Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), 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: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 484.1 | ||
Root | \(0.900969 + 1.56052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.484 |
Dual form | 507.2.e.l.22.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.02446 | − | 1.77441i | −0.724402 | − | 1.25470i | −0.959220 | − | 0.282661i | \(-0.908783\pi\) |
0.234818 | − | 0.972039i | \(-0.424551\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −1.09903 | + | 1.90358i | −0.549516 | + | 0.951789i | ||||
\(5\) | −3.35690 | −1.50125 | −0.750625 | − | 0.660729i | \(-0.770247\pi\) | ||||
−0.750625 | + | 0.660729i | \(0.770247\pi\) | |||||||
\(6\) | 1.02446 | − | 1.77441i | 0.418234 | − | 0.724402i | ||||
\(7\) | 1.12349 | − | 1.94594i | 0.424639 | − | 0.735497i | −0.571747 | − | 0.820430i | \(-0.693734\pi\) |
0.996387 | + | 0.0849330i | \(0.0270676\pi\) | |||||||
\(8\) | 0.405813 | 0.143477 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 3.43900 | + | 5.95652i | 1.08751 | + | 1.88362i | ||||
\(11\) | 2.46950 | + | 4.27730i | 0.744582 | + | 1.28965i | 0.950390 | + | 0.311062i | \(0.100685\pi\) |
−0.205807 | + | 0.978593i | \(0.565982\pi\) | |||||||
\(12\) | −2.19806 | −0.634526 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.60388 | −1.23044 | ||||||||
\(15\) | −1.67845 | − | 2.90716i | −0.433373 | − | 0.750625i | ||||
\(16\) | 1.78232 | + | 3.08707i | 0.445581 | + | 0.771769i | ||||
\(17\) | −0.455927 | + | 0.789689i | −0.110579 | + | 0.191528i | −0.916004 | − | 0.401170i | \(-0.868604\pi\) |
0.805425 | + | 0.592698i | \(0.201937\pi\) | |||||||
\(18\) | 2.04892 | 0.482934 | ||||||||
\(19\) | −1.90097 | + | 3.29257i | −0.436112 | + | 0.755368i | −0.997386 | − | 0.0722619i | \(-0.976978\pi\) |
0.561274 | + | 0.827630i | \(0.310312\pi\) | |||||||
\(20\) | 3.68933 | − | 6.39011i | 0.824960 | − | 1.42887i | ||||
\(21\) | 2.24698 | 0.490331 | ||||||||
\(22\) | 5.05980 | − | 8.76383i | 1.07875 | − | 1.86846i | ||||
\(23\) | −1.01357 | − | 1.75556i | −0.211345 | − | 0.366060i | 0.740791 | − | 0.671736i | \(-0.234451\pi\) |
−0.952136 | + | 0.305676i | \(0.901118\pi\) | |||||||
\(24\) | 0.202907 | + | 0.351445i | 0.0414181 | + | 0.0717383i | ||||
\(25\) | 6.26875 | 1.25375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.46950 | + | 4.27730i | 0.466692 | + | 0.808334i | ||||
\(29\) | 1.96950 | + | 3.41127i | 0.365727 | + | 0.633458i | 0.988893 | − | 0.148632i | \(-0.0474870\pi\) |
−0.623165 | + | 0.782090i | \(0.714154\pi\) | |||||||
\(30\) | −3.43900 | + | 5.95652i | −0.627873 | + | 1.08751i | ||||
\(31\) | 8.82908 | 1.58575 | 0.792875 | − | 0.609384i | \(-0.208583\pi\) | ||||
0.792875 | + | 0.609384i | \(0.208583\pi\) | |||||||
\(32\) | 4.05765 | − | 7.02805i | 0.717297 | − | 1.24240i | ||||
\(33\) | −2.46950 | + | 4.27730i | −0.429885 | + | 0.744582i | ||||
\(34\) | 1.86831 | 0.320413 | ||||||||
\(35\) | −3.77144 | + | 6.53232i | −0.637489 | + | 1.10416i | ||||
\(36\) | −1.09903 | − | 1.90358i | −0.183172 | − | 0.317263i | ||||
\(37\) | 4.40097 | + | 7.62270i | 0.723515 | + | 1.25316i | 0.959582 | + | 0.281428i | \(0.0908080\pi\) |
−0.236068 | + | 0.971737i | \(0.575859\pi\) | |||||||
\(38\) | 7.78986 | 1.26368 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.36227 | −0.215394 | ||||||||
\(41\) | 3.46950 | + | 6.00935i | 0.541845 | + | 0.938503i | 0.998798 | + | 0.0490123i | \(0.0156073\pi\) |
−0.456953 | + | 0.889491i | \(0.651059\pi\) | |||||||
\(42\) | −2.30194 | − | 3.98707i | −0.355197 | − | 0.615219i | ||||
\(43\) | 1.14310 | − | 1.97991i | 0.174322 | − | 0.301934i | −0.765605 | − | 0.643311i | \(-0.777560\pi\) |
0.939926 | + | 0.341377i | \(0.110893\pi\) | |||||||
\(44\) | −10.8562 | −1.63664 | ||||||||
\(45\) | 1.67845 | − | 2.90716i | 0.250208 | − | 0.433373i | ||||
\(46\) | −2.07673 | + | 3.59700i | −0.306197 | + | 0.530349i | ||||
\(47\) | −3.80194 | −0.554570 | −0.277285 | − | 0.960788i | \(-0.589435\pi\) | ||||
−0.277285 | + | 0.960788i | \(0.589435\pi\) | |||||||
\(48\) | −1.78232 | + | 3.08707i | −0.257256 | + | 0.445581i | ||||
\(49\) | 0.975541 | + | 1.68969i | 0.139363 | + | 0.241384i | ||||
\(50\) | −6.42208 | − | 11.1234i | −0.908219 | − | 1.57308i | ||||
\(51\) | −0.911854 | −0.127685 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.542877 | 0.0745698 | 0.0372849 | − | 0.999305i | \(-0.488129\pi\) | ||||
0.0372849 | + | 0.999305i | \(0.488129\pi\) | |||||||
