Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1009,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.r (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2017.2 | ||
Root | \(0.500000 - 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2017 |
Dual form | 3024.2.r.g.1009.2 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.29679 | − | 2.24611i | −0.579942 | − | 1.00449i | −0.995485 | − | 0.0949156i | \(-0.969742\pi\) |
0.415543 | − | 0.909573i | \(-0.363591\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.25729 | + | 3.90975i | −0.680600 | + | 1.17883i | 0.294198 | + | 0.955744i | \(0.404947\pi\) |
−0.974798 | + | 0.223089i | \(0.928386\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.945916 | 0.229418 | 0.114709 | − | 0.993399i | \(-0.463406\pi\) | ||||
0.114709 | + | 0.993399i | \(0.463406\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.05408 | 0.930071 | 0.465035 | − | 0.885292i | \(-0.346042\pi\) | ||||
0.465035 | + | 0.885292i | \(0.346042\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.136673 | + | 0.236725i | 0.0284983 | + | 0.0493605i | 0.879923 | − | 0.475117i | \(-0.157594\pi\) |
−0.851425 | + | 0.524477i | \(0.824261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.863327 | + | 1.49533i | −0.172665 | + | 0.299065i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.23025 | − | 2.13086i | 0.228452 | − | 0.395691i | −0.728897 | − | 0.684623i | \(-0.759967\pi\) |
0.957350 | + | 0.288932i | \(0.0933002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.16372 | + | 2.01561i | 0.209009 | + | 0.362015i | 0.951403 | − | 0.307949i | \(-0.0996427\pi\) |
−0.742393 | + | 0.669964i | \(0.766309\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.59358 | 0.438395 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.78074 | 0.292752 | 0.146376 | − | 0.989229i | \(-0.453239\pi\) | ||||
0.146376 | + | 0.989229i | \(0.453239\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.20321 | − | 5.54812i | −0.500257 | − | 0.866471i | −1.00000 | 0.000297253i | \(-0.999905\pi\) | |
0.499743 | − | 0.866174i | \(-0.333428\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.21780 | + | 9.03749i | −0.795707 | + | 1.37820i | 0.126682 | + | 0.991943i | \(0.459567\pi\) |
−0.922389 | + | 0.386262i | \(0.873766\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.08113 | − | 10.5328i | 0.887023 | − | 1.53637i | 0.0436467 | − | 0.999047i | \(-0.486102\pi\) |
0.843377 | − | 0.537323i | \(-0.180564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.27335 | 0.861710 | 0.430855 | − | 0.902421i | \(-0.358212\pi\) | ||||
0.430855 | + | 0.902421i | \(0.358212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.7089 | 1.57883 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.36333 | + | 2.36135i | 0.177490 | + | 0.307422i | 0.941020 | − | 0.338350i | \(-0.109869\pi\) |
−0.763530 | + | 0.645772i | \(0.776536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.13667 | − | 1.96878i | 0.145536 | − | 0.252076i | −0.784037 | − | 0.620714i | \(-0.786843\pi\) |
0.929573 | + | 0.368639i | \(0.120176\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.29679 | + | 2.24611i | −0.160847 | + | 0.278595i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.90856 | − | 13.6980i | −0.966184 | − | 1.67348i | −0.706400 | − | 0.707813i | \(-0.749682\pi\) |
−0.259784 | − | 0.965667i | \(-0.583651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.27335 | 0.388475 | 0.194237 | − | 0.980955i | \(-0.437777\pi\) | ||||
0.194237 | + | 0.980955i | \(0.437777\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.50739 | −0.176427 | −0.0882134 | − | 0.996102i | \(-0.528116\pi\) | ||||
−0.0882134 | + | 0.996102i | \(0.528116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.25729 | − | 3.90975i | −0.257243 | − | 0.445557i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.35447 | − | 12.7383i | 0.827443 | − | 1.43317i | −0.0725952 | − | 0.997361i | \(-0.523128\pi\) |
0.900038 | − | 0.435811i | \(-0.143539\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.472958 | − | 0.819187i | 0.0519139 | − | 0.0899175i | −0.838901 | − | 0.544285i | \(-0.816801\pi\) |
0.890815 | + | 0.454367i | \(0.150135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.22665 | − | 2.12463i | −0.133049 | − | 0.230448i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.3566 | 1.52180 | 0.760899 | − | 0.648871i | \(-0.224758\pi\) | ||||
0.760899 | + | 0.648871i | \(0.224758\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.25729 | − | 9.10590i | −0.539387 | − | 0.934246i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.74484 | − | 9.95036i | 0.583300 | − | 1.01031i | −0.411785 | − | 0.911281i | \(-0.635094\pi\) |
0.995085 | − | 0.0990246i | \(-0.0315722\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.83988 | + | 3.18677i | −0.183075 | + | 0.317096i | −0.942926 | − | 0.333002i | \(-0.891939\pi\) |
0.759851 | + | 0.650097i | \(0.225272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.86333 | − | 8.42353i | −0.479198 | − | 0.829995i | 0.520518 | − | 0.853851i | \(-0.325739\pi\) |
−0.999715 | + | 0.0238560i | \(0.992406\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.37432 | −0.132860 | −0.0664301 | − | 0.997791i | \(-0.521161\pi\) | ||||
−0.0664301 | + | 0.997791i | \(0.521161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.39922 | −0.325587 | −0.162793 | − | 0.986660i | \(-0.552050\pi\) | ||||
−0.162793 | + | 0.986660i | \(0.552050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.19436 | + | 8.99689i | 0.488644 | + | 0.846356i | 0.999915 | − | 0.0130636i | \(-0.00415840\pi\) |
