Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, 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("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.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: | \(8.04892052375\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.3 | ||
Root | \(0.500000 + 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.337 |
Dual form | 1008.2.r.k.673.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 1.73025 | + | 0.0789082i | 0.998962 | + | 0.0455577i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.29679 | − | 2.24611i | 0.579942 | − | 1.00449i | −0.415543 | − | 0.909573i | \(-0.636409\pi\) |
0.995485 | − | 0.0949156i | \(-0.0302581\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98755 | + | 0.273062i | 0.995849 | + | 0.0910208i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.25729 | + | 3.90975i | 0.680600 | + | 1.17883i | 0.974798 | + | 0.223089i | \(0.0716141\pi\) |
−0.294198 | + | 0.955744i | \(0.595053\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | −0.926995 | − | 0.375073i | \(-0.877618\pi\) |
0.788320 | + | 0.615265i | \(0.210951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.42101 | − | 3.78400i | 0.625102 | − | 0.977025i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.945916 | −0.229418 | −0.114709 | − | 0.993399i | \(-0.536594\pi\) | ||||
−0.114709 | + | 0.993399i | \(0.536594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.05408 | 0.930071 | 0.465035 | − | 0.885292i | \(-0.346042\pi\) | ||||
0.465035 | + | 0.885292i | \(0.346042\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.796790 | − | 1.53790i | −0.173874 | − | 0.335597i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.136673 | + | 0.236725i | −0.0284983 | + | 0.0493605i | −0.879923 | − | 0.475117i | \(-0.842406\pi\) |
0.851425 | + | 0.524477i | \(0.175739\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.863327 | − | 1.49533i | −0.172665 | − | 0.299065i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.14766 | + | 0.708209i | 0.990668 | + | 0.136295i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.23025 | − | 2.13086i | −0.228452 | − | 0.395691i | 0.728897 | − | 0.684623i | \(-0.240033\pi\) |
−0.957350 | + | 0.288932i | \(0.906700\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.16372 | − | 2.01561i | 0.209009 | − | 0.362015i | −0.742393 | − | 0.669964i | \(-0.766309\pi\) |
0.951403 | + | 0.307949i | \(0.0996427\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.59718 | + | 6.94297i | 0.626188 | + | 1.20862i | ||||
\(34\) | 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 | ||||||||
\(39\) | −0.933463 | + | 1.45899i | −0.149474 | + | 0.233625i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.20321 | − | 5.54812i | 0.500257 | − | 0.866471i | −0.499743 | − | 0.866174i | \(-0.666572\pi\) |
1.00000 | 0.000297253i | \(-9.46187e-5\pi\) | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.21780 | − | 9.03749i | −0.795707 | − | 1.37820i | −0.922389 | − | 0.386262i | \(-0.873766\pi\) |
0.126682 | − | 0.991943i | \(-0.459567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.48755 | − | 6.35624i | 0.668964 | − | 0.947533i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.08113 | − | 10.5328i | −0.887023 | − | 1.53637i | −0.843377 | − | 0.537323i | \(-0.819436\pi\) |
−0.0436467 | − | 0.999047i | \(-0.513898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.63667 | − | 0.0746406i | −0.229180 | − | 0.0104518i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.27335 | −0.861710 | −0.430855 | − | 0.902421i | \(-0.641788\pi\) | ||||
−0.430855 | + | 0.902421i | \(0.641788\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.7089 | 1.57883 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.01459 | + | 0.319901i | 0.929105 | + | 0.0423719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.36333 | + | 2.36135i | −0.177490 | + | 0.307422i | −0.941020 | − | 0.338350i | \(-0.890131\pi\) |
0.763530 | + | 0.645772i | \(0.223464\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.13667 | + | 1.96878i | 0.145536 | + | 0.252076i | 0.929573 | − | 0.368639i | \(-0.120176\pi\) |
−0.784037 | + | 0.620714i | \(0.786843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.25729 | − | 2.72382i | −0.158404 | − | 0.343169i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.29679 | + | 2.24611i | 0.160847 | + | 0.278595i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.90856 | + | 13.6980i | −0.966184 | + | 1.67348i | −0.259784 | + | 0.965667i | \(0.583651\pi\) |
−0.706400 | + | 0.707813i | \(0.749682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.255158 | + | 0.398809i | −0.0307175 | + | 0.0480110i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.27335 | −0.388475 | −0.194237 | − | 0.980955i | \(-0.562223\pi\) | ||||
−0.194237 | + | 0.980955i | \(0.562223\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.50739 | −0.176427 | −0.0882134 | − | 0.996102i | \(-0.528116\pi\) | ||||
−0.0882134 | + | 0.996102i | \(0.528116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.37578 | − | 2.65542i | −0.158861 | − | 0.306621i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.25729 | − | 3.90975i | 0.257243 | − | 0.445557i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.35447 | + | 12.7383i | 0.827443 | + | 1.43317i | 0.900038 | + | 0.435811i | \(0.143539\pi\) |
−0.0725952 | + | 0.997361i | \(0.523128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.85087 | + | 1.63157i | 0.983430 | + | 0.181286i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.472958 | − | 0.819187i | −0.0519139 | − | 0.0899175i | 0.838901 | − | 0.544285i | \(-0.183199\pi\) |
−0.890815 | + | 0.454367i | \(0.849865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.22665 | + | 2.12463i | −0.133049 | + | 0.230448i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.96050 | − | 3.78400i | −0.210188 | − | 0.405688i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3566 | −1.52180 | −0.760899 | − | 0.648871i | \(-0.775242\pi\) | ||||
−0.760899 | + | 0.648871i | \(0.775242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.17257 | − | 3.39569i | 0.225285 | − | 0.352117i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.25729 | − | 9.10590i | 0.539387 | − | 0.934246i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.74484 | + | 9.95036i | 0.583300 | + | 1.01031i | 0.995085 | + | 0.0990246i | \(0.0315722\pi\) |
−0.411785 | + | 0.911281i | \(0.635094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.67617 | + | 12.2969i | 0.570476 | + | 1.23589i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.83988 | + | 3.18677i | 0.183075 | + | 0.317096i | 0.942926 | − | 0.333002i | \(-0.108061\pi\) |
−0.759851 | + | 0.650097i | \(0.774728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.86333 | + | 8.42353i | −0.479198 | + | 0.829995i | −0.999715 | − | 0.0238560i | \(-0.992406\pi\) |
