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 | 323.8 | ||
Root | \(-3.24374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.323 |
Dual form | 2070.2.j.i.737.8 |
$q$-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 | \(-0.827361\pi\) | ||
0.856492 | − | 0.516160i | \(-0.172639\pi\) | |||||||
\(12\) | 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 | 0.874896 | − | 0.484310i | \(-0.160929\pi\) |
−0.484310 | + | 0.874896i | \(0.660929\pi\) | |||||||
\(18\) | 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 | \(-0.619235\pi\) | ||||
−0.365888 | + | 0.930659i | \(0.619235\pi\) | |||||||
\(30\) | 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 | \(-0.665743\pi\) | ||
0.497484 | − | 0.867473i | \(-0.334257\pi\) | |||||||
\(42\) | 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 | 0.947046 | − | 0.321099i | \(-0.104052\pi\) |
−0.321099 | + | 0.947046i | \(0.604052\pi\) | |||||||
\(48\) | 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 | −0.549111 | − | 0.835750i | \(-0.685033\pi\) |
0.835750 | + | 0.549111i | \(0.185033\pi\) | |||||||
\(54\) | 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 | \(-0.338357\pi\) | ||||
0.486271 | + | 0.873808i | \(0.338357\pi\) | |||||||
\(60\) | 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 | \(-0.786216\pi\) | ||
0.782813 | − | 0.622257i | \(-0.213784\pi\) | |||||||
\(72\) | 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 | \(0.507560\pi\) |
−0.999718 | + | 0.0237475i | \(0.992440\pi\) | |||||||
\(84\) | 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 | \(-0.640041\pi\) | ||||
−0.425896 | + | 0.904772i | \(0.640041\pi\) | |||||||
\(90\) | 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 | \(-0.976148\pi\) | ||
0.997194 | − | 0.0748634i | \(-0.0238521\pi\) | |||||||
\(102\) | 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 | 0.466768 | − | 0.884380i | \(-0.345418\pi\) |
−0.884380 | + | 0.466768i | \(0.845418\pi\) | |||||||
\(108\) | 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 | −0.141122 | − | 0.989992i | \(-0.545071\pi\) |
0.989992 | + | 0.141122i | \(0.0450710\pi\) | |||||||
\(114\) | 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 | \(0.214035\pi\) | ||||
−0.782323 | + | 0.622873i | \(0.785965\pi\) | |||||||
\(132\) | 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 | \(-0.978305\pi\) |
−0.0681032 | − | 0.997678i | \(-0.521695\pi\) | |||||||
\(138\) | 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 | \(-0.418873\pi\) | ||||
0.252117 | + | 0.967697i | \(0.418873\pi\) | |||||||
\(150\) | 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 | 0.295094 | − | 0.955468i | \(-0.404649\pi\) |
−0.955468 | + | 0.295094i | \(0.904649\pi\) | |||||||
\(168\) | 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 | −0.446223 | − | 0.894922i | \(-0.647231\pi\) |
0.894922 | + | 0.446223i | \(0.147231\pi\) | |||||||
\(174\) | 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 | \(-0.822151\pi\) | ||||
−0.847929 | + | 0.530109i | \(0.822151\pi\) | |||||||
\(180\) | 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 | \(-0.998193\pi\) | ||
0.999984 | − | 0.00567771i | \(-0.00180728\pi\) | |||||||
\(192\) | 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 | 0.913028 | − | 0.407896i | \(-0.133737\pi\) |
−0.407896 | + | 0.913028i | \(0.633737\pi\) | |||||||
\(198\) | 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 | 0.942114 | − | 0.335294i | \(-0.108836\pi\) |
−0.335294 | + | 0.942114i | \(0.608836\pi\) | |||||||
\(228\) | 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 | −0.413313 | − | 0.910589i | \(-0.635628\pi\) |
0.910589 | + | 0.413313i | \(0.135628\pi\) | |||||||
\(234\) | 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 | \(-0.270933\pi\) | ||||
0.659111 | + | 0.752046i | \(0.270933\pi\) | |||||||
\(240\) | 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 | \(0.107587\pi\) | ||||
−0.943421 | + | 0.331596i | \(0.892413\pi\) | |||||||
\(252\) | 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 | 0.894546 | − | 0.446976i | \(-0.147499\pi\) |
−0.446976 | + | 0.894546i | \(0.647499\pi\) | |||||||
\(258\) | 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 | −0.914484 | − | 0.404621i | \(-0.867403\pi\) |
0.404621 | + | 0.914484i | \(0.367403\pi\) | |||||||
\(264\) | 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 | \(-0.622220\pi\) | ||||
−0.374600 | + | 0.927186i | \(0.622220\pi\) | |||||||
\(270\) | 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 | \(0.290023\pi\) | ||||
