Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (of order \(4\), degree \(2\), 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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 28x^{14} + 290x^{12} + 1396x^{10} + 3263x^{8} + 3508x^{6} + 1442x^{4} + 128x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Root | \(1.24374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.323 |
Dual form | 2070.2.j.i.737.1 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.43853 | + | 1.71191i | −0.643331 | + | 0.765588i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.17313 | − | 3.17313i | 1.19933 | − | 1.19933i | 0.224965 | − | 0.974367i | \(-0.427773\pi\) |
0.974367 | − | 0.224965i | \(-0.0722268\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.22770 | − | 0.193306i | 0.704460 | − | 0.0611289i | ||||
\(11\) | 3.42382i | 1.03232i | 0.856492 | + | 0.516160i | \(0.172639\pi\) | ||||
−0.856492 | + | 0.516160i | \(0.827361\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 2.00000i | 0.554700 | + | 0.554700i | 0.927794 | − | 0.373094i | \(-0.121703\pi\) |
−0.373094 | + | 0.927794i | \(0.621703\pi\) | |||||||
\(14\) | −4.48749 | −1.19933 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.61043 | − | 1.61043i | −0.390586 | − | 0.390586i | 0.484310 | − | 0.874896i | \(-0.339071\pi\) |
−0.874896 | + | 0.484310i | \(0.839071\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.45539i | 1.48097i | 0.672074 | + | 0.740484i | \(0.265404\pi\) | ||||
−0.672074 | + | 0.740484i | \(0.734596\pi\) | |||||||
\(20\) | −1.71191 | − | 1.43853i | −0.382794 | − | 0.321665i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.42100 | − | 2.42100i | 0.516160 | − | 0.516160i | ||||
\(23\) | −0.707107 | + | 0.707107i | −0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.861256 | − | 4.92527i | −0.172251 | − | 0.985053i | ||||
\(26\) | − | 2.82843i | − | 0.554700i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.17313 | + | 3.17313i | 0.599666 | + | 0.599666i | ||||
\(29\) | 3.94074 | 0.731776 | 0.365888 | − | 0.930659i | \(-0.380765\pi\) | ||||
0.365888 | + | 0.930659i | \(0.380765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.27749 | −0.409049 | −0.204524 | − | 0.978861i | \(-0.565565\pi\) | ||||
−0.204524 | + | 0.978861i | \(0.565565\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.27749i | 0.390586i | ||||||||
\(35\) | 0.867460 | + | 9.99677i | 0.146628 | + | 1.68976i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.24787 | − | 1.24787i | 0.205148 | − | 0.205148i | −0.597053 | − | 0.802202i | \(-0.703662\pi\) |
0.802202 | + | 0.597053i | \(0.203662\pi\) | |||||||
\(38\) | 4.56465 | − | 4.56465i | 0.740484 | − | 0.740484i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.193306 | + | 2.22770i | 0.0305644 | + | 0.352230i | ||||
\(41\) | 11.1091i | 1.73495i | 0.497484 | + | 0.867473i | \(0.334257\pi\) | ||||
−0.497484 | + | 0.867473i | \(0.665743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.752131 | − | 0.752131i | −0.114699 | − | 0.114699i | 0.647428 | − | 0.762127i | \(-0.275845\pi\) |
−0.762127 | + | 0.647428i | \(0.775845\pi\) | |||||||
\(44\) | −3.42382 | −0.516160 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −4.29128 | − | 4.29128i | −0.625947 | − | 0.625947i | 0.321099 | − | 0.947046i | \(-0.395948\pi\) |
−0.947046 | + | 0.321099i | \(0.895948\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 13.1376i | − | 1.87679i | ||||||
\(50\) | −2.87369 | + | 4.09169i | −0.406401 | + | 0.578652i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | + | 2.00000i | −0.277350 | + | 0.277350i | ||||
\(53\) | −2.08676 | + | 2.08676i | −0.286639 | + | 0.286639i | −0.835750 | − | 0.549111i | \(-0.814967\pi\) |
0.549111 | + | 0.835750i | \(0.314967\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.86126 | − | 4.92527i | −0.790332 | − | 0.664123i | ||||
\(56\) | − | 4.48749i | − | 0.599666i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.78652 | − | 2.78652i | −0.365888 | − | 0.365888i | ||||
\(59\) | −7.47024 | −0.972543 | −0.486271 | − | 0.873808i | \(-0.661643\pi\) | ||||
−0.486271 | + | 0.873808i | \(0.661643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.89087 | −0.498175 | −0.249088 | − | 0.968481i | \(-0.580131\pi\) | ||||
−0.249088 | + | 0.968481i | \(0.580131\pi\) | |||||||
\(62\) | 1.61043 | + | 1.61043i | 0.204524 | + | 0.204524i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −6.30088 | + | 0.546753i | −0.781528 | + | 0.0678164i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.93004 | − | 8.93004i | 1.09098 | − | 1.09098i | 0.0955533 | − | 0.995424i | \(-0.469538\pi\) |
0.995424 | − | 0.0955533i | \(-0.0304620\pi\) | |||||||
\(68\) | 1.61043 | − | 1.61043i | 0.195293 | − | 0.195293i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.45539 | − | 7.68217i | 0.771567 | − | 0.918195i | ||||
\(71\) | 10.4865i | 1.24451i | 0.782813 | + | 0.622257i | \(0.213784\pi\) | ||||
−0.782813 | + | 0.622257i | \(0.786216\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.06401 | + | 6.06401i | 0.709739 | + | 0.709739i | 0.966480 | − | 0.256742i | \(-0.0826489\pi\) |
−0.256742 | + | 0.966480i | \(0.582649\pi\) | |||||||
\(74\) | −1.76475 | −0.205148 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.45539 | −0.740484 | ||||||||
\(77\) | 10.8642 | + | 10.8642i | 1.23809 | + | 1.23809i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3970i | 1.28226i | 0.767432 | + | 0.641130i | \(0.221534\pi\) | ||||
−0.767432 | + | 0.641130i | \(0.778466\pi\) | |||||||
\(80\) | 1.43853 | − | 1.71191i | 0.160833 | − | 0.191397i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.85530 | − | 7.85530i | 0.867473 | − | 0.867473i | ||||
\(83\) | 9.32421 | − | 9.32421i | 1.02347 | − | 1.02347i | 0.0237475 | − | 0.999718i | \(-0.492440\pi\) |
0.999718 | − | 0.0237475i | \(-0.00755976\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.07355 | − | 0.440253i | 0.550304 | − | 0.0477521i | ||||
\(86\) | 1.06367i | 0.114699i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.42100 | + | 2.42100i | 0.258080 | + | 0.258080i | ||||
\(89\) | 8.03580 | 0.851793 | 0.425896 | − | 0.904772i | \(-0.359959\pi\) | ||||
0.425896 | + | 0.904772i | \(0.359959\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6925 | 1.33054 | ||||||||
\(92\) | −0.707107 | − | 0.707107i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.06878i | 0.625947i | ||||||||
\(95\) | −11.0510 | − | 9.28628i | −1.13381 | − | 0.952753i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3510 | + | 11.3510i | −1.15252 | + | 1.15252i | −0.166478 | + | 0.986045i | \(0.553240\pi\) |
−0.986045 | + | 0.166478i | \(0.946760\pi\) | |||||||
\(98\) | −9.28966 | + | 9.28966i | −0.938397 | + | 0.938397i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.92527 | − | 0.861256i | 0.492527 | − | 0.0861256i | ||||
\(101\) | 1.50474i | 0.149727i | 0.997194 | + | 0.0748634i | \(0.0238521\pi\) | ||||
−0.997194 | + | 0.0748634i | \(0.976148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.17313 | − | 3.17313i | −0.312658 | − | 0.312658i | 0.533280 | − | 0.845939i | \(-0.320959\pi\) |
−0.845939 | + | 0.533280i | \(0.820959\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.95113 | 0.286639 | ||||||||
\(107\) | 4.31980 | + | 4.31980i | 0.417611 | + | 0.417611i | 0.884380 | − | 0.466768i | \(-0.154582\pi\) |
−0.466768 | + | 0.884380i | \(0.654582\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9692i | 1.33801i | 0.743259 | + | 0.669003i | \(0.233279\pi\) | ||||
−0.743259 | + | 0.669003i | \(0.766721\pi\) | |||||||
\(110\) | 0.661845 | + | 7.62722i | 0.0631045 | + | 0.727227i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.17313 | + | 3.17313i | −0.299833 | + | 0.299833i | ||||
\(113\) | −9.02361 | + | 9.02361i | −0.848870 | + | 0.848870i | −0.989992 | − | 0.141122i | \(-0.954929\pi\) |
0.141122 | + | 0.989992i | \(0.454929\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.193306 | − | 2.22770i | −0.0180259 | − | 0.207734i | ||||
