Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(589,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 589.5 | ||
Root | \(-0.692297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.589 |
Dual form | 1470.2.g.k.589.1 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.88893 | − | 1.19663i | −0.844756 | − | 0.535151i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.19663 | − | 1.88893i | 0.378409 | − | 0.597333i | ||||
\(11\) | 0.979056 | 0.295197 | 0.147598 | − | 0.989047i | \(-0.452846\pi\) | ||||
0.147598 | + | 0.989047i | \(0.452846\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | − | 0.435157i | − | 0.120691i | −0.998178 | − | 0.0603455i | \(-0.980780\pi\) | ||
0.998178 | − | 0.0603455i | \(-0.0192202\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.19663 | + | 1.88893i | −0.308970 | + | 0.487720i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.79881i | − | 0.678811i | −0.940640 | − | 0.339405i | \(-0.889774\pi\) | ||
0.940640 | − | 0.339405i | \(-0.110226\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −7.34271 | −1.68453 | −0.842266 | − | 0.539062i | \(-0.818779\pi\) | ||||
−0.842266 | + | 0.539062i | \(0.818779\pi\) | |||||||
\(20\) | 1.88893 | + | 1.19663i | 0.422378 | + | 0.267576i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.979056i | 0.208735i | ||||||||
\(23\) | 3.34271i | 0.697003i | 0.937308 | + | 0.348501i | \(0.113309\pi\) | ||||
−0.937308 | + | 0.348501i | \(0.886691\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 2.13613 | + | 4.52072i | 0.427226 | + | 0.904145i | ||||
\(26\) | 0.435157 | 0.0853414 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.74825 | −0.696032 | −0.348016 | − | 0.937489i | \(-0.613144\pi\) | ||||
−0.348016 | + | 0.937489i | \(0.613144\pi\) | |||||||
\(30\) | −1.88893 | − | 1.19663i | −0.344870 | − | 0.218475i | ||||
\(31\) | 4.97906 | 0.894265 | 0.447132 | − | 0.894468i | \(-0.352445\pi\) | ||||
0.447132 | + | 0.894468i | \(0.352445\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 0.979056i | − | 0.170432i | ||||||
\(34\) | 2.79881 | 0.479992 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.63591i | 0.762139i | 0.924546 | + | 0.381069i | \(0.124444\pi\) | ||||
−0.924546 | + | 0.381069i | \(0.875556\pi\) | |||||||
\(38\) | − | 7.34271i | − | 1.19114i | ||||||
\(39\) | −0.435157 | −0.0696809 | ||||||||
\(40\) | −1.19663 | + | 1.88893i | −0.189205 | + | 0.298666i | ||||
\(41\) | 4.94944 | 0.772972 | 0.386486 | − | 0.922295i | \(-0.373689\pi\) | ||||
0.386486 | + | 0.922295i | \(0.373689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.97862i | 1.52172i | 0.648913 | + | 0.760862i | \(0.275224\pi\) | ||||
−0.648913 | + | 0.760862i | \(0.724776\pi\) | |||||||
\(44\) | −0.979056 | −0.147598 | ||||||||
\(45\) | 1.88893 | + | 1.19663i | 0.281585 | + | 0.178384i | ||||
\(46\) | −3.34271 | −0.492855 | ||||||||
\(47\) | 4.40554i | 0.642614i | 0.946975 | + | 0.321307i | \(0.104122\pi\) | ||||
−0.946975 | + | 0.321307i | \(0.895878\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.52072 | + | 2.13613i | −0.639327 | + | 0.302094i | ||||
\(51\) | −2.79881 | −0.391912 | ||||||||
\(52\) | 0.435157i | 0.0603455i | ||||||||
\(53\) | − | 0.657293i | − | 0.0902861i | −0.998981 | − | 0.0451431i | \(-0.985626\pi\) | ||
0.998981 | − | 0.0451431i | \(-0.0143744\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.84937 | − | 1.17157i | −0.249369 | − | 0.157975i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.34271i | 0.972565i | ||||||||
\(58\) | − | 3.74825i | − | 0.492169i | ||||||
\(59\) | −8.27226 | −1.07696 | −0.538478 | − | 0.842639i | \(-0.681001\pi\) | ||||
−0.538478 | + | 0.842639i | \(0.681001\pi\) | |||||||
\(60\) | 1.19663 | − | 1.88893i | 0.154485 | − | 0.243860i | ||||
\(61\) | −11.3336 | −1.45112 | −0.725559 | − | 0.688160i | \(-0.758419\pi\) | ||||
−0.725559 | + | 0.688160i | \(0.758419\pi\) | |||||||
\(62\) | 4.97906i | 0.632341i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.520724 | + | 0.821983i | −0.0645879 | + | 0.101954i | ||||
\(66\) | 0.979056 | 0.120513 | ||||||||
\(67\) | 2.36365i | 0.288766i | 0.989522 | + | 0.144383i | \(0.0461197\pi\) | ||||
−0.989522 | + | 0.144383i | \(0.953880\pi\) | |||||||
\(68\) | 2.79881i | 0.339405i | ||||||||
\(69\) | 3.34271 | 0.402415 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1119 | −1.67477 | −0.837387 | − | 0.546610i | \(-0.815918\pi\) | ||||
−0.837387 | + | 0.546610i | \(0.815918\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 15.3928i | 1.80159i | 0.434240 | + | 0.900797i | \(0.357017\pi\) | ||||
−0.434240 | + | 0.900797i | \(0.642983\pi\) | |||||||
\(74\) | −4.63591 | −0.538914 | ||||||||
\(75\) | 4.52072 | − | 2.13613i | 0.522008 | − | 0.246659i | ||||
\(76\) | 7.34271 | 0.842266 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 0.435157i | − | 0.0492719i | ||||||
\(79\) | 2.88767 | 0.324888 | 0.162444 | − | 0.986718i | \(-0.448062\pi\) | ||||
0.162444 | + | 0.986718i | \(0.448062\pi\) | |||||||
\(80\) | −1.88893 | − | 1.19663i | −0.211189 | − | 0.133788i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.94944i | 0.546574i | ||||||||
\(83\) | − | 14.3842i | − | 1.57887i | −0.613837 | − | 0.789433i | \(-0.710375\pi\) | ||
0.613837 | − | 0.789433i | \(-0.289625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.34915 | + | 5.28676i | −0.363266 | + | 0.573430i | ||||
\(86\) | −9.97862 | −1.07602 | ||||||||
\(87\) | 3.74825i | 0.401854i | ||||||||
\(88\) | − | 0.979056i | − | 0.104368i | ||||||
\(89\) | −10.1210 | −1.07282 | −0.536412 | − | 0.843956i | \(-0.680221\pi\) | ||||
−0.536412 | + | 0.843956i | \(0.680221\pi\) | |||||||
\(90\) | −1.19663 | + | 1.88893i | −0.126136 | + | 0.199111i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 3.34271i | − | 0.348501i | ||||||
\(93\) | − | 4.97906i | − | 0.516304i | ||||||
\(94\) | −4.40554 | −0.454397 | ||||||||
\(95\) | 13.8699 | + | 8.78654i | 1.42302 | + | 0.901480i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 10.6655i | 1.08292i | 0.840726 | + | 0.541460i | \(0.182128\pi\) | ||||
−0.840726 | + | 0.541460i | \(0.817872\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.979056 | −0.0983989 | ||||||||
\(100\) | −2.13613 | − | 4.52072i | −0.213613 | − | 0.452072i | ||||
\(101\) | 14.0328 | 1.39631 | 0.698157 | − | 0.715945i | \(-0.254004\pi\) | ||||
0.698157 | + | 0.715945i | \(0.254004\pi\) | |||||||
\(102\) | − | 2.79881i | − | 0.277123i | ||||||
\(103\) | 10.3842i | 1.02318i | 0.859229 | + | 0.511591i | \(0.170944\pi\) | ||||
−0.859229 | + | 0.511591i | \(0.829056\pi\) | |||||||
\(104\) | −0.435157 | −0.0426707 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.657293 | 0.0638419 | ||||||||
\(107\) | 20.0410i | 1.93744i | 0.248161 | + | 0.968719i | \(0.420174\pi\) | ||||
−0.248161 | + | 0.968719i | \(0.579826\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −18.6564 | −1.78696 | −0.893480 | − | 0.449102i | \(-0.851744\pi\) | ||||
−0.893480 | + | 0.449102i | \(0.851744\pi\) | |||||||
\(110\) | 1.17157 | − | 1.84937i | 0.111705 | − | 0.176331i | ||||
\(111\) | 4.63591 | 0.440021 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.4132i | − | 0.979587i | −0.871838 | − | 0.489794i | \(-0.837072\pi\) | ||
0.871838 | − | 0.489794i | \(-0.162928\pi\) | |||||||
\(114\) | −7.34271 | −0.687708 | ||||||||
\(115\) | 4.00000 | − | 6.31415i | 0.373002 | − | 0.588797i | ||||
\(116\) | 3.74825 | 0.348016 | ||||||||
\(117\) | 0.435157i | 0.0402303i | ||||||||
\(118\) | − | 8.27226i | − | 0.761523i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.88893 | + | 1.19663i | 0.172435 | + | 0.109237i | ||||
\(121\) | −10.0414 | −0.912859 | ||||||||
\(122\) | − | 11.3336i | − | 1.02610i | ||||||
\(123\) | − | 4.94944i | − | 0.446276i | ||||||
\(124\) | −4.97906 | −0.447132 | ||||||||
