Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(139,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.139");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.4 | ||
Character | \(\chi\) | \(=\) | 483.139 |
Dual form | 483.3.g.a.139.3 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.48909 | −1.74454 | −0.872272 | − | 0.489021i | \(-0.837354\pi\) | ||||
−0.872272 | + | 0.489021i | \(0.837354\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 8.17374 | 2.04344 | ||||||||
\(5\) | 1.46096i | 0.292192i | 0.989270 | + | 0.146096i | \(0.0466709\pi\) | ||||
−0.989270 | + | 0.146096i | \(0.953329\pi\) | |||||||
\(6\) | 6.04328i | 1.00721i | ||||||||
\(7\) | 6.91536 | + | 1.08528i | 0.987908 | + | 0.155040i | ||||
\(8\) | −14.5626 | −1.82032 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | − | 5.09743i | − | 0.509743i | ||||||
\(11\) | −8.08381 | −0.734892 | −0.367446 | − | 0.930045i | \(-0.619768\pi\) | ||||
−0.367446 | + | 0.930045i | \(0.619768\pi\) | |||||||
\(12\) | − | 14.1573i | − | 1.17978i | ||||||
\(13\) | − | 10.0187i | − | 0.770671i | −0.922777 | − | 0.385335i | \(-0.874086\pi\) | ||
0.922777 | − | 0.385335i | \(-0.125914\pi\) | |||||||
\(14\) | −24.1283 | − | 3.78664i | −1.72345 | − | 0.270474i | ||||
\(15\) | 2.53046 | 0.168697 | ||||||||
\(16\) | 18.1151 | 1.13219 | ||||||||
\(17\) | − | 14.6817i | − | 0.863632i | −0.901962 | − | 0.431816i | \(-0.857873\pi\) | ||
0.901962 | − | 0.431816i | \(-0.142127\pi\) | |||||||
\(18\) | 10.4673 | 0.581515 | ||||||||
\(19\) | 9.90546i | 0.521340i | 0.965428 | + | 0.260670i | \(0.0839435\pi\) | ||||
−0.965428 | + | 0.260670i | \(0.916057\pi\) | |||||||
\(20\) | 11.9415i | 0.597076i | ||||||||
\(21\) | 1.87976 | − | 11.9778i | 0.0895125 | − | 0.570369i | ||||
\(22\) | 28.2051 | 1.28205 | ||||||||
\(23\) | −4.79583 | −0.208514 | ||||||||
\(24\) | 25.2231i | 1.05096i | ||||||||
\(25\) | 22.8656 | 0.914624 | ||||||||
\(26\) | 34.9562i | 1.34447i | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 56.5243 | + | 8.87081i | 2.01873 | + | 0.316815i | ||||
\(29\) | −0.216442 | −0.00746351 | −0.00373175 | − | 0.999993i | \(-0.501188\pi\) | ||||
−0.00373175 | + | 0.999993i | \(0.501188\pi\) | |||||||
\(30\) | −8.82900 | −0.294300 | ||||||||
\(31\) | − | 27.4353i | − | 0.885010i | −0.896766 | − | 0.442505i | \(-0.854090\pi\) | ||
0.896766 | − | 0.442505i | \(-0.145910\pi\) | |||||||
\(32\) | −4.95494 | −0.154842 | ||||||||
\(33\) | 14.0016i | 0.424290i | ||||||||
\(34\) | 51.2259i | 1.50664i | ||||||||
\(35\) | −1.58555 | + | 10.1031i | −0.0453016 | + | 0.288659i | ||||
\(36\) | −24.5212 | −0.681145 | ||||||||
\(37\) | −12.4301 | −0.335949 | −0.167975 | − | 0.985791i | \(-0.553723\pi\) | ||||
−0.167975 | + | 0.985791i | \(0.553723\pi\) | |||||||
\(38\) | − | 34.5610i | − | 0.909501i | ||||||
\(39\) | −17.3529 | −0.444947 | ||||||||
\(40\) | − | 21.2753i | − | 0.531884i | ||||||
\(41\) | 29.2097i | 0.712431i | 0.934404 | + | 0.356215i | \(0.115933\pi\) | ||||
−0.934404 | + | 0.356215i | \(0.884067\pi\) | |||||||
\(42\) | −6.55866 | + | 41.7914i | −0.156158 | + | 0.995034i | ||||
\(43\) | 16.6889 | 0.388113 | 0.194057 | − | 0.980990i | \(-0.437835\pi\) | ||||
0.194057 | + | 0.980990i | \(0.437835\pi\) | |||||||
\(44\) | −66.0750 | −1.50170 | ||||||||
\(45\) | − | 4.38289i | − | 0.0973975i | ||||||
\(46\) | 16.7331 | 0.363763 | ||||||||
\(47\) | − | 2.99973i | − | 0.0638241i | −0.999491 | − | 0.0319120i | \(-0.989840\pi\) | ||
0.999491 | − | 0.0319120i | \(-0.0101596\pi\) | |||||||
\(48\) | − | 31.3763i | − | 0.653672i | ||||||
\(49\) | 46.6443 | + | 15.0102i | 0.951925 | + | 0.306331i | ||||
\(50\) | −79.7801 | −1.59560 | ||||||||
\(51\) | −25.4295 | −0.498618 | ||||||||
\(52\) | − | 81.8904i | − | 1.57482i | ||||||
\(53\) | 18.5951 | 0.350851 | 0.175425 | − | 0.984493i | \(-0.443870\pi\) | ||||
0.175425 | + | 0.984493i | \(0.443870\pi\) | |||||||
\(54\) | − | 18.1298i | − | 0.335738i | ||||||
\(55\) | − | 11.8101i | − | 0.214730i | ||||||
\(56\) | −100.705 | − | 15.8045i | −1.79831 | − | 0.282223i | ||||
\(57\) | 17.1568 | 0.300996 | ||||||||
\(58\) | 0.755185 | 0.0130204 | ||||||||
\(59\) | − | 106.226i | − | 1.80044i | −0.435434 | − | 0.900221i | \(-0.643405\pi\) | ||
0.435434 | − | 0.900221i | \(-0.356595\pi\) | |||||||
\(60\) | 20.6833 | 0.344722 | ||||||||
\(61\) | − | 100.179i | − | 1.64228i | −0.570725 | − | 0.821142i | \(-0.693338\pi\) | ||
0.570725 | − | 0.821142i | \(-0.306662\pi\) | |||||||
\(62\) | 95.7243i | 1.54394i | ||||||||
\(63\) | −20.7461 | − | 3.25584i | −0.329303 | − | 0.0516800i | ||||
\(64\) | −55.1722 | −0.862065 | ||||||||
\(65\) | 14.6370 | 0.225184 | ||||||||
\(66\) | − | 48.8527i | − | 0.740193i | ||||||
\(67\) | −27.9224 | −0.416752 | −0.208376 | − | 0.978049i | \(-0.566818\pi\) | ||||
−0.208376 | + | 0.978049i | \(0.566818\pi\) | |||||||
\(68\) | − | 120.005i | − | 1.76478i | ||||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | 5.53214 | − | 35.2505i | 0.0790306 | − | 0.503579i | ||||
\(71\) | −14.0375 | −0.197711 | −0.0988556 | − | 0.995102i | \(-0.531518\pi\) | ||||
−0.0988556 | + | 0.995102i | \(0.531518\pi\) | |||||||
\(72\) | 43.6877 | 0.606773 | ||||||||
\(73\) | − | 99.0175i | − | 1.35640i | −0.734876 | − | 0.678202i | \(-0.762759\pi\) | ||
0.734876 | − | 0.678202i | \(-0.237241\pi\) | |||||||
\(74\) | 43.3698 | 0.586078 | ||||||||
\(75\) | − | 39.6044i | − | 0.528058i | ||||||
\(76\) | 80.9647i | 1.06532i | ||||||||
\(77\) | −55.9024 | − | 8.77321i | −0.726006 | − | 0.113938i | ||||
\(78\) | 60.5459 | 0.776230 | ||||||||
\(79\) | −1.25724 | −0.0159144 | −0.00795721 | − | 0.999968i | \(-0.502533\pi\) | ||||
−0.00795721 | + | 0.999968i | \(0.502533\pi\) | |||||||
\(80\) | 26.4655i | 0.330818i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 101.915i | − | 1.24287i | ||||||
\(83\) | − | 50.4640i | − | 0.608000i | −0.952672 | − | 0.304000i | \(-0.901678\pi\) | ||
0.952672 | − | 0.304000i | \(-0.0983224\pi\) | |||||||
\(84\) | 15.3647 | − | 97.9030i | 0.182913 | − | 1.16551i | ||||
\(85\) | 21.4495 | 0.252347 | ||||||||
\(86\) | −58.2290 | −0.677081 | ||||||||
\(87\) | 0.374888i | 0.00430906i | ||||||||
\(88\) | 117.721 | 1.33774 | ||||||||
\(89\) | − | 121.967i | − | 1.37041i | −0.728349 | − | 0.685207i | \(-0.759712\pi\) | ||
0.728349 | − | 0.685207i | \(-0.240288\pi\) | |||||||
\(90\) | 15.2923i | 0.169914i | ||||||||
\(91\) | 10.8731 | − | 69.2830i | 0.119485 | − | 0.761352i | ||||
\(92\) | −39.1999 | −0.426086 | ||||||||
\(93\) | −47.5194 | −0.510961 | ||||||||
\(94\) | 10.4663i | 0.111344i | ||||||||
\(95\) | −14.4715 | −0.152332 | ||||||||
\(96\) | 8.58220i | 0.0893979i | ||||||||
\(97\) | 111.721i | 1.15176i | 0.817533 | + | 0.575882i | \(0.195341\pi\) | ||||
−0.817533 | + | 0.575882i | \(0.804659\pi\) | |||||||
\(98\) | −162.746 | − | 52.3720i | −1.66068 | − | 0.534408i | ||||
\(99\) | 24.2514 | 0.244964 | ||||||||
\(100\) | 186.897 | 1.86897 | ||||||||
\(101\) | − | 114.914i | − | 1.13777i | −0.822418 | − | 0.568884i | \(-0.807375\pi\) | ||
0.822418 | − | 0.568884i | \(-0.192625\pi\) | |||||||
\(102\) | 88.7259 | 0.869862 | ||||||||
\(103\) | − | 52.0049i | − | 0.504902i | −0.967610 | − | 0.252451i | \(-0.918763\pi\) | ||
0.967610 | − | 0.252451i | \(-0.0812367\pi\) | |||||||
\(104\) | 145.898i | 1.40287i | ||||||||
\(105\) | 17.4990 | + | 2.74626i | 0.166658 | + | 0.0261549i | ||||
\(106\) | −64.8800 | −0.612075 | ||||||||
\(107\) | 109.825 | 1.02640 | 0.513202 | − | 0.858268i | \(-0.328459\pi\) | ||||
0.513202 | + | 0.858268i | \(0.328459\pi\) | |||||||
\(108\) | 42.4720i | 0.393259i | ||||||||
\(109\) | −88.6154 | −0.812985 | −0.406493 | − | 0.913654i | \(-0.633248\pi\) | ||||
−0.406493 | + | 0.913654i | \(0.633248\pi\) | |||||||
\(110\) | 41.2066i | 0.374606i | ||||||||
\(111\) | 21.5296i | 0.193960i | ||||||||
\(112\) | 125.272 | + | 19.6600i | 1.11850 | + | 0.175535i | ||||
