Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(149,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.08720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.149 |
Dual form | 150.3.b.a.149.2 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −2.82843 | − | 1.00000i | −0.942809 | − | 0.333333i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.00000 | + | 1.41421i | 0.666667 | + | 0.235702i | ||||
\(7\) | 7.00000i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 8.48528i | − | 0.771389i | −0.922627 | − | 0.385695i | \(-0.873962\pi\) | ||
0.922627 | − | 0.385695i | \(-0.126038\pi\) | |||||||
\(12\) | −5.65685 | − | 2.00000i | −0.471405 | − | 0.166667i | ||||
\(13\) | − | 25.0000i | − | 1.92308i | −0.274670 | − | 0.961538i | \(-0.588569\pi\) | ||
0.274670 | − | 0.961538i | \(-0.411431\pi\) | |||||||
\(14\) | − | 9.89949i | − | 0.707107i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 25.4558 | 1.49740 | 0.748701 | − | 0.662908i | \(-0.230678\pi\) | ||||
0.748701 | + | 0.662908i | \(0.230678\pi\) | |||||||
\(18\) | −9.89949 | − | 8.00000i | −0.549972 | − | 0.444444i | ||||
\(19\) | 7.00000 | 0.368421 | 0.184211 | − | 0.982887i | \(-0.441027\pi\) | ||||
0.184211 | + | 0.982887i | \(0.441027\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.00000 | − | 19.7990i | 0.333333 | − | 0.942809i | ||||
\(22\) | 12.0000i | 0.545455i | ||||||||
\(23\) | 25.4558 | 1.10678 | 0.553388 | − | 0.832924i | \(-0.313335\pi\) | ||||
0.553388 | + | 0.832924i | \(0.313335\pi\) | |||||||
\(24\) | 8.00000 | + | 2.82843i | 0.333333 | + | 0.117851i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 35.3553i | 1.35982i | ||||||||
\(27\) | −14.1421 | − | 23.0000i | −0.523783 | − | 0.851852i | ||||
\(28\) | 14.0000i | 0.500000i | ||||||||
\(29\) | − | 42.4264i | − | 1.46298i | −0.681852 | − | 0.731490i | \(-0.738825\pi\) | ||
0.681852 | − | 0.731490i | \(-0.261175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −0.225806 | −0.112903 | − | 0.993606i | \(-0.536015\pi\) | ||||
−0.112903 | + | 0.993606i | \(0.536015\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | −8.48528 | + | 24.0000i | −0.257130 | + | 0.727273i | ||||
\(34\) | −36.0000 | −1.05882 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 14.0000 | + | 11.3137i | 0.388889 | + | 0.314270i | ||||
\(37\) | − | 2.00000i | − | 0.0540541i | −0.999635 | − | 0.0270270i | \(-0.991396\pi\) | ||
0.999635 | − | 0.0270270i | \(-0.00860402\pi\) | |||||||
\(38\) | −9.89949 | −0.260513 | ||||||||
\(39\) | −25.0000 | + | 70.7107i | −0.641026 | + | 1.81309i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.48528i | 0.206958i | 0.994632 | + | 0.103479i | \(0.0329975\pi\) | ||||
−0.994632 | + | 0.103479i | \(0.967003\pi\) | |||||||
\(42\) | −9.89949 | + | 28.0000i | −0.235702 | + | 0.666667i | ||||
\(43\) | 41.0000i | 0.953488i | 0.879042 | + | 0.476744i | \(0.158183\pi\) | ||||
−0.879042 | + | 0.476744i | \(0.841817\pi\) | |||||||
\(44\) | − | 16.9706i | − | 0.385695i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −36.0000 | −0.782609 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −11.3137 | − | 4.00000i | −0.235702 | − | 0.0833333i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −72.0000 | − | 25.4558i | −1.41176 | − | 0.499134i | ||||
\(52\) | − | 50.0000i | − | 0.961538i | ||||||
\(53\) | 59.3970 | 1.12070 | 0.560349 | − | 0.828257i | \(-0.310667\pi\) | ||||
0.560349 | + | 0.828257i | \(0.310667\pi\) | |||||||
\(54\) | 20.0000 | + | 32.5269i | 0.370370 | + | 0.602350i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 19.7990i | − | 0.353553i | ||||||
\(57\) | −19.7990 | − | 7.00000i | −0.347351 | − | 0.122807i | ||||
\(58\) | 60.0000i | 1.03448i | ||||||||
\(59\) | 33.9411i | 0.575273i | 0.957740 | + | 0.287637i | \(0.0928695\pi\) | ||||
−0.957740 | + | 0.287637i | \(0.907130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.0163934 | −0.00819672 | − | 0.999966i | \(-0.502609\pi\) | ||||
−0.00819672 | + | 0.999966i | \(0.502609\pi\) | |||||||
\(62\) | 9.89949 | 0.159669 | ||||||||
\(63\) | −39.5980 | + | 49.0000i | −0.628539 | + | 0.777778i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.0000 | − | 33.9411i | 0.181818 | − | 0.514259i | ||||
\(67\) | − | 17.0000i | − | 0.253731i | −0.991920 | − | 0.126866i | \(-0.959508\pi\) | ||
0.991920 | − | 0.126866i | \(-0.0404917\pi\) | |||||||
\(68\) | 50.9117 | 0.748701 | ||||||||
\(69\) | −72.0000 | − | 25.4558i | −1.04348 | − | 0.368925i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42.4264i | 0.597555i | 0.954323 | + | 0.298778i | \(0.0965788\pi\) | ||||
−0.954323 | + | 0.298778i | \(0.903421\pi\) | |||||||
\(72\) | −19.7990 | − | 16.0000i | −0.274986 | − | 0.222222i | ||||
\(73\) | − | 70.0000i | − | 0.958904i | −0.877568 | − | 0.479452i | \(-0.840835\pi\) | ||
0.877568 | − | 0.479452i | \(-0.159165\pi\) | |||||||
\(74\) | 2.82843i | 0.0382220i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.0000 | 0.184211 | ||||||||
\(77\) | 59.3970 | 0.771389 | ||||||||
\(78\) | 35.3553 | − | 100.000i | 0.453274 | − | 1.28205i | ||||
\(79\) | 58.0000 | 0.734177 | 0.367089 | − | 0.930186i | \(-0.380355\pi\) | ||||
0.367089 | + | 0.930186i | \(0.380355\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.0000 | + | 79.1960i | 0.209877 | + | 0.977728i | ||||
\(82\) | − | 12.0000i | − | 0.146341i | ||||||
\(83\) | −118.794 | −1.43125 | −0.715626 | − | 0.698484i | \(-0.753859\pi\) | ||||
−0.715626 | + | 0.698484i | \(0.753859\pi\) | |||||||
\(84\) | 14.0000 | − | 39.5980i | 0.166667 | − | 0.471405i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 57.9828i | − | 0.674218i | ||||||
\(87\) | −42.4264 | + | 120.000i | −0.487660 | + | 1.37931i | ||||
\(88\) | 24.0000i | 0.272727i | ||||||||
\(89\) | − | 135.765i | − | 1.52544i | −0.646727 | − | 0.762722i | \(-0.723863\pi\) | ||
0.646727 | − | 0.762722i | \(-0.276137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 175.000 | 1.92308 | ||||||||
\(92\) | 50.9117 | 0.553388 | ||||||||
\(93\) | 19.7990 | + | 7.00000i | 0.212892 | + | 0.0752688i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 16.0000 | + | 5.65685i | 0.166667 | + | 0.0589256i | ||||
\(97\) | 49.0000i | 0.505155i | 0.967577 | + | 0.252577i | \(0.0812782\pi\) | ||||
−0.967577 | + | 0.252577i | \(0.918722\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 48.0000 | − | 59.3970i | 0.484848 | − | 0.599969i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 59.3970i | 0.588089i | 0.955792 | + | 0.294044i | \(0.0950014\pi\) | ||||
−0.955792 | + | 0.294044i | \(0.904999\pi\) | |||||||
\(102\) | 101.823 | + | 36.0000i | 0.998268 | + | 0.352941i | ||||
\(103\) | − | 154.000i | − | 1.49515i | −0.664180 | − | 0.747573i | \(-0.731219\pi\) | ||
0.664180 | − | 0.747573i | \(-0.268781\pi\) | |||||||
\(104\) | 70.7107i | 0.679910i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −84.0000 | −0.792453 | ||||||||
\(107\) | −178.191 | −1.66534 | −0.832668 | − | 0.553773i | \(-0.813188\pi\) | ||||
−0.832668 | + | 0.553773i | \(0.813188\pi\) | |||||||
\(108\) | −28.2843 | − | 46.0000i | −0.261891 | − | 0.425926i | ||||
\(109\) | 25.0000 | 0.229358 | 0.114679 | − | 0.993403i | \(-0.463416\pi\) | ||||
0.114679 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | + | 5.65685i | −0.0180180 | + | 0.0509627i | ||||
\(112\) | 28.0000i | 0.250000i | ||||||||
\(113\) | −16.9706 | −0.150182 | −0.0750910 | − | 0.997177i | \(-0.523925\pi\) | ||||
−0.0750910 | + | 0.997177i | \(0.523925\pi\) | |||||||
\(114\) | 28.0000 | + | 9.89949i | 0.245614 | + | 0.0868377i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 84.8528i | − | 0.731490i | ||||||
\(117\) | 141.421 | − | 175.000i | 1.20873 | − | 1.49573i | ||||
\(118\) | − | 48.0000i | − | 0.406780i | ||||||
\(119\) | 178.191i | 1.49740i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000 | 0.404959 | ||||||||
\(122\) | 1.41421 | 0.0115919 | ||||||||