\(125\) | 1.37465 | − | 11.0955i | 0.122953 | − | 0.992413i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.6987i | − | 1.03810i | −0.854745 | − | 0.519048i | \(-0.826287\pi\) | ||
0.854745 | − | 0.519048i | \(-0.173713\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 9.97862 | 0.878568 | ||||||||
\(130\) | −0.821983 | − | 0.520724i | −0.0720926 | − | 0.0456706i | ||||
\(131\) | 5.38459 | 0.470454 | 0.235227 | − | 0.971940i | \(-0.424417\pi\) | ||||
0.235227 | + | 0.971940i | \(0.424417\pi\) | |||||||
\(132\) | 0.979056i | 0.0852159i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.36365 | −0.204188 | ||||||||
\(135\) | 1.19663 | − | 1.88893i | 0.102990 | − | 0.162573i | ||||
\(136\) | −2.79881 | −0.239996 | ||||||||
\(137\) | 3.68585i | 0.314904i | 0.987527 | + | 0.157452i | \(0.0503279\pi\) | ||||
−0.987527 | + | 0.157452i | \(0.949672\pi\) | |||||||
\(138\) | 3.34271i | 0.284550i | ||||||||
\(139\) | −8.15378 | −0.691595 | −0.345797 | − | 0.938309i | \(-0.612392\pi\) | ||||
−0.345797 | + | 0.938309i | \(0.612392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.40554 | 0.371013 | ||||||||
\(142\) | − | 14.1119i | − | 1.18424i | ||||||
\(143\) | − | 0.426043i | − | 0.0356275i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 7.08018 | + | 4.48528i | 0.587977 | + | 0.372482i | ||||
\(146\) | −15.3928 | −1.27392 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 4.63591i | − | 0.381069i | ||||||
\(149\) | 15.6774 | 1.28434 | 0.642170 | − | 0.766563i | \(-0.278034\pi\) | ||||
0.642170 | + | 0.766563i | \(0.278034\pi\) | |||||||
\(150\) | 2.13613 | + | 4.52072i | 0.174414 | + | 0.369116i | ||||
\(151\) | 4.27226 | 0.347672 | 0.173836 | − | 0.984775i | \(-0.444384\pi\) | ||||
0.173836 | + | 0.984775i | \(0.444384\pi\) | |||||||
\(152\) | 7.34271i | 0.595572i | ||||||||
\(153\) | 2.79881i | 0.226270i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.40510 | − | 5.95811i | −0.755436 | − | 0.478567i | ||||
\(156\) | 0.435157 | 0.0348405 | ||||||||
\(157\) | 15.2498i | 1.21707i | 0.793528 | + | 0.608534i | \(0.208242\pi\) | ||||
−0.793528 | + | 0.608534i | \(0.791758\pi\) | |||||||
\(158\) | 2.88767i | 0.229730i | ||||||||
\(159\) | −0.657293 | −0.0521267 | ||||||||
\(160\) | 1.19663 | − | 1.88893i | 0.0946023 | − | 0.149333i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 7.47599i | 0.585564i | 0.956179 | + | 0.292782i | \(0.0945811\pi\) | ||||
−0.956179 | + | 0.292782i | \(0.905419\pi\) | |||||||
\(164\) | −4.94944 | −0.386486 | ||||||||
\(165\) | −1.17157 | + | 1.84937i | −0.0912068 | + | 0.143973i | ||||
\(166\) | 14.3842 | 1.11643 | ||||||||
\(167\) | − | 12.6640i | − | 0.979972i | −0.871730 | − | 0.489986i | \(-0.837002\pi\) | ||
0.871730 | − | 0.489986i | \(-0.162998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8106 | 0.985434 | ||||||||
\(170\) | −5.28676 | − | 3.34915i | −0.405476 | − | 0.256868i | ||||
\(171\) | 7.34271 | 0.561511 | ||||||||
\(172\) | − | 9.97862i | − | 0.760862i | ||||||
\(173\) | − | 7.12057i | − | 0.541367i | −0.962668 | − | 0.270684i | \(-0.912750\pi\) | ||
0.962668 | − | 0.270684i | \(-0.0872497\pi\) | |||||||
\(174\) | −3.74825 | −0.284154 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.979056 | 0.0737991 | ||||||||
\(177\) | 8.27226i | 0.621781i | ||||||||
\(178\) | − | 10.1210i | − | 0.758602i | ||||||
\(179\) | −3.26420 | −0.243978 | −0.121989 | − | 0.992531i | \(-0.538927\pi\) | ||||
−0.121989 | + | 0.992531i | \(0.538927\pi\) | |||||||
\(180\) | −1.88893 | − | 1.19663i | −0.140793 | − | 0.0891919i | ||||
\(181\) | 1.93823 | 0.144067 | 0.0720337 | − | 0.997402i | \(-0.477051\pi\) | ||||
0.0720337 | + | 0.997402i | \(0.477051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3336i | 0.837803i | ||||||||
\(184\) | 3.34271 | 0.246428 | ||||||||
\(185\) | 5.54749 | − | 8.75692i | 0.407860 | − | 0.643822i | ||||
\(186\) | 4.97906 | 0.365082 | ||||||||
\(187\) | − | 2.74019i | − | 0.200383i | ||||||
\(188\) | − | 4.40554i | − | 0.321307i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.78654 | + | 13.8699i | −0.637443 | + | 1.00623i | ||||
\(191\) | 8.07001 | 0.583925 | 0.291963 | − | 0.956430i | \(-0.405692\pi\) | ||||
0.291963 | + | 0.956430i | \(0.405692\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 1.95811i | − | 0.140948i | −0.997514 | − | 0.0704740i | \(-0.977549\pi\) | ||
0.997514 | − | 0.0704740i | \(-0.0224512\pi\) | |||||||
\(194\) | −10.6655 | −0.765740 | ||||||||
\(195\) | 0.821983 | + | 0.520724i | 0.0588634 | + | 0.0372899i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.3418i | − | 1.23555i | −0.786353 | − | 0.617777i | \(-0.788033\pi\) | ||
0.786353 | − | 0.617777i | \(-0.211967\pi\) | |||||||
\(198\) | − | 0.979056i | − | 0.0695785i | ||||||
\(199\) | −2.59490 | −0.183948 | −0.0919738 | − | 0.995761i | \(-0.529318\pi\) | ||||
−0.0919738 | + | 0.995761i | \(0.529318\pi\) | |||||||
\(200\) | 4.52072 | − | 2.13613i | 0.319663 | − | 0.151047i | ||||
\(201\) | 2.36365 | 0.166719 | ||||||||
\(202\) | 14.0328i | 0.987343i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.79881 | 0.195956 | ||||||||
\(205\) | −9.34915 | − | 5.92267i | −0.652973 | − | 0.413657i | ||||
\(206\) | −10.3842 | −0.723498 | ||||||||
\(207\) | − | 3.34271i | − | 0.232334i | ||||||
\(208\) | − | 0.435157i | − | 0.0301727i | ||||||
\(209\) | −7.18892 | −0.497268 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4127 | 1.06106 | 0.530528 | − | 0.847668i | \(-0.321994\pi\) | ||||
0.530528 | + | 0.847668i | \(0.321994\pi\) | |||||||
\(212\) | 0.657293i | 0.0451431i | ||||||||
\(213\) | 14.1119i | 0.966931i | ||||||||
\(214\) | −20.0410 | −1.36998 | ||||||||
\(215\) | 11.9408 | − | 18.8489i | 0.814353 | − | 1.28549i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 18.6564i | − | 1.26357i | ||||||
\(219\) | 15.3928 | 1.04015 | ||||||||
\(220\) | 1.84937 | + | 1.17157i | 0.124685 | + | 0.0789874i | ||||
\(221\) | −1.21792 | −0.0819263 | ||||||||
\(222\) | 4.63591i | 0.311142i | ||||||||
\(223\) | − | 7.61497i | − | 0.509936i | −0.966950 | − | 0.254968i | \(-0.917935\pi\) | ||
0.966950 | − | 0.254968i | \(-0.0820649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.13613 | − | 4.52072i | −0.142409 | − | 0.301382i | ||||
\(226\) | 10.4132 | 0.692673 | ||||||||
\(227\) | − | 8.34227i | − | 0.553696i | −0.960914 | − | 0.276848i | \(-0.910710\pi\) | ||
0.960914 | − | 0.276848i | \(-0.0892898\pi\) | |||||||
\(228\) | − | 7.34271i | − | 0.486283i | ||||||
\(229\) | −18.6901 | −1.23507 | −0.617537 | − | 0.786542i | \(-0.711869\pi\) | ||||
−0.617537 | + | 0.786542i | \(0.711869\pi\) | |||||||
\(230\) | 6.31415 | + | 4.00000i | 0.416343 | + | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.74825i | 0.246084i | ||||||||
\(233\) | − | 20.0829i | − | 1.31567i | −0.753160 | − | 0.657837i | \(-0.771471\pi\) | ||
0.753160 | − | 0.657837i | \(-0.228529\pi\) | |||||||
\(234\) | −0.435157 | −0.0284471 | ||||||||
\(235\) | 5.27182 | − | 8.32176i | 0.343896 | − | 0.542852i | ||||
\(236\) | 8.27226 | 0.538478 | ||||||||
\(237\) | − | 2.88767i | − | 0.187574i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.2714 | 1.44062 | 0.720308 | − | 0.693654i | \(-0.244000\pi\) | ||||
0.720308 | + | 0.693654i | \(0.244000\pi\) | |||||||
\(240\) | −1.19663 | + | 1.88893i | −0.0772425 | + | 0.121930i | ||||
\(241\) | −6.20075 | −0.399426 | −0.199713 | − | 0.979854i | \(-0.564001\pi\) | ||||
−0.199713 | + | 0.979854i | \(0.564001\pi\) | |||||||
\(242\) | − | 10.0414i | − | 0.645489i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 11.3336 | 0.725559 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.94944 | 0.315565 | ||||||||
\(247\) | 3.19523i | 0.203308i | ||||||||
\(248\) | − | 4.97906i | − | 0.316170i | ||||||
