Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,2,Mod(81,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.t (of order \(6\), 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: | \(1.78864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.951588245534976.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 177.6 | ||
Root | \(-0.716208 - 1.21944i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.177 |
Dual form | 224.2.t.a.81.6 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.13038 | − | 1.22998i | 1.22998 | − | 0.710128i | 0.262952 | − | 0.964809i | \(-0.415304\pi\) |
0.967025 | + | 0.254681i | \(0.0819706\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.28690 | + | 0.742990i | 0.575518 | + | 0.332275i | 0.759350 | − | 0.650682i | \(-0.225517\pi\) |
−0.183832 | + | 0.982958i | \(0.558850\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.129755 | − | 2.64257i | −0.0490429 | − | 0.998797i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.52569 | − | 2.64257i | 0.508562 | − | 0.880856i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.37021 | + | 2.52314i | −1.31767 | + | 0.760756i | −0.983353 | − | 0.181705i | \(-0.941838\pi\) |
−0.334315 | + | 0.942461i | \(0.608505\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.58633i | 0.717320i | 0.933468 | + | 0.358660i | \(0.116766\pi\) | ||||
−0.933468 | + | 0.358660i | \(0.883234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.65544 | 0.943831 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.629755 | − | 1.09077i | −0.152738 | − | 0.264550i | 0.779495 | − | 0.626408i | \(-0.215476\pi\) |
−0.932233 | + | 0.361858i | \(0.882142\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.68324 | + | 1.54917i | 0.615577 | + | 0.355404i | 0.775145 | − | 0.631783i | \(-0.217677\pi\) |
−0.159568 | + | 0.987187i | \(0.551010\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.52673 | − | 5.47008i | −0.769595 | − | 1.19367i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.697966 | + | 1.20891i | −0.145536 | + | 0.252076i | −0.929573 | − | 0.368639i | \(-0.879824\pi\) |
0.784037 | + | 0.620714i | \(0.213157\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.39593 | − | 2.41782i | −0.279186 | − | 0.483565i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.126378i | − | 0.0243215i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.638384i | − | 0.118545i | −0.998242 | − | 0.0592725i | \(-0.981122\pi\) | ||
0.998242 | − | 0.0592725i | \(-0.0188781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.82772 | − | 3.16571i | −0.328268 | − | 0.568578i | 0.653900 | − | 0.756581i | \(-0.273132\pi\) |
−0.982168 | + | 0.188003i | \(0.939798\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.20682 | + | 10.7505i | −1.08047 | + | 1.87143i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.79642 | − | 3.49712i | 0.303650 | − | 0.591121i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.21370 | + | 3.01013i | 0.857127 | + | 0.494862i | 0.863049 | − | 0.505120i | \(-0.168552\pi\) |
−0.00592229 | + | 0.999982i | \(0.501885\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.18113 | + | 5.50988i | 0.509388 | + | 0.882287i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.36226 | 0.993618 | 0.496809 | − | 0.867860i | \(-0.334505\pi\) | ||||
0.496809 | + | 0.867860i | \(0.334505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.02401i | − | 0.156160i | −0.996947 | − | 0.0780801i | \(-0.975121\pi\) | ||
0.996947 | − | 0.0780801i | \(-0.0248790\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.92680 | − | 2.26714i | 0.585373 | − | 0.337965i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.48316 | + | 9.49712i | −0.799802 | + | 1.38530i | 0.119943 | + | 0.992781i | \(0.461729\pi\) |
−0.919745 | + | 0.392516i | \(0.871605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96633 | + | 0.685774i | −0.995190 | + | 0.0979677i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.68324 | − | 1.54917i | −0.375729 | − | 0.216927i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.99481 | + | 2.88375i | −0.686089 | + | 0.396114i | −0.802145 | − | 0.597129i | \(-0.796308\pi\) |
0.116056 | + | 0.993243i | \(0.462975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.49868 | −1.01112 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.62177 | 1.00953 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.01720 | + | 1.74198i | −0.392806 | + | 0.226787i | −0.683375 | − | 0.730067i | \(-0.739489\pi\) |
0.290569 | + | 0.956854i | \(0.406155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1614 | − | 6.44406i | −1.42908 | − | 0.825077i | −0.432028 | − | 0.901860i | \(-0.642202\pi\) |
−0.997048 | + | 0.0767831i | \(0.975535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.18113 | − | 3.68884i | −0.904737 | − | 0.464751i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.92162 | + | 3.32834i | −0.238348 | + | 0.412830i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.443410 | − | 0.256003i | 0.0541711 | − | 0.0312757i | −0.472670 | − | 0.881240i | \(-0.656710\pi\) |
0.526841 | + | 0.849964i | \(0.323376\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.43393i | 0.413396i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.41363 | 0.879836 | 0.439918 | − | 0.898038i | \(-0.355007\pi\) | ||||
0.439918 | + | 0.898038i | \(0.355007\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.94731 | − | 8.56899i | −0.579038 | − | 1.00292i | −0.995590 | − | 0.0938118i | \(-0.970095\pi\) |
0.416552 | − | 0.909112i | \(-0.363239\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.94774 | − | 3.43393i | −0.686786 | − | 0.396516i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.23463 | + | 11.2212i | 0.824463 | + | 1.27877i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.35341 | − | 7.54032i | 0.489797 | − | 0.848353i | −0.510134 | − | 0.860095i | \(-0.670404\pi\) |
0.999931 | + | 0.0117420i | \(0.00373767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.42162 | + | 7.65847i | 0.491291 | + | 0.850941i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.97196i | − | 0.326215i | −0.986608 | − | 0.163107i | \(-0.947848\pi\) | ||
0.986608 | − | 0.163107i | \(-0.0521517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.87161i | − | 0.203004i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.785198 | − | 1.36000i | −0.0841820 | − | 0.145808i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.29186 | − | 2.23757i | 0.136937 | − | 0.237182i | −0.789399 | − | 0.613881i | \(-0.789607\pi\) |
0.926336 | + | 0.376699i | \(0.122941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.83456 | − | 0.335590i | 0.716456 | − | 0.0351794i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.78749 | − | 4.49611i | −0.807525 | − | 0.466225i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.30203 | + | 3.98724i | 0.236184 | + | 0.409082i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.57040 | −0.159449 | −0.0797247 | − | 0.996817i | \(-0.525404\pi\) | ||||
−0.0797247 | + | 0.996817i | \(0.525404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.3981i | 1.54757i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.181183 | − | 0.104606i | 0.0180284 | − | 0.0104087i | −0.490959 | − | 0.871183i | \(-0.663353\pi\) |
0.508987 | + | 0.860774i | \(0.330020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.43846 | − | 5.95558i | 0.338801 | − | 0.586821i | −0.645406 | − | 0.763839i | \(-0.723312\pi\) |
0.984207 | + | 0.177019i | \(0.0566453\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.474313 | − | 9.65975i | −0.0462882 | − | 0.942695i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.2048 | + | 6.46908i | 1.08321 | + | 0.625389i | 0.931759 | − | 0.363076i | \(-0.118274\pi\) |
