Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (of order \(2\), degree \(1\), 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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.32 | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.d.223.31 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.5168 | 1.11954 | 0.559769 | − | 0.828649i | \(-0.310890\pi\) | ||||
0.559769 | + | 0.828649i | \(0.310890\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.2936 | + | 2.88837i | 0.987764 | + | 0.155957i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 55.4008 | 1.51854 | 0.759271 | − | 0.650774i | \(-0.225556\pi\) | ||||
0.759271 | + | 0.650774i | \(0.225556\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 92.1564 | 1.96612 | 0.983061 | − | 0.183276i | \(-0.0586703\pi\) | ||||
0.983061 | + | 0.183276i | \(0.0586703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 37.5504i | 0.646365i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 118.220i | 1.68662i | 0.537430 | + | 0.843309i | \(0.319395\pi\) | ||||
−0.537430 | + | 0.843309i | \(0.680605\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 155.587i | 1.87864i | 0.343041 | + | 0.939321i | \(0.388543\pi\) | ||||
−0.343041 | + | 0.939321i | \(0.611457\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.66510 | + | 54.8809i | −0.0900419 | + | 0.570286i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 125.358i | − | 1.13647i | −0.822865 | − | 0.568236i | \(-0.807626\pi\) | ||
0.822865 | − | 0.568236i | \(-0.192374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 31.6706 | 0.253365 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 131.643i | 0.842947i | 0.906841 | + | 0.421474i | \(0.138487\pi\) | ||||
−0.906841 | + | 0.421474i | \(0.861513\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −66.0511 | −0.382682 | −0.191341 | − | 0.981524i | \(-0.561284\pi\) | ||||
−0.191341 | + | 0.981524i | \(0.561284\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 166.202i | 0.876731i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 228.978 | + | 36.1532i | 1.10584 | + | 0.174600i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 147.117i | − | 0.653671i | −0.945081 | − | 0.326835i | \(-0.894018\pi\) | ||
0.945081 | − | 0.326835i | \(-0.105982\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 276.469i | 1.13514i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.3097i | 0.0773622i | 0.999252 | + | 0.0386811i | \(0.0123156\pi\) | ||||
−0.999252 | + | 0.0386811i | \(0.987684\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −355.210 | −1.25974 | −0.629872 | − | 0.776699i | \(-0.716893\pi\) | ||||
−0.629872 | + | 0.776699i | \(0.716893\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −112.651 | −0.373179 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −79.5977 | −0.247032 | −0.123516 | − | 0.992343i | \(-0.539417\pi\) | ||||
−0.123516 | + | 0.992343i | \(0.539417\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 326.315 | + | 105.678i | 0.951355 | + | 0.308098i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −354.659 | −0.973769 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 463.012i | − | 1.19999i | −0.800003 | − | 0.599996i | \(-0.795169\pi\) | ||
0.800003 | − | 0.599996i | \(-0.204831\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 693.441 | 1.70007 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −466.762 | −1.08463 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 580.211i | − | 1.28029i | −0.768255 | − | 0.640144i | \(-0.778875\pi\) | ||
0.768255 | − | 0.640144i | \(-0.221125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 587.607 | 1.23337 | 0.616683 | − | 0.787212i | \(-0.288476\pi\) | ||||
0.616683 | + | 0.787212i | \(0.288476\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −164.643 | − | 25.9953i | −0.329255 | − | 0.0519857i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1153.50 | 2.20115 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −496.198 | −0.904779 | −0.452390 | − | 0.891820i | \(-0.649428\pi\) | ||||
−0.452390 | + | 0.891820i | \(0.649428\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 376.073 | 0.656143 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 232.774i | 0.389087i | 0.980894 | + | 0.194543i | \(0.0623225\pi\) | ||||
−0.980894 | + | 0.194543i | \(0.937677\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 551.640i | − | 0.884447i | −0.896905 | − | 0.442223i | \(-0.854190\pi\) | ||
0.896905 | − | 0.442223i | \(-0.145810\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 95.0119i | 0.146280i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1013.48 | + | 160.018i | 1.49996 | + | 0.236828i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 437.936i | − | 0.623692i | −0.950133 | − | 0.311846i | \(-0.899053\pi\) | ||
0.950133 | − | 0.311846i | \(-0.100947\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 191.266i | 0.252941i | 0.991970 | + | 0.126471i | \(0.0403650\pi\) | ||||
−0.991970 | + | 0.126471i | \(0.959635\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1479.73i | 1.88823i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −394.929 | −0.486676 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 93.7894i | 0.111704i | 0.998439 | + | 0.0558520i | \(0.0177875\pi\) | ||||
−0.998439 | + | 0.0558520i | \(0.982213\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1685.88 | + | 266.182i | 1.94207 | + | 0.306631i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 198.153i | − | 0.220941i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1947.46i | 2.10321i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 758.892i | − | 0.794369i | −0.917739 | − | 0.397184i | \(-0.869987\pi\) | ||
0.917739 | − | 0.397184i | \(-0.130013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −498.607 | −0.506181 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −803.819 | −0.791910 | −0.395955 | − | 0.918270i | \(-0.629586\pi\) | ||||
−0.395955 | + | 0.918270i | \(0.629586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −946.857 | −0.905792 | −0.452896 | − | 0.891563i | \(-0.649609\pi\) | ||||
−0.452896 | + | 0.891563i | \(0.649609\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −108.459 | + | 686.934i | −0.100805 | + | 0.638456i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1693.10 | −1.52970 | −0.764850 | − | 0.644208i | \(-0.777187\pi\) | ||||
−0.764850 | + | 0.644208i | \(0.777187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 103.927i | 0.0913251i | 0.998957 | + | 0.0456626i | \(0.0145399\pi\) | ||||
−0.998957 | + | 0.0456626i | \(0.985460\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 441.350 | 0.377397 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.0288 | −0.0141764 | −0.00708819 | − | 0.999975i | \(-0.502256\pi\) | ||||
