Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(91,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.h (of order \(5\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 6 x^{10} - 26 x^{9} + 61 x^{8} - 120 x^{7} + 465 x^{6} - 600 x^{5} + 1525 x^{4} + \cdots + 15625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 91.1 | ||
Root | \(1.97131 + 1.05544i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.91 |
Dual form | 450.2.h.g.361.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | −1.97131 | − | 1.05544i | −0.881595 | − | 0.472007i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.04842 | −1.90812 | −0.954061 | − | 0.299612i | \(-0.903143\pi\) | ||||
−0.954061 | + | 0.299612i | \(0.903143\pi\) | |||||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.974449 | − | 2.01257i | −0.308148 | − | 0.636431i | ||||
\(11\) | −4.35193 | − | 3.16186i | −1.31216 | − | 0.953337i | −0.999995 | − | 0.00330824i | \(-0.998947\pi\) |
−0.312162 | − | 0.950029i | \(-0.601053\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.78032 | − | 2.02002i | 0.771123 | − | 0.560254i | −0.131179 | − | 0.991359i | \(-0.541876\pi\) |
0.902302 | + | 0.431105i | \(0.141876\pi\) | |||||||
\(14\) | −4.08426 | − | 2.96739i | −1.09156 | − | 0.793067i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | 1.15320 | − | 3.54919i | 0.279693 | − | 0.860806i | −0.708247 | − | 0.705965i | \(-0.750514\pi\) |
0.987939 | − | 0.154841i | \(-0.0494865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.51156 | + | 4.65210i | −0.346776 | + | 1.06727i | 0.613851 | + | 0.789422i | \(0.289620\pi\) |
−0.960626 | + | 0.277843i | \(0.910380\pi\) | |||||||
\(20\) | 0.394615 | − | 2.20097i | 0.0882386 | − | 0.492152i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.66229 | − | 5.11600i | −0.354401 | − | 1.09073i | ||||
\(23\) | −1.82772 | − | 1.32792i | −0.381106 | − | 0.276890i | 0.380695 | − | 0.924701i | \(-0.375685\pi\) |
−0.761801 | + | 0.647811i | \(0.775685\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.77210 | + | 4.16119i | 0.554419 | + | 0.832238i | ||||
\(26\) | 3.43667 | 0.673986 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.56005 | − | 4.80133i | −0.294821 | − | 0.907366i | ||||
\(29\) | 0.153872 | + | 0.473569i | 0.0285733 | + | 0.0879396i | 0.964326 | − | 0.264717i | \(-0.0852785\pi\) |
−0.935753 | + | 0.352656i | \(0.885278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.05690 | + | 6.33050i | −0.369431 | + | 1.13699i | 0.577729 | + | 0.816229i | \(0.303939\pi\) |
−0.947160 | + | 0.320763i | \(0.896061\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.01912 | − | 2.19352i | 0.517776 | − | 0.376186i | ||||
\(35\) | 9.95198 | + | 5.32830i | 1.68219 | + | 0.900647i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.558667 | + | 0.405896i | −0.0918444 | + | 0.0667288i | −0.632760 | − | 0.774348i | \(-0.718078\pi\) |
0.540915 | + | 0.841077i | \(0.318078\pi\) | |||||||
\(38\) | −3.95731 | + | 2.87516i | −0.641961 | + | 0.466412i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.61295 | − | 1.54867i | 0.255030 | − | 0.244867i | ||||
\(41\) | −9.12111 | + | 6.62688i | −1.42448 | + | 1.03494i | −0.433467 | + | 0.901170i | \(0.642710\pi\) |
−0.991012 | + | 0.133775i | \(0.957290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.179186 | 0.0273257 | 0.0136628 | − | 0.999907i | \(-0.495651\pi\) | ||||
0.0136628 | + | 0.999907i | \(0.495651\pi\) | |||||||
\(44\) | 1.66229 | − | 5.11600i | 0.250600 | − | 0.771266i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.698127 | − | 2.14861i | −0.102933 | − | 0.316796i | ||||
\(47\) | −3.34708 | − | 10.3012i | −0.488221 | − | 1.50259i | −0.827261 | − | 0.561818i | \(-0.810102\pi\) |
0.339040 | − | 0.940772i | \(-0.389898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.4865 | 2.64093 | ||||||||
\(50\) | −0.203212 | + | 4.99587i | −0.0287385 | + | 0.706523i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.78032 | + | 2.02002i | 0.385561 | + | 0.280127i | ||||
\(53\) | −0.526078 | − | 1.61910i | −0.0722624 | − | 0.222401i | 0.908402 | − | 0.418098i | \(-0.137303\pi\) |
−0.980664 | + | 0.195697i | \(0.937303\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.24183 | + | 10.8262i | 0.706809 | + | 1.45980i | ||||
\(56\) | 1.56005 | − | 4.80133i | 0.208470 | − | 0.641605i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.153872 | + | 0.473569i | −0.0202044 | + | 0.0621827i | ||||
\(59\) | 4.45949 | − | 3.24001i | 0.580576 | − | 0.421813i | −0.258356 | − | 0.966050i | \(-0.583181\pi\) |
0.838932 | + | 0.544237i | \(0.183181\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.55174 | − | 6.21320i | −1.09494 | − | 0.795519i | −0.114712 | − | 0.993399i | \(-0.536594\pi\) |
−0.980226 | + | 0.197880i | \(0.936594\pi\) | |||||||
\(62\) | −5.38505 | + | 3.91246i | −0.683901 | + | 0.496884i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −7.61288 | + | 1.04762i | −0.944262 | + | 0.129941i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.86319 | − | 8.81199i | 0.349794 | − | 1.07656i | −0.609173 | − | 0.793038i | \(-0.708498\pi\) |
0.958967 | − | 0.283518i | \(-0.0915016\pi\) | |||||||
\(68\) | 3.73184 | 0.452552 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.91942 | + | 10.1603i | 0.587984 | + | 1.21439i | ||||
\(71\) | 1.15489 | + | 3.55439i | 0.137060 | + | 0.421829i | 0.995905 | − | 0.0904079i | \(-0.0288171\pi\) |
−0.858844 | + | 0.512237i | \(0.828817\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.92773 | − | 2.85366i | −0.459706 | − | 0.333996i | 0.333710 | − | 0.942676i | \(-0.391699\pi\) |
−0.793416 | + | 0.608680i | \(0.791699\pi\) | |||||||
\(74\) | −0.690551 | −0.0802749 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.89151 | −0.561095 | ||||||||
\(77\) | 21.9704 | + | 15.9624i | 2.50375 | + | 1.81908i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.52641 | − | 7.77549i | −0.284243 | − | 0.874811i | −0.986624 | − | 0.163010i | \(-0.947880\pi\) |
0.702381 | − | 0.711801i | \(-0.252120\pi\) | |||||||
\(80\) | 2.21519 | − | 0.304836i | 0.247666 | − | 0.0340818i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.2743 | −1.24504 | ||||||||
\(83\) | −3.72444 | + | 11.4626i | −0.408810 | + | 1.25819i | 0.508861 | + | 0.860849i | \(0.330067\pi\) |
−0.917671 | + | 0.397340i | \(0.869933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.01927 | + | 5.77941i | −0.652882 | + | 0.626865i | ||||
\(86\) | 0.144965 | + | 0.105323i | 0.0156320 | + | 0.0113573i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.35193 | − | 3.16186i | 0.463917 | − | 0.337056i | ||||
\(89\) | −1.89237 | − | 1.37488i | −0.200590 | − | 0.145737i | 0.482956 | − | 0.875645i | \(-0.339563\pi\) |
−0.683546 | + | 0.729907i | \(0.739563\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.0362 | + | 10.1979i | −1.47140 | + | 1.06903i | ||||
\(92\) | 0.698127 | − | 2.14861i | 0.0727848 | − | 0.224009i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.34708 | − | 10.3012i | 0.345224 | − | 1.06249i | ||||
\(95\) | 7.88976 | − | 7.57536i | 0.809472 | − | 0.777215i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.584325 | + | 1.79837i | 0.0593292 | + | 0.182597i | 0.976329 | − | 0.216292i | \(-0.0693962\pi\) |
−0.917000 | + | 0.398888i | \(0.869396\pi\) | |||||||
\(98\) | 14.9559 | + | 10.8661i | 1.51077 | + | 1.09764i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.10090 | + | 3.92230i | −0.310090 | + | 0.392230i | ||||
\(101\) | 4.35256 | 0.433096 | 0.216548 | − | 0.976272i | \(-0.430520\pi\) | ||||
0.216548 | + | 0.976272i | \(0.430520\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.11882 | − | 3.44339i | −0.110241 | − | 0.339287i | 0.880684 | − | 0.473705i | \(-0.157084\pi\) |
−0.990925 | + | 0.134418i | \(0.957084\pi\) | |||||||
\(104\) | 1.06199 | + | 3.26847i | 0.104137 | + | 0.320499i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.526078 | − | 1.61910i | 0.0510972 | − | 0.157261i | ||||
\(107\) | 5.39612 | 0.521662 | 0.260831 | − | 0.965384i | \(-0.416003\pi\) | ||||
0.260831 | + | 0.965384i | \(0.416003\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.43929 | − | 2.49879i | 0.329424 | − | 0.239341i | −0.410762 | − | 0.911743i | \(-0.634737\pi\) |
0.740186 | + | 0.672402i | \(0.234737\pi\) | |||||||
\(110\) | −2.12275 | + | 11.8396i | −0.202396 | + | 1.12887i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.08426 | − | 2.96739i | 0.385926 | − | 0.280392i | ||||
\(113\) | 7.13157 | − | 5.18139i | 0.670882 | − | 0.487424i | −0.199438 | − | 0.979910i | \(-0.563912\pi\) |
0.870320 | + | 0.492486i | \(0.163912\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.20146 | + | 4.54678i | 0.205287 | + | 0.423989i | ||||
