Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.796594176.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 83x^{4} - 104x^{3} + 22x^{2} + 24x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.3 | ||
Root | \(-0.207107 - 2.54762i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.67 |
Dual form | 392.3.k.i.275.3 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26663 | − | 1.54779i | 0.633316 | − | 0.773893i | ||||
\(3\) | −1.70711 | + | 2.95680i | −0.569036 | + | 0.985599i | 0.427626 | + | 0.903956i | \(0.359350\pi\) |
−0.996662 | + | 0.0816428i | \(0.973983\pi\) | |||||||
\(4\) | −0.791288 | − | 3.92095i | −0.197822 | − | 0.980238i | ||||
\(5\) | −1.34221 | + | 0.774923i | −0.268441 | + | 0.154985i | −0.628179 | − | 0.778069i | \(-0.716199\pi\) |
0.359738 | + | 0.933053i | \(0.382866\pi\) | |||||||
\(6\) | 2.41421 | + | 6.38741i | 0.402369 | + | 1.06457i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −7.07107 | − | 3.74166i | −0.883883 | − | 0.467707i | ||||
\(9\) | −1.32843 | − | 2.30090i | −0.147603 | − | 0.255656i | ||||
\(10\) | −0.500665 | + | 3.05899i | −0.0500665 | + | 0.305899i | ||||
\(11\) | 2.24264 | − | 3.88437i | 0.203876 | − | 0.353124i | −0.745898 | − | 0.666060i | \(-0.767979\pi\) |
0.949774 | + | 0.312936i | \(0.101313\pi\) | |||||||
\(12\) | 12.9443 | + | 4.35381i | 1.07869 | + | 0.362817i | ||||
\(13\) | 1.54985i | 0.119219i | 0.998222 | + | 0.0596094i | \(0.0189855\pi\) | ||||
−0.998222 | + | 0.0596094i | \(0.981014\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.29150i | − | 0.352767i | ||||||
\(16\) | −14.7477 | + | 6.20520i | −0.921733 | + | 0.387825i | ||||
\(17\) | −11.8284 | + | 20.4874i | −0.695790 | + | 1.20514i | 0.274124 | + | 0.961694i | \(0.411612\pi\) |
−0.969914 | + | 0.243449i | \(0.921721\pi\) | |||||||
\(18\) | −5.24394 | − | 0.858275i | −0.291330 | − | 0.0476820i | ||||
\(19\) | 12.4350 | + | 21.5381i | 0.654475 | + | 1.13358i | 0.982025 | + | 0.188750i | \(0.0604437\pi\) |
−0.327550 | + | 0.944834i | \(0.606223\pi\) | |||||||
\(20\) | 4.10051 | + | 4.64954i | 0.205025 | + | 0.232477i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.17157 | − | 8.39119i | −0.144162 | − | 0.381418i | ||||
\(23\) | −30.5055 | + | 17.6124i | −1.32633 | + | 0.765756i | −0.984730 | − | 0.174090i | \(-0.944301\pi\) |
−0.341598 | + | 0.939846i | \(0.610968\pi\) | |||||||
\(24\) | 23.1344 | − | 14.5203i | 0.963933 | − | 0.605012i | ||||
\(25\) | −11.2990 | + | 19.5704i | −0.451960 | + | 0.782817i | ||||
\(26\) | 2.39883 | + | 1.96308i | 0.0922627 | + | 0.0755032i | ||||
\(27\) | −21.6569 | −0.802106 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.4499i | 0.774136i | 0.922051 | + | 0.387068i | \(0.126512\pi\) | ||||
−0.922051 | + | 0.387068i | \(0.873488\pi\) | |||||||
\(30\) | −8.19012 | − | 6.70239i | −0.273004 | − | 0.223413i | ||||
\(31\) | −40.4569 | − | 23.3578i | −1.30506 | − | 0.753478i | −0.323795 | − | 0.946127i | \(-0.604959\pi\) |
−0.981268 | + | 0.192649i | \(0.938292\pi\) | |||||||
\(32\) | −9.07561 | + | 30.6860i | −0.283613 | + | 0.958939i | ||||
\(33\) | 7.65685 | + | 13.2621i | 0.232026 | + | 0.401881i | ||||
\(34\) | 16.7279 | + | 44.2579i | 0.491998 | + | 1.30170i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.97056 | + | 7.02938i | −0.221405 | + | 0.195260i | ||||
\(37\) | 50.7340 | − | 29.2913i | 1.37119 | − | 0.791657i | 0.380111 | − | 0.924941i | \(-0.375886\pi\) |
0.991078 | + | 0.133284i | \(0.0425523\pi\) | |||||||
\(38\) | 49.0870 | + | 8.03407i | 1.29176 | + | 0.211423i | ||||
\(39\) | −4.58258 | − | 2.64575i | −0.117502 | − | 0.0678398i | ||||
\(40\) | 12.3903 | − | 0.457458i | 0.309758 | − | 0.0114364i | ||||
\(41\) | −26.9706 | −0.657819 | −0.328909 | − | 0.944362i | \(-0.606681\pi\) | ||||
−0.328909 | + | 0.944362i | \(0.606681\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17.1716 | −0.399339 | −0.199669 | − | 0.979863i | \(-0.563987\pi\) | ||||
−0.199669 | + | 0.979863i | \(0.563987\pi\) | |||||||
\(44\) | −17.0050 | − | 5.71963i | −0.386477 | − | 0.129992i | ||||
\(45\) | 3.56604 | + | 2.05886i | 0.0792454 | + | 0.0457524i | ||||
\(46\) | −11.3791 | + | 69.5245i | −0.247371 | + | 1.51140i | ||||
\(47\) | 31.2918 | − | 18.0663i | 0.665783 | − | 0.384390i | −0.128694 | − | 0.991684i | \(-0.541079\pi\) |
0.794477 | + | 0.607295i | \(0.207745\pi\) | |||||||
\(48\) | 6.82843 | − | 54.1990i | 0.142259 | − | 1.12915i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 15.9792 | + | 42.2769i | 0.319584 | + | 0.845539i | ||||
\(51\) | −40.3848 | − | 69.9485i | −0.791858 | − | 1.37154i | ||||
\(52\) | 6.07687 | − | 1.22637i | 0.116863 | − | 0.0235841i | ||||
\(53\) | 84.7102 | + | 48.9075i | 1.59831 | + | 0.922782i | 0.991814 | + | 0.127693i | \(0.0407571\pi\) |
0.606492 | + | 0.795090i | \(0.292576\pi\) | |||||||
\(54\) | −27.4313 | + | 33.5202i | −0.507986 | + | 0.620744i | ||||
\(55\) | 6.95149i | 0.126391i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −84.9117 | −1.48968 | ||||||||
\(58\) | 34.7477 | + | 28.4358i | 0.599099 | + | 0.490273i | ||||
\(59\) | −30.7782 | + | 53.3094i | −0.521664 | + | 0.903549i | 0.478018 | + | 0.878350i | \(0.341355\pi\) |
−0.999682 | + | 0.0251987i | \(0.991978\pi\) | |||||||
\(60\) | −20.7477 | + | 4.18710i | −0.345795 | + | 0.0697850i | ||||
\(61\) | 32.6340 | − | 18.8412i | 0.534983 | − | 0.308873i | −0.208060 | − | 0.978116i | \(-0.566715\pi\) |
0.743043 | + | 0.669243i | \(0.233382\pi\) | |||||||
\(62\) | −87.3970 | + | 33.0329i | −1.40963 | + | 0.532790i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36.0000 | + | 52.9150i | 0.562500 | + | 0.826797i | ||||
\(65\) | −1.20101 | − | 2.08021i | −0.0184771 | − | 0.0320032i | ||||
\(66\) | 30.2253 | + | 4.94697i | 0.457958 | + | 0.0749541i | ||||
\(67\) | 16.6863 | − | 28.9015i | 0.249049 | − | 0.431366i | −0.714213 | − | 0.699928i | \(-0.753215\pi\) |
0.963262 | + | 0.268563i | \(0.0865486\pi\) | |||||||
\(68\) | 89.6899 | + | 30.1672i | 1.31897 | + | 0.443636i | ||||
\(69\) | − | 120.265i | − | 1.74297i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 102.199i | − | 1.43942i | −0.694277 | − | 0.719708i | \(-0.744276\pi\) | ||
0.694277 | − | 0.719708i | \(-0.255724\pi\) | |||||||
\(72\) | 0.784207 | + | 21.2404i | 0.0108918 | + | 0.295005i | ||||
\(73\) | −34.6569 | + | 60.0274i | −0.474751 | + | 0.822294i | −0.999582 | − | 0.0289132i | \(-0.990795\pi\) |
0.524830 | + | 0.851207i | \(0.324129\pi\) | |||||||
\(74\) | 18.9246 | − | 115.627i | 0.255738 | − | 1.56252i | ||||
\(75\) | −38.5772 | − | 66.8176i | −0.514362 | − | 0.890901i | ||||
\(76\) | 74.6102 | − | 65.8000i | 0.981713 | − | 0.865789i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.89949 | + | 3.74166i | −0.126917 | + | 0.0479700i | ||||
\(79\) | −33.5156 | + | 19.3503i | −0.424248 | + | 0.244940i | −0.696893 | − | 0.717175i | \(-0.745435\pi\) |
0.272645 | + | 0.962115i | \(0.412102\pi\) | |||||||
\(80\) | 14.9859 | − | 19.7570i | 0.187324 | − | 0.246963i | ||||
\(81\) | 48.9264 | − | 84.7430i | 0.604030 | − | 1.04621i | ||||
\(82\) | −34.1618 | + | 41.7447i | −0.416607 | + | 0.509081i | ||||
\(83\) | 3.61522 | 0.0435569 | 0.0217785 | − | 0.999763i | \(-0.493067\pi\) | ||||
0.0217785 | + | 0.999763i | \(0.493067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 36.6645i | − | 0.431347i | ||||||
\(86\) | −21.7501 | + | 26.5779i | −0.252908 | + | 0.309046i | ||||
\(87\) | −66.3799 | − | 38.3245i | −0.762987 | − | 0.440511i | ||||
\(88\) | −30.3918 | + | 19.0754i | −0.345362 | + | 0.216766i | ||||
\(89\) | −22.0294 | − | 38.1561i | −0.247522 | − | 0.428720i | 0.715316 | − | 0.698801i | \(-0.246283\pi\) |
−0.962838 | + | 0.270081i | \(0.912950\pi\) | |||||||
\(90\) | 7.70354 | − | 2.91166i | 0.0855948 | − | 0.0323518i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 93.1960 | + | 105.674i | 1.01300 | + | 1.14863i | ||||
\(93\) | 138.129 | − | 79.7486i | 1.48525 | − | 0.857512i | ||||
\(94\) | 11.6724 | − | 71.3164i | 0.124174 | − | 0.758685i | ||||
\(95\) | −33.3807 | − | 19.2724i | −0.351376 | − | 0.202867i | ||||
\(96\) | −75.2393 | − | 79.2191i | −0.783743 | − | 0.825199i | ||||
\(97\) | 96.1076 | 0.990800 | 0.495400 | − | 0.868665i | \(-0.335021\pi\) | ||||
0.495400 | + | 0.868665i | \(0.335021\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.9167 | −0.120371 | ||||||||
\(100\) | 85.6754 | + | 28.8170i | 0.856754 | + | 0.288170i | ||||
\(101\) | 16.9881 | + | 9.80808i | 0.168199 | + | 0.0971097i | 0.581736 | − | 0.813377i | \(-0.302374\pi\) |
−0.413537 | + | 0.910487i | \(0.635707\pi\) | |||||||
\(102\) | −159.418 | − | 26.0920i | −1.56292 | − | 0.255803i | ||||
\(103\) | −37.3120 | + | 21.5421i | −0.362252 | + | 0.209146i | −0.670068 | − | 0.742300i | \(-0.733735\pi\) |
0.307816 | + | 0.951446i | \(0.400402\pi\) | |||||||
\(104\) | 5.79899 | − | 10.9591i | 0.0557595 | − | 0.105376i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 182.995 | − | 69.1656i | 1.72637 | − | 0.652506i | ||||
\(107\) | −7.79899 | − | 13.5082i | −0.0728878 | − | 0.126245i | 0.827278 | − | 0.561793i | \(-0.189888\pi\) |
−0.900166 | + | 0.435547i | \(0.856555\pi\) | |||||||
\(108\) | 17.1368 | + | 84.9155i | 0.158674 | + | 0.786254i | ||||
\(109\) | 3.33576 | + | 1.92590i | 0.0306033 | + | 0.0176688i | 0.515224 | − | 0.857056i | \(-0.327709\pi\) |
−0.484620 | + | 0.874725i | \(0.661042\pi\) | |||||||
\(110\) | 10.7594 | + | 8.80498i | 0.0978130 | + | 0.0800453i | ||||
\(111\) | 200.013i | 1.80192i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.7746 | −0.121899 | −0.0609496 | − | 0.998141i | \(-0.519413\pi\) | ||||
−0.0609496 | + | 0.998141i | \(0.519413\pi\) | |||||||
\(114\) | −107.552 | + | 131.425i | −0.943437 | + | 1.15285i | ||||
\(115\) | 27.2965 | − | 47.2789i | 0.237361 | − | 0.411121i | ||||