−0.511271 | + | 0.859420i | \(0.670825\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.354473 | − | 0.613964i | 0.0330547 | − | 0.0572525i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.472958 | + | 0.819187i | −0.0433560 | + | 0.0750948i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.69076 | − | 8.12463i | −0.426432 | − | 0.738603i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.48968 | −0.759340 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.672570 | −0.0596809 | −0.0298405 | − | 0.999555i | \(-0.509500\pi\) | ||||
−0.0298405 | + | 0.999555i | \(0.509500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.95691 | − | 6.85356i | −0.345717 | − | 0.598799i | 0.639767 | − | 0.768569i | \(-0.279031\pi\) |
−0.985484 | + | 0.169770i | \(0.945697\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.02704 | + | 3.51094i | −0.175767 | + | 0.304437i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.83628 | + | 3.18054i | −0.156884 | + | 0.271732i | −0.933744 | − | 0.357943i | \(-0.883478\pi\) |
0.776859 | + | 0.629674i | \(0.216812\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.02704 | − | 1.77889i | −0.0871126 | − | 0.150883i | 0.819177 | − | 0.573541i | \(-0.194431\pi\) |
−0.906289 | + | 0.422658i | \(0.861097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.51459 | 0.377529 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.38151 | −0.529956 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.77188 | − | 11.7292i | −0.554774 | − | 0.960897i | −0.997921 | − | 0.0644482i | \(-0.979471\pi\) |
0.443147 | − | 0.896449i | \(-0.353862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.96410 | − | 8.59808i | 0.403973 | − | 0.699702i | −0.590228 | − | 0.807236i | \(-0.700962\pi\) |
0.994201 | + | 0.107535i | \(0.0342956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.01819 | − | 5.22765i | 0.242427 | − | 0.419895i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.02704 | − | 5.24299i | −0.241584 | − | 0.418436i | 0.719581 | − | 0.694408i | \(-0.244334\pi\) |
−0.961166 | + | 0.275972i | \(0.911000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.273346 | −0.0215427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.8171 | −1.39554 | −0.697772 | − | 0.716320i | \(-0.745825\pi\) | ||||
−0.697772 | + | 0.716320i | \(0.745825\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.23385 | + | 7.33325i | 0.327625 | + | 0.567464i | 0.982040 | − | 0.188672i | \(-0.0604183\pi\) |
−0.654415 | + | 0.756136i | \(0.727085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.67830 | − | 15.0313i | 0.659799 | − | 1.14281i | −0.320868 | − | 0.947124i | \(-0.603975\pi\) |
0.980667 | − | 0.195682i | \(-0.0626920\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.863327 | − | 1.49533i | −0.0652614 | − | 0.113036i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.3494 | −0.848295 | −0.424147 | − | 0.905593i | \(-0.639426\pi\) | ||||
−0.424147 | + | 0.905593i | \(0.639426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.8889 | 1.62699 | 0.813495 | − | 0.581572i | \(-0.197562\pi\) | ||||
0.813495 | + | 0.581572i | \(0.197562\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.30924 | − | 3.99973i | −0.169779 | − | 0.294066i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.13521 | + | 3.69829i | −0.156142 | + | 0.270446i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.350874 | − | 0.607731i | 0.0253883 | − | 0.0439739i | −0.853052 | − | 0.521826i | \(-0.825251\pi\) |
0.878440 | + | 0.477852i | \(0.158584\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.07227 | − | 10.5175i | −0.437092 | − | 0.757065i | 0.560372 | − | 0.828241i | \(-0.310658\pi\) |
−0.997464 | + | 0.0711760i | \(0.977325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.4107 | 1.16921 | 0.584607 | − | 0.811317i | \(-0.301249\pi\) | ||||
0.584607 | + | 0.811317i | \(0.301249\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7060 | −1.60959 | −0.804794 | − | 0.593555i | \(-0.797724\pi\) | ||||
−0.804794 | + | 0.593555i | \(0.797724\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.23025 | + | 2.13086i | 0.0863468 | + | 0.149557i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.30778 | + | 14.3895i | −0.580241 | + | 1.00501i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.15126 | + | 15.8505i | −0.633006 | + | 1.09640i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.28074 | + | 3.95035i | 0.157012 | + | 0.271954i | 0.933790 | − | 0.357822i | \(-0.116480\pi\) |
−0.776778 | + | 0.629775i | \(0.783147\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.0656 | 1.84586 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.32743 | −0.157996 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.472958 | − | 0.819187i | −0.0318146 | − | 0.0551045i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.66225 | − | 11.5394i | 0.446137 | − | 0.772733i | −0.551993 | − | 0.833849i | \(-0.686133\pi\) |
0.998131 | + | 0.0611159i | \(0.0194659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.690757 | + | 1.19643i | −0.0458472 | + | 0.0794096i | −0.888038 | − | 0.459769i | \(-0.847932\pi\) |
0.842191 | + | 0.539179i | \(0.181265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.98968 | + | 15.5706i | 0.594055 | + | 1.02893i | 0.993679 | + | 0.112254i | \(0.0358072\pi\) |
−0.399625 | + | 0.916679i | \(0.630859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9823 | 1.24357 | 0.621786 | − | 0.783187i | \(-0.286408\pi\) | ||||
0.621786 | + | 0.783187i | \(0.286408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.5438 | −2.05769 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.44592 | − | 4.23645i | −0.158213 | − | 0.274033i | 0.776011 | − | 0.630719i | \(-0.217240\pi\) |
