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 | 275.1 | ||
Root | \(-0.207107 - 0.0981308i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.275 |
Dual form | 392.3.k.i.67.1 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97374 | − | 0.323042i | −0.986869 | − | 0.161521i | ||||
\(3\) | −1.70711 | − | 2.95680i | −0.569036 | − | 0.985599i | −0.996662 | − | 0.0816428i | \(-0.973983\pi\) |
0.427626 | − | 0.903956i | \(-0.359350\pi\) | |||||||
\(4\) | 3.79129 | + | 1.27520i | 0.947822 | + | 0.318800i | ||||
\(5\) | 1.34221 | + | 0.774923i | 0.268441 | + | 0.154985i | 0.628179 | − | 0.778069i | \(-0.283801\pi\) |
−0.359738 | + | 0.933053i | \(0.617134\pi\) | |||||||
\(6\) | 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 | ||||
\(10\) | −2.39883 | − | 1.96308i | −0.239883 | − | 0.196308i | ||||
\(11\) | 2.24264 | + | 3.88437i | 0.203876 | + | 0.353124i | 0.949774 | − | 0.312936i | \(-0.101313\pi\) |
−0.745898 | + | 0.666060i | \(0.767979\pi\) | |||||||
\(12\) | −2.70163 | − | 13.3870i | −0.225135 | − | 1.11558i | ||||
\(13\) | 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 | ||||||
\(16\) | 12.7477 | + | 9.66930i | 0.796733 | + | 0.604332i | ||||
\(17\) | −11.8284 | − | 20.4874i | −0.695790 | − | 1.20514i | −0.969914 | − | 0.243449i | \(-0.921721\pi\) |
0.274124 | − | 0.961694i | \(-0.411612\pi\) | |||||||
\(18\) | 3.36526 | − | 4.11224i | 0.186959 | − | 0.228458i | ||||
\(19\) | 12.4350 | − | 21.5381i | 0.654475 | − | 1.13358i | −0.327550 | − | 0.944834i | \(-0.606223\pi\) |
0.982025 | − | 0.188750i | \(-0.0604437\pi\) | |||||||
\(20\) | 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 | \(-0.0556985\pi\) |
0.341598 | + | 0.939846i | \(0.389032\pi\) | |||||||
\(24\) | 1.00775 | + | 27.2951i | 0.0419896 | + | 1.13730i | ||||
\(25\) | −11.2990 | − | 19.5704i | −0.451960 | − | 0.782817i | ||||
\(26\) | 0.500665 | − | 3.05899i | 0.0192563 | − | 0.117653i | ||||
\(27\) | −21.6569 | −0.802106 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.4499i | 0.774136i | 0.922051 | + | 0.387068i | \(0.126512\pi\) | ||||
−0.922051 | + | 0.387068i | \(0.873488\pi\) | |||||||
\(30\) | −1.70938 | + | 10.4440i | −0.0569792 | + | 0.348135i | ||||
\(31\) | 40.4569 | − | 23.3578i | 1.30506 | − | 0.753478i | 0.323795 | − | 0.946127i | \(-0.395041\pi\) |
0.981268 | + | 0.192649i | \(0.0617079\pi\) | |||||||
\(32\) | −22.0371 | − | 23.2027i | −0.688659 | − | 0.725085i | ||||
\(33\) | 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 | \(-0.624114\pi\) |
−0.991078 | + | 0.133284i | \(0.957448\pi\) | |||||||
\(38\) | −31.5012 | + | 38.4935i | −0.828979 | + | 1.01299i | ||||
\(39\) | 4.58258 | − | 2.64575i | 0.117502 | − | 0.0678398i | ||||
\(40\) | −6.59133 | − | 10.5016i | −0.164783 | − | 0.262540i | ||||
\(41\) | −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 | \(0.563987\pi\) | |||||||
\(44\) | 3.54915 | + | 17.5866i | 0.0806625 | + | 0.399695i | ||||
\(45\) | −3.56604 | + | 2.05886i | −0.0792454 | + | 0.0457524i | ||||
\(46\) | −54.5204 | − | 44.6168i | −1.18523 | − | 0.969930i | ||||
\(47\) | −31.2918 | − | 18.0663i | −0.665783 | − | 0.384390i | 0.128694 | − | 0.991684i | \(-0.458921\pi\) |
−0.794477 | + | 0.607295i | \(0.792255\pi\) | |||||||
\(48\) | 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 | ||||
\(52\) | −1.97636 | + | 5.87591i | −0.0380070 | + | 0.112998i | ||||
\(53\) | −84.7102 | + | 48.9075i | −1.59831 | + | 0.922782i | −0.606492 | + | 0.795090i | \(0.707424\pi\) |
−0.991814 | + | 0.127693i | \(0.959243\pi\) | |||||||
\(54\) | 42.7450 | + | 6.99607i | 0.791573 | + | 0.129557i | ||||
\(55\) | 6.95149i | 0.126391i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −84.9117 | −1.48968 | ||||||||
\(58\) | 7.25227 | − | 44.3103i | 0.125039 | − | 0.763971i | ||||
\(59\) | −30.7782 | − | 53.3094i | −0.521664 | − | 0.903549i | −0.999682 | − | 0.0251987i | \(-0.991978\pi\) |
0.478018 | − | 0.878350i | \(-0.341355\pi\) | |||||||
\(60\) | 6.74773 | − | 20.0616i | 0.112462 | − | 0.334360i | ||||
\(61\) | −32.6340 | − | 18.8412i | −0.534983 | − | 0.308873i | 0.208060 | − | 0.978116i | \(-0.433285\pi\) |
−0.743043 | + | 0.669243i | \(0.766618\pi\) | |||||||
\(62\) | −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 | ||||
\(66\) | −19.3968 | + | 23.7024i | −0.293891 | + | 0.359127i | ||||
\(67\) | 16.6863 | + | 28.9015i | 0.249049 | + | 0.431366i | 0.963262 | − | 0.268563i | \(-0.0865486\pi\) |
−0.714213 | + | 0.699928i | \(0.753215\pi\) | |||||||
\(68\) | −18.7194 | − | 92.7574i | −0.275285 | − | 1.36408i | ||||
\(69\) | − | 120.265i | − | 1.74297i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 102.199i | − | 1.43942i | −0.694277 | − | 0.719708i | \(-0.744276\pi\) | ||
0.694277 | − | 0.719708i | \(-0.255724\pi\) | |||||||
\(72\) | 18.0026 | − | 11.2993i | 0.250036 | − | 0.156935i | ||||
\(73\) | −34.6569 | − | 60.0274i | −0.474751 | − | 0.822294i | 0.524830 | − | 0.851207i | \(-0.324129\pi\) |
−0.999582 | + | 0.0289132i | \(0.990795\pi\) | |||||||
\(74\) | 90.6733 | + | 74.2026i | 1.22532 | + | 1.00274i | ||||
\(75\) | −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 | \(-0.254565\pi\) |
−0.272645 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(80\) | 9.61710 | + | 22.8567i | 0.120214 | + | 0.285709i | ||||
\(81\) | 48.9264 | + | 84.7430i | 0.604030 | + | 1.04621i | ||||
\(82\) | 53.2328 | + | 8.71262i | 0.649181 | + | 0.106251i | ||||
\(83\) | 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 | ||||||
\(86\) | 33.8922 | + | 5.54714i | 0.394095 | + | 0.0645016i | ||||
\(87\) | 66.3799 | − | 38.3245i | 0.762987 | − | 0.440511i | ||||
\(88\) | −1.32389 | − | 35.8578i | −0.0150442 | − | 0.407475i | ||||
\(89\) | −22.0294 | + | 38.1561i | −0.247522 | + | 0.428720i | −0.962838 | − | 0.270081i | \(-0.912950\pi\) |
0.715316 | + | 0.698801i | \(0.246283\pi\) | |||||||
\(90\) | 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 | ||||
\(94\) | 55.9256 | + | 45.7668i | 0.594953 | + | 0.486880i | ||||
\(95\) | 33.3807 | − | 19.2724i | 0.351376 | − | 0.202867i | ||||
\(96\) | −30.9861 | + | 104.769i | −0.322772 | + | 1.09134i | ||||
\(97\) | 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 | ||||||||
\(100\) | −17.8815 | − | 88.6056i | −0.178815 | − | 0.886056i | ||||
\(101\) | −16.9881 | + | 9.80808i | −0.168199 | + | 0.0971097i | −0.581736 | − | 0.813377i | \(-0.697626\pi\) |
0.413537 | + | 0.910487i | \(0.364293\pi\) | |||||||
\(102\) | 102.305 | − | 125.014i | 1.00299 | − | 1.22563i | ||||
\(103\) | 37.3120 | + | 21.5421i | 0.362252 | + | 0.209146i | 0.670068 | − | 0.742300i | \(-0.266265\pi\) |
−0.307816 | + | 0.951446i | \(0.599598\pi\) | |||||||
\(104\) | 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 | −0.900166 | − | 0.435547i | \(-0.856555\pi\) |
0.827278 | + | 0.561793i | \(0.189888\pi\) | |||||||
\(108\) | −82.1074 | − | 27.6168i | −0.760253 | − | 0.255711i | ||||
\(109\) | −3.33576 | + | 1.92590i | −0.0306033 | + | 0.0176688i | −0.515224 | − | 0.857056i | \(-0.672291\pi\) |
0.484620 | + | 0.874725i | \(0.338958\pi\) | |||||||
\(110\) | 2.24562 | − | 13.7204i | 0.0204148 | − | 0.124731i | ||||
\(111\) | 200.013i | 1.80192i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.7746 | −0.121899 | −0.0609496 | − | 0.998141i | \(-0.519413\pi\) | ||||
−0.0609496 | + | 0.998141i | \(0.519413\pi\) | |||||||