\(116\) | −0.402842 | + | 0.292682i | −0.0374030 | + | 0.0271748i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.51223 | 0.507442 | ||||||||
\(119\) | −5.82185 | + | 17.9178i | −0.533688 | + | 1.64252i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.54273 | + | 17.0588i | 0.503885 | + | 1.55080i | ||||
\(122\) | −3.26647 | − | 10.0532i | −0.295733 | − | 0.910171i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.65628 | −0.597752 | ||||||||
\(125\) | −1.07277 | − | 11.1288i | −0.0959515 | − | 0.995386i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9407 | − | 9.40194i | −1.14830 | − | 0.834287i | −0.160044 | − | 0.987110i | \(-0.551164\pi\) |
−0.988254 | + | 0.152823i | \(0.951164\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.77473 | − | 3.62719i | −0.594183 | − | 0.318126i | ||||
\(131\) | 0.617457 | − | 1.90034i | 0.0539475 | − | 0.166033i | −0.920453 | − | 0.390854i | \(-0.872180\pi\) |
0.974400 | + | 0.224821i | \(0.0721797\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.63098 | − | 23.4858i | 0.661690 | − | 2.03647i | ||||
\(134\) | 7.49592 | − | 5.44611i | 0.647549 | − | 0.470472i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.01912 | + | 2.19352i | 0.258888 | + | 0.188093i | ||||
\(137\) | −1.19061 | + | 0.865029i | −0.101721 | + | 0.0739044i | −0.637483 | − | 0.770464i | \(-0.720024\pi\) |
0.535762 | + | 0.844369i | \(0.320024\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3373 | + | 8.23700i | 0.961614 | + | 0.698654i | 0.953525 | − | 0.301314i | \(-0.0974251\pi\) |
0.00808914 | + | 0.999967i | \(0.497425\pi\) | |||||||
\(140\) | −1.99218 | + | 11.1114i | −0.168370 | + | 0.939087i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.15489 | + | 3.55439i | −0.0969164 | + | 0.298278i | ||||
\(143\) | −18.4868 | −1.54594 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.196495 | − | 1.09595i | 0.0163180 | − | 0.0910139i | ||||
\(146\) | −1.50026 | − | 4.61732i | −0.124162 | − | 0.382133i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.558667 | − | 0.405896i | −0.0459222 | − | 0.0333644i | ||||
\(149\) | −1.86075 | −0.152438 | −0.0762191 | − | 0.997091i | \(-0.524285\pi\) | ||||
−0.0762191 | + | 0.997091i | \(0.524285\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.24990 | −0.345852 | −0.172926 | − | 0.984935i | \(-0.555322\pi\) | ||||
−0.172926 | + | 0.984935i | \(0.555322\pi\) | |||||||
\(152\) | −3.95731 | − | 2.87516i | −0.320981 | − | 0.233206i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.39193 | + | 25.8277i | 0.676241 | + | 2.08126i | ||||
\(155\) | 10.7362 | − | 10.3084i | 0.862356 | − | 0.827992i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.94696 | −0.793854 | −0.396927 | − | 0.917850i | \(-0.629923\pi\) | ||||
−0.396927 | + | 0.917850i | \(0.629923\pi\) | |||||||
\(158\) | 2.52641 | − | 7.77549i | 0.200990 | − | 0.618585i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.97131 | + | 1.05544i | 0.155845 | + | 0.0834398i | ||||
\(161\) | 9.22710 | + | 6.70388i | 0.727197 | + | 0.528340i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.94101 | − | 7.22257i | 0.778640 | − | 0.565715i | −0.125931 | − | 0.992039i | \(-0.540192\pi\) |
0.904571 | + | 0.426324i | \(0.140192\pi\) | |||||||
\(164\) | −9.12111 | − | 6.62688i | −0.712239 | − | 0.517472i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.75071 | + | 7.08430i | −0.756802 | + | 0.549849i | ||||
\(167\) | −3.06099 | + | 9.42075i | −0.236866 | + | 0.729000i | 0.760002 | + | 0.649921i | \(0.225198\pi\) |
−0.996868 | + | 0.0790789i | \(0.974802\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.367517 | + | 1.13110i | −0.0282705 | + | 0.0870078i | ||||
\(170\) | −8.26675 | + | 1.13760i | −0.634031 | + | 0.0872501i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0553716 | + | 0.170416i | 0.00422205 | + | 0.0129941i | ||||
\(173\) | −14.5411 | − | 10.5647i | −1.10554 | − | 0.803221i | −0.123584 | − | 0.992334i | \(-0.539439\pi\) |
−0.981955 | + | 0.189113i | \(0.939439\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.9947 | − | 21.0074i | −1.05790 | − | 1.58801i | ||||
\(176\) | 5.37928 | 0.405479 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.722819 | − | 2.22461i | −0.0541776 | − | 0.166741i | ||||
\(179\) | 5.90754 | + | 18.1815i | 0.441550 | + | 1.35895i | 0.886223 | + | 0.463258i | \(0.153320\pi\) |
−0.444673 | + | 0.895693i | \(0.646680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.58467 | − | 14.1102i | 0.340776 | − | 1.04880i | −0.623031 | − | 0.782197i | \(-0.714099\pi\) |
0.963807 | − | 0.266603i | \(-0.0859011\pi\) | |||||||
\(182\) | −17.3497 | −1.28605 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.82772 | − | 1.32792i | 0.134741 | − | 0.0978953i | ||||
\(185\) | 1.52970 | − | 0.210505i | 0.112466 | − | 0.0154766i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.2407 | + | 11.7996i | −1.18764 | + | 0.862870i | ||||
\(188\) | 8.76276 | − | 6.36652i | 0.639090 | − | 0.464326i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.8356 | − | 1.49111i | 0.786099 | − | 0.108177i | ||||
\(191\) | −10.9557 | + | 7.95979i | −0.792727 | + | 0.575950i | −0.908772 | − | 0.417294i | \(-0.862979\pi\) |
0.116044 | + | 0.993244i | \(0.462979\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.41975 | 0.462104 | 0.231052 | − | 0.972941i | \(-0.425783\pi\) | ||||
0.231052 | + | 0.972941i | \(0.425783\pi\) | |||||||
\(194\) | −0.584325 | + | 1.79837i | −0.0419521 | + | 0.129115i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.71265 | + | 17.5817i | 0.408046 | + | 1.25584i | ||||
\(197\) | 1.57748 | + | 4.85499i | 0.112391 | + | 0.345904i | 0.991394 | − | 0.130913i | \(-0.0417907\pi\) |
−0.879003 | + | 0.476816i | \(0.841791\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3015 | −0.730256 | −0.365128 | − | 0.930957i | \(-0.618975\pi\) | ||||
−0.365128 | + | 0.930957i | \(0.618975\pi\) | |||||||
\(200\) | −4.81415 | + | 1.35054i | −0.340412 | + | 0.0954978i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.52130 | + | 2.55837i | 0.247758 | + | 0.180006i | ||||
\(203\) | −0.776810 | − | 2.39078i | −0.0545214 | − | 0.167800i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.9748 | − | 3.43682i | 1.74431 | − | 0.240038i | ||||
\(206\) | 1.11882 | − | 3.44339i | 0.0779522 | − | 0.239912i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.06199 | + | 3.26847i | −0.0736357 | + | 0.226627i | ||||
\(209\) | 21.2875 | − | 15.4663i | 1.47249 | − | 1.06982i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.11381 | + | 1.53577i | 0.145521 | + | 0.105727i | 0.658164 | − | 0.752875i | \(-0.271334\pi\) |
−0.512643 | + | 0.858602i | \(0.671334\pi\) | |||||||
\(212\) | 1.37729 | − | 1.00066i | 0.0945927 | − | 0.0687256i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.36555 | + | 3.17176i | 0.298423 | + | 0.216817i | ||||
\(215\) | −0.353231 | − | 0.189120i | −0.0240902 | − | 0.0128979i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3841 | − | 31.9590i | 0.704919 | − | 2.16952i | ||||
\(218\) | 4.25120 | 0.287927 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.67651 | + | 8.33076i | −0.584970 | + | 0.561660i | ||||
\(221\) | −3.96318 | − | 12.1974i | −0.266592 | − | 0.820486i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.70751 | − | 1.24058i | −0.114344 | − | 0.0830755i | 0.529144 | − | 0.848532i | \(-0.322513\pi\) |
−0.643488 | + | 0.765457i | \(0.722513\pi\) | |||||||
\(224\) | 5.04842 | 0.337312 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.81511 | 0.586372 | ||||||||
\(227\) | −13.3453 | − | 9.69595i | −0.885760 | − | 0.643543i | 0.0490087 | − | 0.998798i | \(-0.484394\pi\) |
−0.934769 | + | 0.355256i | \(0.884394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.31369 | − | 13.2762i | −0.285057 | − | 0.877315i | −0.986382 | − | 0.164473i | \(-0.947408\pi\) |
0.701325 | − | 0.712842i | \(-0.252592\pi\) | |||||||
\(230\) | −0.891510 | + | 4.97241i | −0.0587844 | + | 0.327871i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.497940 | −0.0326914 | ||||||||
\(233\) | 8.63840 | − | 26.5863i | 0.565920 | − | 1.74172i | −0.0992806 | − | 0.995059i | \(-0.531654\pi\) |
0.665201 | − | 0.746664i | \(-0.268346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.27422 | + | 23.8395i | −0.278819 | + | 1.55512i | ||||
\(236\) | 4.45949 | + | 3.24001i | 0.290288 | + | 0.210906i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.2418 | + | 11.0738i | −0.987979 | + | 0.717809i | ||||
\(239\) | −14.6357 | − | 10.6334i | −0.946704 | − | 0.687821i | 0.00332110 | − | 0.999994i | \(-0.498943\pi\) |
