Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.16 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.b.1609.4 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.63494 | − | 1.52544i | −0.731168 | − | 0.682198i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.48382i | 1.31676i | 0.752686 | + | 0.658380i | \(0.228758\pi\) | ||||
−0.752686 | + | 0.658380i | \(0.771242\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.37949 | −0.415932 | −0.207966 | − | 0.978136i | \(-0.566684\pi\) | ||||
−0.207966 | + | 0.978136i | \(0.566684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.00615147i | 0.00170611i | 1.00000 | 0.000853055i | \(0.000271536\pi\) | |||||
−1.00000 | 0.000853055i | \(0.999728\pi\) | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.52544 | − | 1.63494i | 0.393867 | − | 0.422140i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.950372i | 0.230499i | 0.993337 | + | 0.115250i | \(0.0367668\pi\) | ||||
−0.993337 | + | 0.115250i | \(0.963233\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.93240 | −1.36099 | −0.680493 | − | 0.732754i | \(-0.738234\pi\) | ||||
−0.680493 | + | 0.732754i | \(0.738234\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.48382 | −0.760232 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.79132i | − | 1.20757i | −0.797146 | − | 0.603787i | \(-0.793658\pi\) | ||
0.797146 | − | 0.603787i | \(-0.206342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.346064 | + | 4.98801i | 0.0692129 | + | 0.997602i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.84186 | 0.342025 | 0.171013 | − | 0.985269i | \(-0.445296\pi\) | ||||
0.171013 | + | 0.985269i | \(0.445296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.21197 | −0.756492 | −0.378246 | − | 0.925705i | \(-0.623473\pi\) | ||||
−0.378246 | + | 0.925705i | \(0.623473\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.37949i | − | 0.240138i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.31436 | − | 5.69584i | 0.898290 | − | 0.962773i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.70804i | − | 1.43159i | −0.698309 | − | 0.715796i | \(-0.746064\pi\) | ||
0.698309 | − | 0.715796i | \(-0.253936\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.00615147 | −0.000985023 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.62807 | 0.878957 | 0.439478 | − | 0.898253i | \(-0.355163\pi\) | ||||
0.439478 | + | 0.898253i | \(0.355163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.88362i | 0.287249i | 0.989632 | + | 0.143625i | \(0.0458758\pi\) | ||||
−0.989632 | + | 0.143625i | \(0.954124\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.63494 | + | 1.52544i | 0.243723 | + | 0.227399i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.91697i | − | 0.863079i | −0.902094 | − | 0.431540i | \(-0.857971\pi\) | ||
0.902094 | − | 0.431540i | \(-0.142029\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.13700 | −0.733857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.950372 | −0.133079 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6894i | 1.60566i | 0.596211 | + | 0.802828i | \(0.296672\pi\) | ||||
−0.596211 | + | 0.802828i | \(0.703328\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.25538 | + | 2.10433i | 0.304116 | + | 0.283748i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.93240i | − | 0.785766i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.9173 | 1.68168 | 0.840842 | − | 0.541281i | \(-0.182060\pi\) | ||||
0.840842 | + | 0.541281i | \(0.182060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.73278 | −1.11812 | −0.559059 | − | 0.829128i | \(-0.688837\pi\) | ||||
−0.559059 | + | 0.829128i | \(0.688837\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.48382i | − | 0.438920i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.00938370 | − | 0.0100573i | 0.00116390 | − | 0.00124745i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.79132 | 0.697193 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.85892 | 0.695325 | 0.347663 | − | 0.937620i | \(-0.386975\pi\) | ||||
0.347663 | + | 0.937620i | \(0.386975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.3918i | − | 1.80148i | −0.434364 | − | 0.900738i | \(-0.643027\pi\) | ||
0.434364 | − | 0.900738i | \(-0.356973\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.98801 | + | 0.346064i | −0.575966 | + | 0.0399601i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.80589i | − | 0.547682i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.34143 | 0.825976 | 0.412988 | − | 0.910737i | \(-0.364485\pi\) | ||||
0.412988 | + | 0.910737i | \(0.364485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.1852i | 1.88633i | 0.332331 | + | 0.943163i | \(0.392165\pi\) | ||||
−0.332331 | + | 0.943163i | \(0.607835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.44974 | − | 1.55380i | 0.157246 | − | 0.168533i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.84186i | 0.197468i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.0825605 | −0.00875139 | −0.00437570 | − | 0.999990i | \(-0.501393\pi\) | ||||
−0.00437570 | + | 0.999990i | \(0.501393\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0214306 | −0.00224654 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 4.21197i | − | 0.436761i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.69913 | + | 9.04953i | 0.995110 | + | 0.928462i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.8586i | − | 1.10252i | −0.834333 | − | 0.551260i | \(-0.814147\pi\) | ||
0.834333 | − | 0.551260i | \(-0.185853\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.37949 | 0.138644 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2686 | −1.22077 | −0.610386 | − | 0.792104i | \(-0.708986\pi\) | ||||
−0.610386 | + | 0.792104i | \(0.708986\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.37006i | 0.824726i | 0.911020 | + | 0.412363i | \(0.135296\pi\) | ||||
−0.911020 | + | 0.412363i | \(0.864704\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.69584 | + | 5.31436i | 0.555857 | + | 0.518628i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.42903i | − | 0.911538i | −0.890098 | − | 0.455769i | \(-0.849364\pi\) | ||
0.890098 | − | 0.455769i | \(-0.150636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.11856 | −0.490270 | −0.245135 | − | 0.969489i | \(-0.578832\pi\) | ||||
−0.245135 | + | 0.969489i | \(0.578832\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.70804 | 0.826531 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.7880i | − | 1.39114i | −0.718458 | − | 0.695570i | \(-0.755152\pi\) | ||
