Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(49,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.by (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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 10x^{8} - 6x^{6} + 90x^{4} - 324x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.6 | ||
Root | \(1.62372 - 0.602950i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.529 |
Dual form | 720.2.by.e.49.6 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.62372 | − | 0.602950i | 0.937452 | − | 0.348114i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.194047 | − | 2.22763i | 0.0867804 | − | 0.996227i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.26460 | + | 1.88482i | 1.23390 | + | 0.712394i | 0.967841 | − | 0.251563i | \(-0.0809445\pi\) |
0.266061 | + | 0.963956i | \(0.414278\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.27290 | − | 1.95804i | 0.757634 | − | 0.652680i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.77290 | + | 3.07076i | −0.534550 | + | 0.925868i | 0.464635 | + | 0.885502i | \(0.346186\pi\) |
−0.999185 | + | 0.0403654i | \(0.987148\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.869061 | − | 0.501753i | 0.241034 | − | 0.139161i | −0.374618 | − | 0.927179i | \(-0.622226\pi\) |
0.615652 | + | 0.788018i | \(0.288893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.02807 | − | 3.73404i | −0.265448 | − | 0.964125i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.56023i | − | 0.378410i | −0.981938 | − | 0.189205i | \(-0.939409\pi\) | ||
0.981938 | − | 0.189205i | \(-0.0605911\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.21013 | 1.65412 | 0.827058 | − | 0.562116i | \(-0.190013\pi\) | ||||
0.827058 | + | 0.562116i | \(0.190013\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.43723 | + | 1.09201i | 1.40472 | + | 0.238297i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.35328 | + | 3.09072i | −1.11624 | + | 0.644459i | −0.940437 | − | 0.339967i | \(-0.889584\pi\) |
−0.175799 | + | 0.984426i | \(0.556251\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92469 | − | 0.864531i | −0.984938 | − | 0.172906i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.50994 | − | 4.54975i | 0.483039 | − | 0.875599i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.89142 | − | 5.00809i | −0.519315 | − | 0.899480i | −0.999748 | − | 0.0224486i | \(-0.992854\pi\) |
0.480433 | − | 0.877031i | \(-0.340480\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.02717 | + | 6.05500i | −0.178808 | + | 1.05404i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.83216 | − | 6.90658i | 0.816785 | − | 1.16743i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.851576i | − | 0.139998i | −0.997547 | − | 0.0699991i | \(-0.977700\pi\) | ||
0.997547 | − | 0.0699991i | \(-0.0222996\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.10858 | − | 1.33870i | 0.177514 | − | 0.214364i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.55926 | + | 2.70072i | 0.243516 | + | 0.421782i | 0.961713 | − | 0.274058i | \(-0.0883659\pi\) |
−0.718198 | + | 0.695839i | \(0.755033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.34403 | − | 1.35333i | −0.357462 | − | 0.206381i | 0.310505 | − | 0.950572i | \(-0.399502\pi\) |
−0.667967 | + | 0.744191i | \(0.732835\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.92074 | − | 5.44314i | −0.584470 | − | 0.811415i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.44260 | − | 4.87434i | −1.23148 | − | 0.710995i | −0.264141 | − | 0.964484i | \(-0.585088\pi\) |
−0.967338 | + | 0.253489i | \(0.918422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.60506 | + | 6.24415i | 0.515009 | + | 0.892022i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.940739 | − | 2.53336i | −0.131730 | − | 0.354742i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.2494i | − | 1.54523i | −0.634876 | − | 0.772614i | \(-0.718949\pi\) | ||
0.634876 | − | 0.772614i | \(-0.281051\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.49649 | + | 4.54524i | 0.875986 | + | 0.612881i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.7072 | − | 4.34735i | 1.55066 | − | 0.575821i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.83216 | + | 8.36955i | 0.629094 | + | 1.08962i | 0.987734 | + | 0.156147i | \(0.0499073\pi\) |
−0.358640 | + | 0.933476i | \(0.616759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.10506 | − | 7.11018i | 0.525600 | − | 0.910365i | −0.473956 | − | 0.880549i | \(-0.657174\pi\) |
0.999555 | − | 0.0298166i | \(-0.00949232\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.1107 | − | 2.10821i | 1.39981 | − | 0.265609i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.949082 | − | 2.03331i | −0.117719 | − | 0.252201i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.52711 | + | 1.45903i | −0.308736 | + | 0.178249i | −0.646361 | − | 0.763032i | \(-0.723710\pi\) |
0.337625 | + | 0.941281i | \(0.390376\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.82865 | + | 8.24621i | −0.822073 | + | 0.992727i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.21013 | −0.855685 | −0.427842 | − | 0.903853i | \(-0.640726\pi\) | ||||
−0.427842 | + | 0.903853i | \(0.640726\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.7817i | 1.96415i | 0.188498 | + | 0.982074i | \(0.439638\pi\) | ||||
−0.188498 | + | 0.982074i | \(0.560362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.51757 | + | 1.56559i | −0.983524 | + | 0.180779i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.5756 | + | 6.68319i | −1.31916 | + | 0.761620i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.49649 | + | 9.52020i | −0.618403 | + | 1.07111i | 0.371374 | + | 0.928483i | \(0.378887\pi\) |
−0.989777 | + | 0.142622i | \(0.954447\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.33216 | − | 8.90086i | 0.148018 | − | 0.988985i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.82952 | + | 5.09773i | 0.969166 | + | 0.559548i | 0.898982 | − | 0.437986i | \(-0.144308\pi\) |
0.0701843 | + | 0.997534i | \(0.477641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.47561 | − | 0.302757i | −0.376983 | − | 0.0328386i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.869061 | + | 5.12296i | −0.0931732 | + | 0.549239i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.33567 | 0.565580 | 0.282790 | − | 0.959182i | \(-0.408740\pi\) | ||||
0.282790 | + | 0.959182i | \(0.408740\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.78285 | 0.396550 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.71448 | − | 6.38833i | −0.799954 | − | 0.662439i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.39910 | − | 16.0615i | 0.143545 | − | 1.64788i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.34467 | − | 1.93105i | −0.339600 | − | 0.196068i | 0.320495 | − | 0.947250i | \(-0.396151\pi\) |
−0.660095 | + | 0.751182i | \(0.729484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.98303 | + | 10.4509i | 0.199302 | + | 1.05036i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.37797 | + | 4.11876i | −0.236616 | + | 0.409832i | −0.959741 | − | 0.280886i | \(-0.909372\pi\) |
0.723125 | + | 0.690717i | \(0.242705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.6656 | + | 9.04452i | −1.54357 | + | 0.891183i | −0.544966 | + | 0.838458i | \(0.683457\pi\) |
−0.998609 | + | 0.0527251i | \(0.983209\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.68173 | − | 14.1279i | 0.359300 | − | 1.37874i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.61770i | − | 0.349737i | −0.984592 | − | 0.174868i | \(-0.944050\pi\) | ||
0.984592 | − | 0.174868i | \(-0.0559500\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.63741 | 0.923096 | 0.461548 | − | 0.887115i | \(-0.347294\pi\) | ||||
