Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(419,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 26 x^{18} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.15 | ||
Root | \(1.23709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.419 |
Dual form | 1045.2.b.c.419.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.23709i | 0.874758i | 0.899277 | + | 0.437379i | \(0.144093\pi\) | ||||
−0.899277 | + | 0.437379i | \(0.855907\pi\) | |||||||
\(3\) | 2.07277i | 1.19671i | 0.801230 | + | 0.598357i | \(0.204180\pi\) | ||||
−0.801230 | + | 0.598357i | \(0.795820\pi\) | |||||||
\(4\) | 0.469598 | 0.234799 | ||||||||
\(5\) | 2.13362 | + | 0.669071i | 0.954185 | + | 0.299217i | ||||
\(6\) | −2.56421 | −1.04683 | ||||||||
\(7\) | 0.314194i | 0.118754i | 0.998236 | + | 0.0593771i | \(0.0189115\pi\) | ||||
−0.998236 | + | 0.0593771i | \(0.981089\pi\) | |||||||
\(8\) | 3.05513i | 1.08015i | ||||||||
\(9\) | −1.29637 | −0.432125 | ||||||||
\(10\) | −0.827703 | + | 2.63949i | −0.261743 | + | 0.834681i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.973368i | 0.280987i | ||||||||
\(13\) | 0.897047i | 0.248796i | 0.992232 | + | 0.124398i | \(0.0397000\pi\) | ||||
−0.992232 | + | 0.124398i | \(0.960300\pi\) | |||||||
\(14\) | −0.388688 | −0.103881 | ||||||||
\(15\) | −1.38683 | + | 4.42251i | −0.358078 | + | 1.14189i | ||||
\(16\) | −2.84028 | −0.710070 | ||||||||
\(17\) | − | 0.623404i | − | 0.151198i | −0.997138 | − | 0.0755988i | \(-0.975913\pi\) | ||
0.997138 | − | 0.0755988i | \(-0.0240868\pi\) | |||||||
\(18\) | − | 1.60374i | − | 0.378004i | ||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.00194 | + | 0.314194i | 0.224042 | + | 0.0702560i | ||||
\(21\) | −0.651252 | −0.142115 | ||||||||
\(22\) | 1.23709i | 0.263749i | ||||||||
\(23\) | − | 7.17386i | − | 1.49585i | −0.663782 | − | 0.747926i | \(-0.731050\pi\) | ||
0.663782 | − | 0.747926i | \(-0.268950\pi\) | |||||||
\(24\) | −6.33257 | −1.29263 | ||||||||
\(25\) | 4.10469 | + | 2.85509i | 0.820938 | + | 0.571018i | ||||
\(26\) | −1.10973 | −0.217636 | ||||||||
\(27\) | 3.53123i | 0.679585i | ||||||||
\(28\) | 0.147545i | 0.0278834i | ||||||||
\(29\) | −3.13576 | −0.582295 | −0.291148 | − | 0.956678i | \(-0.594037\pi\) | ||||
−0.291148 | + | 0.956678i | \(0.594037\pi\) | |||||||
\(30\) | −5.47106 | − | 1.71564i | −0.998874 | − | 0.313231i | ||||
\(31\) | −1.16919 | −0.209993 | −0.104997 | − | 0.994473i | \(-0.533483\pi\) | ||||
−0.104997 | + | 0.994473i | \(0.533483\pi\) | |||||||
\(32\) | 2.59655i | 0.459010i | ||||||||
\(33\) | 2.07277i | 0.360823i | ||||||||
\(34\) | 0.771209 | 0.132261 | ||||||||
\(35\) | −0.210218 | + | 0.670372i | −0.0355334 | + | 0.113314i | ||||
\(36\) | −0.608774 | −0.101462 | ||||||||
\(37\) | − | 1.42638i | − | 0.234496i | −0.993103 | − | 0.117248i | \(-0.962593\pi\) | ||
0.993103 | − | 0.117248i | \(-0.0374072\pi\) | |||||||
\(38\) | 1.23709i | 0.200683i | ||||||||
\(39\) | −1.85937 | −0.297738 | ||||||||
\(40\) | −2.04409 | + | 6.51848i | −0.323200 | + | 1.03066i | ||||
\(41\) | −1.02303 | −0.159771 | −0.0798855 | − | 0.996804i | \(-0.525455\pi\) | ||||
−0.0798855 | + | 0.996804i | \(0.525455\pi\) | |||||||
\(42\) | − | 0.805660i | − | 0.124316i | ||||||
\(43\) | − | 5.18696i | − | 0.791004i | −0.918465 | − | 0.395502i | \(-0.870571\pi\) | ||
0.918465 | − | 0.395502i | \(-0.129429\pi\) | |||||||
\(44\) | 0.469598 | 0.0707946 | ||||||||
\(45\) | −2.76597 | − | 0.867365i | −0.412327 | − | 0.129299i | ||||
\(46\) | 8.87474 | 1.30851 | ||||||||
\(47\) | 4.33573i | 0.632431i | 0.948687 | + | 0.316216i | \(0.102412\pi\) | ||||
−0.948687 | + | 0.316216i | \(0.897588\pi\) | |||||||
\(48\) | − | 5.88725i | − | 0.849751i | ||||||
\(49\) | 6.90128 | 0.985897 | ||||||||
\(50\) | −3.53201 | + | 5.07789i | −0.499502 | + | 0.718122i | ||||
\(51\) | 1.29217 | 0.180940 | ||||||||
\(52\) | 0.421252i | 0.0584171i | ||||||||
\(53\) | 3.29122i | 0.452084i | 0.974118 | + | 0.226042i | \(0.0725786\pi\) | ||||
−0.974118 | + | 0.226042i | \(0.927421\pi\) | |||||||
\(54\) | −4.36846 | −0.594472 | ||||||||
\(55\) | 2.13362 | + | 0.669071i | 0.287698 | + | 0.0902175i | ||||
\(56\) | −0.959903 | −0.128272 | ||||||||
\(57\) | 2.07277i | 0.274545i | ||||||||
\(58\) | − | 3.87922i | − | 0.509367i | ||||||
\(59\) | 1.12009 | 0.145823 | 0.0729116 | − | 0.997338i | \(-0.476771\pi\) | ||||
0.0729116 | + | 0.997338i | \(0.476771\pi\) | |||||||
\(60\) | −0.651252 | + | 2.07680i | −0.0840763 | + | 0.268114i | ||||
\(61\) | −5.74190 | −0.735175 | −0.367587 | − | 0.929989i | \(-0.619816\pi\) | ||||
−0.367587 | + | 0.929989i | \(0.619816\pi\) | |||||||
\(62\) | − | 1.44640i | − | 0.183693i | ||||||
\(63\) | − | 0.407313i | − | 0.0513166i | ||||||
\(64\) | −8.89275 | −1.11159 | ||||||||
\(65\) | −0.600188 | + | 1.91396i | −0.0744442 | + | 0.237398i | ||||
\(66\) | −2.56421 | −0.315633 | ||||||||
\(67\) | − | 14.3904i | − | 1.75807i | −0.476759 | − | 0.879034i | \(-0.658188\pi\) | ||
0.476759 | − | 0.879034i | \(-0.341812\pi\) | |||||||
\(68\) | − | 0.292749i | − | 0.0355010i | ||||||
\(69\) | 14.8698 | 1.79011 | ||||||||
\(70\) | −0.829313 | − | 0.260060i | −0.0991219 | − | 0.0310831i | ||||
\(71\) | −5.19451 | −0.616475 | −0.308237 | − | 0.951310i | \(-0.599739\pi\) | ||||
−0.308237 | + | 0.951310i | \(0.599739\pi\) | |||||||
\(72\) | − | 3.96058i | − | 0.466759i | ||||||
\(73\) | − | 14.1336i | − | 1.65422i | −0.562044 | − | 0.827108i | \(-0.689985\pi\) | ||
0.562044 | − | 0.827108i | \(-0.310015\pi\) | |||||||
\(74\) | 1.76457 | 0.205127 | ||||||||
\(75\) | −5.91794 | + | 8.50807i | −0.683345 | + | 0.982428i | ||||
\(76\) | 0.469598 | 0.0538666 | ||||||||
\(77\) | 0.314194i | 0.0358058i | ||||||||
\(78\) | − | 2.30022i | − | 0.260449i | ||||||
\(79\) | −4.00598 | −0.450708 | −0.225354 | − | 0.974277i | \(-0.572354\pi\) | ||||
−0.225354 | + | 0.974277i | \(0.572354\pi\) | |||||||
\(80\) | −6.06009 | − | 1.90035i | −0.677538 | − | 0.212465i | ||||
\(81\) | −11.2085 | −1.24539 | ||||||||
\(82\) | − | 1.26559i | − | 0.139761i | ||||||
\(83\) | − | 1.65116i | − | 0.181239i | −0.995886 | − | 0.0906194i | \(-0.971115\pi\) | ||
0.995886 | − | 0.0906194i | \(-0.0288847\pi\) | |||||||
\(84\) | −0.305827 | −0.0333684 | ||||||||
\(85\) | 0.417101 | − | 1.33011i | 0.0452410 | − | 0.144270i | ||||
\(86\) | 6.41676 | 0.691937 | ||||||||
\(87\) | − | 6.49970i | − | 0.696841i | ||||||
\(88\) | 3.05513i | 0.325677i | ||||||||
\(89\) | 13.9446 | 1.47812 | 0.739062 | − | 0.673638i | \(-0.235269\pi\) | ||||
0.739062 | + | 0.673638i | \(0.235269\pi\) | |||||||
\(90\) | 1.07301 | − | 3.42177i | 0.113105 | − | 0.360686i | ||||
\(91\) | −0.281847 | −0.0295456 | ||||||||
\(92\) | − | 3.36883i | − | 0.351225i | ||||||
\(93\) | − | 2.42347i | − | 0.251302i | ||||||
\(94\) | −5.36371 | −0.553224 | ||||||||
\(95\) | 2.13362 | + | 0.669071i | 0.218905 | + | 0.0686452i | ||||
\(96\) | −5.38206 | −0.549304 | ||||||||
\(97\) | − | 0.809173i | − | 0.0821591i | −0.999156 | − | 0.0410795i | \(-0.986920\pi\) | ||
0.999156 | − | 0.0410795i | \(-0.0130797\pi\) | |||||||
\(98\) | 8.53754i | 0.862421i | ||||||||
\(99\) | −1.29637 | −0.130290 | ||||||||
\(100\) | 1.92755 | + | 1.34074i | 0.192755 | + | 0.134074i | ||||
\(101\) | 7.88444 | 0.784531 | 0.392266 | − | 0.919852i | \(-0.371691\pi\) | ||||
0.392266 | + | 0.919852i | \(0.371691\pi\) | |||||||
\(102\) | 1.59854i | 0.158279i | ||||||||
\(103\) | − | 9.45660i | − | 0.931787i | −0.884841 | − | 0.465893i | \(-0.845733\pi\) | ||
0.884841 | − | 0.465893i | \(-0.154267\pi\) | |||||||
\(104\) | −2.74059 | −0.268737 | ||||||||
\(105\) | −1.38953 | − | 0.435734i | −0.135604 | − | 0.0425233i | ||||
\(106\) | −4.07155 | −0.395464 | ||||||||
\(107\) | − | 4.43836i | − | 0.429072i | −0.976716 | − | 0.214536i | \(-0.931176\pi\) | ||
0.976716 | − | 0.214536i | \(-0.0688240\pi\) | |||||||
\(108\) | 1.65826i | 0.159566i | ||||||||
\(109\) | −11.4134 | −1.09321 | −0.546605 | − | 0.837391i | \(-0.684080\pi\) | ||||
−0.546605 | + | 0.837391i | \(0.684080\pi\) | |||||||
\(110\) | −0.827703 | + | 2.63949i | −0.0789184 | + | 0.251666i | ||||
\(111\) | 2.95656 | 0.280624 | ||||||||
