Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
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: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.432278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.432278 | −0.305667 | −0.152833 | − | 0.988252i | \(-0.548840\pi\) | ||||
−0.152833 | + | 0.988252i | \(0.548840\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.81314 | −0.906568 | ||||||||
\(5\) | 4.10000 | 1.83357 | 0.916787 | − | 0.399376i | \(-0.130773\pi\) | ||||
0.916787 | + | 0.399376i | \(0.130773\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.64833 | 0.582774 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.77234 | −0.560462 | ||||||||
\(11\) | −2.19453 | −0.661676 | −0.330838 | − | 0.943688i | \(-0.607331\pi\) | ||||
−0.330838 | + | 0.943688i | \(0.607331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.36622 | −0.656272 | −0.328136 | − | 0.944631i | \(-0.606420\pi\) | ||||
−0.328136 | + | 0.944631i | \(0.606420\pi\) | |||||||
\(14\) | −0.432278 | −0.115531 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.91373 | 0.728433 | ||||||||
\(17\) | 2.91068 | 0.705944 | 0.352972 | − | 0.935634i | \(-0.385171\pi\) | ||||
0.352972 | + | 0.935634i | \(0.385171\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.73030 | 1.54404 | 0.772018 | − | 0.635601i | \(-0.219247\pi\) | ||||
0.772018 | + | 0.635601i | \(0.219247\pi\) | |||||||
\(20\) | −7.43385 | −1.66226 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.948646 | 0.202252 | ||||||||
\(23\) | −4.56353 | −0.951563 | −0.475781 | − | 0.879564i | \(-0.657835\pi\) | ||||
−0.475781 | + | 0.879564i | \(0.657835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.8100 | 2.36200 | ||||||||
\(26\) | 1.02287 | 0.200600 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.81314 | −0.342650 | ||||||||
\(29\) | 4.17078 | 0.774494 | 0.387247 | − | 0.921976i | \(-0.373426\pi\) | ||||
0.387247 | + | 0.921976i | \(0.373426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.485432 | −0.0871861 | −0.0435931 | − | 0.999049i | \(-0.513881\pi\) | ||||
−0.0435931 | + | 0.999049i | \(0.513881\pi\) | |||||||
\(32\) | −4.55621 | −0.805432 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.25822 | −0.215783 | ||||||||
\(35\) | 4.10000 | 0.693026 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.48926 | 0.902428 | 0.451214 | − | 0.892416i | \(-0.350991\pi\) | ||||
0.451214 | + | 0.892416i | \(0.350991\pi\) | |||||||
\(38\) | −2.90936 | −0.471960 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.75816 | 1.06856 | ||||||||
\(41\) | −10.6000 | −1.65544 | −0.827721 | − | 0.561140i | \(-0.810363\pi\) | ||||
−0.827721 | + | 0.561140i | \(0.810363\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.67190 | −1.01746 | −0.508728 | − | 0.860927i | \(-0.669884\pi\) | ||||
−0.508728 | + | 0.860927i | \(0.669884\pi\) | |||||||
\(44\) | 3.97898 | 0.599854 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.97271 | 0.290861 | ||||||||
\(47\) | 10.8486 | 1.58243 | 0.791215 | − | 0.611538i | \(-0.209449\pi\) | ||||
0.791215 | + | 0.611538i | \(0.209449\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.10519 | −0.721983 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.29028 | 0.594955 | ||||||||
\(53\) | 9.15995 | 1.25822 | 0.629108 | − | 0.777318i | \(-0.283420\pi\) | ||||
0.629108 | + | 0.777318i | \(0.283420\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.99757 | −1.21323 | ||||||||
\(56\) | 1.64833 | 0.220268 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.80293 | −0.236737 | ||||||||
\(59\) | 1.66364 | 0.216587 | 0.108293 | − | 0.994119i | \(-0.465461\pi\) | ||||
0.108293 | + | 0.994119i | \(0.465461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.4307 | −1.84766 | −0.923830 | − | 0.382803i | \(-0.874959\pi\) | ||||
−0.923830 | + | 0.382803i | \(0.874959\pi\) | |||||||
\(62\) | 0.209841 | 0.0266499 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.85792 | −0.482240 | ||||||||
\(65\) | −9.70151 | −1.20332 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4051 | 1.75987 | 0.879933 | − | 0.475097i | \(-0.157587\pi\) | ||||
0.879933 | + | 0.475097i | \(0.157587\pi\) | |||||||
\(68\) | −5.27746 | −0.639986 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.77234 | −0.211835 | ||||||||
\(71\) | −2.63479 | −0.312693 | −0.156346 | − | 0.987702i | \(-0.549972\pi\) | ||||
−0.156346 | + | 0.987702i | \(0.549972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.610455 | −0.0714484 | −0.0357242 | − | 0.999362i | \(-0.511374\pi\) | ||||
−0.0357242 | + | 0.999362i | \(0.511374\pi\) | |||||||
\(74\) | −2.37288 | −0.275842 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.2029 | −1.39977 | ||||||||
\(77\) | −2.19453 | −0.250090 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.36638 | −0.828783 | −0.414391 | − | 0.910099i | \(-0.636006\pi\) | ||||
−0.414391 | + | 0.910099i | \(0.636006\pi\) | |||||||
\(80\) | 11.9463 | 1.33564 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.58214 | 0.506013 | ||||||||
\(83\) | 11.0482 | 1.21269 | 0.606346 | − | 0.795201i | \(-0.292634\pi\) | ||||
0.606346 | + | 0.795201i | \(0.292634\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.9338 | 1.29440 | ||||||||
\(86\) | 2.88412 | 0.311002 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.61732 | −0.385607 | ||||||||
\(89\) | 7.36625 | 0.780821 | 0.390411 | − | 0.920641i | \(-0.372333\pi\) | ||||
0.390411 | + | 0.920641i | \(0.372333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.36622 | −0.248047 | ||||||||
\(92\) | 8.27431 | 0.862656 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.68960 | −0.483696 | ||||||||
\(95\) | 27.5942 | 2.83111 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8692 | 1.10360 | 0.551799 | − | 0.833977i | \(-0.313941\pi\) | ||||
0.551799 | + | 0.833977i | \(0.313941\pi\) | |||||||
\(98\) | −0.432278 | −0.0436666 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −21.4131 | −2.14131 | ||||||||
\(101\) | −19.7064 | −1.96086 | −0.980432 | − | 0.196857i | \(-0.936927\pi\) | ||||
−0.980432 | + | 0.196857i | \(0.936927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.487774 | −0.0480618 | −0.0240309 | − | 0.999711i | \(-0.507650\pi\) | ||||
−0.0240309 | + | 0.999711i | \(0.507650\pi\) | |||||||
\(104\) | −3.90032 | −0.382458 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.95964 | −0.384594 | ||||||||
\(107\) | 13.5828 | 1.31310 | 0.656550 | − | 0.754283i | \(-0.272015\pi\) | ||||
0.656550 | + | 0.754283i | \(0.272015\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.7637 | 1.70146 | 0.850729 | − | 0.525604i | \(-0.176161\pi\) | ||||
