Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(316,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.4 | ||
Root | \(0.385418 - 0.222521i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.316 |
Dual form | 507.2.j.i.361.4 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.77441 | + | 1.02446i | 1.25470 | + | 0.724402i | 0.972039 | − | 0.234818i | \(-0.0754495\pi\) |
0.282661 | + | 0.959220i | \(0.408783\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.09903 | + | 1.90358i | 0.549516 | + | 0.951789i | ||||
\(5\) | 3.35690i | 1.50125i | 0.660729 | + | 0.750625i | \(0.270247\pi\) | ||||
−0.660729 | + | 0.750625i | \(0.729753\pi\) | |||||||
\(6\) | 1.77441 | − | 1.02446i | 0.724402 | − | 0.418234i | ||||
\(7\) | −1.94594 | + | 1.12349i | −0.735497 | + | 0.424639i | −0.820430 | − | 0.571747i | \(-0.806266\pi\) |
0.0849330 | + | 0.996387i | \(0.472932\pi\) | |||||||
\(8\) | 0.405813i | 0.143477i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −3.43900 | + | 5.95652i | −1.08751 | + | 1.88362i | ||||
\(11\) | 4.27730 | + | 2.46950i | 1.28965 | + | 0.744582i | 0.978593 | − | 0.205807i | \(-0.0659820\pi\) |
0.311062 | + | 0.950390i | \(0.399315\pi\) | |||||||
\(12\) | 2.19806 | 0.634526 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.60388 | −1.23044 | ||||||||
\(15\) | 2.90716 | + | 1.67845i | 0.750625 | + | 0.433373i | ||||
\(16\) | 1.78232 | − | 3.08707i | 0.445581 | − | 0.771769i | ||||
\(17\) | 0.455927 | + | 0.789689i | 0.110579 | + | 0.191528i | 0.916004 | − | 0.401170i | \(-0.131396\pi\) |
−0.805425 | + | 0.592698i | \(0.798063\pi\) | |||||||
\(18\) | − | 2.04892i | − | 0.482934i | ||||||
\(19\) | −3.29257 | + | 1.90097i | −0.755368 | + | 0.436112i | −0.827630 | − | 0.561274i | \(-0.810312\pi\) |
0.0722619 | + | 0.997386i | \(0.476978\pi\) | |||||||
\(20\) | −6.39011 | + | 3.68933i | −1.42887 | + | 0.824960i | ||||
\(21\) | 2.24698i | 0.490331i | ||||||||
\(22\) | 5.05980 | + | 8.76383i | 1.07875 | + | 1.86846i | ||||
\(23\) | 1.01357 | − | 1.75556i | 0.211345 | − | 0.366060i | −0.740791 | − | 0.671736i | \(-0.765549\pi\) |
0.952136 | + | 0.305676i | \(0.0988824\pi\) | |||||||
\(24\) | 0.351445 | + | 0.202907i | 0.0717383 | + | 0.0414181i | ||||
\(25\) | −6.26875 | −1.25375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.27730 | − | 2.46950i | −0.808334 | − | 0.466692i | ||||
\(29\) | 1.96950 | − | 3.41127i | 0.365727 | − | 0.633458i | −0.623165 | − | 0.782090i | \(-0.714154\pi\) |
0.988893 | + | 0.148632i | \(0.0474870\pi\) | |||||||
\(30\) | 3.43900 | + | 5.95652i | 0.627873 | + | 1.08751i | ||||
\(31\) | − | 8.82908i | − | 1.58575i | −0.609384 | − | 0.792875i | \(-0.708583\pi\) | ||
0.609384 | − | 0.792875i | \(-0.291417\pi\) | |||||||
\(32\) | 7.02805 | − | 4.05765i | 1.24240 | − | 0.717297i | ||||
\(33\) | 4.27730 | − | 2.46950i | 0.744582 | − | 0.429885i | ||||
\(34\) | 1.86831i | 0.320413i | ||||||||
\(35\) | −3.77144 | − | 6.53232i | −0.637489 | − | 1.10416i | ||||
\(36\) | 1.09903 | − | 1.90358i | 0.183172 | − | 0.317263i | ||||
\(37\) | 7.62270 | + | 4.40097i | 1.25316 | + | 0.723515i | 0.971737 | − | 0.236068i | \(-0.0758587\pi\) |
0.281428 | + | 0.959582i | \(0.409192\pi\) | |||||||
\(38\) | −7.78986 | −1.26368 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.36227 | −0.215394 | ||||||||
\(41\) | −6.00935 | − | 3.46950i | −0.938503 | − | 0.541845i | −0.0490123 | − | 0.998798i | \(-0.515607\pi\) |
−0.889491 | + | 0.456953i | \(0.848941\pi\) | |||||||
\(42\) | −2.30194 | + | 3.98707i | −0.355197 | + | 0.615219i | ||||
\(43\) | −1.14310 | − | 1.97991i | −0.174322 | − | 0.301934i | 0.765605 | − | 0.643311i | \(-0.222440\pi\) |
−0.939926 | + | 0.341377i | \(0.889107\pi\) | |||||||
\(44\) | 10.8562i | 1.63664i | ||||||||
\(45\) | 2.90716 | − | 1.67845i | 0.433373 | − | 0.250208i | ||||
\(46\) | 3.59700 | − | 2.07673i | 0.530349 | − | 0.306197i | ||||
\(47\) | − | 3.80194i | − | 0.554570i | −0.960788 | − | 0.277285i | \(-0.910565\pi\) | ||
0.960788 | − | 0.277285i | \(-0.0894346\pi\) | |||||||
\(48\) | −1.78232 | − | 3.08707i | −0.257256 | − | 0.445581i | ||||
\(49\) | −0.975541 | + | 1.68969i | −0.139363 | + | 0.241384i | ||||
\(50\) | −11.1234 | − | 6.42208i | −1.57308 | − | 0.908219i | ||||
\(51\) | 0.911854 | 0.127685 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.542877 | 0.0745698 | 0.0372849 | − | 0.999305i | \(-0.488129\pi\) | ||||
0.0372849 | + | 0.999305i | \(0.488129\pi\) | |||||||
\(54\) | −1.77441 | − | 1.02446i | −0.241467 | − | 0.139411i | ||||
\(55\) | −8.28986 | + | 14.3585i | −1.11780 | + | 1.93609i | ||||
\(56\) | −0.455927 | − | 0.789689i | −0.0609258 | − | 0.105527i | ||||
\(57\) | 3.80194i | 0.503579i | ||||||||
\(58\) | 6.98942 | − | 4.03534i | 0.917756 | − | 0.529867i | ||||
\(59\) | 4.08226 | − | 2.35690i | 0.531465 | − | 0.306842i | −0.210148 | − | 0.977670i | \(-0.567394\pi\) |
0.741613 | + | 0.670828i | \(0.234061\pi\) | |||||||
\(60\) | 7.37867i | 0.952582i | ||||||||
\(61\) | −1.83997 | − | 3.18692i | −0.235584 | − | 0.408043i | 0.723858 | − | 0.689949i | \(-0.242367\pi\) |
−0.959442 | + | 0.281905i | \(0.909034\pi\) | |||||||
\(62\) | 9.04503 | − | 15.6665i | 1.14872 | − | 1.98964i | ||||
\(63\) | 1.94594 | + | 1.12349i | 0.245166 | + | 0.141546i | ||||
\(64\) | 9.49827 | 1.18728 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.1196 | 1.24564 | ||||||||
\(67\) | 1.31732 | + | 0.760553i | 0.160936 | + | 0.0929164i | 0.578305 | − | 0.815821i | \(-0.303714\pi\) |
−0.417369 | + | 0.908737i | \(0.637048\pi\) | |||||||
\(68\) | −1.00216 | + | 1.73578i | −0.121529 | + | 0.210495i | ||||
\(69\) | −1.01357 | − | 1.75556i | −0.122020 | − | 0.211345i | ||||
\(70\) | − | 15.4547i | − | 1.84719i | ||||||
\(71\) | 2.05999 | − | 1.18933i | 0.244475 | − | 0.141148i | −0.372757 | − | 0.927929i | \(-0.621587\pi\) |
0.617232 | + | 0.786781i | \(0.288254\pi\) | |||||||
\(72\) | 0.351445 | − | 0.202907i | 0.0414181 | − | 0.0239128i | ||||
\(73\) | − | 7.41119i | − | 0.867414i | −0.901054 | − | 0.433707i | \(-0.857205\pi\) | ||
0.901054 | − | 0.433707i | \(-0.142795\pi\) | |||||||
\(74\) | 9.01722 | + | 15.6183i | 1.04823 | + | 1.81559i | ||||
\(75\) | −3.13437 | + | 5.42890i | −0.361926 | + | 0.626875i | ||||
\(76\) | −7.23728 | − | 4.17845i | −0.830173 | − | 0.479301i | ||||
\(77\) | −11.0978 | −1.26472 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.74094 | −0.420888 | −0.210444 | − | 0.977606i | \(-0.567491\pi\) | ||||
−0.210444 | + | 0.977606i | \(0.567491\pi\) | |||||||
\(80\) | 10.3630 | + | 5.98307i | 1.15862 | + | 0.668928i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −7.10872 | − | 12.3127i | −0.785027 | − | 1.35971i | ||||
\(83\) | 2.30798i | 0.253334i | 0.991945 | + | 0.126667i | \(0.0404279\pi\) | ||||
−0.991945 | + | 0.126667i | \(0.959572\pi\) | |||||||
\(84\) | −4.27730 | + | 2.46950i | −0.466692 | + | 0.269445i | ||||
\(85\) | −2.65090 | + | 1.53050i | −0.287531 | + | 0.166006i | ||||
\(86\) | − | 4.68425i | − | 0.505116i | ||||||
\(87\) | −1.96950 | − | 3.41127i | −0.211153 | − | 0.365727i | ||||
\(88\) | −1.00216 | + | 1.73578i | −0.106830 | + | 0.185035i | ||||
\(89\) | −8.71101 | − | 5.02930i | −0.923365 | − | 0.533105i | −0.0386580 | − | 0.999253i | \(-0.512308\pi\) |
−0.884707 | + | 0.466147i | \(0.845642\pi\) | |||||||
\(90\) | 6.87800 | 0.725005 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.45580 | 0.464549 | ||||||||
\(93\) | −7.64621 | − | 4.41454i | −0.792875 | − | 0.457767i | ||||
\(94\) | 3.89493 | − | 6.74621i | 0.401731 | − | 0.695819i | ||||
\(95\) | −6.38135 | − | 11.0528i | −0.654713 | − | 1.13400i | ||||
\(96\) | − | 8.11529i | − | 0.828264i | ||||||
\(97\) | −13.9684 | + | 8.06465i | −1.41827 | + | 0.818841i | −0.996147 | − | 0.0876961i | \(-0.972050\pi\) |
−0.422127 | + | 0.906537i | \(0.638716\pi\) | |||||||
\(98\) | −3.46203 | + | 1.99880i | −0.349718 | + | 0.201910i | ||||
\(99\) | − | 4.93900i | − | 0.496388i | ||||||
\(100\) | −6.88955 | − | 11.9331i | −0.688955 | − | 1.19331i | ||||
\(101\) | −4.97434 | + | 8.61582i | −0.494966 | + | 0.857306i | −0.999983 | − | 0.00580325i | \(-0.998153\pi\) |
0.505017 | + | 0.863109i | \(0.331486\pi\) | |||||||
\(102\) | 1.61801 | + | 0.934157i | 0.160207 | + | 0.0924953i | ||||
\(103\) | 10.9879 | 1.08267 | 0.541336 | − | 0.840806i | \(-0.317919\pi\) | ||||
0.541336 | + | 0.840806i | \(0.317919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.54288 | −0.736109 | ||||||||
\(106\) | 0.963288 | + | 0.556155i | 0.0935628 | + | 0.0540185i | ||||
\(107\) | 4.93631 | − | 8.54994i | 0.477211 | − | 0.826554i | −0.522448 | − | 0.852671i | \(-0.674981\pi\) |
0.999659 | + | 0.0261171i | \(0.00831428\pi\) | |||||||
\(108\) | −1.09903 | − | 1.90358i | −0.105754 | − | 0.183172i | ||||
\(109\) | 20.2446i | 1.93908i | 0.244934 | + | 0.969540i | \(0.421234\pi\) | ||||
−0.244934 | + | 0.969540i | \(0.578766\pi\) | |||||||
\(110\) | −29.4193 | + | 16.9852i | −2.80502 | + | 1.61948i | ||||
\(111\) | 7.62270 | − | 4.40097i | 0.723515 | − | 0.417721i | ||||
\(112\) | 8.00969i | 0.756844i | ||||||||
\(113\) | −4.84601 | − | 8.39354i | −0.455874 | − | 0.789598i | 0.542864 | − | 0.839821i | \(-0.317340\pi\) |
−0.998738 | + | 0.0502233i | \(0.984007\pi\) | |||||||
\(114\) | −3.89493 | + | 6.74621i | −0.364793 | + | 0.631841i | ||||
\(115\) | 5.89324 | + | 3.40246i | 0.549547 | + | 0.317281i | ||||