0.151447 | + | 0.988465i | \(0.451607\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.6430 | − | 9.60883i | 1.59411 | − | 0.920359i | 0.601517 | − | 0.798860i | \(-0.294563\pi\) |
0.992591 | − | 0.121500i | \(-0.0387703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.8096 | 1.40566 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.05137 | −0.0989050 | −0.0494525 | − | 0.998776i | \(-0.515748\pi\) | ||||
−0.0494525 | + | 0.998776i | \(0.515748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.79642 | + | 1.03716i | −0.167517 | + | 0.0967160i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.83456 | + | 3.94593i | 0.631855 | + | 0.364802i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.80071 | + | 1.80570i | −0.256741 | + | 0.165529i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.23250 | − | 12.5271i | 0.657500 | − | 1.13882i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.5540 | − | 7.82543i | 1.22213 | − | 0.705595i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.5786i | − | 1.03562i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.20814 | 0.639619 | 0.319809 | − | 0.947482i | \(-0.396381\pi\) | ||||
0.319809 | + | 0.947482i | \(0.396381\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.25951 | − | 2.18154i | −0.110894 | − | 0.192074i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7767 | − | 7.37662i | −1.11630 | − | 0.644498i | −0.175849 | − | 0.984417i | \(-0.556267\pi\) |
−0.940455 | + | 0.339919i | \(0.889600\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.74562 | − | 7.29165i | 0.324786 | − | 0.632267i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.0938978 | − | 0.162636i | 0.00808144 | − | 0.0139975i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.68113 | + | 8.10795i | 0.399936 | + | 0.692709i | 0.993718 | − | 0.111917i | \(-0.0356991\pi\) |
−0.593782 | + | 0.804626i | \(0.702366\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.69519i | − | 0.143784i | −0.997412 | − | 0.0718921i | \(-0.977096\pi\) | ||
0.997412 | − | 0.0718921i | \(-0.0229037\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.9767i | 2.27184i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.52569 | − | 11.3028i | −0.545705 | − | 0.945189i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.474313 | − | 0.821534i | 0.0393895 | − | 0.0682247i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.9975 | + | 10.0294i | −1.15449 | + | 0.827210i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.19276 | − | 1.84334i | −0.261561 | − | 0.151012i | 0.363485 | − | 0.931600i | \(-0.381587\pi\) |
−0.625047 | + | 0.780587i | \(0.714920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.13861 | − | 12.3644i | −0.580932 | − | 1.00620i | −0.995369 | − | 0.0961252i | \(-0.969355\pi\) |
0.414438 | − | 0.910078i | \(-0.363978\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.84324 | −0.310707 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.43191i | − | 0.436302i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.1614 | + | 6.44406i | −0.890780 | + | 0.514292i | −0.874197 | − | 0.485571i | \(-0.838612\pi\) |
−0.0165822 | + | 0.999863i | \(0.505279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.09390 | + | 12.2870i | −0.562583 | + | 0.974422i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.28520 | + | 1.68756i | 0.258910 | + | 0.132998i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.79831 | − | 1.61560i | −0.219180 | − | 0.126544i | 0.386390 | − | 0.922335i | \(-0.373722\pi\) |
−0.605571 | + | 0.795791i | \(0.707055\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.9751 | + | 9.22320i | −1.24366 | + | 0.718026i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.0487 | 1.08712 | 0.543562 | − | 0.839369i | \(-0.317075\pi\) | ||||
0.543562 | + | 0.839369i | \(0.317075\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.31088 | 0.485453 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.18757 | − | 4.72709i | 0.626119 | − | 0.361490i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.66273 | − | 3.26938i | −0.430529 | − | 0.248566i | 0.269043 | − | 0.963128i | \(-0.413293\pi\) |
−0.699572 | + | 0.714562i | \(0.746626\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.20814 | + | 4.00257i | −0.469291 | + | 0.302566i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.28520 | + | 7.42218i | −0.322095 | + | 0.557885i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.109447 | − | 0.0631891i | 0.00818044 | − | 0.00472298i | −0.495904 | − | 0.868377i | \(-0.665163\pi\) |
0.504085 | + | 0.863654i | \(0.331830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.71920i | 0.202117i | 0.994880 | + | 0.101058i | \(0.0322229\pi\) | ||||
−0.994880 | + | 0.101058i | \(0.967777\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −31.7042 | −2.34364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.47299 | + | 7.74745i | 0.328861 | + | 0.569604i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.50433 | + | 3.17793i | 0.402516 | + | 0.232393i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.333963 | + | 0.0163982i | −0.0242922 | + | 0.00119280i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.22365 | + | 2.11943i | −0.0885404 | + | 0.153357i | −0.906894 | − | 0.421358i | \(-0.861554\pi\) |
0.818354 | + | 0.574715i | \(0.194887\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.97431 | − | 3.41961i | −0.142114 | − | 0.246149i | 0.786178 | − | 0.618000i | \(-0.212057\pi\) |
−0.928293 | + | 0.371851i | \(0.878723\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.45419i | 0.677029i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.5468i | − | 1.39265i | −0.717727 | − | 0.696325i | \(-0.754817\pi\) | ||
0.717727 | − | 0.696325i | \(-0.245183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3981 | + | 18.0101i | 0.737103 | + | 1.27670i | 0.953795 | + | 0.300460i | \(0.0971401\pi\) |
−0.216692 | + | 0.976240i | \(0.569527\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.629755 | − | 1.09077i | 0.0444195 | − | 0.0769369i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.68697 | + | 0.0828337i | −0.118402 | + | 0.00581378i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.18757 | + | 4.72709i | 0.571845 | + | 0.330155i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.12976 | + | 3.68884i | 0.148028 | + | 0.256392i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.6351 | −1.08150 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.2132i | − | 1.18500i | −0.805569 | − | 0.592502i | \(-0.798140\pi\) | ||
0.805569 | − | 0.592502i | \(-0.201860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.7939 | − | 9.11860i | 1.08218 | − | 0.624796i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.760830 | − | 1.31780i | 0.0518882 | − | 0.0898730i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.12844 | + | 5.24064i | −0.551794 | + | 0.355758i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.0793 | − | 12.1701i | −1.42441 | − | 0.822382i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.82109 | − | 1.62876i | 0.189767 | − | 0.109562i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.5164 | −1.17298 | −0.586492 | − | 0.809955i | \(-0.699491\pi\) | ||||
−0.586492 | + | 0.809955i | \(0.699491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.51902 | −0.567935 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.4237 | − | 6.59546i | 0.758215 | − | 0.437756i | −0.0704394 | − | 0.997516i | \(-0.522440\pi\) |
0.828655 | + | 0.559760i | \(0.189107\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8693 | + | 8.58482i | 0.982594 | + | 0.567301i | 0.903052 | − | 0.429531i | \(-0.141321\pi\) |