−0.934224 | + | 0.356686i | \(0.883907\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0797 | − | 22.6546i | 0.842535 | − | 1.45931i | −0.0452094 | − | 0.998978i | \(-0.514396\pi\) |
0.887745 | − | 0.460336i | \(-0.152271\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.29679 | + | 2.24611i | −0.0828489 | + | 0.143498i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.02704 | − | 3.51094i | −0.128978 | − | 0.223396i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.4576 | 1.16503 | 0.582516 | − | 0.812819i | \(-0.302068\pi\) | ||||
0.582516 | + | 0.812819i | \(0.302068\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.23405 | −0.0775838 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.86693 | − | 10.1618i | −0.365969 | − | 0.633876i | 0.622962 | − | 0.782252i | \(-0.285929\pi\) |
−0.988931 | + | 0.148375i | \(0.952596\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.890369 | + | 1.54216i | −0.0553248 | + | 0.0958254i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.76089 | − | 6.51406i | 0.231907 | − | 0.401674i | −0.726463 | − | 0.687206i | \(-0.758837\pi\) |
0.958369 | + | 0.285532i | \(0.0921703\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.13521 | − | 14.0906i | −0.499742 | − | 0.865579i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.8348 | 1.14838 | 0.574190 | − | 0.818722i | \(-0.305317\pi\) | ||||
0.574190 | + | 0.818722i | \(0.305317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.9823 | 1.45682 | 0.728410 | − | 0.685141i | \(-0.240260\pi\) | ||||
0.728410 | + | 0.685141i | \(0.240260\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.89757 | − | 6.75078i | −0.235032 | − | 0.407088i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.58113 | + | 6.20269i | −0.215169 | + | 0.372684i | −0.953325 | − | 0.301947i | \(-0.902364\pi\) |
0.738156 | + | 0.674630i | \(0.235697\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.44085 | − | 12.8879i | 0.443884 | − | 0.768830i | −0.554090 | − | 0.832457i | \(-0.686933\pi\) |
0.997974 | + | 0.0636271i | \(0.0202668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.99854 | + | 17.3180i | 0.594351 | + | 1.02945i | 0.993638 | + | 0.112621i | \(0.0359245\pi\) |
−0.399287 | + | 0.916826i | \(0.630742\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.40642 | 0.378159 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1052 | −0.947367 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.53278 | + | 13.0472i | 0.440070 | + | 0.762223i | 0.997694 | − | 0.0678705i | \(-0.0216205\pi\) |
−0.557625 | + | 0.830093i | \(0.688287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.53590 | − | 6.12435i | 0.205868 | − | 0.356574i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.136673 | − | 0.236725i | 0.00790401 | − | 0.0136901i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.21780 | − | 9.03749i | −0.300749 | − | 0.520912i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.89610 | −0.337610 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.2704 | 1.55641 | 0.778203 | − | 0.628013i | \(-0.216132\pi\) | ||||
0.778203 | + | 0.628013i | \(0.216132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.99115 | + | 13.8411i | 0.453136 | + | 0.784855i | 0.998579 | − | 0.0532931i | \(-0.0169718\pi\) |
−0.545443 | + | 0.838148i | \(0.683638\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.79893 | + | 10.0440i | −0.327775 | + | 0.567722i | −0.982070 | − | 0.188517i | \(-0.939632\pi\) |
0.654295 | + | 0.756239i | \(0.272965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.00885 | + | 1.74739i | −0.0566629 | + | 0.0981430i | −0.892965 | − | 0.450125i | \(-0.851379\pi\) |
0.836303 | + | 0.548268i | \(0.184713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.55408 | + | 9.61996i | 0.310969 | + | 0.538614i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.83482 | 0.213375 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.72665 | 0.0957775 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.08113 | + | 10.5328i | 0.335263 | + | 0.580693i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.85447 | + | 17.0684i | −0.541651 | + | 0.938167i | 0.457159 | + | 0.889385i | \(0.348867\pi\) |
−0.998809 | + | 0.0487815i | \(0.984466\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.5115 | + | 35.5269i | −1.12066 | + | 1.94104i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5256 | + | 25.1590i | 0.791259 | + | 1.37050i | 0.925188 | + | 0.379509i | \(0.123907\pi\) |
−0.133929 | + | 0.990991i | \(0.542759\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5074 | −0.569007 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.5416 | − | 25.1868i | −0.780636 | − | 1.35210i | −0.931572 | − | 0.363557i | \(-0.881562\pi\) |
0.150936 | − | 0.988544i | \(-0.451771\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3815 | + | 21.4454i | −0.662767 | + | 1.14795i | 0.317118 | + | 0.948386i | \(0.397285\pi\) |
−0.979885 | + | 0.199561i | \(0.936049\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.6513 | + | 28.8408i | −0.886257 | + | 1.53504i | −0.0419914 | + | 0.999118i | \(0.513370\pi\) |
−0.844266 | + | 0.535925i | \(0.819963\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.24484 | − | 7.35228i | −0.225293 | − | 0.390219i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.5366 | 1.34777 | 0.673884 | − | 0.738837i | \(-0.264625\pi\) | ||||