\(114\) | 167.593 | + | 27.4300i | 1.47012 | + | 0.240614i | ||||
\(115\) | 27.2965 | + | 47.2789i | 0.237361 | + | 0.411121i | ||||
\(116\) | −28.6282 | + | 85.1142i | −0.246795 | + | 0.733743i | ||||
\(117\) | −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 | ||||
\(122\) | 58.3245 | + | 47.7298i | 0.478069 | + | 0.391228i | ||||
\(123\) | 46.0416 | + | 79.7464i | 0.374322 | + | 0.648345i | ||||
\(124\) | 183.170 | − | 36.9655i | 1.47718 | − | 0.298109i | ||||
\(125\) | − | 73.7695i | − | 0.590156i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 125.025i | − | 0.984445i | −0.870469 | − | 0.492223i | \(-0.836185\pi\) | ||
0.870469 | − | 0.492223i | \(-0.163815\pi\) | |||||||
\(128\) | −53.9608 | − | 116.070i | −0.421569 | − | 0.906796i | ||||
\(129\) | 29.3137 | + | 50.7728i | 0.227238 | + | 0.393588i | ||||
\(130\) | 3.04248 | − | 3.71782i | 0.0234037 | − | 0.0285986i | ||||
\(131\) | −50.1751 | + | 86.9059i | −0.383016 | + | 0.663404i | −0.991492 | − | 0.130169i | \(-0.958448\pi\) |
0.608475 | + | 0.793573i | \(0.291781\pi\) | |||||||
\(132\) | 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 | ||||
\(136\) | 6.98264 | + | 189.126i | 0.0513430 | + | 1.39063i | ||||
\(137\) | −28.6569 | − | 49.6351i | −0.209174 | − | 0.362300i | 0.742280 | − | 0.670089i | \(-0.233744\pi\) |
−0.951455 | + | 0.307789i | \(0.900411\pi\) | |||||||
\(138\) | −38.8506 | + | 237.371i | −0.281526 | + | 1.72008i | ||||
\(139\) | −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 | ||||||||
\(142\) | −33.0144 | + | 201.713i | −0.232496 | + | 1.42052i | ||||
\(143\) | −6.02017 | + | 3.47575i | −0.0420991 | + | 0.0243059i | ||||
\(144\) | −39.1826 | + | 16.4863i | −0.272101 | + | 0.114488i | ||||
\(145\) | −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 | \(-0.110051\pi\) |
0.176927 | + | 0.984224i | \(0.443384\pi\) | |||||||
\(150\) | 97.7261 | − | 119.418i | 0.651508 | − | 0.796123i | ||||
\(151\) | 99.3791 | − | 57.3765i | 0.658140 | − | 0.379977i | −0.133428 | − | 0.991058i | \(-0.542599\pi\) |
0.791568 | + | 0.611081i | \(0.209265\pi\) | |||||||
\(152\) | −168.517 | + | 105.770i | −1.10867 | + | 0.695854i | ||||
\(153\) | 62.8528 | 0.410803 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 72.4020 | 0.467110 | ||||||||
\(156\) | 20.7477 | − | 4.18710i | 0.132998 | − | 0.0268404i | ||||
\(157\) | 183.724 | − | 106.073i | 1.17022 | − | 0.675625i | 0.216486 | − | 0.976286i | \(-0.430540\pi\) |
0.953731 | + | 0.300661i | \(0.0972071\pi\) | |||||||
\(158\) | −59.9001 | − | 49.0193i | −0.379115 | − | 0.310249i | ||||
\(159\) | 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 | −0.215634 | − | 0.976474i | \(-0.569182\pi\) |
0.953469 | − | 0.301493i | \(-0.0974849\pi\) | |||||||
\(164\) | −102.253 | − | 34.3929i | −0.623495 | − | 0.209713i | ||||
\(165\) | 20.5541 | − | 11.8669i | 0.124571 | − | 0.0719208i | ||||
\(166\) | −7.13551 | − | 1.16787i | −0.0429850 | − | 0.00703535i | ||||
\(167\) | 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 | ||||||||
\(170\) | −11.8442 | + | 72.3661i | −0.0696715 | + | 0.425683i | ||||
\(171\) | 33.0381 | + | 57.2236i | 0.193205 | + | 0.334641i | ||||
\(172\) | −65.1024 | − | 21.8972i | −0.378502 | − | 0.127309i | ||||
\(173\) | −157.801 | − | 91.1065i | −0.912145 | − | 0.526627i | −0.0310245 | − | 0.999519i | \(-0.509877\pi\) |
−0.881121 | + | 0.472891i | \(0.843210\pi\) | |||||||
\(174\) | −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 | ||||
\(178\) | 55.8064 | − | 68.1937i | 0.313519 | − | 0.383111i | ||||
\(179\) | −28.6030 | − | 49.5419i | −0.159793 | − | 0.276770i | 0.775001 | − | 0.631960i | \(-0.217749\pi\) |
−0.934794 | + | 0.355190i | \(0.884416\pi\) | |||||||
\(180\) | −16.1454 | + | 3.25830i | −0.0896964 | + | 0.0181016i | ||||
\(181\) | − | 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 | ||||||||
\(184\) | −149.807 | − | 238.680i | −0.814170 | − | 1.29717i | ||||
\(185\) | −45.3970 | − | 78.6299i | −0.245389 | − | 0.425026i | ||||
\(186\) | 246.868 | + | 202.024i | 1.32725 | + | 1.08615i | ||||
\(187\) | 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 | \(-0.251557\pi\) |
−0.263541 | + | 0.964648i | \(0.584890\pi\) | |||||||
\(192\) | 95.0031 | − | 196.776i | 0.494808 | − | 1.02488i | ||||
\(193\) | −78.6518 | − | 136.229i | −0.407522 | − | 0.705849i | 0.587089 | − | 0.809522i | \(-0.300274\pi\) |
−0.994611 | + | 0.103673i | \(0.966940\pi\) | |||||||
\(194\) | −189.691 | − | 31.0468i | −0.977791 | − | 0.160035i | ||||
\(195\) | 8.20101 | 0.0420565 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 124.117i | 0.630034i | 0.949086 | + | 0.315017i | \(0.102010\pi\) | ||||
−0.949086 | + | 0.315017i | \(0.897990\pi\) | |||||||
\(198\) | 23.5205 | + | 3.84961i | 0.118791 | + | 0.0194425i | ||||
\(199\) | −156.729 | + | 90.4874i | −0.787581 | + | 0.454710i | −0.839110 | − | 0.543961i | \(-0.816924\pi\) |
0.0515289 | + | 0.998672i | \(0.483591\pi\) | |||||||
\(200\) | 6.67010 | + | 180.661i | 0.0333505 | + | 0.903304i | ||||
\(201\) | 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 | ||||
\(206\) | −66.6851 | − | 54.5717i | −0.323714 | − | 0.264911i | ||||
\(207\) | −81.0488 | + | 46.7935i | −0.391540 | + | 0.226056i | ||||
\(208\) | −14.9859 | + | 19.7570i | −0.0720477 | + | 0.0949856i | ||||
\(209\) | 111.549 | 0.533728 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 164.049 | 0.777482 | 0.388741 | − | 0.921347i | \(-0.372910\pi\) | ||||
0.388741 | + | 0.921347i | \(0.372910\pi\) | |||||||
\(212\) | −383.528 | + | 77.3998i | −1.80909 | + | 0.365093i | ||||
\(213\) | −302.180 | + | 174.464i | −1.41869 | + | 0.819079i | ||||
\(214\) | 19.7569 | − | 24.1423i | 0.0923219 | − | 0.112815i | ||||
\(215\) | −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 | ||||
\(220\) | −8.86455 | + | 26.3551i | −0.0402934 | + | 0.119796i | ||||
\(221\) | 31.7524 | − | 18.3322i | 0.143676 | − | 0.0829513i | ||||
\(222\) | 64.6127 | − | 394.774i | 0.291048 | − | 1.77826i | ||||
\(223\) | − | 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 | ||||||||
\(226\) | 27.1875 | + | 4.44977i | 0.120299 | + | 0.0196893i | ||||
\(227\) | −52.9031 | − | 91.6308i | −0.233053 | − | 0.403660i | 0.725652 | − | 0.688062i | \(-0.241538\pi\) |
−0.958705 | + | 0.284402i | \(0.908205\pi\) | |||||||
\(228\) | −321.925 | − | 108.279i | −1.41195 | − | 0.474910i | ||||
\(229\) | 64.8469 | + | 37.4394i | 0.283174 | + | 0.163491i | 0.634860 | − | 0.772628i | \(-0.281058\pi\) |
−0.351685 | + | 0.936118i | \(0.614391\pi\) | |||||||
\(230\) | −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 | 0.0712190 | − | 0.997461i | \(-0.477311\pi\) |
0.828217 | − | 0.560408i | \(-0.189356\pi\) | |||||||
\(234\) | 6.37334 | + | 5.21563i | 0.0272365 | + | 0.0222890i | ||||
\(235\) | −28.0000 | − | 48.4974i | −0.119149 | − | 0.206372i | ||||
\(236\) | −48.7088 | − | 241.359i | −0.206393 | − | 1.02271i | ||||
\(237\) | − | 132.132i | − | 0.557518i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 148.318i | 0.620577i | 0.950642 | + | 0.310288i | \(0.100426\pi\) | ||||
−0.950642 | + | 0.310288i | \(0.899574\pi\) | |||||||
\(240\) | 51.1652 | − | 67.4546i | 0.213188 | − | 0.281061i | ||||
\(241\) | 229.936 | + | 398.261i | 0.954092 | + | 1.65254i | 0.736433 | + | 0.676510i | \(0.236508\pi\) |
0.217658 | + | 0.976025i | \(0.430158\pi\) | |||||||
