Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(3849,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.3849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.e (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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3849.3 | ||
Character | \(\chi\) | \(=\) | 4004.3849 |
Dual form | 4004.2.e.a.3849.46 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.04894i | − | 1.76031i | −0.474689 | − | 0.880153i | \(-0.657440\pi\) | ||
0.474689 | − | 0.880153i | \(-0.342560\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.30537i | 1.92542i | 0.270539 | + | 0.962709i | \(0.412798\pi\) | ||||
−0.270539 | + | 0.962709i | \(0.587202\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63608 | − | 0.225969i | −0.996346 | − | 0.0854082i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.29604 | −2.09868 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23073 | + | 2.45435i | 0.672590 | + | 0.740016i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.1268 | 3.38933 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.22792 | 1.51049 | 0.755247 | − | 0.655441i | \(-0.227517\pi\) | ||||
0.755247 | + | 0.655441i | \(0.227517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.815945 | 0.187191 | 0.0935953 | − | 0.995610i | \(-0.470164\pi\) | ||||
0.0935953 | + | 0.995610i | \(0.470164\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.688966 | + | 8.03726i | −0.150345 | + | 1.75387i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.626243 | −0.130581 | −0.0652903 | − | 0.997866i | \(-0.520797\pi\) | ||||
−0.0652903 | + | 0.997866i | \(0.520797\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.5362 | −2.70723 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.0494i | 1.93401i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.50046i | 1.02141i | 0.859756 | + | 0.510705i | \(0.170616\pi\) | ||||
−0.859756 | + | 0.510705i | \(0.829384\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.54277i | − | 0.277090i | −0.990356 | − | 0.138545i | \(-0.955757\pi\) | ||
0.990356 | − | 0.138545i | \(-0.0442426\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.48318 | − | 6.80136i | 1.30265 | − | 1.18396i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.972879 | − | 11.3493i | 0.164446 | − | 1.91838i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.94206 | −0.976869 | −0.488435 | − | 0.872600i | \(-0.662432\pi\) | ||||
−0.488435 | + | 0.872600i | \(0.662432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.04894i | − | 0.488221i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8437 | −1.69350 | −0.846750 | − | 0.531991i | \(-0.821444\pi\) | ||||
−0.846750 | + | 0.531991i | \(0.821444\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96511i | 0.452175i | 0.974107 | + | 0.226087i | \(0.0725935\pi\) | ||||
−0.974107 | + | 0.226087i | \(0.927407\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 27.1068i | − | 4.04084i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.6330i | − | 1.55098i | −0.631359 | − | 0.775491i | \(-0.717502\pi\) | ||
0.631359 | − | 0.775491i | \(-0.282498\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.89788 | + | 1.19135i | 0.985411 | + | 0.170192i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 18.9886i | − | 2.65893i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.1677 | −1.53400 | −0.767000 | − | 0.641647i | \(-0.778251\pi\) | ||||
−0.767000 | + | 0.641647i | \(0.778251\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.5669 | + | 9.60410i | −1.42484 | + | 1.29502i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.48777i | − | 0.329513i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7.99070i | − | 1.04030i | −0.854075 | − | 0.520150i | \(-0.825876\pi\) | ||
0.854075 | − | 0.520150i | \(-0.174124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.4676 | −1.72435 | −0.862176 | − | 0.506609i | \(-0.830899\pi\) | ||||
−0.862176 | + | 0.506609i | \(0.830899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.5969 | + | 1.42271i | 2.09101 | + | 0.179245i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.30537i | 0.534015i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.69312 | 0.329016 | 0.164508 | − | 0.986376i | \(-0.447396\pi\) | ||||
0.164508 | + | 0.986376i | \(0.447396\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.90938i | 0.229862i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.46314 | 0.767033 | 0.383517 | − | 0.923534i | \(-0.374713\pi\) | ||||
0.383517 | + | 0.923534i | \(0.374713\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5984 | 1.24045 | 0.620226 | − | 0.784423i | \(-0.287041\pi\) | ||||
0.620226 | + | 0.784423i | \(0.287041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 41.2710i | 4.76556i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.32578 | − | 6.97396i | −0.606929 | − | 0.794756i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.52349i | 1.07148i | 0.844384 | + | 0.535738i | \(0.179967\pi\) | ||||
−0.844384 | + | 0.535738i | \(0.820033\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.7520 | 1.30578 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.25806 | −0.906440 | −0.453220 | − | 0.891399i | \(-0.649725\pi\) | ||||
−0.453220 | + | 0.891399i | \(0.649725\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.8135i | 2.90833i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.7706 | 1.79799 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.67918i | − | 0.177992i | −0.996032 | − | 0.0889962i | \(-0.971634\pi\) | ||
0.996032 | − | 0.0889962i | \(-0.0283659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.63608 | − | 0.225969i | −0.276337 | − | 0.0236880i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.70382 | −0.487763 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.51294i | 0.360420i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.51534i | − | 0.356928i | −0.983946 | − | 0.178464i | \(-0.942887\pi\) | ||
0.983946 | − | 0.178464i | \(-0.0571129\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.0448 | − | 15.4527i | −1.41155 | − | 1.55306i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.569171 | −0.0566347 | −0.0283173 | − | 0.999599i | \(-0.509015\pi\) | ||||
−0.0283173 | + | 0.999599i | \(0.509015\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.0110i | − | 1.28201i | −0.767537 | − | 0.641004i | \(-0.778518\pi\) | ||
0.767537 | − | 0.641004i | \(-0.221482\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −34.6034 | − | 2.96625i | −3.37694 | − | 0.289476i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.75874i | 0.556718i | 0.960477 | + | 0.278359i | \(0.0897906\pi\) | ||||
−0.960477 | + | 0.278359i | \(0.910209\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.84093i | 0.942590i | 0.881976 | + | 0.471295i | \(0.156213\pi\) | ||||