\(123\) | 8.48528 | − | 24.0000i | 0.0689860 | − | 0.195122i | ||||
\(124\) | −14.0000 | −0.112903 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 56.0000 | − | 69.2965i | 0.444444 | − | 0.549972i | ||||
\(127\) | 34.0000i | 0.267717i | 0.991000 | + | 0.133858i | \(0.0427367\pi\) | ||||
−0.991000 | + | 0.133858i | \(0.957263\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 41.0000 | − | 115.966i | 0.317829 | − | 0.898957i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 195.161i | − | 1.48978i | −0.667186 | − | 0.744891i | \(-0.732501\pi\) | ||
0.667186 | − | 0.744891i | \(-0.267499\pi\) | |||||||
\(132\) | −16.9706 | + | 48.0000i | −0.128565 | + | 0.363636i | ||||
\(133\) | 49.0000i | 0.368421i | ||||||||
\(134\) | 24.0416i | 0.179415i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −72.0000 | −0.529412 | ||||||||
\(137\) | −118.794 | −0.867109 | −0.433555 | − | 0.901127i | \(-0.642741\pi\) | ||||
−0.433555 | + | 0.901127i | \(0.642741\pi\) | |||||||
\(138\) | 101.823 | + | 36.0000i | 0.737851 | + | 0.260870i | ||||
\(139\) | 154.000 | 1.10791 | 0.553957 | − | 0.832545i | \(-0.313117\pi\) | ||||
0.553957 | + | 0.832545i | \(0.313117\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 60.0000i | − | 0.422535i | ||||||
\(143\) | −212.132 | −1.48344 | ||||||||
\(144\) | 28.0000 | + | 22.6274i | 0.194444 | + | 0.157135i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 98.9949i | 0.678048i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 4.00000i | − | 0.0270270i | ||||||
\(149\) | 152.735i | 1.02507i | 0.858667 | + | 0.512534i | \(0.171293\pi\) | ||||
−0.858667 | + | 0.512534i | \(0.828707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −199.000 | −1.31788 | −0.658940 | − | 0.752195i | \(-0.728995\pi\) | ||||
−0.658940 | + | 0.752195i | \(0.728995\pi\) | |||||||
\(152\) | −19.7990 | −0.130257 | ||||||||
\(153\) | 178.191 | + | 144.000i | 1.16465 | + | 0.941176i | ||||
\(154\) | −84.0000 | −0.545455 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −50.0000 | + | 141.421i | −0.320513 | + | 0.906547i | ||||
\(157\) | 145.000i | 0.923567i | 0.886993 | + | 0.461783i | \(0.152790\pi\) | ||||
−0.886993 | + | 0.461783i | \(0.847210\pi\) | |||||||
\(158\) | −82.0244 | −0.519142 | ||||||||
\(159\) | −168.000 | − | 59.3970i | −1.05660 | − | 0.373566i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 178.191i | 1.10678i | ||||||||
\(162\) | −24.0416 | − | 112.000i | −0.148405 | − | 0.691358i | ||||
\(163\) | 161.000i | 0.987730i | 0.869539 | + | 0.493865i | \(0.164416\pi\) | ||||
−0.869539 | + | 0.493865i | \(0.835584\pi\) | |||||||
\(164\) | 16.9706i | 0.103479i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 168.000 | 1.01205 | ||||||||
\(167\) | 110.309 | 0.660531 | 0.330265 | − | 0.943888i | \(-0.392862\pi\) | ||||
0.330265 | + | 0.943888i | \(0.392862\pi\) | |||||||
\(168\) | −19.7990 | + | 56.0000i | −0.117851 | + | 0.333333i | ||||
\(169\) | −456.000 | −2.69822 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 49.0000 | + | 39.5980i | 0.286550 | + | 0.231567i | ||||
\(172\) | 82.0000i | 0.476744i | ||||||||
\(173\) | 178.191 | 1.03001 | 0.515003 | − | 0.857189i | \(-0.327791\pi\) | ||||
0.515003 | + | 0.857189i | \(0.327791\pi\) | |||||||
\(174\) | 60.0000 | − | 169.706i | 0.344828 | − | 0.975320i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 33.9411i | − | 0.192847i | ||||||
\(177\) | 33.9411 | − | 96.0000i | 0.191758 | − | 0.542373i | ||||
\(178\) | 192.000i | 1.07865i | ||||||||
\(179\) | 118.794i | 0.663653i | 0.943340 | + | 0.331827i | \(0.107665\pi\) | ||||
−0.943340 | + | 0.331827i | \(0.892335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −217.000 | −1.19890 | −0.599448 | − | 0.800414i | \(-0.704613\pi\) | ||||
−0.599448 | + | 0.800414i | \(0.704613\pi\) | |||||||
\(182\) | −247.487 | −1.35982 | ||||||||
\(183\) | 2.82843 | + | 1.00000i | 0.0154559 | + | 0.00546448i | ||||
\(184\) | −72.0000 | −0.391304 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −28.0000 | − | 9.89949i | −0.150538 | − | 0.0532231i | ||||
\(187\) | − | 216.000i | − | 1.15508i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 161.000 | − | 98.9949i | 0.851852 | − | 0.523783i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 59.3970i | − | 0.310979i | −0.987838 | − | 0.155489i | \(-0.950305\pi\) | ||
0.987838 | − | 0.155489i | \(-0.0496955\pi\) | |||||||
\(192\) | −22.6274 | − | 8.00000i | −0.117851 | − | 0.0416667i | ||||
\(193\) | − | 25.0000i | − | 0.129534i | −0.997900 | − | 0.0647668i | \(-0.979370\pi\) | ||
0.997900 | − | 0.0647668i | \(-0.0206304\pi\) | |||||||
\(194\) | − | 69.2965i | − | 0.357198i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 135.765 | 0.689160 | 0.344580 | − | 0.938757i | \(-0.388021\pi\) | ||||
0.344580 | + | 0.938757i | \(0.388021\pi\) | |||||||
\(198\) | −67.8823 | + | 84.0000i | −0.342840 | + | 0.424242i | ||||
\(199\) | 103.000 | 0.517588 | 0.258794 | − | 0.965933i | \(-0.416675\pi\) | ||||
0.258794 | + | 0.965933i | \(0.416675\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.0000 | + | 48.0833i | −0.0845771 | + | 0.239220i | ||||
\(202\) | − | 84.0000i | − | 0.415842i | ||||||
\(203\) | 296.985 | 1.46298 | ||||||||
\(204\) | −144.000 | − | 50.9117i | −0.705882 | − | 0.249567i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 217.789i | 1.05723i | ||||||||
\(207\) | 178.191 | + | 144.000i | 0.860826 | + | 0.695652i | ||||
\(208\) | − | 100.000i | − | 0.480769i | ||||||
\(209\) | − | 59.3970i | − | 0.284196i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.00000 | −0.0331754 | −0.0165877 | − | 0.999862i | \(-0.505280\pi\) | ||||
−0.0165877 | + | 0.999862i | \(0.505280\pi\) | |||||||
\(212\) | 118.794 | 0.560349 | ||||||||
\(213\) | 42.4264 | − | 120.000i | 0.199185 | − | 0.563380i | ||||
\(214\) | 252.000 | 1.17757 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 40.0000 | + | 65.0538i | 0.185185 | + | 0.301175i | ||||
\(217\) | − | 49.0000i | − | 0.225806i | ||||||
\(218\) | −35.3553 | −0.162180 | ||||||||
\(219\) | −70.0000 | + | 197.990i | −0.319635 | + | 0.904063i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 636.396i | − | 2.87962i | ||||||
\(222\) | 2.82843 | − | 8.00000i | 0.0127407 | − | 0.0360360i | ||||
\(223\) | 161.000i | 0.721973i | 0.932571 | + | 0.360987i | \(0.117560\pi\) | ||||
−0.932571 | + | 0.360987i | \(0.882440\pi\) | |||||||
\(224\) | − | 39.5980i | − | 0.176777i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.0000 | 0.106195 | ||||||||
\(227\) | −59.3970 | −0.261661 | −0.130830 | − | 0.991405i | \(-0.541764\pi\) | ||||
−0.130830 | + | 0.991405i | \(0.541764\pi\) | |||||||
\(228\) | −39.5980 | − | 14.0000i | −0.173675 | − | 0.0614035i | ||||
\(229\) | 97.0000 | 0.423581 | 0.211790 | − | 0.977315i | \(-0.432071\pi\) | ||||
0.211790 | + | 0.977315i | \(0.432071\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −168.000 | − | 59.3970i | −0.727273 | − | 0.257130i | ||||
\(232\) | 120.000i | 0.517241i | ||||||||
\(233\) | −263.044 | −1.12894 | −0.564472 | − | 0.825453i | \(-0.690920\pi\) | ||||
−0.564472 | + | 0.825453i | \(0.690920\pi\) | |||||||
\(234\) | −200.000 | + | 247.487i | −0.854701 | + | 1.05764i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 67.8823i | 0.287637i | ||||||||
\(237\) | −164.049 | − | 58.0000i | −0.692189 | − | 0.244726i | ||||
\(238\) | − | 252.000i | − | 1.05882i | ||||||
\(239\) | − | 59.3970i | − | 0.248523i | −0.992250 | − | 0.124261i | \(-0.960344\pi\) | ||
0.992250 | − | 0.124261i | \(-0.0396562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 119.000 | 0.493776 | 0.246888 | − | 0.969044i | \(-0.420592\pi\) | ||||
0.246888 | + | 0.969044i | \(0.420592\pi\) | |||||||
\(242\) | −69.2965 | −0.286349 | ||||||||
\(243\) | 31.1127 | − | 241.000i | 0.128036 | − | 0.991770i | ||||
\(244\) | −2.00000 | −0.00819672 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.0000 | + | 33.9411i | −0.0487805 | + | 0.137972i | ||||
