Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(257,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.257");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (of order \(2\), degree \(1\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 99x^{4} + 170x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.8 | ||
Root | \(1.32750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.3.e.b.257.7 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.69031 | + | 1.32750i | 0.896769 | + | 0.442499i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.640013i | 0.128003i | 0.997950 | + | 0.0640013i | \(0.0203862\pi\) | ||||
−0.997950 | + | 0.0640013i | \(0.979614\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.72077 | 0.388681 | 0.194340 | − | 0.980934i | \(-0.437743\pi\) | ||||
0.194340 | + | 0.980934i | \(0.437743\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.47550 | + | 7.14275i | 0.608389 | + | 0.793639i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.2836i | 1.02579i | 0.858452 | + | 0.512893i | \(0.171426\pi\) | ||||
−0.858452 | + | 0.512893i | \(0.828574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.25176 | −0.403982 | −0.201991 | − | 0.979387i | \(-0.564741\pi\) | ||||
−0.201991 | + | 0.979387i | \(0.564741\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.849616 | + | 1.72183i | −0.0566411 | + | 0.114789i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.8718i | 0.874812i | 0.899264 | + | 0.437406i | \(0.144103\pi\) | ||||
−0.899264 | + | 0.437406i | \(0.855897\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.0798 | 0.793676 | 0.396838 | − | 0.917889i | \(-0.370107\pi\) | ||||
0.396838 | + | 0.917889i | \(0.370107\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.31969 | + | 3.61181i | 0.348557 | + | 0.171991i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 36.4411i | − | 1.58439i | −0.610266 | − | 0.792197i | \(-0.708937\pi\) | ||
0.610266 | − | 0.792197i | \(-0.291063\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.5904 | 0.983615 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.24877 | + | 26.4849i | 0.194399 | + | 0.980923i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 51.7310i | 1.78383i | 0.452205 | + | 0.891914i | \(0.350638\pi\) | ||||
−0.452205 | + | 0.891914i | \(0.649362\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.5009 | −1.17745 | −0.588724 | − | 0.808334i | \(-0.700370\pi\) | ||||
−0.588724 | + | 0.808334i | \(0.700370\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.9790 | + | 30.3565i | −0.453910 | + | 0.919893i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.74133i | 0.0497522i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 63.6951 | 1.72149 | 0.860745 | − | 0.509036i | \(-0.169998\pi\) | ||||
0.860745 | + | 0.509036i | \(0.169998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.1289 | − | 6.97170i | −0.362278 | − | 0.178762i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 12.1500i | − | 0.296342i | −0.988962 | − | 0.148171i | \(-0.952661\pi\) | ||
0.988962 | − | 0.148171i | \(-0.0473386\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.8032 | −0.274493 | −0.137247 | − | 0.990537i | \(-0.543825\pi\) | ||||
−0.137247 | + | 0.990537i | \(0.543825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.57146 | + | 3.50439i | −0.101588 | + | 0.0778753i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 61.1247i | − | 1.30053i | −0.759709 | − | 0.650263i | \(-0.774659\pi\) | ||
0.759709 | − | 0.650263i | \(-0.225341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.5974 | −0.848927 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.7423 | + | 40.0097i | −0.387104 | + | 0.784504i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 59.1695i | 1.11641i | 0.829705 | + | 0.558203i | \(0.188509\pi\) | ||||
−0.829705 | + | 0.558203i | \(0.811491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.22168 | −0.131303 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 40.5694 | + | 20.0185i | 0.711744 | + | 0.351201i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 37.2898i | − | 0.632031i | −0.948754 | − | 0.316016i | \(-0.897655\pi\) | ||
0.948754 | − | 0.316016i | \(-0.102345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −58.1987 | −0.954076 | −0.477038 | − | 0.878883i | \(-0.658290\pi\) | ||||
−0.477038 | + | 0.878883i | \(0.658290\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14.8975 | + | 19.4338i | 0.236469 | + | 0.308472i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.36120i | − | 0.0517107i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23.0991 | 0.344762 | 0.172381 | − | 0.985030i | \(-0.444854\pi\) | ||||
0.172381 | + | 0.985030i | \(0.444854\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48.3754 | − | 98.0376i | 0.701093 | − | 1.42084i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.29656i | − | 0.102768i | −0.998679 | − | 0.0513842i | \(-0.983637\pi\) | ||
0.998679 | − | 0.0513842i | \(-0.0163633\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 73.4504 | 1.00617 | 0.503085 | − | 0.864237i | \(-0.332198\pi\) | ||||
0.503085 | + | 0.864237i | \(0.332198\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 66.1557 | + | 32.6437i | 0.882076 | + | 0.435249i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 30.7002i | 0.398703i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.5098 | 0.740630 | 0.370315 | − | 0.928906i | \(-0.379250\pi\) | ||||
0.370315 | + | 0.928906i | \(0.379250\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −21.0379 | + | 78.2203i | −0.259727 | + | 0.965682i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 32.3939i | − | 0.390287i | −0.980775 | − | 0.195144i | \(-0.937483\pi\) | ||
0.980775 | − | 0.195144i | \(-0.0625173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.51815 | −0.111978 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −68.6728 | + | 139.172i | −0.789343 | + | 1.59968i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 112.260i | − | 1.26135i | −0.776046 | − | 0.630677i | \(-0.782777\pi\) | ||
0.776046 | − | 0.630677i | \(-0.217223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.2888 | −0.157020 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −98.1987 | − | 48.4549i | −1.05590 | − | 0.521020i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.65130i | 0.101593i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −80.0338 | −0.825090 | −0.412545 | − | 0.910937i | \(-0.635360\pi\) | ||||
−0.412545 | + | 0.910937i | \(0.635360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −80.5963 | + | 61.7836i | −0.814104 | + | 0.624077i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 119.373i | − | 1.18191i | −0.806705 | − | 0.590954i | \(-0.798751\pi\) | ||
0.806705 | − | 0.590954i | \(-0.201249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 125.522 | 1.21866 | 0.609330 | − | 0.792917i | \(-0.291438\pi\) | ||||
0.609330 | + | 0.792917i | \(0.291438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.31161 | + | 4.68470i | −0.0220153 | + | 0.0446162i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 148.669i | − | 1.38943i | −0.719284 | − | 0.694716i | \(-0.755530\pi\) | ||
0.719284 | − | 0.694716i | \(-0.244470\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −70.6664 | −0.648316 | −0.324158 | − | 0.946003i | \(-0.605081\pi\) | ||||