0.461548 | + | 0.887115i | \(0.347294\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.513458 | − | 1.38272i | −0.0487353 | − | 0.131242i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.08152 | − | 1.77912i | 0.289885 | − | 0.167365i | −0.348005 | − | 0.937493i | \(-0.613141\pi\) |
0.637890 | + | 0.770127i | \(0.279807\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.84619 | + | 12.5249i | 0.545160 | + | 1.16795i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.992839 | − | 2.84209i | 0.0917880 | − | 0.262751i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.94074 | − | 5.09351i | 0.269577 | − | 0.466921i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.786360 | − | 1.36201i | −0.0714872 | − | 0.123820i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.16020 | + | 3.44504i | 0.375112 | + | 0.310629i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.88148 | + | 10.8026i | −0.257727 | + | 0.966218i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.78015i | − | 0.601641i | −0.953681 | − | 0.300820i | \(-0.902739\pi\) | ||
0.953681 | − | 0.300820i | \(-0.0972605\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.62203 | − | 0.784084i | −0.406947 | − | 0.0690347i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.71364 | − | 2.96811i | −0.149721 | − | 0.259325i | 0.781403 | − | 0.624027i | \(-0.214504\pi\) |
−0.931124 | + | 0.364702i | \(0.881171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.5382 | + | 13.5898i | 2.04102 | + | 1.17838i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.64811 | − | 6.47410i | −0.830377 | − | 0.557201i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9268 | − | 7.46330i | −1.10441 | − | 0.637633i | −0.167036 | − | 0.985951i | \(-0.553420\pi\) |
−0.937376 | + | 0.348318i | \(0.886753\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.71364 | + | 4.70016i | 0.230168 | + | 0.398663i | 0.957857 | − | 0.287244i | \(-0.0927391\pi\) |
−0.727689 | + | 0.685907i | \(0.759406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.6474 | − | 2.82406i | −1.40196 | − | 0.237829i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.55823i | 0.297554i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.49649 | + | 3.84560i | 0.456458 | + | 0.319359i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.61851 | + | 7.96505i | 0.793322 | + | 0.656946i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.76939 | + | 4.79672i | 0.226877 | + | 0.392963i | 0.956881 | − | 0.290480i | \(-0.0938150\pi\) |
−0.730004 | + | 0.683443i | \(0.760482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.108576 | − | 0.188059i | 0.00883580 | − | 0.0153041i | −0.861574 | − | 0.507633i | \(-0.830521\pi\) |
0.870409 | + | 0.492328i | \(0.163854\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.05498 | − | 3.54624i | −0.246981 | − | 0.286696i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.7173 | + | 5.46922i | −0.941153 | + | 0.439299i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.86970 | + | 1.07947i | −0.149218 | + | 0.0861511i | −0.572750 | − | 0.819730i | \(-0.694123\pi\) |
0.423532 | + | 0.905881i | \(0.360790\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.78285 | − | 18.2659i | −0.537915 | − | 1.44858i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.3017 | −1.83643 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.39084i | − | 0.657221i | −0.944465 | − | 0.328611i | \(-0.893420\pi\) | ||
0.944465 | − | 0.328611i | \(-0.106580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.2890 | + | 3.46312i | 1.03455 | + | 0.269604i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.00208 | + | 2.31060i | −0.309691 | + | 0.178800i | −0.646788 | − | 0.762670i | \(-0.723888\pi\) |
0.337097 | + | 0.941470i | \(0.390555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.99649 | + | 10.3862i | −0.461268 | + | 0.798940i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.3879 | − | 14.1177i | 1.25321 | − | 1.07961i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.25599 | − | 0.725146i | −0.0954911 | − | 0.0551318i | 0.451494 | − | 0.892274i | \(-0.350891\pi\) |
−0.546985 | + | 0.837142i | \(0.684225\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.4477 | − | 12.1045i | −1.09214 | − | 0.915013i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.8925 | + | 10.6762i | 0.969058 | + | 0.802473i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.4472 | −1.45355 | −0.726775 | − | 0.686876i | \(-0.758982\pi\) | ||||
−0.726775 | + | 0.686876i | \(0.758982\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4273 | −0.775054 | −0.387527 | − | 0.921858i | \(-0.626671\pi\) | ||||
−0.387527 | + | 0.921858i | \(0.626671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.37837 | − | 14.0201i | 0.175814 | − | 1.03639i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.89700 | − | 0.165246i | −0.139470 | − | 0.0121491i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.79107 | + | 2.76613i | 0.350358 | + | 0.202279i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.7694 | − | 10.1223i | 1.21979 | − | 0.736289i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.89142 | + | 3.27604i | −0.136859 | + | 0.237046i | −0.926306 | − | 0.376772i | \(-0.877034\pi\) |
0.789447 | + | 0.613818i | \(0.210367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1893 | + | 7.03751i | −0.877407 | + | 0.506571i | −0.869803 | − | 0.493400i | \(-0.835754\pi\) |
−0.00760445 | + | 0.999971i | \(0.502421\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.76703 | − | 2.72927i | −0.198151 | − | 0.195447i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5044i | 1.53212i | 0.642768 | + | 0.766061i | \(0.277786\pi\) | ||||
−0.642768 | + | 0.766061i | \(0.722214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.21013 | 0.511112 | 0.255556 | − | 0.966794i | \(-0.417741\pi\) | ||||
0.255556 | + | 0.966794i | \(0.417741\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.22359 | + | 3.89277i | −0.227374 | + | 0.274575i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.79379 | + | 5.65445i | −0.687389 | + | 0.396864i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.31878 | − | 2.94939i | 0.441323 | − | 0.205995i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.11573 | + | 17.5068i | −0.425073 | + | 1.21681i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.7828 | + | 22.1405i | −0.884208 | + | 1.53149i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.89142 | + | 3.27604i | 0.130211 | + | 0.225532i | 0.923758 | − | 0.382977i | \(-0.125101\pi\) |
−0.793547 | + | 0.608509i | \(0.791768\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.7072 | + | 4.34735i | −0.802164 | + | 0.297876i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46957 | + | 4.95904i | −0.236623 | + | 0.338204i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 21.7992i | − | 1.47983i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.1185 | + | 27.2487i | 0.683746 | + | 1.84129i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.782848 | − | 1.35593i | −0.0526600 | − | 0.0912099i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.52711 | + | 1.45903i | 0.169228 | + | 0.0977038i | 0.582222 | − | 0.813030i | \(-0.302184\pi\) |
−0.412994 | + | 0.910734i | \(0.635517\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.8861 | + | 7.67775i | −0.859075 | + | 0.511850i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.43272 | − | 2.55923i | −0.294210 | − | 0.169862i | 0.345629 | − | 0.938371i | \(-0.387666\pi\) |
−0.639839 | + | 0.768509i | \(0.720999\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.71013 | − | 8.15818i | −0.311254 | − | 0.539108i | 0.667380 | − | 0.744717i | \(-0.267416\pi\) |
−0.978634 | + | 0.205609i | \(0.934082\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.7659 | + | 17.8311i | −0.971523 | + | 1.17320i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 26.1850i | − | 1.71544i | −0.514118 | − | 0.857719i | \(-0.671881\pi\) | ||