0.520518 | + | 0.853851i | \(0.325739\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.48755 | − | 0.204655i | −0.437940 | − | 0.0199723i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.37432 | 0.132860 | 0.0664301 | − | 0.997791i | \(-0.478839\pi\) | ||||
0.0664301 | + | 0.997791i | \(0.478839\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.39922 | −0.325587 | −0.162793 | − | 0.986660i | \(-0.552050\pi\) | ||||
−0.162793 | + | 0.986660i | \(0.552050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.08113 | + | 0.140515i | 0.292448 | + | 0.0133371i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.19436 | + | 8.99689i | −0.488644 | + | 0.846356i | −0.999915 | − | 0.0130636i | \(-0.995842\pi\) |
0.511271 | + | 0.859420i | \(0.329175\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.354473 | + | 0.613964i | 0.0330547 | + | 0.0572525i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.73025 | + | 2.45076i | −0.159962 | + | 0.226573i | ||||
\(118\) | 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 | ||||||||
\(123\) | 5.98016 | − | 9.34689i | 0.539212 | − | 0.842781i | ||||
\(124\) | 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 | ||||||||
\(129\) | −8.31498 | − | 16.0489i | −0.732093 | − | 1.41302i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.95691 | − | 6.85356i | 0.345717 | − | 0.598799i | −0.639767 | − | 0.768569i | \(-0.720969\pi\) |
0.985484 | + | 0.169770i | \(0.0543026\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.02704 | − | 3.51094i | −0.175767 | − | 0.304437i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.26615 | − | 10.6438i | 0.711437 | − | 0.916072i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.83628 | + | 3.18054i | 0.156884 | + | 0.271732i | 0.933744 | − | 0.357943i | \(-0.116522\pi\) |
−0.776859 | + | 0.629674i | \(0.783188\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.02704 | + | 1.77889i | −0.0871126 | + | 0.150883i | −0.906289 | − | 0.422658i | \(-0.861097\pi\) |
0.819177 | + | 0.573541i | \(0.194431\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.69076 | − | 18.7043i | −0.816109 | − | 1.57519i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.51459 | −0.377529 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.38151 | −0.529956 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.933463 | + | 1.45899i | −0.0769907 | + | 0.120335i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.77188 | − | 11.7292i | 0.554774 | − | 0.960897i | −0.443147 | − | 0.896449i | \(-0.646138\pi\) |
0.997921 | − | 0.0644482i | \(-0.0205287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.96410 | + | 8.59808i | 0.403973 | + | 0.699702i | 0.994201 | − | 0.107535i | \(-0.0342956\pi\) |
−0.590228 | + | 0.807236i | \(0.700962\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.82597 | − | 0.258294i | −0.228466 | − | 0.0208818i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.01819 | − | 5.22765i | −0.242427 | − | 0.419895i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.02704 | + | 5.24299i | −0.241584 | + | 0.418436i | −0.961166 | − | 0.275972i | \(-0.911000\pi\) |
0.719581 | + | 0.694408i | \(0.244334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.8545 | − | 0.495019i | −0.860816 | − | 0.0392575i | ||||
\(160\) | 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 | ||||||||
\(165\) | 20.2594 | + | 0.923932i | 1.57719 | + | 0.0719280i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.23385 | + | 7.33325i | −0.327625 | + | 0.567464i | −0.982040 | − | 0.188672i | \(-0.939582\pi\) |
0.654415 | + | 0.756136i | \(0.272915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.1118 | + | 1.10702i | 0.926210 | + | 0.0846558i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.67830 | − | 15.0313i | −0.659799 | − | 1.14281i | −0.980667 | − | 0.195682i | \(-0.937308\pi\) |
0.320868 | − | 0.947124i | \(-0.396025\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.863327 | + | 1.49533i | −0.0652614 | + | 0.113036i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.54523 | + | 3.97816i | −0.191311 | + | 0.299017i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3494 | 0.848295 | 0.424147 | − | 0.905593i | \(-0.360574\pi\) | ||||
0.424147 | + | 0.905593i | \(0.360574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.8889 | 1.62699 | 0.813495 | − | 0.581572i | \(-0.197562\pi\) | ||||
0.813495 | + | 0.581572i | \(0.197562\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.81138 | + | 3.49617i | 0.133901 | + | 0.258444i | ||||
\(184\) | 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 | ||||||||
\(189\) | −1.96050 | − | 4.81211i | −0.142606 | − | 0.350030i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.350874 | − | 0.607731i | −0.0253883 | − | 0.0439739i | 0.853052 | − | 0.521826i | \(-0.174749\pi\) |
−0.878440 | + | 0.477852i | \(0.841416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.07227 | + | 10.5175i | −0.437092 | + | 0.757065i | −0.997464 | − | 0.0711760i | \(-0.977325\pi\) |
0.560372 | + | 0.828241i | \(0.310658\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.06654 | + | 3.98866i | 0.147988 | + | 0.285634i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4107 | −1.16921 | −0.584607 | − | 0.811317i | \(-0.698751\pi\) | ||||
−0.584607 | + | 0.811317i | \(0.698751\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7060 | −1.60959 | −0.804794 | − | 0.593555i | \(-0.797724\pi\) | ||||
−0.804794 | + | 0.593555i | \(0.797724\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.7647 | + | 23.0770i | −1.04142 | + | 1.62773i | ||||
\(202\) | 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 | ||||||||
\(207\) | −0.472958 | + | 0.669906i | −0.0328728 | + | 0.0465617i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.15126 | + | 15.8505i | 0.633006 | + | 1.09640i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.28074 | − | 3.95035i | 0.157012 | − | 0.271954i | −0.776778 | − | 0.629775i | \(-0.783147\pi\) |
0.933790 | + | 0.357822i | \(0.116480\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.66372 | − | 0.258294i | −0.388071 | − | 0.0176980i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.0656 | −1.84586 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.32743 | −0.157996 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.60817 | − | 0.118946i | −0.176244 | − | 0.00803760i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.472958 | − | 0.819187i | 0.0318146 | − | 0.0551045i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.66225 | + | 11.5394i | 0.446137 | + | 0.772733i | 0.998131 | − | 0.0611159i | \(-0.0194659\pi\) |
−0.551993 | + | 0.833849i | \(0.686133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.17091 | − | 4.70310i | −0.144727 | − | 0.313540i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.690757 | + | 1.19643i | 0.0458472 | + | 0.0794096i | 0.888038 | − | 0.459769i | \(-0.152068\pi\) |