\(113\) | −90.3619 | −0.799663 | −0.399831 | − | 0.916589i | \(-0.630931\pi\) | ||||
−0.399831 | + | 0.916589i | \(0.630931\pi\) | |||||||
\(114\) | −59.8615 | −0.525101 | ||||||||
\(115\) | − | 7.00653i | − | 0.0609263i | ||||||
\(116\) | −1.76914 | −0.0152512 | ||||||||
\(117\) | 30.0562i | 0.256890i | ||||||||
\(118\) | 370.632i | 3.14095i | ||||||||
\(119\) | 15.9338 | − | 101.530i | 0.133898 | − | 0.853189i | ||||
\(120\) | −36.8500 | −0.307083 | ||||||||
\(121\) | −55.6520 | −0.459934 | ||||||||
\(122\) | 349.534i | 2.86504i | ||||||||
\(123\) | 50.5926 | 0.411322 | ||||||||
\(124\) | − | 224.249i | − | 1.80846i | ||||||
\(125\) | 69.9298i | 0.559438i | ||||||||
\(126\) | 72.3849 | + | 11.3599i | 0.574483 | + | 0.0901581i | ||||
\(127\) | 93.8066 | 0.738635 | 0.369318 | − | 0.929303i | \(-0.379591\pi\) | ||||
0.369318 | + | 0.929303i | \(0.379591\pi\) | |||||||
\(128\) | 212.320 | 1.65875 | ||||||||
\(129\) | − | 28.9060i | − | 0.224077i | ||||||
\(130\) | −51.0697 | −0.392844 | ||||||||
\(131\) | 16.6618i | 0.127189i | 0.997976 | + | 0.0635946i | \(0.0202564\pi\) | ||||
−0.997976 | + | 0.0635946i | \(0.979744\pi\) | |||||||
\(132\) | 114.445i | 0.867009i | ||||||||
\(133\) | −10.7502 | + | 68.4998i | −0.0808286 | + | 0.515036i | ||||
\(134\) | 97.4237 | 0.727042 | ||||||||
\(135\) | −7.59138 | −0.0562325 | ||||||||
\(136\) | 213.804i | 1.57209i | ||||||||
\(137\) | −38.0207 | −0.277524 | −0.138762 | − | 0.990326i | \(-0.544312\pi\) | ||||
−0.138762 | + | 0.990326i | \(0.544312\pi\) | |||||||
\(138\) | − | 28.9826i | − | 0.210018i | ||||||
\(139\) | − | 87.3612i | − | 0.628498i | −0.949341 | − | 0.314249i | \(-0.898247\pi\) | ||
0.949341 | − | 0.314249i | \(-0.101753\pi\) | |||||||
\(140\) | −12.9599 | + | 82.5799i | −0.0925708 | + | 0.589857i | ||||
\(141\) | −5.19569 | −0.0368488 | ||||||||
\(142\) | 48.9781 | 0.344916 | ||||||||
\(143\) | 80.9894i | 0.566360i | ||||||||
\(144\) | −54.3453 | −0.377398 | ||||||||
\(145\) | − | 0.316213i | − | 0.00218078i | ||||||
\(146\) | 345.481i | 2.36631i | ||||||||
\(147\) | 25.9984 | − | 80.7904i | 0.176860 | − | 0.549594i | ||||
\(148\) | −101.601 | −0.686491 | ||||||||
\(149\) | −142.960 | −0.959460 | −0.479730 | − | 0.877416i | \(-0.659265\pi\) | ||||
−0.479730 | + | 0.877416i | \(0.659265\pi\) | |||||||
\(150\) | 138.183i | 0.921221i | ||||||||
\(151\) | −172.567 | −1.14282 | −0.571412 | − | 0.820663i | \(-0.693604\pi\) | ||||
−0.571412 | + | 0.820663i | \(0.693604\pi\) | |||||||
\(152\) | − | 144.249i | − | 0.949006i | ||||||
\(153\) | 44.0452i | 0.287877i | ||||||||
\(154\) | 195.049 | + | 30.6105i | 1.26655 | + | 0.198769i | ||||
\(155\) | 40.0820 | 0.258593 | ||||||||
\(156\) | −141.838 | −0.909220 | ||||||||
\(157\) | 81.7870i | 0.520936i | 0.965482 | + | 0.260468i | \(0.0838769\pi\) | ||||
−0.965482 | + | 0.260468i | \(0.916123\pi\) | |||||||
\(158\) | 4.38662 | 0.0277634 | ||||||||
\(159\) | − | 32.2077i | − | 0.202564i | ||||||
\(160\) | − | 7.23897i | − | 0.0452436i | ||||||
\(161\) | −33.1649 | − | 5.20482i | −0.205993 | − | 0.0323281i | ||||
\(162\) | −31.4018 | −0.193838 | ||||||||
\(163\) | −22.4356 | −0.137642 | −0.0688208 | − | 0.997629i | \(-0.521924\pi\) | ||||
−0.0688208 | + | 0.997629i | \(0.521924\pi\) | |||||||
\(164\) | 238.752i | 1.45581i | ||||||||
\(165\) | −20.4558 | −0.123974 | ||||||||
\(166\) | 176.074i | 1.06068i | ||||||||
\(167\) | 104.195i | 0.623920i | 0.950095 | + | 0.311960i | \(0.100985\pi\) | ||||
−0.950095 | + | 0.311960i | \(0.899015\pi\) | |||||||
\(168\) | −27.3741 | + | 174.427i | −0.162941 | + | 1.03825i | ||||
\(169\) | 68.6253 | 0.406067 | ||||||||
\(170\) | −74.8391 | −0.440230 | ||||||||
\(171\) | − | 29.7164i | − | 0.173780i | ||||||
\(172\) | 136.411 | 0.793085 | ||||||||
\(173\) | 61.2668i | 0.354144i | 0.984198 | + | 0.177072i | \(0.0566625\pi\) | ||||
−0.984198 | + | 0.177072i | \(0.943338\pi\) | |||||||
\(174\) | − | 1.30802i | − | 0.00751735i | ||||||
\(175\) | 158.124 | + | 24.8156i | 0.903564 | + | 0.141803i | ||||
\(176\) | −146.439 | −0.832040 | ||||||||
\(177\) | −183.989 | −1.03949 | ||||||||
\(178\) | 425.553i | 2.39075i | ||||||||
\(179\) | 321.989 | 1.79882 | 0.899409 | − | 0.437107i | \(-0.143997\pi\) | ||||
0.899409 | + | 0.437107i | \(0.143997\pi\) | |||||||
\(180\) | − | 35.8246i | − | 0.199025i | ||||||
\(181\) | − | 273.755i | − | 1.51246i | −0.654306 | − | 0.756230i | \(-0.727039\pi\) | ||
0.654306 | − | 0.756230i | \(-0.272961\pi\) | |||||||
\(182\) | −37.9373 | + | 241.735i | −0.208447 | + | 1.32821i | ||||
\(183\) | −173.516 | −0.948173 | ||||||||
\(184\) | 69.8396 | 0.379563 | ||||||||
\(185\) | − | 18.1599i | − | 0.0981618i | ||||||
\(186\) | 165.799 | 0.891394 | ||||||||
\(187\) | 118.684i | 0.634676i | ||||||||
\(188\) | − | 24.5190i | − | 0.130420i | ||||||
\(189\) | −5.63929 | + | 35.9333i | −0.0298375 | + | 0.190123i | ||||
\(190\) | 50.4924 | 0.265749 | ||||||||
\(191\) | 140.743 | 0.736876 | 0.368438 | − | 0.929652i | \(-0.379893\pi\) | ||||
0.368438 | + | 0.929652i | \(0.379893\pi\) | |||||||
\(192\) | 95.5610i | 0.497713i | ||||||||
\(193\) | −252.426 | −1.30791 | −0.653953 | − | 0.756535i | \(-0.726891\pi\) | ||||
−0.653953 | + | 0.756535i | \(0.726891\pi\) | |||||||
\(194\) | − | 389.805i | − | 2.00930i | ||||||
\(195\) | − | 25.3520i | − | 0.130010i | ||||||
\(196\) | 381.259 | + | 122.690i | 1.94520 | + | 0.625967i | ||||
\(197\) | 308.146 | 1.56419 | 0.782097 | − | 0.623156i | \(-0.214150\pi\) | ||||
0.782097 | + | 0.623156i | \(0.214150\pi\) | |||||||
\(198\) | −84.6154 | −0.427351 | ||||||||
\(199\) | 46.9336i | 0.235847i | 0.993023 | + | 0.117924i | \(0.0376238\pi\) | ||||
−0.993023 | + | 0.117924i | \(0.962376\pi\) | |||||||
\(200\) | −332.981 | −1.66491 | ||||||||
\(201\) | 48.3630i | 0.240612i | ||||||||
\(202\) | 400.947i | 1.98489i | ||||||||
\(203\) | −1.49677 | − | 0.234900i | −0.00737326 | − | 0.00115714i | ||||
\(204\) | −207.854 | −1.01889 | ||||||||
\(205\) | −42.6742 | −0.208167 | ||||||||
\(206\) | 181.450i | 0.880824i | ||||||||
\(207\) | 14.3875 | 0.0695048 | ||||||||
\(208\) | − | 181.490i | − | 0.872548i | ||||||
\(209\) | − | 80.0739i | − | 0.383129i | ||||||
\(210\) | −61.0557 | − | 9.58195i | −0.290741 | − | 0.0456283i | ||||
\(211\) | −157.520 | −0.746542 | −0.373271 | − | 0.927722i | \(-0.621764\pi\) | ||||
−0.373271 | + | 0.927722i | \(0.621764\pi\) | |||||||
\(212\) | 151.992 | 0.716941 | ||||||||
\(213\) | 24.3137i | 0.114149i | ||||||||
\(214\) | −383.190 | −1.79061 | ||||||||
\(215\) | 24.3818i | 0.113404i | ||||||||
\(216\) | − | 75.6693i | − | 0.350321i | ||||||
\(217\) | 29.7750 | − | 189.725i | 0.137212 | − | 0.874309i | ||||
\(218\) | 309.187 | 1.41829 | ||||||||
\(219\) | −171.503 | −0.783120 | ||||||||
\(220\) | − | 96.5330i | − | 0.438787i | ||||||
\(221\) | −147.092 | −0.665576 | ||||||||
\(222\) | − | 75.1187i | − | 0.338372i | ||||||
\(223\) | − | 10.4417i | − | 0.0468236i | −0.999726 | − | 0.0234118i | \(-0.992547\pi\) | ||
0.999726 | − | 0.0234118i | \(-0.00745290\pi\) | |||||||
\(224\) | −34.2652 | − | 5.37750i | −0.152969 | − | 0.0240067i | ||||
\(225\) | −68.5968 | −0.304875 | ||||||||
\(226\) | 315.281 | 1.39505 | ||||||||
\(227\) | − | 393.299i | − | 1.73259i | −0.499529 | − | 0.866297i | \(-0.666494\pi\) | ||
0.499529 | − | 0.866297i | \(-0.333506\pi\) | |||||||
\(228\) | 140.235 | 0.615066 | ||||||||
\(229\) | − | 414.362i | − | 1.80944i | −0.426008 | − | 0.904720i | \(-0.640080\pi\) | ||
0.426008 | − | 0.904720i | \(-0.359920\pi\) | |||||||
\(230\) | 24.4464i | 0.106289i | ||||||||
\(231\) | −15.1956 | + | 96.8259i | −0.0657820 | + | 0.419160i | ||||
\(232\) | 3.15195 | 0.0135860 | ||||||||
\(233\) | 316.762 | 1.35950 | 0.679748 | − | 0.733446i | \(-0.262089\pi\) | ||||
0.679748 | + | 0.733446i | \(0.262089\pi\) | |||||||
\(234\) | − | 104.869i | − | 0.448156i | ||||||
\(235\) | 4.38249 | 0.0186489 | ||||||||