\(116\) | 8.65817 | 0.803891 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.65817 | 0.889107 | ||||||||
\(119\) | −1.77441 | − | 1.02446i | −0.162660 | − | 0.0939120i | ||||
\(120\) | −0.681136 | + | 1.17976i | −0.0621790 | + | 0.107697i | ||||
\(121\) | 6.69687 | + | 11.5993i | 0.608806 | + | 1.05448i | ||||
\(122\) | − | 7.53989i | − | 0.682630i | ||||||
\(123\) | −6.00935 | + | 3.46950i | −0.541845 | + | 0.312834i | ||||
\(124\) | 16.8068 | − | 9.70344i | 1.50930 | − | 0.871395i | ||||
\(125\) | − | 4.25906i | − | 0.380942i | ||||||
\(126\) | 2.30194 | + | 3.98707i | 0.205073 | + | 0.355197i | ||||
\(127\) | 6.90581 | − | 11.9612i | 0.612792 | − | 1.06139i | −0.377976 | − | 0.925815i | \(-0.623380\pi\) |
0.990768 | − | 0.135571i | \(-0.0432869\pi\) | |||||||
\(128\) | 2.79777 | + | 1.61529i | 0.247290 | + | 0.142773i | ||||
\(129\) | −2.28621 | −0.201289 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.99462 | 0.261641 | 0.130821 | − | 0.991406i | \(-0.458239\pi\) | ||||
0.130821 | + | 0.991406i | \(0.458239\pi\) | |||||||
\(132\) | 9.40177 | + | 5.42812i | 0.818319 | + | 0.472457i | ||||
\(133\) | 4.27144 | − | 7.39835i | 0.370381 | − | 0.641518i | ||||
\(134\) | 1.55831 | + | 2.69907i | 0.134618 | + | 0.233164i | ||||
\(135\) | − | 3.35690i | − | 0.288916i | ||||||
\(136\) | −0.320466 | + | 0.185021i | −0.0274797 | + | 0.0158654i | ||||
\(137\) | −19.9354 | + | 11.5097i | −1.70319 | + | 0.983339i | −0.760706 | + | 0.649096i | \(0.775147\pi\) |
−0.942487 | + | 0.334243i | \(0.891519\pi\) | |||||||
\(138\) | − | 4.15346i | − | 0.353566i | ||||||
\(139\) | −0.491271 | − | 0.850906i | −0.0416690 | − | 0.0721729i | 0.844439 | − | 0.535652i | \(-0.179934\pi\) |
−0.886108 | + | 0.463479i | \(0.846601\pi\) | |||||||
\(140\) | 8.28986 | − | 14.3585i | 0.700621 | − | 1.21351i | ||||
\(141\) | −3.29257 | − | 1.90097i | −0.277285 | − | 0.160090i | ||||
\(142\) | 4.87369 | 0.408991 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.56465 | −0.297054 | ||||||||
\(145\) | 11.4513 | + | 6.61141i | 0.950978 | + | 0.549048i | ||||
\(146\) | 7.59246 | − | 13.1505i | 0.628356 | − | 1.08835i | ||||
\(147\) | 0.975541 | + | 1.68969i | 0.0804613 | + | 0.139363i | ||||
\(148\) | 19.3472i | 1.59033i | ||||||||
\(149\) | 8.88461 | − | 5.12953i | 0.727855 | − | 0.420228i | −0.0897817 | − | 0.995961i | \(-0.528617\pi\) |
0.817637 | + | 0.575734i | \(0.195284\pi\) | |||||||
\(150\) | −11.1234 | + | 6.42208i | −0.908219 | + | 0.524360i | ||||
\(151\) | 20.1685i | 1.64129i | 0.571438 | + | 0.820646i | \(0.306386\pi\) | ||||
−0.571438 | + | 0.820646i | \(0.693614\pi\) | |||||||
\(152\) | −0.771438 | − | 1.33617i | −0.0625719 | − | 0.108378i | ||||
\(153\) | 0.455927 | − | 0.789689i | 0.0368595 | − | 0.0638425i | ||||
\(154\) | −19.6922 | − | 11.3693i | −1.58684 | − | 0.916162i | ||||
\(155\) | 29.6383 | 2.38061 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4383 | 0.833070 | 0.416535 | − | 0.909120i | \(-0.363244\pi\) | ||||
0.416535 | + | 0.909120i | \(0.363244\pi\) | |||||||
\(158\) | −6.63798 | − | 3.83244i | −0.528089 | − | 0.304892i | ||||
\(159\) | 0.271438 | − | 0.470145i | 0.0215265 | − | 0.0372849i | ||||
\(160\) | 13.6211 | + | 23.5924i | 1.07684 | + | 1.86515i | ||||
\(161\) | 4.55496i | 0.358981i | ||||||||
\(162\) | −1.77441 | + | 1.02446i | −0.139411 | + | 0.0804891i | ||||
\(163\) | 9.56657 | − | 5.52326i | 0.749312 | − | 0.432615i | −0.0761335 | − | 0.997098i | \(-0.524258\pi\) |
0.825445 | + | 0.564482i | \(0.190924\pi\) | |||||||
\(164\) | − | 15.2524i | − | 1.19101i | ||||||
\(165\) | 8.28986 | + | 14.3585i | 0.645364 | + | 1.11780i | ||||
\(166\) | −2.36443 | + | 4.09531i | −0.183515 | + | 0.317858i | ||||
\(167\) | 7.02339 | + | 4.05496i | 0.543487 | + | 0.313782i | 0.746491 | − | 0.665396i | \(-0.231737\pi\) |
−0.203004 | + | 0.979178i | \(0.565071\pi\) | |||||||
\(168\) | −0.911854 | −0.0703511 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.27173 | −0.481020 | ||||||||
\(171\) | 3.29257 | + | 1.90097i | 0.251789 | + | 0.145371i | ||||
\(172\) | 2.51261 | − | 4.35198i | 0.191585 | − | 0.331835i | ||||
\(173\) | −9.02811 | − | 15.6371i | −0.686394 | − | 1.18887i | −0.972996 | − | 0.230820i | \(-0.925859\pi\) |
0.286602 | − | 0.958050i | \(-0.407474\pi\) | |||||||
\(174\) | − | 8.07069i | − | 0.611837i | ||||||
\(175\) | 12.1986 | − | 7.04288i | 0.922129 | − | 0.532391i | ||||
\(176\) | 15.2471 | − | 8.80290i | 1.14929 | − | 0.663543i | ||||
\(177\) | − | 4.71379i | − | 0.354310i | ||||||
\(178\) | −10.3046 | − | 17.8481i | −0.772364 | − | 1.33777i | ||||
\(179\) | −9.93512 | + | 17.2081i | −0.742585 | + | 1.28620i | 0.208729 | + | 0.977974i | \(0.433067\pi\) |
−0.951314 | + | 0.308222i | \(0.900266\pi\) | |||||||
\(180\) | 6.39011 | + | 3.68933i | 0.476291 | + | 0.274987i | ||||
\(181\) | 10.0828 | 0.749446 | 0.374723 | − | 0.927137i | \(-0.377738\pi\) | ||||
0.374723 | + | 0.927137i | \(0.377738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.67994 | −0.272029 | ||||||||
\(184\) | 0.712430 | + | 0.411322i | 0.0525210 | + | 0.0303230i | ||||
\(185\) | −14.7736 | + | 25.5886i | −1.08618 | + | 1.88131i | ||||
\(186\) | −9.04503 | − | 15.6665i | −0.663214 | − | 1.14872i | ||||
\(187\) | 4.50365i | 0.329339i | ||||||||
\(188\) | 7.23728 | − | 4.17845i | 0.527833 | − | 0.304745i | ||||
\(189\) | 1.94594 | − | 1.12349i | 0.141546 | − | 0.0817219i | ||||
\(190\) | − | 26.1497i | − | 1.89710i | ||||||
\(191\) | 3.29374 | + | 5.70493i | 0.238327 | + | 0.412794i | 0.960234 | − | 0.279196i | \(-0.0900678\pi\) |
−0.721908 | + | 0.691990i | \(0.756734\pi\) | |||||||
\(192\) | 4.74914 | − | 8.22574i | 0.342739 | − | 0.593642i | ||||
\(193\) | 9.41131 | + | 5.43362i | 0.677441 | + | 0.391121i | 0.798890 | − | 0.601477i | \(-0.205421\pi\) |
−0.121449 | + | 0.992598i | \(0.538754\pi\) | |||||||
\(194\) | −33.0476 | −2.37268 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.28860 | −0.306329 | ||||||||
\(197\) | −8.00346 | − | 4.62080i | −0.570223 | − | 0.329218i | 0.187015 | − | 0.982357i | \(-0.440119\pi\) |
−0.757238 | + | 0.653139i | \(0.773452\pi\) | |||||||
\(198\) | 5.05980 | − | 8.76383i | 0.359585 | − | 0.622819i | ||||
\(199\) | −0.782323 | − | 1.35502i | −0.0554574 | − | 0.0960551i | 0.836964 | − | 0.547258i | \(-0.184328\pi\) |
−0.892421 | + | 0.451203i | \(0.850995\pi\) | |||||||
\(200\) | − | 2.54394i | − | 0.179884i | ||||||
\(201\) | 1.31732 | − | 0.760553i | 0.0929164 | − | 0.0536453i | ||||
\(202\) | −17.6531 | + | 10.1920i | −1.24207 | + | 0.717108i | ||||
\(203\) | 8.85086i | 0.621208i | ||||||||
\(204\) | 1.00216 | + | 1.73578i | 0.0701649 | + | 0.121529i | ||||
\(205\) | 11.6468 | − | 20.1728i | 0.813444 | − | 1.40893i | ||||
\(206\) | 19.4971 | + | 11.2567i | 1.35843 | + | 0.784289i | ||||
\(207\) | −2.02715 | −0.140896 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.7778 | −1.29889 | ||||||||
\(210\) | −13.3842 | − | 7.72737i | −0.923597 | − | 0.533239i | ||||
\(211\) | −11.6223 | + | 20.1304i | −0.800112 | + | 1.38583i | 0.119430 | + | 0.992843i | \(0.461893\pi\) |
−0.919542 | + | 0.392991i | \(0.871440\pi\) | |||||||
\(212\) | 0.596638 | + | 1.03341i | 0.0409773 | + | 0.0709747i | ||||
\(213\) | − | 2.37867i | − | 0.162984i | ||||||
\(214\) | 17.5181 | − | 10.1141i | 1.19751 | − | 0.691385i | ||||
\(215\) | 6.64637 | − | 3.83728i | 0.453278 | − | 0.261700i | ||||
\(216\) | − | 0.405813i | − | 0.0276121i | ||||||
\(217\) | 9.91939 | + | 17.1809i | 0.673372 | + | 1.16631i | ||||
\(218\) | −20.7397 | + | 35.9223i | −1.40467 | + | 2.43296i | ||||
\(219\) | −6.41828 | − | 3.70560i | −0.433707 | − | 0.250401i | ||||
\(220\) | −36.4432 | −2.45700 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 18.0344 | 1.21039 | ||||||||
\(223\) | −9.29985 | − | 5.36927i | −0.622764 | − | 0.359553i | 0.155180 | − | 0.987886i | \(-0.450404\pi\) |
−0.777944 | + | 0.628333i | \(0.783738\pi\) | |||||||
\(224\) | −9.11745 | + | 15.7919i | −0.609185 | + | 1.05514i | ||||
\(225\) | 3.13437 | + | 5.42890i | 0.208958 | + | 0.361926i | ||||
\(226\) | − | 19.8582i | − | 1.32094i | ||||||
\(227\) | −6.04125 | + | 3.48792i | −0.400972 | + | 0.231501i | −0.686903 | − | 0.726749i | \(-0.741030\pi\) |
0.285931 | + | 0.958250i | \(0.407697\pi\) | |||||||
\(228\) | −7.23728 | + | 4.17845i | −0.479301 | + | 0.276724i | ||||
\(229\) | 16.8049i | 1.11050i | 0.831683 | + | 0.555250i | \(0.187378\pi\) | ||||
−0.831683 | + | 0.555250i | \(0.812622\pi\) | |||||||
\(230\) | 6.97136 | + | 12.0748i | 0.459678 | + | 0.796186i | ||||
\(231\) | −5.54892 | + | 9.61101i | −0.365092 | + | 0.632358i | ||||
\(232\) | 1.38434 | + | 0.799249i | 0.0908864 | + | 0.0524733i | ||||
\(233\) | −8.69202 | −0.569433 | −0.284717 | − | 0.958612i | \(-0.591900\pi\) | ||||
−0.284717 | + | 0.958612i | \(0.591900\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7627 | 0.832547 | ||||||||
\(236\) | 8.97307 | + | 5.18060i | 0.584097 | + | 0.337229i | ||||
\(237\) | −1.87047 | + | 3.23975i | −0.121500 | + | 0.210444i | ||||
\(238\) | −2.09903 | − | 3.63563i | −0.136060 | − | 0.235663i | ||||
\(239\) | − | 22.9191i | − | 1.48252i | −0.671220 | − | 0.741258i | \(-0.734229\pi\) | ||
0.671220 | − | 0.741258i | \(-0.265771\pi\) | |||||||
\(240\) | 10.3630 | − | 5.98307i | 0.668928 | − | 0.386206i | ||||
\(241\) | −19.0354 | + | 10.9901i | −1.22618 | + | 0.707933i | −0.966228 | − | 0.257690i | \(-0.917039\pi\) |
−0.259948 | + | 0.965623i | \(0.583705\pi\) | |||||||
