Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 18x^{8} + 117x^{6} + 333x^{4} + 396x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.8 | ||
Root | \(1.83957i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.w.4049.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.83957i | 1.06208i | 0.847348 | + | 0.531038i | \(0.178198\pi\) | ||||
−0.847348 | + | 0.531038i | \(0.821802\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.97272i | 1.50155i | 0.660559 | + | 0.750774i | \(0.270319\pi\) | ||||
−0.660559 | + | 0.750774i | \(0.729681\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.384010 | −0.128003 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.10339 | 0.634196 | 0.317098 | − | 0.948393i | \(-0.397292\pi\) | ||||
0.317098 | + | 0.948393i | \(0.397292\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.35673i | 1.48569i | 0.669463 | + | 0.742845i | \(0.266524\pi\) | ||||
−0.669463 | + | 0.742845i | \(0.733476\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.29567i | − 0.314246i | −0.987579 | − | 0.157123i | \(-0.949778\pi\) | ||||
0.987579 | − | 0.157123i | \(-0.0502218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.10339 | −0.482551 | −0.241276 | − | 0.970457i | \(-0.577566\pi\) | ||||
−0.241276 | + | 0.970457i | \(0.577566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.30809 | −1.59476 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.81229i | 0.926126i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.03130 | −1.11998 | −0.559992 | − | 0.828498i | \(-0.689196\pi\) | ||||
−0.559992 | + | 0.828498i | \(0.689196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.32489 | −1.49519 | −0.747597 | − | 0.664153i | \(-0.768793\pi\) | ||||
−0.747597 | + | 0.664153i | \(0.768793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.86933i | 0.673564i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.10131i | − 0.838650i | −0.907836 | − | 0.419325i | \(-0.862267\pi\) | ||||
0.907836 | − | 0.419325i | \(-0.137733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.85407 | −1.57791 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.33994 | −1.30248 | −0.651240 | − | 0.758872i | \(-0.725751\pi\) | ||||
−0.651240 | + | 0.758872i | \(0.725751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.78253i | 1.18682i | 0.804899 | + | 0.593412i | \(0.202220\pi\) | ||||
−0.804899 | + | 0.593412i | \(0.797780\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 11.3964i | − 1.66234i | −0.556018 | − | 0.831171i | \(-0.687671\pi\) | ||||
0.556018 | − | 0.831171i | \(-0.312329\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.78253 | −1.25465 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.38347 | 0.333752 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 0.573664i | − 0.0787988i | −0.999224 | − | 0.0393994i | \(-0.987456\pi\) | ||||
0.999224 | − | 0.0393994i | \(-0.0125445\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 3.86933i | − 0.512505i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.17951 | 1.19507 | 0.597535 | − | 0.801843i | \(-0.296147\pi\) | ||||
0.597535 | + | 0.801843i | \(0.296147\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.5149 | 1.73040 | 0.865201 | − | 0.501425i | \(-0.167191\pi\) | ||||
0.865201 | + | 0.501425i | \(0.167191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.52557i | − 0.192203i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.8314i | 1.93411i | 0.254569 | + | 0.967055i | \(0.418066\pi\) | ||||
−0.254569 | + | 0.967055i | \(0.581934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.83957 | 0.221458 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9449 | 1.77363 | 0.886817 | − | 0.462121i | \(-0.152911\pi\) | ||||
0.886817 | + | 0.462121i | \(0.152911\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.36459i | 0.979002i | 0.872003 | + | 0.489501i | \(0.162821\pi\) | ||||
−0.872003 | + | 0.489501i | \(0.837179\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.35619i | 0.952276i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.41149 | 1.05887 | 0.529437 | − | 0.848349i | \(-0.322403\pi\) | ||||
0.529437 | + | 0.848349i | \(0.322403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0046 | −1.11162 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.51206i | 0.165970i | 0.996551 | + | 0.0829849i | \(0.0264453\pi\) | ||||
−0.996551 | + | 0.0829849i | \(0.973555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 11.0950i | − 1.18951i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.5903 | −1.12256 | −0.561282 | − | 0.827624i | \(-0.689692\pi\) | ||||
−0.561282 | + | 0.827624i | \(0.689692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.2808 | −2.23084 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 15.3142i | − 1.58801i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.337451i | 0.0342630i | 0.999853 | + | 0.0171315i | \(0.00545339\pi\) | ||||
−0.999853 | + | 0.0171315i | \(0.994547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.807724 | −0.0811793 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.19119 | −0.616047 | −0.308023 | − | 0.951379i | \(-0.599667\pi\) | ||||
−0.308023 | + | 0.951379i | \(0.599667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.6267i | 1.24414i | 0.782961 | + | 0.622071i | \(0.213708\pi\) | ||||
−0.782961 | + | 0.622071i | \(0.786292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.7940i | − 1.23684i | −0.785848 | − | 0.618419i | \(-0.787773\pi\) | ||||
0.785848 | − | 0.618419i | \(-0.212227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.3165 | −1.37127 | −0.685635 | − | 0.727945i | \(-0.740476\pi\) | ||||