0.673884 | + | 0.738837i | \(0.264625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.56440 | −0.134968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.95477 | + | 3.38576i | 0.102317 | + | 0.177219i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7252 | − | 23.7727i | 0.716449 | − | 1.24093i | −0.245949 | − | 0.969283i | \(-0.579100\pi\) |
0.962398 | − | 0.271644i | \(-0.0875672\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.13667 | + | 5.43288i | −0.162848 | + | 0.282061i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.16372 | − | 14.1400i | −0.422701 | − | 0.732140i | 0.573502 | − | 0.819204i | \(-0.305585\pi\) |
−0.996203 | + | 0.0870646i | \(0.972251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.46050 | −0.126722 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0364 | −0.618267 | −0.309134 | − | 0.951019i | \(-0.600039\pi\) | ||||
−0.309134 | + | 0.951019i | \(0.600039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.21780 | + | 10.7695i | 0.317715 | + | 0.550298i | 0.980011 | − | 0.198944i | \(-0.0637512\pi\) |
−0.662296 | + | 0.749242i | \(0.730418\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.85447 | + | 10.1402i | −0.298372 | + | 0.516795i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.3004 | − | 17.8408i | 0.522250 | − | 0.904564i | −0.477414 | − | 0.878678i | \(-0.658426\pi\) |
0.999665 | − | 0.0258860i | \(-0.00824070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.129281 | + | 0.223922i | 0.00653803 | + | 0.0113242i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −38.1488 | −1.91948 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.6372 | −1.18631 | −0.593157 | − | 0.805087i | \(-0.702119\pi\) | ||||
−0.593157 | + | 0.805087i | \(0.702119\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.28220 | − | 2.22084i | −0.0640300 | − | 0.110903i | 0.832233 | − | 0.554426i | \(-0.187062\pi\) |
−0.896263 | + | 0.443522i | \(0.853729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.16372 | − | 2.01561i | 0.0579688 | − | 0.100405i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.01965 | + | 6.96224i | −0.199247 | + | 0.345105i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.1623 | + | 29.7259i | 0.848619 | + | 1.46985i | 0.882441 | + | 0.470423i | \(0.155899\pi\) |
−0.0338223 | + | 0.999428i | \(0.510768\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.72665 | −0.134170 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.45331 | −0.120428 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.02850 | − | 3.51347i | −0.0990989 | − | 0.171644i | 0.812213 | − | 0.583361i | \(-0.198263\pi\) |
−0.911312 | + | 0.411717i | \(0.864929\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5344 | − | 18.2462i | 0.513417 | − | 0.889264i | −0.486462 | − | 0.873702i | \(-0.661713\pi\) |
0.999879 | − | 0.0155624i | \(-0.00495387\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.816635 | + | 1.41445i | −0.0396126 | + | 0.0686110i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.13667 | + | 1.96878i | 0.0550075 | + | 0.0952757i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.6185 | 1.08949 | 0.544747 | − | 0.838600i | \(-0.316626\pi\) | ||||
0.544747 | + | 0.838600i | \(0.316626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.41789 | 0.116196 | 0.0580982 | − | 0.998311i | \(-0.481496\pi\) | ||||
0.0580982 | + | 0.998311i | \(0.481496\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.554084 | + | 0.959702i | 0.0265054 | + | 0.0459088i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.7448 | + | 20.3427i | −0.560551 | + | 0.970902i | 0.436898 | + | 0.899511i | \(0.356077\pi\) |
−0.997448 | + | 0.0713911i | \(0.977256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.70895 | − | 11.6202i | 0.318752 | − | 0.552094i | −0.661476 | − | 0.749966i | \(-0.730070\pi\) |
0.980228 | + | 0.197872i | \(0.0634031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.6175 | − | 32.2465i | −0.882554 | − | 1.52863i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.16225 | 0.432393 | 0.216197 | − | 0.976350i | \(-0.430635\pi\) | ||||
0.216197 | + | 0.976350i | \(0.430635\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9224 | 1.36190 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.29679 | − | 2.24611i | −0.0607944 | − | 0.105299i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.40856 | + | 7.63584i | −0.206224 | + | 0.357190i | −0.950522 | − | 0.310658i | \(-0.899451\pi\) |
0.744298 | + | 0.667847i | \(0.232784\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.82957 | + | 4.90095i | −0.131786 | + | 0.228260i | −0.924365 | − | 0.381509i | \(-0.875405\pi\) |
0.792579 | + | 0.609769i | \(0.208738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.86333 | + | 13.6197i | 0.365440 | + | 0.632960i | 0.988847 | − | 0.148937i | \(-0.0475853\pi\) |
−0.623407 | + | 0.781898i | \(0.714252\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.9971 | −1.01790 | −0.508952 | − | 0.860795i | \(-0.669967\pi\) | ||||
−0.508952 | + | 0.860795i | \(0.669967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.8171 | 0.730366 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.5562 | − | 40.8006i | −1.08312 | − | 1.87601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50000 | + | 6.06218i | −0.160591 | + | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.4875 | + | 21.6291i | −0.570571 | + | 0.988257i | 0.425937 | + | 0.904753i | \(0.359945\pi\) |
−0.996507 | + | 0.0835043i | \(0.973389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.890369 | − | 1.54216i | −0.0405973 | − | 0.0703166i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.7994 | −1.35312 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5979 | 0.797435 | 0.398717 | − | 0.917074i | \(-0.369455\pi\) | ||||
