Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(343,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.343");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.g (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.7 | ||
Character | \(\chi\) | \(=\) | 684.343 |
Dual form | 684.3.g.d.343.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.55174 | − | 1.26178i | −0.775871 | − | 0.630892i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.815807 | + | 3.91592i | 0.203952 | + | 0.978981i | ||||
\(5\) | 2.61138 | 0.522275 | 0.261138 | − | 0.965302i | \(-0.415902\pi\) | ||||
0.261138 | + | 0.965302i | \(0.415902\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 10.9942i | − | 1.57060i | −0.619118 | − | 0.785298i | \(-0.712510\pi\) | ||
0.619118 | − | 0.785298i | \(-0.287490\pi\) | |||||||
\(8\) | 3.67512 | − | 7.10587i | 0.459391 | − | 0.888234i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.05218 | − | 3.29499i | −0.405218 | − | 0.329499i | ||||
\(11\) | − | 21.8516i | − | 1.98651i | −0.115944 | − | 0.993256i | \(-0.536989\pi\) | ||
0.115944 | − | 0.993256i | \(-0.463011\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.95476 | −0.381135 | −0.190568 | − | 0.981674i | \(-0.561033\pi\) | ||||
−0.190568 | + | 0.981674i | \(0.561033\pi\) | |||||||
\(14\) | −13.8723 | + | 17.0601i | −0.990876 | + | 1.21858i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.6689 | + | 6.38927i | −0.916807 | + | 0.399330i | ||||
\(17\) | 20.1023 | 1.18249 | 0.591243 | − | 0.806493i | \(-0.298637\pi\) | ||||
0.591243 | + | 0.806493i | \(0.298637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890i | 0.229416i | ||||||||
\(20\) | 2.13038 | + | 10.2260i | 0.106519 | + | 0.511298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −27.5720 | + | 33.9081i | −1.25327 | + | 1.54128i | ||||
\(23\) | 9.15603i | 0.398088i | 0.979991 | + | 0.199044i | \(0.0637837\pi\) | ||||
−0.979991 | + | 0.199044i | \(0.936216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.1807 | −0.727228 | ||||||||
\(26\) | 7.68851 | + | 6.25183i | 0.295712 | + | 0.240455i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 43.0523 | − | 8.96912i | 1.53758 | − | 0.320326i | ||||
\(29\) | 1.24974 | 0.0430945 | 0.0215473 | − | 0.999768i | \(-0.493141\pi\) | ||||
0.0215473 | + | 0.999768i | \(0.493141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.9294i | 1.28804i | 0.765007 | + | 0.644022i | \(0.222735\pi\) | ||||
−0.765007 | + | 0.644022i | \(0.777265\pi\) | |||||||
\(32\) | 30.8243 | + | 8.59449i | 0.963258 | + | 0.268578i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −31.1935 | − | 25.3647i | −0.917457 | − | 0.746021i | ||||
\(35\) | − | 28.7099i | − | 0.820284i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −56.6170 | −1.53019 | −0.765094 | − | 0.643918i | \(-0.777308\pi\) | ||||
−0.765094 | + | 0.643918i | \(0.777308\pi\) | |||||||
\(38\) | 5.49999 | − | 6.76389i | 0.144736 | − | 0.177997i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.59714 | − | 18.5561i | 0.239928 | − | 0.463903i | ||||
\(41\) | 31.6717 | 0.772480 | 0.386240 | − | 0.922398i | \(-0.373774\pi\) | ||||
0.386240 | + | 0.922398i | \(0.373774\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 23.3377i | − | 0.542736i | −0.962476 | − | 0.271368i | \(-0.912524\pi\) | ||
0.962476 | − | 0.271368i | \(-0.0874761\pi\) | |||||||
\(44\) | 85.5693 | − | 17.8267i | 1.94476 | − | 0.405152i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.5529 | − | 14.2078i | 0.251151 | − | 0.308865i | ||||
\(47\) | − | 64.7865i | − | 1.37844i | −0.724554 | − | 0.689218i | \(-0.757954\pi\) | ||
0.724554 | − | 0.689218i | \(-0.242046\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −71.8718 | −1.46677 | ||||||||
\(50\) | 28.2118 | + | 22.9401i | 0.564236 | + | 0.458802i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.04213 | − | 19.4025i | −0.0777332 | − | 0.373124i | ||||
\(53\) | −80.8467 | −1.52541 | −0.762705 | − | 0.646747i | \(-0.776129\pi\) | ||||
−0.762705 | + | 0.646747i | \(0.776129\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 57.0628i | − | 1.03751i | ||||||
\(56\) | −78.1232 | − | 40.4050i | −1.39506 | − | 0.721517i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.93928 | − | 1.57690i | −0.0334358 | − | 0.0271880i | ||||
\(59\) | 12.2009i | 0.206795i | 0.994640 | + | 0.103398i | \(0.0329714\pi\) | ||||
−0.994640 | + | 0.103398i | \(0.967029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 64.3769 | 1.05536 | 0.527679 | − | 0.849444i | \(-0.323062\pi\) | ||||
0.527679 | + | 0.849444i | \(0.323062\pi\) | |||||||
\(62\) | 50.3822 | − | 61.9601i | 0.812616 | − | 0.999356i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −36.9869 | − | 52.2300i | −0.577921 | − | 0.816093i | ||||
\(65\) | −12.9387 | −0.199058 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 82.9847i | − | 1.23858i | −0.785163 | − | 0.619289i | \(-0.787421\pi\) | ||
0.785163 | − | 0.619289i | \(-0.212579\pi\) | |||||||
\(68\) | 16.3996 | + | 78.7189i | 0.241170 | + | 1.15763i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −36.2257 | + | 44.5504i | −0.517510 | + | 0.636434i | ||||
\(71\) | 16.4217i | 0.231291i | 0.993291 | + | 0.115646i | \(0.0368937\pi\) | ||||
−0.993291 | + | 0.115646i | \(0.963106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −63.6386 | −0.871761 | −0.435881 | − | 0.900004i | \(-0.643563\pi\) | ||||
−0.435881 | + | 0.900004i | \(0.643563\pi\) | |||||||
\(74\) | 87.8549 | + | 71.4383i | 1.18723 | + | 0.965383i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.0691 | + | 3.55602i | −0.224594 | + | 0.0467897i | ||||
\(77\) | −240.241 | −3.12001 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 19.2738i | − | 0.243972i | −0.992532 | − | 0.121986i | \(-0.961074\pi\) | ||
0.992532 | − | 0.121986i | \(-0.0389264\pi\) | |||||||
\(80\) | −38.3061 | + | 16.6848i | −0.478826 | + | 0.208560i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −49.1463 | − | 39.9628i | −0.599345 | − | 0.487351i | ||||
\(83\) | 29.3102i | 0.353135i | 0.984289 | + | 0.176567i | \(0.0564993\pi\) | ||||
−0.984289 | + | 0.176567i | \(0.943501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 52.4946 | 0.617583 | ||||||||
\(86\) | −29.4471 | + | 36.2140i | −0.342408 | + | 0.421093i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −155.275 | − | 80.3075i | −1.76449 | − | 0.912585i | ||||
\(89\) | 21.4346 | 0.240838 | 0.120419 | − | 0.992723i | \(-0.461576\pi\) | ||||
0.120419 | + | 0.992723i | \(0.461576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 54.4735i | 0.598610i | ||||||||
\(92\) | −35.8543 | + | 7.46955i | −0.389721 | + | 0.0811908i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −81.7465 | + | 100.532i | −0.869644 | + | 1.06949i | ||||
\(95\) | 11.3827i | 0.119818i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 74.7316 | 0.770429 | 0.385214 | − | 0.922827i | \(-0.374128\pi\) | ||||
0.385214 | + | 0.922827i | \(0.374128\pi\) | |||||||
\(98\) | 111.527 | + | 90.6867i | 1.13803 | + | 0.925374i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.8319 | − | 71.1943i | −0.148319 | − | 0.711943i | ||||
\(101\) | 81.5165 | 0.807094 | 0.403547 | − | 0.914959i | \(-0.367777\pi\) | ||||
0.403547 | + | 0.914959i | \(0.367777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 168.311i | 1.63409i | 0.576574 | + | 0.817045i | \(0.304389\pi\) | ||||
−0.576574 | + | 0.817045i | \(0.695611\pi\) | |||||||
\(104\) | −18.2094 | + | 35.2079i | −0.175090 | + | 0.338538i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 125.453 | + | 102.011i | 1.18352 | + | 0.962368i | ||||
\(107\) | − | 133.057i | − | 1.24352i | −0.783207 | − | 0.621761i | \(-0.786418\pi\) | ||
0.783207 | − | 0.621761i | \(-0.213582\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 47.9550 | 0.439954 | 0.219977 | − | 0.975505i | \(-0.429402\pi\) | ||||
0.219977 | + | 0.975505i | \(0.429402\pi\) | |||||||
\(110\) | −72.0009 | + | 88.5468i | −0.654554 | + | 0.804971i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 70.2448 | + | 161.273i | 0.627186 | + | 1.43993i | ||||
