Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5265,2,Mod(1,5265)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5265, 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("5265.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5265 = 3^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5265.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: | \(42.0412366642\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 20 x^{12} + 36 x^{11} + 156 x^{10} - 242 x^{9} - 601 x^{8} + 750 x^{7} + 1188 x^{6} - 1038 x^{5} - 1133 x^{4} + 438 x^{3} + 423 x^{2} + 90 x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.25591\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5265.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25591 | −1.59517 | −0.797584 | − | 0.603207i | \(-0.793889\pi\) | ||||
−0.797584 | + | 0.603207i | \(0.793889\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.08913 | 1.54456 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.21559 | 1.59334 | 0.796671 | − | 0.604413i | \(-0.206592\pi\) | ||||
0.796671 | + | 0.604413i | \(0.206592\pi\) | |||||||
\(8\) | −2.45697 | −0.868671 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.25591 | 0.713381 | ||||||||
\(11\) | −4.32629 | −1.30442 | −0.652212 | − | 0.758036i | \(-0.726159\pi\) | ||||
−0.652212 | + | 0.758036i | \(0.726159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −9.50998 | −2.54165 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.635548 | −0.158887 | ||||||||
\(17\) | −4.03439 | −0.978483 | −0.489241 | − | 0.872148i | \(-0.662726\pi\) | ||||
−0.489241 | + | 0.872148i | \(0.662726\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.09815 | 0.251933 | 0.125967 | − | 0.992034i | \(-0.459797\pi\) | ||||
0.125967 | + | 0.992034i | \(0.459797\pi\) | |||||||
\(20\) | −3.08913 | −0.690750 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.75971 | 2.08078 | ||||||||
\(23\) | 2.39337 | 0.499052 | 0.249526 | − | 0.968368i | \(-0.419725\pi\) | ||||
0.249526 | + | 0.968368i | \(0.419725\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.25591 | −0.442420 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.0225 | 2.46102 | ||||||||
\(29\) | 2.95802 | 0.549290 | 0.274645 | − | 0.961546i | \(-0.411440\pi\) | ||||
0.274645 | + | 0.961546i | \(0.411440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.70367 | −1.74283 | −0.871415 | − | 0.490546i | \(-0.836797\pi\) | ||||
−0.871415 | + | 0.490546i | \(0.836797\pi\) | |||||||
\(32\) | 6.34768 | 1.12212 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.10122 | 1.56085 | ||||||||
\(35\) | −4.21559 | −0.712564 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.76843 | 1.11272 | 0.556361 | − | 0.830940i | \(-0.312197\pi\) | ||||
0.556361 | + | 0.830940i | \(0.312197\pi\) | |||||||
\(38\) | −2.47733 | −0.401876 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.45697 | 0.388481 | ||||||||
\(41\) | 8.83954 | 1.38050 | 0.690252 | − | 0.723569i | \(-0.257500\pi\) | ||||
0.690252 | + | 0.723569i | \(0.257500\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.799491 | 0.121921 | 0.0609606 | − | 0.998140i | \(-0.480584\pi\) | ||||
0.0609606 | + | 0.998140i | \(0.480584\pi\) | |||||||
\(44\) | −13.3645 | −2.01477 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.39923 | −0.796073 | ||||||||
\(47\) | −12.7882 | −1.86535 | −0.932675 | − | 0.360719i | \(-0.882531\pi\) | ||||
−0.932675 | + | 0.360719i | \(0.882531\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.7712 | 1.53874 | ||||||||
\(50\) | −2.25591 | −0.319034 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.08913 | 0.428385 | ||||||||
\(53\) | 5.52360 | 0.758724 | 0.379362 | − | 0.925248i | \(-0.376143\pi\) | ||||
0.379362 | + | 0.925248i | \(0.376143\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.32629 | 0.583357 | ||||||||
\(56\) | −10.3576 | −1.38409 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.67302 | −0.876210 | ||||||||
\(59\) | 2.90495 | 0.378192 | 0.189096 | − | 0.981959i | \(-0.439444\pi\) | ||||
0.189096 | + | 0.981959i | \(0.439444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0980 | −1.67703 | −0.838514 | − | 0.544880i | \(-0.816575\pi\) | ||||
−0.838514 | + | 0.544880i | \(0.816575\pi\) | |||||||
\(62\) | 21.8906 | 2.78011 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0487 | −1.63109 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.66612 | −1.18090 | −0.590452 | − | 0.807073i | \(-0.701051\pi\) | ||||
−0.590452 | + | 0.807073i | \(0.701051\pi\) | |||||||
\(68\) | −12.4627 | −1.51133 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.50998 | 1.13666 | ||||||||
\(71\) | −0.931785 | −0.110583 | −0.0552913 | − | 0.998470i | \(-0.517609\pi\) | ||||
−0.0552913 | + | 0.998470i | \(0.517609\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6631 | 1.59914 | 0.799571 | − | 0.600571i | \(-0.205060\pi\) | ||||
0.799571 | + | 0.600571i | \(0.205060\pi\) | |||||||
\(74\) | −15.2690 | −1.77498 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.39233 | 0.389127 | ||||||||
\(77\) | −18.2378 | −2.07840 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9743 | −1.34722 | −0.673610 | − | 0.739087i | \(-0.735257\pi\) | ||||
−0.673610 | + | 0.739087i | \(0.735257\pi\) | |||||||
\(80\) | 0.635548 | 0.0710564 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −19.9412 | −2.20214 | ||||||||
\(83\) | −7.76044 | −0.851819 | −0.425910 | − | 0.904766i | \(-0.640046\pi\) | ||||
−0.425910 | + | 0.904766i | \(0.640046\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.03439 | 0.437591 | ||||||||
\(86\) | −1.80358 | −0.194485 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.6296 | 1.13312 | ||||||||
\(89\) | 10.2430 | 1.08575 | 0.542875 | − | 0.839813i | \(-0.317336\pi\) | ||||
0.542875 | + | 0.839813i | \(0.317336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.21559 | 0.441914 | ||||||||
\(92\) | 7.39343 | 0.770818 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 28.8490 | 2.97555 | ||||||||
\(95\) | −1.09815 | −0.112668 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.96362 | −0.402445 | −0.201222 | − | 0.979546i | \(-0.564491\pi\) | ||||
−0.201222 | + | 0.979546i | \(0.564491\pi\) | |||||||
\(98\) | −24.2988 | −2.45455 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.08913 | 0.308913 | ||||||||
\(101\) | −4.32854 | −0.430706 | −0.215353 | − | 0.976536i | \(-0.569090\pi\) | ||||
−0.215353 | + | 0.976536i | \(0.569090\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.8309 | −1.65840 | −0.829198 | − | 0.558955i | \(-0.811202\pi\) | ||||
−0.829198 | + | 0.558955i | \(0.811202\pi\) | |||||||
\(104\) | −2.45697 | −0.240926 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.4607 | −1.21029 | ||||||||