\(116\) | 3.94074i | 0.365888i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.28226 | + | 5.28226i | 0.486271 | + | 0.486271i | ||||
\(119\) | −10.2202 | −0.936884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.722512 | −0.0656829 | ||||||||
\(122\) | 2.75126 | + | 2.75126i | 0.249088 | + | 0.249088i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 2.27749i | − | 0.204524i | ||||||
\(125\) | 9.67054 | + | 5.61076i | 0.864960 | + | 0.501841i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6925 | + | 15.6925i | −1.39249 | + | 1.39249i | −0.572774 | + | 0.819713i | \(0.694133\pi\) |
−0.819713 | + | 0.572774i | \(0.805867\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.84201 | + | 4.06878i | 0.424672 | + | 0.356856i | ||||
\(131\) | − | 14.2582i | − | 1.24575i | −0.782323 | − | 0.622873i | \(-0.785965\pi\) | ||
0.782323 | − | 0.622873i | \(-0.214035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.4838 | + | 20.4838i | 1.77617 | + | 1.77617i | ||||
\(134\) | −12.6290 | −1.09098 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.27749 | −0.195293 | ||||||||
\(137\) | 12.4747 | + | 12.4747i | 1.06578 | + | 1.06578i | 0.997678 | + | 0.0681032i | \(0.0216947\pi\) |
0.0681032 | + | 0.997678i | \(0.478305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7021i | 0.907739i | 0.891068 | + | 0.453869i | \(0.149957\pi\) | ||||
−0.891068 | + | 0.453869i | \(0.850043\pi\) | |||||||
\(140\) | −9.99677 | + | 0.867460i | −0.844881 | + | 0.0733138i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.41505 | − | 7.41505i | 0.622257 | − | 0.622257i | ||||
\(143\) | −6.84763 | + | 6.84763i | −0.572628 | + | 0.572628i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.66887 | + | 6.74618i | −0.470774 | + | 0.560240i | ||||
\(146\) | − | 8.57580i | − | 0.709739i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.24787 | + | 1.24787i | 0.102574 | + | 0.102574i | ||||
\(149\) | −6.15497 | −0.504235 | −0.252117 | − | 0.967697i | \(-0.581127\pi\) | ||||
−0.252117 | + | 0.967697i | \(0.581127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.9796 | 1.21902 | 0.609510 | − | 0.792778i | \(-0.291366\pi\) | ||||
0.609510 | + | 0.792778i | \(0.291366\pi\) | |||||||
\(152\) | 4.56465 | + | 4.56465i | 0.370242 | + | 0.370242i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 15.3643i | − | 1.23809i | ||||||
\(155\) | 3.27624 | − | 3.89885i | 0.263154 | − | 0.313163i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.53388 | − | 4.53388i | 0.361843 | − | 0.361843i | −0.502648 | − | 0.864491i | \(-0.667641\pi\) |
0.864491 | + | 0.502648i | \(0.167641\pi\) | |||||||
\(158\) | 8.05888 | − | 8.05888i | 0.641130 | − | 0.641130i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.22770 | + | 0.193306i | −0.176115 | + | 0.0152822i | ||||
\(161\) | 4.48749i | 0.353664i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.1376 | + | 16.1376i | 1.26399 | + | 1.26399i | 0.949141 | + | 0.314850i | \(0.101954\pi\) |
0.314850 | + | 0.949141i | \(0.398046\pi\) | |||||||
\(164\) | −11.1091 | −0.867473 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.1864 | −1.02347 | ||||||||
\(167\) | 8.53392 | + | 8.53392i | 0.660374 | + | 0.660374i | 0.955468 | − | 0.295094i | \(-0.0953510\pi\) |
−0.295094 | + | 0.955468i | \(0.595351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | −3.89885 | − | 3.27624i | −0.299028 | − | 0.251276i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.752131 | − | 0.752131i | 0.0573495 | − | 0.0573495i | ||||
\(173\) | −5.90170 | + | 5.90170i | −0.448698 | + | 0.448698i | −0.894922 | − | 0.446223i | \(-0.852769\pi\) |
0.446223 | + | 0.894922i | \(0.352769\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.3614 | − | 12.8956i | −1.38799 | − | 0.974819i | ||||
\(176\) | − | 3.42382i | − | 0.258080i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.68217 | − | 5.68217i | −0.425896 | − | 0.425896i | ||||
\(179\) | 22.6890 | 1.69586 | 0.847929 | − | 0.530109i | \(-0.177849\pi\) | ||||
0.847929 | + | 0.530109i | \(0.177849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.68217 | −0.422352 | −0.211176 | − | 0.977448i | \(-0.567729\pi\) | ||||
−0.211176 | + | 0.977448i | \(0.567729\pi\) | |||||||
\(182\) | −8.97498 | − | 8.97498i | −0.665270 | − | 0.665270i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | 0.341138 | + | 3.93133i | 0.0250810 | + | 0.289037i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.51381 | − | 5.51381i | 0.403209 | − | 0.403209i | ||||
\(188\) | 4.29128 | − | 4.29128i | 0.312973 | − | 0.312973i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.24787 | + | 14.3807i | 0.0905299 | + | 1.04328i | ||||
\(191\) | 0.156935i | 0.0113554i | 0.999984 | + | 0.00567771i | \(0.00180728\pi\) | ||||
−0.999984 | + | 0.00567771i | \(0.998193\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.6238 | + | 17.6238i | 1.26859 | + | 1.26859i | 0.946819 | + | 0.321767i | \(0.104277\pi\) |
0.321767 | + | 0.946819i | \(0.395723\pi\) | |||||||
\(194\) | 16.0528 | 1.15252 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.1376 | 0.938397 | ||||||||
\(197\) | −7.08987 | − | 7.08987i | −0.505132 | − | 0.505132i | 0.407896 | − | 0.913028i | \(-0.366263\pi\) |
−0.913028 | + | 0.407896i | \(0.866263\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.8601i | − | 1.12429i | −0.827038 | − | 0.562145i | \(-0.809976\pi\) | ||
0.827038 | − | 0.562145i | \(-0.190024\pi\) | |||||||
\(200\) | −4.09169 | − | 2.87369i | −0.289326 | − | 0.203200i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.06401 | − | 1.06401i | 0.0748634 | − | 0.0748634i | ||||
\(203\) | 12.5045 | − | 12.5045i | 0.877643 | − | 0.877643i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0177 | − | 15.9808i | −1.32825 | − | 1.11614i | ||||
\(206\) | 4.48749i | 0.312658i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.00000 | − | 2.00000i | −0.138675 | − | 0.138675i | ||||
\(209\) | −22.1021 | −1.52883 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.68032 | 0.115678 | 0.0578391 | − | 0.998326i | \(-0.481579\pi\) | ||||
0.0578391 | + | 0.998326i | \(0.481579\pi\) | |||||||
\(212\) | −2.08676 | − | 2.08676i | −0.143320 | − | 0.143320i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 6.10913i | − | 0.417611i | ||||||
\(215\) | 2.36954 | − | 0.205615i | 0.161601 | − | 0.0140228i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.22677 | + | 7.22677i | −0.490585 | + | 0.490585i | ||||
\(218\) | 9.87771 | − | 9.87771i | 0.669003 | − | 0.669003i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.92527 | − | 5.86126i | 0.332061 | − | 0.395166i | ||||
\(221\) | − | 6.44171i | − | 0.433316i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.72627 | − | 4.72627i | −0.316494 | − | 0.316494i | 0.530925 | − | 0.847419i | \(-0.321845\pi\) |
−0.847419 | + | 0.530925i | \(0.821845\pi\) | |||||||
\(224\) | 4.48749 | 0.299833 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.7613 | 0.848870 | ||||||||
\(227\) | −9.14266 | − | 9.14266i | −0.606820 | − | 0.606820i | 0.335294 | − | 0.942114i | \(-0.391164\pi\) |
−0.942114 | + | 0.335294i | \(0.891164\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.98963i | 0.329724i | 0.986317 | + | 0.164862i | \(0.0527179\pi\) | ||||
−0.986317 | + | 0.164862i | \(0.947282\pi\) | |||||||
\(230\) | −1.43853 | + | 1.71191i | −0.0948539 | + | 0.112880i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.78652 | − | 2.78652i | 0.182944 | − | 0.182944i | ||||
\(233\) | −7.59060 | + | 7.59060i | −0.497277 | + | 0.497277i | −0.910589 | − | 0.413313i | \(-0.864372\pi\) |
0.413313 | + | 0.910589i | \(0.364372\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5194 | − | 1.17313i | 0.881909 | − | 0.0765268i | ||||
\(236\) | − | 7.47024i | − | 0.486271i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.22677 | + | 7.22677i | 0.468442 | + | 0.468442i | ||||
\(239\) | −20.3792 | −1.31822 | −0.659111 | − | 0.752046i | \(-0.729067\pi\) | ||||
−0.659111 | + | 0.752046i | \(0.729067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.11949 | 0.587438 | 0.293719 | − | 0.955892i | \(-0.405107\pi\) | ||||
