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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 58 x^{13} + 178264 x^{12} - 331354 x^{11} + 307862 x^{10} + \cdots + 22\!\cdots\!01 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.1 | ||
Root | \(-11.9644 - 11.9644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.a.223.9 |
$q$-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 | ||||||||
\(5\) | −16.7103 | −1.49462 | −0.747309 | − | 0.664477i | \(-0.768654\pi\) | ||||
−0.747309 | + | 0.664477i | \(0.768654\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.4816 | − | 8.44725i | −0.889924 | − | 0.456109i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.98444 | −0.246265 | −0.123132 | − | 0.992390i | \(-0.539294\pi\) | ||||
−0.123132 | + | 0.992390i | \(0.539294\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.28960 | −0.134186 | −0.0670931 | − | 0.997747i | \(-0.521372\pi\) | ||||
−0.0670931 | + | 0.997747i | \(0.521372\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 50.1310i | 0.862918i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 106.695i | 1.52220i | 0.648635 | + | 0.761099i | \(0.275340\pi\) | ||||
−0.648635 | + | 0.761099i | \(0.724660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.1841i | 0.304086i | 0.988374 | + | 0.152043i | \(0.0485852\pi\) | ||||
−0.988374 | + | 0.152043i | \(0.951415\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −25.3417 | + | 49.4449i | −0.263334 | + | 0.513798i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.5261i | 0.177020i | 0.996075 | + | 0.0885102i | \(0.0282106\pi\) | ||||
−0.996075 | + | 0.0885102i | \(0.971789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 154.235 | 1.23388 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 132.780i | 0.850231i | 0.905139 | + | 0.425116i | \(0.139767\pi\) | ||||
−0.905139 | + | 0.425116i | \(0.860233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −120.761 | −0.699653 | −0.349826 | − | 0.936815i | \(-0.613759\pi\) | ||||
−0.349826 | + | 0.936815i | \(0.613759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 26.9533i | 0.142181i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 275.413 | + | 141.156i | 1.33010 | + | 0.681708i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 72.1865i | − | 0.320740i | −0.987057 | − | 0.160370i | \(-0.948731\pi\) | ||
0.987057 | − | 0.160370i | \(-0.0512688\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.8688i | 0.0774724i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 410.552i | 1.56384i | 0.623379 | + | 0.781920i | \(0.285759\pi\) | ||||
−0.623379 | + | 0.781920i | \(0.714241\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.1310 | 0.227439 | 0.113720 | − | 0.993513i | \(-0.463723\pi\) | ||||
0.113720 | + | 0.993513i | \(0.463723\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 150.393 | 0.498206 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −281.172 | −0.872619 | −0.436310 | − | 0.899797i | \(-0.643715\pi\) | ||||
−0.436310 | + | 0.899797i | \(0.643715\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 200.288 | + | 278.449i | 0.583930 | + | 0.811804i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 320.085 | 0.878842 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 401.935i | − | 1.04170i | −0.853648 | − | 0.520850i | \(-0.825615\pi\) | ||
0.853648 | − | 0.520850i | \(-0.174385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 150.133 | 0.368071 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 75.5523 | 0.175564 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 584.836i | − | 1.29049i | −0.763974 | − | 0.645247i | \(-0.776755\pi\) | ||
0.763974 | − | 0.645247i | \(-0.223245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −736.702 | −1.54631 | −0.773156 | − | 0.634216i | \(-0.781323\pi\) | ||||
−0.773156 | + | 0.634216i | \(0.781323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 148.335 | + | 76.0252i | 0.296641 | + | 0.152036i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 105.101 | 0.200557 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −643.821 | −1.17396 | −0.586980 | − | 0.809602i | \(-0.699683\pi\) | ||||
−0.586980 | + | 0.809602i | \(0.699683\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 58.5782 | 0.102203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 186.578i | − | 0.311870i | −0.987767 | − | 0.155935i | \(-0.950161\pi\) | ||
0.987767 | − | 0.155935i | \(-0.0498390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 64.5717i | 0.103528i | 0.998659 | + | 0.0517640i | \(0.0164844\pi\) | ||||
−0.998659 | + | 0.0517640i | \(0.983516\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 462.705i | − | 0.712381i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 148.078 | + | 75.8938i | 0.219157 | + | 0.112323i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 50.5244i | − | 0.0719549i | −0.999353 | − | 0.0359775i | \(-0.988546\pi\) | ||
0.999353 | − | 0.0359775i | \(-0.0114545\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.9983i | − | 0.0238020i | −0.999929 | − | 0.0119010i | \(-0.996212\pi\) | ||
0.999929 | − | 0.0119010i | \(-0.00378830\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1782.91i | − | 2.27510i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 398.341 | 0.490881 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 378.330i | 0.450594i | 0.974290 | + | 0.225297i | \(0.0723353\pi\) | ||||
−0.974290 | + | 0.225297i | \(0.927665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 103.663 | + | 53.1298i | 0.119415 | + | 0.0612035i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 362.282i | 0.403945i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 420.834i | − | 0.454492i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 593.957i | − | 0.621724i | −0.950455 | − | 0.310862i | \(-0.899382\pi\) | ||
0.950455 | − | 0.310862i | \(-0.100618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 80.8599 | 0.0820882 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107.294 | 0.105704 | 0.0528522 | − | 0.998602i | \(-0.483169\pi\) | ||||
0.0528522 | + | 0.998602i | \(0.483169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1748.70 | 1.67286 | 0.836430 | − | 0.548073i | \(-0.184639\pi\) | ||||
0.836430 | + | 0.548073i | \(0.184639\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 423.469 | − | 826.240i | 0.393584 | − | 0.767931i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1818.36 | 1.64288 | 0.821439 | − | 0.570297i | \(-0.193172\pi\) | ||||
0.821439 | + | 0.570297i | \(0.193172\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1966.38i | − | 1.72794i | −0.503544 | − | 0.863969i | \(-0.667971\pi\) | ||
0.503544 | − | 0.863969i | \(-0.332029\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −216.559 | −0.185179 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1754.77 | −1.46084 | −0.730419 | − | 0.682999i | \(-0.760675\pi\) | ||||