\(54\) | 1.02446 | + | 1.77441i | 0.139411 | + | 0.241467i | ||||
\(55\) | −8.28986 | − | 14.3585i | −1.11780 | − | 1.93609i | ||||
\(56\) | 0.455927 | − | 0.789689i | 0.0609258 | − | 0.105527i | ||||
\(57\) | −3.80194 | −0.503579 | ||||||||
\(58\) | 4.03534 | − | 6.98942i | 0.529867 | − | 0.917756i | ||||
\(59\) | −2.35690 | + | 4.08226i | −0.306842 | + | 0.531465i | −0.977670 | − | 0.210148i | \(-0.932606\pi\) |
0.670828 | + | 0.741613i | \(0.265939\pi\) | |||||||
\(60\) | 7.37867 | 0.952582 | ||||||||
\(61\) | −1.83997 | + | 3.18692i | −0.235584 | + | 0.408043i | −0.959442 | − | 0.281905i | \(-0.909034\pi\) |
0.723858 | + | 0.689949i | \(0.242367\pi\) | |||||||
\(62\) | −9.04503 | − | 15.6665i | −1.14872 | − | 1.98964i | ||||
\(63\) | 1.12349 | + | 1.94594i | 0.141546 | + | 0.245166i | ||||
\(64\) | −9.49827 | −1.18728 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.1196 | 1.24564 | ||||||||
\(67\) | −0.760553 | − | 1.31732i | −0.0929164 | − | 0.160936i | 0.815821 | − | 0.578305i | \(-0.196286\pi\) |
−0.908737 | + | 0.417369i | \(0.862952\pi\) | |||||||
\(68\) | −1.00216 | − | 1.73578i | −0.121529 | − | 0.210495i | ||||
\(69\) | 1.01357 | − | 1.75556i | 0.122020 | − | 0.211345i | ||||
\(70\) | 15.4547 | 1.84719 | ||||||||
\(71\) | 1.18933 | − | 2.05999i | 0.141148 | − | 0.244475i | −0.786781 | − | 0.617232i | \(-0.788254\pi\) |
0.927929 | + | 0.372757i | \(0.121587\pi\) | |||||||
\(72\) | −0.202907 | + | 0.351445i | −0.0239128 | + | 0.0414181i | ||||
\(73\) | −7.41119 | −0.867414 | −0.433707 | − | 0.901054i | \(-0.642795\pi\) | ||||
−0.433707 | + | 0.901054i | \(0.642795\pi\) | |||||||
\(74\) | 9.01722 | − | 15.6183i | 1.04823 | − | 1.81559i | ||||
\(75\) | 3.13437 | + | 5.42890i | 0.361926 | + | 0.626875i | ||||
\(76\) | −4.17845 | − | 7.23728i | −0.479301 | − | 0.830173i | ||||
\(77\) | 11.0978 | 1.26472 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.74094 | −0.420888 | −0.210444 | − | 0.977606i | \(-0.567491\pi\) | ||||
−0.210444 | + | 0.977606i | \(0.567491\pi\) | |||||||
\(80\) | −5.98307 | − | 10.3630i | −0.668928 | − | 1.15862i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 7.10872 | − | 12.3127i | 0.785027 | − | 1.35971i | ||||
\(83\) | −2.30798 | −0.253334 | −0.126667 | − | 0.991945i | \(-0.540428\pi\) | ||||
−0.126667 | + | 0.991945i | \(0.540428\pi\) | |||||||
\(84\) | −2.46950 | + | 4.27730i | −0.269445 | + | 0.466692i | ||||
\(85\) | 1.53050 | − | 2.65090i | 0.166006 | − | 0.287531i | ||||
\(86\) | −4.68425 | −0.505116 | ||||||||
\(87\) | −1.96950 | + | 3.41127i | −0.211153 | + | 0.365727i | ||||
\(88\) | 1.00216 | + | 1.73578i | 0.106830 | + | 0.185035i | ||||
\(89\) | −5.02930 | − | 8.71101i | −0.533105 | − | 0.923365i | −0.999253 | − | 0.0386580i | \(-0.987692\pi\) |
0.466147 | − | 0.884707i | \(-0.345642\pi\) | |||||||
\(90\) | −6.87800 | −0.725005 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.45580 | 0.464549 | ||||||||
\(93\) | 4.41454 | + | 7.64621i | 0.457767 | + | 0.792875i | ||||
\(94\) | 3.89493 | + | 6.74621i | 0.401731 | + | 0.695819i | ||||
\(95\) | 6.38135 | − | 11.0528i | 0.654713 | − | 1.13400i | ||||
\(96\) | 8.11529 | 0.828264 | ||||||||
\(97\) | −8.06465 | + | 13.9684i | −0.818841 | + | 1.41827i | 0.0876961 | + | 0.996147i | \(0.472050\pi\) |
−0.906537 | + | 0.422127i | \(0.861284\pi\) | |||||||
\(98\) | 1.99880 | − | 3.46203i | 0.201910 | − | 0.349718i | ||||
\(99\) | −4.93900 | −0.496388 | ||||||||
\(100\) | −6.88955 | + | 11.9331i | −0.688955 | + | 1.19331i | ||||
\(101\) | 4.97434 | + | 8.61582i | 0.494966 | + | 0.857306i | 0.999983 | − | 0.00580325i | \(-0.00184724\pi\) |
−0.505017 | + | 0.863109i | \(0.668514\pi\) | |||||||
\(102\) | 0.934157 | + | 1.61801i | 0.0924953 | + | 0.160207i | ||||
\(103\) | −10.9879 | −1.08267 | −0.541336 | − | 0.840806i | \(-0.682081\pi\) | ||||
−0.541336 | + | 0.840806i | \(0.682081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.54288 | −0.736109 | ||||||||
\(106\) | −0.556155 | − | 0.963288i | −0.0540185 | − | 0.0935628i | ||||
\(107\) | 4.93631 | + | 8.54994i | 0.477211 | + | 0.826554i | 0.999659 | − | 0.0261171i | \(-0.00831428\pi\) |
−0.522448 | + | 0.852671i | \(0.674981\pi\) | |||||||
\(108\) | 1.09903 | − | 1.90358i | 0.105754 | − | 0.183172i | ||||
\(109\) | −20.2446 | −1.93908 | −0.969540 | − | 0.244934i | \(-0.921234\pi\) | ||||
−0.969540 | + | 0.244934i | \(0.921234\pi\) | |||||||
\(110\) | −16.9852 | + | 29.4193i | −1.61948 | + | 2.80502i | ||||
\(111\) | −4.40097 | + | 7.62270i | −0.417721 | + | 0.723515i | ||||