\(113\) | −140.249 | −1.24114 | −0.620572 | − | 0.784150i | \(-0.713099\pi\) | ||||
−0.620572 | + | 0.784150i | \(0.713099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.9098i | 0.207912i | ||||||||
\(116\) | 1.01955 | + | 4.89389i | 0.00878920 | + | 0.0421887i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.3949 | − | 18.9327i | 0.130465 | − | 0.160447i | ||||
\(119\) | − | 221.008i | − | 1.85721i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −356.494 | −2.94623 | ||||||||
\(122\) | −99.8963 | − | 81.2297i | −0.818822 | − | 0.665817i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −156.360 | + | 32.5746i | −1.26097 | + | 0.262699i | ||||
\(125\) | −112.761 | −0.902089 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.3426i | − | 0.0971857i | −0.998819 | − | 0.0485929i | \(-0.984526\pi\) | ||
0.998819 | − | 0.0485929i | \(-0.0154737\pi\) | |||||||
\(128\) | −8.50872 | + | 127.717i | −0.0664744 | + | 0.997788i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 20.0776 | + | 16.3259i | 0.154443 | + | 0.125584i | ||||
\(131\) | − | 188.792i | − | 1.44116i | −0.693372 | − | 0.720580i | \(-0.743876\pi\) | ||
0.693372 | − | 0.720580i | \(-0.256124\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47.9225 | 0.360319 | ||||||||
\(134\) | −104.709 | + | 128.771i | −0.781408 | + | 0.960977i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 73.8783 | − | 142.844i | 0.543223 | − | 1.05032i | ||||
\(137\) | 3.88636 | 0.0283676 | 0.0141838 | − | 0.999899i | \(-0.495485\pi\) | ||||
0.0141838 | + | 0.999899i | \(0.495485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 202.870i | 1.45949i | 0.683717 | + | 0.729747i | \(0.260362\pi\) | ||||
−0.683717 | + | 0.729747i | \(0.739638\pi\) | |||||||
\(140\) | 112.426 | − | 23.4218i | 0.803042 | − | 0.167298i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 20.7206 | − | 25.4822i | 0.145920 | − | 0.179452i | ||||
\(143\) | 108.270i | 0.757130i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.26355 | 0.0225072 | ||||||||
\(146\) | 98.7506 | + | 80.2981i | 0.676374 | + | 0.549987i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −46.1885 | − | 221.708i | −0.312085 | − | 1.49803i | ||||
\(149\) | −91.4567 | −0.613803 | −0.306902 | − | 0.951741i | \(-0.599292\pi\) | ||||
−0.306902 | + | 0.951741i | \(0.599292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 170.959i | − | 1.13218i | −0.824344 | − | 0.566089i | \(-0.808456\pi\) | ||
0.824344 | − | 0.566089i | \(-0.191544\pi\) | |||||||
\(152\) | 30.9738 | + | 16.0195i | 0.203775 | + | 0.105391i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 372.791 | + | 303.131i | 2.42072 | + | 1.96839i | ||||
\(155\) | 104.271i | 0.672714i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 259.323 | 1.65174 | 0.825868 | − | 0.563863i | \(-0.190685\pi\) | ||||
0.825868 | + | 0.563863i | \(0.190685\pi\) | |||||||
\(158\) | −24.3194 | + | 29.9080i | −0.153920 | + | 0.189291i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 80.4937 | + | 22.4434i | 0.503086 | + | 0.140272i | ||||
\(161\) | 100.663 | 0.625236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 148.560i | − | 0.911413i | −0.890130 | − | 0.455707i | \(-0.849387\pi\) | ||
0.890130 | − | 0.455707i | \(-0.150613\pi\) | |||||||
\(164\) | 25.8380 | + | 124.024i | 0.157549 | + | 0.756244i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 36.9831 | − | 45.4818i | 0.222790 | − | 0.273987i | ||||
\(167\) | − | 304.827i | − | 1.82531i | −0.408732 | − | 0.912654i | \(-0.634029\pi\) | ||
0.408732 | − | 0.912654i | \(-0.365971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −144.450 | −0.854736 | ||||||||
\(170\) | −81.4581 | − | 66.2368i | −0.479165 | − | 0.389628i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 91.3885 | − | 19.0390i | 0.531328 | − | 0.110692i | ||||
\(173\) | 100.537 | 0.581140 | 0.290570 | − | 0.956854i | \(-0.406155\pi\) | ||||
0.290570 | + | 0.956854i | \(0.406155\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 199.882i | 1.14218i | ||||||||
\(176\) | 139.616 | + | 320.540i | 0.793273 | + | 1.82125i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −33.2610 | − | 27.0458i | −0.186859 | − | 0.151943i | ||||
\(179\) | 247.870i | 1.38475i | 0.721538 | + | 0.692375i | \(0.243435\pi\) | ||||
−0.721538 | + | 0.692375i | \(0.756565\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −151.580 | −0.837457 | −0.418729 | − | 0.908111i | \(-0.637524\pi\) | ||||
−0.418729 | + | 0.908111i | \(0.637524\pi\) | |||||||
\(182\) | 68.7337 | − | 84.5288i | 0.377658 | − | 0.464444i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 65.0616 | + | 33.6496i | 0.353596 | + | 0.182878i | ||||
\(185\) | −147.848 | −0.799180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 439.267i | − | 2.34902i | ||||||
\(188\) | 253.699 | − | 52.8533i | 1.34946 | − | 0.281134i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.3625 | − | 17.6631i | 0.0755923 | − | 0.0929635i | ||||
\(191\) | − | 197.412i | − | 1.03357i | −0.856115 | − | 0.516786i | \(-0.827128\pi\) | ||
0.856115 | − | 0.516786i | \(-0.172872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 367.555 | 1.90443 | 0.952214 | − | 0.305432i | \(-0.0988008\pi\) | ||||
0.952214 | + | 0.305432i | \(0.0988008\pi\) | |||||||
\(194\) | −115.964 | − | 94.2950i | −0.597753 | − | 0.486057i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −58.6335 | − | 281.445i | −0.299151 | − | 1.43594i | ||||
\(197\) | 175.819 | 0.892481 | 0.446240 | − | 0.894913i | \(-0.352763\pi\) | ||||
0.446240 | + | 0.894913i | \(0.352763\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 114.703i | 0.576398i | 0.957571 | + | 0.288199i | \(0.0930564\pi\) | ||||
−0.957571 | + | 0.288199i | \(0.906944\pi\) | |||||||
\(200\) | −66.8164 | + | 129.190i | −0.334082 | + | 0.645949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −126.493 | − | 102.856i | −0.626201 | − | 0.509189i | ||||
\(203\) | − | 13.7399i | − | 0.0676841i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 82.7067 | 0.403447 | ||||||||
\(206\) | 212.372 | − | 261.176i | 1.03093 | − | 1.26784i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 72.6810 | − | 31.6573i | 0.349428 | − | 0.152199i | ||||
\(209\) | 95.2490 | 0.455737 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 95.5737i | − | 0.452956i | −0.974016 | − | 0.226478i | \(-0.927279\pi\) | ||
0.974016 | − | 0.226478i | \(-0.0727211\pi\) | |||||||
\(212\) | −65.9553 | − | 316.589i | −0.311110 | − | 1.49335i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −167.889 | + | 206.470i | −0.784527 | + | 0.964812i | ||||
\(215\) | − | 60.9434i | − | 0.283458i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 438.990 | 2.02300 | ||||||||
\(218\) | −74.4138 | − | 60.5088i | −0.341348 | − | 0.277563i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 223.454 | − | 46.5522i | 1.01570 | − | 0.211601i | ||||
\(221\) | −99.6019 | −0.450687 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 35.6704i | 0.159957i | 0.996797 | + | 0.0799786i | \(0.0254852\pi\) | ||||
−0.996797 | + | 0.0799786i | \(0.974515\pi\) | |||||||
\(224\) | 94.4893 | − | 338.887i | 0.421827 | − | 1.51289i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 217.631 | + | 176.964i | 0.962967 | + | 0.783027i | ||||
\(227\) | 1.37974i | 0.00607816i | 0.999995 | + | 0.00303908i | \(0.000967371\pi\) | ||||
−0.999995 | + | 0.00303908i | \(0.999033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 364.515 | 1.59177 | 0.795884 | − | 0.605449i | \(-0.207006\pi\) | ||||
0.795884 | + | 0.605449i | \(0.207006\pi\) | |||||||
\(230\) | 30.1690 | − | 37.1019i | 0.131170 | − | 0.161313i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.59296 | − | 8.88051i | 0.0197972 | − | 0.0382780i | ||||
\(233\) | −431.919 | −1.85373 | −0.926865 | − | 0.375395i | \(-0.877507\pi\) | ||||
−0.926865 | + | 0.375395i | \(0.877507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 169.182i | − | 0.719923i | ||||||