\(242\) | −127.781 | + | 156.144i | −0.528019 | + | 0.645224i | ||||
\(243\) | 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 | ||||
\(248\) | −373.471 | + | 13.7888i | −1.50593 | + | 0.0555998i | ||||
\(249\) | −6.17157 | − | 10.6895i | −0.0247854 | − | 0.0429296i | ||||
\(250\) | −23.8306 | + | 145.602i | −0.0953226 | + | 0.582407i | ||||
\(251\) | 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 | ||||||||
\(254\) | −40.3882 | + | 246.766i | −0.159009 | + | 0.971519i | ||||
\(255\) | −108.409 | + | 62.5902i | −0.425135 | + | 0.245452i | ||||
\(256\) | 69.0091 | + | 246.523i | 0.269567 | + | 0.962982i | ||||
\(257\) | 213.676 | − | 370.098i | 0.831425 | − | 1.44007i | −0.0654835 | − | 0.997854i | \(-0.520859\pi\) |
0.896908 | − | 0.442216i | \(-0.145808\pi\) | |||||||
\(258\) | −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 | ||||
\(262\) | 127.107 | − | 155.321i | 0.485141 | − | 0.592828i | ||||
\(263\) | 223.109 | − | 128.812i | 0.848322 | − | 0.489779i | −0.0117625 | − | 0.999931i | \(-0.503744\pi\) |
0.860084 | + | 0.510152i | \(0.170411\pi\) | |||||||
\(264\) | −103.764 | + | 65.1276i | −0.393046 | + | 0.246695i | ||||
\(265\) | −151.598 | −0.572068 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 150.426 | 0.563395 | ||||||||
\(268\) | 26.4073 | + | 130.852i | 0.0985348 | + | 0.488255i | ||||
\(269\) | −186.408 | + | 107.623i | −0.692968 | + | 0.400085i | −0.804723 | − | 0.593650i | \(-0.797686\pi\) |
0.111755 | + | 0.993736i | \(0.464353\pi\) | |||||||
\(270\) | 51.9511 | + | 42.5142i | 0.192412 | + | 0.157460i | ||||
\(271\) | −327.833 | − | 189.275i | −1.20972 | − | 0.698431i | −0.247020 | − | 0.969010i | \(-0.579451\pi\) |
−0.962698 | + | 0.270580i | \(0.912785\pi\) | |||||||
\(272\) | 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 | ||||
\(276\) | 153.362 | − | 455.959i | 0.555659 | − | 1.65202i | ||||
\(277\) | −144.149 | + | 83.2243i | −0.520393 | + | 0.300449i | −0.737095 | − | 0.675789i | \(-0.763803\pi\) |
0.216703 | + | 0.976238i | \(0.430470\pi\) | |||||||
\(278\) | 362.505 | + | 59.3312i | 1.30397 | + | 0.213421i | ||||
\(279\) | 124.117i | 0.444863i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −421.765 | −1.50094 | −0.750471 | − | 0.660904i | \(-0.770173\pi\) | ||||
−0.750471 | + | 0.660904i | \(0.770173\pi\) | |||||||
\(282\) | 39.8519 | − | 243.489i | 0.141319 | − | 0.863437i | ||||
\(283\) | 172.719 | + | 299.159i | 0.610316 | + | 1.05710i | 0.991187 | + | 0.132470i | \(0.0422907\pi\) |
−0.380872 | + | 0.924628i | \(0.624376\pi\) | |||||||
\(284\) | 130.324 | − | 387.464i | 0.458886 | − | 1.36431i | ||||
\(285\) | −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 | ||||
\(290\) | 44.0711 | − | 53.8536i | 0.151969 | − | 0.185702i | ||||
\(291\) | −164.066 | − | 284.171i | −0.563801 | − | 0.976532i | ||||
\(292\) | −54.8471 | − | 271.776i | −0.187833 | − | 0.930739i | ||||
\(293\) | 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 | ||||||
\(296\) | 249.146 | + | 396.950i | 0.841708 | + | 1.34105i | ||||
\(297\) | −48.5685 | − | 84.1232i | −0.163530 | − | 0.283243i | ||||
\(298\) | −297.655 | − | 243.586i | −0.998841 | − | 0.817402i | ||||
\(299\) | −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 | ||||
\(304\) | 366.777 | − | 154.324i | 1.20650 | − | 0.507644i | ||||
\(305\) | −29.2010 | − | 50.5776i | −0.0957410 | − | 0.165828i | ||||
\(306\) | −124.055 | − | 20.3041i | −0.405409 | − | 0.0663532i | ||||
\(307\) | 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 | ||||||
\(310\) | −142.903 | − | 23.3889i | −0.460976 | − | 0.0754480i | ||||
\(311\) | −10.7376 | + | 6.19938i | −0.0345262 | + | 0.0199337i | −0.517164 | − | 0.855886i | \(-0.673012\pi\) |
0.482638 | + | 0.875820i | \(0.339679\pi\) | |||||||
\(312\) | −42.3032 | + | 1.56186i | −0.135587 | + | 0.00500596i | ||||
\(313\) | −205.024 | + | 355.113i | −0.655030 | + | 1.13455i | 0.326856 | + | 0.945074i | \(0.394011\pi\) |
−0.981886 | + | 0.189471i | \(0.939323\pi\) | |||||||
\(314\) | −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 | \(-0.267436\pi\) |
−0.311316 | + | 0.950306i | \(0.600770\pi\) | |||||||
\(318\) | −516.900 | − | 423.006i | −1.62547 | − | 1.33021i | ||||
\(319\) | −87.2038 | + | 50.3472i | −0.273366 | + | 0.157828i | ||||
\(320\) | 7.31434 | + | 98.9200i | 0.0228573 | + | 0.309125i | ||||
\(321\) | 53.2548 | 0.165903 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −588.347 | −1.82151 | ||||||||
\(324\) | 77.4297 | + | 383.676i | 0.238981 | + | 1.18419i | ||||
\(325\) | 30.3311 | − | 17.5117i | 0.0933266 | − | 0.0538821i | ||||
\(326\) | −304.668 | + | 372.295i | −0.934565 | + | 1.14201i | ||||
\(327\) | 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 | −0.981239 | − | 0.192794i | \(-0.938245\pi\) |
0.657584 | + | 0.753381i | \(0.271579\pi\) | |||||||
\(332\) | 13.7064 | + | 4.61014i | 0.0412842 | + | 0.0138859i | ||||
\(333\) | 134.793 | − | 77.8227i | 0.404783 | − | 0.233702i | ||||
\(334\) | 68.5174 | − | 418.631i | 0.205142 | − | 1.25339i | ||||
\(335\) | 51.7223i | 0.154395i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 164.049 | 0.486792 | 0.243396 | − | 0.969927i | \(-0.421739\pi\) | ||||
0.243396 | + | 0.969927i | \(0.421739\pi\) | |||||||
\(338\) | −328.821 | − | 53.8181i | −0.972843 | − | 0.159225i | ||||
\(339\) | 23.5147 | + | 40.7287i | 0.0693650 | + | 0.120144i | ||||
\(340\) | 46.7545 | − | 139.006i | 0.137513 | − | 0.408840i | ||||
\(341\) | 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 | ||||
\(346\) | 282.027 | + | 230.797i | 0.815107 | + | 0.667043i | ||||
\(347\) | 54.8457 | + | 94.9955i | 0.158057 | + | 0.273762i | 0.934168 | − | 0.356834i | \(-0.116144\pi\) |
−0.776111 | + | 0.630596i | \(0.782810\pi\) | |||||||
\(348\) | 300.537 | − | 60.6513i | 0.863611 | − | 0.174285i | ||||
\(349\) | 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 | ||||||
\(352\) | 40.7067 | − | 137.636i | 0.115644 | − | 0.391010i | ||||
\(353\) | −39.0488 | − | 67.6345i | −0.110620 | − | 0.191599i | 0.805401 | − | 0.592731i | \(-0.201950\pi\) |
−0.916020 | + | 0.401132i | \(0.868617\pi\) | |||||||
\(354\) | 266.204 | − | 325.293i | 0.751988 | − | 0.918907i | ||||
\(355\) | 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 | \(-0.163528\pi\) |
0.00986020 | + | 0.999951i | \(0.496861\pi\) | |||||||
\(360\) | 32.9193 | − | 1.21540i | 0.0914424 | − | 0.00337611i | ||||
\(361\) | −128.760 | − | 223.019i | −0.356676 | − | 0.617780i | ||||
\(362\) | −105.380 | + | 643.857i | −0.291105 | + | 1.77861i | ||||
\(363\) | −344.434 | −0.948853 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 107.426i | − | 0.294316i | ||||||
\(366\) | 41.5613 | − | 253.933i | 0.113555 | − | 0.693807i | ||||
\(367\) | 191.165 | − | 110.369i | 0.520887 | − | 0.300734i | −0.216411 | − | 0.976302i | \(-0.569435\pi\) |
0.737297 | + | 0.675568i | \(0.236102\pi\) | |||||||
\(368\) | 218.577 | + | 519.485i | 0.593959 | + | 1.41164i | ||||
\(369\) | 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 | \(-0.442814\pi\) |
−0.762742 | + | 0.646703i | \(0.776147\pi\) | |||||||
\(374\) | −134.399 | + | 164.232i | −0.359356 | + | 0.439123i | ||||
\(375\) | −218.121 | + | 125.932i | −0.581657 | + | 0.335820i | ||||
\(376\) | 153.668 | + | 244.831i | 0.408692 | + | 0.651147i | ||||