−0.730419 | + | 0.682999i | \(0.760675\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 326.287i | − | 0.264578i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 56.6064 | 0.0447287 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 901.281 | − | 1758.51i | 0.694288 | − | 1.35464i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1250.28 | −0.939354 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1231.66 | 0.902883 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −488.527 | −0.349562 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1974.40i | 1.37952i | 0.724037 | + | 0.689761i | \(0.242284\pi\) | ||||
−0.724037 | + | 0.689761i | \(0.757716\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 192.393i | − | 0.131312i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1566.88i | − | 1.04503i | −0.852631 | − | 0.522513i | \(-0.824994\pi\) | ||
0.852631 | − | 0.522513i | \(-0.175006\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 212.736 | − | 415.075i | 0.138696 | − | 0.270613i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 451.179i | − | 0.287639i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1903.82 | 1.18726 | 0.593630 | − | 0.804738i | \(-0.297694\pi\) | ||||
0.593630 | + | 0.804738i | \(0.297694\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 935.422i | 0.570802i | 0.958408 | + | 0.285401i | \(0.0921267\pi\) | ||||
−0.958408 | + | 0.285401i | \(0.907873\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 843.515i | 0.503807i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 56.5085 | 0.0330453 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2218.80i | − | 1.27077i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 835.346 | − | 600.864i | 0.468695 | − | 0.337132i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 474.828i | − | 0.261070i | −0.991444 | − | 0.130535i | \(-0.958330\pi\) | ||
0.991444 | − | 0.130535i | \(-0.0416695\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1097.08i | − | 0.591254i | −0.955303 | − | 0.295627i | \(-0.904471\pi\) | ||
0.955303 | − | 0.295627i | \(-0.0955286\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 960.256i | − | 0.507400i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2017.95 | 1.04571 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2782.88 | −1.41464 | −0.707320 | − | 0.706894i | \(-0.750096\pi\) | ||||
−0.707320 | + | 0.706894i | \(0.750096\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1205.81 | −0.601425 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 164.942 | − | 321.822i | 0.0807405 | − | 0.157535i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 58.9320 | 0.0283185 | 0.0141592 | − | 0.999900i | \(-0.495493\pi\) | ||||
0.0141592 | + | 0.999900i | \(0.495493\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 450.399i | − | 0.212506i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1532.53 | 0.710123 | 0.355062 | − | 0.934843i | \(-0.384460\pi\) | ||||
0.355062 | + | 0.934843i | \(0.384460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2157.44 | −0.981994 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 226.657i | − | 0.101362i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1729.85 | −0.760219 | −0.380109 | − | 0.924942i | \(-0.624114\pi\) | ||||
−0.380109 | + | 0.924942i | \(0.624114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2542.04 | − | 1302.86i | −1.09806 | − | 0.562784i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1754.51 | −0.745067 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3137.12 | 1.30994 | 0.654971 | − | 0.755654i | \(-0.272681\pi\) | ||||
0.654971 | + | 0.755654i | \(0.272681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3422.20 | −1.40536 | −0.702681 | − | 0.711506i | \(-0.748014\pi\) | ||||
−0.702681 | + | 0.711506i | \(0.748014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2210.10i | 0.892763i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1206.26i | 0.479384i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 958.596i | − | 0.374864i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 228.076 | − | 445.004i | 0.0877781 | − | 0.171266i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2442.02i | 0.925123i | 0.886587 | + | 0.462562i | \(0.153070\pi\) | ||||
−0.886587 | + | 0.462562i | \(0.846930\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3281.21 | 1.22377 | 0.611883 | − | 0.790948i | \(-0.290412\pi\) | ||||
0.611883 | + | 0.790948i | \(0.290412\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 315.304i | − | 0.115792i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2405.89i | − | 0.870114i | −0.900403 | − | 0.435057i | \(-0.856728\pi\) | ||
0.900403 | − | 0.435057i | \(-0.143272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −949.634 | −0.338280 | −0.169140 | − | 0.985592i | \(-0.554099\pi\) | ||||
−0.169140 | + | 0.985592i | \(0.554099\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1931.46i | 0.677786i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1121.63 | − | 2188.44i | 0.387798 | − | 0.756641i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 6860.46i | − | 2.33734i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 175.735i | − | 0.0590068i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 226.265i | − | 0.0748855i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3535.42 | 1.15350 | 0.576750 | − | 0.816921i | \(-0.304321\pi\) | ||||
0.576750 | + | 0.816921i | \(0.304321\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −559.735 | −0.180058 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1071.65 | −0.339935 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1990.33 | + | 1020.09i | 0.622638 | + | 0.319118i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 193.715 | 0.0597719 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 671.069i | − | 0.204258i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6109.42 | −1.83460 | −0.917302 | − | 0.398192i | \(-0.869638\pi\) | ||||
−0.917302 | + | 0.398192i | \(0.869638\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1388.12 | −0.411293 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 560.043i | 0.163750i | 0.996643 | + | 0.0818752i | \(0.0260909\pi\) | ||||
−0.996643 | + | 0.0818752i | \(0.973909\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4491.68 | 1.29615 | 0.648075 | − | 0.761576i | \(-0.275574\pi\) | ||||
0.648075 | + | 0.761576i | \(0.275574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 227.681 | − | 444.234i | 0.0648499 | − | 0.126530i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2031.76 | 0.571266 | 0.285633 | − | 0.958339i | \(-0.407796\pi\) | ||||
0.285633 | + | 0.958339i | \(0.407796\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4698.47 | 1.30423 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −151.573 | −0.0415432 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6026.95i | 1.63117i | 0.578634 | + | 0.815587i | \(0.303586\pi\) | ||||