0.0795417 | + | 0.996832i | \(0.474654\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 29.2143 | + | 15.0070i | 1.92216 | + | 0.987388i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.4393 | + | 21.5455i | −0.814927 | + | 1.41149i | 0.0944534 | + | 0.995529i | \(0.469890\pi\) |
−0.909380 | + | 0.415966i | \(0.863444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.1125 | + | 8.14787i | −0.920600 | + | 0.531508i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 21.4184i | − | 1.39127i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3242 | 0.861872 | 0.430936 | − | 0.902383i | \(-0.358183\pi\) | ||||
0.430936 | + | 0.902383i | \(0.358183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1218 | + | 19.2635i | 0.716416 | + | 1.24087i | 0.962411 | + | 0.271598i | \(0.0875521\pi\) |
−0.245995 | + | 0.969271i | \(0.579115\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.1678 | + | 11.0665i | 1.22962 | + | 0.709919i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.47446 | − | 4.29339i | −0.605301 | − | 0.274295i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00667 | + | 6.93975i | −0.254938 | + | 0.441566i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.65544 | − | 6.33141i | −0.231654 | − | 0.401237i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.4386i | 1.73191i | 0.500121 | + | 0.865955i | \(0.333289\pi\) | ||||
−0.500121 | + | 0.865955i | \(0.666711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.04427i | − | 0.442870i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.30203 | − | 3.98724i | −0.144159 | − | 0.249691i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.0948 | − | 20.9487i | 0.754451 | − | 1.30675i | −0.191196 | − | 0.981552i | \(-0.561237\pi\) |
0.945647 | − | 0.325195i | \(-0.105430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.27797 | − | 14.1681i | 0.452231 | − | 0.880365i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.68697 | − | 0.973974i | −0.104421 | − | 0.0602875i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.43846 | − | 9.41968i | −0.335350 | − | 0.580842i | 0.648202 | − | 0.761468i | \(-0.275521\pi\) |
−0.983552 | + | 0.180626i | \(0.942188\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.57040 | −0.526475 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.35585i | − | 0.388972i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.7887 | + | 12.0024i | −1.26751 | + | 0.731796i | −0.974516 | − | 0.224319i | \(-0.927984\pi\) |
−0.292992 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.11160 | − | 5.38945i | 0.189016 | − | 0.327386i | −0.755906 | − | 0.654680i | \(-0.772803\pi\) |
0.944922 | + | 0.327294i | \(0.106137\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.1475 | − | 9.12129i | 0.856243 | − | 0.552045i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.2010 | + | 7.04427i | 0.735750 | + | 0.424786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2493 | + | 14.0003i | −1.45700 | + | 0.841199i | −0.998863 | − | 0.0476832i | \(-0.984816\pi\) |
−0.458136 | + | 0.888882i | \(0.651483\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.1541 | −0.667780 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7112 | −0.996906 | −0.498453 | − | 0.866917i | \(-0.666098\pi\) | ||||
−0.498453 | + | 0.866917i | \(0.666098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.1193 | + | 13.9253i | −1.43374 | + | 0.827772i | −0.997404 | − | 0.0720102i | \(-0.977059\pi\) |
−0.436339 | + | 0.899782i | \(0.643725\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.80843 | + | 5.66290i | 0.581001 | + | 0.335441i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.825537 | − | 16.8127i | −0.0487299 | − | 0.992422i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.70682 | − | 13.3486i | 0.453342 | − | 0.785212i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.34554 | + | 1.93155i | −0.196119 | + | 0.113229i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.1851i | 1.17923i | 0.807685 | + | 0.589614i | \(0.200720\pi\) | ||||
−0.807685 | + | 0.589614i | \(0.799280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.17710 | −0.301423 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.318870 | + | 0.552300i | 0.0185027 | + | 0.0320477i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.12665 | − | 1.80517i | −0.180819 | − | 0.104396i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.70602 | + | 0.132871i | −0.155972 | + | 0.00765855i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.257326 | − | 0.445702i | 0.0147830 | − | 0.0256049i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.57574 | − | 16.5857i | −0.548305 | − | 0.949693i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.8844i | − | 1.02071i | −0.859962 | − | 0.510357i | \(-0.829513\pi\) | ||
0.859962 | − | 0.510357i | \(-0.170487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 16.9169i | − | 0.962368i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.715667 | − | 1.23957i | −0.0405818 | − | 0.0702897i | 0.845021 | − | 0.534733i | \(-0.179588\pi\) |
−0.885603 | + | 0.464443i | \(0.846254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.42829 | + | 4.20591i | −0.137255 | + | 0.237732i | −0.926457 | − | 0.376402i | \(-0.877161\pi\) |
0.789202 | + | 0.614134i | \(0.210495\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.50060 | − | 10.0827i | −0.366267 | − | 0.568094i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.78002 | + | 5.64650i | 0.549301 | + | 0.317139i | 0.748840 | − | 0.662751i | \(-0.230611\pi\) |
−0.199539 | + | 0.979890i | \(0.563944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.61073 | + | 2.78987i | 0.0901838 | + | 0.156203i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.8273 | 1.77642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.90239i | − | 0.217135i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.25330 | − | 3.61034i | 0.346871 | − | 0.200266i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.6373 | − | 40.9410i | 1.30714 | − | 2.26404i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.8082 | + | 13.2573i | 1.42285 | + | 0.730900i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.6415 | + | 11.9174i | 1.13456 | + | 0.655039i | 0.945078 | − | 0.326845i | \(-0.105986\pi\) |
0.189483 | + | 0.981884i | \(0.439319\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.9089 | − | 9.18503i | 0.871805 | − | 0.503337i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.760830 | 0.0415686 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4650 | 0.896906 | 0.448453 | − | 0.893806i | \(-0.351975\pi\) | ||||
0.448453 | + | 0.893806i | \(0.351975\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.23983 | + | 1.29317i | −0.121651 | + | 0.0702351i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.9751 | + | 9.22320i | 0.865098 | + | 0.499465i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.71612 | + | 18.3200i | 0.146657 | + | 0.989187i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.55137 | + | 4.41911i | −0.137361 | + | 0.237917i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.78706 | + | 1.60911i | −0.149617 | + | 0.0863817i | −0.572940 | − | 0.819597i | \(-0.694197\pi\) |
0.423322 | + | 0.905979i | \(0.360864\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.8716i | 1.22429i | 0.790747 | + | 0.612143i | \(0.209692\pi\) | ||||
−0.790747 | + | 0.612143i | \(0.790308\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.326856 | 0.0174463 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.6608 | − | 20.1971i | −0.620641 | − | 1.07498i | −0.989367 | − | 0.145444i | \(-0.953539\pi\) |
0.368725 | − | 0.929538i | \(-0.379794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.54058 | + | 5.50826i | 0.506361 | + | 0.292348i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.74562 | + | 7.29165i | −0.198239 | + | 0.385915i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.55488 | + | 4.42518i | −0.134841 | + | 0.233552i | −0.925537 | − | 0.378658i | \(-0.876386\pi\) |