\(236\) | −47.7779 | + | 9.95360i | −0.202449 | + | 0.0421763i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −278.864 | + | 342.947i | −1.17170 | + | 1.44095i | ||||
\(239\) | 126.600i | 0.529706i | 0.964289 | + | 0.264853i | \(0.0853235\pi\) | ||||
−0.964289 | + | 0.264853i | \(0.914677\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −161.602 | −0.670546 | −0.335273 | − | 0.942121i | \(-0.608829\pi\) | ||||
−0.335273 | + | 0.942121i | \(0.608829\pi\) | |||||||
\(242\) | 553.186 | + | 449.818i | 2.28589 | + | 1.85875i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 52.5191 | + | 252.095i | 0.215242 | + | 1.03318i | ||||
\(245\) | −187.684 | −0.766059 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 21.5973i | − | 0.0874385i | ||||||
\(248\) | 283.733 | + | 146.745i | 1.14408 | + | 0.591715i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 174.976 | + | 142.280i | 0.699905 | + | 0.569120i | ||||
\(251\) | − | 137.957i | − | 0.549630i | −0.961497 | − | 0.274815i | \(-0.911383\pi\) | ||
0.961497 | − | 0.274815i | \(-0.0886166\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 200.074 | 0.790807 | ||||||||
\(254\) | −15.5737 | + | 19.1525i | −0.0613137 | + | 0.0754036i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 174.354 | − | 187.447i | 0.681072 | − | 0.732217i | ||||
\(257\) | 250.971 | 0.976541 | 0.488271 | − | 0.872692i | \(-0.337628\pi\) | ||||
0.488271 | + | 0.872692i | \(0.337628\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 622.457i | 2.40331i | ||||||||
\(260\) | −10.5555 | − | 50.6671i | −0.0405981 | − | 0.194874i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −238.215 | + | 292.956i | −0.909216 | + | 1.11815i | ||||
\(263\) | 243.090i | 0.924295i | 0.886803 | + | 0.462147i | \(0.152921\pi\) | ||||
−0.886803 | + | 0.462147i | \(0.847079\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −211.121 | −0.796684 | ||||||||
\(266\) | −74.3633 | − | 60.4678i | −0.279561 | − | 0.227322i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 324.962 | − | 67.6995i | 1.21254 | − | 0.252610i | ||||
\(269\) | 21.9177 | 0.0814784 | 0.0407392 | − | 0.999170i | \(-0.487029\pi\) | ||||
0.0407392 | + | 0.999170i | \(0.487029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 204.167i | 0.753382i | 0.926339 | + | 0.376691i | \(0.122938\pi\) | ||||
−0.926339 | + | 0.376691i | \(0.877062\pi\) | |||||||
\(272\) | −294.878 | + | 128.439i | −1.08411 | + | 0.472202i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.03062 | − | 4.90374i | −0.0220096 | − | 0.0178969i | ||||
\(275\) | 397.278i | 1.44465i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −344.707 | −1.24443 | −0.622214 | − | 0.782847i | \(-0.713767\pi\) | ||||
−0.622214 | + | 0.782847i | \(0.713767\pi\) | |||||||
\(278\) | 255.978 | − | 314.802i | 0.920783 | − | 1.13238i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −204.009 | − | 105.513i | −0.728604 | − | 0.376831i | ||||
\(281\) | 164.108 | 0.584013 | 0.292007 | − | 0.956416i | \(-0.405677\pi\) | ||||
0.292007 | + | 0.956416i | \(0.405677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 395.081i | − | 1.39605i | −0.716076 | − | 0.698023i | \(-0.754063\pi\) | ||
0.716076 | − | 0.698023i | \(-0.245937\pi\) | |||||||
\(284\) | −64.3060 | + | 13.3969i | −0.226430 | + | 0.0471722i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 136.613 | − | 168.006i | 0.477667 | − | 0.587435i | ||||
\(287\) | − | 348.204i | − | 1.21325i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 115.101 | 0.398273 | ||||||||
\(290\) | −5.06418 | − | 4.11789i | −0.0174627 | − | 0.0141996i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −51.9168 | − | 249.204i | −0.177797 | − | 0.853438i | ||||
\(293\) | 485.090 | 1.65560 | 0.827798 | − | 0.561026i | \(-0.189593\pi\) | ||||
0.827798 | + | 0.561026i | \(0.189593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.8612i | 0.108004i | ||||||||
\(296\) | −208.074 | + | 402.313i | −0.702954 | + | 1.35917i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 141.917 | + | 115.399i | 0.476232 | + | 0.387243i | ||||
\(299\) | − | 45.3659i | − | 0.151726i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −256.578 | −0.852419 | ||||||||
\(302\) | −215.713 | + | 265.284i | −0.714282 | + | 0.878424i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −27.8502 | − | 63.9403i | −0.0916125 | − | 0.210330i | ||||
\(305\) | 168.112 | 0.551188 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 271.066i | 0.882953i | 0.897273 | + | 0.441476i | \(0.145545\pi\) | ||||
−0.897273 | + | 0.441476i | \(0.854455\pi\) | |||||||
\(308\) | −195.990 | − | 940.764i | −0.636331 | − | 3.05443i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 131.567 | − | 161.801i | 0.424409 | − | 0.521939i | ||||
\(311\) | 102.844i | 0.330687i | 0.986236 | + | 0.165344i | \(0.0528733\pi\) | ||||
−0.986236 | + | 0.165344i | \(0.947127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.5571 | 0.0784571 | 0.0392285 | − | 0.999230i | \(-0.487510\pi\) | ||||
0.0392285 | + | 0.999230i | \(0.487510\pi\) | |||||||
\(314\) | −402.402 | − | 327.209i | −1.28153 | − | 1.04207i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 75.4748 | − | 15.7237i | 0.238844 | − | 0.0497586i | ||||
\(317\) | 71.3125 | 0.224961 | 0.112480 | − | 0.993654i | \(-0.464120\pi\) | ||||
0.112480 | + | 0.993654i | \(0.464120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 27.3089i | − | 0.0856078i | ||||||
\(320\) | −96.5868 | − | 136.392i | −0.301834 | − | 0.426225i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −156.203 | − | 127.015i | −0.485102 | − | 0.394456i | ||||
\(323\) | 87.6237i | 0.271281i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 90.0811 | 0.277172 | ||||||||
\(326\) | −187.451 | + | 230.527i | −0.575003 | + | 0.707139i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 116.397 | − | 225.055i | 0.354870 | − | 0.686144i | ||||
\(329\) | −712.274 | −2.16497 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 448.461i | 1.35487i | 0.735583 | + | 0.677434i | \(0.236908\pi\) | ||||
−0.735583 | + | 0.677434i | \(0.763092\pi\) | |||||||
\(332\) | −114.776 | + | 23.9114i | −0.345712 | + | 0.0720224i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −384.625 | + | 473.012i | −1.15157 | + | 1.41620i | ||||
\(335\) | − | 216.704i | − | 0.646879i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 300.502 | 0.891699 | 0.445849 | − | 0.895108i | \(-0.352902\pi\) | ||||
0.445849 | + | 0.895108i | \(0.352902\pi\) | |||||||
\(338\) | 224.150 | + | 182.265i | 0.663165 | + | 0.539246i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 42.8254 | + | 205.565i | 0.125957 | + | 0.604602i | ||||
\(341\) | 872.521 | 2.55871 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 251.457i | 0.733110i | ||||||||
\(344\) | −165.834 | − | 85.7688i | −0.482077 | − | 0.249328i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −156.008 | − | 126.856i | −0.450890 | − | 0.366636i | ||||
\(347\) | − | 305.369i | − | 0.880025i | −0.897992 | − | 0.440013i | \(-0.854974\pi\) | ||
0.897992 | − | 0.440013i | \(-0.145026\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −305.406 | −0.875089 | −0.437544 | − | 0.899197i | \(-0.644152\pi\) | ||||
−0.437544 | + | 0.899197i | \(0.644152\pi\) | |||||||
\(350\) | 252.208 | − | 310.165i | 0.720593 | − | 0.886186i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 187.804 | − | 673.560i | 0.533533 | − | 1.91352i | ||||
\(353\) | 273.264 | 0.774119 | 0.387059 | − | 0.922055i | \(-0.373491\pi\) | ||||
0.387059 | + | 0.922055i | \(0.373491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 42.8832i | 0.120798i | ||||||||
\(356\) | 17.4865 | + | 83.9362i | 0.0491193 | + | 0.235776i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 312.758 | − | 384.631i | 0.873627 | − | 1.07439i | ||||
\(359\) | − | 322.334i | − | 0.897866i | −0.893565 | − | 0.448933i | \(-0.851804\pi\) | ||
0.893565 | − | 0.448933i | \(-0.148196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 235.213 | + | 191.261i | 0.649759 | + | 0.528345i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −213.314 | + | 44.4398i | −0.586028 | + | 0.122087i | ||||