\(112\) | − | 0.892400i | − | 0.0843239i | ||||||
\(113\) | 9.60198i | 0.903278i | 0.892201 | + | 0.451639i | \(0.149160\pi\) | ||||
−0.892201 | + | 0.451639i | \(0.850840\pi\) | |||||||
\(114\) | −2.56421 | −0.240160 | ||||||||
\(115\) | 4.79982 | − | 15.3063i | 0.447585 | − | 1.42732i | ||||
\(116\) | −1.47254 | −0.136722 | ||||||||
\(117\) | − | 1.16291i | − | 0.107511i | ||||||
\(118\) | 1.38566i | 0.127560i | ||||||||
\(119\) | 0.195870 | 0.0179554 | ||||||||
\(120\) | −13.5113 | − | 4.23694i | −1.23341 | − | 0.386778i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 7.10327i | − | 0.643100i | ||||||
\(123\) | − | 2.12051i | − | 0.191200i | ||||||
\(124\) | −0.549051 | −0.0493062 | ||||||||
\(125\) | 6.84760 | + | 8.83801i | 0.612468 | + | 0.790495i | ||||
\(126\) | 0.503885 | 0.0448896 | ||||||||
\(127\) | 1.63584i | 0.145158i | 0.997363 | + | 0.0725788i | \(0.0231229\pi\) | ||||
−0.997363 | + | 0.0725788i | \(0.976877\pi\) | |||||||
\(128\) | − | 5.80805i | − | 0.513364i | ||||||
\(129\) | 10.7514 | 0.946606 | ||||||||
\(130\) | −2.36775 | − | 0.742489i | −0.207665 | − | 0.0651206i | ||||
\(131\) | −19.2059 | −1.67803 | −0.839014 | − | 0.544110i | \(-0.816867\pi\) | ||||
−0.839014 | + | 0.544110i | \(0.816867\pi\) | |||||||
\(132\) | 0.973368i | 0.0847209i | ||||||||
\(133\) | 0.314194i | 0.0272441i | ||||||||
\(134\) | 17.8023 | 1.53788 | ||||||||
\(135\) | −2.36264 | + | 7.53430i | −0.203344 | + | 0.648449i | ||||
\(136\) | 1.90458 | 0.163316 | ||||||||
\(137\) | − | 16.2421i | − | 1.38766i | −0.720140 | − | 0.693829i | \(-0.755923\pi\) | ||
0.720140 | − | 0.693829i | \(-0.244077\pi\) | |||||||
\(138\) | 18.3953i | 1.56591i | ||||||||
\(139\) | 0.527173 | 0.0447142 | 0.0223571 | − | 0.999750i | \(-0.492883\pi\) | ||||
0.0223571 | + | 0.999750i | \(0.492883\pi\) | |||||||
\(140\) | −0.0987180 | + | 0.314805i | −0.00834320 | + | 0.0266059i | ||||
\(141\) | −8.98697 | −0.756839 | ||||||||
\(142\) | − | 6.42609i | − | 0.539266i | ||||||
\(143\) | 0.897047i | 0.0750149i | ||||||||
\(144\) | 3.68207 | 0.306839 | ||||||||
\(145\) | −6.69052 | − | 2.09804i | −0.555617 | − | 0.174233i | ||||
\(146\) | 17.4846 | 1.44704 | ||||||||
\(147\) | 14.3048i | 1.17984i | ||||||||
\(148\) | − | 0.669826i | − | 0.0550594i | ||||||
\(149\) | 6.51164 | 0.533454 | 0.266727 | − | 0.963772i | \(-0.414058\pi\) | ||||
0.266727 | + | 0.963772i | \(0.414058\pi\) | |||||||
\(150\) | −10.5253 | − | 7.32105i | −0.859386 | − | 0.597761i | ||||
\(151\) | −15.0375 | −1.22373 | −0.611867 | − | 0.790960i | \(-0.709581\pi\) | ||||
−0.611867 | + | 0.790960i | \(0.709581\pi\) | |||||||
\(152\) | 3.05513i | 0.247803i | ||||||||
\(153\) | 0.808164i | 0.0653362i | ||||||||
\(154\) | −0.388688 | −0.0313214 | ||||||||
\(155\) | −2.49462 | − | 0.782273i | −0.200372 | − | 0.0628337i | ||||
\(156\) | −0.873158 | −0.0699086 | ||||||||
\(157\) | 5.33516i | 0.425792i | 0.977075 | + | 0.212896i | \(0.0682895\pi\) | ||||
−0.977075 | + | 0.212896i | \(0.931710\pi\) | |||||||
\(158\) | − | 4.95578i | − | 0.394260i | ||||||
\(159\) | −6.82194 | −0.541015 | ||||||||
\(160\) | −1.73728 | + | 5.54007i | −0.137344 | + | 0.437981i | ||||
\(161\) | 2.25399 | 0.177639 | ||||||||
\(162\) | − | 13.8660i | − | 1.08942i | ||||||
\(163\) | 0.764022i | 0.0598428i | 0.999552 | + | 0.0299214i | \(0.00952570\pi\) | ||||
−0.999552 | + | 0.0299214i | \(0.990474\pi\) | |||||||
\(164\) | −0.480414 | −0.0375141 | ||||||||
\(165\) | −1.38683 | + | 4.42251i | −0.107965 | + | 0.344292i | ||||
\(166\) | 2.04265 | 0.158540 | ||||||||
\(167\) | 1.61649i | 0.125087i | 0.998042 | + | 0.0625437i | \(0.0199213\pi\) | ||||
−0.998042 | + | 0.0625437i | \(0.980079\pi\) | |||||||
\(168\) | − | 1.98966i | − | 0.153505i | ||||||
\(169\) | 12.1953 | 0.938100 | ||||||||
\(170\) | 1.64547 | + | 0.515993i | 0.126202 | + | 0.0395749i | ||||
\(171\) | −1.29637 | −0.0991362 | ||||||||
\(172\) | − | 2.43579i | − | 0.185727i | ||||||
\(173\) | 11.0950i | 0.843537i | 0.906704 | + | 0.421769i | \(0.138591\pi\) | ||||
−0.906704 | + | 0.421769i | \(0.861409\pi\) | |||||||
\(174\) | 8.04074 | 0.609567 | ||||||||
\(175\) | −0.897052 | + | 1.28967i | −0.0678108 | + | 0.0974899i | ||||
\(176\) | −2.84028 | −0.214094 | ||||||||
\(177\) | 2.32169i | 0.174509i | ||||||||
\(178\) | 17.2508i | 1.29300i | ||||||||
\(179\) | 24.8558 | 1.85781 | 0.928905 | − | 0.370317i | \(-0.120751\pi\) | ||||
0.928905 | + | 0.370317i | \(0.120751\pi\) | |||||||
\(180\) | −1.29889 | − | 0.407313i | −0.0968139 | − | 0.0303593i | ||||
\(181\) | 20.1163 | 1.49524 | 0.747618 | − | 0.664129i | \(-0.231197\pi\) | ||||
0.747618 | + | 0.664129i | \(0.231197\pi\) | |||||||
\(182\) | − | 0.348671i | − | 0.0258452i | ||||||
\(183\) | − | 11.9016i | − | 0.879794i | ||||||
\(184\) | 21.9170 | 1.61575 | ||||||||
\(185\) | 0.954350 | − | 3.04336i | 0.0701652 | − | 0.223752i | ||||
\(186\) | 2.99806 | 0.219828 | ||||||||
\(187\) | − | 0.623404i | − | 0.0455878i | ||||||
\(188\) | 2.03605i | 0.148494i | ||||||||
\(189\) | −1.10949 | −0.0807036 | ||||||||
\(190\) | −0.827703 | + | 2.63949i | −0.0600479 | + | 0.191489i | ||||
\(191\) | 10.2621 | 0.742542 | 0.371271 | − | 0.928524i | \(-0.378922\pi\) | ||||
0.371271 | + | 0.928524i | \(0.378922\pi\) | |||||||
\(192\) | − | 18.4326i | − | 1.33026i | ||||||
\(193\) | 15.1459i | 1.09023i | 0.838363 | + | 0.545113i | \(0.183513\pi\) | ||||
−0.838363 | + | 0.545113i | \(0.816487\pi\) | |||||||
\(194\) | 1.00102 | 0.0718693 | ||||||||
\(195\) | −3.96720 | − | 1.24405i | −0.284097 | − | 0.0890884i | ||||
\(196\) | 3.24083 | 0.231488 | ||||||||
\(197\) | 23.2367i | 1.65554i | 0.561065 | + | 0.827772i | \(0.310392\pi\) | ||||
−0.561065 | + | 0.827772i | \(0.689608\pi\) | |||||||
\(198\) | − | 1.60374i | − | 0.113973i | ||||||
\(199\) | 1.07244 | 0.0760232 | 0.0380116 | − | 0.999277i | \(-0.487898\pi\) | ||||
0.0380116 | + | 0.999277i | \(0.487898\pi\) | |||||||
\(200\) | −8.72265 | + | 12.5403i | −0.616785 | + | 0.886736i | ||||
\(201\) | 29.8280 | 2.10391 | ||||||||
\(202\) | 9.75380i | 0.686275i | ||||||||
\(203\) | − | 0.985236i | − | 0.0691500i | ||||||
\(204\) | 0.606801 | 0.0424846 | ||||||||
\(205\) | −2.18277 | − | 0.684481i | −0.152451 | − | 0.0478063i | ||||
\(206\) | 11.6987 | 0.815087 | ||||||||
\(207\) | 9.30000i | 0.646395i | ||||||||
\(208\) | − | 2.54787i | − | 0.176663i | ||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0.539044 | − | 1.71898i | 0.0371975 | − | 0.118621i | ||||
\(211\) | −11.4154 | −0.785868 | −0.392934 | − | 0.919567i | \(-0.628540\pi\) | ||||
−0.392934 | + | 0.919567i | \(0.628540\pi\) | |||||||
\(212\) | 1.54555i | 0.106149i | ||||||||
\(213\) | − | 10.7670i | − | 0.737744i | ||||||
\(214\) | 5.49067 | 0.375334 | ||||||||
\(215\) | 3.47044 | − | 11.0670i | 0.236682 | − | 0.754764i | ||||
\(216\) | −10.7883 | −0.734053 | ||||||||
\(217\) | − | 0.367354i | − | 0.0249376i | ||||||
\(218\) | − | 14.1195i | − | 0.956294i | ||||||
\(219\) | 29.2957 | 1.97962 | ||||||||
\(220\) | 1.00194 | + | 0.314194i | 0.0675511 | + | 0.0211830i | ||||
\(221\) | 0.559223 | 0.0376174 | ||||||||
\(222\) | 3.65755i | 0.245478i | ||||||||
\(223\) | 14.5284i | 0.972893i | 0.873710 | + | 0.486447i | \(0.161707\pi\) | ||||
−0.873710 | + | 0.486447i | \(0.838293\pi\) | |||||||
\(224\) | −0.815823 | −0.0545094 | ||||||||
\(225\) | −5.32121 | − | 3.70126i | −0.354747 | − | 0.246751i | ||||
\(226\) | −11.8785 | −0.790149 | ||||||||
\(227\) | 12.3529i | 0.819890i | 0.912110 | + | 0.409945i | \(0.134452\pi\) | ||||
−0.912110 | + | 0.409945i | \(0.865548\pi\) | |||||||
\(228\) | 0.973368i | 0.0644629i | ||||||||
\(229\) | −1.41187 | −0.0932990 | −0.0466495 | − | 0.998911i | \(-0.514854\pi\) | ||||
−0.0466495 | + | 0.998911i | \(0.514854\pi\) | |||||||
\(230\) | 18.9353 | + | 5.93783i | 1.24856 | + | 0.391529i | ||||
\(231\) | −0.651252 | −0.0428493 | ||||||||
\(232\) | − | 9.58013i | − | 0.628966i | ||||||
\(233\) | 2.09358i | 0.137155i | 0.997646 | + | 0.0685774i | \(0.0218460\pi\) | ||||
−0.997646 | + | 0.0685774i | \(0.978154\pi\) | |||||||
\(234\) | 1.43863 | 0.0940460 | ||||||||
\(235\) | −2.90091 | + | 9.25081i | −0.189234 | + | 0.603456i | ||||