\(247\) | − | 175.000i | − | 0.708502i | ||||||
\(248\) | 19.7990 | 0.0798346 | ||||||||
\(249\) | 336.000 | + | 118.794i | 1.34940 | + | 0.477084i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 288.500i | 1.14940i | 0.818364 | + | 0.574700i | \(0.194881\pi\) | ||||
−0.818364 | + | 0.574700i | \(0.805119\pi\) | |||||||
\(252\) | −79.1960 | + | 98.0000i | −0.314270 | + | 0.388889i | ||||
\(253\) | − | 216.000i | − | 0.853755i | ||||||
\(254\) | − | 48.0833i | − | 0.189304i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 118.794 | 0.462233 | 0.231117 | − | 0.972926i | \(-0.425762\pi\) | ||||
0.231117 | + | 0.972926i | \(0.425762\pi\) | |||||||
\(258\) | −57.9828 | + | 164.000i | −0.224739 | + | 0.635659i | ||||
\(259\) | 14.0000 | 0.0540541 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 240.000 | − | 296.985i | 0.919540 | − | 1.13787i | ||||
\(262\) | 276.000i | 1.05344i | ||||||||
\(263\) | 8.48528 | 0.0322634 | 0.0161317 | − | 0.999870i | \(-0.494865\pi\) | ||||
0.0161317 | + | 0.999870i | \(0.494865\pi\) | |||||||
\(264\) | 24.0000 | − | 67.8823i | 0.0909091 | − | 0.257130i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 69.2965i | − | 0.260513i | ||||||
\(267\) | −135.765 | + | 384.000i | −0.508481 | + | 1.43820i | ||||
\(268\) | − | 34.0000i | − | 0.126866i | ||||||
\(269\) | − | 59.3970i | − | 0.220807i | −0.993887 | − | 0.110403i | \(-0.964786\pi\) | ||
0.993887 | − | 0.110403i | \(-0.0352142\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 470.000 | 1.73432 | 0.867159 | − | 0.498032i | \(-0.165944\pi\) | ||||
0.867159 | + | 0.498032i | \(0.165944\pi\) | |||||||
\(272\) | 101.823 | 0.374351 | ||||||||
\(273\) | −494.975 | − | 175.000i | −1.81309 | − | 0.641026i | ||||
\(274\) | 168.000 | 0.613139 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −144.000 | − | 50.9117i | −0.521739 | − | 0.184463i | ||||
\(277\) | 217.000i | 0.783394i | 0.920094 | + | 0.391697i | \(0.128112\pi\) | ||||
−0.920094 | + | 0.391697i | \(0.871888\pi\) | |||||||
\(278\) | −217.789 | −0.783413 | ||||||||
\(279\) | −49.0000 | − | 39.5980i | −0.175627 | − | 0.141928i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 517.602i | 1.84200i | 0.389562 | + | 0.921000i | \(0.372626\pi\) | ||||
−0.389562 | + | 0.921000i | \(0.627374\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 65.0000i | 0.229682i | 0.993384 | + | 0.114841i | \(0.0366359\pi\) | ||||
−0.993384 | + | 0.114841i | \(0.963364\pi\) | |||||||
\(284\) | 84.8528i | 0.298778i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 300.000 | 1.04895 | ||||||||
\(287\) | −59.3970 | −0.206958 | ||||||||
\(288\) | −39.5980 | − | 32.0000i | −0.137493 | − | 0.111111i | ||||
\(289\) | 359.000 | 1.24221 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 49.0000 | − | 138.593i | 0.168385 | − | 0.476264i | ||||
\(292\) | − | 140.000i | − | 0.479452i | ||||||
\(293\) | 169.706 | 0.579200 | 0.289600 | − | 0.957148i | \(-0.406478\pi\) | ||||
0.289600 | + | 0.957148i | \(0.406478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.65685i | 0.0191110i | ||||||||
\(297\) | −195.161 | + | 120.000i | −0.657109 | + | 0.404040i | ||||
\(298\) | − | 216.000i | − | 0.724832i | ||||||
\(299\) | − | 636.396i | − | 2.12842i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −287.000 | −0.953488 | ||||||||
\(302\) | 281.428 | 0.931882 | ||||||||
\(303\) | 59.3970 | − | 168.000i | 0.196030 | − | 0.554455i | ||||
\(304\) | 28.0000 | 0.0921053 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −252.000 | − | 203.647i | −0.823529 | − | 0.665512i | ||||
\(307\) | − | 521.000i | − | 1.69707i | −0.529141 | − | 0.848534i | \(-0.677486\pi\) | ||
0.529141 | − | 0.848534i | \(-0.322514\pi\) | |||||||
\(308\) | 118.794 | 0.385695 | ||||||||
\(309\) | −154.000 | + | 435.578i | −0.498382 | + | 1.40964i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 33.9411i | − | 0.109135i | −0.998510 | − | 0.0545677i | \(-0.982622\pi\) | ||
0.998510 | − | 0.0545677i | \(-0.0173781\pi\) | |||||||
\(312\) | 70.7107 | − | 200.000i | 0.226637 | − | 0.641026i | ||||
\(313\) | 119.000i | 0.380192i | 0.981766 | + | 0.190096i | \(0.0608799\pi\) | ||||
−0.981766 | + | 0.190096i | \(0.939120\pi\) | |||||||
\(314\) | − | 205.061i | − | 0.653060i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 116.000 | 0.367089 | ||||||||
\(317\) | 152.735 | 0.481814 | 0.240907 | − | 0.970548i | \(-0.422555\pi\) | ||||
0.240907 | + | 0.970548i | \(0.422555\pi\) | |||||||
\(318\) | 237.588 | + | 84.0000i | 0.747132 | + | 0.264151i | ||||
\(319\) | −360.000 | −1.12853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 504.000 | + | 178.191i | 1.57009 | + | 0.555112i | ||||
\(322\) | − | 252.000i | − | 0.782609i | ||||||
\(323\) | 178.191 | 0.551675 | ||||||||
\(324\) | 34.0000 | + | 158.392i | 0.104938 | + | 0.488864i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 227.688i | − | 0.698431i | ||||||
\(327\) | −70.7107 | − | 25.0000i | −0.216241 | − | 0.0764526i | ||||
\(328\) | − | 24.0000i | − | 0.0731707i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −418.000 | −1.26284 | −0.631420 | − | 0.775441i | \(-0.717528\pi\) | ||||
−0.631420 | + | 0.775441i | \(0.717528\pi\) | |||||||
\(332\) | −237.588 | −0.715626 | ||||||||
\(333\) | 11.3137 | − | 14.0000i | 0.0339751 | − | 0.0420420i | ||||
\(334\) | −156.000 | −0.467066 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 28.0000 | − | 79.1960i | 0.0833333 | − | 0.235702i | ||||
\(337\) | 553.000i | 1.64095i | 0.571683 | + | 0.820475i | \(0.306291\pi\) | ||||
−0.571683 | + | 0.820475i | \(0.693709\pi\) | |||||||
\(338\) | 644.881 | 1.90793 | ||||||||
\(339\) | 48.0000 | + | 16.9706i | 0.141593 | + | 0.0500607i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 59.3970i | 0.174185i | ||||||||
\(342\) | −69.2965 | − | 56.0000i | −0.202621 | − | 0.163743i | ||||
\(343\) | 343.000i | 1.00000i | ||||||||
\(344\) | − | 115.966i | − | 0.337109i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −252.000 | −0.728324 | ||||||||
\(347\) | 644.881 | 1.85845 | 0.929224 | − | 0.369517i | \(-0.120477\pi\) | ||||
0.929224 | + | 0.369517i | \(0.120477\pi\) | |||||||
\(348\) | −84.8528 | + | 240.000i | −0.243830 | + | 0.689655i | ||||
\(349\) | −266.000 | −0.762178 | −0.381089 | − | 0.924538i | \(-0.624451\pi\) | ||||
−0.381089 | + | 0.924538i | \(0.624451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −575.000 | + | 353.553i | −1.63818 | + | 1.00727i | ||||
\(352\) | 48.0000i | 0.136364i | ||||||||
\(353\) | −415.779 | −1.17784 | −0.588922 | − | 0.808190i | \(-0.700447\pi\) | ||||
−0.588922 | + | 0.808190i | \(0.700447\pi\) | |||||||
\(354\) | −48.0000 | + | 135.765i | −0.135593 | + | 0.383516i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 271.529i | − | 0.762722i | ||||||
\(357\) | 178.191 | − | 504.000i | 0.499134 | − | 1.41176i | ||||
\(358\) | − | 168.000i | − | 0.469274i | ||||||
\(359\) | − | 330.926i | − | 0.921799i | −0.887452 | − | 0.460900i | \(-0.847527\pi\) | ||
0.887452 | − | 0.460900i | \(-0.152473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −312.000 | −0.864266 | ||||||||
\(362\) | 306.884 | 0.847747 | ||||||||
\(363\) | −138.593 | − | 49.0000i | −0.381799 | − | 0.134986i | ||||
\(364\) | 350.000 | 0.961538 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.00000 | − | 1.41421i | −0.0109290 | − | 0.00386397i | ||||
\(367\) | 103.000i | 0.280654i | 0.990105 | + | 0.140327i | \(0.0448154\pi\) | ||||
−0.990105 | + | 0.140327i | \(0.955185\pi\) | |||||||
\(368\) | 101.823 | 0.276694 | ||||||||
\(369\) | −48.0000 | + | 59.3970i | −0.130081 | + | 0.160967i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 415.779i | 1.12070i | ||||||||
\(372\) | 39.5980 | + | 14.0000i | 0.106446 | + | 0.0376344i | ||||
\(373\) | 359.000i | 0.962466i | 0.876593 | + | 0.481233i | \(0.159811\pi\) | ||||
−0.876593 | + | 0.481233i | \(0.840189\pi\) | |||||||