−0.578634 | + | 0.815587i | \(0.696414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2390.47i | − | 0.638938i | −0.947597 | − | 0.319469i | \(-0.896496\pi\) | ||
0.947597 | − | 0.319469i | \(-0.103504\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3346.88 | − | 4652.97i | −0.872752 | − | 1.21334i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 158.398i | − | 0.0408041i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −53.9949 | −0.0137421 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1488.61i | − | 0.374344i | −0.982327 | − | 0.187172i | \(-0.940068\pi\) | ||
0.982327 | − | 0.187172i | \(-0.0599322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 175.431i | − | 0.0435938i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5348.73 | −1.31353 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3311.30i | 0.803708i | 0.915704 | + | 0.401854i | \(0.131634\pi\) | ||||
−0.915704 | + | 0.401854i | \(0.868366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −609.777 | + | 1189.75i | −0.146292 | + | 0.285434i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1195.02i | − | 0.283410i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1881.16i | − | 0.441055i | −0.975381 | − | 0.220527i | \(-0.929222\pi\) | ||
0.975381 | − | 0.220527i | \(-0.0707778\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6716.47i | 1.55694i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1134.99 | 0.260151 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3965.12 | 0.898726 | 0.449363 | − | 0.893349i | \(-0.351651\pi\) | ||||
0.449363 | + | 0.893349i | \(0.351651\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −885.508 | −0.198490 | −0.0992450 | − | 0.995063i | \(-0.531643\pi\) | ||||
−0.0992450 | + | 0.995063i | \(0.531643\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 159.389 | − | 310.988i | 0.0353358 | − | 0.0689446i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1385.72 | −0.303861 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3749.11i | 0.813221i | 0.913602 | + | 0.406610i | \(0.133289\pi\) | ||||
−0.913602 | + | 0.406610i | \(0.866711\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1086.85 | 0.233218 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3695.89 | −0.784620 | −0.392310 | − | 0.919833i | \(-0.628324\pi\) | ||||
−0.392310 | + | 0.919833i | \(0.628324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8615.09i | − | 1.80959i | −0.425848 | − | 0.904795i | \(-0.640024\pi\) | ||
0.425848 | − | 0.904795i | \(-0.359976\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1262.50 | −0.262401 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3468.03 | − | 6766.56i | 0.713281 | − | 1.39170i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6470.86 | −1.31709 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1781.87 | −0.358953 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4271.95 | −0.851775 | −0.425888 | − | 0.904776i | \(-0.640038\pi\) | ||||
−0.425888 | + | 0.904776i | \(0.640038\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9772.80i | 1.92879i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 242.580i | − | 0.0473936i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 122.811i | − | 0.0237537i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1056.98 | − | 541.731i | −0.202404 | − | 0.103737i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 321.881i | − | 0.0610284i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12310.5 | 2.31114 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5029.94i | − | 0.935095i | −0.883968 | − | 0.467547i | \(-0.845138\pi\) | ||
0.883968 | − | 0.467547i | \(-0.154862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5246.10i | − | 0.965826i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4564.45 | 0.832238 | 0.416119 | − | 0.909310i | \(-0.363390\pi\) | ||||
0.416119 | + | 0.909310i | \(0.363390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7217.45i | − | 1.30337i | −0.758490 | − | 0.651684i | \(-0.774063\pi\) | ||
0.758490 | − | 0.651684i | \(-0.225937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2478.72 | − | 1270.41i | −0.443365 | − | 0.227236i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5136.65i | − | 0.910104i | −0.890465 | − | 0.455052i | \(-0.849621\pi\) | ||
0.890465 | − | 0.455052i | \(-0.150379\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1192.96i | − | 0.209382i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5455.09i | − | 0.948516i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2687.02 | −0.462879 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −970.076 | −0.165570 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5899.15 | −0.997626 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4634.17 | + | 2375.13i | 0.776565 | + | 0.398009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6895.65 | 1.14507 | 0.572537 | − | 0.819879i | \(-0.305959\pi\) | ||||
0.572537 | + | 0.819879i | \(0.305959\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 649.678i | 0.106913i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10758.5 | 1.75462 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9227.06 | −1.49148 | −0.745742 | − | 0.666235i | \(-0.767905\pi\) | ||||
−0.745742 | + | 0.666235i | \(0.767905\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5264.30i | 0.843415i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1084.97 | 0.172300 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −948.944 | − | 6281.17i | −0.149382 | − | 0.988779i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −978.862 | −0.152754 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1912.98 | 0.295948 | 0.147974 | − | 0.988991i | \(-0.452725\pi\) | ||||
0.147974 | + | 0.988991i | \(0.452725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 115.346 | 0.0176915 | 0.00884577 | − | 0.999961i | \(-0.497184\pi\) | ||||
0.00884577 | + | 0.999961i | \(0.497184\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 169.819i | − | 0.0258241i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5218.75i | 0.786872i | 0.919352 | + | 0.393436i | \(0.128714\pi\) | ||||
−0.919352 | + | 0.393436i | \(0.871286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3117.78i | 0.466126i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5275.53 | − | 2703.84i | −0.782103 | − | 0.400847i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9771.78i | − | 1.43659i | −0.695740 | − | 0.718294i | \(-0.744923\pi\) | ||
0.695740 | − | 0.718294i | \(-0.255077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6224.76 | 0.907532 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3750.84i | 0.542336i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1079.01i | − | 0.154735i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8207.66 | 1.16740 | 0.583701 | − | 0.811969i | \(-0.301604\pi\) | ||||