−0.950025 | + | 0.312174i | \(0.898943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.57117 | − | 5.50078i | 0.487702 | − | 0.354336i | −0.316598 | − | 0.948560i | \(-0.602541\pi\) |
0.804300 | + | 0.594224i | \(0.202541\pi\) | |||||||
\(242\) | −5.54273 | + | 17.0588i | −0.356300 | + | 1.09658i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.26647 | − | 10.0532i | 0.209115 | − | 0.643588i | ||||
\(245\) | −36.4426 | − | 19.5114i | −2.32823 | − | 1.24654i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.19473 | + | 15.9877i | 0.330533 | + | 1.01728i | ||||
\(248\) | −5.38505 | − | 3.91246i | −0.341951 | − | 0.248442i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.67343 | − | 9.63391i | 0.358819 | − | 0.609302i | ||||
\(251\) | −7.00938 | −0.442428 | −0.221214 | − | 0.975225i | \(-0.571002\pi\) | ||||
−0.221214 | + | 0.975225i | \(0.571002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.75542 | + | 11.5580i | 0.236101 | + | 0.726645i | ||||
\(254\) | −4.94289 | − | 15.2127i | −0.310145 | − | 0.954527i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −23.4992 | −1.46584 | −0.732920 | − | 0.680314i | \(-0.761843\pi\) | ||||
−0.732920 | + | 0.680314i | \(0.761843\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.82039 | − | 2.04913i | 0.175250 | − | 0.127327i | ||||
\(260\) | −3.34886 | − | 6.91655i | −0.207687 | − | 0.428946i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.61652 | − | 1.17447i | 0.0998692 | − | 0.0725592i | ||||
\(263\) | −0.591653 | + | 0.429861i | −0.0364829 | + | 0.0265064i | −0.605877 | − | 0.795558i | \(-0.707178\pi\) |
0.569394 | + | 0.822064i | \(0.307178\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.671803 | + | 3.74699i | −0.0412685 | + | 0.230176i | ||||
\(266\) | 19.9782 | − | 14.5150i | 1.22494 | − | 0.889971i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.26547 | 0.565979 | ||||||||
\(269\) | −7.37942 | + | 22.7115i | −0.449931 | + | 1.38475i | 0.427053 | + | 0.904227i | \(0.359552\pi\) |
−0.876984 | + | 0.480519i | \(0.840448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.45801 | − | 22.9534i | −0.453042 | − | 1.39432i | −0.873419 | − | 0.486970i | \(-0.838102\pi\) |
0.420377 | − | 0.907350i | \(-0.361898\pi\) | |||||||
\(272\) | 1.15320 | + | 3.54919i | 0.0699232 | + | 0.215201i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.47168 | −0.0889072 | ||||||||
\(275\) | 1.09313 | − | 26.8742i | 0.0659184 | − | 1.62057i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.7921 | + | 8.56743i | 0.708516 | + | 0.514767i | 0.882694 | − | 0.469947i | \(-0.155727\pi\) |
−0.174179 | + | 0.984714i | \(0.555727\pi\) | |||||||
\(278\) | 4.33045 | + | 13.3278i | 0.259723 | + | 0.799346i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.14284 | + | 7.81836i | −0.486628 | + | 0.467236i | ||||
\(281\) | −5.96598 | + | 18.3614i | −0.355900 | + | 1.09535i | 0.599585 | + | 0.800311i | \(0.295332\pi\) |
−0.955486 | + | 0.295038i | \(0.904668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.57079 | + | 14.0675i | −0.271706 | + | 0.836224i | 0.718367 | + | 0.695665i | \(0.244890\pi\) |
−0.990072 | + | 0.140559i | \(0.955110\pi\) | |||||||
\(284\) | −3.02355 | + | 2.19674i | −0.179414 | + | 0.130352i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.9561 | − | 10.8663i | −0.884375 | − | 0.642536i | ||||
\(287\) | 46.0472 | − | 33.4552i | 2.71808 | − | 1.97480i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.48639 | + | 1.80647i | 0.146258 | + | 0.106263i | ||||
\(290\) | 0.803153 | − | 0.771148i | 0.0471627 | − | 0.0452834i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.50026 | − | 4.61732i | 0.0877961 | − | 0.270209i | ||||
\(293\) | 2.44668 | 0.142936 | 0.0714682 | − | 0.997443i | \(-0.477232\pi\) | ||||
0.0714682 | + | 0.997443i | \(0.477232\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2106 | + | 1.68033i | −0.710931 | + | 0.0978325i | ||||
\(296\) | −0.213392 | − | 0.656753i | −0.0124032 | − | 0.0381730i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.50537 | − | 1.09372i | −0.0872040 | − | 0.0633574i | ||||
\(299\) | −7.76408 | −0.449008 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.904607 | −0.0521407 | ||||||||
\(302\) | −3.43824 | − | 2.49803i | −0.197848 | − | 0.143745i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.51156 | − | 4.65210i | −0.0866939 | − | 0.266816i | ||||
\(305\) | 10.3004 | + | 21.2740i | 0.589801 | + | 1.21814i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.54067 | 0.430369 | 0.215184 | − | 0.976573i | \(-0.430965\pi\) | ||||
0.215184 | + | 0.976573i | \(0.430965\pi\) | |||||||
\(308\) | −8.39193 | + | 25.8277i | −0.478175 | + | 1.47167i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.7449 | − | 2.02908i | 0.837456 | − | 0.115244i | ||||
\(311\) | −8.41518 | − | 6.11399i | −0.477181 | − | 0.346692i | 0.323052 | − | 0.946381i | \(-0.395291\pi\) |
−0.800233 | + | 0.599689i | \(0.795291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.3066 | + | 11.8474i | −0.921701 | + | 0.669655i | −0.943947 | − | 0.330097i | \(-0.892918\pi\) |
0.0222457 | + | 0.999753i | \(0.492918\pi\) | |||||||
\(314\) | −8.04726 | − | 5.84667i | −0.454133 | − | 0.329947i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.61423 | − | 4.80552i | 0.372079 | − | 0.270332i | ||||
\(317\) | −8.23461 | + | 25.3435i | −0.462502 | + | 1.42343i | 0.399595 | + | 0.916692i | \(0.369151\pi\) |
−0.862097 | + | 0.506743i | \(0.830849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.827721 | − | 2.54746i | 0.0463435 | − | 0.142631i | ||||
\(320\) | 0.974449 | + | 2.01257i | 0.0544733 | + | 0.112506i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.52444 | + | 10.8471i | 0.196409 | + | 0.604485i | ||||
\(323\) | 14.7681 | + | 10.7296i | 0.821718 | + | 0.597013i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.1130 | + | 5.96975i | 0.893789 | + | 0.331142i | ||||
\(326\) | 12.2878 | 0.680556 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.48396 | − | 10.7225i | −0.192369 | − | 0.592052i | ||||
\(329\) | 16.8974 | + | 52.0050i | 0.931586 | + | 2.86713i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.63714 | − | 8.11628i | 0.144950 | − | 0.446111i | −0.852054 | − | 0.523453i | \(-0.824643\pi\) |
0.997005 | + | 0.0773422i | \(0.0246434\pi\) | |||||||
\(332\) | −12.0525 | −0.661469 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.01377 | + | 5.82234i | −0.438494 | + | 0.318584i | ||||
\(335\) | −14.9447 | + | 14.3492i | −0.816518 | + | 0.783981i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.62011 | − | 4.80979i | 0.360620 | − | 0.262006i | −0.392691 | − | 0.919671i | \(-0.628456\pi\) |
0.753311 | + | 0.657665i | \(0.228456\pi\) | |||||||
\(338\) | −0.962172 | + | 0.699059i | −0.0523353 | + | 0.0380238i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.35660 | − | 3.93873i | −0.398968 | − | 0.213608i | ||||
\(341\) | 28.9677 | − | 21.0462i | 1.56869 | − | 1.13972i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −57.9888 | −3.13110 | ||||||||
\(344\) | −0.0553716 | + | 0.170416i | −0.00298544 | + | 0.00918823i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.55421 | − | 17.0941i | −0.298596 | − | 0.918984i | ||||
\(347\) | 0.524395 | + | 1.61392i | 0.0281510 | + | 0.0866398i | 0.964145 | − | 0.265376i | \(-0.0854962\pi\) |
−0.935994 | + | 0.352016i | \(0.885496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.6009 | −1.04921 | −0.524605 | − | 0.851346i | \(-0.675787\pi\) | ||||
−0.524605 | + | 0.851346i | \(0.675787\pi\) | |||||||
\(350\) | 1.02590 | − | 25.2212i | 0.0548366 | − | 1.34813i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.35193 | + | 3.16186i | 0.231959 | + | 0.168528i | ||||
\(353\) | −9.55334 | − | 29.4021i | −0.508473 | − | 1.56492i | −0.794853 | − | 0.606802i | \(-0.792452\pi\) |
0.286380 | − | 0.958116i | \(-0.407548\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.47480 | − | 8.22571i | 0.0782742 | − | 0.436576i | ||||
\(356\) | 0.722819 | − | 2.22461i | 0.0383093 | − | 0.117904i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.90754 | + | 18.1815i | −0.312223 | + | 0.960923i | ||||
\(359\) | 16.5150 | − | 11.9988i | 0.871627 | − | 0.633274i | −0.0593962 | − | 0.998234i | \(-0.518918\pi\) |
0.931023 | + | 0.364961i | \(0.118918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.98592 | − | 2.89594i | −0.209785 | − | 0.152418i | ||||
\(362\) | 12.0028 | − | 8.72056i | 0.630854 | − | 0.458342i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.0362 | − | 10.1979i | −0.735698 | − | 0.534516i | ||||