−0.00708819 | + | 0.999975i | \(0.502256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1569.08i | − | 1.27232i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −829.408 | −0.655374 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −341.462 | + | 2162.67i | −0.263040 | + | 1.66598i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1738.25 | 1.30597 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −60.9292 | −0.0446651 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1168.19 | −0.835886 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 481.156i | 0.336187i | 0.985771 | + | 0.168093i | \(0.0537610\pi\) | ||||
−0.985771 | + | 0.168093i | \(0.946239\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1065.63i | − | 0.727314i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1599.97i | − | 1.06710i | −0.845769 | − | 0.533550i | \(-0.820858\pi\) | ||
0.845769 | − | 0.533550i | \(-0.179142\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −449.393 | + | 2846.26i | −0.292988 | + | 1.85565i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 337.954i | − | 0.215455i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −867.738 | −0.541138 | −0.270569 | − | 0.962701i | \(-0.587212\pi\) | ||||
−0.270569 | + | 0.962701i | \(0.587212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 773.391i | − | 0.471929i | −0.971762 | − | 0.235965i | \(-0.924175\pi\) | ||
0.971762 | − | 0.235965i | \(-0.0758249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 238.793i | − | 0.142624i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5105.54 | 2.98564 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1647.75i | 0.943711i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −317.033 | + | 978.944i | −0.177880 | + | 0.549265i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1566.08i | − | 0.861063i | −0.902576 | − | 0.430531i | \(-0.858326\pi\) | ||
0.902576 | − | 0.430531i | \(-0.141674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 168.569i | − | 0.0908474i | −0.998968 | − | 0.0454237i | \(-0.985536\pi\) | ||
0.998968 | − | 0.0454237i | \(-0.0144638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1063.98i | − | 0.562206i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −826.750 | −0.428427 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1378.04 | −0.700506 | −0.350253 | − | 0.936655i | \(-0.613904\pi\) | ||||
−0.350253 | + | 0.936655i | \(0.613904\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1389.03 | 0.692815 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 362.079 | − | 2293.25i | 0.177241 | − | 1.12257i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2078.67 | −0.998858 | −0.499429 | − | 0.866355i | \(-0.666457\pi\) | ||||
−0.499429 | + | 0.866355i | \(0.666457\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2080.32i | 0.981534i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −388.656 | −0.180090 | −0.0900452 | − | 0.995938i | \(-0.528701\pi\) | ||||
−0.0900452 | + | 0.995938i | \(0.528701\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6295.81 | 2.86564 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 1400.29i | − | 0.626214i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2510.22 | 1.10317 | 0.551586 | − | 0.834118i | \(-0.314023\pi\) | ||||
0.551586 | + | 0.834118i | \(0.314023\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 579.371 | + | 91.4764i | 0.250265 | + | 0.0395141i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1740.63 | 0.739175 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1287.12 | −0.537450 | −0.268725 | − | 0.963217i | \(-0.586602\pi\) | ||||
−0.268725 | + | 0.963217i | \(0.586602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2880.43 | −1.18288 | −0.591438 | − | 0.806351i | \(-0.701439\pi\) | ||||
−0.591438 | + | 0.806351i | \(0.701439\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1762.82i | 0.712084i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1841.43i | − | 0.731809i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6549.47i | 2.56120i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 77.9859 | − | 493.928i | 0.0300140 | − | 0.190095i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1264.81i | 0.479155i | 0.970877 | + | 0.239577i | \(0.0770089\pi\) | ||||
−0.970877 | + | 0.239577i | \(0.922991\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3174.10 | 1.18382 | 0.591908 | − | 0.806005i | \(-0.298375\pi\) | ||||
0.591908 | + | 0.806005i | \(0.298375\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3460.51i | 1.27083i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2153.82i | − | 0.778951i | −0.921037 | − | 0.389475i | \(-0.872656\pi\) | ||
0.921037 | − | 0.389475i | \(-0.127344\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5051.78 | −1.79955 | −0.899776 | − | 0.436352i | \(-0.856270\pi\) | ||||
−0.899776 | + | 0.436352i | \(0.856270\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1488.59i | − | 0.522375i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −380.233 | + | 2408.23i | −0.131464 | + | 0.832633i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 254.213i | 0.0866099i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1128.22i | 0.378824i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8619.66i | 2.85280i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1946.49 | −0.635080 | −0.317540 | − | 0.948245i | \(-0.602857\pi\) | ||||
−0.317540 | + | 0.948245i | \(0.602857\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −698.321 | −0.224639 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4446.10 | −1.41033 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1208.32 | − | 190.780i | −0.377999 | − | 0.0596820i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1654.92 | 0.510636 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10894.7i | 3.31610i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 901.888 | 0.270829 | 0.135415 | − | 0.990789i | \(-0.456763\pi\) | ||||
0.135415 | + | 0.990789i | \(0.456763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −285.036 | −0.0844550 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4975.14i | 1.45468i | 0.686278 | + | 0.727339i | \(0.259243\pi\) | ||||
−0.686278 | + | 0.727339i | \(0.740757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3689.85 | 1.06477 | 0.532384 | − | 0.846503i | \(-0.321296\pi\) | ||||
0.532384 | + | 0.846503i | \(0.321296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −480.054 | + | 3040.45i | −0.136733 | + | 0.866003i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3285.97 | 0.923909 | 0.461954 | − | 0.886904i | \(-0.347148\pi\) | ||||
0.461954 | + | 0.886904i | \(0.347148\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −996.309 | −0.276562 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1313.81 | 0.360089 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2662.25i | 0.720529i | 0.932850 | + | 0.360264i | \(0.117314\pi\) | ||||
