − | 0.0990254i | 0.411784 | − | 0.911282i | \(-0.364906\pi\) |
−0.583301 | + | 0.812256i | \(0.698239\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.3927 | + | 12.3511i | −0.918050 | + | 0.530036i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.93204i | 0.168430i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.27444 | −0.182762 | −0.0913808 | − | 0.995816i | \(-0.529128\pi\) | ||||
−0.0913808 | + | 0.995816i | \(0.529128\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.03171 | − | 15.6434i | −0.385464 | − | 0.667644i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.15022 | + | 7.18839i | −0.176805 | + | 0.306236i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.55590 | − | 30.7948i | 0.406358 | − | 1.30953i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.69103 | − | 8.12511i | 0.199123 | − | 0.344892i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.1482 | + | 9.32317i | −0.684221 | + | 0.395035i | −0.801443 | − | 0.598070i | \(-0.795934\pi\) |
0.117222 | + | 0.993106i | \(0.462601\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1885 | −0.430926 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −55.8515 | −2.35805 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.1853 | − | 11.0766i | 0.808565 | − | 0.466825i | −0.0378926 | − | 0.999282i | \(-0.512064\pi\) |
0.846457 | + | 0.532457i | \(0.178731\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.58320 | − | 6.20629i | 0.150746 | − | 0.261101i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.6220 | − | 19.9945i | 0.908039 | − | 0.839688i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.619323 | + | 1.07270i | −0.0259634 | + | 0.0449699i | −0.878715 | − | 0.477346i | \(-0.841599\pi\) |
0.852752 | + | 0.522316i | \(0.174932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.3953 | − | 18.0051i | −0.435028 | − | 0.753490i | 0.562270 | − | 0.826954i | \(-0.309928\pi\) |
−0.997298 | + | 0.0734633i | \(0.976595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.9928 | −0.709883 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.182235i | − | 0.00759971i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.9908 | + | 17.3152i | −1.24853 | + | 0.720842i | −0.970817 | − | 0.239821i | \(-0.922911\pi\) |
−0.277717 | + | 0.960663i | \(0.589578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 44.6103 | + | 25.7558i | 1.85394 | + | 1.07037i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.7888 | + | 9.91675i | −1.81667 | + | 0.411416i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 49.6274 | + | 28.6524i | 2.05536 | + | 1.18666i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.45875 | + | 7.72278i | 0.184347 | + | 0.319298i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 22.4911i | − | 0.928306i | −0.885755 | − | 0.464153i | \(-0.846359\pi\) | ||
0.885755 | − | 0.464153i | \(-0.153641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.71544i | 0.317909i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4815 | + | 38.9392i | 0.924767 | + | 1.60174i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.70525 | − | 2.13923i | −0.152156 | − | 0.0878474i | 0.421989 | − | 0.906601i | \(-0.361332\pi\) |
−0.574145 | + | 0.818754i | \(0.694665\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2699 | + | 2.55227i | −0.462021 | + | 0.104633i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.19719 | − | 2.42325i | −0.171780 | − | 0.0991771i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.50041 | − | 3.17566i | 0.224741 | − | 0.129754i | −0.383403 | − | 0.923581i | \(-0.625248\pi\) |
0.608143 | + | 0.793827i | \(0.291915\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.72971i | − | 0.152138i | −0.997103 | − | 0.0760691i | \(-0.975763\pi\) | ||
0.997103 | − | 0.0760691i | \(-0.0242369\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.3229 | −0.909059 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.3764 | + | 19.7046i | 0.462518 | + | 0.801105i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.66175 | + | 16.7346i | −0.392158 | + | 0.679238i | −0.992734 | − | 0.120330i | \(-0.961605\pi\) |
0.600576 | + | 0.799568i | \(0.294938\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.7661 | − | 17.3535i | 0.760440 | − | 0.703199i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.57626 | + | 7.92631i | −0.185136 | + | 0.320664i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.3430 | − | 15.2092i | 1.06399 | − | 0.614292i | 0.137453 | − | 0.990508i | \(-0.456108\pi\) |
0.926532 | + | 0.376216i | \(0.122775\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.57883 | −0.305608 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.32522 | 0.375419 | 0.187710 | − | 0.982225i | \(-0.439894\pi\) | ||||
