Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9280,2,Mod(1,9280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9280 = 2^{6} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9280.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: | \(74.1011730757\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 145) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9280.1 |
$q$-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 | 0 | ||||||||
\(3\) | 2.90321 | 1.67617 | 0.838085 | − | 0.545540i | \(-0.183675\pi\) | ||||
0.838085 | + | 0.545540i | \(0.183675\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.52543 | 0.576557 | 0.288279 | − | 0.957547i | \(-0.406917\pi\) | ||||
0.288279 | + | 0.957547i | \(0.406917\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.42864 | 1.80955 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.90321 | −1.47837 | −0.739187 | − | 0.673500i | \(-0.764790\pi\) | ||||
−0.739187 | + | 0.673500i | \(0.764790\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.42864 | 1.78298 | 0.891492 | − | 0.453037i | \(-0.149659\pi\) | ||||
0.891492 | + | 0.453037i | \(0.149659\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.90321 | 0.749606 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.14764 | 0.520880 | 0.260440 | − | 0.965490i | \(-0.416132\pi\) | ||||
0.260440 | + | 0.965490i | \(0.416132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.28100 | −0.523296 | −0.261648 | − | 0.965163i | \(-0.584266\pi\) | ||||
−0.261648 | + | 0.965163i | \(0.584266\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.42864 | 0.966408 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.90321 | 1.43942 | 0.719710 | − | 0.694275i | \(-0.244275\pi\) | ||||
0.719710 | + | 0.694275i | \(0.244275\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.05086 | 1.35694 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.71900 | 0.308742 | 0.154371 | − | 0.988013i | \(-0.450665\pi\) | ||||
0.154371 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.2351 | −2.47801 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.52543 | 0.257844 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.95407 | −1.30764 | −0.653820 | − | 0.756650i | \(-0.726835\pi\) | ||||
−0.653820 | + | 0.756650i | \(0.726835\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.6637 | 2.98858 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.37778 | −0.527521 | −0.263761 | − | 0.964588i | \(-0.584963\pi\) | ||||
−0.263761 | + | 0.964588i | \(0.584963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.09679 | 0.167259 | 0.0836293 | − | 0.996497i | \(-0.473349\pi\) | ||||
0.0836293 | + | 0.996497i | \(0.473349\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.42864 | 0.809254 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.7096 | 1.85389 | 0.926945 | − | 0.375196i | \(-0.122425\pi\) | ||||
0.926945 | + | 0.375196i | \(0.122425\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.67307 | −0.667582 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.23506 | 0.873084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.37778 | −0.463974 | −0.231987 | − | 0.972719i | \(-0.574523\pi\) | ||||
−0.231987 | + | 0.972719i | \(0.574523\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.90321 | −0.661149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.62222 | −0.877134 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.18421 | 0.414549 | 0.207274 | − | 0.978283i | \(-0.433541\pi\) | ||||
0.207274 | + | 0.978283i | \(0.433541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.42864 | 0.310955 | 0.155478 | − | 0.987839i | \(-0.450308\pi\) | ||||
0.155478 | + | 0.987839i | \(0.450308\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.28100 | 1.04331 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.42864 | 0.797375 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.09679 | 0.133994 | 0.0669970 | − | 0.997753i | \(-0.478658\pi\) | ||||
0.0669970 | + | 0.997753i | \(0.478658\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.0415 | 2.41271 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.57136 | 0.423843 | 0.211921 | − | 0.977287i | \(-0.432028\pi\) | ||||
0.211921 | + | 0.977287i | \(0.432028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.1891 | 1.66071 | 0.830356 | − | 0.557233i | \(-0.188137\pi\) | ||||
0.830356 | + | 0.557233i | \(0.188137\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.90321 | 0.335234 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.47949 | −0.852368 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.341219 | 0.0383902 | 0.0191951 | − | 0.999816i | \(-0.493890\pi\) | ||||
0.0191951 | + | 0.999816i | \(0.493890\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.18421 | 0.464912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.33185 | 0.804775 | 0.402388 | − | 0.915469i | \(-0.368180\pi\) | ||||
0.402388 | + | 0.915469i | \(0.368180\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.14764 | 0.232945 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.90321 | −0.311257 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.94914 | 0.312609 | 0.156304 | − | 0.987709i | \(-0.450042\pi\) | ||||
0.156304 | + | 0.987709i | \(0.450042\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.80642 | 1.02799 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.99063 | 0.517504 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.28100 | −0.234025 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.5763 | −1.88614 | −0.943068 | − | 0.332600i | \(-0.892074\pi\) | ||||
−0.943068 | + | 0.332600i | \(0.892074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26.6178 | −2.67519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4193 | −1.53427 | −0.767137 | − | 0.641483i | \(-0.778320\pi\) | ||||
−0.767137 | + | 0.641483i | \(0.778320\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.76049 | 0.764664 | 0.382332 | − | 0.924025i | \(-0.375121\pi\) | ||||
0.382332 | + | 0.924025i | \(0.375121\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.42864 | 0.432191 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.03657 | 0.293556 | 0.146778 | − | 0.989169i | \(-0.453110\pi\) | ||||
0.146778 | + | 0.989169i | \(0.453110\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.93978 | 0.760493 | 0.380246 | − | 0.924885i | \(-0.375839\pi\) | ||||