\(112\) | 8.00969 | 0.756844 | ||||||||
\(113\) | −4.84601 | + | 8.39354i | −0.455874 | + | 0.789598i | −0.998738 | − | 0.0502233i | \(-0.984007\pi\) |
0.542864 | + | 0.839821i | \(0.317340\pi\) | |||||||
\(114\) | 3.89493 | + | 6.74621i | 0.364793 | + | 0.631841i | ||||
\(115\) | 3.40246 | + | 5.89324i | 0.317281 | + | 0.549547i | ||||
\(116\) | −8.65817 | −0.803891 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.65817 | 0.889107 | ||||||||
\(119\) | 1.02446 | + | 1.77441i | 0.0939120 | + | 0.162660i | ||||
\(120\) | −0.681136 | − | 1.17976i | −0.0621790 | − | 0.107697i | ||||
\(121\) | −6.69687 | + | 11.5993i | −0.608806 | + | 1.05448i | ||||
\(122\) | 7.53989 | 0.682630 | ||||||||
\(123\) | −3.46950 | + | 6.00935i | −0.312834 | + | 0.541845i | ||||
\(124\) | −9.70344 | + | 16.8068i | −0.871395 | + | 1.50930i | ||||
\(125\) | −4.25906 | −0.380942 | ||||||||
\(126\) | 2.30194 | − | 3.98707i | 0.205073 | − | 0.355197i | ||||
\(127\) | −6.90581 | − | 11.9612i | −0.612792 | − | 1.06139i | −0.990768 | − | 0.135571i | \(-0.956713\pi\) |
0.377976 | − | 0.925815i | \(-0.376620\pi\) | |||||||
\(128\) | 1.61529 | + | 2.79777i | 0.142773 | + | 0.247290i | ||||
\(129\) | 2.28621 | 0.201289 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.99462 | 0.261641 | 0.130821 | − | 0.991406i | \(-0.458239\pi\) | ||||
0.130821 | + | 0.991406i | \(0.458239\pi\) | |||||||
\(132\) | −5.42812 | − | 9.40177i | −0.472457 | − | 0.818319i | ||||
\(133\) | 4.27144 | + | 7.39835i | 0.370381 | + | 0.641518i | ||||
\(134\) | −1.55831 | + | 2.69907i | −0.134618 | + | 0.233164i | ||||
\(135\) | 3.35690 | 0.288916 | ||||||||
\(136\) | −0.185021 | + | 0.320466i | −0.0158654 | + | 0.0274797i | ||||
\(137\) | 11.5097 | − | 19.9354i | 0.983339 | − | 1.70319i | 0.334243 | − | 0.942487i | \(-0.391519\pi\) |
0.649096 | − | 0.760706i | \(-0.275147\pi\) | |||||||
\(138\) | −4.15346 | −0.353566 | ||||||||
\(139\) | −0.491271 | + | 0.850906i | −0.0416690 | + | 0.0721729i | −0.886108 | − | 0.463479i | \(-0.846601\pi\) |
0.844439 | + | 0.535652i | \(0.179934\pi\) | |||||||
\(140\) | −8.28986 | − | 14.3585i | −0.700621 | − | 1.21351i | ||||
\(141\) | −1.90097 | − | 3.29257i | −0.160090 | − | 0.277285i | ||||
\(142\) | −4.87369 | −0.408991 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.56465 | −0.297054 | ||||||||
\(145\) | −6.61141 | − | 11.4513i | −0.549048 | − | 0.950978i | ||||
\(146\) | 7.59246 | + | 13.1505i | 0.628356 | + | 1.08835i | ||||
\(147\) | −0.975541 | + | 1.68969i | −0.0804613 | + | 0.139363i | ||||
\(148\) | −19.3472 | −1.59033 | ||||||||
\(149\) | 5.12953 | − | 8.88461i | 0.420228 | − | 0.727855i | −0.575734 | − | 0.817637i | \(-0.695284\pi\) |
0.995961 | + | 0.0897817i | \(0.0286169\pi\) | |||||||
\(150\) | 6.42208 | − | 11.1234i | 0.524360 | − | 0.908219i | ||||
\(151\) | 20.1685 | 1.64129 | 0.820646 | − | 0.571438i | \(-0.193614\pi\) | ||||
0.820646 | + | 0.571438i | \(0.193614\pi\) | |||||||
\(152\) | −0.771438 | + | 1.33617i | −0.0625719 | + | 0.108378i | ||||
\(153\) | −0.455927 | − | 0.789689i | −0.0368595 | − | 0.0638425i | ||||
\(154\) | −11.3693 | − | 19.6922i | −0.916162 | − | 1.58684i | ||||
\(155\) | −29.6383 | −2.38061 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4383 | 0.833070 | 0.416535 | − | 0.909120i | \(-0.363244\pi\) | ||||
0.416535 | + | 0.909120i | \(0.363244\pi\) | |||||||
\(158\) | 3.83244 | + | 6.63798i | 0.304892 | + | 0.528089i | ||||
\(159\) | 0.271438 | + | 0.470145i | 0.0215265 | + | 0.0372849i | ||||
\(160\) | −13.6211 | + | 23.5924i | −1.07684 | + | 1.86515i | ||||
\(161\) | −4.55496 | −0.358981 | ||||||||
\(162\) | −1.02446 | + | 1.77441i | −0.0804891 | + | 0.139411i | ||||
\(163\) | −5.52326 | + | 9.56657i | −0.432615 | + | 0.749312i | −0.997098 | − | 0.0761335i | \(-0.975742\pi\) |
0.564482 | + | 0.825445i | \(0.309076\pi\) | |||||||
\(164\) | −15.2524 | −1.19101 | ||||||||
\(165\) | 8.28986 | − | 14.3585i | 0.645364 | − | 1.11780i | ||||
\(166\) | 2.36443 | + | 4.09531i | 0.183515 | + | 0.317858i | ||||
\(167\) | 4.05496 | + | 7.02339i | 0.313782 | + | 0.543487i | 0.979178 | − | 0.203004i | \(-0.0650705\pi\) |
−0.665396 | + | 0.746491i | \(0.731737\pi\) | |||||||
\(168\) | 0.911854 | 0.0703511 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.27173 | −0.481020 | ||||||||
\(171\) | −1.90097 | − | 3.29257i | −0.145371 | − | 0.251789i | ||||
\(172\) | 2.51261 | + | 4.35198i | 0.191585 | + | 0.331835i | ||||