0.790696 | + | 0.612210i | \(0.209719\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.70015 | − | 8.14090i | −0.247376 | − | 0.428468i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 35.5833i | − | 1.86764i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 14.7032i | − | 0.769600i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0779 | + | 24.3837i | 0.734862 | + | 1.27282i | 0.954784 | + | 0.297301i | \(0.0960863\pi\) |
−0.219922 | + | 0.975517i | \(0.570580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.70682 | − | 16.8127i | 0.505317 | − | 0.875234i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.26861 | + | 12.8249i | 0.429285 | + | 0.665837i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.10052 | − | 3.52214i | −0.315873 | − | 0.182369i | 0.333679 | − | 0.942687i | \(-0.391710\pi\) |
−0.649551 | + | 0.760318i | \(0.725043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.2414 | − | 24.6667i | −0.735420 | − | 1.27379i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.65107 | 0.0850346 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1974i | 0.677905i | 0.940803 | + | 0.338953i | \(0.110073\pi\) | ||||
−0.940803 | + | 0.338953i | \(0.889927\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3561 | − | 8.86584i | 0.786716 | − | 0.454211i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.46546 | + | 4.27031i | −0.125979 | + | 0.218202i | −0.922115 | − | 0.386915i | \(-0.873541\pi\) |
0.796136 | + | 0.605118i | \(0.206874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.972993 | + | 19.8158i | 0.0495883 | + | 1.00991i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.70602 | − | 1.56232i | −0.137555 | − | 0.0794172i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.8735 | − | 11.4739i | 1.00762 | − | 0.581752i | 0.0971291 | − | 0.995272i | \(-0.469034\pi\) |
0.910495 | + | 0.413520i | \(0.135701\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.75819 | 0.0889155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −36.2923 | −1.83070 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.2048 | − | 6.46908i | 0.563773 | − | 0.325495i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.9079 | − | 14.9579i | −1.30028 | − | 0.750716i | −0.319827 | − | 0.947476i | \(-0.603625\pi\) |
−0.980452 | + | 0.196760i | \(0.936958\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.988965 | − | 20.1410i | −0.0495102 | − | 1.00831i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.83525 | − | 13.5711i | 0.391274 | − | 0.677706i | −0.601344 | − | 0.798990i | \(-0.705368\pi\) |
0.992618 | + | 0.121284i | \(0.0387012\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.18757 | − | 4.72709i | 0.407852 | − | 0.235473i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.1409i | 0.652975i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.3800 | −1.50588 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0434 | + | 22.5918i | 0.644954 | + | 1.11709i | 0.984312 | + | 0.176436i | \(0.0564568\pi\) |
−0.339358 | + | 0.940657i | \(0.610210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.9452 | + | 11.5154i | 0.983824 | + | 0.568011i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.99481 | + | 7.74713i | 0.245778 | + | 0.381211i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.20814 | − | 3.82460i | 0.108393 | − | 0.187742i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.08505 | − | 3.61141i | −0.102105 | − | 0.176851i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 0.252757i | − | 0.0123480i | −0.999981 | − | 0.00617398i | \(-0.998035\pi\) | ||
0.999981 | − | 0.00617398i | \(-0.00196525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3701i | 0.895302i | 0.894208 | + | 0.447651i | \(0.147739\pi\) | ||||
−0.894208 | + | 0.447651i | \(0.852261\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.7312 | + | 28.9793i | 0.813498 | + | 1.40902i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.75819 | + | 3.04528i | −0.0852848 | + | 0.147718i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.5806 | + | 30.3310i | −0.753998 | + | 1.46782i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −27.8044 | − | 16.0529i | −1.34241 | − | 0.775041i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.7223 | + | 23.7678i | 0.660982 | + | 1.14485i | 0.980358 | + | 0.197226i | \(0.0631932\pi\) |
−0.319377 | + | 0.947628i | \(0.603473\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.26215 | −0.348997 | −0.174498 | − | 0.984657i | \(-0.555830\pi\) | ||||
−0.174498 | + | 0.984657i | \(0.555830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 2.33358i | − | 0.111886i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.74562 | + | 2.16253i | −0.179177 | + | 0.103448i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0022 | − | 25.9845i | 0.716015 | − | 1.24017i | −0.246551 | − | 0.969130i | \(-0.579297\pi\) |
0.962567 | − | 0.271045i | \(-0.0873692\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.81623 | + | 19.4553i | −0.419821 | + | 0.926441i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.3838 | − | 17.5421i | −1.44358 | − | 0.833451i | −0.445493 | − | 0.895285i | \(-0.646972\pi\) |
−0.998086 | + | 0.0618342i | \(0.980305\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.32499 | − | 1.91968i | 0.157620 | − | 0.0910017i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.06908 | −0.428953 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.0107 | −0.991556 | −0.495778 | − | 0.868449i | \(-0.665117\pi\) | ||||
−0.495778 | + | 0.868449i | \(0.665117\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.8044 | + | 16.0529i | −1.30926 | + | 0.755901i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.4159 | − | 17.5606i | −1.42906 | − | 0.825071i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.04471 | + | 4.64614i | 0.424022 | + | 0.217814i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.68780 | + | 11.5836i | −0.312842 | + | 0.541858i | −0.978976 | − | 0.203974i | \(-0.934614\pi\) |
0.666135 | + | 0.745832i | \(0.267948\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.137849 | + | 0.0795874i | −0.00643426 | + | 0.00371482i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.68641i | − | 0.125118i | −0.998041 | − | 0.0625592i | \(-0.980074\pi\) | ||
0.998041 | − | 0.0625592i | \(-0.0199262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0380 | 0.977721 | 0.488860 | − | 0.872362i | \(-0.337413\pi\) | ||||
0.488860 | + | 0.872362i | \(0.337413\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.68113 | − | 11.5721i | −0.309830 | − | 0.536641i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.3849 | − | 12.3466i | −0.989574 | − | 0.571331i | −0.0844270 | − | 0.996430i | \(-0.526906\pi\) |
−0.905147 | + | 0.425099i | \(0.860239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.734040 | − | 1.13852i | −0.0338948 | − | 0.0525721i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.8521 | + | 27.4566i | −0.730426 | + | 1.26513i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.58373 | + | 4.47515i | 0.118800 | + | 0.205767i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8.65014i | − | 0.396896i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.5988i | 0.805794i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.4562 | − | 35.4311i | −0.934666 | − | 1.61889i | −0.775229 | − | 0.631680i | \(-0.782366\pi\) |