0.380246 | + | 0.924885i | \(0.375839\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.0923 | −2.19183 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.82071 | 0.735711 | 0.367855 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367855 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.90321 | 0.643728 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 34.8988 | 3.22639 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.27607 | 0.300317 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0415 | 1.18559 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.80642 | −0.884215 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4429 | −1.10413 | −0.552066 | − | 0.833801i | \(-0.686160\pi\) | ||||
−0.552066 | + | 0.833801i | \(0.686160\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.18421 | 0.280354 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.08742 | −0.357120 | −0.178560 | − | 0.983929i | \(-0.557144\pi\) | ||||
−0.178560 | + | 0.983929i | \(0.557144\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.47949 | −0.301710 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.05086 | 0.606841 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.9541 | −1.70479 | −0.852395 | − | 0.522898i | \(-0.824851\pi\) | ||||
−0.852395 | + | 0.522898i | \(0.824851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.90813 | −0.670759 | −0.335380 | − | 0.942083i | \(-0.608865\pi\) | ||||
−0.335380 | + | 0.942083i | \(0.608865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.8988 | 3.10744 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −31.5210 | −2.63592 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | −0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.5669 | −1.11898 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.1017 | 1.31910 | 0.659552 | − | 0.751659i | \(-0.270746\pi\) | ||||
0.659552 | + | 0.751659i | \(0.270746\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.67307 | 0.461668 | 0.230834 | − | 0.972993i | \(-0.425855\pi\) | ||||
0.230834 | + | 0.972993i | \(0.425855\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.6588 | 0.942557 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.71900 | 0.138074 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.89384 | −0.151145 | −0.0755726 | − | 0.997140i | \(-0.524078\pi\) | ||||
−0.0755726 | + | 0.997140i | \(0.524078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.80642 | −0.777700 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.5303 | 0.829908 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.95407 | 0.466359 | 0.233179 | − | 0.972434i | \(-0.425087\pi\) | ||||
0.233179 | + | 0.972434i | \(0.425087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.2351 | −1.10820 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.23951 | 0.328063 | 0.164032 | − | 0.986455i | \(-0.447550\pi\) | ||||
0.164032 | + | 0.986455i | \(0.447550\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.3274 | 2.17903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.3827 | −0.946929 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.4099 | −1.85585 | −0.927925 | − | 0.372766i | \(-0.878409\pi\) | ||||
−0.927925 | + | 0.372766i | \(0.878409\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.52543 | 0.115311 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.24443 | 0.694854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.61285 | 0.270037 | 0.135018 | − | 0.990843i | \(-0.456891\pi\) | ||||
0.135018 | + | 0.990843i | \(0.456891\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0415 | −1.34101 | −0.670507 | − | 0.741904i | \(-0.733923\pi\) | ||||
−0.670507 | + | 0.741904i | \(0.733923\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.05086 | 0.521214 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.95407 | −0.584795 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.5303 | −0.770055 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.7556 | 0.782353 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.85236 | 0.712892 | 0.356446 | − | 0.934316i | \(-0.383988\pi\) | ||||
0.356446 | + | 0.934316i | \(0.383988\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23951 | 0.161203 | 0.0806017 | − | 0.996746i | \(-0.474316\pi\) | ||||
0.0806017 | + | 0.996746i | \(0.474316\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.6637 | 1.33654 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.5620 | 0.752511 | 0.376255 | − | 0.926516i | \(-0.377212\pi\) | ||||
0.376255 | + | 0.926516i | \(0.377212\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.18421 | 0.225723 | 0.112861 | − | 0.993611i | \(-0.463998\pi\) | ||||
0.112861 | + | 0.993611i | \(0.463998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.18421 | 0.224597 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.52543 | −0.107064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.37778 | −0.235915 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 37.4750 | 2.60470 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.1842 | 0.773628 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.76049 | 0.396569 | 0.198284 | − | 0.980145i | \(-0.436463\pi\) | ||||
0.198284 | + | 0.980145i | \(0.436463\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.3684 | 0.710432 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.09679 | 0.0748003 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.62222 | 0.178008 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 41.1941 | 2.78364 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8064 | 0.928721 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.14764 | 0.545607 | 0.272803 | − | 0.962070i | \(-0.412049\pi\) | ||||
0.272803 | + | 0.962070i | \(0.412049\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.42864 | 0.361909 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5161 | −0.697975 | −0.348988 | − | 0.937127i | \(-0.613475\pi\) | ||||
−0.348988 | + | 0.937127i | \(0.613475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.48886 | −0.560960 | −0.280480 | − | 0.959860i | \(-0.590494\pi\) | ||||
−0.280480 | + | 0.959860i | \(0.590494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.7146 | −1.42871 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.5718 | −1.34771 | −0.673853 | − | 0.738866i | \(-0.735362\pi\) | ||||
−0.673853 | + | 0.738866i | \(0.735362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7096 | 0.829085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.990632 | 0.0643485 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.815792 | 0.0527692 | 0.0263846 | − | 0.999652i | \(-0.491601\pi\) | ||||