−0.685635 | + | 0.727945i | \(0.740476\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.38421 | 0.890710 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.59463i | 0.432226i | 0.976368 | + | 0.216113i | \(0.0693380\pi\) | ||||
−0.976368 | + | 0.216113i | \(0.930662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.05704i | − 0.190173i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.14733 | 0.471855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.57574 | −0.597795 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 15.3419i | − 1.38333i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 12.6623i | − 1.12360i | −0.827273 | − | 0.561801i | \(-0.810109\pi\) | ||||
0.827273 | − | 0.561801i | \(-0.189891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.3165 | −1.26050 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.68370 | 0.409217 | 0.204609 | − | 0.978844i | \(-0.434408\pi\) | ||||
0.204609 | + | 0.978844i | \(0.434408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 8.35619i | − 0.724574i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.468120i | 0.0399942i | 0.999800 | + | 0.0199971i | \(0.00636570\pi\) | ||||
−0.999800 | + | 0.0199971i | \(0.993634\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.739205 | −0.0626985 | −0.0313493 | − | 0.999508i | \(-0.509980\pi\) | ||||
−0.0313493 | + | 0.999508i | \(0.509980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.9645 | 1.76553 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.2673i | 0.942220i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 16.1561i | − 1.33253i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.5903 | −1.19528 | −0.597640 | − | 0.801765i | \(-0.703895\pi\) | ||||
−0.597640 | + | 0.801765i | \(0.703895\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6885 | 1.76498 | 0.882491 | − | 0.470329i | \(-0.155865\pi\) | ||||
0.882491 | + | 0.470329i | \(0.155865\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.497550i | 0.0402245i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 7.71253i | − 0.615527i | −0.951463 | − | 0.307763i | \(-0.900420\pi\) | ||||
0.951463 | − | 0.307763i | \(-0.0995805\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.05529 | 0.0836902 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.97272 | 0.313094 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.69177i | − 0.367488i | −0.982974 | − | 0.183744i | \(-0.941178\pi\) | ||||
0.982974 | − | 0.183744i | \(-0.0588217\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 11.6738i | − 0.903343i | −0.892184 | − | 0.451671i | \(-0.850828\pi\) | ||||
0.892184 | − | 0.451671i | \(-0.149172\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.6946 | −1.20728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.807724 | 0.0617682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 8.31723i | − 0.632347i | −0.948701 | − | 0.316174i | \(-0.897602\pi\) | ||||
0.948701 | − | 0.316174i | \(-0.102398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.8863i | 1.26925i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.07517 | 0.304592 | 0.152296 | − | 0.988335i | \(-0.451333\pi\) | ||||
0.152296 | + | 0.988335i | \(0.451333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.52349 | 0.187569 | 0.0937846 | − | 0.995593i | \(-0.470103\pi\) | ||||
0.0937846 | + | 0.995593i | \(0.470103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.8615i | 1.83782i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.72530i | − 0.199293i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.1179 | −1.39062 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.9380 | −1.73210 | −0.866048 | − | 0.499961i | \(-0.833348\pi\) | ||||
−0.866048 | + | 0.499961i | \(0.833348\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.7733i | 1.35133i | 0.737207 | + | 0.675667i | \(0.236144\pi\) | ||||
−0.737207 | + | 0.675667i | \(0.763856\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 15.9052i | − 1.13320i | −0.823993 | − | 0.566600i | \(-0.808259\pi\) | ||||
0.823993 | − | 0.566600i | \(-0.191741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.87544 | −0.700052 | −0.350026 | − | 0.936740i | \(-0.613827\pi\) | ||||
−0.350026 | + | 0.936740i | \(0.613827\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.1229 | −2.05417 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 23.9607i | − 1.68171i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.384010i | 0.0266906i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.42426 | −0.306032 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.06980 | −0.486705 | −0.243353 | − | 0.969938i | \(-0.578247\pi\) | ||||
−0.243353 | + | 0.969938i | \(0.578247\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 27.4922i | 1.88373i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 33.0725i | − 2.24511i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.3872 | −1.03977 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.94055 | 0.466872 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.58817i | 0.575106i | 0.957765 | + | 0.287553i | \(0.0928418\pi\) | ||||
−0.957765 | + | 0.287553i | \(0.907158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 14.2068i | − 0.942937i | −0.881883 | − | 0.471469i | \(-0.843724\pi\) | ||||
0.881883 | − | 0.471469i | \(-0.156276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.49721 | 0.495429 | 0.247715 | − | 0.968833i | \(-0.420320\pi\) | ||||
0.247715 | + | 0.968833i | \(0.420320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.3718 | −1.01139 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 16.9301i | − 1.10912i | −0.832142 | − | 0.554562i | \(-0.812886\pi\) | ||||