0.514118 | − | 0.857719i | \(-0.328119\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.4965 | + | 17.8612i | −0.815181 | + | 1.16513i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.18452 | + | 18.7722i | −0.206857 | + | 1.21939i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3780 | + | 19.7072i | 0.735979 | + | 1.27475i | 0.954292 | + | 0.298875i | \(0.0966113\pi\) |
−0.218313 | + | 0.975879i | \(0.570055\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.31519 | + | 14.4023i | −0.535629 | + | 0.927736i | 0.463504 | + | 0.886095i | \(0.346592\pi\) |
−0.999133 | + | 0.0416412i | \(0.986741\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.20373 | − | 15.2557i | −0.205519 | − | 0.978653i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.6092 | − | 6.81910i | 0.933350 | − | 0.435656i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.26604 | − | 3.61770i | 0.398699 | − | 0.230189i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.4103 | + | 2.95349i | 1.10333 | + | 0.187170i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7758 | 1.31136 | 0.655679 | − | 0.755040i | \(-0.272382\pi\) | ||||
0.655679 | + | 0.755040i | \(0.272382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.9181i | − | 1.37798i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.82595 | + | 1.60403i | −0.364835 | + | 0.100448i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.5061 | − | 9.52978i | 1.02962 | − | 0.594451i | 0.112744 | − | 0.993624i | \(-0.464036\pi\) |
0.916876 | + | 0.399173i | \(0.130703\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.60506 | − | 2.78005i | 0.0997338 | − | 0.172744i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.67778 | + | 8.84223i | 0.103852 | + | 0.547320i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.04770 | − | 4.06899i | −0.434580 | − | 0.250905i | 0.266716 | − | 0.963775i | \(-0.414061\pi\) |
−0.701296 | + | 0.712870i | \(0.747395\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.0596 | − | 2.18292i | −1.53940 | − | 0.134096i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.66362 | − | 3.21715i | 0.530205 | − | 0.196886i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.6374 | 1.56314 | 0.781570 | − | 0.623817i | \(-0.214419\pi\) | ||||
0.781570 | + | 0.623817i | \(0.214419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.21013 | 0.195001 | 0.0975007 | − | 0.995235i | \(-0.468915\pi\) | ||||
0.0975007 | + | 0.995235i | \(0.468915\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.14227 | − | 2.28087i | 0.371747 | − | 0.138045i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.3858 | − | 13.5898i | 0.686587 | − | 0.819496i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.605911 | − | 0.349823i | −0.0364057 | − | 0.0210188i | 0.481687 | − | 0.876343i | \(-0.340024\pi\) |
−0.518092 | + | 0.855325i | \(0.673358\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.3780 | − | 5.72138i | −0.980523 | − | 0.342530i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3152 | − | 26.5267i | 0.913628 | − | 1.58245i | 0.104730 | − | 0.994501i | \(-0.466602\pi\) |
0.808898 | − | 0.587949i | \(-0.200064\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.31882 | − | 4.80287i | 0.494502 | − | 0.285501i | −0.231938 | − | 0.972731i | \(-0.574507\pi\) |
0.726440 | + | 0.687229i | \(0.241173\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.41255 | − | 26.9229i | −0.439082 | − | 1.59478i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.7557i | 0.693916i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.5657 | 0.856806 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.59512 | − | 1.11880i | −0.386613 | − | 0.0655851i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.60718 | + | 1.50526i | −0.152313 | + | 0.0879381i | −0.574220 | − | 0.818701i | \(-0.694694\pi\) |
0.421906 | + | 0.906639i | \(0.361361\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.5819 | − | 9.14020i | 1.14011 | − | 0.532163i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.52127 | + | 15.7737i | 0.552480 | + | 0.915281i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.10155 | + | 5.37205i | −0.179367 | + | 0.310673i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.10155 | − | 8.83615i | −0.294049 | − | 0.509307i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.37773 | + | 8.12148i | −0.0791487 | + | 0.466567i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.0423 | − | 10.5243i | −0.861319 | − | 0.602619i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.8671i | − | 0.848512i | −0.905542 | − | 0.424256i | \(-0.860536\pi\) | ||
0.905542 | − | 0.424256i | \(-0.139464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.9830 | + | 24.1313i | −1.13679 | + | 1.37278i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.53586 | + | 2.66018i | 0.0870905 | + | 0.150845i | 0.906280 | − | 0.422678i | \(-0.138910\pi\) |
−0.819190 | + | 0.573523i | \(0.805576\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.9303 | − | 11.5068i | −1.12653 | − | 0.650402i | −0.183470 | − | 0.983025i | \(-0.558733\pi\) |
−0.943060 | + | 0.332623i | \(0.892066\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.54033 | − | 25.1595i | −0.143131 | − | 1.41758i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.00779729 | + | 0.00450177i | 0.000437939 | + | 0.000252844i | 0.500219 | − | 0.865899i | \(-0.333253\pi\) |
−0.499781 | + | 0.866152i | \(0.666586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.31870 | − | 9.21227i | −0.297790 | − | 0.515788i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.18130 | − | 5.87412i | −0.121748 | − | 0.327861i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.2494i | − | 0.625935i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.71364 | + | 1.71965i | −0.261466 | + | 0.0953889i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.6484 | − | 5.81088i | 0.865359 | − | 0.321342i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.3745 | − | 31.8255i | −1.01302 | − | 1.75460i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.49649 | − | 7.78815i | 0.247149 | − | 0.428075i | −0.715584 | − | 0.698526i | \(-0.753840\pi\) |
0.962734 | + | 0.270451i | \(0.0871728\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.66742 | − | 1.93555i | −0.0913740 | − | 0.106067i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.75980 | + | 5.91259i | 0.150784 | + | 0.323040i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.55649 | − | 2.63069i | 0.248208 | − | 0.143303i | −0.370735 | − | 0.928739i | \(-0.620894\pi\) |
0.618943 | + | 0.785436i | \(0.287561\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.93079 | − | 4.74678i | 0.213491 | − | 0.257810i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.5048 | 1.11040 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.792107i | 0.0427698i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.0444 | + | 16.8119i | 0.917642 | + | 0.905121i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.6155 | + | 10.7477i | −0.999333 | + | 0.576965i | −0.908051 | − | 0.418860i | \(-0.862430\pi\) |
−0.0912825 | + | 0.995825i | \(0.529097\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.28285 | + | 10.8822i | −0.336313 | + | 0.582511i | −0.983736 | − | 0.179619i | \(-0.942513\pi\) |
0.647423 | + | 0.762131i | \(0.275847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.101552 | − | 5.21338i | −0.00542046 | − | 0.278270i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.7048 | + | 12.5313i | 1.15523 | + | 0.666973i | 0.950157 | − | 0.311773i | \(-0.100923\pi\) |
0.205075 | + | 0.978746i | \(0.434256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.39910 | + | 16.0615i | −0.0742567 | + | 0.852457i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.70379 | − | 10.0435i | 0.0901741 | − | 0.531560i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.1961 | 1.22424 | 0.612121 | − | 0.790764i | \(-0.290316\pi\) | ||||