\(116\) | 88.0252 | − | 17.7644i | 0.758838 | − | 0.153141i | ||||
\(117\) | 3.56604 | − | 2.05886i | 0.0304790 | − | 0.0175971i | ||||
\(118\) | 43.5269 | + | 115.161i | 0.368872 | + | 0.975944i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −19.7990 | + | 37.4166i | −0.164992 | + | 0.311805i | ||||
\(121\) | 50.4411 | + | 87.3666i | 0.416869 | + | 0.722038i | ||||
\(122\) | 12.1730 | − | 74.3754i | 0.0997789 | − | 0.609634i | ||||
\(123\) | 46.0416 | − | 79.7464i | 0.374322 | − | 0.648345i | ||||
\(124\) | −59.5718 | + | 177.112i | −0.480418 | + | 1.42833i | ||||
\(125\) | − | 73.7695i | − | 0.590156i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 125.025i | − | 0.984445i | −0.870469 | − | 0.492223i | \(-0.836185\pi\) | ||
0.870469 | − | 0.492223i | \(-0.163815\pi\) | |||||||
\(128\) | 127.500 | + | 11.3035i | 0.996093 | + | 0.0883088i | ||||
\(129\) | 29.3137 | − | 50.7728i | 0.227238 | − | 0.393588i | ||||
\(130\) | −4.74096 | − | 0.775953i | −0.0364689 | − | 0.00596887i | ||||
\(131\) | −50.1751 | − | 86.9059i | −0.383016 | − | 0.663404i | 0.608475 | − | 0.793573i | \(-0.291781\pi\) |
−0.991492 | + | 0.130169i | \(0.958448\pi\) | |||||||
\(132\) | 45.9411 | − | 40.5163i | 0.348039 | − | 0.306941i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −23.5980 | − | 62.4344i | −0.176104 | − | 0.465928i | ||||
\(135\) | 29.0679 | − | 16.7824i | 0.215318 | − | 0.124314i | ||||
\(136\) | 160.297 | − | 100.610i | 1.17865 | − | 0.739780i | ||||
\(137\) | −28.6569 | + | 49.6351i | −0.209174 | + | 0.362300i | −0.951455 | − | 0.307789i | \(-0.900411\pi\) |
0.742280 | + | 0.670089i | \(0.233744\pi\) | |||||||
\(138\) | −186.144 | − | 152.331i | −1.34887 | − | 1.10385i | ||||
\(139\) | −183.664 | −1.32132 | −0.660662 | − | 0.750684i | \(-0.729724\pi\) | ||||
−0.660662 | + | 0.750684i | \(0.729724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 123.365i | 0.874926i | ||||||||
\(142\) | −158.182 | − | 129.448i | −1.11395 | − | 0.911605i | ||||
\(143\) | 6.02017 | + | 3.47575i | 0.0420991 | + | 0.0243059i | ||||
\(144\) | 33.8689 | + | 25.6899i | 0.235200 | + | 0.178402i | ||||
\(145\) | −17.3970 | − | 30.1324i | −0.119979 | − | 0.207810i | ||||
\(146\) | 49.0122 | + | 129.674i | 0.335700 | + | 0.888179i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −154.995 | − | 175.748i | −1.04726 | − | 1.18748i | ||||
\(149\) | −166.545 | + | 96.1549i | −1.11775 | + | 0.645335i | −0.940826 | − | 0.338889i | \(-0.889949\pi\) |
−0.176927 | + | 0.984224i | \(0.556616\pi\) | |||||||
\(150\) | −152.282 | − | 24.9241i | −1.01522 | − | 0.166161i | ||||
\(151\) | −99.3791 | − | 57.3765i | −0.658140 | − | 0.379977i | 0.133428 | − | 0.991058i | \(-0.457401\pi\) |
−0.791568 | + | 0.611081i | \(0.790735\pi\) | |||||||
\(152\) | −7.34073 | − | 198.825i | −0.0482943 | − | 1.30806i | ||||
\(153\) | 62.8528 | 0.410803 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 72.4020 | 0.467110 | ||||||||
\(156\) | −6.74773 | + | 20.0616i | −0.0432547 | + | 0.128600i | ||||
\(157\) | −183.724 | − | 106.073i | −1.17022 | − | 0.675625i | −0.216486 | − | 0.976286i | \(-0.569460\pi\) |
−0.953731 | + | 0.300661i | \(0.902793\pi\) | |||||||
\(158\) | −12.5019 | + | 76.3847i | −0.0791259 | + | 0.483447i | ||||
\(159\) | −289.219 | + | 166.981i | −1.81899 | + | 1.05019i | ||||
\(160\) | −11.5980 | − | 48.2199i | −0.0724874 | − | 0.301374i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −69.1924 | − | 183.066i | −0.427114 | − | 1.13004i | ||||
\(163\) | 120.267 | + | 208.309i | 0.737835 | + | 1.27797i | 0.953469 | + | 0.301493i | \(0.0974849\pi\) |
−0.215634 | + | 0.976474i | \(0.569182\pi\) | |||||||
\(164\) | 21.3415 | + | 105.750i | 0.130131 | + | 0.644819i | ||||
\(165\) | −20.5541 | − | 11.8669i | −0.124571 | − | 0.0719208i | ||||
\(166\) | 4.57916 | − | 5.59560i | 0.0275853 | − | 0.0337084i | ||||
\(167\) | 212.101i | 1.27006i | 0.772486 | + | 0.635032i | \(0.219013\pi\) | ||||
−0.772486 | + | 0.635032i | \(0.780987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 166.598 | 0.985787 | ||||||||
\(170\) | −56.7488 | − | 46.4404i | −0.333816 | − | 0.273179i | ||||
\(171\) | 33.0381 | − | 57.2236i | 0.193205 | − | 0.334641i | ||||
\(172\) | 13.5877 | + | 67.3289i | 0.0789980 | + | 0.391447i | ||||
\(173\) | 157.801 | − | 91.1065i | 0.912145 | − | 0.526627i | 0.0310245 | − | 0.999519i | \(-0.490123\pi\) |
0.881121 | + | 0.472891i | \(0.156790\pi\) | |||||||
\(174\) | −143.397 | + | 54.1990i | −0.824121 | + | 0.311488i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.97056 | + | 71.2016i | −0.0509691 | + | 0.404555i | ||||
\(177\) | −105.083 | − | 182.010i | −0.593691 | − | 1.02830i | ||||
\(178\) | −86.9607 | − | 14.2329i | −0.488543 | − | 0.0799599i | ||||
\(179\) | −28.6030 | + | 49.5419i | −0.159793 | + | 0.276770i | −0.934794 | − | 0.355190i | \(-0.884416\pi\) |
0.775001 | + | 0.631960i | \(0.217749\pi\) | |||||||
\(180\) | 5.25091 | − | 15.6114i | 0.0291717 | − | 0.0867302i | ||||
\(181\) | − | 326.212i | − | 1.80228i | −0.433533 | − | 0.901138i | \(-0.642733\pi\) | ||
0.433533 | − | 0.901138i | \(-0.357267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 128.656i | 0.703039i | ||||||||
\(184\) | 281.606 | − | 10.3971i | 1.53047 | − | 0.0565058i | ||||
\(185\) | −45.3970 | + | 78.6299i | −0.245389 | + | 0.425026i | ||||
\(186\) | 51.5243 | − | 314.806i | 0.277012 | − | 1.69250i | ||||
\(187\) | 53.0538 | + | 91.8919i | 0.283710 | + | 0.491401i | ||||
\(188\) | −95.5980 | − | 108.398i | −0.508500 | − | 0.576585i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −72.1106 | + | 27.2552i | −0.379530 | + | 0.143449i | ||||
\(191\) | −84.0589 | + | 48.5314i | −0.440099 | + | 0.254091i | −0.703639 | − | 0.710557i | \(-0.748443\pi\) |
0.263541 | + | 0.964648i | \(0.415110\pi\) | |||||||
\(192\) | −217.915 | + | 16.1130i | −1.13497 | + | 0.0839221i | ||||
\(193\) | −78.6518 | + | 136.229i | −0.407522 | + | 0.705849i | −0.994611 | − | 0.103673i | \(-0.966940\pi\) |
0.587089 | + | 0.809522i | \(0.300274\pi\) | |||||||
\(194\) | 121.733 | − | 148.754i | 0.627490 | − | 0.766774i | ||||
\(195\) | 8.20101 | 0.0420565 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 124.117i | 0.630034i | 0.949086 | + | 0.315017i | \(0.102010\pi\) | ||||
−0.949086 | + | 0.315017i | \(0.897990\pi\) | |||||||
\(198\) | −15.0941 | + | 18.4446i | −0.0762329 | + | 0.0931544i | ||||
\(199\) | 156.729 | + | 90.4874i | 0.787581 | + | 0.454710i | 0.839110 | − | 0.543961i | \(-0.183076\pi\) |
−0.0515289 | + | 0.998672i | \(0.516409\pi\) | |||||||
\(200\) | 153.122 | − | 96.1069i | 0.765609 | − | 0.480534i | ||||
\(201\) | 56.9706 | + | 98.6759i | 0.283436 | + | 0.490925i | ||||
\(202\) | 36.6985 | − | 13.8707i | 0.181676 | − | 0.0686669i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −242.309 | + | 213.696i | −1.18779 | + | 1.04753i | ||||
\(205\) | 36.2000 | − | 20.9001i | 0.176586 | − | 0.101952i | ||||
\(206\) | −13.9180 | + | 85.0368i | −0.0675630 | + | 0.412800i | ||||
\(207\) | 81.0488 | + | 46.7935i | 0.391540 | + | 0.226056i | ||||
\(208\) | −9.61710 | − | 22.8567i | −0.0462361 | − | 0.109888i | ||||
\(209\) | 111.549 | 0.533728 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 164.049 | 0.777482 | 0.388741 | − | 0.921347i | \(-0.372910\pi\) | ||||
0.388741 | + | 0.921347i | \(0.372910\pi\) | |||||||
\(212\) | 124.734 | − | 370.844i | 0.588366 | − | 1.74927i | ||||
\(213\) | 302.180 | + | 174.464i | 1.41869 | + | 0.819079i | ||||
\(214\) | −30.7863 | − | 5.03880i | −0.143861 | − | 0.0235458i | ||||
\(215\) | 23.0478 | − | 13.3066i | 0.107199 | − | 0.0618913i | ||||
\(216\) | 153.137 | + | 81.0325i | 0.708968 | + | 0.375151i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.20606 | − | 2.72363i | 0.0330553 | − | 0.0124937i | ||||
\(219\) | −118.326 | − | 204.946i | −0.540301 | − | 0.935829i | ||||
\(220\) | 27.2565 | − | 5.50063i | 0.123893 | − | 0.0250029i | ||||
\(221\) | −31.7524 | − | 18.3322i | −0.143676 | − | 0.0829513i | ||||
\(222\) | 309.578 | + | 253.343i | 1.39450 | + | 1.14119i | ||||
\(223\) | − | 10.5830i | − | 0.0474574i | −0.999718 | − | 0.0237287i | \(-0.992446\pi\) | ||
0.999718 | − | 0.0237287i | \(-0.00755379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 60.0395 | 0.266842 | ||||||||
\(226\) | −17.4474 | + | 21.3201i | −0.0772007 | + | 0.0943369i | ||||
\(227\) | −52.9031 | + | 91.6308i | −0.233053 | + | 0.403660i | −0.958705 | − | 0.284402i | \(-0.908205\pi\) |
0.725652 | + | 0.688062i | \(0.241538\pi\) | |||||||
\(228\) | 67.1896 | + | 332.935i | 0.294691 | + | 1.46024i | ||||
\(229\) | −64.8469 | + | 37.4394i | −0.283174 | + | 0.163491i | −0.634860 | − | 0.772628i | \(-0.718942\pi\) |
0.351685 | + | 0.936118i | \(0.385609\pi\) | |||||||
\(230\) | −38.6030 | − | 102.134i | −0.167839 | − | 0.444061i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 84.0000 | − | 158.745i | 0.362069 | − | 0.684246i | ||||
\(233\) | 209.569 | + | 362.983i | 0.899436 | + | 1.55787i | 0.828217 | + | 0.560408i | \(0.189356\pi\) |
0.0712190 | + | 0.997461i | \(0.477311\pi\) | |||||||
\(234\) | 1.33019 | − | 8.12729i | 0.00568459 | − | 0.0347320i | ||||
\(235\) | −28.0000 | + | 48.4974i | −0.119149 | + | 0.206372i | ||||
\(236\) | 233.378 | + | 78.4967i | 0.988889 | + | 0.332613i | ||||
\(237\) | − | 132.132i | − | 0.557518i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 148.318i | 0.620577i | 0.950642 | + | 0.310288i | \(0.100426\pi\) | ||||
−0.950642 | + | 0.310288i | \(0.899574\pi\) | |||||||
\(240\) | 32.8348 | + | 78.0376i | 0.136812 | + | 0.325157i | ||||
\(241\) | 229.936 | − | 398.261i | 0.954092 | − | 1.65254i | 0.217658 | − | 0.976025i | \(-0.430158\pi\) |
0.736433 | − | 0.676510i | \(-0.236508\pi\) | |||||||