\(236\) | 0.525992 | 0.0342392 | ||||||||
\(237\) | − | 8.30348i | − | 0.539369i | ||||||
\(238\) | 0.242309i | 0.0157066i | ||||||||
\(239\) | 24.3275 | 1.57361 | 0.786807 | − | 0.617199i | \(-0.211733\pi\) | ||||
0.786807 | + | 0.617199i | \(0.211733\pi\) | |||||||
\(240\) | 3.93899 | − | 12.5612i | 0.254260 | − | 0.810820i | ||||
\(241\) | 8.11039 | 0.522436 | 0.261218 | − | 0.965280i | \(-0.415876\pi\) | ||||
0.261218 | + | 0.965280i | \(0.415876\pi\) | |||||||
\(242\) | 1.23709i | 0.0795234i | ||||||||
\(243\) | − | 12.6390i | − | 0.810795i | ||||||
\(244\) | −2.69638 | −0.172618 | ||||||||
\(245\) | 14.7247 | + | 4.61745i | 0.940728 | + | 0.294998i | ||||
\(246\) | 2.62327 | 0.167254 | ||||||||
\(247\) | 0.897047i | 0.0570778i | ||||||||
\(248\) | − | 3.57203i | − | 0.226824i | ||||||
\(249\) | 3.42248 | 0.216891 | ||||||||
\(250\) | −10.9334 | + | 8.47113i | −0.691492 | + | 0.535761i | ||||
\(251\) | −15.8691 | −1.00165 | −0.500824 | − | 0.865549i | \(-0.666970\pi\) | ||||
−0.500824 | + | 0.865549i | \(0.666970\pi\) | |||||||
\(252\) | − | 0.191273i | − | 0.0120491i | ||||||
\(253\) | − | 7.17386i | − | 0.451017i | ||||||
\(254\) | −2.02369 | −0.126978 | ||||||||
\(255\) | 2.75701 | + | 0.864554i | 0.172650 | + | 0.0541405i | ||||
\(256\) | −10.6004 | −0.662524 | ||||||||
\(257\) | − | 24.7918i | − | 1.54647i | −0.634120 | − | 0.773234i | \(-0.718638\pi\) | ||
0.634120 | − | 0.773234i | \(-0.281362\pi\) | |||||||
\(258\) | 13.3005i | 0.828051i | ||||||||
\(259\) | 0.448161 | 0.0278474 | ||||||||
\(260\) | −0.281847 | + | 0.898792i | −0.0174794 | + | 0.0557407i | ||||
\(261\) | 4.06511 | 0.251624 | ||||||||
\(262\) | − | 23.7595i | − | 1.46787i | ||||||
\(263\) | − | 0.927458i | − | 0.0571895i | −0.999591 | − | 0.0285948i | \(-0.990897\pi\) | ||
0.999591 | − | 0.0285948i | \(-0.00910323\pi\) | |||||||
\(264\) | −6.33257 | −0.389743 | ||||||||
\(265\) | −2.20206 | + | 7.02222i | −0.135271 | + | 0.431371i | ||||
\(266\) | −0.388688 | −0.0238320 | ||||||||
\(267\) | 28.9039i | 1.76889i | ||||||||
\(268\) | − | 6.75771i | − | 0.412793i | ||||||
\(269\) | 19.3925 | 1.18238 | 0.591190 | − | 0.806533i | \(-0.298658\pi\) | ||||
0.591190 | + | 0.806533i | \(0.298658\pi\) | |||||||
\(270\) | −9.32064 | − | 2.92281i | −0.567236 | − | 0.177876i | ||||
\(271\) | −22.8304 | −1.38685 | −0.693424 | − | 0.720529i | \(-0.743899\pi\) | ||||
−0.693424 | + | 0.720529i | \(0.743899\pi\) | |||||||
\(272\) | 1.77064i | 0.107361i | ||||||||
\(273\) | − | 0.584204i | − | 0.0353576i | ||||||
\(274\) | 20.0930 | 1.21386 | ||||||||
\(275\) | 4.10469 | + | 2.85509i | 0.247522 | + | 0.172168i | ||||
\(276\) | 6.98281 | 0.420316 | ||||||||
\(277\) | 10.5885i | 0.636203i | 0.948057 | + | 0.318102i | \(0.103045\pi\) | ||||
−0.948057 | + | 0.318102i | \(0.896955\pi\) | |||||||
\(278\) | 0.652162i | 0.0391141i | ||||||||
\(279\) | 1.51571 | 0.0907432 | ||||||||
\(280\) | −2.04807 | − | 0.642243i | −0.122396 | − | 0.0383813i | ||||
\(281\) | −6.43575 | −0.383925 | −0.191962 | − | 0.981402i | \(-0.561485\pi\) | ||||
−0.191962 | + | 0.981402i | \(0.561485\pi\) | |||||||
\(282\) | − | 11.1177i | − | 0.662051i | ||||||
\(283\) | − | 10.8999i | − | 0.647930i | −0.946069 | − | 0.323965i | \(-0.894984\pi\) | ||
0.946069 | − | 0.323965i | \(-0.105016\pi\) | |||||||
\(284\) | −2.43933 | −0.144748 | ||||||||
\(285\) | −1.38683 | + | 4.42251i | −0.0821487 | + | 0.261967i | ||||
\(286\) | −1.10973 | −0.0656198 | ||||||||
\(287\) | − | 0.321431i | − | 0.0189735i | ||||||
\(288\) | − | 3.36610i | − | 0.198350i | ||||||
\(289\) | 16.6114 | 0.977139 | ||||||||
\(290\) | 2.59548 | − | 8.27680i | 0.152412 | − | 0.486030i | ||||
\(291\) | 1.67723 | 0.0983209 | ||||||||
\(292\) | − | 6.63712i | − | 0.388408i | ||||||
\(293\) | 6.58240i | 0.384548i | 0.981341 | + | 0.192274i | \(0.0615862\pi\) | ||||
−0.981341 | + | 0.192274i | \(0.938414\pi\) | |||||||
\(294\) | −17.6963 | −1.03207 | ||||||||
\(295\) | 2.38985 | + | 0.749419i | 0.139142 | + | 0.0436329i | ||||
\(296\) | 4.35778 | 0.253291 | ||||||||
\(297\) | 3.53123i | 0.204902i | ||||||||
\(298\) | 8.05551i | 0.466643i | ||||||||
\(299\) | 6.43529 | 0.372163 | ||||||||
\(300\) | −2.77905 | + | 3.99537i | −0.160449 | + | 0.230673i | ||||
\(301\) | 1.62971 | 0.0939351 | ||||||||
\(302\) | − | 18.6028i | − | 1.07047i | ||||||
\(303\) | 16.3426i | 0.938860i | ||||||||
\(304\) | −2.84028 | −0.162901 | ||||||||
\(305\) | −12.2510 | − | 3.84173i | −0.701493 | − | 0.219977i | ||||
\(306\) | −0.999775 | −0.0571533 | ||||||||
\(307\) | 7.65811i | 0.437071i | 0.975829 | + | 0.218536i | \(0.0701280\pi\) | ||||
−0.975829 | + | 0.218536i | \(0.929872\pi\) | |||||||
\(308\) | 0.147545i | 0.00840716i | ||||||||
\(309\) | 19.6014 | 1.11508 | ||||||||
\(310\) | 0.967745 | − | 3.08608i | 0.0549642 | − | 0.175277i | ||||
\(311\) | −2.44749 | −0.138785 | −0.0693923 | − | 0.997589i | \(-0.522106\pi\) | ||||
−0.0693923 | + | 0.997589i | \(0.522106\pi\) | |||||||
\(312\) | − | 5.68062i | − | 0.321602i | ||||||
\(313\) | 9.40612i | 0.531665i | 0.964019 | + | 0.265833i | \(0.0856469\pi\) | ||||
−0.964019 | + | 0.265833i | \(0.914353\pi\) | |||||||
\(314\) | −6.60009 | −0.372465 | ||||||||
\(315\) | 0.272521 | − | 0.869052i | 0.0153548 | − | 0.0489656i | ||||
\(316\) | −1.88120 | −0.105826 | ||||||||
\(317\) | 15.3518i | 0.862243i | 0.902294 | + | 0.431121i | \(0.141882\pi\) | ||||
−0.902294 | + | 0.431121i | \(0.858118\pi\) | |||||||
\(318\) | − | 8.43938i | − | 0.473257i | ||||||
\(319\) | −3.13576 | −0.175569 | ||||||||
\(320\) | −18.9738 | − | 5.94988i | −1.06067 | − | 0.332608i | ||||
\(321\) | 9.19969 | 0.513477 | ||||||||
\(322\) | 2.78839i | 0.155391i | ||||||||
\(323\) | − | 0.623404i | − | 0.0346871i | ||||||
\(324\) | −5.26351 | −0.292417 | ||||||||
\(325\) | −2.56115 | + | 3.68210i | −0.142067 | + | 0.204246i | ||||
\(326\) | −0.945167 | −0.0523480 | ||||||||
\(327\) | − | 23.6574i | − | 1.30826i | ||||||
\(328\) | − | 3.12549i | − | 0.172577i | ||||||
\(329\) | −1.36226 | −0.0751039 | ||||||||
\(330\) | −5.47106 | − | 1.71564i | −0.301172 | − | 0.0944428i | ||||
\(331\) | −30.7373 | −1.68947 | −0.844737 | − | 0.535182i | \(-0.820243\pi\) | ||||
−0.844737 | + | 0.535182i | \(0.820243\pi\) | |||||||
\(332\) | − | 0.775384i | − | 0.0425547i | ||||||
\(333\) | 1.84912i | 0.101331i | ||||||||
\(334\) | −1.99975 | −0.109421 | ||||||||
\(335\) | 9.62820 | − | 30.7037i | 0.526045 | − | 1.67752i | ||||
\(336\) | 1.84974 | 0.100912 | ||||||||
\(337\) | − | 12.0108i | − | 0.654272i | −0.944977 | − | 0.327136i | \(-0.893917\pi\) | ||
0.944977 | − | 0.327136i | \(-0.106083\pi\) | |||||||
\(338\) | 15.0867i | 0.820611i | ||||||||
\(339\) | −19.9027 | −1.08097 | ||||||||
\(340\) | 0.195870 | − | 0.624616i | 0.0106225 | − | 0.0338746i | ||||
\(341\) | −1.16919 | −0.0633154 | ||||||||
\(342\) | − | 1.60374i | − | 0.0867201i | ||||||
\(343\) | 4.36770i | 0.235834i | ||||||||
\(344\) | 15.8468 | 0.854403 | ||||||||
\(345\) | 31.7264 | + | 9.94892i | 1.70809 | + | 0.535632i | ||||
\(346\) | −13.7256 | −0.737891 | ||||||||
\(347\) | − | 6.01606i | − | 0.322959i | −0.986876 | − | 0.161480i | \(-0.948373\pi\) | ||
0.986876 | − | 0.161480i | \(-0.0516266\pi\) | |||||||
\(348\) | − | 3.05225i | − | 0.163618i | ||||||
\(349\) | 31.5085 | 1.68661 | 0.843304 | − | 0.537436i | \(-0.180607\pi\) | ||||
0.843304 | + | 0.537436i | \(0.180607\pi\) | |||||||
\(350\) | −1.59544 | − | 1.10974i | −0.0852800 | − | 0.0593180i | ||||
\(351\) | −3.16768 | −0.169078 | ||||||||
\(352\) | 2.59655i | 0.138397i | ||||||||
\(353\) | 13.6680i | 0.727472i | 0.931502 | + | 0.363736i | \(0.118499\pi\) | ||||
−0.931502 | + | 0.363736i | \(0.881501\pi\) | |||||||
\(354\) | −2.87215 | −0.152653 | ||||||||
\(355\) | −11.0831 | − | 3.47549i | −0.588231 | − | 0.184460i | ||||
\(356\) | 6.54835 | 0.347062 | ||||||||
\(357\) | 0.405993i | 0.0214874i | ||||||||
\(358\) | 30.7490i | 1.62513i | ||||||||
\(359\) | 16.9144 | 0.892708 | 0.446354 | − | 0.894857i | \(-0.352722\pi\) | ||||
0.446354 | + | 0.894857i | \(0.352722\pi\) | |||||||
\(360\) | 2.64991 | − | 8.45039i | 0.139663 | − | 0.445375i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 24.8858i | 1.30797i | ||||||||
