Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(571,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.571");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.b (of order \(2\), degree \(1\), 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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 571.18 | ||
Character | \(\chi\) | \(=\) | 572.571 |
Dual form | 572.2.b.c.571.19 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.883550 | − | 1.10424i | −0.624764 | − | 0.780813i | ||||
\(3\) | − | 2.47596i | − | 1.42950i | −0.699382 | − | 0.714748i | \(-0.746541\pi\) | ||
0.699382 | − | 0.714748i | \(-0.253459\pi\) | |||||||
\(4\) | −0.438678 | + | 1.95130i | −0.219339 | + | 0.975649i | ||||
\(5\) | 2.76928i | 1.23846i | 0.785209 | + | 0.619230i | \(0.212555\pi\) | ||||
−0.785209 | + | 0.619230i | \(0.787445\pi\) | |||||||
\(6\) | −2.73405 | + | 2.18764i | −1.11617 | + | 0.893099i | ||||
\(7\) | 0.534510i | 0.202026i | 0.994885 | + | 0.101013i | \(0.0322083\pi\) | ||||
−0.994885 | + | 0.101013i | \(0.967792\pi\) | |||||||
\(8\) | 2.54229 | − | 1.23966i | 0.898835 | − | 0.438287i | ||||
\(9\) | −3.13038 | −1.04346 | ||||||||
\(10\) | 3.05794 | − | 2.44680i | 0.967007 | − | 0.773746i | ||||
\(11\) | 3.29596 | + | 0.369696i | 0.993768 | + | 0.111468i | ||||
\(12\) | 4.83134 | + | 1.08615i | 1.39469 | + | 0.313545i | ||||
\(13\) | −3.35334 | − | 1.32481i | −0.930049 | − | 0.367435i | ||||
\(14\) | 0.590226 | − | 0.472267i | 0.157745 | − | 0.126219i | ||||
\(15\) | 6.85664 | 1.77038 | ||||||||
\(16\) | −3.61512 | − | 1.71198i | −0.903781 | − | 0.427996i | ||||
\(17\) | − | 5.90649i | − | 1.43253i | −0.697827 | − | 0.716267i | \(-0.745849\pi\) | ||
0.697827 | − | 0.716267i | \(-0.254151\pi\) | |||||||
\(18\) | 2.76585 | + | 3.45669i | 0.651918 | + | 0.814749i | ||||
\(19\) | − | 5.54527i | − | 1.27217i | −0.771618 | − | 0.636086i | \(-0.780552\pi\) | ||
0.771618 | − | 0.636086i | \(-0.219448\pi\) | |||||||
\(20\) | −5.40369 | − | 1.21482i | −1.20830 | − | 0.271643i | ||||
\(21\) | 1.32343 | 0.288795 | ||||||||
\(22\) | −2.50391 | − | 3.96616i | −0.533835 | − | 0.845588i | ||||
\(23\) | − | 4.48555i | − | 0.935301i | −0.883913 | − | 0.467651i | \(-0.845101\pi\) | ||
0.883913 | − | 0.467651i | \(-0.154899\pi\) | |||||||
\(24\) | −3.06936 | − | 6.29461i | −0.626531 | − | 1.28488i | ||||
\(25\) | −2.66893 | −0.533785 | ||||||||
\(26\) | 1.49994 | + | 4.87341i | 0.294163 | + | 0.955755i | ||||
\(27\) | 0.322828i | 0.0621283i | ||||||||
\(28\) | −1.04299 | − | 0.234478i | −0.197106 | − | 0.0443122i | ||||
\(29\) | − | 0.677674i | − | 0.125841i | −0.998019 | − | 0.0629204i | \(-0.979959\pi\) | ||
0.998019 | − | 0.0629204i | \(-0.0200414\pi\) | |||||||
\(30\) | −6.05818 | − | 7.57135i | −1.10607 | − | 1.38233i | ||||
\(31\) | 9.20526 | 1.65331 | 0.826657 | − | 0.562706i | \(-0.190240\pi\) | ||||
0.826657 | + | 0.562706i | \(0.190240\pi\) | |||||||
\(32\) | 1.30371 | + | 5.50458i | 0.230465 | + | 0.973081i | ||||
\(33\) | 0.915354 | − | 8.16066i | 0.159343 | − | 1.42059i | ||||
\(34\) | −6.52216 | + | 5.21868i | −1.11854 | + | 0.894996i | ||||
\(35\) | −1.48021 | −0.250201 | ||||||||
\(36\) | 1.37323 | − | 6.10831i | 0.228872 | − | 1.01805i | ||||
\(37\) | − | 1.55230i | − | 0.255197i | −0.991826 | − | 0.127598i | \(-0.959273\pi\) | ||
0.991826 | − | 0.127598i | \(-0.0407268\pi\) | |||||||
\(38\) | −6.12329 | + | 4.89953i | −0.993329 | + | 0.794808i | ||||
\(39\) | −3.28017 | + | 8.30274i | −0.525248 | + | 1.32950i | ||||
\(40\) | 3.43298 | + | 7.04032i | 0.542802 | + | 1.11317i | ||||
\(41\) | 2.50658 | 0.391462 | 0.195731 | − | 0.980658i | \(-0.437292\pi\) | ||||
0.195731 | + | 0.980658i | \(0.437292\pi\) | |||||||
\(42\) | −1.16931 | − | 1.46138i | −0.180429 | − | 0.225495i | ||||
\(43\) | 8.49046 | 1.29478 | 0.647392 | − | 0.762157i | \(-0.275860\pi\) | ||||
0.647392 | + | 0.762157i | \(0.275860\pi\) | |||||||
\(44\) | −2.16725 | + | 6.26921i | −0.326726 | + | 0.945119i | ||||
\(45\) | − | 8.66892i | − | 1.29229i | ||||||
\(46\) | −4.95311 | + | 3.96321i | −0.730296 | + | 0.584343i | ||||
\(47\) | −10.0993 | −1.47313 | −0.736565 | − | 0.676367i | \(-0.763553\pi\) | ||||
−0.736565 | + | 0.676367i | \(0.763553\pi\) | |||||||
\(48\) | −4.23881 | + | 8.95090i | −0.611819 | + | 1.29195i | ||||
\(49\) | 6.71430 | 0.959186 | ||||||||
\(50\) | 2.35813 | + | 2.94713i | 0.333490 | + | 0.416787i | ||||
\(51\) | −14.6242 | −2.04780 | ||||||||
\(52\) | 4.05613 | − | 5.96220i | 0.562484 | − | 0.826808i | ||||
\(53\) | 4.38869 | 0.602834 | 0.301417 | − | 0.953492i | \(-0.402540\pi\) | ||||
0.301417 | + | 0.953492i | \(0.402540\pi\) | |||||||
\(54\) | 0.356479 | − | 0.285235i | 0.0485106 | − | 0.0388156i | ||||
\(55\) | −1.02379 | + | 9.12743i | −0.138048 | + | 1.23074i | ||||
\(56\) | 0.662613 | + | 1.35888i | 0.0885454 | + | 0.181588i | ||||
\(57\) | −13.7299 | −1.81857 | ||||||||
\(58\) | −0.748313 | + | 0.598759i | −0.0982583 | + | 0.0786209i | ||||
\(59\) | −5.47956 | −0.713378 | −0.356689 | − | 0.934223i | \(-0.616094\pi\) | ||||
−0.356689 | + | 0.934223i | \(0.616094\pi\) | |||||||
\(60\) | −3.00786 | + | 13.3793i | −0.388313 | + | 1.72726i | ||||
\(61\) | 10.3154i | 1.32076i | 0.750933 | + | 0.660378i | \(0.229604\pi\) | ||||
−0.750933 | + | 0.660378i | \(0.770396\pi\) | |||||||
\(62\) | −8.13331 | − | 10.1648i | −1.03293 | − | 1.29093i | ||||
\(63\) | − | 1.67322i | − | 0.210806i | ||||||
\(64\) | 4.92647 | − | 6.30317i | 0.615808 | − | 0.787896i | ||||
\(65\) | 3.66876 | − | 9.28634i | 0.455054 | − | 1.15183i | ||||
\(66\) | −9.82006 | + | 6.19958i | −1.20877 | + | 0.763116i | ||||
\(67\) | 2.88040 | 0.351897 | 0.175949 | − | 0.984399i | \(-0.443701\pi\) | ||||
0.175949 | + | 0.984399i | \(0.443701\pi\) | |||||||
\(68\) | 11.5253 | + | 2.59105i | 1.39765 | + | 0.314211i | ||||
\(69\) | −11.1060 | −1.33701 | ||||||||
\(70\) | 1.30784 | + | 1.63450i | 0.156317 | + | 0.195360i | ||||
\(71\) | −3.09875 | −0.367754 | −0.183877 | − | 0.982949i | \(-0.558865\pi\) | ||||
−0.183877 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(72\) | −7.95834 | + | 3.88063i | −0.937900 | + | 0.457336i | ||||
\(73\) | −9.44310 | −1.10523 | −0.552616 | − | 0.833436i | \(-0.686370\pi\) | ||||
−0.552616 | + | 0.833436i | \(0.686370\pi\) | |||||||
\(74\) | −1.71411 | + | 1.37154i | −0.199261 | + | 0.159438i | ||||
\(75\) | 6.60816i | 0.763044i | ||||||||
\(76\) | 10.8205 | + | 2.43259i | 1.24119 | + | 0.279037i | ||||
\(77\) | −0.197607 | + | 1.76172i | −0.0225194 | + | 0.200767i | ||||
\(78\) | 12.0664 | − | 3.71380i | 1.36625 | − | 0.420505i | ||||
\(79\) | 8.42639 | 0.948043 | 0.474021 | − | 0.880513i | \(-0.342802\pi\) | ||||
0.474021 | + | 0.880513i | \(0.342802\pi\) | |||||||
\(80\) | 4.74097 | − | 10.0113i | 0.530056 | − | 1.11930i | ||||
\(81\) | −8.59184 | −0.954649 | ||||||||
\(82\) | −2.21469 | − | 2.76786i | −0.244572 | − | 0.305659i | ||||
\(83\) | − | 2.83221i | − | 0.310875i | −0.987846 | − | 0.155438i | \(-0.950321\pi\) | ||
0.987846 | − | 0.155438i | \(-0.0496788\pi\) | |||||||
\(84\) | −0.580559 | + | 2.58240i | −0.0633442 | + | 0.281763i | ||||
\(85\) | 16.3567 | 1.77414 | ||||||||
\(86\) | −7.50175 | − | 9.37548i | −0.808935 | − | 1.01098i | ||||
\(87\) | −1.67789 | −0.179889 | ||||||||
\(88\) | 8.83757 | − | 3.14600i | 0.942088 | − | 0.335365i | ||||
\(89\) | − | 6.95222i | − | 0.736933i | −0.929641 | − | 0.368467i | \(-0.879883\pi\) | ||
0.929641 | − | 0.368467i | \(-0.120117\pi\) | |||||||
\(90\) | −9.57254 | + | 7.65943i | −1.00903 | + | 0.807374i | ||||
\(91\) | 0.708123 | − | 1.79239i | 0.0742314 | − | 0.187894i | ||||
\(92\) | 8.75264 | + | 1.96771i | 0.912526 | + | 0.205148i | ||||
\(93\) | − | 22.7919i | − | 2.36341i | ||||||
\(94\) | 8.92321 | + | 11.1520i | 0.920358 | + | 1.15024i | ||||
\(95\) | 15.3564 | 1.57554 | ||||||||
\(96\) | 13.6291 | − | 3.22792i | 1.39102 | − | 0.329449i | ||||
\(97\) | − | 2.27247i | − | 0.230734i | −0.993323 | − | 0.115367i | \(-0.963196\pi\) | ||
0.993323 | − | 0.115367i | \(-0.0368045\pi\) | |||||||
\(98\) | −5.93242 | − | 7.41418i | −0.599265 | − | 0.748945i | ||||
\(99\) | −10.3176 | − | 1.15729i | −1.03696 | − | 0.116312i | ||||
\(100\) | 1.17080 | − | 5.20787i | 0.117080 | − | 0.520787i | ||||
\(101\) | 17.2908i | 1.72050i | 0.509874 | + | 0.860249i | \(0.329692\pi\) | ||||
−0.509874 | + | 0.860249i | \(0.670308\pi\) | |||||||
\(102\) | 12.9212 | + | 16.1486i | 1.27939 | + | 1.59895i | ||||
\(103\) | − | 16.1107i | − | 1.58744i | −0.608285 | − | 0.793718i | \(-0.708142\pi\) | ||
0.608285 | − | 0.793718i | \(-0.291858\pi\) | |||||||
\(104\) | −10.1675 | + | 0.788973i | −0.997003 | + | 0.0773652i | ||||
\(105\) | 3.66494i | 0.357662i | ||||||||
\(106\) | −3.87763 | − | 4.84616i | −0.376629 | − | 0.470701i | ||||
\(107\) | 2.42591 | 0.234522 | 0.117261 | − | 0.993101i | \(-0.462589\pi\) | ||||
0.117261 | + | 0.993101i | \(0.462589\pi\) | |||||||
\(108\) | −0.629934 | − | 0.141618i | −0.0606154 | − | 0.0136272i | ||||
\(109\) | 3.59775 | 0.344602 | 0.172301 | − | 0.985044i | \(-0.444880\pi\) | ||||
0.172301 | + | 0.985044i | \(0.444880\pi\) | |||||||
\(110\) | 10.9834 | − | 6.93403i | 1.04723 | − | 0.661134i | ||||
\(111\) | −3.84344 | −0.364803 | ||||||||
\(112\) | 0.915073 | − | 1.93232i | 0.0864663 | − | 0.182587i | ||||
\(113\) | −16.3185 | −1.53511 | −0.767556 | − | 0.640982i | \(-0.778527\pi\) | ||||