−0.881976 | + | 0.471295i | \(0.843787\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.1170i | 1.71959i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.54776 | −0.898178 | −0.449089 | − | 0.893487i | \(-0.648251\pi\) | ||||
−0.449089 | + | 0.893487i | \(0.648251\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.69620i | − | 0.251422i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.29604 | −0.582069 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.4173 | − | 1.40732i | −1.50497 | − | 0.129009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.04771 | + | 10.9500i | −0.0952466 | + | 0.995454i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 33.0618i | 2.98108i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 36.7514i | − | 3.28714i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.9738i | 1.23997i | 0.784613 | + | 0.619986i | \(0.212862\pi\) | ||||
−0.784613 | + | 0.619986i | \(0.787138\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.04044 | 0.795966 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.7914 | −1.81656 | −0.908278 | − | 0.418367i | \(-0.862603\pi\) | ||||
−0.908278 | + | 0.418367i | \(0.862603\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.15090 | − | 0.184378i | −0.186507 | − | 0.0159876i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −43.2665 | −3.72379 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.44527 | 0.806964 | 0.403482 | − | 0.914988i | \(-0.367800\pi\) | ||||
0.403482 | + | 0.914988i | \(0.367800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.48515 | 0.550063 | 0.275032 | − | 0.961435i | \(-0.411312\pi\) | ||||
0.275032 | + | 0.961435i | \(0.411312\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −32.4194 | −2.73020 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.23073 | + | 2.45435i | 0.186543 | + | 0.205243i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.6815 | −1.96664 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.63234 | − | 21.0312i | 0.299591 | − | 1.73463i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.7382i | 1.45317i | 0.687076 | + | 0.726585i | \(0.258894\pi\) | ||||
−0.687076 | + | 0.726585i | \(0.741106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.30475i | − | 0.187558i | −0.995593 | − | 0.0937791i | \(-0.970105\pi\) | ||
0.995593 | − | 0.0937791i | \(-0.0298948\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −39.2113 | −3.17004 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.64220 | 0.533514 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.2659i | 1.05874i | 0.848393 | + | 0.529368i | \(0.177571\pi\) | ||||
−0.848393 | + | 0.529368i | \(0.822429\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34.0496i | 2.70031i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.65083 | + | 0.141511i | 0.130103 | + | 0.0111527i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.8063 | −0.846418 | −0.423209 | − | 0.906032i | \(-0.639096\pi\) | ||||
−0.423209 | + | 0.906032i | \(0.639096\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 29.2823 | + | 32.2178i | 2.27963 | + | 2.50816i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.852279 | −0.0659513 | −0.0329757 | − | 0.999456i | \(-0.510498\pi\) | ||||
−0.0329757 | + | 0.999456i | \(0.510498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.13722 | −0.392853 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.41091 | 0.259327 | 0.129663 | − | 0.991558i | \(-0.458610\pi\) | ||||
0.129663 | + | 0.991558i | \(0.458610\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 35.6825 | + | 3.05875i | 2.69734 | + | 0.231220i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.3632 | −1.83125 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.78588 | −0.357714 | −0.178857 | − | 0.983875i | \(-0.557240\pi\) | ||||
−0.178857 | + | 0.983875i | \(0.557240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8783i | 1.18023i | 0.807321 | + | 0.590113i | \(0.200917\pi\) | ||||
−0.807321 | + | 0.590113i | \(0.799083\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 41.0620i | 3.03539i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 25.5828i | − | 1.88088i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8928 | + | 15.2855i | 1.01594 | + | 1.11779i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.27086 | − | 26.4912i | 0.165181 | − | 1.92695i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6315 | −0.986341 | −0.493171 | − | 0.869933i | \(-0.664162\pi\) | ||||
−0.493171 | + | 0.869933i | \(0.664162\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 20.0156i | − | 1.44075i | −0.693582 | − | 0.720377i | \(-0.743969\pi\) | ||
0.693582 | − | 0.720377i | \(-0.256031\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.1268 | 0.940030 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22.7364i | − | 1.61990i | −0.586496 | − | 0.809952i | \(-0.699493\pi\) | ||
0.586496 | − | 0.809952i | \(-0.300507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.93627i | 0.562587i | 0.959622 | + | 0.281294i | \(0.0907635\pi\) | ||||
−0.959622 | + | 0.281294i | \(0.909237\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.21115i | − | 0.579170i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.24293 | − | 14.4997i | 0.0872368 | − | 1.01768i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 46.6861i | − | 3.26070i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.94285 | 0.274047 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.82015 | + | 2.00262i | 0.125902 | + | 0.138524i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.89039i | − | 0.267825i | −0.990993 | − | 0.133913i | \(-0.957246\pi\) | ||
0.990993 | − | 0.133913i | \(-0.0427542\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 19.7057i | − | 1.35021i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.7659 | −0.870626 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.348618 | + | 4.06688i | −0.0236658 | + | 0.276078i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 32.3140i | − | 2.18358i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.22792 | 0.418935 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5418i | 1.37558i | 0.725908 | + | 0.687791i | \(0.241420\pi\) | ||||
−0.725908 | + | 0.687791i | \(0.758580\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 85.2243 | 5.68162 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2496 | −0.746660 | −0.373330 | − | 0.927699i | \(-0.621784\pi\) | ||||
−0.373330 | + | 0.927699i | \(0.621784\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.37375i | − | 0.222944i | −0.993768 | − | 0.111472i | \(-0.964443\pi\) | ||
0.993768 | − | 0.111472i | \(-0.0355565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.2632 | + | 16.2380i | −1.39902 | + | 1.06838i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.51559i | 0.164802i | 0.996599 | + | 0.0824009i | \(0.0262588\pi\) | ||||