\(249\) | −14.3842 | −0.911559 | ||||||||
\(250\) | 11.0955 | + | 1.37465i | 0.701742 | + | 0.0869406i | ||||
\(251\) | −27.6560 | −1.74563 | −0.872815 | − | 0.488051i | \(-0.837708\pi\) | ||||
−0.872815 | + | 0.488051i | \(0.837708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.27270i | 0.205753i | ||||||||
\(254\) | 11.6987 | 0.734044 | ||||||||
\(255\) | 5.28676 | + | 3.34915i | 0.331070 | + | 0.209732i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 11.7681i | − | 0.734076i | −0.930206 | − | 0.367038i | \(-0.880372\pi\) | ||
0.930206 | − | 0.367038i | \(-0.119628\pi\) | |||||||
\(258\) | 9.97862i | 0.621242i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.520724 | − | 0.821983i | 0.0322940 | − | 0.0509772i | ||||
\(261\) | 3.74825 | 0.232011 | ||||||||
\(262\) | 5.38459i | 0.332661i | ||||||||
\(263\) | 0.455042i | 0.0280591i | 0.999902 | + | 0.0140295i | \(0.00446589\pi\) | ||||
−0.999902 | + | 0.0140295i | \(0.995534\pi\) | |||||||
\(264\) | −0.979056 | −0.0602567 | ||||||||
\(265\) | −0.786540 | + | 1.24158i | −0.0483167 | + | 0.0762698i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.1210i | 0.619396i | ||||||||
\(268\) | − | 2.36365i | − | 0.144383i | ||||||
\(269\) | −26.1375 | −1.59363 | −0.796815 | − | 0.604223i | \(-0.793484\pi\) | ||||
−0.796815 | + | 0.604223i | \(0.793484\pi\) | |||||||
\(270\) | 1.88893 | + | 1.19663i | 0.114957 | + | 0.0728249i | ||||
\(271\) | 16.7768 | 1.01912 | 0.509559 | − | 0.860436i | \(-0.329808\pi\) | ||||
0.509559 | + | 0.860436i | \(0.329808\pi\) | |||||||
\(272\) | − | 2.79881i | − | 0.169703i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.68585 | −0.222671 | ||||||||
\(275\) | 2.09139 | + | 4.42604i | 0.126116 | + | 0.266900i | ||||
\(276\) | −3.34271 | −0.201207 | ||||||||
\(277\) | − | 20.7478i | − | 1.24661i | −0.781977 | − | 0.623307i | \(-0.785789\pi\) | ||
0.781977 | − | 0.623307i | \(-0.214211\pi\) | |||||||
\(278\) | − | 8.15378i | − | 0.489031i | ||||||
\(279\) | −4.97906 | −0.298088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.3141 | −1.09253 | −0.546265 | − | 0.837612i | \(-0.683951\pi\) | ||||
−0.546265 | + | 0.837612i | \(0.683951\pi\) | |||||||
\(282\) | 4.40554i | 0.262346i | ||||||||
\(283\) | 11.8525i | 0.704560i | 0.935895 | + | 0.352280i | \(0.114593\pi\) | ||||
−0.935895 | + | 0.352280i | \(0.885407\pi\) | |||||||
\(284\) | 14.1119 | 0.837387 | ||||||||
\(285\) | 8.78654 | − | 13.8699i | 0.520470 | − | 0.821581i | ||||
\(286\) | 0.426043 | 0.0251925 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 9.16667 | 0.539216 | ||||||||
\(290\) | −4.48528 | + | 7.08018i | −0.263385 | + | 0.415763i | ||||
\(291\) | 10.6655 | 0.625224 | ||||||||
\(292\) | − | 15.3928i | − | 0.900797i | ||||||
\(293\) | 14.4770i | 0.845758i | 0.906186 | + | 0.422879i | \(0.138980\pi\) | ||||
−0.906186 | + | 0.422879i | \(0.861020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.6257 | + | 9.89887i | 0.909766 | + | 0.576335i | ||||
\(296\) | 4.63591 | 0.269457 | ||||||||
\(297\) | 0.979056i | 0.0568106i | ||||||||
\(298\) | 15.6774i | 0.908165i | ||||||||
\(299\) | 1.45460 | 0.0841219 | ||||||||
\(300\) | −4.52072 | + | 2.13613i | −0.261004 | + | 0.123330i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.27226i | 0.245841i | ||||||||
\(303\) | − | 14.0328i | − | 0.806162i | ||||||
\(304\) | −7.34271 | −0.421133 | ||||||||
\(305\) | 21.4084 | + | 13.5622i | 1.22584 | + | 0.776568i | ||||
\(306\) | −2.79881 | −0.159997 | ||||||||
\(307\) | 30.4252i | 1.73646i | 0.496165 | + | 0.868228i | \(0.334741\pi\) | ||||
−0.496165 | + | 0.868228i | \(0.665259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.3842 | 0.590734 | ||||||||
\(310\) | 5.95811 | − | 9.40510i | 0.338398 | − | 0.534174i | ||||
\(311\) | −9.02856 | −0.511963 | −0.255981 | − | 0.966682i | \(-0.582399\pi\) | ||||
−0.255981 | + | 0.966682i | \(0.582399\pi\) | |||||||
\(312\) | 0.435157i | 0.0246359i | ||||||||
\(313\) | − | 17.1732i | − | 0.970688i | −0.874323 | − | 0.485344i | \(-0.838694\pi\) | ||
0.874323 | − | 0.485344i | \(-0.161306\pi\) | |||||||
\(314\) | −15.2498 | −0.860597 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.88767 | −0.162444 | ||||||||
\(317\) | 2.61541i | 0.146896i | 0.997299 | + | 0.0734479i | \(0.0234003\pi\) | ||||
−0.997299 | + | 0.0734479i | \(0.976600\pi\) | |||||||
\(318\) | − | 0.657293i | − | 0.0368592i | ||||||
\(319\) | −3.66974 | −0.205466 | ||||||||
\(320\) | 1.88893 | + | 1.19663i | 0.105595 | + | 0.0668939i | ||||
\(321\) | 20.0410 | 1.11858 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.5508i | 1.14348i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 1.96723 | − | 0.929553i | 0.109122 | − | 0.0515623i | ||||
\(326\) | −7.47599 | −0.414057 | ||||||||
\(327\) | 18.6564i | 1.03170i | ||||||||
\(328\) | − | 4.94944i | − | 0.273287i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.84937 | − | 1.17157i | −0.101805 | − | 0.0644930i | ||||
\(331\) | −17.7559 | −0.975950 | −0.487975 | − | 0.872857i | \(-0.662264\pi\) | ||||
−0.487975 | + | 0.872857i | \(0.662264\pi\) | |||||||
\(332\) | 14.3842i | 0.789433i | ||||||||
\(333\) | − | 4.63591i | − | 0.254046i | ||||||
\(334\) | 12.6640 | 0.692945 | ||||||||
\(335\) | 2.82843 | − | 4.46478i | 0.154533 | − | 0.243937i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.2304i | − | 1.31991i | −0.751304 | − | 0.659956i | \(-0.770575\pi\) | ||
0.751304 | − | 0.659956i | \(-0.229425\pi\) | |||||||
\(338\) | 12.8106i | 0.696807i | ||||||||
\(339\) | −10.4132 | −0.565565 | ||||||||
\(340\) | 3.34915 | − | 5.28676i | 0.181633 | − | 0.286715i | ||||
\(341\) | 4.87478 | 0.263984 | ||||||||
\(342\) | 7.34271i | 0.397048i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.97862 | 0.538011 | ||||||||
\(345\) | −6.31415 | − | 4.00000i | −0.339942 | − | 0.215353i | ||||
\(346\) | 7.12057 | 0.382804 | ||||||||
\(347\) | 30.4252i | 1.63331i | 0.577127 | + | 0.816654i | \(0.304174\pi\) | ||||
−0.577127 | + | 0.816654i | \(0.695826\pi\) | |||||||
\(348\) | − | 3.74825i | − | 0.200927i | ||||||
\(349\) | −30.2623 | −1.61990 | −0.809951 | − | 0.586497i | \(-0.800506\pi\) | ||||
−0.809951 | + | 0.586497i | \(0.800506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.435157 | 0.0232270 | ||||||||
\(352\) | 0.979056i | 0.0521839i | ||||||||
\(353\) | − | 4.37189i | − | 0.232692i | −0.993209 | − | 0.116346i | \(-0.962882\pi\) | ||
0.993209 | − | 0.116346i | \(-0.0371182\pi\) | |||||||
\(354\) | −8.27226 | −0.439666 | ||||||||
\(355\) | 26.6564 | + | 16.8868i | 1.41478 | + | 0.896258i | ||||
\(356\) | 10.1210 | 0.536412 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.26420i | − | 0.172519i | ||||||
\(359\) | 15.6850 | 0.827821 | 0.413911 | − | 0.910318i | \(-0.364163\pi\) | ||||
0.413911 | + | 0.910318i | \(0.364163\pi\) | |||||||
\(360\) | 1.19663 | − | 1.88893i | 0.0630682 | − | 0.0995555i | ||||
\(361\) | 34.9153 | 1.83765 | ||||||||
\(362\) | 1.93823i | 0.101871i | ||||||||
\(363\) | 10.0414i | 0.527039i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.4196 | − | 29.0760i | 0.964126 | − | 1.52191i | ||||
\(366\) | −11.3336 | −0.592416 | ||||||||
\(367\) | − | 4.94478i | − | 0.258116i | −0.991637 | − | 0.129058i | \(-0.958805\pi\) | ||
0.991637 | − | 0.129058i | \(-0.0411953\pi\) | |||||||
\(368\) | 3.34271i | 0.174251i | ||||||||
\(369\) | −4.94944 | −0.257657 | ||||||||
\(370\) | 8.75692 | + | 5.54749i | 0.455251 | + | 0.288400i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.97906i | 0.258152i | ||||||||
\(373\) | 6.02138i | 0.311775i | 0.987775 | + | 0.155888i | \(0.0498238\pi\) | ||||
−0.987775 | + | 0.155888i | \(0.950176\pi\) | |||||||
\(374\) | 2.74019 | 0.141692 | ||||||||
\(375\) | −11.0955 | − | 1.37465i | −0.572970 | − | 0.0709867i | ||||