0.718458 | − | 0.695570i | \(-0.244848\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.83432 | + | 9.46847i | −0.823804 | + | 0.882939i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.00615147i | − | 0.000568703i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.31092 | −0.303512 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.09701 | −0.827001 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.62807i | 0.507466i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.04312 | − | 8.68300i | 0.629955 | − | 0.776631i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.1851i | − | 1.25873i | −0.777111 | − | 0.629363i | \(-0.783316\pi\) | ||
0.777111 | − | 0.629363i | \(-0.216684\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.88362 | −0.165843 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3659 | 0.905675 | 0.452837 | − | 0.891593i | \(-0.350412\pi\) | ||||
0.452837 | + | 0.891593i | \(0.350412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 20.6674i | − | 1.79209i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.52544 | + | 1.63494i | −0.131289 | + | 0.140713i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.30628i | 0.709653i | 0.934932 | + | 0.354827i | \(0.115460\pi\) | ||||
−0.934932 | + | 0.354827i | \(0.884540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9339 | 1.18186 | 0.590929 | − | 0.806723i | \(-0.298761\pi\) | ||||
0.590929 | + | 0.806723i | \(0.298761\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.91697 | 0.498299 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.00848589i | − | 0.000709626i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.01133 | − | 2.80965i | −0.250078 | − | 0.233329i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5.13700i | − | 0.423692i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.9868 | 1.14584 | 0.572921 | − | 0.819611i | \(-0.305810\pi\) | ||||
0.572921 | + | 0.819611i | \(0.305810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2480 | 1.56638 | 0.783190 | − | 0.621783i | \(-0.213591\pi\) | ||||
0.783190 | + | 0.621783i | \(0.213591\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.950372i | − | 0.0768330i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.88633 | + | 6.42511i | 0.553123 | + | 0.516077i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4863i | 0.836897i | 0.908241 | + | 0.418449i | \(0.137426\pi\) | ||||
−0.908241 | + | 0.418449i | \(0.862574\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.6894 | −0.927026 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.1759 | 1.59009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.57463i | 0.593291i | 0.954988 | + | 0.296645i | \(0.0958680\pi\) | ||||
−0.954988 | + | 0.296645i | \(0.904132\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.10433 | + | 2.25538i | −0.163822 | + | 0.175581i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.1496i | − | 1.32708i | −0.748142 | − | 0.663539i | \(-0.769054\pi\) | ||
0.748142 | − | 0.663539i | \(-0.230946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 0.999997 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.93240 | 0.453662 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 10.7568i | − | 0.817823i | −0.912574 | − | 0.408912i | \(-0.865908\pi\) | ||
0.912574 | − | 0.408912i | \(-0.134092\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.3773 | + | 1.20563i | −1.31360 | + | 0.0911368i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.9173i | 0.970921i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.5022 | 1.83138 | 0.915691 | − | 0.401882i | \(-0.131644\pi\) | ||||
0.915691 | + | 0.401882i | \(0.131644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.467927 | 0.0347807 | 0.0173904 | − | 0.999849i | \(-0.494464\pi\) | ||||
0.0173904 | + | 0.999849i | \(0.494464\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.73278i | − | 0.645546i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.2836 | + | 14.2371i | −0.976629 | + | 1.04673i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.31103i | − | 0.0958719i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.48382 | 0.253411 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.48094 | −0.179515 | −0.0897574 | − | 0.995964i | \(-0.528609\pi\) | ||||
−0.0897574 | + | 0.995964i | \(0.528609\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 24.4200i | − | 1.75779i | −0.477013 | − | 0.878896i | \(-0.658281\pi\) | ||
0.477013 | − | 0.878896i | \(-0.341719\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0100573 | + | 0.00938370i | 0.000720217 | + | 0.000671980i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 24.5278i | − | 1.74754i | −0.486344 | − | 0.873768i | \(-0.661670\pi\) | ||
0.486344 | − | 0.873768i | \(-0.338330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9220 | 1.48312 | 0.741562 | − | 0.670884i | \(-0.234085\pi\) | ||||
0.741562 | + | 0.670884i | \(0.234085\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.41671i | 0.450365i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.20156 | − | 8.58528i | −0.642665 | − | 0.599622i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.79132i | 0.402525i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.18369 | 0.566078 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.45635 | −0.582159 | −0.291080 | − | 0.956699i | \(-0.594014\pi\) | ||||
−0.291080 | + | 0.956699i | \(0.594014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.85892i | 0.401446i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.87335 | − | 3.07961i | 0.195961 | − | 0.210027i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.6737i | − | 0.996119i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.3918 | 1.04008 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.00584618 | −0.000393257 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 27.8779i | − | 1.86684i | −0.358783 | − | 0.933421i | \(-0.616808\pi\) | ||
0.358783 | − | 0.933421i | \(-0.383192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.346064 | − | 4.98801i | −0.0230710 | − | 0.332534i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0632i | 0.800662i | 0.916371 | + | 0.400331i | \(0.131105\pi\) | ||||
−0.916371 | + | 0.400331i | \(0.868895\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.5262 | −1.62074 | −0.810370 | − | 0.585919i | \(-0.800734\pi\) | ||||
−0.810370 | + | 0.585919i | \(0.800734\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.80589 | 0.316205 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.69308i | − | 0.635015i | −0.948256 | − | 0.317507i | \(-0.897154\pi\) | ||
0.948256 | − | 0.317507i | \(-0.102846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.02599 | + | 9.67390i | −0.588791 | + | 0.631056i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.34143i | 0.476877i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.6671 | −1.33684 | −0.668420 | − | 0.743784i | \(-0.733029\pi\) | ||||
−0.668420 | + | 0.743784i | \(0.733029\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.1359 | −1.74798 | −0.873989 | − | 0.485945i | \(-0.838475\pi\) | ||||