\(374\) | 305.470i | 0.816765i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1060.66 | −2.81342 | ||||||||
\(378\) | −227.688 | + | 140.000i | −0.602350 | + | 0.370370i | ||||
\(379\) | −377.000 | −0.994723 | −0.497361 | − | 0.867543i | \(-0.665698\pi\) | ||||
−0.497361 | + | 0.867543i | \(0.665698\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.0000 | − | 96.1665i | 0.0892388 | − | 0.252406i | ||||
\(382\) | 84.0000i | 0.219895i | ||||||||
\(383\) | 610.940 | 1.59514 | 0.797572 | − | 0.603224i | \(-0.206117\pi\) | ||||
0.797572 | + | 0.603224i | \(0.206117\pi\) | |||||||
\(384\) | 32.0000 | + | 11.3137i | 0.0833333 | + | 0.0294628i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 35.3553i | 0.0915941i | ||||||||
\(387\) | −231.931 | + | 287.000i | −0.599305 | + | 0.741602i | ||||
\(388\) | 98.0000i | 0.252577i | ||||||||
\(389\) | 347.897i | 0.894336i | 0.894450 | + | 0.447168i | \(0.147567\pi\) | ||||
−0.894450 | + | 0.447168i | \(0.852433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 648.000 | 1.65729 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −195.161 | + | 552.000i | −0.496594 | + | 1.40458i | ||||
\(394\) | −192.000 | −0.487310 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 96.0000 | − | 118.794i | 0.242424 | − | 0.299985i | ||||
\(397\) | − | 239.000i | − | 0.602015i | −0.953622 | − | 0.301008i | \(-0.902677\pi\) | ||
0.953622 | − | 0.301008i | \(-0.0973229\pi\) | |||||||
\(398\) | −145.664 | −0.365990 | ||||||||
\(399\) | 49.0000 | − | 138.593i | 0.122807 | − | 0.347351i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 93.3381i | − | 0.232763i | −0.993205 | − | 0.116382i | \(-0.962870\pi\) | ||
0.993205 | − | 0.116382i | \(-0.0371296\pi\) | |||||||
\(402\) | 24.0416 | − | 68.0000i | 0.0598051 | − | 0.169154i | ||||
\(403\) | 175.000i | 0.434243i | ||||||||
\(404\) | 118.794i | 0.294044i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −420.000 | −1.03448 | ||||||||
\(407\) | −16.9706 | −0.0416967 | ||||||||
\(408\) | 203.647 | + | 72.0000i | 0.499134 | + | 0.176471i | ||||
\(409\) | −455.000 | −1.11247 | −0.556235 | − | 0.831025i | \(-0.687754\pi\) | ||||
−0.556235 | + | 0.831025i | \(0.687754\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 336.000 | + | 118.794i | 0.817518 | + | 0.289036i | ||||
\(412\) | − | 308.000i | − | 0.747573i | ||||||
\(413\) | −237.588 | −0.575273 | ||||||||
\(414\) | −252.000 | − | 203.647i | −0.608696 | − | 0.491900i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 141.421i | 0.339955i | ||||||||
\(417\) | −435.578 | − | 154.000i | −1.04455 | − | 0.369305i | ||||
\(418\) | 84.0000i | 0.200957i | ||||||||
\(419\) | 296.985i | 0.708794i | 0.935095 | + | 0.354397i | \(0.115314\pi\) | ||||
−0.935095 | + | 0.354397i | \(0.884686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −526.000 | −1.24941 | −0.624703 | − | 0.780862i | \(-0.714780\pi\) | ||||
−0.624703 | + | 0.780862i | \(0.714780\pi\) | |||||||
\(422\) | 9.89949 | 0.0234585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −168.000 | −0.396226 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −60.0000 | + | 169.706i | −0.140845 | + | 0.398370i | ||||
\(427\) | − | 7.00000i | − | 0.0163934i | ||||||
\(428\) | −356.382 | −0.832668 | ||||||||
\(429\) | 600.000 | + | 212.132i | 1.39860 | + | 0.494480i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 280.014i | 0.649685i | 0.945768 | + | 0.324843i | \(0.105311\pi\) | ||||
−0.945768 | + | 0.324843i | \(0.894689\pi\) | |||||||
\(432\) | −56.5685 | − | 92.0000i | −0.130946 | − | 0.212963i | ||||
\(433\) | 119.000i | 0.274827i | 0.990514 | + | 0.137413i | \(0.0438789\pi\) | ||||
−0.990514 | + | 0.137413i | \(0.956121\pi\) | |||||||
\(434\) | 69.2965i | 0.159669i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 50.0000 | 0.114679 | ||||||||
\(437\) | 178.191 | 0.407760 | ||||||||
\(438\) | 98.9949 | − | 280.000i | 0.226016 | − | 0.639269i | ||||
\(439\) | 727.000 | 1.65604 | 0.828018 | − | 0.560701i | \(-0.189468\pi\) | ||||
0.828018 | + | 0.560701i | \(0.189468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 900.000i | 2.03620i | ||||||||
\(443\) | −526.087 | −1.18756 | −0.593778 | − | 0.804629i | \(-0.702364\pi\) | ||||
−0.593778 | + | 0.804629i | \(0.702364\pi\) | |||||||
\(444\) | −4.00000 | + | 11.3137i | −0.00900901 | + | 0.0254813i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 227.688i | − | 0.510512i | ||||||
\(447\) | 152.735 | − | 432.000i | 0.341689 | − | 0.966443i | ||||
\(448\) | 56.0000i | 0.125000i | ||||||||
\(449\) | 254.558i | 0.566945i | 0.958980 | + | 0.283473i | \(0.0914865\pi\) | ||||
−0.958980 | + | 0.283473i | \(0.908513\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 72.0000 | 0.159645 | ||||||||
\(452\) | −33.9411 | −0.0750910 | ||||||||
\(453\) | 562.857 | + | 199.000i | 1.24251 | + | 0.439294i | ||||
\(454\) | 84.0000 | 0.185022 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 56.0000 | + | 19.7990i | 0.122807 | + | 0.0434188i | ||||
\(457\) | 310.000i | 0.678337i | 0.940726 | + | 0.339168i | \(0.110146\pi\) | ||||
−0.940726 | + | 0.339168i | \(0.889854\pi\) | |||||||
\(458\) | −137.179 | −0.299517 | ||||||||
\(459\) | −360.000 | − | 585.484i | −0.784314 | − | 1.27557i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 721.249i | − | 1.56453i | −0.622945 | − | 0.782266i | \(-0.714064\pi\) | ||
0.622945 | − | 0.782266i | \(-0.285936\pi\) | |||||||
\(462\) | 237.588 | + | 84.0000i | 0.514259 | + | 0.181818i | ||||
\(463\) | − | 730.000i | − | 1.57667i | −0.615244 | − | 0.788337i | \(-0.710942\pi\) | ||
0.615244 | − | 0.788337i | \(-0.289058\pi\) | |||||||
\(464\) | − | 169.706i | − | 0.365745i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 372.000 | 0.798283 | ||||||||
\(467\) | 195.161 | 0.417905 | 0.208952 | − | 0.977926i | \(-0.432995\pi\) | ||||
0.208952 | + | 0.977926i | \(0.432995\pi\) | |||||||
\(468\) | 282.843 | − | 350.000i | 0.604365 | − | 0.747863i | ||||
\(469\) | 119.000 | 0.253731 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 145.000 | − | 410.122i | 0.307856 | − | 0.870747i | ||||
\(472\) | − | 96.0000i | − | 0.203390i | ||||||
\(473\) | 347.897 | 0.735511 | ||||||||
\(474\) | 232.000 | + | 82.0244i | 0.489451 | + | 0.173047i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 356.382i | 0.748701i | ||||||||
\(477\) | 415.779 | + | 336.000i | 0.871654 | + | 0.704403i | ||||
\(478\) | 84.0000i | 0.175732i | ||||||||
\(479\) | − | 390.323i | − | 0.814870i | −0.913234 | − | 0.407435i | \(-0.866423\pi\) | ||
0.913234 | − | 0.407435i | \(-0.133577\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −50.0000 | −0.103950 | ||||||||
\(482\) | −168.291 | −0.349152 | ||||||||
\(483\) | 178.191 | − | 504.000i | 0.368925 | − | 1.04348i | ||||
\(484\) | 98.0000 | 0.202479 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −44.0000 | + | 340.825i | −0.0905350 | + | 0.701287i | ||||
\(487\) | − | 473.000i | − | 0.971253i | −0.874167 | − | 0.485626i | \(-0.838592\pi\) | ||
0.874167 | − | 0.485626i | \(-0.161408\pi\) | |||||||
\(488\) | 2.82843 | 0.00579596 | ||||||||
\(489\) | 161.000 | − | 455.377i | 0.329243 | − | 0.931241i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 814.587i | − | 1.65904i | −0.558479 | − | 0.829518i | \(-0.688615\pi\) | ||
0.558479 | − | 0.829518i | \(-0.311385\pi\) | |||||||
\(492\) | 16.9706 | − | 48.0000i | 0.0344930 | − | 0.0975610i | ||||
\(493\) | − | 1080.00i | − | 2.19067i | ||||||
\(494\) | 247.487i | 0.500987i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.0000 | −0.0564516 | ||||||||
\(497\) | −296.985 | −0.597555 | ||||||||
\(498\) | −475.176 | − | 168.000i | −0.954168 | − | 0.337349i | ||||
\(499\) | 175.000 | 0.350701 | 0.175351 | − | 0.984506i | \(-0.443894\pi\) | ||||
0.175351 | + | 0.984506i | \(0.443894\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −312.000 | − | 110.309i | −0.622754 | − | 0.220177i | ||||
\(502\) | − | 408.000i | − | 0.812749i | ||||||