\(242\) | 27.4426i | 1.76408i | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 4.04437 | − | 7.00505i | 0.258914 | − | 0.448452i | ||||
\(245\) | −5.67210 | − | 3.27479i | −0.362377 | − | 0.209219i | ||||
\(246\) | −14.2174 | −0.906471 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.58296 | 0.227518 | ||||||||
\(249\) | 1.99877 | + | 1.15399i | 0.126667 | + | 0.0731311i | ||||
\(250\) | 4.36323 | − | 7.55734i | 0.275955 | − | 0.477968i | ||||
\(251\) | 13.3218 | + | 23.0741i | 0.840868 | + | 1.45643i | 0.889162 | + | 0.457592i | \(0.151288\pi\) |
−0.0482946 | + | 0.998833i | \(0.515379\pi\) | |||||||
\(252\) | 4.93900i | 0.311128i | ||||||||
\(253\) | 8.67072 | − | 5.00604i | 0.545123 | − | 0.314727i | ||||
\(254\) | 24.5075 | − | 14.1494i | 1.53774 | − | 0.887815i | ||||
\(255\) | 3.06100i | 0.191687i | ||||||||
\(256\) | −6.18867 | − | 10.7191i | −0.386792 | − | 0.669943i | ||||
\(257\) | 11.5722 | − | 20.0436i | 0.721853 | − | 1.25029i | −0.238404 | − | 0.971166i | \(-0.576624\pi\) |
0.960256 | − | 0.279119i | \(-0.0900425\pi\) | |||||||
\(258\) | −4.05668 | − | 2.34213i | −0.252558 | − | 0.145814i | ||||
\(259\) | −19.7778 | −1.22893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.93900 | −0.243818 | ||||||||
\(262\) | 5.31370 | + | 3.06787i | 0.328282 | + | 0.189533i | ||||
\(263\) | 9.26420 | − | 16.0461i | 0.571255 | − | 0.989443i | −0.425182 | − | 0.905108i | \(-0.639790\pi\) |
0.996437 | − | 0.0843352i | \(-0.0268766\pi\) | |||||||
\(264\) | 1.00216 | + | 1.73578i | 0.0616784 | + | 0.106830i | ||||
\(265\) | 1.82238i | 0.111948i | ||||||||
\(266\) | 15.1586 | − | 8.75182i | 0.929434 | − | 0.536609i | ||||
\(267\) | −8.71101 | + | 5.02930i | −0.533105 | + | 0.307788i | ||||
\(268\) | 3.34349i | 0.204236i | ||||||||
\(269\) | −4.87920 | − | 8.45102i | −0.297490 | − | 0.515268i | 0.678071 | − | 0.734996i | \(-0.262816\pi\) |
−0.975561 | + | 0.219729i | \(0.929483\pi\) | |||||||
\(270\) | 3.43900 | − | 5.95652i | 0.209291 | − | 0.362503i | ||||
\(271\) | −19.7471 | − | 11.4010i | −1.19955 | − | 0.692560i | −0.239094 | − | 0.970996i | \(-0.576850\pi\) |
−0.960455 | + | 0.278437i | \(0.910184\pi\) | |||||||
\(272\) | 3.25044 | 0.197087 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −47.1648 | −2.84933 | ||||||||
\(275\) | −26.8133 | − | 15.4807i | −1.61690 | − | 0.933520i | ||||
\(276\) | 2.22790 | − | 3.85883i | 0.134104 | − | 0.232274i | ||||
\(277\) | −11.9852 | − | 20.7590i | −0.720123 | − | 1.24729i | −0.960950 | − | 0.276721i | \(-0.910752\pi\) |
0.240828 | − | 0.970568i | \(-0.422581\pi\) | |||||||
\(278\) | − | 2.01315i | − | 0.120741i | ||||||
\(279\) | −7.64621 | + | 4.41454i | −0.457767 | + | 0.264292i | ||||
\(280\) | 2.65090 | − | 1.53050i | 0.158422 | − | 0.0914648i | ||||
\(281\) | 4.12498i | 0.246076i | 0.992402 | + | 0.123038i | \(0.0392637\pi\) | ||||
−0.992402 | + | 0.123038i | \(0.960736\pi\) | |||||||
\(282\) | −3.89493 | − | 6.74621i | −0.231940 | − | 0.401731i | ||||
\(283\) | −7.82789 | + | 13.5583i | −0.465320 | + | 0.805957i | −0.999216 | − | 0.0395927i | \(-0.987394\pi\) |
0.533896 | + | 0.845550i | \(0.320727\pi\) | |||||||
\(284\) | 4.52798 | + | 2.61423i | 0.268686 | + | 0.155126i | ||||
\(285\) | −12.7627 | −0.755998 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5918 | 0.920354 | ||||||||
\(288\) | −7.02805 | − | 4.05765i | −0.414132 | − | 0.239099i | ||||
\(289\) | 8.08426 | − | 14.0024i | 0.475545 | − | 0.823668i | ||||
\(290\) | 13.5462 | + | 23.4628i | 0.795462 | + | 1.37778i | ||||
\(291\) | 16.1293i | 0.945516i | ||||||||
\(292\) | 14.1078 | − | 8.14513i | 0.825595 | − | 0.476658i | ||||
\(293\) | −19.5677 | + | 11.2974i | −1.14315 | + | 0.660001i | −0.947210 | − | 0.320614i | \(-0.896111\pi\) |
−0.195945 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(294\) | 3.99761i | 0.233145i | ||||||||
\(295\) | 7.91185 | + | 13.7037i | 0.460646 | + | 0.797862i | ||||
\(296\) | −1.78597 | + | 3.09339i | −0.103807 | + | 0.179800i | ||||
\(297\) | −4.27730 | − | 2.46950i | −0.248194 | − | 0.143295i | ||||
\(298\) | 21.0200 | 1.21765 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.7791 | −0.795537 | ||||||||
\(301\) | 4.44883 | + | 2.56853i | 0.256426 | + | 0.148048i | ||||
\(302\) | −20.6618 | + | 35.7873i | −1.18895 | + | 2.05933i | ||||
\(303\) | 4.97434 | + | 8.61582i | 0.285769 | + | 0.494966i | ||||
\(304\) | 13.5526i | 0.777293i | ||||||||
\(305\) | 10.6982 | − | 6.17659i | 0.612575 | − | 0.353670i | ||||
\(306\) | 1.61801 | − | 0.934157i | 0.0924953 | − | 0.0534022i | ||||
\(307\) | 6.55496i | 0.374111i | 0.982349 | + | 0.187056i | \(0.0598945\pi\) | ||||
−0.982349 | + | 0.187056i | \(0.940106\pi\) | |||||||
\(308\) | −12.1969 | − | 21.1256i | −0.694981 | − | 1.20374i | ||||
\(309\) | 5.49396 | − | 9.51582i | 0.312540 | − | 0.541336i | ||||
\(310\) | 52.5907 | + | 30.3632i | 2.98695 | + | 1.72452i | ||||
\(311\) | 12.0392 | 0.682682 | 0.341341 | − | 0.939940i | \(-0.389119\pi\) | ||||
0.341341 | + | 0.939940i | \(0.389119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.8950 | −1.91586 | −0.957929 | − | 0.287005i | \(-0.907340\pi\) | ||||
−0.957929 | + | 0.287005i | \(0.907340\pi\) | |||||||
\(314\) | 18.5219 | + | 10.6936i | 1.04525 | + | 0.603477i | ||||
\(315\) | −3.77144 | + | 6.53232i | −0.212496 | + | 0.368055i | ||||
\(316\) | −4.11141 | − | 7.12117i | −0.231285 | − | 0.400597i | ||||
\(317\) | − | 4.49827i | − | 0.252648i | −0.991989 | − | 0.126324i | \(-0.959682\pi\) | ||
0.991989 | − | 0.126324i | \(-0.0403179\pi\) | |||||||
\(318\) | 0.963288 | − | 0.556155i | 0.0540185 | − | 0.0311876i | ||||
\(319\) | 16.8483 | − | 9.72737i | 0.943323 | − | 0.544628i | ||||
\(320\) | 31.8847i | 1.78241i | ||||||||
\(321\) | −4.93631 | − | 8.54994i | −0.275518 | − | 0.477211i | ||||
\(322\) | −4.66637 | + | 8.08238i | −0.260046 | + | 0.450414i | ||||
\(323\) | −3.00235 | − | 1.73341i | −0.167055 | − | 0.0964493i | ||||
\(324\) | −2.19806 | −0.122115 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.6334 | 1.25355 | ||||||||
\(327\) | 17.5323 | + | 10.1223i | 0.969540 | + | 0.559764i | ||||
\(328\) | 1.40797 | − | 2.43867i | 0.0777421 | − | 0.134653i | ||||
\(329\) | 4.27144 | + | 7.39835i | 0.235492 | + | 0.407884i | ||||
\(330\) | 33.9705i | 1.87001i | ||||||||
\(331\) | −9.71085 | + | 5.60656i | −0.533757 | + | 0.308165i | −0.742545 | − | 0.669796i | \(-0.766381\pi\) |
0.208788 | + | 0.977961i | \(0.433048\pi\) | |||||||
\(332\) | −4.39342 | + | 2.53654i | −0.241120 | + | 0.139211i | ||||
\(333\) | − | 8.80194i | − | 0.482343i | ||||||
\(334\) | 8.30827 | + | 14.3904i | 0.454609 | + | 0.787405i | ||||
\(335\) | −2.55310 | + | 4.42209i | −0.139491 | + | 0.241605i | ||||
\(336\) | 6.93659 | + | 4.00484i | 0.378422 | + | 0.218482i | ||||
\(337\) | −7.04892 | −0.383979 | −0.191989 | − | 0.981397i | \(-0.561494\pi\) | ||||
−0.191989 | + | 0.981397i | \(0.561494\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.69202 | −0.526398 | ||||||||
\(340\) | −5.82685 | − | 3.36413i | −0.316005 | − | 0.182446i | ||||
\(341\) | 21.8034 | − | 37.7646i | 1.18072 | − | 2.04507i | ||||
\(342\) | 3.89493 | + | 6.74621i | 0.210614 | + | 0.364793i | ||||
\(343\) | − | 20.1129i | − | 1.08599i | ||||||
\(344\) | 0.803475 | − | 0.463887i | 0.0433205 | − | 0.0250111i | ||||
\(345\) | 5.89324 | − | 3.40246i | 0.317281 | − | 0.183182i | ||||
\(346\) | − | 36.9957i | − | 1.98890i | ||||||
\(347\) | 1.35205 | + | 2.34182i | 0.0725819 | + | 0.125716i | 0.900032 | − | 0.435823i | \(-0.143543\pi\) |
−0.827450 | + | 0.561539i | \(0.810209\pi\) | |||||||
\(348\) | 4.32908 | − | 7.49819i | 0.232063 | − | 0.401945i | ||||
\(349\) | −0.359835 | − | 0.207751i | −0.0192615 | − | 0.0111207i | 0.490338 | − | 0.871532i | \(-0.336873\pi\) |
−0.509600 | + | 0.860412i | \(0.670207\pi\) | |||||||
\(350\) | 28.8605 | 1.54266 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 40.0814 | 2.13635 | ||||||||
\(353\) | 27.8576 | + | 16.0836i | 1.48271 | + | 0.856044i | 0.999807 | − | 0.0196301i | \(-0.00624884\pi\) |
0.482904 | + | 0.875674i | \(0.339582\pi\) | |||||||
\(354\) | 4.82908 | − | 8.36422i | 0.256663 | − | 0.444553i | ||||
\(355\) | 3.99247 | + | 6.91516i | 0.211898 | + | 0.367018i | ||||
\(356\) | − | 22.1094i | − | 1.17180i | ||||||
\(357\) | −1.77441 | + | 1.02446i | −0.0939120 | + | 0.0542201i | ||||
\(358\) | −35.2580 | + | 20.3562i | −1.86344 | + | 1.07586i | ||||
\(359\) | − | 22.3521i | − | 1.17970i | −0.807513 | − | 0.589850i | \(-0.799187\pi\) | ||
0.807513 | − | 0.589850i | \(-0.200813\pi\) | |||||||
\(360\) | 0.681136 | + | 1.17976i | 0.0358990 | + | 0.0621790i | ||||
\(361\) | −2.27263 | + | 3.93632i | −0.119612 | + | 0.207175i | ||||
\(362\) | 17.8910 | + | 10.3294i | 0.940331 | + | 0.542900i | ||||
\(363\) | 13.3937 | 0.702989 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.8786 | 1.30221 | ||||||||
\(366\) | −6.52974 | − | 3.76995i | −0.341315 | − | 0.197058i | ||||
\(367\) | 1.15130 | − | 1.99411i | 0.0600974 | − | 0.104092i | −0.834411 | − | 0.551142i | \(-0.814192\pi\) |
0.894509 | + | 0.447050i | \(0.147526\pi\) | |||||||
\(368\) | −3.61303 | − | 6.25795i | −0.188342 | − | 0.326218i | ||||
\(369\) | 6.93900i | 0.361230i | ||||||||
\(370\) | −52.4290 | + | 30.2699i | −2.72565 | + | 1.57366i | ||||
\(371\) | −1.05641 | + | 0.609916i | −0.0548459 | + | 0.0316653i | ||||
\(372\) | − | 19.4069i | − | 1.00620i | ||||||