\(236\) | − | 868.264i | − | 3.67909i | ||||||
\(237\) | 2.17760i | 0.00918819i | ||||||||
\(238\) | −55.5945 | + | 354.246i | −0.233590 | + | 1.48843i | ||||
\(239\) | 347.307 | 1.45317 | 0.726583 | − | 0.687078i | \(-0.241107\pi\) | ||||
0.726583 | + | 0.687078i | \(0.241107\pi\) | |||||||
\(240\) | 45.8395 | 0.190998 | ||||||||
\(241\) | − | 61.3638i | − | 0.254622i | −0.991863 | − | 0.127311i | \(-0.959365\pi\) | ||
0.991863 | − | 0.127311i | \(-0.0406346\pi\) | |||||||
\(242\) | 194.175 | 0.802375 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | − | 818.840i | − | 3.35590i | ||||||
\(245\) | −21.9293 | + | 68.1456i | −0.0895075 | + | 0.278145i | ||||
\(246\) | −176.522 | −0.717570 | ||||||||
\(247\) | 99.2400 | 0.401781 | ||||||||
\(248\) | 399.528i | 1.61100i | ||||||||
\(249\) | −87.4063 | −0.351029 | ||||||||
\(250\) | − | 243.991i | − | 0.975965i | ||||||
\(251\) | − | 177.416i | − | 0.706838i | −0.935465 | − | 0.353419i | \(-0.885019\pi\) | ||
0.935465 | − | 0.353419i | \(-0.114981\pi\) | |||||||
\(252\) | −169.573 | − | 26.6124i | −0.672909 | − | 0.105605i | ||||
\(253\) | 38.7686 | 0.153236 | ||||||||
\(254\) | −327.300 | −1.28858 | ||||||||
\(255\) | − | 37.1516i | − | 0.145692i | ||||||
\(256\) | −520.116 | −2.03170 | ||||||||
\(257\) | − | 276.116i | − | 1.07438i | −0.843461 | − | 0.537190i | \(-0.819486\pi\) | ||
0.843461 | − | 0.537190i | \(-0.180514\pi\) | |||||||
\(258\) | 100.856i | 0.390913i | ||||||||
\(259\) | −85.9587 | − | 13.4902i | −0.331887 | − | 0.0520856i | ||||
\(260\) | 119.639 | 0.460149 | ||||||||
\(261\) | 0.649325 | 0.00248784 | ||||||||
\(262\) | − | 58.1344i | − | 0.221887i | ||||||
\(263\) | 78.9193 | 0.300074 | 0.150037 | − | 0.988680i | \(-0.452061\pi\) | ||||
0.150037 | + | 0.988680i | \(0.452061\pi\) | |||||||
\(264\) | − | 203.899i | − | 0.772344i | ||||||
\(265\) | 27.1667i | 0.102516i | ||||||||
\(266\) | 37.5084 | − | 239.002i | 0.141009 | − | 0.898503i | ||||
\(267\) | −211.253 | −0.791209 | ||||||||
\(268\) | −228.230 | −0.851606 | ||||||||
\(269\) | − | 233.553i | − | 0.868227i | −0.900858 | − | 0.434113i | \(-0.857062\pi\) | ||
0.900858 | − | 0.434113i | \(-0.142938\pi\) | |||||||
\(270\) | 26.4870 | 0.0981000 | ||||||||
\(271\) | 480.406i | 1.77272i | 0.463000 | + | 0.886358i | \(0.346773\pi\) | ||||
−0.463000 | + | 0.886358i | \(0.653227\pi\) | |||||||
\(272\) | − | 265.961i | − | 0.977798i | ||||||
\(273\) | −120.002 | − | 18.8328i | −0.439567 | − | 0.0689846i | ||||
\(274\) | 132.658 | 0.484152 | ||||||||
\(275\) | −184.841 | −0.672150 | ||||||||
\(276\) | 67.8962i | 0.246001i | ||||||||
\(277\) | −5.33677 | −0.0192663 | −0.00963316 | − | 0.999954i | \(-0.503066\pi\) | ||||
−0.00963316 | + | 0.999954i | \(0.503066\pi\) | |||||||
\(278\) | 304.811i | 1.09644i | ||||||||
\(279\) | 82.3060i | 0.295003i | ||||||||
\(280\) | 23.0897 | − | 147.127i | 0.0824633 | − | 0.525452i | ||||
\(281\) | −247.522 | −0.880860 | −0.440430 | − | 0.897787i | \(-0.645174\pi\) | ||||
−0.440430 | + | 0.897787i | \(0.645174\pi\) | |||||||
\(282\) | 18.1282 | 0.0642845 | ||||||||
\(283\) | 428.419i | 1.51385i | 0.653502 | + | 0.756924i | \(0.273299\pi\) | ||||
−0.653502 | + | 0.756924i | \(0.726701\pi\) | |||||||
\(284\) | −114.739 | −0.404010 | ||||||||
\(285\) | 25.0654i | 0.0879487i | ||||||||
\(286\) | − | 282.579i | − | 0.988040i | ||||||
\(287\) | −31.7007 | + | 201.995i | −0.110455 | + | 0.703816i | ||||
\(288\) | 14.8648 | 0.0516139 | ||||||||
\(289\) | 73.4464 | 0.254140 | ||||||||
\(290\) | 1.10330i | 0.00380447i | ||||||||
\(291\) | 193.507 | 0.664972 | ||||||||
\(292\) | − | 809.343i | − | 2.77172i | ||||||
\(293\) | 433.835i | 1.48067i | 0.672240 | + | 0.740333i | \(0.265332\pi\) | ||||
−0.672240 | + | 0.740333i | \(0.734668\pi\) | |||||||
\(294\) | −90.7109 | + | 281.885i | −0.308540 | + | 0.958792i | ||||
\(295\) | 155.192 | 0.526075 | ||||||||
\(296\) | 181.014 | 0.611535 | ||||||||
\(297\) | − | 42.0047i | − | 0.141430i | ||||||
\(298\) | 498.799 | 1.67382 | ||||||||
\(299\) | 48.0481i | 0.160696i | ||||||||
\(300\) | − | 323.716i | − | 1.07905i | ||||||
\(301\) | 115.410 | + | 18.1121i | 0.383420 | + | 0.0601732i | ||||
\(302\) | 602.100 | 1.99371 | ||||||||
\(303\) | −199.038 | −0.656890 | ||||||||
\(304\) | 179.438i | 0.590258i | ||||||||
\(305\) | 146.358 | 0.479863 | ||||||||
\(306\) | − | 153.678i | − | 0.502215i | ||||||
\(307\) | 257.477i | 0.838687i | 0.907828 | + | 0.419344i | \(0.137740\pi\) | ||||
−0.907828 | + | 0.419344i | \(0.862260\pi\) | |||||||
\(308\) | −456.932 | − | 71.7099i | −1.48355 | − | 0.232824i | ||||
\(309\) | −90.0752 | −0.291505 | ||||||||
\(310\) | −139.850 | −0.451128 | ||||||||
\(311\) | 258.171i | 0.830130i | 0.909792 | + | 0.415065i | \(0.136241\pi\) | ||||
−0.909792 | + | 0.415065i | \(0.863759\pi\) | |||||||
\(312\) | 252.703 | 0.809946 | ||||||||
\(313\) | 273.326i | 0.873246i | 0.899645 | + | 0.436623i | \(0.143826\pi\) | ||||
−0.899645 | + | 0.436623i | \(0.856174\pi\) | |||||||
\(314\) | − | 285.362i | − | 0.908796i | ||||||
\(315\) | 4.75666 | − | 30.3092i | 0.0151005 | − | 0.0962198i | ||||
\(316\) | −10.2763 | −0.0325201 | ||||||||
\(317\) | 143.102 | 0.451426 | 0.225713 | − | 0.974194i | \(-0.427529\pi\) | ||||
0.225713 | + | 0.974194i | \(0.427529\pi\) | |||||||
\(318\) | 112.375i | 0.353382i | ||||||||
\(319\) | 1.74967 | 0.00548487 | ||||||||
\(320\) | − | 80.6044i | − | 0.251889i | ||||||
\(321\) | − | 190.223i | − | 0.592594i | ||||||
\(322\) | 115.715 | + | 18.1601i | 0.359364 | + | 0.0563978i | ||||
\(323\) | 145.429 | 0.450246 | ||||||||
\(324\) | 73.5637 | 0.227048 | ||||||||
\(325\) | − | 229.084i | − | 0.704874i | ||||||
\(326\) | 78.2797 | 0.240122 | ||||||||
\(327\) | 153.486i | 0.469377i | ||||||||
\(328\) | − | 425.367i | − | 1.29685i | ||||||
\(329\) | 3.25555 | − | 20.7442i | 0.00989529 | − | 0.0630523i | ||||
\(330\) | 71.3720 | 0.216279 | ||||||||
\(331\) | −349.567 | −1.05609 | −0.528047 | − | 0.849215i | \(-0.677076\pi\) | ||||
−0.528047 | + | 0.849215i | \(0.677076\pi\) | |||||||
\(332\) | − | 412.480i | − | 1.24241i | ||||||
\(333\) | 37.2904 | 0.111983 | ||||||||
\(334\) | − | 363.544i | − | 1.08846i | ||||||
\(335\) | − | 40.7935i | − | 0.121772i | ||||||
\(336\) | 34.0521 | − | 216.978i | 0.101345 | − | 0.645768i | ||||
\(337\) | −77.8771 | −0.231089 | −0.115545 | − | 0.993302i | \(-0.536861\pi\) | ||||
−0.115545 | + | 0.993302i | \(0.536861\pi\) | |||||||
\(338\) | −239.440 | −0.708401 | ||||||||
\(339\) | 156.511i | 0.461685i | ||||||||
\(340\) | 175.322 | 0.515654 | ||||||||
\(341\) | 221.782i | 0.650387i | ||||||||
\(342\) | 103.683i | 0.303167i | ||||||||
\(343\) | 306.272 | + | 154.423i | 0.892921 | + | 0.450213i | ||||
\(344\) | −243.033 | −0.706491 | ||||||||
\(345\) | −12.1357 | −0.0351758 | ||||||||
\(346\) | − | 213.765i | − | 0.617819i | ||||||
\(347\) | −447.244 | −1.28889 | −0.644444 | − | 0.764651i | \(-0.722911\pi\) | ||||
−0.644444 | + | 0.764651i | \(0.722911\pi\) | |||||||
\(348\) | 3.06424i | 0.00880528i | ||||||||
\(349\) | 383.728i | 1.09951i | 0.835326 | + | 0.549754i | \(0.185279\pi\) | ||||
−0.835326 | + | 0.549754i | \(0.814721\pi\) | |||||||
\(350\) | −551.708 | − | 86.5838i | −1.57631 | − | 0.247382i | ||||
\(351\) | 52.0588 | 0.148316 | ||||||||
\(352\) | 40.0548 | 0.113792 | ||||||||
\(353\) | 550.197i | 1.55863i | 0.626631 | + | 0.779316i | \(0.284433\pi\) | ||||
−0.626631 | + | 0.779316i | \(0.715567\pi\) | |||||||
\(354\) | 641.954 | 1.81343 | ||||||||
\(355\) | − | 20.5083i | − | 0.0577697i | ||||||
\(356\) | − | 996.925i | − | 2.80035i | ||||||
\(357\) | −175.854 | − | 27.5982i | −0.492589 | − | 0.0773058i | ||||
\(358\) | −1123.45 | −3.13812 | ||||||||
\(359\) | 322.417 | 0.898098 | 0.449049 | − | 0.893507i | \(-0.351763\pi\) | ||||
0.449049 | + | 0.893507i | \(0.351763\pi\) | |||||||
\(360\) | 63.8260i | 0.177295i | ||||||||
\(361\) | 262.882 | 0.728205 | ||||||||