\(503\) | −347.897 | −0.691643 | −0.345822 | − | 0.938300i | \(-0.612400\pi\) | ||||
−0.345822 | + | 0.938300i | \(0.612400\pi\) | |||||||
\(504\) | 112.000 | − | 138.593i | 0.222222 | − | 0.274986i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 305.470i | 0.603696i | ||||||||
\(507\) | 1289.76 | + | 456.000i | 2.54391 | + | 0.899408i | ||||
\(508\) | 68.0000i | 0.133858i | ||||||||
\(509\) | 729.734i | 1.43366i | 0.697247 | + | 0.716831i | \(0.254408\pi\) | ||||
−0.697247 | + | 0.716831i | \(0.745592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 490.000 | 0.958904 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −98.9949 | − | 161.000i | −0.192973 | − | 0.313840i | ||||
\(514\) | −168.000 | −0.326848 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 82.0000 | − | 231.931i | 0.158915 | − | 0.449479i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −19.7990 | −0.0382220 | ||||||||
\(519\) | −504.000 | − | 178.191i | −0.971098 | − | 0.343335i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 568.514i | 1.09120i | 0.838047 | + | 0.545599i | \(0.183698\pi\) | ||||
−0.838047 | + | 0.545599i | \(0.816302\pi\) | |||||||
\(522\) | −339.411 | + | 420.000i | −0.650213 | + | 0.804598i | ||||
\(523\) | − | 175.000i | − | 0.334608i | −0.985905 | − | 0.167304i | \(-0.946494\pi\) | ||
0.985905 | − | 0.167304i | \(-0.0535061\pi\) | |||||||
\(524\) | − | 390.323i | − | 0.744891i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | −0.0228137 | ||||||||
\(527\) | −178.191 | −0.338123 | ||||||||
\(528\) | −33.9411 | + | 96.0000i | −0.0642824 | + | 0.181818i | ||||
\(529\) | 119.000 | 0.224953 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −192.000 | + | 237.588i | −0.361582 | + | 0.447435i | ||||
\(532\) | 98.0000i | 0.184211i | ||||||||
\(533\) | 212.132 | 0.397996 | ||||||||
\(534\) | 192.000 | − | 543.058i | 0.359551 | − | 1.01696i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 48.0833i | 0.0897076i | ||||||||
\(537\) | 118.794 | − | 336.000i | 0.221218 | − | 0.625698i | ||||
\(538\) | 84.0000i | 0.156134i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 863.000 | 1.59519 | 0.797597 | − | 0.603191i | \(-0.206104\pi\) | ||||
0.797597 | + | 0.603191i | \(0.206104\pi\) | |||||||
\(542\) | −664.680 | −1.22635 | ||||||||
\(543\) | 613.769 | + | 217.000i | 1.13033 | + | 0.399632i | ||||
\(544\) | −144.000 | −0.264706 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 700.000 | + | 247.487i | 1.28205 | + | 0.453274i | ||||
\(547\) | 778.000i | 1.42230i | 0.703039 | + | 0.711152i | \(0.251826\pi\) | ||||
−0.703039 | + | 0.711152i | \(0.748174\pi\) | |||||||
\(548\) | −237.588 | −0.433555 | ||||||||
\(549\) | −7.00000 | − | 5.65685i | −0.0127505 | − | 0.0103039i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 296.985i | − | 0.538992i | ||||||
\(552\) | 203.647 | + | 72.0000i | 0.368925 | + | 0.130435i | ||||
\(553\) | 406.000i | 0.734177i | ||||||||
\(554\) | − | 306.884i | − | 0.553943i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 308.000 | 0.553957 | ||||||||
\(557\) | 424.264 | 0.761695 | 0.380847 | − | 0.924638i | \(-0.375632\pi\) | ||||
0.380847 | + | 0.924638i | \(0.375632\pi\) | |||||||
\(558\) | 69.2965 | + | 56.0000i | 0.124187 | + | 0.100358i | ||||
\(559\) | 1025.00 | 1.83363 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −216.000 | + | 610.940i | −0.385027 | + | 1.08902i | ||||
\(562\) | − | 732.000i | − | 1.30249i | ||||||
\(563\) | −381.838 | −0.678220 | −0.339110 | − | 0.940747i | \(-0.610126\pi\) | ||||
−0.339110 | + | 0.940747i | \(0.610126\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 91.9239i | − | 0.162410i | ||||||
\(567\) | −554.372 | + | 119.000i | −0.977728 | + | 0.209877i | ||||
\(568\) | − | 120.000i | − | 0.211268i | ||||||
\(569\) | 381.838i | 0.671068i | 0.942028 | + | 0.335534i | \(0.108917\pi\) | ||||
−0.942028 | + | 0.335534i | \(0.891083\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −535.000 | −0.936953 | −0.468476 | − | 0.883476i | \(-0.655197\pi\) | ||||
−0.468476 | + | 0.883476i | \(0.655197\pi\) | |||||||
\(572\) | −424.264 | −0.741720 | ||||||||
\(573\) | −59.3970 | + | 168.000i | −0.103660 | + | 0.293194i | ||||
\(574\) | 84.0000 | 0.146341 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 56.0000 | + | 45.2548i | 0.0972222 | + | 0.0785674i | ||||
\(577\) | 49.0000i | 0.0849220i | 0.999098 | + | 0.0424610i | \(0.0135198\pi\) | ||||
−0.999098 | + | 0.0424610i | \(0.986480\pi\) | |||||||
\(578\) | −507.703 | −0.878378 | ||||||||
\(579\) | −25.0000 | + | 70.7107i | −0.0431779 | + | 0.122126i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 831.558i | − | 1.43125i | ||||||
\(582\) | −69.2965 | + | 196.000i | −0.119066 | + | 0.336770i | ||||
\(583\) | − | 504.000i | − | 0.864494i | ||||||
\(584\) | 197.990i | 0.339024i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −240.000 | −0.409556 | ||||||||
\(587\) | −415.779 | −0.708311 | −0.354156 | − | 0.935186i | \(-0.615232\pi\) | ||||
−0.354156 | + | 0.935186i | \(0.615232\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.0000 | −0.0831919 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −384.000 | − | 135.765i | −0.649746 | − | 0.229720i | ||||
\(592\) | − | 8.00000i | − | 0.0135135i | ||||||
\(593\) | −772.161 | −1.30213 | −0.651063 | − | 0.759024i | \(-0.725677\pi\) | ||||
−0.651063 | + | 0.759024i | \(0.725677\pi\) | |||||||
\(594\) | 276.000 | − | 169.706i | 0.464646 | − | 0.285700i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 305.470i | 0.512534i | ||||||||
\(597\) | −291.328 | − | 103.000i | −0.487987 | − | 0.172529i | ||||
\(598\) | 900.000i | 1.50502i | ||||||||
\(599\) | 644.881i | 1.07660i | 0.842754 | + | 0.538298i | \(0.180933\pi\) | ||||
−0.842754 | + | 0.538298i | \(0.819067\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 455.000 | 0.757072 | 0.378536 | − | 0.925587i | \(-0.376428\pi\) | ||||
0.378536 | + | 0.925587i | \(0.376428\pi\) | |||||||
\(602\) | 405.879 | 0.674218 | ||||||||
\(603\) | 96.1665 | − | 119.000i | 0.159480 | − | 0.197347i | ||||
\(604\) | −398.000 | −0.658940 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −84.0000 | + | 237.588i | −0.138614 | + | 0.392059i | ||||
\(607\) | − | 566.000i | − | 0.932455i | −0.884665 | − | 0.466227i | \(-0.845613\pi\) | ||
0.884665 | − | 0.466227i | \(-0.154387\pi\) | |||||||
\(608\) | −39.5980 | −0.0651283 | ||||||||
\(609\) | −840.000 | − | 296.985i | −1.37931 | − | 0.487660i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 356.382 | + | 288.000i | 0.582323 | + | 0.470588i | ||||
\(613\) | 578.000i | 0.942904i | 0.881892 | + | 0.471452i | \(0.156270\pi\) | ||||
−0.881892 | + | 0.471452i | \(0.843730\pi\) | |||||||
\(614\) | 736.805i | 1.20001i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −168.000 | −0.272727 | ||||||||
\(617\) | 636.396 | 1.03144 | 0.515718 | − | 0.856758i | \(-0.327525\pi\) | ||||
0.515718 | + | 0.856758i | \(0.327525\pi\) | |||||||
\(618\) | 217.789 | − | 616.000i | 0.352409 | − | 0.996764i | ||||
\(619\) | −593.000 | −0.957997 | −0.478998 | − | 0.877816i | \(-0.659000\pi\) | ||||
−0.478998 | + | 0.877816i | \(0.659000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −360.000 | − | 585.484i | −0.579710 | − | 0.942809i | ||||
\(622\) | 48.0000i | 0.0771704i | ||||||||
\(623\) | 950.352 | 1.52544 | ||||||||
\(624\) | −100.000 | + | 282.843i | −0.160256 | + | 0.453274i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 168.291i | − | 0.268836i | ||||||
\(627\) | −59.3970 | + | 168.000i | −0.0947320 | + | 0.267943i | ||||
\(628\) | 290.000i | 0.461783i | ||||||||
\(629\) | − | 50.9117i | − | 0.0809407i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −559.000 | −0.885895 | −0.442948 | − | 0.896547i | \(-0.646067\pi\) | ||||
−0.442948 | + | 0.896547i | \(0.646067\pi\) | |||||||
\(632\) | −164.049 | −0.259571 | ||||||||