−0.324158 | + | 0.946003i | \(0.605081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 171.359 | + | 84.5552i | 1.54378 | + | 0.761758i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 130.968i | − | 1.15901i | −0.814969 | − | 0.579504i | \(-0.803246\pi\) | ||
0.814969 | − | 0.579504i | \(-0.196754\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.3228 | 0.202807 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −28.7560 | − | 37.5120i | −0.245778 | − | 0.320616i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 40.4627i | 0.340023i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.32073 | −0.0522374 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.1291 | − | 32.6873i | 0.131131 | − | 0.265750i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.7385i | 0.253908i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −209.206 | −1.64729 | −0.823647 | − | 0.567103i | \(-0.808064\pi\) | ||||
−0.823647 | + | 0.567103i | \(0.808064\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −31.7543 | − | 15.6687i | −0.246157 | − | 0.121463i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 174.839i | − | 1.33465i | −0.744766 | − | 0.667326i | \(-0.767439\pi\) | ||
0.744766 | − | 0.667326i | \(-0.232561\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41.0287 | 0.308487 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.9507 | + | 3.35929i | −0.125561 | + | 0.0248836i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 162.945i | − | 1.18938i | −0.803956 | − | 0.594689i | \(-0.797275\pi\) | ||
0.803956 | − | 0.594689i | \(-0.202725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −194.227 | −1.39732 | −0.698660 | − | 0.715454i | \(-0.746220\pi\) | ||||
−0.698660 | + | 0.715454i | \(0.746220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 81.1429 | − | 164.444i | 0.575482 | − | 1.16627i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 59.2590i | − | 0.414399i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.1085 | −0.228335 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −111.910 | − | 55.2205i | −0.761291 | − | 0.375650i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 83.4695i | 0.560198i | 0.959971 | + | 0.280099i | \(0.0903673\pi\) | ||||
−0.959971 | + | 0.280099i | \(0.909633\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 60.3488 | 0.399661 | 0.199830 | − | 0.979830i | \(-0.435961\pi\) | ||||
0.199830 | + | 0.979830i | \(0.435961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −106.226 | + | 81.4306i | −0.694285 | + | 0.532226i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 23.3611i | − | 0.150717i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 100.762 | 0.641798 | 0.320899 | − | 0.947113i | \(-0.396015\pi\) | ||||
0.320899 | + | 0.947113i | \(0.396015\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −78.5474 | + | 159.184i | −0.494009 | + | 1.00116i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 99.1476i | − | 0.615824i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 69.7149 | 0.427699 | 0.213849 | − | 0.976867i | \(-0.431400\pi\) | ||||
0.213849 | + | 0.976867i | \(0.431400\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19.4285 | − | 9.58677i | −0.117749 | − | 0.0581016i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 120.823i | − | 0.723491i | −0.932277 | − | 0.361745i | \(-0.882181\pi\) | ||
0.932277 | − | 0.361745i | \(-0.117819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −141.419 | −0.836799 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 82.5697 | + | 107.712i | 0.482863 | + | 0.629893i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 30.0602i | − | 0.173758i | −0.996219 | − | 0.0868791i | \(-0.972311\pi\) | ||
0.996219 | − | 0.0868791i | \(-0.0276894\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 66.9047 | 0.382312 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 49.5022 | − | 100.321i | 0.279673 | − | 0.566786i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 114.784i | − | 0.641250i | −0.947206 | − | 0.320625i | \(-0.896107\pi\) | ||
0.947206 | − | 0.320625i | \(-0.103893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −181.627 | −1.00347 | −0.501733 | − | 0.865022i | \(-0.667304\pi\) | ||||
−0.501733 | + | 0.865022i | \(0.667304\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −156.572 | − | 77.2586i | −0.855586 | − | 0.422178i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 40.7657i | 0.220355i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −167.808 | −0.897370 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.2807 | + | 72.0592i | 0.0755592 | + | 0.381266i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 209.226i | 1.09543i | 0.836666 | + | 0.547713i | \(0.184502\pi\) | ||||
−0.836666 | + | 0.547713i | \(0.815498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 161.330 | 0.835907 | 0.417954 | − | 0.908468i | \(-0.362747\pi\) | ||||
0.417954 | + | 0.908468i | \(0.362747\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.46198 | − | 9.04265i | 0.0228820 | − | 0.0463726i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 144.953i | 0.735801i | 0.929865 | + | 0.367901i | \(0.119923\pi\) | ||||
−0.929865 | + | 0.367901i | \(0.880077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 237.264 | 1.19228 | 0.596140 | − | 0.802880i | \(-0.296700\pi\) | ||||
0.596140 | + | 0.802880i | \(0.296700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 62.1436 | + | 30.6640i | 0.309172 | + | 0.152557i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 140.748i | 0.693340i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.77617 | 0.0379325 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 260.289 | − | 199.533i | 1.25744 | − | 0.963927i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 170.156i | 0.814142i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 307.117 | 1.45553 | 0.727765 | − | 0.685827i | \(-0.240559\pi\) | ||||
0.727765 | + | 0.685827i | \(0.240559\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.68617 | − | 19.6300i | 0.0454750 | − | 0.0921595i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 7.55422i | − | 0.0351359i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −99.3105 | −0.457652 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 197.604 | + | 97.5053i | 0.902302 | + | 0.445230i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 78.1032i | − | 0.353408i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −438.001 | −1.96413 | −0.982065 | − | 0.188544i | \(-0.939623\pi\) | ||||
−0.982065 | + | 0.188544i | \(0.939623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 134.645 | + | 175.643i | 0.598420 | + | 0.780636i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 270.755i | 1.19275i | 0.802705 | + | 0.596376i | \(0.203393\pi\) | ||||
−0.802705 | + | 0.596376i | \(0.796607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −98.6778 | −0.430907 | −0.215454 | − | 0.976514i | \(-0.569123\pi\) | ||||
−0.215454 | + | 0.976514i | \(0.569123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −40.7544 | + | 82.5929i | −0.176426 | + | 0.357545i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 432.405i | 1.85581i | 0.372812 | + | 0.927907i | \(0.378394\pi\) | ||||
−0.372812 | + | 0.927907i | \(0.621606\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39.1206 | 0.166471 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 157.409 | + | 77.6717i | 0.664174 | + | 0.327729i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 275.799i | − | 1.15397i | −0.816754 | − | 0.576986i | \(-0.804229\pi\) | ||