−0.873989 | + | 0.485945i | \(0.838475\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.39869 | + | 7.83618i | 0.536572 | + | 0.500635i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.0364930i | − | 0.00232199i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.1852 | −1.08907 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0570 | −0.761029 | −0.380515 | − | 0.924775i | \(-0.624253\pi\) | ||||
−0.380515 | + | 0.924775i | \(0.624253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.98907i | 0.502269i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.55380 | + | 1.44974i | 0.0973029 | + | 0.0907860i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.53277i | − | 0.594638i | −0.954778 | − | 0.297319i | \(-0.903908\pi\) | ||
0.954778 | − | 0.297319i | \(-0.0960924\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.3372 | 1.88506 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.84186 | −0.114008 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.5536i | − | 1.02074i | −0.859955 | − | 0.510371i | \(-0.829508\pi\) | ||
0.859955 | − | 0.510371i | \(-0.170492\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.8314 | − | 19.1114i | 1.09537 | − | 1.17400i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 0.0825605i | − | 0.00505262i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.03378 | 0.428857 | 0.214429 | − | 0.976740i | \(-0.431211\pi\) | ||||
0.214429 | + | 0.976740i | \(0.431211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.8273 | 1.32591 | 0.662956 | − | 0.748658i | \(-0.269302\pi\) | ||||
0.662956 | + | 0.748658i | \(0.269302\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.0214306i | − | 0.00129704i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.477392 | − | 6.88091i | −0.0287878 | − | 0.414934i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8080i | 1.61074i | 0.592773 | + | 0.805370i | \(0.298033\pi\) | ||||
−0.592773 | + | 0.805370i | \(0.701967\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.21197 | 0.252164 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.3824 | −1.63350 | −0.816750 | − | 0.576992i | \(-0.804226\pi\) | ||||
−0.816750 | + | 0.576992i | \(0.804226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.36562i | − | 0.497284i | −0.968595 | − | 0.248642i | \(-0.920016\pi\) | ||
0.968595 | − | 0.248642i | \(-0.0799843\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.04953 | + | 9.69913i | −0.536048 | + | 0.574527i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.6072i | 1.15738i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0968 | 0.946870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8586 | 0.636540 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.9803i | 0.816736i | 0.912817 | + | 0.408368i | \(0.133902\pi\) | ||||
−0.912817 | + | 0.408368i | \(0.866098\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.1190 | − | 19.7045i | −1.22959 | − | 1.14724i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.37949i | 0.0800461i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0356251 | 0.00206025 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.56219 | −0.378238 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 12.2686i | − | 0.704813i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.2776 | + | 13.3213i | 0.817532 | + | 0.762777i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.9185i | 1.02266i | 0.859384 | + | 0.511331i | \(0.170847\pi\) | ||||
−0.859384 | + | 0.511331i | \(0.829153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.37006 | −0.476156 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.6785 | 1.05916 | 0.529580 | − | 0.848260i | \(-0.322350\pi\) | ||||
0.529580 | + | 0.848260i | \(0.322350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.32650i | 0.527165i | 0.964637 | + | 0.263583i | \(0.0849041\pi\) | ||||
−0.964637 | + | 0.263583i | \(0.915096\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.31436 | + | 5.69584i | −0.299430 | + | 0.320924i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.6307i | − | 0.597080i | −0.954397 | − | 0.298540i | \(-0.903500\pi\) | ||
0.954397 | − | 0.298540i | \(-0.0964996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.54083 | −0.142259 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.42903 | 0.526277 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.63799i | − | 0.313706i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0306836 | + | 0.00212880i | −0.00170202 | + | 0.000118085i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 5.11856i | − | 0.283057i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.6137 | 1.13647 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0440326 | 0.00242025 | 0.00121013 | − | 0.999999i | \(-0.499615\pi\) | ||||
0.00121013 | + | 0.999999i | \(0.499615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.70804i | 0.477198i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.52544 | + | 1.63494i | −0.0833437 | + | 0.0893264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.316789i | 0.0172566i | 0.999963 | + | 0.00862831i | \(0.00274651\pi\) | ||||
−0.999963 | + | 0.00862831i | \(0.997253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.7880 | 0.803175 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.81037 | 0.314649 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.49037i | 0.350447i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.46847 | − | 8.83432i | −0.509765 | − | 0.475624i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6.85062i | − | 0.367760i | −0.982949 | − | 0.183880i | \(-0.941134\pi\) | ||
0.982949 | − | 0.183880i | \(-0.0588658\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1577 | −0.864903 | −0.432452 | − | 0.901657i | \(-0.642351\pi\) | ||||
−0.432452 | + | 0.901657i | \(0.642351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.00615147 | 0.000328341 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.92185i | − | 0.155514i | −0.996972 | − | 0.0777571i | \(-0.975224\pi\) | ||
0.996972 | − | 0.0777571i | \(-0.0247759\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.57898 | − | 8.93742i | −0.508400 | − | 0.474349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.31092i | − | 0.175233i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.8101 | 0.939980 | 0.469990 | − | 0.882672i | \(-0.344257\pi\) | ||||
0.469990 | + | 0.882672i | \(0.344257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1934 | 0.852284 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 9.09701i | − | 0.477469i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.4793 | + | 25.1647i | −1.22896 | + | 1.31718i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.44265i | − | 0.0753055i | −0.999291 | − | 0.0376528i | \(-0.988012\pi\) | ||