0.850729 | + | 0.525604i | \(0.176161\pi\) | |||||||
\(110\) | 3.88945 | 0.370844 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.91373 | 0.275322 | ||||||||
\(113\) | −12.6518 | −1.19019 | −0.595093 | − | 0.803657i | \(-0.702885\pi\) | ||||
−0.595093 | + | 0.803657i | \(0.702885\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.7105 | −1.74476 | ||||||||
\(116\) | −7.56219 | −0.702132 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.719152 | −0.0662033 | ||||||||
\(119\) | 2.91068 | 0.266822 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.18404 | −0.562185 | ||||||||
\(122\) | 6.23806 | 0.564768 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.880154 | 0.0790402 | ||||||||
\(125\) | 27.9209 | 2.49732 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 10.7801 | 0.952836 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.19374 | 0.367816 | ||||||||
\(131\) | 6.74380 | 0.589209 | 0.294604 | − | 0.955619i | \(-0.404812\pi\) | ||||
0.294604 | + | 0.955619i | \(0.404812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.73030 | 0.583591 | ||||||||
\(134\) | −6.22702 | −0.537932 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.79777 | 0.411406 | ||||||||
\(137\) | −4.74982 | −0.405805 | −0.202902 | − | 0.979199i | \(-0.565037\pi\) | ||||
−0.202902 | + | 0.979199i | \(0.565037\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.17516 | −0.184495 | −0.0922473 | − | 0.995736i | \(-0.529405\pi\) | ||||
−0.0922473 | + | 0.995736i | \(0.529405\pi\) | |||||||
\(140\) | −7.43385 | −0.628275 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.13896 | 0.0955796 | ||||||||
\(143\) | 5.19274 | 0.434239 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.1002 | 1.42009 | ||||||||
\(146\) | 0.263886 | 0.0218394 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.95277 | −0.818113 | ||||||||
\(149\) | −4.19763 | −0.343883 | −0.171941 | − | 0.985107i | \(-0.555004\pi\) | ||||
−0.171941 | + | 0.985107i | \(0.555004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4354 | 1.25612 | 0.628059 | − | 0.778166i | \(-0.283850\pi\) | ||||
0.628059 | + | 0.778166i | \(0.283850\pi\) | |||||||
\(152\) | 11.0938 | 0.899824 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.948646 | 0.0764441 | ||||||||
\(155\) | −1.99027 | −0.159862 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.92564 | −0.792152 | −0.396076 | − | 0.918218i | \(-0.629628\pi\) | ||||
−0.396076 | + | 0.918218i | \(0.629628\pi\) | |||||||
\(158\) | 3.18432 | 0.253331 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −18.6805 | −1.47682 | ||||||||
\(161\) | −4.56353 | −0.359657 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.6931 | −0.915875 | −0.457938 | − | 0.888984i | \(-0.651412\pi\) | ||||
−0.457938 | + | 0.888984i | \(0.651412\pi\) | |||||||
\(164\) | 19.2192 | 1.50077 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.77587 | −0.370680 | ||||||||
\(167\) | 15.2201 | 1.17776 | 0.588882 | − | 0.808219i | \(-0.299568\pi\) | ||||
0.588882 | + | 0.808219i | \(0.299568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.40099 | −0.569307 | ||||||||
\(170\) | −5.15871 | −0.395655 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.0971 | 0.922393 | ||||||||
\(173\) | 15.7272 | 1.19572 | 0.597858 | − | 0.801602i | \(-0.296018\pi\) | ||||
0.597858 | + | 0.801602i | \(0.296018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.8100 | 0.892751 | ||||||||
\(176\) | −6.39428 | −0.481987 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.18427 | −0.238671 | ||||||||
\(179\) | 3.56031 | 0.266110 | 0.133055 | − | 0.991109i | \(-0.457521\pi\) | ||||
0.133055 | + | 0.991109i | \(0.457521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1994 | −0.906777 | −0.453389 | − | 0.891313i | \(-0.649785\pi\) | ||||
−0.453389 | + | 0.891313i | \(0.649785\pi\) | |||||||
\(182\) | 1.02287 | 0.0758198 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.52223 | −0.554546 | ||||||||
\(185\) | 22.5059 | 1.65467 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.38758 | −0.467106 | ||||||||
\(188\) | −19.6700 | −1.43458 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.9284 | −0.865374 | ||||||||
\(191\) | 14.2793 | 1.03322 | 0.516608 | − | 0.856222i | \(-0.327194\pi\) | ||||
0.516608 | + | 0.856222i | \(0.327194\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3589 | −1.03358 | −0.516789 | − | 0.856113i | \(-0.672873\pi\) | ||||
−0.516789 | + | 0.856113i | \(0.672873\pi\) | |||||||
\(194\) | −4.69851 | −0.337333 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.81314 | −0.129510 | ||||||||
\(197\) | 24.3173 | 1.73254 | 0.866269 | − | 0.499578i | \(-0.166512\pi\) | ||||
0.866269 | + | 0.499578i | \(0.166512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.20059 | −0.510437 | −0.255218 | − | 0.966883i | \(-0.582147\pi\) | ||||
−0.255218 | + | 0.966883i | \(0.582147\pi\) | |||||||
\(200\) | 19.4668 | 1.37651 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.51866 | 0.599371 | ||||||||
\(203\) | 4.17078 | 0.292731 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −43.4600 | −3.03538 | ||||||||
\(206\) | 0.210854 | 0.0146909 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.89454 | −0.478050 | ||||||||
\(209\) | −14.7698 | −1.02165 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6526 | 1.28410 | 0.642048 | − | 0.766665i | \(-0.278085\pi\) | ||||
0.642048 | + | 0.766665i | \(0.278085\pi\) | |||||||
\(212\) | −16.6082 | −1.14066 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.87155 | −0.401371 | ||||||||
\(215\) | −27.3548 | −1.86558 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.485432 | −0.0329533 | ||||||||
\(218\) | −7.67887 | −0.520079 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16.3138 | 1.09988 | ||||||||
\(221\) | −6.88732 | −0.463291 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2348 | −0.886265 | −0.443132 | − | 0.896456i | \(-0.646133\pi\) | ||||
−0.443132 | + | 0.896456i | \(0.646133\pi\) | |||||||
\(224\) | −4.55621 | −0.304425 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.46911 | 0.363800 | ||||||||
\(227\) | 9.57693 | 0.635643 | 0.317822 | − | 0.948151i | \(-0.397049\pi\) | ||||
0.317822 | + | 0.948151i | \(0.397049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0868 | 0.798717 | 0.399358 | − | 0.916795i | \(-0.369233\pi\) | ||||
0.399358 | + | 0.916795i | \(0.369233\pi\) | |||||||
\(230\) | 8.08812 | 0.533315 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.87484 | 0.451355 | ||||||||
\(233\) | −2.80656 | −0.183864 | −0.0919321 | − | 0.995765i | \(-0.529304\pi\) | ||||