−0.996599 | + | 0.0824009i | \(0.973741\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 45.7789 | 2.98629 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 29.0366 | 1.88613 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8618i | 0.961332i | 0.876904 | + | 0.480666i | \(0.159605\pi\) | ||||
−0.876904 | + | 0.480666i | \(0.840395\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0364 | −0.839746 | −0.419873 | − | 0.907583i | \(-0.637925\pi\) | ||||
−0.419873 | + | 0.907583i | \(0.637925\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 5.68289i | − | 0.364558i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.12918 | + | 29.6979i | −0.327691 | + | 1.89733i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.815945 | 0.0519173 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.1783i | 1.59561i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 23.8441i | − | 1.50502i | −0.658578 | − | 0.752512i | \(-0.728842\pi\) | ||
0.658578 | − | 0.752512i | \(-0.271158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.39698 | − | 1.53702i | −0.0878271 | − | 0.0966317i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 81.7527 | 5.11956 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.1277i | 0.943642i | 0.881694 | + | 0.471821i | \(0.156403\pi\) | ||||
−0.881694 | + | 0.471821i | \(0.843597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.6638 | + | 1.34272i | 0.973300 | + | 0.0834326i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 34.6311i | − | 2.14361i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.2748i | 1.37352i | 0.726883 | + | 0.686761i | \(0.240968\pi\) | ||||
−0.726883 | + | 0.686761i | \(0.759032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 48.0810i | − | 2.95359i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.11971 | −0.313321 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.95027i | − | 0.179881i | −0.995947 | − | 0.0899405i | \(-0.971332\pi\) | ||
0.995947 | − | 0.0899405i | \(-0.0286677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.67235 | −0.344571 | −0.172285 | − | 0.985047i | \(-0.555115\pi\) | ||||
−0.172285 | + | 0.985047i | \(0.555115\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.688966 | + | 8.03726i | −0.0416981 | + | 0.486437i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −30.1955 | − | 33.2226i | −1.82086 | − | 2.00340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.7667i | − | 1.12758i | −0.825918 | − | 0.563791i | \(-0.809342\pi\) | ||
0.825918 | − | 0.563791i | \(-0.190658\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.71336i | 0.581523i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.31081i | − | 0.0781963i | −0.999235 | − | 0.0390982i | \(-0.987551\pi\) | ||
0.999235 | − | 0.0390982i | \(-0.0124485\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.13496 | −0.483573 | −0.241787 | − | 0.970329i | \(-0.577733\pi\) | ||||
−0.241787 | + | 0.970329i | \(0.577733\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.7108 | 0.634450 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.5849 | + | 2.45034i | 1.68731 | + | 0.144639i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.7870 | 1.28159 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.7181 | −0.628303 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6265 | 1.26344 | 0.631718 | − | 0.775199i | \(-0.282350\pi\) | ||||
0.631718 | + | 0.775199i | \(0.282350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.4029 | 2.00301 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.6649 | + | 22.4176i | −1.43120 | + | 1.30080i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.626243 | −0.0362165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.670022 | − | 7.81627i | 0.0386194 | − | 0.450523i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.73537i | 0.0996944i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 57.9830i | − | 3.32010i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.544542 | −0.0310786 | −0.0155393 | − | 0.999879i | \(-0.504947\pi\) | ||||
−0.0155393 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −39.6697 | −2.25673 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.90459i | − | 0.448228i | −0.974563 | − | 0.224114i | \(-0.928051\pi\) | ||
0.974563 | − | 0.224114i | \(-0.0719488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.7353i | 1.11551i | 0.830007 | + | 0.557754i | \(0.188337\pi\) | ||||
−0.830007 | + | 0.557754i | \(0.811663\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.12528 | + | 71.4557i | −0.345121 | + | 4.02607i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.5219 | −1.71428 | −0.857140 | − | 0.515084i | \(-0.827761\pi\) | ||||
−0.857140 | + | 0.515084i | \(0.827761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.5001 | + | 12.2700i | −0.755859 | + | 0.686990i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.5581 | 0.979995 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.08164 | 0.282750 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5362 | −0.750852 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 30.0044 | 1.65925 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.40273 | + | 28.0295i | −0.132467 | + | 1.54531i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.4338 | −1.28804 | −0.644018 | − | 0.765010i | \(-0.722734\pi\) | ||||
−0.644018 | + | 0.765010i | \(0.722734\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 37.4115 | 2.05014 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.5948i | 0.633494i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 30.6525i | − | 1.66975i | −0.550440 | − | 0.834874i | \(-0.685540\pi\) | ||
0.550440 | − | 0.834874i | \(-0.314460\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.1106i | 1.58107i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.78651 | − | 3.44150i | 0.205051 | − | 0.186368i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.9142 | − | 4.69919i | −0.967274 | − | 0.253733i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.22056 | −0.442580 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.65156i | 0.464440i | 0.972663 | + | 0.232220i | \(0.0745989\pi\) | ||||
−0.972663 | + | 0.232220i | \(0.925401\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.0707 | −1.77024 | −0.885118 | − | 0.465367i | \(-0.845922\pi\) | ||||
−0.885118 | + | 0.465367i | \(0.845922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.0494i | 0.536399i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 18.7725i | − | 0.999160i | −0.866268 | − | 0.499580i | \(-0.833488\pi\) | ||
0.866268 | − | 0.499580i | \(-0.166512\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.8262i | 1.47686i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.29083 | + | 50.0555i | −0.227095 | + | 2.64922i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.612151i | 0.0323081i | 0.999870 | + | 0.0161540i | \(0.00514221\pi\) | ||||
