Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(0.500000 + 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.961 |
Dual form | 1008.2.t.h.193.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.09097 | − | 1.34528i | 0.629873 | − | 0.776698i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.18194 | −1.42301 | −0.711504 | − | 0.702682i | \(-0.751986\pi\) | ||||
−0.711504 | + | 0.702682i | \(0.751986\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.710533 | − | 2.54856i | −0.268556 | − | 0.963264i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.619562 | − | 2.93533i | −0.206521 | − | 0.978442i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.18194 | −0.959392 | −0.479696 | − | 0.877435i | \(-0.659253\pi\) | ||||
−0.479696 | + | 0.877435i | \(0.659253\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.85185 | + | 4.93955i | 0.790960 | + | 1.36998i | 0.925373 | + | 0.379058i | \(0.123752\pi\) |
−0.134412 | + | 0.990925i | \(0.542915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.47141 | + | 4.28061i | −0.896314 | + | 1.10525i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.760877 | − | 1.31788i | −0.184540 | − | 0.319632i | 0.758882 | − | 0.651229i | \(-0.225746\pi\) |
−0.943421 | + | 0.331596i | \(0.892413\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.641315 | − | 1.11079i | 0.147128 | − | 0.254833i | −0.783037 | − | 0.621975i | \(-0.786330\pi\) |
0.930165 | + | 0.367142i | \(0.119664\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.20370 | − | 1.82454i | −0.917322 | − | 0.398147i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.23912 | −0.466889 | −0.233445 | − | 0.972370i | \(-0.575000\pi\) | ||||
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.12476 | 1.02495 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.62476 | − | 2.36887i | −0.890036 | − | 0.455890i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.54063 | + | 6.13255i | −0.657478 | + | 1.13879i | 0.323788 | + | 0.946130i | \(0.395043\pi\) |
−0.981266 | + | 0.192656i | \(0.938290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.71053 | + | 8.15888i | −0.846037 | + | 1.46538i | 0.0386810 | + | 0.999252i | \(0.487684\pi\) |
−0.884718 | + | 0.466127i | \(0.845649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.47141 | + | 4.28061i | −0.604295 | + | 0.745158i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.26088 | + | 8.10936i | 0.382158 | + | 1.37073i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.75636 | + | 1.55237i | 1.56227 | + | 0.248578i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.80150 | − | 4.85235i | −0.437522 | − | 0.757810i | 0.559976 | − | 0.828509i | \(-0.310810\pi\) |
−0.997498 | + | 0.0706992i | \(0.977477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.41423 | + | 5.91362i | −0.520665 | + | 0.901819i | 0.479046 | + | 0.877790i | \(0.340983\pi\) |
−0.999711 | + | 0.0240288i | \(0.992351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.97141 | + | 9.34004i | 0.293880 | + | 1.39233i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.91423 | − | 5.04759i | −0.425084 | − | 0.736267i | 0.571344 | − | 0.820711i | \(-0.306422\pi\) |
−0.996428 | + | 0.0844432i | \(0.973089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.99028 | + | 3.62167i | −0.855755 | + | 0.517381i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.60301 | − | 0.414174i | −0.364494 | − | 0.0579959i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.02859 | + | 1.78157i | 0.141288 | + | 0.244717i | 0.927982 | − | 0.372626i | \(-0.121542\pi\) |
−0.786694 | + | 0.617343i | \(0.788209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1248 | 1.36522 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.794668 | − | 2.07459i | −0.105256 | − | 0.274786i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.562382 | + | 0.974074i | −0.0732159 | + | 0.126814i | −0.900309 | − | 0.435251i | \(-0.856660\pi\) |
0.827093 | + | 0.562065i | \(0.189993\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.56238 | − | 2.70612i | −0.200042 | − | 0.346484i | 0.748499 | − | 0.663135i | \(-0.230775\pi\) |
−0.948542 | + | 0.316652i | \(0.897441\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.04063 | + | 3.66464i | −0.887036 | + | 0.461701i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.07442 | − | 15.7174i | −1.12554 | − | 1.94950i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.48345 | − | 9.49761i | 0.669910 | − | 1.16032i | −0.308019 | − | 0.951380i | \(-0.599666\pi\) |
0.977929 | − | 0.208938i | \(-0.0670006\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.44282 | + | 3.01225i | −0.294081 | + | 0.362632i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.69002 | −1.03132 | −0.515658 | − | 0.856794i | \(-0.672452\pi\) | ||||
−0.515658 | + | 0.856794i | \(0.672452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.48345 | − | 4.30146i | −0.290666 | − | 0.503448i | 0.683302 | − | 0.730136i | \(-0.260543\pi\) |
−0.973967 | + | 0.226689i | \(0.927210\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.59097 | − | 6.89425i | 0.645590 | − | 0.796079i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.26088 | + | 8.10936i | 0.257651 | + | 0.924148i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.06922 | − | 3.58399i | −0.232805 | − | 0.403231i | 0.725827 | − | 0.687877i | \(-0.241457\pi\) |
−0.958633 | + | 0.284646i | \(0.908124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.23229 | + | 3.63723i | −0.914699 | + | 0.404137i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.03379 | − | 6.98673i | 0.442766 | − | 0.766893i | −0.555127 | − | 0.831765i | \(-0.687331\pi\) |
0.997894 | + | 0.0648718i | \(0.0206639\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.42107 | + | 4.19341i | 0.262602 | + | 0.454839i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.38727 | + | 11.4536i | 0.470365 | + | 1.22795i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.112725 | − | 0.195246i | 0.0119488 | − | 0.0206960i | −0.859989 | − | 0.510312i | \(-0.829530\pi\) |
0.871938 | + | 0.489616i | \(0.162863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5624 | − | 10.7778i | 1.10724 | − | 1.12982i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.83693 | + | 15.2381i | 0.605262 | + | 1.58012i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.04063 | + | 3.53447i | −0.209364 | + | 0.362629i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.42107 | − | 12.8537i | 0.753495 | − | 1.30509i | −0.192624 | − | 0.981273i | \(-0.561700\pi\) |
0.946119 | − | 0.323819i | \(-0.104967\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.97141 | + | 9.34004i | 0.198134 | + | 0.938710i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.5893 | 1.84971 | 0.924854 | − | 0.380322i | \(-0.124187\pi\) | ||||
0.924854 | + | 0.380322i | \(0.124187\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.282630 | 0.0278484 | 0.0139242 | − | 0.999903i | \(-0.495568\pi\) | ||||
0.0139242 | + | 0.999903i | \(0.495568\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.3759 | + | 5.80557i | 1.30536 | + | 0.566566i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.68878 | + | 9.85326i | −0.549955 | + | 0.952550i | 0.448322 | + | 0.893872i | \(0.352022\pi\) |
−0.998277 | + | 0.0586780i | \(0.981311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21053 | − | 3.82876i | −0.211731 | − | 0.366728i | 0.740526 | − | 0.672028i | \(-0.234577\pi\) |
−0.952256 | + | 0.305300i | \(0.901243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.619562 | − | 1.61745i | −0.0588062 | − | 0.153522i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.60752 | − | 2.78431i | −0.151223 | − | 0.261926i | 0.780454 | − | 0.625213i | \(-0.214988\pi\) |