0.816754 | − | 0.576986i | \(-0.195771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 416.770 | 1.72934 | 0.864669 | − | 0.502343i | \(-0.167528\pi\) | ||||
0.864669 | + | 0.502343i | \(0.167528\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −160.436 | + | 182.509i | −0.660228 | + | 0.751065i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 26.6229i | − | 0.108665i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −79.1958 | −0.320631 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 43.0028 | − | 87.1494i | 0.172702 | − | 0.349998i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 165.903i | 0.660966i | 0.943812 | + | 0.330483i | \(0.107212\pi\) | ||||
−0.943812 | + | 0.330483i | \(0.892788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 411.188 | 1.62525 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −25.6068 | − | 12.6353i | −0.100419 | − | 0.0495503i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 59.6381i | − | 0.232055i | −0.993246 | − | 0.116028i | \(-0.962984\pi\) | ||
0.993246 | − | 0.116028i | \(-0.0370161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 173.300 | 0.669110 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −369.502 | + | 283.253i | −1.41572 | + | 1.08526i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 67.2606i | − | 0.255744i | −0.991791 | − | 0.127872i | \(-0.959185\pi\) | ||
0.991791 | − | 0.127872i | \(-0.0408146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.8693 | −0.142903 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 149.026 | − | 302.015i | 0.558148 | − | 1.13114i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 36.1495i | 0.134385i | 0.997740 | + | 0.0671923i | \(0.0214041\pi\) | ||||
−0.997740 | + | 0.0671923i | \(0.978596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 328.311 | 1.21148 | 0.605741 | − | 0.795662i | \(-0.292877\pi\) | ||||
0.605741 | + | 0.795662i | \(0.292877\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −38.4413 | − | 18.9684i | −0.140811 | − | 0.0694812i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 277.469i | 1.00898i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 60.7455 | 0.219298 | 0.109649 | − | 0.993970i | \(-0.465027\pi\) | ||||
0.109649 | + | 0.993970i | \(0.465027\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −199.861 | − | 260.717i | −0.716347 | − | 0.934470i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 366.827i | 1.30543i | 0.757602 | + | 0.652717i | \(0.226371\pi\) | ||||
−0.757602 | + | 0.652717i | \(0.773629\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 104.032 | 0.367603 | 0.183801 | − | 0.982963i | \(-0.441160\pi\) | ||||
0.183801 | + | 0.982963i | \(0.441160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.8121 | + | 25.9650i | −0.0449547 | + | 0.0911051i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 33.0574i | − | 0.115182i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 67.8293 | 0.234703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −215.315 | − | 106.245i | −0.739915 | − | 0.365102i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 410.579i | 1.40129i | 0.713508 | + | 0.700647i | \(0.247105\pi\) | ||||
−0.713508 | + | 0.700647i | \(0.752895\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.8660 | 0.0809017 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −298.846 | + | 59.2253i | −1.00622 | + | 0.199412i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 191.380i | 0.640066i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.1138 | −0.106690 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 158.467 | − | 321.149i | 0.522994 | − | 1.05990i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 37.2479i | − | 0.122124i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −270.025 | −0.879561 | −0.439781 | − | 0.898105i | \(-0.644944\pi\) | ||||
−0.439781 | + | 0.898105i | \(0.644944\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 337.693 | + | 166.630i | 1.09286 | + | 0.539256i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 251.555i | 0.808858i | 0.914569 | + | 0.404429i | \(0.132530\pi\) | ||||
−0.914569 | + | 0.404429i | \(0.867470\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −83.9560 | −0.268230 | −0.134115 | − | 0.990966i | \(-0.542819\pi\) | ||||
−0.134115 | + | 0.990966i | \(0.542819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.4379 | + | 9.53463i | −0.0394853 | + | 0.0302687i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 270.737i | − | 0.854060i | −0.904238 | − | 0.427030i | \(-0.859560\pi\) | ||
0.904238 | − | 0.427030i | \(-0.140440\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −583.715 | −1.82983 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 197.358 | − | 399.966i | 0.614823 | − | 1.24600i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 224.265i | 0.694318i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −129.143 | −0.397363 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −190.114 | − | 93.8095i | −0.581389 | − | 0.286879i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 166.306i | − | 0.505489i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.91562 | 0.0299566 | 0.0149783 | − | 0.999888i | \(-0.495232\pi\) | ||||
0.0149783 | + | 0.999888i | \(0.495232\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 348.763 | + | 454.959i | 1.04733 | + | 1.36624i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.7837i | 0.0441305i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −289.542 | −0.859174 | −0.429587 | − | 0.903025i | \(-0.641341\pi\) | ||||
−0.429587 | + | 0.903025i | \(0.641341\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 173.860 | − | 352.344i | 0.512860 | − | 1.03936i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 411.864i | − | 1.20781i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −246.494 | −0.718643 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 62.7454 | + | 30.9609i | 0.181871 | + | 0.0897418i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 331.079i | − | 0.954119i | −0.878871 | − | 0.477060i | \(-0.841703\pi\) | ||
0.878871 | − | 0.477060i | \(-0.158297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 302.280 | 0.866133 | 0.433067 | − | 0.901362i | \(-0.357431\pi\) | ||||
0.433067 | + | 0.901362i | \(0.357431\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.5653 | − | 139.092i | −0.0785337 | − | 0.396275i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 528.345i | 1.49673i | 0.663289 | + | 0.748364i | \(0.269160\pi\) | ||||
−0.663289 | + | 0.748364i | \(0.730840\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.66989 | 0.0131546 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −53.7142 | + | 108.857i | −0.150460 | + | 0.304922i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 59.5167i | − | 0.165785i | −0.996559 | − | 0.0828923i | \(-0.973584\pi\) | ||
0.996559 | − | 0.0828923i | \(-0.0264158\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −133.598 | −0.370078 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.0047 | − | 8.39076i | −0.0468449 | − | 0.0231150i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 47.0092i | 0.128792i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 423.762 | 1.15466 | 0.577332 | − | 0.816509i | \(-0.304094\pi\) | ||||