0.293719 | + | 0.955892i | \(0.405107\pi\) | |||||||
\(242\) | 0.510893 | + | 0.510893i | 0.0328415 | + | 0.0328415i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.89087i | − | 0.249088i | ||||||
\(245\) | 22.4903 | + | 18.8988i | 1.43685 | + | 1.20740i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9108 | + | 12.9108i | −0.821494 | + | 0.821494i | ||||
\(248\) | −1.61043 | + | 1.61043i | −0.102262 | + | 0.102262i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.87070 | − | 10.8055i | −0.181559 | − | 0.683401i | ||||
\(251\) | − | 10.5069i | − | 0.663192i | −0.943421 | − | 0.331596i | \(-0.892413\pi\) | ||
0.943421 | − | 0.331596i | \(-0.107587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.42100 | − | 2.42100i | −0.152207 | − | 0.152207i | ||||
\(254\) | 22.1926 | 1.39249 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.17509 | − | 7.17509i | −0.447570 | − | 0.447570i | 0.446976 | − | 0.894546i | \(-0.352501\pi\) |
−0.894546 | + | 0.446976i | \(0.852501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.91931i | − | 0.492082i | ||||||
\(260\) | −0.546753 | − | 6.30088i | −0.0339082 | − | 0.390764i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.0821 | + | 10.0821i | −0.622873 | + | 0.622873i | ||||
\(263\) | 8.26859 | − | 8.26859i | 0.509863 | − | 0.509863i | −0.404621 | − | 0.914484i | \(-0.632597\pi\) |
0.914484 | + | 0.404621i | \(0.132597\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.570473 | − | 6.57423i | −0.0350439 | − | 0.403851i | ||||
\(266\) | − | 28.9685i | − | 1.77617i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.93004 | + | 8.93004i | 0.545489 | + | 0.545489i | ||||
\(269\) | 12.2878 | 0.749200 | 0.374600 | − | 0.927186i | \(-0.377780\pi\) | ||||
0.374600 | + | 0.927186i | \(0.377780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.2666 | −1.29185 | −0.645927 | − | 0.763399i | \(-0.723529\pi\) | ||||
−0.645927 | + | 0.763399i | \(0.723529\pi\) | |||||||
\(272\) | 1.61043 | + | 1.61043i | 0.0976465 | + | 0.0976465i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 17.6418i | − | 1.06578i | ||||||
\(275\) | 16.8632 | − | 2.94878i | 1.01689 | − | 0.177818i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.64182 | − | 7.64182i | 0.459153 | − | 0.459153i | −0.439225 | − | 0.898377i | \(-0.644747\pi\) |
0.898377 | + | 0.439225i | \(0.144747\pi\) | |||||||
\(278\) | 7.56751 | − | 7.56751i | 0.453869 | − | 0.453869i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.68217 | + | 6.45539i | 0.459097 | + | 0.385784i | ||||
\(281\) | − | 26.4923i | − | 1.58040i | −0.612850 | − | 0.790199i | \(-0.709977\pi\) | ||
0.612850 | − | 0.790199i | \(-0.290023\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.20752 | − | 1.20752i | −0.0717799 | − | 0.0717799i | 0.670305 | − | 0.742085i | \(-0.266163\pi\) |
−0.742085 | + | 0.670305i | \(0.766163\pi\) | |||||||
\(284\) | −10.4865 | −0.622257 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.68401 | 0.572628 | ||||||||
\(287\) | 35.2506 | + | 35.2506i | 2.08078 | + | 2.08078i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 11.8130i | − | 0.694885i | ||||||
\(290\) | 8.77877 | − | 0.761770i | 0.515507 | − | 0.0447327i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.06401 | + | 6.06401i | −0.354869 | + | 0.354869i | ||||
\(293\) | −1.04189 | + | 1.04189i | −0.0608681 | + | 0.0608681i | −0.736886 | − | 0.676017i | \(-0.763704\pi\) |
0.676017 | + | 0.736886i | \(0.263704\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.7462 | − | 12.7884i | 0.625667 | − | 0.744567i | ||||
\(296\) | − | 1.76475i | − | 0.102574i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.35222 | + | 4.35222i | 0.252117 | + | 0.252117i | ||||
\(299\) | −2.82843 | −0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.77323 | −0.275124 | ||||||||
\(302\) | −10.5922 | − | 10.5922i | −0.609510 | − | 0.609510i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.45539i | − | 0.370242i | ||||||
\(305\) | 5.59714 | − | 6.66082i | 0.320492 | − | 0.381397i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.0303 | + | 14.0303i | −0.800750 | + | 0.800750i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) |
0.182462 | + | 0.983213i | \(0.441593\pi\) | |||||||
\(308\) | −10.8642 | + | 10.8642i | −0.619047 | + | 0.619047i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.07355 | + | 0.440253i | −0.288158 | + | 0.0250047i | ||||
\(311\) | − | 16.8256i | − | 0.954092i | −0.878878 | − | 0.477046i | \(-0.841708\pi\) | ||
0.878878 | − | 0.477046i | \(-0.158292\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6466 | − | 10.6466i | −0.601781 | − | 0.601781i | 0.339004 | − | 0.940785i | \(-0.389910\pi\) |
−0.940785 | + | 0.339004i | \(0.889910\pi\) | |||||||
\(314\) | −6.41188 | −0.361843 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3970 | −0.641130 | ||||||||
\(317\) | 16.5143 | + | 16.5143i | 0.927537 | + | 0.927537i | 0.997546 | − | 0.0700090i | \(-0.0223028\pi\) |
−0.0700090 | + | 0.997546i | \(0.522303\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.4924i | 0.755427i | ||||||||
\(320\) | 1.71191 | + | 1.43853i | 0.0956986 | + | 0.0804163i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.17313 | − | 3.17313i | 0.176832 | − | 0.176832i | ||||
\(323\) | 10.3959 | − | 10.3959i | 0.578446 | − | 0.578446i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.12802 | − | 11.5730i | 0.450861 | − | 0.641957i | ||||
\(326\) | − | 22.8220i | − | 1.26399i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.85530 | + | 7.85530i | 0.433736 | + | 0.433736i | ||||
\(329\) | −27.2336 | −1.50144 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.20871 | 0.341261 | 0.170631 | − | 0.985335i | \(-0.445419\pi\) | ||||
0.170631 | + | 0.985335i | \(0.445419\pi\) | |||||||
\(332\) | 9.32421 | + | 9.32421i | 0.511733 | + | 0.511733i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 12.0688i | − | 0.660374i | ||||||
\(335\) | 2.44126 | + | 28.1335i | 0.133380 | + | 1.53710i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0436 | + | 14.0436i | −0.765002 | + | 0.765002i | −0.977222 | − | 0.212220i | \(-0.931931\pi\) |
0.212220 | + | 0.977222i | \(0.431931\pi\) | |||||||
\(338\) | −3.53553 | + | 3.53553i | −0.192308 | + | 0.192308i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.440253 | + | 5.07355i | 0.0238761 | + | 0.275152i | ||||
\(341\) | − | 7.79770i | − | 0.422269i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4753 | − | 19.4753i | −1.05157 | − | 1.05157i | ||||
\(344\) | −1.06367 | −0.0573495 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.34627 | 0.448698 | ||||||||
\(347\) | 21.8505 | + | 21.8505i | 1.17300 | + | 1.17300i | 0.981492 | + | 0.191503i | \(0.0613362\pi\) |
0.191503 | + | 0.981492i | \(0.438664\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.57304i | − | 0.191261i | −0.995417 | − | 0.0956303i | \(-0.969513\pi\) | ||
0.995417 | − | 0.0956303i | \(-0.0304867\pi\) | |||||||
\(350\) | 3.86488 | + | 22.1021i | 0.206586 | + | 1.18141i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.42100 | + | 2.42100i | −0.129040 | + | 0.129040i | ||||
\(353\) | 16.1852 | − | 16.1852i | 0.861452 | − | 0.861452i | −0.130055 | − | 0.991507i | \(-0.541515\pi\) |
0.991507 | + | 0.130055i | \(0.0415155\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.9519 | − | 15.0851i | −0.952786 | − | 0.800634i | ||||
\(356\) | 8.03580i | 0.425896i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.0436 | − | 16.0436i | −0.847929 | − | 0.847929i | ||||
\(359\) | 17.8662 | 0.942941 | 0.471471 | − | 0.881882i | \(-0.343723\pi\) | ||||
0.471471 | + | 0.881882i | \(0.343723\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.6721 | −1.19327 | ||||||||
\(362\) | 4.01790 | + | 4.01790i | 0.211176 | + | 0.211176i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.6925i | 0.665270i | ||||||||
\(365\) | −19.1043 | + | 1.65776i | −0.999964 | + | 0.0867710i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.13095 | + | 5.13095i | −0.267833 | + | 0.267833i | −0.828227 | − | 0.560393i | \(-0.810650\pi\) |