\(242\) | 199.115 | + | 32.5892i | 0.822790 | + | 0.134666i | ||||
\(243\) | 69.5894 | + | 120.532i | 0.286376 | + | 0.496018i | ||||
\(244\) | −99.6985 | − | 113.047i | −0.408600 | − | 0.463309i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −65.1127 | − | 172.272i | −0.264686 | − | 0.700293i | ||||
\(247\) | −33.3807 | + | 19.2724i | −0.135145 | + | 0.0780258i | ||||
\(248\) | 198.677 | + | 316.541i | 0.801116 | + | 1.27637i | ||||
\(249\) | −6.17157 | + | 10.6895i | −0.0247854 | + | 0.0429296i | ||||
\(250\) | −114.179 | − | 93.4388i | −0.456718 | − | 0.373755i | ||||
\(251\) | 124.919 | 0.497685 | 0.248842 | − | 0.968544i | \(-0.419950\pi\) | ||||
0.248842 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 157.993i | 0.624478i | ||||||||
\(254\) | −193.511 | − | 158.360i | −0.761856 | − | 0.623465i | ||||
\(255\) | 108.409 | + | 62.5902i | 0.425135 | + | 0.245452i | ||||
\(256\) | 178.991 | − | 183.025i | 0.699183 | − | 0.714943i | ||||
\(257\) | 213.676 | + | 370.098i | 0.831425 | + | 1.44007i | 0.896908 | + | 0.442216i | \(0.145808\pi\) |
−0.0654835 | + | 0.997854i | \(0.520859\pi\) | |||||||
\(258\) | −41.4558 | − | 109.682i | −0.160682 | − | 0.425123i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.20606 | + | 6.35515i | −0.0277156 | + | 0.0244429i | ||||
\(261\) | 51.6552 | − | 29.8231i | 0.197912 | − | 0.114265i | ||||
\(262\) | −198.065 | − | 32.4173i | −0.755974 | − | 0.123730i | ||||
\(263\) | −223.109 | − | 128.812i | −0.848322 | − | 0.489779i | 0.0117625 | − | 0.999931i | \(-0.496256\pi\) |
−0.860084 | + | 0.510152i | \(0.829589\pi\) | |||||||
\(264\) | −4.52005 | − | 122.426i | −0.0171214 | − | 0.463736i | ||||
\(265\) | −151.598 | −0.572068 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 150.426 | 0.563395 | ||||||||
\(268\) | −126.525 | − | 42.5567i | −0.472108 | − | 0.158794i | ||||
\(269\) | 186.408 | + | 107.623i | 0.692968 | + | 0.400085i | 0.804723 | − | 0.593650i | \(-0.202314\pi\) |
−0.111755 | + | 0.993736i | \(0.535647\pi\) | |||||||
\(270\) | 10.8428 | − | 66.2481i | 0.0401586 | − | 0.245363i | ||||
\(271\) | 327.833 | − | 189.275i | 1.20972 | − | 0.698431i | 0.247020 | − | 0.969010i | \(-0.420549\pi\) |
0.962698 | + | 0.270580i | \(0.0872154\pi\) | |||||||
\(272\) | 47.3137 | − | 375.541i | 0.173947 | − | 1.38067i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 40.5269 | + | 107.224i | 0.147908 | + | 0.391329i | ||||
\(275\) | 50.6791 | + | 87.7789i | 0.184288 | + | 0.319196i | ||||
\(276\) | −471.553 | + | 95.1641i | −1.70852 | + | 0.344798i | ||||
\(277\) | 144.149 | + | 83.2243i | 0.520393 | + | 0.300449i | 0.737095 | − | 0.675789i | \(-0.236197\pi\) |
−0.216703 | + | 0.976238i | \(0.569530\pi\) | |||||||
\(278\) | −232.635 | + | 284.273i | −0.836815 | + | 1.02256i | ||||
\(279\) | 124.117i | 0.444863i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −421.765 | −1.50094 | −0.750471 | − | 0.660904i | \(-0.770173\pi\) | ||||
−0.750471 | + | 0.660904i | \(0.770173\pi\) | |||||||
\(282\) | 190.942 | + | 156.257i | 0.677099 | + | 0.554104i | ||||
\(283\) | 172.719 | − | 299.159i | 0.610316 | − | 1.05710i | −0.380872 | − | 0.924628i | \(-0.624376\pi\) |
0.991187 | − | 0.132470i | \(-0.0422907\pi\) | |||||||
\(284\) | −400.716 | + | 80.8685i | −1.41097 | + | 0.284748i | ||||
\(285\) | 113.969 | − | 65.8000i | 0.399891 | − | 0.230877i | ||||
\(286\) | 13.0051 | − | 4.91545i | 0.0454722 | − | 0.0171869i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 82.6619 | − | 19.8821i | 0.287021 | − | 0.0690350i | ||||
\(289\) | −135.323 | − | 234.387i | −0.468247 | − | 0.811028i | ||||
\(290\) | −68.6741 | − | 11.2399i | −0.236807 | − | 0.0387583i | ||||
\(291\) | −164.066 | + | 284.171i | −0.563801 | + | 0.976532i | ||||
\(292\) | 262.788 | + | 88.3889i | 0.899960 | + | 0.302702i | ||||
\(293\) | 511.038i | 1.74416i | 0.489365 | + | 0.872079i | \(0.337229\pi\) | ||||
−0.489365 | + | 0.872079i | \(0.662771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 95.4028i | − | 0.323399i | ||||||
\(296\) | −468.342 | + | 17.2914i | −1.58224 | + | 0.0584170i | ||||
\(297\) | −48.5685 | + | 84.1232i | −0.163530 | + | 0.283243i | ||||
\(298\) | −62.1241 | + | 379.569i | −0.208470 | + | 1.27372i | ||||
\(299\) | −27.2965 | − | 47.2789i | −0.0912925 | − | 0.158123i | ||||
\(300\) | −231.463 | + | 204.131i | −0.771543 | + | 0.680437i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −214.683 | + | 81.1427i | −0.710872 | + | 0.268684i | ||||
\(303\) | −58.0010 | + | 33.4869i | −0.191422 | + | 0.110518i | ||||
\(304\) | −317.037 | − | 240.476i | −1.04288 | − | 0.791040i | ||||
\(305\) | −29.2010 | + | 50.5776i | −0.0957410 | + | 0.165828i | ||||
\(306\) | 79.6114 | − | 97.2828i | 0.260168 | − | 0.317917i | ||||
\(307\) | 223.331 | 0.727462 | 0.363731 | − | 0.931504i | \(-0.381503\pi\) | ||||
0.363731 | + | 0.931504i | \(0.381503\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 147.098i | − | 0.476047i | ||||||
\(310\) | 91.7067 | − | 112.063i | 0.295828 | − | 0.361493i | ||||
\(311\) | 10.7376 | + | 6.19938i | 0.0345262 | + | 0.0199337i | 0.517164 | − | 0.855886i | \(-0.326988\pi\) |
−0.482638 | + | 0.875820i | \(0.660321\pi\) | |||||||
\(312\) | 22.5042 | + | 35.8547i | 0.0721289 | + | 0.114919i | ||||
\(313\) | −205.024 | − | 355.113i | −0.655030 | − | 1.13455i | −0.981886 | − | 0.189471i | \(-0.939323\pi\) |
0.326856 | − | 0.945074i | \(-0.394011\pi\) | |||||||
\(314\) | −396.889 | + | 150.010i | −1.26398 | + | 0.477739i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 102.392 | + | 116.102i | 0.324025 | + | 0.367410i | ||||
\(317\) | −112.857 | + | 65.1580i | −0.356016 | + | 0.205546i | −0.667332 | − | 0.744761i | \(-0.732564\pi\) |
0.311316 | + | 0.950306i | \(0.399230\pi\) | |||||||
\(318\) | −107.883 | + | 659.152i | −0.339256 | + | 2.07280i | ||||
\(319\) | 87.2038 | + | 50.3472i | 0.273366 | + | 0.157828i | ||||
\(320\) | −89.3244 | − | 43.1256i | −0.279139 | − | 0.134768i | ||||
\(321\) | 53.2548 | 0.165903 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −588.347 | −1.82151 | ||||||||
\(324\) | −370.988 | − | 124.782i | −1.14503 | − | 0.385130i | ||||
\(325\) | −30.3311 | − | 17.5117i | −0.0933266 | − | 0.0538821i | ||||
\(326\) | 474.751 | + | 77.7026i | 1.45629 | + | 0.238351i | ||||
\(327\) | −11.3890 | + | 6.57544i | −0.0348287 | + | 0.0201084i | ||||
\(328\) | 190.711 | + | 100.915i | 0.581435 | + | 0.307666i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −44.4020 | + | 16.7824i | −0.134552 | + | 0.0508557i | ||||
\(331\) | −107.130 | − | 185.555i | −0.323655 | − | 0.560588i | 0.657584 | − | 0.753381i | \(-0.271579\pi\) |
−0.981239 | + | 0.192794i | \(0.938245\pi\) | |||||||
\(332\) | −2.86068 | − | 14.1751i | −0.00861651 | − | 0.0426961i | ||||
\(333\) | −134.793 | − | 77.8227i | −0.404783 | − | 0.233702i | ||||
\(334\) | 328.287 | + | 268.653i | 0.982894 | + | 0.804352i | ||||
\(335\) | 51.7223i | 0.154395i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 164.049 | 0.486792 | 0.243396 | − | 0.969927i | \(-0.421739\pi\) | ||||
0.243396 | + | 0.969927i | \(0.421739\pi\) | |||||||
\(338\) | 211.018 | − | 257.858i | 0.624314 | − | 0.762894i | ||||
\(339\) | 23.5147 | − | 40.7287i | 0.0693650 | − | 0.120144i | ||||
\(340\) | −143.760 | + | 29.0121i | −0.422822 | + | 0.0853298i | ||||
\(341\) | −181.461 | + | 104.766i | −0.532143 | + | 0.307233i | ||||
\(342\) | −46.7229 | − | 123.617i | −0.136617 | − | 0.361454i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 121.421 | + | 64.2501i | 0.352969 | + | 0.186774i | ||||
\(345\) | 93.1960 | + | 161.420i | 0.270133 | + | 0.467884i | ||||
\(346\) | 58.8625 | − | 359.641i | 0.170123 | − | 1.03942i | ||||
\(347\) | 54.8457 | − | 94.9955i | 0.158057 | − | 0.273762i | −0.776111 | − | 0.630596i | \(-0.782810\pi\) |
0.934168 | + | 0.356834i | \(0.116144\pi\) | |||||||
\(348\) | −97.7427 | + | 290.598i | −0.280870 | + | 0.835052i | ||||
\(349\) | 463.479i | 1.32802i | 0.747723 | + | 0.664010i | \(0.231147\pi\) | ||||
−0.747723 | + | 0.664010i | \(0.768853\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 33.5648i | − | 0.0956261i | ||||||
\(352\) | 98.8425 | + | 104.071i | 0.280803 | + | 0.295656i | ||||
\(353\) | −39.0488 | + | 67.6345i | −0.110620 | + | 0.191599i | −0.916020 | − | 0.401132i | \(-0.868617\pi\) |
0.805401 | + | 0.592731i | \(0.201950\pi\) | |||||||
\(354\) | −414.814 | − | 67.8926i | −1.17179 | − | 0.191787i | ||||
\(355\) | 79.1960 | + | 137.171i | 0.223087 | + | 0.386398i | ||||
\(356\) | −132.177 | + | 116.569i | −0.371283 | + | 0.327441i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 40.4508 | + | 107.023i | 0.112991 | + | 0.298946i | ||||
\(359\) | −316.198 | + | 182.557i | −0.880774 | + | 0.508515i | −0.870913 | − | 0.491437i | \(-0.836472\pi\) |
−0.00986020 | + | 0.999951i | \(0.503139\pi\) | |||||||
\(360\) | −17.5122 | − | 27.9012i | −0.0486450 | − | 0.0775034i | ||||
\(361\) | −128.760 | + | 223.019i | −0.356676 | + | 0.617780i | ||||
\(362\) | −504.906 | − | 413.190i | −1.39477 | − | 1.14141i | ||||
\(363\) | −344.434 | −0.948853 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 107.426i | − | 0.294316i | ||||||
\(366\) | 199.132 | + | 162.960i | 0.544077 | + | 0.445245i | ||||
\(367\) | −191.165 | − | 110.369i | −0.520887 | − | 0.300734i | 0.216411 | − | 0.976302i | \(-0.430565\pi\) |
−0.737297 | + | 0.675568i | \(0.763898\pi\) | |||||||
\(368\) | 340.599 | − | 449.036i | 0.925541 | − | 1.22021i | ||||
\(369\) | 35.8284 | + | 62.0567i | 0.0970960 | + | 0.168175i | ||||
\(370\) | 64.2010 | + | 169.860i | 0.173516 | + | 0.459081i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −421.990 | − | 478.492i | −1.13438 | − | 1.28627i | ||||
\(373\) | 217.852 | − | 125.777i | 0.584052 | − | 0.337203i | −0.178690 | − | 0.983905i | \(-0.557186\pi\) |