\(633\) | 19.7990 | + | 7.00000i | 0.0312780 | + | 0.0110585i | ||||
\(634\) | −216.000 | −0.340694 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −336.000 | − | 118.794i | −0.528302 | − | 0.186783i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 509.117 | 0.797989 | ||||||||
\(639\) | −240.000 | + | 296.985i | −0.375587 | + | 0.464765i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 543.058i | 0.847204i | 0.905848 | + | 0.423602i | \(0.139235\pi\) | ||||
−0.905848 | + | 0.423602i | \(0.860765\pi\) | |||||||
\(642\) | −712.764 | − | 252.000i | −1.11022 | − | 0.392523i | ||||
\(643\) | 854.000i | 1.32815i | 0.747666 | + | 0.664075i | \(0.231174\pi\) | ||||
−0.747666 | + | 0.664075i | \(0.768826\pi\) | |||||||
\(644\) | 356.382i | 0.553388i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −252.000 | −0.390093 | ||||||||
\(647\) | −322.441 | −0.498363 | −0.249181 | − | 0.968457i | \(-0.580162\pi\) | ||||
−0.249181 | + | 0.968457i | \(0.580162\pi\) | |||||||
\(648\) | −48.0833 | − | 224.000i | −0.0742026 | − | 0.345679i | ||||
\(649\) | 288.000 | 0.443760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −49.0000 | + | 138.593i | −0.0752688 | + | 0.212892i | ||||
\(652\) | 322.000i | 0.493865i | ||||||||
\(653\) | 356.382 | 0.545761 | 0.272880 | − | 0.962048i | \(-0.412024\pi\) | ||||
0.272880 | + | 0.962048i | \(0.412024\pi\) | |||||||
\(654\) | 100.000 | + | 35.3553i | 0.152905 | + | 0.0540602i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 33.9411i | 0.0517395i | ||||||||
\(657\) | 395.980 | − | 490.000i | 0.602709 | − | 0.745814i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 890.955i | 1.35198i | 0.736911 | + | 0.675990i | \(0.236284\pi\) | ||||
−0.736911 | + | 0.675990i | \(0.763716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −910.000 | −1.37670 | −0.688351 | − | 0.725378i | \(-0.741665\pi\) | ||||
−0.688351 | + | 0.725378i | \(0.741665\pi\) | |||||||
\(662\) | 591.141 | 0.892963 | ||||||||
\(663\) | −636.396 | + | 1800.00i | −0.959873 | + | 2.71493i | ||||
\(664\) | 336.000 | 0.506024 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.0000 | + | 19.7990i | −0.0240240 | + | 0.0297282i | ||||
\(667\) | − | 1080.00i | − | 1.61919i | ||||||
\(668\) | 220.617 | 0.330265 | ||||||||
\(669\) | 161.000 | − | 455.377i | 0.240658 | − | 0.680683i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.48528i | 0.0126457i | ||||||||
\(672\) | −39.5980 | + | 112.000i | −0.0589256 | + | 0.166667i | ||||
\(673\) | − | 742.000i | − | 1.10253i | −0.834332 | − | 0.551263i | \(-0.814146\pi\) | ||
0.834332 | − | 0.551263i | \(-0.185854\pi\) | |||||||
\(674\) | − | 782.060i | − | 1.16033i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −912.000 | −1.34911 | ||||||||
\(677\) | −432.749 | −0.639216 | −0.319608 | − | 0.947550i | \(-0.603551\pi\) | ||||
−0.319608 | + | 0.947550i | \(0.603551\pi\) | |||||||
\(678\) | −67.8823 | − | 24.0000i | −0.100121 | − | 0.0353982i | ||||
\(679\) | −343.000 | −0.505155 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 168.000 | + | 59.3970i | 0.246696 | + | 0.0872202i | ||||
\(682\) | − | 84.0000i | − | 0.123167i | ||||||
\(683\) | 661.852 | 0.969037 | 0.484518 | − | 0.874781i | \(-0.338995\pi\) | ||||
0.484518 | + | 0.874781i | \(0.338995\pi\) | |||||||
\(684\) | 98.0000 | + | 79.1960i | 0.143275 | + | 0.115784i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 485.075i | − | 0.707107i | ||||||
\(687\) | −274.357 | − | 97.0000i | −0.399356 | − | 0.141194i | ||||
\(688\) | 164.000i | 0.238372i | ||||||||
\(689\) | − | 1484.92i | − | 2.15519i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 302.000 | 0.437048 | 0.218524 | − | 0.975832i | \(-0.429876\pi\) | ||||
0.218524 | + | 0.975832i | \(0.429876\pi\) | |||||||
\(692\) | 356.382 | 0.515003 | ||||||||
\(693\) | 415.779 | + | 336.000i | 0.599969 | + | 0.484848i | ||||
\(694\) | −912.000 | −1.31412 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 120.000 | − | 339.411i | 0.172414 | − | 0.487660i | ||||
\(697\) | 216.000i | 0.309900i | ||||||||
\(698\) | 376.181 | 0.538941 | ||||||||
\(699\) | 744.000 | + | 263.044i | 1.06438 | + | 0.376314i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 178.191i | 0.254195i | 0.991890 | + | 0.127098i | \(0.0405662\pi\) | ||||
−0.991890 | + | 0.127098i | \(0.959434\pi\) | |||||||
\(702\) | 813.173 | − | 500.000i | 1.15837 | − | 0.712251i | ||||
\(703\) | − | 14.0000i | − | 0.0199147i | ||||||
\(704\) | − | 67.8823i | − | 0.0964237i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 588.000 | 0.832861 | ||||||||
\(707\) | −415.779 | −0.588089 | ||||||||
\(708\) | 67.8823 | − | 192.000i | 0.0958789 | − | 0.271186i | ||||
\(709\) | −95.0000 | −0.133992 | −0.0669958 | − | 0.997753i | \(-0.521341\pi\) | ||||
−0.0669958 | + | 0.997753i | \(0.521341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 406.000 | + | 328.098i | 0.571027 | + | 0.461459i | ||||
\(712\) | 384.000i | 0.539326i | ||||||||
\(713\) | −178.191 | −0.249917 | ||||||||
\(714\) | −252.000 | + | 712.764i | −0.352941 | + | 0.998268i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 237.588i | 0.331827i | ||||||||
\(717\) | −59.3970 | + | 168.000i | −0.0828410 | + | 0.234310i | ||||
\(718\) | 468.000i | 0.651811i | ||||||||
\(719\) | − | 873.984i | − | 1.21555i | −0.794107 | − | 0.607777i | \(-0.792061\pi\) | ||
0.794107 | − | 0.607777i | \(-0.207939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1078.00 | 1.49515 | ||||||||
\(722\) | 441.235 | 0.611128 | ||||||||
\(723\) | −336.583 | − | 119.000i | −0.465536 | − | 0.164592i | ||||
\(724\) | −434.000 | −0.599448 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 196.000 | + | 69.2965i | 0.269972 | + | 0.0954497i | ||||
\(727\) | 871.000i | 1.19807i | 0.800721 | + | 0.599037i | \(0.204450\pi\) | ||||
−0.800721 | + | 0.599037i | \(0.795550\pi\) | |||||||
\(728\) | −494.975 | −0.679910 | ||||||||
\(729\) | −329.000 | + | 650.538i | −0.451303 | + | 0.892371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1043.69i | 1.42776i | ||||||||
\(732\) | 5.65685 | + | 2.00000i | 0.00772794 | + | 0.00273224i | ||||
\(733\) | − | 406.000i | − | 0.553888i | −0.960886 | − | 0.276944i | \(-0.910678\pi\) | ||
0.960886 | − | 0.276944i | \(-0.0893217\pi\) | |||||||
\(734\) | − | 145.664i | − | 0.198452i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −144.000 | −0.195652 | ||||||||
\(737\) | −144.250 | −0.195726 | ||||||||
\(738\) | 67.8823 | − | 84.0000i | 0.0919814 | − | 0.113821i | ||||
\(739\) | −830.000 | −1.12314 | −0.561570 | − | 0.827429i | \(-0.689802\pi\) | ||||
−0.561570 | + | 0.827429i | \(0.689802\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −175.000 | + | 494.975i | −0.236167 | + | 0.667982i | ||||
\(742\) | − | 588.000i | − | 0.792453i | ||||||
\(743\) | −1306.73 | −1.75873 | −0.879363 | − | 0.476152i | \(-0.842031\pi\) | ||||
−0.879363 | + | 0.476152i | \(0.842031\pi\) | |||||||
\(744\) | −56.0000 | − | 19.7990i | −0.0752688 | − | 0.0266115i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 507.703i | − | 0.680567i | ||||||
\(747\) | −831.558 | − | 672.000i | −1.11320 | − | 0.899598i | ||||
\(748\) | − | 432.000i | − | 0.577540i | ||||||
\(749\) | − | 1247.34i | − | 1.66534i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 350.000 | 0.466045 | 0.233023 | − | 0.972471i | \(-0.425138\pi\) | ||||
0.233023 | + | 0.972471i | \(0.425138\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 288.500 | − | 816.000i | 0.383134 | − | 1.08367i | ||||
\(754\) | 1500.00 | 1.98939 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 322.000 | − | 197.990i | 0.425926 | − | 0.261891i | ||||
\(757\) | 265.000i | 0.350066i | 0.984563 | + | 0.175033i | \(0.0560032\pi\) | ||||
−0.984563 | + | 0.175033i | \(0.943997\pi\) | |||||||
\(758\) | 533.159 | 0.703375 | ||||||||
\(759\) | −216.000 | + | 610.940i | −0.284585 | + | 0.804928i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1069.15i | 1.40492i | 0.711722 | + | 0.702461i | \(0.247915\pi\) | ||||