−0.159437 | − | 0.987208i | \(-0.550968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.78520 | + | 13.4844i | −0.354974 | + | 0.614834i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.07439 | − | 0.445570i | 0.412899 | − | 0.0202741i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.02094 | − | 1.16679i | −0.0917660 | − | 0.0529811i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.76704 | + | 15.1850i | 0.397273 | + | 0.688096i | 0.993388 | − | 0.114802i | \(-0.0366234\pi\) |
−0.596116 | + | 0.802898i | \(0.703290\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.94863 | −0.359449 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7509i | 0.710830i | 0.934709 | + | 0.355415i | \(0.115660\pi\) | ||||
−0.934709 | + | 0.355415i | \(0.884340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.696329 | + | 0.402026i | −0.0313611 | + | 0.0181063i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.4406 | + | 19.8158i | −0.514219 | + | 0.890653i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.961958 | − | 19.5910i | −0.0431497 | − | 0.878778i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.82147 | − | 5.09308i | −0.394903 | − | 0.227997i | 0.289379 | − | 0.957215i | \(-0.406551\pi\) |
−0.684282 | + | 0.729217i | \(0.739884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.9292 | − | 17.2796i | 1.33714 | − | 0.771997i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.1001 | −1.20833 | −0.604167 | − | 0.796858i | \(-0.706494\pi\) | ||||
−0.604167 | + | 0.796858i | \(0.706494\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.310885 | 0.0138342 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.4446 | − | 7.76224i | 0.597096 | − | 0.344733i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.4357 | + | 11.2212i | 0.861471 | + | 0.497371i | 0.864505 | − | 0.502625i | \(-0.167632\pi\) |
−0.00303361 | + | 0.999995i | \(0.500966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.0022 | + | 14.1855i | −0.973319 | + | 0.627528i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.195781 | − | 0.339103i | 0.00864396 | − | 0.0149718i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.84987 | − | 5.10948i | 0.389972 | − | 0.225150i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 55.3392i | − | 2.43382i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0850 | −0.706055 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.13510 | + | 8.89426i | 0.224973 | + | 0.389664i | 0.956311 | − | 0.292350i | \(-0.0944373\pi\) |
−0.731338 | + | 0.682015i | \(0.761104\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.4655 | − | 8.92903i | −0.676261 | − | 0.390439i | 0.122184 | − | 0.992507i | \(-0.461010\pi\) |
−0.798445 | + | 0.602068i | \(0.794344\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.30264 | + | 16.1629i | −0.362357 | + | 0.705406i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.30203 | + | 3.98724i | −0.100278 | + | 0.173687i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.5257 | + | 18.2310i | 0.457639 | + | 0.792653i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.6309i | 0.461341i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.4549i | 0.712742i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.61292 | + | 16.6501i | 0.415603 | + | 0.719845i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.155442 | − | 0.269234i | 0.00670783 | − | 0.0116183i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.7140 | − | 20.5740i | 1.23680 | − | 0.886186i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.9303 | + | 11.5067i | 0.856869 | + | 0.494714i | 0.862963 | − | 0.505268i | \(-0.168606\pi\) |
−0.00609356 | + | 0.999981i | \(0.501940\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.34456 | + | 5.79294i | 0.143529 | + | 0.248599i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.5571 | 1.22325 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.10136i | 0.389146i | 0.980888 | + | 0.194573i | \(0.0623321\pi\) | ||||
−0.980888 | + | 0.194573i | \(0.937668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −34.0577 | + | 19.6632i | −1.45355 | + | 0.839206i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.988965 | − | 1.71294i | 0.0421313 | − | 0.0729736i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.4907 | − | 10.5258i | −0.871353 | − | 0.447602i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.0584 | + | 11.0034i | 0.808983 | + | 0.467067i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0016 | + | 8.66116i | −0.635637 | + | 0.366985i | −0.782932 | − | 0.622107i | \(-0.786277\pi\) |
0.147295 | + | 0.989093i | \(0.452943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.64843 | 0.112017 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.6351 | 0.660115 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.91560 | + | 3.99272i | −0.291458 | + | 0.168273i | −0.638599 | − | 0.769540i | \(-0.720486\pi\) |
0.347141 | + | 0.937813i | \(0.387152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.35301 | − | 0.781160i | −0.0569215 | − | 0.0328637i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.6643 | − | 12.6782i | 0.825823 | − | 0.532432i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.98535 | + | 10.3669i | −0.250919 | + | 0.434604i | −0.963779 | − | 0.266702i | \(-0.914066\pi\) |
0.712860 | + | 0.701306i | \(0.247399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.9016 | − | 21.3051i | 1.54428 | − | 0.891592i | 0.545722 | − | 0.837966i | \(-0.316255\pi\) |
0.998561 | − | 0.0536265i | \(-0.0170780\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.02026i | 0.251500i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.89725 | 0.162527 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9650 | + | 25.9202i | 0.623001 | + | 1.07907i | 0.988924 | + | 0.148425i | \(0.0474203\pi\) |
−0.365922 | + | 0.930645i | \(0.619246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.41208 | − | 4.85672i | −0.349594 | − | 0.201838i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.85360 | + | 0.385627i | −0.325822 | + | 0.0159985i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5522 | − | 25.2052i | 0.602692 | − | 1.04389i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.86358 | + | 10.1560i | 0.242429 | + | 0.419900i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.4269i | − | 0.801833i | −0.916115 | − | 0.400916i | \(-0.868692\pi\) | ||
0.916115 | − | 0.400916i | \(-0.131308\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.3258i | − | 0.466671i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.0421 | − | 41.6421i | −0.988959 | − | 1.71293i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.07706 | − | 15.7219i | 0.372750 | − | 0.645622i | −0.617237 | − | 0.786777i | \(-0.711748\pi\) |
0.989988 | + | 0.141155i | \(0.0450815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.94585 | + | 0.242851i | −0.202760 | + | 0.00995592i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.3039 | + | 25.5789i | 1.81324 | + | 1.04687i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.59258 | + | 9.68663i | 0.228507 | + | 0.395785i | 0.957366 | − | 0.288879i | \(-0.0932824\pi\) |
−0.728859 | + | 0.684664i | \(0.759949\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.21883 | −0.172090 | −0.0860448 | − | 0.996291i | \(-0.527423\pi\) | ||||
−0.0860448 | + | 0.996291i | \(0.527423\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.56232i | − | 0.0636226i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.6150 | − | 10.7474i | 0.756806 | − | 0.436942i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.6196 | + | 23.5898i | −0.552802 | + | 0.957481i | 0.445269 | + | 0.895397i | \(0.353108\pi\) |
−0.998071 | + | 0.0620841i | \(0.980225\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.49201 | + | 2.25141i | −0.141504 | + | 0.0912315i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.5627 | − | 14.1813i | −0.993701 | − | 0.573713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.20401 | − | 1.84984i | 0.129409 | − | 0.0747141i | −0.433898 | − | 0.900962i | \(-0.642862\pi\) |