0.398717 | + | 0.917074i | \(0.369455\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.89757 | − | 11.9469i | −0.311283 | − | 0.539158i | 0.667358 | − | 0.744737i | \(-0.267425\pi\) |
−0.978640 | + | 0.205580i | \(0.934092\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.16372 | − | 2.01561i | 0.0524111 | − | 0.0907787i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.63667 | + | 2.83480i | −0.0734148 | + | 0.127158i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.54377 | + | 11.3341i | 0.292939 | + | 0.507386i | 0.974503 | − | 0.224373i | \(-0.0720333\pi\) |
−0.681564 | + | 0.731758i | \(0.738700\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.3068 | −0.994611 | −0.497305 | − | 0.867576i | \(-0.665677\pi\) | ||||
−0.497305 | + | 0.867576i | \(0.665677\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.54377 | 0.424692 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.94659 | − | 13.7639i | −0.352226 | − | 0.610074i | 0.634413 | − | 0.772994i | \(-0.281242\pi\) |
−0.986639 | + | 0.162920i | \(0.947909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.753696 | − | 1.30544i | 0.0333415 | − | 0.0577492i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.6134 | + | 21.8471i | −0.555814 | + | 0.962698i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.4538 | + | 47.5514i | 1.20742 | + | 2.09131i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.41789 | −0.193551 | −0.0967756 | − | 0.995306i | \(-0.530853\pi\) | ||||
−0.0967756 | + | 0.995306i | \(0.530853\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.2733 | −1.10513 | −0.552563 | − | 0.833471i | \(-0.686350\pi\) | ||||
−0.552563 | + | 0.833471i | \(0.686350\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.10078 | + | 1.90660i | 0.0479506 | + | 0.0830528i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4626 | − | 19.8539i | 0.498376 | − | 0.863212i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.20321 | + | 5.54812i | −0.138746 | + | 0.240316i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.78220 | + | 3.08686i | 0.0770513 | + | 0.133457i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.51459 | 0.194457 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.43852 | −0.147834 | −0.0739168 | − | 0.997264i | \(-0.523550\pi\) | ||||
−0.0739168 | + | 0.997264i | \(0.523550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.40808 | + | 7.63501i | 0.188821 | + | 0.327048i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.46410 | + | 6.00000i | −0.148114 | + | 0.256542i | −0.930531 | − | 0.366214i | \(-0.880654\pi\) |
0.782416 | + | 0.622756i | \(0.213987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.98755 | − | 8.63868i | 0.212477 | − | 0.368020i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.35447 | + | 12.7383i | 0.312744 | + | 0.541688i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.5835 | −1.42298 | −0.711488 | − | 0.702698i | \(-0.751979\pi\) | ||||
−0.711488 | + | 0.702698i | \(0.751979\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4356 | 0.441379 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.2396 | − | 36.7880i | −0.895142 | − | 1.55043i | −0.833629 | − | 0.552325i | \(-0.813741\pi\) |
−0.0615128 | − | 0.998106i | \(-0.519593\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.4720 | − | 23.3341i | 0.566770 | − | 0.981675i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.20175 | − | 9.00969i | 0.218069 | − | 0.377706i | −0.736149 | − | 0.676820i | \(-0.763358\pi\) |
0.954217 | + | 0.299114i | \(0.0966910\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.92480 | + | 15.4582i | 0.373491 | + | 0.646906i | 0.990100 | − | 0.140364i | \(-0.0448272\pi\) |
−0.616609 | + | 0.787270i | \(0.711494\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.471974 | −0.0196827 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9430 | 0.497193 | 0.248597 | − | 0.968607i | \(-0.420031\pi\) | ||||
0.248597 | + | 0.968607i | \(0.420031\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.472958 | + | 0.819187i | 0.0196216 | + | 0.0339856i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.1608 | + | 24.5272i | −0.586480 | + | 1.01581i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.9299 | + | 20.6631i | −0.492398 | + | 0.852859i | −0.999962 | − | 0.00875568i | \(-0.997213\pi\) |
0.507563 | + | 0.861614i | \(0.330546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.71780 | + | 8.17147i | 0.194394 | + | 0.336699i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.5801 | −0.804060 | −0.402030 | − | 0.915626i | \(-0.631695\pi\) | ||||
−0.402030 | + | 0.915626i | \(0.631695\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.45331 | 0.100576 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.27335 | − | 16.0619i | −0.378899 | − | 0.656272i | 0.612004 | − | 0.790855i | \(-0.290364\pi\) |
−0.990902 | + | 0.134583i | \(0.957030\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.09931 | − | 15.7605i | 0.371169 | − | 0.642883i | −0.618577 | − | 0.785724i | \(-0.712290\pi\) |
0.989746 | + | 0.142841i | \(0.0456238\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.1659 | + | 21.0719i | −0.494612 | + | 0.856693i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.1549 | − | 19.3208i | −0.452762 | − | 0.784206i | 0.545795 | − | 0.837919i | \(-0.316228\pi\) |
−0.998556 | + | 0.0537125i | \(0.982895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1623 | −0.492032 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.2370 | 0.413467 | 0.206734 | − | 0.978397i | \(-0.433717\pi\) | ||||