\(107\) | −16.1393 | −1.56025 | −0.780125 | − | 0.625624i | \(-0.784844\pi\) | ||||
−0.780125 | + | 0.625624i | \(0.784844\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.91526 | −0.662362 | −0.331181 | − | 0.943567i | \(-0.607447\pi\) | ||||
−0.331181 | + | 0.943567i | \(0.607447\pi\) | |||||||
\(110\) | −9.75971 | −0.930552 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.67921 | −0.253161 | ||||||||
\(113\) | 12.2408 | 1.15152 | 0.575761 | − | 0.817618i | \(-0.304706\pi\) | ||||
0.575761 | + | 0.817618i | \(0.304706\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.39337 | −0.223183 | ||||||||
\(116\) | 9.13769 | 0.848413 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.55329 | −0.603280 | ||||||||
\(119\) | −17.0073 | −1.55906 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.71677 | 0.701524 | ||||||||
\(122\) | 29.5479 | 2.67514 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −29.9759 | −2.69191 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.07671 | 0.184279 | 0.0921393 | − | 0.995746i | \(-0.470630\pi\) | ||||
0.0921393 | + | 0.995746i | \(0.470630\pi\) | |||||||
\(128\) | 16.7413 | 1.47974 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.25591 | 0.197856 | ||||||||
\(131\) | 18.7352 | 1.63690 | 0.818450 | − | 0.574577i | \(-0.194834\pi\) | ||||
0.818450 | + | 0.574577i | \(0.194834\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.62936 | 0.401416 | ||||||||
\(134\) | 21.8059 | 1.88374 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.91238 | 0.849980 | ||||||||
\(137\) | 0.478085 | 0.0408456 | 0.0204228 | − | 0.999791i | \(-0.493499\pi\) | ||||
0.0204228 | + | 0.999791i | \(0.493499\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0222 | 0.850075 | 0.425038 | − | 0.905176i | \(-0.360261\pi\) | ||||
0.425038 | + | 0.905176i | \(0.360261\pi\) | |||||||
\(140\) | −13.0225 | −1.10060 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.10202 | 0.176398 | ||||||||
\(143\) | −4.32629 | −0.361782 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.95802 | −0.245650 | ||||||||
\(146\) | −30.8227 | −2.55090 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.9085 | 1.71867 | ||||||||
\(149\) | −12.3025 | −1.00786 | −0.503931 | − | 0.863744i | \(-0.668113\pi\) | ||||
−0.503931 | + | 0.863744i | \(0.668113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.77828 | 0.795745 | 0.397872 | − | 0.917441i | \(-0.369749\pi\) | ||||
0.397872 | + | 0.917441i | \(0.369749\pi\) | |||||||
\(152\) | −2.69813 | −0.218847 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 41.1429 | 3.31539 | ||||||||
\(155\) | 9.70367 | 0.779417 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.48276 | −0.277954 | −0.138977 | − | 0.990296i | \(-0.544381\pi\) | ||||
−0.138977 | + | 0.990296i | \(0.544381\pi\) | |||||||
\(158\) | 27.0130 | 2.14904 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.34768 | −0.501828 | ||||||||
\(161\) | 10.0895 | 0.795161 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.28319 | 0.492137 | 0.246069 | − | 0.969252i | \(-0.420861\pi\) | ||||
0.246069 | + | 0.969252i | \(0.420861\pi\) | |||||||
\(164\) | 27.3064 | 2.13228 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.5069 | 1.35880 | ||||||||
\(167\) | −19.1729 | −1.48364 | −0.741820 | − | 0.670599i | \(-0.766037\pi\) | ||||
−0.741820 | + | 0.670599i | \(0.766037\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −9.10122 | −0.698031 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.46973 | 0.188315 | ||||||||
\(173\) | −25.4541 | −1.93524 | −0.967620 | − | 0.252413i | \(-0.918776\pi\) | ||||
−0.967620 | + | 0.252413i | \(0.918776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.21559 | 0.318668 | ||||||||
\(176\) | 2.74956 | 0.207256 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −23.1072 | −1.73196 | ||||||||
\(179\) | 0.0384041 | 0.00287046 | 0.00143523 | − | 0.999999i | \(-0.499543\pi\) | ||||
0.00143523 | + | 0.999999i | \(0.499543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.65492 | 0.643315 | 0.321657 | − | 0.946856i | \(-0.395760\pi\) | ||||
0.321657 | + | 0.946856i | \(0.395760\pi\) | |||||||
\(182\) | −9.50998 | −0.704927 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.88044 | −0.433512 | ||||||||
\(185\) | −6.76843 | −0.497625 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.4539 | 1.27636 | ||||||||
\(188\) | −39.5043 | −2.88115 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.47733 | 0.179725 | ||||||||
\(191\) | −0.842914 | −0.0609911 | −0.0304956 | − | 0.999535i | \(-0.509709\pi\) | ||||
−0.0304956 | + | 0.999535i | \(0.509709\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4549 | 0.752560 | 0.376280 | − | 0.926506i | \(-0.377203\pi\) | ||||
0.376280 | + | 0.926506i | \(0.377203\pi\) | |||||||
\(194\) | 8.94157 | 0.641967 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 33.2735 | 2.37668 | ||||||||
\(197\) | 6.60143 | 0.470333 | 0.235166 | − | 0.971955i | \(-0.424436\pi\) | ||||
0.235166 | + | 0.971955i | \(0.424436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.47208 | −0.458794 | −0.229397 | − | 0.973333i | \(-0.573675\pi\) | ||||
−0.229397 | + | 0.973333i | \(0.573675\pi\) | |||||||
\(200\) | −2.45697 | −0.173734 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.76480 | 0.687049 | ||||||||
\(203\) | 12.4698 | 0.875207 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.83954 | −0.617380 | ||||||||
\(206\) | 37.9689 | 2.64542 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.635548 | −0.0440673 | ||||||||
\(209\) | −4.75092 | −0.328628 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1642 | 1.04395 | 0.521974 | − | 0.852961i | \(-0.325196\pi\) | ||||
0.521974 | + | 0.852961i | \(0.325196\pi\) | |||||||
\(212\) | 17.0631 | 1.17190 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 36.4089 | 2.48886 | ||||||||
\(215\) | −0.799491 | −0.0545248 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −40.9067 | −2.77692 | ||||||||
\(218\) | 15.6002 | 1.05658 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 13.3645 | 0.901031 | ||||||||
\(221\) | −4.03439 | −0.271382 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.0022 | −1.54034 | −0.770171 | − | 0.637837i | \(-0.779829\pi\) | ||||
−0.770171 | + | 0.637837i | \(0.779829\pi\) | |||||||
\(224\) | 26.7592 | 1.78792 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.6142 | −1.83687 | ||||||||
\(227\) | 16.5591 | 1.09906 | 0.549532 | − | 0.835473i | \(-0.314806\pi\) | ||||
0.549532 | + | 0.835473i | \(0.314806\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4916 | 1.15588 | 0.577938 | − | 0.816081i | \(-0.303858\pi\) | ||||