0.762742 | + | 0.646703i | \(0.223853\pi\) | |||||||
\(374\) | 209.429 | + | 34.2772i | 0.559970 | + | 0.0916503i | ||||
\(375\) | 218.121 | + | 125.932i | 0.581657 | + | 0.335820i | ||||
\(376\) | −288.864 | + | 10.6650i | −0.768256 | + | 0.0283645i | ||||
\(377\) | −34.7939 | −0.0922916 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 286.024 | 0.754682 | 0.377341 | − | 0.926074i | \(-0.376839\pi\) | ||||
0.377341 | + | 0.926074i | \(0.376839\pi\) | |||||||
\(380\) | −49.1523 | + | 146.134i | −0.129348 | + | 0.384564i | ||||
\(381\) | 369.672 | + | 213.430i | 0.970268 | + | 0.560184i | ||||
\(382\) | −31.3554 | + | 191.577i | −0.0820821 | + | 0.501509i | ||||
\(383\) | −92.5727 | + | 53.4468i | −0.241704 | + | 0.139548i | −0.615960 | − | 0.787778i | \(-0.711232\pi\) |
0.374256 | + | 0.927326i | \(0.377898\pi\) | |||||||
\(384\) | −251.078 | + | 357.695i | −0.653850 | + | 0.931497i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 111.230 | + | 294.288i | 0.288162 | + | 0.762404i | ||||
\(387\) | 22.8112 | + | 39.5101i | 0.0589436 | + | 0.102093i | ||||
\(388\) | −76.0488 | − | 376.833i | −0.196002 | − | 0.971220i | ||||
\(389\) | −66.8405 | − | 38.5904i | −0.171826 | − | 0.0992040i | 0.411620 | − | 0.911355i | \(-0.364963\pi\) |
−0.583447 | + | 0.812151i | \(0.698296\pi\) | |||||||
\(390\) | 10.3877 | − | 12.6934i | 0.0266350 | − | 0.0325472i | ||||
\(391\) | − | 833.307i | − | 2.13122i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 342.617 | 0.871800 | ||||||||
\(394\) | 192.106 | + | 157.210i | 0.487579 | + | 0.399010i | ||||
\(395\) | 29.9899 | − | 51.9440i | 0.0759238 | − | 0.131504i | ||||
\(396\) | 9.42957 | + | 46.7250i | 0.0238120 | + | 0.117992i | ||||
\(397\) | −569.424 | + | 328.757i | −1.43432 | + | 0.828103i | −0.997446 | − | 0.0714218i | \(-0.977246\pi\) |
−0.436870 | + | 0.899525i | \(0.643913\pi\) | |||||||
\(398\) | 338.573 | − | 127.968i | 0.850685 | − | 0.321529i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 45.1960 | − | 358.732i | 0.112990 | − | 0.896830i | ||||
\(401\) | −159.397 | − | 276.084i | −0.397499 | − | 0.688488i | 0.595918 | − | 0.803045i | \(-0.296788\pi\) |
−0.993417 | + | 0.114557i | \(0.963455\pi\) | |||||||
\(402\) | 224.890 | + | 36.8078i | 0.559428 | + | 0.0915616i | ||||
\(403\) | 36.2010 | − | 62.7020i | 0.0898288 | − | 0.155588i | ||||
\(404\) | 25.0145 | − | 74.3705i | 0.0619172 | − | 0.184085i | ||||
\(405\) | 151.657i | 0.374461i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 262.759i | − | 0.645600i | ||||||
\(408\) | 23.8402 | + | 645.716i | 0.0584319 | + | 1.58264i | ||||
\(409\) | −72.6325 | + | 125.803i | −0.177585 | + | 0.307587i | −0.941053 | − | 0.338259i | \(-0.890162\pi\) |
0.763468 | + | 0.645846i | \(0.223495\pi\) | |||||||
\(410\) | 13.5032 | − | 82.5027i | 0.0329347 | − | 0.201226i | ||||
\(411\) | −97.8406 | − | 169.465i | −0.238055 | − | 0.412323i | ||||
\(412\) | 113.990 | + | 129.252i | 0.276675 | + | 0.313719i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 175.085 | − | 66.1760i | 0.422911 | − | 0.159846i | ||||
\(415\) | −4.85237 | + | 2.80152i | −0.0116925 | + | 0.00675065i | ||||
\(416\) | −47.5586 | − | 14.0658i | −0.114324 | − | 0.0338120i | ||||
\(417\) | 313.534 | − | 543.057i | 0.751880 | − | 1.30229i | ||||
\(418\) | 141.292 | − | 172.654i | 0.338019 | − | 0.413049i | ||||
\(419\) | 707.012 | 1.68738 | 0.843690 | − | 0.536831i | \(-0.180379\pi\) | ||||
0.843690 | + | 0.536831i | \(0.180379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 121.989i | − | 0.289761i | −0.989449 | − | 0.144880i | \(-0.953720\pi\) | ||
0.989449 | − | 0.144880i | \(-0.0462798\pi\) | |||||||
\(422\) | 207.789 | − | 253.913i | 0.492392 | − | 0.601688i | ||||
\(423\) | −83.1377 | − | 47.9996i | −0.196543 | − | 0.113474i | ||||
\(424\) | −415.997 | − | 662.784i | −0.981124 | − | 1.56317i | ||||
\(425\) | −267.299 | − | 462.975i | −0.628938 | − | 1.08935i | ||||
\(426\) | 652.784 | − | 246.729i | 1.53236 | − | 0.579176i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −46.7939 | + | 41.2684i | −0.109332 | + | 0.0964214i | ||||
\(429\) | −20.5541 | + | 11.8669i | −0.0479118 | + | 0.0276619i | ||||
\(430\) | 8.59720 | − | 52.5277i | 0.0199935 | − | 0.122157i | ||||
\(431\) | −509.969 | − | 294.431i | −1.18322 | − | 0.683133i | −0.226464 | − | 0.974020i | \(-0.572717\pi\) |
−0.956758 | + | 0.290886i | \(0.906050\pi\) | |||||||
\(432\) | 319.389 | − | 134.385i | 0.739327 | − | 0.311077i | ||||
\(433\) | 137.696 | 0.318004 | 0.159002 | − | 0.987278i | \(-0.449172\pi\) | ||||
0.159002 | + | 0.987278i | \(0.449172\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 118.794 | 0.273090 | ||||||||
\(436\) | 4.91182 | − | 14.6033i | 0.0112656 | − | 0.0334938i | ||||
\(437\) | −758.675 | − | 438.021i | −1.73610 | − | 1.00234i | ||||
\(438\) | −467.089 | − | 76.4485i | −1.06641 | − | 0.174540i | ||||
\(439\) | 381.522 | − | 220.272i | 0.869070 | − | 0.501758i | 0.00203069 | − | 0.999998i | \(-0.499354\pi\) |
0.867039 | + | 0.498240i | \(0.166020\pi\) | |||||||
\(440\) | 26.0101 | − | 49.1545i | 0.0591139 | − | 0.111715i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −68.5929 | + | 25.9257i | −0.155188 | + | 0.0586554i | ||||
\(443\) | 243.529 | + | 421.805i | 0.549727 | + | 0.952155i | 0.998293 | + | 0.0584052i | \(0.0186015\pi\) |
−0.448566 | + | 0.893750i | \(0.648065\pi\) | |||||||
\(444\) | 784.243 | − | 158.268i | 1.76631 | − | 0.356460i | ||||
\(445\) | 59.1361 | + | 34.1422i | 0.132890 | + | 0.0767241i | ||||
\(446\) | −16.3802 | − | 13.4048i | −0.0367270 | − | 0.0300555i | ||||
\(447\) | − | 656.587i | − | 1.46887i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 264.039 | 0.588059 | 0.294030 | − | 0.955796i | \(-0.405004\pi\) | ||||
0.294030 | + | 0.955796i | \(0.405004\pi\) | |||||||
\(450\) | 76.0480 | − | 92.9284i | 0.168996 | − | 0.206508i | ||||
\(451\) | −60.4853 | + | 104.764i | −0.134114 | + | 0.232292i | ||||
\(452\) | 10.8997 | + | 54.0096i | 0.0241143 | + | 0.119490i | ||||
\(453\) | 339.301 | − | 195.896i | 0.749010 | − | 0.432441i | ||||
\(454\) | 74.8162 | + | 197.945i | 0.164793 | + | 0.436003i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 600.416 | + | 317.710i | 1.31670 | + | 0.696733i | ||||
\(457\) | 257.161 | + | 445.417i | 0.562717 | + | 0.974654i | 0.997258 | + | 0.0740019i | \(0.0235771\pi\) |
−0.434542 | + | 0.900652i | \(0.643090\pi\) | |||||||
\(458\) | −24.1890 | + | 147.791i | −0.0528144 | + | 0.322688i | ||||
\(459\) | 256.167 | − | 443.693i | 0.558097 | − | 0.966652i | ||||
\(460\) | −206.978 | − | 69.6169i | −0.449951 | − | 0.151341i | ||||
\(461\) | 202.224i | 0.438664i | 0.975650 | + | 0.219332i | \(0.0703878\pi\) | ||||
−0.975650 | + | 0.219332i | \(0.929612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 722.653i | 1.56081i | 0.625277 | + | 0.780403i | \(0.284986\pi\) | ||||
−0.625277 | + | 0.780403i | \(0.715014\pi\) | |||||||
\(464\) | −139.306 | − | 331.086i | −0.300229 | − | 0.713547i | ||||
\(465\) | −123.598 | + | 214.078i | −0.265802 | + | 0.460383i | ||||
\(466\) | 827.267 | + | 135.399i | 1.77525 | + | 0.290555i | ||||
\(467\) | 173.641 | + | 300.755i | 0.371822 | + | 0.644015i | 0.989846 | − | 0.142144i | \(-0.0453997\pi\) |
−0.618023 | + | 0.786160i | \(0.712066\pi\) | |||||||
\(468\) | −10.8944 | − | 12.3531i | −0.0232787 | − | 0.0263956i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 39.5980 | + | 104.766i | 0.0842510 | + | 0.222907i | ||||
\(471\) | 627.273 | − | 362.156i | 1.33179 | − | 0.768910i | ||||
\(472\) | 417.100 | − | 261.793i | 0.883686 | − | 0.554646i | ||||
\(473\) | −38.5097 | + | 66.7007i | −0.0814158 | + | 0.141016i | ||||
\(474\) | −204.512 | − | 167.362i | −0.431460 | − | 0.353085i | ||||
\(475\) | −562.013 | −1.18319 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 259.880i | − | 0.544822i | ||||||
\(478\) | 229.564 | + | 187.864i | 0.480260 | + | 0.393021i | ||||
\(479\) | 25.2716 | + | 14.5906i | 0.0527591 | + | 0.0304605i | 0.526148 | − | 0.850393i | \(-0.323636\pi\) |
−0.473388 | + | 0.880854i | \(0.656969\pi\) | |||||||
\(480\) | 162.375 | + | 48.0236i | 0.338282 | + | 0.100049i | ||||
\(481\) | 45.3970 | + | 78.6299i | 0.0943804 | + | 0.163472i | ||||
\(482\) | −325.179 | − | 860.342i | −0.674645 | − | 1.78494i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 302.647 | − | 266.909i | 0.625303 | − | 0.551466i | ||||
\(485\) | −128.996 | + | 74.4760i | −0.265972 | + | 0.153559i | ||||
\(486\) | 274.702 | + | 44.9606i | 0.565231 | + | 0.0925114i | ||||
\(487\) | 607.640 | + | 350.821i | 1.24772 | + | 0.720372i | 0.970654 | − | 0.240478i | \(-0.0773043\pi\) |
0.277067 | + | 0.960851i | \(0.410638\pi\) | |||||||
\(488\) | −301.255 | + | 11.1225i | −0.617325 | + | 0.0227920i | ||||
\(489\) | −821.235 | −1.67942 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −59.9512 | −0.122100 | −0.0610501 | − | 0.998135i | \(-0.519445\pi\) | ||||
−0.0610501 | + | 0.998135i | \(0.519445\pi\) | |||||||
\(492\) | −349.114 | − | 117.425i | −0.709582 | − | 0.238668i | ||||
\(493\) | −459.942 | − | 265.548i | −0.932945 | − | 0.538636i | ||||
\(494\) | −12.4516 | + | 76.0772i | −0.0252056 | + | 0.154003i | ||||
\(495\) | 15.9947 | − | 9.23455i | 0.0323125 | − | 0.0186557i | ||||
\(496\) | 741.588 | + | 93.4313i | 1.49514 | + | 0.188370i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.72792 | + | 23.0919i | 0.0175259 | + | 0.0463693i | ||||
\(499\) | 42.1421 | + | 72.9923i | 0.0844532 | + | 0.146277i | 0.905158 | − | 0.425075i | \(-0.139752\pi\) |
−0.820705 | + | 0.571352i | \(0.806419\pi\) | |||||||
\(500\) | −289.247 | + | 58.3729i | −0.578493 | + | 0.116746i | ||||
\(501\) | −627.138 | − | 362.079i | −1.25177 | − | 0.722712i | ||||