0.187710 | + | 0.982225i | \(0.439894\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.29185 | − | 5.36465i | 0.373471 | − | 0.215624i | −0.301503 | − | 0.953465i | \(-0.597488\pi\) |
0.674974 | + | 0.737842i | \(0.264155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.231647 | − | 0.401225i | 0.00929569 | − | 0.0161006i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.63296 | + | 14.9301i | −0.185616 | + | 0.598163i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0923 | + | 20.9445i | 0.482921 | + | 0.836444i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.6159 | −0.742264 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.84644i | − | 0.312362i | −0.987728 | − | 0.156181i | \(-0.950082\pi\) | ||
0.987728 | − | 0.156181i | \(-0.0499183\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −55.1595 | + | 31.8464i | −2.19239 | + | 1.26578i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.49594 | − | 1.44103i | −0.0990484 | − | 0.0571856i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.5321 | − | 14.5767i | 1.20972 | − | 0.577548i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.0715 | − | 8.12420i | −0.556661 | − | 0.321388i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.79977 | + | 11.7775i | 0.268575 | + | 0.465185i | 0.968494 | − | 0.249037i | \(-0.0801141\pi\) |
−0.699919 | + | 0.714222i | \(0.746781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.68857i | − | 0.224335i | −0.993689 | − | 0.112168i | \(-0.964221\pi\) | ||
0.993689 | − | 0.112168i | \(-0.0357794\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.63992i | 0.182697i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.225415 | − | 0.390431i | −0.00886200 | − | 0.0153494i | 0.861560 | − | 0.507655i | \(-0.169488\pi\) |
−0.870422 | + | 0.492306i | \(0.836154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.9234 | + | 21.3178i | 1.44937 | + | 0.836795i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.04127 | − | 22.6911i | 0.275969 | − | 0.889336i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.69894 | + | 2.13559i | 0.144751 | + | 0.0835720i | 0.570626 | − | 0.821210i | \(-0.306700\pi\) |
−0.425875 | + | 0.904782i | \(0.640034\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.92953 | + | 4.00076i | −0.270759 | + | 0.156323i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 15.6586i | − | 0.610901i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5436 | −0.605493 | −0.302746 | − | 0.953071i | \(-0.597903\pi\) | ||||
−0.302746 | + | 0.953071i | \(0.597903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.4897 | + | 25.0969i | 0.563583 | + | 0.976155i | 0.997180 | + | 0.0750479i | \(0.0239110\pi\) |
−0.433597 | + | 0.901107i | \(0.642756\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.2324 | − | 40.2398i | 0.902273 | − | 1.56278i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.39715 | + | 3.67367i | 0.131736 | + | 0.142459i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.399912 | − | 0.692668i | 0.0154846 | − | 0.0268202i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.0707 | − | 12.1652i | 0.814641 | − | 0.470333i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.8797 | 2.19582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.3539 | 1.24715 | 0.623576 | − | 0.781763i | \(-0.285679\pi\) | ||||
0.623576 | + | 0.781763i | \(0.285679\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.20170 | + | 1.27115i | −0.0847433 | + | 0.0489266i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.4527 | − | 38.8892i | 0.862927 | − | 1.49463i | −0.00616405 | − | 0.999981i | \(-0.501962\pi\) |
0.869091 | − | 0.494652i | \(-0.164705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.1616 | + | 7.73649i | −1.31100 | + | 0.296899i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.04722 | − | 15.6703i | 0.346690 | − | 0.600485i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.62256 | − | 9.73856i | −0.215141 | − | 0.372636i | 0.738175 | − | 0.674609i | \(-0.235688\pi\) |
−0.953316 | + | 0.301974i | \(0.902355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1985 | 0.389665 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 22.1754i | − | 0.846043i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.2868 | + | 23.8369i | −1.57290 | + | 0.908115i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.53812 | + | 4.92949i | 0.324805 | + | 0.187527i | 0.653533 | − | 0.756898i | \(-0.273286\pi\) |