−0.0919321 | + | 0.995765i | \(0.529304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 44.4792 | 2.90150 | ||||||||
\(236\) | −3.01640 | −0.196351 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.25822 | −0.0815584 | ||||||||
\(239\) | −9.56442 | −0.618671 | −0.309335 | − | 0.950953i | \(-0.600107\pi\) | ||||
−0.309335 | + | 0.950953i | \(0.600107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4142 | 0.799668 | 0.399834 | − | 0.916588i | \(-0.369068\pi\) | ||||
0.399834 | + | 0.916588i | \(0.369068\pi\) | |||||||
\(242\) | 2.67322 | 0.171841 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.1648 | 1.67503 | ||||||||
\(245\) | 4.10000 | 0.261939 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.9254 | −1.01331 | ||||||||
\(248\) | −0.800154 | −0.0508098 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0696 | −0.763348 | ||||||||
\(251\) | 4.18927 | 0.264424 | 0.132212 | − | 0.991221i | \(-0.457792\pi\) | ||||
0.132212 | + | 0.991221i | \(0.457792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0148 | 0.629626 | ||||||||
\(254\) | −0.432278 | −0.0271235 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.05584 | 0.190990 | ||||||||
\(257\) | −6.16033 | −0.384271 | −0.192135 | − | 0.981368i | \(-0.561541\pi\) | ||||
−0.192135 | + | 0.981368i | \(0.561541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.48926 | 0.341086 | ||||||||
\(260\) | 17.5901 | 1.09089 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.91519 | −0.180101 | ||||||||
\(263\) | 17.8032 | 1.09779 | 0.548895 | − | 0.835891i | \(-0.315049\pi\) | ||||
0.548895 | + | 0.835891i | \(0.315049\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.5558 | 2.30703 | ||||||||
\(266\) | −2.90936 | −0.178384 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −26.1185 | −1.59544 | ||||||||
\(269\) | −5.14395 | −0.313632 | −0.156816 | − | 0.987628i | \(-0.550123\pi\) | ||||
−0.156816 | + | 0.987628i | \(0.550123\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1569 | −0.616990 | −0.308495 | − | 0.951226i | \(-0.599825\pi\) | ||||
−0.308495 | + | 0.951226i | \(0.599825\pi\) | |||||||
\(272\) | 8.48095 | 0.514233 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.05324 | 0.124041 | ||||||||
\(275\) | −25.9174 | −1.56288 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.2773 | −1.39860 | −0.699299 | − | 0.714829i | \(-0.746505\pi\) | ||||
−0.699299 | + | 0.714829i | \(0.746505\pi\) | |||||||
\(278\) | 0.940273 | 0.0563938 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.75816 | 0.403878 | ||||||||
\(281\) | −2.39036 | −0.142597 | −0.0712986 | − | 0.997455i | \(-0.522714\pi\) | ||||
−0.0712986 | + | 0.997455i | \(0.522714\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.7401 | 0.697874 | 0.348937 | − | 0.937146i | \(-0.386543\pi\) | ||||
0.348937 | + | 0.937146i | \(0.386543\pi\) | |||||||
\(284\) | 4.77724 | 0.283477 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.24471 | −0.132732 | ||||||||
\(287\) | −10.6000 | −0.625698 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.52794 | −0.501643 | ||||||||
\(290\) | −7.39203 | −0.434075 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.10684 | 0.0647728 | ||||||||
\(293\) | −11.3005 | −0.660184 | −0.330092 | − | 0.943949i | \(-0.607080\pi\) | ||||
−0.330092 | + | 0.943949i | \(0.607080\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.82090 | 0.397128 | ||||||||
\(296\) | 9.04813 | 0.525912 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.81454 | 0.105113 | ||||||||
\(299\) | 10.7983 | 0.624484 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.67190 | −0.384562 | ||||||||
\(302\) | −6.67239 | −0.383953 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 19.6103 | 1.12473 | ||||||||
\(305\) | −59.1658 | −3.38782 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.1721 | 1.72201 | 0.861006 | − | 0.508595i | \(-0.169835\pi\) | ||||
0.861006 | + | 0.508595i | \(0.169835\pi\) | |||||||
\(308\) | 3.97898 | 0.226723 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.860349 | 0.0488646 | ||||||||
\(311\) | −2.51056 | −0.142361 | −0.0711805 | − | 0.997463i | \(-0.522677\pi\) | ||||
−0.0711805 | + | 0.997463i | \(0.522677\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.42071 | −0.193350 | −0.0966751 | − | 0.995316i | \(-0.530821\pi\) | ||||
−0.0966751 | + | 0.995316i | \(0.530821\pi\) | |||||||
\(314\) | 4.29063 | 0.242134 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.3563 | 0.751348 | ||||||||
\(317\) | 3.84950 | 0.216209 | 0.108105 | − | 0.994140i | \(-0.465522\pi\) | ||||
0.108105 | + | 0.994140i | \(0.465522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.15290 | −0.512464 | ||||||||
\(320\) | −15.8175 | −0.884223 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.97271 | 0.109935 | ||||||||
\(323\) | 19.5897 | 1.09000 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.9450 | −1.55011 | ||||||||
\(326\) | 5.05467 | 0.279952 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.4723 | −0.964748 | ||||||||
\(329\) | 10.8486 | 0.598102 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0166221 | −0.000913635 0 | −0.000456817 | − | 1.00000i | \(-0.500145\pi\) | ||||
−0.000456817 | 1.00000i | \(0.500145\pi\) | ||||||||
\(332\) | −20.0318 | −1.09939 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.57930 | −0.360003 | ||||||||
\(335\) | 59.0610 | 3.22685 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.7639 | 0.640819 | 0.320410 | − | 0.947279i | \(-0.396179\pi\) | ||||
0.320410 | + | 0.947279i | \(0.396179\pi\) | |||||||
\(338\) | 3.19928 | 0.174018 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −21.6376 | −1.17346 | ||||||||
\(341\) | 1.06529 | 0.0576890 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −10.9975 | −0.592947 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.79852 | −0.365491 | ||||||||
\(347\) | −23.9938 | −1.28806 | −0.644028 | − | 0.765002i | \(-0.722738\pi\) | ||||
−0.644028 | + | 0.765002i | \(0.722738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.6506 | −0.837755 | −0.418877 | − | 0.908043i | \(-0.637576\pi\) | ||||
−0.418877 | + | 0.908043i | \(0.637576\pi\) | |||||||
\(350\) | −5.10519 | −0.272884 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.99874 | 0.532935 | ||||||||
\(353\) | −6.48439 | −0.345129 | −0.172565 | − | 0.984998i | \(-0.555205\pi\) | ||||
−0.172565 | + | 0.984998i | \(0.555205\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.8026 | −0.573345 | ||||||||
\(356\) | −13.3560 | −0.707867 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.53904 | −0.0813410 | ||||||||
\(359\) | −6.97556 | −0.368156 | −0.184078 | − | 0.982912i | \(-0.558930\pi\) | ||||