\(365\) | 4.73089 | + | 9.77093i | 0.247626 | + | 0.511434i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.617756 | − | 1.90126i | 0.0322466 | − | 0.0992448i | −0.933638 | − | 0.358218i | \(-0.883384\pi\) |
0.965884 | + | 0.258974i | \(0.0833843\pi\) | |||||||
\(368\) | 2.25919 | 0.117768 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.36129 | + | 0.728834i | 0.0707700 | + | 0.0378903i | ||||
\(371\) | 2.65586 | + | 8.17391i | 0.137886 | + | 0.424368i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.9488 | + | 13.0405i | 0.929352 | + | 0.675214i | 0.945834 | − | 0.324650i | \(-0.105247\pi\) |
−0.0164820 | + | 0.999864i | \(0.505247\pi\) | |||||||
\(374\) | −20.0746 | −1.03803 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.8314 | 0.558585 | ||||||||
\(377\) | 1.38444 | + | 1.00585i | 0.0713020 | + | 0.0518040i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.46397 | + | 7.58332i | 0.126566 | + | 0.389529i | 0.994183 | − | 0.107703i | \(-0.0343497\pi\) |
−0.867617 | + | 0.497232i | \(0.834350\pi\) | |||||||
\(380\) | 9.64266 | + | 5.16269i | 0.494658 | + | 0.264840i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.5420 | −0.692869 | ||||||||
\(383\) | 1.48546 | − | 4.57179i | 0.0759036 | − | 0.233607i | −0.905905 | − | 0.423481i | \(-0.860808\pi\) |
0.981808 | + | 0.189874i | \(0.0608079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.4630 | − | 54.6552i | −1.34868 | − | 2.78548i | ||||
\(386\) | 5.19369 | + | 3.77344i | 0.264352 | + | 0.192063i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.52978 | + | 1.11145i | −0.0776630 | + | 0.0564255i | ||||
\(389\) | −5.32641 | − | 3.86987i | −0.270060 | − | 0.196210i | 0.444510 | − | 0.895774i | \(-0.353378\pi\) |
−0.714570 | + | 0.699564i | \(0.753378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.82077 | + | 4.95558i | −0.344941 | + | 0.250614i | ||||
\(392\) | −5.71265 | + | 17.5817i | −0.288532 | + | 0.888011i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.57748 | + | 4.85499i | −0.0794724 | + | 0.244591i | ||||
\(395\) | −3.22623 | + | 17.9944i | −0.162329 | + | 0.905394i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.42206 | + | 7.45433i | 0.121560 | + | 0.374122i | 0.993259 | − | 0.115920i | \(-0.0369815\pi\) |
−0.871699 | + | 0.490042i | \(0.836982\pi\) | |||||||
\(398\) | −8.33412 | − | 6.05509i | −0.417751 | − | 0.303514i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.68856 | − | 1.73707i | −0.234428 | − | 0.0868537i | ||||
\(401\) | −29.4295 | −1.46964 | −0.734820 | − | 0.678262i | \(-0.762733\pi\) | ||||
−0.734820 | + | 0.678262i | \(0.762733\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.06890 | + | 21.7558i | 0.352127 | + | 1.08374i | ||||
\(404\) | 1.34502 | + | 4.13953i | 0.0669170 | + | 0.205949i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.776810 | − | 2.39078i | 0.0385524 | − | 0.118652i | ||||
\(407\) | 3.71467 | 0.184129 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.24014 | + | 5.98681i | −0.407448 | + | 0.296029i | −0.772568 | − | 0.634932i | \(-0.781028\pi\) |
0.365120 | + | 0.930961i | \(0.381028\pi\) | |||||||
\(410\) | 22.2251 | + | 11.8994i | 1.09762 | + | 0.587667i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.92912 | − | 2.12813i | 0.144307 | − | 0.104846i | ||||
\(413\) | −22.5134 | + | 16.3569i | −1.10781 | + | 0.804871i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.4401 | − | 18.6655i | 0.954279 | − | 0.916251i | ||||
\(416\) | −2.78032 | + | 2.02002i | −0.136317 | + | 0.0990398i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26.3128 | 1.28700 | ||||||||
\(419\) | 1.79741 | − | 5.53185i | 0.0878090 | − | 0.270248i | −0.897504 | − | 0.441006i | \(-0.854622\pi\) |
0.985313 | + | 0.170758i | \(0.0546216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.82013 | + | 30.2233i | 0.478604 | + | 1.47299i | 0.841035 | + | 0.540981i | \(0.181947\pi\) |
−0.362431 | + | 0.932011i | \(0.618053\pi\) | |||||||
\(422\) | 0.807403 | + | 2.48493i | 0.0393038 | + | 0.120965i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.70243 | 0.0826771 | ||||||||
\(425\) | 17.9656 | − | 5.04001i | 0.871462 | − | 0.244477i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.1728 | + | 31.3668i | 2.08928 | + | 1.51795i | ||||
\(428\) | 1.66749 | + | 5.13201i | 0.0806012 | + | 0.248065i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.174608 | − | 0.360626i | −0.00842034 | − | 0.0173909i | ||||
\(431\) | −9.77737 | + | 30.0916i | −0.470959 | + | 1.44946i | 0.380371 | + | 0.924834i | \(0.375796\pi\) |
−0.851331 | + | 0.524630i | \(0.824204\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.96383 | + | 6.04403i | −0.0943754 | + | 0.290458i | −0.987090 | − | 0.160164i | \(-0.948798\pi\) |
0.892715 | + | 0.450622i | \(0.148798\pi\) | |||||||
\(434\) | 27.1860 | − | 19.7518i | 1.30497 | − | 0.948115i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.43929 | + | 2.49879i | 0.164712 | + | 0.119670i | ||||
\(437\) | 8.94031 | − | 6.49552i | 0.427673 | − | 0.310723i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.20060 | − | 3.77846i | −0.248211 | − | 0.180336i | 0.456722 | − | 0.889609i | \(-0.349023\pi\) |
−0.704934 | + | 0.709273i | \(0.749023\pi\) | |||||||
\(440\) | −11.9161 | + | 1.63980i | −0.568080 | + | 0.0781744i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.96318 | − | 12.1974i | 0.188509 | − | 0.580171i | ||||
\(443\) | 39.0619 | 1.85589 | 0.927943 | − | 0.372722i | \(-0.121575\pi\) | ||||
0.927943 | + | 0.372722i | \(0.121575\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.27933 | + | 4.70759i | 0.108050 | + | 0.223161i | ||||
\(446\) | −0.652212 | − | 2.00730i | −0.0308832 | − | 0.0950486i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.08426 | + | 2.96739i | 0.192963 | + | 0.140196i | ||||
\(449\) | 38.7204 | 1.82733 | 0.913665 | − | 0.406468i | \(-0.133240\pi\) | ||||
0.913665 | + | 0.406468i | \(0.133240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 60.6477 | 2.85579 | ||||||||
\(452\) | 7.13157 | + | 5.18139i | 0.335441 | + | 0.243712i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.09746 | − | 15.6884i | −0.239236 | − | 0.736292i | ||||
\(455\) | 38.4330 | − | 5.28883i | 1.80177 | − | 0.247944i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0405 | −0.656786 | −0.328393 | − | 0.944541i | \(-0.606507\pi\) | ||||
−0.328393 | + | 0.944541i | \(0.606507\pi\) | |||||||
\(458\) | 4.31369 | − | 13.2762i | 0.201566 | − | 0.620355i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.64395 | + | 3.49875i | −0.169900 | + | 0.163130i | ||||
\(461\) | 25.3277 | + | 18.4017i | 1.17963 | + | 0.857051i | 0.992130 | − | 0.125214i | \(-0.0399617\pi\) |
0.187500 | + | 0.982265i | \(0.439962\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.6931 | − | 23.0264i | 1.47290 | − | 1.07013i | 0.493143 | − | 0.869948i | \(-0.335848\pi\) |
0.979759 | − | 0.200179i | \(-0.0641522\pi\) | |||||||
\(464\) | −0.402842 | − | 0.292682i | −0.0187015 | − | 0.0135874i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.6156 | − | 16.4312i | 1.04765 | − | 0.761161i | ||||
\(467\) | −5.72675 | + | 17.6251i | −0.265002 | + | 0.815593i | 0.726691 | + | 0.686965i | \(0.241057\pi\) |
−0.991693 | + | 0.128628i | \(0.958943\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.4546 | + | 44.4866i | −0.667450 | + | 2.05420i | ||||
\(470\) | −17.4704 | + | 16.7743i | −0.805851 | + | 0.773739i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.70337 | + | 5.24244i | 0.0784041 | + | 0.241303i | ||||
\(473\) | −0.779806 | − | 0.566562i | −0.0358555 | − | 0.0260506i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.5485 | + | 6.60619i | −1.08048 | + | 0.303113i | ||||
\(476\) | −18.8399 | −0.863525 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.59033 | − | 17.2053i | −0.255696 | − | 0.786951i | ||||
\(479\) | −1.36218 | − | 4.19235i | −0.0622395 | − | 0.191554i | 0.915102 | − | 0.403223i | \(-0.132110\pi\) |
−0.977341 | + | 0.211669i | \(0.932110\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.733357 | + | 2.25704i | −0.0334382 | + | 0.102912i | ||||
\(482\) | 9.35848 | 0.426267 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.5111 | + | 10.5429i | −0.659594 | + | 0.479223i | ||||
\(485\) | 0.746184 | − | 4.16185i | 0.0338825 | − | 0.188980i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.98983 | − | 4.35187i | 0.271425 | − | 0.197202i | −0.443743 | − | 0.896154i | \(-0.646350\pi\) |
0.715169 | + | 0.698952i | \(0.246350\pi\) | |||||||
\(488\) | 8.55174 | − | 6.21320i | 0.387119 | − | 0.281258i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18.0142 | − | 37.2055i | −0.813797 | − | 1.68077i | ||||