\(363\) | 2.07277i | 0.108792i | ||||||||
\(364\) | −0.132355 | −0.00693728 | ||||||||
\(365\) | 9.45639 | − | 30.1558i | 0.494970 | − | 1.57843i | ||||
\(366\) | 14.7234 | 0.769606 | ||||||||
\(367\) | − | 21.8818i | − | 1.14222i | −0.820874 | − | 0.571110i | \(-0.806513\pi\) | ||
0.820874 | − | 0.571110i | \(-0.193487\pi\) | |||||||
\(368\) | 20.3758i | 1.06216i | ||||||||
\(369\) | 1.32623 | 0.0690409 | ||||||||
\(370\) | 3.76492 | + | 1.18062i | 0.195729 | + | 0.0613776i | ||||
\(371\) | −1.03408 | −0.0536869 | ||||||||
\(372\) | − | 1.13806i | − | 0.0590054i | ||||||
\(373\) | − | 21.9840i | − | 1.13829i | −0.822239 | − | 0.569143i | \(-0.807275\pi\) | ||
0.822239 | − | 0.569143i | \(-0.192725\pi\) | |||||||
\(374\) | 0.771209 | 0.0398783 | ||||||||
\(375\) | −18.3192 | + | 14.1935i | −0.945997 | + | 0.732949i | ||||
\(376\) | −13.2462 | −0.683120 | ||||||||
\(377\) | − | 2.81292i | − | 0.144873i | ||||||
\(378\) | − | 1.37254i | − | 0.0705961i | ||||||
\(379\) | −16.3858 | −0.841682 | −0.420841 | − | 0.907134i | \(-0.638265\pi\) | ||||
−0.420841 | + | 0.907134i | \(0.638265\pi\) | |||||||
\(380\) | 1.00194 | + | 0.314194i | 0.0513987 | + | 0.0161178i | ||||
\(381\) | −3.39073 | −0.173712 | ||||||||
\(382\) | 12.6952i | 0.649545i | ||||||||
\(383\) | 7.01836i | 0.358621i | 0.983792 | + | 0.179311i | \(0.0573867\pi\) | ||||
−0.983792 | + | 0.179311i | \(0.942613\pi\) | |||||||
\(384\) | 12.0388 | 0.614350 | ||||||||
\(385\) | −0.210218 | + | 0.670372i | −0.0107137 | + | 0.0341653i | ||||
\(386\) | −18.7369 | −0.953684 | ||||||||
\(387\) | 6.72424i | 0.341812i | ||||||||
\(388\) | − | 0.379986i | − | 0.0192909i | ||||||
\(389\) | −24.4290 | −1.23860 | −0.619300 | − | 0.785154i | \(-0.712584\pi\) | ||||
−0.619300 | + | 0.785154i | \(0.712584\pi\) | |||||||
\(390\) | 1.53901 | − | 4.90780i | 0.0779307 | − | 0.248516i | ||||
\(391\) | −4.47221 | −0.226169 | ||||||||
\(392\) | 21.0843i | 1.06492i | ||||||||
\(393\) | − | 39.8094i | − | 2.00812i | ||||||
\(394\) | −28.7459 | −1.44820 | ||||||||
\(395\) | −8.54725 | − | 2.68028i | −0.430059 | − | 0.134860i | ||||
\(396\) | −0.608774 | −0.0305921 | ||||||||
\(397\) | 20.2563i | 1.01663i | 0.861170 | + | 0.508317i | \(0.169732\pi\) | ||||
−0.861170 | + | 0.508317i | \(0.830268\pi\) | |||||||
\(398\) | 1.32671i | 0.0665019i | ||||||||
\(399\) | −0.651252 | −0.0326034 | ||||||||
\(400\) | −11.6585 | − | 8.10925i | −0.582924 | − | 0.405463i | ||||
\(401\) | 3.36148 | 0.167864 | 0.0839321 | − | 0.996471i | \(-0.473252\pi\) | ||||
0.0839321 | + | 0.996471i | \(0.473252\pi\) | |||||||
\(402\) | 36.9001i | 1.84041i | ||||||||
\(403\) | − | 1.04882i | − | 0.0522455i | ||||||
\(404\) | 3.70252 | 0.184207 | ||||||||
\(405\) | −23.9148 | − | 7.49930i | −1.18834 | − | 0.372643i | ||||
\(406\) | 1.21883 | 0.0604895 | ||||||||
\(407\) | − | 1.42638i | − | 0.0707031i | ||||||
\(408\) | 3.94775i | 0.195443i | ||||||||
\(409\) | −33.5373 | −1.65832 | −0.829158 | − | 0.559015i | \(-0.811179\pi\) | ||||
−0.829158 | + | 0.559015i | \(0.811179\pi\) | |||||||
\(410\) | 0.846768 | − | 2.70029i | 0.0418189 | − | 0.133358i | ||||
\(411\) | 33.6662 | 1.66063 | ||||||||
\(412\) | − | 4.44080i | − | 0.218783i | ||||||
\(413\) | 0.351926i | 0.0173171i | ||||||||
\(414\) | −11.5050 | −0.565439 | ||||||||
\(415\) | 1.10475 | − | 3.52296i | 0.0542298 | − | 0.172935i | ||||
\(416\) | −2.32923 | −0.114200 | ||||||||
\(417\) | 1.09271i | 0.0535101i | ||||||||
\(418\) | 1.23709i | 0.0605083i | ||||||||
\(419\) | −35.9922 | −1.75834 | −0.879168 | − | 0.476513i | \(-0.841901\pi\) | ||||
−0.879168 | + | 0.476513i | \(0.841901\pi\) | |||||||
\(420\) | −0.652519 | − | 0.204620i | −0.0318397 | − | 0.00998442i | ||||
\(421\) | −15.5715 | −0.758907 | −0.379453 | − | 0.925211i | \(-0.623888\pi\) | ||||
−0.379453 | + | 0.925211i | \(0.623888\pi\) | |||||||
\(422\) | − | 14.1219i | − | 0.687444i | ||||||
\(423\) | − | 5.62072i | − | 0.273289i | ||||||
\(424\) | −10.0551 | −0.488318 | ||||||||
\(425\) | 1.77987 | − | 2.55888i | 0.0863365 | − | 0.124124i | ||||
\(426\) | 13.3198 | 0.645347 | ||||||||
\(427\) | − | 1.80407i | − | 0.0873051i | ||||||
\(428\) | − | 2.08424i | − | 0.100746i | ||||||
\(429\) | −1.85937 | −0.0897714 | ||||||||
\(430\) | 13.6909 | + | 4.29327i | 0.660236 | + | 0.207040i | ||||
\(431\) | 19.7186 | 0.949810 | 0.474905 | − | 0.880037i | \(-0.342482\pi\) | ||||
0.474905 | + | 0.880037i | \(0.342482\pi\) | |||||||
\(432\) | − | 10.0297i | − | 0.482553i | ||||||
\(433\) | − | 21.7682i | − | 1.04611i | −0.852298 | − | 0.523056i | \(-0.824792\pi\) | ||
0.852298 | − | 0.523056i | \(-0.175208\pi\) | |||||||
\(434\) | 0.454451 | 0.0218144 | ||||||||
\(435\) | 4.34876 | − | 13.8679i | 0.208507 | − | 0.664915i | ||||
\(436\) | −5.35973 | −0.256685 | ||||||||
\(437\) | − | 7.17386i | − | 0.343172i | ||||||
\(438\) | 36.2416i | 1.73169i | ||||||||
\(439\) | 11.0246 | 0.526174 | 0.263087 | − | 0.964772i | \(-0.415259\pi\) | ||||
0.263087 | + | 0.964772i | \(0.415259\pi\) | |||||||
\(440\) | −2.04409 | + | 6.51848i | −0.0974484 | + | 0.310757i | ||||
\(441\) | −8.94664 | −0.426030 | ||||||||
\(442\) | 0.691811i | 0.0329061i | ||||||||
\(443\) | 14.9049i | 0.708154i | 0.935216 | + | 0.354077i | \(0.115205\pi\) | ||||
−0.935216 | + | 0.354077i | \(0.884795\pi\) | |||||||
\(444\) | 1.38840 | 0.0658903 | ||||||||
\(445\) | 29.7525 | + | 9.32992i | 1.41040 | + | 0.442280i | ||||
\(446\) | −17.9730 | −0.851046 | ||||||||
\(447\) | 13.4971i | 0.638392i | ||||||||
\(448\) | − | 2.79405i | − | 0.132006i | ||||||
\(449\) | −6.75645 | −0.318857 | −0.159428 | − | 0.987209i | \(-0.550965\pi\) | ||||
−0.159428 | + | 0.987209i | \(0.550965\pi\) | |||||||
\(450\) | 4.57881 | − | 6.58284i | 0.215847 | − | 0.310318i | ||||
\(451\) | −1.02303 | −0.0481728 | ||||||||
\(452\) | 4.50907i | 0.212089i | ||||||||
\(453\) | − | 31.1693i | − | 1.46446i | ||||||
\(454\) | −15.2817 | −0.717205 | ||||||||
\(455\) | −0.601355 | − | 0.188576i | −0.0281920 | − | 0.00884056i | ||||
\(456\) | −6.33257 | −0.296550 | ||||||||
\(457\) | − | 9.76392i | − | 0.456737i | −0.973575 | − | 0.228369i | \(-0.926661\pi\) | ||
0.973575 | − | 0.228369i | \(-0.0733391\pi\) | |||||||
\(458\) | − | 1.74662i | − | 0.0816140i | ||||||
\(459\) | 2.20138 | 0.102752 | ||||||||
\(460\) | 2.25399 | − | 7.18781i | 0.105093 | − | 0.335133i | ||||
\(461\) | 24.5389 | 1.14289 | 0.571445 | − | 0.820641i | \(-0.306383\pi\) | ||||
0.571445 | + | 0.820641i | \(0.306383\pi\) | |||||||
\(462\) | − | 0.805660i | − | 0.0374827i | ||||||
\(463\) | − | 31.8776i | − | 1.48148i | −0.671793 | − | 0.740739i | \(-0.734476\pi\) | ||
0.671793 | − | 0.740739i | \(-0.265524\pi\) | |||||||
\(464\) | 8.90643 | 0.413471 | ||||||||
\(465\) | 1.62147 | − | 5.17077i | 0.0751939 | − | 0.239788i | ||||
\(466\) | −2.58995 | −0.119977 | ||||||||
\(467\) | 2.47677i | 0.114611i | 0.998357 | + | 0.0573056i | \(0.0182509\pi\) | ||||
−0.998357 | + | 0.0573056i | \(0.981749\pi\) | |||||||
\(468\) | − | 0.546100i | − | 0.0252435i | ||||||
\(469\) | 4.52138 | 0.208778 | ||||||||
\(470\) | −11.4441 | − | 3.58870i | −0.527878 | − | 0.165534i | ||||
\(471\) | −11.0586 | −0.509551 | ||||||||
\(472\) | 3.42201i | 0.157511i | ||||||||
\(473\) | − | 5.18696i | − | 0.238497i | ||||||
\(474\) | 10.2722 | 0.471817 | ||||||||
\(475\) | 4.10469 | + | 2.85509i | 0.188336 | + | 0.131000i | ||||
\(476\) | 0.0919801 | 0.00421590 | ||||||||
\(477\) | − | 4.26665i | − | 0.195356i | ||||||
\(478\) | 30.0954i | 1.37653i | ||||||||
\(479\) | 11.2179 | 0.512559 | 0.256280 | − | 0.966603i | \(-0.417503\pi\) | ||||
0.256280 | + | 0.966603i | \(0.417503\pi\) | |||||||
\(480\) | −11.4833 | − | 3.60098i | −0.524138 | − | 0.164361i | ||||
\(481\) | 1.27953 | 0.0583417 | ||||||||
\(482\) | 10.0333i | 0.457005i | ||||||||
\(483\) | 4.67199i | 0.212583i | ||||||||
\(484\) | 0.469598 | 0.0213454 | ||||||||
\(485\) | 0.541394 | − | 1.72647i | 0.0245834 | − | 0.0783949i | ||||
\(486\) | 15.6357 | 0.709249 | ||||||||
\(487\) | − | 10.7546i | − | 0.487339i | −0.969858 | − | 0.243669i | \(-0.921649\pi\) | ||
0.969858 | − | 0.243669i | \(-0.0783512\pi\) | |||||||