0.999291 | − | 0.0376528i | \(-0.0119881\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.62807 | −0.292986 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.7236 | −2.11426 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.42957i | − | 0.0740206i | −0.999315 | − | 0.0370103i | \(-0.988217\pi\) | ||
0.999315 | − | 0.0370103i | \(-0.0117834\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.68300 | + | 7.04312i | 0.448388 | + | 0.363705i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0113301i | 0.000583532i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.7653 | −0.655712 | −0.327856 | − | 0.944728i | \(-0.606326\pi\) | ||||
−0.327856 | + | 0.944728i | \(0.606326\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1851 | 0.726726 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 0.494136i | − | 0.0252492i | −0.999920 | − | 0.0126246i | \(-0.995981\pi\) | ||
0.999920 | − | 0.0126246i | \(-0.00401864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.33110 | + | 7.85735i | −0.373628 | + | 0.400448i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 1.88362i | − | 0.0957497i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.28941 | 0.318886 | 0.159443 | − | 0.987207i | \(-0.449030\pi\) | ||||
0.159443 | + | 0.987207i | \(0.449030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.50391 | 0.278345 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.3659i | 0.522892i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0028 | − | 11.1989i | −0.603927 | − | 0.563479i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 21.1867i | − | 1.06333i | −0.846954 | − | 0.531666i | \(-0.821566\pi\) | ||
0.846954 | − | 0.531666i | \(-0.178434\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.6674 | 1.03467 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.25488 | 0.162541 | 0.0812705 | − | 0.996692i | \(-0.474102\pi\) | ||||
0.0812705 | + | 0.996692i | \(0.474102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.0259098i | − | 0.00129066i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.63494 | − | 1.52544i | −0.0812409 | − | 0.0757997i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0127i | 0.595445i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8536 | 0.783913 | 0.391956 | − | 0.919984i | \(-0.371798\pi\) | ||||
0.391956 | + | 0.919984i | \(0.371798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.30628 | −0.409718 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.0014i | 2.21437i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.2151 | − | 28.0969i | 1.28685 | − | 1.37922i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.9339i | 0.682346i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.42505 | 0.167325 | 0.0836624 | − | 0.996494i | \(-0.473338\pi\) | ||||
0.0836624 | + | 0.996494i | \(0.473338\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0605 | 1.70874 | 0.854371 | − | 0.519663i | \(-0.173943\pi\) | ||||
0.854371 | + | 0.519663i | \(0.173943\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.91697i | 0.287693i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.74046 | + | 0.328890i | −0.229946 | + | 0.0159535i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 30.4234i | − | 1.47229i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.00848589 | 0.000409703 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.9897 | −1.78173 | −0.890865 | − | 0.454268i | \(-0.849901\pi\) | ||||
−0.890865 | + | 0.454268i | \(0.849901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 37.4130i | − | 1.79795i | −0.437996 | − | 0.898977i | \(-0.644312\pi\) | ||
0.437996 | − | 0.898977i | \(-0.355688\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.80965 | − | 3.01133i | 0.134712 | − | 0.144382i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.3565i | 1.64349i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.1011 | −0.482098 | −0.241049 | − | 0.970513i | \(-0.577492\pi\) | ||||
−0.241049 | + | 0.970513i | \(0.577492\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.13700 | 0.244619 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0156i | 1.33106i | 0.746370 | + | 0.665531i | \(0.231795\pi\) | ||||
−0.746370 | + | 0.665531i | \(0.768205\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.134982 | + | 0.125941i | 0.00639874 | + | 0.00597018i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.9868i | 0.661552i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8281 | 1.12452 | 0.562258 | − | 0.826962i | \(-0.309933\pi\) | ||||
0.562258 | + | 0.826962i | \(0.309933\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.76386 | −0.365586 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.2480i | 0.904350i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0350378 | + | 0.0326911i | 0.00164260 | + | 0.00153258i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.67425i | 0.358986i | 0.983759 | + | 0.179493i | \(0.0574457\pi\) | ||||
−0.983759 | + | 0.179493i | \(0.942554\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.950372 | 0.0443596 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.39545 | −0.251291 | −0.125646 | − | 0.992075i | \(-0.540100\pi\) | ||||
−0.125646 | + | 0.992075i | \(0.540100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.15948i | − | 0.379203i | −0.981861 | − | 0.189602i | \(-0.939280\pi\) | ||
0.981861 | − | 0.189602i | \(-0.0607197\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.42511 | + | 6.88633i | −0.297957 | + | 0.319346i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 33.9518i | − | 1.57110i | −0.618797 | − | 0.785551i | \(-0.712380\pi\) | ||
0.618797 | − | 0.785551i | \(-0.287620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.48382 | 0.160868 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4863 | −0.483183 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.59843i | − | 0.119476i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.05299 | − | 29.5909i | −0.0941978 | − | 1.35772i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 11.6894i | − | 0.535219i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.97687 | 0.364472 | 0.182236 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182236 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0535672 | 0.00244246 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.1759i | 0.918036i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.5641 | + | 17.7531i | −0.752137 | + | 0.806128i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3.77376i | − | 0.171005i | −0.996338 | − | 0.0855027i | \(-0.972750\pi\) | ||
0.996338 | − | 0.0855027i | \(-0.0272496\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.57463 | −0.342537 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.0282 | 1.53567 | 0.767836 | − | 0.640647i | \(-0.221334\pi\) | ||||