−0.184078 | + | 0.982912i | \(0.558930\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.2969 | 1.38405 | ||||||||
\(362\) | 5.27355 | 0.277171 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.29028 | 0.224872 | ||||||||
\(365\) | −2.50286 | −0.131006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.0425 | −1.30721 | −0.653603 | − | 0.756838i | \(-0.726743\pi\) | ||||
−0.653603 | + | 0.756838i | \(0.726743\pi\) | |||||||
\(368\) | −13.2969 | −0.693150 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.72882 | −0.505777 | ||||||||
\(371\) | 9.15995 | 0.475561 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1651 | 0.629883 | 0.314941 | − | 0.949111i | \(-0.398015\pi\) | ||||
0.314941 | + | 0.949111i | \(0.398015\pi\) | |||||||
\(374\) | 2.76121 | 0.142779 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.8821 | 0.922199 | ||||||||
\(377\) | −9.86899 | −0.508279 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.1220 | −0.776765 | −0.388383 | − | 0.921498i | \(-0.626966\pi\) | ||||
−0.388383 | + | 0.921498i | \(0.626966\pi\) | |||||||
\(380\) | −50.0320 | −2.56659 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.17264 | −0.315820 | ||||||||
\(383\) | −25.4746 | −1.30169 | −0.650845 | − | 0.759211i | \(-0.725585\pi\) | ||||
−0.650845 | + | 0.759211i | \(0.725585\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.99757 | −0.458559 | ||||||||
\(386\) | 6.20704 | 0.315930 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19.7073 | −1.00049 | ||||||||
\(389\) | 20.9955 | 1.06452 | 0.532258 | − | 0.846582i | \(-0.321344\pi\) | ||||
0.532258 | + | 0.846582i | \(0.321344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.2830 | −0.671750 | ||||||||
\(392\) | 1.64833 | 0.0832534 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.5118 | −0.529579 | ||||||||
\(395\) | −30.2022 | −1.51964 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.7159 | −0.537813 | −0.268907 | − | 0.963166i | \(-0.586662\pi\) | ||||
−0.268907 | + | 0.963166i | \(0.586662\pi\) | |||||||
\(398\) | 3.11266 | 0.156023 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 34.4111 | 1.72056 | ||||||||
\(401\) | −20.6307 | −1.03025 | −0.515123 | − | 0.857116i | \(-0.672254\pi\) | ||||
−0.515123 | + | 0.857116i | \(0.672254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.14864 | 0.0572178 | ||||||||
\(404\) | 35.7305 | 1.77766 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.80293 | −0.0894782 | ||||||||
\(407\) | −12.0463 | −0.597115 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.3576 | 0.512150 | 0.256075 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256075 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(410\) | 18.7868 | 0.927813 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.884401 | 0.0435713 | ||||||||
\(413\) | 1.66364 | 0.0818621 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.2974 | 2.22356 | ||||||||
\(416\) | 10.7810 | 0.528582 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.38467 | 0.312284 | ||||||||
\(419\) | 25.7023 | 1.25564 | 0.627820 | − | 0.778359i | \(-0.283947\pi\) | ||||
0.627820 | + | 0.778359i | \(0.283947\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.00604 | −0.341453 | −0.170727 | − | 0.985318i | \(-0.554612\pi\) | ||||
−0.170727 | + | 0.985318i | \(0.554612\pi\) | |||||||
\(422\) | −8.06309 | −0.392505 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.0986 | 0.733255 | ||||||||
\(425\) | 34.3751 | 1.66744 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.4307 | −0.698350 | ||||||||
\(428\) | −24.6275 | −1.19041 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.8249 | 0.570246 | ||||||||
\(431\) | −11.7752 | −0.567193 | −0.283596 | − | 0.958944i | \(-0.591528\pi\) | ||||
−0.283596 | + | 0.958944i | \(0.591528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.7699 | −1.04619 | −0.523097 | − | 0.852273i | \(-0.675224\pi\) | ||||
−0.523097 | + | 0.852273i | \(0.675224\pi\) | |||||||
\(434\) | 0.209841 | 0.0100727 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.2081 | −1.54249 | ||||||||
\(437\) | −30.7139 | −1.46925 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.9471 | 1.52475 | 0.762377 | − | 0.647133i | \(-0.224032\pi\) | ||||
0.762377 | + | 0.647133i | \(0.224032\pi\) | |||||||
\(440\) | −14.8310 | −0.707040 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.97723 | 0.141613 | ||||||||
\(443\) | 36.6620 | 1.74186 | 0.870932 | − | 0.491403i | \(-0.163516\pi\) | ||||
0.870932 | + | 0.491403i | \(0.163516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.2016 | 1.43169 | ||||||||
\(446\) | 5.72109 | 0.270902 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.85792 | −0.182270 | ||||||||
\(449\) | −11.6838 | −0.551394 | −0.275697 | − | 0.961245i | \(-0.588909\pi\) | ||||
−0.275697 | + | 0.961245i | \(0.588909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.2620 | 1.09537 | ||||||||
\(452\) | 22.9395 | 1.07898 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.13989 | −0.194295 | ||||||||
\(455\) | −9.70151 | −0.454814 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.13913 | 0.146842 | 0.0734212 | − | 0.997301i | \(-0.476608\pi\) | ||||
0.0734212 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(458\) | −5.22484 | −0.244141 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 33.9246 | 1.58174 | ||||||||
\(461\) | 37.6820 | 1.75503 | 0.877513 | − | 0.479553i | \(-0.159201\pi\) | ||||
0.877513 | + | 0.479553i | \(0.159201\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.3727 | 1.45801 | 0.729007 | − | 0.684506i | \(-0.239982\pi\) | ||||
0.729007 | + | 0.684506i | \(0.239982\pi\) | |||||||
\(464\) | 12.1525 | 0.564168 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.21321 | 0.0562011 | ||||||||
\(467\) | −0.680845 | −0.0315057 | −0.0157529 | − | 0.999876i | \(-0.505015\pi\) | ||||
−0.0157529 | + | 0.999876i | \(0.505015\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.4051 | 0.665167 | ||||||||
\(470\) | −19.2274 | −0.886892 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.74223 | 0.126221 | ||||||||
\(473\) | 14.6417 | 0.673226 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 79.4847 | 3.64701 | ||||||||
\(476\) | −5.27746 | −0.241892 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.13449 | 0.189107 | ||||||||
\(479\) | 37.0258 | 1.69175 | 0.845876 | − | 0.533379i | \(-0.179078\pi\) | ||||
0.845876 | + | 0.533379i | \(0.179078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.9888 | −0.592238 | ||||||||
\(482\) | −5.36638 | −0.244432 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.2125 | 0.509659 | ||||||||