−0.931677 | + | 0.363287i | \(0.881655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.12476 | 0.664388 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.7323 | − | 11.4315i | 1.17710 | − | 1.05684i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.81806 | + | 2.87553i | −0.258331 | + | 0.263600i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.875237 | −0.0795670 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.58414 | − | 1.52496i | −0.864172 | − | 0.137501i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.396990 | −0.0355079 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.1053 | −1.78406 | −0.892030 | − | 0.451976i | \(-0.850719\pi\) | ||||
−0.892030 | + | 0.451976i | \(0.850719\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.23065 | + | 11.0447i | 0.372488 | + | 0.972431i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.36389 | −0.556015 | −0.278008 | − | 0.960579i | \(-0.589674\pi\) | ||||
−0.278008 | + | 0.960579i | \(0.589674\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.28659 | − | 0.845174i | −0.284983 | − | 0.0732859i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.7157 | + | 7.53762i | 1.26653 | + | 0.648735i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.74145 | 0.234218 | 0.117109 | − | 0.993119i | \(-0.462637\pi\) | ||||
0.117109 | + | 0.993119i | \(0.462637\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.98345 | + | 6.89953i | 0.337872 | + | 0.585211i | 0.984032 | − | 0.177991i | \(-0.0569597\pi\) |
−0.646161 | + | 0.763202i | \(0.723626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.96978 | − | 1.58632i | −0.839607 | − | 0.133593i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.07442 | − | 15.7174i | −0.758841 | − | 1.31435i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2661 | − | 19.5134i | 0.935597 | − | 1.62050i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.66307 | + | 12.0098i | −0.137168 | + | 0.990548i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.2599 | −1.90553 | −0.952764 | − | 0.303712i | \(-0.901774\pi\) | ||||
−0.952764 | + | 0.303712i | \(0.901774\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.12476 | 0.661184 | 0.330592 | − | 0.943774i | \(-0.392752\pi\) | ||||
0.330592 | + | 0.943774i | \(0.392752\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.39699 | + | 3.04993i | −0.274630 | + | 0.246572i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.9887 | − | 25.9611i | 1.20392 | − | 2.08525i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.63160 | − | 9.75422i | 0.449451 | − | 0.778471i | −0.548900 | − | 0.835888i | \(-0.684953\pi\) |
0.998350 | + | 0.0574170i | \(0.0182864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.51887 | + | 0.559900i | 0.279065 | + | 0.0444030i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.59097 | + | 5.70653i | 0.125386 | + | 0.449738i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.99028 | − | 3.44727i | 0.155891 | − | 0.270011i | −0.777492 | − | 0.628893i | \(-0.783508\pi\) |
0.933383 | + | 0.358881i | \(0.116842\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.0458 | − | 13.6207i | 0.859917 | − | 1.06037i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.61956 | − | 4.53721i | −0.202708 | − | 0.351100i | 0.746692 | − | 0.665170i | \(-0.231641\pi\) |
−0.949400 | + | 0.314070i | \(0.898307\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.76608 | + | 16.9153i | −0.751237 | + | 1.30118i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.65787 | − | 1.19427i | −0.279724 | − | 0.0913278i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.27579 | − | 2.20974i | −0.0969968 | − | 0.168003i | 0.813443 | − | 0.581644i | \(-0.197590\pi\) |
−0.910440 | + | 0.413641i | \(0.864257\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.64132 | − | 13.0608i | −0.275258 | − | 0.987300i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.696860 | + | 1.81925i | 0.0523792 | + | 0.136743i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.51887 | − | 6.09487i | −0.263013 | − | 0.455552i | 0.704028 | − | 0.710172i | \(-0.251383\pi\) |
−0.967041 | + | 0.254620i | \(0.918050\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9669 | −0.963822 | −0.481911 | − | 0.876220i | \(-0.660057\pi\) | ||||
−0.481911 | + | 0.876220i | \(0.660057\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.34501 | − | 0.850463i | −0.395115 | − | 0.0628680i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.59097 | + | 2.75564i | −0.116971 | + | 0.202599i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.42107 | + | 4.19341i | 0.177046 | + | 0.306653i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.75116 | + | 13.4696i | −0.200118 | + | 0.979772i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.990285 | + | 1.71522i | 0.0716545 | + | 0.124109i | 0.899627 | − | 0.436660i | \(-0.143839\pi\) |
−0.827972 | + | 0.560769i | \(0.810505\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.27292 | − | 3.93680i | 0.163608 | − | 0.283377i | −0.772552 | − | 0.634951i | \(-0.781020\pi\) |
0.936160 | + | 0.351574i | \(0.114353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −31.0442 | − | 4.93955i | −2.22312 | − | 0.353728i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.8148 | −1.55424 | −0.777120 | − | 0.629353i | \(-0.783320\pi\) | ||||
−0.777120 | + | 0.629353i | \(0.783320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.14132 | − | 10.6371i | −0.435346 | − | 0.754042i | 0.561978 | − | 0.827152i | \(-0.310041\pi\) |
−0.997324 | + | 0.0731106i | \(0.976707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.79467 | − | 17.7384i | −0.479259 | − | 1.25117i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.1449 | + | 4.66611i | 1.27352 | + | 0.327497i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.91423 | + | 15.4399i | 0.622597 | + | 1.07837i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.38727 | + | 6.57256i | 0.0964223 | + | 0.456824i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.04063 | + | 3.53447i | −0.141153 | + | 0.244485i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.32846 | + | 14.4253i | 0.573355 | + | 0.993080i | 0.996218 | + | 0.0868863i | \(0.0276917\pi\) |
−0.422863 | + | 0.906193i | \(0.638975\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.48057 | + | 11.6905i | −0.649598 | + | 0.801021i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.8639 | − | 18.8168i | 0.740911 | − | 1.28330i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.1404 | + | 6.20790i | 1.63876 | + | 0.421420i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.49604 | − | 1.35183i | −0.574109 | − | 0.0913485i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.33981 | − | 7.51677i | 0.291927 | − | 0.505633i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.32846 | − | 9.22916i | 0.356820 | − | 0.618031i | −0.630608 | − | 0.776102i | \(-0.717194\pi\) |
0.987428 | + | 0.158071i | \(0.0505276\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.17511 | − | 15.0429i | −0.211674 | − | 1.00286i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.5081 | 0.962935 | 0.481468 | − | 0.876464i | \(-0.340104\pi\) | ||||
0.481468 | + | 0.876464i | \(0.340104\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2495 | 0.677308 | 0.338654 | − | 0.940911i | \(-0.390028\pi\) | ||||
0.338654 | + | 0.940911i | \(0.390028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.3759 | + | 5.80557i | 0.880071 | + | 0.381979i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.540628 | − | 0.936396i | 0.0354177 | − | 0.0613453i | −0.847773 | − | 0.530359i | \(-0.822057\pi\) |
0.883191 | + | 0.469014i | \(0.155390\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.27292 | + | 16.0612i | 0.604898 | + | 1.04771i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.07893 | − | 1.12635i | −0.459826 | − | 0.0731645i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.16019 | + | 10.6698i | 0.398470 | + | 0.690170i | 0.993537 | − | 0.113506i | \(-0.0362081\pi\) |