0.612121 | + | 0.790764i | \(0.290316\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.9860 | 1.73610 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.09805 | − | 1.73739i | −0.110119 | − | 0.0911892i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.3834 | + | 3.25643i | 1.95674 | + | 0.170450i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.4024 | − | 8.89259i | −0.804000 | − | 0.464190i | 0.0408679 | − | 0.999165i | \(-0.486988\pi\) |
−0.844868 | + | 0.534975i | \(0.820321\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.83216 | + | 3.08537i | 0.459784 | + | 0.160618i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.2031 | − | 36.7249i | 1.10081 | − | 1.90666i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.1887 | − | 6.45979i | 0.579328 | − | 0.334475i | −0.181538 | − | 0.983384i | \(-0.558108\pi\) |
0.760866 | + | 0.648908i | \(0.224774\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.83476 | + | 19.2778i | 0.0947466 | + | 0.995501i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.01052i | 0.155050i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.56570 | −0.285891 | −0.142945 | − | 0.989731i | \(-0.545657\pi\) | ||||
−0.142945 | + | 0.989731i | \(0.545657\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.08809 | − | 11.0090i | −0.209439 | − | 0.564010i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.7584 | − | 14.8716i | 1.31619 | − | 0.759905i | 0.333080 | − | 0.942899i | \(-0.391912\pi\) |
0.983114 | + | 0.182994i | \(0.0585788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.6415 | + | 27.0831i | 0.644269 | + | 1.38028i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.97763 | + | 1.51373i | −0.405526 | + | 0.0769471i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.77641 | + | 6.54094i | −0.191472 | + | 0.331639i | −0.945738 | − | 0.324930i | \(-0.894659\pi\) |
0.754266 | + | 0.656568i | \(0.227993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.82222 | + | 8.35232i | 0.243870 | + | 0.422395i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.57209 | − | 3.78613i | −0.230631 | − | 0.190985i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.1409 | + | 14.0915i | 1.01340 | + | 0.709021i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 30.1571i | − | 1.51354i | −0.653682 | − | 0.756770i | \(-0.726776\pi\) | ||
0.653682 | − | 0.756770i | \(-0.273224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 46.4132 | + | 7.87356i | 2.32357 | + | 0.394171i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.8322 | + | 18.7619i | 0.540932 | + | 0.936922i | 0.998851 | + | 0.0479282i | \(0.0152619\pi\) |
−0.457918 | + | 0.888994i | \(0.651405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.02565 | − | 2.90156i | −0.250345 | − | 0.144537i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.5693 | − | 4.69475i | −0.972409 | − | 0.233284i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.61498 | + | 1.50976i | 0.129620 | + | 0.0748360i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.06921 | − | 7.04807i | −0.201209 | − | 0.348505i | 0.747709 | − | 0.664027i | \(-0.231154\pi\) |
−0.948918 | + | 0.315522i | \(0.897820\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.4895 | − | 4.32404i | −1.25730 | − | 0.213289i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.4310i | 1.79265i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.0692 | − | 18.6797i | 0.641542 | − | 0.916952i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.24014 | + | 5.99553i | 0.354551 | + | 0.293603i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.64736 | − | 11.5136i | −0.324745 | − | 0.562474i | 0.656716 | − | 0.754138i | \(-0.271945\pi\) |
−0.981461 | + | 0.191664i | \(0.938612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0692 | + | 17.4404i | −0.490743 | + | 0.849992i | −0.999943 | − | 0.0106561i | \(-0.996608\pi\) |
0.509200 | + | 0.860648i | \(0.329941\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.7333 | + | 5.45205i | −1.39706 | + | 0.265088i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.34886 | + | 7.68363i | −0.0654295 | + | 0.372711i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.8028 | − | 15.4746i | 1.29708 | − | 0.748868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.14544 | + | 5.77756i | 0.103583 | + | 0.278943i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.8027 | −1.24287 | −0.621437 | − | 0.783464i | \(-0.713451\pi\) | ||||
−0.621437 | + | 0.783464i | \(0.713451\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.38383i | − | 0.306787i | −0.988165 | − | 0.153394i | \(-0.950980\pi\) | ||
0.988165 | − | 0.153394i | \(-0.0490202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.2434 | + | 2.93004i | 0.539081 | + | 0.140485i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.5978 | + | 22.2845i | −1.84638 | + | 1.06601i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.49649 | + | 9.52020i | −0.262333 | + | 0.454374i | −0.966861 | − | 0.255302i | \(-0.917825\pi\) |
0.704528 | + | 0.709676i | \(0.251159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.4203 | + | 7.13349i | 0.972393 | + | 0.339690i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.8515 | + | 12.6160i | 1.03820 | + | 0.599404i | 0.919322 | − | 0.393505i | \(-0.128738\pi\) |
0.118876 | + | 0.992909i | \(0.462071\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.03537 | − | 11.8859i | 0.0490813 | − | 0.563447i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.38889 | + | 6.11871i | 0.349482 | + | 0.289405i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.5657 | 0.923362 | 0.461681 | − | 0.887046i | \(-0.347246\pi\) | ||||
0.461681 | + | 0.887046i | \(0.347246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.0577 | −0.520685 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.0629062 | − | 0.370821i | 0.00295559 | − | 0.0174227i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.734050 | − | 8.42679i | 0.0344128 | − | 0.395054i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.66013 | + | 3.26788i | 0.264770 | + | 0.152865i | 0.626508 | − | 0.779415i | \(-0.284483\pi\) |
−0.361739 | + | 0.932280i | \(0.617817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.09863 | − | 3.91608i | −0.331336 | − | 0.182787i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.7101 | − | 30.6748i | 0.824843 | − | 1.42867i | −0.0771964 | − | 0.997016i | \(-0.524597\pi\) |
0.902039 | − | 0.431654i | \(-0.142070\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0876 | − | 8.13348i | 0.654706 | − | 0.377995i | −0.135551 | − | 0.990770i | \(-0.543280\pi\) |
0.790257 | + | 0.612776i | \(0.209947\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.7278 | + | 15.9454i | −0.729360 | + | 0.739450i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.8112i | 0.731654i | 0.930683 | + | 0.365827i | \(0.119214\pi\) | ||||
−0.930683 | + | 0.365827i | \(0.880786\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0000 | −0.507933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.38499 | + | 2.88009i | −0.109895 | + | 0.132707i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.31148 | − | 4.79864i | 0.382162 | − | 0.220642i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.5077 | − | 6.23338i | −1.62920 | − | 0.286007i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.0268 | − | 25.5688i | −1.00854 | − | 1.17072i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.3709 | − | 28.3553i | 0.748007 | − | 1.29559i | −0.200769 | − | 0.979639i | \(-0.564344\pi\) |