0.767836 | + | 0.640647i | \(0.221334\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.75045i | 0.0788364i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.25538 | − | 2.10433i | −0.101372 | − | 0.0945826i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.4114i | 0.915577i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.3624 | −1.62781 | −0.813903 | − | 0.581001i | \(-0.802661\pi\) | ||||
−0.813903 | + | 0.581001i | \(0.802661\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.1496 | 0.766189 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 24.5726i | − | 1.09564i | −0.836596 | − | 0.547820i | \(-0.815458\pi\) | ||
0.836596 | − | 0.547820i | \(-0.184542\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0584 | + | 18.7150i | 0.892589 | + | 0.832808i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.0000i | 0.577349i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.04776 | 0.268062 | 0.134031 | − | 0.990977i | \(-0.457208\pi\) | ||||
0.134031 | + | 0.990977i | \(0.457208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 53.6223 | 2.37211 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.93240i | 0.261922i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.7680 | − | 13.6845i | 0.562626 | − | 0.603013i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.16240i | 0.358982i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.7568 | 0.472170 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.6035 | −1.91030 | −0.955152 | − | 0.296116i | \(-0.904308\pi\) | ||||
−0.955152 | + | 0.296116i | \(0.904308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.21345i | − | 0.184241i | −0.995748 | − | 0.0921207i | \(-0.970635\pi\) | ||
0.995748 | − | 0.0921207i | \(-0.0293646\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.20563 | − | 17.3773i | −0.0526178 | − | 0.758409i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.00294i | − | 0.174371i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5394 | −0.458235 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.9173 | −0.560561 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0346209i | 0.00149960i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.3834 | + | 15.4159i | −0.621849 | + | 0.666487i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.5022i | 1.05735i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.08643 | 0.305234 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.1030 | −0.434362 | −0.217181 | − | 0.976131i | \(-0.569686\pi\) | ||||
−0.217181 | + | 0.976131i | \(0.569686\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.467927i | 0.0200807i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.36855 | + | 7.80806i | 0.358469 | + | 0.334461i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.1148i | 1.67243i | 0.548404 | + | 0.836214i | \(0.315236\pi\) | ||||
−0.548404 | + | 0.836214i | \(0.684764\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.73278 | 0.372706 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9267 | −0.465491 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.5762i | 1.08761i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.2371 | − | 13.2836i | −0.604333 | − | 0.563857i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.54268i | − | 0.319594i | −0.987150 | − | 0.159797i | \(-0.948916\pi\) | ||
0.987150 | − | 0.159797i | \(-0.0510839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0115870 | −0.000490079 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.31103 | 0.0553517 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.0314i | 1.05495i | 0.849572 | + | 0.527473i | \(0.176860\pi\) | ||||
−0.849572 | + | 0.527473i | \(0.823140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5582 | + | 24.1775i | −0.949032 | + | 1.01716i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.48382i | 0.146307i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.0066 | 0.587188 | 0.293594 | − | 0.955930i | \(-0.405149\pi\) | ||||
0.293594 | + | 0.955930i | \(0.405149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.22997 | −0.135170 | −0.0675849 | − | 0.997714i | \(-0.521529\pi\) | ||||
−0.0675849 | + | 0.997714i | \(0.521529\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.48094i | − | 0.103643i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.8872 | − | 2.00417i | 1.20468 | − | 0.0835797i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.24717i | 0.218443i | 0.994017 | + | 0.109221i | \(0.0348357\pi\) | ||||
−0.994017 | + | 0.109221i | \(0.965164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.4200 | 1.01486 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −59.8703 | −2.48384 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 16.1253i | − | 0.667843i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.00938370 | + | 0.0100573i | −0.000387968 | + | 0.000415818i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.7849i | 1.51827i | 0.650931 | + | 0.759137i | \(0.274379\pi\) | ||||
−0.650931 | + | 0.759137i | \(0.725621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.9871 | 1.02958 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.5278 | 1.00894 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.23589i | 0.215012i | 0.994204 | + | 0.107506i | \(0.0342865\pi\) | ||||
−0.994204 | + | 0.107506i | \(0.965713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.41317 | + | 5.05062i | 0.221918 | + | 0.207055i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.9220i | 0.856282i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.2714 | −1.07342 | −0.536711 | − | 0.843766i | \(-0.680333\pi\) | ||||
−0.536711 | + | 0.843766i | \(0.680333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.1863 | −1.88398 | −0.941990 | − | 0.335641i | \(-0.891047\pi\) | ||||
−0.941990 | + | 0.335641i | \(0.891047\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.8731 | + | 13.8769i | 0.604676 | + | 0.564178i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.4091i | − | 0.584849i | −0.956289 | − | 0.292425i | \(-0.905538\pi\) | ||
0.956289 | − | 0.292425i | \(-0.0944621\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.41671 | −0.260018 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0363981 | 0.00147251 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 31.3208i | − | 1.26504i | −0.774545 | − | 0.632518i | \(-0.782021\pi\) | ||
0.774545 | − | 0.632518i | \(-0.217979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.58528 | − | 9.20156i | 0.346192 | − | 0.371043i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.0998i | 0.688411i | 0.938894 | + | 0.344206i | \(0.111852\pi\) | ||||