0.583701 | + | 0.811969i | \(0.301604\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 3694.97i | − | 0.521280i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3395.25 | + | 6624.55i | −0.475128 | + | 0.927033i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13506.3i | 1.87488i | 0.348152 | + | 0.937438i | \(0.386809\pi\) | ||||
−0.348152 | + | 0.937438i | \(0.613191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1465.58i | 0.201820i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 835.135i | − | 0.114089i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2631.57 | 0.356662 | 0.178331 | − | 0.983971i | \(-0.442930\pi\) | ||||
0.178331 | + | 0.983971i | \(0.442930\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5923.19 | 0.796467 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13787.0 | 1.83938 | 0.919692 | − | 0.392641i | \(-0.128439\pi\) | ||||
0.919692 | + | 0.392641i | \(0.128439\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2474.43 | − | 1268.21i | −0.327555 | − | 0.167880i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −577.179 | −0.0758131 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 4491.05i | − | 0.585360i | −0.956210 | − | 0.292680i | \(-0.905453\pi\) | ||
0.956210 | − | 0.292680i | \(-0.0945471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2083.34 | −0.269460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4700.63 | −0.603347 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 844.279i | 0.107545i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7456.08 | 0.942595 | 0.471297 | − | 0.881974i | \(-0.343786\pi\) | ||||
0.471297 | + | 0.881974i | \(0.343786\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1245.22 | − | 638.209i | −0.156239 | − | 0.0800762i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8374.63 | −1.04292 | −0.521458 | − | 0.853277i | \(-0.674612\pi\) | ||||
−0.521458 | + | 0.853277i | \(0.674612\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 759.535 | 0.0938837 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1353.54 | −0.166069 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 648.555i | 0.0789869i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6640.80i | − | 0.802852i | −0.915891 | − | 0.401426i | \(-0.868515\pi\) | ||
0.915891 | − | 0.401426i | \(-0.131485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5711.47i | − | 0.685464i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4940.25 | + | 9639.04i | −0.588605 | + | 1.14844i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 300.757i | 0.0355749i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2806.27 | 0.329553 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6063.13i | 0.706929i | 0.935448 | + | 0.353465i | \(0.114996\pi\) | ||||
−0.935448 | + | 0.353465i | \(0.885004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12873.6i | 1.49031i | 0.666890 | + | 0.745157i | \(0.267625\pi\) | ||||
−0.666890 | + | 0.745157i | \(0.732375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2530.55 | 0.290873 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16456.1i | 1.87821i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12142.0 | + | 6223.10i | 1.37610 | + | 0.705286i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 169.525i | − | 0.0190787i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8064.52i | − | 0.901286i | −0.892704 | − | 0.450643i | \(-0.851195\pi\) | ||
0.892704 | − | 0.450643i | \(-0.148805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7184.20i | − | 0.797345i | −0.917093 | − | 0.398673i | \(-0.869471\pi\) | ||
0.917093 | − | 0.398673i | \(-0.130529\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6656.41 | −0.733680 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −491.747 | −0.0538294 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1863.44 | 0.202590 | 0.101295 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101295 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1802.59 | − | 2506.04i | −0.194643 | − | 0.270601i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −576.702 | −0.0618509 | −0.0309254 | − | 0.999522i | \(-0.509845\pi\) | ||||
−0.0309254 | + | 0.999522i | \(0.509845\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6322.02i | − | 0.673466i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1424.48 | −0.150729 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8358.04 | 0.878487 | 0.439243 | − | 0.898368i | \(-0.355247\pi\) | ||||
0.439243 | + | 0.898368i | \(0.355247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3688.58i | − | 0.385118i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3291.25 | −0.341361 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1732.24 | − | 887.816i | −0.178480 | − | 0.0914757i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3756.51 | 0.384512 | 0.192256 | − | 0.981345i | \(-0.438420\pi\) | ||||
0.192256 | + | 0.981345i | \(0.438420\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2880.77 | −0.292947 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 866.025 | 0.0874942 | 0.0437471 | − | 0.999043i | \(-0.486070\pi\) | ||||
0.0437471 | + | 0.999043i | \(0.486070\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3348.04i | − | 0.336062i | −0.985782 | − | 0.168031i | \(-0.946259\pi\) | ||
0.985782 | − | 0.168031i | \(-0.0537408\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 6053.85i | − | 0.603743i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12122.4i | − | 1.20119i | −0.799553 | − | 0.600596i | \(-0.794930\pi\) | ||
0.799553 | − | 0.600596i | \(-0.205070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10611.2 | + | 5438.52i | 1.04474 | + | 0.535453i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8348.65i | 0.816742i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −576.181 | −0.0560102 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3884.27i | 0.375205i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3617.42i | 0.347233i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8827.69 | 0.842061 | 0.421031 | − | 0.907046i | \(-0.361668\pi\) | ||||
0.421031 | + | 0.907046i | \(0.361668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 454.024i | 0.0430389i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −965.465 | − | 494.825i | −0.0909527 | − | 0.0466156i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9925.22i | 0.929240i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12562.9i | 1.16895i | 0.811412 | + | 0.584475i | \(0.198699\pi\) | ||||
−0.811412 | + | 0.584475i | \(0.801301\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 176.796i | − | 0.0163497i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3335.07 | 0.306536 | 0.153268 | − | 0.988185i | \(-0.451020\pi\) | ||||