\(488\) | − | 17.5422i | − | 0.794099i | ||||||
\(489\) | −1.58364 | −0.0716147 | ||||||||
\(490\) | −5.71221 | + | 18.2159i | −0.258052 | + | 0.822909i | ||||
\(491\) | −19.2326 | −0.867954 | −0.433977 | − | 0.900924i | \(-0.642890\pi\) | ||||
−0.433977 | + | 0.900924i | \(0.642890\pi\) | |||||||
\(492\) | − | 0.995788i | − | 0.0448936i | ||||||
\(493\) | 1.95484i | 0.0880416i | ||||||||
\(494\) | −1.10973 | −0.0499292 | ||||||||
\(495\) | −2.76597 | − | 0.867365i | −0.124321 | − | 0.0389852i | ||||
\(496\) | 3.32084 | 0.149110 | ||||||||
\(497\) | − | 1.63208i | − | 0.0732090i | ||||||
\(498\) | 4.23394i | 0.189727i | ||||||||
\(499\) | −11.2354 | −0.502967 | −0.251484 | − | 0.967862i | \(-0.580918\pi\) | ||||
−0.251484 | + | 0.967862i | \(0.580918\pi\) | |||||||
\(500\) | 3.21562 | + | 4.15031i | 0.143807 | + | 0.185608i | ||||
\(501\) | −3.35060 | −0.149694 | ||||||||
\(502\) | − | 19.6316i | − | 0.876199i | ||||||
\(503\) | − | 24.5392i | − | 1.09415i | −0.837084 | − | 0.547074i | \(-0.815742\pi\) | ||
0.837084 | − | 0.547074i | \(-0.184258\pi\) | |||||||
\(504\) | 1.24439 | 0.0554297 | ||||||||
\(505\) | 16.8224 | + | 5.27525i | 0.748588 | + | 0.234746i | ||||
\(506\) | 8.87474 | 0.394530 | ||||||||
\(507\) | 25.2781i | 1.12264i | ||||||||
\(508\) | 0.768189i | 0.0340829i | ||||||||
\(509\) | −2.49264 | −0.110484 | −0.0552421 | − | 0.998473i | \(-0.517593\pi\) | ||||
−0.0552421 | + | 0.998473i | \(0.517593\pi\) | |||||||
\(510\) | −1.06954 | + | 3.41068i | −0.0473598 | + | 0.151027i | ||||
\(511\) | 4.44070 | 0.196445 | ||||||||
\(512\) | − | 24.7298i | − | 1.09291i | ||||||
\(513\) | 3.53123i | 0.155907i | ||||||||
\(514\) | 30.6698 | 1.35279 | ||||||||
\(515\) | 6.32713 | − | 20.1768i | 0.278807 | − | 0.889097i | ||||
\(516\) | 5.04883 | 0.222262 | ||||||||
\(517\) | 4.33573i | 0.190685i | ||||||||
\(518\) | 0.554417i | 0.0243597i | ||||||||
\(519\) | −22.9974 | −1.00947 | ||||||||
\(520\) | −5.84739 | − | 1.83365i | −0.256425 | − | 0.0804109i | ||||
\(521\) | 42.6121 | 1.86687 | 0.933435 | − | 0.358747i | \(-0.116796\pi\) | ||||
0.933435 | + | 0.358747i | \(0.116796\pi\) | |||||||
\(522\) | 5.02892i | 0.220110i | ||||||||
\(523\) | 26.0936i | 1.14099i | 0.821300 | + | 0.570497i | \(0.193249\pi\) | ||||
−0.821300 | + | 0.570497i | \(0.806751\pi\) | |||||||
\(524\) | −9.01906 | −0.393999 | ||||||||
\(525\) | −2.67319 | − | 1.85938i | −0.116667 | − | 0.0811501i | ||||
\(526\) | 1.14735 | 0.0500270 | ||||||||
\(527\) | 0.728879i | 0.0317505i | ||||||||
\(528\) | − | 5.88725i | − | 0.256210i | ||||||
\(529\) | −28.4642 | −1.23758 | ||||||||
\(530\) | −8.68715 | − | 2.72415i | −0.377345 | − | 0.118330i | ||||
\(531\) | −1.45205 | −0.0630138 | ||||||||
\(532\) | 0.147545i | 0.00639689i | ||||||||
\(533\) | − | 0.917709i | − | 0.0397504i | ||||||
\(534\) | −35.7569 | −1.54735 | ||||||||
\(535\) | 2.96957 | − | 9.46978i | 0.128386 | − | 0.409414i | ||||
\(536\) | 43.9645 | 1.89898 | ||||||||
\(537\) | 51.5204i | 2.22327i | ||||||||
\(538\) | 23.9903i | 1.03430i | ||||||||
\(539\) | 6.90128 | 0.297259 | ||||||||
\(540\) | −1.10949 | + | 3.53809i | −0.0477449 | + | 0.152255i | ||||
\(541\) | −45.1164 | −1.93971 | −0.969853 | − | 0.243691i | \(-0.921642\pi\) | ||||
−0.969853 | + | 0.243691i | \(0.921642\pi\) | |||||||
\(542\) | − | 28.2434i | − | 1.21316i | ||||||
\(543\) | 41.6966i | 1.78937i | ||||||||
\(544\) | 1.61870 | 0.0694013 | ||||||||
\(545\) | −24.3520 | − | 7.63640i | −1.04312 | − | 0.327108i | ||||
\(546\) | 0.722716 | 0.0309294 | ||||||||
\(547\) | − | 22.8147i | − | 0.975485i | −0.872988 | − | 0.487742i | \(-0.837821\pi\) | ||
0.872988 | − | 0.487742i | \(-0.162179\pi\) | |||||||
\(548\) | − | 7.62726i | − | 0.325821i | ||||||
\(549\) | 7.44364 | 0.317687 | ||||||||
\(550\) | −3.53201 | + | 5.07789i | −0.150606 | + | 0.216522i | ||||
\(551\) | −3.13576 | −0.133588 | ||||||||
\(552\) | 45.4290i | 1.93359i | ||||||||
\(553\) | − | 1.25866i | − | 0.0535235i | ||||||
\(554\) | −13.0990 | −0.556524 | ||||||||
\(555\) | 6.30819 | + | 1.97815i | 0.267768 | + | 0.0839677i | ||||
\(556\) | 0.247559 | 0.0104988 | ||||||||
\(557\) | 30.7731i | 1.30390i | 0.758262 | + | 0.651950i | \(0.226049\pi\) | ||||
−0.758262 | + | 0.651950i | \(0.773951\pi\) | |||||||
\(558\) | 1.87508i | 0.0793783i | ||||||||
\(559\) | 4.65295 | 0.196799 | ||||||||
\(560\) | 0.597079 | − | 1.90404i | 0.0252312 | − | 0.0804606i | ||||
\(561\) | 1.29217 | 0.0545555 | ||||||||
\(562\) | − | 7.96163i | − | 0.335841i | ||||||
\(563\) | − | 12.1120i | − | 0.510462i | −0.966880 | − | 0.255231i | \(-0.917848\pi\) | ||
0.966880 | − | 0.255231i | \(-0.0821515\pi\) | |||||||
\(564\) | −4.22026 | −0.177705 | ||||||||
\(565\) | −6.42440 | + | 20.4870i | −0.270277 | + | 0.861894i | ||||
\(566\) | 13.4842 | 0.566782 | ||||||||
\(567\) | − | 3.52166i | − | 0.147896i | ||||||
\(568\) | − | 15.8699i | − | 0.665885i | ||||||
\(569\) | 25.5023 | 1.06911 | 0.534555 | − | 0.845134i | \(-0.320479\pi\) | ||||
0.534555 | + | 0.845134i | \(0.320479\pi\) | |||||||
\(570\) | −5.47106 | − | 1.71564i | −0.229157 | − | 0.0718602i | ||||
\(571\) | −16.5347 | −0.691955 | −0.345978 | − | 0.938243i | \(-0.612453\pi\) | ||||
−0.345978 | + | 0.938243i | \(0.612453\pi\) | |||||||
\(572\) | 0.421252i | 0.0176134i | ||||||||
\(573\) | 21.2710i | 0.888611i | ||||||||
\(574\) | 0.397641 | 0.0165972 | ||||||||
\(575\) | 20.4820 | − | 29.4465i | 0.854158 | − | 1.22800i | ||||
\(576\) | 11.5283 | 0.480347 | ||||||||
\(577\) | 30.0804i | 1.25226i | 0.779717 | + | 0.626132i | \(0.215363\pi\) | ||||
−0.779717 | + | 0.626132i | \(0.784637\pi\) | |||||||
\(578\) | 20.5498i | 0.854760i | ||||||||
\(579\) | −31.3940 | −1.30469 | ||||||||
\(580\) | −3.14185 | − | 0.985236i | −0.130458 | − | 0.0409097i | ||||
\(581\) | 0.518787 | 0.0215229 | ||||||||
\(582\) | 2.07489i | 0.0860070i | ||||||||
\(583\) | 3.29122i | 0.136308i | ||||||||
\(584\) | 43.1800 | 1.78680 | ||||||||
\(585\) | 0.778068 | − | 2.48121i | 0.0321692 | − | 0.102585i | ||||
\(586\) | −8.14304 | −0.336386 | ||||||||
\(587\) | − | 33.4079i | − | 1.37889i | −0.724337 | − | 0.689446i | \(-0.757854\pi\) | ||
0.724337 | − | 0.689446i | \(-0.242146\pi\) | |||||||
\(588\) | 6.71749i | 0.277025i | ||||||||
\(589\) | −1.16919 | −0.0481758 | ||||||||
\(590\) | −0.927102 | + | 2.95647i | −0.0381682 | + | 0.121716i | ||||
\(591\) | −48.1643 | −1.98121 | ||||||||
\(592\) | 4.05133i | 0.166509i | ||||||||
\(593\) | − | 19.5162i | − | 0.801435i | −0.916202 | − | 0.400717i | \(-0.868761\pi\) | ||
0.916202 | − | 0.400717i | \(-0.131239\pi\) | |||||||
\(594\) | −4.36846 | −0.179240 | ||||||||
\(595\) | 0.417912 | + | 0.131051i | 0.0171327 | + | 0.00537256i | ||||
\(596\) | 3.05785 | 0.125254 | ||||||||
\(597\) | 2.22292i | 0.0909780i | ||||||||
\(598\) | 7.96106i | 0.325552i | ||||||||
\(599\) | −23.8023 | −0.972535 | −0.486267 | − | 0.873810i | \(-0.661642\pi\) | ||||
−0.486267 | + | 0.873810i | \(0.661642\pi\) | |||||||
\(600\) | −25.9932 | − | 18.0800i | −1.06117 | − | 0.738115i | ||||
\(601\) | −19.7433 | −0.805346 | −0.402673 | − | 0.915344i | \(-0.631919\pi\) | ||||
−0.402673 | + | 0.915344i | \(0.631919\pi\) | |||||||
\(602\) | 2.01611i | 0.0821705i | ||||||||
\(603\) | 18.6553i | 0.759704i | ||||||||
\(604\) | −7.06158 | −0.287332 | ||||||||
\(605\) | 2.13362 | + | 0.669071i | 0.0867441 | + | 0.0272016i | ||||
\(606\) | −20.2174 | −0.821275 | ||||||||
\(607\) | − | 21.1111i | − | 0.856875i | −0.903572 | − | 0.428437i | \(-0.859064\pi\) | ||
0.903572 | − | 0.428437i | \(-0.140936\pi\) | |||||||
\(608\) | 2.59655i | 0.105304i | ||||||||
\(609\) | 2.04217 | 0.0827528 | ||||||||
\(610\) | 4.75259 | − | 15.1557i | 0.192427 | − | 0.613636i | ||||
\(611\) | −3.88935 | −0.157346 | ||||||||
\(612\) | 0.379512i | 0.0153409i | ||||||||
\(613\) | − | 29.3006i | − | 1.18344i | −0.806143 | − | 0.591720i | \(-0.798449\pi\) | ||
0.806143 | − | 0.591720i | \(-0.201551\pi\) | |||||||
\(614\) | −9.47380 | −0.382332 | ||||||||
\(615\) | 1.41877 | − | 4.52437i | 0.0572104 | − | 0.182440i | ||||
\(616\) | −0.959903 | −0.0386756 | ||||||||
\(617\) | 13.3644i | 0.538030i | 0.963136 | + | 0.269015i | \(0.0866982\pi\) | ||||