0.560393 | + | 0.828227i | \(0.310650\pi\) | |||||||
\(368\) | 0.707107 | − | 0.707107i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.53865 | − | 3.02109i | 0.131978 | − | 0.157059i | ||||
\(371\) | 13.2432i | 0.687551i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.3469 | − | 19.3469i | −1.00175 | − | 1.00175i | −0.999998 | − | 0.00174761i | \(-0.999444\pi\) |
−0.00174761 | − | 0.999998i | \(-0.500556\pi\) | |||||||
\(374\) | −7.79770 | −0.403209 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.06878 | −0.312973 | ||||||||
\(377\) | 7.88147 | + | 7.88147i | 0.405916 | + | 0.405916i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.0261i | 1.74780i | 0.486104 | + | 0.873901i | \(0.338418\pi\) | ||||
−0.486104 | + | 0.873901i | \(0.661582\pi\) | |||||||
\(380\) | 9.28628 | − | 11.0510i | 0.476376 | − | 0.566906i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.110970 | − | 0.110970i | 0.00567771 | − | 0.00567771i | ||||
\(383\) | 12.7426 | − | 12.7426i | 0.651116 | − | 0.651116i | −0.302146 | − | 0.953262i | \(-0.597703\pi\) |
0.953262 | + | 0.302146i | \(0.0977030\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.2271 | + | 2.97002i | −1.74437 | + | 0.151366i | ||||
\(386\) | − | 24.9238i | − | 1.26859i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.3510 | − | 11.3510i | −0.576262 | − | 0.576262i | ||||
\(389\) | −29.5372 | −1.49759 | −0.748797 | − | 0.662799i | \(-0.769368\pi\) | ||||
−0.748797 | + | 0.662799i | \(0.769368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.27749 | 0.115178 | ||||||||
\(392\) | −9.28966 | − | 9.28966i | −0.469199 | − | 0.469199i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.0266i | 0.505132i | ||||||||
\(395\) | −19.5106 | − | 16.3949i | −0.981684 | − | 0.824918i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.6840 | − | 13.6840i | 0.686781 | − | 0.686781i | −0.274738 | − | 0.961519i | \(-0.588591\pi\) |
0.961519 | + | 0.274738i | \(0.0885912\pi\) | |||||||
\(398\) | −11.2148 | + | 11.2148i | −0.562145 | + | 0.562145i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.861256 | + | 4.92527i | 0.0430628 | + | 0.246263i | ||||
\(401\) | 0.560249i | 0.0279775i | 0.999902 | + | 0.0139887i | \(0.00445290\pi\) | ||||
−0.999902 | + | 0.0139887i | \(0.995547\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.55498 | − | 4.55498i | −0.226899 | − | 0.226899i | ||||
\(404\) | −1.50474 | −0.0748634 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.6840 | −0.877643 | ||||||||
\(407\) | 4.27247 | + | 4.27247i | 0.211779 | + | 0.211779i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.90710i | 0.341534i | 0.985311 | + | 0.170767i | \(0.0546245\pi\) | ||||
−0.985311 | + | 0.170767i | \(0.945375\pi\) | |||||||
\(410\) | 2.14746 | + | 24.7476i | 0.106055 | + | 1.22220i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.17313 | − | 3.17313i | 0.156329 | − | 0.156329i | ||||
\(413\) | −23.7041 | + | 23.7041i | −1.16640 | + | 1.16640i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.54902 | + | 29.3754i | 0.125127 | + | 1.44198i | ||||
\(416\) | 2.82843i | 0.138675i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.6285 | + | 15.6285i | 0.764416 | + | 0.764416i | ||||
\(419\) | −7.98977 | −0.390326 | −0.195163 | − | 0.980771i | \(-0.562524\pi\) | ||||
−0.195163 | + | 0.980771i | \(0.562524\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.9862 | 1.36397 | 0.681983 | − | 0.731368i | \(-0.261118\pi\) | ||||
0.681983 | + | 0.731368i | \(0.261118\pi\) | |||||||
\(422\) | −1.18817 | − | 1.18817i | −0.0578391 | − | 0.0578391i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.95113i | 0.143320i | ||||||||
\(425\) | −6.54479 | + | 9.31877i | −0.317469 | + | 0.452027i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.3463 | + | 12.3463i | −0.597478 | + | 0.597478i | ||||
\(428\) | −4.31980 | + | 4.31980i | −0.208806 | + | 0.208806i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.82091 | − | 1.53013i | −0.0878122 | − | 0.0737893i | ||||
\(431\) | − | 11.1996i | − | 0.539466i | −0.962935 | − | 0.269733i | \(-0.913065\pi\) | ||
0.962935 | − | 0.269733i | \(-0.0869354\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.24376 | − | 7.24376i | −0.348113 | − | 0.348113i | 0.511293 | − | 0.859406i | \(-0.329167\pi\) |
−0.859406 | + | 0.511293i | \(0.829167\pi\) | |||||||
\(434\) | 10.2202 | 0.490585 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.9692 | −0.669003 | ||||||||
\(437\) | −4.56465 | − | 4.56465i | −0.218357 | − | 0.218357i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.9230i | 1.80997i | 0.425448 | + | 0.904983i | \(0.360117\pi\) | ||||
−0.425448 | + | 0.904983i | \(0.639883\pi\) | |||||||
\(440\) | −7.62722 | + | 0.661845i | −0.363614 | + | 0.0315522i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.55498 | + | 4.55498i | −0.216658 | + | 0.216658i | ||||
\(443\) | 8.89120 | − | 8.89120i | 0.422434 | − | 0.422434i | −0.463607 | − | 0.886041i | \(-0.653445\pi\) |
0.886041 | + | 0.463607i | \(0.153445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.5597 | + | 13.7565i | −0.547985 | + | 0.652123i | ||||
\(446\) | 6.68395i | 0.316494i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.17313 | − | 3.17313i | −0.149916 | − | 0.149916i | ||||
\(449\) | −40.7787 | −1.92446 | −0.962232 | − | 0.272231i | \(-0.912239\pi\) | ||||
−0.962232 | + | 0.272231i | \(0.912239\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.0354 | −1.79102 | ||||||||
\(452\) | −9.02361 | − | 9.02361i | −0.424435 | − | 0.424435i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.9297i | 0.606820i | ||||||||
\(455\) | −18.2586 | + | 21.7285i | −0.855977 | + | 1.01865i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.73581 | + | 7.73581i | −0.361866 | + | 0.361866i | −0.864500 | − | 0.502634i | \(-0.832364\pi\) |
0.502634 | + | 0.864500i | \(0.332364\pi\) | |||||||
\(458\) | 3.52820 | − | 3.52820i | 0.164862 | − | 0.164862i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.22770 | − | 0.193306i | 0.103867 | − | 0.00901296i | ||||
\(461\) | − | 21.7525i | − | 1.01311i | −0.862207 | − | 0.506557i | \(-0.830918\pi\) | ||
0.862207 | − | 0.506557i | \(-0.169082\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.5345 | − | 26.5345i | −1.23316 | − | 1.23316i | −0.962742 | − | 0.270423i | \(-0.912836\pi\) |
−0.270423 | − | 0.962742i | \(-0.587164\pi\) | |||||||
\(464\) | −3.94074 | −0.182944 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.7347 | 0.497277 | ||||||||
\(467\) | −10.4936 | − | 10.4936i | −0.485585 | − | 0.485585i | 0.421325 | − | 0.906910i | \(-0.361565\pi\) |
−0.906910 | + | 0.421325i | \(0.861565\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 56.6724i | − | 2.61689i | ||||||
\(470\) | −10.3892 | − | 8.73013i | −0.479218 | − | 0.402691i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.28226 | + | 5.28226i | −0.243136 | + | 0.243136i | ||||
\(473\) | 2.57516 | − | 2.57516i | 0.118406 | − | 0.118406i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.7945 | − | 5.55975i | 1.45883 | − | 0.255099i | ||||
\(476\) | − | 10.2202i | − | 0.468442i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.4103 | + | 14.4103i | 0.659111 | + | 0.659111i | ||||
\(479\) | 8.73949 | 0.399317 | 0.199659 | − | 0.979866i | \(-0.436017\pi\) | ||||
0.199659 | + | 0.979866i | \(0.436017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.99148 | 0.227592 | ||||||||
\(482\) | −6.44846 | − | 6.44846i | −0.293719 | − | 0.293719i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 0.722512i | − | 0.0328415i | ||||||
\(485\) | −3.10311 | − | 35.7608i | −0.140905 | − | 1.62381i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.33673 | − | 7.33673i | 0.332459 | − | 0.332459i | −0.521061 | − | 0.853520i | \(-0.674464\pi\) |
0.853520 | + | 0.521061i | \(0.174464\pi\) | |||||||
\(488\) | −2.75126 | + | 2.75126i | −0.124544 | + | 0.124544i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.53957 | − | 29.2665i | −0.114726 | − | 1.32213i | ||||