\(491\) | −17.8506 | + | 12.9692i | −0.805585 | + | 0.585292i | −0.912547 | − | 0.408971i | \(-0.865888\pi\) |
0.106962 | + | 0.994263i | \(0.465888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.85824 | 0.0836907 | ||||||||
\(494\) | −5.19473 | + | 15.9877i | −0.233722 | + | 0.719322i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.05690 | − | 6.33050i | −0.0923577 | − | 0.284248i | ||||
\(497\) | −5.83038 | − | 17.9441i | −0.261528 | − | 0.804901i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.3376 | −0.820906 | −0.410453 | − | 0.911882i | \(-0.634629\pi\) | ||||
−0.410453 | + | 0.911882i | \(0.634629\pi\) | |||||||
\(500\) | 10.2526 | − | 4.45924i | 0.458509 | − | 0.199423i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.67071 | − | 4.12001i | −0.253096 | − | 0.183885i | ||||
\(503\) | 7.20450 | + | 22.1732i | 0.321233 | + | 0.988653i | 0.973113 | + | 0.230330i | \(0.0739807\pi\) |
−0.651880 | + | 0.758322i | \(0.726019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.58023 | − | 4.59386i | −0.381815 | − | 0.204424i | ||||
\(506\) | −3.75542 | + | 11.5580i | −0.166949 | + | 0.513816i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.94289 | − | 15.2127i | 0.219305 | − | 0.674952i | ||||
\(509\) | 8.63861 | − | 6.27632i | 0.382900 | − | 0.278193i | −0.379640 | − | 0.925134i | \(-0.623952\pi\) |
0.762540 | + | 0.646941i | \(0.223952\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8288 | + | 14.4065i | 0.877176 | + | 0.637305i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.0113 | − | 13.8125i | −0.838551 | − | 0.609243i | ||||
\(515\) | −1.42874 | + | 7.96883i | −0.0629579 | + | 0.351148i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0049 | + | 55.4133i | −0.791853 | + | 2.43707i | ||||
\(518\) | 3.48619 | 0.153174 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.35616 | − | 7.56401i | 0.0594716 | − | 0.331704i | ||||
\(521\) | −6.93220 | − | 21.3351i | −0.303705 | − | 0.934708i | −0.980157 | − | 0.198222i | \(-0.936483\pi\) |
0.676452 | − | 0.736487i | \(-0.263517\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0349 | + | 12.3766i | 0.744885 | + | 0.541190i | 0.894237 | − | 0.447594i | \(-0.147719\pi\) |
−0.149353 | + | 0.988784i | \(0.547719\pi\) | |||||||
\(524\) | 1.99813 | 0.0872889 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.731323 | −0.0318872 | ||||||||
\(527\) | 20.0961 | + | 14.6007i | 0.875402 | + | 0.636017i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.53019 | − | 17.0202i | −0.240443 | − | 0.740008i | ||||
\(530\) | −2.74593 | + | 2.63650i | −0.119275 | + | 0.114522i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.6944 | 1.07064 | ||||||||
\(533\) | −11.9732 | + | 36.8497i | −0.518617 | + | 1.59614i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.6374 | − | 5.69527i | −0.459895 | − | 0.246228i | ||||
\(536\) | 7.49592 | + | 5.44611i | 0.323775 | + | 0.235236i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.3196 | + | 14.0365i | −0.832926 | + | 0.605156i | ||||
\(539\) | −80.4520 | − | 58.4518i | −3.46531 | − | 2.51770i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5520 | − | 16.3850i | 0.969585 | − | 0.704445i | 0.0142281 | − | 0.999899i | \(-0.495471\pi\) |
0.955357 | + | 0.295454i | \(0.0954709\pi\) | |||||||
\(542\) | 7.45801 | − | 22.9534i | 0.320349 | − | 0.985933i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.15320 | + | 3.54919i | −0.0494432 | + | 0.152170i | ||||
\(545\) | −9.41722 | + | 1.29592i | −0.403389 | + | 0.0555111i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.96355 | − | 9.12088i | −0.126712 | − | 0.389981i | 0.867497 | − | 0.497443i | \(-0.165728\pi\) |
−0.994209 | + | 0.107462i | \(0.965728\pi\) | |||||||
\(548\) | −1.19061 | − | 0.865029i | −0.0508604 | − | 0.0369522i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16.6806 | − | 21.0991i | 0.711264 | − | 0.899670i | ||||
\(551\) | −2.43568 | −0.103763 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7544 | + | 39.2539i | 0.542371 | + | 1.66925i | ||||
\(554\) | 4.50416 | + | 13.8624i | 0.191364 | + | 0.588956i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.33045 | + | 13.3278i | −0.183652 | + | 0.565223i | ||||
\(557\) | −14.0946 | −0.597209 | −0.298605 | − | 0.954377i | \(-0.596521\pi\) | ||||
−0.298605 | + | 0.954377i | \(0.596521\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.498196 | − | 0.361961i | 0.0210714 | − | 0.0153093i | ||||
\(560\) | −11.1832 | + | 1.53894i | −0.472577 | + | 0.0650322i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.6191 | + | 11.3480i | −0.658853 | + | 0.478685i | ||||
\(563\) | −13.9439 | + | 10.1308i | −0.587665 | + | 0.426964i | −0.841479 | − | 0.540289i | \(-0.818315\pi\) |
0.253814 | + | 0.967253i | \(0.418315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.5272 | + | 2.68717i | −0.821514 | + | 0.113050i | ||||
\(566\) | −11.9665 | + | 8.69417i | −0.502989 | + | 0.365443i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.73731 | −0.156814 | ||||||||
\(569\) | −3.08527 | + | 9.49547i | −0.129341 | + | 0.398071i | −0.994667 | − | 0.103139i | \(-0.967111\pi\) |
0.865326 | + | 0.501210i | \(0.167111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.81343 | − | 24.0473i | −0.326982 | − | 1.00635i | −0.970538 | − | 0.240948i | \(-0.922542\pi\) |
0.643556 | − | 0.765399i | \(-0.277458\pi\) | |||||||
\(572\) | −5.71274 | − | 17.5820i | −0.238862 | − | 0.735140i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 56.9175 | 2.37569 | ||||||||
\(575\) | 0.459093 | − | 11.2866i | 0.0191455 | − | 0.470684i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.02493 | + | 0.744656i | 0.0426684 | + | 0.0310004i | 0.608915 | − | 0.793235i | \(-0.291605\pi\) |
−0.566247 | + | 0.824236i | \(0.691605\pi\) | |||||||
\(578\) | 0.949717 | + | 2.92293i | 0.0395030 | + | 0.121578i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.10303 | − | 0.151790i | 0.0458010 | − | 0.00630275i | ||||
\(581\) | 18.8025 | − | 57.8682i | 0.780060 | − | 2.40078i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.82992 | + | 8.70961i | −0.117203 | + | 0.360715i | ||||
\(584\) | 3.92773 | − | 2.85366i | 0.162531 | − | 0.118085i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.97940 | + | 1.43812i | 0.0817684 | + | 0.0594082i | ||||
\(587\) | 14.9350 | − | 10.8509i | 0.616434 | − | 0.447865i | −0.235240 | − | 0.971937i | \(-0.575588\pi\) |
0.851674 | + | 0.524072i | \(0.175588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.3410 | − | 19.1379i | −1.08536 | − | 0.788562i | ||||
\(590\) | −10.8663 | − | 5.81782i | −0.447358 | − | 0.239516i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.213392 | − | 0.656753i | 0.00877036 | − | 0.0269924i | ||||
\(593\) | −43.8465 | −1.80056 | −0.900280 | − | 0.435311i | \(-0.856639\pi\) | ||||
−0.900280 | + | 0.435311i | \(0.856639\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.3878 | − | 29.1769i | 1.24578 | − | 1.19614i | ||||
\(596\) | −0.575002 | − | 1.76967i | −0.0235530 | − | 0.0724887i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.28127 | − | 4.56361i | −0.256860 | − | 0.186620i | ||||
\(599\) | −26.3560 | −1.07688 | −0.538439 | − | 0.842664i | \(-0.680986\pi\) | ||||
−0.538439 | + | 0.842664i | \(0.680986\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2074 | −0.824275 | −0.412138 | − | 0.911122i | \(-0.635218\pi\) | ||||
−0.412138 | + | 0.911122i | \(0.635218\pi\) | |||||||
\(602\) | −0.731843 | − | 0.531715i | −0.0298277 | − | 0.0216711i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.31329 | − | 4.04189i | −0.0534370 | − | 0.164462i | ||||
\(605\) | 7.07808 | − | 39.4781i | 0.287765 | − | 1.60501i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.08369 | 0.246929 | 0.123465 | − | 0.992349i | \(-0.460599\pi\) | ||||
0.123465 | + | 0.992349i | \(0.460599\pi\) | |||||||
\(608\) | 1.51156 | − | 4.65210i | 0.0613018 | − | 0.188668i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.17129 | + | 23.2654i | −0.168891 | + | 0.941990i | ||||
\(611\) | −30.1147 | − | 21.8796i | −1.21831 | − | 0.885154i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.6689 | + | 16.4699i | −0.915589 | + | 0.665214i | −0.942422 | − | 0.334426i | \(-0.891458\pi\) |
0.0268331 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(614\) | 6.10053 | + | 4.43229i | 0.246197 | + | 0.178873i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.9704 | + | 15.9624i | −0.885211 | + | 0.643143i | ||||
\(617\) | −0.732565 | + | 2.25460i | −0.0294920 | + | 0.0907669i | −0.964719 | − | 0.263282i | \(-0.915195\pi\) |