\(362\) | 955.157i | 2.63855i | ||||||||
\(363\) | 96.3921i | 0.265543i | ||||||||
\(364\) | 88.8741 | − | 566.302i | 0.244160 | − | 1.55577i | ||||
\(365\) | 144.661 | 0.396331 | ||||||||
\(366\) | 605.411 | 1.65413 | ||||||||
\(367\) | − | 54.1731i | − | 0.147611i | −0.997273 | − | 0.0738053i | \(-0.976486\pi\) | ||
0.997273 | − | 0.0738053i | \(-0.0235143\pi\) | |||||||
\(368\) | −86.8769 | −0.236079 | ||||||||
\(369\) | − | 87.6290i | − | 0.237477i | ||||||
\(370\) | 63.3616i | 0.171248i | ||||||||
\(371\) | 128.592 | + | 20.1809i | 0.346609 | + | 0.0543960i | ||||
\(372\) | −388.411 | −1.04412 | ||||||||
\(373\) | 495.211 | 1.32764 | 0.663822 | − | 0.747890i | \(-0.268933\pi\) | ||||
0.663822 | + | 0.747890i | \(0.268933\pi\) | |||||||
\(374\) | − | 414.101i | − | 1.10722i | ||||||
\(375\) | 121.122 | 0.322992 | ||||||||
\(376\) | 43.6838i | 0.116180i | ||||||||
\(377\) | 2.16847i | 0.00575191i | ||||||||
\(378\) | 19.6760 | − | 125.374i | 0.0520528 | − | 0.331678i | ||||
\(379\) | −305.273 | −0.805470 | −0.402735 | − | 0.915317i | \(-0.631940\pi\) | ||||
−0.402735 | + | 0.915317i | \(0.631940\pi\) | |||||||
\(380\) | −118.286 | −0.311280 | ||||||||
\(381\) | − | 162.478i | − | 0.426451i | ||||||
\(382\) | −491.066 | −1.28551 | ||||||||
\(383\) | 400.831i | 1.04656i | 0.852162 | + | 0.523279i | \(0.175291\pi\) | ||||
−0.852162 | + | 0.523279i | \(0.824709\pi\) | |||||||
\(384\) | − | 367.750i | − | 0.957681i | ||||||
\(385\) | 12.8173 | − | 81.6713i | 0.0332917 | − | 0.212133i | ||||
\(386\) | 880.736 | 2.28170 | ||||||||
\(387\) | −50.0666 | −0.129371 | ||||||||
\(388\) | 913.180i | 2.35356i | ||||||||
\(389\) | −364.606 | −0.937291 | −0.468646 | − | 0.883386i | \(-0.655258\pi\) | ||||
−0.468646 | + | 0.883386i | \(0.655258\pi\) | |||||||
\(390\) | 88.4553i | 0.226808i | ||||||||
\(391\) | 70.4112i | 0.180080i | ||||||||
\(392\) | −679.261 | − | 218.587i | −1.73281 | − | 0.557620i | ||||
\(393\) | 28.8590 | 0.0734327 | ||||||||
\(394\) | −1075.15 | −2.72881 | ||||||||
\(395\) | − | 1.83678i | − | 0.00465007i | ||||||
\(396\) | 198.225 | 0.500568 | ||||||||
\(397\) | − | 43.3239i | − | 0.109128i | −0.998510 | − | 0.0545641i | \(-0.982623\pi\) | ||
0.998510 | − | 0.0545641i | \(-0.0173769\pi\) | |||||||
\(398\) | − | 163.755i | − | 0.411446i | ||||||
\(399\) | 118.645 | + | 18.6199i | 0.297356 | + | 0.0466664i | ||||
\(400\) | 414.212 | 1.03553 | ||||||||
\(401\) | −401.189 | −1.00047 | −0.500235 | − | 0.865890i | \(-0.666753\pi\) | ||||
−0.500235 | + | 0.865890i | \(0.666753\pi\) | |||||||
\(402\) | − | 168.743i | − | 0.419758i | ||||||
\(403\) | −274.867 | −0.682052 | ||||||||
\(404\) | − | 939.281i | − | 2.32495i | ||||||
\(405\) | 13.1487i | 0.0324658i | ||||||||
\(406\) | 5.22237 | + | 0.819587i | 0.0128630 | + | 0.00201869i | ||||
\(407\) | 100.483 | 0.246886 | ||||||||
\(408\) | 370.319 | 0.907645 | ||||||||
\(409\) | − | 138.402i | − | 0.338392i | −0.985582 | − | 0.169196i | \(-0.945883\pi\) | ||
0.985582 | − | 0.169196i | \(-0.0541171\pi\) | |||||||
\(410\) | 148.894 | 0.363156 | ||||||||
\(411\) | 65.8539i | 0.160228i | ||||||||
\(412\) | − | 425.075i | − | 1.03174i | ||||||
\(413\) | 115.285 | − | 734.591i | 0.279141 | − | 1.77867i | ||||
\(414\) | −50.1992 | −0.121254 | ||||||||
\(415\) | 73.7260 | 0.177653 | ||||||||
\(416\) | 49.6421i | 0.119332i | ||||||||
\(417\) | −151.314 | −0.362863 | ||||||||
\(418\) | 279.385i | 0.668385i | ||||||||
\(419\) | 423.644i | 1.01108i | 0.862802 | + | 0.505542i | \(0.168707\pi\) | ||||
−0.862802 | + | 0.505542i | \(0.831293\pi\) | |||||||
\(420\) | 143.033 | + | 22.4472i | 0.340554 | + | 0.0534458i | ||||
\(421\) | −719.394 | −1.70877 | −0.854387 | − | 0.519637i | \(-0.826067\pi\) | ||||
−0.854387 | + | 0.519637i | \(0.826067\pi\) | |||||||
\(422\) | 549.602 | 1.30238 | ||||||||
\(423\) | 8.99919i | 0.0212747i | ||||||||
\(424\) | −270.792 | −0.638661 | ||||||||
\(425\) | − | 335.707i | − | 0.789898i | ||||||
\(426\) | − | 84.8325i | − | 0.199137i | ||||||
\(427\) | 108.723 | − | 692.775i | 0.254620 | − | 1.62242i | ||||
\(428\) | 897.683 | 2.09739 | ||||||||
\(429\) | 140.278 | 0.326988 | ||||||||
\(430\) | − | 85.0703i | − | 0.197838i | ||||||
\(431\) | −227.377 | −0.527557 | −0.263778 | − | 0.964583i | \(-0.584969\pi\) | ||||
−0.263778 | + | 0.964583i | \(0.584969\pi\) | |||||||
\(432\) | 94.1288i | 0.217891i | ||||||||
\(433\) | − | 175.458i | − | 0.405214i | −0.979260 | − | 0.202607i | \(-0.935059\pi\) | ||
0.979260 | − | 0.202607i | \(-0.0649414\pi\) | |||||||
\(434\) | −103.888 | + | 661.968i | −0.239373 | + | 1.52527i | ||||
\(435\) | −0.547697 | −0.00125907 | ||||||||
\(436\) | −724.319 | −1.66128 | ||||||||
\(437\) | − | 47.5049i | − | 0.108707i | ||||||
\(438\) | 598.390 | 1.36619 | ||||||||
\(439\) | 348.758i | 0.794437i | 0.917724 | + | 0.397219i | \(0.130025\pi\) | ||||
−0.917724 | + | 0.397219i | \(0.869975\pi\) | |||||||
\(440\) | 171.986i | 0.390877i | ||||||||
\(441\) | −139.933 | − | 45.0306i | −0.317308 | − | 0.102110i | ||||
\(442\) | 513.218 | 1.16113 | ||||||||
\(443\) | 350.502 | 0.791201 | 0.395601 | − | 0.918423i | \(-0.370536\pi\) | ||||
0.395601 | + | 0.918423i | \(0.370536\pi\) | |||||||
\(444\) | 175.977i | 0.396345i | ||||||||
\(445\) | 178.189 | 0.400424 | ||||||||
\(446\) | 36.4319i | 0.0816859i | ||||||||
\(447\) | 247.613i | 0.553945i | ||||||||
\(448\) | −381.535 | − | 59.8773i | −0.851641 | − | 0.133655i | ||||
\(449\) | 568.236 | 1.26556 | 0.632779 | − | 0.774332i | \(-0.281914\pi\) | ||||
0.632779 | + | 0.774332i | \(0.281914\pi\) | |||||||
\(450\) | 239.340 | 0.531867 | ||||||||
\(451\) | − | 236.125i | − | 0.523560i | ||||||
\(452\) | −738.595 | −1.63406 | ||||||||
\(453\) | 298.894i | 0.659810i | ||||||||
\(454\) | 1372.25i | 3.02259i | ||||||||
\(455\) | 101.220 | + | 15.8852i | 0.222461 | + | 0.0349126i | ||||
\(456\) | −249.846 | −0.547909 | ||||||||
\(457\) | 234.695 | 0.513555 | 0.256778 | − | 0.966470i | \(-0.417339\pi\) | ||||
0.256778 | + | 0.966470i | \(0.417339\pi\) | |||||||
\(458\) | 1445.74i | 3.15665i | ||||||||
\(459\) | 76.2886 | 0.166206 | ||||||||
\(460\) | − | 57.2696i | − | 0.124499i | ||||||
\(461\) | − | 460.577i | − | 0.999082i | −0.866290 | − | 0.499541i | \(-0.833502\pi\) | ||
0.866290 | − | 0.499541i | \(-0.166498\pi\) | |||||||
\(462\) | 53.0189 | − | 337.834i | 0.114760 | − | 0.731243i | ||||
\(463\) | −29.1279 | −0.0629112 | −0.0314556 | − | 0.999505i | \(-0.510014\pi\) | ||||
−0.0314556 | + | 0.999505i | \(0.510014\pi\) | |||||||
\(464\) | −3.92086 | −0.00845013 | ||||||||
\(465\) | − | 69.4240i | − | 0.149299i | ||||||
\(466\) | −1105.21 | −2.37170 | ||||||||
\(467\) | 38.6664i | 0.0827973i | 0.999143 | + | 0.0413987i | \(0.0131814\pi\) | ||||
−0.999143 | + | 0.0413987i | \(0.986819\pi\) | |||||||
\(468\) | 245.671i | 0.524939i | ||||||||
\(469\) | −193.093 | − | 30.3036i | −0.411713 | − | 0.0646133i | ||||
\(470\) | −15.2909 | −0.0325339 | ||||||||
\(471\) | 141.659 | 0.300763 | ||||||||
\(472\) | 1546.92i | 3.27738i | ||||||||
\(473\) | −134.910 | −0.285221 | ||||||||
\(474\) | − | 7.59785i | − | 0.0160292i | ||||||
\(475\) | 226.494i | 0.476830i | ||||||||
\(476\) | 130.239 | − | 829.876i | 0.273611 | − | 1.74344i | ||||
\(477\) | −55.7853 | −0.116950 | ||||||||
\(478\) | −1211.78 | −2.53511 | ||||||||
\(479\) | 579.411i | 1.20963i | 0.796368 | + | 0.604813i | \(0.206752\pi\) | ||||
−0.796368 | + | 0.604813i | \(0.793248\pi\) | |||||||
\(480\) | −12.5383 | −0.0261214 | ||||||||
\(481\) | 124.534i | 0.258906i | ||||||||
\(482\) | 214.104i | 0.444199i | ||||||||
\(483\) | −9.01502 | + | 57.4433i | −0.0186646 | + | 0.118930i | ||||
\(484\) | −454.885 | −0.939845 | ||||||||
\(485\) | −163.220 | −0.336537 | ||||||||
\(486\) | 54.3895i | 0.111913i | ||||||||
\(487\) | 753.901 | 1.54805 | 0.774026 | − | 0.633154i | \(-0.218240\pi\) | ||||
0.774026 | + | 0.633154i | \(0.218240\pi\) | |||||||