\(491\) | 10.0738i | 0.454624i | 0.973822 | + | 0.227312i | \(0.0729937\pi\) | ||||
−0.973822 | + | 0.227312i | \(0.927006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.34627 | − | 6.34627i | −0.285822 | − | 0.285822i | ||||
\(494\) | 18.2586 | 0.821494 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.27749 | 0.102262 | ||||||||
\(497\) | 33.2750 | + | 33.2750i | 1.49259 | + | 1.49259i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 21.0483i | − | 0.942253i | −0.882066 | − | 0.471127i | \(-0.843847\pi\) | ||
0.882066 | − | 0.471127i | \(-0.156153\pi\) | |||||||
\(500\) | −5.61076 | + | 9.67054i | −0.250921 | + | 0.432480i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.42953 | + | 7.42953i | −0.331596 | + | 0.331596i | ||||
\(503\) | 20.0585 | − | 20.0585i | 0.894364 | − | 0.894364i | −0.100566 | − | 0.994930i | \(-0.532065\pi\) |
0.994930 | + | 0.100566i | \(0.0320653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.57597 | − | 2.16461i | −0.114629 | − | 0.0963239i | ||||
\(506\) | 3.42382i | 0.152207i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.6925 | − | 15.6925i | −0.696244 | − | 0.696244i | ||||
\(509\) | −24.8896 | −1.10321 | −0.551605 | − | 0.834105i | \(-0.685984\pi\) | ||||
−0.551605 | + | 0.834105i | \(0.685984\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.4838 | 1.70242 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.1471i | 0.447570i | ||||||||
\(515\) | 9.99677 | − | 0.867460i | 0.440510 | − | 0.0382249i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.6925 | − | 14.6925i | 0.646177 | − | 0.646177i | ||||
\(518\) | −5.59980 | + | 5.59980i | −0.246041 | + | 0.246041i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.06878 | + | 4.84201i | −0.178428 | + | 0.212336i | ||||
\(521\) | − | 37.0211i | − | 1.62193i | −0.585097 | − | 0.810963i | \(-0.698944\pi\) | ||
0.585097 | − | 0.810963i | \(-0.301056\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.83898 | + | 7.83898i | 0.342775 | + | 0.342775i | 0.857409 | − | 0.514635i | \(-0.172073\pi\) |
−0.514635 | + | 0.857409i | \(0.672073\pi\) | |||||||
\(524\) | 14.2582 | 0.622873 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6936 | −0.509863 | ||||||||
\(527\) | 3.66773 | + | 3.66773i | 0.159769 | + | 0.159769i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −4.24529 | + | 5.05206i | −0.184404 | + | 0.219448i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −20.4838 | + | 20.4838i | −0.888087 | + | 0.888087i | ||||
\(533\) | −22.2181 | + | 22.2181i | −0.962375 | + | 0.962375i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6093 | + | 1.18093i | −0.588380 | + | 0.0510562i | ||||
\(536\) | − | 12.6290i | − | 0.545489i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.68878 | − | 8.68878i | −0.374600 | − | 0.374600i | ||||
\(539\) | 44.9806 | 1.93745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 15.0378 | + | 15.0378i | 0.645927 | + | 0.645927i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.27749i | − | 0.0976465i | ||||||
\(545\) | −23.9140 | − | 20.0951i | −1.02436 | − | 0.860781i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.3051 | + | 11.3051i | −0.483371 | + | 0.483371i | −0.906206 | − | 0.422835i | \(-0.861035\pi\) |
0.422835 | + | 0.906206i | \(0.361035\pi\) | |||||||
\(548\) | −12.4747 | + | 12.4747i | −0.532891 | + | 0.532891i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.0092 | − | 9.83898i | −0.597354 | − | 0.419535i | ||||
\(551\) | 25.4390i | 1.08374i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.1642 | + | 36.1642i | 1.53786 | + | 1.53786i | ||||
\(554\) | −10.8072 | −0.459153 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.7021 | −0.453869 | ||||||||
\(557\) | −1.51810 | − | 1.51810i | −0.0643238 | − | 0.0643238i | 0.674213 | − | 0.738537i | \(-0.264483\pi\) |
−0.738537 | + | 0.674213i | \(0.764483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.00852i | − | 0.127247i | ||||||
\(560\) | −0.867460 | − | 9.99677i | −0.0366569 | − | 0.422440i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.7329 | + | 18.7329i | −0.790199 | + | 0.790199i | ||||
\(563\) | 25.1468 | − | 25.1468i | 1.05981 | − | 1.05981i | 0.0617187 | − | 0.998094i | \(-0.480342\pi\) |
0.998094 | − | 0.0617187i | \(-0.0196582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.46684 | − | 28.4283i | −0.103781 | − | 1.19599i | ||||
\(566\) | 1.70770i | 0.0717799i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.41505 | + | 7.41505i | 0.311129 | + | 0.311129i | ||||
\(569\) | 22.6811 | 0.950842 | 0.475421 | − | 0.879758i | \(-0.342296\pi\) | ||||
0.475421 | + | 0.879758i | \(0.342296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2927 | 0.514433 | 0.257217 | − | 0.966354i | \(-0.417195\pi\) | ||||
0.257217 | + | 0.966354i | \(0.417195\pi\) | |||||||
\(572\) | −6.84763 | − | 6.84763i | −0.286314 | − | 0.286314i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 49.8519i | − | 2.08078i | ||||||
\(575\) | 4.09169 | + | 2.87369i | 0.170635 | + | 0.119841i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.22302 | − | 4.22302i | 0.175807 | − | 0.175807i | −0.613718 | − | 0.789525i | \(-0.710327\pi\) |
0.789525 | + | 0.613718i | \(0.210327\pi\) | |||||||
\(578\) | −8.35309 | + | 8.35309i | −0.347443 | + | 0.347443i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.74618 | − | 5.66887i | −0.280120 | − | 0.235387i | ||||
\(581\) | − | 59.1740i | − | 2.45495i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.14470 | − | 7.14470i | −0.295903 | − | 0.295903i | ||||
\(584\) | 8.57580 | 0.354869 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.47346 | 0.0608681 | ||||||||
\(587\) | −4.19233 | − | 4.19233i | −0.173036 | − | 0.173036i | 0.615276 | − | 0.788312i | \(-0.289045\pi\) |
−0.788312 | + | 0.615276i | \(0.789045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 14.7021i | − | 0.605789i | ||||||
\(590\) | −16.6414 | + | 1.44405i | −0.685117 | + | 0.0594504i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.24787 | + | 1.24787i | −0.0512871 | + | 0.0512871i | ||||
\(593\) | −23.0815 | + | 23.0815i | −0.947842 | + | 0.947842i | −0.998706 | − | 0.0508632i | \(-0.983803\pi\) |
0.0508632 | + | 0.998706i | \(0.483803\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.7021 | − | 17.4960i | 0.602727 | − | 0.717268i | ||||
\(596\) | − | 6.15497i | − | 0.252117i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.00000 | + | 2.00000i | 0.0817861 | + | 0.0817861i | ||||
\(599\) | −15.1827 | −0.620349 | −0.310175 | − | 0.950680i | \(-0.600388\pi\) | ||||
−0.310175 | + | 0.950680i | \(0.600388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.1171 | −1.10613 | −0.553065 | − | 0.833138i | \(-0.686542\pi\) | ||||
−0.553065 | + | 0.833138i | \(0.686542\pi\) | |||||||
\(602\) | 3.37518 | + | 3.37518i | 0.137562 | + | 0.137562i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.9796i | 0.609510i | ||||||||
\(605\) | 1.03936 | − | 1.23687i | 0.0422558 | − | 0.0502861i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2608 | − | 10.2608i | 0.416473 | − | 0.416473i | −0.467513 | − | 0.883986i | \(-0.654850\pi\) |
0.883986 | + | 0.467513i | \(0.154850\pi\) | |||||||
\(608\) | −4.56465 | + | 4.56465i | −0.185121 | + | 0.185121i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.66769 | + | 0.752131i | −0.350944 | + | 0.0304529i | ||||
\(611\) | − | 17.1651i | − | 0.694426i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2825 | − | 34.2825i | −1.38466 | − | 1.38466i | −0.836141 | − | 0.548515i | \(-0.815193\pi\) |
−0.548515 | − | 0.836141i | \(-0.684807\pi\) | |||||||
\(614\) | 19.8418 | 0.800750 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.3643 | 0.619047 | ||||||||
\(617\) | −16.4180 | − | 16.4180i | −0.660964 | − | 0.660964i | 0.294644 | − | 0.955607i | \(-0.404799\pi\) |
−0.955607 | + | 0.294644i | \(0.904799\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.4820i | 1.54672i | 0.633966 | + | 0.773361i | \(0.281426\pi\) | ||||
−0.633966 | + | 0.773361i | \(0.718574\pi\) | |||||||