0.0263846 | + | 0.999652i | \(0.491601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.24443 | −0.466655 | −0.233327 | − | 0.972398i | \(-0.574961\pi\) | ||||
−0.233327 | + | 0.972398i | \(0.574961\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.00492 | −0.577666 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.67307 | −0.298552 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.6637 | −0.933029 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.2859 | 1.34894 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.4242 | 1.28916 | 0.644582 | − | 0.764535i | \(-0.277031\pi\) | ||||
0.644582 | + | 0.764535i | \(0.277031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.8479 | −2.12800 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.23506 | 0.390455 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.08250 | 0.192281 | 0.0961405 | − | 0.995368i | \(-0.469350\pi\) | ||||
0.0961405 | + | 0.995368i | \(0.469350\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.1334 | −0.753930 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.42864 | −0.336024 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.0558 | 1.23669 | 0.618346 | − | 0.785906i | \(-0.287803\pi\) | ||||
0.618346 | + | 0.785906i | \(0.287803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.37778 | −0.207496 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.56199 | 0.523985 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.4608 | 1.43043 | 0.715214 | − | 0.698906i | \(-0.246329\pi\) | ||||
0.715214 | + | 0.698906i | \(0.246329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.9353 | −1.33248 | −0.666238 | − | 0.745739i | \(-0.732097\pi\) | ||||
−0.666238 | + | 0.745739i | \(0.732097\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 28.4701 | 1.72309 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.90321 | −0.295675 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.3368 | −1.10175 | −0.550875 | − | 0.834588i | \(-0.685706\pi\) | ||||
−0.550875 | + | 0.834588i | \(0.685706\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.33185 | 0.558683 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.89877 | 0.411546 | 0.205773 | − | 0.978600i | \(-0.434029\pi\) | ||||
0.205773 | + | 0.978600i | \(0.434029\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.0049 | 1.72416 | 0.862082 | − | 0.506769i | \(-0.169160\pi\) | ||||
0.862082 | + | 0.506769i | \(0.169160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.62222 | −0.392266 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.15257 | −0.304146 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3876 | −0.728684 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −53.9309 | −3.16148 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.79213 | −0.455221 | −0.227611 | − | 0.973752i | \(-0.573091\pi\) | ||||
−0.227611 | + | 0.973752i | \(0.573091\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.18421 | 0.185392 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −34.5718 | −2.00606 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 44.3783 | 2.56646 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.67307 | 0.0964342 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −44.7654 | −2.57171 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.42864 | 0.139063 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.92549 | −0.338185 | −0.169093 | − | 0.985600i | \(-0.554084\pi\) | ||||
−0.169093 | + | 0.985600i | \(0.554084\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.5303 | 1.28171 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.94470 | 0.507207 | 0.253604 | − | 0.967308i | \(-0.418384\pi\) | ||||
0.253604 | + | 0.967308i | \(0.418384\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.5116 | −1.72462 | −0.862309 | − | 0.506382i | \(-0.830983\pi\) | ||||
−0.862309 | + | 0.506382i | \(0.830983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.28100 | 0.466581 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.2306 | 1.24860 | 0.624298 | − | 0.781186i | \(-0.285385\pi\) | ||||
0.624298 | + | 0.781186i | \(0.285385\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.90321 | 0.274527 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.81579 | 0.492050 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.89877 | −0.272575 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.42864 | 0.356597 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.0509 | 1.27472 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.3876 | 1.06887 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.54770 | 0.359894 | 0.179947 | − | 0.983676i | \(-0.442407\pi\) | ||||
0.179947 | + | 0.983676i | \(0.442407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −43.1798 | −2.36624 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.09679 | 0.0599239 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.66815 | 0.145343 | 0.0726717 | − | 0.997356i | \(-0.476847\pi\) | ||||
0.0726717 | + | 0.997356i | \(0.476847\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.7052 | 1.23318 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.42864 | −0.456436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8064 | −0.961457 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.0415 | 1.07900 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.6780 | −0.787956 | −0.393978 | − | 0.919120i | \(-0.628901\pi\) | ||||
−0.393978 | + | 0.919120i | \(0.628901\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.1240 | 0.595453 | 0.297727 | − | 0.954651i | \(-0.403772\pi\) | ||||
0.297727 | + | 0.954651i | \(0.403772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 45.3274 | 2.41940 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.4795 | −0.717441 | −0.358721 | − | 0.933445i | \(-0.616787\pi\) | ||||
−0.358721 | + | 0.933445i | \(0.616787\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.57136 | 0.189548 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.51114 | 0.503383 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.1891 | 1.38221 | 0.691105 | − | 0.722755i | \(-0.257124\pi\) | ||||
0.691105 | + | 0.722755i | \(0.257124\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7971 | −0.726161 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 37.8622 | 1.98725 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.1891 | 0.742693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.9862 | −1.19987 | −0.599935 | − | 0.800049i | \(-0.704807\pi\) | ||||