0.577332 | + | 0.816509i | \(0.304094\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 86.7846 | − | 66.5274i | 0.235189 | − | 0.180291i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 160.986i | 0.433925i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.5076 | 0.0710660 | 0.0355330 | − | 0.999369i | \(-0.488687\pi\) | ||||
0.0355330 | + | 0.999369i | \(0.488687\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −42.1328 | + | 85.3863i | −0.112354 | + | 0.227697i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 271.679i | − | 0.720634i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −383.169 | −1.01100 | −0.505500 | − | 0.862827i | \(-0.668692\pi\) | ||||
−0.505500 | + | 0.862827i | \(0.668692\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −562.829 | − | 277.721i | −1.47724 | − | 0.728927i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 299.496i | 0.781973i | 0.920396 | + | 0.390987i | \(0.127866\pi\) | ||||
−0.920396 | + | 0.390987i | \(0.872134\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.6485 | −0.0510351 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −64.6285 | − | 84.3075i | −0.166999 | − | 0.217849i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 437.687i | − | 1.12516i | −0.826743 | − | 0.562580i | \(-0.809809\pi\) | ||
0.826743 | − | 0.562580i | \(-0.190191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 541.944 | 1.38605 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 232.099 | − | 470.372i | 0.590583 | − | 1.19687i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.4470i | 0.0948027i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −669.283 | −1.68585 | −0.842926 | − | 0.538029i | \(-0.819169\pi\) | ||||
−0.842926 | + | 0.538029i | \(0.819169\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 110.380 | + | 54.4656i | 0.276641 | + | 0.136505i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 56.1062i | 0.139916i | 0.997550 | + | 0.0699578i | \(0.0222865\pi\) | ||||
−0.997550 | + | 0.0699578i | \(0.977714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 191.694 | 0.475668 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −50.0620 | − | 13.4645i | −0.123610 | − | 0.0332457i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 718.713i | 1.76588i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 248.582 | 0.607779 | 0.303889 | − | 0.952707i | \(-0.401715\pi\) | ||||
0.303889 | + | 0.952707i | \(0.401715\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 216.309 | − | 438.371i | 0.526299 | − | 1.06660i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 101.457i | − | 0.245658i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.7325 | 0.0499578 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −522.531 | − | 257.836i | −1.25307 | − | 0.618313i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 459.935i | − | 1.09770i | −0.835922 | − | 0.548849i | \(-0.815066\pi\) | ||
0.835922 | − | 0.548849i | \(-0.184934\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −97.4789 | −0.231541 | −0.115771 | − | 0.993276i | \(-0.536934\pi\) | ||||
−0.115771 | + | 0.993276i | \(0.536934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 436.599 | − | 334.688i | 1.03215 | − | 0.791225i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 365.703i | 0.860479i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −158.345 | −0.370831 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 78.6663 | − | 159.425i | 0.183371 | − | 0.371620i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 545.207i | 1.26498i | 0.774568 | + | 0.632490i | \(0.217967\pi\) | ||||
−0.774568 | + | 0.632490i | \(0.782033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.5297 | −0.0566506 | −0.0283253 | − | 0.999599i | \(-0.509017\pi\) | ||||
−0.0283253 | + | 0.999599i | \(0.509017\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −89.0721 | − | 43.9515i | −0.204763 | − | 0.101038i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 549.526i | − | 1.25750i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 81.8743 | 0.186502 | 0.0932509 | − | 0.995643i | \(-0.470274\pi\) | ||||
0.0932509 | + | 0.995643i | \(0.470274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −227.767 | − | 297.120i | −0.516478 | − | 0.673742i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 831.356i | 1.87665i | 0.345753 | + | 0.938325i | \(0.387623\pi\) | ||||
−0.345753 | + | 0.938325i | \(0.612377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 71.8482 | 0.161457 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −110.806 | + | 224.559i | −0.247887 | + | 0.502368i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 259.553i | − | 0.578070i | −0.957319 | − | 0.289035i | \(-0.906666\pi\) | ||
0.957319 | − | 0.289035i | \(-0.0933344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 137.097 | 0.303983 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 162.357 | + | 80.1129i | 0.358403 | + | 0.176850i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 9.14503i | − | 0.0200990i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 373.184 | 0.816596 | 0.408298 | − | 0.912849i | \(-0.366122\pi\) | ||||
0.408298 | + | 0.912849i | \(0.366122\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −393.879 | + | 78.0588i | −0.858123 | + | 0.170063i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 672.996i | − | 1.45986i | −0.683522 | − | 0.729930i | \(-0.739553\pi\) | ||
0.683522 | − | 0.729930i | \(-0.260447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0435 | −0.0605690 | −0.0302845 | − | 0.999541i | \(-0.509641\pi\) | ||||
−0.0302845 | + | 0.999541i | \(0.509641\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.0118 | − | 62.8484i | 0.0666920 | − | 0.135158i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 373.758i | − | 0.800339i | −0.916441 | − | 0.400169i | \(-0.868951\pi\) | ||
0.916441 | − | 0.400169i | \(-0.131049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 62.8472 | 0.134003 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 271.082 | + | 133.762i | 0.575545 | + | 0.283995i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 133.183i | − | 0.281572i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 370.819 | 0.780672 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −422.633 | + | 323.982i | −0.886023 | + | 0.679208i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 915.154i | 1.91055i | 0.295718 | + | 0.955275i | \(0.404441\pi\) | ||||
−0.295718 | + | 0.955275i | \(0.595559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −334.512 | −0.695451 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 131.618 | − | 266.737i | 0.272502 | − | 0.552251i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 51.2227i | − | 0.105614i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −238.560 | −0.489856 | −0.244928 | − | 0.969541i | \(-0.578764\pi\) | ||||
−0.244928 | + | 0.969541i | \(0.578764\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 187.555 | + | 92.5464i | 0.383547 | + | 0.189257i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 435.657i | − | 0.887286i | −0.896204 | − | 0.443643i | \(-0.853686\pi\) | ||
0.896204 | − | 0.443643i | \(-0.146314\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −769.334 | −1.56052 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −39.5423 | − | 51.5827i | −0.0798835 | − | 0.104207i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 19.8522i | − | 0.0399441i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −209.499 | −0.419838 | −0.209919 | − | 0.977719i | \(-0.567320\pi\) | ||||