\(488\) | 1458.87i | 2.98948i | ||||||||
\(489\) | 38.8595i | 0.0794674i | ||||||||
\(490\) | 76.5135 | − | 237.766i | 0.156150 | − | 0.485237i | ||||
\(491\) | −277.996 | −0.566183 | −0.283091 | − | 0.959093i | \(-0.591360\pi\) | ||||
−0.283091 | + | 0.959093i | \(0.591360\pi\) | |||||||
\(492\) | 413.531 | 0.840510 | ||||||||
\(493\) | 3.17774i | 0.00644573i | ||||||||
\(494\) | −346.257 | −0.700926 | ||||||||
\(495\) | 35.4304i | 0.0715766i | ||||||||
\(496\) | − | 496.993i | − | 1.00200i | ||||||
\(497\) | −97.0743 | − | 15.2346i | −0.195321 | − | 0.0306532i | ||||
\(498\) | 304.968 | 0.612386 | ||||||||
\(499\) | 760.839 | 1.52473 | 0.762364 | − | 0.647149i | \(-0.224039\pi\) | ||||
0.762364 | + | 0.647149i | \(0.224039\pi\) | |||||||
\(500\) | 571.588i | 1.14318i | ||||||||
\(501\) | 180.470 | 0.360220 | ||||||||
\(502\) | 619.021i | 1.23311i | ||||||||
\(503\) | 815.950i | 1.62217i | 0.584931 | + | 0.811083i | \(0.301122\pi\) | ||||
−0.584931 | + | 0.811083i | \(0.698878\pi\) | |||||||
\(504\) | 302.116 | + | 47.4134i | 0.599436 | + | 0.0940742i | ||||
\(505\) | 167.886 | 0.332447 | ||||||||
\(506\) | −135.267 | −0.267326 | ||||||||
\(507\) | − | 118.862i | − | 0.234443i | ||||||
\(508\) | 766.751 | 1.50935 | ||||||||
\(509\) | 63.1818i | 0.124129i | 0.998072 | + | 0.0620647i | \(0.0197685\pi\) | ||||
−0.998072 | + | 0.0620647i | \(0.980231\pi\) | |||||||
\(510\) | 129.625i | 0.254167i | ||||||||
\(511\) | 107.462 | − | 684.741i | 0.210297 | − | 1.34000i | ||||
\(512\) | 965.449 | 1.88564 | ||||||||
\(513\) | −51.4703 | −0.100332 | ||||||||
\(514\) | 963.393i | 1.87431i | ||||||||
\(515\) | 75.9772 | 0.147529 | ||||||||
\(516\) | − | 236.270i | − | 0.457888i | ||||||
\(517\) | 24.2493i | 0.0469038i | ||||||||
\(518\) | 299.918 | + | 47.0684i | 0.578992 | + | 0.0908657i | ||||
\(519\) | 106.117 | 0.204465 | ||||||||
\(520\) | −213.152 | −0.409907 | ||||||||
\(521\) | 113.598i | 0.218038i | 0.994040 | + | 0.109019i | \(0.0347710\pi\) | ||||
−0.994040 | + | 0.109019i | \(0.965229\pi\) | |||||||
\(522\) | −2.26555 | −0.00434014 | ||||||||
\(523\) | 839.032i | 1.60427i | 0.597144 | + | 0.802134i | \(0.296302\pi\) | ||||
−0.597144 | + | 0.802134i | \(0.703698\pi\) | |||||||
\(524\) | 136.189i | 0.259903i | ||||||||
\(525\) | 42.9819 | − | 273.878i | 0.0818702 | − | 0.521673i | ||||
\(526\) | −275.357 | −0.523492 | ||||||||
\(527\) | −402.798 | −0.764323 | ||||||||
\(528\) | 253.640i | 0.480378i | ||||||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | − | 94.7872i | − | 0.178844i | ||||||
\(531\) | 318.678i | 0.600147i | ||||||||
\(532\) | −87.8694 | + | 559.900i | −0.165168 | + | 1.05244i | ||||
\(533\) | 292.643 | 0.549049 | ||||||||
\(534\) | 737.079 | 1.38030 | ||||||||
\(535\) | 160.450i | 0.299907i | ||||||||
\(536\) | 406.621 | 0.758622 | ||||||||
\(537\) | − | 557.701i | − | 1.03855i | ||||||
\(538\) | 814.887i | 1.51466i | ||||||||
\(539\) | −377.064 | − | 121.340i | −0.699562 | − | 0.225120i | ||||
\(540\) | −62.0500 | −0.114907 | ||||||||
\(541\) | −111.214 | −0.205571 | −0.102785 | − | 0.994704i | \(-0.532775\pi\) | ||||
−0.102785 | + | 0.994704i | \(0.532775\pi\) | |||||||
\(542\) | − | 1676.18i | − | 3.09258i | ||||||
\(543\) | −474.158 | −0.873220 | ||||||||
\(544\) | 72.7471i | 0.133726i | ||||||||
\(545\) | − | 129.464i | − | 0.237548i | ||||||
\(546\) | 418.697 | + | 65.7093i | 0.766844 | + | 0.120347i | ||||
\(547\) | 29.0925 | 0.0531856 | 0.0265928 | − | 0.999646i | \(-0.491534\pi\) | ||||
0.0265928 | + | 0.999646i | \(0.491534\pi\) | |||||||
\(548\) | −310.772 | −0.567102 | ||||||||
\(549\) | 300.538i | 0.547428i | ||||||||
\(550\) | 644.927 | 1.17259 | ||||||||
\(551\) | − | 2.14396i | − | 0.00389103i | ||||||
\(552\) | − | 120.966i | − | 0.219141i | ||||||
\(553\) | −8.69426 | − | 1.36446i | −0.0157220 | − | 0.00246737i | ||||
\(554\) | 18.6205 | 0.0336110 | ||||||||
\(555\) | −31.4539 | −0.0566737 | ||||||||
\(556\) | − | 714.068i | − | 1.28429i | ||||||
\(557\) | −932.764 | −1.67462 | −0.837310 | − | 0.546728i | \(-0.815873\pi\) | ||||
−0.837310 | + | 0.546728i | \(0.815873\pi\) | |||||||
\(558\) | − | 287.173i | − | 0.514647i | ||||||
\(559\) | − | 167.201i | − | 0.299108i | ||||||
\(560\) | −28.7225 | + | 183.018i | −0.0512901 | + | 0.326818i | ||||
\(561\) | 205.568 | 0.366430 | ||||||||
\(562\) | 863.625 | 1.53670 | ||||||||
\(563\) | − | 549.628i | − | 0.976249i | −0.872774 | − | 0.488124i | \(-0.837681\pi\) | ||
0.872774 | − | 0.488124i | \(-0.162319\pi\) | |||||||
\(564\) | −42.4682 | −0.0752982 | ||||||||
\(565\) | − | 132.015i | − | 0.233655i | ||||||
\(566\) | − | 1494.79i | − | 2.64098i | ||||||
\(567\) | 62.2382 | + | 9.76753i | 0.109768 | + | 0.0172267i | ||||
\(568\) | 204.422 | 0.359898 | ||||||||
\(569\) | 223.921 | 0.393534 | 0.196767 | − | 0.980450i | \(-0.436956\pi\) | ||||
0.196767 | + | 0.980450i | \(0.436956\pi\) | |||||||
\(570\) | − | 87.4553i | − | 0.153430i | ||||||
\(571\) | 650.294 | 1.13887 | 0.569435 | − | 0.822037i | \(-0.307162\pi\) | ||||
0.569435 | + | 0.822037i | \(0.307162\pi\) | |||||||
\(572\) | 661.987i | 1.15732i | ||||||||
\(573\) | − | 243.774i | − | 0.425435i | ||||||
\(574\) | 110.607 | − | 704.779i | 0.192694 | − | 1.22784i | ||||
\(575\) | −109.660 | −0.190712 | ||||||||
\(576\) | 165.516 | 0.287355 | ||||||||
\(577\) | − | 1120.34i | − | 1.94166i | −0.239772 | − | 0.970829i | \(-0.577073\pi\) | ||
0.239772 | − | 0.970829i | \(-0.422927\pi\) | |||||||
\(578\) | −256.261 | −0.443358 | ||||||||
\(579\) | 437.214i | 0.755120i | ||||||||
\(580\) | − | 2.58465i | − | 0.00445628i | ||||||
\(581\) | 54.7677 | − | 348.977i | 0.0942645 | − | 0.600649i | ||||
\(582\) | −675.162 | −1.16007 | ||||||||
\(583\) | −150.319 | −0.257838 | ||||||||
\(584\) | 1441.95i | 2.46909i | ||||||||
\(585\) | −43.9109 | −0.0750614 | ||||||||
\(586\) | − | 1513.69i | − | 2.58309i | ||||||
\(587\) | 519.842i | 0.885592i | 0.896622 | + | 0.442796i | \(0.146013\pi\) | ||||
−0.896622 | + | 0.442796i | \(0.853987\pi\) | |||||||
\(588\) | 212.505 | − | 660.359i | 0.361402 | − | 1.12306i | ||||
\(589\) | 271.760 | 0.461391 | ||||||||
\(590\) | −541.479 | −0.917762 | ||||||||
\(591\) | − | 533.725i | − | 0.903088i | ||||||
\(592\) | −225.173 | −0.380359 | ||||||||
\(593\) | 289.795i | 0.488692i | 0.969688 | + | 0.244346i | \(0.0785733\pi\) | ||||
−0.969688 | + | 0.244346i | \(0.921427\pi\) | |||||||
\(594\) | 146.558i | 0.246731i | ||||||||
\(595\) | 148.331 | + | 23.2787i | 0.249295 | + | 0.0391239i | ||||
\(596\) | −1168.51 | −1.96059 | ||||||||
\(597\) | 81.2913 | 0.136166 | ||||||||
\(598\) | − | 167.644i | − | 0.280341i | ||||||
\(599\) | −591.525 | −0.987521 | −0.493761 | − | 0.869598i | \(-0.664378\pi\) | ||||
−0.493761 | + | 0.869598i | \(0.664378\pi\) | |||||||
\(600\) | 576.741i | 0.961235i | ||||||||
\(601\) | 125.235i | 0.208377i | 0.994558 | + | 0.104188i | \(0.0332245\pi\) | ||||
−0.994558 | + | 0.104188i | \(0.966775\pi\) | |||||||
\(602\) | −402.674 | − | 63.1948i | −0.668894 | − | 0.104975i | ||||
\(603\) | 83.7671 | 0.138917 | ||||||||
\(604\) | −1410.51 | −2.33529 | ||||||||
\(605\) | − | 81.3055i | − | 0.134389i | ||||||
\(606\) | 694.460 | 1.14597 | ||||||||
\(607\) | 96.8852i | 0.159613i | 0.996810 | + | 0.0798066i | \(0.0254303\pi\) | ||||
−0.996810 | + | 0.0798066i | \(0.974570\pi\) | |||||||
\(608\) | − | 49.0809i | − | 0.0807252i | ||||||
\(609\) | −0.406859 | + | 2.59249i | −0.000668077 | + | 0.00425695i | ||||
\(610\) | −510.656 | −0.837142 | ||||||||
\(611\) | −30.0535 | −0.0491873 | ||||||||
\(612\) | 360.014i | 0.588259i | ||||||||
\(613\) | 557.666 | 0.909732 | 0.454866 | − | 0.890560i | \(-0.349687\pi\) | ||||
0.454866 | + | 0.890560i | \(0.349687\pi\) | |||||||
\(614\) | − | 898.360i | − | 1.46313i | ||||||
\(615\) | 73.9139i | 0.120185i | ||||||||
\(616\) | 814.083 | + | 127.760i | 1.32156 | + | 0.207403i | ||||