−0.938894 | + | 0.344206i | \(0.888148\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.1087 | −1.29056 | −0.645278 | − | 0.763948i | \(-0.723259\pi\) | ||||
−0.645278 | + | 0.763948i | \(0.723259\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.79132 | −0.232398 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.287626i | − | 0.0115235i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7605 | + | 3.45235i | −0.990419 | + | 0.138094i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.18369i | 0.326825i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.27588 | 0.329981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4447 | −1.01294 | −0.506469 | − | 0.862258i | \(-0.669049\pi\) | ||||
−0.506469 | + | 0.862258i | \(0.669049\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 8.45635i | − | 0.336110i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.6386 | + | 23.1919i | −0.858701 | + | 0.920341i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.0316001i | − | 0.00125204i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.85892 | −0.231775 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −50.1762 | −1.98184 | −0.990920 | − | 0.134455i | \(-0.957071\pi\) | ||||
−0.990920 | + | 0.134455i | \(0.957071\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18.6849i | − | 0.736860i | −0.929655 | − | 0.368430i | \(-0.879895\pi\) | ||
0.929655 | − | 0.368430i | \(-0.120105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.07961 | + | 2.87335i | 0.121259 | + | 0.113138i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.6483i | 1.08697i | 0.839420 | + | 0.543483i | \(0.182895\pi\) | ||||
−0.839420 | + | 0.543483i | \(0.817105\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.8192 | −0.699466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.6737 | 0.575110 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 32.8195i | − | 1.28433i | −0.766568 | − | 0.642163i | \(-0.778037\pi\) | ||
0.766568 | − | 0.642163i | \(-0.221963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.9477 | − | 15.8126i | −0.662200 | − | 0.617849i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.3918i | 0.600492i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9909 | 0.856642 | 0.428321 | − | 0.903627i | \(-0.359105\pi\) | ||||
0.428321 | + | 0.903627i | \(0.359105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.8094 | −1.70399 | −0.851995 | − | 0.523550i | \(-0.824607\pi\) | ||||
−0.851995 | + | 0.523550i | \(0.824607\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 0.00584618i | − | 0.000227047i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −31.5269 | + | 33.7900i | −1.22256 | + | 1.31032i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.6668i | − | 0.413021i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.8779 | 1.07782 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0468 | 0.465061 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.5926i | − | 0.601051i | −0.953774 | − | 0.300526i | \(-0.902838\pi\) | ||
0.953774 | − | 0.300526i | \(-0.0971621\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.98801 | − | 0.346064i | 0.191989 | − | 0.0133200i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.15504i | 0.236558i | 0.992980 | + | 0.118279i | \(0.0377376\pi\) | ||||
−0.992980 | + | 0.118279i | \(0.962262\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.8293 | 1.45175 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0632 | −0.462263 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 46.6388i | − | 1.78459i | −0.451457 | − | 0.892293i | \(-0.649096\pi\) | ||
0.451457 | − | 0.892293i | \(-0.350904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.6707 | − | 13.5803i | 0.484124 | − | 0.518876i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 24.5262i | − | 0.935735i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0719067 | −0.00273943 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.8639 | −1.02195 | −0.510975 | − | 0.859595i | \(-0.670716\pi\) | ||||
−0.510975 | + | 0.859595i | \(0.670716\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.80589i | 0.182561i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.7811 | − | 21.2553i | −0.864137 | − | 0.806261i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.34876i | 0.202599i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.69308 | 0.366626 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.9337 | 0.564037 | 0.282019 | − | 0.959409i | \(-0.408996\pi\) | ||||
0.282019 | + | 0.959409i | \(0.408996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 51.6596i | 1.94838i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.67390 | − | 9.02599i | −0.364340 | − | 0.339938i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 42.7416i | − | 1.60746i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.23386 | −0.159006 | −0.0795030 | − | 0.996835i | \(-0.525333\pi\) | ||||
−0.0795030 | + | 0.996835i | \(0.525333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.34143 | −0.275325 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.3929i | 0.913521i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0129447 | + | 0.0138739i | −0.000484105 | + | 0.000518855i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 20.6671i | − | 0.771825i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.71665 | −0.175901 | −0.0879507 | − | 0.996125i | \(-0.528032\pi\) | ||||
−0.0879507 | + | 0.996125i | \(0.528032\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.1598 | −1.08597 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 27.1359i | − | 1.00920i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.637403 | + | 9.18722i | 0.0236725 | + | 0.341205i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.54853i | 0.168695i | 0.996436 | + | 0.0843477i | \(0.0268807\pi\) | ||||
−0.996436 | + | 0.0843477i | \(0.973119\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.79014 | −0.0662106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11.8615i | − | 0.438114i | −0.975712 | − | 0.219057i | \(-0.929702\pi\) | ||
0.975712 | − | 0.219057i | \(-0.0702980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.83618 | + | 8.39869i | −0.289042 | + | 0.309790i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.37949i | 0.0508142i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.2083 | 0.816946 | 0.408473 | − | 0.912770i | \(-0.366061\pi\) | ||||
0.408473 | + | 0.912770i | \(0.366061\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0364930 | 0.00134060 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 29.7672i | − | 1.09205i | −0.837768 | − | 0.546027i | \(-0.816140\pi\) | ||