\(365\) | −166.184 | −0.455299 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 489.127i | − | 1.33277i | −0.745608 | − | 0.666385i | \(-0.767841\pi\) | ||
0.745608 | − | 0.666385i | \(-0.232159\pi\) | |||||||
\(368\) | −58.5004 | − | 134.309i | −0.158968 | − | 0.364970i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 229.422 | + | 186.552i | 0.620060 | + | 0.504196i | ||||
\(371\) | 888.842i | 2.39580i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 56.5754 | 0.151677 | 0.0758383 | − | 0.997120i | \(-0.475837\pi\) | ||||
0.0758383 | + | 0.997120i | \(0.475837\pi\) | |||||||
\(374\) | −554.260 | + | 681.629i | −1.48198 | + | 1.82254i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −460.365 | − | 238.098i | −1.22437 | − | 0.633241i | ||||
\(377\) | −6.19217 | −0.0164248 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 427.669i | − | 1.12842i | −0.825633 | − | 0.564208i | \(-0.809182\pi\) | ||
0.825633 | − | 0.564208i | \(-0.190818\pi\) | |||||||
\(380\) | −44.5739 | + | 9.28611i | −0.117300 | + | 0.0244371i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −249.091 | + | 306.333i | −0.652072 | + | 0.801918i | ||||
\(383\) | 592.062i | 1.54585i | 0.634494 | + | 0.772927i | \(0.281208\pi\) | ||||
−0.634494 | + | 0.772927i | \(0.718792\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −627.359 | −1.62950 | ||||||||
\(386\) | −570.350 | − | 463.774i | −1.47759 | − | 1.20149i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 60.9665 | + | 292.643i | 0.157130 | + | 0.754235i | ||||
\(389\) | 318.932 | 0.819877 | 0.409938 | − | 0.912113i | \(-0.365550\pi\) | ||||
0.409938 | + | 0.912113i | \(0.365550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 184.057i | 0.470734i | ||||||||
\(392\) | −264.138 | + | 510.712i | −0.673821 | + | 1.30284i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −272.825 | − | 221.845i | −0.692450 | − | 0.563059i | ||||
\(395\) | − | 50.3312i | − | 0.127421i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 543.126 | 1.36808 | 0.684038 | − | 0.729446i | \(-0.260222\pi\) | ||||
0.684038 | + | 0.729446i | \(0.260222\pi\) | |||||||
\(398\) | 144.730 | − | 177.990i | 0.363644 | − | 0.447210i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 266.691 | − | 116.162i | 0.666728 | − | 0.290404i | ||||
\(401\) | 149.069 | 0.371743 | 0.185872 | − | 0.982574i | \(-0.440489\pi\) | ||||
0.185872 | + | 0.982574i | \(0.440489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 197.840i | − | 0.490919i | ||||||
\(404\) | 66.5017 | + | 319.213i | 0.164608 | + | 0.790130i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.3367 | + | 21.3207i | −0.0427013 | + | 0.0525141i | ||||
\(407\) | 1237.17i | 3.03974i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 239.293 | 0.585069 | 0.292535 | − | 0.956255i | \(-0.405501\pi\) | ||||
0.292535 | + | 0.956255i | \(0.405501\pi\) | |||||||
\(410\) | −128.340 | − | 104.358i | −0.313023 | − | 0.254532i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −659.094 | + | 137.310i | −1.59974 | + | 0.333275i | ||||
\(413\) | 134.139 | 0.324792 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 76.5399i | 0.184434i | ||||||||
\(416\) | −152.727 | − | 42.5836i | −0.367132 | − | 0.102364i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −147.802 | − | 120.184i | −0.353593 | − | 0.287521i | ||||
\(419\) | − | 60.5956i | − | 0.144620i | −0.997382 | − | 0.0723098i | \(-0.976963\pi\) | ||
0.997382 | − | 0.0723098i | \(-0.0230370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −356.491 | −0.846771 | −0.423385 | − | 0.905950i | \(-0.639158\pi\) | ||||
−0.423385 | + | 0.905950i | \(0.639158\pi\) | |||||||
\(422\) | −120.593 | + | 148.306i | −0.285766 | + | 0.351435i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −297.122 | + | 574.486i | −0.700759 | + | 1.35492i | ||||
\(425\) | −365.473 | −0.859938 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 707.771i | − | 1.65754i | ||||||
\(428\) | 521.040 | − | 108.549i | 1.21738 | − | 0.253618i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −76.8974 | + | 94.5685i | −0.178831 | + | 0.219927i | ||||
\(431\) | 413.002i | 0.958241i | 0.877749 | + | 0.479120i | \(0.159044\pi\) | ||||
−0.877749 | + | 0.479120i | \(0.840956\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 267.426 | 0.617612 | 0.308806 | − | 0.951125i | \(-0.400071\pi\) | ||||
0.308806 | + | 0.951125i | \(0.400071\pi\) | |||||||
\(434\) | −681.200 | − | 553.910i | −1.56958 | − | 1.27629i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 39.1220 | + | 187.788i | 0.0897294 | + | 0.430707i | ||||
\(437\) | −39.9102 | −0.0913277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 137.021i | 0.312121i | 0.987747 | + | 0.156061i | \(0.0498796\pi\) | ||||
−0.987747 | + | 0.156061i | \(0.950120\pi\) | |||||||
\(440\) | −405.481 | − | 209.713i | −0.921548 | − | 0.476620i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 154.556 | + | 125.676i | 0.349675 | + | 0.284335i | ||||
\(443\) | − | 192.762i | − | 0.435129i | −0.976046 | − | 0.217565i | \(-0.930189\pi\) | ||
0.976046 | − | 0.217565i | \(-0.0698113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 55.9738 | 0.125784 | ||||||||
\(446\) | 45.0084 | − | 55.3513i | 0.100916 | − | 0.124106i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −574.225 | + | 406.641i | −1.28175 | + | 0.907680i | ||||
\(449\) | −157.944 | −0.351768 | −0.175884 | − | 0.984411i | \(-0.556278\pi\) | ||||
−0.175884 | + | 0.984411i | \(0.556278\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 692.078i | − | 1.53454i | ||||||
\(452\) | −114.416 | − | 549.205i | −0.253133 | − | 1.21506i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.74094 | − | 2.14100i | 0.00383466 | − | 0.00471587i | ||||
\(455\) | 142.251i | 0.312639i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −810.971 | −1.77455 | −0.887277 | − | 0.461237i | \(-0.847406\pi\) | ||||
−0.887277 | + | 0.461237i | \(0.847406\pi\) | |||||||
\(458\) | −565.633 | − | 459.939i | −1.23501 | − | 1.00423i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −93.6291 | + | 19.5058i | −0.203542 | + | 0.0424039i | ||||
\(461\) | −437.664 | −0.949379 | −0.474689 | − | 0.880153i | \(-0.657440\pi\) | ||||
−0.474689 | + | 0.880153i | \(0.657440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 220.543i | 0.476335i | 0.971224 | + | 0.238168i | \(0.0765468\pi\) | ||||
−0.971224 | + | 0.238168i | \(0.923453\pi\) | |||||||
\(464\) | −18.3324 | + | 7.98494i | −0.0395094 | + | 0.0172089i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 670.227 | + | 544.988i | 1.43826 | + | 1.16950i | ||||
\(467\) | − | 339.834i | − | 0.727695i | −0.931458 | − | 0.363848i | \(-0.881463\pi\) | ||
0.931458 | − | 0.363848i | \(-0.118537\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −912.348 | −1.94531 | ||||||||
\(470\) | −213.471 | + | 262.527i | −0.454194 | + | 0.558568i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 86.6983 | + | 44.8399i | 0.183683 | + | 0.0949999i | ||||
\(473\) | −509.966 | −1.07815 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 79.2479i | − | 0.166838i | ||||||
\(476\) | 865.450 | − | 180.300i | 1.81817 | − | 0.378781i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 159.741 | − | 196.450i | 0.334187 | − | 0.410984i | ||||
\(479\) | − | 22.5784i | − | 0.0471366i | −0.999722 | − | 0.0235683i | \(-0.992497\pi\) | ||
0.999722 | − | 0.0235683i | \(-0.00750271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 280.523 | 0.583209 | ||||||||
\(482\) | 250.764 | + | 203.906i | 0.520257 | + | 0.423042i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −290.830 | − | 1396.00i | −0.600888 | − | 2.88430i | ||||
\(485\) | 195.152 | 0.402376 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 75.8170i | 0.155682i | 0.996966 | + | 0.0778409i | \(0.0248026\pi\) | ||||
−0.996966 | + | 0.0778409i | \(0.975197\pi\) | |||||||