0.832142 | − | 0.554562i | \(-0.187114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.3131i | 1.12460i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.7850 | 1.15042 | 0.575208 | − | 0.818007i | \(-0.304921\pi\) | ||||
0.575208 | + | 0.818007i | \(0.304921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.55263 | −0.615339 | −0.307669 | − | 0.951493i | \(-0.599549\pi\) | ||||
−0.307669 | + | 0.951493i | \(0.599549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3.96721i | − 0.254497i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 11.2673i | − 0.716922i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.78153 | −0.176272 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.2075 | −0.833651 | −0.416826 | − | 0.908986i | \(-0.636857\pi\) | ||||
−0.416826 | + | 0.908986i | \(0.636857\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.10339i | − 0.132239i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.41506i | 0.213025i | 0.994311 | + | 0.106513i | \(0.0339685\pi\) | ||||
−0.994311 | + | 0.106513i | \(0.966032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.2661 | 1.25927 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.31608 | 0.143362 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.6589i | 1.15056i | 0.817957 | + | 0.575279i | \(0.195106\pi\) | ||||
−0.817957 | + | 0.575279i | \(0.804894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 19.4815i | − 1.19225i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.2224 | 1.47687 | 0.738434 | − | 0.674326i | \(-0.235566\pi\) | ||||
0.738434 | + | 0.674326i | \(0.235566\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1201 | −0.614749 | −0.307375 | − | 0.951589i | \(-0.599450\pi\) | ||||
−0.307375 | + | 0.951589i | \(0.599450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 39.1475i | − 2.36932i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.5298i | 1.41377i | 0.707329 | + | 0.706884i | \(0.249900\pi\) | ||||
−0.707329 | + | 0.706884i | \(0.750100\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.19684 | 0.191390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.77314 | 0.105776 | 0.0528882 | − | 0.998600i | \(-0.483157\pi\) | ||||
0.0528882 | + | 0.998600i | \(0.483157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.96641i | 0.354666i | 0.984151 | + | 0.177333i | \(0.0567470\pi\) | ||||
−0.984151 | + | 0.177333i | \(0.943253\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 33.1323i | − 1.95574i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.3212 | 0.901250 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.620765 | −0.0363899 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.2404i | 0.715090i | 0.933896 | + | 0.357545i | \(0.116386\pi\) | ||||
−0.933896 | + | 0.357545i | \(0.883614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.1221i | 0.587346i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.35673 | 0.309788 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.9178 | −1.78207 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 11.3891i | − 0.654288i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.82713i | 0.503791i | 0.967754 | + | 0.251896i | \(0.0810539\pi\) | ||||
−0.967754 | + | 0.251896i | \(0.918946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.2276 | −1.32137 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.9202 | −0.789345 | −0.394672 | − | 0.918822i | \(-0.629142\pi\) | ||||
−0.394672 | + | 0.918822i | \(0.629142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.5030i | 1.32847i | 0.747523 | + | 0.664235i | \(0.231243\pi\) | ||||
−0.747523 | + | 0.664235i | \(0.768757\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 13.3279i | − 0.748570i | −0.927314 | − | 0.374285i | \(-0.877888\pi\) | ||||
0.927314 | − | 0.374285i | \(-0.122112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.6862 | −0.710290 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.5354 | 1.31362 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.72530i | 0.151640i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 26.3362i | − 1.45639i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 45.2749 | 2.49609 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.270137 | −0.0148481 | −0.00742404 | − | 0.999972i | \(-0.502363\pi\) | ||||
−0.00742404 | + | 0.999972i | \(0.502363\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.95896i | 0.107350i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0205i | 1.09058i | 0.838246 | + | 0.545292i | \(0.183581\pi\) | ||||
−0.838246 | + | 0.545292i | \(0.816419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.45213 | −0.459057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.5105 | −0.948247 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 7.08149i | − 0.382364i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1156i | 0.811448i | 0.913996 | + | 0.405724i | \(0.132981\pi\) | ||||
−0.913996 | + | 0.405724i | \(0.867019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5673 | 0.779771 | 0.389886 | − | 0.920863i | \(-0.372515\pi\) | ||||
0.389886 | + | 0.920863i | \(0.372515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.7782 | −1.37594 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.5376i | 0.986656i | 0.869843 | + | 0.493328i | \(0.164220\pi\) | ||||
−0.869843 | + | 0.493328i | \(0.835780\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.46886i | 0.501145i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.1834 | 1.27635 | 0.638175 | − | 0.769891i | \(-0.279689\pi\) | ||||