−0.595068 | + | 0.803676i | \(0.702875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | −0.837404 | −0.418702 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.08809 | + | 15.0429i | −0.262251 | + | 0.965000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.0607 | − | 11.5239i | 1.21775 | − | 0.736238i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.31573 | 0.465489 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.99837 | − | 13.0489i | −0.316759 | − | 0.826941i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.11109 | −0.322609 | −0.161305 | − | 0.986905i | \(-0.551570\pi\) | ||||
−0.161305 | + | 0.986905i | \(0.551570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.12476 | 0.447930 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.28263 | + | 1.31788i | 0.518678 | + | 0.0825287i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.66019 | 0.477830 | 0.238915 | − | 0.971041i | \(-0.423208\pi\) | ||||
0.238915 | + | 0.971041i | \(0.423208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.56238 | − | 0.658939i | −0.159219 | − | 0.0409445i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.1947 | + | 6.59341i | 1.25002 | + | 0.408122i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.09493 | 0.190842 | 0.0954208 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954208 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.27292 | − | 5.66886i | −0.201054 | − | 0.348235i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.139680 | − | 0.364654i | −0.00854830 | − | 0.0223165i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4451 | − | 23.2877i | −0.819765 | − | 1.41987i | −0.905855 | − | 0.423587i | \(-0.860771\pi\) |
0.0860906 | − | 0.996287i | \(-0.472563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.1082 | − | 19.2400i | 0.674776 | − | 1.16875i | −0.301759 | − | 0.953384i | \(-0.597574\pi\) |
0.976534 | − | 0.215362i | \(-0.0690930\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.97592 | − | 25.9677i | −0.180111 | − | 1.57163i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.3067 | −0.983331 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6375 | −0.879482 | −0.439741 | − | 0.898125i | \(-0.644930\pi\) | ||||
−0.439741 | + | 0.898125i | \(0.644930\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.8675 | + | 8.77202i | 1.60851 | + | 0.525167i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.6992 | − | 20.2636i | 0.697915 | − | 1.20882i | −0.271273 | − | 0.962502i | \(-0.587445\pi\) |
0.969188 | − | 0.246322i | \(-0.0792219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0624 | + | 22.6247i | −0.776478 | + | 1.34490i | 0.157482 | + | 0.987522i | \(0.449662\pi\) |
−0.933960 | + | 0.357377i | \(0.883671\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.52859 | + | 6.60123i | 0.149781 | + | 0.391023i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3759 | + | 10.5876i | −0.612471 | + | 0.624963i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.34213 | − | 12.7169i | 0.431890 | − | 0.748056i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.19562 | − | 24.0064i | −0.539057 | − | 1.40728i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.9315 | + | 22.3980i | 0.755465 | + | 1.30850i | 0.945143 | + | 0.326657i | \(0.105922\pi\) |
−0.189678 | + | 0.981846i | \(0.560745\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.78947 | − | 3.09945i | 0.104187 | − | 0.180457i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.7157 | + | 7.53762i | 0.853894 | + | 0.437377i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.38564 | − | 11.0603i | −0.369291 | − | 0.639631i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.4971 | + | 4.49954i | 1.00852 | + | 0.259349i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.2804 | − | 25.0079i | 1.16508 | − | 1.43667i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.97141 | + | 8.61073i | 0.284662 | + | 0.493049i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.53216 | −0.201591 | −0.100795 | − | 0.994907i | \(-0.532139\pi\) | ||||
−0.100795 | + | 0.994907i | \(0.532139\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.308342 | − | 0.380217i | 0.0175409 | − | 0.0216298i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.851848 | − | 1.47544i | 0.0483039 | − | 0.0836648i | −0.840863 | − | 0.541249i | \(-0.817952\pi\) |
0.889166 | + | 0.457584i | \(0.151285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.42107 | + | 2.46136i | 0.0803234 | + | 0.139124i | 0.903389 | − | 0.428822i | \(-0.141071\pi\) |
−0.823065 | + | 0.567947i | \(0.807738\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22.4029 | − | 11.6607i | 1.26226 | − | 0.657004i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4601 | + | 21.5815i | 0.699827 | + | 1.21214i | 0.968526 | + | 0.248911i | \(0.0800728\pi\) |
−0.268700 | + | 0.963224i | \(0.586594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.2661 | − | 19.5134i | 0.630779 | − | 1.09254i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.04910 | + | 18.4026i | 0.393442 | + | 1.02713i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.95185 | −0.108604 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.6150 | + | 25.3140i | 0.810697 | + | 1.40417i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.56238 | − | 1.20328i | −0.418201 | − | 0.0665413i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.7934 | + | 11.0136i | −0.595061 | + | 0.607198i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.58577 | − | 6.21074i | −0.197092 | − | 0.341373i | 0.750492 | − | 0.660879i | \(-0.229816\pi\) |
−0.947584 | + | 0.319506i | \(0.896483\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.85185 | − | 0.931107i | −0.156280 | − | 0.0510244i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.4480 | + | 30.2209i | −0.953287 | + | 1.65114i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9211 | − | 18.9158i | −0.594908 | − | 1.03041i | −0.993560 | − | 0.113309i | \(-0.963855\pi\) |
0.398651 | − | 0.917103i | \(-0.369478\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.49944 | − | 0.875035i | −0.298689 | − | 0.0475254i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.9887 | − | 25.9611i | 0.811681 | − | 1.40587i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4863 | + | 12.6933i | 0.728193 | + | 0.685372i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.77292 | − | 9.58481i | 0.418480 | − | 0.516029i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.05555 | + | 1.82826i | −0.0566646 | + | 0.0981460i | −0.892966 | − | 0.450124i | \(-0.851380\pi\) |
0.836302 | + | 0.548270i | \(0.184713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1082 | − | 31.3643i | 0.969310 | − | 1.67889i | 0.271751 | − | 0.962368i | \(-0.412397\pi\) |
0.697559 | − | 0.716527i | \(-0.254269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.48796 | − | 29.5999i | −0.0794215 | − | 1.57993i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4887 | −0.558255 | −0.279127 | − | 0.960254i | \(-0.590045\pi\) | ||||
−0.279127 | + | 0.960254i | \(0.590045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.6512 | 1.46757 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.793980 | + | 6.92820i | 0.0420219 | + | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.2209 | + | 28.0955i | −0.856108 | + | 1.48282i | 0.0195047 | + | 0.999810i | \(0.493791\pi\) |
−0.875613 | + | 0.483013i | \(0.839542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.67743 | + | 15.0297i | 0.456707 | + | 0.791039i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.954858 | + | 1.17744i | −0.0501171 | + | 0.0617995i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.90219 | + | 13.6870i | 0.413620 | + | 0.716410i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.1111 | 0.945391 | 0.472696 | − | 0.881226i | \(-0.343281\pi\) | ||||