−0.842191 | + | 0.539179i | \(0.818735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.98968 | − | 15.5706i | 0.594055 | − | 1.02893i | −0.399625 | − | 0.916679i | \(-0.630859\pi\) |
0.993679 | − | 0.112254i | \(-0.0358072\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.21420 | − | 6.58673i | 0.277274 | − | 0.433375i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.9823 | −1.24357 | −0.621786 | − | 0.783187i | \(-0.713592\pi\) | ||||
−0.621786 | + | 0.783187i | \(0.713592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.5438 | −2.05769 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.7199 | + | 22.6208i | 0.761292 | + | 1.46938i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.44592 | − | 4.23645i | 0.158213 | − | 0.274033i | −0.776011 | − | 0.630719i | \(-0.782760\pi\) |
0.934224 | + | 0.356686i | \(0.116093\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0797 | + | 22.6546i | 0.842535 | + | 1.45931i | 0.887745 | + | 0.460336i | \(0.152271\pi\) |
−0.0452094 | + | 0.998978i | \(0.514396\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1855 | + | 3.52144i | 0.974150 | + | 0.225901i | ||||
\(244\) | 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 | ||||||||
\(249\) | −0.753696 | − | 1.45472i | −0.0477635 | − | 0.0921892i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4576 | −1.16503 | −0.582516 | − | 0.812819i | \(-0.697932\pi\) | ||||
−0.582516 | + | 0.812819i | \(0.697932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.23405 | −0.0775838 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.29007 | + | 3.57935i | −0.143410 | + | 0.224147i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.86693 | − | 10.1618i | 0.365969 | − | 0.633876i | −0.622962 | − | 0.782252i | \(-0.714071\pi\) |
0.988931 | + | 0.148375i | \(0.0474044\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.890369 | − | 1.54216i | −0.0553248 | − | 0.0958254i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.09358 | − | 6.70198i | −0.191488 | − | 0.414842i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.76089 | − | 6.51406i | −0.231907 | − | 0.401674i | 0.726463 | − | 0.687206i | \(-0.241163\pi\) |
−0.958369 | + | 0.285532i | \(0.907830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.13521 | + | 14.0906i | −0.499742 | + | 0.865579i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.8406 | − | 1.13285i | −1.52022 | − | 0.0693296i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.8348 | −1.14838 | −0.574190 | − | 0.818722i | \(-0.694683\pi\) | ||||
−0.574190 | + | 0.818722i | \(0.694683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.9823 | 1.45682 | 0.728410 | − | 0.685141i | \(-0.240260\pi\) | ||||
0.728410 | + | 0.685141i | \(0.240260\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73025 | + | 0.0789082i | 0.104720 | + | 0.00477574i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.89757 | − | 6.75078i | 0.235032 | − | 0.407088i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.58113 | − | 6.20269i | −0.215169 | − | 0.372684i | 0.738156 | − | 0.674630i | \(-0.235697\pi\) |
−0.953325 | + | 0.301947i | \(0.902364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.02704 | − | 5.70397i | 0.241093 | − | 0.341488i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.44085 | − | 12.8879i | −0.443884 | − | 0.768830i | 0.554090 | − | 0.832457i | \(-0.313067\pi\) |
−0.997974 | + | 0.0636271i | \(0.979733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.99854 | − | 17.3180i | 0.594351 | − | 1.02945i | −0.399287 | − | 0.916826i | \(-0.630742\pi\) |
0.993638 | − | 0.112621i | \(-0.0359245\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.81498 | − | 15.3407i | 0.581389 | − | 0.908703i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.40642 | −0.378159 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1052 | −0.947367 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.15486 | + | 17.6699i | 0.536667 | + | 1.03583i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.53278 | + | 13.0472i | −0.440070 | + | 0.762223i | −0.997694 | − | 0.0678705i | \(-0.978380\pi\) |
0.557625 | + | 0.830093i | \(0.311713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.53590 | + | 6.12435i | 0.205868 | + | 0.356574i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.85087 | + | 21.7247i | 0.513580 | + | 1.26060i | ||||
\(298\) | 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 | ||||||||
\(303\) | 2.93200 | + | 5.65910i | 0.168439 | + | 0.325107i | ||||
\(304\) | 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 | ||||||||
\(309\) | −9.07947 | + | 14.1911i | −0.516513 | + | 0.807302i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.99115 | + | 13.8411i | −0.453136 | + | 0.784855i | −0.998579 | − | 0.0532931i | \(-0.983028\pi\) |
0.545443 | + | 0.838148i | \(0.316362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.79893 | − | 10.0440i | −0.327775 | − | 0.567722i | 0.654295 | − | 0.756239i | \(-0.272965\pi\) |
−0.982070 | + | 0.188517i | \(0.939632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.74844 | − | 0.708209i | −0.436575 | − | 0.0399031i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.00885 | + | 1.74739i | 0.0566629 | + | 0.0981430i | 0.892965 | − | 0.450125i | \(-0.148621\pi\) |
−0.836303 | + | 0.548268i | \(0.815287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.55408 | − | 9.61996i | 0.310969 | − | 0.538614i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.37792 | + | 0.108445i | 0.132722 | + | 0.00605281i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.83482 | −0.213375 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.72665 | 0.0957775 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.88151 | − | 0.268227i | −0.325249 | − | 0.0148330i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.08113 | + | 10.5328i | −0.335263 | + | 0.580693i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.85447 | − | 17.0684i | −0.541651 | − | 0.938167i | −0.998809 | − | 0.0487815i | \(-0.984466\pi\) |
0.457159 | − | 0.889385i | \(-0.348867\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.32004 | + | 0.486253i | 0.291536 | + | 0.0266465i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.5115 | + | 35.5269i | 1.12066 | + | 1.94104i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5256 | − | 25.1590i | 0.791259 | − | 1.37050i | −0.133929 | − | 0.990991i | \(-0.542759\pi\) |
0.925188 | − | 0.379509i | \(-0.123907\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.69748 | + | 15.1570i | −0.526695 | + | 0.823216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.5074 | 0.569007 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.564880 | + | 1.09028i | 0.0304121 | + | 0.0586989i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.5416 | − | 25.1868i | 0.780636 | − | 1.35210i | −0.150936 | − | 0.988544i | \(-0.548229\pi\) |