0.638175 | + | 0.769891i | \(0.279689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5757 | −0.767144 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 12.0965i | − 0.634903i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 5.79604i | − 0.302551i | −0.988492 | − | 0.151275i | \(-0.951662\pi\) | ||||
0.988492 | − | 0.151275i | \(-0.0483380\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.20262 | 0.166722 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.27901 | 0.118320 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 25.5753i | − 1.32424i | −0.749399 | − | 0.662119i | \(-0.769657\pi\) | ||||
0.749399 | − | 0.662119i | \(-0.230343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 32.3081i | − 1.66395i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.82223 | 0.504534 | 0.252267 | − | 0.967658i | \(-0.418824\pi\) | ||||
0.252267 | + | 0.967658i | \(0.418824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.2932 | 1.19335 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 33.9797i | − 1.73628i | −0.496319 | − | 0.868141i | \(-0.665315\pi\) | ||||
0.496319 | − | 0.868141i | \(-0.334685\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2.98857i | − 0.151918i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.6744 | 1.25104 | 0.625521 | − | 0.780207i | \(-0.284886\pi\) | ||||
0.625521 | + | 0.780207i | \(0.284886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.29567 | −0.0655247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.61599i | 0.434619i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.17340i | 0.159268i | 0.996824 | + | 0.0796342i | \(0.0253752\pi\) | ||||
−0.996824 | + | 0.0796342i | \(0.974625\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.3718 | 0.769552 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.07720 | 0.203606 | 0.101803 | − | 0.994805i | \(-0.467539\pi\) | ||||
0.101803 | + | 0.994805i | \(0.467539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 44.5942i | − 2.22140i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 10.7301i | − 0.531869i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.5426 | −0.916871 | −0.458435 | − | 0.888728i | \(-0.651590\pi\) | ||||
−0.458435 | + | 0.888728i | \(0.651590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.861138 | −0.0424768 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.4676i | 1.79445i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 1.35982i | − 0.0665906i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.22587 | 0.157594 | 0.0787970 | − | 0.996891i | \(-0.474892\pi\) | ||||
0.0787970 | + | 0.996891i | \(0.474892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0595 | 0.880167 | 0.440084 | − | 0.897957i | \(-0.354949\pi\) | ||||
0.440084 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.37635i | 0.212785i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 53.6909i | 2.59828i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.7270 | −1.00071 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.62458 | −0.463600 | −0.231800 | − | 0.972763i | \(-0.574461\pi\) | ||||
−0.231800 | + | 0.972763i | \(0.574461\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1.83990i | − 0.0884200i | −0.999022 | − | 0.0442100i | \(-0.985923\pi\) | ||||
0.999022 | − | 0.0442100i | \(-0.0140771\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.10339i | 0.100619i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.73907 | −0.321638 | −0.160819 | − | 0.986984i | \(-0.551414\pi\) | ||||
−0.160819 | + | 0.986984i | \(0.551414\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.37258 | 0.160599 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.4099i | 0.542103i | 0.962565 | + | 0.271051i | \(0.0873714\pi\) | ||||
−0.962565 | + | 0.271051i | \(0.912629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 26.8398i | − 1.26948i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.8081 | −1.31235 | −0.656173 | − | 0.754610i | \(-0.727826\pi\) | ||||
−0.656173 | + | 0.754610i | \(0.727826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.5422 | −0.826028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 39.8974i | 1.87454i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 26.6835i | − 1.24820i | −0.781343 | − | 0.624102i | \(-0.785465\pi\) | ||||
0.781343 | − | 0.624102i | \(-0.214535\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.23513 | 0.291031 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.0398 | −1.07307 | −0.536534 | − | 0.843879i | \(-0.680267\pi\) | ||||
−0.536534 | + | 0.843879i | \(0.680267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 23.3998i | − 1.08748i | −0.839253 | − | 0.543740i | \(-0.817008\pi\) | ||||
0.839253 | − | 0.543740i | \(-0.182992\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 4.29380i | − 0.198693i | −0.995053 | − | 0.0993467i | \(-0.968325\pi\) | ||||
0.995053 | − | 0.0993467i | \(-0.0316753\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −62.8936 | −2.90416 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.1877 | 0.653735 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.3697i | 0.752680i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.220293i | 0.0100865i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.6694 | 1.21856 | 0.609278 | − | 0.792957i | \(-0.291459\pi\) | ||||
0.609278 | + | 0.792957i | \(0.291459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.3264 | 1.24597 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.30809i | 0.332530i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.67114i | 0.392927i | 0.980511 | + | 0.196463i | \(0.0629457\pi\) | ||||