0.153268 | + | 0.988185i | \(0.451020\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14167.0 | −1.29422 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1351.20 | −0.122690 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1576.07 | + | 3075.11i | −0.142247 | + | 0.277541i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17947.1 | −1.61007 | −0.805033 | − | 0.593230i | \(-0.797852\pi\) | ||||
−0.805033 | + | 0.593230i | \(0.797852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 4597.58i | − | 0.409990i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3789.15 | −0.335885 | −0.167942 | − | 0.985797i | \(-0.553712\pi\) | ||||
−0.167942 | + | 0.985797i | \(0.553712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1792.92 | −0.157987 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6472.32i | 0.566955i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10041.2 | 0.874399 | 0.437199 | − | 0.899365i | \(-0.355970\pi\) | ||||
0.437199 | + | 0.899365i | \(0.355970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 545.453 | − | 1064.25i | 0.0472200 | − | 0.0921321i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −679.971 | −0.0585213 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29221.4 | −2.50029 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2526.17 | 0.214895 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5189.54i | 0.438912i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16041.1i | 1.34890i | 0.738322 | + | 0.674448i | \(0.235618\pi\) | ||||
−0.738322 | + | 0.674448i | \(0.764382\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3627.15i | − | 0.303259i | −0.988437 | − | 0.151629i | \(-0.951548\pi\) | ||
0.988437 | − | 0.151629i | \(-0.0484520\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3908.59 | + | 7626.13i | −0.324923 | + | 0.633965i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12884.6i | − | 1.06501i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11785.7 | 0.968664 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5263.52i | 0.430165i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2582.21i | − | 0.209846i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30385.5 | −2.45547 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9411.37i | − | 0.756295i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1799.47 | − | 2501.71i | −0.143801 | − | 0.199919i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 181.348i | 0.0144118i | 0.999974 | + | 0.00720588i | \(0.00229372\pi\) | ||||
−0.999974 | + | 0.00720588i | \(0.997706\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10266.6i | 0.811386i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 32858.9i | 2.58261i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18922.2 | −1.47908 | −0.739539 | − | 0.673114i | \(-0.764956\pi\) | ||||
−0.739539 | + | 0.673114i | \(0.764956\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6630.31 | 0.515437 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3343.96 | −0.258543 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −426.792 | + | 832.724i | −0.0328193 | + | 0.0640344i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3618.78 | 0.276772 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11700.6i | 0.890075i | 0.895512 | + | 0.445037i | \(0.146810\pi\) | ||||
−0.895512 | + | 0.445037i | \(0.853190\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −403.358 | −0.0305192 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2875.79 | −0.216428 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22989.7i | 1.72096i | 0.509485 | + | 0.860479i | \(0.329836\pi\) | ||||
−0.509485 | + | 0.860479i | \(0.670164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29322.7 | 2.18339 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1335.01 | − | 684.227i | −0.0988805 | − | 0.0506787i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −837.958 | −0.0617382 | −0.0308691 | − | 0.999523i | \(-0.509827\pi\) | ||||
−0.0308691 | + | 0.999523i | \(0.509827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16018.3 | −1.17399 | −0.586993 | − | 0.809592i | \(-0.699689\pi\) | ||||
−0.586993 | + | 0.809592i | \(0.699689\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7326.07 | 0.534120 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3011.61i | 0.218422i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1914.68i | − | 0.138144i | −0.997612 | − | 0.0690722i | \(-0.977996\pi\) | ||
0.997612 | − | 0.0690722i | \(-0.0220039\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 9843.64i | − | 0.706542i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −152.036 | + | 296.641i | −0.0108563 | + | 0.0211820i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3611.16i | 0.256534i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −945.911 | −0.0668523 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17100.9i | 1.20243i | 0.799086 | + | 0.601217i | \(0.205317\pi\) | ||||
−0.799086 | + | 0.601217i | \(0.794683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3041.25i | − | 0.212754i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7217.66 | −0.502360 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5989.45i | 0.414768i | 0.978260 | + | 0.207384i | \(0.0664949\pi\) | ||||
−0.978260 | + | 0.207384i | \(0.933505\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15060.7 | + | 29385.3i | −1.03769 | + | 2.02467i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2848.90i | 0.195306i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6751.78i | 0.460551i | 0.973125 | + | 0.230276i | \(0.0739628\pi\) | ||||
−0.973125 | + | 0.230276i | \(0.926037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24461.5i | − | 1.66024i | −0.557582 | − | 0.830122i | \(-0.688271\pi\) | ||
0.557582 | − | 0.830122i | \(-0.311729\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5794.39 | 0.391320 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20892.6 | 1.40397 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22238.9 | −1.48707 | −0.743533 | − | 0.668699i | \(-0.766852\pi\) | ||||
−0.743533 | + | 0.668699i | \(0.766852\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6565.31 | − | 3364.89i | −0.436847 | − | 0.223895i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1768.46 | 0.117093 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10848.5i | 0.714792i | 0.933953 | + | 0.357396i | \(0.116335\pi\) | ||||
−0.933953 | + | 0.357396i | \(0.883665\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20581.4 | −1.34946 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19769.2 | 1.28991 | 0.644957 | − | 0.764219i | \(-0.276875\pi\) | ||||
0.644957 | + | 0.764219i | \(0.276875\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26002.5i | − | 1.68842i | −0.536016 | − | 0.844208i | \(-0.680071\pi\) | ||