−0.767556 | + | 0.640982i | \(0.778527\pi\) | |||||||
\(114\) | 12.1310 | + | 15.1610i | 1.13618 | + | 1.41996i | ||||
\(115\) | 12.4217 | 1.15833 | ||||||||
\(116\) | 1.32234 | + | 0.297281i | 0.122776 | + | 0.0276018i | ||||
\(117\) | 10.4972 | + | 4.14715i | 0.970471 | + | 0.383405i | ||||
\(118\) | 4.84147 | + | 6.05074i | 0.445693 | + | 0.557015i | ||||
\(119\) | 3.15708 | 0.289409 | ||||||||
\(120\) | 17.4316 | − | 8.49993i | 1.59128 | − | 0.775933i | ||||
\(121\) | 10.7266 | + | 2.43701i | 0.975150 | + | 0.221546i | ||||
\(122\) | 11.3907 | − | 9.11420i | 1.03126 | − | 0.825161i | ||||
\(123\) | − | 6.20620i | − | 0.559594i | ||||||
\(124\) | −4.03815 | + | 17.9622i | −0.362637 | + | 1.61305i | ||||
\(125\) | 6.45540i | 0.577389i | ||||||||
\(126\) | −1.84763 | + | 1.47838i | −0.164600 | + | 0.131704i | ||||
\(127\) | 13.6785 | 1.21377 | 0.606887 | − | 0.794788i | \(-0.292418\pi\) | ||||
0.606887 | + | 0.794788i | \(0.292418\pi\) | |||||||
\(128\) | −11.3130 | + | 0.129179i | −0.999935 | + | 0.0114179i | ||||
\(129\) | − | 21.0221i | − | 1.85089i | ||||||
\(130\) | −13.4959 | + | 4.15377i | −1.18367 | + | 0.364309i | ||||
\(131\) | −5.26829 | −0.460292 | −0.230146 | − | 0.973156i | \(-0.573920\pi\) | ||||
−0.230146 | + | 0.973156i | \(0.573920\pi\) | |||||||
\(132\) | 15.5223 | + | 5.36603i | 1.35105 | + | 0.467053i | ||||
\(133\) | 2.96400 | 0.257012 | ||||||||
\(134\) | −2.54498 | − | 3.18065i | −0.219853 | − | 0.274766i | ||||
\(135\) | −0.894002 | −0.0769435 | ||||||||
\(136\) | −7.32206 | − | 15.0160i | −0.627861 | − | 1.28761i | ||||
\(137\) | 14.4042i | 1.23063i | 0.788281 | + | 0.615315i | \(0.210971\pi\) | ||||
−0.788281 | + | 0.615315i | \(0.789029\pi\) | |||||||
\(138\) | 9.81275 | + | 12.2637i | 0.835316 | + | 1.04396i | ||||
\(139\) | −10.9164 | −0.925915 | −0.462958 | − | 0.886380i | \(-0.653212\pi\) | ||||
−0.462958 | + | 0.886380i | \(0.653212\pi\) | |||||||
\(140\) | 0.649336 | − | 2.88833i | 0.0548789 | − | 0.244108i | ||||
\(141\) | 25.0054i | 2.10583i | ||||||||
\(142\) | 2.73790 | + | 3.42175i | 0.229760 | + | 0.287147i | ||||
\(143\) | −10.5627 | − | 5.60622i | −0.883296 | − | 0.468816i | ||||
\(144\) | 11.3167 | + | 5.35917i | 0.943060 | + | 0.446597i | ||||
\(145\) | 1.87667 | 0.155849 | ||||||||
\(146\) | 8.34345 | + | 10.4274i | 0.690509 | + | 0.862980i | ||||
\(147\) | − | 16.6243i | − | 1.37115i | ||||||
\(148\) | 3.02900 | + | 0.680961i | 0.248982 | + | 0.0559746i | ||||
\(149\) | −17.4380 | −1.42857 | −0.714287 | − | 0.699853i | \(-0.753249\pi\) | ||||
−0.714287 | + | 0.699853i | \(0.753249\pi\) | |||||||
\(150\) | 7.29697 | − | 5.83864i | 0.595795 | − | 0.476723i | ||||
\(151\) | 11.6811i | 0.950595i | 0.879825 | + | 0.475298i | \(0.157660\pi\) | ||||
−0.879825 | + | 0.475298i | \(0.842340\pi\) | |||||||
\(152\) | −6.87427 | − | 14.0977i | −0.557577 | − | 1.14347i | ||||
\(153\) | 18.4896i | 1.49479i | ||||||||
\(154\) | 2.11995 | − | 1.33837i | 0.170831 | − | 0.107849i | ||||
\(155\) | 25.4920i | 2.04756i | ||||||||
\(156\) | −14.7622 | − | 10.0428i | −1.18192 | − | 0.804069i | ||||
\(157\) | −8.98086 | −0.716750 | −0.358375 | − | 0.933578i | \(-0.616669\pi\) | ||||
−0.358375 | + | 0.933578i | \(0.616669\pi\) | |||||||
\(158\) | −7.44514 | − | 9.30473i | −0.592303 | − | 0.740245i | ||||
\(159\) | − | 10.8662i | − | 0.861749i | ||||||
\(160\) | −15.2437 | + | 3.61033i | −1.20512 | + | 0.285422i | ||||
\(161\) | 2.39757 | 0.188955 | ||||||||
\(162\) | 7.59133 | + | 9.48743i | 0.596431 | + | 0.745403i | ||||
\(163\) | 11.2972 | 0.884862 | 0.442431 | − | 0.896803i | \(-0.354116\pi\) | ||||
0.442431 | + | 0.896803i | \(0.354116\pi\) | |||||||
\(164\) | −1.09958 | + | 4.89108i | −0.0858630 | + | 0.381929i | ||||
\(165\) | 22.5992 | + | 2.53487i | 1.75934 | + | 0.197340i | ||||
\(166\) | −3.12743 | + | 2.50240i | −0.242736 | + | 0.194224i | ||||
\(167\) | − | 8.52950i | − | 0.660032i | −0.943975 | − | 0.330016i | \(-0.892946\pi\) | ||
0.943975 | − | 0.330016i | \(-0.107054\pi\) | |||||||
\(168\) | 3.36453 | − | 1.64060i | 0.259579 | − | 0.126575i | ||||
\(169\) | 9.48977 | + | 8.88505i | 0.729983 | + | 0.683466i | ||||
\(170\) | −14.4520 | − | 18.0617i | −1.10842 | − | 1.38527i | ||||
\(171\) | 17.3588i | 1.32746i | ||||||||
\(172\) | −3.72458 | + | 16.5674i | −0.283997 | + | 1.26325i | ||||
\(173\) | 13.0482i | 0.992033i | 0.868313 | + | 0.496017i | \(0.165204\pi\) | ||||
−0.868313 | + | 0.496017i | \(0.834796\pi\) | |||||||
\(174\) | 1.48250 | + | 1.85279i | 0.112388 | + | 0.140460i | ||||
\(175\) | − | 1.42657i | − | 0.107838i | ||||||
\(176\) | −11.2824 | − | 6.97912i | −0.850441 | − | 0.526071i | ||||
\(177\) | 13.5672i | 1.01977i | ||||||||
\(178\) | −7.67689 | + | 6.14263i | −0.575408 | + | 0.460410i | ||||
\(179\) | − | 7.19411i | − | 0.537713i | −0.963180 | − | 0.268857i | \(-0.913354\pi\) | ||
0.963180 | − | 0.268857i | \(-0.0866458\pi\) | |||||||
\(180\) | 16.9156 | + | 3.80287i | 1.26082 | + | 0.283449i | ||||
\(181\) | 6.78219 | 0.504116 | 0.252058 | − | 0.967712i | \(-0.418893\pi\) | ||||
0.252058 | + | 0.967712i | \(0.418893\pi\) | |||||||
\(182\) | −2.60489 | + | 0.801735i | −0.193087 | + | 0.0594286i | ||||
\(183\) | 25.5406 | 1.88802 | ||||||||
\(184\) | −5.56057 | − | 11.4036i | −0.409931 | − | 0.840682i | ||||
\(185\) | 4.29876 | 0.316051 | ||||||||
\(186\) | −25.1676 | + | 20.1378i | −1.84538 | + | 1.47657i | ||||
\(187\) | 2.18361 | − | 19.4675i | 0.159681 | − | 1.42361i | ||||
\(188\) | 4.43033 | − | 19.7067i | 0.323115 | − | 1.43726i | ||||
\(189\) | −0.172555 | −0.0125515 | ||||||||
\(190\) | −13.5682 | − | 16.9571i | −0.984338 | − | 1.23020i | ||||
\(191\) | − | 2.12348i | − | 0.153650i | −0.997045 | − | 0.0768248i | \(-0.975522\pi\) | ||
0.997045 | − | 0.0768248i | \(-0.0244782\pi\) | |||||||
\(192\) | −15.6064 | − | 12.1977i | −1.12629 | − | 0.880296i | ||||
\(193\) | 13.1530 | 0.946770 | 0.473385 | − | 0.880856i | \(-0.343032\pi\) | ||||
0.473385 | + | 0.880856i | \(0.343032\pi\) | |||||||
\(194\) | −2.50935 | + | 2.00784i | −0.180161 | + | 0.144155i | ||||
\(195\) | −22.9926 | − | 9.08372i | −1.64654 | − | 0.650499i | ||||
\(196\) | −2.94542 | + | 13.1016i | −0.210387 | + | 0.935828i | ||||
\(197\) | 2.47118 | 0.176064 | 0.0880321 | − | 0.996118i | \(-0.471942\pi\) | ||||
0.0880321 | + | 0.996118i | \(0.471942\pi\) | |||||||
\(198\) | 7.83820 | + | 12.4156i | 0.557037 | + | 0.882339i | ||||
\(199\) | 17.6493i | 1.25113i | 0.780174 | + | 0.625563i | \(0.215131\pi\) | ||||
−0.780174 | + | 0.625563i | \(0.784869\pi\) | |||||||
\(200\) | −6.78518 | + | 3.30857i | −0.479785 | + | 0.233951i | ||||
\(201\) | − | 7.13177i | − | 0.503036i | ||||||
\(202\) | 19.0931 | − | 15.2773i | 1.34339 | − | 1.07491i | ||||
\(203\) | 0.362224 | 0.0254231 | ||||||||
\(204\) | 6.41534 | − | 28.5362i | 0.449163 | − | 1.99794i | ||||
\(205\) | 6.94143i | 0.484810i | ||||||||
\(206\) | −17.7901 | + | 14.2346i | −1.23949 | + | 0.991774i | ||||
\(207\) | 14.0415i | 0.975951i | ||||||||
\(208\) | 9.85469 | + | 10.5302i | 0.683300 | + | 0.730138i | ||||
\(209\) | 2.05007 | − | 18.2770i | 0.141806 | − | 1.26424i | ||||
\(210\) | 4.04696 | − | 3.23816i | 0.279267 | − | 0.223454i | ||||
\(211\) | −25.0448 | −1.72416 | −0.862078 | − | 0.506775i | \(-0.830837\pi\) | ||||
−0.862078 | + | 0.506775i | \(0.830837\pi\) | |||||||
\(212\) | −1.92523 | + | 8.56365i | −0.132225 | + | 0.588154i | ||||
\(213\) | 7.67239i | 0.525703i | ||||||||
\(214\) | −2.14342 | − | 2.67878i | −0.146521 | − | 0.183118i | ||||
\(215\) | 23.5125i | 1.60354i | ||||||||
\(216\) | 0.400199 | + | 0.820723i | 0.0272301 | + | 0.0558431i | ||||
\(217\) | 4.92031i | 0.334012i | ||||||||
\(218\) | −3.17879 | − | 3.97276i | −0.215295 | − | 0.269070i | ||||
\(219\) | 23.3808i | 1.57993i | ||||||||
\(220\) | −17.3612 | − | 6.00173i | −1.17049 | − | 0.404637i | ||||
\(221\) | −7.82495 | + | 19.8065i | −0.526363 | + | 1.33233i | ||||
\(222\) | 3.39587 | + | 4.24406i | 0.227916 | + | 0.284843i | ||||
\(223\) | 1.33070 | 0.0891100 | 0.0445550 | − | 0.999007i | \(-0.485813\pi\) | ||||
0.0445550 | + | 0.999007i | \(0.485813\pi\) | |||||||
\(224\) | −2.94225 | + | 0.696844i | −0.196587 | + | 0.0465598i | ||||
\(225\) | 8.35476 | 0.556984 | ||||||||
\(226\) | 14.4182 | + | 18.0195i | 0.959083 | + | 1.19864i | ||||
\(227\) | 18.9517i | 1.25787i | 0.777458 | + | 0.628935i | \(0.216509\pi\) | ||||
−0.777458 | + | 0.628935i | \(0.783491\pi\) | |||||||
\(228\) | 6.02300 | − | 26.7911i | 0.398883 | − | 1.77428i | ||||
\(229\) | − | 11.3147i | − | 0.747697i | −0.927490 | − | 0.373848i | \(-0.878038\pi\) | ||
0.927490 | − | 0.373848i | \(-0.121962\pi\) | |||||||
\(230\) | −10.9752 | − | 13.7166i | −0.723686 | − | 0.904443i | ||||
\(231\) | 4.36196 | + | 0.489266i | 0.286996 | + | 0.0321913i | ||||
\(232\) | −0.840088 | − | 1.72284i | −0.0551545 | − | 0.113110i | ||||
\(233\) | − | 27.0748i | − | 1.77373i | −0.462028 | − | 0.886865i | \(-0.652878\pi\) | ||
0.462028 | − | 0.886865i | \(-0.347122\pi\) | |||||||
\(234\) | −4.69540 | − | 15.2557i | −0.306948 | − | 0.997294i | ||||
\(235\) | − | 27.9677i | − | 1.82441i | ||||||
\(236\) | 2.40377 | − | 10.6923i | 0.156472 | − | 0.696007i | ||||
\(237\) | − | 20.8634i | − | 1.35522i | ||||||
\(238\) | −2.78944 | − | 3.48616i | −0.180812 | − | 0.225974i | ||||
\(239\) | − | 14.6552i | − | 0.947969i | −0.880533 | − | 0.473984i | \(-0.842815\pi\) | ||
