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: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.8 | ||
Character | \(\chi\) | \(=\) | 684.343 |
Dual form | 684.3.g.c.343.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.78242 | + | 0.907175i | −0.891212 | + | 0.453588i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.35407 | − | 3.23394i | 0.588517 | − | 0.808485i | ||||
\(5\) | 3.42194 | 0.684389 | 0.342194 | − | 0.939629i | \(-0.388830\pi\) | ||||
0.342194 | + | 0.939629i | \(0.388830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.09734i | − | 0.156762i | −0.996923 | − | 0.0783811i | \(-0.975025\pi\) | ||
0.996923 | − | 0.0783811i | \(-0.0249751\pi\) | |||||||
\(8\) | −1.26219 | + | 7.89980i | −0.157774 | + | 0.987475i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.09935 | + | 3.10430i | −0.609935 | + | 0.310430i | ||||
\(11\) | 15.1885i | 1.38077i | 0.723442 | + | 0.690386i | \(0.242559\pi\) | ||||
−0.723442 | + | 0.690386i | \(0.757441\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.52450 | −0.271115 | −0.135558 | − | 0.990769i | \(-0.543283\pi\) | ||||
−0.135558 | + | 0.990769i | \(0.543283\pi\) | |||||||
\(14\) | 0.995475 | + | 1.95592i | 0.0711054 | + | 0.139708i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.91674 | − | 15.2258i | −0.307296 | − | 0.951614i | ||||
\(17\) | −12.8708 | −0.757104 | −0.378552 | − | 0.925580i | \(-0.623578\pi\) | ||||
−0.378552 | + | 0.925580i | \(0.623578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890i | 0.229416i | ||||||||
\(20\) | 8.05549 | − | 11.0664i | 0.402774 | − | 0.553318i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −13.7786 | − | 27.0723i | −0.626301 | − | 1.23056i | ||||
\(23\) | − | 4.00522i | − | 0.174140i | −0.996202 | − | 0.0870699i | \(-0.972250\pi\) | ||
0.996202 | − | 0.0870699i | \(-0.0277504\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.2903 | −0.531612 | ||||||||
\(26\) | 6.28215 | − | 3.19734i | 0.241621 | − | 0.122974i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.54872 | − | 2.58320i | −0.126740 | − | 0.0922572i | ||||
\(29\) | −42.9404 | −1.48070 | −0.740351 | − | 0.672220i | \(-0.765341\pi\) | ||||
−0.740351 | + | 0.672220i | \(0.765341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.9996i | 1.19354i | 0.802414 | + | 0.596768i | \(0.203549\pi\) | ||||
−0.802414 | + | 0.596768i | \(0.796451\pi\) | |||||||
\(32\) | 22.5762 | + | 22.6785i | 0.705506 | + | 0.708704i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 22.9412 | − | 11.6760i | 0.674740 | − | 0.343413i | ||||
\(35\) | − | 3.75502i | − | 0.107286i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 56.3720 | 1.52357 | 0.761784 | − | 0.647831i | \(-0.224324\pi\) | ||||
0.761784 | + | 0.647831i | \(0.224324\pi\) | |||||||
\(38\) | −3.95428 | − | 7.76940i | −0.104060 | − | 0.204458i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.31915 | + | 27.0327i | −0.107979 | + | 0.675817i | ||||
\(41\) | 1.67907 | 0.0409530 | 0.0204765 | − | 0.999790i | \(-0.493482\pi\) | ||||
0.0204765 | + | 0.999790i | \(0.493482\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.06487i | − | 0.117788i | −0.998264 | − | 0.0588939i | \(-0.981243\pi\) | ||
0.998264 | − | 0.0588939i | \(-0.0187574\pi\) | |||||||
\(44\) | 49.1187 | + | 35.7547i | 1.11633 | + | 0.812607i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.63343 | + | 7.13899i | 0.0789877 | + | 0.155195i | ||||
\(47\) | 32.3170i | 0.687595i | 0.939044 | + | 0.343798i | \(0.111713\pi\) | ||||
−0.939044 | + | 0.343798i | \(0.888287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.7959 | 0.975426 | ||||||||
\(50\) | 23.6889 | − | 12.0566i | 0.473779 | − | 0.241132i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.29690 | + | 11.3980i | −0.159556 | + | 0.219193i | ||||
\(53\) | −69.3744 | −1.30895 | −0.654475 | − | 0.756083i | \(-0.727110\pi\) | ||||
−0.654475 | + | 0.756083i | \(0.727110\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 51.9742i | 0.944985i | ||||||||
\(56\) | 8.66873 | + | 1.38505i | 0.154799 | + | 0.0247330i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 76.5379 | − | 38.9544i | 1.31962 | − | 0.671628i | ||||
\(59\) | 32.2677i | 0.546910i | 0.961885 | + | 0.273455i | \(0.0881665\pi\) | ||||
−0.961885 | + | 0.273455i | \(0.911834\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −68.1965 | −1.11798 | −0.558988 | − | 0.829176i | \(-0.688810\pi\) | ||||
−0.558988 | + | 0.829176i | \(0.688810\pi\) | |||||||
\(62\) | −33.5651 | − | 65.9490i | −0.541373 | − | 1.06369i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −60.8137 | − | 19.9421i | −0.950215 | − | 0.311596i | ||||
\(65\) | −12.0606 | −0.185548 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 52.6766i | 0.786219i | 0.919492 | + | 0.393109i | \(0.128601\pi\) | ||||
−0.919492 | + | 0.393109i | \(0.871399\pi\) | |||||||
\(68\) | −30.2987 | + | 41.6233i | −0.445568 | + | 0.612107i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.40646 | + | 6.69304i | 0.0486637 | + | 0.0956148i | ||||
\(71\) | − | 3.42161i | − | 0.0481917i | −0.999710 | − | 0.0240959i | \(-0.992329\pi\) | ||
0.999710 | − | 0.0240959i | \(-0.00767069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 29.6657 | 0.406380 | 0.203190 | − | 0.979139i | \(-0.434869\pi\) | ||||
0.203190 | + | 0.979139i | \(0.434869\pi\) | |||||||
\(74\) | −100.479 | + | 51.1393i | −1.35782 | + | 0.691072i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.0964 | + | 10.2611i | 0.185479 | + | 0.135015i | ||||
\(77\) | 16.6669 | 0.216453 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 68.4637i | 0.866629i | 0.901243 | + | 0.433314i | \(0.142656\pi\) | ||||
−0.901243 | + | 0.433314i | \(0.857344\pi\) | |||||||
\(80\) | −16.8248 | − | 52.1019i | −0.210310 | − | 0.651274i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.99282 | + | 1.52321i | −0.0364978 | + | 0.0185758i | ||||
\(83\) | − | 51.1729i | − | 0.616541i | −0.951299 | − | 0.308270i | \(-0.900250\pi\) | ||
0.951299 | − | 0.308270i | \(-0.0997502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44.0431 | −0.518154 | ||||||||
\(86\) | 4.59473 | + | 9.02775i | 0.0534270 | + | 0.104974i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −119.986 | − | 19.1708i | −1.36348 | − | 0.217850i | ||||
\(89\) | −1.78749 | −0.0200841 | −0.0100421 | − | 0.999950i | \(-0.503197\pi\) | ||||
−0.0100421 | + | 0.999950i | \(0.503197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.86756i | 0.0425006i | ||||||||
\(92\) | −12.9526 | − | 9.42855i | −0.140789 | − | 0.102484i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −29.3172 | − | 57.6025i | −0.311885 | − | 0.612793i | ||||
\(95\) | 14.9159i | 0.157010i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −114.257 | −1.17790 | −0.588952 | − | 0.808168i | \(-0.700459\pi\) | ||||
−0.588952 | + | 0.808168i | \(0.700459\pi\) | |||||||
\(98\) | −85.1925 | + | 43.3592i | −0.869311 | + | 0.442441i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −31.2862 | + | 42.9800i | −0.312862 | + | 0.429800i | ||||
\(101\) | −142.326 | −1.40917 | −0.704583 | − | 0.709622i | \(-0.748866\pi\) | ||||
−0.704583 | + | 0.709622i | \(0.748866\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56.5941i | 0.549457i | 0.961522 | + | 0.274729i | \(0.0885880\pi\) | ||||
−0.961522 | + | 0.274729i | \(0.911412\pi\) | |||||||
\(104\) | 4.44860 | − | 27.8428i | 0.0427750 | − | 0.267719i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 123.655 | − | 62.9347i | 1.16655 | − | 0.593724i | ||||
\(107\) | 190.866i | 1.78380i | 0.452237 | + | 0.891898i | \(0.350626\pi\) | ||||
−0.452237 | + | 0.891898i | \(0.649374\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −136.983 | −1.25672 | −0.628361 | − | 0.777922i | \(-0.716274\pi\) | ||||
−0.628361 | + | 0.777922i | \(0.716274\pi\) | |||||||
\(110\) | −47.1497 | − | 92.6400i | −0.428633 | − | 0.842181i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −16.7078 | + | 5.39531i | −0.149177 | + | 0.0481724i | ||||