−0.999870 | + | 0.0161540i | \(0.994858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3342 | −0.964960 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 33.3859 | + | 3.19441i | 1.75230 | + | 0.167663i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 45.6301i | 2.38839i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.7775i | 0.980180i | 0.871672 | + | 0.490090i | \(0.163036\pi\) | ||||
−0.871672 | + | 0.490090i | \(0.836964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 68.2723 | 3.55412 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.4390 | + | 2.52355i | 1.52839 | + | 0.131016i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.97321i | 0.464615i | 0.972642 | + | 0.232308i | \(0.0746276\pi\) | ||||
−0.972642 | + | 0.232308i | \(0.925372\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −112.053 | −5.78638 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.50046i | 0.283288i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.6889 | −0.754520 | −0.377260 | − | 0.926107i | \(-0.623134\pi\) | ||||
−0.377260 | + | 0.926107i | \(0.623134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.6052 | 2.18273 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.4863i | 0.535823i | 0.963443 | + | 0.267912i | \(0.0863336\pi\) | ||||
−0.963443 | + | 0.267912i | \(0.913666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.0254 | − | 22.9294i | 1.53024 | − | 1.16859i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 18.6684i | − | 0.948970i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.0993 | −1.72890 | −0.864452 | − | 0.502715i | \(-0.832335\pi\) | ||||
−0.864452 | + | 0.502715i | \(0.832335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.90019 | −0.197241 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 63.3919i | 3.19770i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −41.0021 | −2.06304 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.0340i | − | 0.955290i | −0.878553 | − | 0.477645i | \(-0.841491\pi\) | ||
0.878553 | − | 0.477645i | \(-0.158509\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.562158 | + | 6.55796i | −0.0281431 | + | 0.328309i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.40109 | 0.419531 | 0.209765 | − | 0.977752i | \(-0.432730\pi\) | ||||
0.209765 | + | 0.977752i | \(0.432730\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.54277i | − | 0.0768509i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 50.5967i | 2.51417i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.2551 | − | 14.5839i | −0.657032 | − | 0.722899i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8928 | 0.785850 | 0.392925 | − | 0.919571i | \(-0.371463\pi\) | ||||
0.392925 | + | 0.919571i | \(0.371463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 28.7981i | − | 1.42050i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.80565 | + | 21.0641i | −0.0888501 | + | 1.03650i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 35.5540i | − | 1.74528i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 19.7728i | − | 0.968280i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 8.64392i | − | 0.422283i | −0.977455 | − | 0.211142i | \(-0.932282\pi\) | ||
0.977455 | − | 0.211142i | \(-0.0677181\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.76359 | −0.475848 | −0.237924 | − | 0.971284i | \(-0.576467\pi\) | ||||
−0.237924 | + | 0.971284i | \(0.576467\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 66.9458i | 3.25502i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −84.3023 | −4.08926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.5018 | + | 3.04326i | 1.71805 | + | 0.147274i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.48318 | − | 6.80136i | 0.361291 | − | 0.328373i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.6870i | 0.755617i | 0.925884 | + | 0.377808i | \(0.123322\pi\) | ||||
−0.925884 | + | 0.377808i | \(0.876678\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.43221i | − | 0.309112i | −0.987984 | − | 0.154556i | \(-0.950605\pi\) | ||
0.987984 | − | 0.154556i | \(-0.0493947\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 72.2035i | 3.46189i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.510979 | −0.0244435 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.9418 | 1.66768 | 0.833841 | − | 0.552004i | \(-0.186137\pi\) | ||||
0.833841 | + | 0.552004i | \(0.186137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.4293 | − | 7.50076i | −2.06806 | − | 0.357179i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.4733 | −1.49534 | −0.747670 | − | 0.664070i | \(-0.768828\pi\) | ||||
−0.747670 | + | 0.664070i | \(0.768828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.22947 | 0.342710 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 54.0827 | 2.55803 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.19601 | 0.0564433 | 0.0282216 | − | 0.999602i | \(-0.491016\pi\) | ||||
0.0282216 | + | 0.999602i | \(0.491016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.1893 | − | 26.6143i | −1.13903 | − | 1.25322i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.02706 | −0.330160 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.972879 | − | 11.3493i | 0.0456093 | − | 0.532064i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14.6420i | − | 0.684924i | −0.939532 | − | 0.342462i | \(-0.888739\pi\) | ||
0.939532 | − | 0.342462i | \(-0.111261\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 62.5871i | 2.92132i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.33845 | 0.295211 | 0.147606 | − | 0.989046i | \(-0.452843\pi\) | ||||
0.147606 | + | 0.989046i | \(0.452843\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.12809 | 0.191849 | 0.0959243 | − | 0.995389i | \(-0.469419\pi\) | ||||
0.0959243 | + | 0.995389i | \(0.469419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 20.2517i | − | 0.939149i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.77050i | 0.0819288i | 0.999161 | + | 0.0409644i | \(0.0130430\pi\) | ||||
−0.999161 | + | 0.0409644i | \(0.986957\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.09928 | − | 0.608560i | −0.327814 | − | 0.0281007i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.4470 | 1.86370 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.27743 | + | 6.61435i | −0.334616 | + | 0.304128i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0448 | −0.506769 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 70.3122 | 3.21938 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.6868 | −0.579675 | −0.289837 | − | 0.957076i | \(-0.593601\pi\) | ||||
−0.289837 | + | 0.957076i | \(0.593601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.94206 | −0.270935 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.431460 | − | 5.03328i | 0.0196321 | − | 0.229022i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.1348 | 0.687236 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.1009 | 1.36400 | 0.682002 | − | 0.731351i | \(-0.261110\pi\) | ||||