0.948776 | − | 0.315948i | \(-0.102323\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.427281 | − | 0.740072i | −0.0194823 | − | 0.0337444i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −37.8354 | + | 14.0498i | −1.72157 | + | 0.639288i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.95069 | + | 7.07598i | −0.224799 | + | 0.321304i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.4220i | − | 1.65044i | −0.564814 | − | 0.825218i | \(-0.691052\pi\) | ||
0.564814 | − | 0.825218i | \(-0.308948\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.05926 | − | 13.6243i | −0.228788 | − | 0.616114i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.71364 | − | 2.96811i | −0.0773355 | − | 0.133949i | 0.824764 | − | 0.565477i | \(-0.191308\pi\) |
−0.902100 | + | 0.431528i | \(0.857975\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.05359 | + | 2.34034i | 0.182564 | + | 0.105404i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.6656 | − | 2.38949i | 1.06369 | − | 0.107400i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.5382 | − | 13.5898i | −1.05583 | − | 0.609584i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.71364 | − | 2.96811i | −0.0767131 | − | 0.132871i | 0.825117 | − | 0.564962i | \(-0.191109\pi\) |
−0.901830 | + | 0.432091i | \(0.857776\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.10506 | + | 6.16482i | −0.228077 | + | 0.275424i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 17.4219i | − | 0.776802i | −0.921490 | − | 0.388401i | \(-0.873027\pi\) | ||
0.921490 | − | 0.388401i | \(-0.126973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.71364 | + | 6.09647i | 0.387752 | + | 0.271289i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.47421 | + | 20.4799i | −0.154295 | + | 0.909542i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.07272 | − | 12.2503i | −0.313493 | − | 0.542985i | 0.665623 | − | 0.746288i | \(-0.268166\pi\) |
−0.979116 | + | 0.203303i | \(0.934832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.6304 | + | 54.7854i | −1.39925 | + | 2.42356i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.0970 | − | 32.8042i | 0.799003 | − | 1.44834i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.1080 | + | 36.6522i | 0.753869 | + | 1.61509i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.9358 | − | 17.2834i | 1.31657 | − | 0.760125i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.47660 | − | 0.420131i | −0.108710 | − | 0.0184417i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2300 | −0.886293 | −0.443147 | − | 0.896449i | \(-0.646138\pi\) | ||||
−0.443147 | + | 0.896449i | \(0.646138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.3295i | 1.58858i | 0.607540 | + | 0.794289i | \(0.292156\pi\) | ||||
−0.607540 | + | 0.794289i | \(0.707844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −30.7573 | − | 10.9430i | −1.34236 | − | 0.477592i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.81376 | + | 4.51127i | −0.340373 | + | 0.196514i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.60506 | − | 13.1724i | 0.330655 | − | 0.572711i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.3709 | + | 9.56160i | 1.18780 | + | 0.414938i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.71019 | + | 1.56473i | 0.117391 | + | 0.0677759i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.05891 | − | 0.702004i | −0.348417 | − | 0.0303503i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.5767 | + | 11.7257i | −1.36263 | + | 0.506001i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.5657 | −1.10119 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.8475 | 1.06828 | 0.534140 | − | 0.845396i | \(-0.320636\pi\) | ||||
0.534140 | + | 0.845396i | \(0.320636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.9309 | + | 6.28713i | −0.726576 | + | 0.269807i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.87011 | − | 21.4686i | 0.0801067 | − | 0.919614i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8034 | − | 16.0523i | −1.18879 | − | 0.686347i | −0.230757 | − | 0.973012i | \(-0.574120\pi\) |
−0.958031 | + | 0.286665i | \(0.907453\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.59161 | − | 24.1986i | −0.195965 | − | 1.03277i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.8152 | + | 18.7325i | −0.460743 | + | 0.798030i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.8876 | + | 20.7197i | −1.52610 | + | 0.881093i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.17982 | + | 0.875484i | −0.134976 | + | 0.0371622i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17.3894i | − | 0.736813i | −0.929665 | − | 0.368406i | \(-0.879904\pi\) | ||
0.929665 | − | 0.368406i | \(-0.120096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.71615 | −0.114881 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.44717 | + | 1.60262i | 0.398860 | + | 0.0676628i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.6771 | − | 13.6700i | 0.997870 | − | 0.576120i | 0.0902525 | − | 0.995919i | \(-0.471233\pi\) |
0.907617 | + | 0.419799i | \(0.137899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.36526 | − | 7.20973i | −0.141577 | − | 0.303316i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.1255 | − | 26.5468i | 0.887186 | − | 1.11486i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.59512 | + | 13.1551i | −0.318404 | + | 0.551492i | −0.980155 | − | 0.198232i | \(-0.936480\pi\) |
0.661751 | + | 0.749723i | \(0.269813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.3510 | − | 33.5170i | −0.809816 | − | 1.40264i | −0.912991 | − | 0.407980i | \(-0.866233\pi\) |
0.103175 | − | 0.994663i | \(-0.467100\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.09584 | + | 6.45979i | −0.0457795 | + | 0.269862i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.0353 | − | 10.5928i | 1.21085 | − | 0.441748i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.82910i | 0.159408i | 0.996819 | + | 0.0797038i | \(0.0253974\pi\) | ||||
−0.996819 | + | 0.0797038i | \(0.974603\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.5487 | + | 18.7765i | −0.646183 | + | 0.780324i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.2166 | + | 33.2841i | 0.797237 | + | 1.38086i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.5442 | + | 19.9441i | 1.43068 | + | 0.826001i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.13848 | − | 2.76318i | −0.253795 | − | 0.114243i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.3772 | − | 12.3421i | −0.882332 | − | 0.509415i | −0.0109053 | − | 0.999941i | \(-0.503471\pi\) |
−0.871427 | + | 0.490526i | \(0.836805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.8475 | − | 36.1090i | −0.859008 | − | 1.48785i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.9661 | + | 34.9169i | 0.533352 | + | 1.43629i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.4290i | 1.57809i | 0.614336 | + | 0.789044i | \(0.289424\pi\) | ||||
−0.614336 | + | 0.789044i | \(0.710576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.7758 | − | 7.53926i | −0.441766 | − | 0.309080i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.7072 | − | 4.34735i | 0.479144 | − | 0.177925i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.71364 | − | 13.3604i | −0.315171 | − | 0.545892i | 0.664303 | − | 0.747463i | \(-0.268728\pi\) |
−0.979474 | + | 0.201572i | \(0.935395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.286360 | − | 0.495989i | 0.0116809 | − | 0.0202318i | −0.860126 | − | 0.510082i | \(-0.829615\pi\) |
0.871807 | + | 0.489850i | \(0.162948\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.88704 | + | 8.26441i | −0.117569 | + | 0.336553i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.18666 | + | 1.48743i | −0.129556 | + | 0.0604724i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.84448 | + | 4.52901i | −0.318398 | + | 0.183827i | −0.650678 | − | 0.759354i | \(-0.725515\pi\) |