−0.963136 | + | 0.269015i | \(0.913302\pi\) | |||||||
\(618\) | 24.2487i | 0.975427i | ||||||||
\(619\) | −5.07280 | −0.203893 | −0.101947 | − | 0.994790i | \(-0.532507\pi\) | ||||
−0.101947 | + | 0.994790i | \(0.532507\pi\) | |||||||
\(620\) | −1.17147 | − | 0.367354i | −0.0470472 | − | 0.0147533i | ||||
\(621\) | 25.3325 | 1.01656 | ||||||||
\(622\) | − | 3.02778i | − | 0.121403i | ||||||
\(623\) | 4.38131i | 0.175533i | ||||||||
\(624\) | 5.28114 | 0.211415 | ||||||||
\(625\) | 8.69694 | + | 23.4385i | 0.347878 | + | 0.937540i | ||||
\(626\) | −11.6363 | −0.465078 | ||||||||
\(627\) | 2.07277i | 0.0827784i | ||||||||
\(628\) | 2.50538i | 0.0999755i | ||||||||
\(629\) | −0.889212 | −0.0354552 | ||||||||
\(630\) | 1.07510 | + | 0.337134i | 0.0428330 | + | 0.0134318i | ||||
\(631\) | −10.8359 | −0.431371 | −0.215686 | − | 0.976463i | \(-0.569199\pi\) | ||||
−0.215686 | + | 0.976463i | \(0.569199\pi\) | |||||||
\(632\) | − | 12.2388i | − | 0.486832i | ||||||
\(633\) | − | 23.6615i | − | 0.940459i | ||||||
\(634\) | −18.9916 | −0.754253 | ||||||||
\(635\) | −1.09449 | + | 3.49027i | −0.0434337 | + | 0.138507i | ||||
\(636\) | −3.20357 | −0.127030 | ||||||||
\(637\) | 6.19078i | 0.245288i | ||||||||
\(638\) | − | 3.87922i | − | 0.153580i | ||||||
\(639\) | 6.73402 | 0.266394 | ||||||||
\(640\) | 3.88600 | − | 12.3922i | 0.153608 | − | 0.489845i | ||||
\(641\) | −3.60462 | −0.142374 | −0.0711869 | − | 0.997463i | \(-0.522679\pi\) | ||||
−0.0711869 | + | 0.997463i | \(0.522679\pi\) | |||||||
\(642\) | 11.3809i | 0.449168i | ||||||||
\(643\) | − | 10.1882i | − | 0.401785i | −0.979613 | − | 0.200893i | \(-0.935616\pi\) | ||
0.979613 | − | 0.200893i | \(-0.0643842\pi\) | |||||||
\(644\) | 1.05847 | 0.0417094 | ||||||||
\(645\) | 22.9394 | + | 7.19343i | 0.903237 | + | 0.283241i | ||||
\(646\) | 0.771209 | 0.0303428 | ||||||||
\(647\) | 17.0298i | 0.669509i | 0.942305 | + | 0.334754i | \(0.108653\pi\) | ||||
−0.942305 | + | 0.334754i | \(0.891347\pi\) | |||||||
\(648\) | − | 34.2435i | − | 1.34521i | ||||||
\(649\) | 1.12009 | 0.0439674 | ||||||||
\(650\) | −4.55511 | − | 3.16838i | −0.178666 | − | 0.124274i | ||||
\(651\) | 0.761440 | 0.0298432 | ||||||||
\(652\) | 0.358783i | 0.0140510i | ||||||||
\(653\) | 8.11964i | 0.317746i | 0.987299 | + | 0.158873i | \(0.0507860\pi\) | ||||
−0.987299 | + | 0.158873i | \(0.949214\pi\) | |||||||
\(654\) | 29.2665 | 1.14441 | ||||||||
\(655\) | −40.9782 | − | 12.8501i | −1.60115 | − | 0.502095i | ||||
\(656\) | 2.90570 | 0.113449 | ||||||||
\(657\) | 18.3225i | 0.714827i | ||||||||
\(658\) | − | 1.68525i | − | 0.0656977i | ||||||
\(659\) | −30.5197 | −1.18888 | −0.594439 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594439 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(660\) | −0.651252 | + | 2.07680i | −0.0253500 | + | 0.0808394i | ||||
\(661\) | −5.45074 | −0.212009 | −0.106005 | − | 0.994366i | \(-0.533806\pi\) | ||||
−0.106005 | + | 0.994366i | \(0.533806\pi\) | |||||||
\(662\) | − | 38.0249i | − | 1.47788i | ||||||
\(663\) | 1.15914i | 0.0450173i | ||||||||
\(664\) | 5.04452 | 0.195765 | ||||||||
\(665\) | −0.210218 | + | 0.670372i | −0.00815191 | + | 0.0259959i | ||||
\(666\) | −2.28754 | −0.0886404 | ||||||||
\(667\) | 22.4955i | 0.871028i | ||||||||
\(668\) | 0.759099i | 0.0293704i | ||||||||
\(669\) | −30.1140 | −1.16428 | ||||||||
\(670\) | 37.9834 | + | 11.9110i | 1.46743 | + | 0.460162i | ||||
\(671\) | −5.74190 | −0.221663 | ||||||||
\(672\) | − | 1.69101i | − | 0.0652322i | ||||||
\(673\) | − | 12.2864i | − | 0.473605i | −0.971558 | − | 0.236802i | \(-0.923901\pi\) | ||
0.971558 | − | 0.236802i | \(-0.0760994\pi\) | |||||||
\(674\) | 14.8585 | 0.572329 | ||||||||
\(675\) | −10.0820 | + | 14.4946i | −0.388055 | + | 0.557897i | ||||
\(676\) | 5.72689 | 0.220265 | ||||||||
\(677\) | 7.06832i | 0.271658i | 0.990732 | + | 0.135829i | \(0.0433697\pi\) | ||||
−0.990732 | + | 0.135829i | \(0.956630\pi\) | |||||||
\(678\) | − | 24.6215i | − | 0.945583i | ||||||
\(679\) | 0.254237 | 0.00975674 | ||||||||
\(680\) | 4.06365 | + | 1.27430i | 0.155834 | + | 0.0488670i | ||||
\(681\) | −25.6047 | −0.981174 | ||||||||
\(682\) | − | 1.44640i | − | 0.0553856i | ||||||
\(683\) | 41.6548i | 1.59388i | 0.604062 | + | 0.796938i | \(0.293548\pi\) | ||||
−0.604062 | + | 0.796938i | \(0.706452\pi\) | |||||||
\(684\) | −0.608774 | −0.0232771 | ||||||||
\(685\) | 10.8671 | − | 34.6545i | 0.415211 | − | 1.32408i | ||||
\(686\) | −5.40326 | −0.206297 | ||||||||
\(687\) | − | 2.92648i | − | 0.111652i | ||||||
\(688\) | 14.7324i | 0.561669i | ||||||||
\(689\) | −2.95238 | −0.112477 | ||||||||
\(690\) | −12.3077 | + | 39.2486i | −0.468548 | + | 1.49417i | ||||
\(691\) | −19.7340 | −0.750717 | −0.375358 | − | 0.926880i | \(-0.622480\pi\) | ||||
−0.375358 | + | 0.926880i | \(0.622480\pi\) | |||||||
\(692\) | 5.21019i | 0.198062i | ||||||||
\(693\) | − | 0.407313i | − | 0.0154725i | ||||||
\(694\) | 7.44244 | 0.282511 | ||||||||
\(695\) | 1.12479 | + | 0.352716i | 0.0426656 | + | 0.0133793i | ||||
\(696\) | 19.8574 | 0.752692 | ||||||||
\(697\) | 0.637763i | 0.0241570i | ||||||||
\(698\) | 38.9789i | 1.47537i | ||||||||
\(699\) | −4.33950 | −0.164135 | ||||||||
\(700\) | −0.421254 | + | 0.605626i | −0.0159219 | + | 0.0228905i | ||||
\(701\) | −37.0168 | −1.39810 | −0.699052 | − | 0.715070i | \(-0.746395\pi\) | ||||
−0.699052 | + | 0.715070i | \(0.746395\pi\) | |||||||
\(702\) | − | 3.91871i | − | 0.147902i | ||||||
\(703\) | − | 1.42638i | − | 0.0537970i | ||||||
\(704\) | −8.89275 | −0.335158 | ||||||||
\(705\) | −19.1748 | − | 6.01292i | −0.722165 | − | 0.226460i | ||||
\(706\) | −16.9086 | −0.636362 | ||||||||
\(707\) | 2.47725i | 0.0931665i | ||||||||
\(708\) | 1.09026i | 0.0409745i | ||||||||
\(709\) | −30.0213 | −1.12748 | −0.563738 | − | 0.825954i | \(-0.690637\pi\) | ||||
−0.563738 | + | 0.825954i | \(0.690637\pi\) | |||||||
\(710\) | 4.29951 | − | 13.7109i | 0.161358 | − | 0.514559i | ||||
\(711\) | 5.19325 | 0.194762 | ||||||||
\(712\) | 42.6025i | 1.59660i | ||||||||
\(713\) | 8.38763i | 0.314119i | ||||||||
\(714\) | −0.502252 | −0.0187963 | ||||||||
\(715\) | −0.600188 | + | 1.91396i | −0.0224458 | + | 0.0715781i | ||||
\(716\) | 11.6722 | 0.436212 | ||||||||
\(717\) | 50.4252i | 1.88317i | ||||||||
\(718\) | 20.9247i | 0.780903i | ||||||||
\(719\) | −19.9674 | −0.744659 | −0.372330 | − | 0.928101i | \(-0.621441\pi\) | ||||
−0.372330 | + | 0.928101i | \(0.621441\pi\) | |||||||
\(720\) | 7.85614 | + | 2.46356i | 0.292781 | + | 0.0918115i | ||||
\(721\) | 2.97121 | 0.110654 | ||||||||
\(722\) | 1.23709i | 0.0460399i | ||||||||
\(723\) | 16.8110i | 0.625207i | ||||||||
\(724\) | 9.44660 | 0.351080 | ||||||||
\(725\) | −12.8713 | − | 8.95286i | −0.478028 | − | 0.332501i | ||||
\(726\) | −2.56421 | −0.0951668 | ||||||||
\(727\) | − | 27.8780i | − | 1.03394i | −0.856005 | − | 0.516968i | \(-0.827061\pi\) | ||
0.856005 | − | 0.516968i | \(-0.172939\pi\) | |||||||
\(728\) | − | 0.861078i | − | 0.0319137i | ||||||
\(729\) | −7.42780 | −0.275104 | ||||||||
\(730\) | 37.3056 | + | 11.6984i | 1.38074 | + | 0.432979i | ||||
\(731\) | −3.23357 | −0.119598 | ||||||||
\(732\) | − | 5.58898i | − | 0.206575i | ||||||
\(733\) | − | 6.72664i | − | 0.248454i | −0.992254 | − | 0.124227i | \(-0.960355\pi\) | ||
0.992254 | − | 0.124227i | \(-0.0396451\pi\) | |||||||
\(734\) | 27.0698 | 0.999166 | ||||||||
\(735\) | −9.57090 | + | 30.5210i | −0.353028 | + | 1.12578i | ||||
\(736\) | 18.6273 | 0.686612 | ||||||||
\(737\) | − | 14.3904i | − | 0.530078i | ||||||
\(738\) | 1.64068i | 0.0603941i | ||||||||
\(739\) | 32.6139 | 1.19972 | 0.599862 | − | 0.800104i | \(-0.295222\pi\) | ||||
0.599862 | + | 0.800104i | \(0.295222\pi\) | |||||||
\(740\) | 0.448161 | − | 1.42916i | 0.0164747 | − | 0.0525368i | ||||
\(741\) | −1.85937 | −0.0683058 | ||||||||
\(742\) | − | 1.27926i | − | 0.0469630i | ||||||
\(743\) | 1.17457i | 0.0430907i | 0.999768 | + | 0.0215454i | \(0.00685863\pi\) | ||||
−0.999768 | + | 0.0215454i | \(0.993141\pi\) | |||||||
\(744\) | 7.40400 | 0.271444 | ||||||||
\(745\) | 13.8934 | + | 4.35674i | 0.509014 | + | 0.159619i | ||||