0.931572 | − | 0.363557i | \(-0.118438\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3815 | − | 21.4454i | −0.662767 | − | 1.14795i | −0.979885 | − | 0.199561i | \(-0.936049\pi\) |
0.317118 | − | 0.948386i | \(-0.397285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.18716 | + | 4.10390i | −0.170118 | + | 0.219050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.6513 | + | 28.8408i | 0.886257 | + | 1.53504i | 0.844266 | + | 0.535925i | \(0.180037\pi\) |
0.0419914 | + | 0.999118i | \(0.486630\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.24484 | + | 7.35228i | −0.225293 | + | 0.390219i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.753696 | + | 1.45472i | 0.0398898 | + | 0.0769920i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.5366 | −1.34777 | −0.673884 | − | 0.738837i | \(-0.735375\pi\) | ||||
−0.673884 | + | 0.738837i | \(0.735375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.56440 | −0.134968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.75729 | + | 13.6875i | −0.459639 | + | 0.718409i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.95477 | + | 3.38576i | −0.102317 | + | 0.177219i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7252 | + | 23.7727i | 0.716449 | + | 1.24093i | 0.962398 | + | 0.271644i | \(0.0875672\pi\) |
−0.245949 | + | 0.969283i | \(0.579100\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.0847 | − | 15.7006i | 0.577048 | − | 0.817341i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.13667 | + | 5.43288i | 0.162848 | + | 0.282061i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.16372 | + | 14.1400i | −0.422701 | + | 0.732140i | −0.996203 | − | 0.0870646i | \(-0.972251\pi\) |
0.573502 | + | 0.819204i | \(0.305585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.6893 | + | 0.669906i | 0.758552 | + | 0.0345938i | ||||
\(376\) | 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 | ||||||||
\(381\) | −1.16372 | − | 0.0530713i | −0.0596189 | − | 0.00271892i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.21780 | + | 10.7695i | −0.317715 | + | 0.550298i | −0.980011 | − | 0.198944i | \(-0.936249\pi\) |
0.662296 | + | 0.749242i | \(0.269582\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.85447 | − | 10.1402i | −0.298372 | − | 0.516795i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.1206 | − | 28.4247i | −0.666959 | − | 1.44491i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.3004 | − | 17.8408i | −0.522250 | − | 0.904564i | −0.999665 | − | 0.0258860i | \(-0.991759\pi\) |
0.477414 | − | 0.878678i | \(-0.341574\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.129281 | − | 0.223922i | 0.00653803 | − | 0.0113242i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.38725 | − | 11.5462i | 0.372637 | − | 0.582427i | ||||
\(394\) | 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 | ||||||||
\(399\) | −3.23025 | − | 6.23476i | −0.161715 | − | 0.312129i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.28220 | − | 2.22084i | 0.0640300 | − | 0.110903i | −0.832233 | − | 0.554426i | \(-0.812938\pi\) |
0.896263 | + | 0.443522i | \(0.146271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.16372 | + | 2.01561i | 0.0579688 | + | 0.100405i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.1424 | − | 17.7642i | 0.752432 | − | 0.882710i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.01965 | + | 6.96224i | 0.199247 | + | 0.345105i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.1623 | − | 29.7259i | 0.848619 | − | 1.46985i | −0.0338223 | − | 0.999428i | \(-0.510768\pi\) |
0.882441 | − | 0.470423i | \(-0.155899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.92627 | + | 5.64803i | 0.144342 | + | 0.278597i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.72665 | 0.134170 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.45331 | −0.120428 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.91741 | + | 2.99689i | −0.0938960 | + | 0.146758i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.02850 | − | 3.51347i | 0.0990989 | − | 0.171644i | −0.812213 | − | 0.583361i | \(-0.801737\pi\) |
0.911312 | + | 0.411717i | \(0.135071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5344 | + | 18.2462i | 0.513417 | + | 0.889264i | 0.999879 | + | 0.0155624i | \(0.00495387\pi\) |
−0.486462 | + | 0.873702i | \(0.661713\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.2915 | − | 33.1278i | −0.743500 | − | 1.61073i | ||||
\(424\) | 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 | ||||||||
\(429\) | −7.81138 | − | 0.356238i | −0.377137 | − | 0.0171993i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.6185 | −1.08949 | −0.544747 | − | 0.838600i | \(-0.683374\pi\) | ||||
−0.544747 | + | 0.838600i | \(0.683374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.41789 | 0.116196 | 0.0580982 | − | 0.998311i | \(-0.481496\pi\) | ||||
0.0580982 | + | 0.998311i | \(0.481496\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.0416 | − | 0.503554i | −0.529406 | − | 0.0241436i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.554084 | + | 0.959702i | −0.0265054 | + | 0.0459088i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.7448 | − | 20.3427i | −0.560551 | − | 0.970902i | −0.997448 | − | 0.0713911i | \(-0.977256\pi\) |
0.436898 | − | 0.899511i | \(-0.356077\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.73025 | + | 2.45076i | −0.0823930 | + | 0.116703i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.70895 | − | 11.6202i | −0.318752 | − | 0.552094i | 0.661476 | − | 0.749966i | \(-0.269930\pi\) |
−0.980228 | + | 0.197872i | \(0.936597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.6175 | + | 32.2465i | −0.882554 | + | 1.52863i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.6426 | − | 19.7602i | 0.597975 | − | 0.934625i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.16225 | −0.432393 | −0.216197 | − | 0.976350i | \(-0.569365\pi\) | ||||
−0.216197 | + | 0.976350i | \(0.569365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9224 | 1.36190 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.91069 | + | 15.2686i | 0.371677 | + | 0.717379i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.29679 | − | 2.24611i | 0.0607944 | − | 0.105299i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.40856 | − | 7.63584i | −0.206224 | − | 0.357190i | 0.744298 | − | 0.667847i | \(-0.232784\pi\) |
−0.950522 | + | 0.310658i | \(0.899451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.86926 | − | 0.669906i | −0.227277 | − | 0.0312685i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.82957 | + | 4.90095i | 0.131786 | + | 0.228260i | 0.924365 | − | 0.381509i | \(-0.124595\pi\) |
−0.792579 | + | 0.609769i | \(0.791262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.86333 | − | 13.6197i | 0.365440 | − | 0.632960i | −0.623407 | − | 0.781898i | \(-0.714252\pi\) |