\(173\) | 9.02811 | − | 15.6371i | 0.686394 | − | 1.18887i | −0.286602 | − | 0.958050i | \(-0.592526\pi\) |
0.972996 | − | 0.230820i | \(-0.0741409\pi\) | |||||||
\(174\) | 8.07069 | 0.611837 | ||||||||
\(175\) | 7.04288 | − | 12.1986i | 0.532391 | − | 0.922129i | ||||
\(176\) | −8.80290 | + | 15.2471i | −0.663543 | + | 1.14929i | ||||
\(177\) | −4.71379 | −0.354310 | ||||||||
\(178\) | −10.3046 | + | 17.8481i | −0.772364 | + | 1.33777i | ||||
\(179\) | 9.93512 | + | 17.2081i | 0.742585 | + | 1.28620i | 0.951314 | + | 0.308222i | \(0.0997340\pi\) |
−0.208729 | + | 0.977974i | \(0.566933\pi\) | |||||||
\(180\) | 3.68933 | + | 6.39011i | 0.274987 | + | 0.476291i | ||||
\(181\) | −10.0828 | −0.749446 | −0.374723 | − | 0.927137i | \(-0.622262\pi\) | ||||
−0.374723 | + | 0.927137i | \(0.622262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.67994 | −0.272029 | ||||||||
\(184\) | −0.411322 | − | 0.712430i | −0.0303230 | − | 0.0525210i | ||||
\(185\) | −14.7736 | − | 25.5886i | −1.08618 | − | 1.88131i | ||||
\(186\) | 9.04503 | − | 15.6665i | 0.663214 | − | 1.14872i | ||||
\(187\) | −4.50365 | −0.329339 | ||||||||
\(188\) | 4.17845 | − | 7.23728i | 0.304745 | − | 0.527833i | ||||
\(189\) | −1.12349 | + | 1.94594i | −0.0817219 | + | 0.141546i | ||||
\(190\) | −26.1497 | −1.89710 | ||||||||
\(191\) | 3.29374 | − | 5.70493i | 0.238327 | − | 0.412794i | −0.721908 | − | 0.691990i | \(-0.756734\pi\) |
0.960234 | + | 0.279196i | \(0.0900678\pi\) | |||||||
\(192\) | −4.74914 | − | 8.22574i | −0.342739 | − | 0.593642i | ||||
\(193\) | 5.43362 | + | 9.41131i | 0.391121 | + | 0.677441i | 0.992598 | − | 0.121449i | \(-0.0387541\pi\) |
−0.601477 | + | 0.798890i | \(0.705421\pi\) | |||||||
\(194\) | 33.0476 | 2.37268 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.28860 | −0.306329 | ||||||||
\(197\) | 4.62080 | + | 8.00346i | 0.329218 | + | 0.570223i | 0.982357 | − | 0.187015i | \(-0.0598814\pi\) |
−0.653139 | + | 0.757238i | \(0.726548\pi\) | |||||||
\(198\) | 5.05980 | + | 8.76383i | 0.359585 | + | 0.622819i | ||||
\(199\) | 0.782323 | − | 1.35502i | 0.0554574 | − | 0.0960551i | −0.836964 | − | 0.547258i | \(-0.815672\pi\) |
0.892421 | + | 0.451203i | \(0.149005\pi\) | |||||||
\(200\) | 2.54394 | 0.179884 | ||||||||
\(201\) | 0.760553 | − | 1.31732i | 0.0536453 | − | 0.0929164i | ||||
\(202\) | 10.1920 | − | 17.6531i | 0.717108 | − | 1.24207i | ||||
\(203\) | 8.85086 | 0.621208 | ||||||||
\(204\) | 1.00216 | − | 1.73578i | 0.0701649 | − | 0.121529i | ||||
\(205\) | −11.6468 | − | 20.1728i | −0.813444 | − | 1.40893i | ||||
\(206\) | 11.2567 | + | 19.4971i | 0.784289 | + | 1.35843i | ||||
\(207\) | 2.02715 | 0.140896 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.7778 | −1.29889 | ||||||||
\(210\) | 7.72737 | + | 13.3842i | 0.533239 | + | 0.923597i | ||||
\(211\) | −11.6223 | − | 20.1304i | −0.800112 | − | 1.38583i | −0.919542 | − | 0.392991i | \(-0.871440\pi\) |
0.119430 | − | 0.992843i | \(-0.461893\pi\) | |||||||
\(212\) | −0.596638 | + | 1.03341i | −0.0409773 | + | 0.0709747i | ||||
\(213\) | 2.37867 | 0.162984 | ||||||||
\(214\) | 10.1141 | − | 17.5181i | 0.691385 | − | 1.19751i | ||||
\(215\) | −3.83728 | + | 6.64637i | −0.261700 | + | 0.453278i | ||||
\(216\) | −0.405813 | −0.0276121 | ||||||||
\(217\) | 9.91939 | − | 17.1809i | 0.673372 | − | 1.16631i | ||||
\(218\) | 20.7397 | + | 35.9223i | 1.40467 | + | 2.43296i | ||||
\(219\) | −3.70560 | − | 6.41828i | −0.250401 | − | 0.433707i | ||||
\(220\) | 36.4432 | 2.45700 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 18.0344 | 1.21039 | ||||||||
\(223\) | 5.36927 | + | 9.29985i | 0.359553 | + | 0.622764i | 0.987886 | − | 0.155180i | \(-0.0495958\pi\) |
−0.628333 | + | 0.777944i | \(0.716262\pi\) | |||||||
\(224\) | −9.11745 | − | 15.7919i | −0.609185 | − | 1.05514i | ||||
\(225\) | −3.13437 | + | 5.42890i | −0.208958 | + | 0.361926i | ||||
\(226\) | 19.8582 | 1.32094 | ||||||||
\(227\) | −3.48792 | + | 6.04125i | −0.231501 | + | 0.400972i | −0.958250 | − | 0.285931i | \(-0.907697\pi\) |
0.726749 | + | 0.686903i | \(0.241030\pi\) | |||||||
\(228\) | 4.17845 | − | 7.23728i | 0.276724 | − | 0.479301i | ||||
\(229\) | 16.8049 | 1.11050 | 0.555250 | − | 0.831683i | \(-0.312622\pi\) | ||||
0.555250 | + | 0.831683i | \(0.312622\pi\) | |||||||
\(230\) | 6.97136 | − | 12.0748i | 0.459678 | − | 0.796186i | ||||
\(231\) | 5.54892 | + | 9.61101i | 0.365092 | + | 0.632358i | ||||
\(232\) | 0.799249 | + | 1.38434i | 0.0524733 | + | 0.0908864i | ||||
\(233\) | 8.69202 | 0.569433 | 0.284717 | − | 0.958612i | \(-0.408100\pi\) | ||||