\(373\) | 9.63802 | + | 16.6935i | 0.499038 | + | 0.864359i | 0.999999 | − | 0.00111058i | \(-0.000353507\pi\) |
−0.500961 | + | 0.865470i | \(0.667020\pi\) | |||||||
\(374\) | −4.61380 | + | 7.99134i | −0.238574 | + | 0.413222i | ||||
\(375\) | −3.68846 | − | 2.12953i | −0.190471 | − | 0.109968i | ||||
\(376\) | 1.54288 | 0.0795678 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.60388 | 0.236798 | ||||||||
\(379\) | 6.35614 | + | 3.66972i | 0.326493 | + | 0.188501i | 0.654283 | − | 0.756250i | \(-0.272971\pi\) |
−0.327790 | + | 0.944751i | \(0.606304\pi\) | |||||||
\(380\) | 14.0266 | − | 24.2948i | 0.719550 | − | 1.24630i | ||||
\(381\) | −6.90581 | − | 11.9612i | −0.353796 | − | 0.612792i | ||||
\(382\) | 13.4972i | 0.690577i | ||||||||
\(383\) | 16.5325 | − | 9.54503i | 0.844770 | − | 0.487728i | −0.0141126 | − | 0.999900i | \(-0.504492\pi\) |
0.858883 | + | 0.512172i | \(0.171159\pi\) | |||||||
\(384\) | 2.79777 | − | 1.61529i | 0.142773 | − | 0.0824301i | ||||
\(385\) | − | 37.2543i | − | 1.89865i | ||||||
\(386\) | 11.1330 | + | 19.2830i | 0.566657 | + | 0.981479i | ||||
\(387\) | −1.14310 | + | 1.97991i | −0.0581072 | + | 0.100645i | ||||
\(388\) | −30.7034 | − | 17.7266i | −1.55873 | − | 0.899932i | ||||
\(389\) | 23.9879 | 1.21624 | 0.608118 | − | 0.793847i | \(-0.291925\pi\) | ||||
0.608118 | + | 0.793847i | \(0.291925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.84846 | 0.0934807 | ||||||||
\(392\) | −0.685697 | − | 0.395888i | −0.0346329 | − | 0.0199953i | ||||
\(393\) | 1.49731 | − | 2.59342i | 0.0755294 | − | 0.130821i | ||||
\(394\) | −9.46764 | − | 16.3984i | −0.476973 | − | 0.826141i | ||||
\(395\) | − | 12.5579i | − | 0.631859i | ||||||
\(396\) | 9.40177 | − | 5.42812i | 0.472457 | − | 0.272773i | ||||
\(397\) | 3.82601 | − | 2.20895i | 0.192022 | − | 0.110864i | −0.400907 | − | 0.916119i | \(-0.631305\pi\) |
0.592929 | + | 0.805255i | \(0.297972\pi\) | |||||||
\(398\) | − | 3.20583i | − | 0.160694i | ||||||
\(399\) | −4.27144 | − | 7.39835i | −0.213839 | − | 0.370381i | ||||
\(400\) | −11.1729 | + | 19.3521i | −0.558647 | + | 0.967605i | ||||
\(401\) | −17.6745 | − | 10.2044i | −0.882624 | − | 0.509583i | −0.0111015 | − | 0.999938i | \(-0.503534\pi\) |
−0.871523 | + | 0.490355i | \(0.836867\pi\) | |||||||
\(402\) | 3.11662 | 0.155443 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −21.8678 | −1.08797 | ||||||||
\(405\) | −2.90716 | − | 1.67845i | −0.144458 | − | 0.0834027i | ||||
\(406\) | −9.06734 | + | 15.7051i | −0.450004 | + | 0.779430i | ||||
\(407\) | 21.7364 | + | 37.6485i | 1.07743 | + | 1.86617i | ||||
\(408\) | 0.370042i | 0.0183198i | ||||||||
\(409\) | −19.1817 | + | 11.0746i | −0.948475 | + | 0.547602i | −0.892607 | − | 0.450836i | \(-0.851126\pi\) |
−0.0558682 | + | 0.998438i | \(0.517793\pi\) | |||||||
\(410\) | 41.3323 | − | 23.8632i | 2.04126 | − | 1.17852i | ||||
\(411\) | 23.0194i | 1.13546i | ||||||||
\(412\) | 12.0761 | + | 20.9164i | 0.594945 | + | 1.03047i | ||||
\(413\) | −5.29590 | + | 9.17276i | −0.260594 | + | 0.451362i | ||||
\(414\) | −3.59700 | − | 2.07673i | −0.176783 | − | 0.102066i | ||||
\(415\) | −7.74764 | −0.380317 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.982542 | −0.0481153 | ||||||||
\(418\) | −33.3196 | − | 19.2371i | −1.62971 | − | 0.940915i | ||||
\(419\) | −7.37800 | + | 12.7791i | −0.360439 | + | 0.624299i | −0.988033 | − | 0.154242i | \(-0.950706\pi\) |
0.627594 | + | 0.778541i | \(0.284040\pi\) | |||||||
\(420\) | −8.28986 | − | 14.3585i | −0.404504 | − | 0.700621i | ||||
\(421\) | 8.47219i | 0.412909i | 0.978456 | + | 0.206455i | \(0.0661926\pi\) | ||||
−0.978456 | + | 0.206455i | \(0.933807\pi\) | |||||||
\(422\) | −41.2455 | + | 23.8131i | −2.00780 | + | 1.15920i | ||||
\(423\) | −3.29257 | + | 1.90097i | −0.160090 | + | 0.0924283i | ||||
\(424\) | 0.220306i | 0.0106990i | ||||||||
\(425\) | −2.85809 | − | 4.95036i | −0.138638 | − | 0.240128i | ||||
\(426\) | 2.43685 | − | 4.22074i | 0.118066 | − | 0.204496i | ||||
\(427\) | 7.16095 | + | 4.13437i | 0.346543 | + | 0.200076i | ||||
\(428\) | 21.7006 | 1.04894 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.7245 | 0.758305 | ||||||||
\(431\) | −2.07137 | − | 1.19591i | −0.0997744 | − | 0.0576048i | 0.449283 | − | 0.893390i | \(-0.351680\pi\) |
−0.549057 | + | 0.835785i | \(0.685013\pi\) | |||||||
\(432\) | −1.78232 | + | 3.08707i | −0.0857521 | + | 0.148527i | ||||
\(433\) | −5.21432 | − | 9.03147i | −0.250584 | − | 0.434025i | 0.713102 | − | 0.701060i | \(-0.247289\pi\) |
−0.963687 | + | 0.267035i | \(0.913956\pi\) | |||||||
\(434\) | 40.6480i | 1.95117i | ||||||||
\(435\) | 11.4513 | − | 6.61141i | 0.549048 | − | 0.316993i | ||||
\(436\) | −38.5371 | + | 22.2494i | −1.84559 | + | 1.06555i | ||||
\(437\) | 7.70709i | 0.368680i | ||||||||
\(438\) | −7.59246 | − | 13.1505i | −0.362782 | − | 0.628356i | ||||
\(439\) | −16.2751 | + | 28.1893i | −0.776767 | + | 1.34540i | 0.157028 | + | 0.987594i | \(0.449809\pi\) |
−0.933796 | + | 0.357807i | \(0.883525\pi\) | |||||||
\(440\) | −5.82685 | − | 3.36413i | −0.277784 | − | 0.160379i | ||||
\(441\) | 1.95108 | 0.0929087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.58211 | 0.455260 | 0.227630 | − | 0.973748i | \(-0.426902\pi\) | ||||
0.227630 | + | 0.973748i | \(0.426902\pi\) | |||||||
\(444\) | 16.7552 | + | 9.67360i | 0.795165 | + | 0.459089i | ||||
\(445\) | 16.8828 | − | 29.2419i | 0.800324 | − | 1.38620i | ||||
\(446\) | −11.0012 | − | 19.0546i | −0.520922 | − | 0.902263i | ||||
\(447\) | − | 10.2591i | − | 0.485237i | ||||||
\(448\) | −18.4831 | + | 10.6712i | −0.873243 | + | 0.504167i | ||||
\(449\) | 24.5897 | − | 14.1969i | 1.16046 | − | 0.669992i | 0.209045 | − | 0.977906i | \(-0.432964\pi\) |
0.951414 | + | 0.307914i | \(0.0996311\pi\) | |||||||
\(450\) | 12.8442i | 0.605479i | ||||||||
\(451\) | −17.1359 | − | 29.6802i | −0.806896 | − | 1.39759i | ||||
\(452\) | 10.6518 | − | 18.4495i | 0.501020 | − | 0.867792i | ||||
\(453\) | 17.4665 | + | 10.0843i | 0.820646 | + | 0.473800i | ||||
\(454\) | −14.2929 | −0.670800 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.54288 | −0.0722518 | ||||||||
\(457\) | −4.32639 | − | 2.49784i | −0.202380 | − | 0.116844i | 0.395385 | − | 0.918515i | \(-0.370611\pi\) |
−0.597765 | + | 0.801671i | \(0.703944\pi\) | |||||||
\(458\) | −17.2159 | + | 29.8189i | −0.804448 | + | 1.39335i | ||||
\(459\) | −0.455927 | − | 0.789689i | −0.0212808 | − | 0.0368595i | ||||
\(460\) | 14.9576i | 0.697404i | ||||||||
\(461\) | 1.17137 | − | 0.676292i | 0.0545562 | − | 0.0314981i | −0.472474 | − | 0.881345i | \(-0.656639\pi\) |
0.527030 | + | 0.849847i | \(0.323306\pi\) | |||||||
\(462\) | −19.6922 | + | 11.3693i | −0.916162 | + | 0.528946i | ||||
\(463\) | 3.36467i | 0.156369i | 0.996939 | + | 0.0781846i | \(0.0249124\pi\) | ||||
−0.996939 | + | 0.0781846i | \(0.975088\pi\) | |||||||
\(464\) | −7.02057 | − | 12.1600i | −0.325922 | − | 0.564513i | ||||
\(465\) | 14.8192 | − | 25.6675i | 0.687222 | − | 1.19030i | ||||
\(466\) | −15.4232 | − | 8.90462i | −0.714468 | − | 0.412498i | ||||
\(467\) | −6.91079 | −0.319793 | −0.159897 | − | 0.987134i | \(-0.551116\pi\) | ||||
−0.159897 | + | 0.987134i | \(0.551116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.41789 | −0.157824 | ||||||||
\(470\) | 22.6463 | + | 13.0749i | 1.04460 | + | 0.603099i | ||||
\(471\) | 5.21917 | − | 9.03987i | 0.240487 | − | 0.416535i | ||||
\(472\) | 0.956459 | + | 1.65664i | 0.0440246 | + | 0.0762529i | ||||
\(473\) | − | 11.2916i | − | 0.519188i | ||||||
\(474\) | −6.63798 | + | 3.83244i | −0.304892 | + | 0.176030i | ||||
\(475\) | 20.6403 | − | 11.9167i | 0.947043 | − | 0.546776i | ||||
\(476\) | − | 4.50365i | − | 0.206424i | ||||||
\(477\) | −0.271438 | − | 0.470145i | −0.0124283 | − | 0.0215265i | ||||
\(478\) | 23.4797 | − | 40.6681i | 1.07394 | − | 1.86011i | ||||
\(479\) | 3.04471 | + | 1.75786i | 0.139116 | + | 0.0803189i | 0.567943 | − | 0.823068i | \(-0.307739\pi\) |
−0.428826 | + | 0.903387i | \(0.641073\pi\) | |||||||
\(480\) | 27.2422 | 1.24343 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −45.0355 | −2.05131 | ||||||||
\(483\) | 3.94471 | + | 2.27748i | 0.179490 | + | 0.103629i | ||||
\(484\) | −14.7201 | + | 25.4960i | −0.669097 | + | 1.15891i | ||||
\(485\) | −27.0722 | − | 46.8904i | −1.22928 | − | 2.12918i | ||||
\(486\) | 2.04892i | 0.0929408i | ||||||||
\(487\) | −11.1266 | + | 6.42394i | −0.504194 | + | 0.291096i | −0.730444 | − | 0.682973i | \(-0.760687\pi\) |
0.226250 | + | 0.974069i | \(0.427353\pi\) | |||||||
\(488\) | 1.29329 | − | 0.746684i | 0.0585447 | − | 0.0338008i | ||||
\(489\) | − | 11.0465i | − | 0.499541i | ||||||
\(490\) | −6.70978 | − | 11.6217i | −0.303117 | − | 0.525014i | ||||
\(491\) | 14.3354 | − | 24.8297i | 0.646948 | − | 1.12055i | −0.336899 | − | 0.941541i | \(-0.609378\pi\) |
0.983848 | − | 0.179007i | \(-0.0572885\pi\) | |||||||
\(492\) | −13.2089 | − | 7.62618i | −0.595504 | − | 0.343815i | ||||
\(493\) | 3.59179 | 0.161766 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.5797 | 0.745203 | ||||||||
\(496\) | −27.2560 | − | 15.7363i | −1.22383 | − | 0.706580i | ||||
\(497\) | −2.67241 | + | 4.62874i | −0.119874 | + | 0.207628i | ||||
\(498\) | 2.36443 | + | 4.09531i | 0.105953 | + | 0.183515i | ||||
\(499\) | − | 33.5555i | − | 1.50215i | −0.660215 | − | 0.751076i | \(-0.729535\pi\) | ||
0.660215 | − | 0.751076i | \(-0.270465\pi\) | |||||||