\(113\) | 63.0026 | 0.557545 | 0.278773 | − | 0.960357i | \(-0.410072\pi\) | ||||
0.278773 | + | 0.960357i | \(0.410072\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.7056i | − | 0.119179i | ||||||
\(116\) | −101.085 | + | 138.867i | −0.871418 | + | 1.19713i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.2724 | − | 57.5147i | −0.248072 | − | 0.487413i | ||||
\(119\) | 14.1236i | 0.118685i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −109.690 | −0.906529 | ||||||||
\(122\) | 121.555 | − | 61.8662i | 0.996353 | − | 0.507100i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 119.655 | + | 87.0996i | 0.964956 | + | 0.702416i | ||||
\(125\) | −131.027 | −1.04822 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 131.614i | 1.03633i | 0.855280 | + | 0.518166i | \(0.173385\pi\) | ||||
−0.855280 | + | 0.518166i | \(0.826615\pi\) | |||||||
\(128\) | 126.487 | − | 19.6234i | 0.988179 | − | 0.153307i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 21.4972 | − | 10.9411i | 0.165363 | − | 0.0841624i | ||||
\(131\) | − | 126.299i | − | 0.964113i | −0.876140 | − | 0.482056i | \(-0.839890\pi\) | ||
0.876140 | − | 0.482056i | \(-0.160110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.78317 | 0.0359637 | ||||||||
\(134\) | −47.7869 | − | 93.8921i | −0.356619 | − | 0.700687i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.2454 | − | 101.677i | 0.119451 | − | 0.747622i | ||||
\(137\) | 206.449 | 1.50693 | 0.753465 | − | 0.657488i | \(-0.228381\pi\) | ||||
0.753465 | + | 0.657488i | \(0.228381\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 169.116i | 1.21666i | 0.793684 | + | 0.608330i | \(0.208160\pi\) | ||||
−0.793684 | + | 0.608330i | \(0.791840\pi\) | |||||||
\(140\) | −12.1435 | − | 8.83957i | −0.0867394 | − | 0.0631398i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.10400 | + | 6.09876i | 0.0218592 | + | 0.0429490i | ||||
\(143\) | − | 53.5318i | − | 0.374348i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −146.940 | −1.01338 | ||||||||
\(146\) | −52.8769 | + | 26.9120i | −0.362170 | + | 0.184329i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 132.703 | − | 182.304i | 0.896645 | − | 1.23178i | ||||
\(149\) | 16.2018 | 0.108737 | 0.0543685 | − | 0.998521i | \(-0.482685\pi\) | ||||
0.0543685 | + | 0.998521i | \(0.482685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 228.478i | − | 1.51310i | −0.653935 | − | 0.756551i | \(-0.726883\pi\) | ||
0.653935 | − | 0.756551i | \(-0.273117\pi\) | |||||||
\(152\) | −34.4344 | − | 5.50177i | −0.226542 | − | 0.0361959i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −29.7074 | + | 15.1198i | −0.192905 | + | 0.0981803i | ||||
\(155\) | 126.611i | 0.816843i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.5361 | 0.137173 | 0.0685863 | − | 0.997645i | \(-0.478151\pi\) | ||||
0.0685863 | + | 0.997645i | \(0.478151\pi\) | |||||||
\(158\) | −62.1085 | − | 122.031i | −0.393092 | − | 0.772350i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 77.2545 | + | 77.6046i | 0.482841 | + | 0.485029i | ||||
\(161\) | −4.39507 | −0.0272985 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 167.384i | − | 1.02689i | −0.858121 | − | 0.513447i | \(-0.828368\pi\) | ||
0.858121 | − | 0.513447i | \(-0.171632\pi\) | |||||||
\(164\) | 3.95265 | − | 5.43003i | 0.0241015 | − | 0.0331099i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 46.4228 | + | 91.2118i | 0.279655 | + | 0.549468i | ||||
\(167\) | 2.31649i | 0.0138712i | 0.999976 | + | 0.00693560i | \(0.00220769\pi\) | ||||
−0.999976 | + | 0.00693560i | \(0.997792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −156.578 | −0.926497 | ||||||||
\(170\) | 78.5034 | − | 39.9548i | 0.461785 | − | 0.235028i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.3795 | − | 11.9230i | −0.0952296 | − | 0.0693200i | ||||
\(173\) | 103.387 | 0.597612 | 0.298806 | − | 0.954314i | \(-0.403412\pi\) | ||||
0.298806 | + | 0.954314i | \(0.403412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.5839i | 0.0833366i | ||||||||
\(176\) | 231.257 | − | 74.6778i | 1.31396 | − | 0.424306i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.18606 | − | 1.62156i | 0.0178992 | − | 0.00910990i | ||||
\(179\) | 261.074i | 1.45851i | 0.684240 | + | 0.729257i | \(0.260134\pi\) | ||||
−0.684240 | + | 0.729257i | \(0.739866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 41.3242 | 0.228310 | 0.114155 | − | 0.993463i | \(-0.463584\pi\) | ||||
0.114155 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(182\) | −3.50855 | − | 6.89362i | −0.0192777 | − | 0.0378770i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 31.6404 | + | 5.05536i | 0.171959 | + | 0.0274748i | ||||
\(185\) | 192.902 | 1.04271 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 195.488i | − | 1.04539i | ||||||
\(188\) | 104.511 | + | 76.0763i | 0.555910 | + | 0.404661i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.5313 | − | 26.5865i | −0.0712176 | − | 0.139929i | ||||
\(191\) | 204.518i | 1.07077i | 0.844607 | + | 0.535387i | \(0.179834\pi\) | ||||
−0.844607 | + | 0.535387i | \(0.820166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 74.7204 | 0.387152 | 0.193576 | − | 0.981085i | \(-0.437991\pi\) | ||||
0.193576 | + | 0.981085i | \(0.437991\pi\) | |||||||
\(194\) | 203.654 | − | 103.651i | 1.04976 | − | 0.534282i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 112.515 | − | 154.569i | 0.574054 | − | 0.788617i | ||||
\(197\) | 241.437 | 1.22557 | 0.612784 | − | 0.790250i | \(-0.290049\pi\) | ||||
0.612784 | + | 0.790250i | \(0.290049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 41.2820i | 0.207447i | 0.994606 | + | 0.103724i | \(0.0330758\pi\) | ||||
−0.994606 | + | 0.103724i | \(0.966924\pi\) | |||||||
\(200\) | 16.7749 | − | 104.991i | 0.0838746 | − | 0.524953i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 253.685 | − | 129.114i | 1.25586 | − | 0.639180i | ||||
\(203\) | 47.1200i | 0.232118i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.74570 | 0.0280278 | ||||||||
\(206\) | −51.3408 | − | 100.875i | −0.249227 | − | 0.489683i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.3290 | + | 53.6634i | 0.0833127 | + | 0.257997i | ||||
\(209\) | −66.2051 | −0.316771 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.2564i | 0.0723051i | 0.999346 | + | 0.0361526i | \(0.0115102\pi\) | ||||
−0.999346 | + | 0.0361526i | \(0.988490\pi\) | |||||||
\(212\) | −163.312 | + | 224.353i | −0.770339 | + | 1.05827i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −173.149 | − | 340.204i | −0.809108 | − | 1.58974i | ||||
\(215\) | − | 17.3317i | − | 0.0806126i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 40.6010 | 0.187101 | ||||||||
\(218\) | 244.161 | − | 124.267i | 1.12001 | − | 0.570034i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 168.081 | + | 122.351i | 0.764006 | + | 0.556139i | ||||
\(221\) | 45.3630 | 0.205262 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 376.770i | 1.68955i | 0.535119 | + | 0.844776i | \(0.320267\pi\) | ||||
−0.535119 | + | 0.844776i | \(0.679733\pi\) | |||||||
\(224\) | 24.8859 | − | 24.7737i | 0.111098 | − | 0.110597i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −112.297 | + | 57.1544i | −0.496891 | + | 0.252896i | ||||
\(227\) | 10.7868i | 0.0475191i | 0.999718 | + | 0.0237596i | \(0.00756362\pi\) | ||||
−0.999718 | + | 0.0237596i | \(0.992436\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 409.128 | 1.78659 | 0.893293 | − | 0.449475i | \(-0.148389\pi\) | ||||
0.893293 | + | 0.449475i | \(0.148389\pi\) | |||||||
\(230\) | 12.4334 | + | 24.4292i | 0.0540583 | + | 0.106214i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 54.1990 | − | 339.220i | 0.233617 | − | 1.46216i | ||||
\(233\) | −136.723 | −0.586792 | −0.293396 | − | 0.955991i | \(-0.594785\pi\) | ||||
−0.293396 | + | 0.955991i | \(0.594785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 110.587i | 0.470582i | ||||||||
\(236\) | 104.352 | + | 75.9603i | 0.442169 | + | 0.321866i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.8125 | − | 25.1742i | −0.0538342 | − | 0.105774i | ||||