\(488\) | 236.593 | − | 457.454i | 0.484822 | − | 0.937406i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 291.238 | + | 236.817i | 0.594363 | + | 0.483300i | ||||
\(491\) | − | 576.470i | − | 1.17407i | −0.809560 | − | 0.587037i | \(-0.800294\pi\) | ||
0.809560 | − | 0.587037i | \(-0.199706\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.1226 | 0.0509587 | ||||||||
\(494\) | −27.2511 | + | 33.5134i | −0.0551642 | + | 0.0678410i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −255.120 | − | 585.721i | −0.514354 | − | 1.18089i | ||||
\(497\) | 180.543 | 0.363265 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 74.3934i | − | 0.149085i | −0.997218 | − | 0.0745425i | \(-0.976250\pi\) | ||
0.997218 | − | 0.0745425i | \(-0.0237496\pi\) | |||||||
\(500\) | −91.9913 | − | 441.564i | −0.183983 | − | 0.883128i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −174.072 | + | 214.074i | −0.346757 | + | 0.426442i | ||||
\(503\) | − | 52.1597i | − | 0.103697i | −0.998655 | − | 0.0518486i | \(-0.983489\pi\) | ||
0.998655 | − | 0.0518486i | \(-0.0165113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 212.870 | 0.421526 | ||||||||
\(506\) | −310.464 | − | 252.450i | −0.613564 | − | 0.498913i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 48.3326 | − | 10.0692i | 0.0951430 | − | 0.0198212i | ||||
\(509\) | −356.915 | −0.701208 | −0.350604 | − | 0.936524i | \(-0.614024\pi\) | ||||
−0.350604 | + | 0.936524i | \(0.614024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 699.653i | 1.36918i | ||||||||
\(512\) | −507.071 | + | 70.8728i | −0.990373 | + | 0.138423i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −389.442 | − | 316.671i | −0.757670 | − | 0.616092i | ||||
\(515\) | 439.524i | 0.853445i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1415.69 | −2.73828 | ||||||||
\(518\) | 785.405 | − | 965.892i | 1.51623 | − | 1.86466i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −47.5515 | + | 91.9411i | −0.0914452 | + | 0.176810i | ||||
\(521\) | 690.445 | 1.32523 | 0.662615 | − | 0.748960i | \(-0.269446\pi\) | ||||
0.662615 | + | 0.748960i | \(0.269446\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 223.239i | 0.426843i | 0.976960 | + | 0.213421i | \(0.0684607\pi\) | ||||
−0.976960 | + | 0.213421i | \(0.931539\pi\) | |||||||
\(524\) | 739.295 | − | 154.018i | 1.41087 | − | 0.293927i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 306.726 | − | 377.212i | 0.583130 | − | 0.717134i | ||||
\(527\) | 802.671i | 1.52309i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 445.167 | 0.841526 | ||||||||
\(530\) | 327.606 | + | 266.389i | 0.618124 | + | 0.502621i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 39.0955 | + | 187.661i | 0.0734878 | + | 0.352746i | ||||
\(533\) | −156.926 | −0.294420 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 347.461i | − | 0.649460i | ||||||
\(536\) | −589.679 | − | 304.979i | −1.10015 | − | 0.568991i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.0106 | − | 27.6554i | −0.0632168 | − | 0.0514041i | ||||
\(539\) | 1570.52i | 2.91376i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −457.379 | −0.845433 | −0.422717 | − | 0.906262i | \(-0.638923\pi\) | ||||
−0.422717 | + | 0.906262i | \(0.638923\pi\) | |||||||
\(542\) | 257.614 | − | 316.814i | 0.475302 | − | 0.584527i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 619.637 | + | 172.769i | 1.13904 | + | 0.317589i | ||||
\(545\) | 125.229 | 0.229777 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 861.942i | − | 1.57576i | −0.615827 | − | 0.787881i | \(-0.711178\pi\) | ||
0.615827 | − | 0.787881i | \(-0.288822\pi\) | |||||||
\(548\) | 3.17052 | + | 15.2187i | 0.00578561 | + | 0.0277713i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 501.279 | − | 616.473i | 0.911416 | − | 1.12086i | ||||
\(551\) | 5.44750i | 0.00988656i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −211.900 | −0.383182 | ||||||||
\(554\) | 534.896 | + | 434.945i | 0.965516 | + | 0.785099i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −794.423 | + | 165.503i | −1.42882 | + | 0.297666i | ||||
\(557\) | 843.824 | 1.51494 | 0.757472 | − | 0.652868i | \(-0.226434\pi\) | ||||
0.757472 | + | 0.652868i | \(0.226434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 115.632i | 0.206856i | ||||||||
\(560\) | 183.436 | + | 421.144i | 0.327564 | + | 0.752042i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −254.653 | − | 207.068i | −0.453119 | − | 0.368449i | ||||
\(563\) | − | 1004.70i | − | 1.78454i | −0.451503 | − | 0.892270i | \(-0.649112\pi\) | ||
0.451503 | − | 0.892270i | \(-0.350888\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −366.244 | −0.648219 | ||||||||
\(566\) | −498.506 | + | 613.064i | −0.880753 | + | 1.08315i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 116.690 | + | 60.3517i | 0.205441 | + | 0.106253i | ||||
\(569\) | 878.437 | 1.54383 | 0.771913 | − | 0.635728i | \(-0.219300\pi\) | ||||
0.771913 | + | 0.635728i | \(0.219300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 269.358i | − | 0.471731i | −0.971786 | − | 0.235865i | \(-0.924208\pi\) | ||
0.971786 | − | 0.235865i | \(-0.0757924\pi\) | |||||||
\(572\) | −423.975 | + | 88.3270i | −0.741216 | + | 0.154418i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −439.358 | + | 540.323i | −0.765432 | + | 0.941329i | ||||
\(575\) | − | 166.463i | − | 0.289501i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 882.889 | 1.53014 | 0.765068 | − | 0.643949i | \(-0.222705\pi\) | ||||
0.765068 | + | 0.643949i | \(0.222705\pi\) | |||||||
\(578\) | −178.607 | − | 145.233i | −0.309009 | − | 0.251267i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.66242 | + | 12.7798i | 0.00459038 | + | 0.0220341i | ||||
\(581\) | 322.241 | 0.554632 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1766.63i | 3.03024i | ||||||||
\(584\) | −233.880 | + | 452.208i | −0.400479 | + | 0.774328i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −752.734 | − | 612.078i | −1.28453 | − | 1.04450i | ||||
\(587\) | 461.666i | 0.786484i | 0.919435 | + | 0.393242i | \(0.128646\pi\) | ||||
−0.919435 | + | 0.393242i | \(0.871354\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −174.048 | −0.295498 | ||||||||
\(590\) | 40.2019 | − | 49.4404i | 0.0681389 | − | 0.0837973i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 830.510 | − | 361.741i | 1.40289 | − | 0.611050i | ||||
\(593\) | 788.632 | 1.32990 | 0.664951 | − | 0.746887i | \(-0.268453\pi\) | ||||
0.664951 | + | 0.746887i | \(0.268453\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 577.135i | − | 0.969974i | ||||||
\(596\) | −74.6110 | − | 358.138i | −0.125186 | − | 0.600902i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −57.2420 | + | 70.3962i | −0.0957224 | + | 0.117719i | ||||
\(599\) | − | 284.551i | − | 0.475043i | −0.971382 | − | 0.237521i | \(-0.923665\pi\) | ||
0.971382 | − | 0.237521i | \(-0.0763350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −290.399 | −0.483192 | −0.241596 | − | 0.970377i | \(-0.577671\pi\) | ||||
−0.241596 | + | 0.970377i | \(0.577671\pi\) | |||||||
\(602\) | 398.143 | + | 323.746i | 0.661367 | + | 0.537784i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 669.462 | − | 139.469i | 1.10838 | − | 0.230910i | ||||
\(605\) | −930.939 | −1.53874 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 886.175i | 1.45993i | 0.683487 | + | 0.729963i | \(0.260463\pi\) | ||||
−0.683487 | + | 0.729963i | \(0.739537\pi\) | |||||||
\(608\) | −37.4625 | + | 134.360i | −0.0616160 | + | 0.220987i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −260.867 | − | 212.121i | −0.427651 | − | 0.347740i | ||||
\(611\) | 321.002i | 0.525371i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 196.758 | 0.320975 | 0.160488 | − | 0.987038i | \(-0.448693\pi\) | ||||
0.160488 | + | 0.987038i | \(0.448693\pi\) | |||||||
\(614\) | 342.027 | − | 420.625i | 0.557047 | − | 0.685057i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −882.914 | + | 1707.12i | −1.43330 | + | 2.77130i | ||||
\(617\) | 601.962 | 0.975628 | 0.487814 | − | 0.872948i | \(-0.337795\pi\) | ||||