\(620\) | 3.89885 | + | 3.27624i | 0.156582 | + | 0.131577i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.8975 | + | 11.8975i | −0.477046 | + | 0.477046i | ||||
\(623\) | 25.4987 | − | 25.4987i | 1.02158 | − | 1.02158i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.5165 | + | 8.48383i | −0.940659 | + | 0.339353i | ||||
\(626\) | 15.0566i | 0.601781i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.53388 | + | 4.53388i | 0.180922 | + | 0.180922i | ||||
\(629\) | −4.01920 | −0.160256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.89888 | −0.115403 | −0.0577013 | − | 0.998334i | \(-0.518377\pi\) | ||||
−0.0577013 | + | 0.998334i | \(0.518377\pi\) | |||||||
\(632\) | 8.05888 | + | 8.05888i | 0.320565 | + | 0.320565i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 23.3548i | − | 0.927537i | ||||||
\(635\) | −4.28997 | − | 49.4384i | −0.170242 | − | 1.96190i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.2751 | − | 26.2751i | 1.04106 | − | 1.04106i | ||||
\(638\) | 9.54053 | − | 9.54053i | 0.377713 | − | 0.377713i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.193306 | − | 2.22770i | −0.00764111 | − | 0.0880574i | ||||
\(641\) | 31.0985i | 1.22832i | 0.789183 | + | 0.614158i | \(0.210504\pi\) | ||||
−0.789183 | + | 0.614158i | \(0.789496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.34745 | + | 5.34745i | 0.210883 | + | 0.210883i | 0.804642 | − | 0.593760i | \(-0.202357\pi\) |
−0.593760 | + | 0.804642i | \(0.702357\pi\) | |||||||
\(644\) | −4.48749 | −0.176832 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.7021 | −0.578446 | ||||||||
\(647\) | 1.72817 | + | 1.72817i | 0.0679415 | + | 0.0679415i | 0.740261 | − | 0.672320i | \(-0.234702\pi\) |
−0.672320 | + | 0.740261i | \(0.734702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 25.5767i | − | 1.00397i | ||||||
\(650\) | −13.9308 | + | 2.43600i | −0.546409 | + | 0.0955478i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.1376 | + | 16.1376i | −0.631996 | + | 0.631996i | ||||
\(653\) | 15.3048 | − | 15.3048i | 0.598921 | − | 0.598921i | −0.341104 | − | 0.940025i | \(-0.610801\pi\) |
0.940025 | + | 0.341104i | \(0.110801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.4087 | + | 20.5109i | 0.953728 | + | 0.801426i | ||||
\(656\) | − | 11.1091i | − | 0.433736i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 19.2571 | + | 19.2571i | 0.750718 | + | 0.750718i | ||||
\(659\) | −18.0992 | −0.705045 | −0.352523 | − | 0.935803i | \(-0.614676\pi\) | ||||
−0.352523 | + | 0.935803i | \(0.614676\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.87044 | −0.189438 | −0.0947191 | − | 0.995504i | \(-0.530195\pi\) | ||||
−0.0947191 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(662\) | −4.39022 | − | 4.39022i | −0.170631 | − | 0.170631i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 13.1864i | − | 0.511733i | ||||||
\(665\) | −64.5331 | + | 5.59980i | −2.50248 | + | 0.217151i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.78652 | + | 2.78652i | −0.107895 | + | 0.107895i | ||||
\(668\) | −8.53392 | + | 8.53392i | −0.330187 | + | 0.330187i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.1672 | − | 21.6196i | 0.701859 | − | 0.835240i | ||||
\(671\) | − | 13.3216i | − | 0.514276i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4886 | − | 30.4886i | −1.17525 | − | 1.17525i | −0.980940 | − | 0.194309i | \(-0.937754\pi\) |
−0.194309 | − | 0.980940i | \(-0.562246\pi\) | |||||||
\(674\) | 19.8606 | 0.765002 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | 3.12903 | + | 3.12903i | 0.120258 | + | 0.120258i | 0.764675 | − | 0.644416i | \(-0.222900\pi\) |
−0.644416 | + | 0.764675i | \(0.722900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.0367i | 2.76452i | ||||||||
\(680\) | 3.27624 | − | 3.89885i | 0.125638 | − | 0.149514i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.51381 | + | 5.51381i | −0.211135 | + | 0.211135i | ||||
\(683\) | 27.5040 | − | 27.5040i | 1.05241 | − | 1.05241i | 0.0538625 | − | 0.998548i | \(-0.482847\pi\) |
0.998548 | − | 0.0538625i | \(-0.0171533\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.3006 | + | 3.41028i | −1.50160 | + | 0.130300i | ||||
\(686\) | 27.5422i | 1.05157i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.752131 | + | 0.752131i | 0.0286747 | + | 0.0286747i | ||||
\(689\) | −8.34706 | −0.317998 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.6033 | 0.821829 | 0.410915 | − | 0.911674i | \(-0.365209\pi\) | ||||
0.410915 | + | 0.911674i | \(0.365209\pi\) | |||||||
\(692\) | −5.90170 | − | 5.90170i | −0.224349 | − | 0.224349i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 30.9012i | − | 1.17300i | ||||||
\(695\) | −18.3210 | − | 15.3953i | −0.694954 | − | 0.583976i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.8904 | − | 17.8904i | 0.677645 | − | 0.677645i | ||||
\(698\) | −2.52652 | + | 2.52652i | −0.0956303 | + | 0.0956303i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.8956 | − | 18.3614i | 0.487410 | − | 0.693996i | ||||
\(701\) | 0.544287i | 0.0205574i | 0.999947 | + | 0.0102787i | \(0.00327187\pi\) | ||||
−0.999947 | + | 0.0102787i | \(0.996728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.05548 | + | 8.05548i | 0.303818 | + | 0.303818i | ||||
\(704\) | 3.42382 | 0.129040 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.8893 | −0.861452 | ||||||||
\(707\) | 4.77473 | + | 4.77473i | 0.179572 | + | 0.179572i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.6848i | 1.00217i | 0.865398 | + | 0.501085i | \(0.167066\pi\) | ||||
−0.865398 | + | 0.501085i | \(0.832934\pi\) | |||||||
\(710\) | 2.02710 | + | 23.3607i | 0.0760757 | + | 0.876710i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.68217 | − | 5.68217i | 0.212948 | − | 0.212948i | ||||
\(713\) | 1.61043 | − | 1.61043i | 0.0603110 | − | 0.0603110i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.87198 | − | 21.5730i | −0.0700081 | − | 0.806786i | ||||
\(716\) | 22.6890i | 0.847929i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.6333 | − | 12.6333i | −0.471471 | − | 0.471471i | ||||
\(719\) | 0.851266 | 0.0317469 | 0.0158734 | − | 0.999874i | \(-0.494947\pi\) | ||||
0.0158734 | + | 0.999874i | \(0.494947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.1376 | −0.749962 | ||||||||
\(722\) | 16.0316 | + | 16.0316i | 0.596634 | + | 0.596634i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 5.68217i | − | 0.211176i | ||||||
\(725\) | −3.39398 | − | 19.4092i | −0.126049 | − | 0.720839i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.5858 | − | 21.5858i | 0.800574 | − | 0.800574i | −0.182611 | − | 0.983185i | \(-0.558455\pi\) |
0.983185 | + | 0.182611i | \(0.0584550\pi\) | |||||||
\(728\) | 8.97498 | − | 8.97498i | 0.332635 | − | 0.332635i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.6810 | + | 12.3366i | 0.543368 | + | 0.456597i | ||||
\(731\) | 2.42250i | 0.0895996i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0410 | + | 11.0410i | 0.407809 | + | 0.407809i | 0.880974 | − | 0.473165i | \(-0.156889\pi\) |
−0.473165 | + | 0.880974i | \(0.656889\pi\) | |||||||
\(734\) | 7.25625 | 0.267833 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 30.5748 | + | 30.5748i | 1.12624 | + | 1.12624i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 46.0967i | − | 1.69569i | −0.530241 | − | 0.847847i | \(-0.677898\pi\) | ||
0.530241 | − | 0.847847i | \(-0.322102\pi\) | |||||||
\(740\) | −3.93133 | + | 0.341138i | −0.144519 | + | 0.0125405i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.36434 | − | 9.36434i | 0.343776 | − | 0.343776i | ||||
\(743\) | 12.6723 | − | 12.6723i | 0.464902 | − | 0.464902i | −0.435356 | − | 0.900258i | \(-0.643378\pi\) |
0.900258 | + | 0.435356i | \(0.143378\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.85412 | − | 10.5367i | 0.324390 | − | 0.386036i | ||||
\(746\) | 27.3607i | 1.00175i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.51381 | + | 5.51381i | 0.201605 | + | 0.201605i | ||||