\(239\) | − | 252.663i | − | 1.05717i | −0.848882 | − | 0.528583i | \(-0.822724\pi\) | ||
0.848882 | − | 0.528583i | \(-0.177276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 352.816 | 1.46397 | 0.731983 | − | 0.681323i | \(-0.238595\pi\) | ||||
0.731983 | + | 0.681323i | \(0.238595\pi\) | |||||||
\(242\) | 195.514 | − | 99.5081i | 0.807910 | − | 0.411190i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −160.539 | + | 220.543i | −0.657947 | + | 0.903866i | ||||
\(245\) | 163.555 | 0.667571 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 15.3629i | − | 0.0621981i | ||||||
\(248\) | −292.290 | − | 46.7007i | −1.17859 | − | 0.188309i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 233.546 | − | 118.865i | 0.934184 | − | 0.475459i | ||||
\(251\) | − | 456.020i | − | 1.81681i | −0.418089 | − | 0.908406i | \(-0.637300\pi\) | ||
0.418089 | − | 0.908406i | \(-0.362700\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 60.8332 | 0.240447 | ||||||||
\(254\) | −119.397 | − | 234.592i | −0.470067 | − | 0.923591i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −207.651 | + | 149.723i | −0.811138 | + | 0.584855i | ||||
\(257\) | 466.591 | 1.81553 | 0.907764 | − | 0.419480i | \(-0.137788\pi\) | ||||
0.907764 | + | 0.419480i | \(0.137788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 61.8590i | − | 0.238838i | ||||||
\(260\) | −28.3915 | + | 39.0034i | −0.109198 | + | 0.150013i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 114.575 | + | 225.118i | 0.437310 | + | 0.859229i | ||||
\(263\) | − | 254.295i | − | 0.966901i | −0.875372 | − | 0.483450i | \(-0.839383\pi\) | ||
0.875372 | − | 0.483450i | \(-0.160617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −237.395 | −0.895832 | ||||||||
\(266\) | −8.52564 | + | 4.33918i | −0.0320513 | + | 0.0163127i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 170.353 | + | 124.004i | 0.635646 | + | 0.462703i | ||||
\(269\) | −361.778 | −1.34490 | −0.672451 | − | 0.740142i | \(-0.734758\pi\) | ||||
−0.672451 | + | 0.740142i | \(0.734758\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 110.301i | − | 0.407016i | −0.979073 | − | 0.203508i | \(-0.934766\pi\) | ||
0.979073 | − | 0.203508i | \(-0.0652342\pi\) | |||||||
\(272\) | 63.2823 | + | 195.968i | 0.232655 | + | 0.720471i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −367.980 | + | 187.286i | −1.34299 | + | 0.683525i | ||||
\(275\) | − | 201.859i | − | 0.734034i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 395.836 | 1.42901 | 0.714505 | − | 0.699631i | \(-0.246652\pi\) | ||||
0.714505 | + | 0.699631i | \(0.246652\pi\) | |||||||
\(278\) | −153.418 | − | 301.436i | −0.551862 | − | 1.08430i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 29.6639 | + | 4.73956i | 0.105943 | + | 0.0169270i | ||||
\(281\) | −395.060 | −1.40591 | −0.702954 | − | 0.711235i | \(-0.748136\pi\) | ||||
−0.702954 | + | 0.711235i | \(0.748136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 253.450i | 0.895582i | 0.894138 | + | 0.447791i | \(0.147789\pi\) | ||||
−0.894138 | + | 0.447791i | \(0.852211\pi\) | |||||||
\(284\) | −11.0653 | − | 8.05470i | −0.0389623 | − | 0.0283616i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 48.5627 | + | 95.4163i | 0.169800 | + | 0.333623i | ||||
\(287\) | − | 1.84251i | − | 0.00641989i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −123.343 | −0.426793 | ||||||||
\(290\) | 261.909 | − | 133.300i | 0.903133 | − | 0.459655i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 69.8351 | − | 95.9372i | 0.239161 | − | 0.328552i | ||||
\(293\) | −187.619 | −0.640338 | −0.320169 | − | 0.947360i | \(-0.603740\pi\) | ||||
−0.320169 | + | 0.947360i | \(0.603740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 110.418i | 0.374299i | ||||||||
\(296\) | −71.1524 | + | 445.328i | −0.240380 | + | 1.50449i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.8785 | + | 14.6979i | −0.0969076 | + | 0.0493217i | ||||
\(299\) | 14.1164i | 0.0472120i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.55786 | −0.0184647 | ||||||||
\(302\) | 207.270 | + | 407.245i | 0.686324 | + | 1.34849i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 66.3678 | − | 21.4316i | 0.218315 | − | 0.0704986i | ||||
\(305\) | −233.365 | −0.765130 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 55.4720i | 0.180691i | 0.995911 | + | 0.0903453i | \(0.0287971\pi\) | ||||
−0.995911 | + | 0.0903453i | \(0.971203\pi\) | |||||||
\(308\) | 39.2349 | − | 53.8996i | 0.127386 | − | 0.174999i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −114.858 | − | 225.674i | −0.370510 | − | 0.727980i | ||||
\(311\) | − | 342.779i | − | 1.10218i | −0.834445 | − | 0.551091i | \(-0.814212\pi\) | ||
0.834445 | − | 0.551091i | \(-0.185788\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 227.749 | 0.727633 | 0.363817 | − | 0.931471i | \(-0.381473\pi\) | ||||
0.363817 | + | 0.931471i | \(0.381473\pi\) | |||||||
\(314\) | −38.3865 | + | 19.5370i | −0.122250 | + | 0.0622198i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 221.407 | + | 161.168i | 0.700656 | + | 0.510025i | ||||
\(317\) | 182.998 | 0.577280 | 0.288640 | − | 0.957438i | \(-0.406797\pi\) | ||||
0.288640 | + | 0.957438i | \(0.406797\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 652.199i | − | 2.04451i | ||||||
\(320\) | −208.101 | − | 68.2409i | −0.650316 | − | 0.213253i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.83387 | − | 3.98709i | 0.0243288 | − | 0.0123823i | ||||
\(323\) | − | 56.1024i | − | 0.173692i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 46.8416 | 0.144128 | ||||||||
\(326\) | 151.846 | + | 298.349i | 0.465787 | + | 0.915180i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.11932 | + | 13.2644i | −0.00646133 | + | 0.0404401i | ||||
\(329\) | 35.4626 | 0.107789 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 228.937i | 0.691653i | 0.938298 | + | 0.345826i | \(0.112401\pi\) | ||||
−0.938298 | + | 0.345826i | \(0.887599\pi\) | |||||||
\(332\) | −165.490 | − | 120.464i | −0.498464 | − | 0.362845i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.10146 | − | 4.12897i | −0.00629181 | − | 0.0123622i | ||||
\(335\) | 180.257i | 0.538079i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −301.984 | −0.896095 | −0.448048 | − | 0.894010i | \(-0.647881\pi\) | ||||
−0.448048 | + | 0.894010i | \(0.647881\pi\) | |||||||
\(338\) | 279.088 | − | 142.044i | 0.825705 | − | 0.420247i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −103.680 | + | 142.433i | −0.304942 | + | 0.418920i | ||||
\(341\) | −561.968 | −1.64800 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 106.218i | − | 0.309672i | ||||||
\(344\) | 40.0115 | + | 6.39285i | 0.116312 | + | 0.0185839i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −184.279 | + | 93.7901i | −0.532599 | + | 0.271070i | ||||
\(347\) | − | 45.9375i | − | 0.132385i | −0.997807 | − | 0.0661923i | \(-0.978915\pi\) | ||
0.997807 | − | 0.0661923i | \(-0.0210851\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 310.999 | 0.891116 | 0.445558 | − | 0.895253i | \(-0.353005\pi\) | ||||
0.445558 | + | 0.895253i | \(0.353005\pi\) | |||||||
\(350\) | −13.2302 | − | 25.9947i | −0.0378005 | − | 0.0742706i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −344.452 | + | 342.898i | −0.978558 | + | 0.974143i | ||||
\(353\) | 238.500 | 0.675637 | 0.337818 | − | 0.941211i | \(-0.390311\pi\) | ||||
0.337818 | + | 0.941211i | \(0.390311\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 11.7086i | − | 0.0329819i | ||||||
\(356\) | −4.20786 | + | 5.78062i | −0.0118198 | + | 0.0162377i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −236.840 | − | 465.344i | −0.661563 | − | 1.29984i | ||||
\(359\) | − | 530.898i | − | 1.47882i | −0.673253 | − | 0.739412i | \(-0.735104\pi\) | ||
0.673253 | − | 0.739412i | \(-0.264896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | −73.6572 | + | 37.4883i | −0.203473 | + | 0.103559i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.5074 | + | 9.10448i | 0.0343611 | + | 0.0250123i | ||||