0.472696 | + | 0.881226i | \(0.343281\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.5075 | + | 11.2297i | −0.651116 | + | 0.584593i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.80959 | − | 3.88728i | 0.197784 | − | 0.201818i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.6706 | −0.604280 | −0.302140 | − | 0.953263i | \(-0.597701\pi\) | ||||
−0.302140 | + | 0.953263i | \(0.597701\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.433105 | + | 0.534063i | −0.0223654 | + | 0.0275789i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.3893 | −2.08016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.2690 | −0.732947 | −0.366474 | − | 0.930428i | \(-0.619435\pi\) | ||||
−0.366474 | + | 0.930428i | \(0.619435\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.9343 | + | 27.0473i | −1.12373 | + | 1.38568i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.64979 | 0.0843001 | 0.0421501 | − | 0.999111i | \(-0.486579\pi\) | ||||
0.0421501 | + | 0.999111i | \(0.486579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.19398 | − | 25.8035i | −0.366639 | − | 1.31507i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.4737 | + | 6.35803i | 0.989905 | + | 0.323197i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.0676 | −1.62589 | −0.812946 | − | 0.582340i | \(-0.802137\pi\) | ||||
−0.812946 | + | 0.582340i | \(0.802137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.70370 | + | 2.95089i | 0.0861596 | + | 0.149233i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.94282 | + | 8.56122i | −0.350219 | + | 0.431856i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.58414 | + | 11.4041i | 0.331284 | + | 0.573800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.9669 | + | 32.8516i | −0.951921 | + | 1.64878i | −0.210660 | + | 0.977559i | \(0.567561\pi\) |
−0.741261 | + | 0.671217i | \(0.765772\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.72257 | + | 3.49932i | −0.236424 | + | 0.175185i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6192 | 0.530296 | 0.265148 | − | 0.964208i | \(-0.414579\pi\) | ||||
0.265148 | + | 0.964208i | \(0.414579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −53.7349 | −2.67673 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 26.1947 | − | 11.5735i | 1.30162 | − | 0.575090i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.59097 | + | 2.75564i | −0.0788615 | + | 0.136592i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.77292 | + | 4.80283i | −0.137112 | + | 0.237485i | −0.926402 | − | 0.376535i | \(-0.877115\pi\) |
0.789290 | + | 0.614020i | \(0.210449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.99084 | − | 3.68802i | 0.147527 | − | 0.181916i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.88207 | + | 0.741150i | 0.141818 | + | 0.0364696i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8353 | + | 22.2314i | −0.630060 | + | 1.09130i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6276 | + | 2.16834i | 0.667349 | + | 0.106184i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.77455 | − | 4.80566i | −0.135546 | − | 0.234772i | 0.790260 | − | 0.612772i | \(-0.209945\pi\) |
−0.925806 | + | 0.378000i | \(0.876612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.42107 | + | 5.92546i | −0.166733 | + | 0.288789i | −0.937269 | − | 0.348606i | \(-0.886655\pi\) |
0.770537 | + | 0.637396i | \(0.219988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.0108 | + | 11.6815i | −0.632606 | + | 0.567975i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.89931 | − | 6.75381i | −0.189144 | − | 0.327608i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.78659 | + | 5.90461i | −0.280033 | + | 0.285744i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.0442 | − | 4.93955i | −1.49883 | − | 0.238484i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.5539 | − | 28.6722i | −0.797374 | − | 1.38109i | −0.921321 | − | 0.388803i | \(-0.872889\pi\) |
0.123947 | − | 0.992289i | \(-0.460445\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1111 | −0.582022 | −0.291011 | − | 0.956720i | \(-0.593992\pi\) | ||||
−0.291011 | + | 0.956720i | \(0.593992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.9601 | − | 36.4446i | −0.669334 | − | 1.74739i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.43598 | + | 2.48720i | −0.0686924 | + | 0.118979i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.41711 | − | 7.65066i | −0.210817 | − | 0.365146i | 0.741153 | − | 0.671336i | \(-0.234279\pi\) |
−0.951970 | + | 0.306190i | \(0.900946\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.3421 | + | 15.3396i | 0.682959 | + | 0.730457i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.75924 | + | 15.1715i | 0.416164 | + | 0.720817i | 0.995550 | − | 0.0942360i | \(-0.0300408\pi\) |
−0.579386 | + | 0.815053i | \(0.696708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.358685 | + | 0.621261i | −0.0170033 | + | 0.0294506i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.3759 | + | 31.2911i | −1.20024 | + | 1.48002i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.2301 | 1.47384 | 0.736920 | − | 0.675980i | \(-0.236280\pi\) | ||||
0.736920 | + | 0.675980i | \(0.236280\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.91423 | + | 15.4399i | 0.419755 | + | 0.727036i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.86389 | − | 10.9301i | 0.416462 | − | 0.513540i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −33.6089 | + | 34.2944i | −1.57561 | + | 1.60775i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0624 | + | 27.8209i | 0.751367 | + | 1.30140i | 0.947161 | + | 0.320760i | \(0.103938\pi\) |
−0.195794 | + | 0.980645i | \(0.562728\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.396990 | + | 7.89729i | 0.0185299 | + | 0.368614i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.23229 | − | 2.13438i | 0.0573933 | − | 0.0994081i | −0.835901 | − | 0.548880i | \(-0.815054\pi\) |
0.893295 | + | 0.449472i | \(0.148388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.1735 | − | 26.2812i | −0.705171 | − | 1.22139i | −0.966630 | − | 0.256177i | \(-0.917537\pi\) |
0.261459 | − | 0.965215i | \(-0.415796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.5728 | − | 48.4868i | −0.861292 | − | 2.24852i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.98181 | − | 13.8249i | 0.369354 | − | 0.639740i | −0.620110 | − | 0.784515i | \(-0.712912\pi\) |
0.989465 | + | 0.144774i | \(0.0462456\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.1014 | − | 7.22651i | −1.29760 | − | 0.333689i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.97825 | − | 18.2177i | −0.321541 | − | 0.839425i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.8639 | − | 18.8168i | 0.499522 | − | 0.865198i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.28659 | − | 5.69254i | 0.150799 | − | 0.261192i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.59222 | − | 4.12304i | 0.210263 | − | 0.188781i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.1729 | 1.05880 | 0.529399 | − | 0.848373i | \(-0.322418\pi\) | ||||
0.529399 | + | 0.848373i | \(0.322418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.70370 | 0.260066 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.41260 | + | 4.08536i | 0.428288 | + | 0.185890i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.6134 | + | 40.8996i | −1.07223 | + | 1.85716i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.70658 | − | 2.95588i | −0.0773323 | − | 0.133943i | 0.824766 | − | 0.565474i | \(-0.191307\pi\) |