0.880533 | − | 0.473984i | \(-0.157185\pi\) | |||||||
\(240\) | −24.7876 | − | 11.7385i | −1.60003 | − | 0.757714i | ||||
\(241\) | −7.37547 | −0.475096 | −0.237548 | − | 0.971376i | \(-0.576344\pi\) | ||||
−0.237548 | + | 0.971376i | \(0.576344\pi\) | |||||||
\(242\) | −6.78650 | − | 13.9980i | −0.436253 | − | 0.899824i | ||||
\(243\) | 22.2416i | 1.42680i | ||||||||
\(244\) | −20.1285 | − | 4.52516i | −1.28859 | − | 0.289694i | ||||
\(245\) | 18.5938i | 1.18791i | ||||||||
\(246\) | −6.85311 | + | 5.48349i | −0.436938 | + | 0.349614i | ||||
\(247\) | −7.34641 | + | 18.5952i | −0.467441 | + | 1.18318i | ||||
\(248\) | 23.4024 | − | 11.4114i | 1.48606 | − | 0.724627i | ||||
\(249\) | −7.01244 | −0.444395 | ||||||||
\(250\) | 7.12830 | − | 5.70367i | 0.450833 | − | 0.360732i | ||||
\(251\) | 2.77747i | 0.175312i | 0.996151 | + | 0.0876562i | \(0.0279377\pi\) | ||||
−0.996151 | + | 0.0876562i | \(0.972062\pi\) | |||||||
\(252\) | 3.26496 | + | 0.734007i | 0.205673 | + | 0.0462381i | ||||
\(253\) | 1.65829 | − | 14.7842i | 0.104256 | − | 0.929473i | ||||
\(254\) | −12.0857 | − | 15.1043i | −0.758322 | − | 0.947730i | ||||
\(255\) | − | 40.4986i | − | 2.53612i | ||||||
\(256\) | 10.1382 | + | 12.3781i | 0.633639 | + | 0.773629i | ||||
\(257\) | 15.1479 | 0.944903 | 0.472452 | − | 0.881357i | \(-0.343369\pi\) | ||||
0.472452 | + | 0.881357i | \(0.343369\pi\) | |||||||
\(258\) | −23.2133 | + | 18.5740i | −1.44520 | + | 1.15637i | ||||
\(259\) | 0.829720 | 0.0515563 | ||||||||
\(260\) | 16.5110 | + | 11.2326i | 1.02397 | + | 0.696614i | ||||
\(261\) | 2.12138i | 0.131310i | ||||||||
\(262\) | 4.65479 | + | 5.81744i | 0.287574 | + | 0.359402i | ||||
\(263\) | 3.46372 | 0.213582 | 0.106791 | − | 0.994281i | \(-0.465942\pi\) | ||||
0.106791 | + | 0.994281i | \(0.465942\pi\) | |||||||
\(264\) | −7.78938 | − | 21.8815i | −0.479403 | − | 1.34671i | ||||
\(265\) | 12.1535i | 0.746586i | ||||||||
\(266\) | −2.61885 | − | 3.27296i | −0.160572 | − | 0.200678i | ||||
\(267\) | −17.2134 | −1.05344 | ||||||||
\(268\) | −1.26357 | + | 5.62052i | −0.0771849 | + | 0.343328i | ||||
\(269\) | 20.6283 | 1.25773 | 0.628863 | − | 0.777516i | \(-0.283520\pi\) | ||||
0.628863 | + | 0.777516i | \(0.283520\pi\) | |||||||
\(270\) | 0.789896 | + | 0.987191i | 0.0480715 | + | 0.0600785i | ||||
\(271\) | − | 14.0761i | − | 0.855065i | −0.904000 | − | 0.427532i | \(-0.859383\pi\) | ||
0.904000 | − | 0.427532i | \(-0.140617\pi\) | |||||||
\(272\) | −10.1118 | + | 21.3527i | −0.613119 | + | 1.29470i | ||||
\(273\) | −4.43790 | − | 1.75328i | −0.268594 | − | 0.106114i | ||||
\(274\) | 15.9056 | − | 12.7268i | 0.960892 | − | 0.768854i | ||||
\(275\) | −8.79666 | − | 0.986692i | −0.530459 | − | 0.0594998i | ||||
\(276\) | 4.87198 | − | 21.6712i | 0.293259 | − | 1.30445i | ||||
\(277\) | 26.1430i | 1.57078i | 0.619000 | + | 0.785391i | \(0.287538\pi\) | ||||
−0.619000 | + | 0.785391i | \(0.712462\pi\) | |||||||
\(278\) | 9.64517 | + | 12.0543i | 0.578479 | + | 0.722967i | ||||
\(279\) | −28.8160 | −1.72517 | ||||||||
\(280\) | −3.76312 | + | 1.83496i | −0.224889 | + | 0.109660i | ||||
\(281\) | 22.8496 | 1.36309 | 0.681545 | − | 0.731776i | \(-0.261308\pi\) | ||||
0.681545 | + | 0.731776i | \(0.261308\pi\) | |||||||
\(282\) | 27.6119 | − | 22.0935i | 1.64426 | − | 1.31565i | ||||
\(283\) | 13.1440 | 0.781331 | 0.390666 | − | 0.920533i | \(-0.372245\pi\) | ||||
0.390666 | + | 0.920533i | \(0.372245\pi\) | |||||||
\(284\) | 1.35936 | − | 6.04658i | 0.0806629 | − | 0.358799i | ||||
\(285\) | − | 38.0219i | − | 2.25222i | ||||||
\(286\) | 3.14206 | + | 16.6171i | 0.185794 | + | 0.982589i | ||||
\(287\) | 1.33979i | 0.0790855i | ||||||||
\(288\) | −4.08110 | − | 17.2314i | −0.240481 | − | 1.01537i | ||||
\(289\) | −17.8866 | −1.05215 | ||||||||
\(290\) | −1.65813 | − | 2.07229i | −0.0973689 | − | 0.121689i | ||||
\(291\) | −5.62655 | −0.329834 | ||||||||
\(292\) | 4.14249 | − | 18.4263i | 0.242421 | − | 1.07832i | ||||
\(293\) | −11.1419 | −0.650917 | −0.325459 | − | 0.945556i | \(-0.605519\pi\) | ||||
−0.325459 | + | 0.945556i | \(0.605519\pi\) | |||||||
\(294\) | −18.3572 | + | 14.6884i | −1.07061 | + | 0.856647i | ||||
\(295\) | − | 15.1745i | − | 0.883491i | ||||||
\(296\) | −1.92433 | − | 3.94640i | −0.111849 | − | 0.229380i | ||||
\(297\) | −0.119348 | + | 1.06403i | −0.00692530 | + | 0.0617411i | ||||
\(298\) | 15.4073 | + | 19.2556i | 0.892521 | + | 1.11545i | ||||
\(299\) | −5.94248 | + | 15.0416i | −0.343663 | + | 0.869876i | ||||
\(300\) | −12.8945 | − | 2.89886i | −0.744463 | − | 0.167366i | ||||
\(301\) | 4.53824i | 0.261580i | ||||||||
\(302\) | 12.8987 | − | 10.3208i | 0.742238 | − | 0.593898i | ||||
\(303\) | 42.8113 | 2.45945 | ||||||||
\(304\) | −9.49342 | + | 20.0468i | −0.544485 | + | 1.14976i | ||||
\(305\) | −28.5663 | −1.63570 | ||||||||
\(306\) | 20.4169 | − | 16.3365i | 1.16716 | − | 0.933894i | ||||
\(307\) | 28.8175i | 1.64470i | 0.568980 | + | 0.822351i | \(0.307338\pi\) | ||||
−0.568980 | + | 0.822351i | \(0.692662\pi\) | |||||||
\(308\) | −3.35096 | − | 1.15842i | −0.190939 | − | 0.0660070i | ||||
\(309\) | −39.8895 | −2.26924 | ||||||||
\(310\) | 28.1492 | − | 22.5234i | 1.59877 | − | 1.27924i | ||||
\(311\) | − | 14.7627i | − | 0.837114i | −0.908190 | − | 0.418557i | \(-0.862536\pi\) | ||
0.908190 | − | 0.418557i | \(-0.137464\pi\) | |||||||
\(312\) | 1.95347 | + | 25.1743i | 0.110593 | + | 1.42521i | ||||
\(313\) | −12.4148 | −0.701726 | −0.350863 | − | 0.936427i | \(-0.614112\pi\) | ||||
−0.350863 | + | 0.936427i | \(0.614112\pi\) | |||||||
\(314\) | 7.93504 | + | 9.91699i | 0.447800 | + | 0.559648i | ||||
\(315\) | 4.63363 | 0.261075 | ||||||||
\(316\) | −3.69648 | + | 16.4424i | −0.207943 | + | 0.924957i | ||||
\(317\) | 8.15212i | 0.457869i | 0.973442 | + | 0.228934i | \(0.0735241\pi\) | ||||
−0.973442 | + | 0.228934i | \(0.926476\pi\) | |||||||
\(318\) | −11.9989 | + | 9.60087i | −0.672865 | + | 0.538390i | ||||
\(319\) | 0.250534 | − | 2.23358i | 0.0140272 | − | 0.125057i | ||||
\(320\) | 17.4553 | + | 13.6428i | 0.975778 | + | 0.762654i | ||||
\(321\) | − | 6.00647i | − | 0.335248i | ||||||
\(322\) | −2.11837 | − | 2.64749i | −0.118052 | − | 0.147539i | ||||
\(323\) | −32.7531 | −1.82243 | ||||||||
\(324\) | 3.76906 | − | 16.7652i | 0.209392 | − | 0.931402i | ||||
\(325\) | 8.94981 | + | 3.53581i | 0.496446 | + | 0.196131i | ||||
\(326\) | −9.98161 | − | 12.4747i | −0.552830 | − | 0.690912i | ||||
\(327\) | − | 8.90788i | − | 0.492607i | ||||||
\(328\) | 6.37245 | − | 3.10732i | 0.351860 | − | 0.171573i | ||||
\(329\) | − | 5.39816i | − | 0.297610i | ||||||
\(330\) | −17.1684 | − | 27.1945i | −0.945089 | − | 1.49701i | ||||
\(331\) | 10.6108 | 0.583223 | 0.291611 | − | 0.956537i | \(-0.405809\pi\) | ||||
0.291611 | + | 0.956537i | \(0.405809\pi\) | |||||||
\(332\) | 5.52648 | + | 1.24243i | 0.303305 | + | 0.0681871i | ||||
\(333\) | 4.85930i | 0.266288i | ||||||||
\(334\) | −9.41859 | + | 7.53624i | −0.515362 | + | 0.412365i | ||||
\(335\) | 7.97665i | 0.435811i | ||||||||
\(336\) | −4.78435 | − | 2.26569i | −0.261008 | − | 0.123603i | ||||
\(337\) | − | 9.58696i | − | 0.522235i | −0.965307 | − | 0.261117i | \(-0.915909\pi\) | ||
0.965307 | − | 0.261117i | \(-0.0840910\pi\) | |||||||
\(338\) | 1.42651 | − | 18.3293i | 0.0775921 | − | 0.996985i | ||||
\(339\) | 40.4039i | 2.19444i | ||||||||
\(340\) | −7.17534 | + | 31.9168i | −0.389138 | + | 1.73093i | ||||
\(341\) | 30.3401 | + | 3.40315i | 1.64301 | + | 0.184291i | ||||
\(342\) | 19.1683 | − | 15.3374i | 1.03650 | − | 0.829352i | ||||
\(343\) | 7.33043i | 0.395806i | ||||||||
\(344\) | 21.5852 | − | 10.5253i | 1.16380 | − | 0.567487i | ||||
\(345\) | − | 30.7558i | − | 1.65584i | ||||||
\(346\) | 14.4083 | − | 11.5287i | 0.774593 | − | 0.619787i | ||||
\(347\) | −15.7991 | −0.848142 | −0.424071 | − | 0.905629i | \(-0.639399\pi\) | ||||
−0.424071 | + | 0.905629i | \(0.639399\pi\) | |||||||
\(348\) | 0.736056 | − | 3.27407i | 0.0394568 | − | 0.175509i | ||||
\(349\) | −18.7254 | −1.00235 | −0.501174 | − | 0.865346i | \(-0.667098\pi\) | ||||
−0.501174 | + | 0.865346i | \(0.667098\pi\) | |||||||
\(350\) | −1.57527 | + | 1.26044i | −0.0842017 | + | 0.0673736i | ||||
\(351\) | 0.427685 | − | 1.08255i | 0.0228281 | − | 0.0577824i | ||||
\(352\) | 2.26193 | + | 18.6248i | 0.120562 | + | 0.992706i | ||||
\(353\) | 4.16295i | 0.221571i | 0.993844 | + | 0.110786i | \(0.0353367\pi\) | ||||
−0.993844 | + | 0.110786i | \(0.964663\pi\) | |||||||
\(354\) | 14.9814 | − | 11.9873i | 0.796252 | − | 0.637117i | ||||
\(355\) | − | 8.58132i | − | 0.455449i | ||||||
\(356\) | 13.5658 | + | 3.04979i | 0.718988 | + | 0.161638i | ||||
\(357\) | − | 7.81680i | − | 0.413709i | ||||||
\(358\) | −7.94401 | + | 6.35636i | −0.419854 | + | 0.335944i | ||||
\(359\) | − | 9.90104i | − | 0.522557i | −0.965264 | − | 0.261278i | \(-0.915856\pi\) | ||
0.965264 | − | 0.261278i | \(-0.0841440\pi\) | |||||||
\(360\) | −10.7465 | − | 22.0389i | −0.566393 | − | 1.16155i | ||||
\(361\) | −11.7500 | −0.618423 | ||||||||
\(362\) | −5.99240 | − | 7.48914i | −0.314954 | − | 0.393621i | ||||
\(363\) | 6.03393 | − | 26.5588i | 0.316699 | − | 1.39397i | ||||
\(364\) | 3.18686 | + | 2.16804i | 0.167037 | + | 0.113636i | ||||
\(365\) | − | 26.1506i | − | 1.36879i | ||||||
\(366\) | −22.5664 | − | 28.2029i | −1.17957 | − | 1.47419i | ||||