\(749\) | 27.4146 | 1.00171 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.16652 | −0.152038 | −0.0760192 | − | 0.997106i | \(-0.524221\pi\) | ||||
−0.0760192 | + | 0.997106i | \(0.524221\pi\) | |||||||
\(752\) | 4.29128 | + | 4.29128i | 0.156487 | + | 0.156487i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 11.1461i | − | 0.405916i | ||||||
\(755\) | −21.5486 | + | 25.6436i | −0.784233 | + | 0.933268i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.74443 | − | 6.74443i | 0.245131 | − | 0.245131i | −0.573838 | − | 0.818969i | \(-0.694546\pi\) |
0.818969 | + | 0.573838i | \(0.194546\pi\) | |||||||
\(758\) | 24.0601 | − | 24.0601i | 0.873901 | − | 0.873901i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.3807 | + | 1.24787i | −0.521641 | + | 0.0452650i | ||||
\(761\) | 6.87318i | 0.249153i | 0.992210 | + | 0.124576i | \(0.0397572\pi\) | ||||
−0.992210 | + | 0.124576i | \(0.960243\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.3261 | + | 44.3261i | 1.60471 | + | 1.60471i | ||||
\(764\) | −0.156935 | −0.00567771 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0207 | −0.651116 | ||||||||
\(767\) | −14.9405 | − | 14.9405i | −0.539470 | − | 0.539470i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 29.5826i | − | 1.06678i | −0.845871 | − | 0.533388i | \(-0.820919\pi\) | ||
0.845871 | − | 0.533388i | \(-0.179081\pi\) | |||||||
\(770\) | 26.3023 | + | 22.1021i | 0.947870 | + | 0.796504i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.6238 | + | 17.6238i | −0.634293 | + | 0.634293i | ||||
\(773\) | 8.79887 | − | 8.79887i | 0.316473 | − | 0.316473i | −0.530938 | − | 0.847411i | \(-0.678160\pi\) |
0.847411 | + | 0.530938i | \(0.178160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.96150 | + | 11.2172i | 0.0704592 | + | 0.402935i | ||||
\(776\) | 16.0528i | 0.576262i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.8859 | + | 20.8859i | 0.748797 | + | 0.748797i | ||||
\(779\) | −71.7134 | −2.56940 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.9037 | −1.28474 | ||||||||
\(782\) | −1.61043 | − | 1.61043i | −0.0575888 | − | 0.0575888i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.1376i | 0.469199i | ||||||||
\(785\) | 1.23946 | + | 14.2837i | 0.0442381 | + | 0.509808i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.76250 | + | 1.76250i | −0.0628263 | + | 0.0628263i | −0.737822 | − | 0.674996i | \(-0.764146\pi\) |
0.674996 | + | 0.737822i | \(0.264146\pi\) | |||||||
\(788\) | 7.08987 | − | 7.08987i | 0.252566 | − | 0.252566i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.20311 | + | 25.3890i | 0.0783831 | + | 0.903301i | ||||
\(791\) | 57.2663i | 2.03615i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.78175 | − | 7.78175i | −0.276338 | − | 0.276338i | ||||
\(794\) | −19.3521 | −0.686781 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.8601 | 0.562145 | ||||||||
\(797\) | 15.3709 | + | 15.3709i | 0.544465 | + | 0.544465i | 0.924834 | − | 0.380370i | \(-0.124203\pi\) |
−0.380370 | + | 0.924834i | \(0.624203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.8216i | 0.488972i | ||||||||
\(800\) | 2.87369 | − | 4.09169i | 0.101600 | − | 0.144663i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.396156 | − | 0.396156i | 0.0139887 | − | 0.0139887i | ||||
\(803\) | −20.7620 | + | 20.7620i | −0.732677 | + | 0.732677i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.68217 | − | 6.45539i | −0.270761 | − | 0.227523i | ||||
\(806\) | 6.44171i | 0.226899i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.06401 | + | 1.06401i | 0.0374317 | + | 0.0374317i | ||||
\(809\) | 46.8226 | 1.64620 | 0.823098 | − | 0.567899i | \(-0.192244\pi\) | ||||
0.823098 | + | 0.567899i | \(0.192244\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.1955 | 1.51680 | 0.758399 | − | 0.651791i | \(-0.225982\pi\) | ||||
0.758399 | + | 0.651791i | \(0.225982\pi\) | |||||||
\(812\) | 12.5045 | + | 12.5045i | 0.438821 | + | 0.438821i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 6.04219i | − | 0.211779i | ||||||
\(815\) | −50.8404 | + | 4.41163i | −1.78086 | + | 0.154533i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.85530 | − | 4.85530i | 0.169866 | − | 0.169866i | ||||
\(818\) | 4.88406 | − | 4.88406i | 0.170767 | − | 0.170767i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.9808 | − | 19.0177i | 0.558072 | − | 0.664127i | ||||
\(821\) | 34.5656i | 1.20635i | 0.797610 | + | 0.603174i | \(0.206098\pi\) | ||||
−0.797610 | + | 0.603174i | \(0.793902\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.4910 | + | 10.4910i | 0.365692 | + | 0.365692i | 0.865903 | − | 0.500211i | \(-0.166744\pi\) |
−0.500211 | + | 0.865903i | \(0.666744\pi\) | |||||||
\(824\) | −4.48749 | −0.156329 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.5226 | 1.16640 | ||||||||
\(827\) | 5.84595 | + | 5.84595i | 0.203284 | + | 0.203284i | 0.801405 | − | 0.598122i | \(-0.204086\pi\) |
−0.598122 | + | 0.801405i | \(0.704086\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.7287i | − | 0.719937i | −0.932965 | − | 0.359968i | \(-0.882788\pi\) | ||
0.932965 | − | 0.359968i | \(-0.117212\pi\) | |||||||
\(830\) | 18.9691 | − | 22.5740i | 0.658427 | − | 0.783553i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | − | 2.00000i | 0.0693375 | − | 0.0693375i | ||||
\(833\) | −21.1571 | + | 21.1571i | −0.733050 | + | 0.733050i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.8856 | + | 2.33297i | −0.930414 | + | 0.0807358i | ||||
\(836\) | − | 22.1021i | − | 0.764416i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.64962 | + | 5.64962i | 0.195163 | + | 0.195163i | ||||
\(839\) | 13.9495 | 0.481589 | 0.240795 | − | 0.970576i | \(-0.422592\pi\) | ||||
0.240795 | + | 0.970576i | \(0.422592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4706 | −0.464503 | ||||||||
\(842\) | −19.7893 | − | 19.7893i | −0.681983 | − | 0.681983i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.68032i | 0.0578391i | ||||||||
\(845\) | 8.55954 | + | 7.19266i | 0.294457 | + | 0.247435i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.29263 | + | 2.29263i | −0.0787756 | + | 0.0787756i | ||||
\(848\) | 2.08676 | − | 2.08676i | 0.0716598 | − | 0.0716598i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.2172 | − | 1.96150i | 0.384748 | − | 0.0672789i | ||||
\(851\) | 1.76475i | 0.0604950i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.8890 | − | 11.8890i | −0.407073 | − | 0.407073i | 0.473644 | − | 0.880716i | \(-0.342938\pi\) |
−0.880716 | + | 0.473644i | \(0.842938\pi\) | |||||||
\(854\) | 17.4603 | 0.597478 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.10913 | 0.208806 | ||||||||
\(857\) | −5.82156 | − | 5.82156i | −0.198861 | − | 0.198861i | 0.600651 | − | 0.799512i | \(-0.294908\pi\) |
−0.799512 | + | 0.600651i | \(0.794908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.91549i | 0.270073i | 0.990841 | + | 0.135037i | \(0.0431152\pi\) | ||||
−0.990841 | + | 0.135037i | \(0.956885\pi\) | |||||||
\(860\) | 0.205615 | + | 2.36954i | 0.00701141 | + | 0.0808007i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.91931 | + | 7.91931i | −0.269733 | + | 0.269733i | ||||
\(863\) | 19.3695 | − | 19.3695i | 0.659345 | − | 0.659345i | −0.295880 | − | 0.955225i | \(-0.595613\pi\) |
0.955225 | + | 0.295880i | \(0.0956130\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.61339 | − | 18.5930i | −0.0548568 | − | 0.632179i | ||||
\(866\) | 10.2442i | 0.348113i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.22677 | − | 7.22677i | −0.245293 | − | 0.245293i | ||||
\(869\) | −39.0212 | −1.32370 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.7201 | 1.21033 | ||||||||
\(872\) | 9.87771 | + | 9.87771i | 0.334502 | + | 0.334502i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.45539i | 0.218357i | ||||||||
\(875\) | 48.4896 | − | 12.8822i | 1.63925 | − | 0.435499i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.2329 | + | 26.2329i | −0.885823 | + | 0.885823i | −0.994119 | − | 0.108296i | \(-0.965461\pi\) |
0.108296 | + | 0.994119i | \(0.465461\pi\) | |||||||