\(377\) | −34.7939 | −0.0922916 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 286.024 | 0.754682 | 0.377341 | − | 0.926074i | \(-0.376839\pi\) | ||||
0.377341 | + | 0.926074i | \(0.376839\pi\) | |||||||
\(380\) | 151.132 | − | 30.5000i | 0.397716 | − | 0.0802631i | ||||
\(381\) | −369.672 | + | 213.430i | −0.970268 | + | 0.560184i | ||||
\(382\) | −150.233 | − | 122.943i | −0.393279 | − | 0.321840i | ||||
\(383\) | 92.5727 | + | 53.4468i | 0.241704 | + | 0.139548i | 0.615960 | − | 0.787778i | \(-0.288768\pi\) |
−0.374256 | + | 0.927326i | \(0.622102\pi\) | |||||||
\(384\) | −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 | ||||
\(388\) | 364.372 | + | 122.557i | 0.939102 | + | 0.315867i | ||||
\(389\) | 66.8405 | − | 38.5904i | 0.171826 | − | 0.0992040i | −0.411620 | − | 0.911355i | \(-0.635037\pi\) |
0.583447 | + | 0.812151i | \(0.301704\pi\) | |||||||
\(390\) | −16.1866 | − | 2.64927i | −0.0415042 | − | 0.00679300i | ||||
\(391\) | − | 833.307i | − | 2.13122i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 342.617 | 0.871800 | ||||||||
\(394\) | 40.0949 | − | 244.974i | 0.101764 | − | 0.621761i | ||||
\(395\) | 29.9899 | + | 51.9440i | 0.0759238 | + | 0.131504i | ||||
\(396\) | −45.1798 | − | 15.1962i | −0.114090 | − | 0.0383743i | ||||
\(397\) | 569.424 | + | 328.757i | 1.43432 | + | 0.828103i | 0.997446 | − | 0.0714218i | \(-0.0227536\pi\) |
0.436870 | + | 0.899525i | \(0.356087\pi\) | |||||||
\(398\) | 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 | −0.993417 | − | 0.114557i | \(-0.963455\pi\) |
0.595918 | + | 0.803045i | \(0.296788\pi\) | |||||||
\(402\) | −144.321 | + | 176.357i | −0.359009 | + | 0.438698i | ||||
\(403\) | 36.2010 | + | 62.7020i | 0.0898288 | + | 0.155588i | ||||
\(404\) | −76.9140 | + | 15.5220i | −0.190381 | + | 0.0384209i | ||||
\(405\) | 151.657i | 0.374461i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 262.759i | − | 0.645600i | ||||||
\(408\) | 547.287 | − | 343.504i | 1.34139 | − | 0.841923i | ||||
\(409\) | −72.6325 | − | 125.803i | −0.177585 | − | 0.307587i | 0.763468 | − | 0.645846i | \(-0.223495\pi\) |
−0.941053 | + | 0.338259i | \(0.890162\pi\) | |||||||
\(410\) | 64.6978 | + | 52.9455i | 0.157799 | + | 0.129135i | ||||
\(411\) | −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 | ||||
\(416\) | 35.9606 | − | 34.1541i | 0.0864438 | − | 0.0821012i | ||||
\(417\) | 313.534 | + | 543.057i | 0.751880 | + | 1.30229i | ||||
\(418\) | −220.169 | − | 36.0351i | −0.526720 | − | 0.0862083i | ||||
\(419\) | 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 | \(-0.0462798\pi\) | |||||||
\(422\) | −323.789 | − | 52.9946i | −0.767273 | − | 0.125580i | ||||
\(423\) | 83.1377 | − | 47.9996i | 0.196543 | − | 0.113474i | ||||
\(424\) | 781.987 | − | 28.8714i | 1.84431 | − | 0.0680929i | ||||
\(425\) | −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 | ||||
\(430\) | 41.1917 | + | 33.7092i | 0.0957946 | + | 0.0783936i | ||||
\(431\) | 509.969 | − | 294.431i | 1.18322 | − | 0.683133i | 0.226464 | − | 0.974020i | \(-0.427283\pi\) |
0.956758 | + | 0.290886i | \(0.0939501\pi\) | |||||||
\(432\) | −276.076 | − | 209.407i | −0.639064 | − | 0.484738i | ||||
\(433\) | 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 | ||||||||
\(436\) | −15.1027 | + | 3.04788i | −0.0346393 | + | 0.00699056i | ||||
\(437\) | 758.675 | − | 438.021i | 1.73610 | − | 1.00234i | ||||
\(438\) | 299.751 | − | 366.287i | 0.684362 | − | 0.836271i | ||||
\(439\) | −381.522 | − | 220.272i | −0.869070 | − | 0.501758i | −0.00203069 | − | 0.999998i | \(-0.500646\pi\) |
−0.867039 | + | 0.498240i | \(0.833980\pi\) | |||||||
\(440\) | 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 | −0.448566 | − | 0.893750i | \(-0.648065\pi\) |
0.998293 | − | 0.0584052i | \(-0.0186015\pi\) | |||||||
\(444\) | −255.057 | + | 758.309i | −0.574453 | + | 1.70790i | ||||
\(445\) | −59.1361 | + | 34.1422i | −0.132890 | + | 0.0767241i | ||||
\(446\) | −3.41875 | + | 20.8881i | −0.00766537 | + | 0.0468343i | ||||
\(447\) | − | 656.587i | − | 1.46887i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 264.039 | 0.588059 | 0.294030 | − | 0.955796i | \(-0.405004\pi\) | ||||
0.294030 | + | 0.955796i | \(0.405004\pi\) | |||||||
\(450\) | −118.502 | − | 19.3953i | −0.263339 | − | 0.0431006i | ||||
\(451\) | −60.4853 | − | 104.764i | −0.134114 | − | 0.232292i | ||||
\(452\) | −52.2235 | − | 17.5654i | −0.115539 | − | 0.0388615i | ||||
\(453\) | −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 | −0.434542 | − | 0.900652i | \(-0.643090\pi\) |
0.997258 | − | 0.0740019i | \(-0.0235771\pi\) | |||||||
\(458\) | −115.896 | − | 94.8438i | −0.253049 | − | 0.207083i | ||||
\(459\) | 256.167 | + | 443.693i | 0.558097 | + | 0.966652i | ||||
\(460\) | 43.1987 | + | 214.056i | 0.0939103 | + | 0.465340i | ||||
\(461\) | 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 | \(0.715014\pi\) | |||||||
\(464\) | −217.075 | + | 286.186i | −0.467835 | + | 0.616780i | ||||
\(465\) | −123.598 | − | 214.078i | −0.265802 | − | 0.460383i | ||||
\(466\) | −530.892 | + | 648.735i | −1.13925 | + | 1.39213i | ||||
\(467\) | 173.641 | − | 300.755i | 0.371822 | − | 0.644015i | −0.618023 | − | 0.786160i | \(-0.712066\pi\) |
0.989846 | + | 0.142144i | \(0.0453997\pi\) | |||||||
\(468\) | −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 | ||||
\(472\) | 18.1692 | + | 492.115i | 0.0384940 | + | 1.04262i | ||||
\(473\) | −38.5097 | − | 66.7007i | −0.0814158 | − | 0.141016i | ||||
\(474\) | −42.6841 | + | 260.794i | −0.0900509 | + | 0.550198i | ||||
\(475\) | −562.013 | −1.18319 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 259.880i | − | 0.544822i | ||||||
\(478\) | 47.9129 | − | 292.741i | 0.100236 | − | 0.612428i | ||||
\(479\) | −25.2716 | + | 14.5906i | −0.0527591 | + | 0.0304605i | −0.526148 | − | 0.850393i | \(-0.676364\pi\) |
0.473388 | + | 0.880854i | \(0.343031\pi\) | |||||||
\(480\) | −122.777 | + | 116.609i | −0.255786 | + | 0.242936i | ||||
\(481\) | 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 | ||||
\(486\) | −176.288 | + | 215.419i | −0.362733 | + | 0.443249i | ||||
\(487\) | −607.640 | + | 350.821i | −1.24772 | + | 0.720372i | −0.970654 | − | 0.240478i | \(-0.922696\pi\) |
−0.277067 | + | 0.960851i | \(0.589362\pi\) | |||||||
\(488\) | 160.260 | + | 255.333i | 0.328401 | + | 0.523223i | ||||
\(489\) | −821.235 | −1.67942 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −59.9512 | −0.122100 | −0.0610501 | − | 0.998135i | \(-0.519445\pi\) | ||||
−0.0610501 | + | 0.998135i | \(0.519445\pi\) | |||||||
\(492\) | 72.8644 | + | 361.054i | 0.148098 | + | 0.733850i | ||||
\(493\) | 459.942 | − | 265.548i | 0.932945 | − | 0.538636i | ||||
\(494\) | −59.6590 | − | 48.8220i | −0.120767 | − | 0.0988299i | ||||
\(495\) | −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 | −0.820705 | − | 0.571352i | \(-0.806419\pi\) |
0.905158 | + | 0.425075i | \(0.139752\pi\) | |||||||
\(500\) | 94.0709 | − | 279.681i | 0.188142 | − | 0.559363i | ||||
\(501\) | 627.138 | − | 362.079i | 1.25177 | − | 0.722712i | ||||
\(502\) | −246.557 | − | 40.3540i | −0.491150 | − | 0.0803865i | ||||
\(503\) | − | 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 | ||||||||
\(506\) | 51.0384 | − | 311.837i | 0.100866 | − | 0.616278i | ||||
\(507\) | −284.401 | − | 492.596i | −0.560948 | − | 0.971590i | ||||