\(485\) | 44.5636 | 2.02353 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.9255 | 0.495081 | 0.247541 | − | 0.968877i | \(-0.420378\pi\) | ||||
0.247541 | + | 0.968877i | \(0.420378\pi\) | |||||||
\(488\) | −23.7866 | −1.07677 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.77234 | −0.0800661 | ||||||||
\(491\) | 25.0361 | 1.12987 | 0.564933 | − | 0.825137i | \(-0.308902\pi\) | ||||
0.564933 | + | 0.825137i | \(0.308902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.1398 | 0.546749 | ||||||||
\(494\) | 6.88419 | 0.309734 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.41442 | −0.0635093 | ||||||||
\(497\) | −2.63479 | −0.118187 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.5673 | −1.54744 | −0.773721 | − | 0.633526i | \(-0.781607\pi\) | ||||
−0.773721 | + | 0.633526i | \(0.781607\pi\) | |||||||
\(500\) | −50.6244 | −2.26399 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.81093 | −0.0808256 | ||||||||
\(503\) | 18.9830 | 0.846410 | 0.423205 | − | 0.906034i | \(-0.360905\pi\) | ||||
0.423205 | + | 0.906034i | \(0.360905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −80.7964 | −3.59539 | ||||||||
\(506\) | −4.32918 | −0.192456 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.81314 | −0.0804449 | ||||||||
\(509\) | 1.07444 | 0.0476237 | 0.0238119 | − | 0.999716i | \(-0.492420\pi\) | ||||
0.0238119 | + | 0.999716i | \(0.492420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.610455 | −0.0270049 | ||||||||
\(512\) | −22.8812 | −1.01122 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.66297 | 0.117459 | ||||||||
\(515\) | −1.99987 | −0.0881249 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.8076 | −1.04706 | ||||||||
\(518\) | −2.37288 | −0.104259 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15.9913 | −0.701266 | ||||||||
\(521\) | −1.02818 | −0.0450456 | −0.0225228 | − | 0.999746i | \(-0.507170\pi\) | ||||
−0.0225228 | + | 0.999746i | \(0.507170\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0103 | −0.831264 | −0.415632 | − | 0.909533i | \(-0.636440\pi\) | ||||
−0.415632 | + | 0.909533i | \(0.636440\pi\) | |||||||
\(524\) | −12.2274 | −0.534158 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.69591 | −0.335558 | ||||||||
\(527\) | −1.41294 | −0.0615485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.17416 | −0.0945286 | ||||||||
\(530\) | −16.2345 | −0.705182 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.2029 | −0.529065 | ||||||||
\(533\) | 25.0820 | 1.08642 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 55.6895 | 2.40767 | ||||||||
\(536\) | 23.7445 | 1.02560 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.22362 | 0.0958669 | ||||||||
\(539\) | −2.19453 | −0.0945251 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.4975 | −1.31119 | −0.655594 | − | 0.755113i | \(-0.727582\pi\) | ||||
−0.655594 | + | 0.755113i | \(0.727582\pi\) | |||||||
\(542\) | 4.39062 | 0.188593 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.2617 | −0.568590 | ||||||||
\(545\) | 72.8313 | 3.11975 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.5343 | 0.450415 | 0.225207 | − | 0.974311i | \(-0.427694\pi\) | ||||
0.225207 | + | 0.974311i | \(0.427694\pi\) | |||||||
\(548\) | 8.61207 | 0.367889 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.2035 | 0.477719 | ||||||||
\(551\) | 28.0706 | 1.19585 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.36638 | −0.313251 | ||||||||
\(554\) | 10.0623 | 0.427505 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.94386 | 0.167257 | ||||||||
\(557\) | −20.4261 | −0.865480 | −0.432740 | − | 0.901519i | \(-0.642453\pi\) | ||||
−0.432740 | + | 0.901519i | \(0.642453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.7872 | 0.667728 | ||||||||
\(560\) | 11.9463 | 0.504823 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.03330 | 0.0435872 | ||||||||
\(563\) | 41.1411 | 1.73389 | 0.866945 | − | 0.498404i | \(-0.166080\pi\) | ||||
0.866945 | + | 0.498404i | \(0.166080\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −51.8725 | −2.18229 | ||||||||
\(566\) | −5.07496 | −0.213317 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.34302 | −0.182229 | ||||||||
\(569\) | 11.3486 | 0.475759 | 0.237879 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237879 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.4620 | −1.48404 | −0.742020 | − | 0.670378i | \(-0.766132\pi\) | ||||
−0.742020 | + | 0.670378i | \(0.766132\pi\) | |||||||
\(572\) | −9.41515 | −0.393667 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.58214 | 0.191255 | ||||||||
\(575\) | −53.8953 | −2.24759 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.7787 | 1.69764 | 0.848819 | − | 0.528683i | \(-0.177314\pi\) | ||||
0.848819 | + | 0.528683i | \(0.177314\pi\) | |||||||
\(578\) | 3.68644 | 0.153336 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −31.0050 | −1.28741 | ||||||||
\(581\) | 11.0482 | 0.458355 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.1018 | −0.832530 | ||||||||
\(584\) | −1.00623 | −0.0416383 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.88497 | 0.201796 | ||||||||
\(587\) | 30.2579 | 1.24888 | 0.624439 | − | 0.781073i | \(-0.285327\pi\) | ||||
0.624439 | + | 0.781073i | \(0.285327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.26710 | −0.134619 | ||||||||
\(590\) | −2.94852 | −0.121389 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.9942 | 0.657359 | ||||||||
\(593\) | 44.4426 | 1.82504 | 0.912519 | − | 0.409034i | \(-0.134134\pi\) | ||||
0.912519 | + | 0.409034i | \(0.134134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9338 | 0.489237 | ||||||||
\(596\) | 7.61087 | 0.311753 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.66788 | −0.190884 | ||||||||
\(599\) | −20.4984 | −0.837540 | −0.418770 | − | 0.908092i | \(-0.637539\pi\) | ||||
−0.418770 | + | 0.908092i | \(0.637539\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.2297 | −0.621234 | −0.310617 | − | 0.950535i | \(-0.600536\pi\) | ||||
−0.310617 | + | 0.950535i | \(0.600536\pi\) | |||||||
\(602\) | 2.88412 | 0.117548 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −27.9865 | −1.13876 | ||||||||
\(605\) | −25.3545 | −1.03081 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.8705 | 1.37476 | 0.687380 | − | 0.726298i | \(-0.258761\pi\) | ||||
0.687380 | + | 0.726298i | \(0.258761\pi\) | |||||||
\(608\) | −30.6646 | −1.24362 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.5760 | 1.03554 | ||||||||
\(611\) | −25.6702 | −1.03850 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.78220 | 0.395099 | 0.197550 | − | 0.980293i | \(-0.436702\pi\) | ||||
0.197550 | + | 0.980293i | \(0.436702\pi\) | |||||||