\(500\) | 8.10745 | − | 4.68084i | 0.362576 | − | 0.209334i | ||||
\(501\) | 7.02339 | − | 4.05496i | 0.313782 | − | 0.181162i | ||||
\(502\) | 54.5907i | 2.43650i | ||||||||
\(503\) | −10.7817 | − | 18.6744i | −0.480730 | − | 0.832650i | 0.519025 | − | 0.854759i | \(-0.326295\pi\) |
−0.999756 | + | 0.0221094i | \(0.992962\pi\) | |||||||
\(504\) | −0.455927 | + | 0.789689i | −0.0203086 | + | 0.0351755i | ||||
\(505\) | −28.9224 | − | 16.6984i | −1.28703 | − | 0.743067i | ||||
\(506\) | 20.5139 | 0.911955 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.3588 | 1.34695 | ||||||||
\(509\) | 7.69904 | + | 4.44504i | 0.341254 | + | 0.197023i | 0.660826 | − | 0.750539i | \(-0.270206\pi\) |
−0.319572 | + | 0.947562i | \(0.603539\pi\) | |||||||
\(510\) | −3.13587 | + | 5.43148i | −0.138859 | + | 0.240510i | ||||
\(511\) | 8.32640 | + | 14.4217i | 0.368338 | + | 0.637980i | ||||
\(512\) | − | 31.8213i | − | 1.40632i | ||||||
\(513\) | 3.29257 | − | 1.90097i | 0.145371 | − | 0.0839298i | ||||
\(514\) | 41.0677 | − | 23.7104i | 1.81142 | − | 1.04582i | ||||
\(515\) | 36.8853i | 1.62536i | ||||||||
\(516\) | −2.51261 | − | 4.35198i | −0.110612 | − | 0.191585i | ||||
\(517\) | 9.38889 | − | 16.2620i | 0.412923 | − | 0.715203i | ||||
\(518\) | −35.0940 | − | 20.2615i | −1.54194 | − | 0.890240i | ||||
\(519\) | −18.0562 | −0.792580 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.3478 | 0.847642 | 0.423821 | − | 0.905746i | \(-0.360688\pi\) | ||||
0.423821 | + | 0.905746i | \(0.360688\pi\) | |||||||
\(522\) | −6.98942 | − | 4.03534i | −0.305919 | − | 0.176622i | ||||
\(523\) | 6.29739 | − | 10.9074i | 0.275366 | − | 0.476947i | −0.694862 | − | 0.719143i | \(-0.744534\pi\) |
0.970227 | + | 0.242196i | \(0.0778678\pi\) | |||||||
\(524\) | 3.29118 | + | 5.70050i | 0.143776 | + | 0.249027i | ||||
\(525\) | − | 14.0858i | − | 0.614753i | ||||||
\(526\) | 32.8771 | − | 18.9816i | 1.43351 | − | 0.827636i | ||||
\(527\) | 6.97223 | − | 4.02542i | 0.303715 | − | 0.175350i | ||||
\(528\) | − | 17.6058i | − | 0.766194i | ||||||
\(529\) | 9.44534 | + | 16.3598i | 0.410667 | + | 0.711296i | ||||
\(530\) | −1.86695 | + | 3.23366i | −0.0810953 | + | 0.140461i | ||||
\(531\) | −4.08226 | − | 2.35690i | −0.177155 | − | 0.102281i | ||||
\(532\) | 18.7778 | 0.814120 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −20.6093 | −0.891850 | ||||||||
\(535\) | 28.7013 | + | 16.5707i | 1.24086 | + | 0.716413i | ||||
\(536\) | −0.308643 | + | 0.534585i | −0.0133313 | + | 0.0230905i | ||||
\(537\) | 9.93512 | + | 17.2081i | 0.428732 | + | 0.742585i | ||||
\(538\) | − | 19.9941i | − | 0.862009i | ||||||
\(539\) | −8.34537 | + | 4.81820i | −0.359460 | + | 0.207535i | ||||
\(540\) | 6.39011 | − | 3.68933i | 0.274987 | − | 0.158764i | ||||
\(541\) | − | 29.0019i | − | 1.24689i | −0.781867 | − | 0.623445i | \(-0.785733\pi\) | ||
0.781867 | − | 0.623445i | \(-0.214267\pi\) | |||||||
\(542\) | −23.3596 | − | 40.4601i | −1.00338 | − | 1.73791i | ||||
\(543\) | 5.04138 | − | 8.73193i | 0.216347 | − | 0.374723i | ||||
\(544\) | 6.40856 | + | 3.69998i | 0.274765 | + | 0.158635i | ||||
\(545\) | −67.9590 | −2.91104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.7006 | 1.18439 | 0.592197 | − | 0.805793i | \(-0.298261\pi\) | ||||
0.592197 | + | 0.805793i | \(0.298261\pi\) | |||||||
\(548\) | −43.8192 | − | 25.2990i | −1.87186 | − | 1.08072i | ||||
\(549\) | −1.83997 | + | 3.18692i | −0.0785280 | + | 0.136014i | ||||
\(550\) | −31.7186 | − | 54.9383i | −1.35249 | − | 2.34258i | ||||
\(551\) | 14.9758i | 0.637992i | ||||||||
\(552\) | 0.712430 | − | 0.411322i | 0.0303230 | − | 0.0175070i | ||||
\(553\) | 7.27965 | − | 4.20291i | 0.309562 | − | 0.178726i | ||||
\(554\) | − | 49.1135i | − | 2.08663i | ||||||
\(555\) | 14.7736 | + | 25.5886i | 0.627104 | + | 1.08618i | ||||
\(556\) | 1.07984 | − | 1.87034i | 0.0457956 | − | 0.0793203i | ||||
\(557\) | 5.89738 | + | 3.40485i | 0.249880 | + | 0.144268i | 0.619709 | − | 0.784831i | \(-0.287251\pi\) |
−0.369829 | + | 0.929100i | \(0.620584\pi\) | |||||||
\(558\) | −18.0901 | −0.765814 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −26.8877 | −1.13621 | ||||||||
\(561\) | 3.90027 | + | 2.25182i | 0.164670 | + | 0.0950721i | ||||
\(562\) | −4.22587 | + | 7.31943i | −0.178258 | + | 0.308751i | ||||
\(563\) | −9.62618 | − | 16.6730i | −0.405695 | − | 0.702684i | 0.588707 | − | 0.808346i | \(-0.299637\pi\) |
−0.994402 | + | 0.105662i | \(0.966304\pi\) | |||||||
\(564\) | − | 8.35690i | − | 0.351889i | ||||||
\(565\) | 28.1762 | − | 16.2676i | 1.18538 | − | 0.684381i | ||||
\(566\) | −27.7798 | + | 16.0387i | −1.16767 | + | 0.674157i | ||||
\(567\) | − | 2.24698i | − | 0.0943643i | ||||||
\(568\) | 0.482647 | + | 0.835969i | 0.0202514 | + | 0.0350765i | ||||
\(569\) | 3.92423 | − | 6.79697i | 0.164512 | − | 0.284944i | −0.771970 | − | 0.635659i | \(-0.780728\pi\) |
0.936482 | + | 0.350716i | \(0.114062\pi\) | |||||||
\(570\) | −22.6463 | − | 13.0749i | −0.948551 | − | 0.547646i | ||||
\(571\) | −29.8568 | −1.24947 | −0.624735 | − | 0.780837i | \(-0.714793\pi\) | ||||
−0.624735 | + | 0.780837i | \(0.714793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.58748 | 0.275196 | ||||||||
\(574\) | 27.6663 | + | 15.9731i | 1.15477 | + | 0.666706i | ||||
\(575\) | −6.35384 | + | 11.0052i | −0.264973 | + | 0.458947i | ||||
\(576\) | −4.74914 | − | 8.22574i | −0.197881 | − | 0.342739i | ||||
\(577\) | 8.97823i | 0.373769i | 0.982382 | + | 0.186884i | \(0.0598389\pi\) | ||||
−0.982382 | + | 0.186884i | \(0.940161\pi\) | |||||||
\(578\) | 28.6897 | − | 16.5640i | 1.19333 | − | 0.688971i | ||||
\(579\) | 9.41131 | − | 5.43362i | 0.391121 | − | 0.225814i | ||||
\(580\) | 29.0646i | 1.20684i | ||||||||
\(581\) | −2.59299 | − | 4.49119i | −0.107575 | − | 0.186326i | ||||
\(582\) | −16.5238 | + | 28.6201i | −0.684933 | + | 1.18634i | ||||
\(583\) | 2.32205 | + | 1.34063i | 0.0961693 | + | 0.0555234i | ||||
\(584\) | 3.00756 | 0.124454 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46.2948 | −1.91242 | ||||||||
\(587\) | −20.6580 | − | 11.9269i | −0.852648 | − | 0.492277i | 0.00889531 | − | 0.999960i | \(-0.497168\pi\) |
−0.861543 | + | 0.507684i | \(0.830502\pi\) | |||||||
\(588\) | −2.14430 | + | 3.71404i | −0.0884295 | + | 0.153164i | ||||
\(589\) | 16.7838 | + | 29.0704i | 0.691565 | + | 1.19783i | ||||
\(590\) | 32.4215i | 1.33477i | ||||||||
\(591\) | −8.00346 | + | 4.62080i | −0.329218 | + | 0.190074i | ||||
\(592\) | 27.1722 | − | 15.6879i | 1.11677 | − | 0.644769i | ||||
\(593\) | − | 11.9866i | − | 0.492230i | −0.969241 | − | 0.246115i | \(-0.920846\pi\) | ||
0.969241 | − | 0.246115i | \(-0.0791541\pi\) | |||||||
\(594\) | −5.05980 | − | 8.76383i | −0.207606 | − | 0.359585i | ||||
\(595\) | 3.43900 | − | 5.95652i | 0.140985 | − | 0.244194i | ||||
\(596\) | 19.5289 | + | 11.2750i | 0.799936 | + | 0.461843i | ||||
\(597\) | −1.56465 | −0.0640367 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.1142 | 1.18958 | 0.594788 | − | 0.803883i | \(-0.297236\pi\) | ||||
0.594788 | + | 0.803883i | \(0.297236\pi\) | |||||||
\(600\) | −2.20312 | − | 1.27197i | −0.0899419 | − | 0.0519280i | ||||
\(601\) | −18.5683 | + | 32.1612i | −0.757417 | + | 1.31188i | 0.186747 | + | 0.982408i | \(0.440205\pi\) |
−0.944164 | + | 0.329476i | \(0.893128\pi\) | |||||||
\(602\) | 5.26271 | + | 9.11528i | 0.214492 | + | 0.371511i | ||||
\(603\) | − | 1.52111i | − | 0.0619442i | ||||||
\(604\) | −38.3924 | + | 22.1658i | −1.56216 | + | 0.901915i | ||||
\(605\) | −38.9377 | + | 22.4807i | −1.58304 | + | 0.913970i | ||||
\(606\) | 20.3840i | 0.828045i | ||||||||
\(607\) | 7.11625 | + | 12.3257i | 0.288840 | + | 0.500285i | 0.973533 | − | 0.228546i | \(-0.0733972\pi\) |
−0.684693 | + | 0.728831i | \(0.740064\pi\) | |||||||
\(608\) | −15.4269 | + | 26.7202i | −0.625644 | + | 1.08365i | ||||
\(609\) | 7.66507 | + | 4.42543i | 0.310604 | + | 0.179327i | ||||
\(610\) | 25.3106 | 1.02480 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.00431 | 0.0810195 | ||||||||
\(613\) | −26.2526 | − | 15.1570i | −1.06033 | − | 0.612184i | −0.134810 | − | 0.990872i | \(-0.543042\pi\) |
−0.925525 | + | 0.378687i | \(0.876376\pi\) | |||||||
\(614\) | −6.71528 | + | 11.6312i | −0.271007 | + | 0.469398i | ||||
\(615\) | −11.6468 | − | 20.1728i | −0.469642 | − | 0.813444i | ||||
\(616\) | − | 4.50365i | − | 0.181457i | ||||||
\(617\) | −21.6192 | + | 12.4819i | −0.870358 | + | 0.502501i | −0.867467 | − | 0.497494i | \(-0.834254\pi\) |
−0.00289086 | + | 0.999996i | \(0.500920\pi\) | |||||||
\(618\) | 19.4971 | − | 11.2567i | 0.784289 | − | 0.452810i | ||||
\(619\) | − | 35.6122i | − | 1.43138i | −0.698420 | − | 0.715688i | \(-0.746113\pi\) | ||
0.698420 | − | 0.715688i | \(-0.253887\pi\) | |||||||
\(620\) | 32.5734 | + | 56.4188i | 1.30818 | + | 2.26584i | ||||
\(621\) | −1.01357 | + | 1.75556i | −0.0406733 | + | 0.0704482i | ||||
\(622\) | 21.3626 | + | 12.3337i | 0.856561 | + | 0.494536i | ||||
\(623\) | 22.6015 | 0.905509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0465 | −0.681861 | ||||||||
\(626\) | −60.1438 | − | 34.7240i | −2.40383 | − | 1.38785i | ||||
\(627\) | −9.38889 | + | 16.2620i | −0.374956 | + | 0.649443i | ||||
\(628\) | 11.4721 | + | 19.8702i | 0.457785 | + | 0.792907i | ||||
\(629\) | 8.02608i | 0.320021i | ||||||||
\(630\) | −13.3842 | + | 7.72737i | −0.533239 | + | 0.307866i | ||||