−0.902098 | + | 0.431531i | \(0.857974\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.46621 | − | 6.43837i | −0.111526 | − | 0.291153i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.58414 | + | 16.6002i | 0.432526 | + | 0.749157i | 0.997090 | − | 0.0762323i | \(-0.0242890\pi\) |
−0.564564 | + | 0.825389i | \(0.690956\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.7759 | 0.485323 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.27292 | − | 29.7195i | −0.281947 | − | 1.33579i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.17455 | + | 22.1470i | 0.276966 | + | 0.993430i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.1696 | −1.84301 | −0.921503 | − | 0.388371i | \(-0.873038\pi\) | ||||
−0.921503 | + | 0.388371i | \(0.873038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.96169 | − | 1.42593i | −0.400379 | − | 0.0637056i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.4542 | 1.17953 | 0.589767 | − | 0.807574i | \(-0.299220\pi\) | ||||
0.589767 | + | 0.807574i | \(0.299220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −59.1502 | −2.63215 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.1014 | + | 31.5923i | 0.537441 | + | 1.40306i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.7713 | 0.566077 | 0.283039 | − | 0.959109i | \(-0.408658\pi\) | ||||
0.283039 | + | 0.959109i | \(0.408658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.19794 | + | 9.38554i | −0.406893 | + | 0.415192i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.59725 | + | 3.61795i | −0.247125 | + | 0.159736i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.899313 | −0.0396285 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.27292 | + | 16.0612i | 0.407822 | + | 0.706369i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.36458 | − | 0.694462i | −0.191584 | − | 0.0304835i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.40615 | − | 5.89962i | −0.149226 | − | 0.258467i | 0.781716 | − | 0.623635i | \(-0.214345\pi\) |
−0.930942 | + | 0.365168i | \(0.881012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7535 | + | 25.5538i | −0.645125 | + | 1.11739i | 0.339148 | + | 0.940733i | \(0.389861\pi\) |
−0.984273 | + | 0.176656i | \(0.943472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.5430 | − | 9.35032i | −0.940211 | − | 0.408081i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.3365 | 0.624510 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9863 | −0.782014 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.20765 | + | 1.04728i | 0.139200 | + | 0.0454479i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.9789 | − | 27.6763i | 0.692125 | − | 1.19879i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.1014 | − | 31.3525i | 0.782591 | − | 1.35549i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0383 | − | 1.91546i | −0.519491 | − | 0.0826580i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.0607 | − | 11.5239i | 0.821004 | − | 0.496371i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7008 | − | 25.4626i | 0.632038 | − | 1.09472i | −0.355097 | − | 0.934829i | \(-0.615552\pi\) |
0.987135 | − | 0.159892i | \(-0.0511145\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.1465 | + | 17.4441i | −0.607085 | + | 0.748599i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.03379 | + | 12.1829i | 0.301295 | + | 0.521857i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6150 | + | 30.5102i | −0.753165 | + | 1.30452i | 0.193116 | + | 0.981176i | \(0.438141\pi\) |
−0.946281 | + | 0.323344i | \(0.895193\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.97537 | + | 6.26271i | −0.297701 | + | 0.267286i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.54132 | + | 7.86579i | 0.193467 | + | 0.335094i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.66376 | + | 7.82007i | −0.325896 | + | 0.332543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.97141 | + | 5.14663i | 0.0836817 | + | 0.218462i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.36909 | − | 5.83543i | −0.142753 | − | 0.247255i | 0.785779 | − | 0.618507i | \(-0.212262\pi\) |
−0.928532 | + | 0.371252i | \(0.878929\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.9475 | −1.64730 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.28263 | + | 1.31788i | 0.349693 | + | 0.0556408i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.729964 | + | 1.26433i | −0.0307643 | + | 0.0532853i | −0.880998 | − | 0.473121i | \(-0.843127\pi\) |
0.850233 | + | 0.526406i | \(0.176461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.11505 | + | 8.85952i | 0.215192 | + | 0.372723i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.1190 | + | 18.3961i | 0.634939 | + | 0.772563i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.78263 | − | 16.9440i | −0.410109 | − | 0.710330i | 0.584792 | − | 0.811183i | \(-0.301176\pi\) |
−0.994901 | + | 0.100853i | \(0.967843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.9629 | + | 18.9884i | −0.458785 | + | 0.794638i | −0.998897 | − | 0.0469545i | \(-0.985048\pi\) |
0.540112 | + | 0.841593i | \(0.318382\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.38783 | + | 0.539049i | 0.141529 | + | 0.0225191i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.4750 | −0.478540 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3655 | + | 21.4177i | 0.514783 | + | 0.891631i | 0.999853 | + | 0.0171554i | \(0.00546099\pi\) |
−0.485069 | + | 0.874476i | \(0.661206\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.81642 | − | 7.35265i | −0.117046 | − | 0.305566i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.6722 | − | 5.31604i | −0.857629 | − | 0.220547i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.27292 | − | 5.66886i | −0.135550 | − | 0.234780i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −40.5134 | + | 36.3743i | −1.67502 | + | 1.50389i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0796 | − | 31.3148i | 0.746226 | − | 1.29250i | −0.203394 | − | 0.979097i | \(-0.565197\pi\) |
0.949620 | − | 0.313404i | \(-0.101469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.04187 | + | 10.4648i | 0.248951 | + | 0.431196i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.7993 | + | 29.3470i | −0.978973 | + | 1.20717i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.55391 | + | 13.0838i | −0.310202 | + | 0.537285i | −0.978406 | − | 0.206693i | \(-0.933730\pi\) |
0.668204 | + | 0.743978i | \(0.267063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.96690 | − | 9.14978i | 0.367607 | − | 0.375105i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0098 | − | 3.34295i | −0.859876 | − | 0.136818i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.72708 | + | 4.72345i | −0.111426 | + | 0.192995i | −0.916345 | − | 0.400389i | \(-0.868875\pi\) |
0.804920 | + | 0.593384i | \(0.202208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.36840 | + | 5.83424i | −0.137400 | + | 0.237984i | −0.926512 | − | 0.376266i | \(-0.877208\pi\) |
0.789112 | + | 0.614250i | \(0.210541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.2759 | − | 10.2114i | −1.27365 | − | 0.415839i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.78495 | 0.113224 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.67059 | −0.270751 | −0.135376 | − | 0.990794i | \(-0.543224\pi\) | ||||
−0.135376 | + | 0.990794i | \(0.543224\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.0728 | − | 19.3194i | 1.05652 | − | 0.782860i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.6219 | − | 28.7899i | 0.672449 | − | 1.16472i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.654988 | + | 1.13447i | 0.0264547 | + | 0.0458209i | 0.878950 | − | 0.476915i | \(-0.158245\pi\) |
−0.852495 | + | 0.522735i | \(0.824912\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.4962 | + | 4.85235i | 1.22972 | + | 0.195666i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.2483 | + | 29.8749i | 0.694390 | + | 1.20272i | 0.970386 | + | 0.241560i | \(0.0776589\pi\) |