0.682002 | + | 0.731351i | \(0.261110\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.9479i | 1.48996i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 35.0014i | − | 1.57959i | −0.613370 | − | 0.789795i | \(-0.710187\pi\) | ||
0.613370 | − | 0.789795i | \(-0.289813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.2564i | 1.54283i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 66.5296 | − | 60.4678i | 2.99028 | − | 2.71783i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.0374 | − | 1.46047i | −0.764231 | − | 0.0655109i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.00138 | 0.268659 | 0.134329 | − | 0.990937i | \(-0.457112\pi\) | ||||
0.134329 | + | 0.990937i | \(0.457112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.59855i | 0.116095i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.8342 | 1.19648 | 0.598238 | − | 0.801318i | \(-0.295868\pi\) | ||||
0.598238 | + | 0.801318i | \(0.295868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.45049i | − | 0.109045i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3.04894i | − | 0.135408i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 21.3512i | − | 0.946375i | −0.880962 | − | 0.473188i | \(-0.843103\pi\) | ||
0.880962 | − | 0.473188i | \(-0.156897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.9384 | − | 2.39492i | −1.23592 | − | 0.105945i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.19979i | 0.362029i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 56.0170 | 2.46840 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.0971 | − | 23.7193i | 1.14775 | − | 1.04317i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.3997i | − | 0.456495i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.9400i | − | 0.610721i | −0.952237 | − | 0.305360i | \(-0.901223\pi\) | ||
0.952237 | − | 0.305360i | \(-0.0987769\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.20406 | −0.227558 | −0.113779 | − | 0.993506i | \(-0.536296\pi\) | ||||
−0.113779 | + | 0.993506i | \(0.536296\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.32596 | − | 108.794i | 0.407018 | − | 4.74815i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 9.60826i | − | 0.418543i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6078 | −0.982949 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 50.3097i | 2.18326i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.8437 | −0.469692 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.7935 | −1.07192 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.5919i | 0.629686i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.4633 | + | 19.5874i | 0.536832 | + | 0.843689i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 4.17722i | − | 0.179593i | −0.995960 | − | 0.0897963i | \(-0.971378\pi\) | ||
0.995960 | − | 0.0897963i | \(-0.0286216\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 48.4120 | 2.07756 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −42.3688 | −1.81488 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.8440i | − | 1.14777i | −0.818937 | − | 0.573883i | \(-0.805436\pi\) | ||
0.818937 | − | 0.573883i | \(-0.194564\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 84.7927 | 3.61886 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.48807i | 0.191198i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.15201 | − | 25.1047i | 0.0915129 | − | 1.06756i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −78.0003 | −3.31093 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.21249i | 0.136118i | 0.997681 | + | 0.0680588i | \(0.0216805\pi\) | ||||
−0.997681 | + | 0.0680588i | \(0.978319\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.96511i | 0.125411i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 46.6047 | − | 42.3583i | 1.96765 | − | 1.78837i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5707 | 0.445504 | 0.222752 | − | 0.974875i | \(-0.428496\pi\) | ||||
0.222752 | + | 0.974875i | \(0.428496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 41.1066i | − | 1.72937i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −30.9793 | − | 2.65559i | −1.30101 | − | 0.111524i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.0687i | 0.799401i | 0.916646 | + | 0.399700i | \(0.130886\pi\) | ||||
−0.916646 | + | 0.399700i | \(0.869114\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.87982i | − | 0.0786680i | −0.999226 | − | 0.0393340i | \(-0.987476\pi\) | ||
0.999226 | − | 0.0393340i | \(-0.0125236\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 41.5617i | 1.73626i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.47693 | 0.353512 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.7990i | 1.15729i | 0.815581 | + | 0.578643i | \(0.196417\pi\) | ||||
−0.815581 | + | 0.578643i | \(0.803583\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −61.0264 | −2.53617 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.7689 | + | 1.86606i | 0.903128 | + | 0.0774174i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.9121 | − | 27.4095i | −1.03175 | − | 1.13518i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 27.1068i | − | 1.12073i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 10.4469i | − | 0.431190i | −0.976483 | − | 0.215595i | \(-0.930831\pi\) | ||
0.976483 | − | 0.215595i | \(-0.0691692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.25882i | − | 0.0518686i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −69.3221 | −2.85153 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.91927 | −0.407336 | −0.203668 | − | 0.979040i | \(-0.565286\pi\) | ||||
−0.203668 | + | 0.979040i | \(0.565286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.05901 | − | 70.6826i | 0.248395 | − | 2.89770i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.1972 | 0.990326 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.3821 | 1.03708 | 0.518542 | − | 0.855052i | \(-0.326475\pi\) | ||||
0.518542 | + | 0.855052i | \(0.326475\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3480 | 0.911592 | 0.455796 | − | 0.890084i | \(-0.349355\pi\) | ||||
0.455796 | + | 0.890084i | \(0.349355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.9560 | −0.690500 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −47.1437 | − | 4.51079i | −1.91666 | − | 0.183390i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.7769 | 0.518599 | 0.259300 | − | 0.965797i | \(-0.416508\pi\) | ||||
0.259300 | + | 0.965797i | \(0.416508\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −44.2087 | − | 3.78963i | −1.79142 | − | 0.153563i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 10.6330i | − | 0.430165i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.0433i | 1.73850i | 0.494371 | + | 0.869251i | \(0.335398\pi\) | ||||
−0.494371 | + | 0.869251i | \(0.664602\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −142.343 | −5.73982 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.1068 | 1.13154 | 0.565768 | − | 0.824565i | \(-0.308580\pi\) | ||||