0.284717 | + | 0.958612i | \(0.408100\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7627 | 0.832547 | ||||||||
\(236\) | −5.18060 | − | 8.97307i | −0.337229 | − | 0.584097i | ||||
\(237\) | −1.87047 | − | 3.23975i | −0.121500 | − | 0.210444i | ||||
\(238\) | 2.09903 | − | 3.63563i | 0.136060 | − | 0.235663i | ||||
\(239\) | 22.9191 | 1.48252 | 0.741258 | − | 0.671220i | \(-0.234229\pi\) | ||||
0.741258 | + | 0.671220i | \(0.234229\pi\) | |||||||
\(240\) | 5.98307 | − | 10.3630i | 0.386206 | − | 0.668928i | ||||
\(241\) | 10.9901 | − | 19.0354i | 0.707933 | − | 1.22618i | −0.257690 | − | 0.966228i | \(-0.582961\pi\) |
0.965623 | − | 0.259948i | \(-0.0837054\pi\) | |||||||
\(242\) | 27.4426 | 1.76408 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −4.04437 | − | 7.00505i | −0.258914 | − | 0.448452i | ||||
\(245\) | −3.27479 | − | 5.67210i | −0.209219 | − | 0.362377i | ||||
\(246\) | 14.2174 | 0.906471 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.58296 | 0.227518 | ||||||||
\(249\) | −1.15399 | − | 1.99877i | −0.0731311 | − | 0.126667i | ||||
\(250\) | 4.36323 | + | 7.55734i | 0.275955 | + | 0.477968i | ||||
\(251\) | −13.3218 | + | 23.0741i | −0.840868 | + | 1.45643i | 0.0482946 | + | 0.998833i | \(0.484621\pi\) |
−0.889162 | + | 0.457592i | \(0.848712\pi\) | |||||||
\(252\) | −4.93900 | −0.311128 | ||||||||
\(253\) | 5.00604 | − | 8.67072i | 0.314727 | − | 0.545123i | ||||
\(254\) | −14.1494 | + | 24.5075i | −0.887815 | + | 1.53774i | ||||
\(255\) | 3.06100 | 0.191687 | ||||||||
\(256\) | −6.18867 | + | 10.7191i | −0.386792 | + | 0.669943i | ||||
\(257\) | −11.5722 | − | 20.0436i | −0.721853 | − | 1.25029i | −0.960256 | − | 0.279119i | \(-0.909957\pi\) |
0.238404 | − | 0.971166i | \(-0.423376\pi\) | |||||||
\(258\) | −2.34213 | − | 4.05668i | −0.145814 | − | 0.252558i | ||||
\(259\) | 19.7778 | 1.22893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.93900 | −0.243818 | ||||||||
\(262\) | −3.06787 | − | 5.31370i | −0.189533 | − | 0.328282i | ||||
\(263\) | 9.26420 | + | 16.0461i | 0.571255 | + | 0.989443i | 0.996437 | + | 0.0843352i | \(0.0268766\pi\) |
−0.425182 | + | 0.905108i | \(0.639790\pi\) | |||||||
\(264\) | −1.00216 | + | 1.73578i | −0.0616784 | + | 0.106830i | ||||
\(265\) | −1.82238 | −0.111948 | ||||||||
\(266\) | 8.75182 | − | 15.1586i | 0.536609 | − | 0.929434i | ||||
\(267\) | 5.02930 | − | 8.71101i | 0.307788 | − | 0.533105i | ||||
\(268\) | 3.34349 | 0.204236 | ||||||||
\(269\) | −4.87920 | + | 8.45102i | −0.297490 | + | 0.515268i | −0.975561 | − | 0.219729i | \(-0.929483\pi\) |
0.678071 | + | 0.734996i | \(0.262816\pi\) | |||||||
\(270\) | −3.43900 | − | 5.95652i | −0.209291 | − | 0.362503i | ||||
\(271\) | −11.4010 | − | 19.7471i | −0.692560 | − | 1.19955i | −0.970996 | − | 0.239094i | \(-0.923150\pi\) |
0.278437 | − | 0.960455i | \(-0.410184\pi\) | |||||||
\(272\) | −3.25044 | −0.197087 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −47.1648 | −2.84933 | ||||||||
\(275\) | 15.4807 | + | 26.8133i | 0.933520 | + | 1.61690i | ||||
\(276\) | 2.22790 | + | 3.85883i | 0.134104 | + | 0.232274i | ||||
\(277\) | 11.9852 | − | 20.7590i | 0.720123 | − | 1.24729i | −0.240828 | − | 0.970568i | \(-0.577419\pi\) |
0.960950 | − | 0.276721i | \(-0.0892478\pi\) | |||||||
\(278\) | 2.01315 | 0.120741 | ||||||||
\(279\) | −4.41454 | + | 7.64621i | −0.264292 | + | 0.457767i | ||||
\(280\) | −1.53050 | + | 2.65090i | −0.0914648 | + | 0.158422i | ||||
\(281\) | 4.12498 | 0.246076 | 0.123038 | − | 0.992402i | \(-0.460736\pi\) | ||||
0.123038 | + | 0.992402i | \(0.460736\pi\) | |||||||
\(282\) | −3.89493 | + | 6.74621i | −0.231940 | + | 0.401731i | ||||
\(283\) | 7.82789 | + | 13.5583i | 0.465320 | + | 0.805957i | 0.999216 | − | 0.0395927i | \(-0.0126060\pi\) |
−0.533896 | + | 0.845550i | \(0.679273\pi\) | |||||||
\(284\) | 2.61423 | + | 4.52798i | 0.155126 | + | 0.268686i | ||||
\(285\) | 12.7627 | 0.755998 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5918 | 0.920354 | ||||||||
\(288\) | 4.05765 | + | 7.02805i | 0.239099 | + | 0.414132i | ||||
\(289\) | 8.08426 | + | 14.0024i | 0.475545 | + | 0.823668i | ||||
\(290\) | −13.5462 | + | 23.4628i | −0.795462 | + | 1.37778i | ||||
\(291\) | −16.1293 | −0.945516 | ||||||||
\(292\) | 8.14513 | − | 14.1078i | 0.476658 | − | 0.825595i | ||||
\(293\) | 11.2974 | − | 19.5677i | 0.660001 | − | 1.14315i | −0.320614 | − | 0.947210i | \(-0.603889\pi\) |
0.980615 | − | 0.195945i | \(-0.0627773\pi\) | |||||||