−0.209919 | + | 0.977719i | \(0.567320\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 160.392 | − | 325.051i | 0.320144 | − | 0.648804i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 558.314i | − | 1.10997i | −0.831861 | − | 0.554984i | \(-0.812724\pi\) | ||
0.831861 | − | 0.554984i | \(-0.187276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 76.4002 | 0.151287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −380.460 | − | 187.733i | −0.750415 | − | 0.370283i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 319.621i | 0.627939i | 0.949433 | + | 0.313969i | \(0.101659\pi\) | ||||
−0.949433 | + | 0.313969i | \(0.898341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 199.841 | 0.391079 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 79.1507 | + | 399.388i | 0.154290 | + | 0.778535i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 80.3357i | 0.155992i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 689.710 | 1.33406 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 39.9048 | − | 80.8710i | 0.0768879 | − | 0.155821i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 771.602i | − | 1.48100i | −0.672055 | − | 0.740501i | \(-0.734588\pi\) | ||
0.672055 | − | 0.740501i | \(-0.265412\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 288.856 | 0.552306 | 0.276153 | − | 0.961114i | \(-0.410940\pi\) | ||||
0.276153 | + | 0.961114i | \(0.410940\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 179.994 | + | 88.8158i | 0.342846 | + | 0.169173i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 542.835i | − | 1.03005i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −798.951 | −1.51030 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 266.352 | − | 204.180i | 0.501605 | − | 0.384521i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 63.8090i | 0.119717i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 95.1503 | 0.177851 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 152.375 | − | 308.803i | 0.283753 | − | 0.575053i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 469.371i | − | 0.870818i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 232.871 | 0.430446 | 0.215223 | − | 0.976565i | \(-0.430952\pi\) | ||||
0.215223 | + | 0.976565i | \(0.430952\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −488.633 | − | 241.110i | −0.899877 | − | 0.444033i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 45.2274i | − | 0.0829861i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −910.003 | −1.66363 | −0.831813 | − | 0.555056i | \(-0.812697\pi\) | ||||
−0.831813 | + | 0.555056i | \(0.812697\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −318.667 | − | 415.699i | −0.580449 | − | 0.757192i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 780.096i | 1.41578i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 159.191 | 0.287869 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −54.1164 | + | 109.672i | −0.0975071 | + | 0.197608i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 297.809i | 0.534666i | 0.963604 | + | 0.267333i | \(0.0861424\pi\) | ||||
−0.963604 | + | 0.267333i | \(0.913858\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 61.9877 | 0.110890 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −451.456 | − | 222.765i | −0.804734 | − | 0.397086i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 184.465i | 0.327647i | 0.986490 | + | 0.163824i | \(0.0523828\pi\) | ||||
−0.986490 | + | 0.163824i | \(0.947617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 83.8212 | 0.148356 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −57.2391 | + | 212.819i | −0.100951 | + | 0.375342i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 404.137i | 0.710258i | 0.934817 | + | 0.355129i | \(0.115563\pi\) | ||||
−0.934817 | + | 0.355129i | \(0.884437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −762.365 | −1.33514 | −0.667570 | − | 0.744547i | \(-0.732666\pi\) | ||||
−0.667570 | + | 0.744547i | \(0.732666\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −277.748 | + | 562.883i | −0.484726 | + | 0.982344i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 896.100i | − | 1.55843i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −290.766 | −0.503927 | −0.251964 | − | 0.967737i | \(-0.581076\pi\) | ||||
−0.251964 | + | 0.967737i | \(0.581076\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 434.027 | + | 214.165i | 0.749616 | + | 0.369888i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 88.1361i | − | 0.151697i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −667.648 | −1.14519 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0082 | − | 18.4042i | 0.0410397 | − | 0.0314602i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 224.506i | 0.382464i | 0.981545 | + | 0.191232i | \(0.0612482\pi\) | ||||
−0.981545 | + | 0.191232i | \(0.938752\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −550.428 | −0.934513 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −192.425 | + | 389.968i | −0.325592 | + | 0.659844i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 482.620i | 0.813862i | 0.913459 | + | 0.406931i | \(0.133401\pi\) | ||||
−0.913459 | + | 0.406931i | \(0.866599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.8967 | −0.0435238 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 638.312 | + | 314.967i | 1.06920 | + | 0.527583i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 803.277i | − | 1.34103i | −0.741896 | − | 0.670515i | \(-0.766073\pi\) | ||
0.741896 | − | 0.670515i | \(-0.233927\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −126.365 | −0.210258 | −0.105129 | − | 0.994459i | \(-0.533526\pi\) | ||||
−0.105129 | + | 0.994459i | \(0.533526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 126.479 | + | 164.991i | 0.209750 | + | 0.273617i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 4.04535i | − | 0.00668653i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 397.356 | 0.654623 | 0.327312 | − | 0.944916i | \(-0.393857\pi\) | ||||
0.327312 | + | 0.944916i | \(0.393857\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −186.843 | + | 378.655i | −0.306802 | + | 0.621766i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 321.012i | 0.525388i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1056.55 | 1.72357 | 0.861785 | − | 0.507275i | \(-0.169347\pi\) | ||||
0.861785 | + | 0.507275i | \(0.169347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.9203 | + | 10.3229i | 0.0340167 | + | 0.0167851i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 411.284i | − | 0.666586i | −0.942823 | − | 0.333293i | \(-0.891840\pi\) | ||
0.942823 | − | 0.333293i | \(-0.108160\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 691.383 | 1.11693 | 0.558467 | − | 0.829526i | \(-0.311390\pi\) | ||||
0.558467 | + | 0.829526i | \(0.311390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 965.138 | − | 191.271i | 1.55417 | − | 0.308005i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 305.435i | − | 0.490264i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 594.447 | 0.951114 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −225.881 | + | 457.771i | −0.360257 | + | 0.730097i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 947.262i | 1.50598i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −528.057 | −0.836858 | −0.418429 | − | 0.908250i | \(-0.637419\pi\) | ||||