0.565768 | + | 0.824565i | \(0.308580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.8211i | 0.635902i | 0.948107 | + | 0.317951i | \(0.102995\pi\) | ||||
−0.948107 | + | 0.317951i | \(0.897005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 6.29338i | − | 0.252545i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.379442 | + | 4.42645i | −0.0152020 | + | 0.177342i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 90.5472 | 3.62189 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.10586 | − | 5.54953i | 0.243845 | − | 0.221627i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.0067 | −1.47555 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.82300 | 0.0725725 | 0.0362863 | − | 0.999341i | \(-0.488447\pi\) | ||||
0.0362863 | + | 0.999341i | \(0.488447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.8616 | −0.471455 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −60.1622 | −2.38746 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.89788 | + | 1.19135i | 0.273304 | + | 0.0472028i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.6922 | −1.60976 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.8720 | 1.06138 | 0.530690 | − | 0.847566i | \(-0.321933\pi\) | ||||
0.530690 | + | 0.847566i | \(0.321933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.22230i | − | 0.0876391i | −0.999039 | − | 0.0438195i | \(-0.986047\pi\) | ||
0.999039 | − | 0.0438195i | \(-0.0139527\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.9224i | 1.53257i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 31.7005i | − | 1.24628i | −0.782112 | − | 0.623138i | \(-0.785857\pi\) | ||
0.782112 | − | 0.623138i | \(-0.214143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.6120 | − | 17.8251i | 0.769838 | − | 0.699695i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.3997 | + | 1.06292i | 0.485981 | + | 0.0416590i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.35326 | −0.326888 | −0.163444 | − | 0.986553i | \(-0.552260\pi\) | ||||
−0.163444 | + | 0.986553i | \(0.552260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 89.5147i | − | 3.49763i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −66.7282 | −2.60331 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.2630i | 0.945153i | 0.881290 | + | 0.472577i | \(0.156676\pi\) | ||||
−0.881290 | + | 0.472577i | \(0.843324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.7909i | 1.08094i | 0.841363 | + | 0.540471i | \(0.181754\pi\) | ||||
−0.841363 | + | 0.540471i | \(0.818246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 18.9886i | − | 0.737455i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.793815 | − | 9.26041i | 0.0307828 | − | 0.359103i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.44462i | − | 0.133376i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 62.6308 | 2.42145 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0426 | − | 33.0543i | −1.15978 | − | 1.27605i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.3618i | 1.82566i | 0.408334 | + | 0.912832i | \(0.366110\pi\) | ||||
−0.408334 | + | 0.912832i | \(0.633890\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 136.031i | − | 5.23583i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.49513 | 0.326494 | 0.163247 | − | 0.986585i | \(-0.447803\pi\) | ||||
0.163247 | + | 0.986585i | \(0.447803\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.794357 | + | 9.26672i | −0.0304846 | + | 0.355624i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.2992i | 1.31435i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3789 | 1.35374 | 0.676869 | − | 0.736104i | \(-0.263337\pi\) | ||||
0.676869 | + | 0.736104i | \(0.263337\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6654i | 1.55374i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.2864 | −0.392450 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1677 | −0.425455 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 4.72419i | − | 0.179717i | −0.995955 | − | 0.0898583i | \(-0.971359\pi\) | ||
0.995955 | − | 0.0898583i | \(-0.0286414\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.5313 | + | 43.9083i | 1.27375 | + | 1.66794i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.9209i | 1.05910i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −67.5337 | −2.55802 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.66989 | 0.290102 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.5468i | − | 1.34258i | −0.741193 | − | 0.671292i | \(-0.765740\pi\) | ||
0.741193 | − | 0.671292i | \(-0.234260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.84840 | −0.182861 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 139.577i | − | 5.25678i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.50038 | + | 0.128615i | 0.0564277 | + | 0.00483706i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.38729 | −0.239880 | −0.119940 | − | 0.992781i | \(-0.538270\pi\) | ||||
−0.119940 | + | 0.992781i | \(0.538270\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 59.9603i | − | 2.24869i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.966149i | 0.0361826i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5669 | + | 9.60410i | −0.395179 | + | 0.359173i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 45.3129 | 1.69224 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.32828i | 0.198711i | 0.995052 | + | 0.0993556i | \(0.0316781\pi\) | ||||
−0.995052 | + | 0.0993556i | \(0.968322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.94007 | + | 34.2980i | −0.109494 | + | 1.27732i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.7471i | 1.47821i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 74.4552i | − | 2.76520i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.2630i | 0.640248i | 0.947376 | + | 0.320124i | \(0.103725\pi\) | ||||
−0.947376 | + | 0.320124i | \(0.896275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.9292 | 0.664046 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.4665i | 0.683007i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.57837 | 0.242978 | 0.121489 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121489 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 90.5471 | + | 15.6386i | 3.33988 | + | 0.576837i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.00761 | + | 6.60986i | 0.221293 | + | 0.243477i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 0.0295860i | − | 0.00108834i | −1.00000 | 0.000544169i | \(-0.999827\pi\) | |||
1.00000 | 0.000544169i | \(-0.000173215\pi\) | ||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2.48777i | − | 0.0913904i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 46.2496i | − | 1.69673i | −0.529409 | − | 0.848367i | \(-0.677586\pi\) | ||