\(746\) | 27.1962 | 0.995724 | ||||||||
\(747\) | 2.14053i | 0.0783178i | ||||||||
\(748\) | − | 0.292749i | − | 0.0107040i | ||||||
\(749\) | 1.39451 | 0.0509542 | ||||||||
\(750\) | −17.5587 | − | 22.6625i | −0.641153 | − | 0.827518i | ||||
\(751\) | 29.1972 | 1.06542 | 0.532711 | − | 0.846297i | \(-0.321173\pi\) | ||||
0.532711 | + | 0.846297i | \(0.321173\pi\) | |||||||
\(752\) | − | 12.3147i | − | 0.449071i | ||||||
\(753\) | − | 32.8930i | − | 1.19869i | ||||||
\(754\) | 3.47985 | 0.126729 | ||||||||
\(755\) | −32.0844 | − | 10.0612i | −1.16767 | − | 0.366163i | ||||
\(756\) | −0.521015 | −0.0189491 | ||||||||
\(757\) | 5.16599i | 0.187761i | 0.995583 | + | 0.0938806i | \(0.0299272\pi\) | ||||
−0.995583 | + | 0.0938806i | \(0.970073\pi\) | |||||||
\(758\) | − | 20.2708i | − | 0.736268i | ||||||
\(759\) | 14.8698 | 0.539738 | ||||||||
\(760\) | −2.04409 | + | 6.51848i | −0.0741471 | + | 0.236450i | ||||
\(761\) | −16.5957 | −0.601595 | −0.300798 | − | 0.953688i | \(-0.597253\pi\) | ||||
−0.300798 | + | 0.953688i | \(0.597253\pi\) | |||||||
\(762\) | − | 4.19465i | − | 0.151956i | ||||||
\(763\) | − | 3.58604i | − | 0.129823i | ||||||
\(764\) | 4.81908 | 0.174348 | ||||||||
\(765\) | −0.540719 | + | 1.72432i | −0.0195497 | + | 0.0623428i | ||||
\(766\) | −8.68237 | −0.313707 | ||||||||
\(767\) | 1.00477i | 0.0362803i | ||||||||
\(768\) | − | 21.9721i | − | 0.792852i | ||||||
\(769\) | 11.8283 | 0.426538 | 0.213269 | − | 0.976993i | \(-0.431589\pi\) | ||||
0.213269 | + | 0.976993i | \(0.431589\pi\) | |||||||
\(770\) | −0.829313 | − | 0.260060i | −0.0298864 | − | 0.00937190i | ||||
\(771\) | 51.3877 | 1.85068 | ||||||||
\(772\) | 7.11249i | 0.255984i | ||||||||
\(773\) | − | 14.7844i | − | 0.531757i | −0.964007 | − | 0.265878i | \(-0.914338\pi\) | ||
0.964007 | − | 0.265878i | \(-0.0856619\pi\) | |||||||
\(774\) | −8.31852 | −0.299003 | ||||||||
\(775\) | −4.79917 | − | 3.33815i | −0.172391 | − | 0.119910i | ||||
\(776\) | 2.47212 | 0.0887441 | ||||||||
\(777\) | 0.928935i | 0.0333253i | ||||||||
\(778\) | − | 30.2210i | − | 1.08347i | ||||||
\(779\) | −1.02303 | −0.0366540 | ||||||||
\(780\) | −1.86299 | − | 0.584204i | −0.0667057 | − | 0.0209179i | ||||
\(781\) | −5.19451 | −0.185874 | ||||||||
\(782\) | − | 5.53254i | − | 0.197843i | ||||||
\(783\) | − | 11.0731i | − | 0.395719i | ||||||
\(784\) | −19.6016 | −0.700057 | ||||||||
\(785\) | −3.56960 | + | 11.3832i | −0.127404 | + | 0.406284i | ||||
\(786\) | 49.2480 | 1.75662 | ||||||||
\(787\) | − | 53.9408i | − | 1.92278i | −0.275183 | − | 0.961392i | \(-0.588739\pi\) | ||
0.275183 | − | 0.961392i | \(-0.411261\pi\) | |||||||
\(788\) | 10.9119i | 0.388720i | ||||||||
\(789\) | 1.92241 | 0.0684395 | ||||||||
\(790\) | 3.31576 | − | 10.5738i | 0.117970 | − | 0.376197i | ||||
\(791\) | −3.01689 | −0.107268 | ||||||||
\(792\) | − | 3.96058i | − | 0.140733i | ||||||
\(793\) | − | 5.15075i | − | 0.182909i | ||||||
\(794\) | −25.0589 | −0.889309 | ||||||||
\(795\) | −14.5554 | − | 4.56436i | −0.516228 | − | 0.161881i | ||||
\(796\) | 0.503615 | 0.0178502 | ||||||||
\(797\) | − | 8.19451i | − | 0.290264i | −0.989412 | − | 0.145132i | \(-0.953639\pi\) | ||
0.989412 | − | 0.145132i | \(-0.0463607\pi\) | |||||||
\(798\) | − | 0.805660i | − | 0.0285201i | ||||||
\(799\) | 2.70291 | 0.0956221 | ||||||||
\(800\) | −7.41339 | + | 10.6581i | −0.262103 | + | 0.376819i | ||||
\(801\) | −18.0774 | −0.638733 | ||||||||
\(802\) | 4.15846i | 0.146840i | ||||||||
\(803\) | − | 14.1336i | − | 0.498765i | ||||||
\(804\) | 14.0072 | 0.493995 | ||||||||
\(805\) | 4.80915 | + | 1.50808i | 0.169500 | + | 0.0531527i | ||||
\(806\) | 1.29749 | 0.0457022 | ||||||||
\(807\) | 40.1961i | 1.41497i | ||||||||
\(808\) | 24.0880i | 0.847412i | ||||||||
\(809\) | −12.5113 | −0.439872 | −0.219936 | − | 0.975514i | \(-0.570585\pi\) | ||||
−0.219936 | + | 0.975514i | \(0.570585\pi\) | |||||||
\(810\) | 9.27734 | − | 29.5848i | 0.325973 | − | 1.03951i | ||||
\(811\) | 38.8266 | 1.36339 | 0.681693 | − | 0.731638i | \(-0.261244\pi\) | ||||
0.681693 | + | 0.731638i | \(0.261244\pi\) | |||||||
\(812\) | − | 0.462665i | − | 0.0162364i | ||||||
\(813\) | − | 47.3222i | − | 1.65966i | ||||||
\(814\) | 1.76457 | 0.0618481 | ||||||||
\(815\) | −0.511185 | + | 1.63013i | −0.0179060 | + | 0.0571011i | ||||
\(816\) | −3.67013 | −0.128480 | ||||||||
\(817\) | − | 5.18696i | − | 0.181469i | ||||||
\(818\) | − | 41.4889i | − | 1.45062i | ||||||
\(819\) | 0.365379 | 0.0127674 | ||||||||
\(820\) | −1.02502 | − | 0.321431i | −0.0357954 | − | 0.0112249i | ||||
\(821\) | 48.3052 | 1.68586 | 0.842932 | − | 0.538021i | \(-0.180828\pi\) | ||||
0.842932 | + | 0.538021i | \(0.180828\pi\) | |||||||
\(822\) | 41.6482i | 1.45265i | ||||||||
\(823\) | − | 29.2789i | − | 1.02060i | −0.859997 | − | 0.510299i | \(-0.829535\pi\) | ||
0.859997 | − | 0.510299i | \(-0.170465\pi\) | |||||||
\(824\) | 28.8911 | 1.00647 | ||||||||
\(825\) | −5.91794 | + | 8.50807i | −0.206036 | + | 0.296213i | ||||
\(826\) | −0.435365 | −0.0151483 | ||||||||
\(827\) | 2.34864i | 0.0816702i | 0.999166 | + | 0.0408351i | \(0.0130018\pi\) | ||||
−0.999166 | + | 0.0408351i | \(0.986998\pi\) | |||||||
\(828\) | 4.36726i | 0.151773i | ||||||||
\(829\) | 25.9906 | 0.902691 | 0.451346 | − | 0.892349i | \(-0.350944\pi\) | ||||
0.451346 | + | 0.892349i | \(0.350944\pi\) | |||||||
\(830\) | 4.35824 | + | 1.36667i | 0.151277 | + | 0.0474380i | ||||
\(831\) | −21.9476 | −0.761354 | ||||||||
\(832\) | − | 7.97722i | − | 0.276560i | ||||||
\(833\) | − | 4.30228i | − | 0.149065i | ||||||
\(834\) | −1.35178 | −0.0468084 | ||||||||
\(835\) | −1.08154 | + | 3.44897i | −0.0374284 | + | 0.119357i | ||||
\(836\) | 0.469598 | 0.0162414 | ||||||||
\(837\) | − | 4.12868i | − | 0.142708i | ||||||
\(838\) | − | 44.5258i | − | 1.53812i | ||||||
\(839\) | 5.06723 | 0.174940 | 0.0874701 | − | 0.996167i | \(-0.472122\pi\) | ||||
0.0874701 | + | 0.996167i | \(0.472122\pi\) | |||||||
\(840\) | 1.33122 | − | 4.24518i | 0.0459315 | − | 0.146473i | ||||
\(841\) | −19.1670 | −0.660932 | ||||||||
\(842\) | − | 19.2634i | − | 0.663859i | ||||||
\(843\) | − | 13.3398i | − | 0.459448i | ||||||
\(844\) | −5.36065 | −0.184521 | ||||||||
\(845\) | 26.0202 | + | 8.15952i | 0.895121 | + | 0.280696i | ||||
\(846\) | 6.95337 | 0.239062 | ||||||||
\(847\) | 0.314194i | 0.0107958i | ||||||||
\(848\) | − | 9.34799i | − | 0.321011i | ||||||
\(849\) | 22.5929 | 0.775387 | ||||||||
\(850\) | 3.16557 | + | 2.20187i | 0.108578 | + | 0.0755235i | ||||
\(851\) | −10.2327 | −0.350771 | ||||||||
\(852\) | − | 5.05617i | − | 0.173221i | ||||||
\(853\) | 1.16933i | 0.0400371i | 0.999800 | + | 0.0200186i | \(0.00637253\pi\) | ||||
−0.999800 | + | 0.0200186i | \(0.993627\pi\) | |||||||
\(854\) | 2.23181 | 0.0763708 | ||||||||
\(855\) | −2.76597 | − | 0.867365i | −0.0945942 | − | 0.0296633i | ||||
\(856\) | 13.5597 | 0.463462 | ||||||||
\(857\) | − | 20.5020i | − | 0.700336i | −0.936687 | − | 0.350168i | \(-0.886124\pi\) | ||
0.936687 | − | 0.350168i | \(-0.113876\pi\) | |||||||
\(858\) | − | 2.30022i | − | 0.0785282i | ||||||
\(859\) | 51.2221 | 1.74768 | 0.873838 | − | 0.486216i | \(-0.161623\pi\) | ||||
0.873838 | + | 0.486216i | \(0.161623\pi\) | |||||||
\(860\) | 1.62971 | − | 5.19705i | 0.0555728 | − | 0.177218i | ||||
\(861\) | 0.666253 | 0.0227058 | ||||||||
\(862\) | 24.3937i | 0.830854i | ||||||||
\(863\) | 40.4511i | 1.37697i | 0.725250 | + | 0.688486i | \(0.241724\pi\) | ||||
−0.725250 | + | 0.688486i | \(0.758276\pi\) | |||||||
\(864\) | −9.16902 | −0.311936 | ||||||||
\(865\) | −7.42334 | + | 23.6725i | −0.252401 | + | 0.804890i | ||||
\(866\) | 26.9293 | 0.915095 | ||||||||
\(867\) | 34.4315i | 1.16936i | ||||||||
\(868\) | − | 0.172509i | − | 0.00585532i | ||||||
\(869\) | −4.00598 | −0.135894 | ||||||||
\(870\) | 17.1559 | + | 5.37982i | 0.581639 | + | 0.182393i | ||||
\(871\) | 12.9089 | 0.437401 | ||||||||
\(872\) | − | 34.8695i | − | 1.18083i | ||||||
\(873\) | 1.04899i | 0.0355029i | ||||||||
\(874\) | 8.87474 | 0.300192 | ||||||||
\(875\) | −2.77685 | + | 2.15148i | −0.0938747 | + | 0.0727332i | ||||
\(876\) | 13.7572 | 0.464813 | ||||||||