\(367\) | − | 4.13130i | − | 0.215652i | −0.994170 | − | 0.107826i | \(-0.965611\pi\) | ||
0.994170 | − | 0.107826i | \(-0.0343890\pi\) | |||||||
\(368\) | −7.67919 | + | 16.2158i | −0.400305 | + | 0.845307i | ||||
\(369\) | −7.84656 | −0.408476 | ||||||||
\(370\) | −3.79817 | − | 4.74685i | −0.197457 | − | 0.246777i | ||||
\(371\) | 2.34580i | 0.121788i | ||||||||
\(372\) | 44.4737 | + | 9.99830i | 2.30585 | + | 0.518388i | ||||
\(373\) | 34.4449i | 1.78349i | 0.452538 | + | 0.891745i | \(0.350519\pi\) | ||||
−0.452538 | + | 0.891745i | \(0.649481\pi\) | |||||||
\(374\) | −23.4261 | + | 14.7893i | −1.21133 | + | 0.764737i | ||||
\(375\) | 15.9833 | 0.825376 | ||||||||
\(376\) | −25.6752 | + | 12.5197i | −1.32410 | + | 0.645654i | ||||
\(377\) | −0.897787 | + | 2.27247i | −0.0462384 | + | 0.117038i | ||||
\(378\) | 0.152461 | + | 0.190542i | 0.00784175 | + | 0.00980040i | ||||
\(379\) | −29.3313 | −1.50665 | −0.753323 | − | 0.657651i | \(-0.771550\pi\) | ||||
−0.753323 | + | 0.657651i | \(0.771550\pi\) | |||||||
\(380\) | −6.73653 | + | 29.9649i | −0.345577 | + | 1.53717i | ||||
\(381\) | − | 33.8675i | − | 1.73509i | ||||||
\(382\) | −2.34482 | + | 1.87620i | −0.119972 | + | 0.0959948i | ||||
\(383\) | −23.6902 | −1.21051 | −0.605255 | − | 0.796032i | \(-0.706929\pi\) | ||||
−0.605255 | + | 0.796032i | \(0.706929\pi\) | |||||||
\(384\) | 0.319842 | + | 28.0105i | 0.0163218 | + | 1.42940i | ||||
\(385\) | −4.87871 | − | 0.547228i | −0.248642 | − | 0.0278893i | ||||
\(386\) | −11.6213 | − | 14.5240i | −0.591508 | − | 0.739251i | ||||
\(387\) | −26.5784 | −1.35106 | ||||||||
\(388\) | 4.43427 | + | 0.996884i | 0.225116 | + | 0.0506091i | ||||
\(389\) | −18.0886 | −0.917130 | −0.458565 | − | 0.888661i | \(-0.651636\pi\) | ||||
−0.458565 | + | 0.888661i | \(0.651636\pi\) | |||||||
\(390\) | 10.2846 | + | 33.4152i | 0.520779 | + | 1.69205i | ||||
\(391\) | −26.4938 | −1.33985 | ||||||||
\(392\) | 17.0697 | − | 8.32347i | 0.862149 | − | 0.420399i | ||||
\(393\) | 13.0441i | 0.657986i | ||||||||
\(394\) | −2.18341 | − | 2.72877i | −0.109999 | − | 0.137473i | ||||
\(395\) | 23.3351i | 1.17411i | ||||||||
\(396\) | 6.78433 | − | 19.6250i | 0.340926 | − | 0.986196i | ||||
\(397\) | − | 27.1183i | − | 1.36103i | −0.732735 | − | 0.680514i | \(-0.761757\pi\) | ||
0.732735 | − | 0.680514i | \(-0.238243\pi\) | |||||||
\(398\) | 19.4890 | − | 15.5940i | 0.976896 | − | 0.781659i | ||||
\(399\) | − | 7.33876i | − | 0.367398i | ||||||
\(400\) | 9.64849 | + | 4.56916i | 0.482425 | + | 0.228458i | ||||
\(401\) | 30.7606i | 1.53611i | 0.640383 | + | 0.768056i | \(0.278776\pi\) | ||||
−0.640383 | + | 0.768056i | \(0.721224\pi\) | |||||||
\(402\) | −7.87516 | + | 6.30128i | −0.392777 | + | 0.314279i | ||||
\(403\) | −30.8684 | − | 12.1952i | −1.53766 | − | 0.607486i | ||||
\(404\) | −33.7395 | − | 7.58510i | −1.67860 | − | 0.377373i | ||||
\(405\) | − | 23.7932i | − | 1.18230i | ||||||
\(406\) | −0.320043 | − | 0.399981i | −0.0158835 | − | 0.0198507i | ||||
\(407\) | 0.573880 | − | 5.11631i | 0.0284462 | − | 0.253606i | ||||
\(408\) | −37.1790 | + | 18.1291i | −1.84064 | + | 0.897526i | ||||
\(409\) | 30.4703 | 1.50666 | 0.753331 | − | 0.657642i | \(-0.228446\pi\) | ||||
0.753331 | + | 0.657642i | \(0.228446\pi\) | |||||||
\(410\) | 7.66498 | − | 6.13310i | 0.378546 | − | 0.302892i | ||||
\(411\) | 35.6641 | 1.75918 | ||||||||
\(412\) | 31.4368 | + | 7.06743i | 1.54878 | + | 0.348187i | ||||
\(413\) | − | 2.92888i | − | 0.144121i | ||||||
\(414\) | 15.5051 | − | 12.4064i | 0.762036 | − | 0.609739i | ||||
\(415\) | 7.84318 | 0.385007 | ||||||||
\(416\) | 2.92073 | − | 20.1859i | 0.143201 | − | 0.989694i | ||||
\(417\) | 27.0285i | 1.32359i | ||||||||
\(418\) | −21.9934 | + | 13.8849i | −1.07573 | + | 0.679131i | ||||
\(419\) | 3.97053i | 0.193973i | 0.995286 | + | 0.0969866i | \(0.0309204\pi\) | ||||
−0.995286 | + | 0.0969866i | \(0.969080\pi\) | |||||||
\(420\) | −7.15139 | − | 1.60773i | −0.348952 | − | 0.0784493i | ||||
\(421\) | 20.6838i | 1.00807i | 0.863684 | + | 0.504033i | \(0.168151\pi\) | ||||
−0.863684 | + | 0.504033i | \(0.831849\pi\) | |||||||
\(422\) | 22.1284 | + | 27.6554i | 1.07719 | + | 1.34624i | ||||
\(423\) | 31.6146 | 1.53715 | ||||||||
\(424\) | 11.1573 | − | 5.44051i | 0.541848 | − | 0.264214i | ||||
\(425\) | 15.7640i | 0.764665i | ||||||||
\(426\) | 8.47213 | − | 6.77894i | 0.410476 | − | 0.328441i | ||||
\(427\) | −5.51370 | −0.266827 | ||||||||
\(428\) | −1.06420 | + | 4.73368i | −0.0514399 | + | 0.228811i | ||||
\(429\) | −13.8808 | + | 26.1528i | −0.670171 | + | 1.26267i | ||||
\(430\) | 25.9634 | − | 20.7745i | 1.25206 | − | 1.00183i | ||||
\(431\) | − | 28.8707i | − | 1.39065i | −0.718693 | − | 0.695327i | \(-0.755260\pi\) | ||
0.718693 | − | 0.695327i | \(-0.244740\pi\) | |||||||
\(432\) | 0.552677 | − | 1.16706i | 0.0265907 | − | 0.0561504i | ||||
\(433\) | 0.958185 | 0.0460474 | 0.0230237 | − | 0.999735i | \(-0.492671\pi\) | ||||
0.0230237 | + | 0.999735i | \(0.492671\pi\) | |||||||
\(434\) | 5.43318 | − | 4.34734i | 0.260801 | − | 0.208679i | ||||
\(435\) | − | 4.64656i | − | 0.222786i | ||||||
\(436\) | −1.57825 | + | 7.02027i | −0.0755846 | + | 0.336210i | ||||
\(437\) | −24.8736 | −1.18986 | ||||||||
\(438\) | 25.8179 | − | 20.6581i | 1.23363 | − | 0.987081i | ||||
\(439\) | −1.22798 | −0.0586083 | −0.0293042 | − | 0.999571i | \(-0.509329\pi\) | ||||
−0.0293042 | + | 0.999571i | \(0.509329\pi\) | |||||||
\(440\) | 8.71217 | + | 24.4737i | 0.415336 | + | 1.16674i | ||||
\(441\) | −21.0183 | −1.00087 | ||||||||
\(442\) | 28.7848 | − | 8.85939i | 1.36915 | − | 0.421398i | ||||
\(443\) | 31.4487i | 1.49417i | 0.664727 | + | 0.747086i | \(0.268548\pi\) | ||||
−0.664727 | + | 0.747086i | \(0.731452\pi\) | |||||||
\(444\) | 1.68603 | − | 7.49969i | 0.0800156 | − | 0.355919i | ||||
\(445\) | 19.2526 | 0.912663 | ||||||||
\(446\) | −1.17574 | − | 1.46940i | −0.0556727 | − | 0.0695783i | ||||
\(447\) | 43.1757i | 2.04214i | ||||||||
\(448\) | 3.36911 | + | 2.63325i | 0.159175 | + | 0.124409i | ||||
\(449\) | 4.36055i | 0.205787i | 0.994692 | + | 0.102894i | \(0.0328101\pi\) | ||||
−0.994692 | + | 0.102894i | \(0.967190\pi\) | |||||||
\(450\) | −7.38185 | − | 9.22564i | −0.347984 | − | 0.434901i | ||||
\(451\) | 8.26158 | + | 0.926674i | 0.389023 | + | 0.0436354i | ||||
\(452\) | 7.15856 | − | 31.8422i | 0.336710 | − | 1.49773i | ||||
\(453\) | 28.9220 | 1.35887 | ||||||||
\(454\) | 20.9272 | − | 16.7448i | 0.982161 | − | 0.785872i | ||||
\(455\) | 4.96365 | + | 1.96099i | 0.232699 | + | 0.0919327i | ||||
\(456\) | −34.9053 | + | 17.0204i | −1.63459 | + | 0.797055i | ||||
\(457\) | 30.1840 | 1.41195 | 0.705974 | − | 0.708237i | \(-0.250509\pi\) | ||||
0.705974 | + | 0.708237i | \(0.250509\pi\) | |||||||
\(458\) | −12.4941 | + | 9.99711i | −0.583812 | + | 0.467134i | ||||
\(459\) | 1.90678 | 0.0890009 | ||||||||
\(460\) | −5.44915 | + | 24.2385i | −0.254068 | + | 1.13013i | ||||
\(461\) | 32.5822 | 1.51751 | 0.758753 | − | 0.651378i | \(-0.225809\pi\) | ||||
0.758753 | + | 0.651378i | \(0.225809\pi\) | |||||||
\(462\) | −3.31374 | − | 5.24892i | −0.154169 | − | 0.244202i | ||||
\(463\) | 4.03113 | 0.187343 | 0.0936713 | − | 0.995603i | \(-0.470140\pi\) | ||||
0.0936713 | + | 0.995603i | \(0.470140\pi\) | |||||||
\(464\) | −1.16017 | + | 2.44987i | −0.0538594 | + | 0.113733i | ||||
\(465\) | 63.1171 | 2.92699 | ||||||||
\(466\) | −29.8970 | + | 23.9220i | −1.38495 | + | 1.10816i | ||||
\(467\) | 3.41015i | 0.157803i | 0.996882 | + | 0.0789014i | \(0.0251412\pi\) | ||||
−0.996882 | + | 0.0789014i | \(0.974859\pi\) | |||||||
\(468\) | −12.6972 | + | 18.6640i | −0.586930 | + | 0.862743i | ||||
\(469\) | 1.53961i | 0.0710924i | ||||||||
\(470\) | −30.8830 | + | 24.7109i | −1.42453 | + | 1.13983i | ||||
\(471\) | 22.2363i | 1.02459i | ||||||||
\(472\) | −13.9306 | + | 6.79282i | −0.641209 | + | 0.312665i | ||||
\(473\) | 27.9842 | + | 3.13889i | 1.28671 | + | 0.144326i | ||||
\(474\) | −23.0382 | + | 18.4339i | −1.05818 | + | 0.846696i | ||||
\(475\) | 14.7999i | 0.679067i | ||||||||
\(476\) | −1.38494 | + | 6.16040i | −0.0634787 | + | 0.282361i | ||||
\(477\) | −13.7383 | −0.629034 | ||||||||
\(478\) | −16.1829 | + | 12.9486i | −0.740187 | + | 0.592257i | ||||
\(479\) | − | 7.23882i | − | 0.330750i | −0.986231 | − | 0.165375i | \(-0.947117\pi\) | ||
0.986231 | − | 0.165375i | \(-0.0528834\pi\) | |||||||
\(480\) | 8.93904 | + | 37.7429i | 0.408009 | + | 1.72272i | ||||
\(481\) | −2.05650 | + | 5.20539i | −0.0937682 | + | 0.237345i | ||||
\(482\) | 6.51660 | + | 8.14427i | 0.296823 | + | 0.370961i | ||||
\(483\) | − | 5.93629i | − | 0.270111i | ||||||
\(484\) | −9.46087 | + | 19.8618i | −0.430040 | + | 0.902810i | ||||
\(485\) | 6.29311 | 0.285756 | ||||||||
\(486\) | 24.5600 | − | 19.6515i | 1.11406 | − | 0.891412i | ||||
\(487\) | 22.4374 | 1.01674 | 0.508368 | − | 0.861140i | \(-0.330249\pi\) | ||||
0.508368 | + | 0.861140i | \(0.330249\pi\) | |||||||
\(488\) | 12.7877 | + | 26.2248i | 0.578871 | + | 1.18714i | ||||
\(489\) | − | 27.9713i | − | 1.26491i | ||||||
\(490\) | 20.5319 | − | 16.4285i | 0.927539 | − | 0.742166i | ||||
\(491\) | 21.1277 | 0.953480 | 0.476740 | − | 0.879044i | \(-0.341818\pi\) | ||||
0.476740 | + | 0.879044i | \(0.341818\pi\) | |||||||
\(492\) | 12.1101 | + | 2.72252i | 0.545967 | + | 0.122741i | ||||