\(365\) | 101.514 | 0.278122 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 338.362i | − | 0.921968i | −0.887408 | − | 0.460984i | \(-0.847496\pi\) | ||
0.887408 | − | 0.460984i | \(-0.152504\pi\) | |||||||
\(368\) | −60.9827 | + | 19.6926i | −0.165714 | + | 0.0535125i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −343.833 | + | 174.996i | −0.929278 | + | 0.472962i | ||||
\(371\) | 76.1270i | 0.205194i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 108.938 | 0.292060 | 0.146030 | − | 0.989280i | \(-0.453350\pi\) | ||||
0.146030 | + | 0.989280i | \(0.453350\pi\) | |||||||
\(374\) | 177.341 | + | 348.442i | 0.474175 | + | 0.931662i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −255.298 | − | 40.7903i | −0.678983 | − | 0.108485i | ||||
\(377\) | 151.343 | 0.401441 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 495.638i | − | 1.30775i | −0.756602 | − | 0.653876i | \(-0.773142\pi\) | ||
0.756602 | − | 0.653876i | \(-0.226858\pi\) | |||||||
\(380\) | 48.2372 | + | 35.1130i | 0.126940 | + | 0.0924028i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −185.533 | − | 364.537i | −0.485690 | − | 0.954286i | ||||
\(383\) | 69.6825i | 0.181939i | 0.995854 | + | 0.0909694i | \(0.0289965\pi\) | ||||
−0.995854 | + | 0.0909694i | \(0.971003\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 57.0331 | 0.148138 | ||||||||
\(386\) | −133.183 | + | 67.7845i | −0.345035 | + | 0.175608i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −268.968 | + | 369.499i | −0.693216 | + | 0.952317i | ||||
\(389\) | −276.727 | −0.711381 | −0.355690 | − | 0.934604i | \(-0.615754\pi\) | ||||
−0.355690 | + | 0.934604i | \(0.615754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51.5502i | 0.131842i | ||||||||
\(392\) | −60.3276 | + | 377.578i | −0.153897 | + | 0.963209i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −430.343 | + | 219.026i | −1.09224 | + | 0.555903i | ||||
\(395\) | 234.279i | 0.593111i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −455.070 | −1.14627 | −0.573136 | − | 0.819460i | \(-0.694273\pi\) | ||||
−0.573136 | + | 0.819460i | \(0.694273\pi\) | |||||||
\(398\) | −37.4500 | − | 73.5820i | −0.0940955 | − | 0.184880i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 65.3449 | + | 202.356i | 0.163362 | + | 0.505889i | ||||
\(401\) | 38.5054 | 0.0960235 | 0.0480117 | − | 0.998847i | \(-0.484712\pi\) | ||||
0.0480117 | + | 0.998847i | \(0.484712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 130.405i | − | 0.323586i | ||||||
\(404\) | −335.044 | + | 460.273i | −0.829317 | + | 1.13929i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −42.7461 | − | 83.9878i | −0.105286 | − | 0.206866i | ||||
\(407\) | 856.205i | 2.10370i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −423.191 | −1.03470 | −0.517348 | − | 0.855775i | \(-0.673081\pi\) | ||||
−0.517348 | + | 0.855775i | \(0.673081\pi\) | |||||||
\(410\) | −10.2413 | + | 5.21236i | −0.0249787 | + | 0.0127131i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 183.022 | + | 133.226i | 0.444228 | + | 0.323365i | ||||
\(413\) | 35.4085 | 0.0857348 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 175.111i | − | 0.421954i | ||||||
\(416\) | −79.5698 | − | 79.9304i | −0.191273 | − | 0.192140i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 118.005 | − | 60.0596i | 0.282310 | − | 0.143683i | ||||
\(419\) | 782.531i | 1.86762i | 0.357775 | + | 0.933808i | \(0.383536\pi\) | ||||
−0.357775 | + | 0.933808i | \(0.616464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 735.211 | 1.74634 | 0.873172 | − | 0.487412i | \(-0.162059\pi\) | ||||
0.873172 | + | 0.487412i | \(0.162059\pi\) | |||||||
\(422\) | −13.8402 | − | 27.1933i | −0.0327967 | − | 0.0644392i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 87.5639 | − | 548.044i | 0.206519 | − | 1.29256i | ||||
\(425\) | 171.056 | 0.402485 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 74.8344i | 0.175256i | ||||||||
\(428\) | 617.250 | + | 449.312i | 1.44217 | + | 1.04979i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.7229 | + | 30.8924i | 0.0365649 | + | 0.0718429i | ||||
\(431\) | 225.461i | 0.523111i | 0.965188 | + | 0.261555i | \(0.0842354\pi\) | ||||
−0.965188 | + | 0.261555i | \(0.915765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −213.659 | −0.493438 | −0.246719 | − | 0.969087i | \(-0.579352\pi\) | ||||
−0.246719 | + | 0.969087i | \(0.579352\pi\) | |||||||
\(434\) | −72.3682 | + | 36.8322i | −0.166747 | + | 0.0848669i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −322.467 | + | 442.994i | −0.739602 | + | 1.01604i | ||||
\(437\) | 17.4583 | 0.0399504 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 641.592i | − | 1.46149i | −0.682653 | − | 0.730743i | \(-0.739174\pi\) | ||
0.682653 | − | 0.730743i | \(-0.260826\pi\) | |||||||
\(440\) | −410.586 | − | 65.6014i | −0.933149 | − | 0.149094i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −80.8561 | + | 41.1522i | −0.182932 | + | 0.0931045i | ||||
\(443\) | − | 831.547i | − | 1.87708i | −0.345168 | − | 0.938541i | \(-0.612178\pi\) | ||
0.345168 | − | 0.938541i | \(-0.387822\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.11668 | −0.0137453 | ||||||||
\(446\) | −341.797 | − | 671.564i | −0.766360 | − | 1.50575i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.8832 | + | 66.7331i | −0.0488465 | + | 0.148958i | ||||
\(449\) | 222.733 | 0.496065 | 0.248032 | − | 0.968752i | \(-0.420216\pi\) | ||||
0.248032 | + | 0.968752i | \(0.420216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.5026i | 0.0565468i | ||||||||
\(452\) | 148.312 | − | 203.747i | 0.328125 | − | 0.450767i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.78555 | − | 19.2267i | −0.0215541 | − | 0.0423496i | ||||
\(455\) | 13.2346i | 0.0290869i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −625.280 | −1.36823 | −0.684114 | − | 0.729376i | \(-0.739811\pi\) | ||||
−0.684114 | + | 0.729376i | \(0.739811\pi\) | |||||||
\(458\) | −729.240 | + | 371.151i | −1.59223 | + | 0.810373i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −44.3232 | − | 32.2640i | −0.0963548 | − | 0.0701391i | ||||
\(461\) | 38.6449 | 0.0838284 | 0.0419142 | − | 0.999121i | \(-0.486654\pi\) | ||||
0.0419142 | + | 0.999121i | \(0.486654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 129.791i | 0.280327i | 0.990128 | + | 0.140163i | \(0.0447628\pi\) | ||||
−0.990128 | + | 0.140163i | \(0.955237\pi\) | |||||||
\(464\) | 211.127 | + | 653.803i | 0.455014 | + | 1.40906i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 243.698 | − | 124.031i | 0.522956 | − | 0.266162i | ||||
\(467\) | 560.733i | 1.20071i | 0.799732 | + | 0.600357i | \(0.204975\pi\) | ||||
−0.799732 | + | 0.600357i | \(0.795025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 57.8039 | 0.123249 | ||||||||
\(470\) | −100.322 | − | 197.113i | −0.213450 | − | 0.419389i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −254.908 | − | 40.7281i | −0.540060 | − | 0.0862883i | ||||
\(473\) | 76.9277 | 0.162638 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 57.9310i | − | 0.121960i | ||||||
\(476\) | 45.6747 | + | 33.2478i | 0.0959553 | + | 0.0698483i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 229.209 | + | 450.352i | 0.479517 | + | 0.942158i | ||||
\(479\) | − | 216.834i | − | 0.452681i | −0.974048 | − | 0.226341i | \(-0.927324\pi\) | ||
0.974048 | − | 0.226341i | \(-0.0726763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −198.683 | −0.413062 | ||||||||
\(482\) | −628.867 | + | 320.066i | −1.30470 | + | 0.664037i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −258.218 | + | 354.731i | −0.533508 | + | 0.732915i | ||||
\(485\) | −390.980 | −0.806144 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 494.674i | 1.01576i | 0.861428 | + | 0.507879i | \(0.169570\pi\) | ||||
−0.861428 | + | 0.507879i | \(0.830430\pi\) | |||||||
\(488\) | 86.0771 | − | 538.739i | 0.176388 | − | 1.10397i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −291.524 | + | 148.373i | −0.594947 | + | 0.302802i | ||||