\(631\) | −20.6832 | + | 11.9415i | −0.823385 | + | 0.475382i | −0.851582 | − | 0.524221i | \(-0.824357\pi\) |
0.0281972 | + | 0.999602i | \(0.491023\pi\) | |||||||
\(632\) | − | 1.51812i | − | 0.0603877i | ||||||
\(633\) | 11.6223 | + | 20.1304i | 0.461945 | + | 0.800112i | ||||
\(634\) | 4.60829 | − | 7.98180i | 0.183019 | − | 0.316998i | ||||
\(635\) | 40.1526 | + | 23.1821i | 1.59341 | + | 0.919953i | ||||
\(636\) | 1.19328 | 0.0473165 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 39.8611 | 1.57812 | ||||||||
\(639\) | −2.05999 | − | 1.18933i | −0.0814918 | − | 0.0470493i | ||||
\(640\) | −5.42237 | + | 9.39182i | −0.214338 | + | 0.371244i | ||||
\(641\) | −12.3288 | − | 21.3542i | −0.486960 | − | 0.843440i | 0.512927 | − | 0.858432i | \(-0.328561\pi\) |
−0.999888 | + | 0.0149922i | \(0.995228\pi\) | |||||||
\(642\) | − | 20.2282i | − | 0.798343i | ||||||
\(643\) | 41.4103 | − | 23.9083i | 1.63306 | − | 0.942850i | 0.649923 | − | 0.760000i | \(-0.274801\pi\) |
0.983141 | − | 0.182850i | \(-0.0585323\pi\) | |||||||
\(644\) | −8.67072 | + | 5.00604i | −0.341674 | + | 0.197266i | ||||
\(645\) | − | 7.67456i | − | 0.302186i | ||||||
\(646\) | −3.55161 | − | 6.15156i | −0.139736 | − | 0.242030i | ||||
\(647\) | −2.69471 | + | 4.66737i | −0.105940 | + | 0.183493i | −0.914122 | − | 0.405440i | \(-0.867118\pi\) |
0.808182 | + | 0.588933i | \(0.200452\pi\) | |||||||
\(648\) | −0.351445 | − | 0.202907i | −0.0138060 | − | 0.00797092i | ||||
\(649\) | 23.2814 | 0.913876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.8388 | 0.777543 | ||||||||
\(652\) | 21.0279 | + | 12.1405i | 0.823517 | + | 0.475458i | ||||
\(653\) | 2.51895 | − | 4.36295i | 0.0985741 | − | 0.170735i | −0.812521 | − | 0.582933i | \(-0.801905\pi\) |
0.911095 | + | 0.412197i | \(0.135239\pi\) | |||||||
\(654\) | 20.7397 | + | 35.9223i | 0.810988 | + | 1.40467i | ||||
\(655\) | 10.0526i | 0.392789i | ||||||||
\(656\) | −21.4212 | + | 12.3675i | −0.836358 | + | 0.482871i | ||||
\(657\) | −6.41828 | + | 3.70560i | −0.250401 | + | 0.144569i | ||||
\(658\) | 17.5036i | 0.682363i | ||||||||
\(659\) | 21.9906 | + | 38.0888i | 0.856632 | + | 1.48373i | 0.875122 | + | 0.483902i | \(0.160781\pi\) |
−0.0184899 | + | 0.999829i | \(0.505886\pi\) | |||||||
\(660\) | −18.2216 | + | 31.5608i | −0.709276 | + | 1.22850i | ||||
\(661\) | −33.0989 | − | 19.1097i | −1.28740 | − | 0.743280i | −0.309210 | − | 0.950994i | \(-0.600064\pi\) |
−0.978190 | + | 0.207714i | \(0.933398\pi\) | |||||||
\(662\) | −22.9748 | −0.892940 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.936608 | −0.0363474 | ||||||||
\(665\) | 24.8355 | + | 14.3388i | 0.963079 | + | 0.556034i | ||||
\(666\) | 9.01722 | − | 15.6183i | 0.349410 | − | 0.605196i | ||||
\(667\) | −3.99247 | − | 6.91516i | −0.154589 | − | 0.267756i | ||||
\(668\) | 17.8261i | 0.689713i | ||||||||
\(669\) | −9.29985 | + | 5.36927i | −0.359553 | + | 0.207588i | ||||
\(670\) | −9.06051 | + | 5.23109i | −0.350038 | + | 0.202094i | ||||
\(671\) | − | 18.1752i | − | 0.701647i | ||||||
\(672\) | 9.11745 | + | 15.7919i | 0.351713 | + | 0.609185i | ||||
\(673\) | −3.33244 | + | 5.77195i | −0.128456 | + | 0.222492i | −0.923079 | − | 0.384611i | \(-0.874335\pi\) |
0.794623 | + | 0.607104i | \(0.207669\pi\) | |||||||
\(674\) | −12.5077 | − | 7.22132i | −0.481779 | − | 0.278155i | ||||
\(675\) | 6.26875 | 0.241284 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.80194 | 0.184553 | 0.0922767 | − | 0.995733i | \(-0.470586\pi\) | ||||
0.0922767 | + | 0.995733i | \(0.470586\pi\) | |||||||
\(678\) | −17.1977 | − | 9.92908i | −0.660472 | − | 0.381324i | ||||
\(679\) | 18.1211 | − | 31.3867i | 0.695424 | − | 1.20451i | ||||
\(680\) | −0.621097 | − | 1.07577i | −0.0238180 | − | 0.0412539i | ||||
\(681\) | 6.97584i | 0.267315i | ||||||||
\(682\) | 77.3766 | − | 44.6734i | 2.96290 | − | 1.71063i | ||||
\(683\) | −9.75063 | + | 5.62953i | −0.373098 | + | 0.215408i | −0.674811 | − | 0.737991i | \(-0.735775\pi\) |
0.301713 | + | 0.953399i | \(0.402441\pi\) | |||||||
\(684\) | 8.35690i | 0.319534i | ||||||||
\(685\) | −38.6368 | − | 66.9209i | −1.47624 | − | 2.55692i | ||||
\(686\) | 20.6048 | − | 35.6886i | 0.786696 | − | 1.36260i | ||||
\(687\) | 14.5535 | + | 8.40246i | 0.555250 | + | 0.320574i | ||||
\(688\) | −8.14952 | −0.310698 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 13.9427 | 0.530790 | ||||||||
\(691\) | 21.4033 | + | 12.3572i | 0.814219 | + | 0.470090i | 0.848419 | − | 0.529325i | \(-0.177555\pi\) |
−0.0341997 | + | 0.999415i | \(0.510888\pi\) | |||||||
\(692\) | 19.8443 | − | 34.3714i | 0.754369 | − | 1.30660i | ||||
\(693\) | 5.54892 | + | 9.61101i | 0.210786 | + | 0.365092i | ||||
\(694\) | 5.54048i | 0.210314i | ||||||||
\(695\) | 2.85640 | − | 1.64914i | 0.108350 | − | 0.0625556i | ||||
\(696\) | 1.38434 | − | 0.799249i | 0.0524733 | − | 0.0302955i | ||||
\(697\) | − | 6.32736i | − | 0.239666i | ||||||
\(698\) | −0.425665 | − | 0.737273i | −0.0161116 | − | 0.0279062i | ||||
\(699\) | −4.34601 | + | 7.52751i | −0.164381 | + | 0.284717i | ||||
\(700\) | 26.8133 | + | 15.4807i | 1.01345 | + | 0.585115i | ||||
\(701\) | −25.8920 | −0.977927 | −0.488964 | − | 0.872304i | \(-0.662625\pi\) | ||||
−0.488964 | + | 0.872304i | \(0.662625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.4644 | −1.26213 | ||||||||
\(704\) | 40.6270 | + | 23.4560i | 1.53119 | + | 0.884031i | ||||
\(705\) | 6.38135 | − | 11.0528i | 0.240336 | − | 0.416274i | ||||
\(706\) | 32.9540 | + | 57.0779i | 1.24024 | + | 2.14816i | ||||
\(707\) | − | 22.3545i | − | 0.840728i | ||||||
\(708\) | 8.97307 | − | 5.18060i | 0.337229 | − | 0.194699i | ||||
\(709\) | −0.0737525 | + | 0.0425810i | −0.00276983 | + | 0.00159916i | −0.501384 | − | 0.865225i | \(-0.667176\pi\) |
0.498614 | + | 0.866824i | \(0.333842\pi\) | |||||||
\(710\) | 16.3605i | 0.613998i | ||||||||
\(711\) | 1.87047 | + | 3.23975i | 0.0701481 | + | 0.121500i | ||||
\(712\) | 2.04096 | − | 3.53504i | 0.0764881 | − | 0.132481i | ||||
\(713\) | −15.5000 | − | 8.94893i | −0.580479 | − | 0.335140i | ||||
\(714\) | −4.19806 | −0.157109 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −43.6760 | −1.63225 | ||||||||
\(717\) | −19.8486 | − | 11.4596i | −0.741258 | − | 0.427966i | ||||
\(718\) | 22.8988 | − | 39.6619i | 0.854576 | − | 1.48017i | ||||
\(719\) | 13.5254 | + | 23.4267i | 0.504413 | + | 0.873669i | 0.999987 | + | 0.00510319i | \(0.00162440\pi\) |
−0.495574 | + | 0.868566i | \(0.665042\pi\) | |||||||
\(720\) | − | 11.9661i | − | 0.445952i | ||||||
\(721\) | −21.3818 | + | 12.3448i | −0.796302 | + | 0.459745i | ||||
\(722\) | −8.06519 | + | 4.65644i | −0.300155 | + | 0.173295i | ||||
\(723\) | 21.9801i | 0.817451i | ||||||||
\(724\) | 11.0813 | + | 19.1933i | 0.411832 | + | 0.713315i | ||||
\(725\) | −12.3463 | + | 21.3844i | −0.458530 | + | 0.794198i | ||||
\(726\) | 23.7660 | + | 13.7213i | 0.882040 | + | 0.509246i | ||||
\(727\) | 47.1584 | 1.74901 | 0.874503 | − | 0.485019i | \(-0.161187\pi\) | ||||
0.874503 | + | 0.485019i | \(0.161187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 44.1449 | + | 25.4871i | 1.63388 | + | 0.943320i | ||||
\(731\) | 1.04234 | − | 1.80539i | 0.0385525 | − | 0.0667749i | ||||
\(732\) | −4.04437 | − | 7.00505i | −0.149484 | − | 0.258914i | ||||
\(733\) | − | 9.68186i | − | 0.357608i | −0.983885 | − | 0.178804i | \(-0.942777\pi\) | ||
0.983885 | − | 0.178804i | \(-0.0572227\pi\) | |||||||
\(734\) | 4.08577 | − | 2.35892i | 0.150809 | − | 0.0870693i | ||||
\(735\) | −5.67210 | + | 3.27479i | −0.209219 | + | 0.120792i | ||||
\(736\) | − | 16.4509i | − | 0.606388i | ||||||
\(737\) | 3.75637 | + | 6.50623i | 0.138368 | + | 0.239660i | ||||
\(738\) | −7.10872 | + | 12.3127i | −0.261676 | + | 0.453235i | ||||
\(739\) | 31.4488 | + | 18.1570i | 1.15686 | + | 0.667915i | 0.950550 | − | 0.310571i | \(-0.100520\pi\) |
0.206313 | + | 0.978486i | \(0.433854\pi\) | |||||||
\(740\) | −64.9466 | −2.38748 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.49934 | −0.0917535 | ||||||||
\(743\) | 36.1597 | + | 20.8768i | 1.32657 | + | 0.765896i | 0.984768 | − | 0.173876i | \(-0.0556292\pi\) |
0.341803 | + | 0.939772i | \(0.388963\pi\) | |||||||
\(744\) | 1.79148 | − | 3.10293i | 0.0656788 | − | 0.113759i | ||||
\(745\) | 17.2193 | + | 29.8247i | 0.630866 | + | 1.09269i | ||||
\(746\) | 39.4950i | 1.44602i | ||||||||
\(747\) | 1.99877 | − | 1.15399i | 0.0731311 | − | 0.0422223i | ||||
\(748\) | −8.57304 | + | 4.94965i | −0.313462 | + | 0.180977i | ||||
\(749\) | 22.1836i | 0.810571i | ||||||||
\(750\) | −4.36323 | − | 7.55734i | −0.159323 | − | 0.275955i | ||||
\(751\) | −11.0963 | + | 19.2194i | −0.404911 | + | 0.701327i | −0.994311 | − | 0.106515i | \(-0.966031\pi\) |
0.589400 | + | 0.807841i | \(0.299364\pi\) | |||||||
\(752\) | −11.7369 | − | 6.77628i | −0.427999 | − | 0.247106i | ||||
\(753\) | 26.6437 | 0.970950 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −67.7036 | −2.46399 | ||||||||
\(756\) | 4.27730 | + | 2.46950i | 0.155564 | + | 0.0898149i | ||||
\(757\) | −4.61865 | + | 7.99973i | −0.167868 | + | 0.290755i | −0.937670 | − | 0.347527i | \(-0.887021\pi\) |
0.769802 | + | 0.638282i | \(0.220355\pi\) | |||||||
\(758\) | 7.51895 | + | 13.0232i | 0.273101 | + | 0.473024i | ||||
\(759\) | − | 10.0121i | − | 0.363416i | ||||||
\(760\) | 4.48538 | − | 2.58964i | 0.162702 | − | 0.0939360i | ||||