0.837768 | − | 0.546027i | \(-0.183860\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.8676 | − | 21.3360i | −0.837802 | − | 0.781690i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 17.1852i | − | 0.628775i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.8490 | 1.20028 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9738 | −0.692363 | −0.346182 | − | 0.938168i | \(-0.612522\pi\) | ||||
−0.346182 | + | 0.938168i | \(0.612522\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 12.0570i | − | 0.439380i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.4693 | − | 29.3617i | −1.14529 | − | 1.06858i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.59503i | 0.130664i | 0.997864 | + | 0.0653319i | \(0.0208106\pi\) | ||||
−0.997864 | + | 0.0653319i | \(0.979189\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.98907 | −0.289985 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.3749 | 1.57234 | 0.786169 | − | 0.618012i | \(-0.212062\pi\) | ||||
0.786169 | + | 0.618012i | \(0.212062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 17.8322i | − | 0.645567i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.44974 | + | 1.55380i | −0.0524153 | + | 0.0561778i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.0794601i | 0.00286914i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.2888 | −1.20042 | −0.600212 | − | 0.799841i | \(-0.704917\pi\) | ||||
−0.600212 | + | 0.799841i | \(0.704917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.53277 | 0.343314 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.75564i | 0.314918i | 0.987525 | + | 0.157459i | \(0.0503303\pi\) | ||||
−0.987525 | + | 0.157459i | \(0.949670\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.45761 | − | 21.0094i | −0.0523590 | − | 0.754678i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.3372i | 1.08834i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.3880 | −1.19625 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.08231 | −0.289208 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.84186i | − | 0.0658227i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.9962 | − | 17.1445i | 0.570929 | − | 0.611912i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.5156i | 1.26600i | 0.774154 | + | 0.632998i | \(0.218176\pi\) | ||||
−0.774154 | + | 0.632998i | \(0.781824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.5536 | 0.589325 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.5188 | 1.83180 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.0537194i | − | 0.00190763i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.1114 | + | 17.8314i | 0.677812 | + | 0.632415i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 19.8606i | − | 0.703500i | −0.936094 | − | 0.351750i | \(-0.885587\pi\) | ||
0.936094 | − | 0.351750i | \(-0.114413\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.62332 | 0.198939 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.0825605 | 0.00291713 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.2328i | 0.749291i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.9864 | − | 30.7772i | −1.16262 | − | 1.08475i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.03378i | 0.247601i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.1079 | 1.86717 | 0.933587 | − | 0.358352i | \(-0.116661\pi\) | ||||
0.933587 | + | 0.358352i | \(0.116661\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.45248 | 0.121233 | 0.0606166 | − | 0.998161i | \(-0.480693\pi\) | ||||
0.0606166 | + | 0.998161i | \(0.480693\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.8273i | 0.765516i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.5546 | − | 12.3841i | 0.404742 | − | 0.433795i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 11.1744i | − | 0.390942i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0214306 | 0.000748846 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.4174 | 1.65488 | 0.827439 | − | 0.561556i | \(-0.189797\pi\) | ||||
0.827439 | + | 0.561556i | \(0.189797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.81465i | 0.0632546i | 0.999500 | + | 0.0316273i | \(0.0100690\pi\) | ||||
−0.999500 | + | 0.0316273i | \(0.989931\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.88091 | − | 0.477392i | 0.239562 | − | 0.0166207i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 26.7154i | − | 0.928985i | −0.885577 | − | 0.464492i | \(-0.846237\pi\) | ||
0.885577 | − | 0.464492i | \(-0.153763\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.0126 | −1.25077 | −0.625384 | − | 0.780317i | \(-0.715058\pi\) | ||||
−0.625384 | + | 0.780317i | \(0.715058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.8080 | −0.929961 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.88206i | − | 0.169153i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.1607 | + | 28.0386i | −0.905329 | + | 0.970317i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.21197i | 0.145587i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.88016 | −0.0994342 | −0.0497171 | − | 0.998763i | \(-0.515832\pi\) | ||||
−0.0497171 | + | 0.998763i | \(0.515832\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6075 | −0.883019 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 27.3824i | − | 0.943101i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.2542 | − | 19.8307i | −0.731166 | − | 0.682196i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 31.6923i | − | 1.08896i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.36562 | 0.287107 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.4311 | −1.72875 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.2580i | 0.933297i | 0.884443 | + | 0.466648i | \(0.154539\pi\) | ||||
−0.884443 | + | 0.466648i | \(0.845461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.69913 | − | 9.04953i | −0.331703 | − | 0.309487i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 26.1104i | − | 0.891916i | −0.895054 | − | 0.445958i | \(-0.852863\pi\) | ||
0.895054 | − | 0.445958i | \(-0.147137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.32404 | 0.181654 | 0.0908270 | − | 0.995867i | \(-0.471049\pi\) | ||||
0.0908270 | + | 0.995867i | \(0.471049\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.6072 | −0.668211 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.0033i | − | 0.408596i | −0.978909 | − | 0.204298i | \(-0.934509\pi\) | ||
0.978909 | − | 0.204298i | \(-0.0654911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.4088 | + | 17.5867i | −0.557917 | + | 0.597966i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.0968i | 0.546676i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.1274 | −0.343550 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.00615147 | 0.000208435 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.8586i | 0.367507i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.2500 | + | 24.5369i | 1.02264 | + | 0.829500i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.18961i | 0.209008i | 0.994524 | + | 0.104504i | \(0.0333255\pi\) | ||||