0.529409 | − | 0.848367i | \(-0.322414\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −76.3695 | −2.79796 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 51.9931 | 1.90233 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.30130 | − | 15.1805i | 0.0475483 | − | 0.554684i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5975 | 0.459688 | 0.229844 | − | 0.973227i | \(-0.426178\pi\) | ||||
0.229844 | + | 0.973227i | \(0.426178\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −72.6992 | −2.64931 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.92281 | 0.361128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.3686 | 1.72164 | 0.860821 | − | 0.508908i | \(-0.169951\pi\) | ||||
0.860821 | + | 0.508908i | \(0.169951\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.68629 | + | 4.25930i | −0.170101 | + | 0.154603i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.3236 | 1.24423 | 0.622115 | − | 0.782926i | \(-0.286274\pi\) | ||||
0.622115 | + | 0.782926i | \(0.286274\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.22374 | − | 25.9415i | 0.0805049 | − | 0.939146i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 168.819i | − | 6.10366i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 7.99070i | − | 0.288527i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.4091 | −0.699910 | −0.349955 | − | 0.936767i | \(-0.613803\pi\) | ||||
−0.349955 | + | 0.936767i | \(0.613803\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 46.1236 | 1.66110 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.6784i | 1.13939i | 0.821855 | + | 0.569697i | \(0.192940\pi\) | ||||
−0.821855 | + | 0.569697i | \(0.807060\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.8832i | 0.750148i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.09388 | − | 47.7579i | 0.146867 | − | 1.71331i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.84785 | −0.317007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.4175 | + | 15.8628i | 0.515899 | + | 0.567617i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.2765 | −1.97542 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −57.1146 | −2.03851 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.0390 | 1.60547 | 0.802733 | − | 0.596339i | \(-0.203379\pi\) | ||||
0.802733 | + | 0.596339i | \(0.203379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 67.9145 | 2.41782 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.1687 | + | 2.15750i | 0.894896 | + | 0.0767118i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.4676 | −0.478249 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −146.596 | −5.19923 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.7427i | 1.12438i | 0.827006 | + | 0.562192i | \(0.190042\pi\) | ||||
−0.827006 | + | 0.562192i | \(0.809958\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 66.2215i | − | 2.34275i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.5722i | 0.373549i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.6422 | + | 26.0123i | 0.834316 | + | 0.917955i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.609258 | + | 7.10742i | −0.0214735 | + | 0.250504i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.99519 | −0.316646 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.08147i | 0.178655i | 0.996002 | + | 0.0893275i | \(0.0284718\pi\) | ||||
−0.996002 | + | 0.0893275i | \(0.971528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6887 | −1.04251 | −0.521255 | − | 0.853401i | \(-0.674536\pi\) | ||||
−0.521255 | + | 0.853401i | \(0.674536\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.2947i | 0.606550i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 46.5252i | − | 1.62971i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.41937i | 0.0846429i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.5969 | + | 1.42271i | 0.579942 | + | 0.0497135i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.1933i | 1.29805i | 0.760765 | + | 0.649027i | \(0.224824\pi\) | ||||
−0.760765 | + | 0.649027i | \(0.775176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6722 | 0.825160 | 0.412580 | − | 0.910921i | \(-0.364628\pi\) | ||||
0.412580 | + | 0.910921i | \(0.364628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −101.294 | + | 92.0643i | −3.52659 | + | 3.20527i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.9003i | − | 0.413814i | −0.978361 | − | 0.206907i | \(-0.933660\pi\) | ||
0.978361 | − | 0.206907i | \(-0.0663398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 11.1597i | − | 0.387593i | −0.981042 | − | 0.193796i | \(-0.937920\pi\) | ||
0.981042 | − | 0.193796i | \(-0.0620801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.2185 | −1.98489 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 42.9594 | + | 7.41961i | 1.48846 | + | 0.257074i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.66937i | − | 0.126984i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.5040 | 0.535896 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 56.8859i | − | 1.96392i | −0.189086 | − | 0.981960i | \(-0.560553\pi\) | ||
0.189086 | − | 0.981960i | \(-0.439447\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.25506 | −0.0432779 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.99658 | −0.137650 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.30537i | 0.148109i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.23622 | − | 28.6283i | 0.179918 | − | 0.983682i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.8030i | 0.851237i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.72117 | 0.127560 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.5307 | −0.805676 | −0.402838 | − | 0.915271i | \(-0.631976\pi\) | ||||
−0.402838 | + | 0.915271i | \(0.631976\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 22.1176i | − | 0.756407i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.3336 | −0.899538 | −0.449769 | − | 0.893145i | \(-0.648494\pi\) | ||||
−0.449769 | + | 0.893145i | \(0.648494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.3084i | − | 0.863512i | −0.901990 | − | 0.431756i | \(-0.857894\pi\) | ||
0.901990 | − | 0.431756i | \(-0.142106\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.47093 | − | 87.1536i | 0.254609 | − | 2.97019i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.09350 | 0.241466 | 0.120733 | − | 0.992685i | \(-0.461476\pi\) | ||||
0.120733 | + | 0.992685i | \(0.461476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.6852i | 0.499312i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 66.4274i | − | 2.25599i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.3740 | + | 21.2443i | −0.792910 | + | 0.720664i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.69312 | 0.0912527 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.1327i | 0.749079i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.30466 | + | 96.8797i | −0.280749 | + | 3.27513i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.6667i | 0.630331i | 0.949037 | + | 0.315165i | \(0.102060\pi\) | ||||