\(491\) | − | 253.258i | − | 0.515801i | −0.966171 | − | 0.257901i | \(-0.916969\pi\) | ||
0.966171 | − | 0.257901i | \(-0.0830307\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 552.676 | 1.12105 | ||||||||
\(494\) | 13.9369 | + | 27.3832i | 0.0282123 | + | 0.0554317i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 563.350 | − | 181.918i | 1.13579 | − | 0.366769i | ||||
\(497\) | −3.75466 | −0.00755464 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 137.797i | 0.276147i | 0.990422 | + | 0.138073i | \(0.0440910\pi\) | ||||
−0.990422 | + | 0.138073i | \(0.955909\pi\) | |||||||
\(500\) | −308.447 | + | 423.734i | −0.616894 | + | 0.847469i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 413.690 | + | 812.820i | 0.824083 | + | 1.61916i | ||||
\(503\) | − | 170.929i | − | 0.339818i | −0.985460 | − | 0.169909i | \(-0.945653\pi\) | ||
0.985460 | − | 0.169909i | \(-0.0543475\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −487.031 | −0.964417 | ||||||||
\(506\) | −108.430 | + | 55.1863i | −0.214289 | + | 0.109064i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 425.632 | + | 309.828i | 0.837858 | + | 0.609898i | ||||
\(509\) | 5.97470 | 0.0117381 | 0.00586906 | − | 0.999983i | \(-0.498132\pi\) | ||||
0.00586906 | + | 0.999983i | \(0.498132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 32.5532i | − | 0.0637050i | ||||||
\(512\) | 234.298 | − | 455.246i | 0.457613 | − | 0.889152i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −831.663 | + | 423.280i | −1.61802 | + | 0.823501i | ||||
\(515\) | 193.662i | 0.376043i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −490.846 | −0.949412 | ||||||||
\(518\) | 56.1170 | + | 110.259i | 0.108334 | + | 0.212855i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.2228 | − | 95.2766i | 0.0292747 | − | 0.183224i | ||||
\(521\) | 695.484 | 1.33490 | 0.667451 | − | 0.744654i | \(-0.267385\pi\) | ||||
0.667451 | + | 0.744654i | \(0.267385\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 622.889i | 1.19099i | 0.803358 | + | 0.595496i | \(0.203044\pi\) | ||||
−0.803358 | + | 0.595496i | \(0.796956\pi\) | |||||||
\(524\) | −408.443 | − | 297.316i | −0.779471 | − | 0.567396i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 230.690 | + | 453.261i | 0.438574 | + | 0.861713i | ||||
\(527\) | − | 476.214i | − | 0.903631i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 512.958 | 0.969675 | ||||||||
\(530\) | 423.139 | − | 215.359i | 0.798376 | − | 0.406338i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.2599 | − | 15.4685i | 0.0211652 | − | 0.0290761i | ||||
\(533\) | −5.91789 | −0.0111030 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 653.133i | 1.22081i | ||||||||
\(536\) | −416.135 | − | 66.4881i | −0.776371 | − | 0.124045i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 644.842 | − | 328.196i | 1.19859 | − | 0.610031i | ||||
\(539\) | 725.947i | 1.34684i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −960.900 | −1.77615 | −0.888077 | − | 0.459694i | \(-0.847959\pi\) | ||||
−0.888077 | + | 0.459694i | \(0.847959\pi\) | |||||||
\(542\) | 100.063 | + | 196.603i | 0.184617 | + | 0.362737i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −290.573 | − | 291.890i | −0.534142 | − | 0.536563i | ||||
\(545\) | −468.747 | −0.860087 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 987.060i | − | 1.80450i | −0.431215 | − | 0.902249i | \(-0.641915\pi\) | ||
0.431215 | − | 0.902249i | \(-0.358085\pi\) | |||||||
\(548\) | 485.996 | − | 667.645i | 0.886853 | − | 1.21833i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 183.122 | + | 359.799i | 0.332949 | + | 0.654180i | ||||
\(551\) | − | 187.173i | − | 0.339696i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 75.1276 | 0.135855 | ||||||||
\(554\) | −705.547 | + | 359.092i | −1.27355 | + | 0.648181i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 546.910 | + | 398.110i | 0.983651 | + | 0.716025i | ||||
\(557\) | −75.4101 | −0.135386 | −0.0676931 | − | 0.997706i | \(-0.521564\pi\) | ||||
−0.0676931 | + | 0.997706i | \(0.521564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.8511i | 0.0319340i | ||||||||
\(560\) | −57.1733 | + | 18.4625i | −0.102095 | + | 0.0329687i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 704.165 | − | 358.389i | 1.25296 | − | 0.637703i | ||||
\(563\) | − | 825.440i | − | 1.46615i | −0.680150 | − | 0.733073i | \(-0.738086\pi\) | ||
0.680150 | − | 0.733073i | \(-0.261914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 215.591 | 0.381578 | ||||||||
\(566\) | −229.923 | − | 451.755i | −0.406225 | − | 0.798153i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.0301 | + | 4.31873i | 0.0475881 | + | 0.00760341i | ||||
\(569\) | −929.541 | −1.63364 | −0.816820 | − | 0.576893i | \(-0.804265\pi\) | ||||
−0.816820 | + | 0.576893i | \(0.804265\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 443.030i | − | 0.775885i | −0.921684 | − | 0.387942i | \(-0.873186\pi\) | ||
0.921684 | − | 0.387942i | \(-0.126814\pi\) | |||||||
\(572\) | −173.119 | − | 126.017i | −0.302655 | − | 0.220310i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.67148 | + | 3.28413i | 0.00291198 | + | 0.00572148i | ||||
\(575\) | 53.2305i | 0.0925748i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 744.989 | 1.29114 | 0.645571 | − | 0.763700i | \(-0.276620\pi\) | ||||
0.645571 | + | 0.763700i | \(0.276620\pi\) | |||||||
\(578\) | 219.850 | − | 111.894i | 0.380363 | − | 0.193588i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −345.906 | + | 475.194i | −0.596389 | + | 0.819300i | ||||
\(581\) | −56.1538 | −0.0966503 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1053.69i | − | 1.80736i | ||||||
\(584\) | −37.4439 | + | 234.353i | −0.0641162 | + | 0.401290i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 334.417 | − | 170.203i | 0.570677 | − | 0.290450i | ||||
\(587\) | 509.617i | 0.868172i | 0.900871 | + | 0.434086i | \(0.142929\pi\) | ||||
−0.900871 | + | 0.434086i | \(0.857071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −161.278 | −0.273816 | ||||||||
\(590\) | −100.169 | − | 196.812i | −0.169777 | − | 0.333580i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −277.167 | − | 858.310i | −0.468187 | − | 1.44985i | ||||
\(593\) | 1087.55 | 1.83399 | 0.916994 | − | 0.398902i | \(-0.130608\pi\) | ||||
0.916994 | + | 0.398902i | \(0.130608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.3300i | 0.0812269i | ||||||||
\(596\) | 38.1401 | − | 52.3957i | 0.0639935 | − | 0.0879122i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.8060 | − | 25.1614i | −0.0214148 | − | 0.0420758i | ||||
\(599\) | − | 898.934i | − | 1.50073i | −0.661027 | − | 0.750363i | \(-0.729879\pi\) | ||
0.661027 | − | 0.750363i | \(-0.270121\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 188.733 | 0.314032 | 0.157016 | − | 0.987596i | \(-0.449813\pi\) | ||||
0.157016 | + | 0.987596i | \(0.449813\pi\) | |||||||
\(602\) | 9.90646 | − | 5.04195i | 0.0164559 | − | 0.00837534i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −738.885 | − | 537.853i | −1.22332 | − | 0.890486i | ||||
\(605\) | −375.353 | −0.620419 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1073.94i | − | 1.76925i | −0.466300 | − | 0.884626i | \(-0.654413\pi\) | ||
0.466300 | − | 0.884626i | \(-0.345587\pi\) | |||||||
\(608\) | −98.8534 | + | 98.4074i | −0.162588 | + | 0.161854i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 415.955 | − | 211.703i | 0.681893 | − | 0.347053i | ||||
\(611\) | − | 113.901i | − | 0.186417i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 520.604 | 0.849272 | 0.424636 | − | 0.905364i | \(-0.360402\pi\) | ||||
0.424636 | + | 0.905364i | \(0.360402\pi\) | |||||||
\(614\) | −50.3228 | − | 98.8746i | −0.0819590 | − | 0.161034i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.0368 | + | 131.665i | −0.0341506 | + | 0.213742i | ||||
\(617\) | 972.303 | 1.57586 | 0.787928 | − | 0.615767i | \(-0.211154\pi\) | ||||