\(508\) | 159.431 | − | 474.004i | 0.313841 | − | 0.933079i | ||||
\(509\) | 413.123 | + | 238.516i | 0.811636 | + | 0.468598i | 0.847524 | − | 0.530758i | \(-0.178093\pi\) |
−0.0358878 | + | 0.999356i | \(0.511426\pi\) | |||||||
\(510\) | 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 | ||||
\(514\) | −541.298 | + | 661.450i | −1.05311 | + | 1.28687i | ||||
\(515\) | 33.3869 | + | 57.8278i | 0.0648289 | + | 0.112287i | ||||
\(516\) | 46.3912 | + | 229.875i | 0.0899054 | + | 0.445495i | ||||
\(517\) | − | 162.065i | − | 0.313472i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 622.114i | 1.19868i | ||||||||
\(520\) | 16.2759 | − | 10.2155i | 0.0312997 | − | 0.0196453i | ||||
\(521\) | −105.437 | − | 182.621i | −0.202373 | − | 0.350521i | 0.746919 | − | 0.664915i | \(-0.231532\pi\) |
−0.949293 | + | 0.314394i | \(0.898199\pi\) | |||||||
\(522\) | 92.3196 | + | 75.5498i | 0.176858 | + | 0.144731i | ||||
\(523\) | −255.783 | + | 443.030i | −0.489069 | + | 0.847093i | −0.999921 | − | 0.0125761i | \(-0.995997\pi\) |
0.510852 | + | 0.859669i | \(0.329330\pi\) | |||||||
\(524\) | −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 | ||||
\(528\) | 225.842 | − | 95.0247i | 0.427732 | − | 0.179971i | ||||
\(529\) | 355.892 | + | 616.423i | 0.672764 | + | 1.16526i | ||||
\(530\) | 299.215 | + | 48.9725i | 0.564556 | + | 0.0924009i | ||||
\(531\) | 163.546 | 0.307997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 41.8002i | − | 0.0784244i | ||||||
\(534\) | −296.902 | − | 48.5940i | −0.555997 | − | 0.0910001i | ||||
\(535\) | −20.9357 | + | 12.0872i | −0.0391321 | + | 0.0225929i | ||||
\(536\) | −9.85037 | − | 266.799i | −0.0183776 | − | 0.497759i | ||||
\(537\) | −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 | \(-0.230837\pi\) |
−0.200234 | + | 0.979748i | \(0.564170\pi\) | |||||||
\(542\) | 585.914 | + | 479.483i | 1.08102 | + | 0.884654i | ||||
\(543\) | −964.542 | + | 556.878i | −1.77632 | + | 1.02556i | ||||
\(544\) | −214.700 | + | 725.935i | −0.394670 | + | 1.33444i | ||||
\(545\) | −5.96970 | −0.0109536 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −441.976 | −0.807999 | −0.404000 | − | 0.914759i | \(-0.632380\pi\) | ||||
−0.404000 | + | 0.914759i | \(0.632380\pi\) | |||||||
\(548\) | −45.3516 | − | 224.724i | −0.0827585 | − | 0.410081i | ||||
\(549\) | 86.7038 | − | 50.0584i | 0.157930 | − | 0.0911811i | ||||
\(550\) | −128.384 | + | 156.881i | −0.233425 | + | 0.285238i | ||||
\(551\) | 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 | ||||
\(556\) | −696.323 | − | 234.208i | −1.25238 | − | 0.421238i | ||||
\(557\) | −316.714 | + | 182.855i | −0.568607 | + | 0.328285i | −0.756593 | − | 0.653886i | \(-0.773137\pi\) |
0.187986 | + | 0.982172i | \(0.439804\pi\) | |||||||
\(558\) | 40.0949 | − | 244.974i | 0.0718546 | − | 0.439021i | ||||
\(559\) | − | 26.6133i | − | 0.0476087i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −362.274 | −0.645765 | ||||||||
\(562\) | 832.453 | + | 136.248i | 1.48123 | + | 0.242433i | ||||
\(563\) | −403.194 | − | 698.353i | −0.716154 | − | 1.24041i | −0.962513 | − | 0.271236i | \(-0.912568\pi\) |
0.246359 | − | 0.969179i | \(-0.420766\pi\) | |||||||
\(564\) | −157.315 | + | 467.711i | −0.278926 | + | 0.829274i | ||||
\(565\) | −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 | −0.947183 | − | 0.320694i | \(-0.896084\pi\) |
0.751320 | + | 0.659938i | \(0.229417\pi\) | |||||||
\(570\) | 203.689 | + | 166.689i | 0.357349 | + | 0.292436i | ||||
\(571\) | −286.541 | − | 496.304i | −0.501823 | − | 0.869184i | −0.999998 | − | 0.00210683i | \(-0.999329\pi\) |
0.498174 | − | 0.867077i | \(-0.334004\pi\) | |||||||
\(572\) | −27.2565 | + | 5.50063i | −0.0476512 | + | 0.00961649i | ||||
\(573\) | − | 331.393i | − | 0.578348i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 796.008i | − | 1.38436i | ||||||
\(576\) | −169.576 | + | 12.5388i | −0.294402 | + | 0.0217687i | ||||
\(577\) | 361.950 | + | 626.916i | 0.627297 | + | 1.08651i | 0.988092 | + | 0.153865i | \(0.0491721\pi\) |
−0.360795 | + | 0.932645i | \(0.617495\pi\) | |||||||
\(578\) | 342.810 | − | 418.903i | 0.593097 | − | 0.724746i | ||||
\(579\) | −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 | ||||
\(584\) | 20.4589 | + | 554.132i | 0.0350323 | + | 0.948856i | ||||
\(585\) | −3.19091 | − | 5.52682i | −0.00545455 | − | 0.00944755i | ||||
\(586\) | 165.087 | − | 1008.66i | 0.281718 | − | 1.72126i | ||||
\(587\) | 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 | ||||||
\(590\) | −30.8191 | + | 188.300i | −0.0522358 | + | 0.319153i | ||||
\(591\) | 366.988 | − | 211.880i | 0.620960 | − | 0.358512i | ||||
\(592\) | −363.517 | − | 863.960i | −0.614049 | − | 1.45939i | ||||
\(593\) | 64.3726 | − | 111.497i | 0.108554 | − | 0.188021i | −0.806631 | − | 0.591056i | \(-0.798711\pi\) |
0.915185 | + | 0.403035i | \(0.132045\pi\) | |||||||
\(594\) | 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 | ||||
\(598\) | 69.1491 | − | 84.4982i | 0.115634 | − | 0.141301i | ||||
\(599\) | 280.705 | − | 162.065i | 0.468623 | − | 0.270559i | −0.247040 | − | 0.969005i | \(-0.579458\pi\) |
0.715663 | + | 0.698446i | \(0.246125\pi\) | |||||||
\(600\) | 522.790 | − | 328.129i | 0.871317 | − | 0.546882i | ||||
\(601\) | −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 | ||||||||
\(604\) | 449.941 | − | 90.8027i | 0.744936 | − | 0.150336i | ||||
\(605\) | 135.405 | − | 78.1759i | 0.223809 | − | 0.129216i | ||||
\(606\) | −103.661 | − | 84.8311i | −0.171058 | − | 0.139985i | ||||
\(607\) | −611.413 | − | 353.000i | −1.00727 | − | 0.581548i | −0.0968795 | − | 0.995296i | \(-0.530886\pi\) |
−0.910391 | + | 0.413748i | \(0.864219\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | 238.293 | + | 80.1499i | 0.389368 | + | 0.130964i | ||||
\(613\) | 18.9026 | − | 10.9134i | 0.0308363 | − | 0.0178033i | −0.484503 | − | 0.874790i | \(-0.660999\pi\) |
0.515339 | + | 0.856986i | \(0.327666\pi\) | |||||||
\(614\) | −440.797 | − | 72.1453i | −0.717910 | − | 0.117500i | ||||
\(615\) | 142.715i | 0.232057i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −699.578 | −1.13384 | −0.566919 | − | 0.823774i | \(-0.691865\pi\) | ||||
−0.566919 | + | 0.823774i | \(0.691865\pi\) | |||||||
\(618\) | −47.5190 | + | 290.334i | −0.0768915 | + | 0.469796i | ||||
\(619\) | −48.0990 | − | 83.3100i | −0.0777044 | − | 0.134588i | 0.824555 | − | 0.565782i | \(-0.191426\pi\) |
−0.902259 | + | 0.431194i | \(0.858092\pi\) | |||||||
\(620\) | 274.497 | + | 92.3271i | 0.442737 | + | 0.148915i | ||||
\(621\) | −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 | ||||
\(626\) | 519.381 | − | 634.668i | 0.829682 | − | 1.01385i | ||||
\(627\) | −190.426 | − | 329.828i | −0.303710 | − | 0.526042i | ||||
\(628\) | 831.815 | − | 167.869i | 1.32455 | − | 0.267307i | ||||
\(629\) | 1385.88i | 2.20331i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 269.399i | 0.426940i | 0.976950 | + | 0.213470i | \(0.0684766\pi\) | ||||
−0.976950 | + | 0.213470i | \(0.931523\pi\) | |||||||
\(632\) | −164.589 | − | 262.231i | −0.260426 | − | 0.414922i | ||||
\(633\) | −280.049 | − | 485.059i | −0.442415 | − | 0.766285i | ||||
\(634\) | −201.701 | − | 165.062i | −0.318141 | − | 0.260351i | ||||
\(635\) | 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 | ||||