−0.275996 | + | 0.961159i | \(0.589008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.4484 | 0.661118 | 0.330559 | − | 0.943785i | \(-0.392763\pi\) | ||||
0.330559 | + | 0.943785i | \(0.392763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.3554 | + | 5.30420i | 0.415549 | + | 0.212850i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.577690 | − | 0.148558i | −0.0231446 | − | 0.00595184i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3606 | −0.974425 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.52859 | + | 6.60123i | 0.100982 | + | 0.263628i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.52175 | −0.0606763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0118 | 1.19475 | 0.597375 | − | 0.801962i | \(-0.296210\pi\) | ||||
0.597375 | + | 0.801962i | \(0.296210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.4922 | + | 4.53349i | 1.13246 | + | 0.180190i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 63.9740 | 2.53873 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.9728 | − | 19.2608i | −1.38567 | − | 0.763142i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.38401 | + | 25.5081i | 0.212988 | + | 1.00908i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.8993 | 1.10196 | 0.550978 | − | 0.834520i | \(-0.314255\pi\) | ||||
0.550978 | + | 0.834520i | \(0.314255\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.2524 | − | 24.6859i | −0.562060 | − | 0.973516i | −0.997317 | − | 0.0732100i | \(-0.976676\pi\) |
0.435257 | − | 0.900306i | \(-0.356658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.4617 | − | 35.1436i | −0.530054 | − | 1.38378i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.35705 | − | 14.4748i | −0.328550 | − | 0.569065i | 0.653675 | − | 0.756776i | \(-0.273226\pi\) |
−0.982224 | + | 0.187711i | \(0.939893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.78947 | − | 3.09945i | 0.0702427 | − | 0.121664i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 34.6878 | − | 25.7029i | 1.35952 | − | 1.00738i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.1650 | 1.49351 | 0.746756 | − | 0.665098i | \(-0.231610\pi\) | ||||
0.746756 | + | 0.665098i | \(0.231610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.2495 | 0.791214 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.0875 | + | 9.95475i | −0.432566 | + | 0.388372i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.37072 | + | 7.57031i | −0.170259 | + | 0.294898i | −0.938510 | − | 0.345251i | \(-0.887794\pi\) |
0.768251 | + | 0.640148i | \(0.221127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0419 | − | 17.3930i | 0.390584 | − | 0.676511i | −0.601943 | − | 0.798539i | \(-0.705607\pi\) |
0.992527 | + | 0.122028i | \(0.0389399\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.37756 | − | 14.0388i | −0.208847 | − | 0.545224i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.4577 | + | 2.68930i | 0.405534 | + | 0.104286i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.92790 | − | 13.7315i | 0.306970 | − | 0.531687i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.60262 | − | 17.2370i | −0.255272 | − | 0.666422i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.97141 | + | 8.61073i | 0.191919 | + | 0.332414i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.0264 | + | 29.4906i | −0.656319 | + | 1.13678i | 0.325242 | + | 0.945631i | \(0.394554\pi\) |
−0.981561 | + | 0.191148i | \(0.938779\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.7008 | − | 12.1399i | −0.912245 | − | 0.467266i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.358685 | + | 0.621261i | 0.0137854 | + | 0.0238770i | 0.872836 | − | 0.488014i | \(-0.162279\pi\) |
−0.859050 | + | 0.511891i | \(0.828945\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.0312 | − | 9.78005i | −1.45950 | − | 0.375324i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.8279 | − | 19.5174i | 0.606527 | − | 0.747910i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5270 | + | 18.2332i | 0.402803 | + | 0.697675i | 0.994063 | − | 0.108806i | \(-0.0347027\pi\) |
−0.591260 | + | 0.806481i | \(0.701369\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.72313 | −0.333294 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.1819 | − | 13.7885i | 0.426618 | − | 0.526064i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.86677 | + | 10.1615i | −0.223506 | + | 0.387124i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.92395 | + | 5.06442i | 0.111232 | + | 0.192660i | 0.916267 | − | 0.400567i | \(-0.131187\pi\) |
−0.805035 | + | 0.593227i | \(0.797854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.4029 | − | 11.6607i | 0.851015 | − | 0.442952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.6751 | − | 21.9539i | −0.480794 | − | 0.832760i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.26320 | + | 7.38408i | −0.161480 | + | 0.279692i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.669905 | − | 1.74888i | −0.0253381 | − | 0.0661486i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.2711 | 0.387935 | 0.193967 | − | 0.981008i | \(-0.437864\pi\) | ||||
0.193967 | + | 0.981008i | \(0.437864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.641315 | − | 1.11079i | −0.0241877 | − | 0.0418942i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.7233 | + | 5.04759i | 1.19477 | + | 0.190103i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.2083 | − | 47.3760i | −0.496751 | − | 1.78176i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.7427 | − | 37.6594i | −0.816564 | − | 1.41433i | −0.908200 | − | 0.418538i | \(-0.862543\pi\) |
0.0916356 | − | 0.995793i | \(-0.470790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.23818 | + | 8.29434i | −0.346459 | + | 0.311062i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.5475 | − | 18.2687i | 0.395006 | − | 0.684170i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.8743 | + | 50.0117i | 1.07984 | + | 1.87033i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.0744 | + | 3.35322i | 0.787039 | + | 0.125228i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.4412 | + | 44.0654i | −0.948796 | + | 1.64336i | −0.200830 | + | 0.979626i | \(0.564364\pi\) |
−0.747966 | + | 0.663737i | \(0.768969\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.200818 | − | 0.720299i | −0.00747886 | − | 0.0268253i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.1826 | + | 17.4887i | −0.527458 | + | 0.650410i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.1449 | + | 31.4279i | −0.673884 | + | 1.16720i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.07210 | + | 10.5172i | −0.225202 | + | 0.390061i | −0.956380 | − | 0.292126i | \(-0.905637\pi\) |
0.731178 | + | 0.682186i | \(0.238971\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.7769 | + | 21.9110i | 0.584329 | + | 0.811517i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.3912 | 0.384334 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.1696 | −1.70531 | −0.852657 | − | 0.522470i | \(-0.825011\pi\) | ||||
−0.852657 | + | 0.522470i | \(0.825011\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.29179 | − | 38.2144i | 0.195191 | − | 1.40956i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.4480 | + | 30.2209i | −0.642706 | + | 1.11320i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.49604 | + | 4.32327i | 0.0918184 | + | 0.159034i | 0.908276 | − | 0.418371i | \(-0.137399\pi\) |
−0.816458 | + | 0.577405i | \(0.804065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.98126 | − | 9.84172i | 0.293199 | − | 0.361545i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7060 | + | 27.2036i | 0.576198 | + | 0.998004i | 0.995910 | + | 0.0903470i | \(0.0287976\pi\) |