\(376\) | 4.40554 | 0.227198 | ||||||||
\(377\) | 1.63108i | 0.0840047i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.8030 | 1.89044 | 0.945222 | − | 0.326429i | \(-0.105845\pi\) | ||||
0.945222 | + | 0.326429i | \(0.105845\pi\) | |||||||
\(380\) | −13.8699 | − | 8.78654i | −0.711510 | − | 0.450740i | ||||
\(381\) | −11.6987 | −0.599345 | ||||||||
\(382\) | 8.07001i | 0.412898i | ||||||||
\(383\) | − | 9.03383i | − | 0.461607i | −0.973000 | − | 0.230804i | \(-0.925864\pi\) | ||
0.973000 | − | 0.230804i | \(-0.0741355\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.95811 | 0.0996653 | ||||||||
\(387\) | − | 9.97862i | − | 0.507242i | ||||||
\(388\) | − | 10.6655i | − | 0.541460i | ||||||
\(389\) | −33.5646 | −1.70179 | −0.850896 | − | 0.525334i | \(-0.823940\pi\) | ||||
−0.850896 | + | 0.525334i | \(0.823940\pi\) | |||||||
\(390\) | −0.520724 | + | 0.821983i | −0.0263679 | + | 0.0416227i | ||||
\(391\) | 9.35560 | 0.473133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.38459i | − | 0.271617i | ||||||
\(394\) | 17.3418 | 0.873669 | ||||||||
\(395\) | −5.45460 | − | 3.45548i | −0.274451 | − | 0.173864i | ||||
\(396\) | 0.979056 | 0.0491994 | ||||||||
\(397\) | − | 33.9792i | − | 1.70537i | −0.522426 | − | 0.852685i | \(-0.674973\pi\) | ||
0.522426 | − | 0.852685i | \(-0.325027\pi\) | |||||||
\(398\) | − | 2.59490i | − | 0.130071i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.13613 | + | 4.52072i | 0.106806 | + | 0.226036i | ||||
\(401\) | −4.27226 | −0.213346 | −0.106673 | − | 0.994294i | \(-0.534020\pi\) | ||||
−0.106673 | + | 0.994294i | \(0.534020\pi\) | |||||||
\(402\) | 2.36365i | 0.117888i | ||||||||
\(403\) | − | 2.16667i | − | 0.107930i | ||||||
\(404\) | −14.0328 | −0.698157 | ||||||||
\(405\) | −1.88893 | − | 1.19663i | −0.0938618 | − | 0.0594613i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.53882i | 0.224981i | ||||||||
\(408\) | 2.79881i | 0.138562i | ||||||||
\(409\) | −3.63888 | −0.179931 | −0.0899656 | − | 0.995945i | \(-0.528676\pi\) | ||||
−0.0899656 | + | 0.995945i | \(0.528676\pi\) | |||||||
\(410\) | 5.92267 | − | 9.34915i | 0.292500 | − | 0.461722i | ||||
\(411\) | 3.68585 | 0.181810 | ||||||||
\(412\) | − | 10.3842i | − | 0.511591i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.34271 | 0.164285 | ||||||||
\(415\) | −17.2126 | + | 27.1707i | −0.844932 | + | 1.33376i | ||||
\(416\) | 0.435157 | 0.0213353 | ||||||||
\(417\) | 8.15378i | 0.399293i | ||||||||
\(418\) | − | 7.18892i | − | 0.351622i | ||||||
\(419\) | 26.6274 | 1.30083 | 0.650417 | − | 0.759577i | \(-0.274594\pi\) | ||||
0.650417 | + | 0.759577i | \(0.274594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1880 | −0.740220 | −0.370110 | − | 0.928988i | \(-0.620680\pi\) | ||||
−0.370110 | + | 0.928988i | \(0.620680\pi\) | |||||||
\(422\) | 15.4127i | 0.750279i | ||||||||
\(423\) | − | 4.40554i | − | 0.214205i | ||||||
\(424\) | −0.657293 | −0.0319210 | ||||||||
\(425\) | 12.6526 | − | 5.97862i | 0.613743 | − | 0.290006i | ||||
\(426\) | −14.1119 | −0.683724 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 20.0410i | − | 0.968719i | ||||||
\(429\) | −0.426043 | −0.0205696 | ||||||||
\(430\) | 18.8489 | + | 11.9408i | 0.908976 | + | 0.575835i | ||||
\(431\) | −4.23125 | −0.203812 | −0.101906 | − | 0.994794i | \(-0.532494\pi\) | ||||
−0.101906 | + | 0.994794i | \(0.532494\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 33.9352i | 1.63082i | 0.578882 | + | 0.815412i | \(0.303489\pi\) | ||||
−0.578882 | + | 0.815412i | \(0.696511\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.48528 | − | 7.08018i | 0.215053 | − | 0.339469i | ||||
\(436\) | 18.6564 | 0.893480 | ||||||||
\(437\) | − | 24.5445i | − | 1.17412i | ||||||
\(438\) | 15.3928i | 0.735498i | ||||||||
\(439\) | −5.48257 | −0.261669 | −0.130834 | − | 0.991404i | \(-0.541766\pi\) | ||||
−0.130834 | + | 0.991404i | \(0.541766\pi\) | |||||||
\(440\) | −1.17157 | + | 1.84937i | −0.0558525 | + | 0.0881653i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.21792i | − | 0.0579306i | ||||||
\(443\) | − | 1.23081i | − | 0.0584776i | −0.999572 | − | 0.0292388i | \(-0.990692\pi\) | ||
0.999572 | − | 0.0292388i | \(-0.00930832\pi\) | |||||||
\(444\) | −4.63591 | −0.220011 | ||||||||
\(445\) | 19.1179 | + | 12.1112i | 0.906275 | + | 0.574124i | ||||
\(446\) | 7.61497 | 0.360579 | ||||||||
\(447\) | − | 15.6774i | − | 0.741514i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.6435 | −0.691071 | −0.345535 | − | 0.938406i | \(-0.612303\pi\) | ||||
−0.345535 | + | 0.938406i | \(0.612303\pi\) | |||||||
\(450\) | 4.52072 | − | 2.13613i | 0.213109 | − | 0.100698i | ||||
\(451\) | 4.84578 | 0.228179 | ||||||||
\(452\) | 10.4132i | 0.489794i | ||||||||
\(453\) | − | 4.27226i | − | 0.200728i | ||||||
\(454\) | 8.34227 | 0.391522 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.34271 | 0.343854 | ||||||||
\(457\) | − | 31.3289i | − | 1.46551i | −0.680495 | − | 0.732753i | \(-0.738235\pi\) | ||
0.680495 | − | 0.732753i | \(-0.261765\pi\) | |||||||
\(458\) | − | 18.6901i | − | 0.873329i | ||||||
\(459\) | 2.79881 | 0.130637 | ||||||||
\(460\) | −4.00000 | + | 6.31415i | −0.186501 | + | 0.294399i | ||||
\(461\) | −12.7667 | −0.594602 | −0.297301 | − | 0.954784i | \(-0.596087\pi\) | ||||
−0.297301 | + | 0.954784i | \(0.596087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.7112i | 1.24137i | 0.784058 | + | 0.620687i | \(0.213146\pi\) | ||||
−0.784058 | + | 0.620687i | \(0.786854\pi\) | |||||||
\(464\) | −3.74825 | −0.174008 | ||||||||
\(465\) | −5.95811 | + | 9.40510i | −0.276301 | + | 0.436151i | ||||
\(466\) | 20.0829 | 0.930322 | ||||||||
\(467\) | 37.6141i | 1.74057i | 0.492546 | + | 0.870286i | \(0.336066\pi\) | ||||
−0.492546 | + | 0.870286i | \(0.663934\pi\) | |||||||
\(468\) | − | 0.435157i | − | 0.0201152i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.32176 | + | 5.27182i | 0.383854 | + | 0.243171i | ||||
\(471\) | 15.2498 | 0.702675 | ||||||||
\(472\) | 8.27226i | 0.380762i | ||||||||
\(473\) | 9.76963i | 0.449208i | ||||||||
\(474\) | 2.88767 | 0.132635 | ||||||||
\(475\) | −15.6850 | − | 33.1944i | −0.719676 | − | 1.52306i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.657293i | 0.0300954i | ||||||||
\(478\) | 22.2714i | 1.01867i | ||||||||
\(479\) | −23.8235 | −1.08852 | −0.544262 | − | 0.838915i | \(-0.683190\pi\) | ||||
−0.544262 | + | 0.838915i | \(0.683190\pi\) | |||||||
\(480\) | −1.88893 | − | 1.19663i | −0.0862176 | − | 0.0546187i | ||||
\(481\) | 2.01735 | 0.0919833 | ||||||||
\(482\) | − | 6.20075i | − | 0.282437i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.0414 | 0.456429 | ||||||||
\(485\) | 12.7627 | − | 20.1465i | 0.579526 | − | 0.914804i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − | 3.75674i | − | 0.170234i | −0.996371 | − | 0.0851170i | \(-0.972874\pi\) | ||
0.996371 | − | 0.0851170i | \(-0.0271264\pi\) | |||||||
\(488\) | 11.3336i | 0.513048i | ||||||||
\(489\) | 7.47599 | 0.338076 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00762 | 0.0906025 | 0.0453012 | − | 0.998973i | \(-0.485575\pi\) | ||||
0.0453012 | + | 0.998973i | \(0.485575\pi\) | |||||||
\(492\) | 4.94944i | 0.223138i | ||||||||
\(493\) | 10.4906i | 0.472474i | ||||||||
\(494\) | −3.19523 | −0.143760 | ||||||||
\(495\) | 1.84937 | + | 1.17157i | 0.0831230 | + | 0.0526583i | ||||
\(496\) | 4.97906 | 0.223566 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 14.3842i | − | 0.644569i | ||||||
\(499\) | 0.628294 | 0.0281263 | 0.0140632 | − | 0.999901i | \(-0.495523\pi\) | ||||
0.0140632 | + | 0.999901i | \(0.495523\pi\) | |||||||
\(500\) | −1.37465 | + | 11.0955i | −0.0614763 | + | 0.496206i | ||||
\(501\) | −12.6640 | −0.565787 | ||||||||
\(502\) | − | 27.6560i | − | 1.23435i | ||||||