−0.949037 | + | 0.315165i | \(0.897940\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 65.9380i | − | 2.22403i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 33.2091i | − | 1.11884i | −0.828883 | − | 0.559422i | \(-0.811023\pi\) | ||
0.828883 | − | 0.559422i | \(-0.188977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.221802 | −0.00746423 | −0.00373212 | − | 0.999993i | \(-0.501188\pi\) | ||||
−0.00373212 | + | 0.999993i | \(0.501188\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 104.892i | − | 3.52592i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.8697 | −0.700736 | −0.350368 | − | 0.936612i | \(-0.613943\pi\) | ||||
−0.350368 | + | 0.936612i | \(0.613943\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.15764 | − | 36.8360i | 0.105904 | − | 1.23544i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.2155 | + | 28.8436i | 0.878254 | + | 0.966297i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8.67594i | − | 0.290329i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 20.6050i | − | 0.688749i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.90938i | 0.0637522i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.48595 | 0.283022 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69.5515 | −2.31710 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.8314 | − | 2.04286i | −0.793058 | − | 0.0679821i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −68.3619 | −2.27243 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.3950 | −1.67334 | −0.836669 | − | 0.547708i | \(-0.815500\pi\) | ||||
−0.836669 | + | 0.547708i | \(0.815500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.58353 | 0.118858 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.7787 | −1.31793 | −0.658964 | − | 0.752174i | \(-0.729005\pi\) | ||||
−0.658964 | + | 0.752174i | \(0.729005\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.4215 | − | 20.2682i | −0.609662 | − | 0.670780i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −176.787 | −5.84439 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54.8080 | + | 4.69822i | 1.80992 | + | 0.155149i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.4011i | 0.574009i | 0.957929 | + | 0.287004i | \(0.0926594\pi\) | ||||
−0.957929 | + | 0.287004i | \(0.907341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.66028i | 0.0547079i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.46314 | 0.212737 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 80.4328 | 2.64461 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 81.9176i | 2.69053i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.7888i | 0.878912i | 0.898264 | + | 0.439456i | \(0.144829\pi\) | ||||
−0.898264 | + | 0.439456i | \(0.855171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.62829 | + | 0.972072i | 0.184460 | + | 0.0318584i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.1006 | −0.789019 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −65.8098 | + | 59.8136i | −2.15221 | + | 1.95611i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.5445 | −1.03051 | −0.515256 | − | 0.857036i | \(-0.672303\pi\) | ||||
−0.515256 | + | 0.857036i | \(0.672303\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.1719 | 1.96364 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.3278 | 1.80364 | 0.901818 | − | 0.432116i | \(-0.142233\pi\) | ||||
0.901818 | + | 0.432116i | \(0.142233\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.79078 | 0.221138 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 114.054 | + | 9.77688i | 3.71018 | + | 0.318042i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.6400 | 1.71057 | 0.855285 | − | 0.518157i | \(-0.173382\pi\) | ||||
0.855285 | + | 0.518157i | \(0.173382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5984 | 0.344040 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 93.0594i | 3.01766i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.60473i | − | 0.181555i | −0.995871 | − | 0.0907775i | \(-0.971065\pi\) | ||
0.995871 | − | 0.0907775i | \(-0.0289352\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 58.6886i | − | 1.89912i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.4106 | + | 41.1609i | 1.20931 | + | 1.33054i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.8985 | − | 2.13434i | −0.804016 | − | 0.0689214i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.6199 | 0.923221 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 36.2573i | − | 1.16837i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 86.1745 | 2.77405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.5560i | 1.07909i | 0.841957 | + | 0.539544i | \(0.181403\pi\) | ||||
−0.841957 | + | 0.539544i | \(0.818597\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 15.4936i | − | 0.497727i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.83687i | − | 0.155223i | −0.996984 | − | 0.0776113i | \(-0.975271\pi\) | ||
0.996984 | − | 0.0776113i | \(-0.0247293\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0954 | − | 1.46544i | −0.548053 | − | 0.0469799i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41.2710i | 1.32173i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.7375 | 0.887402 | 0.443701 | − | 0.896175i | \(-0.353665\pi\) | ||||
0.443701 | + | 0.896175i | \(0.353665\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.12130 | − | 3.74579i | 0.131717 | − | 0.119716i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 61.9589i | − | 1.97820i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 53.3096i | − | 1.70031i | −0.526531 | − | 0.850156i | \(-0.676508\pi\) | ||
0.526531 | − | 0.850156i | \(-0.323492\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 97.8887 | 3.11899 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 85.4602 | + | 7.32577i | 2.72023 | + | 0.233182i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.85688i | − | 0.0590453i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.4003 | 1.37866 | 0.689328 | − | 0.724449i | \(-0.257906\pi\) | ||||
0.689328 | + | 0.724449i | \(0.257906\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 71.4482i | 2.26734i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.1685 | −1.08322 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.47459 | 0.0783711 | 0.0391855 | − | 0.999232i | \(-0.487524\pi\) | ||||
0.0391855 | + | 0.999232i | \(0.487524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 59.7144i | − | 1.88928i |
(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 | 4004.2.e.a.3849.3 | ✓ | 48 | |
7.6 | odd | 2 | 4004.2.e.b.3849.46 | yes | 48 | ||
11.10 | odd | 2 | 4004.2.e.b.3849.3 | yes | 48 | ||
77.76 | even | 2 | inner | 4004.2.e.a.3849.46 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.e.a.3849.3 | ✓ | 48 | 1.1 | even | 1 | trivial | |
4004.2.e.a.3849.46 | yes | 48 | 77.76 | even | 2 | inner | |
4004.2.e.b.3849.3 | yes | 48 | 11.10 | odd | 2 | ||
4004.2.e.b.3849.46 | yes | 48 | 7.6 | odd | 2 |