\(493\) | −4.00267 | −0.180271 | ||||||||
\(494\) | 27.0244 | − | 8.31759i | 1.21589 | − | 0.374226i | ||||
\(495\) | 3.20487 | − | 28.5724i | 0.144048 | − | 1.28423i | ||||
\(496\) | −33.2781 | − | 15.7593i | −1.49423 | − | 0.707612i | ||||
\(497\) | − | 1.65631i | − | 0.0742958i | ||||||
\(498\) | 6.19584 | + | 7.74339i | 0.277642 | + | 0.346990i | ||||
\(499\) | 8.39062 | 0.375616 | 0.187808 | − | 0.982206i | \(-0.439862\pi\) | ||||
0.187808 | + | 0.982206i | \(0.439862\pi\) | |||||||
\(500\) | −12.5964 | − | 2.83185i | −0.563329 | − | 0.126644i | ||||
\(501\) | −21.1187 | −0.943514 | ||||||||
\(502\) | 3.06699 | − | 2.45403i | 0.136886 | − | 0.109529i | ||||
\(503\) | −20.0923 | −0.895870 | −0.447935 | − | 0.894066i | \(-0.647840\pi\) | ||||
−0.447935 | + | 0.894066i | \(0.647840\pi\) | |||||||
\(504\) | −2.07423 | − | 4.25382i | −0.0923937 | − | 0.189480i | ||||
\(505\) | −47.8831 | −2.13077 | ||||||||
\(506\) | −17.7904 | + | 11.2314i | −0.790880 | + | 0.499297i | ||||
\(507\) | 21.9990 | − | 23.4963i | 0.977012 | − | 1.04351i | ||||
\(508\) | −6.00048 | + | 26.6909i | −0.266228 | + | 1.18422i | ||||
\(509\) | − | 19.2550i | − | 0.853463i | −0.904378 | − | 0.426732i | \(-0.859665\pi\) | ||
0.904378 | − | 0.426732i | \(-0.140335\pi\) | |||||||
\(510\) | −44.7201 | + | 35.7826i | −1.98024 | + | 1.58448i | ||||
\(511\) | − | 5.04743i | − | 0.223285i | ||||||
\(512\) | 4.71069 | − | 22.1316i | 0.208185 | − | 0.978089i | ||||
\(513\) | 1.79017 | 0.0790379 | ||||||||
\(514\) | −13.3840 | − | 16.7269i | −0.590342 | − | 0.737793i | ||||
\(515\) | 44.6151 | 1.96598 | ||||||||
\(516\) | 41.0203 | + | 9.22193i | 1.80582 | + | 0.405973i | ||||
\(517\) | −33.2867 | − | 3.73366i | −1.46395 | − | 0.164206i | ||||
\(518\) | −0.733100 | − | 0.916208i | −0.0322105 | − | 0.0402559i | ||||
\(519\) | 32.3067 | 1.41811 | ||||||||
\(520\) | −2.18489 | − | 28.1566i | −0.0958137 | − | 1.23475i | ||||
\(521\) | 37.4309 | 1.63988 | 0.819939 | − | 0.572451i | \(-0.194007\pi\) | ||||
0.819939 | + | 0.572451i | \(0.194007\pi\) | |||||||
\(522\) | 2.34251 | − | 1.87435i | 0.102529 | − | 0.0820379i | ||||
\(523\) | −7.29447 | −0.318965 | −0.159482 | − | 0.987201i | \(-0.550983\pi\) | ||||
−0.159482 | + | 0.987201i | \(0.550983\pi\) | |||||||
\(524\) | 2.31108 | − | 10.2800i | 0.100960 | − | 0.449084i | ||||
\(525\) | −3.53213 | −0.154155 | ||||||||
\(526\) | −3.06037 | − | 3.82477i | −0.133439 | − | 0.166768i | ||||
\(527\) | − | 54.3708i | − | 2.36843i | ||||||
\(528\) | −17.2800 | + | 27.9347i | −0.752017 | + | 1.21570i | ||||
\(529\) | 2.87986 | 0.125211 | ||||||||
\(530\) | 13.4204 | − | 10.7383i | 0.582944 | − | 0.466440i | ||||
\(531\) | 17.1531 | 0.744383 | ||||||||
\(532\) | −1.30024 | + | 5.78365i | −0.0563728 | + | 0.250753i | ||||
\(533\) | −8.40542 | − | 3.32073i | −0.364079 | − | 0.143837i | ||||
\(534\) | 15.2089 | + | 19.0077i | 0.658154 | + | 0.822543i | ||||
\(535\) | 6.71804i | 0.290446i | ||||||||
\(536\) | 7.32282 | − | 3.57073i | 0.316298 | − | 0.154232i | ||||
\(537\) | −17.8124 | −0.768660 | ||||||||
\(538\) | −18.2261 | − | 22.7785i | −0.785783 | − | 0.982050i | ||||
\(539\) | 22.1300 | + | 2.48225i | 0.953208 | + | 0.106918i | ||||
\(540\) | 0.392180 | − | 1.74446i | 0.0168767 | − | 0.0750698i | ||||
\(541\) | −4.63441 | −0.199249 | −0.0996243 | − | 0.995025i | \(-0.531764\pi\) | ||||
−0.0996243 | + | 0.995025i | \(0.531764\pi\) | |||||||
\(542\) | −15.5434 | + | 12.4370i | −0.667646 | + | 0.534214i | ||||
\(543\) | − | 16.7924i | − | 0.720632i | ||||||
\(544\) | 32.5127 | − | 7.70032i | 1.39397 | − | 0.330149i | ||||
\(545\) | 9.96318i | 0.426776i | ||||||||
\(546\) | 1.98506 | + | 6.44961i | 0.0849529 | + | 0.276018i | ||||
\(547\) | 17.5177 | 0.749002 | 0.374501 | − | 0.927226i | \(-0.377814\pi\) | ||||
0.374501 | + | 0.927226i | \(0.377814\pi\) | |||||||
\(548\) | −28.1068 | − | 6.31879i | −1.20066 | − | 0.269925i | ||||
\(549\) | − | 32.2913i | − | 1.37816i | ||||||
\(550\) | 6.68275 | + | 10.5854i | 0.284953 | + | 0.451362i | ||||
\(551\) | −3.75789 | −0.160091 | ||||||||
\(552\) | −28.2348 | + | 13.7678i | −1.20175 | + | 0.585995i | ||||
\(553\) | 4.50399i | 0.191529i | ||||||||
\(554\) | 28.8681 | − | 23.0987i | 1.22649 | − | 0.981369i | ||||
\(555\) | − | 10.6436i | − | 0.451794i | ||||||
\(556\) | 4.78878 | − | 21.3011i | 0.203090 | − | 0.903368i | ||||
\(557\) | 34.5051 | 1.46203 | 0.731014 | − | 0.682363i | \(-0.239048\pi\) | ||||
0.731014 | + | 0.682363i | \(0.239048\pi\) | |||||||
\(558\) | 25.4604 | + | 31.8197i | 1.07782 | + | 1.34704i | ||||
\(559\) | −28.4714 | − | 11.2482i | −1.20421 | − | 0.475749i | ||||
\(560\) | 5.35114 | + | 2.53410i | 0.226127 | + | 0.107085i | ||||
\(561\) | −48.2008 | − | 5.40653i | −2.03504 | − | 0.228264i | ||||
\(562\) | −20.1887 | − | 25.2313i | −0.851610 | − | 1.06432i | ||||
\(563\) | 3.29489 | 0.138863 | 0.0694314 | − | 0.997587i | \(-0.477881\pi\) | ||||
0.0694314 | + | 0.997587i | \(0.477881\pi\) | |||||||
\(564\) | −48.7929 | − | 10.9693i | −2.05455 | − | 0.461892i | ||||
\(565\) | − | 45.1904i | − | 1.90118i | ||||||
\(566\) | −11.6134 | − | 14.5141i | −0.488148 | − | 0.610074i | ||||
\(567\) | − | 4.59243i | − | 0.192864i | ||||||
\(568\) | −7.87792 | + | 3.84141i | −0.330550 | + | 0.161182i | ||||
\(569\) | 36.4540i | 1.52823i | 0.645080 | + | 0.764115i | \(0.276824\pi\) | ||||
−0.645080 | + | 0.764115i | \(0.723176\pi\) | |||||||
\(570\) | −41.9852 | + | 33.5943i | −1.75857 | + | 1.40711i | ||||
\(571\) | 35.0455 | 1.46661 | 0.733305 | − | 0.679900i | \(-0.237977\pi\) | ||||
0.733305 | + | 0.679900i | \(0.237977\pi\) | |||||||
\(572\) | 15.5730 | − | 18.1516i | 0.651141 | − | 0.758957i | ||||
\(573\) | −5.25765 | −0.219642 | ||||||||
\(574\) | 1.47945 | − | 1.18377i | 0.0617510 | − | 0.0494098i | ||||
\(575\) | 11.9716i | 0.499250i | ||||||||
\(576\) | −15.4217 | + | 19.7313i | −0.642572 | + | 0.822139i | ||||
\(577\) | − | 22.6920i | − | 0.944681i | −0.881416 | − | 0.472340i | \(-0.843409\pi\) | ||
0.881416 | − | 0.472340i | \(-0.156591\pi\) | |||||||
\(578\) | 15.8037 | + | 19.7510i | 0.657347 | + | 0.821535i | ||||
\(579\) | − | 32.5662i | − | 1.35341i | ||||||
\(580\) | −0.823255 | + | 3.66194i | −0.0341838 | + | 0.152054i | ||||
\(581\) | 1.51384 | 0.0628048 | ||||||||
\(582\) | 4.97134 | + | 6.21304i | 0.206069 | + | 0.257539i | ||||
\(583\) | 14.4649 | + | 1.62248i | 0.599077 | + | 0.0671964i | ||||
\(584\) | −24.0071 | + | 11.7063i | −0.993421 | + | 0.484409i | ||||
\(585\) | −11.4846 | + | 29.0698i | −0.474832 | + | 1.20189i | ||||
\(586\) | 9.84443 | + | 12.3033i | 0.406670 | + | 0.508245i | ||||
\(587\) | −23.1795 | −0.956722 | −0.478361 | − | 0.878163i | \(-0.658769\pi\) | ||||
−0.478361 | + | 0.878163i | \(0.658769\pi\) | |||||||
\(588\) | 32.4390 | + | 7.29274i | 1.33776 | + | 0.300748i | ||||
\(589\) | − | 51.0457i | − | 2.10330i | ||||||
\(590\) | −16.7562 | + | 13.4074i | −0.689842 | + | 0.551974i | ||||
\(591\) | − | 6.11855i | − | 0.251683i | ||||||
\(592\) | −2.65751 | + | 5.61176i | −0.109223 | + | 0.230642i | ||||
\(593\) | −1.34031 | −0.0550399 | −0.0275200 | − | 0.999621i | \(-0.508761\pi\) | ||||
−0.0275200 | + | 0.999621i | \(0.508761\pi\) | |||||||
\(594\) | 1.28039 | − | 0.808333i | 0.0525350 | − | 0.0331663i | ||||
\(595\) | 8.74284i | 0.358421i | ||||||||
\(596\) | 7.64966 | − | 34.0266i | 0.313342 | − | 1.39379i | ||||
\(597\) | 43.6990 | 1.78848 | ||||||||
\(598\) | 21.8599 | − | 6.72807i | 0.893919 | − | 0.275131i | ||||
\(599\) | − | 34.7876i | − | 1.42138i | −0.703504 | − | 0.710691i | \(-0.748382\pi\) | ||
0.703504 | − | 0.710691i | \(-0.251618\pi\) | |||||||
\(600\) | 8.19189 | + | 16.7998i | 0.334433 | + | 0.685851i | ||||
\(601\) | 34.3990i | 1.40317i | 0.712588 | + | 0.701583i | \(0.247523\pi\) | ||||
−0.712588 | + | 0.701583i | \(0.752477\pi\) | |||||||
\(602\) | 5.01129 | − | 4.00976i | 0.204245 | − | 0.163426i | ||||
\(603\) | −9.01677 | −0.367191 | ||||||||
\(604\) | −22.7933 | − | 5.12425i | −0.927447 | − | 0.208503i | ||||
\(605\) | −6.74876 | + | 29.7051i | −0.274376 | + | 1.20768i | ||||
\(606\) | −37.8260 | − | 47.2739i | −1.53657 | − | 1.92037i | ||||
\(607\) | 14.0802 | 0.571498 | 0.285749 | − | 0.958305i | \(-0.407758\pi\) | ||||
0.285749 | + | 0.958305i | \(0.407758\pi\) | |||||||
\(608\) | 30.5244 | − | 7.22940i | 1.23793 | − | 0.293191i | ||||
\(609\) | − | 0.896852i | − | 0.0363423i | ||||||
\(610\) | 25.2398 | + | 31.5440i | 1.02193 | + | 1.27718i | ||||
\(611\) | 33.8663 | + | 13.3796i | 1.37008 | + | 0.541280i | ||||
\(612\) | −36.0787 | − | 8.11098i | −1.45839 | − | 0.327867i | ||||
\(613\) | 10.9545 | 0.442447 | 0.221224 | − | 0.975223i | \(-0.428995\pi\) | ||||
0.221224 | + | 0.975223i | \(0.428995\pi\) | |||||||
\(614\) | 31.8214 | − | 25.4617i | 1.28421 | − | 1.02755i | ||||
\(615\) | 17.1867 | 0.693035 | ||||||||
\(616\) | 1.68157 | + | 4.72377i | 0.0677524 | + | 0.190326i | ||||
\(617\) | 6.00315i | 0.241678i | 0.992672 | + | 0.120839i | \(0.0385584\pi\) | ||||
−0.992672 | + | 0.120839i | \(0.961442\pi\) | |||||||
\(618\) | 35.2444 | + | 44.0475i | 1.41774 | + | 1.77185i | ||||
\(619\) | 13.0392 | 0.524088 | 0.262044 | − | 0.965056i | \(-0.415603\pi\) | ||||
0.262044 | + | 0.965056i | \(0.415603\pi\) | |||||||
\(620\) | −49.7424 | − | 11.1828i | −1.99770 | − | 0.449111i | ||||