0.487814 | + | 0.872948i | \(0.337795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 186.061i | − | 0.300583i | −0.988642 | − | 0.150292i | \(-0.951979\pi\) | ||
0.988642 | − | 0.150292i | \(-0.0480212\pi\) | |||||||
\(620\) | −408.316 | + | 85.0647i | −0.658574 | + | 0.137201i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 129.766 | − | 159.587i | 0.208628 | − | 0.256571i | ||||
\(623\) | − | 235.656i | − | 0.378259i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 160.056 | 0.256090 | ||||||||
\(626\) | −38.1062 | − | 30.9857i | −0.0608726 | − | 0.0494979i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 211.557 | + | 1015.49i | 0.336874 | + | 1.61702i | ||||
\(629\) | −1138.13 | −1.80943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 719.486i | 1.14023i | 0.821564 | + | 0.570116i | \(0.193102\pi\) | ||||
−0.821564 | + | 0.570116i | \(0.806898\pi\) | |||||||
\(632\) | −136.957 | − | 70.8337i | −0.216705 | − | 0.112079i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −110.659 | − | 89.9810i | −0.174540 | − | 0.141926i | ||||
\(635\) | − | 32.2311i | − | 0.0507577i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 356.108 | 0.559039 | ||||||||
\(638\) | −34.4579 | + | 42.3763i | −0.0540092 | + | 0.0664206i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −22.2195 | + | 333.517i | −0.0347179 | + | 0.521120i | ||||
\(641\) | 948.094 | 1.47909 | 0.739543 | − | 0.673110i | \(-0.235042\pi\) | ||||
0.739543 | + | 0.673110i | \(0.235042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 72.1092i | − | 0.112145i | −0.998427 | − | 0.0560725i | \(-0.982142\pi\) | ||
0.998427 | − | 0.0560725i | \(-0.0178578\pi\) | |||||||
\(644\) | 82.1216 | + | 394.189i | 0.127518 | + | 0.612094i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 110.562 | − | 135.969i | 0.171149 | − | 0.210479i | ||||
\(647\) | − | 323.878i | − | 0.500584i | −0.968170 | − | 0.250292i | \(-0.919473\pi\) | ||
0.968170 | − | 0.250292i | \(-0.0805266\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 266.610 | 0.410801 | ||||||||
\(650\) | −139.783 | − | 113.663i | −0.215050 | − | 0.174866i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 581.751 | − | 121.197i | 0.892256 | − | 0.185884i | ||||
\(653\) | 200.031 | 0.306326 | 0.153163 | − | 0.988201i | \(-0.451054\pi\) | ||||
0.153163 | + | 0.988201i | \(0.451054\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 493.007i | − | 0.752682i | ||||||
\(656\) | −464.590 | + | 202.359i | −0.708216 | + | 0.308474i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1105.27 | + | 898.735i | 1.67973 | + | 1.36586i | ||||
\(659\) | − | 599.936i | − | 0.910374i | −0.890396 | − | 0.455187i | \(-0.849572\pi\) | ||
0.890396 | − | 0.455187i | \(-0.150428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 220.336 | 0.333337 | 0.166668 | − | 0.986013i | \(-0.446699\pi\) | ||||
0.166668 | + | 0.986013i | \(0.446699\pi\) | |||||||
\(662\) | 565.861 | − | 695.896i | 0.854775 | − | 1.05120i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 208.274 | + | 107.719i | 0.313666 | + | 0.162227i | ||||
\(665\) | 125.144 | 0.188186 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.4427i | 0.0171554i | ||||||||
\(668\) | 1193.68 | − | 248.680i | 1.78694 | − | 0.372275i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −273.434 | + | 336.269i | −0.408110 | + | 0.501894i | ||||
\(671\) | − | 1406.74i | − | 2.09648i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −786.871 | −1.16920 | −0.584599 | − | 0.811322i | \(-0.698748\pi\) | ||||
−0.584599 | + | 0.811322i | \(0.698748\pi\) | |||||||
\(674\) | −466.302 | − | 379.169i | −0.691843 | − | 0.562565i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −117.844 | − | 565.657i | −0.174325 | − | 0.836770i | ||||
\(677\) | 385.498 | 0.569421 | 0.284711 | − | 0.958613i | \(-0.408102\pi\) | ||||
0.284711 | + | 0.958613i | \(0.408102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 821.612i | − | 1.21003i | ||||||
\(680\) | 192.924 | − | 373.020i | 0.283712 | − | 0.548559i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1353.93 | − | 1100.93i | −1.98523 | − | 1.61427i | ||||
\(683\) | − | 474.430i | − | 0.694626i | −0.937749 | − | 0.347313i | \(-0.887094\pi\) | ||
0.937749 | − | 0.347313i | \(-0.112906\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1487 | 0.0148157 | ||||||||
\(686\) | 317.284 | − | 390.196i | 0.462513 | − | 0.568799i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 149.111 | + | 342.338i | 0.216731 | + | 0.497585i | ||||
\(689\) | 400.576 | 0.581387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 317.710i | − | 0.459784i | −0.973216 | − | 0.229892i | \(-0.926163\pi\) | ||
0.973216 | − | 0.229892i | \(-0.0738372\pi\) | |||||||
\(692\) | 82.0189 | + | 393.696i | 0.118524 | + | 0.568925i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −385.309 | + | 473.854i | −0.555201 | + | 0.682786i | ||||
\(695\) | 529.769i | 0.762258i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 636.673 | 0.913447 | ||||||||
\(698\) | 473.911 | + | 385.356i | 0.678956 | + | 0.552086i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −782.722 | + | 163.065i | −1.11817 | + | 0.232950i | ||||
\(701\) | 1220.64 | 1.74128 | 0.870640 | − | 0.491921i | \(-0.163705\pi\) | ||||
0.870640 | + | 0.491921i | \(0.163705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 246.788i | − | 0.351049i | ||||||
\(704\) | −1141.31 | + | 808.224i | −1.62118 | + | 1.14805i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −424.035 | − | 344.800i | −0.600616 | − | 0.488385i | ||||
\(707\) | − | 896.207i | − | 1.26762i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 448.866 | 0.633097 | 0.316548 | − | 0.948576i | \(-0.397476\pi\) | ||||
0.316548 | + | 0.948576i | \(0.397476\pi\) | |||||||
\(710\) | 54.1092 | − | 66.5436i | 0.0762102 | − | 0.0937234i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 78.7748 | − | 152.312i | 0.110639 | − | 0.213921i | ||||
\(713\) | −365.594 | −0.512755 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 282.733i | 0.395430i | ||||||||
\(716\) | −970.641 | + | 202.214i | −1.35564 | + | 0.282422i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −406.716 | + | 500.179i | −0.566456 | + | 0.696629i | ||||
\(719\) | 256.712i | 0.357040i | 0.983936 | + | 0.178520i | \(0.0571309\pi\) | ||||
−0.983936 | + | 0.178520i | \(0.942869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1850.44 | 2.56650 | ||||||||
\(722\) | 29.4831 | + | 23.9739i | 0.0408353 | + | 0.0332048i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −123.660 | − | 593.575i | −0.170801 | − | 0.819854i | ||||
\(725\) | −22.7212 | −0.0313396 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.0120i | 0.0344043i | 0.999852 | + | 0.0172022i | \(0.00547589\pi\) | ||||
−0.999852 | + | 0.0172022i | \(0.994524\pi\) | |||||||
\(728\) | 387.082 | + | 200.197i | 0.531706 | + | 0.274996i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 257.875 | + | 209.689i | 0.353254 | + | 0.287245i | ||||
\(731\) | − | 469.140i | − | 0.641778i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1006.20 | 1.37271 | 0.686356 | − | 0.727266i | \(-0.259209\pi\) | ||||
0.686356 | + | 0.727266i | \(0.259209\pi\) | |||||||
\(734\) | −617.172 | + | 758.998i | −0.840833 | + | 1.03406i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −78.6914 | + | 282.228i | −0.106918 | + | 0.383462i | ||||
\(737\) | −1813.35 | −2.46045 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 710.886i | 0.961956i | 0.876733 | + | 0.480978i | \(0.159718\pi\) | ||||
−0.876733 | + | 0.480978i | \(0.840282\pi\) | |||||||
\(740\) | −120.616 | − | 578.962i | −0.162994 | − | 0.782382i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1121.53 | − | 1379.25i | 1.51149 | − | 1.85883i | ||||
\(743\) | − | 521.430i | − | 0.701790i | −0.936415 | − | 0.350895i | \(-0.885877\pi\) | ||
0.936415 | − | 0.350895i | \(-0.114123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −238.828 | −0.320574 | ||||||||