0.935227 | + | 0.354048i | \(0.115195\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.116715 | − | 0.359213i | 0.00469119 | − | 0.0144380i | −0.948684 | − | 0.316227i | \(-0.897584\pi\) |
0.953375 | + | 0.301789i | \(0.0975838\pi\) | |||||||
\(620\) | 13.1216 | + | 7.02530i | 0.526975 | + | 0.282143i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.21431 | − | 9.89264i | −0.128882 | − | 0.396659i | ||||
\(623\) | 9.55345 | + | 6.94099i | 0.382751 | + | 0.278085i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.63097 | + | 23.0704i | −0.385239 | + | 0.922817i | ||||
\(626\) | −20.1560 | −0.805596 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.07378 | − | 9.46012i | −0.122657 | − | 0.377500i | ||||
\(629\) | 0.796345 | + | 2.45090i | 0.0317524 | + | 0.0977237i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.1538 | − | 31.2501i | 0.404216 | − | 1.24405i | −0.517332 | − | 0.855785i | \(-0.673075\pi\) |
0.921548 | − | 0.388264i | \(-0.126925\pi\) | |||||||
\(632\) | 8.17564 | 0.325209 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.5585 | + | 15.6632i | −0.856197 | + | 0.622064i | ||||
\(635\) | 15.5868 | + | 32.1922i | 0.618544 | + | 1.27751i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 51.3985 | − | 37.3432i | 2.03648 | − | 1.47959i | ||||
\(638\) | 2.16700 | − | 1.57442i | 0.0857924 | − | 0.0623318i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.394615 | + | 2.20097i | −0.0155985 | + | 0.0870011i | ||||
\(641\) | 34.3726 | − | 24.9731i | 1.35764 | − | 0.986380i | 0.359044 | − | 0.933321i | \(-0.383103\pi\) |
0.998591 | − | 0.0530594i | \(-0.0168973\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.70055 | 0.0670633 | 0.0335316 | − | 0.999438i | \(-0.489325\pi\) | ||||
0.0335316 | + | 0.999438i | \(0.489325\pi\) | |||||||
\(644\) | −3.52444 | + | 10.8471i | −0.138882 | + | 0.427436i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.64090 | + | 17.3609i | 0.221938 | + | 0.683056i | ||||
\(647\) | −10.6378 | − | 32.7399i | −0.418217 | − | 1.28714i | −0.909342 | − | 0.416050i | \(-0.863414\pi\) |
0.491125 | − | 0.871089i | \(-0.336586\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.6518 | −1.16394 | ||||||||
\(650\) | 9.52678 | + | 14.3006i | 0.373671 | + | 0.560917i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.94101 | + | 7.22257i | 0.389320 | + | 0.282858i | ||||
\(653\) | 2.57723 | + | 7.93189i | 0.100855 | + | 0.310399i | 0.988735 | − | 0.149675i | \(-0.0478228\pi\) |
−0.887880 | + | 0.460074i | \(0.847823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.22289 | + | 3.09446i | −0.125929 | + | 0.120911i | ||||
\(656\) | 3.48396 | − | 10.7225i | 0.136026 | − | 0.418644i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.8974 | + | 52.0050i | −0.658731 | + | 2.02736i | ||||
\(659\) | 19.4275 | − | 14.1149i | 0.756789 | − | 0.549839i | −0.141135 | − | 0.989990i | \(-0.545075\pi\) |
0.897924 | + | 0.440151i | \(0.145075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.3548 | − | 23.5071i | −1.25845 | − | 0.914321i | −0.259774 | − | 0.965669i | \(-0.583648\pi\) |
−0.998681 | + | 0.0513486i | \(0.983648\pi\) | |||||||
\(662\) | 6.90412 | − | 5.01614i | 0.268336 | − | 0.194958i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.75071 | − | 7.08430i | −0.378401 | − | 0.274924i | ||||
\(665\) | −39.8308 | + | 38.2436i | −1.54457 | + | 1.48302i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.347626 | − | 1.06988i | 0.0134601 | − | 0.0414260i | ||||
\(668\) | −9.90556 | −0.383258 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.5248 | + | 2.82445i | −0.792942 | + | 0.109118i | ||||
\(671\) | 17.5713 | + | 54.0788i | 0.678332 | + | 2.08769i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.2296 | − | 27.7754i | −1.47364 | − | 1.07066i | −0.979538 | − | 0.201260i | \(-0.935496\pi\) |
−0.494104 | − | 0.869403i | \(-0.664504\pi\) | |||||||
\(674\) | 8.18290 | 0.315194 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.18931 | −0.0457427 | ||||||||
\(677\) | 24.4111 | + | 17.7357i | 0.938194 | + | 0.681638i | 0.947985 | − | 0.318314i | \(-0.103117\pi\) |
−0.00979088 | + | 0.999952i | \(0.503117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.94992 | − | 9.07891i | −0.113207 | − | 0.348417i | ||||
\(680\) | −3.63649 | − | 7.51061i | −0.139453 | − | 0.288019i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.8060 | 1.37108 | ||||||||
\(683\) | 1.18283 | − | 3.64038i | 0.0452598 | − | 0.139295i | −0.925873 | − | 0.377835i | \(-0.876669\pi\) |
0.971133 | + | 0.238540i | \(0.0766687\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.26004 | − | 0.448620i | 0.124560 | − | 0.0171409i | ||||
\(686\) | −46.9139 | − | 34.0849i | −1.79118 | − | 1.30137i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.144965 | + | 0.105323i | −0.00552673 | + | 0.00401541i | ||||
\(689\) | −4.73329 | − | 3.43894i | −0.180324 | − | 0.131013i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.0464 | + | 10.2053i | −0.534351 | + | 0.388229i | −0.821983 | − | 0.569512i | \(-0.807132\pi\) |
0.287632 | + | 0.957741i | \(0.407132\pi\) | |||||||
\(692\) | 5.55421 | − | 17.0941i | 0.211139 | − | 0.649820i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.524395 | + | 1.61392i | −0.0199058 | + | 0.0612636i | ||||
\(695\) | −13.6556 | − | 28.2035i | −0.517985 | − | 1.06982i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.0016 | + | 40.0147i | 0.492470 | + | 1.51567i | ||||
\(698\) | −15.8574 | − | 11.5211i | −0.600213 | − | 0.436080i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15.6546 | − | 19.8014i | 0.591690 | − | 0.748422i | ||||
\(701\) | 30.6938 | 1.15929 | 0.579644 | − | 0.814870i | \(-0.303192\pi\) | ||||
0.579644 | + | 0.814870i | \(0.303192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.04381 | − | 3.21251i | −0.0393680 | − | 0.121162i | ||||
\(704\) | 1.66229 | + | 5.11600i | 0.0626499 | + | 0.192817i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.55334 | − | 29.4021i | 0.359545 | − | 1.10656i | ||||
\(707\) | −21.9736 | −0.826400 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.3044 | − | 27.8297i | 1.43855 | − | 1.04517i | 0.450207 | − | 0.892924i | \(-0.351350\pi\) |
0.988343 | − | 0.152244i | \(-0.0486498\pi\) | |||||||
\(710\) | 6.02809 | − | 5.78788i | 0.226230 | − | 0.217215i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.89237 | − | 1.37488i | 0.0709194 | − | 0.0515260i | ||||
\(713\) | 12.1658 | − | 8.83899i | 0.455614 | − | 0.331023i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.4432 | + | 19.5117i | 1.36290 | + | 0.729696i | ||||
\(716\) | −15.4661 | + | 11.2368i | −0.577996 | + | 0.419939i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.4136 | 0.761830 | ||||||||
\(719\) | 8.85041 | − | 27.2387i | 0.330064 | − | 1.01583i | −0.639038 | − | 0.769175i | \(-0.720667\pi\) |
0.969102 | − | 0.246659i | \(-0.0793327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.64830 | + | 17.3837i | 0.210354 | + | 0.647402i | ||||
\(722\) | −1.52249 | − | 4.68573i | −0.0566610 | − | 0.174385i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.8363 | 0.551387 | ||||||||
\(725\) | −1.54406 | + | 1.95307i | −0.0573451 | + | 0.0725352i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.72535 | + | 2.70662i | 0.138166 | + | 0.100383i | 0.654721 | − | 0.755870i | \(-0.272786\pi\) |
−0.516556 | + | 0.856254i | \(0.672786\pi\) | |||||||
\(728\) | −5.36136 | − | 16.5006i | −0.198705 | − | 0.611552i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.91583 | + | 10.6856i | −0.0709082 | + | 0.395492i | ||||
\(731\) | 0.206638 | − | 0.635967i | 0.00764279 | − | 0.0235221i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.33453 | − | 16.4180i | 0.197036 | − | 0.606413i | −0.802911 | − | 0.596099i | \(-0.796717\pi\) |
0.999947 | − | 0.0103145i | \(-0.00328325\pi\) | |||||||
\(734\) | 1.61731 | − | 1.17504i | 0.0596958 | − | 0.0433716i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.82772 | + | 1.32792i | 0.0673707 | + | 0.0489477i | ||||
\(737\) | −40.3227 | + | 29.2961i | −1.48531 | + | 1.07914i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.3468 | + | 8.97048i | 0.454184 | + | 0.329984i | 0.791246 | − | 0.611498i | \(-0.209433\pi\) |
−0.337061 | + | 0.941483i | \(0.609433\pi\) | |||||||
\(740\) | 0.672906 | + | 1.38978i | 0.0247365 | + | 0.0510895i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.65586 | + | 8.17391i | −0.0974998 | + | 0.300074i | ||||
\(743\) | 5.21102 | 0.191174 | 0.0955869 | − | 0.995421i | \(-0.469527\pi\) | ||||
0.0955869 | + | 0.995421i | \(0.469527\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.66810 | + | 1.96390i | 0.134389 | + | 0.0719518i | ||||