0.577938 | + | 0.816081i | \(0.303858\pi\) | |||||||
\(230\) | 5.39923 | 0.356014 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.26776 | −0.477152 | ||||||||
\(233\) | −10.5425 | −0.690660 | −0.345330 | − | 0.938481i | \(-0.612233\pi\) | ||||
−0.345330 | + | 0.938481i | \(0.612233\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7882 | 0.834210 | ||||||||
\(236\) | 8.97375 | 0.584141 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 38.3670 | 2.48696 | ||||||||
\(239\) | −3.19160 | −0.206447 | −0.103224 | − | 0.994658i | \(-0.532916\pi\) | ||||
−0.103224 | + | 0.994658i | \(0.532916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9488 | 0.705272 | 0.352636 | − | 0.935761i | \(-0.385285\pi\) | ||||
0.352636 | + | 0.935761i | \(0.385285\pi\) | |||||||
\(242\) | −17.4083 | −1.11905 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −40.4614 | −2.59028 | ||||||||
\(245\) | −10.7712 | −0.688145 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.09815 | 0.0698737 | ||||||||
\(248\) | 23.8416 | 1.51395 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.25591 | 0.142676 | ||||||||
\(251\) | 1.57317 | 0.0992975 | 0.0496488 | − | 0.998767i | \(-0.484190\pi\) | ||||
0.0496488 | + | 0.998767i | \(0.484190\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.3544 | −0.650976 | ||||||||
\(254\) | −4.68488 | −0.293955 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.6695 | −0.729344 | ||||||||
\(257\) | −13.0843 | −0.816178 | −0.408089 | − | 0.912942i | \(-0.633805\pi\) | ||||
−0.408089 | + | 0.912942i | \(0.633805\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.5329 | 1.77295 | ||||||||
\(260\) | −3.08913 | −0.191580 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −42.2649 | −2.61113 | ||||||||
\(263\) | −14.5499 | −0.897182 | −0.448591 | − | 0.893737i | \(-0.648074\pi\) | ||||
−0.448591 | + | 0.893737i | \(0.648074\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.52360 | −0.339312 | ||||||||
\(266\) | −10.4434 | −0.640326 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −29.8599 | −1.82398 | ||||||||
\(269\) | −12.2822 | −0.748857 | −0.374429 | − | 0.927256i | \(-0.622161\pi\) | ||||
−0.374429 | + | 0.927256i | \(0.622161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.7884 | −1.87026 | −0.935131 | − | 0.354303i | \(-0.884718\pi\) | ||||
−0.935131 | + | 0.354303i | \(0.884718\pi\) | |||||||
\(272\) | 2.56405 | 0.155468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.07852 | −0.0651556 | ||||||||
\(275\) | −4.32629 | −0.260885 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.24859 | 0.195189 | 0.0975944 | − | 0.995226i | \(-0.468885\pi\) | ||||
0.0975944 | + | 0.995226i | \(0.468885\pi\) | |||||||
\(278\) | −22.6093 | −1.35601 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.3576 | 0.618984 | ||||||||
\(281\) | −10.3407 | −0.616871 | −0.308436 | − | 0.951245i | \(-0.599805\pi\) | ||||
−0.308436 | + | 0.951245i | \(0.599805\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.21779 | −0.488497 | −0.244248 | − | 0.969713i | \(-0.578541\pi\) | ||||
−0.244248 | + | 0.969713i | \(0.578541\pi\) | |||||||
\(284\) | −2.87840 | −0.170802 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.75971 | 0.577104 | ||||||||
\(287\) | 37.2638 | 2.19961 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.723709 | −0.0425711 | ||||||||
\(290\) | 6.67302 | 0.391853 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 42.2070 | 2.46998 | ||||||||
\(293\) | 3.66476 | 0.214098 | 0.107049 | − | 0.994254i | \(-0.465860\pi\) | ||||
0.107049 | + | 0.994254i | \(0.465860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.90495 | −0.169132 | ||||||||
\(296\) | −16.6298 | −0.966590 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.7534 | 1.60771 | ||||||||
\(299\) | 2.39337 | 0.138412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.37032 | 0.194262 | ||||||||
\(302\) | −22.0589 | −1.26935 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.697928 | −0.0400289 | ||||||||
\(305\) | 13.0980 | 0.749990 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.85132 | −0.448099 | −0.224049 | − | 0.974578i | \(-0.571928\pi\) | ||||
−0.224049 | + | 0.974578i | \(0.571928\pi\) | |||||||
\(308\) | −56.3390 | −3.21021 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21.8906 | −1.24330 | ||||||||
\(311\) | 4.60248 | 0.260983 | 0.130491 | − | 0.991449i | \(-0.458345\pi\) | ||||
0.130491 | + | 0.991449i | \(0.458345\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.98950 | −0.564640 | −0.282320 | − | 0.959320i | \(-0.591104\pi\) | ||||
−0.282320 | + | 0.959320i | \(0.591104\pi\) | |||||||
\(314\) | 7.85679 | 0.443384 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −36.9903 | −2.08087 | ||||||||
\(317\) | 27.2236 | 1.52903 | 0.764514 | − | 0.644607i | \(-0.222979\pi\) | ||||
0.764514 | + | 0.644607i | \(0.222979\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.7972 | −0.716507 | ||||||||
\(320\) | 13.0487 | 0.729445 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.7609 | −1.26842 | ||||||||
\(323\) | −4.43037 | −0.246513 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −14.1743 | −0.785042 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −21.7185 | −1.19920 | ||||||||
\(329\) | −53.9097 | −2.97214 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.3945 | −1.61567 | −0.807834 | − | 0.589411i | \(-0.799360\pi\) | ||||
−0.807834 | + | 0.589411i | \(0.799360\pi\) | |||||||
\(332\) | −23.9730 | −1.31569 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 43.2522 | 2.36666 | ||||||||
\(335\) | 9.66612 | 0.528116 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2391 | −1.32039 | −0.660194 | − | 0.751095i | \(-0.729526\pi\) | ||||
−0.660194 | + | 0.751095i | \(0.729526\pi\) | |||||||
\(338\) | −2.25591 | −0.122705 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.4627 | 0.675887 | ||||||||
\(341\) | 41.9809 | 2.27339 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.8977 | 0.858395 | ||||||||
\(344\) | −1.96433 | −0.105909 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 57.4221 | 3.08703 | ||||||||
\(347\) | −11.8083 | −0.633903 | −0.316951 | − | 0.948442i | \(-0.602659\pi\) | ||||
−0.316951 | + | 0.948442i | \(0.602659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9748 | 1.28334 | 0.641670 | − | 0.766980i | \(-0.278242\pi\) | ||||
0.641670 | + | 0.766980i | \(0.278242\pi\) | |||||||
\(350\) | −9.50998 | −0.508330 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.4619 | −1.46372 | ||||||||
\(353\) | −14.4690 | −0.770107 | −0.385054 | − | 0.922894i | \(-0.625817\pi\) | ||||
−0.385054 | + | 0.922894i | \(0.625817\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.931785 | 0.0494540 | ||||||||