0.563307 | + | 0.826248i | \(0.309529\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.2569 | 0.937808 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.0487 | 1.04868 | 0.524341 | − | 0.851508i | \(-0.324312\pi\) | ||||
0.524341 | + | 0.851508i | \(0.324312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.7816 | − | 16.0397i | 1.11664 | − | 0.644692i | 0.176098 | − | 0.984373i | \(-0.443652\pi\) |
0.940541 | + | 0.339681i | \(0.110319\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.152780 | + | 0.0882077i | 0.00613086 | + | 0.00353965i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.08057 | − | 3.12350i | −0.243613 | − | 0.125140i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.62309 | − | 2.81127i | 0.0649236 | − | 0.112451i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −33.3088 | + | 19.2308i | −1.33022 | + | 0.768005i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.58258i | − | 0.302337i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.7538 | −0.467912 | −0.233956 | − | 0.972247i | \(-0.575167\pi\) | ||||
−0.233956 | + | 0.972247i | \(0.575167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.1718 | − | 36.6707i | −0.841504 | − | 1.45753i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.27612 | + | 5.35557i | 0.368112 | + | 0.212529i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.77364 | − | 18.0172i | −0.0702742 | − | 0.713869i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3109 | − | 19.5910i | 0.447452 | − | 0.775009i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.9136 | − | 36.2235i | −0.826039 | − | 1.43074i | −0.901123 | − | 0.433564i | \(-0.857256\pi\) |
0.0750839 | − | 0.997177i | \(-0.476078\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.9368i | 1.69326i | 0.532180 | + | 0.846631i | \(0.321373\pi\) | ||||
−0.532180 | + | 0.846631i | \(0.678627\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 3.74321i | − | 0.147389i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.55891 | − | 7.89626i | −0.179229 | − | 0.310434i | 0.762388 | − | 0.647121i | \(-0.224027\pi\) |
−0.941617 | + | 0.336687i | \(0.890694\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.79054 | − | 15.2257i | 0.345059 | − | 0.597660i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.8708 | + | 21.1624i | −0.426061 | + | 0.829419i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.8716 | − | 10.8955i | −0.738502 | − | 0.426374i | 0.0830227 | − | 0.996548i | \(-0.473543\pi\) |
−0.821524 | + | 0.570174i | \(0.806876\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.9615 | − | 18.9859i | −0.428301 | − | 0.741840i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.1922 | −1.17791 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.152682i | 0.00594765i | 0.999996 | + | 0.00297383i | \(0.000946600\pi\) | ||||
−0.999996 | + | 0.00297383i | \(0.999053\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.6004 | + | 14.2031i | −0.956845 | + | 0.552435i | −0.895201 | − | 0.445663i | \(-0.852968\pi\) |
−0.0616446 | + | 0.998098i | \(0.519635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.00667 | − | 6.93975i | 0.155606 | − | 0.269518i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.2379 | − | 6.60065i | 0.397007 | − | 0.255962i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.771750 | + | 0.445570i | 0.0298823 | + | 0.0172525i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.3166 | + | 21.5447i | −1.44274 | + | 0.832968i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 65.0371 | 2.51073 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.2542 | 1.01203 | 0.506013 | − | 0.862526i | \(-0.331119\pi\) | ||||
0.506013 | + | 0.862526i | \(0.331119\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.305561 | + | 0.176415i | −0.0117610 | + | 0.00679023i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.00416 | − | 2.31180i | −0.153892 | − | 0.0888498i | 0.421076 | − | 0.907025i | \(-0.361652\pi\) |
−0.574969 | + | 0.818175i | \(0.694986\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.203767 | + | 4.14988i | 0.00781986 | + | 0.159258i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.2245 | − | 28.1017i | 0.621725 | − | 1.07686i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.8469 | + | 9.72659i | −0.644631 | + | 0.372178i | −0.786396 | − | 0.617723i | \(-0.788055\pi\) |
0.141765 | + | 0.989900i | \(0.454722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.9121i | 0.531555i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.2365 | 1.61142 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.45834 | − | 12.9182i | −0.284140 | − | 0.492145i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.0449 | − | 8.68618i | −0.572335 | − | 0.330438i | 0.185746 | − | 0.982598i | \(-0.440530\pi\) |
−0.758081 | + | 0.652160i | \(0.773863\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 40.6905 | − | 1.99799i | 1.54571 | − | 0.0758972i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.25951 | − | 2.18154i | 0.0477760 | − | 0.0827504i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00667 | − | 6.93975i | −0.151763 | − | 0.262862i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 61.2003i | 2.31481i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.1180i | − | 0.948695i | −0.880338 | − | 0.474348i | \(-0.842684\pi\) | ||
0.880338 | − | 0.474348i | \(-0.157316\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.32640 | + | 16.1538i | 0.351752 | + | 0.609252i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.0434 | + | 34.7162i | −0.754878 | + | 1.30749i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.299938 | − | 0.465215i | −0.0112803 | − | 0.0174962i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.4147 | − | 10.0544i | −0.654024 | − | 0.377601i | 0.135972 | − | 0.990713i | \(-0.456584\pi\) |
−0.789996 | + | 0.613112i | \(0.789918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.2839 | − | 23.0084i | −0.498184 | − | 0.862881i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.10275 | 0.191099 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 19.3941i | − | 0.725297i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.3857 | − | 16.3885i | 1.06008 | − | 0.612039i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.1966 | + | 33.2496i | −0.715914 | + | 1.24000i | 0.246692 | + | 0.969094i | \(0.420656\pi\) |
−0.962606 | + | 0.270906i | \(0.912677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.1842 | − | 8.31358i | −0.602730 | − | 0.309614i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.3873 | + | 27.3590i | 1.76235 | + | 1.01749i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.54350 | + | 0.891141i | −0.0573242 | + | 0.0330961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.8679 | −0.551422 | −0.275711 | − | 0.961241i | \(-0.588913\pi\) | ||||
−0.275711 | + | 0.961241i | \(0.588913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.9167 | 1.03395 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.11696 | + | 0.644877i | −0.0413122 | + | 0.0238516i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.4503 | + | 21.0446i | 1.34632 | + | 0.777300i | 0.987727 | − | 0.156192i | \(-0.0499219\pi\) |
0.358597 | + | 0.933492i | \(0.383255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −25.4650 | + | 2.50681i | −0.939291 | + | 0.0924650i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.29186 | + | 2.23757i | −0.0475864 | + | 0.0824221i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.9859 | − | 6.34270i | 0.404122 | − | 0.233320i | −0.284139 | − | 0.958783i | \(-0.591708\pi\) |