\(640\) | 17.5187 | − | 197.605i | 0.0273730 | − | 0.308758i | ||||
\(641\) | −317.907 | − | 550.630i | −0.495954 | − | 0.859018i | 0.504035 | − | 0.863683i | \(-0.331848\pi\) |
−0.999989 | + | 0.00466541i | \(0.998515\pi\) | |||||||
\(642\) | −105.111 | − | 17.2035i | −0.163724 | − | 0.0267968i | ||||
\(643\) | 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 | ||||||||
\(646\) | 1161.24 | + | 190.061i | 1.79759 | + | 0.294212i | ||||
\(647\) | −225.826 | + | 130.381i | −0.349035 | + | 0.201516i | −0.664260 | − | 0.747501i | \(-0.731253\pi\) |
0.315225 | + | 0.949017i | \(0.397920\pi\) | |||||||
\(648\) | −28.8826 | − | 782.290i | −0.0445719 | − | 1.20724i | ||||
\(649\) | 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 | \(-0.0187693\pi\) |
0.448095 | + | 0.893986i | \(0.352103\pi\) | |||||||
\(654\) | −20.3547 | − | 16.6573i | −0.0311235 | − | 0.0254699i | ||||
\(655\) | −134.691 | + | 77.7637i | −0.205635 | + | 0.118723i | ||||
\(656\) | −343.813 | − | 260.787i | −0.524106 | − | 0.397541i | ||||
\(657\) | 184.156 | 0.280299 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −362.780 | −0.550500 | −0.275250 | − | 0.961373i | \(-0.588761\pi\) | ||||
−0.275250 | + | 0.961373i | \(0.588761\pi\) | |||||||
\(660\) | 93.0594 | − | 18.7803i | 0.140999 | − | 0.0284550i | ||||
\(661\) | 102.047 | − | 58.9169i | 0.154383 | − | 0.0891330i | −0.420818 | − | 0.907145i | \(-0.638257\pi\) |
0.575201 | + | 0.818012i | \(0.304924\pi\) | |||||||
\(662\) | 271.388 | − | 331.629i | 0.409952 | − | 0.500950i | ||||
\(663\) | −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 | ||||
\(668\) | −270.471 | + | 804.135i | −0.404897 | + | 1.20379i | ||||
\(669\) | −31.2918 | + | 18.0663i | −0.0467740 | + | 0.0270050i | ||||
\(670\) | 16.7085 | − | 102.086i | 0.0249380 | − | 0.152368i | ||||
\(671\) | − | 169.017i | − | 0.251888i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.56854 | −0.00976009 | −0.00488005 | − | 0.999988i | \(-0.501553\pi\) | ||||
−0.00488005 | + | 0.999988i | \(0.501553\pi\) | |||||||
\(674\) | −323.789 | − | 52.9946i | −0.480400 | − | 0.0786270i | ||||
\(675\) | 244.701 | + | 423.834i | 0.362519 | + | 0.627902i | ||||
\(676\) | 631.621 | + | 212.446i | 0.934350 | + | 0.314269i | ||||
\(677\) | −108.942 | − | 62.8978i | −0.160919 | − | 0.0929066i | 0.417378 | − | 0.908733i | \(-0.362949\pi\) |
−0.578297 | + | 0.815826i | \(0.696282\pi\) | |||||||
\(678\) | −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 | ||||
\(682\) | −324.312 | − | 265.401i | −0.475531 | − | 0.389151i | ||||
\(683\) | 276.887 | + | 479.583i | 0.405399 | + | 0.702171i | 0.994368 | − | 0.105984i | \(-0.0337994\pi\) |
−0.588969 | + | 0.808156i | \(0.700466\pi\) | |||||||
\(684\) | 52.2852 | + | 259.081i | 0.0764404 | + | 0.378774i | ||||
\(685\) | − | 88.8274i | − | 0.129675i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 255.652i | − | 0.372128i | ||||||
\(688\) | −218.899 | − | 166.037i | −0.318166 | − | 0.241333i | ||||
\(689\) | −75.7990 | − | 131.288i | −0.110013 | − | 0.190548i | ||||
\(690\) | −236.090 | + | 288.495i | −0.342159 | + | 0.418109i | ||||
\(691\) | 523.413 | − | 906.577i | 0.757471 | − | 1.31198i | −0.186665 | − | 0.982424i | \(-0.559768\pi\) |
0.944136 | − | 0.329555i | \(-0.106899\pi\) | |||||||
\(692\) | −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 | ||||
\(696\) | −612.774 | + | 22.6240i | −0.880422 | + | 0.0325057i | ||||
\(697\) | 319.019 | + | 552.558i | 0.457703 | + | 0.792766i | ||||
\(698\) | 149.723 | − | 914.787i | 0.214503 | − | 1.31058i | ||||
\(699\) | −1431.02 | −2.04724 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 625.993i | − | 0.893000i | −0.894784 | − | 0.446500i | \(-0.852670\pi\) | ||
0.894784 | − | 0.446500i | \(-0.147330\pi\) | |||||||
\(702\) | −10.8428 | + | 66.2481i | −0.0154456 | + | 0.0943705i | ||||
\(703\) | −1261.76 | + | 728.476i | −1.79482 | + | 1.03624i | ||||
\(704\) | −124.806 | + | 258.507i | −0.177282 | + | 0.367197i | ||||
\(705\) | −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 | \(-0.470792\pi\) |
−0.816566 | + | 0.577252i | \(0.804125\pi\) | |||||||
\(710\) | −200.624 | + | 245.157i | −0.282569 | + | 0.345291i | ||||
\(711\) | −89.0461 | + | 51.4108i | −0.125241 | + | 0.0723077i | ||||
\(712\) | 298.539 | − | 187.378i | 0.419296 | − | 0.263171i | ||||
\(713\) | 1645.55 | 2.30792 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.7737 | −0.0150682 | ||||||||
\(716\) | −45.2665 | − | 224.302i | −0.0632213 | − | 0.313271i | ||||
\(717\) | 438.546 | − | 253.194i | 0.611640 | − | 0.353130i | ||||
\(718\) | −565.118 | − | 462.465i | −0.787073 | − | 0.644101i | ||||
\(719\) | 529.578 | + | 305.752i | 0.736549 | + | 0.425247i | 0.820813 | − | 0.571197i | \(-0.193521\pi\) |
−0.0842645 | + | 0.996443i | \(0.526854\pi\) | |||||||
\(720\) | −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 | ||||
\(724\) | 415.985 | − | 1236.76i | 0.574566 | − | 1.70824i | ||||
\(725\) | 439.355 | − | 253.662i | 0.606007 | − | 0.349878i | ||||
\(726\) | 679.822 | + | 111.266i | 0.936394 | + | 0.153260i | ||||
\(727\) | 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 | ||||||||
\(730\) | −34.7029 | + | 212.030i | −0.0475383 | + | 0.290452i | ||||
\(731\) | 203.113 | + | 351.802i | 0.277856 | + | 0.481261i | ||||
\(732\) | −164.062 | + | 487.772i | −0.224129 | + | 0.666355i | ||||
\(733\) | 189.014 | + | 109.127i | 0.257863 | + | 0.148878i | 0.623360 | − | 0.781935i | \(-0.285767\pi\) |
−0.365496 | + | 0.930813i | \(0.619101\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | −90.7628 | + | 110.910i | −0.122985 | + | 0.150284i | ||||
\(739\) | 3.64971 | + | 6.32149i | 0.00493872 | + | 0.00855411i | 0.868484 | − | 0.495717i | \(-0.165095\pi\) |
−0.863545 | + | 0.504271i | \(0.831761\pi\) | |||||||
\(740\) | −71.8441 | − | 355.999i | −0.0970867 | − | 0.481079i | ||||
\(741\) | − | 131.600i | − | 0.177598i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 106.867i | − | 0.143832i | −0.997411 | − | 0.0719159i | \(-0.977089\pi\) | ||
0.997411 | − | 0.0719159i | \(-0.0229113\pi\) | |||||||
\(744\) | 678.325 | + | 1080.74i | 0.911727 | + | 1.45260i | ||||
\(745\) | 149.025 | + | 258.119i | 0.200034 | + | 0.346469i | ||||
\(746\) | 389.351 | + | 318.625i | 0.521918 | + | 0.427112i | ||||
\(747\) | −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 | \(-0.360378\pi\) |
−0.571689 | + | 0.820470i | \(0.693712\pi\) | |||||||
\(752\) | −224.210 | − | 532.874i | −0.298152 | − | 0.708609i | ||||
\(753\) | −213.250 | − | 369.359i | −0.283200 | − | 0.490517i | ||||
\(754\) | 68.6741 | + | 11.2399i | 0.0910798 | + | 0.0149070i | ||||
\(755\) | 177.849 | 0.235562 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 704.275i | 0.930350i | 0.885219 | + | 0.465175i | \(0.154009\pi\) | ||||
−0.885219 | + | 0.465175i | \(0.845991\pi\) | |||||||
\(758\) | −564.537 | − | 92.3979i | −0.744772 | − | 0.121897i | ||||
\(759\) | 467.153 | − | 269.711i | 0.615485 | − | 0.355350i | ||||
\(760\) | −308.148 | + | 11.3770i | −0.405458 | + | 0.0149697i | ||||
\(761\) | 501.465 | − | 868.563i | 0.658955 | − | 1.14134i | −0.321931 | − | 0.946763i | \(-0.604332\pi\) |
0.980886 | − | 0.194581i | \(-0.0623348\pi\) | |||||||
\(762\) | 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 | ||||
\(766\) | −165.449 | − | 135.395i | −0.215990 | − | 0.176756i | ||||