\(621\) | 1.44806 | 0.0581087 | ||||||||
\(622\) | −16.3015 | + | 13.0436i | −0.653630 | + | 0.522999i | ||||
\(623\) | 3.71603 | 0.148880 | ||||||||
\(624\) | 26.0724 | − | 24.3998i | 1.04373 | − | 0.976775i | ||||
\(625\) | −31.2215 | −1.24886 | ||||||||
\(626\) | 10.9691 | + | 13.7089i | 0.438413 | + | 0.547917i | ||||
\(627\) | −45.2531 | − | 5.07589i | −1.80723 | − | 0.202711i | ||||
\(628\) | 3.93971 | − | 17.5243i | 0.157211 | − | 0.699297i | ||||
\(629\) | −9.16864 | −0.365578 | ||||||||
\(630\) | −4.09404 | − | 5.11662i | −0.163111 | − | 0.203851i | ||||
\(631\) | −19.0168 | −0.757046 | −0.378523 | − | 0.925592i | \(-0.623568\pi\) | ||||
−0.378523 | + | 0.925592i | \(0.623568\pi\) | |||||||
\(632\) | 21.4223 | − | 10.4459i | 0.852134 | − | 0.415515i | ||||
\(633\) | 62.0100i | 2.46468i | ||||||||
\(634\) | 9.00187 | − | 7.20281i | 0.357510 | − | 0.286060i | ||||
\(635\) | 37.8797i | 1.50321i | ||||||||
\(636\) | 21.2033 | + | 4.76678i | 0.840764 | + | 0.189015i | ||||
\(637\) | −22.5153 | − | 8.89515i | −0.892090 | − | 0.352439i | ||||
\(638\) | −2.68776 | + | 1.69683i | −0.106410 | + | 0.0671783i | ||||
\(639\) | 9.70028 | 0.383737 | ||||||||
\(640\) | −0.357732 | − | 31.3288i | −0.0141406 | − | 1.23838i | ||||
\(641\) | −18.2023 | −0.718949 | −0.359475 | − | 0.933155i | \(-0.617044\pi\) | ||||
−0.359475 | + | 0.933155i | \(0.617044\pi\) | |||||||
\(642\) | −6.63257 | + | 5.30702i | −0.261767 | + | 0.209451i | ||||
\(643\) | 18.4562 | 0.727840 | 0.363920 | − | 0.931430i | \(-0.381438\pi\) | ||||
0.363920 | + | 0.931430i | \(0.381438\pi\) | |||||||
\(644\) | −1.05176 | + | 4.67837i | −0.0414453 | + | 0.184354i | ||||
\(645\) | 58.2160 | 2.29225 | ||||||||
\(646\) | 28.9390 | + | 36.1672i | 1.13859 | + | 1.42298i | ||||
\(647\) | 16.4584i | 0.647047i | 0.946220 | + | 0.323524i | \(0.104868\pi\) | ||||
−0.946220 | + | 0.323524i | \(0.895132\pi\) | |||||||
\(648\) | −21.8430 | + | 10.6510i | −0.858072 | + | 0.418411i | ||||
\(649\) | −18.0604 | − | 2.02577i | −0.708933 | − | 0.0795186i | ||||
\(650\) | −4.00324 | − | 13.0068i | −0.157020 | − | 0.510168i | ||||
\(651\) | 12.1825 | 0.477469 | ||||||||
\(652\) | −4.95582 | + | 22.0441i | −0.194085 | + | 0.863315i | ||||
\(653\) | −2.39687 | −0.0937967 | −0.0468983 | − | 0.998900i | \(-0.514934\pi\) | ||||
−0.0468983 | + | 0.998900i | \(0.514934\pi\) | |||||||
\(654\) | −9.83641 | + | 7.87056i | −0.384634 | + | 0.307763i | ||||
\(655\) | − | 14.5894i | − | 0.570054i | ||||||
\(656\) | −9.06159 | − | 4.29123i | −0.353796 | − | 0.167544i | ||||
\(657\) | 29.5605 | 1.15327 | ||||||||
\(658\) | −5.96085 | + | 4.76954i | −0.232378 | + | 0.185936i | ||||
\(659\) | −37.1638 | −1.44770 | −0.723848 | − | 0.689959i | \(-0.757629\pi\) | ||||
−0.723848 | + | 0.689959i | \(0.757629\pi\) | |||||||
\(660\) | −14.8601 | + | 42.9857i | −0.578427 | + | 1.67322i | ||||
\(661\) | 47.4011i | 1.84369i | 0.387562 | + | 0.921844i | \(0.373317\pi\) | ||||
−0.387562 | + | 0.921844i | \(0.626683\pi\) | |||||||
\(662\) | −9.37518 | − | 11.7168i | −0.364377 | − | 0.455388i | ||||
\(663\) | 49.0400 | + | 19.3743i | 1.90456 | + | 0.752435i | ||||
\(664\) | −3.51099 | − | 7.20029i | −0.136253 | − | 0.279425i | ||||
\(665\) | 8.20817i | 0.318299i | ||||||||
\(666\) | 5.36582 | − | 4.29343i | 0.207921 | − | 0.166367i | ||||
\(667\) | −3.03974 | −0.117699 | ||||||||
\(668\) | 16.6436 | + | 3.74171i | 0.643960 | + | 0.144771i | ||||
\(669\) | − | 3.29475i | − | 0.127382i | ||||||
\(670\) | 8.80811 | − | 7.04777i | 0.340287 | − | 0.272279i | ||||
\(671\) | −3.81358 | + | 33.9992i | −0.147222 | + | 1.31252i | ||||
\(672\) | 1.72536 | + | 7.28490i | 0.0665572 | + | 0.281021i | ||||
\(673\) | − | 5.26521i | − | 0.202959i | −0.994838 | − | 0.101479i | \(-0.967642\pi\) | ||
0.994838 | − | 0.101479i | \(-0.0323576\pi\) | |||||||
\(674\) | −10.5863 | + | 8.47056i | −0.407768 | + | 0.326274i | ||||
\(675\) | − | 0.861604i | − | 0.0331632i | ||||||
\(676\) | −21.5003 | + | 14.6197i | −0.826936 | + | 0.562296i | ||||
\(677\) | − | 0.333277i | − | 0.0128089i | −0.999979 | − | 0.00640444i | \(-0.997961\pi\) | ||
0.999979 | − | 0.00640444i | \(-0.00203861\pi\) | |||||||
\(678\) | 44.6155 | − | 35.6989i | 1.71345 | − | 1.37101i | ||||
\(679\) | 1.21466 | 0.0466143 | ||||||||
\(680\) | 41.5835 | − | 20.2768i | 1.59466 | − | 0.777582i | ||||
\(681\) | 46.9237 | 1.79812 | ||||||||
\(682\) | −23.0491 | − | 36.5096i | −0.882597 | − | 1.39802i | ||||
\(683\) | −2.49175 | −0.0953442 | −0.0476721 | − | 0.998863i | \(-0.515180\pi\) | ||||
−0.0476721 | + | 0.998863i | \(0.515180\pi\) | |||||||
\(684\) | −33.8722 | − | 7.61495i | −1.29514 | − | 0.291165i | ||||
\(685\) | −39.8892 | −1.52409 | ||||||||
\(686\) | 8.09453 | − | 6.47680i | 0.309051 | − | 0.247286i | ||||
\(687\) | −28.0148 | −1.06883 | ||||||||
\(688\) | −30.6941 | − | 14.5355i | −1.17020 | − | 0.554162i | ||||
\(689\) | −14.7168 | − | 5.81417i | −0.560665 | − | 0.221502i | ||||
\(690\) | −33.9617 | + | 27.1743i | −1.29290 | + | 1.03451i | ||||
\(691\) | −39.4033 | −1.49897 | −0.749486 | − | 0.662020i | \(-0.769699\pi\) | ||||
−0.749486 | + | 0.662020i | \(0.769699\pi\) | |||||||
\(692\) | −25.4608 | − | 5.72395i | −0.967876 | − | 0.217592i | ||||
\(693\) | 0.618584 | − | 5.51487i | 0.0234981 | − | 0.209493i | ||||
\(694\) | 13.9593 | + | 17.4460i | 0.529889 | + | 0.662241i | ||||
\(695\) | − | 30.2305i | − | 1.14671i | ||||||
\(696\) | −4.26569 | + | 2.08003i | −0.161691 | + | 0.0788432i | ||||
\(697\) | − | 14.8051i | − | 0.560783i | ||||||
\(698\) | 16.5448 | + | 20.6773i | 0.626232 | + | 0.782647i | ||||
\(699\) | −67.0362 | −2.53554 | ||||||||
\(700\) | 2.78366 | + | 0.625805i | 0.105212 | + | 0.0236532i | ||||
\(701\) | − | 14.3122i | − | 0.540565i | −0.962781 | − | 0.270283i | \(-0.912883\pi\) | ||
0.962781 | − | 0.270283i | \(-0.0871171\pi\) | |||||||
\(702\) | −1.57328 | + | 0.484224i | −0.0593795 | + | 0.0182759i | ||||
\(703\) | −8.60793 | −0.324654 | ||||||||
\(704\) | 18.5677 | − | 18.9537i | 0.699796 | − | 0.714343i | ||||
\(705\) | −69.2470 | −2.60799 | ||||||||
\(706\) | 4.59688 | − | 3.67817i | 0.173006 | − | 0.138430i | ||||
\(707\) | −9.24210 | −0.347585 | ||||||||
\(708\) | −26.4736 | − | 5.95163i | −0.994939 | − | 0.223676i | ||||
\(709\) | − | 26.4836i | − | 0.994612i | −0.867575 | − | 0.497306i | \(-0.834323\pi\) | ||
0.867575 | − | 0.497306i | \(-0.165677\pi\) | |||||||
\(710\) | −9.47581 | + | 7.58202i | −0.355621 | + | 0.284548i | ||||
\(711\) | −26.3778 | −0.989246 | ||||||||
\(712\) | −8.61841 | − | 17.6745i | −0.322989 | − | 0.662381i | ||||
\(713\) | − | 41.2906i | − | 1.54635i | ||||||
\(714\) | −8.63160 | + | 6.90654i | −0.323030 | + | 0.258471i | ||||
\(715\) | 15.5252 | − | 29.2511i | 0.580610 | − | 1.09393i | ||||
\(716\) | 14.0379 | + | 3.15590i | 0.524619 | + | 0.117942i | ||||
\(717\) | −36.2858 | −1.35512 | ||||||||
\(718\) | −10.9331 | + | 8.74806i | −0.408019 | + | 0.326475i | ||||
\(719\) | 28.7663i | 1.07280i | 0.843963 | + | 0.536401i | \(0.180217\pi\) | ||||
−0.843963 | + | 0.536401i | \(0.819783\pi\) | |||||||
\(720\) | −14.8411 | + | 31.3392i | −0.553093 | + | 1.16794i | ||||
\(721\) | 8.61135 | 0.320703 | ||||||||
\(722\) | 10.3817 | + | 12.9748i | 0.386369 | + | 0.482873i | ||||
\(723\) | 18.2614i | 0.679148i | ||||||||
\(724\) | −2.97520 | + | 13.2341i | −0.110572 | + | 0.491840i | ||||
\(725\) | 1.80866i | 0.0671720i | ||||||||
\(726\) | −34.6585 | + | 16.8031i | −1.28630 | + | 0.623622i | ||||
\(727\) | 23.8682i | 0.885221i | 0.896714 | + | 0.442610i | \(0.145948\pi\) | ||||
−0.896714 | + | 0.442610i | \(0.854052\pi\) | |||||||
\(728\) | −0.421714 | − | 5.43462i | −0.0156298 | − | 0.201420i | ||||
\(729\) | 29.2937 | 1.08495 | ||||||||
\(730\) | −28.8765 | + | 23.1054i | −1.06877 | + | 0.855168i | ||||
\(731\) | − | 50.1488i | − | 1.85482i | ||||||
\(732\) | −11.2041 | + | 49.8373i | −0.414116 | + | 1.84204i | ||||
\(733\) | 0.489259 | 0.0180712 | 0.00903560 | − | 0.999959i | \(-0.497124\pi\) | ||||
0.00903560 | + | 0.999959i | \(0.497124\pi\) | |||||||
\(734\) | −4.56193 | + | 3.65021i | −0.168384 | + | 0.134732i | ||||
\(735\) | 46.0375 | 1.69812 | ||||||||
\(736\) | 24.6910 | − | 5.84783i | 0.910124 | − | 0.215554i | ||||
\(737\) | 9.49368 | + | 1.06487i | 0.349704 | + | 0.0392252i | ||||
\(738\) | 6.93283 | + | 8.66446i | 0.255201 | + | 0.318943i | ||||
\(739\) | 4.59628i | 0.169077i | 0.996420 | + | 0.0845384i | \(0.0269416\pi\) | ||||
−0.996420 | + | 0.0845384i | \(0.973058\pi\) | |||||||
\(740\) | −1.88577 | + | 8.38816i | −0.0693224 | + | 0.308355i | ||||
\(741\) | 46.0409 | + | 18.1894i | 1.69136 | + | 0.668206i | ||||
\(742\) | 2.59032 | − | 2.07263i | 0.0950937 | − | 0.0760888i | ||||
\(743\) | 38.4847i | 1.41187i | 0.708278 | + | 0.705934i | \(0.249472\pi\) | ||||
−0.708278 | + | 0.705934i | \(0.750528\pi\) | |||||||
\(744\) | −28.2543 | − | 57.9435i | −1.03585 | − | 2.12431i | ||||
\(745\) | − | 48.2906i | − | 1.76923i | ||||||
\(746\) | 38.0354 | − | 30.4338i | 1.39257 | − | 1.11426i | ||||
\(747\) | 8.86590i | 0.324386i | ||||||||
\(748\) | 37.0290 | + | 12.8008i | 1.35391 | + | 0.468045i | ||||
\(749\) | 1.29668i | 0.0473795i | ||||||||
\(750\) | −14.1221 | − | 17.6494i | −0.515665 | − | 0.644464i | ||||
\(751\) | 2.60106i | 0.0949141i | 0.998873 | + | 0.0474571i | \(0.0151117\pi\) | ||||
−0.998873 | + | 0.0474571i | \(0.984888\pi\) | |||||||