\(356\) | 31.6418 | 1.67701 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.0866362 | −0.00457887 | ||||||||
\(359\) | 23.2724 | 1.22827 | 0.614135 | − | 0.789201i | \(-0.289505\pi\) | ||||
0.614135 | + | 0.789201i | \(0.289505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7941 | −0.936530 | ||||||||
\(362\) | −19.5247 | −1.02620 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.0225 | 0.682564 | ||||||||
\(365\) | −13.6631 | −0.715158 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.6268 | 1.70311 | 0.851553 | − | 0.524268i | \(-0.175661\pi\) | ||||
0.851553 | + | 0.524268i | \(0.175661\pi\) | |||||||
\(368\) | −1.52110 | −0.0792929 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15.2690 | 0.793795 | ||||||||
\(371\) | 23.2852 | 1.20891 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.7273 | −1.84989 | −0.924945 | − | 0.380101i | \(-0.875889\pi\) | ||||
−0.924945 | + | 0.380101i | \(0.875889\pi\) | |||||||
\(374\) | −39.3745 | −2.03601 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.4202 | 1.62037 | ||||||||
\(377\) | 2.95802 | 0.152346 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.26986 | 0.270695 | 0.135347 | − | 0.990798i | \(-0.456785\pi\) | ||||
0.135347 | + | 0.990798i | \(0.456785\pi\) | |||||||
\(380\) | −3.39233 | −0.174023 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.90154 | 0.0972911 | ||||||||
\(383\) | −32.5075 | −1.66105 | −0.830527 | − | 0.556978i | \(-0.811961\pi\) | ||||
−0.830527 | + | 0.556978i | \(0.811961\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.2378 | 0.929487 | ||||||||
\(386\) | −23.5853 | −1.20046 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.2441 | −0.621601 | ||||||||
\(389\) | 28.0499 | 1.42219 | 0.711093 | − | 0.703098i | \(-0.248200\pi\) | ||||
0.711093 | + | 0.703098i | \(0.248200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.65579 | −0.488314 | ||||||||
\(392\) | −26.4645 | −1.33666 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.8922 | −0.750260 | ||||||||
\(395\) | 11.9743 | 0.602495 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.4381 | 1.02576 | 0.512880 | − | 0.858460i | \(-0.328578\pi\) | ||||
0.512880 | + | 0.858460i | \(0.328578\pi\) | |||||||
\(398\) | 14.6004 | 0.731854 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.635548 | −0.0317774 | ||||||||
\(401\) | −15.4383 | −0.770952 | −0.385476 | − | 0.922718i | \(-0.625963\pi\) | ||||
−0.385476 | + | 0.922718i | \(0.625963\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.70367 | −0.483374 | ||||||||
\(404\) | −13.3714 | −0.665253 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −28.1307 | −1.39610 | ||||||||
\(407\) | −29.2822 | −1.45146 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.01427 | −0.445727 | −0.222863 | − | 0.974850i | \(-0.571540\pi\) | ||||
−0.222863 | + | 0.974850i | \(0.571540\pi\) | |||||||
\(410\) | 19.9412 | 0.984825 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −51.9927 | −2.56150 | ||||||||
\(413\) | 12.2461 | 0.602589 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.76044 | 0.380945 | ||||||||
\(416\) | 6.34768 | 0.311221 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.7176 | 0.524217 | ||||||||
\(419\) | 24.1705 | 1.18081 | 0.590403 | − | 0.807108i | \(-0.298969\pi\) | ||||
0.590403 | + | 0.807108i | \(0.298969\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6219 | −0.712628 | −0.356314 | − | 0.934366i | \(-0.615967\pi\) | ||||
−0.356314 | + | 0.934366i | \(0.615967\pi\) | |||||||
\(422\) | −34.2091 | −1.66527 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.5713 | −0.659082 | ||||||||
\(425\) | −4.03439 | −0.195697 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −55.2158 | −2.67208 | ||||||||
\(428\) | −49.8565 | −2.40990 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.80358 | 0.0869763 | ||||||||
\(431\) | 19.1759 | 0.923672 | 0.461836 | − | 0.886965i | \(-0.347191\pi\) | ||||
0.461836 | + | 0.886965i | \(0.347191\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.0916 | −1.83056 | −0.915282 | − | 0.402813i | \(-0.868032\pi\) | ||||
−0.915282 | + | 0.402813i | \(0.868032\pi\) | |||||||
\(434\) | 92.2817 | 4.42966 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.3621 | −1.02306 | ||||||||
\(437\) | 2.62828 | 0.125728 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.16322 | 0.389609 | 0.194805 | − | 0.980842i | \(-0.437593\pi\) | ||||
0.194805 | + | 0.980842i | \(0.437593\pi\) | |||||||
\(440\) | −10.6296 | −0.506745 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.10122 | 0.432901 | ||||||||
\(443\) | −14.7454 | −0.700573 | −0.350286 | − | 0.936643i | \(-0.613916\pi\) | ||||
−0.350286 | + | 0.936643i | \(0.613916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.2430 | −0.485562 | ||||||||
\(446\) | 51.8909 | 2.45711 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −55.0079 | −2.59888 | ||||||||
\(449\) | 27.8207 | 1.31294 | 0.656469 | − | 0.754353i | \(-0.272049\pi\) | ||||
0.656469 | + | 0.754353i | \(0.272049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.2424 | −1.80076 | ||||||||
\(452\) | 37.8135 | 1.77860 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −37.3557 | −1.75319 | ||||||||
\(455\) | −4.21559 | −0.197630 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2011 | 1.31919 | 0.659597 | − | 0.751620i | \(-0.270727\pi\) | ||||
0.659597 | + | 0.751620i | \(0.270727\pi\) | |||||||
\(458\) | −39.4594 | −1.84382 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.39343 | −0.344720 | ||||||||
\(461\) | −12.2631 | −0.571151 | −0.285576 | − | 0.958356i | \(-0.592185\pi\) | ||||
−0.285576 | + | 0.958356i | \(0.592185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.68122 | 0.356977 | 0.178488 | − | 0.983942i | \(-0.442879\pi\) | ||||
0.178488 | + | 0.983942i | \(0.442879\pi\) | |||||||
\(464\) | −1.87996 | −0.0872750 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.7829 | 1.10172 | ||||||||
\(467\) | 31.6557 | 1.46485 | 0.732426 | − | 0.680847i | \(-0.238388\pi\) | ||||
0.732426 | + | 0.680847i | \(0.238388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.7484 | −1.88158 | ||||||||
\(470\) | −28.8490 | −1.33071 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.13737 | −0.328524 | ||||||||
\(473\) | −3.45883 | −0.159037 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.09815 | 0.0503867 | ||||||||
\(476\) | −52.5378 | −2.40806 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.19995 | 0.329318 | ||||||||
\(479\) | −21.5067 | −0.982665 | −0.491332 | − | 0.870972i | \(-0.663490\pi\) | ||||
−0.491332 | + | 0.870972i | \(0.663490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.76843 | 0.308614 | ||||||||