−0.328727 | + | 0.944425i | \(0.606620\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.26394 | − | 27.6593i | −0.237948 | − | 1.05069i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.60629 | − | 4.96884i | −0.326455 | − | 0.188479i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.51896 | + | 13.0232i | 0.284801 | + | 0.493289i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.2249i | 0.613681i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.00307i | − | 0.226733i | −0.993553 | − | 0.113366i | \(-0.963837\pi\) | ||
0.993553 | − | 0.113366i | \(-0.0361634\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.03050 | + | 6.98103i | 0.152013 | + | 0.263294i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.60972 | + | 2.08407i | 0.135950 | + | 0.0784907i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.79573 | − | 4.43474i | 0.180362 | − | 0.166785i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.2323 | + | 5.90764i | 0.384283 | + | 0.221866i | 0.679680 | − | 0.733508i | \(-0.262119\pi\) |
−0.295397 | + | 0.955375i | \(0.595452\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.4724 | − | 11.2424i | 0.730272 | − | 0.421623i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 0.743454i | − | 0.0278426i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.0802 | −1.05014 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.0607 | − | 39.9423i | −0.861217 | − | 1.49167i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.06796 | − | 5.31386i | 0.114415 | − | 0.198173i | −0.803130 | − | 0.595803i | \(-0.796834\pi\) |
0.917546 | + | 0.397630i | \(0.130167\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.65122 | − | 1.44332i | −0.173221 | − | 0.0537520i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.07708 | − | 5.32966i | 0.114438 | − | 0.198212i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.80097 | + | 2.19449i | −0.141164 | + | 0.0815013i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.8986 | −0.552558 | −0.276279 | − | 0.961077i | \(-0.589101\pi\) | ||||
−0.276279 | + | 0.961077i | \(0.589101\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.74887 | 0.138847 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.97308 | − | 4.60326i | 0.294895 | − | 0.170258i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.7602 | + | 41.1539i | −0.877604 | + | 1.52006i | −0.0236421 | + | 0.999720i | \(0.507526\pi\) |
−0.853962 | + | 0.520335i | \(0.825807\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.63835 | − | 13.9046i | −0.244859 | − | 0.512879i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.1462 | − | 60.8750i | 1.29463 | − | 2.24236i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.95274 | − | 3.38225i | −0.0718328 | − | 0.124418i | 0.827872 | − | 0.560917i | \(-0.189551\pi\) |
−0.899705 | + | 0.436499i | \(0.856218\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.1201 | −0.739130 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 48.0392i | − | 1.76239i | −0.472755 | − | 0.881194i | \(-0.656741\pi\) | ||
0.472755 | − | 0.881194i | \(-0.343259\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.6559 | + | 7.88422i | −0.500312 | + | 0.288855i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.1146 | − | 15.6546i | −0.992073 | − | 0.572773i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.9223 | + | 14.2501i | 1.67797 | + | 0.520688i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.139857 | − | 0.0807464i | −0.00510345 | − | 0.00294648i | 0.497446 | − | 0.867495i | \(-0.334271\pi\) |
−0.502550 | + | 0.864548i | \(0.667605\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.6529 | − | 35.7718i | −0.752633 | − | 1.30360i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.05243i | 0.220270i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0175i | 0.618513i | 0.950979 | + | 0.309257i | \(0.100080\pi\) | ||||
−0.950979 | + | 0.309257i | \(0.899920\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.16521 | − | 2.01820i | −0.0422944 | − | 0.0732560i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.5345 | + | 13.5876i | 0.853125 | + | 0.492552i | 0.861704 | − | 0.507411i | \(-0.169398\pi\) |
−0.00857924 | + | 0.999963i | \(0.502731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.06309 | + | 7.63803i | 0.255701 | + | 0.276515i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.97848 | − | 4.02903i | −0.252308 | − | 0.145670i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.7179 | + | 17.7350i | −1.10916 | + | 0.640374i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16.2516i | − | 0.586049i | −0.956105 | − | 0.293025i | \(-0.905338\pi\) | ||
0.956105 | − | 0.293025i | \(-0.0946618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.1959 | 0.619296 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.07903 | + | 3.60098i | 0.0747774 | + | 0.129518i | 0.900989 | − | 0.433841i | \(-0.142842\pi\) |