\(761\) | 6.49669 | − | 3.75086i | 0.235505 | − | 0.135969i | −0.377604 | − | 0.925967i | \(-0.623252\pi\) |
0.613109 | + | 0.789998i | \(0.289919\pi\) | |||||||
\(762\) | − | 28.2989i | − | 1.02516i | ||||||
\(763\) | −22.7446 | − | 39.3948i | −0.823409 | − | 1.42619i | ||||
\(764\) | −7.23985 | + | 12.5398i | −0.261929 | + | 0.453673i | ||||
\(765\) | 2.65090 | + | 1.53050i | 0.0958436 | + | 0.0553353i | ||||
\(766\) | 39.1140 | 1.41325 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.3773 | −0.446629 | ||||||||
\(769\) | −4.45141 | − | 2.57002i | −0.160522 | − | 0.0926774i | 0.417587 | − | 0.908637i | \(-0.362876\pi\) |
−0.578109 | + | 0.815959i | \(0.696209\pi\) | |||||||
\(770\) | 38.1655 | − | 66.1045i | 1.37539 | − | 2.38224i | ||||
\(771\) | −11.5722 | − | 20.0436i | −0.416762 | − | 0.721853i | ||||
\(772\) | 23.8869i | 0.859708i | ||||||||
\(773\) | −7.36271 | + | 4.25086i | −0.264818 | + | 0.152893i | −0.626531 | − | 0.779397i | \(-0.715526\pi\) |
0.361712 | + | 0.932290i | \(0.382192\pi\) | |||||||
\(774\) | −4.05668 | + | 2.34213i | −0.145814 | + | 0.0841860i | ||||
\(775\) | 55.3473i | 1.98813i | ||||||||
\(776\) | −3.27274 | − | 5.66855i | −0.117485 | − | 0.203489i | ||||
\(777\) | −9.88889 | + | 17.1281i | −0.354762 | + | 0.614466i | ||||
\(778\) | 42.5645 | + | 24.5746i | 1.52601 | + | 0.881043i | ||||
\(779\) | 26.3817 | 0.945221 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7482 | 0.420385 | ||||||||
\(782\) | 3.27994 | + | 1.89367i | 0.117290 | + | 0.0677176i | ||||
\(783\) | −1.96950 | + | 3.41127i | −0.0703842 | + | 0.121909i | ||||
\(784\) | 3.47746 | + | 6.02314i | 0.124195 | + | 0.215112i | ||||
\(785\) | 35.0404i | 1.25065i | ||||||||
\(786\) | 5.31370 | − | 3.06787i | 0.189533 | − | 0.109427i | ||||
\(787\) | 6.74248 | − | 3.89277i | 0.240343 | − | 0.138762i | −0.374991 | − | 0.927028i | \(-0.622354\pi\) |
0.615335 | + | 0.788266i | \(0.289021\pi\) | |||||||
\(788\) | − | 20.3136i | − | 0.723643i | ||||||
\(789\) | −9.26420 | − | 16.0461i | −0.329814 | − | 0.571255i | ||||
\(790\) | 12.8651 | − | 22.2830i | 0.457719 | − | 0.792793i | ||||
\(791\) | 18.8601 | + | 10.8889i | 0.670588 | + | 0.387164i | ||||
\(792\) | 2.00431 | 0.0712201 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.05190 | 0.321240 | ||||||||
\(795\) | 1.57823 | + | 0.911190i | 0.0559740 | + | 0.0323166i | ||||
\(796\) | 1.71960 | − | 2.97843i | 0.0609494 | − | 0.105568i | ||||
\(797\) | 10.6920 | + | 18.5191i | 0.378731 | + | 0.655981i | 0.990878 | − | 0.134763i | \(-0.0430273\pi\) |
−0.612147 | + | 0.790744i | \(0.709694\pi\) | |||||||
\(798\) | − | 17.5036i | − | 0.619622i | ||||||
\(799\) | 3.00235 | − | 1.73341i | 0.106215 | − | 0.0613235i | ||||
\(800\) | −44.0571 | + | 25.4364i | −1.55765 | + | 0.899312i | ||||
\(801\) | 10.0586i | 0.355403i | ||||||||
\(802\) | −20.9080 | − | 36.2137i | −0.738286 | − | 1.27875i | ||||
\(803\) | 18.3019 | − | 31.6999i | 0.645861 | − | 1.11866i | ||||
\(804\) | 2.89554 | + | 1.67174i | 0.102118 | + | 0.0589578i | ||||
\(805\) | −15.2905 | −0.538920 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.75840 | −0.343512 | ||||||||
\(808\) | −3.49641 | − | 2.01865i | −0.123003 | − | 0.0710160i | ||||
\(809\) | −1.14310 | + | 1.97991i | −0.0401894 | + | 0.0696101i | −0.885420 | − | 0.464791i | \(-0.846129\pi\) |
0.845231 | + | 0.534401i | \(0.179463\pi\) | |||||||
\(810\) | −3.43900 | − | 5.95652i | −0.120834 | − | 0.209291i | ||||
\(811\) | 17.8079i | 0.625320i | 0.949865 | + | 0.312660i | \(0.101220\pi\) | ||||
−0.949865 | + | 0.312660i | \(0.898780\pi\) | |||||||
\(812\) | −16.8483 | + | 9.72737i | −0.591259 | + | 0.341364i | ||||
\(813\) | −19.7471 | + | 11.4010i | −0.692560 | + | 0.399849i | ||||
\(814\) | 89.0721i | 3.12198i | ||||||||
\(815\) | 18.5410 | + | 32.1140i | 0.649463 | + | 1.12490i | ||||
\(816\) | 1.62522 | − | 2.81496i | 0.0568940 | − | 0.0985434i | ||||
\(817\) | 7.52751 | + | 4.34601i | 0.263354 | + | 0.152048i | ||||
\(818\) | −45.3818 | −1.58674 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 51.2006 | 1.78800 | ||||||||
\(821\) | −12.0424 | − | 6.95271i | −0.420284 | − | 0.242651i | 0.274915 | − | 0.961469i | \(-0.411350\pi\) |
−0.695199 | + | 0.718817i | \(0.744684\pi\) | |||||||
\(822\) | −23.5824 | + | 40.8459i | −0.822531 | + | 1.42466i | ||||
\(823\) | −3.62415 | − | 6.27722i | −0.126330 | − | 0.218810i | 0.795922 | − | 0.605399i | \(-0.206987\pi\) |
−0.922252 | + | 0.386589i | \(0.873653\pi\) | |||||||
\(824\) | 4.45904i | 0.155338i | ||||||||
\(825\) | −26.8133 | + | 15.4807i | −0.933520 | + | 0.538968i | ||||
\(826\) | −18.7942 | + | 10.8509i | −0.653935 | + | 0.377550i | ||||
\(827\) | − | 54.1191i | − | 1.88191i | −0.338536 | − | 0.940953i | \(-0.609932\pi\) | ||
0.338536 | − | 0.940953i | \(-0.390068\pi\) | |||||||
\(828\) | −2.22790 | − | 3.85883i | −0.0774248 | − | 0.134104i | ||||
\(829\) | −2.89589 | + | 5.01582i | −0.100578 | + | 0.174207i | −0.911923 | − | 0.410361i | \(-0.865403\pi\) |
0.811345 | + | 0.584568i | \(0.198736\pi\) | |||||||
\(830\) | −13.7475 | − | 7.93714i | −0.477184 | − | 0.275502i | ||||
\(831\) | −23.9705 | −0.831526 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.77910 | −0.0616422 | ||||||||
\(834\) | −1.74344 | − | 1.00657i | −0.0603703 | − | 0.0348548i | ||||
\(835\) | −13.6121 | + | 23.5768i | −0.471065 | + | 0.815909i | ||||
\(836\) | −20.6374 | − | 35.7450i | −0.713758 | − | 1.23627i | ||||
\(837\) | 8.82908i | 0.305178i | ||||||||
\(838\) | −26.1833 | + | 15.1169i | −0.904486 | + | 0.522205i | ||||
\(839\) | 4.58431 | − | 2.64675i | 0.158268 | − | 0.0913760i | −0.418774 | − | 0.908090i | \(-0.637540\pi\) |
0.577042 | + | 0.816714i | \(0.304207\pi\) | |||||||
\(840\) | − | 3.06100i | − | 0.105614i | ||||||
\(841\) | 6.74214 | + | 11.6777i | 0.232487 | + | 0.402680i | ||||
\(842\) | −8.67941 | + | 15.0332i | −0.299112 | + | 0.518077i | ||||
\(843\) | 3.57234 | + | 2.06249i | 0.123038 | + | 0.0710360i | ||||
\(844\) | −51.0930 | −1.75870 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.78986 | −0.267821 | ||||||||
\(847\) | −26.0634 | − | 15.0477i | −0.895550 | − | 0.517046i | ||||
\(848\) | 0.967582 | − | 1.67590i | 0.0332269 | − | 0.0575507i | ||||
\(849\) | 7.82789 | + | 13.5583i | 0.268652 | + | 0.465320i | ||||
\(850\) | − | 11.7120i | − | 0.401718i | ||||||
\(851\) | 15.4523 | − | 8.92141i | 0.529699 | − | 0.305822i | ||||
\(852\) | 4.52798 | − | 2.61423i | 0.155126 | − | 0.0895620i | ||||
\(853\) | 13.5961i | 0.465522i | 0.972534 | + | 0.232761i | \(0.0747760\pi\) | ||||
−0.972534 | + | 0.232761i | \(0.925224\pi\) | |||||||
\(854\) | 8.47099 | + | 14.6722i | 0.289871 | + | 0.502072i | ||||
\(855\) | −6.38135 | + | 11.0528i | −0.218238 | + | 0.377999i | ||||
\(856\) | 3.46968 | + | 2.00322i | 0.118591 | + | 0.0684687i | ||||
\(857\) | 23.8323 | 0.814097 | 0.407048 | − | 0.913407i | \(-0.366558\pi\) | ||||
0.407048 | + | 0.913407i | \(0.366558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.9861 | −0.920754 | −0.460377 | − | 0.887723i | \(-0.652286\pi\) | ||||
−0.460377 | + | 0.887723i | \(0.652286\pi\) | |||||||
\(860\) | 14.6091 | + | 8.43458i | 0.498167 | + | 0.287617i | ||||
\(861\) | 7.79590 | − | 13.5029i | 0.265683 | − | 0.460177i | ||||
\(862\) | −2.45031 | − | 4.24407i | −0.0834580 | − | 0.144553i | ||||
\(863\) | − | 27.0291i | − | 0.920080i | −0.887898 | − | 0.460040i | \(-0.847835\pi\) | ||
0.887898 | − | 0.460040i | \(-0.152165\pi\) | |||||||
\(864\) | −7.02805 | + | 4.05765i | −0.239099 | + | 0.138044i | ||||
\(865\) | 52.4922 | − | 30.3064i | 1.78479 | − | 1.03045i | ||||
\(866\) | − | 21.3674i | − | 0.726095i | ||||||
\(867\) | −8.08426 | − | 14.0024i | −0.274556 | − | 0.475545i | ||||
\(868\) | −21.8034 | + | 37.7646i | −0.740057 | + | 1.28182i | ||||
\(869\) | −16.0011 | − | 9.23825i | −0.542801 | − | 0.313386i | ||||
\(870\) | 27.0925 | 0.918520 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.21552 | −0.278213 | ||||||||
\(873\) | 13.9684 | + | 8.06465i | 0.472758 | + | 0.272947i | ||||
\(874\) | −7.89559 | + | 13.6756i | −0.267072 | + | 0.462583i | ||||
\(875\) | 4.78501 | + | 8.28788i | 0.161763 | + | 0.280182i | ||||
\(876\) | − | 16.2903i | − | 0.550397i | ||||||
\(877\) | 35.4014 | − | 20.4390i | 1.19542 | − | 0.690176i | 0.235889 | − | 0.971780i | \(-0.424200\pi\) |
0.959531 | + | 0.281604i | \(0.0908664\pi\) | |||||||
\(878\) | −57.7575 | + | 33.3463i | −1.94922 | + | 1.12538i | ||||
\(879\) | 22.5948i | 0.762103i | ||||||||
\(880\) | 29.5504 | + | 51.1828i | 0.996144 | + | 1.72537i | ||||
\(881\) | −11.2482 | + | 19.4824i | −0.378961 | + | 0.656379i | −0.990911 | − | 0.134517i | \(-0.957052\pi\) |
0.611951 | + | 0.790896i | \(0.290385\pi\) | |||||||
\(882\) | 3.46203 | + | 1.99880i | 0.116573 | + | 0.0673032i | ||||
\(883\) | 4.16315 | 0.140101 | 0.0700505 | − | 0.997543i | \(-0.477684\pi\) | ||||
0.0700505 | + | 0.997543i | \(0.477684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.8237 | 0.531908 | ||||||||
\(886\) | 17.0026 | + | 9.81647i | 0.571214 | + | 0.329791i | ||||
\(887\) | 13.1501 | − | 22.7766i | 0.441537 | − | 0.764765i | −0.556266 | − | 0.831004i | \(-0.687767\pi\) |
0.997804 | + | 0.0662389i | \(0.0211000\pi\) | |||||||
\(888\) | 1.78597 | + | 3.09339i | 0.0599333 | + | 0.103807i | ||||
\(889\) | 31.0344i | 1.04086i | ||||||||
\(890\) | 59.9143 | − | 34.5916i | 2.00833 | − | 1.15951i | ||||