\(482\) | −24.6994 | −1.12503 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 23.8381 | 1.08355 | ||||||||
\(485\) | 3.96362 | 0.179979 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5371 | 1.29314 | 0.646571 | − | 0.762854i | \(-0.276203\pi\) | ||||
0.646571 | + | 0.762854i | \(0.276203\pi\) | |||||||
\(488\) | 32.1814 | 1.45679 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 24.2988 | 1.09771 | ||||||||
\(491\) | 15.4443 | 0.696991 | 0.348495 | − | 0.937310i | \(-0.386693\pi\) | ||||
0.348495 | + | 0.937310i | \(0.386693\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.9338 | −0.537471 | ||||||||
\(494\) | −2.47733 | −0.111460 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.16715 | 0.276913 | ||||||||
\(497\) | −3.92802 | −0.176196 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.52244 | 0.336751 | 0.168375 | − | 0.985723i | \(-0.446148\pi\) | ||||
0.168375 | + | 0.985723i | \(0.446148\pi\) | |||||||
\(500\) | −3.08913 | −0.138150 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.54893 | −0.158396 | ||||||||
\(503\) | −26.3229 | −1.17368 | −0.586839 | − | 0.809704i | \(-0.699628\pi\) | ||||
−0.586839 | + | 0.809704i | \(0.699628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.32854 | 0.192618 | ||||||||
\(506\) | 23.3586 | 1.03842 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.41523 | 0.284630 | ||||||||
\(509\) | −4.38464 | −0.194346 | −0.0971729 | − | 0.995268i | \(-0.530980\pi\) | ||||
−0.0971729 | + | 0.995268i | \(0.530980\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 57.5979 | 2.54798 | ||||||||
\(512\) | −7.15730 | −0.316311 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.5170 | 1.30194 | ||||||||
\(515\) | 16.8309 | 0.741657 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 55.3254 | 2.43321 | ||||||||
\(518\) | −64.3676 | −2.82815 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.45697 | 0.107745 | ||||||||
\(521\) | −26.4071 | −1.15692 | −0.578458 | − | 0.815712i | \(-0.696345\pi\) | ||||
−0.578458 | + | 0.815712i | \(0.696345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.4053 | −0.804807 | −0.402404 | − | 0.915462i | \(-0.631825\pi\) | ||||
−0.402404 | + | 0.915462i | \(0.631825\pi\) | |||||||
\(524\) | 57.8754 | 2.52830 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.8231 | 1.43116 | ||||||||
\(527\) | 39.1484 | 1.70533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.2718 | −0.750947 | ||||||||
\(530\) | 12.4607 | 0.541260 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.3007 | 0.620013 | ||||||||
\(533\) | 8.83954 | 0.382883 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.1393 | 0.697765 | ||||||||
\(536\) | 23.7494 | 1.02582 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.7075 | 1.19455 | ||||||||
\(539\) | −46.5992 | −2.00717 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.49220 | −0.107148 | −0.0535739 | − | 0.998564i | \(-0.517061\pi\) | ||||
−0.0535739 | + | 0.998564i | \(0.517061\pi\) | |||||||
\(542\) | 69.4558 | 2.98338 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25.6090 | −1.09798 | ||||||||
\(545\) | 6.91526 | 0.296217 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.0530 | −0.900161 | −0.450081 | − | 0.892988i | \(-0.648605\pi\) | ||||
−0.450081 | + | 0.892988i | \(0.648605\pi\) | |||||||
\(548\) | 1.47687 | 0.0630886 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.75971 | 0.416156 | ||||||||
\(551\) | 3.24835 | 0.138384 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −50.4789 | −2.14658 | ||||||||
\(554\) | −7.32852 | −0.311359 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.9600 | 1.31300 | ||||||||
\(557\) | −22.8244 | −0.967102 | −0.483551 | − | 0.875316i | \(-0.660653\pi\) | ||||
−0.483551 | + | 0.875316i | \(0.660653\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.799491 | 0.0338149 | ||||||||
\(560\) | 2.67921 | 0.113217 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.3276 | 0.984014 | ||||||||
\(563\) | −15.4201 | −0.649878 | −0.324939 | − | 0.945735i | \(-0.605344\pi\) | ||||
−0.324939 | + | 0.945735i | \(0.605344\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.2408 | −0.514976 | ||||||||
\(566\) | 18.5386 | 0.779235 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.28937 | 0.0960598 | ||||||||
\(569\) | −4.76808 | −0.199888 | −0.0999442 | − | 0.994993i | \(-0.531866\pi\) | ||||
−0.0999442 | + | 0.994993i | \(0.531866\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.3824 | −1.18777 | −0.593883 | − | 0.804552i | \(-0.702406\pi\) | ||||
−0.593883 | + | 0.804552i | \(0.702406\pi\) | |||||||
\(572\) | −13.3645 | −0.558796 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −84.0638 | −3.50876 | ||||||||
\(575\) | 2.39337 | 0.0998104 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5884 | −0.773844 | −0.386922 | − | 0.922112i | \(-0.626462\pi\) | ||||
−0.386922 | + | 0.922112i | \(0.626462\pi\) | |||||||
\(578\) | 1.63262 | 0.0679081 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.13769 | −0.379422 | ||||||||
\(581\) | −32.7148 | −1.35724 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.8967 | −0.989699 | ||||||||
\(584\) | −33.5698 | −1.38913 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.26737 | −0.341522 | ||||||||
\(587\) | −10.2852 | −0.424515 | −0.212257 | − | 0.977214i | \(-0.568082\pi\) | ||||
−0.212257 | + | 0.977214i | \(0.568082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.6561 | −0.439077 | ||||||||
\(590\) | 6.55329 | 0.269795 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.30166 | −0.176797 | ||||||||
\(593\) | −29.9608 | −1.23034 | −0.615171 | − | 0.788394i | \(-0.710913\pi\) | ||||
−0.615171 | + | 0.788394i | \(0.710913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.0073 | 0.697232 | ||||||||
\(596\) | −38.0040 | −1.55671 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.39923 | −0.220791 | ||||||||
\(599\) | −34.1173 | −1.39399 | −0.696997 | − | 0.717074i | \(-0.745481\pi\) | ||||
−0.696997 | + | 0.717074i | \(0.745481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.7701 | −1.54068 | −0.770338 | − | 0.637636i | \(-0.779913\pi\) | ||||
−0.770338 | + | 0.637636i | \(0.779913\pi\) | |||||||
\(602\) | −7.60314 | −0.309881 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30.2063 | 1.22908 | ||||||||
\(605\) | −7.71677 | −0.313731 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.3129 | −1.39272 | −0.696358 | − | 0.717694i | \(-0.745198\pi\) | ||||
−0.696358 | + | 0.717694i | \(0.745198\pi\) | |||||||
\(608\) | 6.97072 | 0.282700 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29.5479 | −1.19636 | ||||||||