0.787928 | + | 0.615767i | \(0.211154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1216.61i | 1.96544i | 0.185106 | + | 0.982718i | \(0.440737\pi\) | ||||
−0.185106 | + | 0.982718i | \(0.559263\pi\) | |||||||
\(620\) | 409.451 | + | 298.050i | 0.660405 | + | 0.480726i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 310.960 | + | 610.977i | 0.499936 | + | 0.982278i | ||||
\(623\) | 1.96147i | 0.00314843i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −116.111 | −0.185777 | ||||||||
\(626\) | −405.945 | + | 206.608i | −0.648475 | + | 0.330045i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 50.6974 | − | 69.6465i | 0.0807284 | − | 0.110902i | ||||
\(629\) | −725.551 | −1.15350 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 118.157i | − | 0.187254i | −0.995607 | − | 0.0936268i | \(-0.970154\pi\) | ||
0.995607 | − | 0.0936268i | \(-0.0298461\pi\) | |||||||
\(632\) | −540.849 | − | 86.4144i | −0.855774 | − | 0.136732i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −326.180 | + | 166.011i | −0.514479 | + | 0.261847i | ||||
\(635\) | 450.376i | 0.709254i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −168.456 | −0.264453 | ||||||||
\(638\) | 591.659 | + | 1162.50i | 0.927365 | + | 1.82209i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 432.831 | − | 67.1500i | 0.676298 | − | 0.104922i | ||||
\(641\) | −1009.00 | −1.57411 | −0.787055 | − | 0.616883i | \(-0.788395\pi\) | ||||
−0.787055 | + | 0.616883i | \(0.788395\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 596.414i | − | 0.927550i | −0.885953 | − | 0.463775i | \(-0.846495\pi\) | ||
0.885953 | − | 0.463775i | \(-0.153505\pi\) | |||||||
\(644\) | −10.3463 | + | 14.2134i | −0.0160656 | + | 0.0220705i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 50.8947 | + | 99.9982i | 0.0787844 | + | 0.154796i | ||||
\(647\) | − | 428.660i | − | 0.662535i | −0.943537 | − | 0.331267i | \(-0.892524\pi\) | ||
0.943537 | − | 0.331267i | \(-0.107476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −490.097 | −0.755158 | ||||||||
\(650\) | −83.4916 | + | 42.4935i | −0.128449 | + | 0.0653747i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −541.309 | − | 394.033i | −0.830229 | − | 0.604344i | ||||
\(653\) | 710.928 | 1.08871 | 0.544355 | − | 0.838855i | \(-0.316774\pi\) | ||||
0.544355 | + | 0.838855i | \(0.316774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 432.187i | − | 0.659828i | ||||||
\(656\) | −8.25557 | − | 25.5653i | −0.0125847 | − | 0.0389715i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −63.2093 | + | 32.1707i | −0.0960627 | + | 0.0488917i | ||||
\(659\) | 882.670i | 1.33941i | 0.742628 | + | 0.669704i | \(0.233579\pi\) | ||||
−0.742628 | + | 0.669704i | \(0.766421\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 982.979 | 1.48711 | 0.743555 | − | 0.668675i | \(-0.233138\pi\) | ||||
0.743555 | + | 0.668675i | \(0.233138\pi\) | |||||||
\(662\) | −207.686 | − | 408.063i | −0.313725 | − | 0.616409i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 404.256 | + | 64.5901i | 0.608819 | + | 0.0972742i | ||||
\(665\) | 16.3678 | 0.0246132 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 171.986i | 0.257849i | ||||||||
\(668\) | 7.49139 | + | 5.45317i | 0.0112147 | + | 0.00816343i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −163.524 | − | 321.294i | −0.244066 | − | 0.479543i | ||||
\(671\) | − | 1035.80i | − | 1.54367i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1277.40 | 1.89807 | 0.949035 | − | 0.315170i | \(-0.102061\pi\) | ||||
0.949035 | + | 0.315170i | \(0.102061\pi\) | |||||||
\(674\) | 538.264 | − | 273.953i | 0.798611 | − | 0.406458i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −368.595 | + | 506.364i | −0.545259 | + | 0.749059i | ||||
\(677\) | 1157.24 | 1.70937 | 0.854685 | − | 0.519147i | \(-0.173750\pi\) | ||||
0.854685 | + | 0.519147i | \(0.173750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 125.378i | 0.184651i | ||||||||
\(680\) | 55.5909 | − | 347.932i | 0.0817513 | − | 0.511664i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1001.67 | − | 509.804i | 1.46872 | − | 0.747513i | ||||
\(683\) | 1193.34i | 1.74720i | 0.486647 | + | 0.873599i | \(0.338220\pi\) | ||||
−0.486647 | + | 0.873599i | \(0.661780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 706.458 | 1.03133 | ||||||||
\(686\) | 96.3579 | + | 189.325i | 0.140463 | + | 0.275983i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −77.1168 | + | 24.9027i | −0.112088 | + | 0.0361957i | ||||
\(689\) | 244.510 | 0.354876 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 864.424i | 1.25098i | 0.780234 | + | 0.625488i | \(0.215100\pi\) | ||||
−0.780234 | + | 0.625488i | \(0.784900\pi\) | |||||||
\(692\) | 243.380 | − | 334.347i | 0.351705 | − | 0.483161i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 41.6733 | + | 81.8800i | 0.0600480 | + | 0.117983i | ||||
\(695\) | 578.705i | 0.832669i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.6110 | −0.0310057 | ||||||||
\(698\) | −554.333 | + | 282.131i | −0.794173 | + | 0.404199i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 47.1635 | + | 34.3315i | 0.0673764 | + | 0.0490450i | ||||
\(701\) | 459.736 | 0.655828 | 0.327914 | − | 0.944708i | \(-0.393654\pi\) | ||||
0.327914 | + | 0.944708i | \(0.393654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 245.720i | 0.349530i | ||||||||
\(704\) | 302.891 | − | 923.668i | 0.430243 | − | 1.31203i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −425.107 | + | 216.361i | −0.602135 | + | 0.306460i | ||||
\(707\) | 156.179i | 0.220904i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1008.64 | −1.42262 | −0.711310 | − | 0.702878i | \(-0.751898\pi\) | ||||
−0.711310 | + | 0.702878i | \(0.751898\pi\) | |||||||
\(710\) | 10.6217 | + | 20.8696i | 0.0149602 | + | 0.0293938i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.25615 | − | 14.1208i | 0.00316875 | − | 0.0198326i | ||||
\(713\) | 148.192 | 0.207842 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 183.183i | − | 0.256200i | ||||||
\(716\) | 844.297 | + | 614.585i | 1.17919 | + | 0.858359i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 481.617 | + | 946.285i | 0.670776 | + | 1.31795i | ||||
\(719\) | − | 404.053i | − | 0.561965i | −0.959713 | − | 0.280983i | \(-0.909340\pi\) | ||
0.959713 | − | 0.280983i | \(-0.0906603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 62.1027 | 0.0861341 | ||||||||
\(722\) | 33.8660 | − | 17.2363i | 0.0469059 | − | 0.0238730i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 97.2799 | − | 133.640i | 0.134364 | − | 0.184586i | ||||
\(725\) | 570.690 | 0.787159 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 256.630i | − | 0.352999i | −0.984301 | − | 0.176500i | \(-0.943523\pi\) | ||
0.984301 | − | 0.176500i | \(-0.0564774\pi\) | |||||||
\(728\) | −30.5529 | − | 4.88160i | −0.0419683 | − | 0.00670550i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −180.942 | + | 92.0914i | −0.247865 | + | 0.126153i | ||||
\(731\) | 65.1888i | 0.0891776i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −204.399 | −0.278852 | −0.139426 | − | 0.990232i | \(-0.544526\pi\) | ||||
−0.139426 | + | 0.990232i | \(0.544526\pi\) | |||||||
\(734\) | 306.954 | + | 603.105i | 0.418193 | + | 0.821669i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 90.8324 | − | 90.4226i | 0.123414 | − | 0.122857i | ||||
\(737\) | −800.078 | −1.08559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1459.41i | 1.97485i | 0.158100 | + | 0.987423i | \(0.449463\pi\) | ||||
−0.158100 | + | 0.987423i | \(0.550537\pi\) | |||||||
\(740\) | 454.104 | − | 623.833i | 0.613654 | − | 0.843018i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −69.0605 | − | 135.691i | −0.0930735 | − | 0.182871i | ||||
\(743\) | − | 1022.36i | − | 1.37599i | −0.725717 | − | 0.687993i | \(-0.758492\pi\) | ||
0.725717 | − | 0.687993i | \(-0.241508\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.4417 | 0.0744183 | ||||||||