0.988847 | + | 0.148937i | \(0.0475853\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.80972 | − | 9.28332i | −0.223045 | − | 0.430504i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.9971 | 1.01790 | 0.508952 | − | 0.860795i | \(-0.330033\pi\) | ||||
0.508952 | + | 0.860795i | \(0.330033\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.8171 | 0.730366 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.65126 | + | 8.83284i | −0.260396 | + | 0.406996i | ||||
\(472\) | 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 | ||||||||
\(477\) | −18.7419 | − | 1.71301i | −0.858133 | − | 0.0784336i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.4875 | + | 21.6291i | 0.570571 | + | 0.988257i | 0.996507 | + | 0.0835043i | \(0.0266112\pi\) |
−0.425937 | + | 0.904753i | \(0.640055\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.890369 | + | 1.54216i | −0.0405973 | + | 0.0703166i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.472958 | + | 0.0215693i | 0.0215203 | + | 0.000981436i | ||||
\(484\) | 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 | ||||||||
\(489\) | −30.8281 | − | 1.40592i | −1.39410 | − | 0.0635778i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.89757 | − | 11.9469i | 0.311283 | − | 0.539158i | −0.667358 | − | 0.744737i | \(-0.732575\pi\) |
0.978640 | + | 0.205580i | \(0.0659080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.16372 | + | 2.01561i | 0.0524111 | + | 0.0907787i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 34.9810 | + | 3.19727i | 1.57228 | + | 0.143707i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.63667 | + | 2.83480i | 0.0734148 | + | 0.127158i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.54377 | − | 11.3341i | 0.292939 | − | 0.507386i | −0.681564 | − | 0.731758i | \(-0.738700\pi\) |
0.974503 | + | 0.224373i | \(0.0720333\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.90428 | + | 12.3543i | −0.353137 | + | 0.551949i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.3068 | 0.994611 | 0.497305 | − | 0.867576i | \(-0.334323\pi\) | ||||
0.497305 | + | 0.867576i | \(0.334323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.54377 | 0.424692 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.56148 | + | 18.4548i | 0.424640 | + | 0.819605i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.94659 | − | 13.7639i | 0.352226 | − | 0.610074i | −0.634413 | − | 0.772994i | \(-0.718758\pi\) |
0.986639 | + | 0.162920i | \(0.0520914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.753696 | + | 1.30544i | 0.0333415 | + | 0.0577492i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.8691 | + | 2.87114i | 0.921392 | + | 0.126764i | ||||
\(514\) | 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 | ||||||||
\(519\) | −13.8296 | − | 26.6927i | −0.607051 | − | 1.17168i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.41789 | 0.193551 | 0.0967756 | − | 0.995306i | \(-0.469147\pi\) | ||||
0.0967756 | + | 0.995306i | \(0.469147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.2733 | −1.10513 | −0.552563 | − | 0.833471i | \(-0.686350\pi\) | ||||
−0.552563 | + | 0.833471i | \(0.686350\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.61177 | + | 2.51917i | −0.0703433 | + | 0.109946i | ||||
\(526\) | 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 | ||||||||
\(531\) | −4.71780 | + | 6.68238i | −0.204735 | + | 0.289990i | ||||
\(532\) | 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 | ||||||||
\(537\) | 19.6373 | + | 0.895562i | 0.847414 | + | 0.0386464i | ||||
\(538\) | 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 | ||||||||
\(543\) | 37.8733 | + | 1.72722i | 1.62530 | + | 0.0741219i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.40808 | + | 7.63501i | −0.188821 | + | 0.327048i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.46410 | − | 6.00000i | −0.148114 | − | 0.256542i | 0.782416 | − | 0.622756i | \(-0.213987\pi\) |
−0.930531 | + | 0.366214i | \(0.880654\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.85827 | + | 6.19219i | 0.121988 | + | 0.264276i | ||||
\(550\) | 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 | ||||||||
\(555\) | 4.31118 | − | 6.73832i | 0.183000 | − | 0.286026i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.5835 | 1.42298 | 0.711488 | − | 0.702698i | \(-0.248021\pi\) | ||||
0.711488 | + | 0.702698i | \(0.248021\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4356 | 0.441379 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.40263 | − | 6.56747i | −0.143659 | − | 0.277279i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.2396 | − | 36.7880i | 0.895142 | − | 1.55043i | 0.0615128 | − | 0.998106i | \(-0.480407\pi\) |
0.833629 | − | 0.552325i | \(-0.186259\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.4720 | + | 23.3341i | 0.566770 | + | 0.981675i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.01245 | − | 8.48087i | −0.126511 | − | 0.356163i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.20175 | − | 9.00969i | −0.218069 | − | 0.377706i | 0.736149 | − | 0.676820i | \(-0.236642\pi\) |
−0.954217 | + | 0.299114i | \(0.903309\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.92480 | − | 15.4582i | 0.373491 | − | 0.646906i | −0.616609 | − | 0.787270i | \(-0.711494\pi\) |
0.990100 | + | 0.140364i | \(0.0448272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.559145 | − | 1.07922i | −0.0233586 | − | 0.0450849i | ||||
\(574\) | 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 | ||||||||
\(579\) | −11.3365 | + | 17.7187i | −0.471128 | + | 0.736366i | ||||
\(580\) | 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 | ||||||||
\(585\) | 3.26089 | + | 7.06445i | 0.134821 | + | 0.292079i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.9299 | + | 20.6631i | 0.492398 | + | 0.852859i | 0.999962 | − | 0.00875568i | \(-0.00278706\pi\) |
−0.507563 | + | 0.861614i | \(0.669454\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.71780 | − | 8.17147i | 0.194394 | − | 0.336699i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.3946 | − | 1.29494i | −1.16800 | − | 0.0532667i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5801 | 0.804060 | 0.402030 | − | 0.915626i | \(-0.368305\pi\) | ||||
0.402030 | + | 0.915626i | \(0.368305\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.45331 | 0.100576 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −39.2871 | − | 1.79169i | −1.60792 | − | 0.0733291i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.27335 | − | 16.0619i | 0.378899 | − | 0.656272i | −0.612004 | − | 0.790855i | \(-0.709636\pi\) |
0.990902 | + | 0.134583i | \(0.0429696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.09931 | + | 15.7605i | 0.371169 | + | 0.642883i | 0.989746 | − | 0.142841i | \(-0.0456238\pi\) |
−0.618577 | + | 0.785724i | \(0.712290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.3676 | + | 38.7640i | −1.11449 | + | 1.57859i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1659 | + | 21.0719i | 0.494612 | + | 0.856693i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.1549 | + | 19.3208i | −0.452762 | + | 0.784206i | −0.998556 | − | 0.0537125i | \(-0.982895\pi\) |