−0.826212 | + | 0.563359i | \(0.809509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.03983 | + | 3.53308i | −0.0732727 | + | 0.126912i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.48268 | − | 24.2095i | −0.196690 | − | 0.868513i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.25584 | − | 5.63928i | 0.116652 | − | 0.202048i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.3097 | − | 25.5822i | 1.58552 | − | 0.915403i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.1581 | −0.398758 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.4149 | 0.728637 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.346588 | + | 0.200103i | −0.0123545 | + | 0.00713289i | −0.506165 | − | 0.862437i | \(-0.668937\pi\) |
0.493810 | + | 0.869570i | \(0.335604\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.40478 | + | 11.0934i | −0.228016 | + | 0.394936i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.18790 | − | 18.4922i | −0.148904 | − | 0.657509i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.6601 | + | 40.9806i | −0.840196 | + | 1.45526i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.8556 | + | 18.8024i | 0.385007 | + | 0.666852i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.32443 | −0.153179 | −0.0765895 | − | 0.997063i | \(-0.524403\pi\) | ||||
−0.0765895 | + | 0.997063i | \(0.524403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.27042i | − | 0.292586i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.44075 | + | 5.45062i | −0.333572 | + | 0.192588i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.7014 | + | 24.6536i | 1.50690 | + | 0.870008i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.327346 | − | 0.353992i | −0.0115374 | − | 0.0124766i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.1120 | + | 26.6228i | 1.62322 | + | 0.937165i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.2699 | − | 31.6444i | −0.642335 | − | 1.11256i | −0.984910 | − | 0.173066i | \(-0.944633\pi\) |
0.342576 | − | 0.939490i | \(-0.388701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6473i | 0.619680i | 0.950789 | + | 0.309840i | \(0.100275\pi\) | ||||
−0.950789 | + | 0.309840i | \(0.899725\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.5025i | 1.21005i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.91267 | + | 3.31285i | 0.0669981 | + | 0.116044i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.45248 | − | 1.99329i | −0.120787 | − | 0.0697364i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.5335 | + | 6.99236i | 0.787385 | + | 0.244333i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.1429 | − | 21.4445i | −1.29630 | − | 0.748418i | −0.316535 | − | 0.948581i | \(-0.602520\pi\) |
−0.979763 | + | 0.200163i | \(0.935853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.2832 | − | 18.0614i | 1.09046 | − | 0.629580i | 0.156764 | − | 0.987636i | \(-0.449894\pi\) |
0.933700 | + | 0.358056i | \(0.116560\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.7880i | 0.445221i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.53954 | 0.262176 | 0.131088 | − | 0.991371i | \(-0.458153\pi\) | ||||
0.131088 | + | 0.991371i | \(0.458153\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.0133 | − | 48.5204i | −0.972941 | − | 1.68518i | −0.686570 | − | 0.727063i | \(-0.740885\pi\) |
−0.286370 | − | 0.958119i | \(-0.592449\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.1375 | − | 27.9509i | 0.559802 | − | 0.969606i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.3073 | + | 25.2018i | −0.599662 | + | 0.873192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.8265 | + | 18.7521i | −0.374667 | + | 0.648943i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.98215 | + | 5.18585i | −0.310469 | + | 0.179249i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.7497 | −1.16517 | −0.582584 | − | 0.812770i | \(-0.697958\pi\) | ||||
−0.582584 | + | 0.812770i | \(0.697958\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.73688 | 0.335755 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.6733 | + | 16.5546i | −0.987562 | + | 0.570169i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.18047 | − | 8.97285i | 0.178214 | − | 0.308675i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57.4940 | + | 17.8409i | 1.97552 | + | 0.613021i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.45705 | − | 9.45188i | 0.187285 | − | 0.324388i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.388376 | − | 0.672687i | −0.0133133 | − | 0.0230594i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.4433 | 1.82987 | 0.914933 | − | 0.403607i | \(-0.132244\pi\) | ||||
0.914933 | + | 0.403607i | \(0.132244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.48928i | 0.119331i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.9412 | − | 17.8639i | 1.05693 | − | 0.610220i | 0.132350 | − | 0.991203i | \(-0.457748\pi\) |