0.332280 | + | 0.943181i | \(0.392182\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.4930 | + | 15.0864i | −0.506241 | + | 0.611331i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.78285 | −0.395772 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.99155i | 0.282386i | 0.989982 | + | 0.141193i | \(0.0450938\pi\) | ||||
−0.989982 | + | 0.141193i | \(0.954906\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.48156 | − | 8.59889i | 0.342010 | − | 0.346741i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.1769 | + | 9.91710i | −0.691517 | + | 0.399247i | −0.804180 | − | 0.594386i | \(-0.797395\pi\) |
0.112663 | + | 0.993633i | \(0.464062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.1016 | − | 24.4246i | 0.566789 | − | 0.981708i | −0.430092 | − | 0.902785i | \(-0.641519\pi\) |
0.996881 | − | 0.0789225i | \(-0.0251480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.625546 | + | 32.1136i | 0.0251023 | + | 1.28867i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.4188 | + | 10.0568i | 0.697871 | + | 0.402916i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5052 | + | 8.51509i | 0.940207 | + | 0.340604i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.40605 | + | 43.6574i | −0.295769 | + | 1.74351i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.32865 | −0.0529768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.27482 | 0.289606 | 0.144803 | − | 0.989461i | \(-0.453745\pi\) | ||||
0.144803 | + | 0.989461i | \(0.453745\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.04642 | + | 4.17892i | 0.200577 | + | 0.166097i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.1037 | − | 1.31567i | −0.599371 | − | 0.0522107i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.26604 | + | 3.61770i | 0.248270 | + | 0.143339i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.3879 | + | 14.1177i | −0.648296 | + | 0.558488i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.43372 | + | 11.1435i | −0.254116 | + | 0.440143i | −0.964655 | − | 0.263515i | \(-0.915118\pi\) |
0.710539 | + | 0.703658i | \(0.248451\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.8515 | + | 12.6160i | −0.861741 | + | 0.497526i | −0.864595 | − | 0.502470i | \(-0.832425\pi\) |
0.00285403 | + | 0.999996i | \(0.499092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.64354 | + | 10.1440i | −0.104089 | + | 0.399421i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.5618i | 0.926311i | 0.886277 | + | 0.463156i | \(0.153283\pi\) | ||||
−0.886277 | + | 0.463156i | \(0.846717\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.2678 | −1.34513 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.1438 | − | 35.3957i | −0.515148 | − | 1.38727i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.0519 | + | 8.69020i | −0.589025 | + | 0.340074i | −0.764712 | − | 0.644372i | \(-0.777119\pi\) |
0.175687 | + | 0.984446i | \(0.443785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.94439 | + | 3.24141i | −0.271340 | + | 0.126652i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.8592 | + | 38.1431i | 1.28196 | + | 1.48810i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.83216 | − | 13.5657i | 0.305098 | − | 0.528445i | −0.672185 | − | 0.740383i | \(-0.734644\pi\) |
0.977283 | + | 0.211938i | \(0.0679775\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.7136 | − | 20.2886i | −0.455608 | − | 0.789136i | 0.543115 | − | 0.839658i | \(-0.317245\pi\) |
−0.998723 | + | 0.0505224i | \(0.983911\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.08868 | − | 1.72963i | −0.0811177 | − | 0.0671732i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 34.8405 | − | 49.7973i | 1.35106 | − | 1.93106i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 18.5443i | − | 0.718038i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.98303 | + | 0.845323i | 0.192655 | + | 0.0326821i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.5557 | + | 25.2113i | 0.561918 | + | 0.973271i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.8816 | − | 14.3654i | −0.959114 | − | 0.553745i | −0.0632136 | − | 0.998000i | \(-0.520135\pi\) |
−0.895900 | + | 0.444255i | \(0.853468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.2941 | + | 20.2362i | −0.627160 | + | 0.778891i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.6079 | + | 25.1770i | 1.67599 | + | 0.967632i | 0.964177 | + | 0.265260i | \(0.0854577\pi\) |
0.711810 | + | 0.702372i | \(0.247876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.27934 | − | 12.6082i | −0.279355 | − | 0.483858i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.74056 | − | 1.48275i | −0.334939 | − | 0.0568192i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 11.5953i | − | 0.443681i | −0.975083 | − | 0.221841i | \(-0.928794\pi\) | ||
0.975083 | − | 0.221841i | \(-0.0712065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.1339 | + | 27.3480i | −0.731069 | + | 1.04491i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.5669 | − | 10.4066i | −0.479457 | − | 0.397036i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.64443 | − | 9.77644i | −0.215036 | − | 0.372453i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.9238 | − | 39.7051i | 0.872061 | − | 1.51045i | 0.0122006 | − | 0.999926i | \(-0.496116\pi\) |
0.859861 | − | 0.510529i | \(-0.170550\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.2243 | + | 37.8557i | −0.502350 | + | 1.43802i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.9968 | − | 5.13294i | 0.417133 | − | 0.194704i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.21373 | − | 2.43280i | 0.159606 | − | 0.0921489i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.7883 | − | 42.5170i | −0.597167 | − | 1.60814i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.1115 | −1.43945 | −0.719726 | − | 0.694259i | \(-0.755732\pi\) | ||||
−0.719726 | + | 0.694259i | \(0.755732\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.13997i | − | 0.231573i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.52135 | + | 36.5362i | −0.358595 | + | 1.37603i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.5262 | + | 8.96406i | −0.583923 | + | 0.337128i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.14443 | + | 1.98222i | −0.0429801 | + | 0.0744437i | −0.886715 | − | 0.462316i | \(-0.847019\pi\) |
0.843735 | + | 0.536760i | \(0.180352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.14794 | + | 32.4008i | 0.230566 | + | 1.21513i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.9572 | + | 17.8731i | 1.15936 | + | 0.669355i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.92644 | + | 0.690464i | 0.296432 | + | 0.0258219i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.3570 | + | 25.1386i | 1.13370 | + | 0.938816i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.6035 | −0.619205 | −0.309602 | − | 0.950866i | \(-0.600196\pi\) | ||||
−0.309602 | + | 0.950866i | \(0.600196\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −68.1891 | −2.53949 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.81761 | + | 28.3989i | −0.179169 | + | 1.05617i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.63315 | − | 11.4979i | 0.357766 | − | 0.427022i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.4350 | + | 19.3037i | 1.24003 | + | 0.715934i | 0.969101 | − | 0.246664i | \(-0.0793345\pi\) |
0.270933 | + | 0.962598i | \(0.412668\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.4004 | − | 22.8392i | −0.533347 | − | 0.845897i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.11150 | + | 3.65722i | −0.0780966 | + | 0.135267i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.3584 | − | 16.9501i | 1.08438 | − | 0.626066i | 0.152305 | − | 0.988334i | \(-0.451331\pi\) |
0.932074 | + | 0.362267i | \(0.117997\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.6097 | − | 19.8809i | 0.723313 | − | 0.733319i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.3469i | − | 0.381131i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.8405 | −1.35520 | −0.677600 | − | 0.735431i | \(-0.736980\pi\) | ||||