\(503\) | 28.9911i | 1.29265i | 0.763063 | + | 0.646324i | \(0.223695\pi\) | ||||
−0.763063 | + | 0.646324i | \(0.776305\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.5070 | − | 16.7921i | −1.17954 | − | 0.747239i | ||||
\(506\) | −3.27270 | −0.145489 | ||||||||
\(507\) | − | 12.8106i | − | 0.568940i | ||||||
\(508\) | 11.6987i | 0.519048i | ||||||||
\(509\) | −15.5056 | −0.687274 | −0.343637 | − | 0.939103i | \(-0.611659\pi\) | ||||
−0.343637 | + | 0.939103i | \(0.611659\pi\) | |||||||
\(510\) | −3.34915 | + | 5.28676i | −0.148303 | + | 0.234102i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 7.34271i | − | 0.324188i | ||||||
\(514\) | 11.7681 | 0.519070 | ||||||||
\(515\) | 12.4260 | − | 19.6150i | 0.547557 | − | 0.864339i | ||||
\(516\) | −9.97862 | −0.439284 | ||||||||
\(517\) | 4.31327i | 0.189697i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.12057 | −0.312558 | ||||||||
\(520\) | 0.821983 | + | 0.520724i | 0.0360463 | + | 0.0228353i | ||||
\(521\) | 13.5532 | 0.593776 | 0.296888 | − | 0.954912i | \(-0.404051\pi\) | ||||
0.296888 | + | 0.954912i | \(0.404051\pi\) | |||||||
\(522\) | 3.74825i | 0.164056i | ||||||||
\(523\) | 22.4542i | 0.981852i | 0.871201 | + | 0.490926i | \(0.163341\pi\) | ||||
−0.871201 | + | 0.490926i | \(0.836659\pi\) | |||||||
\(524\) | −5.38459 | −0.235227 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.455042 | −0.0198408 | ||||||||
\(527\) | − | 13.9354i | − | 0.607037i | ||||||
\(528\) | − | 0.979056i | − | 0.0426080i | ||||||
\(529\) | 11.8263 | 0.514187 | ||||||||
\(530\) | −1.24158 | − | 0.786540i | −0.0539309 | − | 0.0341651i | ||||
\(531\) | 8.27226 | 0.358985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.15378i | − | 0.0932907i | ||||||
\(534\) | −10.1210 | −0.437979 | ||||||||
\(535\) | 23.9818 | − | 37.8561i | 1.03682 | − | 1.63666i | ||||
\(536\) | 2.36365 | 0.102094 | ||||||||
\(537\) | 3.26420i | 0.140861i | ||||||||
\(538\) | − | 26.1375i | − | 1.12687i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.19663 | + | 1.88893i | −0.0514950 | + | 0.0812867i | ||||
\(541\) | 10.8111 | 0.464804 | 0.232402 | − | 0.972620i | \(-0.425341\pi\) | ||||
0.232402 | + | 0.972620i | \(0.425341\pi\) | |||||||
\(542\) | 16.7768i | 0.720625i | ||||||||
\(543\) | − | 1.93823i | − | 0.0831773i | ||||||
\(544\) | 2.79881 | 0.119998 | ||||||||
\(545\) | 35.2407 | + | 22.3249i | 1.50955 | + | 0.956294i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.1881i | − | 1.03421i | −0.855923 | − | 0.517103i | \(-0.827010\pi\) | ||
0.855923 | − | 0.517103i | \(-0.172990\pi\) | |||||||
\(548\) | − | 3.68585i | − | 0.157452i | ||||||
\(549\) | 11.3336 | 0.483706 | ||||||||
\(550\) | −4.42604 | + | 2.09139i | −0.188727 | + | 0.0891772i | ||||
\(551\) | 27.5223 | 1.17249 | ||||||||
\(552\) | − | 3.34271i | − | 0.142275i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.7478 | 0.881490 | ||||||||
\(555\) | −8.75692 | − | 5.54749i | −0.371711 | − | 0.235478i | ||||
\(556\) | 8.15378 | 0.345797 | ||||||||
\(557\) | − | 26.1529i | − | 1.10813i | −0.832472 | − | 0.554067i | \(-0.813075\pi\) | ||
0.832472 | − | 0.554067i | \(-0.186925\pi\) | |||||||
\(558\) | − | 4.97906i | − | 0.210780i | ||||||
\(559\) | 4.34227 | 0.183658 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.74019 | −0.115691 | ||||||||
\(562\) | − | 18.3141i | − | 0.772536i | ||||||
\(563\) | 10.5864i | 0.446164i | 0.974800 | + | 0.223082i | \(0.0716117\pi\) | ||||
−0.974800 | + | 0.223082i | \(0.928388\pi\) | |||||||
\(564\) | −4.40554 | −0.185507 | ||||||||
\(565\) | −12.4607 | + | 19.6697i | −0.524227 | + | 0.827512i | ||||
\(566\) | −11.8525 | −0.498199 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.1119i | 0.592122i | ||||||||
\(569\) | −15.6440 | −0.655829 | −0.327915 | − | 0.944707i | \(-0.606346\pi\) | ||||
−0.327915 | + | 0.944707i | \(0.606346\pi\) | |||||||
\(570\) | 13.8699 | + | 8.78654i | 0.580945 | + | 0.368028i | ||||
\(571\) | 8.50982 | 0.356125 | 0.178062 | − | 0.984019i | \(-0.443017\pi\) | ||||
0.178062 | + | 0.984019i | \(0.443017\pi\) | |||||||
\(572\) | 0.426043i | 0.0178138i | ||||||||
\(573\) | − | 8.07001i | − | 0.337129i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.1115 | + | 7.14046i | −0.630191 | + | 0.297778i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 9.67798i | 0.402900i | 0.979499 | + | 0.201450i | \(0.0645653\pi\) | ||||
−0.979499 | + | 0.201450i | \(0.935435\pi\) | |||||||
\(578\) | 9.16667i | 0.381283i | ||||||||
\(579\) | −1.95811 | −0.0813764 | ||||||||
\(580\) | −7.08018 | − | 4.48528i | −0.293989 | − | 0.186241i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.6655i | 0.442100i | ||||||||
\(583\) | − | 0.643527i | − | 0.0266522i | ||||||
\(584\) | 15.3928 | 0.636960 | ||||||||
\(585\) | 0.520724 | − | 0.821983i | 0.0215293 | − | 0.0339848i | ||||
\(586\) | −14.4770 | −0.598041 | ||||||||
\(587\) | − | 16.3013i | − | 0.672825i | −0.941715 | − | 0.336412i | \(-0.890786\pi\) | ||
0.941715 | − | 0.336412i | \(-0.109214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.5598 | −1.50642 | ||||||||
\(590\) | −9.89887 | + | 15.6257i | −0.407530 | + | 0.643301i | ||||
\(591\) | −17.3418 | −0.713348 | ||||||||
\(592\) | 4.63591i | 0.190535i | ||||||||
\(593\) | 12.4802i | 0.512500i | 0.966610 | + | 0.256250i | \(0.0824871\pi\) | ||||
−0.966610 | + | 0.256250i | \(0.917513\pi\) | |||||||
\(594\) | −0.979056 | −0.0401712 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.6774 | −0.642170 | ||||||||
\(597\) | 2.59490i | 0.106202i | ||||||||
\(598\) | 1.45460i | 0.0594832i | ||||||||
\(599\) | −40.7545 | −1.66519 | −0.832593 | − | 0.553886i | \(-0.813144\pi\) | ||||
−0.832593 | + | 0.553886i | \(0.813144\pi\) | |||||||
\(600\) | −2.13613 | − | 4.52072i | −0.0872071 | − | 0.184558i | ||||
\(601\) | −4.94541 | −0.201727 | −0.100864 | − | 0.994900i | \(-0.532161\pi\) | ||||
−0.100864 | + | 0.994900i | \(0.532161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.36365i | − | 0.0962553i | ||||||
\(604\) | −4.27226 | −0.173836 | ||||||||
\(605\) | 18.9676 | + | 12.0159i | 0.771143 | + | 0.488518i | ||||
\(606\) | 14.0328 | 0.570042 | ||||||||
\(607\) | − | 0.871555i | − | 0.0353753i | −0.999844 | − | 0.0176877i | \(-0.994370\pi\) | ||
0.999844 | − | 0.0176877i | \(-0.00563045\pi\) | |||||||
\(608\) | − | 7.34271i | − | 0.297786i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.5622 | + | 21.4084i | −0.549116 | + | 0.866800i | ||||
\(611\) | 1.91710 | 0.0775577 | ||||||||
\(612\) | − | 2.79881i | − | 0.113135i | ||||||
\(613\) | − | 36.9007i | − | 1.49041i | −0.666838 | − | 0.745203i | \(-0.732353\pi\) | ||
0.666838 | − | 0.745203i | \(-0.267647\pi\) | |||||||
\(614\) | −30.4252 | −1.22786 | ||||||||
\(615\) | −5.92267 | + | 9.34915i | −0.238825 | + | 0.376994i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6911i | 1.15506i | 0.816369 | + | 0.577530i | \(0.195984\pi\) | ||||
−0.816369 | + | 0.577530i | \(0.804016\pi\) | |||||||
\(618\) | 10.3842i | 0.417712i | ||||||||
\(619\) | −6.31415 | −0.253787 | −0.126894 | − | 0.991916i | \(-0.540501\pi\) | ||||
−0.126894 | + | 0.991916i | \(0.540501\pi\) | |||||||
\(620\) | 9.40510 | + | 5.95811i | 0.377718 | + | 0.239284i | ||||
\(621\) | −3.34271 | −0.134138 | ||||||||
\(622\) | − | 9.02856i | − | 0.362012i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.435157 | −0.0174202 | ||||||||
\(625\) | −15.8739 | + | 19.3137i | −0.634956 | + | 0.772548i | ||||
\(626\) | 17.1732 | 0.686380 | ||||||||
\(627\) | 7.18892i | 0.287098i | ||||||||
\(628\) | − | 15.2498i | − | 0.608534i | ||||||
\(629\) | 12.9750 | 0.517348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.237559 | −0.00945707 | −0.00472853 | − | 0.999989i | \(-0.501505\pi\) | ||||
−0.00472853 | + | 0.999989i | \(0.501505\pi\) | |||||||