−0.932850 | + | 0.360264i | \(0.882686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 494.863i | 0.132269i | 0.997811 | + | 0.0661347i | \(0.0210667\pi\) | ||||
−0.997811 | + | 0.0661347i | \(0.978933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4084.42 | + | 1322.75i | 1.06508 | + | 0.344927i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14338.4i | 3.69364i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −573.797 | −0.146036 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4465.24i | − | 1.12288i | −0.827516 | − | 0.561442i | \(-0.810247\pi\) | ||
0.827516 | − | 0.561442i | \(-0.189753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6944.91i | − | 1.72578i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4439.20 | −1.09017 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3874.34i | − | 0.940369i | −0.882568 | − | 0.470185i | \(-0.844187\pi\) | ||
0.882568 | − | 0.470185i | \(-0.155813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 424.927 | − | 2691.30i | 0.101945 | − | 0.645672i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1184.79i | − | 0.280982i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4291.91i | − | 1.00628i | −0.864206 | − | 0.503138i | \(-0.832179\pi\) | ||
0.864206 | − | 0.503138i | \(-0.167821\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5795.43i | − | 1.34344i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −281.368 | −0.0644923 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4934.08 | 1.11835 | 0.559175 | − | 0.829050i | \(-0.311118\pi\) | ||||
0.559175 | + | 0.829050i | \(0.311118\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3796.02 | 0.850893 | 0.425446 | − | 0.904984i | \(-0.360117\pi\) | ||||
0.425446 | + | 0.904984i | \(0.360117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −798.545 | + | 5057.63i | −0.177033 | + | 1.12125i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1754.58 | 0.384745 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6822.56i | 1.47988i | 0.672671 | + | 0.739942i | \(0.265147\pi\) | ||||
−0.672671 | + | 0.739942i | \(0.734853\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 594.460 | 0.127561 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7537.89 | 1.60026 | 0.800129 | − | 0.599827i | \(-0.204764\pi\) | ||||
0.800129 | + | 0.599827i | \(0.204764\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1945.91i | 0.408736i | 0.978894 | + | 0.204368i | \(0.0655139\pi\) | ||||
−0.978894 | + | 0.204368i | \(0.934486\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5842.37 | −1.21429 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −58.6620 | + | 371.539i | −0.0120652 | + | 0.0764155i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9062.90 | −1.84468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2276.67 | 0.458629 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4658.84 | 0.928916 | 0.464458 | − | 0.885595i | \(-0.346249\pi\) | ||||
0.464458 | + | 0.885595i | \(0.346249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7262.39i | − | 1.43333i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1495.82i | − | 0.292244i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 11552.5i | − | 2.23444i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6498.09 | − | 1025.98i | −1.24433 | − | 0.196466i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2411.46i | − | 0.457210i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7354.96 | 1.38080 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3147.04i | 0.585053i | 0.956257 | + | 0.292526i | \(0.0944959\pi\) | ||||
−0.956257 | + | 0.292526i | \(0.905504\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2840.57i | − | 0.522959i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9786.74 | 1.78442 | 0.892211 | − | 0.451619i | \(-0.149153\pi\) | ||||
0.892211 | + | 0.451619i | \(0.149153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7053.24i | − | 1.27372i | −0.770981 | − | 0.636858i | \(-0.780234\pi\) | ||
0.770981 | − | 0.636858i | \(-0.219766\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2060.80 | − | 325.378i | −0.368613 | − | 0.0582000i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7111.48i | 1.26000i | 0.776595 | + | 0.630001i | \(0.216945\pi\) | ||||
−0.776595 | + | 0.630001i | \(0.783055\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7293.12i | 1.28005i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5079.29i | − | 0.883173i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18393.5 | −3.16855 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2918.65 | 0.498147 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −311.782 | −0.0527266 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1456.13 | − | 229.907i | −0.244009 | − | 0.0385265i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4383.51 | 0.727914 | 0.363957 | − | 0.931416i | \(-0.381425\pi\) | ||||
0.363957 | + | 0.931416i | \(0.381425\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1324.05i | 0.217890i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6210.82 | −1.01293 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3696.74 | 0.597549 | 0.298775 | − | 0.954324i | \(-0.403422\pi\) | ||||
0.298775 | + | 0.954324i | \(0.403422\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 51.0863i | − | 0.00818474i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3659.29 | −0.581119 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5664.25 | + | 2875.74i | 0.891664 | + | 0.452698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4707.23 | 0.734577 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6007.60 | 0.929408 | 0.464704 | − | 0.885466i | \(-0.346161\pi\) | ||||
0.464704 | + | 0.885466i | \(0.346161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1376.99 | −0.211199 | −0.105600 | − | 0.994409i | \(-0.533676\pi\) | ||||
−0.105600 | + | 0.994409i | \(0.533676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2488.22i | − | 0.378381i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3533.89i | 0.532833i | 0.963858 | + | 0.266417i | \(0.0858397\pi\) | ||||
−0.963858 | + | 0.266417i | \(0.914160\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2913.59i | 0.435597i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6488.01 | − | 1024.39i | −0.961854 | − | 0.151866i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4792.38i | − | 0.704547i | −0.935897 | − | 0.352273i | \(-0.885409\pi\) | ||
0.935897 | − | 0.352273i | \(-0.114591\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17348.4 | −2.52929 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5214.75i | 0.754003i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6904.78i | − | 0.990172i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10145.7 | −1.44305 | −0.721526 | − | 0.692387i | \(-0.756559\pi\) | ||||