0.924582 | + | 0.380983i | \(0.124414\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.24262 | − | 2.44948i | −0.144756 | − | 0.0835751i | 0.425873 | − | 0.904783i | \(-0.359967\pi\) |
−0.570629 | + | 0.821208i | \(0.693300\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.7220 | + | 13.6138i | −0.501723 | + | 0.463957i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0242 | − | 15.6024i | −0.919914 | − | 0.531113i | −0.0363065 | − | 0.999341i | \(-0.511559\pi\) |
−0.883608 | + | 0.468228i | \(0.844893\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.20160 | + | 9.00944i | 0.176860 | + | 0.306330i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.56736i | 0.155116i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 70.8021i | 2.40180i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.2394 | + | 50.6441i | 0.990738 | + | 1.71601i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.1533 | − | 12.2129i | −0.715931 | − | 0.413343i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.584379 | + | 2.58041i | 0.0197556 | + | 0.0872337i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.65217 | − | 2.68593i | −0.157092 | − | 0.0906974i | 0.419393 | − | 0.907805i | \(-0.362243\pi\) |
−0.576485 | + | 0.817107i | \(0.695576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.89545 | − | 2.82639i | 0.165120 | − | 0.0953318i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.9255i | 0.435471i | 0.976008 | + | 0.217736i | \(0.0698670\pi\) | ||||
−0.976008 | + | 0.217736i | \(0.930133\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.5290 | −1.43122 | −0.715608 | − | 0.698502i | \(-0.753850\pi\) | ||||
−0.715608 | + | 0.698502i | \(0.753850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.07669 | + | 13.9892i | 0.271495 | + | 0.470243i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.2391 | + | 33.3231i | −0.645987 | + | 1.11888i | 0.338086 | + | 0.941115i | \(0.390220\pi\) |
−0.984073 | + | 0.177766i | \(0.943113\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.43690 | + | 1.68422i | −0.249426 | + | 0.0564868i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.3339 | + | 56.0040i | −1.08323 | + | 1.87620i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.10144 | + | 1.79062i | −0.103786 | + | 0.0599207i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.61028 | −0.254383 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.93876 | 0.0647332 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.5066 | + | 8.95275i | −0.517175 | + | 0.298591i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.5396 | − | 37.3077i | 0.717588 | − | 1.24290i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.33464 | + | 9.01308i | 0.277359 | + | 0.299937i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.61124 | − | 9.71894i | 0.186524 | − | 0.323069i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.8056 | − | 51.6248i | −0.989679 | − | 1.71417i | −0.618941 | − | 0.785438i | \(-0.712438\pi\) |
−0.370738 | − | 0.928737i | \(-0.620895\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.55501 | 0.151080 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.9457i | 1.35659i | 0.734790 | + | 0.678295i | \(0.237281\pi\) | ||||
−0.734790 | + | 0.678295i | \(0.762719\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 85.3810 | − | 49.2947i | 2.82570 | − | 1.63142i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.6629 | + | 10.7751i | 0.616978 | + | 0.356212i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.27413 | + | 20.2190i | −0.207190 | + | 0.667689i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.8509 | + | 13.1930i | 0.753781 | + | 0.435196i | 0.827058 | − | 0.562116i | \(-0.190013\pi\) |
−0.0732776 | + | 0.997312i | \(0.523346\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.8950 | − | 27.5310i | −0.523759 | − | 0.907177i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.5655i | 1.40106i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.26237i | 0.140146i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.69805 | − | 2.94110i | −0.0557711 | − | 0.0965984i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.7083 | − | 22.3482i | −1.26998 | − | 0.733222i | −0.294994 | − | 0.955499i | \(-0.595318\pi\) |
−0.974984 | + | 0.222277i | \(0.928651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1980 | + | 1.03388i | 0.432546 | + | 0.0338842i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.5182 | + | 18.1971i | 1.03186 | + | 0.595745i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.9745 | − | 12.6870i | 0.718642 | − | 0.414908i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14.4033i | − | 0.470535i | −0.971931 | − | 0.235268i | \(-0.924403\pi\) | ||