−0.711722 | + | 0.702461i | \(0.752085\pi\) | |||||||
\(762\) | −48.0833 | + | 136.000i | −0.0631014 | + | 0.178478i | ||||
\(763\) | 175.000i | 0.229358i | ||||||||
\(764\) | − | 118.794i | − | 0.155489i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −864.000 | −1.12794 | ||||||||
\(767\) | 848.528 | 1.10629 | ||||||||
\(768\) | −45.2548 | − | 16.0000i | −0.0589256 | − | 0.0208333i | ||||
\(769\) | 529.000 | 0.687906 | 0.343953 | − | 0.938987i | \(-0.388234\pi\) | ||||
0.343953 | + | 0.938987i | \(0.388234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −336.000 | − | 118.794i | −0.435798 | − | 0.154078i | ||||
\(772\) | − | 50.0000i | − | 0.0647668i | ||||||
\(773\) | 1009.75 | 1.30627 | 0.653136 | − | 0.757240i | \(-0.273453\pi\) | ||||
0.653136 | + | 0.757240i | \(0.273453\pi\) | |||||||
\(774\) | 328.000 | − | 405.879i | 0.423773 | − | 0.524392i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 138.593i | − | 0.178599i | ||||||
\(777\) | −39.5980 | − | 14.0000i | −0.0509627 | − | 0.0180180i | ||||
\(778\) | − | 492.000i | − | 0.632391i | ||||||
\(779\) | 59.3970i | 0.0762477i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 360.000 | 0.460948 | ||||||||
\(782\) | −916.410 | −1.17188 | ||||||||
\(783\) | −975.807 | + | 600.000i | −1.24624 | + | 0.766284i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 276.000 | − | 780.646i | 0.351145 | − | 0.993188i | ||||
\(787\) | 1519.00i | 1.93011i | 0.262039 | + | 0.965057i | \(0.415605\pi\) | ||||
−0.262039 | + | 0.965057i | \(0.584395\pi\) | |||||||
\(788\) | 271.529 | 0.344580 | ||||||||
\(789\) | −24.0000 | − | 8.48528i | −0.0304183 | − | 0.0107545i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 118.794i | − | 0.150182i | ||||||
\(792\) | −135.765 | + | 168.000i | −0.171420 | + | 0.212121i | ||||
\(793\) | 25.0000i | 0.0315259i | ||||||||
\(794\) | 337.997i | 0.425689i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 206.000 | 0.258794 | ||||||||
\(797\) | 526.087 | 0.660085 | 0.330042 | − | 0.943966i | \(-0.392937\pi\) | ||||
0.330042 | + | 0.943966i | \(0.392937\pi\) | |||||||
\(798\) | −69.2965 | + | 196.000i | −0.0868377 | + | 0.245614i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 768.000 | − | 950.352i | 0.958801 | − | 1.18646i | ||||
\(802\) | 132.000i | 0.164589i | ||||||||
\(803\) | −593.970 | −0.739688 | ||||||||
\(804\) | −34.0000 | + | 96.1665i | −0.0422886 | + | 0.119610i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 247.487i | − | 0.307056i | ||||||
\(807\) | −59.3970 | + | 168.000i | −0.0736022 | + | 0.208178i | ||||
\(808\) | − | 168.000i | − | 0.207921i | ||||||
\(809\) | − | 823.072i | − | 1.01739i | −0.860945 | − | 0.508697i | \(-0.830127\pi\) | ||
0.860945 | − | 0.508697i | \(-0.169873\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −319.000 | −0.393342 | −0.196671 | − | 0.980470i | \(-0.563013\pi\) | ||||
−0.196671 | + | 0.980470i | \(0.563013\pi\) | |||||||
\(812\) | 593.970 | 0.731490 | ||||||||
\(813\) | −1329.36 | − | 470.000i | −1.63513 | − | 0.578106i | ||||
\(814\) | 24.0000 | 0.0294840 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −288.000 | − | 101.823i | −0.352941 | − | 0.124784i | ||||
\(817\) | 287.000i | 0.351285i | ||||||||
\(818\) | 643.467 | 0.786635 | ||||||||
\(819\) | 1225.00 | + | 989.949i | 1.49573 | + | 1.20873i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 118.794i | 0.144694i | 0.997380 | + | 0.0723471i | \(0.0230489\pi\) | ||||
−0.997380 | + | 0.0723471i | \(0.976951\pi\) | |||||||
\(822\) | −475.176 | − | 168.000i | −0.578073 | − | 0.204380i | ||||
\(823\) | − | 1375.00i | − | 1.67072i | −0.549706 | − | 0.835358i | \(-0.685260\pi\) | ||
0.549706 | − | 0.835358i | \(-0.314740\pi\) | |||||||
\(824\) | 435.578i | 0.528614i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 336.000 | 0.406780 | ||||||||
\(827\) | 280.014 | 0.338590 | 0.169295 | − | 0.985565i | \(-0.445851\pi\) | ||||
0.169295 | + | 0.985565i | \(0.445851\pi\) | |||||||
\(828\) | 356.382 | + | 288.000i | 0.430413 | + | 0.347826i | ||||
\(829\) | 142.000 | 0.171291 | 0.0856454 | − | 0.996326i | \(-0.472705\pi\) | ||||
0.0856454 | + | 0.996326i | \(0.472705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 217.000 | − | 613.769i | 0.261131 | − | 0.738590i | ||||
\(832\) | − | 200.000i | − | 0.240385i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 616.000 | + | 217.789i | 0.738609 | + | 0.261138i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 118.794i | − | 0.142098i | ||||||
\(837\) | 98.9949 | + | 161.000i | 0.118274 | + | 0.192354i | ||||
\(838\) | − | 420.000i | − | 0.501193i | ||||||
\(839\) | 1247.34i | 1.48669i | 0.668906 | + | 0.743347i | \(0.266763\pi\) | ||||
−0.668906 | + | 0.743347i | \(0.733237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −959.000 | −1.14031 | ||||||||
\(842\) | 743.876 | 0.883464 | ||||||||
\(843\) | 517.602 | − | 1464.00i | 0.614000 | − | 1.73665i | ||||
\(844\) | −14.0000 | −0.0165877 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 343.000i | 0.404959i | ||||||||
\(848\) | 237.588 | 0.280174 | ||||||||
\(849\) | 65.0000 | − | 183.848i | 0.0765607 | − | 0.216546i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 50.9117i | − | 0.0598257i | ||||||
\(852\) | 84.8528 | − | 240.000i | 0.0995925 | − | 0.281690i | ||||
\(853\) | − | 1057.00i | − | 1.23916i | −0.784935 | − | 0.619578i | \(-0.787304\pi\) | ||
0.784935 | − | 0.619578i | \(-0.212696\pi\) | |||||||
\(854\) | 9.89949i | 0.0115919i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 504.000 | 0.588785 | ||||||||
\(857\) | 627.911 | 0.732685 | 0.366342 | − | 0.930480i | \(-0.380610\pi\) | ||||
0.366342 | + | 0.930480i | \(0.380610\pi\) | |||||||
\(858\) | −848.528 | − | 300.000i | −0.988961 | − | 0.349650i | ||||
\(859\) | 946.000 | 1.10128 | 0.550640 | − | 0.834743i | \(-0.314384\pi\) | ||||
0.550640 | + | 0.834743i | \(0.314384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 168.000 | + | 59.3970i | 0.195122 | + | 0.0689860i | ||||
\(862\) | − | 396.000i | − | 0.459397i | ||||||
\(863\) | −390.323 | −0.452286 | −0.226143 | − | 0.974094i | \(-0.572612\pi\) | ||||
−0.226143 | + | 0.974094i | \(0.572612\pi\) | |||||||
\(864\) | 80.0000 | + | 130.108i | 0.0925926 | + | 0.150588i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 168.291i | − | 0.194332i | ||||||
\(867\) | −1015.41 | − | 359.000i | −1.17117 | − | 0.414072i | ||||
\(868\) | − | 98.0000i | − | 0.112903i | ||||||
\(869\) | − | 492.146i | − | 0.566336i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −425.000 | −0.487945 | ||||||||
\(872\) | −70.7107 | −0.0810902 | ||||||||
\(873\) | −277.186 | + | 343.000i | −0.317510 | + | 0.392898i | ||||
\(874\) | −252.000 | −0.288330 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −140.000 | + | 395.980i | −0.159817 | + | 0.452032i | ||||
\(877\) | − | 1463.00i | − | 1.66819i | −0.551623 | − | 0.834094i | \(-0.685991\pi\) | ||
0.551623 | − | 0.834094i | \(-0.314009\pi\) | |||||||
\(878\) | −1028.13 | −1.17099 | ||||||||
\(879\) | −480.000 | − | 169.706i | −0.546075 | − | 0.193067i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1069.15i | − | 1.21356i | −0.794870 | − | 0.606779i | \(-0.792461\pi\) | ||
0.794870 | − | 0.606779i | \(-0.207539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1289.00i | 1.45980i | 0.683556 | + | 0.729898i | \(0.260432\pi\) | ||||
−0.683556 | + | 0.729898i | \(0.739568\pi\) | |||||||
\(884\) | − | 1272.79i | − | 1.43981i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 744.000 | 0.839729 | ||||||||
\(887\) | −1289.76 | −1.45407 | −0.727037 | − | 0.686599i | \(-0.759103\pi\) | ||||
−0.727037 | + | 0.686599i | \(0.759103\pi\) | |||||||
\(888\) | 5.65685 | − | 16.0000i | 0.00637033 | − | 0.0180180i | ||||
\(889\) | −238.000 | −0.267717 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 672.000 | − | 144.250i | 0.754209 | − | 0.161897i | ||||