\(614\) | −13.0427 | −0.526361 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.61732 | −0.145746 | ||||||||
\(617\) | −27.4862 | −1.10655 | −0.553276 | − | 0.832998i | \(-0.686622\pi\) | ||||
−0.553276 | + | 0.832998i | \(0.686622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.0270 | 1.84998 | 0.924990 | − | 0.379992i | \(-0.124073\pi\) | ||||
0.924990 | + | 0.379992i | \(0.124073\pi\) | |||||||
\(620\) | 3.60863 | 0.144926 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.08526 | 0.0435150 | ||||||||
\(623\) | 7.36625 | 0.295123 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 55.4258 | 2.21703 | ||||||||
\(626\) | 1.47870 | 0.0591007 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.9965 | 0.718140 | ||||||||
\(629\) | 15.9775 | 0.637064 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.88781 | 0.274199 | 0.137100 | − | 0.990557i | \(-0.456222\pi\) | ||||
0.137100 | + | 0.990557i | \(0.456222\pi\) | |||||||
\(632\) | −12.1423 | −0.482993 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.66405 | −0.0660880 | ||||||||
\(635\) | 4.10000 | 0.162703 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.36622 | −0.0937531 | ||||||||
\(638\) | 3.95659 | 0.156643 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 44.1984 | 1.74710 | ||||||||
\(641\) | 18.6043 | 0.734827 | 0.367414 | − | 0.930058i | \(-0.380243\pi\) | ||||
0.367414 | + | 0.930058i | \(0.380243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.1894 | −1.26942 | −0.634712 | − | 0.772749i | \(-0.718881\pi\) | ||||
−0.634712 | + | 0.772749i | \(0.718881\pi\) | |||||||
\(644\) | 8.27431 | 0.326053 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.46821 | −0.333177 | ||||||||
\(647\) | −0.965623 | −0.0379626 | −0.0189813 | − | 0.999820i | \(-0.506042\pi\) | ||||
−0.0189813 | + | 0.999820i | \(0.506042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.65090 | −0.143310 | ||||||||
\(650\) | 12.0800 | 0.473817 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.2012 | 0.830303 | ||||||||
\(653\) | 38.7135 | 1.51498 | 0.757489 | − | 0.652848i | \(-0.226426\pi\) | ||||
0.757489 | + | 0.652848i | \(0.226426\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.6496 | 1.08036 | ||||||||
\(656\) | −30.8856 | −1.20588 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.68960 | −0.182820 | ||||||||
\(659\) | 19.8754 | 0.774235 | 0.387117 | − | 0.922030i | \(-0.373471\pi\) | ||||
0.387117 | + | 0.922030i | \(0.373471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.6662 | 1.58173 | 0.790865 | − | 0.611990i | \(-0.209631\pi\) | ||||
0.790865 | + | 0.611990i | \(0.209631\pi\) | |||||||
\(662\) | 0.00718538 | 0.000279268 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.2111 | 0.706726 | ||||||||
\(665\) | 27.5942 | 1.07006 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.0335 | −0.736980 | ||||||||
\(668\) | −27.5961 | −1.06772 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.5308 | −0.986339 | ||||||||
\(671\) | 31.6686 | 1.22255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.5654 | −0.869832 | −0.434916 | − | 0.900471i | \(-0.643222\pi\) | ||||
−0.434916 | + | 0.900471i | \(0.643222\pi\) | |||||||
\(674\) | −5.08526 | −0.195877 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.4190 | 0.516116 | ||||||||
\(677\) | 28.7074 | 1.10332 | 0.551658 | − | 0.834070i | \(-0.313995\pi\) | ||||
0.551658 | + | 0.834070i | \(0.313995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.8692 | 0.417121 | ||||||||
\(680\) | 19.6709 | 0.754343 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.460503 | −0.0176336 | ||||||||
\(683\) | −11.0647 | −0.423379 | −0.211690 | − | 0.977337i | \(-0.567897\pi\) | ||||
−0.211690 | + | 0.977337i | \(0.567897\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.4743 | −0.744073 | ||||||||
\(686\) | −0.432278 | −0.0165044 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.4402 | −0.741149 | ||||||||
\(689\) | −21.6745 | −0.825731 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.8585 | 0.907619 | 0.453809 | − | 0.891099i | \(-0.350065\pi\) | ||||
0.453809 | + | 0.891099i | \(0.350065\pi\) | |||||||
\(692\) | −28.5156 | −1.08400 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.3720 | 0.393716 | ||||||||
\(695\) | −8.91815 | −0.338285 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.8532 | −1.16865 | ||||||||
\(698\) | 6.76538 | 0.256074 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −21.4131 | −0.809339 | ||||||||
\(701\) | 38.1381 | 1.44046 | 0.720229 | − | 0.693737i | \(-0.244037\pi\) | ||||
0.720229 | + | 0.693737i | \(0.244037\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.9443 | 1.39338 | ||||||||
\(704\) | 8.46632 | 0.319086 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.80306 | 0.105495 | ||||||||
\(707\) | −19.7064 | −0.741137 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.87952 | 0.145698 | 0.0728492 | − | 0.997343i | \(-0.476791\pi\) | ||||
0.0728492 | + | 0.997343i | \(0.476791\pi\) | |||||||
\(710\) | 4.66974 | 0.175252 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.1420 | 0.455042 | ||||||||
\(713\) | 2.21529 | 0.0829631 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.2902 | 0.796210 | ||||||||
\(716\) | −6.45533 | −0.241247 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.01538 | 0.112533 | ||||||||
\(719\) | 3.10342 | 0.115738 | 0.0578691 | − | 0.998324i | \(-0.481569\pi\) | ||||
0.0578691 | + | 0.998324i | \(0.481569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.487774 | −0.0181657 | ||||||||
\(722\) | −11.3676 | −0.423057 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.1192 | 0.822055 | ||||||||
\(725\) | 49.2568 | 1.82935 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.6900 | −1.76872 | −0.884362 | − | 0.466802i | \(-0.845406\pi\) | ||||
−0.884362 | + | 0.466802i | \(0.845406\pi\) | |||||||
\(728\) | −3.90032 | −0.144556 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.08193 | 0.0400441 | ||||||||
\(731\) | −19.4198 | −0.718267 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.5015 | −1.38515 | −0.692574 | − | 0.721346i | \(-0.743524\pi\) | ||||
−0.692574 | + | 0.721346i | \(0.743524\pi\) | |||||||
\(734\) | 10.8253 | 0.399569 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.7924 | 0.766419 | ||||||||
\(737\) | −31.6125 | −1.16446 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.09825 | 0.150757 | 0.0753783 | − | 0.997155i | \(-0.475984\pi\) | ||||
0.0753783 | + | 0.997155i | \(0.475984\pi\) | |||||||
\(740\) | −40.8063 | −1.50007 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.95964 | −0.145363 | ||||||||