\(611\) | −12.7882 | −0.517355 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6306 | 0.712095 | 0.356048 | − | 0.934468i | \(-0.384124\pi\) | ||||
0.356048 | + | 0.934468i | \(0.384124\pi\) | |||||||
\(614\) | 17.7119 | 0.714793 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 44.8099 | 1.80544 | ||||||||
\(617\) | 3.05417 | 0.122956 | 0.0614782 | − | 0.998108i | \(-0.480419\pi\) | ||||
0.0614782 | + | 0.998108i | \(0.480419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.6857 | −0.751041 | −0.375521 | − | 0.926814i | \(-0.622536\pi\) | ||||
−0.375521 | + | 0.926814i | \(0.622536\pi\) | |||||||
\(620\) | 29.9759 | 1.20386 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.3828 | −0.416311 | ||||||||
\(623\) | 43.1800 | 1.72997 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.5354 | 0.900696 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.7587 | −0.429318 | ||||||||
\(629\) | −27.3065 | −1.08878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1057 | 0.919823 | 0.459911 | − | 0.887965i | \(-0.347881\pi\) | ||||
0.459911 | + | 0.887965i | \(0.347881\pi\) | |||||||
\(632\) | 29.4206 | 1.17029 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −61.4139 | −2.43906 | ||||||||
\(635\) | −2.07671 | −0.0824119 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.7712 | 0.426769 | ||||||||
\(638\) | 28.8694 | 1.14295 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.7413 | −0.661759 | ||||||||
\(641\) | 36.0663 | 1.42454 | 0.712268 | − | 0.701908i | \(-0.247668\pi\) | ||||
0.712268 | + | 0.701908i | \(0.247668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.19636 | −0.165488 | −0.0827441 | − | 0.996571i | \(-0.526368\pi\) | ||||
−0.0827441 | + | 0.996571i | \(0.526368\pi\) | |||||||
\(644\) | 31.1676 | 1.22818 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.99452 | 0.393229 | ||||||||
\(647\) | 0.325332 | 0.0127901 | 0.00639506 | − | 0.999980i | \(-0.497964\pi\) | ||||
0.00639506 | + | 0.999980i | \(0.497964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.5676 | −0.493323 | ||||||||
\(650\) | −2.25591 | −0.0884840 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.4096 | 0.760137 | ||||||||
\(653\) | 17.5931 | 0.688471 | 0.344235 | − | 0.938883i | \(-0.388138\pi\) | ||||
0.344235 | + | 0.938883i | \(0.388138\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.7352 | −0.732044 | ||||||||
\(656\) | −5.61795 | −0.219344 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 121.615 | 4.74106 | ||||||||
\(659\) | −41.6237 | −1.62143 | −0.810714 | − | 0.585442i | \(-0.800921\pi\) | ||||
−0.810714 | + | 0.585442i | \(0.800921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.29887 | −0.206102 | −0.103051 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103051 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(662\) | 66.3113 | 2.57726 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.0672 | 0.739950 | ||||||||
\(665\) | −4.62936 | −0.179519 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.07963 | 0.274124 | ||||||||
\(668\) | −59.2274 | −2.29158 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.8059 | −0.842435 | ||||||||
\(671\) | 56.6658 | 2.18756 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.91548 | 0.228025 | 0.114012 | − | 0.993479i | \(-0.463630\pi\) | ||||
0.114012 | + | 0.993479i | \(0.463630\pi\) | |||||||
\(674\) | 54.6812 | 2.10624 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.08913 | 0.118813 | ||||||||
\(677\) | 1.13425 | 0.0435928 | 0.0217964 | − | 0.999762i | \(-0.493061\pi\) | ||||
0.0217964 | + | 0.999762i | \(0.493061\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.7090 | −0.641232 | ||||||||
\(680\) | −9.91238 | −0.380122 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −94.7050 | −3.62644 | ||||||||
\(683\) | 36.6543 | 1.40254 | 0.701268 | − | 0.712898i | \(-0.252618\pi\) | ||||
0.701268 | + | 0.712898i | \(0.252618\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.478085 | −0.0182667 | ||||||||
\(686\) | −35.8638 | −1.36929 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.508115 | −0.0193717 | ||||||||
\(689\) | 5.52360 | 0.210432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.106753 | 0.00406106 | 0.00203053 | − | 0.999998i | \(-0.499354\pi\) | ||||
0.00203053 | + | 0.999998i | \(0.499354\pi\) | |||||||
\(692\) | −78.6309 | −2.98910 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.6384 | 1.01118 | ||||||||
\(695\) | −10.0222 | −0.380165 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.6621 | −1.35080 | ||||||||
\(698\) | −54.0849 | −2.04715 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.0225 | 0.492204 | ||||||||
\(701\) | −32.7446 | −1.23674 | −0.618372 | − | 0.785885i | \(-0.712208\pi\) | ||||
−0.618372 | + | 0.785885i | \(0.712208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.43276 | 0.280332 | ||||||||
\(704\) | 56.4524 | 2.12763 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32.6408 | 1.22845 | ||||||||
\(707\) | −18.2473 | −0.686262 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.10454 | −0.191705 | −0.0958524 | − | 0.995396i | \(-0.530558\pi\) | ||||
−0.0958524 | + | 0.995396i | \(0.530558\pi\) | |||||||
\(710\) | −2.10202 | −0.0788875 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25.1666 | −0.943160 | ||||||||
\(713\) | −23.2245 | −0.869763 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.32629 | 0.161794 | ||||||||
\(716\) | 0.118635 | 0.00443361 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −52.5004 | −1.95930 | ||||||||
\(719\) | −35.4870 | −1.32344 | −0.661722 | − | 0.749750i | \(-0.730174\pi\) | ||||
−0.661722 | + | 0.749750i | \(0.730174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −70.9520 | −2.64239 | ||||||||
\(722\) | 40.1418 | 1.49392 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.7361 | 0.993641 | ||||||||
\(725\) | 2.95802 | 0.109858 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1780 | −1.08215 | −0.541076 | − | 0.840974i | \(-0.681983\pi\) | ||||
−0.541076 | + | 0.840974i | \(0.681983\pi\) | |||||||
\(728\) | −10.3576 | −0.383877 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 30.8227 | 1.14080 | ||||||||
\(731\) | −3.22546 | −0.119298 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.5000 | 1.27429 | 0.637144 | − | 0.770745i | \(-0.280116\pi\) | ||||
0.637144 | + | 0.770745i | \(0.280116\pi\) | |||||||
\(734\) | −73.6031 | −2.71674 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.1924 | 0.559998 | ||||||||
\(737\) | 41.8184 | 1.54040 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.1371 | −0.740756 | −0.370378 | − | 0.928881i | \(-0.620772\pi\) | ||||
−0.370378 | + | 0.928881i | \(0.620772\pi\) | |||||||