−0.612850 | + | 0.790199i | \(0.709977\pi\) | |||||||
\(282\) | 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 | −0.676017 | − | 0.736886i | \(-0.736296\pi\) |
0.736886 | + | 0.676017i | \(0.236296\pi\) | |||||||
\(294\) | 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 | \(0.158292\pi\) | ||||
−0.878878 | + | 0.477046i | \(0.841708\pi\) | |||||||
\(312\) | 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 | 0.0700090 | − | 0.997546i | \(-0.477697\pi\) |
−0.997546 | + | 0.0700090i | \(0.977697\pi\) | |||||||
\(318\) | 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 | \(-0.938664\pi\) |
−0.191503 | − | 0.981492i | \(-0.561336\pi\) | |||||||
\(348\) | 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 | −0.991507 | − | 0.130055i | \(-0.958485\pi\) |
0.130055 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(354\) | 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 | \(-0.656277\pi\) | ||||
−0.471471 | + | 0.881882i | \(0.656277\pi\) | |||||||
\(360\) | 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 | −0.953262 | − | 0.302146i | \(-0.902297\pi\) |
0.302146 | + | 0.953262i | \(0.402297\pi\) | |||||||
\(384\) | 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 | \(-0.230632\pi\) | ||||
0.748797 | + | 0.662799i | \(0.230632\pi\) | |||||||
\(390\) | 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 | \(-0.995547\pi\) | ||
0.999902 | − | 0.0139887i | \(-0.00445290\pi\) | |||||||
\(402\) | 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 | \(-0.437476\pi\) | ||||
0.195163 | + | 0.980771i | \(0.437476\pi\) | |||||||
\(420\) | 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 | \(0.0869354\pi\) | ||||
−0.962935 | + | 0.269733i | \(0.913065\pi\) | |||||||
\(432\) | 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 | −0.886041 | − | 0.463607i | \(-0.846555\pi\) |
0.463607 | + | 0.886041i | \(0.346555\pi\) | |||||||
\(444\) | 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 | \(-0.0877613\pi\) | ||||
0.962232 | + | 0.272231i | \(0.0877613\pi\) | |||||||
\(450\) | 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 | \(0.169082\pi\) | ||||
−0.862207 | + | 0.506557i | \(0.830918\pi\) | |||||||
\(462\) | 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 | 0.906910 | − | 0.421325i | \(-0.138435\pi\) |
−0.421325 | + | 0.906910i | \(0.638435\pi\) | |||||||
\(468\) | 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 | \(-0.563983\pi\) | ||||
−0.199659 | + | 0.979866i | \(0.563983\pi\) | |||||||
\(480\) | 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 | \(-0.927006\pi\) | ||
0.973822 | − | 0.227312i | \(-0.0729937\pi\) | |||||||
\(492\) | 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 | −0.994930 | − | 0.100566i | \(-0.967935\pi\) |
0.100566 | + | 0.994930i | \(0.467935\pi\) | |||||||
\(504\) | 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 | \(-0.314016\pi\) | ||||
0.551605 | + | 0.834105i | \(0.314016\pi\) | |||||||
\(510\) | 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 | \(0.301056\pi\) | ||||
−0.585097 | + | 0.810963i | \(0.698944\pi\) | |||||||
\(522\) | 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 | 0.738537 | − | 0.674213i | \(-0.235517\pi\) |
−0.674213 | + | 0.738537i | \(0.735517\pi\) | |||||||
\(558\) | 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 | \(0.519658\pi\) |
−0.998094 | + | 0.0617187i | \(0.980342\pi\) | |||||||
\(564\) | 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 | \(-0.657704\pi\) | ||||
−0.475421 | + | 0.879758i | \(0.657704\pi\) | |||||||
\(570\) | 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 | 0.788312 | − | 0.615276i | \(-0.210955\pi\) |
−0.615276 | + | 0.788312i | \(0.710955\pi\) | |||||||
\(588\) | 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 | −0.0508632 | − | 0.998706i | \(-0.516197\pi\) |
0.998706 | + | 0.0508632i | \(0.0161973\pi\) | |||||||
\(594\) | 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 | \(-0.399612\pi\) | ||||
0.310175 | + | 0.950680i | \(0.399612\pi\) | |||||||
\(600\) | 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 | 0.955607 | − | 0.294644i | \(-0.0952009\pi\) |
−0.294644 | + | 0.955607i | \(0.595201\pi\) | |||||||
\(618\) | 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 | \(-0.789496\pi\) | ||
0.789183 | − | 0.614158i | \(-0.210504\pi\) | |||||||
\(642\) | 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 | 0.672320 | − | 0.740261i | \(-0.265298\pi\) |
−0.740261 | + | 0.672320i | \(0.765298\pi\) | |||||||