\(617\) | −6.30866 | −0.0102247 | −0.00511237 | − | 0.999987i | \(-0.501627\pi\) | ||||
−0.00511237 | + | 0.999987i | \(0.501627\pi\) | |||||||
\(618\) | 314.280 | 0.508544 | ||||||||
\(619\) | 355.187i | 0.573808i | 0.957959 | + | 0.286904i | \(0.0926260\pi\) | ||||
−0.957959 | + | 0.286904i | \(0.907374\pi\) | |||||||
\(620\) | 327.620 | 0.528419 | ||||||||
\(621\) | − | 24.9199i | − | 0.0401286i | ||||||
\(622\) | − | 900.780i | − | 1.44820i | ||||||
\(623\) | 132.368 | − | 843.444i | 0.212469 | − | 1.35384i | ||||
\(624\) | −314.350 | −0.503766 | ||||||||
\(625\) | 469.475 | 0.751160 | ||||||||
\(626\) | − | 953.658i | − | 1.52342i | ||||||
\(627\) | −138.692 | −0.221199 | ||||||||
\(628\) | 668.506i | 1.06450i | ||||||||
\(629\) | 182.496i | 0.290137i | ||||||||
\(630\) | −16.5964 | + | 105.752i | −0.0263435 | + | 0.167860i | ||||
\(631\) | 711.988 | 1.12835 | 0.564175 | − | 0.825656i | \(-0.309194\pi\) | ||||
0.564175 | + | 0.825656i | \(0.309194\pi\) | |||||||
\(632\) | 18.3086 | 0.0289693 | ||||||||
\(633\) | 272.833i | 0.431016i | ||||||||
\(634\) | −499.296 | −0.787533 | ||||||||
\(635\) | 137.048i | 0.215824i | ||||||||
\(636\) | − | 263.257i | − | 0.413926i | ||||||
\(637\) | 150.383 | − | 467.316i | 0.236080 | − | 0.733621i | ||||
\(638\) | −6.10477 | −0.00956860 | ||||||||
\(639\) | 42.1125 | 0.0659037 | ||||||||
\(640\) | 310.192i | 0.484675i | ||||||||
\(641\) | −341.832 | −0.533279 | −0.266639 | − | 0.963796i | \(-0.585913\pi\) | ||||
−0.266639 | + | 0.963796i | \(0.585913\pi\) | |||||||
\(642\) | 663.704i | 1.03381i | ||||||||
\(643\) | − | 331.892i | − | 0.516162i | −0.966123 | − | 0.258081i | \(-0.916910\pi\) | ||
0.966123 | − | 0.258081i | \(-0.0830902\pi\) | |||||||
\(644\) | −271.081 | − | 42.5429i | −0.420934 | − | 0.0660604i | ||||
\(645\) | 42.2305 | 0.0654737 | ||||||||
\(646\) | −507.416 | −0.785474 | ||||||||
\(647\) | − | 663.004i | − | 1.02474i | −0.858766 | − | 0.512368i | \(-0.828768\pi\) | ||
0.858766 | − | 0.512368i | \(-0.171232\pi\) | |||||||
\(648\) | −131.063 | −0.202258 | ||||||||
\(649\) | 858.711i | 1.32313i | ||||||||
\(650\) | 799.294i | 1.22968i | ||||||||
\(651\) | −328.613 | − | 51.5719i | −0.504783 | − | 0.0792195i | ||||
\(652\) | −183.383 | −0.281262 | ||||||||
\(653\) | 784.805 | 1.20184 | 0.600922 | − | 0.799307i | \(-0.294800\pi\) | ||||
0.600922 | + | 0.799307i | \(0.294800\pi\) | |||||||
\(654\) | − | 535.528i | − | 0.818850i | ||||||
\(655\) | −24.3422 | −0.0371637 | ||||||||
\(656\) | 529.136i | 0.806609i | ||||||||
\(657\) | 297.052i | 0.452135i | ||||||||
\(658\) | −11.3589 | + | 72.3784i | −0.0172628 | + | 0.109998i | ||||
\(659\) | −1308.17 | −1.98509 | −0.992543 | − | 0.121898i | \(-0.961102\pi\) | ||||
−0.992543 | + | 0.121898i | \(0.961102\pi\) | |||||||
\(660\) | −167.200 | −0.253334 | ||||||||
\(661\) | − | 1061.20i | − | 1.60545i | −0.596349 | − | 0.802725i | \(-0.703382\pi\) | ||
0.596349 | − | 0.802725i | \(-0.296618\pi\) | |||||||
\(662\) | 1219.67 | 1.84240 | ||||||||
\(663\) | 254.771i | 0.384270i | ||||||||
\(664\) | 734.885i | 1.10676i | ||||||||
\(665\) | −100.076 | − | 15.7056i | −0.150490 | − | 0.0236175i | ||||
\(666\) | −130.109 | −0.195359 | ||||||||
\(667\) | 1.03802 | 0.00155625 | ||||||||
\(668\) | 851.660i | 1.27494i | ||||||||
\(669\) | −18.0855 | −0.0270336 | ||||||||
\(670\) | 142.332i | 0.212436i | ||||||||
\(671\) | 809.830i | 1.20690i | ||||||||
\(672\) | −9.31410 | + | 59.3490i | −0.0138603 | + | 0.0883169i | ||||
\(673\) | −482.238 | −0.716549 | −0.358275 | − | 0.933616i | \(-0.616635\pi\) | ||||
−0.358275 | + | 0.933616i | \(0.616635\pi\) | |||||||
\(674\) | 271.720 | 0.403146 | ||||||||
\(675\) | 118.813i | 0.176019i | ||||||||
\(676\) | 560.925 | 0.829771 | ||||||||
\(677\) | 5.11810i | 0.00755997i | 0.999993 | + | 0.00377998i | \(0.00120321\pi\) | ||||
−0.999993 | + | 0.00377998i | \(0.998797\pi\) | |||||||
\(678\) | − | 546.082i | − | 0.805431i | ||||||
\(679\) | −121.249 | + | 772.592i | −0.178570 | + | 1.13784i | ||||
\(680\) | −312.359 | −0.459352 | ||||||||
\(681\) | −681.214 | −1.00031 | ||||||||
\(682\) | − | 773.817i | − | 1.13463i | ||||||
\(683\) | −601.461 | −0.880616 | −0.440308 | − | 0.897847i | \(-0.645131\pi\) | ||||
−0.440308 | + | 0.897847i | \(0.645131\pi\) | |||||||
\(684\) | − | 242.894i | − | 0.355108i | ||||||
\(685\) | − | 55.5469i | − | 0.0810903i | ||||||
\(686\) | −1068.61 | − | 538.796i | −1.55774 | − | 0.785417i | ||||
\(687\) | −717.695 | −1.04468 | ||||||||
\(688\) | 302.321 | 0.439419 | ||||||||
\(689\) | − | 186.299i | − | 0.270391i | ||||||
\(690\) | 42.3424 | 0.0613658 | ||||||||
\(691\) | 575.488i | 0.832834i | 0.909174 | + | 0.416417i | \(0.136714\pi\) | ||||
−0.909174 | + | 0.416417i | \(0.863286\pi\) | |||||||
\(692\) | 500.779i | 0.723670i | ||||||||
\(693\) | 167.707 | + | 26.3196i | 0.242002 | + | 0.0379792i | ||||
\(694\) | 1560.47 | 2.24852 | ||||||||
\(695\) | 127.631 | 0.183642 | ||||||||
\(696\) | − | 5.45933i | − | 0.00784386i | ||||||
\(697\) | 428.849 | 0.615278 | ||||||||
\(698\) | − | 1338.86i | − | 1.91814i | ||||||
\(699\) | − | 548.649i | − | 0.784905i | ||||||
\(700\) | 1292.46 | + | 202.836i | 1.84638 | + | 0.289766i | ||||
\(701\) | −328.856 | −0.469124 | −0.234562 | − | 0.972101i | \(-0.575366\pi\) | ||||
−0.234562 | + | 0.972101i | \(0.575366\pi\) | |||||||
\(702\) | −181.638 | −0.258743 | ||||||||
\(703\) | − | 123.126i | − | 0.175144i | ||||||
\(704\) | 446.001 | 0.633525 | ||||||||
\(705\) | − | 7.59070i | − | 0.0107670i | ||||||
\(706\) | − | 1919.69i | − | 2.71910i | ||||||
\(707\) | 124.715 | − | 794.675i | 0.176400 | − | 1.12401i | ||||
\(708\) | −1503.88 | −2.12412 | ||||||||
\(709\) | −1214.87 | −1.71349 | −0.856746 | − | 0.515738i | \(-0.827518\pi\) | ||||
−0.856746 | + | 0.515738i | \(0.827518\pi\) | |||||||
\(710\) | 71.5551i | 0.100782i | ||||||||
\(711\) | 3.77172 | 0.00530481 | ||||||||
\(712\) | 1776.15i | 2.49459i | ||||||||
\(713\) | 131.575i | 0.184537i | ||||||||
\(714\) | 613.571 | + | 96.2925i | 0.859343 | + | 0.134863i | ||||
\(715\) | −118.322 | −0.165486 | ||||||||
\(716\) | 2631.85 | 3.67577 | ||||||||
\(717\) | − | 601.553i | − | 0.838986i | ||||||
\(718\) | −1124.94 | −1.56677 | ||||||||
\(719\) | 1056.98i | 1.47008i | 0.678026 | + | 0.735038i | \(0.262836\pi\) | ||||
−0.678026 | + | 0.735038i | \(0.737164\pi\) | |||||||
\(720\) | − | 79.3964i | − | 0.110273i | ||||||
\(721\) | 56.4400 | − | 359.633i | 0.0782801 | − | 0.498797i | ||||
\(722\) | −917.218 | −1.27039 | ||||||||
\(723\) | −106.285 | −0.147006 | ||||||||
\(724\) | − | 2237.61i | − | 3.09062i | ||||||
\(725\) | −4.94907 | −0.00682630 | ||||||||
\(726\) | − | 336.321i | − | 0.463251i | ||||||
\(727\) | − | 1130.45i | − | 1.55495i | −0.628911 | − | 0.777477i | \(-0.716499\pi\) | ||
0.628911 | − | 0.777477i | \(-0.283501\pi\) | |||||||
\(728\) | −158.341 | + | 1008.94i | −0.217501 | + | 1.38590i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −504.734 | −0.691417 | ||||||||
\(731\) | − | 245.022i | − | 0.335187i | ||||||
\(732\) | −1418.27 | −1.93753 | ||||||||
\(733\) | 630.457i | 0.860105i | 0.902804 | + | 0.430052i | \(0.141505\pi\) | ||||
−0.902804 | + | 0.430052i | \(0.858495\pi\) | |||||||
\(734\) | 189.015i | 0.257513i | ||||||||
\(735\) | 118.032 | + | 37.9827i | 0.160587 | + | 0.0516772i | ||||
\(736\) | 23.7630 | 0.0322867 | ||||||||
\(737\) | 225.719 | 0.306268 | ||||||||
\(738\) | 305.745i | 0.414289i | ||||||||
\(739\) | 1068.43 | 1.44578 | 0.722890 | − | 0.690963i | \(-0.242813\pi\) | ||||
0.722890 | + | 0.690963i | \(0.242813\pi\) | |||||||
\(740\) | − | 148.435i | − | 0.200587i | ||||||
\(741\) | − | 171.889i | − | 0.231969i | ||||||
\(742\) | −448.668 | − | 70.4130i | −0.604674 | − | 0.0948962i | ||||
\(743\) | 823.811 | 1.10876 | 0.554382 | − | 0.832263i | \(-0.312955\pi\) | ||||
0.554382 | + | 0.832263i | \(0.312955\pi\) | |||||||