−0.599935 | + | 0.800049i | \(0.704807\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.3368 | −0.954574 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.15257 | −0.267508 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.2766 | 1.25699 | 0.628496 | − | 0.777813i | \(-0.283671\pi\) | ||||
0.628496 | + | 0.777813i | \(0.283671\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.90321 | 0.149921 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.42864 | −0.331092 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.7605 | −1.52869 | −0.764347 | − | 0.644805i | \(-0.776938\pi\) | ||||
−0.764347 | + | 0.644805i | \(0.776938\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.1245 | −1.85071 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.8020 | 1.21622 | 0.608112 | − | 0.793851i | \(-0.291927\pi\) | ||||
0.608112 | + | 0.793851i | \(0.291927\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.47949 | −0.381190 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.95407 | 0.302662 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.52051 | 0.330603 | 0.165301 | − | 0.986243i | \(-0.447140\pi\) | ||||
0.165301 | + | 0.986243i | \(0.447140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8256 | 0.749765 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.8666 | −0.598593 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.341219 | 0.0171686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7654 | 0.741055 | 0.370527 | − | 0.928822i | \(-0.379177\pi\) | ||||
0.370527 | + | 0.928822i | \(0.379177\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.1017 | −0.505718 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.81579 | 0.340364 | 0.170182 | − | 0.985413i | \(-0.445564\pi\) | ||||
0.170182 | + | 0.985413i | \(0.445564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0509 | 0.550482 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.18421 | 0.207915 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.0005 | 1.93318 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0825 | −0.547994 | −0.273997 | − | 0.961731i | \(-0.588346\pi\) | ||||
−0.273997 | + | 0.961731i | \(0.588346\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −57.9309 | −2.85752 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.85728 | 0.239011 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.33185 | 0.359906 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.9590 | −1.12431 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.9719 | −1.51308 | −0.756538 | − | 0.653950i | \(-0.773111\pi\) | ||||
−0.756538 | + | 0.653950i | \(0.773111\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.8988 | −1.11602 | −0.558009 | − | 0.829835i | \(-0.688434\pi\) | ||||
−0.558009 | + | 0.829835i | \(0.688434\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 68.9960 | 3.35470 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.14764 | 0.104176 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.70471 | 0.179284 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −91.5121 | −4.41825 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.0830 | −1.35271 | −0.676355 | − | 0.736576i | \(-0.736441\pi\) | ||||
−0.676355 | + | 0.736576i | \(0.736441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.0049 | 1.10555 | 0.552773 | − | 0.833332i | \(-0.313570\pi\) | ||||
0.552773 | + | 0.833332i | \(0.313570\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.90321 | −0.139198 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.7462 | −0.753243 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.7462 | 0.560616 | 0.280308 | − | 0.959910i | \(-0.409563\pi\) | ||||
0.280308 | + | 0.959910i | \(0.409563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.3684 | −1.20802 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6874 | −0.840352 | −0.420176 | − | 0.907443i | \(-0.638032\pi\) | ||||
−0.420176 | + | 0.907443i | \(0.638032\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.94914 | 0.139803 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 46.7467 | 2.21104 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.57136 | 0.0741571 | 0.0370785 | − | 0.999312i | \(-0.488195\pi\) | ||||
0.0370785 | + | 0.999312i | \(0.488195\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.5620 | 0.779874 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.4701 | 0.773834 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.80642 | 0.459732 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.47949 | 0.0692078 | 0.0346039 | − | 0.999401i | \(-0.488983\pi\) | ||||
0.0346039 | + | 0.999401i | \(0.488983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.1427 | 0.706802 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.2543 | 1.92140 | 0.960702 | − | 0.277583i | \(-0.0895334\pi\) | ||||
0.960702 | + | 0.277583i | \(0.0895334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.4242 | −1.59983 | −0.799914 | − | 0.600115i | \(-0.795122\pi\) | ||||
−0.799914 | + | 0.600115i | \(0.795122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.99063 | 0.231435 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.1699 | −0.701980 | −0.350990 | − | 0.936379i | \(-0.614155\pi\) | ||||
−0.350990 | + | 0.936379i | \(0.614155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.67307 | 0.0772552 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.49823 | −0.253345 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.37778 | −0.247271 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.28100 | −0.104659 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.3368 | −0.839583 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.9763 | −0.867051 | −0.433526 | − | 0.901141i | \(-0.642731\pi\) | ||||
−0.433526 | + | 0.901141i | \(0.642731\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −51.1338 | −2.33150 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.5718 | 1.39107 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.5763 | −0.843506 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.3926 | −1.46785 | −0.733923 | − | 0.679232i | \(-0.762313\pi\) | ||||
−0.733923 | + | 0.679232i | \(0.762313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.2859 | 0.781696 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.69673 | −0.121702 | −0.0608508 | − | 0.998147i | \(-0.519381\pi\) | ||||