−0.980511 | + | 0.196463i | \(0.937054\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.63083 | 0.390300 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.0900 | −1.13229 | −0.566147 | − | 0.824304i | \(-0.691566\pi\) | ||||
−0.566147 | + | 0.824304i | \(0.691566\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.81456i | 0.351950i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 59.3720i | 2.66320i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.9323 | 1.56379 | 0.781893 | − | 0.623412i | \(-0.214254\pi\) | ||||
0.781893 | + | 0.623412i | \(0.214254\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.4747 | 0.959418 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.7782i | 1.14939i | 0.818367 | + | 0.574695i | \(0.194879\pi\) | ||||
−0.818367 | + | 0.574695i | \(0.805121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 28.8713i | − 1.28222i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.21667 | −0.186900 | −0.0934502 | − | 0.995624i | \(-0.529790\pi\) | ||||
−0.0934502 | + | 0.995624i | \(0.529790\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.2302 | −1.47002 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 10.1221i | − 0.446903i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 23.9712i | − 1.05425i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.3001 | 0.671600 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3112 | 1.28415 | 0.642073 | − | 0.766644i | \(-0.278075\pi\) | ||||
0.642073 | + | 0.766644i | \(0.278075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 31.1549i | − 1.36231i | −0.732140 | − | 0.681154i | \(-0.761478\pi\) | ||||
0.732140 | − | 0.681154i | \(-0.238522\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.7863i | 0.469858i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.52502 | −0.152973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 44.6748i | − 1.93508i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.49655i | 0.323500i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.4731 | −0.795692 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7393 | 0.676683 | 0.338342 | − | 0.941023i | \(-0.390134\pi\) | ||||
0.338342 | + | 0.941023i | \(0.390134\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.64212i | 0.199213i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.2935i | 1.68007i | 0.542534 | + | 0.840034i | \(0.317465\pi\) | ||||
−0.542534 | + | 0.840034i | \(0.682535\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.18985 | −0.221497 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6862 | 0.540450 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.3892i | 1.58995i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 38.1005i | − 1.61437i | −0.590297 | − | 0.807186i | \(-0.700990\pi\) | ||||
0.590297 | − | 0.807186i | \(-0.299010\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.6889 | −1.76325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.01337 | 0.211665 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.6868i | 1.37758i | 0.724959 | + | 0.688792i | \(0.241859\pi\) | ||||
−0.724959 | + | 0.688792i | \(0.758141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 39.7454i | − 1.66915i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.0256 | −0.881438 | −0.440719 | − | 0.897645i | \(-0.645276\pi\) | ||||
−0.440719 | + | 0.897645i | \(0.645276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.43876 | −0.311303 | −0.155651 | − | 0.987812i | \(-0.549748\pi\) | ||||
−0.155651 | + | 0.987812i | \(0.549748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 44.0357i | − 1.83962i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.4148i | 1.26618i | 0.774077 | + | 0.633091i | \(0.218214\pi\) | ||||
−0.774077 | + | 0.633091i | \(0.781786\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.5348 | −1.43522 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00698 | −0.249212 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.20664i | − 0.0499739i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.7544i | 1.39319i | 0.717464 | + | 0.696596i | \(0.245303\pi\) | ||||
−0.717464 | + | 0.696596i | \(0.754697\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.5105 | 0.721508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.2587 | 1.20354 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.3980i | 1.12510i | 0.826763 | + | 0.562550i | \(0.190180\pi\) | ||||
−0.826763 | + | 0.562550i | \(0.809820\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 18.1666i | − 0.743507i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.2927 | −1.52374 | −0.761869 | − | 0.647731i | \(-0.775718\pi\) | ||||
−0.761869 | + | 0.647731i | \(0.775718\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.26039 | −0.0922032 | −0.0461016 | − | 0.998937i | \(-0.514680\pi\) | ||||
−0.0461016 | + | 0.998937i | \(0.514680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 6.07941i | − 0.247573i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.4782i | 0.952951i | 0.879188 | + | 0.476476i | \(0.158086\pi\) | ||||
−0.879188 | + | 0.476476i | \(0.841914\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 44.0773 | 1.78610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 61.0477 | 2.46972 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 25.0418i | − 1.01143i | −0.862701 | − | 0.505714i | \(-0.831229\pi\) | ||||
0.862701 | − | 0.505714i | \(-0.168771\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.2705i | 0.735541i | 0.929916 | + | 0.367771i | \(0.119879\pi\) | ||||