\(502\) | 158.226 | − | 193.348i | 0.315192 | − | 0.385155i | ||||
\(503\) | − | 409.987i | − | 0.815083i | −0.913187 | − | 0.407542i | \(-0.866386\pi\) | ||
0.913187 | − | 0.407542i | \(-0.133614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.4020 | −0.0602020 | ||||||||
\(506\) | 244.539 | + | 200.119i | 0.483280 | + | 0.395492i | ||||
\(507\) | −284.401 | + | 492.596i | −0.560948 | + | 0.971590i | ||||
\(508\) | −490.215 | + | 98.9304i | −0.964991 | + | 0.194745i | ||||
\(509\) | −413.123 | + | 238.516i | −0.811636 | + | 0.468598i | −0.847524 | − | 0.530758i | \(-0.821907\pi\) |
0.0358878 | + | 0.999356i | \(0.488574\pi\) | |||||||
\(510\) | 234.191 | − | 88.5158i | 0.459198 | − | 0.173560i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −56.5685 | − | 508.865i | −0.110485 | − | 0.993878i | ||||
\(513\) | −269.304 | − | 466.448i | −0.524958 | − | 0.909254i | ||||
\(514\) | 843.482 | + | 138.053i | 1.64102 | + | 0.268585i | ||||
\(515\) | 33.3869 | − | 57.8278i | 0.0648289 | − | 0.112287i | ||||
\(516\) | −222.273 | − | 74.7617i | −0.430762 | − | 0.144887i | ||||
\(517\) | − | 162.065i | − | 0.313472i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 622.114i | 1.19868i | ||||||||
\(520\) | 0.708989 | + | 19.2031i | 0.00136344 | + | 0.0369290i | ||||
\(521\) | −105.437 | + | 182.621i | −0.202373 | + | 0.350521i | −0.949293 | − | 0.314394i | \(-0.898199\pi\) |
0.746919 | + | 0.664915i | \(0.231532\pi\) | |||||||
\(522\) | 19.2682 | − | 117.726i | 0.0369123 | − | 0.225529i | ||||
\(523\) | −255.783 | − | 443.030i | −0.489069 | − | 0.847093i | 0.510852 | − | 0.859669i | \(-0.329330\pi\) |
−0.999921 | + | 0.0125761i | \(0.995997\pi\) | |||||||
\(524\) | −301.051 | + | 265.502i | −0.574525 | + | 0.506683i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −481.970 | + | 182.167i | −0.916292 | + | 0.346326i | ||||
\(527\) | 957.084 | − | 552.573i | 1.81610 | − | 1.04852i | ||||
\(528\) | −195.215 | − | 148.073i | −0.369725 | − | 0.280441i | ||||
\(529\) | 355.892 | − | 616.423i | 0.672764 | − | 1.16526i | ||||
\(530\) | −192.019 | + | 234.641i | −0.362300 | + | 0.442720i | ||||
\(531\) | 163.546 | 0.307997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 41.8002i | − | 0.0784244i | ||||||
\(534\) | 190.535 | − | 232.828i | 0.356807 | − | 0.436007i | ||||
\(535\) | 20.9357 | + | 12.0872i | 0.0391321 | + | 0.0225929i | ||||
\(536\) | −226.129 | + | 141.930i | −0.421883 | + | 0.264795i | ||||
\(537\) | −97.6569 | − | 169.147i | −0.181856 | − | 0.314984i | ||||
\(538\) | 402.688 | − | 152.202i | 0.748491 | − | 0.282903i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −88.8040 | − | 100.694i | −0.164452 | − | 0.186471i | ||||
\(541\) | −296.542 | + | 171.208i | −0.548136 | + | 0.316466i | −0.748370 | − | 0.663282i | \(-0.769163\pi\) |
0.200234 | + | 0.979748i | \(0.435830\pi\) | |||||||
\(542\) | 122.287 | − | 747.157i | 0.225622 | − | 1.37852i | ||||
\(543\) | 964.542 | + | 556.878i | 1.77632 | + | 1.02556i | ||||
\(544\) | −521.328 | − | 548.904i | −0.958324 | − | 1.00901i | ||||
\(545\) | −5.96970 | −0.0109536 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −441.976 | −0.807999 | −0.404000 | − | 0.914759i | \(-0.632380\pi\) | ||||
−0.404000 | + | 0.914759i | \(0.632380\pi\) | |||||||
\(548\) | 217.293 | + | 73.0865i | 0.396520 | + | 0.133369i | ||||
\(549\) | −86.7038 | − | 50.0584i | −0.157930 | − | 0.0911811i | ||||
\(550\) | 200.055 | + | 32.7430i | 0.363736 | + | 0.0595327i | ||||
\(551\) | −483.529 | + | 279.166i | −0.877548 | + | 0.506653i | ||||
\(552\) | −449.990 | + | 850.401i | −0.815199 | + | 1.54058i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 311.397 | − | 117.697i | 0.562088 | − | 0.212449i | ||||
\(555\) | −154.995 | − | 268.459i | −0.279270 | − | 0.483710i | ||||
\(556\) | 145.331 | + | 720.138i | 0.261387 | + | 1.29521i | ||||
\(557\) | 316.714 | + | 182.855i | 0.568607 | + | 0.328285i | 0.756593 | − | 0.653886i | \(-0.226863\pi\) |
−0.187986 | + | 0.982172i | \(0.560196\pi\) | |||||||
\(558\) | 192.106 | + | 157.210i | 0.344276 | + | 0.281739i | ||||
\(559\) | − | 26.6133i | − | 0.0476087i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −362.274 | −0.645765 | ||||||||
\(562\) | −534.220 | + | 652.802i | −0.950570 | + | 1.16157i | ||||
\(563\) | −403.194 | + | 698.353i | −0.716154 | + | 1.24041i | 0.246359 | + | 0.969179i | \(0.420766\pi\) |
−0.962513 | + | 0.271236i | \(0.912568\pi\) | |||||||
\(564\) | 483.706 | − | 97.6169i | 0.857636 | − | 0.173080i | ||||
\(565\) | 18.4883 | − | 10.6743i | 0.0327227 | − | 0.0188925i | ||||
\(566\) | −244.262 | − | 646.256i | −0.431558 | − | 1.14180i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −382.392 | + | 722.653i | −0.673225 | + | 1.27228i | ||||
\(569\) | −111.446 | − | 193.030i | −0.195862 | − | 0.339244i | 0.751320 | − | 0.659938i | \(-0.229417\pi\) |
−0.947183 | + | 0.320694i | \(0.896084\pi\) | |||||||
\(570\) | 42.5123 | − | 259.744i | 0.0745830 | − | 0.455691i | ||||
\(571\) | −286.541 | + | 496.304i | −0.501823 | + | 0.869184i | 0.498174 | + | 0.867077i | \(0.334004\pi\) |
−0.999998 | + | 0.00210683i | \(0.999329\pi\) | |||||||
\(572\) | 8.86455 | − | 26.3551i | 0.0154975 | − | 0.0460754i | ||||
\(573\) | − | 331.393i | − | 0.578348i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 796.008i | − | 1.38436i | ||||||
\(576\) | 73.9290 | − | 153.126i | 0.128349 | − | 0.265844i | ||||
\(577\) | 361.950 | − | 626.916i | 0.627297 | − | 1.08651i | −0.360795 | − | 0.932645i | \(-0.617495\pi\) |
0.988092 | − | 0.153865i | \(-0.0491721\pi\) | |||||||
\(578\) | −534.186 | − | 87.4302i | −0.924197 | − | 0.151263i | ||||
\(579\) | −268.534 | − | 465.115i | −0.463789 | − | 0.803307i | ||||
\(580\) | −104.382 | + | 92.0561i | −0.179969 | + | 0.158717i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 232.024 | + | 613.879i | 0.398667 | + | 1.05477i | ||||
\(583\) | 379.949 | − | 219.364i | 0.651714 | − | 0.376267i | ||||
\(584\) | 469.663 | − | 294.784i | 0.804218 | − | 0.504767i | ||||
\(585\) | −3.19091 | + | 5.52682i | −0.00545455 | + | 0.00944755i | ||||
\(586\) | 790.978 | + | 647.297i | 1.34979 | + | 1.10460i | ||||
\(587\) | 21.1198 | 0.0359793 | 0.0179896 | − | 0.999838i | \(-0.494273\pi\) | ||||
0.0179896 | + | 0.999838i | \(0.494273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1161.82i | − | 1.97253i | ||||||
\(590\) | −147.663 | − | 120.840i | −0.250277 | − | 0.204814i | ||||
\(591\) | −366.988 | − | 211.880i | −0.620960 | − | 0.358512i | ||||
\(592\) | −566.453 | + | 746.795i | −0.956846 | + | 1.26148i | ||||
\(593\) | 64.3726 | + | 111.497i | 0.108554 | + | 0.188021i | 0.915185 | − | 0.403035i | \(-0.132045\pi\) |
−0.806631 | + | 0.591056i | \(0.798711\pi\) | |||||||
\(594\) | 68.6863 | + | 181.727i | 0.115633 | + | 0.305937i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 508.804 | + | 576.930i | 0.853698 | + | 0.968003i | ||||
\(597\) | −535.105 | + | 308.943i | −0.896324 | + | 0.517493i | ||||
\(598\) | −107.752 | − | 17.6358i | −0.180188 | − | 0.0294913i | ||||
\(599\) | −280.705 | − | 162.065i | −0.468623 | − | 0.270559i | 0.247040 | − | 0.969005i | \(-0.420542\pi\) |
−0.715663 | + | 0.698446i | \(0.753875\pi\) | |||||||
\(600\) | 22.7731 | + | 616.814i | 0.0379552 | + | 1.02802i | ||||
\(601\) | −721.862 | −1.20110 | −0.600551 | − | 0.799587i | \(-0.705052\pi\) | ||||
−0.600551 | + | 0.799587i | \(0.705052\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −88.6661 | −0.147042 | ||||||||
\(604\) | −146.333 | + | 435.062i | −0.242273 | + | 0.720301i | ||||
\(605\) | −135.405 | − | 78.1759i | −0.223809 | − | 0.129216i | ||||
\(606\) | −21.6353 | + | 132.189i | −0.0357019 | + | 0.218133i | ||||
\(607\) | 611.413 | − | 353.000i | 1.00727 | − | 0.581548i | 0.0968795 | − | 0.995296i | \(-0.469114\pi\) |
0.910391 | + | 0.413748i | \(0.135781\pi\) | |||||||
\(608\) | −773.775 | + | 186.110i | −1.27266 | + | 0.306103i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 41.2965 | + | 109.260i | 0.0676991 | + | 0.179115i | ||||
\(611\) | 28.0000 | + | 48.4974i | 0.0458265 | + | 0.0793739i | ||||
\(612\) | −49.7347 | − | 246.443i | −0.0812658 | − | 0.402684i | ||||
\(613\) | −18.9026 | − | 10.9134i | −0.0308363 | − | 0.0178033i | 0.484503 | − | 0.874790i | \(-0.339001\pi\) |
−0.515339 | + | 0.856986i | \(0.672334\pi\) | |||||||
\(614\) | 282.878 | − | 345.669i | 0.460713 | − | 0.562978i | ||||
\(615\) | 142.715i | 0.232057i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −699.578 | −1.13384 | −0.566919 | − | 0.823774i | \(-0.691865\pi\) | ||||
−0.566919 | + | 0.823774i | \(0.691865\pi\) | |||||||
\(618\) | −227.677 | − | 186.320i | −0.368409 | − | 0.301488i | ||||
\(619\) | −48.0990 | + | 83.3100i | −0.0777044 | + | 0.134588i | −0.902259 | − | 0.431194i | \(-0.858092\pi\) |
0.824555 | + | 0.565782i | \(0.191426\pi\) | |||||||
\(620\) | −57.2908 | − | 283.885i | −0.0924046 | − | 0.457879i | ||||
\(621\) | 660.654 | − | 381.429i | 1.06386 | − | 0.614217i | ||||
\(622\) | 23.1960 | − | 8.76725i | 0.0372925 | − | 0.0140953i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 84.0000 | + | 10.5830i | 0.134615 | + | 0.0169599i | ||||
\(625\) | −225.309 | − | 390.247i | −0.360495 | − | 0.624395i | ||||
\(626\) | −809.329 | − | 132.463i | −1.29286 | − | 0.211602i | ||||
\(627\) | −190.426 | + | 329.828i | −0.303710 | + | 0.526042i | ||||
\(628\) | −270.529 | + | 804.308i | −0.430779 | + | 1.28074i | ||||
\(629\) | 1385.88i | 2.20331i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 269.399i | 0.426940i | 0.976950 | + | 0.213470i | \(0.0684766\pi\) | ||||
−0.976950 | + | 0.213470i | \(0.931523\pi\) | |||||||
\(632\) | 309.393 | − | 11.4230i | 0.489546 | − | 0.0180743i | ||||
\(633\) | −280.049 | + | 485.059i | −0.442415 | + | 0.766285i | ||||