\(746\) | −87.7904 | − | 71.3858i | −0.117681 | − | 0.0956915i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1720.14 | − | 358.357i | 2.29965 | − | 0.479087i | ||||
\(749\) | −1462.85 | −1.95307 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 650.897i | 0.866707i | 0.901224 | + | 0.433354i | \(0.142670\pi\) | ||||
−0.901224 | + | 0.433354i | \(0.857330\pi\) | |||||||
\(752\) | 413.939 | + | 950.348i | 0.550451 | + | 1.26376i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.60865 | + | 7.81317i | 0.0127436 | + | 0.0103623i | ||||
\(755\) | − | 446.438i | − | 0.591309i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 744.251 | 0.983159 | 0.491579 | − | 0.870833i | \(-0.336420\pi\) | ||||
0.491579 | + | 0.870833i | \(0.336420\pi\) | |||||||
\(758\) | −539.626 | + | 663.633i | −0.711908 | + | 0.875505i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 80.8842 | + | 41.8329i | 0.106427 | + | 0.0550433i | ||||
\(761\) | −378.670 | −0.497595 | −0.248797 | − | 0.968556i | \(-0.580035\pi\) | ||||
−0.248797 | + | 0.968556i | \(0.580035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 527.226i | − | 0.690990i | ||||||
\(764\) | 773.051 | − | 161.050i | 1.01185 | − | 0.210799i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 747.054 | − | 918.728i | 0.975267 | − | 1.19938i | ||||
\(767\) | − | 60.4527i | − | 0.0788170i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.255290 | −0.000331977 | −0.000165989 | − | 1.00000i | \(-0.500053\pi\) | ||||
−0.000165989 | 1.00000i | \(0.500053\pi\) | ||||||||
\(770\) | 973.499 | + | 791.590i | 1.26428 | + | 1.02804i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 299.854 | + | 1439.32i | 0.388411 | + | 1.86440i | ||||
\(773\) | 398.489 | 0.515510 | 0.257755 | − | 0.966210i | \(-0.417017\pi\) | ||||
0.257755 | + | 0.966210i | \(0.417017\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 725.944i | − | 0.936702i | ||||||
\(776\) | 274.648 | − | 531.033i | 0.353928 | − | 0.684321i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −494.900 | − | 402.423i | −0.636118 | − | 0.517253i | ||||
\(779\) | 138.054i | 0.177219i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 358.840 | 0.459462 | ||||||||
\(782\) | 232.240 | − | 285.609i | 0.296982 | − | 0.365229i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1054.28 | − | 459.209i | 1.34475 | − | 0.585726i | ||||
\(785\) | 677.189 | 0.862661 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 530.707i | 0.674342i | 0.941443 | + | 0.337171i | \(0.109470\pi\) | ||||
−0.941443 | + | 0.337171i | \(0.890530\pi\) | |||||||
\(788\) | 143.434 | + | 688.493i | 0.182023 | + | 0.873722i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −63.5071 | + | 78.1011i | −0.0803887 | + | 0.0988621i | ||||
\(791\) | 1541.92i | 1.94934i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −318.972 | −0.402235 | ||||||||
\(794\) | −842.792 | − | 685.308i | −1.06145 | − | 0.863108i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −449.169 | + | 93.5756i | −0.564282 | + | 0.117557i | ||||
\(797\) | −1343.23 | −1.68536 | −0.842678 | − | 0.538418i | \(-0.819022\pi\) | ||||
−0.842678 | + | 0.538418i | \(0.819022\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1302.36i | − | 1.62998i | ||||||
\(800\) | −560.407 | − | 156.254i | −0.700509 | − | 0.195317i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −231.317 | − | 188.093i | −0.288425 | − | 0.234530i | ||||
\(803\) | 1390.61i | 1.73176i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 262.869 | 0.326545 | ||||||||
\(806\) | −249.632 | + | 306.997i | −0.309717 | + | 0.380890i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 299.583 | − | 579.246i | 0.370772 | − | 0.716889i | ||||
\(809\) | −596.997 | −0.737945 | −0.368972 | − | 0.929440i | \(-0.620290\pi\) | ||||
−0.368972 | + | 0.929440i | \(0.620290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 254.062i | − | 0.313270i | −0.987657 | − | 0.156635i | \(-0.949935\pi\) | ||
0.987657 | − | 0.156635i | \(-0.0500647\pi\) | |||||||
\(812\) | 53.8043 | − | 11.2091i | 0.0662614 | − | 0.0138043i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1561.04 | − | 1919.77i | 1.91774 | − | 2.35844i | ||||
\(815\) | − | 387.947i | − | 0.476009i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 101.726 | 0.124512 | ||||||||
\(818\) | −371.321 | − | 301.936i | −0.453938 | − | 0.369115i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 67.4727 | + | 323.873i | 0.0822838 | + | 0.394967i | ||||
\(821\) | −1111.21 | −1.35348 | −0.676739 | − | 0.736223i | \(-0.736607\pi\) | ||||
−0.676739 | + | 0.736223i | \(0.736607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 745.561i | − | 0.905906i | −0.891534 | − | 0.452953i | \(-0.850371\pi\) | ||
0.891534 | − | 0.452953i | \(-0.149629\pi\) | |||||||
\(824\) | 1196.00 | + | 618.565i | 1.45146 | + | 0.750686i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −208.149 | − | 169.254i | −0.251997 | − | 0.204909i | ||||
\(827\) | − | 108.732i | − | 0.131477i | −0.997837 | − | 0.0657387i | \(-0.979060\pi\) | ||
0.997837 | − | 0.0657387i | \(-0.0209404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −342.192 | −0.412777 | −0.206388 | − | 0.978470i | \(-0.566171\pi\) | ||||
−0.206388 | + | 0.978470i | \(0.566171\pi\) | |||||||
\(830\) | 96.5768 | − | 118.770i | 0.116358 | − | 0.143097i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 183.261 | + | 258.787i | 0.220266 | + | 0.311042i | ||||
\(833\) | −1444.79 | −1.73444 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 796.017i | − | 0.953314i | ||||||
\(836\) | 77.7048 | + | 372.988i | 0.0929483 | + | 0.446158i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −76.4586 | + | 94.0288i | −0.0912393 | + | 0.112206i | ||||
\(839\) | 1448.05i | 1.72592i | 0.505270 | + | 0.862961i | \(0.331393\pi\) | ||||
−0.505270 | + | 0.862961i | \(0.668607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −839.438 | −0.998143 | ||||||||
\(842\) | 553.181 | + | 449.814i | 0.656985 | + | 0.534221i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 374.259 | − | 77.9697i | 0.443435 | − | 0.0923811i | ||||
\(845\) | −377.214 | −0.446407 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3919.35i | 4.62733i | ||||||||
\(848\) | 1185.93 | − | 516.552i | 1.39851 | − | 0.609141i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 567.121 | + | 461.148i | 0.667201 | + | 0.542527i | ||||
\(851\) | − | 518.387i | − | 0.609150i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 474.240 | 0.555968 | 0.277984 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277984 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(854\) | −893.053 | + | 1098.28i | −1.04573 | + | 1.28604i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −945.485 | − | 489.000i | −1.10454 | − | 0.571262i | ||||
\(857\) | 1081.61 | 1.26209 | 0.631046 | − | 0.775746i | \(-0.282626\pi\) | ||||
0.631046 | + | 0.775746i | \(0.282626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 412.312i | 0.479991i | 0.970774 | + | 0.239995i | \(0.0771459\pi\) | ||||
−0.970774 | + | 0.239995i | \(0.922854\pi\) | |||||||
\(860\) | 238.650 | − | 49.7181i | 0.277500 | − | 0.0578117i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 521.119 | − | 640.872i | 0.604546 | − | 0.743471i | ||||
\(863\) | − | 714.308i | − | 0.827703i | −0.910344 | − | 0.413852i | \(-0.864183\pi\) | ||
0.910344 | − | 0.413852i | \(-0.135817\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 262.540 | 0.303515 | ||||||||
\(866\) | −414.976 | − | 337.434i | −0.479188 | − | 0.389646i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 358.131 | + | 1719.05i | 0.412594 | + | 1.98048i | ||||
\(869\) | −421.164 | −0.484654 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 411.169i | 0.472066i | ||||||||
\(872\) | 176.241 | − | 340.762i | 0.202111 | − | 0.390782i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 61.9304 | + | 50.3580i | 0.0708585 | + | 0.0576179i | ||||
\(875\) | 1239.72i | 1.41682i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −953.647 | −1.08740 | −0.543698 | − | 0.839281i | \(-0.682976\pi\) | ||||