−0.929916 | + | 0.367771i | \(0.880121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.17743 | −0.288485 | −0.144243 | − | 0.989542i | \(-0.546075\pi\) | ||||
−0.144243 | + | 0.989542i | \(0.546075\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.81229 | 0.193111 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 42.0721i | − 1.68558i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 8.13872i | − 0.325029i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.60960 | −0.263542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.7621 | −1.14500 | −0.572500 | − | 0.819904i | \(-0.694026\pi\) | ||||
−0.572500 | + | 0.819904i | \(0.694026\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 13.0054i | − 0.516917i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 47.0457i | − 1.86402i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.73900 | −0.227031 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.7383 | −1.60907 | −0.804533 | − | 0.593907i | \(-0.797585\pi\) | ||||
−0.804533 | + | 0.593907i | \(0.797585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 8.24043i | − 0.324971i | −0.986711 | − | 0.162485i | \(-0.948049\pi\) | ||||
0.986711 | − | 0.162485i | \(-0.0519510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.1134i | 1.30182i | 0.759154 | + | 0.650911i | \(0.225613\pi\) | ||||
−0.759154 | + | 0.650911i | \(0.774387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.3081 | 0.757909 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 60.8391 | 2.38447 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.5452i | 0.569199i | 0.958647 | + | 0.284599i | \(0.0918605\pi\) | ||||
−0.958647 | + | 0.284599i | \(0.908139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 3.21209i | − 0.125316i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.4498 | 0.952427 | 0.476214 | − | 0.879330i | \(-0.342009\pi\) | ||||
0.476214 | + | 0.879330i | \(0.342009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.43400 | 0.0557763 | 0.0278882 | − | 0.999611i | \(-0.491122\pi\) | ||||
0.0278882 | + | 0.999611i | \(0.491122\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.7676i | 0.495853i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.03130i | 0.233533i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.7985 | −0.610806 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.4271 | 1.09742 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 3.39873i | − 0.131011i | −0.997852 | − | 0.0655056i | \(-0.979134\pi\) | ||||
0.997852 | − | 0.0655056i | \(-0.0208660\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.7751i | 0.606287i | 0.952945 | + | 0.303144i | \(0.0980362\pi\) | ||||
−0.952945 | + | 0.303144i | \(0.901964\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.34060 | −0.0514475 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.1343 | 1.00147 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 4.99979i | − 0.191312i | −0.995414 | − | 0.0956559i | \(-0.969505\pi\) | ||||
0.995414 | − | 0.0956559i | \(-0.0304948\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.7916i | 0.526183i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.07296 | 0.117071 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.6864 | 1.54779 | 0.773893 | − | 0.633317i | \(-0.218307\pi\) | ||||
0.773893 | + | 0.633317i | \(0.218307\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3.20886i | − 0.121895i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8058i | 0.409298i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.1440 | 1.17797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.30372 | −0.0492407 | −0.0246204 | − | 0.999697i | \(-0.507838\pi\) | ||||
−0.0246204 | + | 0.999697i | \(0.507838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7301i | 0.404692i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 24.5959i | − 0.925024i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −52.5228 | −1.97253 | −0.986267 | − | 0.165157i | \(-0.947187\pi\) | ||||
−0.986267 | + | 0.165157i | \(0.947187\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.61411 | −0.135540 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.32489i | 0.311770i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.7167i | 1.22183i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.2329 | 0.903735 | 0.451868 | − | 0.892085i | \(-0.350758\pi\) | ||||
0.451868 | + | 0.892085i | \(0.350758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.1622 | −1.86814 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 17.5727i | − 0.653536i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 37.0943i | − 1.37575i | −0.725829 | − | 0.687875i | \(-0.758544\pi\) | ||||
0.725829 | − | 0.687875i | \(-0.241456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.7158 | −0.841324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0836 | 0.372954 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.3065i | 1.71037i | 0.518325 | + | 0.855184i | \(0.326556\pi\) | ||||
−0.518325 | + | 0.855184i | \(0.673444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.2996i | 1.22660i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.3516 | 1.19007 | 0.595037 | − | 0.803698i | \(-0.297137\pi\) | ||||
0.595037 | + | 0.803698i | \(0.297137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.7270 | 0.761425 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.73343i | − 0.0635935i | −0.999494 | − | 0.0317967i | \(-0.989877\pi\) | ||||
0.999494 | − | 0.0317967i | \(-0.0101229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 0.580645i | − 0.0212447i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.8268 | 1.85717 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.9983 | 1.56903 | 0.784515 | − | 0.620110i | \(-0.212912\pi\) | ||||