0.206734 | + | 0.978397i | \(0.433717\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.66372 | − | 9.80984i | −0.228013 | − | 0.394929i | 0.729206 | − | 0.684294i | \(-0.239889\pi\) |
−0.957219 | + | 0.289364i | \(0.906556\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.31663 | − | 7.47663i | 0.173500 | − | 0.300511i | −0.766141 | − | 0.642672i | \(-0.777826\pi\) |
0.939641 | + | 0.342161i | \(0.111159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.17830 | + | 12.4332i | −0.287593 | + | 0.498125i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3260 | + | 26.5454i | 0.613039 | + | 1.06181i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.68443 | 0.0671626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.8535 | 0.591308 | 0.295654 | − | 0.955295i | \(-0.404462\pi\) | ||||
0.295654 | + | 0.955295i | \(0.404462\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.872181 | + | 1.51066i | 0.0346115 | + | 0.0599488i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.500000 | + | 0.866025i | −0.0198107 | + | 0.0343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0797 | + | 29.5828i | −0.674606 | + | 1.16845i | 0.301978 | + | 0.953315i | \(0.402353\pi\) |
−0.976584 | + | 0.215137i | \(0.930980\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.41741 | − | 9.38323i | −0.213642 | − | 0.370039i | 0.739210 | − | 0.673475i | \(-0.235199\pi\) |
−0.952852 | + | 0.303437i | \(0.901866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.9692 | 1.29615 | 0.648077 | − | 0.761575i | \(-0.275573\pi\) | ||||
0.648077 | + | 0.761575i | \(0.275573\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.3097 | −0.483199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.96557 | − | 3.40446i | −0.0769185 | − | 0.133227i | 0.825000 | − | 0.565132i | \(-0.191175\pi\) |
−0.901919 | + | 0.431905i | \(0.857841\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.2626 | + | 17.7753i | −0.400991 | + | 0.694537i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.40856 | + | 14.5640i | −0.327551 | + | 0.567335i | −0.982025 | − | 0.188749i | \(-0.939557\pi\) |
0.654474 | + | 0.756084i | \(0.272890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.51080 | + | 14.7411i | 0.331032 | + | 0.573364i | 0.982714 | − | 0.185128i | \(-0.0592700\pi\) |
−0.651683 | + | 0.758492i | \(0.725937\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.5146 | 0.407738 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.672570 | 0.0260420 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.13161 | + | 8.88821i | 0.198104 | + | 0.343126i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.3727 | + | 24.8942i | −0.554025 | + | 0.959600i | 0.443953 | + | 0.896050i | \(0.353576\pi\) |
−0.997979 | + | 0.0635501i | \(0.979758\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.01819 | + | 5.22765i | −0.115998 | + | 0.200915i | −0.918178 | − | 0.396167i | \(-0.870340\pi\) |
0.802180 | + | 0.597082i | \(0.203673\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.74484 | + | 9.95036i | 0.220467 | + | 0.381860i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.5113 | 0.784842 | 0.392421 | − | 0.919786i | \(-0.371638\pi\) | ||||
0.392421 | + | 0.919786i | \(0.371638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.52510 | 0.363935 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.13667 | − | 5.43288i | −0.119498 | − | 0.206976i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.50146 | + | 12.9929i | −0.285369 | + | 0.494274i | −0.972699 | − | 0.232072i | \(-0.925450\pi\) |
0.687330 | + | 0.726346i | \(0.258783\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.66372 | + | 4.61369i | −0.101040 | + | 0.175007i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.02997 | − | 5.24806i | −0.114768 | − | 0.198784i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.5113 | −1.45455 | −0.727275 | − | 0.686346i | \(-0.759214\pi\) | ||||
−0.727275 | + | 0.686346i | \(0.759214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.21926 | 0.272280 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.83988 | − | 3.18677i | −0.0691959 | − | 0.119851i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.82004 | + | 6.61650i | −0.143465 | + | 0.248488i | −0.928799 | − | 0.370584i | \(-0.879158\pi\) |
0.785334 | + | 0.619072i | \(0.212491\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.318097 | + | 0.550960i | −0.0119128 | + | 0.0206336i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.85447 | − | 10.1402i | −0.218945 | − | 0.379224i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.0364 | −1.12017 | −0.560084 | − | 0.828436i | \(-0.689231\pi\) | ||||
−0.560084 | + | 0.828436i | \(0.689231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.72665 | 0.362240 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.12422 | + | 3.67926i | 0.0788916 | + | 0.136644i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.72812 | − | 2.99319i | 0.0640923 | − | 0.111011i | −0.832199 | − | 0.554478i | \(-0.812918\pi\) |
0.896291 | + | 0.443466i | \(0.146251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.93560 | + | 8.54871i | −0.182550 | + | 0.316185i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.2630 | − | 33.3645i | −0.711496 | − | 1.23235i | −0.964295 | − | 0.264829i | \(-0.914685\pi\) |
0.252799 | − | 0.967519i | \(-0.418649\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 71.4078 | 2.63034 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.1239 | −1.65991 | −0.829955 | − | 0.557830i | \(-0.811634\pi\) | ||||