0.545795 | + | 0.837919i | \(0.316228\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.29679 | + | 3.58985i | −0.0930706 | + | 0.145468i | ||||
\(610\) | 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 | ||||||||
\(615\) | −13.2391 | − | 25.5530i | −0.533852 | − | 1.03040i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.66372 | − | 9.80984i | 0.228013 | − | 0.394929i | −0.729206 | − | 0.684294i | \(-0.760111\pi\) |
0.957219 | + | 0.289364i | \(0.0934439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.31663 | + | 7.47663i | 0.173500 | + | 0.300511i | 0.939641 | − | 0.342161i | \(-0.111159\pi\) |
−0.766141 | + | 0.642672i | \(0.777826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.871198 | + | 1.12179i | −0.0349600 | + | 0.0450157i | ||||
\(622\) | 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 | ||||||||
\(627\) | 14.5833 | + | 28.1474i | 0.582399 | + | 1.12410i | ||||
\(628\) | 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 | ||||||||
\(633\) | 4.25797 | − | 6.65514i | 0.169239 | − | 0.264518i | ||||
\(634\) | 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 | ||||||||
\(639\) | −9.77928 | − | 0.893828i | −0.386862 | − | 0.0353593i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.0797 | + | 29.5828i | 0.674606 | + | 1.16845i | 0.976584 | + | 0.215137i | \(0.0690199\pi\) |
−0.301978 | + | 0.953315i | \(0.597647\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.41741 | + | 9.38323i | −0.213642 | + | 0.370039i | −0.952852 | − | 0.303437i | \(-0.901866\pi\) |
0.739210 | + | 0.673475i | \(0.235199\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −46.8302 | − | 2.13570i | −1.84394 | − | 0.0840929i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.9692 | −1.29615 | −0.648077 | − | 0.761575i | \(-0.724427\pi\) | ||||
−0.648077 | + | 0.761575i | \(0.724427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.3097 | −0.483199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.02704 | − | 0.183653i | −0.157832 | − | 0.00719795i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.96557 | − | 3.40446i | 0.0769185 | − | 0.133227i | −0.825000 | − | 0.565132i | \(-0.808825\pi\) |
0.901919 | + | 0.431905i | \(0.142159\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.2626 | − | 17.7753i | −0.400991 | − | 0.694537i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.50340 | − | 0.411612i | −0.175695 | − | 0.0160585i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.40856 | + | 14.5640i | 0.327551 | + | 0.567335i | 0.982025 | − | 0.188749i | \(-0.0604434\pi\) |
−0.654474 | + | 0.756084i | \(0.727110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.51080 | − | 14.7411i | 0.331032 | − | 0.573364i | −0.651683 | − | 0.758492i | \(-0.725937\pi\) |
0.982714 | + | 0.185128i | \(0.0592700\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.882977 | − | 1.38008i | 0.0342920 | − | 0.0535979i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.5146 | −0.407738 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.672570 | 0.0260420 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.6168 | + | 20.4917i | 0.410470 | + | 0.792255i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.13161 | + | 8.88821i | −0.198104 | + | 0.343126i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.3727 | − | 24.8942i | −0.554025 | − | 0.959600i | −0.997979 | − | 0.0635501i | \(-0.979758\pi\) |
0.443953 | − | 0.896050i | \(-0.353576\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.38511 | − | 8.30885i | −0.130293 | − | 0.319808i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.01819 | + | 5.22765i | 0.115998 | + | 0.200915i | 0.918178 | − | 0.396167i | \(-0.129660\pi\) |
−0.802180 | + | 0.597082i | \(0.796327\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.74484 | − | 9.95036i | 0.220467 | − | 0.381860i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.10078 | + | 2.12463i | 0.0421818 | + | 0.0814159i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.5113 | −0.784842 | −0.392421 | − | 0.919786i | \(-0.628362\pi\) | ||||
−0.392421 | + | 0.919786i | \(0.628362\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.52510 | 0.363935 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.7831 | − | 26.2317i | 0.640314 | − | 1.00080i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.13667 | − | 5.43288i | 0.119498 | − | 0.206976i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.50146 | − | 12.9929i | −0.285369 | − | 0.494274i | 0.687330 | − | 0.726346i | \(-0.258783\pi\) |
−0.972699 | + | 0.232072i | \(0.925450\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.81138 | − | 11.0642i | 0.296730 | − | 0.420293i | ||||
\(694\) | 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 | ||||||||
\(699\) | −32.8442 | − | 1.49786i | −1.24228 | − | 0.0566542i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.5113 | 1.45455 | 0.727275 | − | 0.686346i | \(-0.240786\pi\) | ||||
0.727275 | + | 0.686346i | \(0.240786\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.21926 | 0.272280 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −54.5787 | − | 2.48906i | −2.05555 | − | 0.0937435i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.83988 | − | 3.18677i | 0.0691959 | − | 0.119851i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.82004 | − | 6.61650i | −0.143465 | − | 0.248488i | 0.785334 | − | 0.619072i | \(-0.212491\pi\) |
−0.928799 | + | 0.370584i | \(0.879158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.4935 | + | 40.0646i | 0.693560 | + | 1.50254i | ||||
\(712\) | 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 | ||||||||
\(717\) | 4.56634 | − | 7.13713i | 0.170533 | − | 0.266541i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.0364 | 1.12017 | 0.560084 | − | 0.828436i | \(-0.310769\pi\) | ||||
0.560084 | + | 0.828436i | \(0.310769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.72665 | 0.362240 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.8435 | + | 40.2303i | 0.775177 | + | 1.49618i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.12422 | + | 3.67926i | −0.0788916 | + | 0.136644i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.72812 | + | 2.99319i | 0.0640923 | + | 0.111011i | 0.896291 | − | 0.443466i | \(-0.146251\pi\) |
−0.832199 | + | 0.554478i | \(0.812918\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9969 | + | 7.29124i | 0.962847 | + | 0.270046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.93560 | + | 8.54871i | 0.182550 | + | 0.316185i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.2630 | + | 33.3645i | −0.711496 | + | 1.23235i | 0.252799 | + | 0.967519i | \(0.418649\pi\) |