−0.721526 | + | 0.692387i | \(0.756559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 182.788i | − | 0.0257874i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1337.35 | − | 8470.17i | 0.187147 | − | 1.18531i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8427.27i | − | 1.16983i | −0.811094 | − | 0.584916i | \(-0.801127\pi\) | ||
0.811094 | − | 0.584916i | \(-0.198873\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3504.56i | − | 0.482599i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12131.7i | 1.65734i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6309.37 | −0.855121 | −0.427560 | − | 0.903987i | \(-0.640627\pi\) | ||||
−0.427560 | + | 0.903987i | \(0.640627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1443.47 | −0.194098 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6889.51 | 0.919158 | 0.459579 | − | 0.888137i | \(-0.348000\pi\) | ||||
0.459579 | + | 0.888137i | \(0.348000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12685.6 | + | 2002.91i | 1.67926 | + | 0.265138i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3196.89 | 0.419915 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3025.39i | − | 0.394327i | −0.980371 | − | 0.197164i | \(-0.936827\pi\) | ||
0.980371 | − | 0.197164i | \(-0.0631730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14819.7 | 1.91679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4799.91 | 0.616090 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 5481.56i | − | 0.698247i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1565.33 | 0.197889 | 0.0989444 | − | 0.995093i | \(-0.468453\pi\) | ||||
0.0989444 | + | 0.995093i | \(0.468453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8538.78 | − | 1348.18i | −1.07136 | − | 0.169156i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2687.03 | 0.334623 | 0.167312 | − | 0.985904i | \(-0.446491\pi\) | ||||
0.167312 | + | 0.985904i | \(0.446491\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6087.04 | −0.752399 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1013.86 | 0.124393 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8150.38i | − | 0.992627i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11421.7i | 1.38084i | 0.723407 | + | 0.690422i | \(0.242575\pi\) | ||||
−0.723407 | + | 0.690422i | \(0.757425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2603.21i | − | 0.312426i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1675.86 | − | 10614.2i | 0.199670 | − | 1.26462i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2394.04i | 0.283178i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2320.17 | 0.272468 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5192.62i | − | 0.605432i | −0.953081 | − | 0.302716i | \(-0.902107\pi\) | ||
0.953081 | − | 0.302716i | \(-0.0978934\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11047.1i | 1.27887i | 0.768846 | + | 0.639434i | \(0.220831\pi\) | ||||
−0.768846 | + | 0.639434i | \(0.779169\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 716.379 | 0.0823441 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3744.09i | 0.427330i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10749.5 | + | 1697.22i | 1.21827 | + | 0.192352i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15316.6i | 1.72376i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7402.32i | 0.827279i | 0.910441 | + | 0.413640i | \(0.135743\pi\) | ||||
−0.910441 | + | 0.413640i | \(0.864257\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 304.730i | 0.0338208i | 0.999857 | + | 0.0169104i | \(0.00538300\pi\) | ||||
−0.999857 | + | 0.0169104i | \(0.994617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4943.25 | −0.544852 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19504.1 | 2.13502 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7752.82 | −0.842875 | −0.421437 | − | 0.906857i | \(-0.638474\pi\) | ||||
−0.421437 | + | 0.906857i | \(0.638474\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2936.83 | − | 951.098i | −0.317118 | − | 0.102699i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14980.0 | 1.60660 | 0.803298 | − | 0.595577i | \(-0.203077\pi\) | ||||
0.803298 | + | 0.595577i | \(0.203077\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1173.94i | 0.125057i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4698.24 | 0.497135 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17523.6 | −1.84185 | −0.920925 | − | 0.389740i | \(-0.872565\pi\) | ||||
−0.920925 | + | 0.389740i | \(0.872565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1125.18i | 0.117478i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 505.707 | 0.0524508 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21101.8 | + | 3331.75i | 2.17422 | + | 0.343285i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3264.38 | −0.334139 | −0.167069 | − | 0.985945i | \(-0.553430\pi\) | ||||
−0.167069 | + | 0.985945i | \(0.553430\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3191.93 | 0.324590 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4096.53 | −0.413870 | −0.206935 | − | 0.978355i | \(-0.566349\pi\) | ||||
−0.206935 | + | 0.978355i | \(0.566349\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12281.3i | − | 1.23275i | −0.787455 | − | 0.616373i | \(-0.788602\pi\) | ||
0.787455 | − | 0.616373i | \(-0.211398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 2480.25i | − | 0.247352i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 14919.7i | − | 1.47838i | −0.673499 | − | 0.739188i | \(-0.735209\pi\) | ||
0.673499 | − | 0.739188i | \(-0.264791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9077.26 | − | 1433.20i | −0.893708 | − | 0.141107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 4134.12i | − | 0.404438i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19678.9 | −1.91298 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4927.55i | 0.475982i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4167.10i | 0.399997i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3253.39 | 0.310337 | 0.155168 | − | 0.987888i | \(-0.450408\pi\) | ||||
0.155168 | + | 0.987888i | \(0.450408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 13557.7i | − | 1.28520i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6879.74 | + | 1086.24i | 0.648114 | + | 0.102330i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9498.90i | − | 0.889326i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 367.609i | 0.0342053i | 0.999854 | + | 0.0171026i | \(0.00544420\pi\) | ||||
−0.999854 | + | 0.0171026i | \(0.994556\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6236.01i | − | 0.576691i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8656.19 | 0.795618 | 0.397809 | − | 0.917468i | \(-0.369771\pi\) | ||||