−0.677600 | + | 0.735431i | \(0.736980\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.99298 | − | 9.65223i | 0.293629 | − | 0.354584i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.89680 | + | 5.71392i | −0.363078 | + | 0.209623i | −0.670430 | − | 0.741973i | \(-0.733890\pi\) |
0.307352 | + | 0.951596i | \(0.400557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.2227 | − | 5.23839i | 0.411169 | − | 0.191920i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.0502 | − | 5.70192i | 1.09948 | − | 0.208622i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.81870 | − | 11.8103i | 0.249150 | − | 0.431541i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.10155 | − | 14.0323i | −0.295630 | − | 0.512046i | 0.679501 | − | 0.733674i | \(-0.262196\pi\) |
−0.975131 | + | 0.221628i | \(0.928863\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.7340 | − | 12.5268i | 1.22934 | − | 0.456502i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.397858 | − | 0.278360i | −0.0144795 | − | 0.0101306i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.08698i | − | 0.293926i | −0.989142 | − | 0.146963i | \(-0.953050\pi\) | ||
0.989142 | − | 0.146963i | \(-0.0469499\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.2156 | − | 35.5888i | −0.479694 | − | 1.29179i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.7031 | − | 18.5383i | −0.387987 | − | 0.672014i | 0.604191 | − | 0.796839i | \(-0.293496\pi\) |
−0.992179 | + | 0.124826i | \(0.960163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.4623 | + | 18.1647i | 1.13901 | + | 0.657608i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.49253 | + | 6.11724i | −0.307048 | + | 0.221169i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.39889 | + | 4.84910i | 0.303266 | + | 0.175091i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.7031 | + | 44.5191i | 0.926878 | + | 1.60540i | 0.788513 | + | 0.615018i | \(0.210851\pi\) |
0.138364 | + | 0.990381i | \(0.455815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.0552 | − | 25.4260i | 0.758283 | − | 0.915695i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.90972 | + | 27.1630i | 0.355968 | + | 0.975725i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.929933 | − | 5.48179i | 0.0333612 | − | 0.196658i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.2425 | + | 19.4725i | 0.402803 | + | 0.697676i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.7828 | − | 22.1405i | 0.457406 | − | 0.792251i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.05567 | + | 13.3456i | 0.287886 | + | 0.476934i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.04185 | + | 4.37447i | 0.0728769 | + | 0.156131i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.08216 | + | 2.35683i | −0.145513 | + | 0.0840121i | −0.570989 | − | 0.820958i | \(-0.693440\pi\) |
0.425476 | + | 0.904970i | \(0.360107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.8969 | − | 2.35747i | −0.494741 | − | 0.0839281i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.4132 | 0.476920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 8.23891i | − | 0.292572i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −42.0058 | + | 11.5653i | −1.48979 | + | 0.410177i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.88882 | − | 5.13196i | 0.314858 | − | 0.181784i | −0.334240 | − | 0.942488i | \(-0.608480\pi\) |
0.649098 | + | 0.760704i | \(0.275146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.60506 | + | 13.1724i | −0.269048 | + | 0.466005i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.1275 | − | 10.4475i | 0.428503 | − | 0.369143i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −51.5324 | − | 29.7523i | −1.81854 | − | 1.04993i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.52163 | + | 51.9077i | −0.159367 | + | 1.82951i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 41.6278 | − | 15.4581i | 1.46537 | − | 0.544150i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.9860 | −0.772985 | −0.386492 | − | 0.922293i | \(-0.626313\pi\) | ||||
−0.386492 | + | 0.922293i | \(0.626313\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6951 | 0.902276 | 0.451138 | − | 0.892454i | \(-0.351018\pi\) | ||||
0.451138 | + | 0.892454i | \(0.351018\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.21233 | − | 1.93555i | 0.182805 | − | 0.0678826i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.6917 | − | 1.62822i | −0.654742 | − | 0.0570340i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.9008 | − | 9.75767i | −0.591284 | − | 0.341378i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.59804 | − | 7.40697i | 0.300440 | − | 0.258820i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.1967 | + | 21.1253i | −0.425667 | + | 0.737276i | −0.996482 | − | 0.0838018i | \(-0.973294\pi\) |
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.26396 | − | 1.30710i | 0.0789167 | − | 0.0455626i | −0.460022 | − | 0.887907i | \(-0.652159\pi\) |
0.538939 | + | 0.842345i | \(0.318825\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.2932 | − | 28.9310i | 0.358365 | − | 1.00725i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.0684725i | 0.00238102i | 0.999999 | + | 0.00119051i | \(0.000378951\pi\) | ||||
−0.999999 | + | 0.00119051i | \(0.999621\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.7828 | 0.860744 | 0.430372 | − | 0.902652i | \(-0.358382\pi\) | ||||
0.430372 | + | 0.902652i | \(0.358382\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.19475 | − | 0.202679i | −0.0414455 | − | 0.00703084i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.74229 | − | 5.62471i | 0.337550 | − | 0.194885i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.37058 | + | 9.36354i | 0.151250 | + | 0.324039i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.0429 | + | 0.585210i | −1.03843 | + | 0.0202278i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.6204 | + | 39.1797i | −0.780944 | + | 1.35264i | 0.150448 | + | 0.988618i | \(0.451928\pi\) |
−0.931392 | + | 0.364017i | \(0.881405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.87323 | − | 52.3061i | 0.305610 | − | 1.80152i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.9731 | + | 15.3734i | 0.755897 | + | 0.528861i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.92857i | − | 0.203708i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.6115 | − | 12.8143i | 0.364186 | − | 0.439787i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.63198 | + | 4.55872i | 0.0902231 | + | 0.156271i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5067 | − | 10.1075i | −0.599418 | − | 0.346074i | 0.169395 | − | 0.985548i | \(-0.445819\pi\) |
−0.768813 | + | 0.639474i | \(0.779152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −28.2691 | − | 39.2457i | −0.966781 | − | 1.34218i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.2464 | − | 13.4213i | −0.794083 | − | 0.458464i | 0.0473147 | − | 0.998880i | \(-0.484934\pi\) |
−0.841398 | + | 0.540416i | \(0.818267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.68130 | − | 2.91209i | −0.0573651 | − | 0.0993592i | 0.835917 | − | 0.548856i | \(-0.184937\pi\) |
−0.893282 | + | 0.449497i | \(0.851603\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.08809 | + | 19.0879i | 0.241562 | + | 0.650513i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.4524i | 0.628126i | 0.949402 | + | 0.314063i | \(0.101690\pi\) | ||||