−0.418429 | + | 0.908250i | \(0.637419\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 826.238 | + | 407.697i | 1.30527 | + | 0.644071i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 133.895i | − | 0.210858i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 218.460 | 0.342951 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 52.1175 | − | 39.9523i | 0.0815611 | − | 0.0625232i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 134.165i | 0.209306i | 0.994509 | + | 0.104653i | \(0.0333731\pi\) | ||||
−0.994509 | + | 0.104653i | \(0.966627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 633.985 | 0.985979 | 0.492990 | − | 0.870035i | \(-0.335904\pi\) | ||||
0.492990 | + | 0.870035i | \(0.335904\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.0282 | − | 20.3232i | 0.0155476 | − | 0.0315088i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 227.758i | 0.352021i | 0.984388 | + | 0.176011i | \(0.0563193\pi\) | ||||
−0.984388 | + | 0.176011i | \(0.943681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 420.766 | 0.648329 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −267.176 | − | 131.834i | −0.410408 | − | 0.202511i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1190.65i | 1.82336i | 0.410906 | + | 0.911678i | \(0.365212\pi\) | ||||
−0.410906 | + | 0.911678i | \(0.634788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 111.900 | 0.170839 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 402.178 | + | 524.638i | 0.612142 | + | 0.798536i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 266.873i | 0.404967i | 0.979286 | + | 0.202484i | \(0.0649013\pi\) | ||||
−0.979286 | + | 0.202484i | \(0.935099\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1045.10 | −1.58109 | −0.790544 | − | 0.612405i | \(-0.790202\pi\) | ||||
−0.790544 | + | 0.612405i | \(0.790202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 103.682 | − | 210.122i | 0.156383 | − | 0.316925i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.2589i | 0.0394871i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1885.13 | 2.82629 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1178.36 | − | 581.445i | −1.76137 | − | 0.869126i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 656.693i | − | 0.978678i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 408.300 | 0.606687 | 0.303343 | − | 0.952881i | \(-0.401897\pi\) | ||||
0.303343 | + | 0.952881i | \(0.401897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 129.069 | + | 651.274i | 0.191214 | + | 0.964850i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 749.557i | − | 1.10717i | −0.832791 | − | 0.553587i | \(-0.813259\pi\) | ||
0.832791 | − | 0.553587i | \(-0.186741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −217.753 | −0.320697 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −359.426 | + | 728.413i | −0.527792 | + | 1.06962i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 258.242i | 0.378099i | 0.981968 | + | 0.189050i | \(0.0605407\pi\) | ||||
−0.981968 | + | 0.189050i | \(0.939459\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 104.287 | 0.152244 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −265.474 | − | 130.995i | −0.386424 | − | 0.190676i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 310.744i | − | 0.451007i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −929.714 | −1.34546 | −0.672731 | − | 0.739887i | \(-0.734879\pi\) | ||||
−0.672731 | + | 0.739887i | \(0.734879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −219.284 | + | 168.099i | −0.316427 | + | 0.242567i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 124.308i | − | 0.178861i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 180.693 | 0.259244 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −574.016 | + | 1163.30i | −0.821197 | + | 1.66424i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 335.731i | 0.478932i | 0.970905 | + | 0.239466i | \(0.0769724\pi\) | ||||
−0.970905 | + | 0.239466i | \(0.923028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 960.513 | 1.36631 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 105.246 | + | 51.9325i | 0.149286 | + | 0.0736632i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 324.785i | − | 0.459385i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 356.121 | 0.502287 | 0.251143 | − | 0.967950i | \(-0.419193\pi\) | ||||
0.251143 | + | 0.967950i | \(0.419193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 320.370 | + | 417.921i | 0.450591 | + | 0.587793i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1330.13i | 1.86554i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.9266 | 0.0530442 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 366.123 | − | 741.985i | 0.510632 | − | 1.03485i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 31.7234i | − | 0.0441216i | −0.999757 | − | 0.0220608i | \(-0.992977\pi\) | ||
0.999757 | − | 0.0220608i | \(-0.00702274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 341.516 | 0.473670 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1121.24 | + | 553.262i | 1.55082 | + | 0.765231i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1272.09i | 1.75460i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −234.202 | −0.322148 | −0.161074 | − | 0.986942i | \(-0.551496\pi\) | ||||
−0.161074 | + | 0.986942i | \(0.551496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −673.901 | + | 278.027i | −0.924418 | + | 0.381381i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 175.535i | − | 0.240130i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 616.813 | 0.841491 | 0.420745 | − | 0.907179i | \(-0.361769\pi\) | ||||
0.420745 | + | 0.907179i | \(0.361769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.3419 | − | 71.6238i | 0.0480842 | − | 0.0974473i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 260.642i | 0.353653i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −605.806 | −0.819764 | −0.409882 | − | 0.912138i | \(-0.634430\pi\) | ||||
−0.409882 | + | 0.912138i | \(0.634430\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −213.061 | − | 105.132i | −0.287532 | − | 0.141879i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1033.33i | − | 1.39076i | −0.718642 | − | 0.695380i | \(-0.755236\pi\) | ||
0.718642 | − | 0.695380i | \(-0.244764\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53.4216 | −0.0717068 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 231.381 | − | 177.372i | 0.309747 | − | 0.237446i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 404.494i | − | 0.540046i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −969.301 | −1.29068 | −0.645340 | − | 0.763896i | \(-0.723284\pi\) | ||||
−0.645340 | + | 0.763896i | \(0.723284\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −220.235 | + | 446.329i | −0.292477 | + | 0.592734i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.6240i | 0.0511577i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −533.594 | −0.704880 | −0.352440 | − | 0.935835i | \(-0.614648\pi\) | ||||
−0.352440 | + | 0.935835i | \(0.614648\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1106.22 | + | 545.851i | 1.45747 | + | 0.719172i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 867.717i | − | 1.14023i | −0.821564 | − | 0.570116i | \(-0.806898\pi\) | ||