−0.994524 | + | 0.104504i | \(0.966674\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.9803 | −0.471543 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.6288 | −0.425474 | −0.212737 | − | 0.977110i | \(-0.568238\pi\) | ||||
−0.212737 | + | 0.977110i | \(0.568238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.1877i | 1.55434i | 0.629291 | + | 0.777170i | \(0.283346\pi\) | ||||
−0.629291 | + | 0.777170i | \(0.716654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.7045 | − | 21.1190i | 0.662360 | − | 0.709906i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.1189i | 0.742682i | 0.928497 | + | 0.371341i | \(0.121102\pi\) | ||||
−0.928497 | + | 0.371341i | \(0.878898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.4184 | 1.65744 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.37949 | −0.0462147 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.1019i | 1.17464i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.0597 | − | 37.3767i | −1.33905 | − | 1.24936i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0356251i | 0.00118949i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.75787 | −0.258739 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.1092 | −0.370102 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 6.56219i | − | 0.218376i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.765033 | − | 0.713794i | −0.0254305 | − | 0.0237273i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.7759i | 0.424217i | 0.977246 | + | 0.212108i | \(0.0680330\pi\) | ||||
−0.977246 | + | 0.212108i | \(0.931967\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.2686 | 0.406924 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.19007 | −0.105692 | −0.0528459 | − | 0.998603i | \(-0.516829\pi\) | ||||
−0.0528459 | + | 0.998603i | \(0.516829\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.7069i | − | 0.784583i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.3213 | + | 14.2776i | −0.440390 | + | 0.472002i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.1130i | 1.19256i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.0087 | 0.890935 | 0.445468 | − | 0.895298i | \(-0.353037\pi\) | ||||
0.445468 | + | 0.895298i | \(0.353037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.9185 | −0.590434 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0360409i | 0.00118630i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.4358 | − | 3.01354i | 1.42816 | − | 0.0990847i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 8.37006i | − | 0.274909i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.4873 | −1.39396 | −0.696981 | − | 0.717089i | \(-0.745474\pi\) | ||||
−0.696981 | + | 0.717089i | \(0.745474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.4747 | 0.998769 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.6785i | 0.611506i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.99990 | + | 2.14345i | −0.0654036 | + | 0.0700984i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.3512i | 1.25288i | 0.779470 | + | 0.626440i | \(0.215489\pi\) | ||||
−0.779470 | + | 0.626440i | \(0.784511\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.32650 | −0.304359 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.24423 | −0.0405607 | −0.0202803 | − | 0.999794i | \(-0.506456\pi\) | ||||
−0.0202803 | + | 0.999794i | \(0.506456\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 32.5940i | − | 1.06141i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.69584 | − | 5.31436i | −0.185286 | − | 0.172876i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.1202i | 0.393853i | 0.980418 | + | 0.196926i | \(0.0630960\pi\) | ||||
−0.980418 | + | 0.196926i | \(0.936904\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0946822 | 0.00307352 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.6307 | 0.344724 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.9713i | 0.452576i | 0.974060 | + | 0.226288i | \(0.0726591\pi\) | ||||
−0.974060 | + | 0.226288i | \(0.927341\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.05619 | + | 3.78453i | 0.131255 | + | 0.122465i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 2.54083i | − | 0.0821333i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.9376 | −0.934443 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.2593 | −0.427719 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.42903i | 0.303846i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37.2513 | + | 39.9253i | −1.19916 | + | 1.28524i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.52975i | − | 0.242140i | −0.992644 | − | 0.121070i | \(-0.961367\pi\) | ||
0.992644 | − | 0.121070i | \(-0.0386326\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.63799 | 0.181118 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.60699 | 0.244120 | 0.122060 | − | 0.992523i | \(-0.461050\pi\) | ||||
0.122060 | + | 0.992523i | \(0.461050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.5432i | 1.55622i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.00212880 | − | 0.0306836i | −6.81763e−5 | − | 0.000982661i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 16.8460i | − | 0.538952i | −0.963007 | − | 0.269476i | \(-0.913149\pi\) | ||
0.963007 | − | 0.269476i | \(-0.0868506\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.113891 | 0.00363998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.11856 | 0.163423 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 12.3613i | − | 0.394263i | −0.980377 | − | 0.197132i | \(-0.936837\pi\) | ||
0.980377 | − | 0.197132i | \(-0.0631627\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.4157 | + | 40.1015i | −1.19216 | + | 1.27774i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.6137i | 0.656140i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.9086 | 0.346875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.4738 | 1.31746 | 0.658729 | − | 0.752380i | \(-0.271094\pi\) | ||||
0.658729 | + | 0.752380i | \(0.271094\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.0440326i | 0.00139733i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.2063 | − | 31.9153i | −1.08441 | − | 1.01178i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 17.8188i | − | 0.564328i | −0.959366 | − | 0.282164i | \(-0.908948\pi\) | ||
0.959366 | − | 0.282164i | \(-0.0910523\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.70804 | −0.275510 |
(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 | 4020.2.g.b.1609.16 | yes | 24 | |
5.4 | even | 2 | inner | 4020.2.g.b.1609.4 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.b.1609.4 | ✓ | 24 | 5.4 | even | 2 | inner | |
4020.2.g.b.1609.16 | yes | 24 | 1.1 | even | 1 | trivial |