−0.829955 | + | 0.557830i | \(0.811634\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.74338 | − | 8.21577i | −0.174018 | − | 0.301407i | 0.765803 | − | 0.643075i | \(-0.222342\pi\) |
−0.939821 | + | 0.341668i | \(0.889008\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.5634 | + | 30.4207i | −0.643474 | + | 1.11453i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.687159 | − | 1.19019i | 0.0251082 | − | 0.0434887i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.91595 | − | 8.51467i | −0.179386 | − | 0.310705i | 0.762285 | − | 0.647242i | \(-0.224078\pi\) |
−0.941670 | + | 0.336537i | \(0.890744\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.7496 | −0.937124 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.8171 | −1.51987 | −0.759934 | − | 0.650000i | \(-0.774769\pi\) | ||||
−0.759934 | + | 0.650000i | \(0.774769\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.4897 | + | 19.9007i | 0.416501 | + | 0.721400i | 0.995585 | − | 0.0938675i | \(-0.0299230\pi\) |
−0.579084 | + | 0.815268i | \(0.696590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69961 | − | 2.94381i | 0.0615301 | − | 0.106573i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.36333 | − | 2.36135i | 0.0492269 | − | 0.0852635i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.04329 | − | 5.27113i | −0.109744 | − | 0.190082i | 0.805923 | − | 0.592021i | \(-0.201670\pi\) |
−0.915666 | + | 0.401939i | \(0.868336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.8214 | 1.50421 | 0.752105 | − | 0.659043i | \(-0.229038\pi\) | ||||
0.752105 | + | 0.659043i | \(0.229038\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.01867 | −0.144355 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.9861 | − | 22.4926i | −0.465275 | − | 0.805880i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.38891 | + | 12.7980i | −0.264396 | + | 0.457947i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.85087 | + | 13.5981i | −0.280210 | + | 0.485337i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1460 | + | 27.9657i | 0.575543 | + | 0.996870i | 0.995982 | + | 0.0895491i | \(0.0285426\pi\) |
−0.420439 | + | 0.907321i | \(0.638124\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3887 | −0.369380 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.27335 | −0.0807289 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.2829 | + | 40.3271i | 0.824722 | + | 1.42846i | 0.902132 | + | 0.431461i | \(0.142002\pi\) |
−0.0774101 | + | 0.996999i | \(0.524665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.75223 | − | 9.96316i | 0.203499 | − | 0.352471i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.40263 | − | 5.89352i | 0.120076 | − | 0.207978i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.354473 | + | 0.613964i | 0.0124935 | + | 0.0216394i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.8023 | 0.379790 | 0.189895 | − | 0.981804i | \(-0.439185\pi\) | ||||
0.189895 | + | 0.981804i | \(0.439185\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.58307 | −0.196048 | −0.0980240 | − | 0.995184i | \(-0.531252\pi\) | ||||
−0.0980240 | + | 0.995184i | \(0.531252\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.1050 | + | 40.0191i | 0.809335 | + | 1.40181i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.1534 | + | 36.6388i | −0.740064 | + | 1.28183i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.8940 | + | 27.5292i | −0.554703 | + | 0.960774i | 0.443223 | + | 0.896411i | \(0.353835\pi\) |
−0.997927 | + | 0.0643630i | \(0.979498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.0000 | − | 31.1769i | −0.627441 | − | 1.08676i | −0.988063 | − | 0.154047i | \(-0.950769\pi\) |
0.360623 | − | 0.932712i | \(-0.382564\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.9224 | 0.553675 | 0.276837 | − | 0.960917i | \(-0.410714\pi\) | ||||
0.276837 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.4720 | 1.23199 | 0.615996 | − | 0.787749i | \(-0.288754\pi\) | ||||
0.615996 | + | 0.787749i | \(0.288754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.472958 | − | 0.819187i | −0.0163870 | − | 0.0283832i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.9808 | − | 19.0194i | 0.380007 | − | 0.658192i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.3391 | − | 47.3527i | 0.943850 | − | 1.63480i | 0.185814 | − | 0.982585i | \(-0.440508\pi\) |
0.758037 | − | 0.652212i | \(-0.226159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4730 | + | 19.8717i | 0.395619 | + | 0.685233i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.1230 | −1.07066 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.38151 | 0.322353 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.243379 | + | 0.421545i | 0.00834292 | + | 0.0144504i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.09884 | − | 1.90324i | 0.0376234 | − | 0.0651656i | −0.846601 | − | 0.532229i | \(-0.821355\pi\) |
0.884224 | + | 0.467063i | \(0.154688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.88823 | + | 13.6628i | −0.269457 | + | 0.466713i | −0.968722 | − | 0.248150i | \(-0.920178\pi\) |
0.699265 | + | 0.714863i | \(0.253511\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.78813 | + | 4.82918i | 0.0951298 | + | 0.164770i | 0.909663 | − | 0.415348i | \(-0.136340\pi\) |
−0.814533 | + | 0.580117i | \(0.803007\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.1268 | 0.787247 | 0.393623 | − | 0.919272i | \(-0.371221\pi\) | ||||