0.784515 | + | 0.620110i | \(0.212912\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 24.2961i | − 0.885400i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 48.3219i | − 1.75629i | −0.478397 | − | 0.878144i | \(-0.658782\pi\) | ||||
0.478397 | − | 0.878144i | \(-0.341218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.86933 | 0.140448 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.2528 | 0.697915 | 0.348958 | − | 0.937139i | \(-0.386536\pi\) | ||||
0.348958 | + | 0.937139i | \(0.386536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 56.8754i | − 2.05903i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 49.1722i | 1.77550i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.05816 | −0.326645 | −0.163323 | − | 0.986573i | \(-0.552221\pi\) | ||||
−0.163323 | + | 0.986573i | \(0.552221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.28223 | −0.226249 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.1276i | 1.04765i | 0.851827 | + | 0.523824i | \(0.175495\pi\) | ||||
−0.851827 | + | 0.523824i | \(0.824505\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 37.2809i | 1.33744i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.5422 | 0.628513 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.4350 | 1.12483 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 29.0244i | − 1.03725i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.8771i | 0.851128i | 0.904928 | + | 0.425564i | \(0.139924\pi\) | ||||
−0.904928 | + | 0.425564i | \(0.860076\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −34.3243 | −1.22198 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.2532 | −0.649008 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 72.3956i | 2.57084i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.8896i | 0.704526i | 0.935901 | + | 0.352263i | \(0.114588\pi\) | ||||
−0.935901 | + | 0.352263i | \(0.885412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7660 | −0.522383 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.06677 | 0.143692 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.5940i | 0.620879i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.5588i | 1.56854i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.3598 | −0.926760 | −0.463380 | − | 0.886160i | \(-0.653363\pi\) | ||||
−0.463380 | + | 0.886160i | \(0.653363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.2482 | −0.500323 | −0.250161 | − | 0.968204i | \(-0.580484\pi\) | ||||
−0.250161 | + | 0.968204i | \(0.580484\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 18.6165i | − 0.652910i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 16.3697i | − 0.572703i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.17205 | 0.285555 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.56520 | 0.194227 | 0.0971134 | − | 0.995273i | \(-0.469039\pi\) | ||||
0.0971134 | + | 0.995273i | \(0.469039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 34.1312i | − 1.18974i | −0.803823 | − | 0.594869i | \(-0.797204\pi\) | ||||
0.803823 | − | 0.594869i | \(-0.202796\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.5085i | 0.817472i | 0.912653 | + | 0.408736i | \(0.134030\pi\) | ||||
−0.912653 | + | 0.408736i | \(0.865970\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.7442 | 1.10252 | 0.551260 | − | 0.834333i | \(-0.314147\pi\) | ||||
0.551260 | + | 0.834333i | \(0.314147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.2846 | −1.50153 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.3792i | 0.394267i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 40.0618i | − 1.38474i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.5409 | −0.847247 | −0.423623 | − | 0.905838i | \(-0.639242\pi\) | ||||
−0.423623 | + | 0.905838i | \(0.639242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.37661 | 0.254366 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.26180i | 0.112343i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 26.1236i | − 0.897618i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.9756 | −0.376682 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.10131 | −0.174871 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 23.7499i | − 0.813183i | −0.913610 | − | 0.406591i | \(-0.866717\pi\) | ||||
0.913610 | − | 0.406591i | \(-0.133283\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.0643i | 1.47105i | 0.677499 | + | 0.735524i | \(0.263064\pi\) | ||||
−0.677499 | + | 0.735524i | \(0.736936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.0591 | 0.855006 | 0.427503 | − | 0.904014i | \(-0.359393\pi\) | ||||
0.427503 | + | 0.904014i | \(0.359393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60.9490 | 2.07714 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.0967i | 1.56915i | 0.620033 | + | 0.784575i | \(0.287119\pi\) | ||||
−0.620033 | + | 0.784575i | \(0.712881\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.1845i | 0.957195i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.7960 | 0.671535 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −84.8044 | −2.87349 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 0.129585i | − 0.00438578i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.1644i | 1.18742i | 0.804680 | + | 0.593709i | \(0.202337\pi\) | ||||
−0.804680 | + | 0.593709i | \(0.797663\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.5170 | −0.759480 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.8350 | −1.30838 | −0.654192 | − | 0.756329i | \(-0.726991\pi\) | ||||