0.536016 | − | 0.844208i | \(-0.319929\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −527.204 | −0.0340676 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3195.85 | − | 6235.49i | 0.205520 | − | 0.400995i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11115.9 | −0.711419 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −678.795 | −0.0432352 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7701.95 | 0.488230 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 420.513i | − | 0.0265299i | −0.999912 | − | 0.0132650i | \(-0.995778\pi\) | ||
0.999912 | − | 0.0132650i | \(-0.00422249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10606.3i | − | 0.665974i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 32992.8i | − | 2.06186i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1259.73 | − | 1751.33i | −0.0783553 | − | 0.108933i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1679.20i | 0.103957i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14251.4 | 0.878154 | 0.439077 | − | 0.898449i | \(-0.355306\pi\) | ||||
0.439077 | + | 0.898449i | \(0.355306\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22847.4i | 1.40126i | 0.713523 | + | 0.700632i | \(0.247098\pi\) | ||||
−0.713523 | + | 0.700632i | \(0.752902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3214.95i | 0.196261i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17057.9 | 1.03650 | 0.518248 | − | 0.855230i | \(-0.326584\pi\) | ||||
0.518248 | + | 0.855230i | \(0.326584\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5254.42i | 0.317803i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3060.28 | − | 5970.99i | 0.184243 | − | 0.359480i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23995.8i | 1.43802i | 0.694999 | + | 0.719010i | \(0.255405\pi\) | ||||
−0.694999 | + | 0.719010i | \(0.744595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26183.0i | 1.56192i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 581.145i | − | 0.0345093i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29296.8 | −1.73177 | −0.865887 | − | 0.500239i | \(-0.833246\pi\) | ||||
−0.865887 | + | 0.500239i | \(0.833246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20769.2 | −1.22213 | −0.611066 | − | 0.791580i | \(-0.709259\pi\) | ||||
−0.611066 | + | 0.791580i | \(0.709259\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2013.21 | −0.117928 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3554.89 | + | 6936.04i | −0.207298 | + | 0.404463i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2592.68 | −0.150508 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18328.2i | 1.05921i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6618.85 | 0.380802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15326.2 | 0.877835 | 0.438918 | − | 0.898527i | \(-0.355362\pi\) | ||||
0.438918 | + | 0.898527i | \(0.355362\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4164.35i | 0.237460i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3440.17 | −0.195298 | −0.0976488 | − | 0.995221i | \(-0.531132\pi\) | ||||
−0.0976488 | + | 0.995221i | \(0.531132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5017.31 | + | 9789.38i | −0.283574 | + | 0.553287i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1680.13 | 0.0945413 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31000.6 | 1.73676 | 0.868378 | − | 0.495902i | \(-0.165163\pi\) | ||||
0.868378 | + | 0.495902i | \(0.165163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31813.5 | −1.77450 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 13475.0i | − | 0.748333i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2528.01i | 0.139782i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19379.3i | 1.06689i | 0.845834 | + | 0.533447i | \(0.179103\pi\) | ||||
−0.845834 | + | 0.533447i | \(0.820897\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1332.70 | − | 683.044i | −0.0730522 | − | 0.0374411i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 15631.2i | − | 0.853130i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43803.9 | −2.38047 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 6095.27i | − | 0.329820i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35585.2i | 1.91731i | 0.284572 | + | 0.958655i | \(0.408148\pi\) | ||||
−0.284572 | + | 0.958655i | \(0.591852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1817.95 | 0.0975325 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 14095.4i | − | 0.752999i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1768.38 | − | 906.338i | −0.0940688 | − | 0.0482126i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 12432.6i | − | 0.658558i | −0.944233 | − | 0.329279i | \(-0.893194\pi\) | ||
0.944233 | − | 0.329279i | \(-0.106806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 454.719i | 0.0239850i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2357.98i | − | 0.123853i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −944.275 | −0.0493900 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18080.8 | 0.941759 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25374.8 | 1.31616 | 0.658082 | − | 0.752946i | \(-0.271368\pi\) | ||||
0.658082 | + | 0.752946i | \(0.271368\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28821.4 | − | 14771.7i | −1.48872 | − | 0.763006i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7171.42 | −0.368891 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20479.4i | 1.04908i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28559.3 | 1.45696 | 0.728478 | − | 0.685069i | \(-0.240228\pi\) | ||||
0.728478 | + | 0.685069i | \(0.240228\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6842.47i | 0.346208i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31475.5 | 1.58605 | 0.793025 | − | 0.609189i | \(-0.208505\pi\) | ||||
0.793025 | + | 0.609189i | \(0.208505\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13958.9 | + | 10040.6i | −0.700520 | + | 0.503883i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5784.37 | 0.289105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17164.7 | −0.854416 | −0.427208 | − | 0.904153i | \(-0.640503\pi\) | ||||
−0.427208 | + | 0.904153i | \(0.640503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −475.193 | −0.0235582 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 29385.8i | − | 1.45095i | −0.688247 | − | 0.725477i | \(-0.741619\pi\) | ||
0.688247 | − | 0.725477i | \(-0.258381\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7934.54i | 0.390200i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 161.985i | 0.00793401i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29969.6 | − | 15360.2i | −1.46204 | − | 0.749330i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2143.28i | − | 0.104140i | −0.998643 | − | 0.0520701i | \(-0.983418\pi\) | ||