\(878\) | 26.8156 | − | 26.8156i | 0.904983 | − | 0.904983i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.86126 | + | 4.92527i | 0.197583 | + | 0.166031i | ||||
\(881\) | 45.8820i | 1.54580i | 0.634525 | + | 0.772902i | \(0.281196\pi\) | ||||
−0.634525 | + | 0.772902i | \(0.718804\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8627 | + | 18.8627i | 0.634782 | + | 0.634782i | 0.949264 | − | 0.314482i | \(-0.101831\pi\) |
−0.314482 | + | 0.949264i | \(0.601831\pi\) | |||||||
\(884\) | 6.44171 | 0.216658 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.5741 | −0.422434 | ||||||||
\(887\) | −15.4909 | − | 15.4909i | −0.520133 | − | 0.520133i | 0.397479 | − | 0.917611i | \(-0.369885\pi\) |
−0.917611 | + | 0.397479i | \(0.869885\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 99.5890i | 3.34011i | ||||||||
\(890\) | 17.9013 | − | 1.55337i | 0.600054 | − | 0.0520691i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.72627 | − | 4.72627i | 0.158247 | − | 0.158247i | ||||
\(893\) | 27.7019 | − | 27.7019i | 0.927008 | − | 0.927008i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.6389 | + | 38.8415i | −1.09100 | + | 1.29833i | ||||
\(896\) | 4.48749i | 0.149916i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.8349 | + | 28.8349i | 0.962232 | + | 0.962232i | ||||
\(899\) | −8.97498 | −0.299332 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.72117 | 0.223914 | ||||||||
\(902\) | 26.8951 | + | 26.8951i | 0.895509 | + | 0.895509i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.7613i | 0.424435i | ||||||||
\(905\) | 8.17398 | − | 9.72735i | 0.271712 | − | 0.323348i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.41571 | − | 9.41571i | 0.312644 | − | 0.312644i | −0.533289 | − | 0.845933i | \(-0.679044\pi\) |
0.845933 | + | 0.533289i | \(0.179044\pi\) | |||||||
\(908\) | 9.14266 | − | 9.14266i | 0.303410 | − | 0.303410i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28.2751 | − | 2.45355i | 0.937311 | − | 0.0813343i | ||||
\(911\) | − | 24.2752i | − | 0.804274i | −0.915580 | − | 0.402137i | \(-0.868268\pi\) | ||
0.915580 | − | 0.402137i | \(-0.131732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.9244 | + | 31.9244i | 1.05654 | + | 1.05654i | ||||
\(914\) | 10.9401 | 0.361866 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.98963 | −0.164862 | ||||||||
\(917\) | −45.2432 | − | 45.2432i | −1.49406 | − | 1.49406i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 45.8495i | − | 1.51244i | −0.654320 | − | 0.756218i | \(-0.727045\pi\) | ||
0.654320 | − | 0.756218i | \(-0.272955\pi\) | |||||||
\(920\) | −1.71191 | − | 1.43853i | −0.0564399 | − | 0.0474270i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.3813 | + | 15.3813i | −0.506557 | + | 0.506557i | ||||
\(923\) | −20.9729 | + | 20.9729i | −0.690332 | + | 0.690332i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.22082 | − | 5.07135i | −0.237419 | − | 0.166745i | ||||
\(926\) | 37.5255i | 1.23316i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.78652 | + | 2.78652i | 0.0914720 | + | 0.0914720i | ||||
\(929\) | −51.5944 | −1.69276 | −0.846379 | − | 0.532582i | \(-0.821222\pi\) | ||||
−0.846379 | + | 0.532582i | \(0.821222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 84.8081 | 2.77947 | ||||||||
\(932\) | −7.59060 | − | 7.59060i | −0.248638 | − | 0.248638i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14.8402i | 0.485585i | ||||||||
\(935\) | 1.50734 | + | 17.3709i | 0.0492955 | + | 0.568089i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.15455 | + | 8.15455i | −0.266397 | + | 0.266397i | −0.827647 | − | 0.561249i | \(-0.810321\pi\) |
0.561249 | + | 0.827647i | \(0.310321\pi\) | |||||||
\(938\) | −40.0734 | + | 40.0734i | −1.30844 | + | 1.30844i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.17313 | + | 13.5194i | 0.0382634 | + | 0.440954i | ||||
\(941\) | − | 19.0545i | − | 0.621159i | −0.950547 | − | 0.310579i | \(-0.899477\pi\) | ||
0.950547 | − | 0.310579i | \(-0.100523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.85530 | − | 7.85530i | −0.255804 | − | 0.255804i | ||||
\(944\) | 7.47024 | 0.243136 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.64182 | −0.118406 | ||||||||
\(947\) | 39.5188 | + | 39.5188i | 1.28419 | + | 1.28419i | 0.938262 | + | 0.345926i | \(0.112435\pi\) |
0.345926 | + | 0.938262i | \(0.387565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.2560i | 0.787384i | ||||||||
\(950\) | −26.4135 | − | 18.5508i | −0.856966 | − | 0.601867i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.22677 | + | 7.22677i | −0.234221 | + | 0.234221i | ||||
\(953\) | 13.1971 | − | 13.1971i | 0.427497 | − | 0.427497i | −0.460278 | − | 0.887775i | \(-0.652250\pi\) |
0.887775 | + | 0.460278i | \(0.152250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.268658 | − | 0.225756i | −0.00869357 | − | 0.00730528i | ||||
\(956\) | − | 20.3792i | − | 0.659111i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.17975 | − | 6.17975i | −0.199659 | − | 0.199659i | ||||
\(959\) | 79.1675 | 2.55645 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.8130 | −0.832679 | ||||||||
\(962\) | −3.52951 | − | 3.52951i | −0.113796 | − | 0.113796i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.11949i | 0.293719i | ||||||||
\(965\) | −55.5226 | + | 4.81792i | −1.78733 | + | 0.155094i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.0265 | + | 27.0265i | −0.869115 | + | 0.869115i | −0.992374 | − | 0.123260i | \(-0.960665\pi\) |
0.123260 | + | 0.992374i | \(0.460665\pi\) | |||||||
\(968\) | −0.510893 | + | 0.510893i | −0.0164207 | + | 0.0164207i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.0924 | + | 27.4809i | −0.741454 | + | 0.882359i | ||||
\(971\) | 23.1061i | 0.741510i | 0.928731 | + | 0.370755i | \(0.120901\pi\) | ||||
−0.928731 | + | 0.370755i | \(0.879099\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.9591 | + | 33.9591i | 1.08868 | + | 1.08868i | ||||
\(974\) | −10.3757 | −0.332459 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.89087 | 0.124544 | ||||||||
\(977\) | −15.3977 | − | 15.3977i | −0.492617 | − | 0.492617i | 0.416513 | − | 0.909130i | \(-0.363252\pi\) |
−0.909130 | + | 0.416513i | \(0.863252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.5131i | 0.879322i | ||||||||
\(980\) | −18.8988 | + | 22.4903i | −0.603700 | + | 0.718426i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.12325 | − | 7.12325i | 0.227312 | − | 0.227312i | ||||
\(983\) | 10.6126 | − | 10.6126i | 0.338490 | − | 0.338490i | −0.517309 | − | 0.855799i | \(-0.673066\pi\) |
0.855799 | + | 0.517309i | \(0.173066\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.3362 | − | 1.93820i | 0.711691 | − | 0.0617563i | ||||
\(986\) | 8.97498i | 0.285822i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.9108 | − | 12.9108i | −0.410747 | − | 0.410747i | ||||
\(989\) | 1.06367 | 0.0338229 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0072 | 0.572017 | 0.286008 | − | 0.958227i | \(-0.407671\pi\) | ||||
0.286008 | + | 0.958227i | \(0.407671\pi\) | |||||||
\(992\) | −1.61043 | − | 1.61043i | −0.0511311 | − | 0.0511311i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 47.0579i | − | 1.49259i | ||||||
\(995\) | 27.1510 | + | 22.8152i | 0.860744 | + | 0.723291i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.81541 | + | 4.81541i | −0.152506 | + | 0.152506i | −0.779236 | − | 0.626730i | \(-0.784393\pi\) |
0.626730 | + | 0.779236i | \(0.284393\pi\) | |||||||
\(998\) | −14.8834 | + | 14.8834i | −0.471127 | + | 0.471127i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2070.2.j.i.323.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 2070.2.j.i.323.8 | yes | 16 | |
5.2 | odd | 4 | inner | 2070.2.j.i.737.8 | yes | 16 | |
15.2 | even | 4 | inner | 2070.2.j.i.737.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.i.323.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2070.2.j.i.323.8 | yes | 16 | 3.2 | odd | 2 | inner | |
2070.2.j.i.737.1 | yes | 16 | 15.2 | even | 4 | inner | |
2070.2.j.i.737.8 | yes | 16 | 5.2 | odd | 4 | inner |