0.971931 | − | 0.235268i | \(-0.0755967\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.58701 | −0.182325 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.58349 | + | 9.67088i | 0.182016 | + | 0.315262i | 0.942567 | − | 0.334017i | \(-0.108404\pi\) |
−0.760551 | + | 0.649279i | \(0.775071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.313730 | + | 0.543396i | −0.0102165 | + | 0.0176954i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.99346 | + | 6.42410i | −0.0648472 | + | 0.208976i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.3303 | − | 17.8927i | 0.335691 | − | 0.581434i | −0.647926 | − | 0.761703i | \(-0.724364\pi\) |
0.983617 | + | 0.180269i | \(0.0576968\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.5248 | + | 20.5102i | −1.15318 | + | 0.665791i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37.7262 | −1.22336 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6708 | 0.961132 | 0.480566 | − | 0.876959i | \(-0.340431\pi\) | ||||
0.480566 | + | 0.876959i | \(0.340431\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.68571 | − | 3.86000i | 0.216344 | − | 0.124907i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28.0631 | + | 48.6067i | −0.907152 | + | 1.57123i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.8107 | − | 18.3195i | 0.639720 | − | 0.591566i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.17822 | − | 12.4330i | 0.231555 | − | 0.401066i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.7651 | + | 29.0380i | 0.540248 | + | 0.935736i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.4022 | −0.753345 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.5419i | − | 1.62532i | −0.582740 | − | 0.812658i | \(-0.698020\pi\) | ||
0.582740 | − | 0.812658i | \(-0.301980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.7452 | − | 9.09048i | 0.505808 | − | 0.292028i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.5599 | − | 17.6438i | −0.980715 | − | 0.566216i | −0.0782293 | − | 0.996935i | \(-0.524927\pi\) |
−0.902486 | + | 0.430719i | \(0.858260\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.6433 | + | 5.80737i | −0.822086 | + | 0.186176i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.21347 | − | 5.31940i | −0.295067 | − | 0.170357i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.3142 | − | 23.0609i | −0.425960 | − | 0.737784i | 0.570550 | − | 0.821263i | \(-0.306730\pi\) |
−0.996510 | + | 0.0834788i | \(0.973397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 34.3268i | − | 1.09709i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.25465i | 0.231623i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.60664 | + | 16.6392i | 0.306404 | + | 0.530708i | 0.977573 | − | 0.210597i | \(-0.0675408\pi\) |
−0.671169 | + | 0.741305i | \(0.734207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.6905 | − | 10.2136i | −0.563666 | − | 0.325432i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.7555 | − | 2.43577i | 0.342351 | − | 0.0775315i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.332678 | + | 0.192072i | 0.0105786 | + | 0.00610753i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.2605 | + | 30.1726i | −1.66011 | + | 0.958465i | −0.687450 | + | 0.726232i | \(0.741270\pi\) |
−0.972660 | + | 0.232233i | \(0.925397\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 52.3991i | 1.66283i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.20182 | 0.0698023 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.59147 | + | 14.8809i | 0.272095 | + | 0.471282i | 0.969398 | − | 0.245495i | \(-0.0789503\pi\) |
−0.697303 | + | 0.716776i | \(0.745617\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.41811 | + | 9.38444i | −0.171421 | + | 0.296911i |
(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 | 1120.2.bz.f.271.4 | 24 | ||
4.3 | odd | 2 | 280.2.bj.e.131.11 | ✓ | 24 | ||
7.3 | odd | 6 | 1120.2.bz.e.591.4 | 24 | |||
8.3 | odd | 2 | 1120.2.bz.e.271.4 | 24 | |||
8.5 | even | 2 | 280.2.bj.f.131.2 | yes | 24 | ||
28.3 | even | 6 | 280.2.bj.f.171.2 | yes | 24 | ||
56.3 | even | 6 | inner | 1120.2.bz.f.591.4 | 24 | ||
56.45 | odd | 6 | 280.2.bj.e.171.11 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bj.e.131.11 | ✓ | 24 | 4.3 | odd | 2 | ||
280.2.bj.e.171.11 | yes | 24 | 56.45 | odd | 6 | ||
280.2.bj.f.131.2 | yes | 24 | 8.5 | even | 2 | ||
280.2.bj.f.171.2 | yes | 24 | 28.3 | even | 6 | ||
1120.2.bz.e.271.4 | 24 | 8.3 | odd | 2 | |||
1120.2.bz.e.591.4 | 24 | 7.3 | odd | 6 | |||
1120.2.bz.f.271.4 | 24 | 1.1 | even | 1 | trivial | ||
1120.2.bz.f.591.4 | 24 | 56.3 | even | 6 | inner |