0.397809 | + | 0.917468i | \(0.369771\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15562.8 | −1.42173 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6240.97 | −0.566689 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −672.336 | + | 4258.28i | −0.0606809 | + | 0.384326i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14675.5 | −1.31656 | −0.658280 | − | 0.752773i | \(-0.728716\pi\) | ||||
−0.658280 | + | 0.752773i | \(0.728716\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 1165.97i | − | 0.103975i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4451.92 | 0.394635 | 0.197317 | − | 0.980340i | \(-0.436777\pi\) | ||||
0.197317 | + | 0.980340i | \(0.436777\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10061.2 | −0.886573 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18887.4i | 1.65448i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17750.3 | 1.54572 | 0.772858 | − | 0.634579i | \(-0.218826\pi\) | ||||
0.772858 | + | 0.634579i | \(0.218826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1593.34 | − | 10091.5i | 0.137936 | − | 0.873624i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4200.86 | 0.361545 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11851.6 | −1.01407 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4409.78 | −0.375129 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7530.67i | 0.636916i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8202.49i | − | 0.689746i | −0.938649 | − | 0.344873i | \(-0.887922\pi\) | ||
0.938649 | − | 0.344873i | \(-0.112078\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14583.3i | − | 1.21928i | −0.792678 | − | 0.609641i | \(-0.791314\pi\) | ||
0.792678 | − | 0.609641i | \(-0.208686\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −274.429 | + | 1738.11i | −0.0228135 | + | 0.144490i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 7808.55i | − | 0.645438i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3547.53 | −0.291570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5221.90i | 0.426763i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1871.67i | 0.152104i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21192.2 | −1.71256 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 3861.35i | − | 0.310297i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18078.1 | + | 5854.62i | 1.44467 | + | 0.467860i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 18146.0i | − | 1.44207i | −0.692900 | − | 0.721033i | \(-0.743667\pi\) | ||
0.692900 | − | 0.721033i | \(-0.256333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8641.28i | − | 0.682933i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1300.84i | 0.102242i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10223.9 | 0.799164 | 0.399582 | − | 0.916698i | \(-0.369155\pi\) | ||||
0.399582 | + | 0.916698i | \(0.369155\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5288.46 | −0.411122 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20482.0 | −1.58360 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1264.92 | − | 8011.44i | 0.0972692 | − | 0.616060i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5524.29 | 0.422510 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18894.8i | − | 1.43734i | −0.695352 | − | 0.718669i | \(-0.744752\pi\) | ||
0.695352 | − | 0.718669i | \(-0.255248\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32734.9 | −2.47681 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19648.4 | −1.47871 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 4811.00i | − | 0.360141i | −0.983654 | − | 0.180071i | \(-0.942367\pi\) | ||
0.983654 | − | 0.180071i | \(-0.0576326\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −213.146 | −0.0158710 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1481.78 | + | 233.958i | 0.109752 | + | 0.0173286i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15811.2 | 1.16492 | 0.582460 | − | 0.812859i | \(-0.302090\pi\) | ||||
0.582460 | + | 0.812859i | \(0.302090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12377.3 | 0.907131 | 0.453566 | − | 0.891223i | \(-0.350152\pi\) | ||||
0.453566 | + | 0.891223i | \(0.350152\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3794.43 | −0.276640 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3970.15i | − | 0.287942i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17225.6i | 1.24283i | 0.783484 | + | 0.621413i | \(0.213441\pi\) | ||||
−0.783484 | + | 0.621413i | \(0.786559\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9522.30i | 0.683477i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −552.446 | + | 3498.95i | −0.0394480 | + | 0.249846i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 25651.2i | − | 1.82224i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10381.5 | −0.733716 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 17524.8i | − | 1.23224i | −0.787651 | − | 0.616121i | \(-0.788703\pi\) | ||
0.787651 | − | 0.616121i | \(-0.211297\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10276.7i | − | 0.718922i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6461.46 | 0.449727 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17080.1i | 1.18279i | 0.806382 | + | 0.591394i | \(0.201422\pi\) | ||||
−0.806382 | + | 0.591394i | \(0.798578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4274.02 | + | 27069.7i | −0.294483 | + | 1.86513i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 15155.3i | − | 1.03897i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 18593.0i | − | 1.26826i | −0.773225 | − | 0.634132i | \(-0.781358\pi\) | ||
0.773225 | − | 0.634132i | \(-0.218642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22600.9i | 1.53396i | 0.641670 | + | 0.766981i | \(0.278242\pi\) | ||||
−0.641670 | + | 0.766981i | \(0.721758\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4465.78 | 0.301593 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21757.3 | 1.46209 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7870.14 | −0.526259 | −0.263130 | − | 0.964761i | \(-0.584755\pi\) | ||||
−0.263130 | + | 0.964761i | \(0.584755\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7224.68 | − | 1140.70i | −0.480721 | − | 0.0759006i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7335.44 | −0.485696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5829.16i | 0.384074i | 0.981388 | + | 0.192037i | \(0.0615094\pi\) | ||||
−0.981388 | + | 0.192037i | \(0.938491\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −762.640 | −0.0500042 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3132.87 | 0.204416 | 0.102208 | − | 0.994763i | \(-0.467409\pi\) | ||||
0.102208 | + | 0.994763i | \(0.467409\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1967.51i | − | 0.127756i | −0.997958 | − | 0.0638779i | \(-0.979653\pi\) | ||