\(746\) | −194.174 | + | 98.8261i | −0.260287 | + | 0.132475i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −632.195 | − | 460.191i | −0.845180 | − | 0.615228i | ||||
\(749\) | 209.444 | 0.279632 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 299.399i | 0.398667i | 0.979932 | + | 0.199334i | \(0.0638777\pi\) | ||||
−0.979932 | + | 0.199334i | \(0.936122\pi\) | |||||||
\(752\) | 492.052 | − | 158.894i | 0.654325 | − | 0.211295i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −269.758 | + | 137.295i | −0.357769 | + | 0.182089i | ||||
\(755\) | − | 781.840i | − | 1.03555i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −931.935 | −1.23109 | −0.615545 | − | 0.788102i | \(-0.711064\pi\) | ||||
−0.615545 | + | 0.788102i | \(0.711064\pi\) | |||||||
\(758\) | 449.631 | + | 883.437i | 0.593180 | + | 1.16548i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −117.833 | − | 18.8268i | −0.155043 | − | 0.0247721i | ||||
\(761\) | 119.523 | 0.157060 | 0.0785300 | − | 0.996912i | \(-0.474977\pi\) | ||||
0.0785300 | + | 0.996912i | \(0.474977\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 150.316i | 0.197007i | ||||||||
\(764\) | 661.398 | + | 481.449i | 0.865705 | + | 0.630168i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −63.2143 | − | 124.204i | −0.0825251 | − | 0.162146i | ||||
\(767\) | − | 113.727i | − | 0.148276i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −219.147 | −0.284977 | −0.142489 | − | 0.989796i | \(-0.545510\pi\) | ||||
−0.142489 | + | 0.989796i | \(0.545510\pi\) | |||||||
\(770\) | −101.657 | + | 51.7390i | −0.132022 | + | 0.0671935i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 175.897 | − | 241.641i | 0.227846 | − | 0.313007i | ||||
\(773\) | 908.079 | 1.17475 | 0.587373 | − | 0.809316i | \(-0.300162\pi\) | ||||
0.587373 | + | 0.809316i | \(0.300162\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 491.736i | − | 0.634498i | ||||||
\(776\) | 144.214 | − | 902.605i | 0.185843 | − | 1.16315i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 493.245 | − | 251.040i | 0.633991 | − | 0.322673i | ||||
\(779\) | 7.31892i | 0.00939527i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.9691 | 0.0665417 | ||||||||
\(782\) | −46.7651 | − | 91.8843i | −0.0598019 | − | 0.117499i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −235.000 | − | 727.731i | −0.299745 | − | 0.928229i | ||||
\(785\) | 73.6954 | 0.0938794 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 276.800i | − | 0.351715i | −0.984416 | − | 0.175857i | \(-0.943730\pi\) | ||
0.984416 | − | 0.175857i | \(-0.0562698\pi\) | |||||||
\(788\) | 568.359 | − | 780.793i | 0.721267 | − | 0.990854i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −212.532 | − | 417.584i | −0.269028 | − | 0.528588i | ||||
\(791\) | − | 69.1350i | − | 0.0874020i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 240.358 | 0.303100 | ||||||||
\(794\) | 811.128 | − | 412.828i | 1.02157 | − | 0.519935i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 133.504 | + | 97.1806i | 0.167718 | + | 0.122086i | ||||
\(797\) | −669.972 | −0.840617 | −0.420309 | − | 0.907381i | \(-0.638078\pi\) | ||||
−0.420309 | + | 0.907381i | \(0.638078\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 415.944i | − | 0.520581i | ||||||
\(800\) | −300.044 | − | 301.404i | −0.375055 | − | 0.376755i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −68.6329 | + | 34.9312i | −0.0855772 | + | 0.0435551i | ||||
\(803\) | 450.577i | 0.561117i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.0397 | −0.0186828 | ||||||||
\(806\) | 118.300 | + | 232.437i | 0.146774 | + | 0.288383i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 179.643 | − | 1124.35i | 0.222330 | − | 1.39152i | ||||
\(809\) | 192.312 | 0.237716 | 0.118858 | − | 0.992911i | \(-0.462077\pi\) | ||||
0.118858 | + | 0.992911i | \(0.462077\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 973.092i | 1.19987i | 0.800050 | + | 0.599934i | \(0.204806\pi\) | ||||
−0.800050 | + | 0.599934i | \(0.795194\pi\) | |||||||
\(812\) | 152.383 | + | 110.924i | 0.187664 | + | 0.136605i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −776.728 | − | 1526.12i | −0.954212 | − | 1.87484i | ||||
\(815\) | − | 572.778i | − | 0.702795i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.0773 | 0.0270224 | ||||||||
\(818\) | 754.305 | − | 383.908i | 0.922134 | − | 0.469326i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5258 | − | 18.5813i | 0.0164948 | − | 0.0226601i | ||||
\(821\) | −1069.44 | −1.30261 | −0.651306 | − | 0.758815i | \(-0.725779\pi\) | ||||
−0.651306 | + | 0.758815i | \(0.725779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 82.3572i | − | 0.100069i | −0.998747 | − | 0.0500347i | \(-0.984067\pi\) | ||
0.998747 | − | 0.0500347i | \(-0.0159332\pi\) | |||||||
\(824\) | −447.082 | − | 71.4327i | −0.542576 | − | 0.0866902i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −63.1129 | + | 32.1217i | −0.0764079 | + | 0.0388882i | ||||
\(827\) | 1243.38i | 1.50348i | 0.659458 | + | 0.751741i | \(0.270786\pi\) | ||||
−0.659458 | + | 0.751741i | \(0.729214\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −991.491 | −1.19601 | −0.598004 | − | 0.801493i | \(-0.704039\pi\) | ||||
−0.598004 | + | 0.801493i | \(0.704039\pi\) | |||||||
\(830\) | 158.856 | + | 312.122i | 0.191393 | + | 0.376050i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 214.338 | + | 70.2860i | 0.257618 | + | 0.0844784i | ||||
\(833\) | −615.170 | −0.738499 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.92690i | 0.00949330i | ||||||||
\(836\) | −155.851 | + | 214.103i | −0.186425 | + | 0.256104i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −709.893 | − | 1394.80i | −0.847127 | − | 1.66444i | ||||
\(839\) | − | 518.848i | − | 0.618412i | −0.950995 | − | 0.309206i | \(-0.899937\pi\) | ||
0.950995 | − | 0.309206i | \(-0.100063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1002.88 | 1.19248 | ||||||||
\(842\) | −1310.46 | + | 666.965i | −1.55636 | + | 0.792120i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 49.3382 | + | 35.9145i | 0.0584576 | + | 0.0425528i | ||||
\(845\) | −535.801 | −0.634084 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 120.367i | 0.142110i | ||||||||
\(848\) | 341.096 | + | 1056.28i | 0.402236 | + | 1.24562i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −304.895 | + | 155.178i | −0.358700 | + | 0.182562i | ||||
\(851\) | − | 225.782i | − | 0.265314i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −682.035 | −0.799572 | −0.399786 | − | 0.916609i | \(-0.630916\pi\) | ||||
−0.399786 | + | 0.916609i | \(0.630916\pi\) | |||||||
\(854\) | −67.8879 | − | 133.387i | −0.0794941 | − | 0.156190i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1507.80 | − | 240.910i | −1.76145 | − | 0.281437i | ||||
\(857\) | −257.918 | −0.300955 | −0.150477 | − | 0.988613i | \(-0.548081\pi\) | ||||
−0.150477 | + | 0.988613i | \(0.548081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 800.297i | 0.931661i | 0.884874 | + | 0.465831i | \(0.154244\pi\) | ||||
−0.884874 | + | 0.465831i | \(0.845756\pi\) | |||||||
\(860\) | −56.0497 | − | 40.8000i | −0.0651741 | − | 0.0474419i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −204.532 | − | 401.867i | −0.237277 | − | 0.466202i | ||||
\(863\) | − | 97.9073i | − | 0.113450i | −0.998390 | − | 0.0567250i | \(-0.981934\pi\) | ||
0.998390 | − | 0.0567250i | \(-0.0180658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 353.784 | 0.408999 | ||||||||
\(866\) | 380.830 | − | 193.826i | 0.439757 | − | 0.223817i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 95.5774 | − | 131.301i | 0.110112 | − | 0.151269i | ||||
\(869\) | −1039.86 | −1.19662 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 185.659i | − | 0.213156i | ||||||
\(872\) | 172.899 | − | 1082.14i | 0.198278 | − | 1.24098i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −31.1181 | + | 15.8378i | −0.0356043 | + | 0.0181210i | ||||
\(875\) | 143.781i | 0.164321i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −286.418 | −0.326588 | −0.163294 | − | 0.986577i | \(-0.552212\pi\) | ||||