−0.419712 | + | 0.907657i | \(0.637869\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 74.0118 | 2.71158 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −23.0075 | − | 7.51179i | −0.841801 | − | 0.274842i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.1537 | + | 7.49711i | 1.06525 | + | 0.273939i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.29630 | −0.120284 | −0.0601419 | − | 0.998190i | \(-0.519155\pi\) | ||||
−0.0601419 | + | 0.998190i | \(0.519155\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.57605 | + | 6.87585i | −0.203203 | + | 0.250570i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.8525 | −0.940870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1384 | −0.368488 | −0.184244 | − | 0.982881i | \(-0.558984\pi\) | ||||
−0.184244 | + | 0.982881i | \(0.558984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.77292 | − | 9.58481i | 0.282139 | − | 0.347907i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0676 | 0.509950 | 0.254975 | − | 0.966948i | \(-0.417933\pi\) | ||||
0.254975 | + | 0.966948i | \(0.417933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.18715 | + | 8.35413i | −0.296395 | + | 0.302440i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.8090 | − | 9.70470i | 0.390801 | − | 0.350874i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.41531 | −0.231643 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3461 | + | 19.6520i | 0.409151 | + | 0.708669i | 0.994795 | − | 0.101899i | \(-0.0324918\pi\) |
−0.585644 | + | 0.810568i | \(0.699158\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.35705 | − | 10.3051i | 0.300972 | − | 0.371129i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.327772 | + | 0.567717i | 0.0117891 | + | 0.0204194i | 0.871860 | − | 0.489756i | \(-0.162914\pi\) |
−0.860071 | + | 0.510175i | \(0.829581\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.1404 | + | 41.8123i | −0.867148 | + | 1.50194i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.68194 | + | 2.72824i | −0.132089 | + | 0.0978751i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.18659 | −0.257486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.6512 | 0.989436 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.9018 | − | 19.9743i | 1.10434 | − | 0.713823i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.9194 | + | 31.0374i | −0.639572 | + | 1.10777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.270036 | − | 0.467717i | 0.00962576 | − | 0.0166723i | −0.861172 | − | 0.508313i | \(-0.830269\pi\) |
0.870798 | + | 0.491641i | \(0.163603\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.37648 | − | 4.16355i | 0.120206 | − | 0.148226i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.95378 | + | 6.07521i | −0.211692 | + | 0.216010i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.91135 | − | 15.4349i | 0.316451 | − | 0.548110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.1969 | − | 1.78157i | −0.397112 | − | 0.0631858i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.5550 | − | 21.7459i | −0.444721 | − | 0.770279i | 0.553312 | − | 0.832974i | \(-0.313364\pi\) |
−0.998033 | + | 0.0626954i | \(0.980030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.43474 | + | 7.68119i | −0.156890 | + | 0.271741i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.642950 | − | 0.209918i | −0.0227175 | − | 0.00741710i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.90219 | + | 13.6870i | 0.278862 | + | 0.483004i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.06238 | − | 18.1579i | −0.178426 | − | 0.639981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −45.9967 | − | 7.31869i | −1.61916 | − | 0.257630i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.5865 | − | 25.2645i | −0.512833 | − | 0.888252i | −0.999889 | − | 0.0148817i | \(-0.995263\pi\) |
0.487057 | − | 0.873370i | \(-0.338071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4290 | 0.541785 | 0.270892 | − | 0.962610i | \(-0.412681\pi\) | ||||
0.270892 | + | 0.962610i | \(0.412681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.7644 | − | 35.9339i | −0.482740 | − | 1.26026i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.33297 | + | 10.9690i | −0.221834 | + | 0.384228i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.37919 | + | 7.58499i | 0.153209 | + | 0.265365i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.1804 | − | 24.3265i | −1.33413 | − | 0.850038i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.24364 | − | 7.35019i | −0.148104 | − | 0.256524i | 0.782423 | − | 0.622748i | \(-0.213984\pi\) |
−0.930527 | + | 0.366224i | \(0.880650\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.5487 | − | 25.1991i | 0.507136 | − | 0.878385i | −0.492830 | − | 0.870126i | \(-0.664037\pi\) |
0.999966 | − | 0.00825976i | \(-0.00262919\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.7902 | + | 21.9371i | −0.619374 | + | 0.763752i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.9396 | 0.902007 | 0.451003 | − | 0.892522i | \(-0.351066\pi\) | ||||
0.451003 | + | 0.892522i | \(0.351066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.10821 | + | 5.38358i | 0.107953 | + | 0.186979i | 0.914941 | − | 0.403588i | \(-0.132237\pi\) |
−0.806988 | + | 0.590568i | \(0.798904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.9691 | + | 19.6915i | −0.553961 | + | 0.683092i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.33078 | + | 5.13882i | 0.323292 | + | 0.178049i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.33530 | + | 14.4372i | 0.288455 | + | 0.499618i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.1125 | − | 26.5742i | 1.42105 | − | 0.918540i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.2947 | + | 36.8834i | −0.735174 | + | 1.27336i | 0.219474 | + | 0.975618i | \(0.429566\pi\) |
−0.954647 | + | 0.297740i | \(0.903767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5721 | − | 18.3114i | −0.364555 | − | 0.631428i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.4967 | − | 37.8457i | −0.499294 | − | 1.30347i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.0751 | − | 53.8237i | 1.06902 | − | 1.85159i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.621885 | + | 2.23059i | 0.0213682 | + | 0.0766440i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.1859 | + | 42.2555i | 0.555499 | + | 1.45020i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.11956 | + | 1.93914i | −0.0383781 | + | 0.0664728i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.6969 | + | 18.5275i | −0.366254 | + | 0.634370i | −0.988976 | − | 0.148073i | \(-0.952693\pi\) |
0.622723 | + | 0.782442i | \(0.286026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.6391 | + | 3.80009i | 0.398050 | + | 0.129960i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.8435 | −1.25855 | −0.629275 | − | 0.777183i | \(-0.716648\pi\) | ||||
−0.629275 | + | 0.777183i | \(0.716648\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.6375 | 0.601783 | 0.300892 | − | 0.953658i | \(-0.402716\pi\) | ||||
0.300892 | + | 0.953658i | \(0.402716\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.92339 | + | 25.5093i | 0.0996289 | + | 0.869353i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.380438 | − | 0.658939i | 0.0129503 | − | 0.0224305i | −0.859478 | − | 0.511173i | \(-0.829211\pi\) |
0.872428 | + | 0.488743i | \(0.162544\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.05950 | + | 7.03127i | 0.138027 | + | 0.239070i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.09781 | − | 23.7511i | −0.308978 | − | 0.806628i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.58414 | + | 11.4041i | 0.223351 | + | 0.386856i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 62.5519 | 2.11949 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.3275 | − | 13.8196i | −1.43257 | − | 0.467723i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.282075 | + | 1.01175i | 0.00953586 | + | 0.0342035i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.4991 | −1.40132 | −0.700662 | − | 0.713494i | \(-0.747112\pi\) | ||||