0.997958 | − | 0.0638779i | \(-0.0203468\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3384.66 | −0.218714 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −270.898 | + | 1715.75i | −0.0174210 | + | 0.110337i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18580.8 | −1.18917 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25859.0 | −1.64706 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17392.1 | 1.10249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12821.2i | 0.808883i | 0.914564 | + | 0.404441i | \(0.132534\pi\) | ||||
−0.914564 | + | 0.404441i | \(0.867466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5839.47i | − | 0.366664i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6022.54i | 0.376374i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30072.0 | + | 9738.86i | 1.87048 | + | 0.605758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 2094.96i | − | 0.129696i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7100.25 | 0.437509 | 0.218754 | − | 0.975780i | \(-0.429801\pi\) | ||||
0.218754 | + | 0.975780i | \(0.429801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22717.2i | 1.39328i | 0.717421 | + | 0.696640i | \(0.245323\pi\) | ||||
−0.717421 | + | 0.696640i | \(0.754677\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 13338.3i | − | 0.814256i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 333.262 | 0.0202502 | 0.0101251 | − | 0.999949i | \(-0.496777\pi\) | ||||
0.0101251 | + | 0.999949i | \(0.496777\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 32144.1i | − | 1.94417i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 572.340 | − | 3624.95i | 0.0344574 | − | 0.218238i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 27002.5i | − | 1.61821i | −0.587666 | − | 0.809103i | \(-0.699953\pi\) | ||
0.587666 | − | 0.809103i | \(-0.300047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 20026.5i | − | 1.19466i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4964.76i | 0.294816i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17790.1 | 1.05160 | 0.525799 | − | 0.850609i | \(-0.323766\pi\) | ||||
0.525799 | + | 0.850609i | \(0.323766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28922.6 | −1.70190 | −0.850951 | − | 0.525246i | \(-0.823973\pi\) | ||||
−0.850951 | + | 0.525246i | \(0.823973\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −32684.1 | −1.91455 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5624.97 | + | 35626.1i | −0.328011 | + | 2.07747i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16502.4 | 0.957987 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2705.66i | 0.156363i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32553.9 | 1.87292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9655.76 | −0.553049 | −0.276525 | − | 0.961007i | \(-0.589183\pi\) | ||||
−0.276525 | + | 0.961007i | \(0.589183\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 855.107i | − | 0.0487601i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 97.6916 | 0.00554593 | 0.00277296 | − | 0.999996i | \(-0.499117\pi\) | ||||
0.00277296 | + | 0.999996i | \(0.499117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2191.96 | − | 13882.9i | 0.123888 | − | 0.784649i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14925.4 | −0.839859 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9136.04 | −0.511831 | −0.255916 | − | 0.966699i | \(-0.582377\pi\) | ||||
−0.255916 | + | 0.966699i | \(0.582377\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10861.3 | −0.605824 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11069.5i | 0.614744i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 42669.5i | − | 2.35933i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20090.0i | 1.10602i | 0.833174 | + | 0.553011i | \(0.186521\pi\) | ||||
−0.833174 | + | 0.553011i | \(0.813479\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9121.34 | − | 1440.16i | −0.499987 | − | 0.0789426i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 9680.39i | − | 0.528342i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2401.01 | −0.130480 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9857.90i | 0.533419i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28733.6i | 1.54815i | 0.633095 | + | 0.774074i | \(0.281784\pi\) | ||||
−0.633095 | + | 0.774074i | \(0.718216\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22889.5 | 1.22801 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2988.93i | − | 0.159673i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14704.8 | − | 2321.72i | −0.782220 | − | 0.123504i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1873.43i | 0.0992360i | 0.998768 | + | 0.0496180i | \(0.0158004\pi\) | ||||
−0.998768 | + | 0.0496180i | \(0.984200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3941.42i | 0.207897i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8280.01i | 0.434907i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 63905.1 | 3.34254 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7986.74 | −0.415998 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2073.02 | −0.107525 | −0.0537625 | − | 0.998554i | \(-0.517121\pi\) | ||||
−0.0537625 | + | 0.998554i | \(0.517121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17321.5 | − | 2734.87i | −0.894709 | − | 0.141265i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1484.59 | −0.0763658 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4169.21i | 0.213573i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26274.3 | 1.34038 | 0.670191 | − | 0.742188i | \(-0.266212\pi\) | ||||
0.670191 | + | 0.742188i | \(0.266212\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 41992.8i | − | 2.12471i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18164.4 | −0.915304 | −0.457652 | − | 0.889131i | \(-0.651309\pi\) | ||||
−0.457652 | + | 0.889131i | \(0.651309\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3968.24 | + | 12253.3i | −0.199144 | + | 0.614923i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27489.8 | −1.37395 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9438.47 | −0.469824 | −0.234912 | − | 0.972017i | \(-0.575480\pi\) | ||||
−0.234912 | + | 0.972017i | \(0.575480\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −43015.1 | −2.13252 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8531.76i | 0.421265i | 0.977565 | + | 0.210633i | \(0.0675524\pi\) | ||||
−0.977565 | + | 0.210633i | \(0.932448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 19602.3i | − | 0.963992i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1721.39i | − | 0.0843138i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30972.9 | − | 4890.29i | −1.51098 | − | 0.238568i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20258.1i | 0.984325i | 0.870503 | + | 0.492163i | \(0.163794\pi\) | ||||