\(743\) | 33.2979 | 1.22158 | 0.610791 | − | 0.791792i | \(-0.290852\pi\) | ||||
0.610791 | + | 0.791792i | \(0.290852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.2103 | −0.630535 | ||||||||
\(746\) | −5.25868 | −0.192534 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.5815 | 0.423463 | ||||||||
\(749\) | 13.5828 | 0.496305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.6824 | 0.900674 | 0.450337 | − | 0.892859i | \(-0.351304\pi\) | ||||
0.450337 | + | 0.892859i | \(0.351304\pi\) | |||||||
\(752\) | 31.6099 | 1.15269 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.26614 | 0.155364 | ||||||||
\(755\) | 63.2852 | 2.30319 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2286 | 0.953295 | 0.476647 | − | 0.879095i | \(-0.341852\pi\) | ||||
0.476647 | + | 0.879095i | \(0.341852\pi\) | |||||||
\(758\) | 6.53690 | 0.237431 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 45.4845 | 1.64989 | ||||||||
\(761\) | 25.9623 | 0.941131 | 0.470566 | − | 0.882365i | \(-0.344050\pi\) | ||||
0.470566 | + | 0.882365i | \(0.344050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.7637 | 0.643091 | ||||||||
\(764\) | −25.8904 | −0.936681 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.0121 | 0.397883 | ||||||||
\(767\) | −3.93653 | −0.142140 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.1020 | 1.15763 | 0.578814 | − | 0.815459i | \(-0.303516\pi\) | ||||
0.578814 | + | 0.815459i | \(0.303516\pi\) | |||||||
\(770\) | 3.88945 | 0.140166 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 26.0347 | 0.937008 | ||||||||
\(773\) | 35.2474 | 1.26776 | 0.633880 | − | 0.773431i | \(-0.281461\pi\) | ||||
0.633880 | + | 0.773431i | \(0.281461\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.73294 | −0.205933 | ||||||||
\(776\) | 17.9160 | 0.643148 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.07591 | −0.325387 | ||||||||
\(779\) | −71.3411 | −2.55606 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.78213 | 0.206901 | ||||||||
\(782\) | 5.74194 | 0.205331 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.91373 | 0.104062 | ||||||||
\(785\) | −40.6951 | −1.45247 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.54430 | 0.340218 | 0.170109 | − | 0.985425i | \(-0.445588\pi\) | ||||
0.170109 | + | 0.985425i | \(0.445588\pi\) | |||||||
\(788\) | −44.0906 | −1.57066 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.0557 | 0.464502 | ||||||||
\(791\) | −12.6518 | −0.449848 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.1462 | 1.21257 | ||||||||
\(794\) | 4.63223 | 0.164392 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.0557 | 0.462745 | ||||||||
\(797\) | −29.9392 | −1.06050 | −0.530251 | − | 0.847841i | \(-0.677902\pi\) | ||||
−0.530251 | + | 0.847841i | \(0.677902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.5768 | 1.11711 | ||||||||
\(800\) | −53.8088 | −1.90243 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.91817 | 0.314912 | ||||||||
\(803\) | 1.33966 | 0.0472756 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.7105 | −0.659458 | ||||||||
\(806\) | −0.496531 | −0.0174896 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −32.4828 | −1.14274 | ||||||||
\(809\) | 52.3491 | 1.84049 | 0.920247 | − | 0.391337i | \(-0.127987\pi\) | ||||
0.920247 | + | 0.391337i | \(0.127987\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.5843 | −1.31976 | −0.659882 | − | 0.751369i | \(-0.729394\pi\) | ||||
−0.659882 | + | 0.751369i | \(0.729394\pi\) | |||||||
\(812\) | −7.56219 | −0.265381 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.20736 | 0.182518 | ||||||||
\(815\) | −47.9417 | −1.67933 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44.9039 | −1.57099 | ||||||||
\(818\) | −4.47736 | −0.156547 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 78.7988 | 2.75178 | ||||||||
\(821\) | −22.0108 | −0.768181 | −0.384090 | − | 0.923296i | \(-0.625485\pi\) | ||||
−0.384090 | + | 0.923296i | \(0.625485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.1421 | −1.25983 | −0.629917 | − | 0.776662i | \(-0.716911\pi\) | ||||
−0.629917 | + | 0.776662i | \(0.716911\pi\) | |||||||
\(824\) | −0.804014 | −0.0280092 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.719152 | −0.0250225 | ||||||||
\(827\) | 6.82706 | 0.237400 | 0.118700 | − | 0.992930i | \(-0.462127\pi\) | ||||
0.118700 | + | 0.992930i | \(0.462127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.01103 | −0.312966 | −0.156483 | − | 0.987681i | \(-0.550016\pi\) | ||||
−0.156483 | + | 0.987681i | \(0.550016\pi\) | |||||||
\(830\) | −19.5811 | −0.679669 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.12870 | 0.316481 | ||||||||
\(833\) | 2.91068 | 0.100849 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 62.4023 | 2.15952 | ||||||||
\(836\) | 26.7797 | 0.926196 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.1105 | −0.383807 | ||||||||
\(839\) | −20.9726 | −0.724056 | −0.362028 | − | 0.932167i | \(-0.617915\pi\) | ||||
−0.362028 | + | 0.932167i | \(0.617915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.6046 | −0.400159 | ||||||||
\(842\) | 3.02855 | 0.104371 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33.8196 | −1.16412 | ||||||||
\(845\) | −30.3441 | −1.04387 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.18404 | −0.212486 | ||||||||
\(848\) | 26.6896 | 0.916526 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.8596 | −0.509680 | ||||||||
\(851\) | −25.0504 | −0.858717 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.0956 | 1.09893 | 0.549466 | − | 0.835516i | \(-0.314831\pi\) | ||||
0.549466 | + | 0.835516i | \(0.314831\pi\) | |||||||
\(854\) | 6.23806 | 0.213462 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.3890 | 0.765240 | ||||||||
\(857\) | −35.7115 | −1.21988 | −0.609941 | − | 0.792447i | \(-0.708807\pi\) | ||||
−0.609941 | + | 0.792447i | \(0.708807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0861 | 0.685330 | 0.342665 | − | 0.939458i | \(-0.388670\pi\) | ||||
0.342665 | + | 0.939458i | \(0.388670\pi\) | |||||||
\(860\) | 49.5980 | 1.69128 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.09017 | 0.173372 | ||||||||
\(863\) | −10.7248 | −0.365077 | −0.182538 | − | 0.983199i | \(-0.558431\pi\) | ||||
−0.182538 | + | 0.983199i | \(0.558431\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 64.4815 | 2.19244 | ||||||||
\(866\) | 9.41064 | 0.319787 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.880154 | 0.0298744 | ||||||||
\(869\) | 16.1657 | 0.548385 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.0857 | −1.15495 | ||||||||