−0.163294 | + | 0.986577i | \(0.552212\pi\) | |||||||
\(878\) | 582.037 | + | 1143.59i | 0.662912 | + | 1.30249i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 791.349 | − | 255.543i | 0.899260 | − | 0.290390i | ||||
\(881\) | −401.330 | −0.455539 | −0.227770 | − | 0.973715i | \(-0.573143\pi\) | ||||
−0.227770 | + | 0.973715i | \(0.573143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 675.471i | − | 0.764973i | −0.923961 | − | 0.382486i | \(-0.875068\pi\) | ||
0.923961 | − | 0.382486i | \(-0.124932\pi\) | |||||||
\(884\) | 106.788 | − | 146.701i | 0.120800 | − | 0.165952i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 754.359 | + | 1482.17i | 0.851421 | + | 1.67288i | ||||
\(887\) | 906.749i | 1.02227i | 0.859502 | + | 0.511133i | \(0.170774\pi\) | ||||
−0.859502 | + | 0.511133i | \(0.829226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 144.425 | 0.162458 | ||||||||
\(890\) | 10.9025 | − | 5.54890i | 0.0122500 | − | 0.00623471i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1218.45 | + | 886.942i | 1.36598 | + | 0.994330i | ||||
\(893\) | −140.866 | −0.157745 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 893.380i | 0.998190i | ||||||||
\(896\) | −21.5334 | − | 138.798i | −0.0240328 | − | 0.154909i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −397.004 | + | 202.058i | −0.442098 | + | 0.225009i | ||||
\(899\) | − | 1588.78i | − | 1.76727i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 892.902 | 0.991012 | ||||||||
\(902\) | −23.1353 | − | 45.4564i | −0.0256489 | − | 0.0503951i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −79.5214 | + | 497.708i | −0.0879662 | + | 0.550562i | ||||
\(905\) | 141.409 | 0.156253 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 114.996i | − | 0.126787i | −0.997989 | − | 0.0633935i | \(-0.979808\pi\) | ||
0.997989 | − | 0.0633935i | \(-0.0201923\pi\) | |||||||
\(908\) | 34.8840 | + | 25.3929i | 0.0384185 | + | 0.0279658i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.0061 | − | 23.5896i | −0.0131935 | − | 0.0259226i | ||||
\(911\) | 522.402i | 0.573439i | 0.958015 | + | 0.286719i | \(0.0925647\pi\) | ||||
−0.958015 | + | 0.286719i | \(0.907435\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 777.239 | 0.851302 | ||||||||
\(914\) | 1114.51 | − | 567.238i | 1.21938 | − | 0.620611i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 963.115 | − | 1323.10i | 1.05144 | − | 1.44443i | ||||
\(917\) | −138.592 | −0.151136 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1145.11i | 1.24604i | 0.782206 | + | 0.623020i | \(0.214095\pi\) | ||||
−0.782206 | + | 0.623020i | \(0.785905\pi\) | |||||||
\(920\) | 108.272 | + | 17.2992i | 0.117687 | + | 0.0188034i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −68.8816 | + | 35.0577i | −0.0747088 | + | 0.0380235i | ||||
\(923\) | 12.0595i | 0.0130655i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −749.201 | −0.809947 | ||||||||
\(926\) | −117.743 | − | 231.343i | −0.127153 | − | 0.249830i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −969.431 | − | 973.824i | −1.04465 | − | 1.04938i | ||||
\(929\) | −854.884 | −0.920220 | −0.460110 | − | 0.887862i | \(-0.652190\pi\) | ||||
−0.460110 | + | 0.887862i | \(0.652190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 208.337i | 0.223778i | ||||||||
\(932\) | −321.854 | + | 442.153i | −0.345337 | + | 0.474413i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −508.683 | − | 999.464i | −0.544629 | − | 1.07009i | ||||
\(935\) | − | 668.947i | − | 0.715452i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1305.11 | −1.39286 | −0.696432 | − | 0.717623i | \(-0.745230\pi\) | ||||
−0.696432 | + | 0.717623i | \(0.745230\pi\) | |||||||
\(938\) | −103.031 | + | 52.4383i | −0.109841 | + | 0.0559044i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 357.631 | + | 260.329i | 0.380459 | + | 0.276946i | ||||
\(941\) | 1007.79 | 1.07098 | 0.535491 | − | 0.844541i | \(-0.320127\pi\) | ||||
0.535491 | + | 0.844541i | \(0.320127\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.72506i | − | 0.00713156i | ||||||
\(944\) | 491.302 | − | 158.652i | 0.520447 | − | 0.168063i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −137.118 | + | 69.7869i | −0.144945 | + | 0.0737705i | ||||
\(947\) | 1192.09i | 1.25880i | 0.777080 | + | 0.629401i | \(0.216700\pi\) | ||||
−0.777080 | + | 0.629401i | \(0.783300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −104.557 | −0.110176 | ||||||||
\(950\) | 52.5536 | + | 103.258i | 0.0553196 | + | 0.108692i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −111.573 | − | 17.8267i | −0.117199 | − | 0.0187255i | ||||
\(953\) | 728.571 | 0.764503 | 0.382251 | − | 0.924058i | \(-0.375149\pi\) | ||||
0.382251 | + | 0.924058i | \(0.375149\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 699.849i | 0.732826i | ||||||||
\(956\) | −817.096 | − | 594.784i | −0.854703 | − | 0.622159i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 196.707 | + | 386.491i | 0.205331 | + | 0.403435i | ||||
\(959\) | − | 226.544i | − | 0.236230i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −407.972 | −0.424529 | ||||||||
\(962\) | 354.137 | − | 180.240i | 0.368126 | − | 0.187360i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 830.552 | − | 1140.99i | 0.861568 | − | 1.18359i | ||||
\(965\) | 255.689 | 0.264963 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 571.802i | 0.591315i | 0.955294 | + | 0.295657i | \(0.0955387\pi\) | ||||
−0.955294 | + | 0.295657i | \(0.904461\pi\) | |||||||
\(968\) | 138.450 | − | 866.530i | 0.143027 | − | 0.895175i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 696.892 | − | 354.687i | 0.718445 | − | 0.365657i | ||||
\(971\) | 456.799i | 0.470442i | 0.971942 | + | 0.235221i | \(0.0755814\pi\) | ||||
−0.971942 | + | 0.235221i | \(0.924419\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 185.577 | 0.190726 | ||||||||
\(974\) | −448.756 | − | 881.719i | −0.460735 | − | 0.905256i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 335.304 | + | 1038.35i | 0.343550 | + | 1.06388i | ||||
\(977\) | −565.223 | −0.578529 | −0.289264 | − | 0.957249i | \(-0.593411\pi\) | ||||
−0.289264 | + | 0.957249i | \(0.593411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 27.1492i | − | 0.0277316i | ||||||
\(980\) | 385.019 | − | 528.926i | 0.392876 | − | 0.539721i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 229.750 | + | 451.414i | 0.233961 | + | 0.459688i | ||||
\(983\) | 838.013i | 0.852506i | 0.904604 | + | 0.426253i | \(0.140167\pi\) | ||||
−0.904604 | + | 0.426253i | \(0.859833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 826.184 | 0.838766 | ||||||||
\(986\) | −985.102 | + | 501.374i | −0.999089 | + | 0.508493i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −49.6828 | − | 36.1653i | −0.0502862 | − | 0.0366046i | ||||
\(989\) | −20.2859 | −0.0205115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 993.095i | 1.00211i | 0.865414 | + | 0.501057i | \(0.167055\pi\) | ||||
−0.865414 | + | 0.501057i | \(0.832945\pi\) | |||||||
\(992\) | −839.097 | + | 835.311i | −0.845863 | + | 0.842047i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.69239 | − | 3.40613i | 0.00673278 | − | 0.00342669i | ||||
\(995\) | 141.265i | 0.141975i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −203.135 | −0.203746 | −0.101873 | − | 0.994797i | \(-0.532484\pi\) | ||||
−0.101873 | + | 0.994797i | \(0.532484\pi\) | |||||||
\(998\) | −125.006 | − | 245.613i | −0.125257 | − | 0.246105i | ||||
\(999\) | 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.c.343.8 | 36 | ||
3.2 | odd | 2 | 228.3.g.a.115.29 | ✓ | 36 | ||
4.3 | odd | 2 | inner | 684.3.g.c.343.7 | 36 | ||
12.11 | even | 2 | 228.3.g.a.115.30 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.g.a.115.29 | ✓ | 36 | 3.2 | odd | 2 | ||
228.3.g.a.115.30 | yes | 36 | 12.11 | even | 2 | ||
684.3.g.c.343.7 | 36 | 4.3 | odd | 2 | inner | ||
684.3.g.c.343.8 | 36 | 1.1 | even | 1 | trivial |