0.821564 | − | 0.570116i | \(-0.193102\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −192.267 | −0.251988 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −52.1166 | − | 67.9858i | −0.0681263 | − | 0.0888704i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 195.837i | 0.255329i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 194.555 | 0.252997 | 0.126498 | − | 0.991967i | \(-0.459626\pi\) | ||||
0.126498 | + | 0.991967i | \(0.459626\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 79.1695 | − | 160.445i | 0.102684 | − | 0.208100i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 420.140i | 0.543519i | 0.962365 | + | 0.271760i | \(0.0876056\pi\) | ||||
−0.962365 | + | 0.271760i | \(0.912394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −897.572 | −1.15816 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 466.229 | + | 230.055i | 0.600037 | + | 0.296081i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 183.220i | − | 0.235199i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 82.3318 | 0.105418 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1370.09 | + | 271.524i | −1.74980 | + | 0.346775i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 64.4892i | 0.0821519i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 849.081 | 1.07888 | 0.539441 | − | 0.842023i | \(-0.318635\pi\) | ||||
0.539441 | + | 0.842023i | \(0.318635\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 89.2883 | − | 180.952i | 0.113166 | − | 0.229343i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 356.333i | − | 0.450484i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 305.646 | 0.385429 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −101.880 | − | 50.2714i | −0.128151 | − | 0.0632344i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 779.186i | 0.977648i | 0.872382 | + | 0.488824i | \(0.162574\pi\) | ||||
−0.872382 | + | 0.488824i | \(0.837426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 909.035 | 1.13772 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 801.849 | − | 614.682i | 1.00106 | − | 0.767393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 828.789i | 1.03212i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 63.4558 | 0.0788270 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.9884 | + | 97.2532i | −0.0594651 | + | 0.120512i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 865.140i | − | 1.06939i | −0.845044 | − | 0.534697i | \(-0.820426\pi\) | ||
0.845044 | − | 0.534697i | \(-0.179574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −251.360 | −0.309938 | −0.154969 | − | 0.987919i | \(-0.549528\pi\) | ||||
−0.154969 | + | 0.987919i | \(0.549528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 883.258 | + | 435.833i | 1.08642 | + | 0.536080i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.6185i | 0.0547466i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −177.991 | −0.217859 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −78.2384 | − | 102.061i | −0.0955292 | − | 0.124617i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 103.359i | 0.125894i | 0.998017 | + | 0.0629470i | \(0.0200499\pi\) | ||||
−0.998017 | + | 0.0629470i | \(0.979950\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 474.728 | 0.576826 | 0.288413 | − | 0.957506i | \(-0.406872\pi\) | ||||
0.288413 | + | 0.957506i | \(0.406872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −368.340 | + | 746.477i | −0.446473 | + | 0.904821i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 471.776i | − | 0.570467i | −0.958458 | − | 0.285234i | \(-0.907929\pi\) | ||
0.958458 | − | 0.285234i | \(-0.0920712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 771.883 | 0.931102 | 0.465551 | − | 0.885021i | \(-0.345856\pi\) | ||||
0.465551 | + | 0.885021i | \(0.345856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 163.424 | + | 80.6396i | 0.196660 | + | 0.0970392i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 618.629i | − | 0.742652i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 77.3283 | 0.0926087 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −191.585 | − | 966.723i | −0.228895 | − | 1.15499i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 510.944i | − | 0.608992i | −0.952514 | − | 0.304496i | \(-0.901512\pi\) | ||
0.952514 | − | 0.304496i | \(-0.0984881\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1835.10 | −2.18204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −486.962 | + | 986.877i | −0.577654 | + | 1.17067i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 90.5100i | − | 0.107112i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.1972 | −0.0203037 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 279.877 | + | 138.102i | 0.329655 | + | 0.162664i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2321.12i | − | 2.72752i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −581.090 | −0.681231 | −0.340616 | − | 0.940203i | \(-0.610635\pi\) | ||||
−0.340616 | + | 0.940203i | \(0.610635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −68.9369 | + | 52.8457i | −0.0806279 | + | 0.0618078i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.21760i | − | 0.00842193i | −0.999991 | − | 0.00421097i | \(-0.998660\pi\) | ||
0.999991 | − | 0.00421097i | \(-0.00134040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −104.856 | −0.122068 | −0.0610339 | − | 0.998136i | \(-0.519440\pi\) | ||||
−0.0610339 | + | 0.998136i | \(0.519440\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 43.8836 | − | 88.9344i | 0.0509681 | − | 0.103292i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1213.72i | − | 1.40640i | −0.710992 | − | 0.703200i | \(-0.751754\pi\) | ||
0.710992 | − | 0.703200i | \(-0.248246\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.2389 | 0.0222415 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 182.482 | + | 90.0432i | 0.210475 | + | 0.103856i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 660.204i | 0.759729i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −121.311 | −0.139278 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −438.225 | − | 571.661i | −0.501975 | − | 0.654824i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 86.3530i | 0.0986892i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −706.591 | −0.805691 | −0.402846 | − | 0.915268i | \(-0.631979\pi\) | ||||
−0.402846 | + | 0.915268i | \(0.631979\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −545.043 | + | 1104.58i | −0.620072 | + | 1.25664i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1715.95i | − | 1.94773i | −0.227134 | − | 0.973864i | \(-0.572935\pi\) | ||
0.227134 | − | 0.973864i | \(-0.427065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1472.11 | −1.66717 | −0.833586 | − | 0.552390i | \(-0.813716\pi\) | ||||
−0.833586 | + | 0.552390i | \(0.813716\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 64.2068 | + | 31.6821i | 0.0725501 | + | 0.0357989i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 277.658i | 0.313030i | 0.987676 | + | 0.156515i | \(0.0500259\pi\) | ||||