\(746\) | 6.85582 | + | 21.1000i | 0.251009 | + | 0.772528i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.2407 | − | 11.7996i | −0.593819 | − | 0.431435i | ||||
\(749\) | −27.2418 | −0.995395 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.8064 | −1.12414 | −0.562070 | − | 0.827090i | \(-0.689995\pi\) | ||||
−0.562070 | + | 0.827090i | \(0.689995\pi\) | |||||||
\(752\) | 8.76276 | + | 6.36652i | 0.319545 | + | 0.232163i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.528807 | + | 1.62750i | 0.0192580 | + | 0.0592701i | ||||
\(755\) | 8.37785 | + | 4.48551i | 0.304901 | + | 0.163244i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.4137 | −0.850985 | −0.425492 | − | 0.904962i | \(-0.639899\pi\) | ||||
−0.425492 | + | 0.904962i | \(0.639899\pi\) | |||||||
\(758\) | −2.46397 | + | 7.58332i | −0.0894954 | + | 0.275439i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.76652 | + | 9.84452i | 0.172900 | + | 0.357098i | ||||
\(761\) | −26.9935 | − | 19.6119i | −0.978514 | − | 0.710932i | −0.0211379 | − | 0.999777i | \(-0.506729\pi\) |
−0.957376 | + | 0.288845i | \(0.906729\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.3630 | + | 12.6149i | −0.628582 | + | 0.456692i | ||||
\(764\) | −10.9557 | − | 7.95979i | −0.396364 | − | 0.287975i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.88899 | − | 2.82552i | 0.140515 | − | 0.102090i | ||||
\(767\) | 5.85393 | − | 18.0165i | 0.211373 | − | 0.650539i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1223 | − | 37.3087i | 0.437142 | − | 1.34538i | −0.453734 | − | 0.891137i | \(-0.649908\pi\) |
0.890876 | − | 0.454247i | \(-0.150092\pi\) | |||||||
\(770\) | 10.7165 | − | 59.7715i | 0.386196 | − | 2.15401i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.98381 | + | 6.10555i | 0.0713990 | + | 0.219744i | ||||
\(773\) | −7.58903 | − | 5.51376i | −0.272959 | − | 0.198316i | 0.442882 | − | 0.896580i | \(-0.353956\pi\) |
−0.715840 | + | 0.698264i | \(0.753956\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.0443 | + | 8.98959i | −1.15107 | + | 0.322916i | ||||
\(776\) | −1.89092 | −0.0678799 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.03451 | − | 6.26157i | −0.0729407 | − | 0.224488i | ||||
\(779\) | −17.0418 | − | 52.4493i | −0.610586 | − | 1.87919i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.21249 | − | 19.1201i | 0.222300 | − | 0.684170i | ||||
\(782\) | −8.43093 | −0.301489 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14.9559 | + | 10.8661i | −0.534140 | + | 0.388075i | ||||
\(785\) | 19.6085 | + | 10.4984i | 0.699857 | + | 0.374704i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.32633 | + | 3.86981i | −0.189863 | + | 0.137944i | −0.678656 | − | 0.734456i | \(-0.737437\pi\) |
0.488793 | + | 0.872400i | \(0.337437\pi\) | |||||||
\(788\) | −4.12990 | + | 3.00055i | −0.147122 | + | 0.106890i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.1869 | + | 12.6614i | −0.469168 | + | 0.450473i | ||||
\(791\) | −36.0032 | + | 26.1578i | −1.28012 | + | 0.930065i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.3274 | −1.29002 | ||||||||
\(794\) | −2.42206 | + | 7.45433i | −0.0859557 | + | 0.264544i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.18335 | − | 9.79734i | −0.112831 | − | 0.347258i | ||||
\(797\) | −3.44128 | − | 10.5912i | −0.121896 | − | 0.375158i | 0.871427 | − | 0.490526i | \(-0.163195\pi\) |
−0.993323 | + | 0.115368i | \(0.963195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.4209 | −1.42999 | ||||||||
\(800\) | −2.77210 | − | 4.16119i | −0.0980084 | − | 0.147120i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.8090 | − | 17.2982i | −0.840724 | − | 0.610822i | ||||
\(803\) | 8.07032 | + | 24.8379i | 0.284795 | + | 0.876510i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.1139 | − | 22.9540i | −0.391713 | − | 0.809024i | ||||
\(806\) | −7.06890 | + | 21.7558i | −0.248991 | + | 0.766317i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.34502 | + | 4.13953i | −0.0473175 | + | 0.145628i | ||||
\(809\) | 27.7387 | − | 20.1533i | 0.975241 | − | 0.708554i | 0.0186007 | − | 0.999827i | \(-0.494079\pi\) |
0.956640 | + | 0.291273i | \(0.0940789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.0793 | + | 26.9397i | 1.30203 | + | 0.945980i | 0.999973 | − | 0.00731019i | \(-0.00232693\pi\) |
0.302056 | + | 0.953290i | \(0.402327\pi\) | |||||||
\(812\) | 2.03372 | − | 1.47758i | 0.0713694 | − | 0.0518529i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.00523 | + | 2.18343i | 0.105333 | + | 0.0765291i | ||||
\(815\) | −27.2198 | + | 3.74576i | −0.953466 | + | 0.131208i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.270851 | + | 0.833593i | −0.00947587 | + | 0.0291637i | ||||
\(818\) | −10.1854 | −0.356123 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.9862 | + | 22.6904i | 0.383656 | + | 0.792383i | ||||
\(821\) | 2.49186 | + | 7.66917i | 0.0869667 | + | 0.267656i | 0.985077 | − | 0.172114i | \(-0.0550599\pi\) |
−0.898110 | + | 0.439770i | \(0.855060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.7737 | + | 14.3664i | 0.689267 | + | 0.500782i | 0.876419 | − | 0.481549i | \(-0.159926\pi\) |
−0.187152 | + | 0.982331i | \(0.559926\pi\) | |||||||
\(824\) | 3.62059 | 0.126129 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.8280 | −0.968261 | ||||||||
\(827\) | 14.2534 | + | 10.3557i | 0.495641 | + | 0.360104i | 0.807349 | − | 0.590074i | \(-0.200901\pi\) |
−0.311709 | + | 0.950178i | \(0.600901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.9374 | + | 49.0502i | 0.553528 | + | 1.70358i | 0.699800 | + | 0.714338i | \(0.253272\pi\) |
−0.146273 | + | 0.989244i | \(0.546728\pi\) | |||||||
\(830\) | 26.6987 | − | 3.67405i | 0.926725 | − | 0.127528i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.43667 | −0.119145 | ||||||||
\(833\) | 21.3187 | − | 65.6122i | 0.738649 | − | 2.27333i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.9772 | − | 15.3405i | 0.552913 | − | 0.530880i | ||||
\(836\) | 21.2875 | + | 15.4663i | 0.736244 | + | 0.534912i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.70567 | − | 3.41887i | 0.162555 | − | 0.118103i | ||||
\(839\) | 36.0522 | + | 26.1935i | 1.24466 | + | 0.904298i | 0.997900 | − | 0.0647781i | \(-0.0206340\pi\) |
0.246760 | + | 0.969077i | \(0.420634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2609 | − | 16.9000i | 0.802100 | − | 0.582760i | ||||
\(842\) | −9.82013 | + | 30.2233i | −0.338424 | + | 1.04156i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.807403 | + | 2.48493i | −0.0277920 | + | 0.0855349i | ||||
\(845\) | 1.91830 | − | 1.84185i | 0.0659914 | − | 0.0633617i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.9820 | − | 86.1198i | −0.961474 | − | 2.95911i | ||||
\(848\) | 1.37729 | + | 1.00066i | 0.0472964 | + | 0.0343628i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.4970 | + | 6.48249i | 0.600141 | + | 0.222348i | ||||
\(851\) | 1.56008 | 0.0534790 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.80437 | + | 30.1747i | 0.335695 | + | 1.03316i | 0.966379 | + | 0.257123i | \(0.0827746\pi\) |
−0.630683 | + | 0.776040i | \(0.717225\pi\) | |||||||
\(854\) | 16.4905 | + | 50.7526i | 0.564294 | + | 1.73672i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.66749 | + | 5.13201i | −0.0569937 | + | 0.175409i | ||||
\(857\) | −42.8506 | −1.46375 | −0.731874 | − | 0.681440i | \(-0.761354\pi\) | ||||
−0.731874 | + | 0.681440i | \(0.761354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0964 | − | 18.9602i | 0.890399 | − | 0.646912i | −0.0455834 | − | 0.998961i | \(-0.514515\pi\) |
0.935982 | + | 0.352048i | \(0.114515\pi\) | |||||||
\(860\) | 0.0707097 | − | 0.394384i | 0.00241118 | − | 0.0134484i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.5975 | + | 18.5977i | −0.871854 | + | 0.633439i | ||||
\(863\) | 4.38976 | − | 3.18935i | 0.149429 | − | 0.108567i | −0.510559 | − | 0.859843i | \(-0.670561\pi\) |
0.659988 | + | 0.751276i | \(0.270561\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.5145 | + | 36.1736i | 0.595512 | + | 1.22994i | ||||
\(866\) | −5.14136 | + | 3.73542i | −0.174711 | + | 0.126935i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 33.6037 | 1.14058 | ||||||||
\(869\) | −13.5903 | + | 41.8266i | −0.461018 | + | 1.41887i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.83983 | − | 30.2839i | −0.333410 | − | 1.02613i | ||||
\(872\) | 1.31369 | + | 4.04313i | 0.0444872 | + | 0.136918i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.0508 | 0.373800 | ||||||||
\(875\) | 5.41579 | + | 56.1826i | 0.183087 | + | 1.89932i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.5102 | − | 30.8855i | −1.43547 | − | 1.04293i | −0.988965 | − | 0.148147i | \(-0.952669\pi\) |