−0.0608508 | + | 0.998147i | \(0.519381\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.14764 | −0.0967250 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26.6178 | −1.19638 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.44785 | 0.244370 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5718 | −0.652325 | −0.326163 | − | 0.945314i | \(-0.605756\pi\) | ||||
−0.326163 | + | 0.945314i | \(0.605756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.3082 | 0.549890 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.2494 | −0.992050 | −0.496025 | − | 0.868308i | \(-0.665208\pi\) | ||||
−0.496025 | + | 0.868308i | \(0.665208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.4193 | −0.686149 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 82.2405 | 3.65243 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.18421 | 0.407083 | 0.203541 | − | 0.979066i | \(-0.434755\pi\) | ||||
0.203541 | + | 0.979066i | \(0.434755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.6445 | 0.957496 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.0830 | −0.710081 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.76049 | 0.341968 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −62.3180 | −2.74074 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −70.8671 | −3.11072 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.01921 | 0.307517 | 0.153759 | − | 0.988108i | \(-0.450862\pi\) | ||||
0.153759 | + | 0.988108i | \(0.450862\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.29036 | 0.318785 | 0.159393 | − | 0.987215i | \(-0.449046\pi\) | ||||
0.159393 | + | 0.987215i | \(0.449046\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.42864 | 0.193282 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.69181 | 0.160818 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.6543 | 1.07193 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.2859 | 0.750145 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.7146 | −0.940562 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.03657 | 0.131282 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.4889 | 0.452628 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.9131 | 0.986935 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.9491 | −1.33061 | −0.665304 | − | 0.746573i | \(-0.731698\pi\) | ||||
−0.665304 | + | 0.746573i | \(0.731698\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −52.3783 | −2.24777 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.93978 | 0.340103 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4237 | 0.830498 | 0.415249 | − | 0.909708i | \(-0.363694\pi\) | ||||
0.415249 | + | 0.909708i | \(0.363694\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.1842 | 0.562688 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.28100 | 0.0971737 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.520505 | 0.0221341 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.0923 | −0.980215 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.3497 | −1.28596 | −0.642979 | − | 0.765884i | \(-0.722302\pi\) | ||||
−0.642979 | + | 0.765884i | \(0.722302\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.05086 | 0.298219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.5718 | −1.29074 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.1798 | 1.39836 | 0.699180 | − | 0.714946i | \(-0.253549\pi\) | ||||
0.699180 | + | 0.714946i | \(0.253549\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.82071 | 0.329020 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.38271 | 0.268048 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.06022 | −0.170213 | −0.0851067 | − | 0.996372i | \(-0.527123\pi\) | ||||
−0.0851067 | + | 0.996372i | \(0.527123\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.5496 | 1.32031 | 0.660154 | − | 0.751130i | \(-0.270491\pi\) | ||||
0.660154 | + | 0.751130i | \(0.270491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.6035 | 1.19493 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.90321 | 0.287884 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.7891 | 1.40666 | 0.703329 | − | 0.710865i | \(-0.251696\pi\) | ||||
0.703329 | + | 0.710865i | \(0.251696\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.50177 | 0.270204 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.1842 | 0.463999 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.5620 | 0.685928 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 34.8988 | 1.44289 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.5669 | 1.05526 | 0.527630 | − | 0.849474i | \(-0.323081\pi\) | ||||
0.527630 | + | 0.849474i | \(0.323081\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.92104 | −0.161564 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.6637 | 1.26134 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.96836 | 0.327221 | 0.163611 | − | 0.986525i | \(-0.447686\pi\) | ||||
0.163611 | + | 0.986525i | \(0.447686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.27607 | 0.134306 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.24443 | 0.378349 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.2815 | 1.52328 | 0.761640 | − | 0.648001i | \(-0.224395\pi\) | ||||
0.761640 | + | 0.648001i | \(0.224395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.9496 | −1.22167 | −0.610835 | − | 0.791758i | \(-0.709166\pi\) | ||||
−0.610835 | + | 0.791758i | \(0.709166\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.95407 | 0.242468 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.0415 | 0.530212 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8435 | −1.29249 | −0.646243 | − | 0.763132i | \(-0.723661\pi\) | ||||
−0.646243 | + | 0.763132i | \(0.723661\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.42864 | −0.179458 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 81.7057 | 3.30546 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.65386 | 0.107188 | 0.0535942 | − | 0.998563i | \(-0.482932\pi\) | ||||
0.0535942 | + | 0.998563i | \(0.482932\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.80642 | −0.395433 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.3096 | −0.737116 | −0.368558 | − | 0.929605i | \(-0.620148\pi\) | ||||
−0.368558 | + | 0.929605i | \(0.620148\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8113 | −0.514931 | −0.257466 | − | 0.966287i | \(-0.582887\pi\) | ||||