−0.870503 | + | 0.492163i | \(0.836206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13395.7 | 0.648297 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2109.95i | − | 0.101707i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30742.9i | 1.47605i | 0.674772 | + | 0.738026i | \(0.264242\pi\) | ||||
−0.674772 | + | 0.738026i | \(0.735758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20834.7 | 0.996381 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22602.8i | 1.07667i | 0.842730 | + | 0.538337i | \(0.180947\pi\) | ||||
−0.842730 | + | 0.538337i | \(0.819053\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −300.181 | + | 1901.21i | −0.0142428 | + | 0.0902077i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 13317.6i | − | 0.629411i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 53470.2i | − | 2.51720i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6329.77i | 0.296823i | 0.988926 | + | 0.148412i | \(0.0474161\pi\) | ||||
−0.988926 | + | 0.148412i | \(0.952584\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11623.0 | 0.542922 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13945.2 | −0.648867 | −0.324433 | − | 0.945909i | \(-0.605174\pi\) | ||||
−0.324433 | + | 0.945909i | \(0.605174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2091.88 | −0.0969581 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8073.89 | + | 1274.78i | 0.372779 | + | 0.0588578i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3159.94 | −0.145336 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12895.9i | 0.590845i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3554.36 | 0.162225 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17248.7 | −0.784243 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38929.4i | − | 1.76326i | −0.471946 | − | 0.881628i | \(-0.656448\pi\) | ||
0.471946 | − | 0.881628i | \(-0.343552\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12875.7 | 0.580973 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −311.518 | − | 49.1853i | −0.0140029 | − | 0.00221091i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54151.7 | 2.42495 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17386.3 | 0.775633 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5612.71 | −0.249451 | −0.124726 | − | 0.992191i | \(-0.539805\pi\) | ||||
−0.124726 | + | 0.992191i | \(0.539805\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9410.02i | − | 0.416649i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 844.104i | − | 0.0372346i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 30561.3i | − | 1.34307i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4532.07 | − | 28704.2i | 0.198428 | − | 1.25676i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14802.2i | 0.645679i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13074.7 | −0.568210 | −0.284105 | − | 0.958793i | \(-0.591696\pi\) | ||||
−0.284105 | + | 0.958793i | \(0.591696\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3773.85i | 0.163400i | 0.996657 | + | 0.0817002i | \(0.0260350\pi\) | ||||
−0.996657 | + | 0.0817002i | \(0.973965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11388.1i | 0.491263i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26018.3 | −1.11826 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 55266.2i | − | 2.36661i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15172.9 | − | 2395.64i | −0.647355 | − | 0.102210i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15494.5i | 0.658661i | 0.944215 | + | 0.329331i | \(0.106823\pi\) | ||||
−0.944215 | + | 0.329331i | \(0.893177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32765.2i | − | 1.38776i | −0.720092 | − | 0.693879i | \(-0.755900\pi\) | ||
0.720092 | − | 0.693879i | \(-0.244100\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5263.73i | 0.222133i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8067.05 | 0.339200 | 0.169600 | − | 0.985513i | \(-0.445752\pi\) | ||||
0.169600 | + | 0.985513i | \(0.445752\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19574.3 | −0.820078 | −0.410039 | − | 0.912068i | \(-0.634485\pi\) | ||||
−0.410039 | + | 0.912068i | \(0.634485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20467.7 | −0.854411 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12493.2 | + | 38576.8i | −0.519643 | + | 1.60457i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4864.74 | −0.201618 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1783.38i | 0.0736471i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41602.1 | 1.71187 | 0.855937 | − | 0.517079i | \(-0.172981\pi\) | ||||
0.855937 | + | 0.517079i | \(0.172981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7059.15 | 0.289440 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22613.7i | 0.923910i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 78803.5 | 3.20819 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31798.9 | + | 5020.70i | 1.28999 | + | 0.203676i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5837.73 | −0.235984 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18442.2 | −0.742879 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21967.3 | −0.881765 | −0.440882 | − | 0.897565i | \(-0.645334\pi\) | ||||
−0.440882 | + | 0.897565i | \(0.645334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 17527.1i | − | 0.701070i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40486.3i | 1.61375i | 0.590720 | + | 0.806877i | \(0.298844\pi\) | ||||
−0.590720 | + | 0.806877i | \(0.701156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 26419.8i | − | 1.04940i | −0.851289 | − | 0.524698i | \(-0.824178\pi\) | ||
0.851289 | − | 0.524698i | \(-0.175822\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1114.62 | − | 175.986i | −0.0441185 | − | 0.00696584i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31789.9i | 1.25393i | 0.779048 | + | 0.626964i | \(0.215703\pi\) | ||||
−0.779048 | + | 0.626964i | \(0.784297\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31420.0 | 1.23504 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 27188.7i | − | 1.06503i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 24262.0i | − | 0.947103i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45727.8 | −1.77891 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6830.02i | 0.264790i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21370.4 | − | 3374.15i | −0.825658 | − | 0.130362i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 8034.36i | − | 0.309351i | −0.987965 | − | 0.154676i | \(-0.950567\pi\) | ||
0.987965 | − | 0.154676i | \(-0.0494332\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13976.5i | 0.536310i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 17579.3i | − | 0.672262i | −0.941815 | − | 0.336131i | \(-0.890882\pi\) | ||
0.941815 | − | 0.336131i | \(-0.109118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31775.9 | −1.21104 | −0.605518 | − | 0.795832i | \(-0.707034\pi\) | ||||