\(634\) | −42.0975 | + | 257.210i | −0.0663999 | + | 0.405694i | ||||
\(635\) | 96.8843 | + | 167.809i | 0.152574 | + | 0.264266i | ||||
\(636\) | 883.578 | + | 1001.88i | 1.38927 | + | 1.57529i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 188.382 | − | 71.2016i | 0.295269 | − | 0.111601i | ||||
\(639\) | −235.149 | + | 135.763i | −0.367995 | + | 0.212462i | ||||
\(640\) | −179.890 | + | 83.6309i | −0.281079 | + | 0.130673i | ||||
\(641\) | −317.907 | + | 550.630i | −0.495954 | + | 0.859018i | −0.999989 | − | 0.00466541i | \(-0.998515\pi\) |
0.504035 | + | 0.863683i | \(0.331848\pi\) | |||||||
\(642\) | 67.4543 | − | 82.4271i | 0.105069 | − | 0.128391i | ||||
\(643\) | 1281.70 | 1.99332 | 0.996658 | − | 0.0816828i | \(-0.0260295\pi\) | ||||
0.996658 | + | 0.0816828i | \(0.0260295\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 90.8634i | 0.140874i | ||||||||
\(646\) | −745.219 | + | 910.636i | −1.15359 | + | 1.40965i | ||||
\(647\) | 225.826 | + | 130.381i | 0.349035 | + | 0.201516i | 0.664260 | − | 0.747501i | \(-0.268747\pi\) |
−0.315225 | + | 0.949017i | \(0.602080\pi\) | |||||||
\(648\) | −663.041 | + | 416.158i | −1.02321 | + | 0.642219i | ||||
\(649\) | 138.049 | + | 239.107i | 0.212710 | + | 0.368424i | ||||
\(650\) | −65.5227 | + | 24.7653i | −0.100804 | + | 0.0381004i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 721.602 | − | 636.393i | 1.10675 | − | 0.976063i | ||||
\(653\) | −944.471 | + | 545.291i | −1.44636 | + | 0.835055i | −0.998262 | − | 0.0589313i | \(-0.981231\pi\) |
−0.448095 | + | 0.893986i | \(0.647897\pi\) | |||||||
\(654\) | −4.24828 | + | 25.9564i | −0.00649585 | + | 0.0396887i | ||||
\(655\) | 134.691 | + | 77.7637i | 0.205635 | + | 0.118723i | ||||
\(656\) | 397.754 | − | 167.358i | 0.606333 | − | 0.255119i | ||||
\(657\) | 184.156 | 0.280299 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −362.780 | −0.550500 | −0.275250 | − | 0.961373i | \(-0.588761\pi\) | ||||
−0.275250 | + | 0.961373i | \(0.588761\pi\) | |||||||
\(660\) | −30.2655 | + | 89.9820i | −0.0458567 | + | 0.136336i | ||||
\(661\) | −102.047 | − | 58.9169i | −0.154383 | − | 0.0891330i | 0.420818 | − | 0.907145i | \(-0.361743\pi\) |
−0.575201 | + | 0.818012i | \(0.695076\pi\) | |||||||
\(662\) | −422.893 | − | 69.2149i | −0.638811 | − | 0.104554i | ||||
\(663\) | 108.409 | − | 62.5902i | 0.163513 | − | 0.0944045i | ||||
\(664\) | −25.5635 | − | 13.5269i | −0.0384992 | − | 0.0203719i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −291.186 | + | 110.058i | −0.437216 | + | 0.165252i | ||||
\(667\) | −395.397 | − | 684.848i | −0.592799 | − | 1.02676i | ||||
\(668\) | 831.637 | − | 167.833i | 1.24496 | − | 0.251247i | ||||
\(669\) | 31.2918 | + | 18.0663i | 0.0467740 | + | 0.0270050i | ||||
\(670\) | 80.0552 | + | 65.5132i | 0.119485 | + | 0.0977808i | ||||
\(671\) | − | 169.017i | − | 0.251888i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.56854 | −0.00976009 | −0.00488005 | − | 0.999988i | \(-0.501553\pi\) | ||||
−0.00488005 | + | 0.999988i | \(0.501553\pi\) | |||||||
\(674\) | 207.789 | − | 253.913i | 0.308293 | − | 0.376725i | ||||
\(675\) | 244.701 | − | 423.834i | 0.362519 | − | 0.627902i | ||||
\(676\) | −131.827 | − | 653.223i | −0.195010 | − | 0.966306i | ||||
\(677\) | 108.942 | − | 62.8978i | 0.160919 | − | 0.0929066i | −0.417378 | − | 0.908733i | \(-0.637051\pi\) |
0.578297 | + | 0.815826i | \(0.303718\pi\) | |||||||
\(678\) | −33.2548 | − | 87.9840i | −0.0490484 | − | 0.129770i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −137.186 | + | 259.257i | −0.201744 | + | 0.381260i | ||||
\(681\) | −180.622 | − | 312.847i | −0.265231 | − | 0.459394i | ||||
\(682\) | −67.6879 | + | 413.563i | −0.0992491 | + | 0.606397i | ||||
\(683\) | 276.887 | − | 479.583i | 0.405399 | − | 0.702171i | −0.588969 | − | 0.808156i | \(-0.700466\pi\) |
0.994368 | + | 0.105984i | \(0.0337994\pi\) | |||||||
\(684\) | −250.514 | − | 84.2603i | −0.366248 | − | 0.123188i | ||||
\(685\) | − | 88.8274i | − | 0.129675i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 255.652i | − | 0.372128i | ||||||
\(688\) | 253.242 | − | 106.553i | 0.368084 | − | 0.154874i | ||||
\(689\) | −75.7990 | + | 131.288i | −0.110013 | + | 0.190548i | ||||
\(690\) | 367.889 | + | 60.2124i | 0.533172 | + | 0.0872644i | ||||
\(691\) | 523.413 | + | 906.577i | 0.757471 | + | 1.31198i | 0.944136 | + | 0.329555i | \(0.106899\pi\) |
−0.186665 | + | 0.982424i | \(0.559768\pi\) | |||||||
\(692\) | −482.090 | − | 546.639i | −0.696662 | − | 0.789941i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −77.5635 | − | 205.214i | −0.111763 | − | 0.295697i | ||||
\(695\) | 246.515 | − | 142.325i | 0.354698 | − | 0.204785i | ||||
\(696\) | 325.980 | + | 519.366i | 0.468362 | + | 0.746215i | ||||
\(697\) | 319.019 | − | 552.558i | 0.457703 | − | 0.792766i | ||||
\(698\) | 717.367 | + | 587.058i | 1.02775 | + | 0.841057i | ||||
\(699\) | −1431.02 | −2.04724 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 625.993i | − | 0.893000i | −0.894784 | − | 0.446500i | \(-0.852670\pi\) | ||
0.894784 | − | 0.446500i | \(-0.147330\pi\) | |||||||
\(702\) | −51.9511 | − | 42.5142i | −0.0740044 | − | 0.0605615i | ||||
\(703\) | 1261.76 | + | 728.476i | 1.79482 | + | 1.03624i | ||||
\(704\) | 286.276 | − | 21.1678i | 0.406643 | − | 0.0300680i | ||||
\(705\) | −95.5980 | − | 165.581i | −0.135600 | − | 0.234866i | ||||
\(706\) | 55.2233 | + | 146.107i | 0.0782200 | + | 0.206951i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −630.500 | + | 556.048i | −0.890536 | + | 0.785379i | ||||
\(709\) | 513.979 | − | 296.746i | 0.724935 | − | 0.418541i | −0.0916314 | − | 0.995793i | \(-0.529208\pi\) |
0.816566 | + | 0.577252i | \(0.195875\pi\) | |||||||
\(710\) | 312.624 | + | 51.1672i | 0.440316 | + | 0.0720665i | ||||
\(711\) | 89.0461 | + | 51.4108i | 0.125241 | + | 0.0723077i | ||||
\(712\) | 13.0046 | + | 352.231i | 0.0182649 | + | 0.494706i | ||||
\(713\) | 1645.55 | 2.30792 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.7737 | −0.0150682 | ||||||||
\(716\) | 216.885 | + | 72.9492i | 0.302912 | + | 0.101884i | ||||
\(717\) | −438.546 | − | 253.194i | −0.611640 | − | 0.353130i | ||||
\(718\) | −117.947 | + | 720.639i | −0.164272 | + | 1.00368i | ||||
\(719\) | −529.578 | + | 305.752i | −0.736549 | + | 0.425247i | −0.820813 | − | 0.571197i | \(-0.806479\pi\) |
0.0842645 | + | 0.996443i | \(0.473146\pi\) | |||||||
\(720\) | −65.3667 | − | 8.23543i | −0.0907870 | − | 0.0114381i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 182.094 | + | 481.775i | 0.252208 | + | 0.667279i | ||||
\(723\) | 785.051 | + | 1359.75i | 1.08582 | + | 1.88070i | ||||
\(724\) | −1279.06 | + | 258.127i | −1.76666 | + | 0.356530i | ||||
\(725\) | −439.355 | − | 253.662i | −0.606007 | − | 0.349878i | ||||
\(726\) | −436.270 | + | 533.110i | −0.600924 | + | 0.734311i | ||||
\(727\) | 944.144i | 1.29868i | 0.760496 | + | 0.649342i | \(0.224956\pi\) | ||||
−0.760496 | + | 0.649342i | \(0.775044\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 405.489 | 0.556227 | ||||||||
\(730\) | −166.272 | − | 136.069i | −0.227770 | − | 0.186395i | ||||
\(731\) | 203.113 | − | 351.802i | 0.277856 | − | 0.481261i | ||||
\(732\) | 504.454 | − | 101.804i | 0.689145 | − | 0.139076i | ||||
\(733\) | −189.014 | + | 109.127i | −0.257863 | + | 0.148878i | −0.623360 | − | 0.781935i | \(-0.714233\pi\) |
0.365496 | + | 0.930813i | \(0.380899\pi\) | |||||||
\(734\) | −412.965 | + | 156.086i | −0.562622 | + | 0.212651i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −263.598 | − | 1095.94i | −0.358149 | − | 1.48905i | ||||
\(737\) | −74.8427 | − | 129.631i | −0.101550 | − | 0.175891i | ||||
\(738\) | 141.432 | + | 23.1482i | 0.191642 | + | 0.0313661i | ||||
\(739\) | 3.64971 | − | 6.32149i | 0.00493872 | − | 0.00855411i | −0.863545 | − | 0.504271i | \(-0.831761\pi\) |
0.868484 | + | 0.495717i | \(0.165095\pi\) | |||||||
\(740\) | 344.226 | + | 115.780i | 0.465170 | + | 0.156460i | ||||
\(741\) | − | 131.600i | − | 0.177598i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 106.867i | − | 0.143832i | −0.997411 | − | 0.0719159i | \(-0.977089\pi\) | ||
0.997411 | − | 0.0719159i | \(-0.0229113\pi\) | |||||||
\(744\) | −1275.11 | + | 47.0778i | −1.71386 | + | 0.0632766i | ||||
\(745\) | 149.025 | − | 258.119i | 0.200034 | − | 0.346469i | ||||
\(746\) | 81.2623 | − | 496.500i | 0.108931 | − | 0.665550i | ||||
\(747\) | −4.80256 | − | 8.31828i | −0.00642913 | − | 0.0111356i | ||||
\(748\) | 318.323 | − | 280.734i | 0.425565 | − | 0.375313i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 471.196 | − | 178.095i | 0.628261 | − | 0.237460i | ||||
\(751\) | 110.387 | − | 63.7317i | 0.146986 | − | 0.0848624i | −0.424703 | − | 0.905333i | \(-0.639622\pi\) |
0.571689 | + | 0.820470i | \(0.306288\pi\) | |||||||
\(752\) | −349.378 | + | 460.609i | −0.464598 | + | 0.612512i | ||||
\(753\) | −213.250 | + | 369.359i | −0.283200 | + | 0.490517i | ||||
\(754\) | −44.0711 | + | 53.8536i | −0.0584497 | + | 0.0714239i | ||||
\(755\) | 177.849 | 0.235562 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 704.275i | 0.930350i | 0.885219 | + | 0.465175i | \(0.154009\pi\) | ||||
−0.885219 | + | 0.465175i | \(0.845991\pi\) | |||||||
\(758\) | 362.288 | − | 442.705i | 0.477952 | − | 0.584043i | ||||
\(759\) | −467.153 | − | 269.711i | −0.615485 | − | 0.355350i | ||||
\(760\) | 163.927 | + | 261.175i | 0.215693 | + | 0.343652i | ||||
\(761\) | 501.465 | + | 868.563i | 0.658955 | + | 1.14134i | 0.980886 | + | 0.194581i | \(0.0623348\pi\) |
−0.321931 | + | 0.946763i | \(0.604332\pi\) | |||||||
\(762\) | 798.583 | − | 301.836i | 1.04801 | − | 0.396110i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 256.804 | + | 291.188i | 0.336131 | + | 0.381137i | ||||