−0.543698 | + | 0.839281i | \(0.682976\pi\) | |||||||
\(878\) | 172.891 | − | 212.622i | 0.196915 | − | 0.242166i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 364.590 | + | 837.050i | 0.414307 | + | 0.951193i | ||||
\(881\) | −685.401 | −0.777981 | −0.388990 | − | 0.921242i | \(-0.627176\pi\) | ||||
−0.388990 | + | 0.921242i | \(0.627176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 761.761i | − | 0.862696i | −0.902186 | − | 0.431348i | \(-0.858038\pi\) | ||
0.902186 | − | 0.431348i | \(-0.141962\pi\) | |||||||
\(884\) | −81.2559 | − | 390.033i | −0.0919184 | − | 0.441214i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −243.224 | + | 299.117i | −0.274519 | + | 0.337604i | ||||
\(887\) | − | 1281.41i | − | 1.44465i | −0.691553 | − | 0.722325i | \(-0.743073\pi\) | ||
0.691553 | − | 0.722325i | \(-0.256927\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −135.697 | −0.152640 | ||||||||
\(890\) | −86.8569 | − | 70.6268i | −0.0975920 | − | 0.0793559i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −139.683 | + | 29.1002i | −0.156595 | + | 0.0326235i | ||||
\(893\) | 282.398 | 0.316235 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 647.282i | 0.723221i | ||||||||
\(896\) | 1404.14 | + | 93.5463i | 1.56712 | + | 0.104404i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 245.088 | + | 199.291i | 0.272926 | + | 0.221927i | ||||
\(899\) | 49.9014i | 0.0555076i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1625.20 | −1.80378 | ||||||||
\(902\) | −873.252 | + | 1073.93i | −0.968129 | + | 1.19061i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −515.433 | + | 996.594i | −0.570170 | + | 1.10243i | ||||
\(905\) | −395.832 | −0.437383 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 895.017i | − | 0.986788i | −0.869806 | − | 0.493394i | \(-0.835756\pi\) | ||
0.869806 | − | 0.493394i | \(-0.164244\pi\) | |||||||
\(908\) | −5.40297 | + | 1.12560i | −0.00595040 | + | 0.00123965i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 179.490 | − | 220.737i | 0.197241 | − | 0.242568i | ||||
\(911\) | − | 1336.00i | − | 1.46652i | −0.679948 | − | 0.733260i | \(-0.737998\pi\) | ||
0.679948 | − | 0.733260i | \(-0.262002\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 640.475 | 0.701506 | ||||||||
\(914\) | 1258.42 | + | 1023.27i | 1.37683 | + | 1.11955i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 297.374 | + | 1427.41i | 0.324644 | + | 1.55831i | ||||
\(917\) | −2075.61 | −2.26348 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1242.95i | 1.35250i | 0.736673 | + | 0.676249i | \(0.236396\pi\) | ||||
−0.736673 | + | 0.676249i | \(0.763604\pi\) | |||||||
\(920\) | 169.900 | + | 87.8717i | 0.184674 | + | 0.0955127i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 679.141 | + | 552.237i | 0.736595 | + | 0.598955i | ||||
\(923\) | − | 81.3654i | − | 0.0881532i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1029.34 | 1.11280 | ||||||||
\(926\) | 278.278 | − | 342.226i | 0.300516 | − | 0.369575i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 38.5223 | + | 10.7409i | 0.0415112 | + | 0.0115742i | ||||
\(929\) | 1198.80 | 1.29042 | 0.645212 | − | 0.764004i | \(-0.276769\pi\) | ||||
0.645212 | + | 0.764004i | \(0.276769\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 313.282i | − | 0.336501i | ||||||
\(932\) | −352.363 | − | 1691.36i | −0.378071 | − | 1.81477i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −428.796 | + | 527.334i | −0.459097 | + | 0.564598i | ||||
\(935\) | − | 1147.09i | − | 1.22684i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1480.41 | −1.57994 | −0.789971 | − | 0.613144i | \(-0.789904\pi\) | ||||
−0.789971 | + | 0.613144i | \(0.789904\pi\) | |||||||
\(938\) | 1415.73 | + | 1151.19i | 1.50931 | + | 1.22728i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 662.504 | − | 138.020i | 0.704791 | − | 0.146830i | ||||
\(941\) | 638.982 | 0.679046 | 0.339523 | − | 0.940598i | \(-0.389734\pi\) | ||||
0.339523 | + | 0.940598i | \(0.389734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 289.987i | 0.307515i | ||||||||
\(944\) | −77.9551 | − | 178.974i | −0.0825795 | − | 0.189592i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 791.335 | + | 643.466i | 0.836507 | + | 0.680197i | ||||
\(947\) | − | 715.258i | − | 0.755288i | −0.925951 | − | 0.377644i | \(-0.876734\pi\) | ||
0.925951 | − | 0.377644i | \(-0.123266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 315.314 | 0.332259 | ||||||||
\(950\) | −99.9936 | + | 122.972i | −0.105256 | + | 0.129445i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1570.45 | − | 812.231i | −1.64964 | − | 0.853184i | ||||
\(953\) | −1419.89 | −1.48992 | −0.744959 | − | 0.667110i | \(-0.767531\pi\) | ||||
−0.744959 | + | 0.667110i | \(0.767531\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 515.518i | − | 0.539809i | ||||||
\(956\) | −495.755 | + | 103.281i | −0.518572 | + | 0.108034i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.4891 | + | 35.0359i | −0.0297381 | + | 0.0365719i | ||||
\(959\) | − | 42.7273i | − | 0.0445540i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −633.354 | −0.659057 | ||||||||
\(962\) | −435.300 | − | 353.960i | −0.452495 | − | 0.367942i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −131.836 | − | 632.819i | −0.136759 | − | 0.656452i | ||||
\(965\) | 959.824 | 0.994636 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 289.245i | − | 0.299116i | −0.988753 | − | 0.149558i | \(-0.952215\pi\) | ||
0.988753 | − | 0.149558i | \(-0.0477851\pi\) | |||||||
\(968\) | −1310.16 | + | 2533.20i | −1.35347 | + | 2.61694i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −302.826 | − | 246.240i | −0.312192 | − | 0.253856i | ||||
\(971\) | − | 1893.95i | − | 1.95051i | −0.221073 | − | 0.975257i | \(-0.570956\pi\) | ||
0.221073 | − | 0.975257i | \(-0.429044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2230.39 | 2.29228 | ||||||||
\(974\) | 95.6646 | − | 117.648i | 0.0982183 | − | 0.120789i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −944.339 | + | 411.322i | −0.967561 | + | 0.421436i | ||||
\(977\) | −1575.22 | −1.61230 | −0.806150 | − | 0.591711i | \(-0.798453\pi\) | ||||
−0.806150 | + | 0.591711i | \(0.798453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 468.381i | − | 0.478428i | ||||||
\(980\) | −153.114 | − | 734.958i | −0.156239 | − | 0.749957i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −727.380 | + | 894.533i | −0.740713 | + | 0.910929i | ||||
\(983\) | 906.607i | 0.922286i | 0.887326 | + | 0.461143i | \(0.152560\pi\) | ||||
−0.887326 | + | 0.461143i | \(0.847440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 459.129 | 0.466121 | ||||||||
\(986\) | −38.9838 | − | 31.6993i | −0.0395374 | − | 0.0321494i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 84.5734 | − | 17.6192i | 0.0856006 | − | 0.0178332i | ||||
\(989\) | 213.680 | 0.216057 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1283.89i | − | 1.29555i | −0.761831 | − | 0.647776i | \(-0.775699\pi\) | ||
0.761831 | − | 0.647776i | \(-0.224301\pi\) | |||||||
\(992\) | −343.172 | + | 1230.79i | −0.345940 | + | 1.24072i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −280.156 | − | 227.806i | −0.281847 | − | 0.229181i | ||||
\(995\) | 299.533i | 0.301038i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 153.327 | 0.153789 | 0.0768944 | − | 0.997039i | \(-0.475500\pi\) | ||||
0.0768944 | + | 0.997039i | \(0.475500\pi\) | |||||||
\(998\) | −93.8683 | + | 115.439i | −0.0940565 | + | 0.115671i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.3.g.d.343.7 | ✓ | 36 | |
3.2 | odd | 2 | inner | 684.3.g.d.343.30 | yes | 36 | |
4.3 | odd | 2 | inner | 684.3.g.d.343.8 | yes | 36 | |
12.11 | even | 2 | inner | 684.3.g.d.343.29 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.g.d.343.7 | ✓ | 36 | 1.1 | even | 1 | trivial | |
684.3.g.d.343.8 | yes | 36 | 4.3 | odd | 2 | inner | |
684.3.g.d.343.29 | yes | 36 | 12.11 | even | 2 | inner | |
684.3.g.d.343.30 | yes | 36 | 3.2 | odd | 2 | inner |