\(294\) | 3.99761 | 0.233145 | ||||||||
\(295\) | 7.91185 | − | 13.7037i | 0.460646 | − | 0.797862i | ||||
\(296\) | 1.78597 | + | 3.09339i | 0.103807 | + | 0.179800i | ||||
\(297\) | −2.46950 | − | 4.27730i | −0.143295 | − | 0.248194i | ||||
\(298\) | −21.0200 | −1.21765 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.7791 | −0.795537 | ||||||||
\(301\) | −2.56853 | − | 4.44883i | −0.148048 | − | 0.256426i | ||||
\(302\) | −20.6618 | − | 35.7873i | −1.18895 | − | 2.05933i | ||||
\(303\) | −4.97434 | + | 8.61582i | −0.285769 | + | 0.494966i | ||||
\(304\) | −13.5526 | −0.777293 | ||||||||
\(305\) | 6.17659 | − | 10.6982i | 0.353670 | − | 0.612575i | ||||
\(306\) | −0.934157 | + | 1.61801i | −0.0534022 | + | 0.0924953i | ||||
\(307\) | 6.55496 | 0.374111 | 0.187056 | − | 0.982349i | \(-0.440106\pi\) | ||||
0.187056 | + | 0.982349i | \(0.440106\pi\) | |||||||
\(308\) | −12.1969 | + | 21.1256i | −0.694981 | + | 1.20374i | ||||
\(309\) | −5.49396 | − | 9.51582i | −0.312540 | − | 0.541336i | ||||
\(310\) | 30.3632 | + | 52.5907i | 1.72452 | + | 2.98695i | ||||
\(311\) | −12.0392 | −0.682682 | −0.341341 | − | 0.939940i | \(-0.610881\pi\) | ||||
−0.341341 | + | 0.939940i | \(0.610881\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.8950 | −1.91586 | −0.957929 | − | 0.287005i | \(-0.907340\pi\) | ||||
−0.957929 | + | 0.287005i | \(0.907340\pi\) | |||||||
\(314\) | −10.6936 | − | 18.5219i | −0.603477 | − | 1.04525i | ||||
\(315\) | −3.77144 | − | 6.53232i | −0.212496 | − | 0.368055i | ||||
\(316\) | 4.11141 | − | 7.12117i | 0.231285 | − | 0.400597i | ||||
\(317\) | 4.49827 | 0.252648 | 0.126324 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126324 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(318\) | 0.556155 | − | 0.963288i | 0.0311876 | − | 0.0540185i | ||||
\(319\) | −9.72737 | + | 16.8483i | −0.544628 | + | 0.943323i | ||||
\(320\) | 31.8847 | 1.78241 | ||||||||
\(321\) | −4.93631 | + | 8.54994i | −0.275518 | + | 0.477211i | ||||
\(322\) | 4.66637 | + | 8.08238i | 0.260046 | + | 0.450414i | ||||
\(323\) | −1.73341 | − | 3.00235i | −0.0964493 | − | 0.167055i | ||||
\(324\) | 2.19806 | 0.122115 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.6334 | 1.25355 | ||||||||
\(327\) | −10.1223 | − | 17.5323i | −0.559764 | − | 0.969540i | ||||
\(328\) | 1.40797 | + | 2.43867i | 0.0777421 | + | 0.134653i | ||||
\(329\) | −4.27144 | + | 7.39835i | −0.235492 | + | 0.407884i | ||||
\(330\) | −33.9705 | −1.87001 | ||||||||
\(331\) | −5.60656 | + | 9.71085i | −0.308165 | + | 0.533757i | −0.977961 | − | 0.208788i | \(-0.933048\pi\) |
0.669796 | + | 0.742545i | \(0.266381\pi\) | |||||||
\(332\) | 2.53654 | − | 4.39342i | 0.139211 | − | 0.241120i | ||||
\(333\) | −8.80194 | −0.482343 | ||||||||
\(334\) | 8.30827 | − | 14.3904i | 0.454609 | − | 0.787405i | ||||
\(335\) | 2.55310 | + | 4.42209i | 0.139491 | + | 0.241605i | ||||
\(336\) | 4.00484 | + | 6.93659i | 0.218482 | + | 0.378422i | ||||
\(337\) | 7.04892 | 0.383979 | 0.191989 | − | 0.981397i | \(-0.438506\pi\) | ||||
0.191989 | + | 0.981397i | \(0.438506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.69202 | −0.526398 | ||||||||
\(340\) | 3.36413 | + | 5.82685i | 0.182446 | + | 0.316005i | ||||
\(341\) | 21.8034 | + | 37.7646i | 1.18072 | + | 2.04507i | ||||
\(342\) | −3.89493 | + | 6.74621i | −0.210614 | + | 0.364793i | ||||
\(343\) | 20.1129 | 1.08599 | ||||||||
\(344\) | 0.463887 | − | 0.803475i | 0.0250111 | − | 0.0433205i | ||||
\(345\) | −3.40246 | + | 5.89324i | −0.183182 | + | 0.317281i | ||||
\(346\) | −36.9957 | −1.98890 | ||||||||
\(347\) | 1.35205 | − | 2.34182i | 0.0725819 | − | 0.125716i | −0.827450 | − | 0.561539i | \(-0.810209\pi\) |
0.900032 | + | 0.435823i | \(0.143543\pi\) | |||||||
\(348\) | −4.32908 | − | 7.49819i | −0.232063 | − | 0.401945i | ||||
\(349\) | −0.207751 | − | 0.359835i | −0.0111207 | − | 0.0192615i | 0.860412 | − | 0.509600i | \(-0.170207\pi\) |
−0.871532 | + | 0.490338i | \(0.836873\pi\) | |||||||
\(350\) | −28.8605 | −1.54266 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 40.0814 | 2.13635 | ||||||||
\(353\) | −16.0836 | − | 27.8576i | −0.856044 | − | 1.48271i | −0.875674 | − | 0.482904i | \(-0.839582\pi\) |
0.0196301 | − | 0.999807i | \(-0.493751\pi\) | |||||||
\(354\) | 4.82908 | + | 8.36422i | 0.256663 | + | 0.444553i | ||||
\(355\) | −3.99247 | + | 6.91516i | −0.211898 | + | 0.367018i | ||||
\(356\) | 22.1094 | 1.17180 | ||||||||
\(357\) | −1.02446 | + | 1.77441i | −0.0542201 | + | 0.0939120i | ||||