\(765\) | −84.3614 | + | 48.7061i | −0.110276 | + | 0.0636681i | ||||
\(766\) | −34.5311 | + | 210.980i | −0.0450798 | + | 0.275431i | ||||
\(767\) | −82.6213 | − | 47.7014i | −0.107720 | − | 0.0621922i | ||||
\(768\) | 235.612 | + | 841.683i | 0.306786 | + | 1.09594i | ||||
\(769\) | −646.950 | −0.841288 | −0.420644 | − | 0.907226i | \(-0.638196\pi\) | ||||
−0.420644 | + | 0.907226i | \(0.638196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1459.07 | −1.89244 | ||||||||
\(772\) | 596.383 | + | 200.594i | 0.772517 | + | 0.259836i | ||||
\(773\) | 488.668 | + | 282.132i | 0.632170 | + | 0.364984i | 0.781592 | − | 0.623790i | \(-0.214408\pi\) |
−0.149422 | + | 0.988774i | \(0.547741\pi\) | |||||||
\(774\) | 90.0466 | + | 14.7379i | 0.116339 | + | 0.0190413i | ||||
\(775\) | 914.245 | − | 527.840i | 1.17967 | − | 0.681083i | ||||
\(776\) | −679.584 | − | 359.602i | −0.875752 | − | 0.463404i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −144.392 | + | 54.5750i | −0.185594 | + | 0.0701478i | ||||
\(779\) | −335.380 | − | 580.895i | −0.430526 | − | 0.745693i | ||||
\(780\) | −6.48936 | − | 32.1558i | −0.00831969 | − | 0.0412253i | ||||
\(781\) | −396.977 | − | 229.195i | −0.508293 | − | 0.293463i | ||||
\(782\) | −1289.78 | − | 1055.49i | −1.64934 | − | 1.34974i | ||||
\(783\) | − | 486.195i | − | 0.620939i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 328.794 | 0.418846 | ||||||||
\(786\) | 433.970 | − | 530.299i | 0.552125 | − | 0.674680i | ||||
\(787\) | −461.673 | + | 799.640i | −0.586623 | + | 1.01606i | 0.408048 | + | 0.912961i | \(0.366210\pi\) |
−0.994671 | + | 0.103101i | \(0.967124\pi\) | |||||||
\(788\) | 486.655 | − | 98.2120i | 0.617583 | − | 0.124635i | ||||
\(789\) | 761.740 | − | 439.791i | 0.965451 | − | 0.557403i | ||||
\(790\) | −42.4121 | − | 112.212i | −0.0536862 | − | 0.142040i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 84.2641 | + | 44.5884i | 0.106394 | + | 0.0562984i | ||||
\(793\) | 29.2010 | + | 50.5776i | 0.0368235 | + | 0.0637801i | ||||
\(794\) | −212.404 | + | 1297.76i | −0.267512 | + | 1.63446i | ||||
\(795\) | 258.794 | − | 448.244i | 0.325527 | − | 0.563829i | ||||
\(796\) | 230.779 | − | 686.127i | 0.289923 | − | 0.861969i | ||||
\(797\) | − | 207.983i | − | 0.260957i | −0.991451 | − | 0.130479i | \(-0.958349\pi\) | ||
0.991451 | − | 0.130479i | \(-0.0416514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 854.785i | 1.06982i | ||||||||
\(800\) | −497.994 | − | 524.335i | −0.622492 | − | 0.655419i | ||||
\(801\) | −58.5290 | + | 101.375i | −0.0730699 | + | 0.126561i | ||||
\(802\) | −629.216 | − | 102.984i | −0.784558 | − | 0.128409i | ||||
\(803\) | 155.446 | + | 269.240i | 0.193581 | + | 0.335293i | ||||
\(804\) | 341.823 | − | 301.460i | 0.425153 | − | 0.374950i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −51.1960 | − | 135.452i | −0.0635186 | − | 0.168054i | ||||
\(807\) | −636.438 | + | 367.448i | −0.788647 | + | 0.455326i | ||||
\(808\) | −83.4255 | − | 132.917i | −0.103249 | − | 0.164502i | ||||
\(809\) | −170.270 | + | 294.916i | −0.210470 | + | 0.364544i | −0.951862 | − | 0.306528i | \(-0.900833\pi\) |
0.741392 | + | 0.671072i | \(0.234166\pi\) | |||||||
\(810\) | 234.732 | + | 192.093i | 0.289793 | + | 0.237152i | ||||
\(811\) | −907.380 | −1.11884 | −0.559420 | − | 0.828884i | \(-0.688976\pi\) | ||||
−0.559420 | + | 0.828884i | \(0.688976\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1292.45i | 1.58973i | ||||||||
\(814\) | −406.695 | − | 332.819i | −0.499626 | − | 0.408869i | ||||
\(815\) | −322.846 | − | 186.395i | −0.396130 | − | 0.228706i | ||||
\(816\) | 1029.63 | + | 780.985i | 1.26180 | + | 0.957090i | ||||
\(817\) | −213.529 | − | 369.843i | −0.261357 | − | 0.452684i | ||||
\(818\) | 102.718 | + | 271.766i | 0.125572 | + | 0.332232i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −110.593 | − | 125.401i | −0.134869 | − | 0.152928i | ||||
\(821\) | 548.560 | − | 316.711i | 0.668161 | − | 0.385763i | −0.127219 | − | 0.991875i | \(-0.540605\pi\) |
0.795379 | + | 0.606112i | \(0.207272\pi\) | |||||||
\(822\) | −386.224 | − | 63.2132i | −0.469858 | − | 0.0769018i | ||||
\(823\) | 124.404 | + | 71.8247i | 0.151159 | + | 0.0872718i | 0.573672 | − | 0.819085i | \(-0.305518\pi\) |
−0.422513 | + | 0.906357i | \(0.638852\pi\) | |||||||
\(824\) | 344.438 | − | 12.7169i | 0.418008 | − | 0.0154331i | ||||
\(825\) | −346.059 | −0.419465 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1545.57 | 1.86888 | 0.934442 | − | 0.356114i | \(-0.115899\pi\) | ||||
0.934442 | + | 0.356114i | \(0.115899\pi\) | |||||||
\(828\) | 119.342 | − | 354.815i | 0.144133 | − | 0.428521i | ||||
\(829\) | 644.285 | + | 371.978i | 0.777183 | + | 0.448707i | 0.835431 | − | 0.549595i | \(-0.185218\pi\) |
−0.0582482 | + | 0.998302i | \(0.518551\pi\) | |||||||
\(830\) | −1.81002 | + | 11.0589i | −0.00218074 | + | 0.0133240i | ||||
\(831\) | −492.155 | + | 284.146i | −0.592244 | + | 0.341932i | ||||
\(832\) | −82.0101 | + | 55.7944i | −0.0985698 | + | 0.0670606i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −443.404 | − | 1173.14i | −0.531660 | − | 1.40664i | ||||
\(835\) | −164.362 | − | 284.683i | −0.196840 | − | 0.340937i | ||||
\(836\) | −88.2675 | − | 437.379i | −0.105583 | − | 0.523181i | ||||
\(837\) | 876.170 | + | 505.857i | 1.04680 | + | 0.604369i | ||||
\(838\) | 895.524 | − | 1094.30i | 1.06864 | − | 1.30585i | ||||
\(839\) | 96.3107i | 0.114792i | 0.998351 | + | 0.0573961i | \(0.0182798\pi\) | ||||
−0.998351 | + | 0.0573961i | \(0.981720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 337.000 | 0.400713 | ||||||||
\(842\) | −188.814 | − | 154.516i | −0.224244 | − | 0.183510i | ||||
\(843\) | 719.997 | − | 1247.07i | 0.854089 | − | 1.47933i | ||||
\(844\) | −129.810 | − | 643.227i | −0.153803 | − | 0.762118i | ||||
\(845\) | −223.609 | + | 129.101i | −0.264626 | + | 0.152782i | ||||
\(846\) | −179.598 | + | 67.8817i | −0.212291 | + | 0.0802384i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1552.76 | − | 195.630i | −1.83109 | − | 0.230696i | ||||
\(849\) | 589.701 | + | 1021.39i | 0.694583 | + | 1.20305i | ||||
\(850\) | −1055.15 | − | 172.697i | −1.24136 | − | 0.203173i | ||||
\(851\) | −1031.78 | + | 1787.09i | −1.21243 | + | 2.09999i | ||||
\(852\) | 444.953 | − | 1322.89i | 0.522245 | − | 1.55268i | ||||
\(853\) | − | 904.866i | − | 1.06080i | −0.847746 | − | 0.530402i | \(-0.822041\pi\) | ||
0.847746 | − | 0.530402i | \(-0.177959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 102.408i | 0.119775i | ||||||||
\(856\) | 4.60396 | + | 124.699i | 0.00537845 | + | 0.145676i | ||||
\(857\) | −80.4659 | + | 139.371i | −0.0938926 | + | 0.162627i | −0.909146 | − | 0.416478i | \(-0.863264\pi\) |
0.815253 | + | 0.579105i | \(0.196598\pi\) | |||||||
\(858\) | −7.66704 | + | 46.8445i | −0.00893594 | + | 0.0545973i | ||||
\(859\) | −115.846 | − | 200.652i | −0.134862 | − | 0.233587i | 0.790683 | − | 0.612226i | \(-0.209726\pi\) |
−0.925545 | + | 0.378638i | \(0.876392\pi\) | |||||||
\(860\) | −70.4121 | − | 79.8398i | −0.0818746 | − | 0.0928370i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1101.66 | + | 416.388i | −1.27803 | + | 0.483048i | ||||
\(863\) | −1158.18 | + | 668.674i | −1.34204 | + | 0.774825i | −0.987106 | − | 0.160068i | \(-0.948829\pi\) |
−0.354931 | + | 0.934893i | \(0.615495\pi\) | |||||||
\(864\) | 196.549 | − | 664.563i | 0.227487 | − | 0.769170i | ||||
\(865\) | −141.201 | + | 244.567i | −0.163238 | + | 0.282737i | ||||
\(866\) | 174.410 | − | 213.123i | 0.201397 | − | 0.246101i | ||||
\(867\) | 924.046 | 1.06580 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 173.583i | 0.199750i | ||||||||
\(870\) | 150.468 | − | 183.868i | 0.172952 | − | 0.211342i | ||||
\(871\) | 44.7929 | + | 25.8612i | 0.0514269 | + | 0.0296914i | ||||
\(872\) | −16.3813 | − | 26.0994i | −0.0187859 | − | 0.0299305i | ||||
\(873\) | −127.672 | − | 221.134i | −0.146245 | − | 0.253304i | ||||
\(874\) | −1638.92 | + | 619.455i | −1.87520 | + | 0.708759i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −709.955 | + | 626.122i | −0.810451 | + | 0.714751i | ||||
\(877\) | 1243.73 | − | 718.068i | 1.41816 | − | 0.818777i | 0.422026 | − | 0.906584i | \(-0.361319\pi\) |
0.996138 | + | 0.0878061i | \(0.0279856\pi\) | |||||||
\(878\) | 142.314 | − | 869.517i | 0.162089 | − | 0.990338i | ||||
\(879\) | −1511.04 | − | 872.397i | −1.71904 | − | 0.992488i | ||||
\(880\) | −43.1354 | − | 102.519i | −0.0490175 | − | 0.116499i | ||||
\(881\) | −186.706 | −0.211926 | −0.105963 | − | 0.994370i | \(-0.533792\pi\) | ||||
−0.105963 | + | 0.994370i | \(0.533792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1277.99 | 1.44733 | 0.723664 | − | 0.690153i | \(-0.242457\pi\) | ||||
0.723664 | + | 0.690153i | \(0.242457\pi\) | |||||||
\(884\) | −46.7545 | + | 139.006i | −0.0528898 | + | 0.157246i | ||||
\(885\) | 282.087 | + | 162.863i | 0.318742 | + | 0.184026i | ||||
\(886\) | 961.325 | + | 157.340i | 1.08502 | + | 0.177585i | ||||
\(887\) | −849.326 | + | 490.359i | −0.957526 | + | 0.552828i | −0.895411 | − | 0.445241i | \(-0.853118\pi\) |
−0.0621155 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(888\) | 748.382 | − | 1414.31i | 0.842772 | − | 1.59269i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 127.748 | − | 48.2844i | 0.143538 | − | 0.0542521i | ||||
\(891\) | −219.449 | − | 380.096i | −0.246295 | − | 0.426595i | ||||
\(892\) | −41.4955 | + | 8.37420i | −0.0465196 | + | 0.00938812i | ||||
\(893\) | 778.228 | + | 449.310i | 0.871476 | + | 0.503147i | ||||
\(894\) | −1016.26 | − | 831.654i | −1.13675 | − | 0.930262i | ||||
\(895\) | − | 88.6605i | − | 0.0990621i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 186.392 | 0.207795 | ||||||||