−0.964295 | + | 0.264829i | \(0.914685\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.06654 | + | 3.98866i | 0.0762254 | + | 0.147124i | ||||
\(736\) | 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 | ||||||||
\(741\) | −3.78434 | + | 5.91486i | −0.139021 | + | 0.217288i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.74338 | − | 8.21577i | 0.174018 | − | 0.301407i | −0.765803 | − | 0.643075i | \(-0.777658\pi\) |
0.939821 | + | 0.341668i | \(0.110992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.5634 | − | 30.4207i | −0.643474 | − | 1.11453i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.18929 | − | 2.57651i | −0.0435140 | − | 0.0942695i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.687159 | − | 1.19019i | −0.0251082 | − | 0.0434887i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.91595 | + | 8.51467i | −0.179386 | + | 0.310705i | −0.941670 | − | 0.336537i | \(-0.890744\pi\) |
0.762285 | + | 0.647242i | \(0.224078\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.9363 | − | 1.45646i | −1.16382 | − | 0.0530762i | ||||
\(754\) | 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 | ||||||||
\(759\) | −2.13521 | − | 0.0973764i | −0.0775032 | − | 0.00353454i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.4897 | + | 19.9007i | −0.416501 | + | 0.721400i | −0.995585 | − | 0.0938675i | \(-0.970077\pi\) |
0.579084 | + | 0.815268i | \(0.303410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69961 | + | 2.94381i | 0.0615301 | + | 0.106573i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.24484 | + | 6.01247i | −0.153473 | + | 0.217381i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.36333 | − | 2.36135i | −0.0492269 | − | 0.0852635i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.04329 | + | 5.27113i | −0.109744 | + | 0.190082i | −0.915666 | − | 0.401939i | \(-0.868336\pi\) |
0.805923 | + | 0.592021i | \(0.201670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9531 | − | 17.1196i | 0.394467 | − | 0.616546i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.8214 | −1.50421 | −0.752105 | − | 0.659043i | \(-0.770962\pi\) | ||||
−0.752105 | + | 0.659043i | \(0.770962\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.01867 | −0.144355 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.41887 | − | 2.73859i | −0.0509018 | − | 0.0982464i | ||||
\(778\) | 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 | ||||||||
\(783\) | −4.82383 | − | 11.8402i | −0.172390 | − | 0.423135i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.85087 | + | 13.5981i | 0.280210 | + | 0.485337i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1460 | − | 27.9657i | 0.575543 | − | 0.996870i | −0.420439 | − | 0.907321i | \(-0.638124\pi\) |
0.995982 | − | 0.0895491i | \(-0.0285426\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.99328 | − | 11.5677i | −0.213366 | − | 0.411822i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.3887 | 0.369380 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.27335 | −0.0807289 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.1878 | + | 23.7384i | −0.538657 | + | 0.841913i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.2829 | + | 40.3271i | −0.824722 | + | 1.42846i | 0.0774101 | + | 0.996999i | \(0.475335\pi\) |
−0.902132 | + | 0.431461i | \(0.857998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.75223 | + | 9.96316i | 0.203499 | + | 0.352471i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −42.8910 | − | 3.92025i | −1.51548 | − | 0.138515i | ||||
\(802\) | 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 | ||||||||
\(807\) | −32.5890 | − | 1.48622i | −1.14719 | − | 0.0523175i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.8023 | −0.379790 | −0.189895 | − | 0.981804i | \(-0.560815\pi\) | ||||
−0.189895 | + | 0.981804i | \(0.560815\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.58307 | −0.196048 | −0.0980240 | − | 0.995184i | \(-0.531252\pi\) | ||||
−0.0980240 | + | 0.995184i | \(0.531252\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.4954 | + | 1.89240i | 1.45531 | + | 0.0663694i | ||||
\(814\) | 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 | ||||||||
\(819\) | 2.98755 | + | 0.273062i | 0.104393 | + | 0.00954157i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.8940 | + | 27.5292i | 0.554703 | + | 0.960774i | 0.997927 | + | 0.0643630i | \(0.0205016\pi\) |
−0.443223 | + | 0.896411i | \(0.646165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.0000 | + | 31.1769i | −0.627441 | + | 1.08676i | 0.360623 | + | 0.932712i | \(0.382564\pi\) |
−0.988063 | + | 0.154047i | \(0.950769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.27647 | − | 11.3730i | 0.253334 | − | 0.395957i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.9224 | −0.553675 | −0.276837 | − | 0.960917i | \(-0.589286\pi\) | ||||
−0.276837 | + | 0.960917i | \(0.589286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.4720 | 1.23199 | 0.615996 | − | 0.787749i | \(-0.288754\pi\) | ||||
0.615996 | + | 0.787749i | \(0.288754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.70681 | − | 11.0148i | −0.197967 | − | 0.382099i | ||||
\(832\) | 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 | ||||||||
\(837\) | 7.41789 | − | 9.55155i | 0.256400 | − | 0.330150i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.3391 | − | 47.3527i | −0.943850 | − | 1.63480i | −0.758037 | − | 0.652212i | \(-0.773841\pi\) |
−0.185814 | − | 0.982585i | \(-0.559492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4730 | − | 19.8717i | 0.395619 | − | 0.685233i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.8576 | − | 22.8865i | −0.408397 | − | 0.788254i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.1230 | 1.07066 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.38151 | 0.322353 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.6665 | − | 29.1755i | 0.640633 | − | 1.00130i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.243379 | + | 0.421545i | −0.00834292 | + | 0.0144504i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.09884 | + | 1.90324i | 0.0376234 | + | 0.0651656i | 0.884224 | − | 0.467063i | \(-0.154688\pi\) |
−0.846601 | + | 0.532229i | \(0.821355\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.1929 | − | 25.7687i | 0.622184 | − | 0.881272i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.88823 | + | 13.6628i | 0.269457 | + | 0.466713i | 0.968722 | − | 0.248150i | \(-0.0798225\pi\) |
−0.699265 | + | 0.714863i | \(0.746489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.78813 | − | 4.82918i | 0.0951298 | − | 0.164770i | −0.814533 | − | 0.580117i | \(-0.803007\pi\) |
0.909663 | + | 0.415348i | \(0.136340\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.0847 | − | 0.505519i | −0.377766 | − | 0.0172281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.1268 | −0.787247 | −0.393623 | − | 0.919272i | \(-0.628779\pi\) | ||||