\(752\) | 36.5101 | + | 17.2898i | 1.33139 | + | 0.630493i | ||||
\(753\) | 6.87691 | 0.250609 | ||||||||
\(754\) | 3.30259 | − | 1.01647i | 0.120273 | − | 0.0370177i | ||||
\(755\) | −32.3483 | −1.17727 | ||||||||
\(756\) | 0.0756962 | − | 0.336706i | 0.00275304 | − | 0.0122459i | ||||
\(757\) | −15.6223 | −0.567802 | −0.283901 | − | 0.958854i | \(-0.591629\pi\) | ||||
−0.283901 | + | 0.958854i | \(0.591629\pi\) | |||||||
\(758\) | 25.9156 | + | 32.3887i | 0.941299 | + | 1.17641i | ||||
\(759\) | −36.6050 | − | 4.10586i | −1.32868 | − | 0.149033i | ||||
\(760\) | 39.0405 | − | 19.0368i | 1.41615 | − | 0.690537i | ||||
\(761\) | 16.2114 | 0.587662 | 0.293831 | − | 0.955857i | \(-0.405070\pi\) | ||||
0.293831 | + | 0.955857i | \(0.405070\pi\) | |||||||
\(762\) | −37.3978 | + | 29.9236i | −1.35478 | + | 1.08402i | ||||
\(763\) | 1.92303i | 0.0696184i | ||||||||
\(764\) | 4.14354 | + | 0.931525i | 0.149908 | + | 0.0337014i | ||||
\(765\) | −51.2029 | −1.85124 | ||||||||
\(766\) | 20.9314 | + | 26.1595i | 0.756284 | + | 0.945183i | ||||
\(767\) | 18.3748 | + | 7.25936i | 0.663477 | + | 0.262120i | ||||
\(768\) | 30.6476 | − | 25.1018i | 1.10590 | − | 0.905785i | ||||
\(769\) | 12.0546 | 0.434700 | 0.217350 | − | 0.976094i | \(-0.430259\pi\) | ||||
0.217350 | + | 0.976094i | \(0.430259\pi\) | |||||||
\(770\) | 3.70631 | + | 5.87075i | 0.133566 | + | 0.211567i | ||||
\(771\) | − | 37.5057i | − | 1.35074i | ||||||
\(772\) | −5.76992 | + | 25.6653i | −0.207664 | + | 0.923715i | ||||
\(773\) | − | 29.6851i | − | 1.06770i | −0.845579 | − | 0.533850i | \(-0.820745\pi\) | ||
0.845579 | − | 0.533850i | \(-0.179255\pi\) | |||||||
\(774\) | 23.4834 | + | 29.3489i | 0.844092 | + | 1.05492i | ||||
\(775\) | −24.5682 | −0.882514 | ||||||||
\(776\) | −2.81710 | − | 5.77728i | −0.101128 | − | 0.207392i | ||||
\(777\) | − | 2.05436i | − | 0.0736996i | ||||||
\(778\) | 15.9822 | + | 19.9741i | 0.572990 | + | 0.716107i | ||||
\(779\) | − | 13.8997i | − | 0.498007i | ||||||
\(780\) | 27.8114 | − | 40.8806i | 0.995808 | − | 1.46376i | ||||
\(781\) | −10.2133 | − | 1.14560i | −0.365462 | − | 0.0409927i | ||||
\(782\) | 23.4086 | + | 29.2555i | 0.837091 | + | 1.04617i | ||||
\(783\) | 0.218772 | 0.00781828 | ||||||||
\(784\) | −24.2730 | − | 11.4948i | −0.866893 | − | 0.410528i | ||||
\(785\) | − | 24.8705i | − | 0.887667i | ||||||
\(786\) | 14.4037 | − | 11.5251i | 0.513765 | − | 0.411086i | ||||
\(787\) | 6.17918i | 0.220264i | 0.993917 | + | 0.110132i | \(0.0351274\pi\) | ||||
−0.993917 | + | 0.110132i | \(0.964873\pi\) | |||||||
\(788\) | −1.08405 | + | 4.82201i | −0.0386178 | + | 0.171777i | ||||
\(789\) | − | 8.57605i | − | 0.305315i | ||||||
\(790\) | 25.7674 | − | 20.6177i | 0.916764 | − | 0.733544i | ||||
\(791\) | − | 8.72239i | − | 0.310132i | ||||||
\(792\) | −27.6650 | + | 9.84820i | −0.983033 | + | 0.349941i | ||||
\(793\) | 13.6660 | − | 34.5911i | 0.485292 | − | 1.22837i | ||||
\(794\) | −29.9450 | + | 23.9604i | −1.06271 | + | 0.850322i | ||||
\(795\) | 30.0917 | 1.06724 | ||||||||
\(796\) | −34.4390 | − | 7.74237i | −1.22066 | − | 0.274421i | ||||
\(797\) | −10.8368 | −0.383861 | −0.191930 | − | 0.981409i | \(-0.561475\pi\) | ||||
−0.191930 | + | 0.981409i | \(0.561475\pi\) | |||||||
\(798\) | −8.10373 | + | 6.48416i | −0.286869 | + | 0.229537i | ||||
\(799\) | 59.6512i | 2.11031i | ||||||||
\(800\) | −3.47949 | − | 14.6913i | −0.123019 | − | 0.519416i | ||||
\(801\) | 21.7631i | 0.768962i | ||||||||
\(802\) | 33.9670 | − | 27.1785i | 1.19942 | − | 0.959708i | ||||
\(803\) | −31.1240 | − | 3.49108i | −1.09834 | − | 0.123198i | ||||
\(804\) | 13.9162 | + | 3.12855i | 0.490787 | + | 0.110336i | ||||
\(805\) | 6.63955i | 0.234013i | ||||||||
\(806\) | 13.8074 | + | 44.8611i | 0.486344 | + | 1.58016i | ||||
\(807\) | − | 51.0748i | − | 1.79792i | ||||||
\(808\) | 21.4348 | + | 43.9582i | 0.754073 | + | 1.54644i | ||||
\(809\) | − | 17.7739i | − | 0.624897i | −0.949935 | − | 0.312448i | \(-0.898851\pi\) | ||
0.949935 | − | 0.312448i | \(-0.101149\pi\) | |||||||
\(810\) | −26.2734 | + | 21.0225i | −0.923152 | + | 0.738656i | ||||
\(811\) | − | 49.2510i | − | 1.72944i | −0.502256 | − | 0.864719i | \(-0.667497\pi\) | ||
0.502256 | − | 0.864719i | \(-0.332503\pi\) | |||||||
\(812\) | −0.158900 | + | 0.706806i | −0.00557629 | + | 0.0248040i | ||||
\(813\) | −34.8520 | −1.22231 | ||||||||
\(814\) | −6.15667 | + | 3.88682i | −0.215791 | + | 0.136233i | ||||
\(815\) | 31.2850i | 1.09587i | ||||||||
\(816\) | 52.8684 | + | 25.0365i | 1.85076 | + | 0.876451i | ||||
\(817\) | − | 47.0819i | − | 1.64719i | ||||||
\(818\) | −26.9221 | − | 33.6465i | −0.941308 | − | 1.17642i | ||||
\(819\) | −2.21670 | + | 5.61088i | −0.0774577 | + | 0.196060i | ||||
\(820\) | −13.5448 | − | 3.04506i | −0.473005 | − | 0.106338i | ||||
\(821\) | −30.7585 | −1.07348 | −0.536739 | − | 0.843748i | \(-0.680344\pi\) | ||||
−0.536739 | + | 0.843748i | \(0.680344\pi\) | |||||||
\(822\) | −31.5110 | − | 39.3816i | −1.09907 | − | 1.37359i | ||||
\(823\) | − | 12.7499i | − | 0.444433i | −0.974997 | − | 0.222217i | \(-0.928671\pi\) | ||
0.974997 | − | 0.222217i | \(-0.0713292\pi\) | |||||||
\(824\) | −19.9719 | − | 40.9581i | −0.695753 | − | 1.42684i | ||||
\(825\) | −2.44301 | + | 21.7802i | −0.0850547 | + | 0.758289i | ||||
\(826\) | −3.23418 | + | 2.58781i | −0.112532 | + | 0.0900416i | ||||
\(827\) | − | 15.8622i | − | 0.551584i | −0.961217 | − | 0.275792i | \(-0.911060\pi\) | ||
0.961217 | − | 0.275792i | \(-0.0889400\pi\) | |||||||
\(828\) | −27.3991 | − | 6.15970i | −0.952185 | − | 0.214064i | ||||
\(829\) | 48.1345 | 1.67178 | 0.835890 | − | 0.548897i | \(-0.184952\pi\) | ||||
0.835890 | + | 0.548897i | \(0.184952\pi\) | |||||||
\(830\) | −6.92984 | − | 8.66073i | −0.240538 | − | 0.300618i | ||||
\(831\) | 64.7291 | 2.24543 | ||||||||
\(832\) | −24.8706 | + | 14.6100i | −0.862233 | + | 0.506512i | ||||
\(833\) | − | 39.6579i | − | 1.37407i | ||||||
\(834\) | 29.8459 | − | 23.8811i | 1.03348 | − | 0.826934i | ||||
\(835\) | 23.6206 | 0.817424 | ||||||||
\(836\) | 34.7645 | + | 12.0180i | 1.20235 | + | 0.415651i | ||||
\(837\) | 2.97172i | 0.102718i | ||||||||
\(838\) | 4.38441 | − | 3.50816i | 0.151457 | − | 0.121188i | ||||
\(839\) | −31.6487 | −1.09264 | −0.546318 | − | 0.837578i | \(-0.683971\pi\) | ||||
−0.546318 | + | 0.837578i | \(0.683971\pi\) | |||||||
\(840\) | 4.54330 | + | 9.31734i | 0.156759 | + | 0.321479i | ||||
\(841\) | 28.5408 | 0.984164 | ||||||||
\(842\) | 22.8398 | − | 18.2752i | 0.787112 | − | 0.629804i | ||||
\(843\) | − | 56.5746i | − | 1.94853i | ||||||
\(844\) | 10.9866 | − | 48.8699i | 0.378175 | − | 1.68217i | ||||
\(845\) | −24.6052 | + | 26.2799i | −0.846445 | + | 0.904055i | ||||
\(846\) | −27.9331 | − | 34.9100i | −0.960359 | − | 1.20023i | ||||
\(847\) | −1.30260 | + | 5.73350i | −0.0447580 | + | 0.197006i | ||||
\(848\) | −15.8657 | − | 7.51338i | −0.544829 | − | 0.258010i | ||||
\(849\) | − | 32.5441i | − | 1.11691i | ||||||
\(850\) | 17.4072 | − | 13.9283i | 0.597061 | − | 0.477735i | ||||
\(851\) | −6.96292 | −0.238686 | ||||||||
\(852\) | −14.9711 | − | 3.36571i | −0.512902 | − | 0.115307i | ||||
\(853\) | −42.8801 | −1.46819 | −0.734094 | − | 0.679048i | \(-0.762393\pi\) | ||||
−0.734094 | + | 0.679048i | \(0.762393\pi\) | |||||||
\(854\) | 4.87163 | + | 6.08844i | 0.166704 | + | 0.208342i | ||||
\(855\) | −48.0715 | −1.64401 | ||||||||
\(856\) | 6.16738 | − | 3.00732i | 0.210797 | − | 0.102788i | ||||
\(857\) | 37.0942i | 1.26711i | 0.773696 | + | 0.633557i | \(0.218406\pi\) | ||||
−0.773696 | + | 0.633557i | \(0.781594\pi\) | |||||||
\(858\) | 41.1433 | − | 7.77963i | 1.40461 | − | 0.265592i | ||||
\(859\) | 53.4127i | 1.82242i | 0.411944 | + | 0.911209i | \(0.364850\pi\) | ||||
−0.411944 | + | 0.911209i | \(0.635150\pi\) | |||||||
\(860\) | −45.8799 | − | 10.3144i | −1.56449 | − | 0.351719i | ||||
\(861\) | 3.31728 | 0.113052 | ||||||||
\(862\) | −31.8801 | + | 25.5087i | −1.08584 | + | 0.868831i | ||||
\(863\) | 13.3427 | 0.454190 | 0.227095 | − | 0.973873i | \(-0.427077\pi\) | ||||
0.227095 | + | 0.973873i | \(0.427077\pi\) | |||||||
\(864\) | −1.77703 | + | 0.420873i | −0.0604559 | + | 0.0143184i | ||||
\(865\) | −36.1340 | −1.22859 | ||||||||
\(866\) | −0.846605 | − | 1.05806i | −0.0287688 | − | 0.0359545i | ||||
\(867\) | 44.2865i | 1.50405i | ||||||||
\(868\) | −9.60098 | − | 2.15843i | −0.325879 | − | 0.0732620i | ||||
\(869\) | 27.7730 | + | 3.11521i | 0.942135 | + | 0.105676i | ||||
\(870\) | −5.13091 | + | 4.10547i | −0.173954 | + | 0.139189i | ||||
\(871\) | −9.65897 | − | 3.81598i | −0.327282 | − | 0.129299i | ||||
\(872\) | 9.14651 | − | 4.46000i | 0.309740 | − | 0.151035i | ||||
\(873\) | 7.11371i | 0.240763i | ||||||||
\(874\) | 21.9771 | + | 27.4663i | 0.743385 | + | 0.929062i | ||||
\(875\) | −3.45048 | −0.116648 | ||||||||
\(876\) | −45.6228 | − | 10.2566i | −1.54145 | − | 0.346540i | ||||
\(877\) | −7.39316 | −0.249649 | −0.124825 | − | 0.992179i | \(-0.539837\pi\) | ||||
−0.124825 | + | 0.992179i | \(0.539837\pi\) | |||||||
\(878\) | 1.08498 | + | 1.35598i | 0.0366164 | + | 0.0457622i | ||||
\(879\) | 27.5869i | 0.930484i | ||||||||
\(880\) | 19.3272 | − | 31.2441i | 0.651518 | − | 1.05324i | ||||
\(881\) | 1.04846 | 0.0353235 | 0.0176618 | − | 0.999844i | \(-0.494378\pi\) | ||||
0.0176618 | + | 0.999844i | \(0.494378\pi\) | |||||||