0.393623 | + | 0.919272i | \(0.371221\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.0157 | −1.53058 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.2024 | + | 57.5083i | 1.12631 | + | 1.95083i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.90856 | + | 13.6980i | −0.267971 | + | 0.464140i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.24484 | − | 7.35228i | 0.143502 | − | 0.248552i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.96264 | − | 3.39939i | −0.0662737 | − | 0.114789i | 0.830985 | − | 0.556295i | \(-0.187778\pi\) |
−0.897258 | + | 0.441506i | \(0.854444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.1986 | −0.916345 | −0.458173 | − | 0.888863i | \(-0.651496\pi\) | ||||
−0.458173 | + | 0.888863i | \(0.651496\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.21341 | −0.276403 | −0.138202 | − | 0.990404i | \(-0.544132\pi\) | ||||
−0.138202 | + | 0.990404i | \(0.544132\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.24057 | + | 5.61283i | 0.108808 | + | 0.188460i | 0.915287 | − | 0.402801i | \(-0.131963\pi\) |
−0.806480 | + | 0.591262i | \(0.798630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.336285 | − | 0.582462i | 0.0112786 | − | 0.0195352i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.6534 | − | 42.7009i | 0.824995 | − | 1.42893i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.7178 | + | 25.4920i | 0.491962 | + | 0.852103i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.72665 | 0.190995 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.93406 | 0.197692 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.3853 | − | 49.1648i | −0.943560 | − | 1.63429i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.06440 | − | 8.77180i | 0.168161 | − | 0.291263i | −0.769613 | − | 0.638511i | \(-0.779551\pi\) |
0.937773 | + | 0.347248i | \(0.112884\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.9612 | + | 39.7699i | −0.760738 | + | 1.31764i | 0.181733 | + | 0.983348i | \(0.441829\pi\) |
−0.942471 | + | 0.334289i | \(0.891504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.13521 | + | 3.69829i | 0.0706652 | + | 0.122396i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.91381 | 0.261337 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.92432 | 0.162438 | 0.0812192 | − | 0.996696i | \(-0.474119\pi\) | ||||
0.0812192 | + | 0.996696i | \(0.474119\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.63667 | − | 2.83480i | −0.0538718 | − | 0.0933086i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.53736 | + | 2.66278i | −0.0505481 | + | 0.0875518i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.00379324 | − | 0.00657009i | 0.000124452 | − | 0.000215558i | −0.865963 | − | 0.500108i | \(-0.833294\pi\) |
0.866088 | + | 0.499892i | \(0.166627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.02704 | − | 3.51094i | −0.0664336 | − | 0.115066i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.0757 | 0.362213 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.1623 | 0.691341 | 0.345670 | − | 0.938356i | \(-0.387652\pi\) | ||||
0.345670 | + | 0.938356i | \(0.387652\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.27908 | + | 3.94748i | 0.0742959 | + | 0.128684i | 0.900780 | − | 0.434276i | \(-0.142996\pi\) |
−0.826484 | + | 0.562960i | \(0.809662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.875585 | − | 1.51656i | 0.0285130 | − | 0.0493859i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.86760 | + | 11.8950i | −0.223167 | + | 0.386537i | −0.955768 | − | 0.294122i | \(-0.904973\pi\) |
0.732601 | + | 0.680658i | \(0.238306\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.753696 | + | 1.30544i | 0.0244660 | + | 0.0423764i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.80699 | −0.285286 | −0.142643 | − | 0.989774i | \(-0.545560\pi\) | ||||
−0.142643 | + | 0.989774i | \(0.545560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.82004 | −0.0588951 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.83628 | − | 3.18054i | −0.0592967 | − | 0.102705i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7915 | − | 22.1556i | 0.412630 | − | 0.714696i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.7489 | + | 27.2779i | −0.506976 | + | 0.878108i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.1642 | + | 33.1934i | 0.616279 | + | 1.06743i | 0.990159 | + | 0.139949i | \(0.0446939\pi\) |
−0.373880 | + | 0.927477i | \(0.621973\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.0187 | −0.995436 | −0.497718 | − | 0.867339i | \(-0.665829\pi\) | ||||
−0.497718 | + | 0.867339i | \(0.665829\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.05408 | 0.0658509 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.3712 | − | 45.6763i | −0.843689 | − | 1.46131i | −0.886755 | − | 0.462241i | \(-0.847046\pi\) |
0.0430652 | − | 0.999072i | \(-0.486288\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.4071 | + | 56.1307i | −1.03574 | + | 1.79395i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.15146 | − | 15.8508i | 0.291886 | − | 0.505562i | −0.682370 | − | 0.731007i | \(-0.739050\pi\) |
0.974256 | + | 0.225446i | \(0.0723838\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.2812 | − | 36.8601i | −0.678076 | − | 1.17446i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.85253 | −0.0907052 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.6008 | 0.400277 | 0.200138 | − | 0.979768i | \(-0.435861\pi\) | ||||
0.200138 | + | 0.979768i | \(0.435861\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.4449 | + | 51.0001i | 0.933467 | + | 1.61681i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.87120 | + | 10.1692i | −0.185943 | + | 0.322062i | −0.943894 | − | 0.330249i | \(-0.892867\pi\) |
0.757951 | + | 0.652311i | \(0.226201\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))