−0.446503 | − | 0.894782i | \(-0.647331\pi\) | |||||||
\(878\) | −1.98645 | − | 6.11368i | −0.0670396 | − | 0.206327i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.6042 | − | 5.67750i | −0.357468 | − | 0.191389i | ||||
\(881\) | 3.81610 | − | 11.7448i | 0.128568 | − | 0.395691i | −0.865966 | − | 0.500102i | \(-0.833296\pi\) |
0.994534 | + | 0.104411i | \(0.0332958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.2451 | − | 46.9197i | 0.513040 | − | 1.57897i | −0.273781 | − | 0.961792i | \(-0.588274\pi\) |
0.786821 | − | 0.617182i | \(-0.211726\pi\) | |||||||
\(884\) | 10.3757 | − | 7.53841i | 0.348974 | − | 0.253544i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.6017 | + | 22.9600i | 1.06168 | + | 0.771356i | ||||
\(887\) | −10.3174 | + | 7.49602i | −0.346424 | + | 0.251692i | −0.747367 | − | 0.664411i | \(-0.768682\pi\) |
0.400943 | + | 0.916103i | \(0.368682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 65.3298 | + | 47.4649i | 2.19109 | + | 1.59192i | ||||
\(890\) | −0.923041 | + | 5.14828i | −0.0309404 | + | 0.172571i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.652212 | − | 2.00730i | 0.0218377 | − | 0.0672095i | ||||
\(893\) | 52.9817 | 1.77297 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.54393 | − | 42.0764i | 0.252166 | − | 1.40646i | ||||
\(896\) | 1.56005 | + | 4.80133i | 0.0521175 | + | 0.160401i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.3255 | + | 22.7593i | 1.04534 | + | 0.759487i | ||||
\(899\) | −3.31443 | −0.110542 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.35318 | −0.211655 | ||||||||
\(902\) | 49.0650 | + | 35.6478i | 1.63369 | + | 1.18694i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.72402 | + | 8.38367i | 0.0905995 | + | 0.278837i | ||||
\(905\) | −23.9302 | + | 22.9766i | −0.795467 | + | 0.763768i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.0967 | 1.13216 | 0.566082 | − | 0.824349i | \(-0.308459\pi\) | ||||
0.566082 | + | 0.824349i | \(0.308459\pi\) | |||||||
\(908\) | 5.09746 | − | 15.6884i | 0.169165 | − | 0.520637i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 34.2016 | + | 18.3116i | 1.13377 | + | 0.607023i | ||||
\(911\) | 16.4225 | + | 11.9316i | 0.544100 | + | 0.395312i | 0.825606 | − | 0.564248i | \(-0.190834\pi\) |
−0.281505 | + | 0.959560i | \(0.590834\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.4518 | − | 38.1085i | 1.73590 | − | 1.26121i | ||||
\(914\) | −11.3590 | − | 8.25279i | −0.375722 | − | 0.272978i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.2934 | − | 8.20513i | 0.373144 | − | 0.271105i | ||||
\(917\) | −3.11718 | + | 9.59370i | −0.102938 | + | 0.316812i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.96344 | − | 12.1982i | 0.130742 | − | 0.402382i | −0.864162 | − | 0.503214i | \(-0.832151\pi\) |
0.994903 | + | 0.100833i | \(0.0321507\pi\) | |||||||
\(920\) | −5.00453 | + | 0.688683i | −0.164995 | + | 0.0227052i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.67433 | + | 29.7745i | 0.318607 | + | 0.980571i | ||||
\(923\) | 10.3909 | + | 7.54945i | 0.342022 | + | 0.248493i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.23769 | − | 1.19954i | −0.106455 | − | 0.0394406i | ||||
\(926\) | 39.1748 | 1.28736 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.153872 | − | 0.473569i | −0.00505110 | − | 0.0155457i | ||||
\(929\) | 8.92328 | + | 27.4630i | 0.292763 | + | 0.901033i | 0.983964 | + | 0.178370i | \(0.0570823\pi\) |
−0.691200 | + | 0.722663i | \(0.742918\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.9435 | + | 86.0012i | −0.915810 | + | 2.81857i | ||||
\(932\) | 27.9544 | 0.915678 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.9928 | + | 10.8929i | −0.490580 | + | 0.356427i | ||||
\(935\) | 44.4692 | − | 6.11948i | 1.45430 | − | 0.200128i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.2904 | + | 32.1789i | −1.44690 | + | 1.05124i | −0.460363 | + | 0.887731i | \(0.652281\pi\) |
−0.986542 | + | 0.163507i | \(0.947719\pi\) | |||||||
\(938\) | −37.8426 | + | 27.4942i | −1.23560 | + | 0.897718i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −23.9935 | + | 3.30179i | −0.782583 | + | 0.107693i | ||||
\(941\) | 10.6128 | − | 7.71063i | 0.345967 | − | 0.251359i | −0.401208 | − | 0.915987i | \(-0.631410\pi\) |
0.747175 | + | 0.664627i | \(0.231410\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.4708 | 0.829443 | ||||||||
\(944\) | −1.70337 | + | 5.24244i | −0.0554400 | + | 0.170627i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.297860 | − | 0.916717i | −0.00968425 | − | 0.0298051i | ||||
\(947\) | −17.7342 | − | 54.5802i | −0.576283 | − | 1.77362i | −0.631767 | − | 0.775158i | \(-0.717670\pi\) |
0.0554842 | − | 0.998460i | \(-0.482330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.6848 | −0.541612 | ||||||||
\(950\) | −22.9341 | − | 8.49692i | −0.744081 | − | 0.275676i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.2418 | − | 11.0738i | −0.493990 | − | 0.358904i | ||||
\(953\) | 9.86978 | + | 30.3761i | 0.319713 | + | 0.983977i | 0.973771 | + | 0.227532i | \(0.0730655\pi\) |
−0.654057 | + | 0.756445i | \(0.726934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.9981 | − | 4.12810i | 0.970717 | − | 0.133582i | ||||
\(956\) | 5.59033 | − | 17.2053i | 0.180804 | − | 0.556459i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.36218 | − | 4.19235i | 0.0440100 | − | 0.135449i | ||||
\(959\) | 6.01070 | − | 4.36703i | 0.194096 | − | 0.141019i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.7649 | − | 7.82113i | −0.347253 | − | 0.252294i | ||||
\(962\) | −1.91995 | + | 1.39493i | −0.0619018 | + | 0.0449743i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.57117 | + | 5.50078i | 0.243851 | + | 0.177168i | ||||
\(965\) | −12.6553 | − | 6.77566i | −0.407389 | − | 0.218116i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.12337 | − | 9.61274i | 0.100441 | − | 0.309125i | −0.888193 | − | 0.459471i | \(-0.848039\pi\) |
0.988633 | + | 0.150346i | \(0.0480389\pi\) | |||||||
\(968\) | −17.9367 | −0.576506 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.04995 | − | 2.92841i | 0.0979281 | − | 0.0940257i | ||||
\(971\) | −8.57960 | − | 26.4053i | −0.275333 | − | 0.847386i | −0.989131 | − | 0.147036i | \(-0.953027\pi\) |
0.713799 | − | 0.700351i | \(-0.246973\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −57.2352 | − | 41.5838i | −1.83488 | − | 1.33312i | ||||
\(974\) | 7.40384 | 0.237234 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.5705 | 0.338354 | ||||||||
\(977\) | 17.9779 | + | 13.0617i | 0.575165 | + | 0.417882i | 0.836978 | − | 0.547237i | \(-0.184320\pi\) |
−0.261813 | + | 0.965119i | \(0.584320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.88825 | + | 11.9668i | 0.124269 | + | 0.382460i | ||||
\(980\) | 7.29506 | − | 40.6883i | 0.233032 | − | 1.29974i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.0645 | −0.704107 | ||||||||
\(983\) | −14.0395 | + | 43.2090i | −0.447789 | + | 1.37815i | 0.431606 | + | 0.902062i | \(0.357947\pi\) |
−0.879396 | + | 0.476092i | \(0.842053\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.01445 | − | 11.2356i | 0.0641856 | − | 0.357996i | ||||
\(986\) | 1.50334 | + | 1.09224i | 0.0478762 | + | 0.0347841i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.6000 | + | 9.88096i | −0.432673 | + | 0.314355i | ||||
\(989\) | −0.327503 | − | 0.237945i | −0.0104140 | − | 0.00756620i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5332 | − | 9.10592i | 0.398131 | − | 0.289259i | −0.370648 | − | 0.928773i | \(-0.620864\pi\) |
0.768779 | + | 0.639514i | \(0.220864\pi\) | |||||||
\(992\) | 2.05690 | − | 6.33050i | 0.0653068 | − | 0.200994i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.83038 | − | 17.9441i | 0.184928 | − | 0.569151i | ||||
\(995\) | 20.3075 | + | 10.8726i | 0.643790 | + | 0.344686i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.66765 | − | 20.5209i | −0.211167 | − | 0.649904i | −0.999404 | − | 0.0345322i | \(-0.989006\pi\) |
0.788237 | − | 0.615372i | \(-0.210994\pi\) | |||||||
\(998\) | −14.8355 | − | 10.7786i | −0.469608 | − | 0.341191i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.2.h.g.91.1 | yes | 12 | |
3.2 | odd | 2 | 450.2.h.f.91.3 | ✓ | 12 | ||
25.11 | even | 5 | inner | 450.2.h.g.361.1 | yes | 12 | |
75.11 | odd | 10 | 450.2.h.f.361.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.h.f.91.3 | ✓ | 12 | 3.2 | odd | 2 | ||
450.2.h.f.361.3 | yes | 12 | 75.11 | odd | 10 | ||
450.2.h.g.91.1 | yes | 12 | 1.1 | even | 1 | trivial | |
450.2.h.g.361.1 | yes | 12 | 25.11 | even | 5 | inner |