−0.949402 | + | 0.314063i | \(0.898310\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.85908 | + | 2.65717i | −0.0632106 | + | 0.0903465i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.6505 | − | 8.78239i | 0.803214 | − | 0.298266i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.4895 | − | 33.7567i | −0.661135 | − | 1.14512i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.46414 | + | 2.53597i | −0.0496106 | + | 0.0859281i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.3832 | + | 2.15992i | −0.385262 | + | 0.0731022i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.7679 | + | 29.8352i | −1.00634 | + | 1.00861i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0905 | + | 11.5993i | −0.678408 | + | 0.391679i | −0.799255 | − | 0.600992i | \(-0.794772\pi\) |
0.120847 | + | 0.992671i | \(0.461439\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.32573 | + | 4.01611i | −0.112174 | + | 0.135460i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.34854 | 0.0791244 | 0.0395622 | − | 0.999217i | \(-0.487404\pi\) | ||||
0.0395622 | + | 0.999217i | \(0.487404\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.3264i | 0.549428i | 0.961526 | + | 0.274714i | \(0.0885832\pi\) | ||||
−0.961526 | + | 0.274714i | \(0.911417\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.2844 | − | 26.6480i | 0.883541 | − | 0.895763i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.2464 | + | 13.4213i | −0.780539 | + | 0.450645i | −0.836621 | − | 0.547782i | \(-0.815472\pi\) |
0.0560821 | + | 0.998426i | \(0.482139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.7793 | − | 22.1345i | 0.428605 | − | 0.742366i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.9706 | + | 19.8711i | 0.836546 | + | 0.665707i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.8722 | − | 35.1446i | −2.03701 | − | 1.17607i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.77366 | + | 43.3212i | −0.126140 | + | 1.44807i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.79696 | + | 10.5928i | −0.0599987 | + | 0.353682i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.3485 | 0.578606 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.5516 | −0.584730 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.6112 | − | 11.2714i | −0.452953 | − | 0.375089i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.02338 | + | 23.2281i | −0.0672595 | + | 0.772130i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.79188 | + | 3.92130i | 0.225521 | + | 0.130204i | 0.608504 | − | 0.793551i | \(-0.291770\pi\) |
−0.382983 | + | 0.923755i | \(0.625103\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.65981 | + | 14.0177i | 0.0882203 | + | 0.464937i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.28636 | − | 2.22804i | 0.0426190 | − | 0.0738183i | −0.843929 | − | 0.536455i | \(-0.819763\pi\) |
0.886548 | + | 0.462637i | \(0.153097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.3078 | + | 18.0755i | −1.03614 | + | 0.598213i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −30.7700 | − | 8.01868i | −1.01723 | − | 0.265089i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 12.9196i | − | 0.426642i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.4062 | 1.39885 | 0.699426 | − | 0.714705i | \(-0.253439\pi\) | ||||
0.699426 | + | 0.714705i | \(0.253439\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.96414 | − | 24.1400i | −0.295379 | − | 0.795440i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.26604 | + | 3.61770i | −0.206249 | + | 0.119078i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.736213 | + | 4.19375i | −0.0242065 | + | 0.137890i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.8968 | + | 51.2311i | −0.587807 | + | 1.68265i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.9167 | − | 44.8891i | 0.850301 | − | 1.47276i | −0.0306361 | − | 0.999531i | \(-0.509753\pi\) |
0.880937 | − | 0.473234i | \(-0.156913\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.9930 | + | 45.0212i | 0.851885 | + | 1.47551i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.09775 | + | 3.39333i | 0.134154 | + | 0.111093i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.09161 | − | 10.1360i | 0.231920 | − | 0.331482i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.9666i | − | 0.554275i | −0.960830 | − | 0.277137i | \(-0.910614\pi\) | ||
0.960830 | − | 0.277137i | \(-0.0893857\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −39.2992 | − | 6.66674i | −1.28248 | − | 0.217561i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.82865 | − | 4.89937i | −0.0922114 | − | 0.159715i | 0.816230 | − | 0.577727i | \(-0.196060\pi\) |
−0.908441 | + | 0.418012i | \(0.862727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.6943 | − | 9.63847i | −0.543642 | − | 0.313872i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −19.2947 | − | 39.3202i | −0.627657 | − | 1.27909i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.6452 | + | 17.6930i | 0.995834 | + | 0.574945i | 0.907013 | − | 0.421103i | \(-0.138357\pi\) |
0.0888210 | + | 0.996048i | \(0.471690\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.42026 | + | 14.5843i | 0.273333 | + | 0.473427i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.0153749 | + | 0.00260821i | 0.000498566 | + | 8.45770e-5i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.66116i | 0.0538101i | 0.999638 | + | 0.0269051i | \(0.00856518\pi\) | ||||
−0.999638 | + | 0.0269051i | \(0.991435\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.93079 | + | 4.84910i | 0.224275 | + | 0.156913i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.1906 | − | 11.7512i | −0.458717 | − | 0.379862i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.1339 | − | 48.7293i | −0.908491 | − | 1.57355i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.22066 | + | 2.11425i | −0.0393763 | + | 0.0682017i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.08360 | − | 8.22268i | −0.228266 | − | 0.264972i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.3117 | + | 28.5189i | 0.428518 | + | 0.918057i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.9581 | + | 10.3681i | −0.577494 | + | 0.333416i | −0.760137 | − | 0.649763i | \(-0.774868\pi\) |
0.182643 | + | 0.983179i | \(0.441535\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.78285 | − | 18.2659i | −0.217896 | − | 0.586784i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.9193 | −0.671331 | −0.335665 | − | 0.941981i | \(-0.608961\pi\) | ||||
−0.335665 | + | 0.941981i | \(0.608961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.4589i | 0.655881i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.61675 | + | 5.63431i | −0.211905 | + | 0.180442i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.50418 | − | 1.44579i | 0.0801159 | − | 0.0462549i | −0.459407 | − | 0.888226i | \(-0.651938\pi\) |
0.539523 | + | 0.841971i | \(0.318605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.45963 | + | 16.3846i | −0.302331 | + | 0.523653i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.9049 | − | 18.8704i | 0.699369 | − | 0.602486i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.45628 | − | 3.15019i | −0.174028 | − | 0.100475i | 0.410456 | − | 0.911881i | \(-0.365370\pi\) |
−0.584484 | + | 0.811405i | \(0.698703\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 47.9038 | + | 4.17285i | 1.52634 | + | 0.132958i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.0241 | − | 40.5966i | −1.56045 | − | 1.29221i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.7310 | 0.532016 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.60515 | − | 15.3569i | 0.0826719 | − | 0.487336i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.39910 | − | 16.0615i | 0.0443546 | − | 0.509184i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.29589 | − | 4.78963i | −0.262733 | − | 0.151689i | 0.362847 | − | 0.931849i | \(-0.381805\pi\) |
−0.625581 | + | 0.780159i | \(0.715138\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.87445 | − | 2.13741i | −0.122582 | − | 0.0676246i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))