0.688261 | + | 0.725463i | \(0.258374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.7124i | 0.724154i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.7219 | 0.943644 | 0.471822 | − | 0.881694i | \(-0.343596\pi\) | ||||
0.471822 | + | 0.881694i | \(0.343596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.73917 | − | 4.74438i | −0.100355 | − | 0.173821i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.85360 | − | 4.53428i | −0.287348 | − | 0.165901i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.6411 | − | 30.4488i | 0.571513 | − | 1.11257i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9305 | − | 31.0565i | 0.654292 | − | 1.13327i | −0.327779 | − | 0.944755i | \(-0.606300\pi\) |
0.982071 | − | 0.188513i | \(-0.0603667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.7489 | + | 58.4548i | 1.22988 | + | 2.13021i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 21.2157i | − | 0.772117i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.7289i | 1.11686i | 0.829551 | + | 0.558431i | \(0.188597\pi\) | ||||
−0.829551 | + | 0.558431i | \(0.811403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.66429 | − | 15.0070i | −0.314494 | − | 0.544719i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5624 | + | 39.0792i | −0.817887 | + | 1.41662i | 0.0893497 | + | 0.996000i | \(0.471521\pi\) |
−0.907236 | + | 0.420621i | \(0.861812\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.5515 | − | 42.7334i | −0.997431 | − | 1.54705i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.94585 | − | 2.85549i | −0.178818 | − | 0.103240i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.50535 | − | 7.80349i | −0.162679 | − | 0.281768i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.0168 | −1.01031 | −0.505156 | − | 0.863028i | \(-0.668565\pi\) | ||||
−0.505156 | + | 0.863028i | \(0.668565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 59.5051i | − | 2.14302i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.9953 | − | 17.3178i | 1.07886 | − | 0.622878i | 0.148268 | − | 0.988947i | \(-0.452630\pi\) |
0.930588 | + | 0.366069i | \(0.119297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.10275 | + | 8.83822i | −0.183296 | + | 0.317478i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.92162 | − | 39.1353i | −0.0689377 | − | 1.40397i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.0715 | + | 9.85621i | 0.611649 | + | 0.353136i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.3992 | + | 18.7057i | −1.15933 | + | 0.669341i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0806779 | −0.00288319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.1515 | −0.683546 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.6763 | − | 17.1336i | 1.05784 | − | 0.610747i | 0.133009 | − | 0.991115i | \(-0.457536\pi\) |
0.924835 | + | 0.380368i | \(0.124203\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.1720 | − | 13.3784i | −0.824944 | − | 0.476282i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.136421 | + | 2.77833i | 0.00485058 | + | 0.0987860i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.6665 | − | 28.8672i | 0.591844 | − | 1.02510i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.2582 | + | 10.5414i | −0.647552 | + | 0.373865i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.5838i | 0.729114i | 0.931181 | + | 0.364557i | \(0.118780\pi\) | ||||
−0.931181 | + | 0.364557i | \(0.881220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.8122 | 0.488641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.94196 | − | 6.82767i | −0.139282 | − | 0.241244i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 43.2416 | + | 24.9655i | 1.52596 | + | 0.881014i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.97387 | + | 4.61258i | 0.104815 | + | 0.162572i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.5252 | + | 51.1392i | −1.03934 | + | 1.80019i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.4504 | + | 40.6172i | 0.824471 | + | 1.42802i | 0.902323 | + | 0.431060i | \(0.141860\pi\) |
−0.0778526 | + | 0.996965i | \(0.524806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.2462i | − | 0.781168i | −0.920567 | − | 0.390584i | \(-0.872273\pi\) | ||
0.920567 | − | 0.390584i | \(-0.127727\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 15.3088i | − | 0.536902i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.40076 | − | 4.15823i | −0.0840948 | − | 0.145656i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.58637 | − | 2.74767i | 0.0554999 | − | 0.0961287i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.54058 | − | 18.5728i | 0.333375 | − | 0.648986i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.4062 | − | 16.4003i | −0.991384 | − | 0.572376i | −0.0856966 | − | 0.996321i | \(-0.527312\pi\) |
−0.905688 | + | 0.423945i | \(0.860645\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.88576 | − | 11.9265i | −0.240023 | − | 0.415731i | 0.720698 | − | 0.693249i | \(-0.243822\pi\) |
−0.960720 | + | 0.277518i | \(0.910488\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.6572 | 1.20661 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0460i | 0.766615i | 0.923621 | + | 0.383307i | \(0.125215\pi\) | ||||
−0.923621 | + | 0.383307i | \(0.874785\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.74751 | − | 2.74098i | 0.164888 | − | 0.0951980i | −0.415285 | − | 0.909691i | \(-0.636318\pi\) |
0.580173 | + | 0.814493i | \(0.302985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.4402 | + | 59.6522i | −1.19472 | + | 2.06931i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.13510 | + | 7.16678i | 0.177921 | + | 0.248314i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0793 | + | 10.4381i | 0.625659 | + | 0.361224i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.400076 | + | 0.230984i | −0.0138287 | + | 0.00798398i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.7512 | −0.992601 | −0.496301 | − | 0.868151i | \(-0.665309\pi\) | ||||
−0.496301 | + | 0.868151i | \(0.665309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5925 | 0.985947 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.6012 | + | 20.5544i | −1.22617 | + | 0.707930i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.12145 | + | 4.68892i | 0.279387 | + | 0.161304i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.0421 | − | 17.4869i | −1.16970 | − | 0.600858i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.2556 | + | 59.3324i | −1.17565 | + | 2.03628i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.27797 | + | 4.20194i | −0.249486 | + | 0.144041i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 21.7605i | − | 0.745064i | −0.928019 | − | 0.372532i | \(-0.878490\pi\) | ||
0.928019 | − | 0.372532i | \(-0.121510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.0487 | 0.480457 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.89593 | − | 10.2121i | −0.201401 | − | 0.348837i | 0.747579 | − | 0.664173i | \(-0.231216\pi\) |
−0.948980 | + | 0.315336i | \(0.897883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.15132 | − | 2.39676i | −0.141641 | − | 0.0817766i | 0.427505 | − | 0.904013i | \(-0.359393\pi\) |
−0.569146 | + | 0.822237i | \(0.692726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.4379 | − | 34.8021i | −0.764683 | − | 1.18605i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.0628642 | + | 0.108884i | −0.00213992 | + | 0.00370646i | −0.867093 | − | 0.498146i | \(-0.834014\pi\) |