\(877\) | − | 18.9754i | − | 0.640754i | −0.947290 | − | 0.320377i | \(-0.896190\pi\) | ||
0.947290 | − | 0.320377i | \(-0.103810\pi\) | |||||||
\(878\) | 13.6384i | 0.460275i | ||||||||
\(879\) | −13.6438 | −0.460194 | ||||||||
\(880\) | −6.06009 | − | 1.90035i | −0.204286 | − | 0.0640608i | ||||
\(881\) | 7.37496 | 0.248469 | 0.124234 | − | 0.992253i | \(-0.460353\pi\) | ||||
0.124234 | + | 0.992253i | \(0.460353\pi\) | |||||||
\(882\) | − | 11.0678i | − | 0.372673i | ||||||
\(883\) | − | 31.6616i | − | 1.06550i | −0.846274 | − | 0.532748i | \(-0.821159\pi\) | ||
0.846274 | − | 0.532748i | \(-0.178841\pi\) | |||||||
\(884\) | 0.262610 | 0.00883253 | ||||||||
\(885\) | −1.55337 | + | 4.95360i | −0.0522161 | + | 0.166514i | ||||
\(886\) | −18.4388 | −0.619463 | ||||||||
\(887\) | 44.5979i | 1.49745i | 0.662880 | + | 0.748726i | \(0.269334\pi\) | ||||
−0.662880 | + | 0.748726i | \(0.730666\pi\) | |||||||
\(888\) | 9.03267i | 0.303116i | ||||||||
\(889\) | −0.513973 | −0.0172381 | ||||||||
\(890\) | −11.5420 | + | 36.8066i | −0.386888 | + | 1.23376i | ||||
\(891\) | −11.2085 | −0.375500 | ||||||||
\(892\) | 6.82251i | 0.228434i | ||||||||
\(893\) | 4.33573i | 0.145090i | ||||||||
\(894\) | −16.6972 | −0.558438 | ||||||||
\(895\) | 53.0329 | + | 16.6303i | 1.77269 | + | 0.555889i | ||||
\(896\) | 1.82486 | 0.0609642 | ||||||||
\(897\) | 13.3389i | 0.445372i | ||||||||
\(898\) | − | 8.35837i | − | 0.278922i | ||||||
\(899\) | 3.66630 | 0.122278 | ||||||||
\(900\) | −2.49883 | − | 1.73810i | −0.0832943 | − | 0.0579368i | ||||
\(901\) | 2.05176 | 0.0683540 | ||||||||
\(902\) | − | 1.26559i | − | 0.0421395i | ||||||
\(903\) | 3.37802i | 0.112414i | ||||||||
\(904\) | −29.3352 | −0.975676 | ||||||||
\(905\) | 42.9207 | + | 13.4593i | 1.42673 | + | 0.447401i | ||||
\(906\) | 38.5593 | 1.28105 | ||||||||
\(907\) | 19.8230i | 0.658211i | 0.944293 | + | 0.329105i | \(0.106747\pi\) | ||||
−0.944293 | + | 0.329105i | \(0.893253\pi\) | |||||||
\(908\) | 5.80089i | 0.192509i | ||||||||
\(909\) | −10.2212 | −0.339015 | ||||||||
\(910\) | 0.233286 | − | 0.743933i | 0.00773335 | − | 0.0246611i | ||||
\(911\) | −46.0464 | −1.52559 | −0.762793 | − | 0.646642i | \(-0.776173\pi\) | ||||
−0.762793 | + | 0.646642i | \(0.776173\pi\) | |||||||
\(912\) | − | 5.88725i | − | 0.194946i | ||||||
\(913\) | − | 1.65116i | − | 0.0546456i | ||||||
\(914\) | 12.0789 | 0.399534 | ||||||||
\(915\) | 7.96303 | − | 25.3936i | 0.263250 | − | 0.839486i | ||||
\(916\) | −0.663011 | −0.0219065 | ||||||||
\(917\) | − | 6.03439i | − | 0.199273i | ||||||
\(918\) | 2.72331i | 0.0898827i | ||||||||
\(919\) | −1.40785 | −0.0464406 | −0.0232203 | − | 0.999730i | \(-0.507392\pi\) | ||||
−0.0232203 | + | 0.999730i | \(0.507392\pi\) | |||||||
\(920\) | 46.7627 | + | 14.6640i | 1.54172 | + | 0.483459i | ||||
\(921\) | −15.8735 | −0.523050 | ||||||||
\(922\) | 30.3569i | 0.999751i | ||||||||
\(923\) | − | 4.65972i | − | 0.153377i | ||||||
\(924\) | −0.305827 | −0.0100610 | ||||||||
\(925\) | 4.07245 | − | 5.85486i | 0.133901 | − | 0.192506i | ||||
\(926\) | 39.4356 | 1.29593 | ||||||||
\(927\) | 12.2593i | 0.402648i | ||||||||
\(928\) | − | 8.14216i | − | 0.267280i | ||||||
\(929\) | −2.06693 | −0.0678137 | −0.0339068 | − | 0.999425i | \(-0.510795\pi\) | ||||
−0.0339068 | + | 0.999425i | \(0.510795\pi\) | |||||||
\(930\) | 6.39672 | + | 2.00591i | 0.209757 | + | 0.0657765i | ||||
\(931\) | 6.90128 | 0.226180 | ||||||||
\(932\) | 0.983139i | 0.0322038i | ||||||||
\(933\) | − | 5.07309i | − | 0.166085i | ||||||
\(934\) | −3.06400 | −0.100257 | ||||||||
\(935\) | 0.417101 | − | 1.33011i | 0.0136407 | − | 0.0434992i | ||||
\(936\) | 3.55283 | 0.116128 | ||||||||
\(937\) | − | 56.0643i | − | 1.83154i | −0.401704 | − | 0.915770i | \(-0.631582\pi\) | ||
0.401704 | − | 0.915770i | \(-0.368418\pi\) | |||||||
\(938\) | 5.59338i | 0.182630i | ||||||||
\(939\) | −19.4967 | −0.636251 | ||||||||
\(940\) | −1.36226 | + | 4.34416i | −0.0444321 | + | 0.141691i | ||||
\(941\) | 13.0112 | 0.424152 | 0.212076 | − | 0.977253i | \(-0.431978\pi\) | ||||
0.212076 | + | 0.977253i | \(0.431978\pi\) | |||||||
\(942\) | − | 13.6805i | − | 0.445734i | ||||||
\(943\) | 7.33910i | 0.238994i | ||||||||
\(944\) | −3.18137 | −0.103545 | ||||||||
\(945\) | −2.36723 | − | 0.742328i | −0.0770061 | − | 0.0241479i | ||||
\(946\) | 6.41676 | 0.208627 | ||||||||
\(947\) | − | 12.2916i | − | 0.399422i | −0.979855 | − | 0.199711i | \(-0.936000\pi\) | ||
0.979855 | − | 0.199711i | \(-0.0640003\pi\) | |||||||
\(948\) | − | 3.89930i | − | 0.126643i | ||||||
\(949\) | 12.6785 | 0.411562 | ||||||||
\(950\) | −3.53201 | + | 5.07789i | −0.114594 | + | 0.164748i | ||||
\(951\) | −31.8207 | −1.03186 | ||||||||
\(952\) | 0.598407i | 0.0193945i | ||||||||
\(953\) | 3.46550i | 0.112259i | 0.998424 | + | 0.0561293i | \(0.0178759\pi\) | ||||
−0.998424 | + | 0.0561293i | \(0.982124\pi\) | |||||||
\(954\) | 5.27825 | 0.170890 | ||||||||
\(955\) | 21.8955 | + | 6.86610i | 0.708523 | + | 0.222182i | ||||
\(956\) | 11.4241 | 0.369483 | ||||||||
\(957\) | − | 6.49970i | − | 0.210105i | ||||||
\(958\) | 13.8776i | 0.448365i | ||||||||
\(959\) | 5.10318 | 0.164790 | ||||||||
\(960\) | 12.3327 | − | 39.3282i | 0.398037 | − | 1.26931i | ||||
\(961\) | −29.6330 | −0.955903 | ||||||||
\(962\) | 1.58290i | 0.0510348i | ||||||||
\(963\) | 5.75377i | 0.185413i | ||||||||
\(964\) | 3.80862 | 0.122668 | ||||||||
\(965\) | −10.1337 | + | 32.3156i | −0.326215 | + | 1.04028i | ||||
\(966\) | −5.77969 | −0.185959 | ||||||||
\(967\) | 50.4829i | 1.62342i | 0.584061 | + | 0.811710i | \(0.301463\pi\) | ||||
−0.584061 | + | 0.811710i | \(0.698537\pi\) | |||||||
\(968\) | 3.05513i | 0.0981954i | ||||||||
\(969\) | 1.29217 | 0.0415105 | ||||||||
\(970\) | 2.13581 | + | 0.669755i | 0.0685766 | + | 0.0215045i | ||||
\(971\) | 47.0493 | 1.50989 | 0.754943 | − | 0.655791i | \(-0.227665\pi\) | ||||
0.754943 | + | 0.655791i | \(0.227665\pi\) | |||||||
\(972\) | − | 5.93527i | − | 0.190374i | ||||||
\(973\) | 0.165635i | 0.00531000i | ||||||||
\(974\) | 13.3045 | 0.426303 | ||||||||
\(975\) | −7.63215 | − | 5.30867i | −0.244424 | − | 0.170014i | ||||
\(976\) | 16.3086 | 0.522026 | ||||||||
\(977\) | − | 39.3093i | − | 1.25762i | −0.777560 | − | 0.628808i | \(-0.783543\pi\) | ||
0.777560 | − | 0.628808i | \(-0.216457\pi\) | |||||||
\(978\) | − | 1.95911i | − | 0.0626455i | ||||||
\(979\) | 13.9446 | 0.445671 | ||||||||
\(980\) | 6.91470 | + | 2.16834i | 0.220882 | + | 0.0692652i | ||||
\(981\) | 14.7961 | 0.472403 | ||||||||
\(982\) | − | 23.7925i | − | 0.759250i | ||||||
\(983\) | 8.58356i | 0.273773i | 0.990587 | + | 0.136887i | \(0.0437096\pi\) | ||||
−0.990587 | + | 0.136887i | \(0.956290\pi\) | |||||||
\(984\) | 6.47843 | 0.206525 | ||||||||
\(985\) | −15.5470 | + | 49.5783i | −0.495368 | + | 1.57970i | ||||
\(986\) | −2.41832 | −0.0770151 | ||||||||
\(987\) | − | 2.82365i | − | 0.0898779i | ||||||
\(988\) | 0.421252i | 0.0134018i | ||||||||
\(989\) | −37.2105 | −1.18323 | ||||||||
\(990\) | 1.07301 | − | 3.42177i | 0.0341026 | − | 0.108751i | ||||
\(991\) | −50.1272 | −1.59234 | −0.796172 | − | 0.605070i | \(-0.793145\pi\) | ||||
−0.796172 | + | 0.605070i | \(0.793145\pi\) | |||||||
\(992\) | − | 3.03587i | − | 0.0963891i | ||||||
\(993\) | − | 63.7113i | − | 2.02182i | ||||||
\(994\) | 2.01904 | 0.0640401 | ||||||||
\(995\) | 2.28818 | + | 0.717538i | 0.0725402 | + | 0.0227475i | ||||
\(996\) | 1.60719 | 0.0509258 | ||||||||
\(997\) | 58.8564i | 1.86400i | 0.362457 | + | 0.932001i | \(0.381938\pi\) | ||||
−0.362457 | + | 0.932001i | \(0.618062\pi\) | |||||||
\(998\) | − | 13.8993i | − | 0.439974i | ||||||
\(999\) | 5.03688 | 0.159360 |
(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 | 1045.2.b.c.419.15 | yes | 20 | |
5.2 | odd | 4 | 5225.2.a.ba.1.6 | 20 | |||
5.3 | odd | 4 | 5225.2.a.ba.1.15 | 20 | |||
5.4 | even | 2 | inner | 1045.2.b.c.419.6 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.b.c.419.6 | ✓ | 20 | 5.4 | even | 2 | inner | |
1045.2.b.c.419.15 | yes | 20 | 1.1 | even | 1 | trivial | |
5225.2.a.ba.1.6 | 20 | 5.2 | odd | 4 | |||
5225.2.a.ba.1.15 | 20 | 5.3 | odd | 4 |