\(872\) | 29.2806 | 0.991566 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.2770 | 0.449100 | ||||||||
\(875\) | 27.9209 | 0.943899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0168 | −0.777223 | −0.388612 | − | 0.921402i | \(-0.627045\pi\) | ||||
−0.388612 | + | 0.921402i | \(0.627045\pi\) | |||||||
\(878\) | −13.8100 | −0.466066 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −26.2165 | −0.883759 | ||||||||
\(881\) | 5.44399 | 0.183413 | 0.0917063 | − | 0.995786i | \(-0.470768\pi\) | ||||
0.0917063 | + | 0.995786i | \(0.470768\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2700 | −0.816750 | −0.408375 | − | 0.912814i | \(-0.633904\pi\) | ||||
−0.408375 | + | 0.912814i | \(0.633904\pi\) | |||||||
\(884\) | 12.4876 | 0.420005 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.8482 | −0.532430 | ||||||||
\(887\) | 44.8788 | 1.50688 | 0.753441 | − | 0.657516i | \(-0.228393\pi\) | ||||
0.753441 | + | 0.657516i | \(0.228393\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −13.0555 | −0.437621 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.9964 | 0.803459 | ||||||||
\(893\) | 73.0142 | 2.44333 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.5973 | 0.487933 | ||||||||
\(896\) | 10.7801 | 0.360138 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.05066 | 0.168543 | ||||||||
\(899\) | −2.02463 | −0.0675252 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.6617 | 0.888229 | ||||||||
\(902\) | −10.0557 | −0.334817 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.8545 | −0.693609 | ||||||||
\(905\) | −50.0177 | −1.66264 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.6797 | 1.88202 | 0.941009 | − | 0.338382i | \(-0.109880\pi\) | ||||
0.941009 | + | 0.338382i | \(0.109880\pi\) | |||||||
\(908\) | −17.3643 | −0.576254 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.19374 | 0.139021 | ||||||||
\(911\) | 1.65229 | 0.0547428 | 0.0273714 | − | 0.999625i | \(-0.491286\pi\) | ||||
0.0273714 | + | 0.999625i | \(0.491286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.2455 | −0.802409 | ||||||||
\(914\) | −1.35698 | −0.0448848 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.9150 | −0.724091 | ||||||||
\(917\) | 6.74380 | 0.222700 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.1884 | −0.995823 | −0.497912 | − | 0.867228i | \(-0.665900\pi\) | ||||
−0.497912 | + | 0.867228i | \(0.665900\pi\) | |||||||
\(920\) | −30.8411 | −1.01680 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.2891 | −0.536453 | ||||||||
\(923\) | 6.23451 | 0.205211 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 64.8280 | 2.13153 | ||||||||
\(926\) | −13.5617 | −0.445666 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19.0029 | −0.623802 | ||||||||
\(929\) | −48.4510 | −1.58963 | −0.794813 | − | 0.606854i | \(-0.792431\pi\) | ||||
−0.794813 | + | 0.606854i | \(0.792431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.73030 | 0.220577 | ||||||||
\(932\) | 5.08868 | 0.166685 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.294314 | 0.00963025 | ||||||||
\(935\) | −26.1890 | −0.856473 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.7524 | −1.52734 | −0.763668 | − | 0.645609i | \(-0.776604\pi\) | ||||
−0.763668 | + | 0.645609i | \(0.776604\pi\) | |||||||
\(938\) | −6.22702 | −0.203319 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −80.6468 | −2.63041 | ||||||||
\(941\) | 55.8314 | 1.82005 | 0.910026 | − | 0.414550i | \(-0.136061\pi\) | ||||
0.910026 | + | 0.414550i | \(0.136061\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48.3735 | 1.57526 | ||||||||
\(944\) | 4.84739 | 0.157769 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.32928 | −0.205783 | ||||||||
\(947\) | −42.8711 | −1.39312 | −0.696561 | − | 0.717497i | \(-0.745288\pi\) | ||||
−0.696561 | + | 0.717497i | \(0.745288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.44447 | 0.0468896 | ||||||||
\(950\) | −34.3595 | −1.11477 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.79777 | 0.155497 | ||||||||
\(953\) | 15.0549 | 0.487677 | 0.243838 | − | 0.969816i | \(-0.421593\pi\) | ||||
0.243838 | + | 0.969816i | \(0.421593\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 58.5453 | 1.89448 | ||||||||
\(956\) | 17.3416 | 0.560867 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.0054 | −0.517112 | ||||||||
\(959\) | −4.74982 | −0.153380 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7644 | −0.992399 | ||||||||
\(962\) | 5.61477 | 0.181027 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.5086 | −0.724953 | ||||||||
\(965\) | −58.8715 | −1.89514 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.6827 | −0.761585 | −0.380793 | − | 0.924660i | \(-0.624349\pi\) | ||||
−0.380793 | + | 0.924660i | \(0.624349\pi\) | |||||||
\(968\) | −10.1934 | −0.327627 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.2639 | −0.618525 | ||||||||
\(971\) | −25.6083 | −0.821810 | −0.410905 | − | 0.911678i | \(-0.634787\pi\) | ||||
−0.410905 | + | 0.911678i | \(0.634787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.17516 | −0.0697324 | ||||||||
\(974\) | −4.72285 | −0.151330 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.0472 | −1.34590 | ||||||||
\(977\) | −10.4357 | −0.333869 | −0.166935 | − | 0.985968i | \(-0.553387\pi\) | ||||
−0.166935 | + | 0.985968i | \(0.553387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.1655 | −0.516650 | ||||||||
\(980\) | −7.43385 | −0.237466 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.8226 | −0.345362 | ||||||||
\(983\) | 31.3815 | 1.00092 | 0.500458 | − | 0.865761i | \(-0.333165\pi\) | ||||
0.500458 | + | 0.865761i | \(0.333165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 99.7010 | 3.17674 | ||||||||
\(986\) | −5.24777 | −0.167123 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.8749 | 0.918632 | ||||||||
\(989\) | 30.4475 | 0.968173 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.0297 | −0.540967 | −0.270483 | − | 0.962725i | \(-0.587184\pi\) | ||||
−0.270483 | + | 0.962725i | \(0.587184\pi\) | |||||||
\(992\) | 2.21173 | 0.0702225 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.13896 | 0.0361257 | ||||||||
\(995\) | −29.5224 | −0.935924 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.32135 | 0.0418476 | 0.0209238 | − | 0.999781i | \(-0.493339\pi\) | ||||
0.0209238 | + | 0.999781i | \(0.493339\pi\) | |||||||
\(998\) | 14.9427 | 0.473001 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.u.1.7 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.12 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.12 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.7 | 18 | 1.1 | even | 1 | trivial |