−0.700662 | + | 0.713494i | \(0.747112\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.2394 | + | 7.03908i | 1.49216 | + | 0.237422i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.35486 | 0.281482 | 0.140741 | − | 0.990046i | \(-0.455051\pi\) | ||||
0.140741 | + | 0.990046i | \(0.455051\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6181 | −1.19864 | −0.599322 | − | 0.800508i | \(-0.704563\pi\) | ||||
−0.599322 | + | 0.800508i | \(0.704563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.21737 | − | 5.78874i | −0.0745361 | − | 0.194587i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.1100 | 1.24603 | 0.623016 | − | 0.782209i | \(-0.285907\pi\) | ||||
0.623016 | + | 0.782209i | \(0.285907\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.2855 | + | 51.2396i | 0.479121 | + | 1.71852i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.1947 | − | 11.5735i | 0.877554 | − | 0.387726i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.47576 | −0.250167 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1969 | + | 19.3935i | 0.374270 | + | 0.648254i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.8457 | − | 3.47594i | −0.729407 | − | 0.116058i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.3565 | − | 57.7751i | −1.11250 | − | 1.92691i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.56526 | − | 2.71111i | 0.0521464 | − | 0.0903202i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.1420 | − | 18.6297i | 0.836673 | − | 0.619957i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.2599 | 1.37153 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.1502 | 1.59880 | 0.799401 | − | 0.600798i | \(-0.205150\pi\) | ||||
0.799401 | + | 0.600798i | \(0.205150\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.5172 | − | 54.5658i | −0.382003 | − | 1.80983i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.4428 | + | 30.2119i | −0.577906 | + | 1.00096i | 0.417813 | + | 0.908533i | \(0.362797\pi\) |
−0.995719 | + | 0.0924301i | \(0.970537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.8353 | + | 22.2314i | −0.424786 | + | 0.735751i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.0075 | + | 2.70612i | 0.562251 | + | 0.0894617i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.52175 | + | 16.2187i | 0.149321 | + | 0.535590i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.8675 | − | 44.8037i | 0.853289 | − | 1.47794i | −0.0249351 | − | 0.999689i | \(-0.507938\pi\) |
0.878224 | − | 0.478250i | \(-0.158729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.85348 | + | 4.75174i | −0.126977 | + | 0.156575i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.7826 | − | 42.9248i | −0.815730 | − | 1.41289i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.56238 | − | 4.43818i | 0.0842506 | − | 0.145926i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.175107 | − | 0.829612i | −0.00575126 | − | 0.0272480i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.4142 | + | 44.0187i | 0.833814 | + | 1.44421i | 0.894993 | + | 0.446081i | \(0.147181\pi\) |
−0.0611787 | + | 0.998127i | \(0.519486\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.181255 | + | 8.97658i | 0.00594039 | + | 0.294196i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.05555 | − | 2.75564i | −0.0345570 | − | 0.0902157i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.70370 | − | 13.3432i | −0.251938 | − | 0.436369i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.54583 | 0.0831686 | 0.0415843 | − | 0.999135i | \(-0.486759\pi\) | ||||
0.0415843 | + | 0.999135i | \(0.486759\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.86156 | + | 0.773540i | 0.158651 | + | 0.0252435i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.578933 | + | 1.00274i | −0.0188727 | + | 0.0326885i | −0.875308 | − | 0.483567i | \(-0.839341\pi\) |
0.856435 | + | 0.516255i | \(0.172674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.27292 | + | 10.8650i | 0.204274 | + | 0.353813i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.75404 | − | 42.8596i | 0.284769 | − | 1.39422i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.90739 | + | 8.49985i | 0.159469 | + | 0.276208i | 0.934677 | − | 0.355497i | \(-0.115689\pi\) |
−0.775208 | + | 0.631706i | \(0.782355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.1648 | − | 24.5342i | 0.459810 | − | 0.796414i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.6267 | + | 6.78248i | 1.38227 | + | 0.219937i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.53791 | 0.211784 | 0.105892 | − | 0.994378i | \(-0.466230\pi\) | ||||
0.105892 | + | 0.994378i | \(0.466230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.15103 | − | 5.45774i | −0.101965 | − | 0.176608i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.9601 | − | 36.4446i | −0.451265 | − | 1.17809i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.94789 | − | 6.98673i | −0.0629006 | − | 0.225613i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8782 | − | 50.0186i | −0.931556 | − | 1.61350i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 32.4471 | + | 10.5937i | 1.04559 | + | 0.341378i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.23229 | + | 12.5267i | −0.232816 | + | 0.403248i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.4445 | − | 25.0185i | −0.464502 | − | 0.804542i | 0.534677 | − | 0.845057i | \(-0.320433\pi\) |
−0.999179 | + | 0.0405151i | \(0.987100\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.12941 | + | 2.62578i | −0.0684065 | + | 0.0843523i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.66827 | + | 4.62158i | −0.0856289 | + | 0.148314i | −0.905659 | − | 0.424007i | \(-0.860623\pi\) |
0.820030 | + | 0.572320i | \(0.193957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.7535 | − | 15.0544i | 0.472975 | − | 0.482622i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 49.9991 | + | 7.95552i | 1.60125 | + | 0.254780i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.0361 | − | 41.6318i | 0.768983 | − | 1.33192i | −0.169131 | − | 0.985594i | \(-0.554096\pi\) |
0.938115 | − | 0.346325i | \(-0.112571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.358685 | + | 0.621261i | −0.0114636 | + | 0.0198556i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.86909 | + | 8.86079i | −0.315096 | + | 0.282903i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.4627 | −0.939714 | −0.469857 | − | 0.882743i | \(-0.655694\pi\) | ||||
−0.469857 | + | 0.882743i | \(0.655694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 69.4134 | 2.21170 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.04102 | + | 26.5357i | 0.0967967 | + | 0.844640i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.64488 | − | 13.2413i | 0.243093 | − | 0.421050i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.4142 | − | 26.6982i | −0.489649 | − | 0.848097i | 0.510280 | − | 0.860008i | \(-0.329542\pi\) |
−0.999929 | + | 0.0119112i | \(0.996208\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.2672 | − | 1.95187i | −0.389286 | − | 0.0619407i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.5413 | + | 33.8466i | 0.619501 | + | 1.07301i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.54583 | 0.175638 | 0.0878191 | − | 0.996136i | \(-0.472010\pi\) | ||||
0.0878191 | + | 0.996136i | \(0.472010\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.36389 | + | 2.82073i | −0.138067 | + | 0.0892438i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))