−0.605518 | + | 0.795832i | \(0.707034\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21787.2 | 0.827534 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6353.28 | −0.240498 | −0.120249 | − | 0.992744i | \(-0.538369\pi\) | ||||
−0.120249 | + | 0.992744i | \(0.538369\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1389.76 | + | 8802.10i | −0.0524308 | + | 0.332073i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4487.46 | 0.168727 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 12384.4i | − | 0.464085i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16110.6 | −0.601696 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34657.5 | 1.29006 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 8695.16i | − | 0.322581i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54737.1 | 2.02393 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3077.93 | − | 19494.3i | 0.113430 | − | 0.718414i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36053.8 | −1.32427 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21510.5 | −0.787480 | −0.393740 | − | 0.919222i | \(-0.628819\pi\) | ||||
−0.393740 | + | 0.919222i | \(0.628819\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7234.37 | 0.263970 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14005.7i | − | 0.509363i | −0.967025 | − | 0.254681i | \(-0.918029\pi\) | ||
0.967025 | − | 0.254681i | \(-0.0819706\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10596.3i | 0.384102i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22064.9i | 0.797205i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4621.30 | − | 29269.3i | 0.166422 | − | 1.05404i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 17108.7i | − | 0.614106i | −0.951692 | − | 0.307053i | \(-0.900657\pi\) | ||
0.951692 | − | 0.307053i | \(-0.0993428\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9441.12 | −0.337780 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21451.6i | 0.764993i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4659.27i | − | 0.165617i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8521.71 | 0.301931 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 50366.6i | − | 1.77877i | −0.457162 | − | 0.889384i | \(-0.651134\pi\) | ||
0.457162 | − | 0.889384i | \(-0.348866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16442.1 | + | 50770.4i | −0.578805 | + | 1.78725i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29360.2i | 1.03024i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 81978.5i | 2.86736i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34447.3i | 1.20101i | 0.799621 | + | 0.600505i | \(0.205034\pi\) | ||||
−0.799621 | + | 0.600505i | \(0.794966\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21159.7 | 0.735380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21746.7 | 0.753372 | 0.376686 | − | 0.926341i | \(-0.377064\pi\) | ||||
0.376686 | + | 0.926341i | \(0.377064\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2545.98 | 0.0879200 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 976.135 | − | 6182.41i | 0.0336018 | − | 0.212819i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20179.9 | −0.692460 | −0.346230 | − | 0.938150i | \(-0.612538\pi\) | ||||
−0.346230 | + | 0.938150i | \(0.612538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 50837.2i | − | 1.73893i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21334.4 | −0.727462 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49322.8 | −1.67652 | −0.838259 | − | 0.545272i | \(-0.816426\pi\) | ||||
−0.838259 | + | 0.545272i | \(0.816426\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15831.4i | 0.536432i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21879.4 | −0.739038 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15874.1 | − | 2506.35i | −0.534516 | − | 0.0843943i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25428.2 | −0.853555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15237.9 | 0.509900 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39729.6 | 1.32533 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41458.2i | 1.37870i | 0.724427 | + | 0.689352i | \(0.242105\pi\) | ||||
−0.724427 | + | 0.689352i | \(0.757895\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 55180.5i | − | 1.82936i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19762.1i | 0.653136i | 0.945174 | + | 0.326568i | \(0.105892\pi\) | ||||
−0.945174 | + | 0.326568i | \(0.894108\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2233.84 | − | 14148.1i | 0.0736007 | − | 0.466154i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8755.95i | 0.287605i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 59693.7 | 1.95473 | 0.977365 | − | 0.211561i | \(-0.0678547\pi\) | ||||
0.977365 | + | 0.211561i | \(0.0678547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5196.01i | 0.169627i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 935.347i | − | 0.0304417i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6590.24 | −0.213831 | −0.106916 | − | 0.994268i | \(-0.534097\pi\) | ||||
−0.106916 | + | 0.994268i | \(0.534097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 26959.0i | − | 0.872065i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 689.722 | − | 4368.39i | 0.0222433 | − | 0.140879i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44528.3i | 1.43167i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 8611.31i | − | 0.276031i | −0.990430 | − | 0.138016i | \(-0.955928\pi\) | ||
0.990430 | − | 0.138016i | \(-0.0440724\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13150.5i | 0.420261i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −63232.1 | −2.01467 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13666.7 | 0.434130 | 0.217065 | − | 0.976157i | \(-0.430352\pi\) | ||||
0.217065 | + | 0.976157i | \(0.430352\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3972.15 | −0.125799 |
(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 | 1344.4.p.d.223.32 | yes | 32 | |
4.3 | odd | 2 | inner | 1344.4.p.d.223.1 | yes | 32 | |
7.6 | odd | 2 | 1344.4.p.c.223.7 | yes | 32 | ||
8.3 | odd | 2 | 1344.4.p.c.223.8 | yes | 32 | ||
8.5 | even | 2 | 1344.4.p.c.223.1 | ✓ | 32 | ||
28.27 | even | 2 | 1344.4.p.c.223.2 | yes | 32 | ||
56.13 | odd | 2 | inner | 1344.4.p.d.223.2 | yes | 32 | |
56.27 | even | 2 | inner | 1344.4.p.d.223.31 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.c.223.1 | ✓ | 32 | 8.5 | even | 2 | ||
1344.4.p.c.223.2 | yes | 32 | 28.27 | even | 2 | ||
1344.4.p.c.223.7 | yes | 32 | 7.6 | odd | 2 | ||
1344.4.p.c.223.8 | yes | 32 | 8.3 | odd | 2 | ||
1344.4.p.d.223.1 | yes | 32 | 4.3 | odd | 2 | inner | |
1344.4.p.d.223.2 | yes | 32 | 56.13 | odd | 2 | inner | |
1344.4.p.d.223.31 | yes | 32 | 56.27 | even | 2 | inner | |
1344.4.p.d.223.32 | yes | 32 | 1.1 | even | 1 | trivial |