\(632\) | − | 2.88767i | − | 0.114865i | ||||||
\(633\) | − | 15.4127i | − | 0.612600i | ||||||
\(634\) | −2.61541 | −0.103871 | ||||||||
\(635\) | −13.9991 | + | 22.0981i | −0.555538 | + | 0.876938i | ||||
\(636\) | 0.657293 | 0.0260634 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 3.66974i | − | 0.145287i | ||||||
\(639\) | 14.1119 | 0.558258 | ||||||||
\(640\) | −1.19663 | + | 1.88893i | −0.0473011 | + | 0.0746666i | ||||
\(641\) | −15.3490 | −0.606250 | −0.303125 | − | 0.952951i | \(-0.598030\pi\) | ||||
−0.303125 | + | 0.952951i | \(0.598030\pi\) | |||||||
\(642\) | 20.0410i | 0.790956i | ||||||||
\(643\) | 8.77577i | 0.346083i | 0.984915 | + | 0.173041i | \(0.0553594\pi\) | ||||
−0.984915 | + | 0.173041i | \(0.944641\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.8489 | − | 11.9408i | −0.742176 | − | 0.470167i | ||||
\(646\) | −20.5508 | −0.808562 | ||||||||
\(647\) | 19.2504i | 0.756813i | 0.925640 | + | 0.378406i | \(0.123528\pi\) | ||||
−0.925640 | + | 0.378406i | \(0.876472\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −8.09901 | −0.317914 | ||||||||
\(650\) | 0.929553 | + | 1.96723i | 0.0364600 | + | 0.0771610i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 7.47599i | − | 0.292782i | ||||||
\(653\) | − | 7.45460i | − | 0.291721i | −0.989305 | − | 0.145861i | \(-0.953405\pi\) | ||
0.989305 | − | 0.145861i | \(-0.0465951\pi\) | |||||||
\(654\) | −18.6564 | −0.729524 | ||||||||
\(655\) | −10.1711 | − | 6.44339i | −0.397419 | − | 0.251764i | ||||
\(656\) | 4.94944 | 0.193243 | ||||||||
\(657\) | − | 15.3928i | − | 0.600532i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.93717 | −0.114416 | −0.0572079 | − | 0.998362i | \(-0.518220\pi\) | ||||
−0.0572079 | + | 0.998362i | \(0.518220\pi\) | |||||||
\(660\) | 1.17157 | − | 1.84937i | 0.0456034 | − | 0.0719867i | ||||
\(661\) | −23.6361 | −0.919337 | −0.459669 | − | 0.888090i | \(-0.652032\pi\) | ||||
−0.459669 | + | 0.888090i | \(0.652032\pi\) | |||||||
\(662\) | − | 17.7559i | − | 0.690101i | ||||||
\(663\) | 1.21792i | 0.0473002i | ||||||||
\(664\) | −14.3842 | −0.558214 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.63591 | 0.179638 | ||||||||
\(667\) | − | 12.5293i | − | 0.485136i | ||||||
\(668\) | 12.6640i | 0.489986i | ||||||||
\(669\) | −7.61497 | −0.294412 | ||||||||
\(670\) | 4.46478 | + | 2.82843i | 0.172489 | + | 0.109272i | ||||
\(671\) | −11.0962 | −0.428365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.9568i | 1.96424i | 0.188256 | + | 0.982120i | \(0.439717\pi\) | ||||
−0.188256 | + | 0.982120i | \(0.560283\pi\) | |||||||
\(674\) | 24.2304 | 0.933319 | ||||||||
\(675\) | −4.52072 | + | 2.13613i | −0.174003 | + | 0.0822197i | ||||
\(676\) | −12.8106 | −0.492717 | ||||||||
\(677\) | − | 5.23992i | − | 0.201387i | −0.994918 | − | 0.100693i | \(-0.967894\pi\) | ||
0.994918 | − | 0.100693i | \(-0.0321061\pi\) | |||||||
\(678\) | − | 10.4132i | − | 0.399915i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.28676 | + | 3.34915i | 0.202738 | + | 0.128434i | ||||
\(681\) | −8.34227 | −0.319676 | ||||||||
\(682\) | 4.87478i | 0.186665i | ||||||||
\(683\) | − | 32.2648i | − | 1.23458i | −0.786736 | − | 0.617289i | \(-0.788231\pi\) | ||
0.786736 | − | 0.617289i | \(-0.211769\pi\) | |||||||
\(684\) | −7.34271 | −0.280755 | ||||||||
\(685\) | 4.41062 | − | 6.96233i | 0.168521 | − | 0.266017i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.6901i | 0.713071i | ||||||||
\(688\) | 9.97862i | 0.380431i | ||||||||
\(689\) | −0.286026 | −0.0108967 | ||||||||
\(690\) | 4.00000 | − | 6.31415i | 0.152277 | − | 0.240375i | ||||
\(691\) | −20.4470 | −0.777840 | −0.388920 | − | 0.921272i | \(-0.627152\pi\) | ||||
−0.388920 | + | 0.921272i | \(0.627152\pi\) | |||||||
\(692\) | 7.12057i | 0.270684i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.4252 | −1.15492 | ||||||||
\(695\) | 15.4019 | + | 9.75710i | 0.584229 | + | 0.370108i | ||||
\(696\) | 3.74825 | 0.142077 | ||||||||
\(697\) | − | 13.8525i | − | 0.524702i | ||||||
\(698\) | − | 30.2623i | − | 1.14544i | ||||||
\(699\) | −20.0829 | −0.759605 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.4969 | −0.585311 | −0.292655 | − | 0.956218i | \(-0.594539\pi\) | ||||
−0.292655 | + | 0.956218i | \(0.594539\pi\) | |||||||
\(702\) | 0.435157i | 0.0164240i | ||||||||
\(703\) | − | 34.0401i | − | 1.28385i | ||||||
\(704\) | −0.979056 | −0.0368996 | ||||||||
\(705\) | −8.32176 | − | 5.27182i | −0.313416 | − | 0.198548i | ||||
\(706\) | 4.37189 | 0.164538 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 8.27226i | − | 0.310891i | ||||||
\(709\) | −38.9212 | −1.46172 | −0.730859 | − | 0.682529i | \(-0.760880\pi\) | ||||
−0.730859 | + | 0.682529i | \(0.760880\pi\) | |||||||
\(710\) | −16.8868 | + | 26.6564i | −0.633750 | + | 1.00040i | ||||
\(711\) | −2.88767 | −0.108296 | ||||||||
\(712\) | 10.1210i | 0.379301i | ||||||||
\(713\) | 16.6435i | 0.623305i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.509819 | + | 0.804767i | −0.0190661 | + | 0.0300966i | ||||
\(716\) | 3.26420 | 0.121989 | ||||||||
\(717\) | − | 22.2714i | − | 0.831740i | ||||||
\(718\) | 15.6850i | 0.585358i | ||||||||
\(719\) | −3.53119 | −0.131691 | −0.0658456 | − | 0.997830i | \(-0.520974\pi\) | ||||
−0.0658456 | + | 0.997830i | \(0.520974\pi\) | |||||||
\(720\) | 1.88893 | + | 1.19663i | 0.0703963 | + | 0.0445959i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 34.9153i | 1.29941i | ||||||||
\(723\) | 6.20075i | 0.230608i | ||||||||
\(724\) | −1.93823 | −0.0720337 | ||||||||
\(725\) | −8.00674 | − | 16.9448i | −0.297363 | − | 0.629314i | ||||
\(726\) | −10.0414 | −0.372673 | ||||||||
\(727\) | − | 45.2934i | − | 1.67984i | −0.542712 | − | 0.839919i | \(-0.682602\pi\) | ||
0.542712 | − | 0.839919i | \(-0.317398\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 29.0760 | + | 18.4196i | 1.07615 | + | 0.681740i | ||||
\(731\) | 27.9282 | 1.03296 | ||||||||
\(732\) | − | 11.3336i | − | 0.418902i | ||||||
\(733\) | 48.5462i | 1.79309i | 0.442949 | + | 0.896547i | \(0.353932\pi\) | ||||
−0.442949 | + | 0.896547i | \(0.646068\pi\) | |||||||
\(734\) | 4.94478 | 0.182515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.34271 | −0.123214 | ||||||||
\(737\) | 2.31415i | 0.0852427i | ||||||||
\(738\) | − | 4.94944i | − | 0.182191i | ||||||
\(739\) | −25.7969 | −0.948953 | −0.474477 | − | 0.880268i | \(-0.657363\pi\) | ||||
−0.474477 | + | 0.880268i | \(0.657363\pi\) | |||||||
\(740\) | −5.54749 | + | 8.75692i | −0.203930 | + | 0.321911i | ||||
\(741\) | 3.19523 | 0.117380 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.7192i | 1.05361i | 0.849987 | + | 0.526803i | \(0.176610\pi\) | ||||
−0.849987 | + | 0.526803i | \(0.823390\pi\) | |||||||
\(744\) | −4.97906 | −0.182541 | ||||||||
\(745\) | −29.6135 | − | 18.7601i | −1.08495 | − | 0.687316i | ||||
\(746\) | −6.02138 | −0.220458 | ||||||||
\(747\) | 14.3842i | 0.526289i | ||||||||
\(748\) | 2.74019i | 0.100191i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.37465 | − | 11.0955i | 0.0501952 | − | 0.405151i | ||||
\(751\) | −34.1876 | −1.24752 | −0.623762 | − | 0.781615i | \(-0.714396\pi\) | ||||
−0.623762 | + | 0.781615i | \(0.714396\pi\) | |||||||
\(752\) | 4.40554i | 0.160653i | ||||||||
\(753\) | 27.6560i | 1.00784i | ||||||||
\(754\) | −1.63108 | −0.0594003 | ||||||||
\(755\) | −8.07001 | − | 5.11233i | −0.293698 | − | 0.186057i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 41.4622i | − | 1.50697i | −0.657465 | − | 0.753485i | \(-0.728371\pi\) | ||
0.657465 | − | 0.753485i | \(-0.271629\pi\) | |||||||
\(758\) | 36.8030i | 1.33675i | ||||||||
\(759\) | 3.27270 | 0.118791 | ||||||||
\(760\) | 8.78654 | − | 13.8699i | 0.318721 | − | 0.503113i | ||||
\(761\) | −27.6941 | −1.00391 | −0.501955 | − | 0.864894i | \(-0.667386\pi\) | ||||