\(767\) | 82.6213 | − | 47.7014i | 0.107720 | − | 0.0621922i | ||||
\(768\) | 611.113 | − | 624.887i | 0.795720 | − | 0.813655i | ||||
\(769\) | −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 | ||||||||
\(772\) | −124.472 | − | 616.780i | −0.161234 | − | 0.798938i | ||||
\(773\) | −488.668 | + | 282.132i | −0.632170 | + | 0.364984i | −0.781592 | − | 0.623790i | \(-0.785592\pi\) |
0.149422 | + | 0.988774i | \(0.452259\pi\) | |||||||
\(774\) | −57.7867 | + | 70.6137i | −0.0746599 | + | 0.0912322i | ||||
\(775\) | −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 | ||||
\(780\) | 31.0924 | + | 10.4579i | 0.0398620 | + | 0.0134076i | ||||
\(781\) | 396.977 | − | 229.195i | 0.508293 | − | 0.293463i | ||||
\(782\) | −269.193 | + | 1644.73i | −0.344237 | + | 2.10324i | ||||
\(783\) | − | 486.195i | − | 0.620939i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 328.794 | 0.418846 | ||||||||
\(786\) | −676.237 | − | 110.680i | −0.860352 | − | 0.140814i | ||||
\(787\) | −461.673 | − | 799.640i | −0.586623 | − | 1.01606i | −0.994671 | − | 0.103101i | \(-0.967124\pi\) |
0.408048 | − | 0.912961i | \(-0.366210\pi\) | |||||||
\(788\) | −158.274 | + | 470.562i | −0.200855 | + | 0.597160i | ||||
\(789\) | −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 | ||||
\(794\) | −1017.69 | − | 832.828i | −1.28173 | − | 1.04890i | ||||
\(795\) | 258.794 | + | 448.244i | 0.325527 | + | 0.563829i | ||||
\(796\) | −709.593 | + | 143.203i | −0.891449 | + | 0.179903i | ||||
\(797\) | − | 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 | ||||||||
\(800\) | −205.090 | + | 693.443i | −0.256363 | + | 0.866803i | ||||
\(801\) | −58.5290 | − | 101.375i | −0.0730699 | − | 0.126561i | ||||
\(802\) | 403.795 | − | 493.425i | 0.503484 | − | 0.615243i | ||||
\(803\) | 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 | ||||
\(808\) | 156.822 | − | 5.78998i | 0.194087 | − | 0.00716581i | ||||
\(809\) | −170.270 | − | 294.916i | −0.210470 | − | 0.364544i | 0.741392 | − | 0.671072i | \(-0.234166\pi\) |
−0.951862 | + | 0.306528i | \(0.900833\pi\) | |||||||
\(810\) | 48.9915 | − | 299.331i | 0.0604833 | − | 0.369544i | ||||
\(811\) | −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 | ||||||||
\(814\) | −84.8823 | + | 518.618i | −0.104278 | + | 0.637123i | ||||
\(815\) | 322.846 | − | 186.395i | 0.396130 | − | 0.228706i | ||||
\(816\) | −1191.17 | + | 501.191i | −1.45976 | + | 0.614205i | ||||
\(817\) | −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 | \(-0.459395\pi\) |
−0.795379 | + | 0.606112i | \(0.792728\pi\) | |||||||
\(822\) | 247.856 | − | 302.873i | 0.301528 | − | 0.368458i | ||||
\(823\) | −124.404 | + | 71.8247i | −0.151159 | + | 0.0872718i | −0.573672 | − | 0.819085i | \(-0.694482\pi\) |
0.422513 | + | 0.906357i | \(0.361148\pi\) | |||||||
\(824\) | −183.232 | − | 291.934i | −0.222369 | − | 0.354289i | ||||
\(825\) | −346.059 | −0.419465 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1545.57 | 1.86888 | 0.934442 | − | 0.356114i | \(-0.115899\pi\) | ||||
0.934442 | + | 0.356114i | \(0.115899\pi\) | |||||||
\(828\) | −366.950 | + | 74.0543i | −0.443177 | + | 0.0894376i | ||||
\(829\) | −644.285 | + | 371.978i | −0.777183 | + | 0.448707i | −0.835431 | − | 0.549595i | \(-0.814782\pi\) |
0.0582482 | + | 0.998302i | \(0.481449\pi\) | |||||||
\(830\) | −8.67231 | − | 7.09699i | −0.0104486 | − | 0.00855058i | ||||
\(831\) | 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 | ||||
\(836\) | 422.915 | + | 142.248i | 0.505879 | + | 0.170153i | ||||
\(837\) | −876.170 | + | 505.857i | −1.04680 | + | 0.604369i | ||||
\(838\) | −1395.46 | − | 228.395i | −1.66522 | − | 0.272547i | ||||
\(839\) | 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 | ||||||||
\(842\) | −39.4077 | + | 240.775i | −0.0468025 | + | 0.285956i | ||||
\(843\) | 719.997 | + | 1247.07i | 0.854089 | + | 1.47933i | ||||
\(844\) | 621.956 | + | 209.195i | 0.736915 | + | 0.247861i | ||||
\(845\) | 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 | ||||
\(850\) | 677.138 | − | 827.442i | 0.796633 | − | 0.973462i | ||||
\(851\) | −1031.78 | − | 1787.09i | −1.21243 | − | 2.09999i | ||||
\(852\) | −1368.13 | + | 276.102i | −1.60578 | + | 0.324064i | ||||
\(853\) | − | 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 | ||||||||
\(856\) | 105.690 | − | 66.3366i | 0.123470 | − | 0.0774960i | ||||
\(857\) | −80.4659 | − | 139.371i | −0.0938926 | − | 0.162627i | 0.815253 | − | 0.579105i | \(-0.196598\pi\) |
−0.909146 | + | 0.416478i | \(0.863264\pi\) | |||||||
\(858\) | −36.7350 | − | 30.0621i | −0.0428147 | − | 0.0350374i | ||||
\(859\) | −115.846 | + | 200.652i | −0.134862 | + | 0.233587i | −0.925545 | − | 0.378638i | \(-0.876392\pi\) |
0.790683 | + | 0.612226i | \(0.209726\pi\) | |||||||
\(860\) | −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 | \(-0.0511712\pi\) |
0.354931 | + | 0.934893i | \(0.384505\pi\) | |||||||
\(864\) | 477.254 | + | 502.498i | 0.552377 | + | 0.581595i | ||||
\(865\) | −141.201 | − | 244.567i | −0.163238 | − | 0.282737i | ||||
\(866\) | −271.775 | − | 44.4814i | −0.313828 | − | 0.0513642i | ||||
\(867\) | 924.046 | 1.06580 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 173.583i | 0.199750i | ||||||||
\(870\) | −234.468 | − | 38.3754i | −0.269504 | − | 0.0441097i | ||||
\(871\) | −44.7929 | + | 25.8612i | −0.0514269 | + | 0.0296914i | ||||
\(872\) | 30.7934 | − | 1.13691i | 0.0353136 | − | 0.00130380i | ||||
\(873\) | −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 | \(-0.638681\pi\) |
−0.996138 | + | 0.0878061i | \(0.972014\pi\) | |||||||
\(878\) | 681.867 | + | 558.006i | 0.776614 | + | 0.635542i | ||||
\(879\) | 1511.04 | − | 872.397i | 1.71904 | − | 0.992488i | ||||
\(880\) | −67.2161 | + | 88.6157i | −0.0763819 | + | 0.100700i | ||||
\(881\) | −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 | \(0.242457\pi\) | |||||||
\(884\) | 143.760 | − | 29.0121i | 0.162624 | − | 0.0328192i | ||||
\(885\) | −282.087 | + | 162.863i | −0.318742 | + | 0.184026i | ||||
\(886\) | −616.923 | + | 753.862i | −0.696302 | + | 0.850860i | ||||
\(887\) | 849.326 | + | 490.359i | 0.957526 | + | 0.552828i | 0.895411 | − | 0.445241i | \(-0.146882\pi\) |
0.0621155 | + | 0.998069i | \(0.480215\pi\) | |||||||
\(888\) | 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 | ||||
\(892\) | 13.4955 | − | 40.1232i | 0.0151294 | − | 0.0449812i | ||||
\(893\) | −778.228 | + | 449.310i | −0.871476 | + | 0.503147i | ||||
\(894\) | −212.105 | + | 1295.93i | −0.237254 | + | 1.44959i | ||||
\(895\) | − | 88.6605i | − | 0.0990621i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 186.392 | 0.207795 | ||||||||
\(898\) | −521.143 | − | 85.2956i | −0.580338 | − | 0.0949839i | ||||
\(899\) | 524.382 | + | 908.256i | 0.583295 | + | 1.01030i | ||||
\(900\) | 227.627 | + | 76.5625i | 0.252919 | + | 0.0850694i | ||||
\(901\) | 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 | ||||
\(906\) | 606.410 | + | 496.256i | 0.669326 | + | 0.547743i | ||||
\(907\) | 329.186 | + | 570.167i | 0.362939 | + | 0.628629i | 0.988443 | − | 0.151592i | \(-0.0484399\pi\) |
−0.625504 | + | 0.780221i | \(0.715107\pi\) | |||||||
\(908\) | −83.7231 | − | 414.861i | −0.0922061 | − | 0.456895i | ||||