\(898\) | 334.440 | − | 408.676i | 0.372427 | − | 0.455095i | ||||
\(899\) | 524.382 | − | 908.256i | 0.583295 | − | 1.01030i | ||||
\(900\) | −47.5086 | − | 235.412i | −0.0527873 | − | 0.261569i | ||||
\(901\) | −2003.98 | + | 1157.00i | −2.22417 | + | 1.28412i | ||||
\(902\) | 85.5391 | + | 226.315i | 0.0948327 | + | 0.250904i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 97.4012 | + | 51.5398i | 0.107745 | + | 0.0570131i | ||||
\(905\) | 252.789 | + | 437.843i | 0.279325 | + | 0.483805i | ||||
\(906\) | 126.565 | − | 773.294i | 0.139697 | − | 0.853525i | ||||
\(907\) | 329.186 | − | 570.167i | 0.362939 | − | 0.628629i | −0.625504 | − | 0.780221i | \(-0.715107\pi\) |
0.988443 | + | 0.151592i | \(0.0484399\pi\) | |||||||
\(908\) | 401.142 | + | 134.924i | 0.441786 | + | 0.148595i | ||||
\(909\) | − | 52.1173i | − | 0.0573348i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 276.507i | − | 0.303520i | −0.988417 | − | 0.151760i | \(-0.951506\pi\) | ||
0.988417 | − | 0.151760i | \(-0.0484941\pi\) | |||||||
\(912\) | 1252.25 | − | 526.894i | 1.37309 | − | 0.577735i | ||||
\(913\) | 8.10765 | − | 14.0429i | 0.00888023 | − | 0.0153810i | ||||
\(914\) | 1015.14 | + | 166.148i | 1.11066 | + | 0.181781i | ||||
\(915\) | −99.6985 | − | 172.683i | −0.108960 | − | 0.188724i | ||||
\(916\) | 198.111 | + | 224.636i | 0.216278 | + | 0.245236i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −362.274 | − | 958.487i | −0.394634 | − | 1.04410i | ||||
\(919\) | −1160.24 | + | 669.867i | −1.26251 | + | 0.728908i | −0.973559 | − | 0.228437i | \(-0.926639\pi\) |
−0.288948 | + | 0.957345i | \(0.593305\pi\) | |||||||
\(920\) | −369.916 | + | 232.178i | −0.402083 | + | 0.252367i | ||||
\(921\) | −381.250 | + | 660.344i | −0.413952 | + | 0.716986i | ||||
\(922\) | 313.000 | + | 256.144i | 0.339479 | + | 0.277813i | ||||
\(923\) | 158.392 | 0.171606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1323.85i | 1.43119i | ||||||||
\(926\) | 1118.51 | + | 915.335i | 1.20790 | + | 0.988483i | ||||
\(927\) | 99.1324 | + | 57.2341i | 0.106939 | + | 0.0617412i | ||||
\(928\) | −688.900 | − | 203.747i | −0.742349 | − | 0.219555i | ||||
\(929\) | −17.7006 | − | 30.6583i | −0.0190534 | − | 0.0330014i | 0.856342 | − | 0.516410i | \(-0.172732\pi\) |
−0.875395 | + | 0.483409i | \(0.839399\pi\) | |||||||
\(930\) | 174.794 | + | 462.461i | 0.187950 | + | 0.497270i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1257.41 | − | 1108.93i | 1.34915 | − | 1.18984i | ||||
\(933\) | −36.6606 | + | 21.1660i | −0.0392933 | + | 0.0226860i | ||||
\(934\) | 685.444 | + | 112.187i | 0.733880 | + | 0.120114i | ||||
\(935\) | −142.418 | − | 82.2252i | −0.152319 | − | 0.0879414i | ||||
\(936\) | −32.9193 | + | 1.21540i | −0.0351702 | + | 0.00129850i | ||||
\(937\) | 610.235 | 0.651265 | 0.325633 | − | 0.945496i | \(-0.394423\pi\) | ||||
0.325633 | + | 0.945496i | \(0.394423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1399.99 | 1.49094 | ||||||||
\(940\) | 212.312 | + | 71.4112i | 0.225864 | + | 0.0759694i | ||||
\(941\) | 1604.66 | + | 926.450i | 1.70527 | + | 0.984537i | 0.940222 | + | 0.340563i | \(0.110618\pi\) |
0.765047 | + | 0.643975i | \(0.222716\pi\) | |||||||
\(942\) | 233.983 | − | 1429.60i | 0.248390 | − | 1.51763i | ||||
\(943\) | 822.752 | − | 475.016i | 0.872483 | − | 0.503728i | ||||
\(944\) | 123.113 | − | 977.177i | 0.130416 | − | 1.03514i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 54.4609 | + | 144.090i | 0.0575697 | + | 0.152315i | ||||
\(947\) | 916.448 | + | 1587.33i | 0.967738 | + | 1.67617i | 0.702072 | + | 0.712106i | \(0.252259\pi\) |
0.265666 | + | 0.964065i | \(0.414408\pi\) | |||||||
\(948\) | −518.082 | + | 104.554i | −0.546500 | + | 0.110289i | ||||
\(949\) | −93.0332 | − | 53.7128i | −0.0980329 | − | 0.0565993i | ||||
\(950\) | −711.864 | + | 869.876i | −0.749330 | + | 0.915659i | ||||
\(951\) | − | 444.927i | − | 0.467852i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 349.687 | 0.366933 | 0.183467 | − | 0.983026i | \(-0.441268\pi\) | ||||
0.183467 | + | 0.983026i | \(0.441268\pi\) | |||||||
\(954\) | −402.239 | − | 329.172i | −0.421634 | − | 0.345044i | ||||
\(955\) | 75.2162 | − | 130.278i | 0.0787604 | − | 0.136417i | ||||
\(956\) | 581.547 | − | 117.362i | 0.608313 | − | 0.122764i | ||||
\(957\) | −297.733 | + | 171.896i | −0.311110 | + | 0.179620i | ||||
\(958\) | 54.5929 | − | 20.6342i | 0.0569864 | − | 0.0215388i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 280.000 | − | 190.494i | 0.291667 | − | 0.198431i | ||||
\(961\) | 610.676 | + | 1057.72i | 0.635459 | + | 1.10065i | ||||
\(962\) | 179.203 | + | 29.3302i | 0.186282 | + | 0.0304888i | ||||
\(963\) | −20.7208 | + | 35.8894i | −0.0215169 | + | 0.0372684i | ||||
\(964\) | −1743.51 | − | 586.429i | −1.80862 | − | 0.608329i | ||||
\(965\) | − | 243.796i | − | 0.252639i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 632.128i | − | 0.653700i | −0.945076 | − | 0.326850i | \(-0.894013\pi\) | ||
0.945076 | − | 0.326850i | \(-0.105987\pi\) | |||||||
\(968\) | −29.7768 | − | 806.509i | −0.0307611 | − | 0.833170i | ||||
\(969\) | 1004.37 | − | 1739.62i | 1.03650 | − | 1.79528i | ||||
\(970\) | −48.1177 | + | 293.992i | −0.0496059 | + | 0.303085i | ||||
\(971\) | −328.248 | − | 568.543i | −0.338052 | − | 0.585523i | 0.646014 | − | 0.763325i | \(-0.276435\pi\) |
−0.984066 | + | 0.177802i | \(0.943101\pi\) | |||||||
\(972\) | 417.536 | − | 368.232i | 0.429564 | − | 0.378840i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1312.65 | − | 496.136i | 1.34769 | − | 0.509380i | ||||
\(975\) | 103.557 | − | 59.7886i | 0.106212 | − | 0.0613217i | ||||
\(976\) | −364.363 | + | 480.366i | −0.373323 | + | 0.492178i | ||||
\(977\) | −84.6569 | + | 146.630i | −0.0866498 | + | 0.150082i | −0.906093 | − | 0.423078i | \(-0.860949\pi\) |
0.819443 | + | 0.573160i | \(0.194283\pi\) | |||||||
\(978\) | −1040.20 | + | 1271.10i | −1.06360 | + | 1.29969i | ||||
\(979\) | −197.616 | −0.201855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 10.2337i | − | 0.0104319i | ||||||
\(982\) | −75.9361 | + | 92.7917i | −0.0773280 | + | 0.0944926i | ||||
\(983\) | −605.012 | − | 349.304i | −0.615475 | − | 0.355345i | 0.159630 | − | 0.987177i | \(-0.448970\pi\) |
−0.775105 | + | 0.631832i | \(0.782303\pi\) | |||||||
\(984\) | −623.947 | + | 391.621i | −0.634093 | + | 0.397988i | ||||
\(985\) | −96.1808 | − | 166.590i | −0.0976455 | − | 0.169127i | ||||
\(986\) | −993.588 | + | 375.541i | −1.00770 | + | 0.380873i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 101.980 | + | 115.634i | 0.103218 | + | 0.117039i | ||||
\(989\) | 523.828 | − | 302.432i | 0.529654 | − | 0.305796i | ||||
\(990\) | 5.96629 | − | 36.4532i | 0.00602656 | − | 0.0368214i | ||||
\(991\) | −372.133 | − | 214.851i | −0.375513 | − | 0.216802i | 0.300352 | − | 0.953829i | \(-0.402896\pi\) |
−0.675864 | + | 0.737026i | \(0.736229\pi\) | |||||||
\(992\) | 1083.93 | − | 1029.48i | 1.09267 | − | 1.03778i | ||||
\(993\) | 731.529 | 0.736686 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −280.483 | −0.281892 | ||||||||
\(996\) | 46.7964 | + | 15.7400i | 0.0469844 | + | 0.0158032i | ||||
\(997\) | 45.3720 | + | 26.1955i | 0.0455085 | + | 0.0262743i | 0.522582 | − | 0.852589i | \(-0.324969\pi\) |
−0.477073 | + | 0.878864i | \(0.658302\pi\) | |||||||
\(998\) | 166.355 | + | 27.2274i | 0.166688 | + | 0.0272819i | ||||
\(999\) | −1098.74 | + | 634.357i | −1.09984 | + | 0.634992i |
(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 | 392.3.k.i.67.3 | 8 | ||
7.2 | even | 3 | inner | 392.3.k.i.275.1 | 8 | ||
7.3 | odd | 6 | 392.3.g.h.99.4 | 4 | |||
7.4 | even | 3 | 56.3.g.a.43.4 | yes | 4 | ||
7.5 | odd | 6 | 392.3.k.j.275.1 | 8 | |||
7.6 | odd | 2 | 392.3.k.j.67.3 | 8 | |||
8.3 | odd | 2 | inner | 392.3.k.i.67.1 | 8 | ||
21.11 | odd | 6 | 504.3.g.a.379.1 | 4 | |||
28.3 | even | 6 | 1568.3.g.h.687.4 | 4 | |||
28.11 | odd | 6 | 224.3.g.a.15.1 | 4 | |||
56.3 | even | 6 | 392.3.g.h.99.3 | 4 | |||
56.11 | odd | 6 | 56.3.g.a.43.3 | ✓ | 4 | ||
56.19 | even | 6 | 392.3.k.j.275.3 | 8 | |||
56.27 | even | 2 | 392.3.k.j.67.1 | 8 | |||
56.45 | odd | 6 | 1568.3.g.h.687.3 | 4 | |||
56.51 | odd | 6 | inner | 392.3.k.i.275.3 | 8 | ||
56.53 | even | 6 | 224.3.g.a.15.2 | 4 | |||
84.11 | even | 6 | 2016.3.g.a.1135.3 | 4 | |||
112.11 | odd | 12 | 1792.3.d.g.1023.8 | 8 | |||
112.53 | even | 12 | 1792.3.d.g.1023.2 | 8 | |||
112.67 | odd | 12 | 1792.3.d.g.1023.1 | 8 | |||
112.109 | even | 12 | 1792.3.d.g.1023.7 | 8 | |||
168.11 | even | 6 | 504.3.g.a.379.2 | 4 | |||
168.53 | odd | 6 | 2016.3.g.a.1135.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.a.43.3 | ✓ | 4 | 56.11 | odd | 6 | ||
56.3.g.a.43.4 | yes | 4 | 7.4 | even | 3 | ||
224.3.g.a.15.1 | 4 | 28.11 | odd | 6 | |||
224.3.g.a.15.2 | 4 | 56.53 | even | 6 | |||
392.3.g.h.99.3 | 4 | 56.3 | even | 6 | |||
392.3.g.h.99.4 | 4 | 7.3 | odd | 6 | |||
392.3.k.i.67.1 | 8 | 8.3 | odd | 2 | inner | ||
392.3.k.i.67.3 | 8 | 1.1 | even | 1 | trivial | ||
392.3.k.i.275.1 | 8 | 7.2 | even | 3 | inner | ||
392.3.k.i.275.3 | 8 | 56.51 | odd | 6 | inner | ||
392.3.k.j.67.1 | 8 | 56.27 | even | 2 | |||
392.3.k.j.67.3 | 8 | 7.6 | odd | 2 | |||
392.3.k.j.275.1 | 8 | 7.5 | odd | 6 | |||
392.3.k.j.275.3 | 8 | 56.19 | even | 6 | |||
504.3.g.a.379.1 | 4 | 21.11 | odd | 6 | |||
504.3.g.a.379.2 | 4 | 168.11 | even | 6 | |||
1568.3.g.h.687.3 | 4 | 56.45 | odd | 6 | |||
1568.3.g.h.687.4 | 4 | 28.3 | even | 6 | |||
1792.3.d.g.1023.1 | 8 | 112.67 | odd | 12 | |||
1792.3.d.g.1023.2 | 8 | 112.53 | even | 12 | |||
1792.3.d.g.1023.7 | 8 | 112.109 | even | 12 | |||
1792.3.d.g.1023.8 | 8 | 112.11 | odd | 12 | |||
2016.3.g.a.1135.2 | 4 | 168.53 | odd | 6 | |||
2016.3.g.a.1135.3 | 4 | 84.11 | even | 6 |