−0.501955 | + | 0.864894i | \(0.667386\pi\) | |||||||
\(762\) | − | 11.6987i | − | 0.423801i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.07001 | −0.291963 | ||||||||
\(765\) | 3.34915 | − | 5.28676i | 0.121089 | − | 0.191143i | ||||
\(766\) | 9.03383 | 0.326406 | ||||||||
\(767\) | 3.59973i | 0.129979i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 9.74001 | 0.351234 | 0.175617 | − | 0.984459i | \(-0.443808\pi\) | ||||
0.175617 | + | 0.984459i | \(0.443808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.7681 | −0.423819 | ||||||||
\(772\) | 1.95811i | 0.0704740i | ||||||||
\(773\) | 30.6171i | 1.10122i | 0.834763 | + | 0.550610i | \(0.185605\pi\) | ||||
−0.834763 | + | 0.550610i | \(0.814395\pi\) | |||||||
\(774\) | 9.97862 | 0.358674 | ||||||||
\(775\) | 10.6359 | + | 22.5089i | 0.382053 | + | 0.808545i | ||||
\(776\) | 10.6655 | 0.382870 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 33.5646i | − | 1.20335i | ||||||
\(779\) | −36.3423 | −1.30210 | ||||||||
\(780\) | −0.821983 | − | 0.520724i | −0.0294317 | − | 0.0186449i | ||||
\(781\) | −13.8163 | −0.494388 | ||||||||
\(782\) | 9.35560i | 0.334555i | ||||||||
\(783\) | − | 3.74825i | − | 0.133951i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.2485 | − | 28.8059i | 0.651316 | − | 1.02813i | ||||
\(786\) | 5.38459 | 0.192062 | ||||||||
\(787\) | − | 15.7977i | − | 0.563129i | −0.959542 | − | 0.281564i | \(-0.909147\pi\) | ||
0.959542 | − | 0.281564i | \(-0.0908533\pi\) | |||||||
\(788\) | 17.3418i | 0.617777i | ||||||||
\(789\) | 0.455042 | 0.0161999 | ||||||||
\(790\) | 3.45548 | − | 5.45460i | 0.122940 | − | 0.194066i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.979056i | 0.0347892i | ||||||||
\(793\) | 4.93190i | 0.175137i | ||||||||
\(794\) | 33.9792 | 1.20588 | ||||||||
\(795\) | 1.24158 | + | 0.786540i | 0.0440344 | + | 0.0278957i | ||||
\(796\) | 2.59490 | 0.0919738 | ||||||||
\(797\) | − | 47.6651i | − | 1.68838i | −0.536041 | − | 0.844192i | \(-0.680081\pi\) | ||
0.536041 | − | 0.844192i | \(-0.319919\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.3303 | 0.436213 | ||||||||
\(800\) | −4.52072 | + | 2.13613i | −0.159832 | + | 0.0755236i | ||||
\(801\) | 10.1210 | 0.357608 | ||||||||
\(802\) | − | 4.27226i | − | 0.150859i | ||||||
\(803\) | 15.0704i | 0.531825i | ||||||||
\(804\) | −2.36365 | −0.0833595 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.16667 | 0.0763178 | ||||||||
\(807\) | 26.1375i | 0.920083i | ||||||||
\(808\) | − | 14.0328i | − | 0.493671i | ||||||
\(809\) | 17.2709 | 0.607214 | 0.303607 | − | 0.952797i | \(-0.401809\pi\) | ||||
0.303607 | + | 0.952797i | \(0.401809\pi\) | |||||||
\(810\) | 1.19663 | − | 1.88893i | 0.0420455 | − | 0.0663703i | ||||
\(811\) | 14.7901 | 0.519351 | 0.259676 | − | 0.965696i | \(-0.416384\pi\) | ||||
0.259676 | + | 0.965696i | \(0.416384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.7768i | − | 0.588388i | ||||||
\(814\) | −4.53882 | −0.159085 | ||||||||
\(815\) | 8.94603 | − | 14.1216i | 0.313366 | − | 0.494659i | ||||
\(816\) | −2.79881 | −0.0979779 | ||||||||
\(817\) | − | 73.2701i | − | 2.56340i | ||||||
\(818\) | − | 3.63888i | − | 0.127231i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.34915 | + | 5.92267i | 0.326487 | + | 0.206829i | ||||
\(821\) | −45.6917 | −1.59465 | −0.797326 | − | 0.603549i | \(-0.793753\pi\) | ||||
−0.797326 | + | 0.603549i | \(0.793753\pi\) | |||||||
\(822\) | 3.68585i | 0.128559i | ||||||||
\(823\) | 4.99386i | 0.174075i | 0.996205 | + | 0.0870375i | \(0.0277400\pi\) | ||||
−0.996205 | + | 0.0870375i | \(0.972260\pi\) | |||||||
\(824\) | 10.3842 | 0.361749 | ||||||||
\(825\) | 4.42604 | − | 2.09139i | 0.154095 | − | 0.0728129i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.5946i | 1.86367i | 0.362885 | + | 0.931834i | \(0.381792\pi\) | ||||
−0.362885 | + | 0.931834i | \(0.618208\pi\) | |||||||
\(828\) | 3.34271i | 0.116167i | ||||||||
\(829\) | −1.16692 | −0.0405288 | −0.0202644 | − | 0.999795i | \(-0.506451\pi\) | ||||
−0.0202644 | + | 0.999795i | \(0.506451\pi\) | |||||||
\(830\) | −27.1707 | − | 17.2126i | −0.943109 | − | 0.597457i | ||||
\(831\) | −20.7478 | −0.719733 | ||||||||
\(832\) | 0.435157i | 0.0150864i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.15378 | −0.282342 | ||||||||
\(835\) | −15.1542 | + | 23.9215i | −0.524433 | + | 0.827838i | ||||
\(836\) | 7.18892 | 0.248634 | ||||||||
\(837\) | 4.97906i | 0.172101i | ||||||||
\(838\) | 26.6274i | 0.919829i | ||||||||
\(839\) | 31.2709 | 1.07959 | 0.539796 | − | 0.841796i | \(-0.318501\pi\) | ||||
0.539796 | + | 0.841796i | \(0.318501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.9507 | −0.515540 | ||||||||
\(842\) | − | 15.1880i | − | 0.523415i | ||||||
\(843\) | 18.3141i | 0.630773i | ||||||||
\(844\) | −15.4127 | −0.530528 | ||||||||
\(845\) | −24.1984 | − | 15.3297i | −0.832451 | − | 0.527356i | ||||
\(846\) | 4.40554 | 0.151466 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 0.657293i | − | 0.0225715i | ||||||
\(849\) | 11.8525 | 0.406778 | ||||||||
\(850\) | 5.97862 | + | 12.6526i | 0.205065 | + | 0.433982i | ||||
\(851\) | −15.4965 | −0.531213 | ||||||||
\(852\) | − | 14.1119i | − | 0.483466i | ||||||
\(853\) | − | 11.3154i | − | 0.387431i | −0.981058 | − | 0.193715i | \(-0.937946\pi\) | ||
0.981058 | − | 0.193715i | \(-0.0620538\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.8699 | − | 8.78654i | −0.474340 | − | 0.300493i | ||||
\(856\) | 20.0410 | 0.684988 | ||||||||
\(857\) | − | 36.8572i | − | 1.25902i | −0.776994 | − | 0.629508i | \(-0.783256\pi\) | ||
0.776994 | − | 0.629508i | \(-0.216744\pi\) | |||||||
\(858\) | − | 0.426043i | − | 0.0145449i | ||||||
\(859\) | −18.6974 | −0.637948 | −0.318974 | − | 0.947763i | \(-0.603338\pi\) | ||||
−0.318974 | + | 0.947763i | \(0.603338\pi\) | |||||||
\(860\) | −11.9408 | + | 18.8489i | −0.407177 | + | 0.642743i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 4.23125i | − | 0.144117i | ||||||
\(863\) | − | 29.5384i | − | 1.00550i | −0.864432 | − | 0.502749i | \(-0.832322\pi\) | ||
0.864432 | − | 0.502749i | \(-0.167678\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −8.52072 | + | 13.4503i | −0.289713 | + | 0.457323i | ||||
\(866\) | −33.9352 | −1.15317 | ||||||||
\(867\) | − | 9.16667i | − | 0.311317i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.82719 | 0.0959057 | ||||||||
\(870\) | 7.08018 | + | 4.48528i | 0.240041 | + | 0.152065i | ||||
\(871\) | 1.02856 | 0.0348514 | ||||||||
\(872\) | 18.6564i | 0.631786i | ||||||||
\(873\) | − | 10.6655i | − | 0.360973i | ||||||
\(874\) | 24.5445 | 0.830231 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.3928 | −0.520076 | ||||||||
\(877\) | − | 14.2581i | − | 0.481461i | −0.970592 | − | 0.240730i | \(-0.922613\pi\) | ||
0.970592 | − | 0.240730i | \(-0.0773869\pi\) | |||||||
\(878\) | − | 5.48257i | − | 0.185028i | ||||||
\(879\) | 14.4770 | 0.488299 | ||||||||
\(880\) | −1.84937 | − | 1.17157i | −0.0623423 | − | 0.0394937i | ||||
\(881\) | 31.2744 | 1.05366 | 0.526830 | − | 0.849971i | \(-0.323380\pi\) | ||||
0.526830 | + | 0.849971i | \(0.323380\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.3566i | − | 1.12254i | −0.827633 | − | 0.561270i | \(-0.810313\pi\) | ||
0.827633 | − | 0.561270i | \(-0.189687\pi\) | |||||||
\(884\) | 1.21792 | 0.0409631 | ||||||||
\(885\) | 9.89887 | − | 15.6257i | 0.332747 | − | 0.525253i | ||||
\(886\) | 1.23081 | 0.0413499 | ||||||||
\(887\) | 42.1444i | 1.41507i | 0.706678 | + | 0.707535i | \(0.250193\pi\) | ||||
−0.706678 | + | 0.707535i | \(0.749807\pi\) | |||||||
\(888\) | − | 4.63591i | − | 0.155571i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.1112 | + | 19.1179i | −0.405967 | + | 0.640834i | ||||