\(744\) | 692.004 | 0.930112 | ||||||||
\(745\) | − | 208.858i | − | 0.280347i | ||||||
\(746\) | −1727.84 | −2.31613 | ||||||||
\(747\) | 151.392i | 0.202667i | ||||||||
\(748\) | 970.096i | 1.29692i | ||||||||
\(749\) | 759.481 | + | 119.191i | 1.01399 | + | 0.159134i | ||||
\(750\) | −422.605 | −0.563474 | ||||||||
\(751\) | 1167.64 | 1.55477 | 0.777387 | − | 0.629022i | \(-0.216545\pi\) | ||||
0.777387 | + | 0.629022i | \(0.216545\pi\) | |||||||
\(752\) | − | 54.3404i | − | 0.0722612i | ||||||
\(753\) | −307.294 | −0.408093 | ||||||||
\(754\) | − | 7.56598i | − | 0.0100345i | ||||||
\(755\) | − | 252.113i | − | 0.333925i | ||||||
\(756\) | −46.0941 | + | 293.709i | −0.0609710 | + | 0.388504i | ||||
\(757\) | 564.937 | 0.746283 | 0.373142 | − | 0.927774i | \(-0.378281\pi\) | ||||
0.373142 | + | 0.927774i | \(0.378281\pi\) | |||||||
\(758\) | 1065.12 | 1.40518 | ||||||||
\(759\) | − | 67.1492i | − | 0.0884706i | ||||||
\(760\) | 210.742 | 0.277292 | ||||||||
\(761\) | 1346.43i | 1.76929i | 0.466264 | + | 0.884646i | \(0.345600\pi\) | ||||
−0.466264 | + | 0.884646i | \(0.654400\pi\) | |||||||
\(762\) | 566.900i | 0.743963i | ||||||||
\(763\) | −612.807 | − | 96.1726i | −0.803155 | − | 0.126045i | ||||
\(764\) | 1150.40 | 1.50576 | ||||||||
\(765\) | −64.3484 | −0.0841156 | ||||||||
\(766\) | − | 1398.54i | − | 1.82577i | ||||||
\(767\) | −1064.25 | −1.38755 | ||||||||
\(768\) | 900.867i | 1.17300i | ||||||||
\(769\) | 854.281i | 1.11090i | 0.831550 | + | 0.555450i | \(0.187454\pi\) | ||||
−0.831550 | + | 0.555450i | \(0.812546\pi\) | |||||||
\(770\) | −44.7208 | + | 284.959i | −0.0580789 | + | 0.370076i | ||||
\(771\) | −478.247 | −0.620294 | ||||||||
\(772\) | −2063.26 | −2.67262 | ||||||||
\(773\) | − | 532.431i | − | 0.688785i | −0.938826 | − | 0.344392i | \(-0.888085\pi\) | ||
0.938826 | − | 0.344392i | \(-0.111915\pi\) | |||||||
\(774\) | 174.687 | 0.225694 | ||||||||
\(775\) | − | 627.325i | − | 0.809451i | ||||||
\(776\) | − | 1626.95i | − | 2.09658i | ||||||
\(777\) | −23.3657 | + | 148.885i | −0.0300716 | + | 0.191615i | ||||
\(778\) | 1272.14 | 1.63515 | ||||||||
\(779\) | −289.335 | −0.371419 | ||||||||
\(780\) | − | 207.220i | − | 0.265667i | ||||||
\(781\) | 113.476 | 0.145296 | ||||||||
\(782\) | − | 245.671i | − | 0.314157i | ||||||
\(783\) | − | 1.12466i | − | 0.00143635i | ||||||
\(784\) | 844.966 | + | 271.911i | 1.07776 | + | 0.346826i | ||||
\(785\) | −119.488 | −0.152214 | ||||||||
\(786\) | −100.692 | −0.128107 | ||||||||
\(787\) | − | 5.75166i | − | 0.00730833i | −0.999993 | − | 0.00365417i | \(-0.998837\pi\) | ||
0.999993 | − | 0.00365417i | \(-0.00116316\pi\) | |||||||
\(788\) | 2518.71 | 3.19633 | ||||||||
\(789\) | − | 136.692i | − | 0.173248i | ||||||
\(790\) | 6.40868i | 0.00811226i | ||||||||
\(791\) | −624.885 | − | 98.0680i | −0.789993 | − | 0.123980i | ||||
\(792\) | −353.163 | −0.445913 | ||||||||
\(793\) | −1003.67 | −1.26566 | ||||||||
\(794\) | 151.161i | 0.190379i | ||||||||
\(795\) | 47.0542 | 0.0591876 | ||||||||
\(796\) | 383.623i | 0.481938i | ||||||||
\(797\) | − | 1260.72i | − | 1.58183i | −0.611924 | − | 0.790917i | \(-0.709604\pi\) | ||
0.611924 | − | 0.790917i | \(-0.290396\pi\) | |||||||
\(798\) | −413.963 | − | 64.9665i | −0.518751 | − | 0.0814117i | ||||
\(799\) | −44.0413 | −0.0551205 | ||||||||
\(800\) | −113.298 | −0.141622 | ||||||||
\(801\) | 365.900i | 0.456804i | ||||||||
\(802\) | 1399.78 | 1.74537 | ||||||||
\(803\) | 800.439i | 0.996810i | ||||||||
\(804\) | 395.306i | 0.491675i | ||||||||
\(805\) | 7.60405 | − | 48.4526i | 0.00944603 | − | 0.0601896i | ||||
\(806\) | 959.035 | 1.18987 | ||||||||
\(807\) | −404.526 | −0.501271 | ||||||||
\(808\) | 1673.45i | 2.07110i | ||||||||
\(809\) | −105.646 | −0.130589 | −0.0652943 | − | 0.997866i | \(-0.520799\pi\) | ||||
−0.0652943 | + | 0.997866i | \(0.520799\pi\) | |||||||
\(810\) | − | 45.8768i | − | 0.0566381i | ||||||
\(811\) | 1181.24i | 1.45652i | 0.685299 | + | 0.728262i | \(0.259672\pi\) | ||||
−0.685299 | + | 0.728262i | \(0.740328\pi\) | |||||||
\(812\) | −12.2342 | − | 1.92001i | −0.0150668 | − | 0.00236455i | ||||
\(813\) | 832.088 | 1.02348 | ||||||||
\(814\) | −350.593 | −0.430704 | ||||||||
\(815\) | − | 32.7775i | − | 0.0402178i | ||||||
\(816\) | −460.658 | −0.564532 | ||||||||
\(817\) | 165.311i | 0.202339i | ||||||||
\(818\) | 482.898i | 0.590340i | ||||||||
\(819\) | −32.6194 | + | 207.849i | −0.0398283 | + | 0.253784i | ||||
\(820\) | −348.808 | −0.425375 | ||||||||
\(821\) | 479.585 | 0.584147 | 0.292073 | − | 0.956396i | \(-0.405655\pi\) | ||||
0.292073 | + | 0.956396i | \(0.405655\pi\) | |||||||
\(822\) | − | 229.770i | − | 0.279526i | ||||||
\(823\) | −525.864 | −0.638960 | −0.319480 | − | 0.947593i | \(-0.603508\pi\) | ||||
−0.319480 | + | 0.947593i | \(0.603508\pi\) | |||||||
\(824\) | 757.325i | 0.919083i | ||||||||
\(825\) | 320.154i | 0.388066i | ||||||||
\(826\) | −402.240 | + | 2563.05i | −0.486973 | + | 3.10297i | ||||
\(827\) | −451.526 | −0.545980 | −0.272990 | − | 0.962017i | \(-0.588013\pi\) | ||||
−0.272990 | + | 0.962017i | \(0.588013\pi\) | |||||||
\(828\) | 117.600 | 0.142029 | ||||||||
\(829\) | 1247.66i | 1.50502i | 0.658580 | + | 0.752511i | \(0.271157\pi\) | ||||
−0.658580 | + | 0.752511i | \(0.728843\pi\) | |||||||
\(830\) | −257.237 | −0.309924 | ||||||||
\(831\) | 9.24356i | 0.0111234i | ||||||||
\(832\) | 552.754i | 0.664368i | ||||||||
\(833\) | 220.376 | − | 684.820i | 0.264557 | − | 0.822113i | ||||
\(834\) | 527.948 | 0.633031 | ||||||||
\(835\) | −152.224 | −0.182305 | ||||||||
\(836\) | − | 654.503i | − | 0.782899i | ||||||
\(837\) | 142.558 | 0.170320 | ||||||||
\(838\) | − | 1478.13i | − | 1.76388i | ||||||
\(839\) | − | 118.810i | − | 0.141609i | −0.997490 | − | 0.0708047i | \(-0.977443\pi\) | ||
0.997490 | − | 0.0708047i | \(-0.0225567\pi\) | |||||||
\(840\) | −254.831 | − | 39.9926i | −0.303370 | − | 0.0476102i | ||||
\(841\) | −840.953 | −0.999944 | ||||||||
\(842\) | 2510.03 | 2.98103 | ||||||||
\(843\) | 428.720i | 0.508565i | ||||||||
\(844\) | −1287.53 | −1.52551 | ||||||||
\(845\) | 100.259i | 0.118650i | ||||||||
\(846\) | − | 31.3990i | − | 0.0371146i | ||||||
\(847\) | −384.853 | − | 60.3981i | −0.454372 | − | 0.0713082i | ||||
\(848\) | 336.852 | 0.397231 | ||||||||
\(849\) | 742.044 | 0.874021 | ||||||||
\(850\) | 1171.31i | 1.37801i | ||||||||
\(851\) | 59.6128 | 0.0700503 | ||||||||
\(852\) | 198.734i | 0.233255i | ||||||||
\(853\) | 445.451i | 0.522217i | 0.965309 | + | 0.261109i | \(0.0840881\pi\) | ||||
−0.965309 | + | 0.261109i | \(0.915912\pi\) | |||||||
\(854\) | −379.343 | + | 2417.16i | −0.444196 | + | 2.83039i | ||||
\(855\) | 43.4145 | 0.0507772 | ||||||||
\(856\) | −1599.34 | −1.86838 | ||||||||
\(857\) | 778.359i | 0.908236i | 0.890941 | + | 0.454118i | \(0.150046\pi\) | ||||
−0.890941 | + | 0.454118i | \(0.849954\pi\) | |||||||
\(858\) | −489.442 | −0.570445 | ||||||||
\(859\) | − | 1143.51i | − | 1.33121i | −0.746305 | − | 0.665604i | \(-0.768174\pi\) | ||
0.746305 | − | 0.665604i | \(-0.231826\pi\) | |||||||
\(860\) | 199.291i | 0.231733i | ||||||||
\(861\) | 349.866 | + | 54.9072i | 0.406348 | + | 0.0637714i | ||||
\(862\) | 793.339 | 0.920347 | ||||||||
\(863\) | 1298.91 | 1.50511 | 0.752554 | − | 0.658531i | \(-0.228822\pi\) | ||||
0.752554 | + | 0.658531i | \(0.228822\pi\) | |||||||
\(864\) | − | 25.7466i | − | 0.0297993i | ||||||
\(865\) | −89.5085 | −0.103478 | ||||||||
\(866\) | 612.187i | 0.706913i | ||||||||
\(867\) | − | 127.213i | − | 0.146728i | ||||||
\(868\) | 243.373 | − | 1550.76i | 0.280384 | − | 1.78659i | ||||
\(869\) | 10.1633 | 0.0116954 | ||||||||
\(870\) | 1.91096 | 0.00219651 | ||||||||
\(871\) | 279.746i | 0.321178i | ||||||||
\(872\) | 1290.47 | 1.47989 | ||||||||
\(873\) | − | 335.164i | − | 0.383922i | ||||||
\(874\) | 165.749i | 0.189644i | ||||||||
\(875\) | −75.8935 | + | 483.590i | −0.0867354 | + | 0.552674i | ||||