\(648\) | 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 | −0.940025 | − | 0.341104i | \(-0.889199\pi\) |
0.341104 | + | 0.940025i | \(0.389199\pi\) | |||||||
\(654\) | 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 | \(-0.385324\pi\) | ||||
0.352523 | + | 0.935803i | \(0.385324\pi\) | |||||||
\(660\) | 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 | 0.644416 | − | 0.764675i | \(-0.277100\pi\) |
−0.764675 | + | 0.644416i | \(0.777100\pi\) | |||||||
\(678\) | 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 | \(0.517153\pi\) |
−0.998548 | + | 0.0538625i | \(0.982847\pi\) | |||||||
\(684\) | 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 | \(-0.996728\pi\) | ||
0.999947 | − | 0.0102787i | \(-0.00327187\pi\) | |||||||
\(702\) | 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 | \(-0.505053\pi\) | ||||
−0.0158734 | + | 0.999874i | \(0.505053\pi\) | |||||||
\(720\) | 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 | −0.900258 | − | 0.435356i | \(-0.856622\pi\) |
0.435356 | + | 0.900258i | \(0.356622\pi\) | |||||||
\(744\) | 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 | \(-0.960243\pi\) | ||
0.992210 | − | 0.124576i | \(-0.0397572\pi\) | |||||||
\(762\) | 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 | −0.847411 | − | 0.530938i | \(-0.821840\pi\) |
0.530938 | + | 0.847411i | \(0.321840\pi\) | |||||||
\(774\) | 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 | 0.380370 | − | 0.924834i | \(-0.375797\pi\) |
−0.924834 | + | 0.380370i | \(0.875797\pi\) | |||||||
\(798\) | 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 | \(-0.807756\pi\) | ||||
−0.823098 | + | 0.567899i | \(0.807756\pi\) | |||||||
\(810\) | 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 | \(-0.793902\pi\) | ||
0.797610 | − | 0.603174i | \(-0.206098\pi\) | |||||||
\(822\) | 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 | 0.598122 | − | 0.801405i | \(-0.295914\pi\) |
−0.801405 | + | 0.598122i | \(0.795914\pi\) | |||||||
\(828\) | 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 | \(-0.577408\pi\) | ||||
−0.240795 | + | 0.970576i | \(0.577408\pi\) | |||||||
\(840\) | 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 | 0.799512 | − | 0.600651i | \(-0.205092\pi\) |
−0.600651 | + | 0.799512i | \(0.705092\pi\) | |||||||
\(858\) | 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 | −0.955225 | − | 0.295880i | \(-0.904387\pi\) |
0.295880 | + | 0.955225i | \(0.404387\pi\) | |||||||
\(864\) | 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 | \(-0.718804\pi\) | ||
0.634525 | − | 0.772902i | \(-0.281196\pi\) | |||||||
\(882\) | 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 | 0.917611 | − | 0.397479i | \(-0.130115\pi\) |
−0.397479 | + | 0.917611i | \(0.630115\pi\) | |||||||
\(888\) | 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 | \(0.131732\pi\) | ||||
−0.915580 | + | 0.402137i | \(0.868268\pi\) | |||||||
\(912\) | 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 | \(-0.178778\pi\) | ||||
0.846379 | + | 0.532582i | \(0.178778\pi\) | |||||||
\(930\) | 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 | \(0.100523\pi\) | ||||
−0.950547 | + | 0.310579i | \(0.899477\pi\) | |||||||
\(942\) | 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 | \(-0.887565\pi\) |
−0.345926 | − | 0.938262i | \(-0.612435\pi\) | |||||||
\(948\) | 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 | −0.887775 | − | 0.460278i | \(-0.847750\pi\) |
0.460278 | + | 0.887775i | \(0.347750\pi\) | |||||||
\(954\) | 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 | \(-0.879099\pi\) | ||
0.928731 | − | 0.370755i | \(-0.120901\pi\) | |||||||
\(972\) | 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 | 0.909130 | − | 0.416513i | \(-0.136748\pi\) |
−0.416513 | + | 0.909130i | \(0.636748\pi\) | |||||||
\(978\) | 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 | −0.855799 | − | 0.517309i | \(-0.826934\pi\) |
0.517309 | + | 0.855799i | \(0.326934\pi\) | |||||||
\(984\) | 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.323.8 | yes | 16 | |
3.2 | odd | 2 | inner | 2070.2.j.i.323.1 | ✓ | 16 | |
5.2 | odd | 4 | inner | 2070.2.j.i.737.1 | yes | 16 | |
15.2 | even | 4 | inner | 2070.2.j.i.737.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.i.323.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
2070.2.j.i.323.8 | yes | 16 | 1.1 | even | 1 | trivial | |
2070.2.j.i.737.1 | yes | 16 | 5.2 | odd | 4 | inner | |
2070.2.j.i.737.8 | yes | 16 | 15.2 | even | 4 | inner |