−0.654192 | + | 0.756329i | \(0.726991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.5954i | 0.356562i | 0.983980 | + | 0.178281i | \(0.0570536\pi\) | ||||
−0.983980 | + | 0.178281i | \(0.942946\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.8733i | 0.902316i | 0.892444 | + | 0.451158i | \(0.148989\pi\) | ||||
−0.892444 | + | 0.451158i | \(0.851011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.3040 | 1.68714 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.0435 | −0.704984 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.9712i | 0.802165i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.85407i | 0.329018i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 50.2099 | 1.67459 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.743278 | −0.0247622 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 56.8754i | − 1.89270i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 58.3210i | − 1.93652i | −0.249949 | − | 0.968259i | \(-0.580414\pi\) | ||||
0.249949 | − | 0.968259i | \(-0.419586\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.37748 | 0.0788561 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.3287 | 1.33615 | 0.668074 | − | 0.744095i | \(-0.267119\pi\) | ||||
0.668074 | + | 0.744095i | \(0.267119\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.18045i | 0.105257i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.6071i | 0.614459i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.6333 | 1.24141 | 0.620704 | − | 0.784045i | \(-0.286847\pi\) | ||||
0.620704 | + | 0.784045i | \(0.286847\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.2381 | −0.535064 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80.0559i | 2.63507i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 4.84877i | − 0.159254i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.7190 | −1.00786 | −0.503929 | − | 0.863745i | \(-0.668113\pi\) | ||||
−0.503929 | + | 0.863745i | \(0.668113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.4731 | 0.605431 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 25.6072i | − 0.838343i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.5843i | 1.32583i | 0.748694 | + | 0.662915i | \(0.230681\pi\) | ||||
−0.748694 | + | 0.662915i | \(0.769319\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43.2355 | −1.41094 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.5104 | 1.19020 | 0.595102 | − | 0.803650i | \(-0.297112\pi\) | ||||
0.595102 | + | 0.803650i | \(0.297112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.33994i | 0.271586i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 34.9681i | − 1.13631i | −0.822921 | − | 0.568155i | \(-0.807657\pi\) | ||||
0.822921 | − | 0.568155i | \(-0.192343\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.8069 | −1.45449 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.5176 | 0.795038 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.7164i | 1.15697i | 0.815694 | + | 0.578484i | \(0.196355\pi\) | ||||
−0.815694 | + | 0.578484i | \(0.803645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 23.3371i | − 0.754382i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.85971 | −0.0600532 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.3038 | 1.23561 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.91301i | 0.158320i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.0422i | 1.38414i | 0.721829 | + | 0.692072i | \(0.243302\pi\) | ||||
−0.721829 | + | 0.692072i | \(0.756698\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.01337 | −0.161053 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.76196 | −0.313276 | −0.156638 | − | 0.987656i | \(-0.550066\pi\) | ||||
−0.156638 | + | 0.987656i | \(0.550066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.93666i | − 0.0941449i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 24.0469i | − 0.769329i | −0.923056 | − | 0.384665i | \(-0.874317\pi\) | ||||
0.923056 | − | 0.384665i | \(-0.125683\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.2754 | −0.711926 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.49768 | 0.175527 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 19.2418i | − 0.613717i | −0.951755 | − | 0.306859i | \(-0.900722\pi\) | ||||
0.951755 | − | 0.306859i | \(-0.0992778\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 83.2862i | 2.65103i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.78253 | 0.247470 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.1944 | −1.21328 | −0.606642 | − | 0.794975i | \(-0.707484\pi\) | ||||
−0.606642 | + | 0.794975i | \(0.707484\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 0.496936i | − 0.0157698i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.5981i | 1.31742i | 0.752395 | + | 0.658712i | \(0.228899\pi\) | ||||
−0.752395 | + | 0.658712i | \(0.771101\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.5490 | 0.776696 |
(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 | 4600.2.e.w.4049.8 | 10 | ||
5.2 | odd | 4 | 4600.2.a.bf.1.4 | yes | 5 | ||
5.3 | odd | 4 | 4600.2.a.bd.1.2 | ✓ | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.w.4049.3 | 10 | ||
20.3 | even | 4 | 9200.2.a.cv.1.4 | 5 | |||
20.7 | even | 4 | 9200.2.a.ct.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bd.1.2 | ✓ | 5 | 5.3 | odd | 4 | ||
4600.2.a.bf.1.4 | yes | 5 | 5.2 | odd | 4 | ||
4600.2.e.w.4049.3 | 10 | 5.4 | even | 2 | inner | ||
4600.2.e.w.4049.8 | 10 | 1.1 | even | 1 | trivial | ||
9200.2.a.ct.1.2 | 5 | 20.7 | even | 4 | |||
9200.2.a.cv.1.4 | 5 | 20.3 | even | 4 |