−0.257466 | + | 0.966287i | \(0.582887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 48.6735 | 1.95320 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.49871 | 0.180237 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 32.4701 | 1.29673 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.0825 | −0.681124 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.2766 | 1.20529 | 0.602645 | − | 0.798009i | \(-0.294113\pi\) | ||||
0.602645 | + | 0.798009i | \(0.294113\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.7239 | 0.664716 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.4429 | −0.493783 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.0415 | −1.19029 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.3876 | 0.766963 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50177 | −0.177809 | −0.0889046 | − | 0.996040i | \(-0.528337\pi\) | ||||
−0.0889046 | + | 0.996040i | \(0.528337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.0272 | 1.57852 | 0.789259 | − | 0.614060i | \(-0.210465\pi\) | ||||
0.789259 | + | 0.614060i | \(0.210465\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.18421 | 0.125378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.3604 | 1.07565 | 0.537825 | − | 0.843057i | \(-0.319246\pi\) | ||||
0.537825 | + | 0.843057i | \(0.319246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.6128 | −0.612858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.61285 | 0.298371 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.8430 | −0.893915 | −0.446958 | − | 0.894555i | \(-0.647493\pi\) | ||||
−0.446958 | + | 0.894555i | \(0.647493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.08742 | −0.159709 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 77.0277 | 3.00514 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0178 | −0.585012 | −0.292506 | − | 0.956264i | \(-0.594489\pi\) | ||||
−0.292506 | + | 0.956264i | \(0.594489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.65080 | 0.180895 | 0.0904475 | − | 0.995901i | \(-0.471170\pi\) | ||||
0.0904475 | + | 0.995901i | \(0.471170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 40.0830 | 1.55669 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.47949 | −0.134929 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.90321 | −0.267293 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.6543 | 0.914529 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.9081 | −0.459708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.8671 | −1.72950 | −0.864750 | − | 0.502202i | \(-0.832523\pi\) | ||||
−0.864750 | + | 0.502202i | \(0.832523\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.05086 | 0.271388 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.2212 | −1.04620 | −0.523099 | − | 0.852272i | \(-0.675224\pi\) | ||||
−0.523099 | + | 0.852272i | \(0.675224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.3368 | −1.08747 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.5303 | −1.16993 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0558 | −0.461301 | −0.230651 | − | 0.973037i | \(-0.574085\pi\) | ||||
−0.230651 | + | 0.973037i | \(0.574085\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.9541 | −0.762406 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.6450 | −0.940264 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.7146 | −0.827259 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.5812 | −1.42966 | −0.714828 | − | 0.699300i | \(-0.753495\pi\) | ||||
−0.714828 | + | 0.699300i | \(0.753495\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −40.6035 | −1.54240 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.90813 | −0.299973 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.25428 | −0.274775 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −59.7244 | −2.25898 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.04149 | −0.0771059 | −0.0385530 | − | 0.999257i | \(-0.512275\pi\) | ||||
−0.0385530 | + | 0.999257i | \(0.512275\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.1432 | 0.684284 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36.8988 | 1.38969 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.5210 | −0.884598 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.1432 | 1.20716 | 0.603582 | − | 0.797301i | \(-0.293740\pi\) | ||||
0.603582 | + | 0.797301i | \(0.293740\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.85236 | 0.0694688 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.8666 | 0.444409 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.5210 | −1.17882 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.36842 | 0.0884501 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.01921 | 0.0380102 | 0.0190051 | − | 0.999819i | \(-0.493950\pi\) | ||||
0.0190051 | + | 0.999819i | \(0.493950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.8381 | 0.440873 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.0321 | −0.782193 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.1476 | −0.895587 | −0.447793 | − | 0.894137i | \(-0.647790\pi\) | ||||
−0.447793 | + | 0.894137i | \(0.647790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.6958 | −1.43318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.35551 | 0.0871217 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.8845 | −0.697514 | −0.348757 | − | 0.937213i | \(-0.613396\pi\) | ||||
−0.348757 | + | 0.937213i | \(0.613396\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.5669 | −0.500423 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.37778 | −0.198093 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.31312 | 0.121875 | 0.0609375 | − | 0.998142i | \(-0.480591\pi\) | ||||
0.0609375 | + | 0.998142i | \(0.480591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −42.5718 | −1.56392 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.99508 | 0.109879 | 0.0549394 | − | 0.998490i | \(-0.482503\pi\) | ||||
0.0549394 | + | 0.998490i | \(0.482503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.1017 | 0.589921 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.8020 | 1.45628 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.63206 | 0.169252 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9956 | 0.437724 | 0.218862 | − | 0.975756i | \(-0.429766\pi\) | ||||
0.218862 | + | 0.975756i | \(0.429766\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 59.2958 | 2.16086 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.67307 | 0.206464 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.5763 | −0.675166 | −0.337583 | − | 0.941296i | \(-0.609609\pi\) | ||||