\(891\) | 0.979056 | 0.0327996 | ||||||||
\(892\) | 7.61497i | 0.254968i | ||||||||
\(893\) | − | 32.3486i | − | 1.08250i | ||||||
\(894\) | 15.6774 | 0.524329 | ||||||||
\(895\) | 6.16586 | + | 3.90606i | 0.206102 | + | 0.130565i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.45460i | − | 0.0485678i | ||||||
\(898\) | − | 14.6435i | − | 0.488661i | ||||||
\(899\) | −18.6627 | −0.622437 | ||||||||
\(900\) | 2.13613 | + | 4.52072i | 0.0712043 | + | 0.150691i | ||||
\(901\) | −1.83964 | −0.0612872 | ||||||||
\(902\) | 4.84578i | 0.161347i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.4132 | −0.346336 | ||||||||
\(905\) | −3.66118 | − | 2.31935i | −0.121702 | − | 0.0770978i | ||||
\(906\) | 4.27226 | 0.141936 | ||||||||
\(907\) | 55.9840i | 1.85892i | 0.368923 | + | 0.929460i | \(0.379727\pi\) | ||||
−0.368923 | + | 0.929460i | \(0.620273\pi\) | |||||||
\(908\) | 8.34227i | 0.276848i | ||||||||
\(909\) | −14.0328 | −0.465438 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4389 | 1.00849 | 0.504243 | − | 0.863562i | \(-0.331771\pi\) | ||||
0.504243 | + | 0.863562i | \(0.331771\pi\) | |||||||
\(912\) | 7.34271i | 0.243141i | ||||||||
\(913\) | − | 14.0829i | − | 0.466076i | ||||||
\(914\) | 31.3289 | 1.03627 | ||||||||
\(915\) | 13.5622 | − | 21.4084i | 0.448352 | − | 0.707740i | ||||
\(916\) | 18.6901 | 0.617537 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.79881i | 0.0923744i | ||||||||
\(919\) | 28.1538 | 0.928708 | 0.464354 | − | 0.885650i | \(-0.346287\pi\) | ||||
0.464354 | + | 0.885650i | \(0.346287\pi\) | |||||||
\(920\) | −6.31415 | − | 4.00000i | −0.208171 | − | 0.131876i | ||||
\(921\) | 30.4252 | 1.00254 | ||||||||
\(922\) | − | 12.7667i | − | 0.420447i | ||||||
\(923\) | 6.14089i | 0.202130i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.9577 | + | 9.90291i | −0.689084 | + | 0.325606i | ||||
\(926\) | −26.7112 | −0.877784 | ||||||||
\(927\) | − | 10.3842i | − | 0.341060i | ||||||
\(928\) | − | 3.74825i | − | 0.123042i | ||||||
\(929\) | 25.8955 | 0.849603 | 0.424801 | − | 0.905287i | \(-0.360344\pi\) | ||||
0.424801 | + | 0.905287i | \(0.360344\pi\) | |||||||
\(930\) | −9.40510 | − | 5.95811i | −0.308405 | − | 0.195374i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.0829i | 0.657837i | ||||||||
\(933\) | 9.02856i | 0.295582i | ||||||||
\(934\) | −37.6141 | −1.23077 | ||||||||
\(935\) | −3.27901 | + | 5.17603i | −0.107235 | + | 0.169274i | ||||
\(936\) | 0.435157 | 0.0142236 | ||||||||
\(937\) | 48.1184i | 1.57196i | 0.618253 | + | 0.785979i | \(0.287841\pi\) | ||||
−0.618253 | + | 0.785979i | \(0.712159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.1732 | −0.560427 | ||||||||
\(940\) | −5.27182 | + | 8.32176i | −0.171948 | + | 0.271426i | ||||
\(941\) | 52.2066 | 1.70189 | 0.850944 | − | 0.525257i | \(-0.176031\pi\) | ||||
0.850944 | + | 0.525257i | \(0.176031\pi\) | |||||||
\(942\) | 15.2498i | 0.496866i | ||||||||
\(943\) | 16.5445i | 0.538764i | ||||||||
\(944\) | −8.27226 | −0.269239 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.76963 | −0.317638 | ||||||||
\(947\) | − | 20.2995i | − | 0.659645i | −0.944043 | − | 0.329823i | \(-0.893011\pi\) | ||
0.944043 | − | 0.329823i | \(-0.106989\pi\) | |||||||
\(948\) | 2.88767i | 0.0937870i | ||||||||
\(949\) | 6.69830 | 0.217436 | ||||||||
\(950\) | 33.1944 | − | 15.6850i | 1.07697 | − | 0.508888i | ||||
\(951\) | 2.61541 | 0.0848103 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.9511i | 0.549100i | 0.961573 | + | 0.274550i | \(0.0885289\pi\) | ||||
−0.961573 | + | 0.274550i | \(0.911471\pi\) | |||||||
\(954\) | −0.657293 | −0.0212806 | ||||||||
\(955\) | −15.2437 | − | 9.65685i | −0.493275 | − | 0.312488i | ||||
\(956\) | −22.2714 | −0.720308 | ||||||||
\(957\) | 3.66974i | 0.118626i | ||||||||
\(958\) | − | 23.8235i | − | 0.769703i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.19663 | − | 1.88893i | 0.0386212 | − | 0.0609650i | ||||
\(961\) | −6.20900 | −0.200290 | ||||||||
\(962\) | 2.01735i | 0.0650420i | ||||||||
\(963\) | − | 20.0410i | − | 0.645813i | ||||||
\(964\) | 6.20075 | 0.199713 | ||||||||
\(965\) | −2.34315 | + | 3.69874i | −0.0754285 | + | 0.119067i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.0294i | − | 0.740577i | −0.928917 | − | 0.370288i | \(-0.879259\pi\) | ||
0.928917 | − | 0.370288i | \(-0.120741\pi\) | |||||||
\(968\) | 10.0414i | 0.322744i | ||||||||
\(969\) | 20.5508 | 0.660188 | ||||||||
\(970\) | 20.1465 | + | 12.7627i | 0.646864 | + | 0.409787i | ||||
\(971\) | 12.3770 | 0.397196 | 0.198598 | − | 0.980081i | \(-0.436361\pi\) | ||||
0.198598 | + | 0.980081i | \(0.436361\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.75674 | 0.120374 | ||||||||
\(975\) | −0.929553 | − | 1.96723i | −0.0297695 | − | 0.0630017i | ||||
\(976\) | −11.3336 | −0.362779 | ||||||||
\(977\) | − | 1.00614i | − | 0.0321893i | −0.999870 | − | 0.0160946i | \(-0.994877\pi\) | ||
0.999870 | − | 0.0160946i | \(-0.00512331\pi\) | |||||||
\(978\) | 7.47599i | 0.239056i | ||||||||
\(979\) | −9.90904 | −0.316694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.6564 | 0.595654 | ||||||||
\(982\) | 2.00762i | 0.0640656i | ||||||||
\(983\) | 42.1444i | 1.34420i | 0.740461 | + | 0.672099i | \(0.234607\pi\) | ||||
−0.740461 | + | 0.672099i | \(0.765393\pi\) | |||||||
\(984\) | −4.94944 | −0.157782 | ||||||||
\(985\) | −20.7518 | + | 32.7575i | −0.661209 | + | 1.04374i | ||||
\(986\) | −10.4906 | −0.334089 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 3.19523i | − | 0.101654i | ||||||
\(989\) | −33.3556 | −1.06065 | ||||||||
\(990\) | −1.17157 | + | 1.84937i | −0.0372350 | + | 0.0587769i | ||||
\(991\) | −34.0691 | −1.08224 | −0.541121 | − | 0.840945i | \(-0.682000\pi\) | ||||
−0.541121 | + | 0.840945i | \(0.682000\pi\) | |||||||
\(992\) | 4.97906i | 0.158085i | ||||||||
\(993\) | 17.7559i | 0.563465i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.90159 | + | 3.10515i | 0.155391 | + | 0.0984398i | ||||
\(996\) | 14.3842 | 0.455779 | ||||||||
\(997\) | − | 6.02076i | − | 0.190679i | −0.995445 | − | 0.0953397i | \(-0.969606\pi\) | ||
0.995445 | − | 0.0953397i | \(-0.0303937\pi\) | |||||||
\(998\) | 0.628294i | 0.0198883i | ||||||||
\(999\) | −4.63591 | −0.146674 |
(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 | 1470.2.g.k.589.5 | yes | 8 | |
5.2 | odd | 4 | 7350.2.a.dr.1.3 | 4 | |||
5.3 | odd | 4 | 7350.2.a.du.1.3 | 4 | |||
5.4 | even | 2 | inner | 1470.2.g.k.589.1 | yes | 8 | |
7.2 | even | 3 | 1470.2.n.k.949.7 | 16 | |||
7.3 | odd | 6 | 1470.2.n.l.79.1 | 16 | |||
7.4 | even | 3 | 1470.2.n.k.79.4 | 16 | |||
7.5 | odd | 6 | 1470.2.n.l.949.6 | 16 | |||
7.6 | odd | 2 | 1470.2.g.j.589.8 | yes | 8 | ||
35.4 | even | 6 | 1470.2.n.k.79.7 | 16 | |||
35.9 | even | 6 | 1470.2.n.k.949.4 | 16 | |||
35.13 | even | 4 | 7350.2.a.dt.1.3 | 4 | |||
35.19 | odd | 6 | 1470.2.n.l.949.1 | 16 | |||
35.24 | odd | 6 | 1470.2.n.l.79.6 | 16 | |||
35.27 | even | 4 | 7350.2.a.ds.1.3 | 4 | |||
35.34 | odd | 2 | 1470.2.g.j.589.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.g.j.589.4 | ✓ | 8 | 35.34 | odd | 2 | ||
1470.2.g.j.589.8 | yes | 8 | 7.6 | odd | 2 | ||
1470.2.g.k.589.1 | yes | 8 | 5.4 | even | 2 | inner | |
1470.2.g.k.589.5 | yes | 8 | 1.1 | even | 1 | trivial | |
1470.2.n.k.79.4 | 16 | 7.4 | even | 3 | |||
1470.2.n.k.79.7 | 16 | 35.4 | even | 6 | |||
1470.2.n.k.949.4 | 16 | 35.9 | even | 6 | |||
1470.2.n.k.949.7 | 16 | 7.2 | even | 3 | |||
1470.2.n.l.79.1 | 16 | 7.3 | odd | 6 | |||
1470.2.n.l.79.6 | 16 | 35.24 | odd | 6 | |||
1470.2.n.l.949.1 | 16 | 35.19 | odd | 6 | |||
1470.2.n.l.949.6 | 16 | 7.5 | odd | 6 | |||
7350.2.a.dr.1.3 | 4 | 5.2 | odd | 4 | |||
7350.2.a.ds.1.3 | 4 | 35.27 | even | 4 | |||
7350.2.a.dt.1.3 | 4 | 35.13 | even | 4 | |||
7350.2.a.du.1.3 | 4 | 5.3 | odd | 4 |