−0.393623 | + | 0.919272i | \(0.628779\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.0157 | −1.53058 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.8661 | − | 1.27084i | −0.946384 | − | 0.0431599i | ||||
\(868\) | 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 | ||||||||
\(873\) | 14.4459 | + | 31.2959i | 0.488920 | + | 1.05920i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.24484 | − | 7.35228i | −0.143502 | − | 0.248552i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.96264 | + | 3.39939i | −0.0662737 | + | 0.114789i | −0.897258 | − | 0.441506i | \(-0.854444\pi\) |
0.830985 | + | 0.556295i | \(0.187778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.0631 | + | 21.9805i | −0.474338 | + | 0.741383i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.1986 | 0.916345 | 0.458173 | − | 0.888863i | \(-0.348504\pi\) | ||||
0.458173 | + | 0.888863i | \(0.348504\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.21341 | −0.276403 | −0.138202 | − | 0.990404i | \(-0.544132\pi\) | ||||
−0.138202 | + | 0.990404i | \(0.544132\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.63473 | + | 10.8757i | 0.189409 | + | 0.365582i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.24057 | + | 5.61283i | −0.108808 | + | 0.188460i | −0.915287 | − | 0.402801i | \(-0.868037\pi\) |
0.806480 | + | 0.591262i | \(0.201370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.336285 | + | 0.582462i | 0.0112786 | + | 0.0195352i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.6000 | + | 38.2876i | 0.455617 | + | 1.28268i | ||||
\(892\) | 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 | ||||||||
\(897\) | −0.217799 | − | 0.420378i | −0.00727211 | − | 0.0140360i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.72665 | −0.190995 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.93406 | 0.197692 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.74124 | + | 15.2254i | −0.324168 | + | 0.506670i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.3853 | − | 49.1648i | 0.943560 | − | 1.63429i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.06440 | + | 8.77180i | 0.168161 | + | 0.291263i | 0.937773 | − | 0.347248i | \(-0.112884\pi\) |
−0.769613 | + | 0.638511i | \(0.779551\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.62655 | + | 10.0230i | 0.153453 | + | 0.332443i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.9612 | + | 39.7699i | 0.760738 | + | 1.31764i | 0.942471 | + | 0.334289i | \(0.108496\pi\) |
−0.181733 | + | 0.983348i | \(0.558171\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.13521 | − | 3.69829i | 0.0706652 | − | 0.122396i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.2017 | + | 0.465251i | 0.337259 | + | 0.0153807i | ||||
\(916\) | 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 | ||||||||
\(921\) | 47.1847 | + | 2.15186i | 1.55479 | + | 0.0709062i | ||||
\(922\) | 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 | ||||||||
\(927\) | −16.8296 | + | 23.8377i | −0.552755 | + | 0.782933i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.00379324 | − | 0.00657009i | −0.000124452 | − | 0.000215558i | 0.865963 | − | 0.500108i | \(-0.166706\pi\) |
−0.866088 | + | 0.499892i | \(0.833373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.02704 | + | 3.51094i | −0.0664336 | + | 0.115066i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.9189 | + | 23.3180i | −0.488422 | + | 0.763396i | ||||
\(934\) | 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 | ||||||||
\(939\) | −9.24105 | − | 17.8363i | −0.301570 | − | 0.582066i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.27908 | + | 3.94748i | −0.0742959 | + | 0.128684i | −0.900780 | − | 0.434276i | \(-0.857004\pi\) |
0.826484 | + | 0.562960i | \(0.190338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.875585 | + | 1.51656i | 0.0285130 | + | 0.0493859i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.3509 | − | 1.83680i | −0.434304 | − | 0.0597510i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.86760 | + | 11.8950i | 0.223167 | + | 0.386537i | 0.955768 | − | 0.294122i | \(-0.0950271\pi\) |
−0.732601 | + | 0.680658i | \(0.761694\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.753696 | − | 1.30544i | 0.0244660 | − | 0.0423764i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.60769 | + | 3.10303i | 0.0521329 | + | 0.100623i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.80699 | 0.285286 | 0.142643 | − | 0.989774i | \(-0.454440\pi\) | ||||
0.142643 | + | 0.989774i | \(0.454440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.82004 | −0.0588951 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.3691 | − | 16.2067i | 0.335184 | − | 0.523888i | ||||
\(958\) | 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 | ||||||||
\(963\) | 4.10584 | + | 0.375274i | 0.132309 | + | 0.0120930i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.7489 | + | 27.2779i | 0.506976 | + | 0.878108i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.1642 | − | 33.1934i | 0.616279 | − | 1.06743i | −0.373880 | − | 0.927477i | \(-0.621973\pi\) |
0.990159 | − | 0.139949i | \(-0.0446939\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.63521 | − | 0.302599i | −0.213154 | − | 0.00972088i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.0187 | 0.995436 | 0.497718 | − | 0.867339i | \(-0.334171\pi\) | ||||
0.497718 | + | 0.867339i | \(0.334171\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.05408 | 0.0658509 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.98755 | + | 0.136247i | 0.0956781 | + | 0.00436340i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.3712 | − | 45.6763i | 0.843689 | − | 1.46131i | −0.0430652 | − | 0.999072i | \(-0.513712\pi\) |
0.886755 | − | 0.462241i | \(-0.152954\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.4071 | − | 56.1307i | −1.03574 | − | 1.79395i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.1553 | − | 0.928200i | −0.324235 | − | 0.0296351i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.15146 | − | 15.8508i | −0.291886 | − | 0.505562i | 0.682370 | − | 0.731007i | \(-0.260950\pi\) |
−0.974256 | + | 0.225446i | \(0.927616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.2812 | + | 36.8601i | −0.678076 | + | 1.17446i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.3530 | + | 17.7446i | −0.361370 | + | 0.564816i | ||||
\(988\) | 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 | ||||||||
\(993\) | −15.7039 | − | 30.3103i | −0.498348 | − | 0.961869i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.4449 | + | 51.0001i | −0.933467 | + | 1.61681i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.87120 | − | 10.1692i | −0.185943 | − | 0.322062i | 0.757951 | − | 0.652311i | \(-0.226201\pi\) |
−0.943894 | + | 0.330249i | \(0.892867\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.16664 | + | 1.26113i | 0.290020 | + | 0.0399005i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))