\(740\) | −20.9085 | −0.768613 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −52.5293 | −1.92841 | ||||||||
\(743\) | −11.8986 | −0.436518 | −0.218259 | − | 0.975891i | \(-0.570038\pi\) | ||||
−0.218259 | + | 0.975891i | \(0.570038\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.3025 | 0.450729 | ||||||||
\(746\) | 80.5976 | 2.95089 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 53.9174 | 1.97142 | ||||||||
\(749\) | −68.0368 | −2.48601 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.42721 | 0.125061 | 0.0625303 | − | 0.998043i | \(-0.480083\pi\) | ||||
0.0625303 | + | 0.998043i | \(0.480083\pi\) | |||||||
\(752\) | 8.12751 | 0.296380 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.67302 | −0.243017 | ||||||||
\(755\) | −9.77828 | −0.355868 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.8498 | −0.576070 | −0.288035 | − | 0.957620i | \(-0.593002\pi\) | ||||
−0.288035 | + | 0.957620i | \(0.593002\pi\) | |||||||
\(758\) | −11.8883 | −0.431804 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.69813 | 0.0978714 | ||||||||
\(761\) | 1.25854 | 0.0456222 | 0.0228111 | − | 0.999740i | \(-0.492738\pi\) | ||||
0.0228111 | + | 0.999740i | \(0.492738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.1519 | −1.05537 | ||||||||
\(764\) | −2.60387 | −0.0942047 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 73.3339 | 2.64966 | ||||||||
\(767\) | 2.90495 | 0.104892 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.8522 | 1.32892 | 0.664462 | − | 0.747322i | \(-0.268661\pi\) | ||||
0.664462 | + | 0.747322i | \(0.268661\pi\) | |||||||
\(770\) | −41.1429 | −1.48269 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 32.2965 | 1.16238 | ||||||||
\(773\) | −46.8403 | −1.68473 | −0.842364 | − | 0.538909i | \(-0.818837\pi\) | ||||
−0.842364 | + | 0.538909i | \(0.818837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.70367 | −0.348566 | ||||||||
\(776\) | 9.73850 | 0.349592 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −63.2780 | −2.26863 | ||||||||
\(779\) | 9.70715 | 0.347795 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.03117 | 0.144247 | ||||||||
\(782\) | 21.7826 | 0.778943 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.84560 | −0.244486 | ||||||||
\(785\) | 3.48276 | 0.124305 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.5720 | −1.33930 | −0.669649 | − | 0.742678i | \(-0.733555\pi\) | ||||
−0.669649 | + | 0.742678i | \(0.733555\pi\) | |||||||
\(788\) | 20.3927 | 0.726459 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27.0130 | −0.961081 | ||||||||
\(791\) | 51.6024 | 1.83477 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0980 | −0.465124 | ||||||||
\(794\) | −46.1066 | −1.63626 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.9931 | −0.708636 | ||||||||
\(797\) | −10.4391 | −0.369771 | −0.184886 | − | 0.982760i | \(-0.559191\pi\) | ||||
−0.184886 | + | 0.982760i | \(0.559191\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.5925 | 1.82521 | ||||||||
\(800\) | 6.34768 | 0.224424 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34.8274 | 1.22980 | ||||||||
\(803\) | −59.1104 | −2.08596 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.0895 | −0.355607 | ||||||||
\(806\) | 21.8906 | 0.771063 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.6351 | 0.374142 | ||||||||
\(809\) | −37.5611 | −1.32058 | −0.660289 | − | 0.751012i | \(-0.729566\pi\) | ||||
−0.660289 | + | 0.751012i | \(0.729566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.2183 | 1.51760 | 0.758800 | − | 0.651324i | \(-0.225786\pi\) | ||||
0.758800 | + | 0.651324i | \(0.225786\pi\) | |||||||
\(812\) | 38.5207 | 1.35181 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 66.0579 | 2.31533 | ||||||||
\(815\) | −6.28319 | −0.220091 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.877962 | 0.0307160 | ||||||||
\(818\) | 20.3354 | 0.711010 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.3064 | −0.953583 | ||||||||
\(821\) | −3.68430 | −0.128583 | −0.0642914 | − | 0.997931i | \(-0.520479\pi\) | ||||
−0.0642914 | + | 0.997931i | \(0.520479\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −51.3253 | −1.78909 | −0.894544 | − | 0.446981i | \(-0.852499\pi\) | ||||
−0.894544 | + | 0.446981i | \(0.852499\pi\) | |||||||
\(824\) | 41.3530 | 1.44060 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.6260 | −0.961231 | ||||||||
\(827\) | −32.3392 | −1.12454 | −0.562272 | − | 0.826953i | \(-0.690072\pi\) | ||||
−0.562272 | + | 0.826953i | \(0.690072\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.9258 | −1.66453 | −0.832265 | − | 0.554378i | \(-0.812956\pi\) | ||||
−0.832265 | + | 0.554378i | \(0.812956\pi\) | |||||||
\(830\) | −17.5069 | −0.607672 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.0487 | −0.452382 | ||||||||
\(833\) | −43.4551 | −1.50563 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.1729 | 0.663504 | ||||||||
\(836\) | −14.6762 | −0.507587 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −54.5265 | −1.88359 | ||||||||
\(839\) | 6.54467 | 0.225947 | 0.112974 | − | 0.993598i | \(-0.463962\pi\) | ||||
0.112974 | + | 0.993598i | \(0.463962\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.2501 | −0.698281 | ||||||||
\(842\) | 32.9857 | 1.13676 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 46.8442 | 1.61244 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.5307 | 1.11777 | ||||||||
\(848\) | −3.51051 | −0.120551 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.10122 | 0.312169 | ||||||||
\(851\) | 16.1994 | 0.555307 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.5312 | 1.04537 | 0.522684 | − | 0.852527i | \(-0.324931\pi\) | ||||
0.522684 | + | 0.852527i | \(0.324931\pi\) | |||||||
\(854\) | 124.562 | 4.26242 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.6539 | 1.35534 | ||||||||
\(857\) | 51.7653 | 1.76827 | 0.884134 | − | 0.467234i | \(-0.154749\pi\) | ||||
0.884134 | + | 0.467234i | \(0.154749\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.73672 | 0.263973 | 0.131987 | − | 0.991251i | \(-0.457864\pi\) | ||||
0.131987 | + | 0.991251i | \(0.457864\pi\) | |||||||
\(860\) | −2.46973 | −0.0842170 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.2592 | −1.47341 | ||||||||
\(863\) | 33.8502 | 1.15228 | 0.576138 | − | 0.817353i | \(-0.304559\pi\) | ||||
0.576138 | + | 0.817353i | \(0.304559\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.4541 | 0.865465 | ||||||||
\(866\) | 85.9312 | 2.92006 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −126.366 | −4.28914 | ||||||||
\(869\) | 51.8045 | 1.75735 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.66612 | −0.327524 | ||||||||