\(892\) | 322.000i | 0.360987i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −216.000 | + | 610.940i | −0.241611 | + | 0.683378i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 79.1960i | − | 0.0883883i | ||||||
\(897\) | −636.396 | + | 1800.00i | −0.709472 | + | 2.00669i | ||||
\(898\) | − | 360.000i | − | 0.400891i | ||||||
\(899\) | 296.985i | 0.330350i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1512.00 | 1.67814 | ||||||||
\(902\) | −101.823 | −0.112886 | ||||||||
\(903\) | 811.759 | + | 287.000i | 0.898957 | + | 0.317829i | ||||
\(904\) | 48.0000 | 0.0530973 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −796.000 | − | 281.428i | −0.878587 | − | 0.310627i | ||||
\(907\) | − | 14.0000i | − | 0.0154355i | −0.999970 | − | 0.00771775i | \(-0.997543\pi\) | ||
0.999970 | − | 0.00771775i | \(-0.00245666\pi\) | |||||||
\(908\) | −118.794 | −0.130830 | ||||||||
\(909\) | −336.000 | + | 415.779i | −0.369637 | + | 0.457402i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 695.793i | − | 0.763768i | −0.924210 | − | 0.381884i | \(-0.875275\pi\) | ||
0.924210 | − | 0.381884i | \(-0.124725\pi\) | |||||||
\(912\) | −79.1960 | − | 28.0000i | −0.0868377 | − | 0.0307018i | ||||
\(913\) | 1008.00i | 1.10405i | ||||||||
\(914\) | − | 438.406i | − | 0.479657i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 194.000 | 0.211790 | ||||||||
\(917\) | 1366.13 | 1.48978 | ||||||||
\(918\) | 509.117 | + | 828.000i | 0.554594 | + | 0.901961i | ||||
\(919\) | 1423.00 | 1.54842 | 0.774211 | − | 0.632927i | \(-0.218147\pi\) | ||||
0.774211 | + | 0.632927i | \(0.218147\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −521.000 | + | 1473.61i | −0.565689 | + | 1.60001i | ||||
\(922\) | 1020.00i | 1.10629i | ||||||||
\(923\) | 1060.66 | 1.14914 | ||||||||
\(924\) | −336.000 | − | 118.794i | −0.363636 | − | 0.128565i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1032.38i | 1.11488i | ||||||||
\(927\) | 871.156 | − | 1078.00i | 0.939758 | − | 1.16289i | ||||
\(928\) | 240.000i | 0.258621i | ||||||||
\(929\) | − | 415.779i | − | 0.447555i | −0.974640 | − | 0.223778i | \(-0.928161\pi\) | ||
0.974640 | − | 0.223778i | \(-0.0718389\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −526.087 | −0.564472 | ||||||||
\(933\) | −33.9411 | + | 96.0000i | −0.0363785 | + | 0.102894i | ||||
\(934\) | −276.000 | −0.295503 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −400.000 | + | 494.975i | −0.427350 | + | 0.528819i | ||||
\(937\) | − | 1655.00i | − | 1.76628i | −0.469114 | − | 0.883138i | \(-0.655427\pi\) | ||
0.469114 | − | 0.883138i | \(-0.344573\pi\) | |||||||
\(938\) | −168.291 | −0.179415 | ||||||||
\(939\) | 119.000 | − | 336.583i | 0.126731 | − | 0.358448i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1663.12i | 1.76739i | 0.468062 | + | 0.883696i | \(0.344952\pi\) | ||||
−0.468062 | + | 0.883696i | \(0.655048\pi\) | |||||||
\(942\) | −205.061 | + | 580.000i | −0.217687 | + | 0.615711i | ||||
\(943\) | 216.000i | 0.229056i | ||||||||
\(944\) | 135.765i | 0.143818i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −492.000 | −0.520085 | ||||||||
\(947\) | −415.779 | −0.439048 | −0.219524 | − | 0.975607i | \(-0.570450\pi\) | ||||
−0.219524 | + | 0.975607i | \(0.570450\pi\) | |||||||
\(948\) | −328.098 | − | 116.000i | −0.346094 | − | 0.122363i | ||||
\(949\) | −1750.00 | −1.84405 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −432.000 | − | 152.735i | −0.454259 | − | 0.160605i | ||||
\(952\) | − | 504.000i | − | 0.529412i | ||||||
\(953\) | 1680.09 | 1.76294 | 0.881472 | − | 0.472236i | \(-0.156553\pi\) | ||||
0.881472 | + | 0.472236i | \(0.156553\pi\) | |||||||
\(954\) | −588.000 | − | 475.176i | −0.616352 | − | 0.498088i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 118.794i | − | 0.124261i | ||||||
\(957\) | 1018.23 | + | 360.000i | 1.06399 | + | 0.376176i | ||||
\(958\) | 552.000i | 0.576200i | ||||||||
\(959\) | − | 831.558i | − | 0.867109i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −912.000 | −0.949011 | ||||||||
\(962\) | 70.7107 | 0.0735038 | ||||||||
\(963\) | −1247.34 | − | 1008.00i | −1.29526 | − | 1.04673i | ||||
\(964\) | 238.000 | 0.246888 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −252.000 | + | 712.764i | −0.260870 | + | 0.737851i | ||||
\(967\) | 1162.00i | 1.20165i | 0.799379 | + | 0.600827i | \(0.205162\pi\) | ||||
−0.799379 | + | 0.600827i | \(0.794838\pi\) | |||||||
\(968\) | −138.593 | −0.143175 | ||||||||
\(969\) | −504.000 | − | 178.191i | −0.520124 | − | 0.183892i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 712.764i | − | 0.734051i | −0.930211 | − | 0.367026i | \(-0.880376\pi\) | ||
0.930211 | − | 0.367026i | \(-0.119624\pi\) | |||||||
\(972\) | 62.2254 | − | 482.000i | 0.0640179 | − | 0.495885i | ||||
\(973\) | 1078.00i | 1.10791i | ||||||||
\(974\) | 668.923i | 0.686779i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | −0.00409836 | ||||||||
\(977\) | −899.440 | −0.920614 | −0.460307 | − | 0.887760i | \(-0.652261\pi\) | ||||
−0.460307 | + | 0.887760i | \(0.652261\pi\) | |||||||
\(978\) | −227.688 | + | 644.000i | −0.232810 | + | 0.658487i | ||||
\(979\) | −1152.00 | −1.17671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 175.000 | + | 141.421i | 0.178389 | + | 0.144160i | ||||
\(982\) | 1152.00i | 1.17312i | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | −24.0000 | + | 67.8823i | −0.0243902 | + | 0.0689860i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1527.35i | 1.54904i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 350.000i | − | 0.354251i | ||||||
\(989\) | 1043.69i | 1.05530i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −535.000 | −0.539859 | −0.269929 | − | 0.962880i | \(-0.587000\pi\) | ||||
−0.269929 | + | 0.962880i | \(0.587000\pi\) | |||||||
\(992\) | 39.5980 | 0.0399173 | ||||||||
\(993\) | 1182.28 | + | 418.000i | 1.19062 | + | 0.420947i | ||||
\(994\) | 420.000 | 0.422535 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 672.000 | + | 237.588i | 0.674699 | + | 0.238542i | ||||
\(997\) | − | 1274.00i | − | 1.27783i | −0.769276 | − | 0.638917i | \(-0.779383\pi\) | ||
0.769276 | − | 0.638917i | \(-0.220617\pi\) | |||||||
\(998\) | −247.487 | −0.247983 | ||||||||
\(999\) | −46.0000 | + | 28.2843i | −0.0460460 | + | 0.0283126i |
(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 | 150.3.b.a.149.1 | 4 | ||
3.2 | odd | 2 | inner | 150.3.b.a.149.3 | 4 | ||
4.3 | odd | 2 | 1200.3.c.h.449.4 | 4 | |||
5.2 | odd | 4 | 150.3.d.a.101.1 | ✓ | 2 | ||
5.3 | odd | 4 | 150.3.d.b.101.2 | yes | 2 | ||
5.4 | even | 2 | inner | 150.3.b.a.149.4 | 4 | ||
12.11 | even | 2 | 1200.3.c.h.449.2 | 4 | |||
15.2 | even | 4 | 150.3.d.a.101.2 | yes | 2 | ||
15.8 | even | 4 | 150.3.d.b.101.1 | yes | 2 | ||
15.14 | odd | 2 | inner | 150.3.b.a.149.2 | 4 | ||
20.3 | even | 4 | 1200.3.l.i.401.2 | 2 | |||
20.7 | even | 4 | 1200.3.l.p.401.1 | 2 | |||
20.19 | odd | 2 | 1200.3.c.h.449.1 | 4 | |||
60.23 | odd | 4 | 1200.3.l.i.401.1 | 2 | |||
60.47 | odd | 4 | 1200.3.l.p.401.2 | 2 | |||
60.59 | even | 2 | 1200.3.c.h.449.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.3.b.a.149.1 | 4 | 1.1 | even | 1 | trivial | ||
150.3.b.a.149.2 | 4 | 15.14 | odd | 2 | inner | ||
150.3.b.a.149.3 | 4 | 3.2 | odd | 2 | inner | ||
150.3.b.a.149.4 | 4 | 5.4 | even | 2 | inner | ||
150.3.d.a.101.1 | ✓ | 2 | 5.2 | odd | 4 | ||
150.3.d.a.101.2 | yes | 2 | 15.2 | even | 4 | ||
150.3.d.b.101.1 | yes | 2 | 15.8 | even | 4 | ||
150.3.d.b.101.2 | yes | 2 | 5.3 | odd | 4 | ||
1200.3.c.h.449.1 | 4 | 20.19 | odd | 2 | |||
1200.3.c.h.449.2 | 4 | 12.11 | even | 2 | |||
1200.3.c.h.449.3 | 4 | 60.59 | even | 2 | |||
1200.3.c.h.449.4 | 4 | 4.3 | odd | 2 | |||
1200.3.l.i.401.1 | 2 | 60.23 | odd | 4 | |||
1200.3.l.i.401.2 | 2 | 20.3 | even | 4 | |||
1200.3.l.p.401.1 | 2 | 20.7 | even | 4 | |||
1200.3.l.p.401.2 | 2 | 60.47 | odd | 4 |