\(876\) | −1401.82 | −1.60026 | ||||||||
\(877\) | −1381.00 | −1.57469 | −0.787346 | − | 0.616512i | \(-0.788545\pi\) | ||||
−0.787346 | + | 0.616512i | \(0.788545\pi\) | |||||||
\(878\) | − | 1216.85i | − | 1.38593i | ||||||
\(879\) | 751.425 | 0.854863 | ||||||||
\(880\) | − | 213.942i | − | 0.243116i | ||||||
\(881\) | − | 1468.58i | − | 1.66695i | −0.552558 | − | 0.833475i | \(-0.686348\pi\) | ||
0.552558 | − | 0.833475i | \(-0.313652\pi\) | |||||||
\(882\) | 488.239 | + | 157.116i | 0.553559 | + | 0.178136i | ||||
\(883\) | 453.515 | 0.513607 | 0.256804 | − | 0.966464i | \(-0.417331\pi\) | ||||
0.256804 | + | 0.966464i | \(0.417331\pi\) | |||||||
\(884\) | −1202.29 | −1.36006 | ||||||||
\(885\) | − | 268.801i | − | 0.303730i | ||||||
\(886\) | −1222.93 | −1.38029 | ||||||||
\(887\) | 748.985i | 0.844403i | 0.906502 | + | 0.422201i | \(0.138742\pi\) | ||||
−0.906502 | + | 0.422201i | \(0.861258\pi\) | |||||||
\(888\) | − | 313.526i | − | 0.353070i | ||||||
\(889\) | 648.706 | + | 101.807i | 0.729704 | + | 0.114518i | ||||
\(890\) | −621.717 | −0.698558 | ||||||||
\(891\) | −72.7543 | −0.0816547 | ||||||||
\(892\) | − | 85.3475i | − | 0.0956811i | ||||||
\(893\) | 29.7137 | 0.0332740 | ||||||||
\(894\) | − | 863.945i | − | 0.966381i | ||||||
\(895\) | 470.413i | 0.525601i | ||||||||
\(896\) | 1468.27 | + | 230.427i | 1.63869 | + | 0.257173i | ||||
\(897\) | 83.2217 | 0.0927778 | ||||||||
\(898\) | −1982.63 | −2.20782 | ||||||||
\(899\) | 5.93815i | 0.00660528i | ||||||||
\(900\) | −560.692 | −0.622991 | ||||||||
\(901\) | − | 273.009i | − | 0.303006i | ||||||
\(902\) | 823.862i | 0.913373i | ||||||||
\(903\) | 31.3711 | − | 199.895i | 0.0347410 | − | 0.221368i | ||||
\(904\) | 1315.90 | 1.45564 | ||||||||
\(905\) | 399.946 | 0.441930 | ||||||||
\(906\) | − | 1042.87i | − | 1.15107i | ||||||
\(907\) | 1704.51 | 1.87928 | 0.939641 | − | 0.342163i | \(-0.111159\pi\) | ||||
0.939641 | + | 0.342163i | \(0.111159\pi\) | |||||||
\(908\) | − | 3214.72i | − | 3.54044i | ||||||
\(909\) | 344.743i | 0.379256i | ||||||||
\(910\) | −353.165 | − | 55.4250i | −0.388094 | − | 0.0609065i | ||||
\(911\) | −668.129 | −0.733402 | −0.366701 | − | 0.930339i | \(-0.619513\pi\) | ||||
−0.366701 | + | 0.930339i | \(0.619513\pi\) | |||||||
\(912\) | 310.796 | 0.340785 | ||||||||
\(913\) | 407.942i | 0.446815i | ||||||||
\(914\) | −818.871 | −0.895920 | ||||||||
\(915\) | − | 253.500i | − | 0.277049i | ||||||
\(916\) | − | 3386.88i | − | 3.69747i | ||||||
\(917\) | −18.0827 | + | 115.222i | −0.0197194 | + | 0.125651i | ||||
\(918\) | −266.178 | −0.289954 | ||||||||
\(919\) | −867.877 | −0.944371 | −0.472185 | − | 0.881499i | \(-0.656535\pi\) | ||||
−0.472185 | + | 0.881499i | \(0.656535\pi\) | |||||||
\(920\) | 102.033i | 0.110905i | ||||||||
\(921\) | 445.963 | 0.484216 | ||||||||
\(922\) | 1606.99i | 1.74294i | ||||||||
\(923\) | 140.638i | 0.152370i | ||||||||
\(924\) | −124.205 | + | 791.430i | −0.134421 | + | 0.856526i | ||||
\(925\) | −284.222 | −0.307267 | ||||||||
\(926\) | 101.630 | 0.109751 | ||||||||
\(927\) | 156.015i | 0.168301i | ||||||||
\(928\) | 1.07246 | 0.00115566 | ||||||||
\(929\) | − | 1209.41i | − | 1.30184i | −0.759147 | − | 0.650919i | \(-0.774384\pi\) | ||
0.759147 | − | 0.650919i | \(-0.225616\pi\) | |||||||
\(930\) | 242.227i | 0.260459i | ||||||||
\(931\) | −148.683 | + | 462.034i | −0.159703 | + | 0.496277i | ||||
\(932\) | 2589.13 | 2.77804 | ||||||||
\(933\) | 447.164 | 0.479276 | ||||||||
\(934\) | − | 134.910i | − | 0.144444i | ||||||
\(935\) | −173.393 | −0.185448 | ||||||||
\(936\) | − | 437.695i | − | 0.467622i | ||||||
\(937\) | 106.970i | 0.114162i | 0.998370 | + | 0.0570811i | \(0.0181794\pi\) | ||||
−0.998370 | + | 0.0570811i | \(0.981821\pi\) | |||||||
\(938\) | 673.719 | + | 105.732i | 0.718251 | + | 0.112721i | ||||
\(939\) | 473.414 | 0.504169 | ||||||||
\(940\) | 35.8214 | 0.0381078 | ||||||||
\(941\) | 930.978i | 0.989350i | 0.869078 | + | 0.494675i | \(0.164713\pi\) | ||||
−0.869078 | + | 0.494675i | \(0.835287\pi\) | |||||||
\(942\) | −494.261 | −0.524694 | ||||||||
\(943\) | − | 140.085i | − | 0.148552i | ||||||
\(944\) | − | 1924.29i | − | 2.03845i | ||||||
\(945\) | −52.4971 | − | 8.23878i | −0.0555525 | − | 0.00871829i | ||||
\(946\) | 470.712 | 0.497581 | ||||||||
\(947\) | −594.943 | −0.628239 | −0.314120 | − | 0.949383i | \(-0.601709\pi\) | ||||
−0.314120 | + | 0.949383i | \(0.601709\pi\) | |||||||
\(948\) | 17.7992i | 0.0187755i | ||||||||
\(949\) | −992.028 | −1.04534 | ||||||||
\(950\) | − | 790.258i | − | 0.831851i | ||||||
\(951\) | − | 247.860i | − | 0.260631i | ||||||
\(952\) | −232.037 | + | 1478.53i | −0.243737 | + | 1.55308i | ||||
\(953\) | −563.659 | −0.591457 | −0.295729 | − | 0.955272i | \(-0.595562\pi\) | ||||
−0.295729 | + | 0.955272i | \(0.595562\pi\) | |||||||
\(954\) | 194.640 | 0.204025 | ||||||||
\(955\) | 205.621i | 0.215309i | ||||||||
\(956\) | 2838.80 | 2.96945 | ||||||||
\(957\) | − | 3.03052i | − | 0.00316669i | ||||||
\(958\) | − | 2021.62i | − | 2.11025i | ||||||
\(959\) | −262.927 | − | 41.2632i | −0.274168 | − | 0.0430273i | ||||
\(960\) | −139.611 | −0.145428 | ||||||||
\(961\) | 208.303 | 0.216757 | ||||||||
\(962\) | − | 434.510i | − | 0.451673i | ||||||
\(963\) | −329.476 | −0.342135 | ||||||||
\(964\) | − | 501.572i | − | 0.520303i | ||||||
\(965\) | − | 368.785i | − | 0.382160i | ||||||
\(966\) | 31.4542 | − | 200.425i | 0.0325613 | − | 0.207479i | ||||
\(967\) | −533.769 | −0.551984 | −0.275992 | − | 0.961160i | \(-0.589006\pi\) | ||||
−0.275992 | + | 0.961160i | \(0.589006\pi\) | |||||||
\(968\) | 810.435 | 0.837227 | ||||||||
\(969\) | − | 251.891i | − | 0.259950i | ||||||
\(970\) | 569.490 | 0.587104 | ||||||||
\(971\) | 237.067i | 0.244147i | 0.992521 | + | 0.122073i | \(0.0389543\pi\) | ||||
−0.992521 | + | 0.122073i | \(0.961046\pi\) | |||||||
\(972\) | − | 127.416i | − | 0.131086i | ||||||
\(973\) | 94.8114 | − | 604.134i | 0.0974424 | − | 0.620898i | ||||
\(974\) | −2630.43 | −2.70064 | ||||||||
\(975\) | −396.785 | −0.406959 | ||||||||
\(976\) | − | 1814.76i | − | 1.85938i | ||||||
\(977\) | −317.705 | −0.325185 | −0.162592 | − | 0.986693i | \(-0.551986\pi\) | ||||
−0.162592 | + | 0.986693i | \(0.551986\pi\) | |||||||
\(978\) | − | 135.584i | − | 0.138634i | ||||||
\(979\) | 985.957i | 1.00711i | ||||||||
\(980\) | −179.245 | + | 557.005i | −0.182903 | + | 0.568372i | ||||
\(981\) | 265.846 | 0.270995 | ||||||||
\(982\) | 969.952 | 0.987731 | ||||||||
\(983\) | − | 187.630i | − | 0.190874i | −0.995435 | − | 0.0954372i | \(-0.969575\pi\) | ||
0.995435 | − | 0.0954372i | \(-0.0304249\pi\) | |||||||
\(984\) | −736.758 | −0.748738 | ||||||||
\(985\) | 450.190i | 0.457046i | ||||||||
\(986\) | − | 11.0874i | − | 0.0112449i | ||||||
\(987\) | −35.9300 | − | 5.63878i | −0.0364033 | − | 0.00571305i | ||||
\(988\) | 811.162 | 0.821015 | ||||||||
\(989\) | −80.0370 | −0.0809272 | ||||||||
\(990\) | − | 123.620i | − | 0.124869i | ||||||
\(991\) | 1895.27 | 1.91248 | 0.956241 | − | 0.292579i | \(-0.0945135\pi\) | ||||
0.956241 | + | 0.292579i | \(0.0945135\pi\) | |||||||
\(992\) | 135.940i | 0.137037i | ||||||||
\(993\) | 605.468i | 0.609736i | ||||||||
\(994\) | 338.701 | + | 53.1550i | 0.340745 | + | 0.0534758i | ||||
\(995\) | −68.5681 | −0.0689127 | ||||||||
\(996\) | −714.436 | −0.717306 | ||||||||
\(997\) | − | 828.968i | − | 0.831462i | −0.909488 | − | 0.415731i | \(-0.863526\pi\) | ||
0.909488 | − | 0.415731i | \(-0.136474\pi\) | |||||||
\(998\) | −2654.63 | −2.65995 | ||||||||
\(999\) | − | 64.5888i | − | 0.0646535i |
(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 | 483.3.g.a.139.4 | yes | 60 | |
7.6 | odd | 2 | inner | 483.3.g.a.139.3 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.g.a.139.3 | ✓ | 60 | 7.6 | odd | 2 | inner | |
483.3.g.a.139.4 | yes | 60 | 1.1 | even | 1 | trivial |