\(909\) | − | 52.1173i | − | 0.0573348i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 276.507i | − | 0.303520i | −0.988417 | − | 0.151760i | \(-0.951506\pi\) | ||
0.988417 | − | 0.151760i | \(-0.0484941\pi\) | |||||||
\(912\) | −1082.43 | − | 821.037i | −1.18688 | − | 0.900260i | ||||
\(913\) | 8.10765 | + | 14.0429i | 0.00888023 | + | 0.0153810i | ||||
\(914\) | −651.458 | + | 796.062i | −0.712755 | + | 0.870965i | ||||
\(915\) | −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 | \(-0.0733613\pi\) |
0.288948 | + | 0.957345i | \(0.406695\pi\) | |||||||
\(920\) | −16.1138 | − | 436.446i | −0.0175150 | − | 0.474398i | ||||
\(921\) | −381.250 | − | 660.344i | −0.413952 | − | 0.716986i | ||||
\(922\) | 65.3269 | − | 399.138i | 0.0708534 | − | 0.432904i | ||||
\(923\) | 158.392 | 0.171606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1323.85i | 1.43119i | ||||||||
\(926\) | 233.447 | − | 1426.33i | 0.252103 | − | 1.54031i | ||||
\(927\) | −99.1324 | + | 57.2341i | −0.106939 | + | 0.0617412i | ||||
\(928\) | 520.900 | − | 494.731i | 0.561315 | − | 0.533116i | ||||
\(929\) | −17.7006 | + | 30.6583i | −0.0190534 | + | 0.0330014i | −0.875395 | − | 0.483409i | \(-0.839399\pi\) |
0.856342 | + | 0.516410i | \(0.172732\pi\) | |||||||
\(930\) | 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 | ||||
\(934\) | −439.879 | + | 537.519i | −0.470962 | + | 0.575502i | ||||
\(935\) | 142.418 | − | 82.2252i | 0.152319 | − | 0.0879414i | ||||
\(936\) | 17.5122 | + | 27.9012i | 0.0187096 | + | 0.0298090i | ||||
\(937\) | 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 | ||||||||
\(940\) | −44.3121 | − | 219.573i | −0.0471406 | − | 0.233589i | ||||
\(941\) | −1604.66 | + | 926.450i | −1.70527 | + | 0.984537i | −0.765047 | + | 0.643975i | \(0.777284\pi\) |
−0.940222 | + | 0.340563i | \(0.889382\pi\) | |||||||
\(942\) | 1121.08 | + | 917.438i | 1.19011 | + | 0.973925i | ||||
\(943\) | −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 | 0.265666 | − | 0.964065i | \(-0.414408\pi\) |
0.702072 | − | 0.712106i | \(-0.252259\pi\) | |||||||
\(948\) | 168.495 | − | 500.950i | 0.177737 | − | 0.528428i | ||||
\(949\) | 93.0332 | − | 53.7128i | 0.0980329 | − | 0.0565993i | ||||
\(950\) | 1109.27 | + | 181.554i | 1.16765 | + | 0.191109i | ||||
\(951\) | − | 444.927i | − | 0.467852i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 349.687 | 0.366933 | 0.183467 | − | 0.983026i | \(-0.441268\pi\) | ||||
0.183467 | + | 0.983026i | \(0.441268\pi\) | |||||||
\(954\) | −83.9521 | + | 512.935i | −0.0880001 | + | 0.537668i | ||||
\(955\) | 75.2162 | + | 130.278i | 0.0787604 | + | 0.136417i | ||||
\(956\) | −189.135 | + | 562.316i | −0.197840 | + | 0.588196i | ||||
\(957\) | 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 | ||||
\(962\) | −115.002 | + | 140.530i | −0.119545 | + | 0.146081i | ||||
\(963\) | −20.7208 | − | 35.8894i | −0.0215169 | − | 0.0372684i | ||||
\(964\) | 363.891 | + | 1803.14i | 0.377481 | + | 1.87047i | ||||
\(965\) | − | 243.796i | − | 0.252639i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 632.128i | − | 0.653700i | −0.945076 | − | 0.326850i | \(-0.894013\pi\) | ||
0.945076 | − | 0.326850i | \(-0.105987\pi\) | |||||||
\(968\) | −683.568 | + | 429.042i | −0.706166 | + | 0.443225i | ||||
\(969\) | 1004.37 | + | 1739.62i | 1.03650 | + | 1.79528i | ||||
\(970\) | −230.546 | − | 188.667i | −0.237676 | − | 0.194502i | ||||
\(971\) | −328.248 | + | 568.543i | −0.338052 | + | 0.585523i | −0.984066 | − | 0.177802i | \(-0.943101\pi\) |
0.646014 | + | 0.763325i | \(0.276435\pi\) | |||||||
\(972\) | 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 | ||||
\(976\) | −233.827 | − | 555.731i | −0.239577 | − | 0.569397i | ||||
\(977\) | −84.6569 | − | 146.630i | −0.0866498 | − | 0.150082i | 0.819443 | − | 0.573160i | \(-0.194283\pi\) |
−0.906093 | + | 0.423078i | \(0.860949\pi\) | |||||||
\(978\) | 1620.90 | + | 265.293i | 1.65736 | + | 0.271261i | ||||
\(979\) | −197.616 | −0.201855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 10.2337i | − | 0.0104319i | ||||||
\(982\) | 118.328 | + | 19.3668i | 0.120497 | + | 0.0197218i | ||||
\(983\) | 605.012 | − | 349.304i | 0.615475 | − | 0.355345i | −0.159630 | − | 0.987177i | \(-0.551030\pi\) |
0.775105 | + | 0.631832i | \(0.217697\pi\) | |||||||
\(984\) | −27.1796 | − | 736.165i | −0.0276216 | − | 0.748135i | ||||
\(985\) | −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 | ||||
\(990\) | 28.5862 | + | 23.3936i | 0.0288750 | + | 0.0236298i | ||||
\(991\) | 372.133 | − | 214.851i | 0.375513 | − | 0.216802i | −0.300352 | − | 0.953829i | \(-0.597104\pi\) |
0.675864 | + | 0.737026i | \(0.263771\pi\) | |||||||
\(992\) | −1433.52 | − | 423.973i | −1.44508 | − | 0.427392i | ||||
\(993\) | 731.529 | 0.736686 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −280.483 | −0.281892 | ||||||||
\(996\) | −9.76698 | − | 48.3969i | −0.00980621 | − | 0.0485912i | ||||
\(997\) | −45.3720 | + | 26.1955i | −0.0455085 | + | 0.0262743i | −0.522582 | − | 0.852589i | \(-0.675031\pi\) |
0.477073 | + | 0.878864i | \(0.341698\pi\) | |||||||
\(998\) | −106.757 | + | 130.454i | −0.106971 | + | 0.130716i | ||||
\(999\) | 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.275.1 | 8 | ||
7.2 | even | 3 | 56.3.g.a.43.4 | yes | 4 | ||
7.3 | odd | 6 | 392.3.k.j.67.3 | 8 | |||
7.4 | even | 3 | inner | 392.3.k.i.67.3 | 8 | ||
7.5 | odd | 6 | 392.3.g.h.99.4 | 4 | |||
7.6 | odd | 2 | 392.3.k.j.275.1 | 8 | |||
8.3 | odd | 2 | inner | 392.3.k.i.275.3 | 8 | ||
21.2 | odd | 6 | 504.3.g.a.379.1 | 4 | |||
28.19 | even | 6 | 1568.3.g.h.687.4 | 4 | |||
28.23 | odd | 6 | 224.3.g.a.15.1 | 4 | |||
56.3 | even | 6 | 392.3.k.j.67.1 | 8 | |||
56.5 | odd | 6 | 1568.3.g.h.687.3 | 4 | |||
56.11 | odd | 6 | inner | 392.3.k.i.67.1 | 8 | ||
56.19 | even | 6 | 392.3.g.h.99.3 | 4 | |||
56.27 | even | 2 | 392.3.k.j.275.3 | 8 | |||
56.37 | even | 6 | 224.3.g.a.15.2 | 4 | |||
56.51 | odd | 6 | 56.3.g.a.43.3 | ✓ | 4 | ||
84.23 | even | 6 | 2016.3.g.a.1135.3 | 4 | |||
112.37 | even | 12 | 1792.3.d.g.1023.2 | 8 | |||
112.51 | odd | 12 | 1792.3.d.g.1023.1 | 8 | |||
112.93 | even | 12 | 1792.3.d.g.1023.7 | 8 | |||
112.107 | odd | 12 | 1792.3.d.g.1023.8 | 8 | |||
168.107 | even | 6 | 504.3.g.a.379.2 | 4 | |||
168.149 | 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 | 56.51 | odd | 6 | ||
56.3.g.a.43.4 | yes | 4 | 7.2 | even | 3 | ||
224.3.g.a.15.1 | 4 | 28.23 | odd | 6 | |||
224.3.g.a.15.2 | 4 | 56.37 | even | 6 | |||
392.3.g.h.99.3 | 4 | 56.19 | even | 6 | |||
392.3.g.h.99.4 | 4 | 7.5 | odd | 6 | |||
392.3.k.i.67.1 | 8 | 56.11 | odd | 6 | inner | ||
392.3.k.i.67.3 | 8 | 7.4 | even | 3 | inner | ||
392.3.k.i.275.1 | 8 | 1.1 | even | 1 | trivial | ||
392.3.k.i.275.3 | 8 | 8.3 | odd | 2 | inner | ||
392.3.k.j.67.1 | 8 | 56.3 | even | 6 | |||
392.3.k.j.67.3 | 8 | 7.3 | odd | 6 | |||
392.3.k.j.275.1 | 8 | 7.6 | odd | 2 | |||
392.3.k.j.275.3 | 8 | 56.27 | even | 2 | |||
504.3.g.a.379.1 | 4 | 21.2 | odd | 6 | |||
504.3.g.a.379.2 | 4 | 168.107 | even | 6 | |||
1568.3.g.h.687.3 | 4 | 56.5 | odd | 6 | |||
1568.3.g.h.687.4 | 4 | 28.19 | even | 6 | |||
1792.3.d.g.1023.1 | 8 | 112.51 | odd | 12 | |||
1792.3.d.g.1023.2 | 8 | 112.37 | even | 12 | |||
1792.3.d.g.1023.7 | 8 | 112.93 | even | 12 | |||
1792.3.d.g.1023.8 | 8 | 112.107 | odd | 12 | |||
2016.3.g.a.1135.2 | 4 | 168.149 | odd | 6 | |||
2016.3.g.a.1135.3 | 4 | 84.23 | even | 6 |