\(358\) | 20.3562 | − | 35.2580i | 1.07586 | − | 1.86344i | ||||
\(359\) | −22.3521 | −1.17970 | −0.589850 | − | 0.807513i | \(-0.700813\pi\) | ||||
−0.589850 | + | 0.807513i | \(0.700813\pi\) | |||||||
\(360\) | 0.681136 | − | 1.17976i | 0.0358990 | − | 0.0621790i | ||||
\(361\) | 2.27263 | + | 3.93632i | 0.119612 | + | 0.207175i | ||||
\(362\) | 10.3294 | + | 17.8910i | 0.542900 | + | 0.940331i | ||||
\(363\) | −13.3937 | −0.702989 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.8786 | 1.30221 | ||||||||
\(366\) | 3.76995 | + | 6.52974i | 0.197058 | + | 0.341315i | ||||
\(367\) | 1.15130 | + | 1.99411i | 0.0600974 | + | 0.104092i | 0.894509 | − | 0.447050i | \(-0.147526\pi\) |
−0.834411 | + | 0.551142i | \(0.814192\pi\) | |||||||
\(368\) | 3.61303 | − | 6.25795i | 0.188342 | − | 0.326218i | ||||
\(369\) | −6.93900 | −0.361230 | ||||||||
\(370\) | −30.2699 | + | 52.4290i | −1.57366 | + | 2.72565i | ||||
\(371\) | 0.609916 | − | 1.05641i | 0.0316653 | − | 0.0548459i | ||||
\(372\) | −19.4069 | −1.00620 | ||||||||
\(373\) | 9.63802 | − | 16.6935i | 0.499038 | − | 0.864359i | −0.500961 | − | 0.865470i | \(-0.667020\pi\) |
0.999999 | + | 0.00111058i | \(0.000353507\pi\) | |||||||
\(374\) | 4.61380 | + | 7.99134i | 0.238574 | + | 0.413222i | ||||
\(375\) | −2.12953 | − | 3.68846i | −0.109968 | − | 0.190471i | ||||
\(376\) | −1.54288 | −0.0795678 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.60388 | 0.236798 | ||||||||
\(379\) | −3.66972 | − | 6.35614i | −0.188501 | − | 0.326493i | 0.756250 | − | 0.654283i | \(-0.227029\pi\) |
−0.944751 | + | 0.327790i | \(0.893696\pi\) | |||||||
\(380\) | 14.0266 | + | 24.2948i | 0.719550 | + | 1.24630i | ||||
\(381\) | 6.90581 | − | 11.9612i | 0.353796 | − | 0.612792i | ||||
\(382\) | −13.4972 | −0.690577 | ||||||||
\(383\) | 9.54503 | − | 16.5325i | 0.487728 | − | 0.844770i | −0.512172 | − | 0.858883i | \(-0.671159\pi\) |
0.999900 | + | 0.0141126i | \(0.00449231\pi\) | |||||||
\(384\) | −1.61529 | + | 2.79777i | −0.0824301 | + | 0.142773i | ||||
\(385\) | −37.2543 | −1.89865 | ||||||||
\(386\) | 11.1330 | − | 19.2830i | 0.566657 | − | 0.981479i | ||||
\(387\) | 1.14310 | + | 1.97991i | 0.0581072 | + | 0.100645i | ||||
\(388\) | −17.7266 | − | 30.7034i | −0.899932 | − | 1.55873i | ||||
\(389\) | −23.9879 | −1.21624 | −0.608118 | − | 0.793847i | \(-0.708075\pi\) | ||||
−0.608118 | + | 0.793847i | \(0.708075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.84846 | 0.0934807 | ||||||||
\(392\) | 0.395888 | + | 0.685697i | 0.0199953 | + | 0.0346329i | ||||
\(393\) | 1.49731 | + | 2.59342i | 0.0755294 | + | 0.130821i | ||||
\(394\) | 9.46764 | − | 16.3984i | 0.476973 | − | 0.826141i | ||||
\(395\) | 12.5579 | 0.631859 | ||||||||
\(396\) | 5.42812 | − | 9.40177i | 0.272773 | − | 0.472457i | ||||
\(397\) | −2.20895 | + | 3.82601i | −0.110864 | + | 0.192022i | −0.916119 | − | 0.400907i | \(-0.868695\pi\) |
0.805255 | + | 0.592929i | \(0.202028\pi\) | |||||||
\(398\) | −3.20583 | −0.160694 | ||||||||
\(399\) | −4.27144 | + | 7.39835i | −0.213839 | + | 0.370381i | ||||
\(400\) | 11.1729 | + | 19.3521i | 0.558647 | + | 0.967605i | ||||
\(401\) | −10.2044 | − | 17.6745i | −0.509583 | − | 0.882624i | −0.999938 | − | 0.0111015i | \(-0.996466\pi\) |
0.490355 | − | 0.871523i | \(-0.336867\pi\) | |||||||
\(402\) | −3.11662 | −0.155443 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −21.8678 | −1.08797 | ||||||||
\(405\) | 1.67845 | + | 2.90716i | 0.0834027 | + | 0.144458i | ||||
\(406\) | −9.06734 | − | 15.7051i | −0.450004 | − | 0.779430i | ||||
\(407\) | −21.7364 | + | 37.6485i | −1.07743 | + | 1.86617i | ||||
\(408\) | −0.370042 | −0.0183198 | ||||||||
\(409\) | −11.0746 | + | 19.1817i | −0.547602 | + | 0.948475i | 0.450836 | + | 0.892607i | \(0.351126\pi\) |
−0.998438 | + | 0.0558682i | \(0.982207\pi\) | |||||||
\(410\) | −23.8632 | + | 41.3323i | −1.17852 | + | 2.04126i | ||||
\(411\) | 23.0194 | 1.13546 | ||||||||
\(412\) | 12.0761 | − | 20.9164i | 0.594945 | − | 1.03047i | ||||
\(413\) | 5.29590 | + | 9.17276i | 0.260594 | + | 0.451362i | ||||
\(414\) | −2.07673 | − | 3.59700i | −0.102066 | − | 0.176783i | ||||
\(415\) | 7.74764 | 0.380317 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.982542 | −0.0481153 | ||||||||
\(418\) | 19.2371 | + | 33.3196i | 0.940915 | + | 1.62971i | ||||
\(419\) | −7.37800 | − | 12.7791i | −0.360439 | − | 0.624299i | 0.627594 | − | 0.778541i | \(-0.284040\pi\) |