−0.337583 | + | 0.941296i | \(0.609609\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −98.2677 | −3.56689 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.59057 | 0.0939082 | 0.0469541 | − | 0.998897i | \(-0.485049\pi\) | ||||
0.0469541 | + | 0.998897i | \(0.485049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1116 | 0.438468 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.6588 | 0.421524 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.4701 | 0.739133 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.7467 | 1.18088 | 0.590438 | − | 0.807083i | \(-0.298955\pi\) | ||||
0.590438 | + | 0.807083i | \(0.298955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.94914 | 0.322296 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.2208 | −1.01503 | −0.507515 | − | 0.861643i | \(-0.669436\pi\) | ||||
−0.507515 | + | 0.861643i | \(0.669436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.71900 | 0.0617484 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.2257 | −1.26371 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.70471 | 0.276050 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.5111 | −0.626598 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.05086 | −0.251977 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.89384 | −0.0675942 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.9857 | −0.427244 | −0.213622 | − | 0.976916i | \(-0.568526\pi\) | ||||
−0.213622 | + | 0.976916i | \(0.568526\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 58.2262 | 2.07291 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.9299 | 0.424180 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.6128 | 0.554428 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.80642 | −0.347798 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.0366 | 1.17022 | 0.585108 | − | 0.810956i | \(-0.301052\pi\) | ||||
0.585108 | + | 0.810956i | \(0.301052\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.2958 | 0.965655 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.0098 | 0.565680 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −69.5723 | −2.45515 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.5303 | 0.371146 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 68.1116 | 2.39764 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.1303 | −1.12964 | −0.564820 | − | 0.825214i | \(-0.691055\pi\) | ||||
−0.564820 | + | 0.825214i | \(0.691055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.3176 | −0.537872 | −0.268936 | − | 0.963158i | \(-0.586672\pi\) | ||||
−0.268936 | + | 0.963158i | \(0.586672\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −63.6829 | −2.23346 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.95407 | 0.208562 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.50177 | −0.0875258 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 53.2355 | 1.86020 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.1427 | 0.598285 | 0.299143 | − | 0.954208i | \(-0.403299\pi\) | ||||
0.299143 | + | 0.954208i | \(0.403299\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.6400 | −1.24233 | −0.621167 | − | 0.783678i | \(-0.713341\pi\) | ||||
−0.621167 | + | 0.783678i | \(0.713341\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.2351 | −0.495601 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.70964 | −0.163770 | −0.0818850 | − | 0.996642i | \(-0.526094\pi\) | ||||
−0.0818850 | + | 0.996642i | \(0.526094\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.25380 | −0.0782777 | −0.0391388 | − | 0.999234i | \(-0.512461\pi\) | ||||
−0.0391388 | + | 0.999234i | \(0.512461\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −53.2355 | −1.84672 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.0361 | −0.347730 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.23951 | 0.146714 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.1204 | 0.418944 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.42419 | −0.290835 | −0.145418 | − | 0.989370i | \(-0.546453\pi\) | ||||
−0.145418 | + | 0.989370i | \(0.546453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.0286 | 0.689821 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.3274 | 0.974492 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.8938 | 0.683561 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 84.2074 | 2.88999 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.9086 | −1.88224 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.8247 | −1.77444 | −0.887222 | − | 0.461342i | \(-0.847368\pi\) | ||||
−0.887222 | + | 0.461342i | \(0.847368\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.3827 | −0.423480 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.0415 | −1.02620 | −0.513099 | − | 0.858330i | \(-0.671503\pi\) | ||||
−0.513099 | + | 0.858330i | \(0.671503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.6874 | −0.671724 | −0.335862 | − | 0.941911i | \(-0.609028\pi\) | ||||
−0.335862 | + | 0.941911i | \(0.609028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.9590 | −0.509801 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5986 | 0.667143 | 0.333571 | − | 0.942725i | \(-0.391746\pi\) | ||||
0.333571 | + | 0.942725i | \(0.391746\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.4099 | −0.829962 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −35.9639 | −1.22140 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.67307 | −0.0567550 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.05086 | 0.238909 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −100.844 | −3.41305 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.52543 | 0.0515689 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.2351 | 0.548219 | 0.274110 | − | 0.961698i | \(-0.411617\pi\) | ||||
0.274110 | + | 0.961698i | \(0.411617\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.6222 | −0.763028 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.7052 | −0.697576 | −0.348788 | − | 0.937202i | \(-0.613407\pi\) | ||||
−0.348788 | + | 0.937202i | \(0.613407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.75112 | −0.294499 | −0.147249 | − | 0.989099i | \(-0.547042\pi\) | ||||
−0.147249 | + | 0.989099i | \(0.547042\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.24443 | 0.310748 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.414349 | 0.0139125 | 0.00695625 | − | 0.999976i | \(-0.497786\pi\) | ||||