\(882\) | 18.5708 | + | 23.2092i | 0.625310 | + | 0.781495i | ||||
\(883\) | 16.7074i | 0.562249i | 0.959671 | + | 0.281124i | \(0.0907073\pi\) | ||||
−0.959671 | + | 0.281124i | \(0.909293\pi\) | |||||||
\(884\) | −35.2156 | − | 23.9575i | −1.18443 | − | 0.805777i | ||||
\(885\) | −37.5714 | −1.26295 | ||||||||
\(886\) | 34.7268 | − | 27.7865i | 1.16667 | − | 0.933505i | ||||
\(887\) | 53.5161 | 1.79690 | 0.898448 | − | 0.439080i | \(-0.144696\pi\) | ||||
0.898448 | + | 0.439080i | \(0.144696\pi\) | |||||||
\(888\) | −9.77113 | + | 4.76457i | −0.327897 | + | 0.159888i | ||||
\(889\) | 7.31131i | 0.245214i | ||||||||
\(890\) | −17.0107 | − | 21.2595i | −0.570199 | − | 0.712620i | ||||
\(891\) | −28.3183 | − | 3.17637i | −0.948700 | − | 0.106413i | ||||
\(892\) | −0.583747 | + | 2.59658i | −0.0195453 | + | 0.0869400i | ||||
\(893\) | 56.0032i | 1.87407i | ||||||||
\(894\) | 47.6762 | − | 38.1479i | 1.59453 | − | 1.27586i | ||||
\(895\) | 19.9225 | 0.665937 | ||||||||
\(896\) | −0.0690473 | − | 6.04690i | −0.00230671 | − | 0.202013i | ||||
\(897\) | 37.2423 | + | 14.7134i | 1.24349 | + | 0.491265i | ||||
\(898\) | 4.81508 | − | 3.85276i | 0.160681 | − | 0.128568i | ||||
\(899\) | − | 6.23817i | − | 0.208054i | ||||||
\(900\) | −3.66505 | + | 16.3026i | −0.122168 | + | 0.543421i | ||||
\(901\) | − | 25.9218i | − | 0.863579i | ||||||
\(902\) | −6.27625 | − | 9.94150i | −0.208976 | − | 0.331016i | ||||
\(903\) | 11.2365 | 0.373928 | ||||||||
\(904\) | −41.4863 | + | 20.2294i | −1.37981 | + | 0.672820i | ||||
\(905\) | 18.7818i | 0.624328i | ||||||||
\(906\) | −25.5540 | − | 31.9367i | −0.848975 | − | 1.06103i | ||||
\(907\) | − | 20.6013i | − | 0.684054i | −0.939690 | − | 0.342027i | \(-0.888887\pi\) | ||
0.939690 | − | 0.342027i | \(-0.111113\pi\) | |||||||
\(908\) | −36.9804 | − | 8.31371i | −1.22724 | − | 0.275900i | ||||
\(909\) | − | 54.1268i | − | 1.79527i | ||||||
\(910\) | −2.22023 | − | 7.21368i | −0.0735999 | − | 0.239131i | ||||
\(911\) | 16.0253i | 0.530941i | 0.964119 | + | 0.265470i | \(0.0855272\pi\) | ||||
−0.964119 | + | 0.265470i | \(0.914473\pi\) | |||||||
\(912\) | 49.6352 | + | 23.5053i | 1.64359 | + | 0.778339i | ||||
\(913\) | 1.04706 | − | 9.33483i | 0.0346525 | − | 0.308938i | ||||
\(914\) | −26.6691 | − | 33.3303i | −0.882135 | − | 1.10247i | ||||
\(915\) | 70.7292i | 2.33823i | ||||||||
\(916\) | 22.0783 | + | 4.96352i | 0.729489 | + | 0.163999i | ||||
\(917\) | − | 2.81595i | − | 0.0929910i | ||||||
\(918\) | −1.68474 | − | 2.10554i | −0.0556046 | − | 0.0694931i | ||||
\(919\) | 15.6755 | 0.517088 | 0.258544 | − | 0.966000i | \(-0.416757\pi\) | ||||
0.258544 | + | 0.966000i | \(0.416757\pi\) | |||||||
\(920\) | 31.5797 | − | 15.3988i | 1.04115 | − | 0.507683i | ||||
\(921\) | 71.3511 | 2.35110 | ||||||||
\(922\) | −28.7880 | − | 35.9785i | −0.948084 | − | 1.18489i | ||||
\(923\) | 10.3912 | + | 4.10525i | 0.342029 | + | 0.135126i | ||||
\(924\) | −2.86820 | + | 8.29684i | −0.0943568 | + | 0.272946i | ||||
\(925\) | 4.14297i | 0.136220i | ||||||||
\(926\) | −3.56171 | − | 4.45132i | −0.117045 | − | 0.146280i | ||||
\(927\) | 50.4328i | 1.65643i | ||||||||
\(928\) | 3.73031 | − | 0.883487i | 0.122453 | − | 0.0290019i | ||||
\(929\) | 17.5641i | 0.576258i | 0.957592 | + | 0.288129i | \(0.0930332\pi\) | ||||
−0.957592 | + | 0.288129i | \(0.906967\pi\) | |||||||
\(930\) | −55.7671 | − | 69.6963i | −1.82868 | − | 2.28543i | ||||
\(931\) | − | 37.2326i | − | 1.22025i | ||||||
\(932\) | 52.8310 | + | 11.8771i | 1.73054 | + | 0.389049i | ||||
\(933\) | −36.5518 | −1.19665 | ||||||||
\(934\) | 3.76561 | − | 3.01303i | 0.123214 | − | 0.0985895i | ||||
\(935\) | 53.9111 | + | 6.04702i | 1.76308 | + | 0.197759i | ||||
\(936\) | 31.8281 | − | 2.46979i | 1.04033 | − | 0.0807276i | ||||
\(937\) | − | 51.2539i | − | 1.67439i | −0.546904 | − | 0.837195i | \(-0.684194\pi\) | ||
0.546904 | − | 0.837195i | \(-0.315806\pi\) | |||||||
\(938\) | 1.70009 | − | 1.36032i | 0.0555099 | − | 0.0444160i | ||||
\(939\) | 30.7386i | 1.00312i | ||||||||
\(940\) | 54.5733 | + | 12.2688i | 1.77999 | + | 0.400165i | ||||
\(941\) | −5.44008 | −0.177342 | −0.0886708 | − | 0.996061i | \(-0.528262\pi\) | ||||
−0.0886708 | + | 0.996061i | \(0.528262\pi\) | |||||||
\(942\) | 24.5541 | − | 19.6468i | 0.800016 | − | 0.640129i | ||||
\(943\) | − | 11.2434i | − | 0.366135i | ||||||
\(944\) | 19.8093 | + | 9.38092i | 0.644737 | + | 0.305323i | ||||
\(945\) | − | 0.477853i | − | 0.0155446i | ||||||
\(946\) | −21.2594 | − | 33.6746i | −0.691201 | − | 1.09485i | ||||
\(947\) | −21.5672 | −0.700841 | −0.350420 | − | 0.936593i | \(-0.613961\pi\) | ||||
−0.350420 | + | 0.936593i | \(0.613961\pi\) | |||||||
\(948\) | 40.7107 | + | 9.15233i | 1.32222 | + | 0.297254i | ||||
\(949\) | 31.6659 | + | 12.5103i | 1.02792 | + | 0.406101i | ||||
\(950\) | 16.3426 | − | 13.0765i | 0.530224 | − | 0.424257i | ||||
\(951\) | 20.1843 | 0.654522 | ||||||||
\(952\) | 8.02620 | − | 3.91372i | 0.260131 | − | 0.126844i | ||||
\(953\) | 7.87118i | 0.254972i | 0.991840 | + | 0.127486i | \(0.0406909\pi\) | ||||
−0.991840 | + | 0.127486i | \(0.959309\pi\) | |||||||
\(954\) | 12.1385 | + | 15.1703i | 0.392998 | + | 0.491158i | ||||
\(955\) | 5.88051 | 0.190289 | ||||||||
\(956\) | 28.5967 | + | 6.42894i | 0.924885 | + | 0.207927i | ||||
\(957\) | −5.53027 | − | 0.620312i | −0.178768 | − | 0.0200518i | ||||
\(958\) | −7.99337 | + | 6.39586i | −0.258254 | + | 0.206641i | ||||
\(959\) | −7.69917 | −0.248619 | ||||||||
\(960\) | 33.7790 | − | 43.2185i | 1.09021 | − | 1.39487i | ||||
\(961\) | 53.7368 | 1.73345 | ||||||||
\(962\) | 7.56500 | − | 2.32836i | 0.243906 | − | 0.0750694i | ||||
\(963\) | −7.59405 | −0.244715 | ||||||||
\(964\) | 3.23546 | − | 14.3917i | 0.104207 | − | 0.463527i | ||||
\(965\) | 36.4242i | 1.17254i | ||||||||
\(966\) | −6.55508 | + | 5.24501i | −0.210906 | + | 0.168756i | ||||
\(967\) | 2.04860i | 0.0658785i | 0.999457 | + | 0.0329392i | \(0.0104868\pi\) | ||||
−0.999457 | + | 0.0329392i | \(0.989513\pi\) | |||||||
\(968\) | 30.2913 | − | 7.10187i | 0.973600 | − | 0.228263i | ||||
\(969\) | 81.0953i | 2.60516i | ||||||||
\(970\) | −5.56028 | − | 6.94909i | −0.178530 | − | 0.223122i | ||||
\(971\) | 24.7936i | 0.795663i | 0.917458 | + | 0.397832i | \(0.130237\pi\) | ||||
−0.917458 | + | 0.397832i | \(0.869763\pi\) | |||||||
\(972\) | −43.3999 | − | 9.75689i | −1.39205 | − | 0.312953i | ||||
\(973\) | − | 5.83492i | − | 0.187059i | ||||||
\(974\) | −19.8246 | − | 24.7762i | −0.635221 | − | 0.793881i | ||||
\(975\) | 8.75453 | − | 22.1594i | 0.280369 | − | 0.709668i | ||||
\(976\) | 17.6599 | − | 37.2915i | 0.565278 | − | 1.19367i | ||||
\(977\) | 41.2555i | 1.31988i | 0.751318 | + | 0.659940i | \(0.229418\pi\) | ||||
−0.751318 | + | 0.659940i | \(0.770582\pi\) | |||||||
\(978\) | −30.8870 | + | 24.7141i | −0.987657 | + | 0.790269i | ||||
\(979\) | 2.57021 | − | 22.9142i | 0.0821442 | − | 0.732341i | ||||
\(980\) | −36.2820 | − | 8.15669i | −1.15899 | − | 0.260556i | ||||
\(981\) | −11.2623 | −0.359579 | ||||||||
\(982\) | −18.6674 | − | 23.3300i | −0.595700 | − | 0.744490i | ||||
\(983\) | −27.3410 | −0.872042 | −0.436021 | − | 0.899936i | \(-0.643613\pi\) | ||||
−0.436021 | + | 0.899936i | \(0.643613\pi\) | |||||||
\(984\) | −7.69360 | − | 15.7779i | −0.245263 | − | 0.502982i | ||||
\(985\) | 6.84340i | 0.218049i | ||||||||
\(986\) | 3.53656 | + | 4.41990i | 0.112627 | + | 0.140758i | ||||
\(987\) | −13.3656 | −0.425433 | ||||||||
\(988\) | −33.0620 | − | 22.4923i | −1.05184 | − | 0.715577i | ||||
\(989\) | − | 38.0844i | − | 1.21101i | ||||||
\(990\) | −34.3823 | + | 21.7062i | −1.09274 | + | 0.689868i | ||||
\(991\) | 10.0759i | 0.320072i | 0.987111 | + | 0.160036i | \(0.0511611\pi\) | ||||
−0.987111 | + | 0.160036i | \(0.948839\pi\) | |||||||
\(992\) | 12.0010 | + | 50.6711i | 0.381031 | + | 1.60881i | ||||
\(993\) | − | 26.2719i | − | 0.833715i | ||||||
\(994\) | −1.82896 | + | 1.46344i | −0.0580112 | + | 0.0464174i | ||||
\(995\) | −48.8759 | −1.54947 | ||||||||
\(996\) | 3.07620 | − | 13.6833i | 0.0974733 | − | 0.433573i | ||||
\(997\) | − | 33.7038i | − | 1.06741i | −0.845670 | − | 0.533706i | \(-0.820799\pi\) | ||
0.845670 | − | 0.533706i | \(-0.179201\pi\) | |||||||
\(998\) | −7.41353 | − | 9.26523i | −0.234671 | − | 0.293286i | ||||
\(999\) | 0.501126 | 0.0158549 |
(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 | 572.2.b.c.571.18 | yes | 56 | |
4.3 | odd | 2 | inner | 572.2.b.c.571.20 | yes | 56 | |
11.10 | odd | 2 | inner | 572.2.b.c.571.40 | yes | 56 | |
13.12 | even | 2 | inner | 572.2.b.c.571.39 | yes | 56 | |
44.43 | even | 2 | inner | 572.2.b.c.571.38 | yes | 56 | |
52.51 | odd | 2 | inner | 572.2.b.c.571.37 | yes | 56 | |
143.142 | odd | 2 | inner | 572.2.b.c.571.17 | ✓ | 56 | |
572.571 | even | 2 | inner | 572.2.b.c.571.19 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.b.c.571.17 | ✓ | 56 | 143.142 | odd | 2 | inner | |
572.2.b.c.571.18 | yes | 56 | 1.1 | even | 1 | trivial | |
572.2.b.c.571.19 | yes | 56 | 572.571 | even | 2 | inner | |
572.2.b.c.571.20 | yes | 56 | 4.3 | odd | 2 | inner | |
572.2.b.c.571.37 | yes | 56 | 52.51 | odd | 2 | inner | |
572.2.b.c.571.38 | yes | 56 | 44.43 | even | 2 | inner | |
572.2.b.c.571.39 | yes | 56 | 13.12 | even | 2 | inner | |
572.2.b.c.571.40 | yes | 56 | 11.10 | odd | 2 | inner |