\(891\) | −4.27730 | + | 2.46950i | −0.143295 | + | 0.0827314i | ||||
\(892\) | − | 23.6040i | − | 0.790320i | ||||||
\(893\) | 7.22737 | + | 12.5182i | 0.241855 | + | 0.418904i | ||||
\(894\) | 10.5100 | − | 18.2038i | 0.351506 | − | 0.608827i | ||||
\(895\) | −57.7659 | − | 33.3512i | −1.93090 | − | 1.11481i | ||||
\(896\) | −7.25906 | −0.242508 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 58.1764 | 1.94137 | ||||||||
\(899\) | −30.1184 | − | 17.3889i | −1.00451 | − | 0.579952i | ||||
\(900\) | −6.88955 | + | 11.9331i | −0.229652 | + | 0.397768i | ||||
\(901\) | 0.247512 | + | 0.428703i | 0.00824582 | + | 0.0142822i | ||||
\(902\) | − | 70.2199i | − | 2.33807i | ||||||
\(903\) | 4.44883 | − | 2.56853i | 0.148048 | − | 0.0854754i | ||||
\(904\) | 3.40621 | − | 1.96658i | 0.113289 | − | 0.0654073i | ||||
\(905\) | 33.8468i | 1.12511i | ||||||||
\(906\) | 20.6618 | + | 35.7873i | 0.686443 | + | 1.18895i | ||||
\(907\) | −28.9557 | + | 50.1527i | −0.961458 | + | 1.66529i | −0.242613 | + | 0.970123i | \(0.578005\pi\) |
−0.718845 | + | 0.695171i | \(0.755329\pi\) | |||||||
\(908\) | −13.2790 | − | 7.66666i | −0.440681 | − | 0.254427i | ||||
\(909\) | 9.94869 | 0.329977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.286799 | −0.00950208 | −0.00475104 | − | 0.999989i | \(-0.501512\pi\) | ||||
−0.00475104 | + | 0.999989i | \(0.501512\pi\) | |||||||
\(912\) | 11.7369 | + | 6.77628i | 0.388646 | + | 0.224385i | ||||
\(913\) | −5.69955 | + | 9.87192i | −0.188628 | + | 0.326713i | ||||
\(914\) | −5.11788 | − | 8.86442i | −0.169284 | − | 0.293209i | ||||
\(915\) | − | 12.3532i | − | 0.408383i | ||||||
\(916\) | −31.9895 | + | 18.4691i | −1.05696 | + | 0.610237i | ||||
\(917\) | −5.82736 | + | 3.36443i | −0.192436 | + | 0.111103i | ||||
\(918\) | − | 1.86831i | − | 0.0616635i | ||||||
\(919\) | 15.5620 | + | 26.9541i | 0.513342 | + | 0.889134i | 0.999880 | + | 0.0154747i | \(0.00492596\pi\) |
−0.486539 | + | 0.873659i | \(0.661741\pi\) | |||||||
\(920\) | −1.38076 | + | 2.39155i | −0.0455224 | + | 0.0788472i | ||||
\(921\) | 5.67676 | + | 3.27748i | 0.187056 | + | 0.107997i | ||||
\(922\) | 2.77133 | 0.0912690 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −24.3937 | −0.802495 | ||||||||
\(925\) | −47.7848 | − | 27.5886i | −1.57115 | − | 0.907107i | ||||
\(926\) | −3.44696 | + | 5.97031i | −0.113274 | + | 0.196197i | ||||
\(927\) | −5.49396 | − | 9.51582i | −0.180445 | − | 0.312540i | ||||
\(928\) | − | 31.9661i | − | 1.04934i | ||||||
\(929\) | 6.60493 | − | 3.81336i | 0.216701 | − | 0.125112i | −0.387721 | − | 0.921777i | \(-0.626738\pi\) |
0.604422 | + | 0.796665i | \(0.293404\pi\) | |||||||
\(930\) | 52.5907 | − | 30.3632i | 1.72452 | − | 0.995650i | ||||
\(931\) | − | 7.41789i | − | 0.243112i | ||||||
\(932\) | −9.55280 | − | 16.5459i | −0.312912 | − | 0.541980i | ||||
\(933\) | 6.01961 | − | 10.4263i | 0.197073 | − | 0.341341i | ||||
\(934\) | −12.2626 | − | 7.07982i | −0.401245 | − | 0.231659i | ||||
\(935\) | −15.1183 | −0.494421 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.67324 | −0.185337 | −0.0926683 | − | 0.995697i | \(-0.529540\pi\) | ||||
−0.0926683 | + | 0.995697i | \(0.529540\pi\) | |||||||
\(938\) | −6.06476 | − | 3.50149i | −0.198021 | − | 0.114328i | ||||
\(939\) | −16.9475 | + | 29.3539i | −0.553061 | + | 0.957929i | ||||
\(940\) | 14.0266 | + | 24.2948i | 0.457498 | + | 0.792409i | ||||
\(941\) | 41.5394i | 1.35415i | 0.735916 | + | 0.677073i | \(0.236752\pi\) | ||||
−0.735916 | + | 0.677073i | \(0.763248\pi\) | |||||||
\(942\) | 18.5219 | − | 10.6936i | 0.603477 | − | 0.348418i | ||||
\(943\) | −12.1818 | + | 7.03319i | −0.396695 | + | 0.229032i | ||||
\(944\) | − | 16.8030i | − | 0.546891i | ||||||
\(945\) | 3.77144 | + | 6.53232i | 0.122685 | + | 0.212496i | ||||
\(946\) | 11.5678 | − | 20.0360i | 0.376100 | − | 0.651425i | ||||
\(947\) | −40.9725 | − | 23.6555i | −1.33143 | − | 0.768700i | −0.345909 | − | 0.938268i | \(-0.612429\pi\) |
−0.985518 | + | 0.169568i | \(0.945763\pi\) | |||||||
\(948\) | −8.22282 | −0.267065 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 48.8327 | 1.58434 | ||||||||
\(951\) | −3.89562 | − | 2.24914i | −0.126324 | − | 0.0729332i | ||||
\(952\) | 0.415739 | − | 0.720081i | 0.0134742 | − | 0.0233380i | ||||
\(953\) | −17.1717 | − | 29.7423i | −0.556247 | − | 0.963449i | −0.997805 | − | 0.0662159i | \(-0.978907\pi\) |
0.441558 | − | 0.897233i | \(-0.354426\pi\) | |||||||
\(954\) | − | 1.11231i | − | 0.0360123i | ||||||
\(955\) | −19.1508 | + | 11.0567i | −0.619707 | + | 0.357788i | ||||
\(956\) | 43.6284 | − | 25.1889i | 1.41104 | − | 0.814666i | ||||
\(957\) | − | 19.4547i | − | 0.628882i | ||||||
\(958\) | 3.60172 | + | 6.23836i | 0.116366 | + | 0.201552i | ||||
\(959\) | 25.8620 | − | 44.7944i | 0.835129 | − | 1.44649i | ||||
\(960\) | 27.6130 | + | 15.9424i | 0.891205 | + | 0.514537i | ||||
\(961\) | −46.9527 | −1.51460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.87263 | −0.318141 | ||||||||
\(964\) | −41.8409 | − | 24.1569i | −1.34761 | − | 0.778040i | ||||
\(965\) | −18.2401 | + | 31.5928i | −0.587170 | + | 1.01701i | ||||
\(966\) | 4.66637 | + | 8.08238i | 0.150138 | + | 0.260046i | ||||
\(967\) | 48.5096i | 1.55996i | 0.625802 | + | 0.779982i | \(0.284772\pi\) | ||||
−0.625802 | + | 0.779982i | \(0.715228\pi\) | |||||||
\(968\) | −4.70715 | + | 2.71768i | −0.151294 | + | 0.0873494i | ||||
\(969\) | −3.00235 | + | 1.73341i | −0.0964493 | + | 0.0556850i | ||||
\(970\) | − | 110.937i | − | 3.56198i | ||||||
\(971\) | −20.7325 | − | 35.9098i | −0.665338 | − | 1.15240i | −0.979194 | − | 0.202928i | \(-0.934954\pi\) |
0.313856 | − | 0.949471i | \(-0.398379\pi\) | |||||||
\(972\) | −1.09903 | + | 1.90358i | −0.0352514 | + | 0.0610573i | ||||
\(973\) | 1.91197 | + | 1.10388i | 0.0612949 | + | 0.0353886i | ||||
\(974\) | −26.3242 | −0.843483 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.1177 | −0.419887 | ||||||||
\(977\) | 1.81586 | + | 1.04838i | 0.0580944 | + | 0.0335408i | 0.528766 | − | 0.848768i | \(-0.322655\pi\) |
−0.470671 | + | 0.882309i | \(0.655988\pi\) | |||||||
\(978\) | 11.3167 | − | 19.6011i | 0.361868 | − | 0.626774i | ||||
\(979\) | −24.8397 | − | 43.0237i | −0.793881 | − | 1.37504i | ||||
\(980\) | − | 14.3964i | − | 0.459876i | ||||||
\(981\) | 17.5323 | − | 10.1223i | 0.559764 | − | 0.323180i | ||||
\(982\) | 50.8740 | − | 29.3721i | 1.62345 | − | 0.937301i | ||||
\(983\) | − | 25.2336i | − | 0.804826i | −0.915458 | − | 0.402413i | \(-0.868172\pi\) | ||
0.915458 | − | 0.402413i | \(-0.131828\pi\) | |||||||
\(984\) | −1.40797 | − | 2.43867i | −0.0448844 | − | 0.0777421i | ||||
\(985\) | 15.5115 | − | 26.8668i | 0.494239 | − | 0.856047i | ||||
\(986\) | 6.37333 | + | 3.67964i | 0.202968 | + | 0.117184i | ||||
\(987\) | 8.54288 | 0.271923 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.63448 | −0.147368 | ||||||||
\(990\) | 29.4193 | + | 16.9852i | 0.935006 | + | 0.539826i | ||||
\(991\) | −6.02446 | + | 10.4347i | −0.191373 | + | 0.331468i | −0.945706 | − | 0.325025i | \(-0.894627\pi\) |
0.754332 | + | 0.656493i | \(0.227961\pi\) | |||||||
\(992\) | −35.8253 | − | 62.0512i | −1.13745 | − | 1.97013i | ||||
\(993\) | 11.2131i | 0.355838i | ||||||||
\(994\) | −9.48392 | + | 5.47554i | −0.300812 | + | 0.173674i | ||||
\(995\) | 4.54867 | − | 2.62618i | 0.144203 | − | 0.0832554i | ||||
\(996\) | 5.07308i | 0.160747i | ||||||||
\(997\) | 0.717013 | + | 1.24190i | 0.0227080 | + | 0.0393314i | 0.877156 | − | 0.480205i | \(-0.159438\pi\) |
−0.854448 | + | 0.519537i | \(0.826105\pi\) | |||||||
\(998\) | 34.3763 | − | 59.5415i | 1.08816 | − | 1.88475i | ||||
\(999\) | −7.62270 | − | 4.40097i | −0.241172 | − | 0.139240i |
(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 | 507.2.j.i.316.4 | 12 | ||
13.2 | odd | 12 | 507.2.e.i.484.3 | 6 | |||
13.3 | even | 3 | inner | 507.2.j.i.361.3 | 12 | ||
13.4 | even | 6 | 507.2.b.f.337.4 | 6 | |||
13.5 | odd | 4 | 507.2.e.i.22.3 | 6 | |||
13.6 | odd | 12 | 507.2.a.l.1.1 | yes | 3 | ||
13.7 | odd | 12 | 507.2.a.i.1.3 | ✓ | 3 | ||
13.8 | odd | 4 | 507.2.e.l.22.1 | 6 | |||
13.9 | even | 3 | 507.2.b.f.337.3 | 6 | |||
13.10 | even | 6 | inner | 507.2.j.i.361.4 | 12 | ||
13.11 | odd | 12 | 507.2.e.l.484.1 | 6 | |||
13.12 | even | 2 | inner | 507.2.j.i.316.3 | 12 | ||
39.17 | odd | 6 | 1521.2.b.k.1351.3 | 6 | |||
39.20 | even | 12 | 1521.2.a.s.1.1 | 3 | |||
39.32 | even | 12 | 1521.2.a.n.1.3 | 3 | |||
39.35 | odd | 6 | 1521.2.b.k.1351.4 | 6 | |||
52.7 | even | 12 | 8112.2.a.cg.1.2 | 3 | |||
52.19 | even | 12 | 8112.2.a.cp.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.3 | ✓ | 3 | 13.7 | odd | 12 | ||
507.2.a.l.1.1 | yes | 3 | 13.6 | odd | 12 | ||
507.2.b.f.337.3 | 6 | 13.9 | even | 3 | |||
507.2.b.f.337.4 | 6 | 13.4 | even | 6 | |||
507.2.e.i.22.3 | 6 | 13.5 | odd | 4 | |||
507.2.e.i.484.3 | 6 | 13.2 | odd | 12 | |||
507.2.e.l.22.1 | 6 | 13.8 | odd | 4 | |||
507.2.e.l.484.1 | 6 | 13.11 | odd | 12 | |||
507.2.j.i.316.3 | 12 | 13.12 | even | 2 | inner | ||
507.2.j.i.316.4 | 12 | 1.1 | even | 1 | trivial | ||
507.2.j.i.361.3 | 12 | 13.3 | even | 3 | inner | ||
507.2.j.i.361.4 | 12 | 13.10 | even | 6 | inner | ||
1521.2.a.n.1.3 | 3 | 39.32 | even | 12 | |||
1521.2.a.s.1.1 | 3 | 39.20 | even | 12 | |||
1521.2.b.k.1351.3 | 6 | 39.17 | odd | 6 | |||
1521.2.b.k.1351.4 | 6 | 39.35 | odd | 6 | |||
8112.2.a.cg.1.2 | 3 | 52.7 | even | 12 | |||
8112.2.a.cp.1.2 | 3 | 52.19 | even | 12 |