0.998643 | − | 0.0520701i | \(-0.0165819\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4465.83 | −0.216128 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18332.6i | 0.883698i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5880.09i | − | 0.282319i | −0.989987 | − | 0.141160i | \(-0.954917\pi\) | ||
0.989987 | − | 0.141160i | \(-0.0450831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −526.292 | −0.0251689 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 36013.8i | − | 1.71551i | −0.514062 | − | 0.857753i | \(-0.671860\pi\) | ||
0.514062 | − | 0.857753i | \(-0.328140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16610.5 | + | 32409.2i | −0.788128 | + | 1.53773i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16046.2i | 0.758368i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3678.38i | 0.173166i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16133.5i | − | 0.756555i | −0.925692 | − | 0.378277i | \(-0.876517\pi\) | ||
0.925692 | − | 0.378277i | \(-0.123483\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9933.89 | 0.464021 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33017.3 | 1.53629 | 0.768143 | − | 0.640278i | \(-0.221181\pi\) | ||||
0.768143 | + | 0.640278i | \(0.221181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18625.5 | −0.863288 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3569.25 | + | 1829.33i | 0.164796 | + | 0.0844619i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10339.4 | −0.475541 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1676.30i | 0.0768025i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3585.07 | −0.163627 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46502.9 | 2.11434 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28920.2i | − | 1.30990i | −0.755672 | − | 0.654951i | \(-0.772689\pi\) | ||
0.755672 | − | 0.654951i | \(-0.227311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5643.48 | −0.254643 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28921.4 | + | 14823.0i | 1.30003 | + | 0.666301i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4633.56 | 0.207494 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20149.4 | 0.898901 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12634.5 | −0.561529 | −0.280764 | − | 0.959777i | \(-0.590588\pi\) | ||||
−0.280764 | + | 0.959777i | \(0.590588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 29999.7i | − | 1.32830i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3404.97i | − | 0.150198i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 580.140i | − | 0.0254953i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2756.23 | + | 5377.74i | −0.120676 | + | 0.235454i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 11895.3i | − | 0.518880i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41369.9 | −1.79788 | −0.898941 | − | 0.438070i | \(-0.855662\pi\) | ||||
−0.898941 | + | 0.438070i | \(0.855662\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 32.6724i | − | 0.00141465i | −1.00000 | 0.000707326i | \(-0.999775\pi\) | |||
1.00000 | 0.000707326i | \(-0.000225149\pi\) | ||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2656.52i | 0.114598i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −984.773 | −0.0423253 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1615.08i | 0.0691610i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −932.965 | − | 478.168i | −0.0398052 | − | 0.0204012i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 33836.1i | − | 1.43835i | −0.694828 | − | 0.719176i | \(-0.744519\pi\) | ||
0.694828 | − | 0.719176i | \(-0.255481\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9891.61i | − | 0.418955i | −0.977813 | − | 0.209477i | \(-0.932824\pi\) | ||
0.977813 | − | 0.209477i | \(-0.0671763\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4157.15i | 0.175434i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32492.4 | 1.36623 | 0.683114 | − | 0.730311i | \(-0.260625\pi\) | ||||
0.683114 | + | 0.730311i | \(0.260625\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5778.92 | −0.242111 | −0.121056 | − | 0.992646i | \(-0.538628\pi\) | ||||
−0.121056 | + | 0.992646i | \(0.538628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11247.3 | 0.469513 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29709.1 | + | 21369.8i | −1.23573 | + | 0.888857i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25609.0 | −1.06136 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3260.54i | − | 0.134648i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26855.3 | 1.10506 | 0.552532 | − | 0.833492i | \(-0.313662\pi\) | ||||
0.552532 | + | 0.833492i | \(0.313662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6758.35 | 0.277107 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11087.7i | 0.453001i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36051.5 | 1.46771 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20606.6 | + | 10561.4i | 0.835954 | + | 0.428447i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25845.3 | −1.04477 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1409.52 | 0.0567776 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32717.6 | −1.31328 | −0.656641 | − | 0.754203i | \(-0.728023\pi\) | ||||
−0.656641 | + | 0.754203i | \(0.728023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3787.51i | 0.151497i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 16998.3i | − | 0.677538i | −0.940870 | − | 0.338769i | \(-0.889989\pi\) | ||
0.940870 | − | 0.338769i | \(-0.110011\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7023.27i | − | 0.278965i | −0.990225 | − | 0.139482i | \(-0.955456\pi\) | ||
0.990225 | − | 0.139482i | \(-0.0445439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20299.7 | − | 10404.1i | −0.803498 | − | 0.411813i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21301.7i | 0.840231i | 0.907471 | + | 0.420115i | \(0.138010\pi\) | ||||
−0.907471 | + | 0.420115i | \(0.861990\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28906.3 | 1.13624 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19412.6i | 0.760422i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 453.933i | 0.0177199i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4049.38 | 0.157529 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5345.62i | 0.207241i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8051.73 | + | 4126.71i | 0.311083 | + | 0.159438i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 6855.04i | − | 0.263943i | −0.991253 | − | 0.131972i | \(-0.957869\pi\) | ||
0.991253 | − | 0.131972i | \(-0.0421308\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12815.9i | 0.491773i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12391.1i | 0.473855i | 0.971527 | + | 0.236927i | \(0.0761404\pi\) | ||||
−0.971527 | + | 0.236927i | \(0.923860\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7078.73 | −0.269783 | −0.134891 | − | 0.990860i | \(-0.543069\pi\) | ||||