−0.987676 | + | 0.156515i | \(0.949974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −569.202 | −0.640272 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −882.610 | − | 237.384i | −0.990584 | − | 0.266424i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 921.751i | − | 1.03220i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 73.4631 | 0.0820817 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −254.056 | + | 514.870i | −0.283229 | + | 0.573991i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1888.23i | − | 2.10037i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −879.957 | −0.976645 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −86.3959 | − | 42.6310i | −0.0956766 | − | 0.0472104i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 116.244i | − | 0.128446i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −365.591 | −0.403078 | −0.201539 | − | 0.979481i | \(-0.564594\pi\) | ||||
−0.201539 | + | 0.979481i | \(0.564594\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 852.650 | − | 653.625i | 0.938009 | − | 0.719060i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1664.90i | 1.82755i | 0.406223 | + | 0.913774i | \(0.366846\pi\) | ||||
−0.406223 | + | 0.913774i | \(0.633154\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 365.521 | 0.400351 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 49.4465 | − | 100.208i | 0.0540399 | − | 0.109517i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 475.697i | − | 0.518754i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 195.745 | 0.212998 | 0.106499 | − | 0.994313i | \(-0.466036\pi\) | ||||
0.106499 | + | 0.994313i | \(0.466036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −726.451 | − | 358.458i | −0.788763 | − | 0.389205i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.3198i | 0.0415166i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1566.29 | 1.69328 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 687.295 | + | 896.573i | 0.741419 | + | 0.967177i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 769.046i | − | 0.827822i | −0.910317 | − | 0.413911i | \(-0.864163\pi\) | ||
0.910317 | − | 0.413911i | \(-0.135837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −627.283 | −0.673773 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −333.939 | + | 676.760i | −0.357919 | + | 0.725359i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 107.400i | − | 0.114866i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.0296961 | −3.16928e−5 | −1.58464e−5 | − | 1.00000i | \(-0.500005\pi\) | ||||
−1.58464e−5 | 1.00000i | \(0.500005\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −225.867 | − | 111.451i | −0.240540 | − | 0.118692i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1283.68i | − | 1.36416i | −0.731277 | − | 0.682081i | \(-0.761075\pi\) | ||
0.731277 | − | 0.682081i | \(-0.238925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −442.760 | −0.469522 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −46.1189 | + | 9.13983i | −0.0488030 | + | 0.00967178i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1514.62i | 1.59938i | 0.600410 | + | 0.799692i | \(0.295004\pi\) | ||||
−0.600410 | + | 0.799692i | \(0.704996\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −385.744 | −0.406474 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 359.403 | − | 728.365i | 0.377921 | − | 0.765894i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 937.870i | 0.984124i | 0.870560 | + | 0.492062i | \(0.163757\pi\) | ||||
−0.870560 | + | 0.492062i | \(0.836243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −133.908 | −0.140218 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1570.37 | − | 774.880i | −1.64093 | − | 0.809697i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 443.335i | − | 0.462288i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 371.317 | 0.386386 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1061.91 | − | 814.038i | 1.10271 | − | 0.845315i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 103.253i | 0.106998i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 461.673 | 0.477428 | 0.238714 | − | 0.971090i | \(-0.423274\pi\) | ||||
0.238714 | + | 0.971090i | \(0.423274\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −297.711 | + | 603.340i | −0.307235 | + | 0.622642i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1360.95i | − | 1.40160i | −0.713360 | − | 0.700798i | \(-0.752827\pi\) | ||
0.713360 | − | 0.700798i | \(-0.247173\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −528.447 | −0.543111 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −347.434 | − | 171.437i | −0.356342 | − | 0.175833i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1162.17i | − | 1.18953i | −0.803901 | − | 0.594763i | \(-0.797246\pi\) | ||
0.803901 | − | 0.594763i | \(-0.202754\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1266.71 | 1.29388 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −386.934 | − | 504.753i | −0.394428 | − | 0.514529i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 969.961i | 0.986735i | 0.869821 | + | 0.493368i | \(0.164234\pi\) | ||||
−0.869821 | + | 0.493368i | \(0.835766\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −92.7717 | −0.0941845 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 220.771 | − | 447.414i | 0.223679 | − | 0.453307i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 430.122i | 0.434906i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1602.81 | 1.61737 | 0.808684 | − | 0.588243i | \(-0.200180\pi\) | ||||
0.808684 | + | 0.588243i | \(0.200180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.6761 | + | 13.1630i | 0.0268641 | + | 0.0132558i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 151.852i | 0.152615i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −742.855 | −0.745090 | −0.372545 | − | 0.928014i | \(-0.621515\pi\) | ||||
−0.372545 | + | 0.928014i | \(0.621515\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 334.321 | + | 1686.96i | 0.334656 | + | 1.68865i |
(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 | 384.3.e.b.257.8 | yes | 8 | |
3.2 | odd | 2 | inner | 384.3.e.b.257.7 | yes | 8 | |
4.3 | odd | 2 | 384.3.e.c.257.1 | yes | 8 | ||
8.3 | odd | 2 | 384.3.e.a.257.8 | yes | 8 | ||
8.5 | even | 2 | 384.3.e.d.257.1 | yes | 8 | ||
12.11 | even | 2 | 384.3.e.c.257.2 | yes | 8 | ||
16.3 | odd | 4 | 768.3.h.h.641.11 | 16 | |||
16.5 | even | 4 | 768.3.h.g.641.11 | 16 | |||
16.11 | odd | 4 | 768.3.h.h.641.6 | 16 | |||
16.13 | even | 4 | 768.3.h.g.641.6 | 16 | |||
24.5 | odd | 2 | 384.3.e.d.257.2 | yes | 8 | ||
24.11 | even | 2 | 384.3.e.a.257.7 | ✓ | 8 | ||
48.5 | odd | 4 | 768.3.h.g.641.5 | 16 | |||
48.11 | even | 4 | 768.3.h.h.641.12 | 16 | |||
48.29 | odd | 4 | 768.3.h.g.641.12 | 16 | |||
48.35 | even | 4 | 768.3.h.h.641.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.7 | ✓ | 8 | 24.11 | even | 2 | ||
384.3.e.a.257.8 | yes | 8 | 8.3 | odd | 2 | ||
384.3.e.b.257.7 | yes | 8 | 3.2 | odd | 2 | inner | |
384.3.e.b.257.8 | yes | 8 | 1.1 | even | 1 | trivial | |
384.3.e.c.257.1 | yes | 8 | 4.3 | odd | 2 | ||
384.3.e.c.257.2 | yes | 8 | 12.11 | even | 2 | ||
384.3.e.d.257.1 | yes | 8 | 8.5 | even | 2 | ||
384.3.e.d.257.2 | yes | 8 | 24.5 | odd | 2 | ||
768.3.h.g.641.5 | 16 | 48.5 | odd | 4 | |||
768.3.h.g.641.6 | 16 | 16.13 | even | 4 | |||
768.3.h.g.641.11 | 16 | 16.5 | even | 4 | |||
768.3.h.g.641.12 | 16 | 48.29 | odd | 4 | |||
768.3.h.h.641.5 | 16 | 48.35 | even | 4 | |||
768.3.h.h.641.6 | 16 | 16.11 | odd | 4 | |||
768.3.h.h.641.11 | 16 | 16.3 | odd | 4 | |||
768.3.h.h.641.12 | 16 | 48.11 | even | 4 |