0.864953 | + | 0.501852i | \(0.167348\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.85823 | − | 8.41471i | −0.165185 | − | 0.286109i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 37.9168i | − | 1.28772i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.9371i | 1.49046i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.662108 | + | 1.14681i | 0.0224347 | + | 0.0388580i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.39593 | + | 4.14988i | −0.0810900 | + | 0.140452i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.5971 | + | 1.50238i | −1.03437 | + | 0.0507897i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.9534 | + | 14.9842i | 0.876385 | + | 0.505981i | 0.869465 | − | 0.493995i | \(-0.164464\pi\) |
0.00692013 | + | 0.999976i | \(0.497797\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.8273 | + | 43.0021i | 0.837403 | + | 1.45042i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.2728 | −1.01992 | −0.509959 | − | 0.860199i | \(-0.670339\pi\) | ||||
−0.509959 | + | 0.860199i | \(0.670339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.3423i | 1.45858i | 0.684203 | + | 0.729291i | \(0.260150\pi\) | ||||
−0.684203 | + | 0.729291i | \(0.739850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.0292 | + | 6.36772i | −0.370743 | + | 0.214048i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.56821 | − | 13.1085i | 0.254116 | − | 0.440141i | −0.710539 | − | 0.703658i | \(-0.751549\pi\) |
0.964655 | + | 0.263516i | \(0.0848823\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.935294 | − | 19.0480i | −0.0313687 | − | 0.638849i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.6468 | − | 22.3128i | −1.29472 | − | 0.747505i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.4253 | + | 16.9887i | −0.984680 | + | 0.568505i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.187796 | 0.00627731 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.88128 | −0.296537 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.02094 | + | 1.16679i | −0.0674020 | + | 0.0389146i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.29101 | + | 3.63212i | 0.209584 | + | 0.121003i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.60143 | + | 3.61141i | −0.186404 | + | 0.120180i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.02034 | + | 3.49933i | −0.0671584 | + | 0.116322i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.4761 | + | 15.8633i | −0.912328 | + | 0.526733i | −0.881180 | − | 0.472782i | \(-0.843250\pi\) |
−0.0311488 | + | 0.999515i | \(0.509917\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 0.638384i | − | 0.0211739i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.4757 | −0.976574 | −0.488287 | − | 0.872683i | \(-0.662378\pi\) | ||||
−0.488287 | + | 0.872683i | \(0.662378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.49868 | + | 12.9881i | 0.248170 | + | 0.429843i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −40.8000 | − | 23.5559i | −1.34881 | − | 0.778734i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.8354 | + | 34.7204i | −0.588976 | + | 1.14657i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.85875 | − | 15.3438i | 0.292223 | − | 0.506146i | −0.682112 | − | 0.731248i | \(-0.738938\pi\) |
0.974335 | + | 0.225102i | \(0.0722716\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.9974 | − | 38.1005i | −0.724838 | − | 1.25546i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.1741i | 0.631124i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 16.8077i | − | 0.552635i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.4920 | − | 18.1727i | −0.344603 | − | 0.596870i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.6338 | + | 46.1311i | −0.873826 | + | 1.51351i | −0.0158180 | + | 0.999875i | \(0.505035\pi\) |
−0.858008 | + | 0.513636i | \(0.828298\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.7547 | − | 8.95192i | −0.647434 | − | 0.293387i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.04929 | − | 1.76051i | −0.0998293 | − | 0.0576365i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.72233 | + | 8.17932i | 0.154437 | + | 0.267492i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.2055 | −1.24812 | −0.624060 | − | 0.781377i | \(-0.714518\pi\) | ||||
−0.624060 | + | 0.781377i | \(0.714518\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.9469i | 0.389874i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.31195 | + | 4.79890i | −0.270962 | + | 0.156440i | −0.629325 | − | 0.777143i | \(-0.716668\pi\) |
0.358363 | + | 0.933582i | \(0.383335\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.44064 | + | 7.69141i | −0.144607 | + | 0.250467i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.441960 | − | 0.227028i | −0.0143769 | − | 0.00738523i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.3314 | + | 8.27425i | 0.465709 | + | 0.268877i | 0.714442 | − | 0.699695i | \(-0.246681\pi\) |
−0.248733 | + | 0.968572i | \(0.580014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.1622 | − | 12.7954i | 0.719417 | − | 0.415356i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.7803 | 0.900837 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.08942 | 0.197256 | 0.0986278 | − | 0.995124i | \(-0.468555\pi\) | ||||
0.0986278 | + | 0.995124i | \(0.468555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.14943 | + | 1.81832i | −0.101913 | + | 0.0588396i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.86296 | + | 3.96233i | 0.221848 | + | 0.128084i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.8184 | − | 13.4223i | 0.672262 | − | 0.433427i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.81887 | − | 15.2747i | 0.284480 | − | 0.492733i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.1899 | − | 19.7396i | 1.10176 | − | 0.636099i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 5.86758i | − | 0.188884i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.5430 | −0.692778 | −0.346389 | − | 0.938091i | \(-0.612592\pi\) | ||||
−0.346389 | + | 0.938091i | \(0.612592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.79985 | − | 8.31358i | −0.154193 | − | 0.267071i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.27385 | − | 1.31281i | −0.0729715 | − | 0.0421301i | 0.463070 | − | 0.886322i | \(-0.346748\pi\) |
−0.536042 | + | 0.844191i | \(0.680081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.47966 | + | 0.219960i | −0.143611 | + | 0.00705160i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.88128 | − | 15.3828i | 0.284429 | − | 0.492645i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.2338 | + | 29.8499i | 0.551359 | + | 0.954982i | 0.998177 | + | 0.0603567i | \(0.0192238\pi\) |
−0.446818 | + | 0.894625i | \(0.647443\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.0382i | 0.416704i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 58.6403i | − | 1.87224i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.2210 | + | 45.4161i | 0.836320 | + | 1.44855i | 0.892951 | + | 0.450154i | \(0.148631\pi\) |
−0.0566303 | + | 0.998395i | \(0.518036\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.5230 | − | 25.1547i | 0.462743 | − | 0.801494i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 71.2877 | − | 3.50036i | 2.26911 | − | 0.111418i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.23794 | + | 0.714725i | 0.0393642 | + | 0.0227269i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.08057 | − | 13.9960i | −0.256688 | − | 0.444596i | 0.708665 | − | 0.705545i | \(-0.249298\pi\) |
−0.965353 | + | 0.260949i | \(0.915964\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 58.6325 | 1.86064 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.9028i | 0.979684i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.0954 | − | 19.6850i | 1.07981 | − | 0.623430i | 0.148967 | − | 0.988842i | \(-0.452405\pi\) |
0.930846 | + | 0.365412i | \(0.119072\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.380415 | − | 0.658898i | 0.0120358 | − | 0.0208466i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))