\(872\) | 16.9906 | 0.575375 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.92917 | −0.200557 | ||||||||
\(875\) | −4.21559 | −0.142513 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.7722 | 1.37678 | 0.688389 | − | 0.725341i | \(-0.258318\pi\) | ||||
0.688389 | + | 0.725341i | \(0.258318\pi\) | |||||||
\(878\) | −18.4155 | −0.621493 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.74956 | −0.0926877 | ||||||||
\(881\) | 29.1285 | 0.981363 | 0.490681 | − | 0.871339i | \(-0.336748\pi\) | ||||
0.490681 | + | 0.871339i | \(0.336748\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4971 | −0.757086 | −0.378543 | − | 0.925584i | \(-0.623575\pi\) | ||||
−0.378543 | + | 0.925584i | \(0.623575\pi\) | |||||||
\(884\) | −12.4627 | −0.419167 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33.2642 | 1.11753 | ||||||||
\(887\) | −25.8907 | −0.869323 | −0.434662 | − | 0.900594i | \(-0.643132\pi\) | ||||
−0.434662 | + | 0.900594i | \(0.643132\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.75457 | 0.293619 | ||||||||
\(890\) | 23.1072 | 0.774554 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −71.0568 | −2.37916 | ||||||||
\(893\) | −14.0434 | −0.469944 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.0384041 | −0.00128371 | ||||||||
\(896\) | 70.5745 | 2.35773 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −62.7609 | −2.09436 | ||||||||
\(899\) | −28.7036 | −0.957319 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.2843 | −0.742399 | ||||||||
\(902\) | 86.2713 | 2.87252 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.0754 | −1.00029 | ||||||||
\(905\) | −8.65492 | −0.287699 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.90315 | 0.196011 | 0.0980055 | − | 0.995186i | \(-0.468754\pi\) | ||||
0.0980055 | + | 0.995186i | \(0.468754\pi\) | |||||||
\(908\) | 51.1531 | 1.69757 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.50998 | 0.315253 | ||||||||
\(911\) | 17.8384 | 0.591012 | 0.295506 | − | 0.955341i | \(-0.404512\pi\) | ||||
0.295506 | + | 0.955341i | \(0.404512\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.5739 | 1.11113 | ||||||||
\(914\) | −63.6192 | −2.10434 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 54.0337 | 1.78532 | ||||||||
\(917\) | 78.9798 | 2.60814 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.3670 | −1.66145 | −0.830727 | − | 0.556680i | \(-0.812075\pi\) | ||||
−0.830727 | + | 0.556680i | \(0.812075\pi\) | |||||||
\(920\) | 5.88044 | 0.193873 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.6645 | 0.911082 | ||||||||
\(923\) | −0.931785 | −0.0306701 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.76843 | 0.222545 | ||||||||
\(926\) | −17.3281 | −0.569438 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 18.7765 | 0.616370 | ||||||||
\(929\) | −30.6296 | −1.00492 | −0.502462 | − | 0.864599i | \(-0.667572\pi\) | ||||
−0.502462 | + | 0.864599i | \(0.667572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.8284 | 0.387660 | ||||||||
\(932\) | −32.5670 | −1.06677 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −71.4124 | −2.33669 | ||||||||
\(935\) | −17.4539 | −0.570804 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3784 | −0.763740 | −0.381870 | − | 0.924216i | \(-0.624720\pi\) | ||||
−0.381870 | + | 0.924216i | \(0.624720\pi\) | |||||||
\(938\) | 91.9246 | 3.00144 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 39.5043 | 1.28849 | ||||||||
\(941\) | −23.5653 | −0.768208 | −0.384104 | − | 0.923290i | \(-0.625490\pi\) | ||||
−0.384104 | + | 0.923290i | \(0.625490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.1563 | 0.688943 | ||||||||
\(944\) | −1.84623 | −0.0600897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.80280 | 0.253691 | ||||||||
\(947\) | −4.17712 | −0.135738 | −0.0678690 | − | 0.997694i | \(-0.521620\pi\) | ||||
−0.0678690 | + | 0.997694i | \(0.521620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.6631 | 0.443522 | ||||||||
\(950\) | −2.47733 | −0.0803753 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 41.7865 | 1.35431 | ||||||||
\(953\) | 26.3851 | 0.854697 | 0.427348 | − | 0.904087i | \(-0.359448\pi\) | ||||
0.427348 | + | 0.904087i | \(0.359448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.842914 | 0.0272761 | ||||||||
\(956\) | −9.85925 | −0.318871 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 48.5171 | 1.56752 | ||||||||
\(959\) | 2.01541 | 0.0650810 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.1612 | 2.03746 | ||||||||
\(962\) | −15.2690 | −0.492291 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 33.8221 | 1.08934 | ||||||||
\(965\) | −10.4549 | −0.336555 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2763 | 0.330464 | 0.165232 | − | 0.986255i | \(-0.447163\pi\) | ||||
0.165232 | + | 0.986255i | \(0.447163\pi\) | |||||||
\(968\) | −18.9599 | −0.609394 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.94157 | −0.287096 | ||||||||
\(971\) | 50.4571 | 1.61925 | 0.809623 | − | 0.586951i | \(-0.199672\pi\) | ||||
0.809623 | + | 0.586951i | \(0.199672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.2496 | 1.35446 | ||||||||
\(974\) | −64.3772 | −2.06278 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.32441 | 0.266458 | ||||||||
\(977\) | 21.5111 | 0.688202 | 0.344101 | − | 0.938933i | \(-0.388184\pi\) | ||||
0.344101 | + | 0.938933i | \(0.388184\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.3140 | −1.41628 | ||||||||
\(980\) | −33.2735 | −1.06288 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.8409 | −1.11182 | ||||||||
\(983\) | 3.34360 | 0.106644 | 0.0533221 | − | 0.998577i | \(-0.483019\pi\) | ||||
0.0533221 | + | 0.998577i | \(0.483019\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.60143 | −0.210339 | ||||||||
\(986\) | 26.9215 | 0.857357 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.39233 | 0.107924 | ||||||||
\(989\) | 1.91348 | 0.0608450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.2253 | 0.356584 | 0.178292 | − | 0.983978i | \(-0.442943\pi\) | ||||
0.178292 | + | 0.983978i | \(0.442943\pi\) | |||||||
\(992\) | −61.5958 | −1.95567 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.86126 | 0.281062 | ||||||||
\(995\) | 6.47208 | 0.205179 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.8375 | −1.29334 | −0.646669 | − | 0.762771i | \(-0.723838\pi\) | ||||
−0.646669 | + | 0.762771i | \(0.723838\pi\) | |||||||
\(998\) | −16.9699 | −0.537174 | ||||||||
\(999\) | 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 | 5265.2.a.bi.1.3 | ✓ | 14 | |
3.2 | odd | 2 | 5265.2.a.bj.1.12 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5265.2.a.bi.1.3 | ✓ | 14 | 1.1 | even | 1 | trivial | |
5265.2.a.bj.1.12 | yes | 14 | 3.2 | odd | 2 |