−0.134891 | + | 0.990860i | \(0.543069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29318.4 | 1.11359 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47526.1 | 1.79906 | 0.899532 | − | 0.436854i | \(-0.143907\pi\) | ||||
0.899532 | + | 0.436854i | \(0.143907\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16678.2 | − | 32541.3i | 0.629212 | − | 1.22767i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −727.739 | −0.0273627 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7081.06i | − | 0.265351i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −52422.4 | −1.95786 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −368.433 | −0.0137142 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 16034.6i | − | 0.594867i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42884.6 | 1.58567 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1625.19 | + | 3170.95i | −0.0598926 | + | 0.116858i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 57186.1 | 2.10048 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31328.6 | 1.14691 | 0.573457 | − | 0.819236i | \(-0.305602\pi\) | ||||
0.573457 | + | 0.819236i | \(0.305602\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −965.644 | −0.0352348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 21649.9i | − | 0.787367i | −0.919246 | − | 0.393684i | \(-0.871201\pi\) | ||
0.919246 | − | 0.393684i | \(-0.128799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 161.705i | 0.00586160i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 36931.6i | − | 1.33434i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13235.8 | + | 25824.7i | −0.476646 | + | 0.929995i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 39980.3i | − | 1.43507i | −0.696522 | − | 0.717535i | \(-0.745270\pi\) | ||
0.696522 | − | 0.717535i | \(-0.254730\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15089.8 | −0.539877 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1173.50i | 0.0418486i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 11133.7i | − | 0.395755i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15738.3 | −0.557620 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50671.5i | 1.78954i | 0.446531 | + | 0.894768i | \(0.352659\pi\) | ||||
−0.446531 | + | 0.894768i | \(0.647341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7012.48 | + | 5044.07i | −0.246858 | + | 0.177565i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 13693.3i | − | 0.480493i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16018.5i | 0.560277i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25149.9i | 0.876853i | 0.898767 | + | 0.438427i | \(0.144464\pi\) | ||||
−0.898767 | + | 0.438427i | \(0.855536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21652.4 | −0.752500 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3742.64 | 0.129656 | 0.0648282 | − | 0.997896i | \(-0.479350\pi\) | ||||
0.0648282 | + | 0.997896i | \(0.479350\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8016.47 | −0.276832 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3811.22 | + | 7436.16i | −0.131195 | + | 0.255977i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37380.8 | −1.28270 | −0.641348 | − | 0.767250i | \(-0.721625\pi\) | ||||
−0.641348 | + | 0.767250i | \(0.721625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 406.130i | − | 0.0138920i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15409.9 | −0.525449 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2567.62 | 0.0872753 | 0.0436376 | − | 0.999047i | \(-0.486105\pi\) | ||||
0.0436376 | + | 0.999047i | \(0.486105\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 40807.0i | − | 1.38270i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3578.87 | −0.120887 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31378.1 | − | 16082.1i | −1.05657 | − | 0.541519i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15207.9 | −0.510486 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16365.3 | −0.547626 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54830.2 | −1.82906 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 20902.7i | − | 0.695126i | −0.937657 | − | 0.347563i | \(-0.887009\pi\) | ||
0.937657 | − | 0.347563i | \(-0.112991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8061.06i | 0.267243i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 52144.6i | − | 1.72338i | −0.507436 | − | 0.861689i | \(-0.669407\pi\) | ||
0.507436 | − | 0.861689i | \(-0.330593\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7901.74 | − | 15417.3i | 0.260348 | − | 0.507970i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2910.23i | 0.0955917i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25818.9 | 0.845466 | 0.422733 | − | 0.906254i | \(-0.361071\pi\) | ||||
0.422733 | + | 0.906254i | \(0.361071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3399.08i | − | 0.110965i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17697.4i | 0.575980i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27741.0 | 0.900104 | 0.450052 | − | 0.893002i | \(-0.351405\pi\) | ||||
0.450052 | + | 0.893002i | \(0.351405\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40203.2i | 1.30049i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7125.38 | − | 13902.5i | 0.229791 | − | 0.448350i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1252.23i | 0.0402614i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39220.7i | 1.25720i | 0.777729 | + | 0.628600i | \(0.216372\pi\) | ||||
−0.777729 | + | 0.628600i | \(0.783628\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 20687.0i | − | 0.661108i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15868.7 | 0.505599 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25324.2 | −0.804440 | −0.402220 | − | 0.915543i | \(-0.631761\pi\) | ||||
−0.402220 | + | 0.915543i | \(0.631761\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1949.04 | 0.0617265 |
(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.a.223.1 | ✓ | 16 | |
4.3 | odd | 2 | inner | 1344.4.p.a.223.10 | yes | 16 | |
7.6 | odd | 2 | 1344.4.p.b.223.16 | yes | 16 | ||
8.3 | odd | 2 | 1344.4.p.b.223.8 | yes | 16 | ||
8.5 | even | 2 | 1344.4.p.b.223.15 | yes | 16 | ||
28.27 | even | 2 | 1344.4.p.b.223.7 | yes | 16 | ||
56.13 | odd | 2 | inner | 1344.4.p.a.223.2 | yes | 16 | |
56.27 | even | 2 | inner | 1344.4.p.a.223.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.a.223.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1344.4.p.a.223.2 | yes | 16 | 56.13 | odd | 2 | inner | |
1344.4.p.a.223.9 | yes | 16 | 56.27 | even | 2 | inner | |
1344.4.p.a.223.10 | yes | 16 | 4.3 | odd | 2 | inner | |
1344.4.p.b.223.7 | yes | 16 | 28.27 | even | 2 | ||
1344.4.p.b.223.8 | yes | 16 | 8.3 | odd | 2 | ||
1344.4.p.b.223.15 | yes | 16 | 8.5 | even | 2 | ||
1344.4.p.b.223.16 | yes | 16 | 7.6 | odd | 2 |