0.00695625 | + | 0.999976i | \(0.497786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.9808 | −0.636595 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.5161 | −0.687314 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.9906 | −0.970135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.61285 | 0.120764 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 128.839 | 4.30183 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.71900 | −0.0573320 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.25428 | −0.241675 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.85728 | 0.161640 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0415 | −0.599719 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.9862 | 1.56015 | 0.780075 | − | 0.625686i | \(-0.215181\pi\) | ||||
0.780075 | + | 0.625686i | \(0.215181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −83.7057 | −2.77634 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.1704 | −0.403223 | −0.201612 | − | 0.979466i | \(-0.564618\pi\) | ||||
−0.201612 | + | 0.979466i | \(0.564618\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.9496 | −1.18976 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.05086 | 0.233094 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.23506 | −0.205900 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.2672 | −0.767514 | −0.383757 | − | 0.923434i | \(-0.625370\pi\) | ||||
−0.383757 | + | 0.923434i | \(0.625370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.2029 | −0.566856 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.9590 | 0.755704 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.95407 | −0.261528 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42.1289 | 1.38369 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.7556 | 1.46838 | 0.734191 | − | 0.678943i | \(-0.237562\pi\) | ||||
0.734191 | + | 0.678943i | \(0.237562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.6593 | 0.349343 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.9684 | 0.850166 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.5303 | −0.344379 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.7239 | −0.742358 | −0.371179 | − | 0.928561i | \(-0.621046\pi\) | ||||
−0.371179 | + | 0.928561i | \(0.621046\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −88.5817 | −2.89075 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.10171 | −0.133712 | −0.0668560 | − | 0.997763i | \(-0.521297\pi\) | ||||
−0.0668560 | + | 0.997763i | \(0.521297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.3176 | −0.759324 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.7556 | 0.349879 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6178 | −0.540005 | −0.270002 | − | 0.962860i | \(-0.587025\pi\) | ||||
−0.270002 | + | 0.962860i | \(0.587025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 91.2168 | 2.96102 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 64.5402 | 2.09286 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.85728 | 0.0925563 | 0.0462782 | − | 0.998929i | \(-0.485264\pi\) | ||||
0.0462782 | + | 0.998929i | \(0.485264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.85236 | 0.318815 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.2351 | 0.460154 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.4385 | −0.982910 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.0450 | −0.904678 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.4844 | 0.531203 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.23951 | 0.0720923 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.8015 | 0.540300 | 0.270150 | − | 0.962818i | \(-0.412927\pi\) | ||||
0.270150 | + | 0.962818i | \(0.412927\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.2222 | −0.456881 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.3640 | −1.23116 | −0.615579 | − | 0.788075i | \(-0.711078\pi\) | ||||
−0.615579 | + | 0.788075i | \(0.711078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0633 | −0.386731 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.6637 | 0.597717 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.6356 | 1.01211 | 0.506056 | − | 0.862500i | \(-0.331103\pi\) | ||||
0.506056 | + | 0.862500i | \(0.331103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4603 | −0.462153 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.1022 | 1.37615 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.3733 | −1.12823 | −0.564117 | − | 0.825695i | \(-0.690783\pi\) | ||||
−0.564117 | + | 0.825695i | \(0.690783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5620 | 0.336533 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 56.2864 | 1.79162 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.57136 | 0.240755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.6953 | 0.784474 | 0.392237 | − | 0.919864i | \(-0.371701\pi\) | ||||
0.392237 | + | 0.919864i | \(0.371701\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.0094 | 0.603244 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.18421 | 0.100946 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4050 | 0.361199 | 0.180600 | − | 0.983557i | \(-0.442196\pi\) | ||||
0.180600 | + | 0.983557i | \(0.442196\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −56.0830 | −1.77439 |
(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 | 9280.2.a.bu.1.3 | 3 | ||
4.3 | odd | 2 | 9280.2.a.bm.1.1 | 3 | |||
8.3 | odd | 2 | 2320.2.a.s.1.3 | 3 | |||
8.5 | even | 2 | 145.2.a.d.1.1 | ✓ | 3 | ||
24.5 | odd | 2 | 1305.2.a.o.1.3 | 3 | |||
40.13 | odd | 4 | 725.2.b.d.349.4 | 6 | |||
40.29 | even | 2 | 725.2.a.d.1.3 | 3 | |||
40.37 | odd | 4 | 725.2.b.d.349.3 | 6 | |||
56.13 | odd | 2 | 7105.2.a.p.1.1 | 3 | |||
120.29 | odd | 2 | 6525.2.a.bh.1.1 | 3 | |||
232.173 | even | 2 | 4205.2.a.e.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
145.2.a.d.1.1 | ✓ | 3 | 8.5 | even | 2 | ||
725.2.a.d.1.3 | 3 | 40.29 | even | 2 | |||
725.2.b.d.349.3 | 6 | 40.37 | odd | 4 | |||
725.2.b.d.349.4 | 6 | 40.13 | odd | 4 | |||
1305.2.a.o.1.3 | 3 | 24.5 | odd | 2 | |||
2320.2.a.s.1.3 | 3 | 8.3 | odd | 2 | |||
4205.2.a.e.1.3 | 3 | 232.173 | even | 2 | |||
6525.2.a.bh.1.1 | 3 | 120.29 | odd | 2 | |||
7105.2.a.p.1.1 | 3 | 56.13 | odd | 2 | |||
9280.2.a.bm.1.1 | 3 | 4.3 | odd | 2 | |||
9280.2.a.bu.1.3 | 3 | 1.1 | even | 1 | trivial |