−0.988033 | + | 0.154242i | \(0.950706\pi\) | |||||||
\(420\) | 8.28986 | − | 14.3585i | 0.404504 | − | 0.700621i | ||||
\(421\) | −8.47219 | −0.412909 | −0.206455 | − | 0.978456i | \(-0.566193\pi\) | ||||
−0.206455 | + | 0.978456i | \(0.566193\pi\) | |||||||
\(422\) | −23.8131 | + | 41.2455i | −1.15920 | + | 2.00780i | ||||
\(423\) | 1.90097 | − | 3.29257i | 0.0924283 | − | 0.160090i | ||||
\(424\) | 0.220306 | 0.0106990 | ||||||||
\(425\) | −2.85809 | + | 4.95036i | −0.138638 | + | 0.240128i | ||||
\(426\) | −2.43685 | − | 4.22074i | −0.118066 | − | 0.204496i | ||||
\(427\) | 4.13437 | + | 7.16095i | 0.200076 | + | 0.346543i | ||||
\(428\) | −21.7006 | −1.04894 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.7245 | 0.758305 | ||||||||
\(431\) | 1.19591 | + | 2.07137i | 0.0576048 | + | 0.0997744i | 0.893390 | − | 0.449283i | \(-0.148320\pi\) |
−0.835785 | + | 0.549057i | \(0.814987\pi\) | |||||||
\(432\) | −1.78232 | − | 3.08707i | −0.0857521 | − | 0.148527i | ||||
\(433\) | 5.21432 | − | 9.03147i | 0.250584 | − | 0.434025i | −0.713102 | − | 0.701060i | \(-0.752711\pi\) |
0.963687 | + | 0.267035i | \(0.0860439\pi\) | |||||||
\(434\) | −40.6480 | −1.95117 | ||||||||
\(435\) | 6.61141 | − | 11.4513i | 0.316993 | − | 0.549048i | ||||
\(436\) | 22.2494 | − | 38.5371i | 1.06555 | − | 1.84559i | ||||
\(437\) | 7.70709 | 0.368680 | ||||||||
\(438\) | −7.59246 | + | 13.1505i | −0.362782 | + | 0.628356i | ||||
\(439\) | 16.2751 | + | 28.1893i | 0.776767 | + | 1.34540i | 0.933796 | + | 0.357807i | \(0.116475\pi\) |
−0.157028 | + | 0.987594i | \(0.550191\pi\) | |||||||
\(440\) | −3.36413 | − | 5.82685i | −0.160379 | − | 0.277784i | ||||
\(441\) | −1.95108 | −0.0929087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.58211 | 0.455260 | 0.227630 | − | 0.973748i | \(-0.426902\pi\) | ||||
0.227630 | + | 0.973748i | \(0.426902\pi\) | |||||||
\(444\) | −9.67360 | − | 16.7552i | −0.459089 | − | 0.795165i | ||||
\(445\) | 16.8828 | + | 29.2419i | 0.800324 | + | 1.38620i | ||||
\(446\) | 11.0012 | − | 19.0546i | 0.520922 | − | 0.902263i | ||||
\(447\) | 10.2591 | 0.485237 | ||||||||
\(448\) | −10.6712 | + | 18.4831i | −0.504167 | + | 0.873243i | ||||
\(449\) | −14.1969 | + | 24.5897i | −0.669992 | + | 1.16046i | 0.307914 | + | 0.951414i | \(0.400369\pi\) |
−0.977906 | + | 0.209045i | \(0.932964\pi\) | |||||||
\(450\) | 12.8442 | 0.605479 | ||||||||
\(451\) | −17.1359 | + | 29.6802i | −0.806896 | + | 1.39759i | ||||
\(452\) | −10.6518 | − | 18.4495i | −0.501020 | − | 0.867792i | ||||
\(453\) | 10.0843 | + | 17.4665i | 0.473800 | + | 0.820646i | ||||
\(454\) | 14.2929 | 0.670800 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.54288 | −0.0722518 | ||||||||
\(457\) | 2.49784 | + | 4.32639i | 0.116844 | + | 0.202380i | 0.918515 | − | 0.395385i | \(-0.129389\pi\) |
−0.801671 | + | 0.597765i | \(0.796056\pi\) | |||||||
\(458\) | −17.2159 | − | 29.8189i | −0.804448 | − | 1.39335i | ||||
\(459\) | 0.455927 | − | 0.789689i | 0.0212808 | − | 0.0368595i | ||||
\(460\) | −14.9576 | −0.697404 | ||||||||
\(461\) | 0.676292 | − | 1.17137i | 0.0314981 | − | 0.0545562i | −0.849847 | − | 0.527030i | \(-0.823306\pi\) |
0.881345 | + | 0.472474i | \(0.156639\pi\) | |||||||
\(462\) | 11.3693 | − | 19.6922i | 0.528946 | − | 0.916162i | ||||
\(463\) | 3.36467 | 0.156369 | 0.0781846 | − | 0.996939i | \(-0.475088\pi\) | ||||
0.0781846 | + | 0.996939i | \(0.475088\pi\) | |||||||
\(464\) | −7.02057 | + | 12.1600i | −0.325922 | + | 0.564513i | ||||
\(465\) | −14.8192 | − | 25.6675i | −0.687222 | − | 1.19030i | ||||
\(466\) | −8.90462 | − | 15.4232i | −0.412498 | − | 0.714468i | ||||
\(467\) | 6.91079 | 0.319793 | 0.159897 | − | 0.987134i | \(-0.448884\pi\) | ||||
0.159897 | + | 0.987134i | \(0.448884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.41789 | −0.157824 | ||||||||
\(470\) | −13.0749 | − | 22.6463i | −0.603099 | − | 1.04460i | ||||
\(471\) | 5.21917 | + | 9.03987i | 0.240487 | + | 0.416535i | ||||
\(472\) | −0.956459 | + | 1.65664i | −0.0440246 | + | 0.0762529i | ||||
\(473\) | 11.2916 | 0.519188 | ||||||||
\(474\) | −3.83244 | + | 6.63798i | −0.176030 | + | 0.304892i | ||||
\(475\) | −11.9167 | + | 20.6403i | −0.546776 | + | 0.947043i | ||||
\(476\) | −4.50365 | −0.206424 | ||||||||
\(477\) | −0.271438 | + | 0.470145i | −0.0124283 | + | 0.0215265i | ||||
\(478\) | −23.4797 | − | 40.6681i | −1.07394 | − | 1.86011i | ||||
\(479\) | 1.75786 | + | 3.04471i | 0.0803189 | + | 0.139116i | 0.903387 | − | 0.428826i | \(-0.141073\pi\) |
−0.823068 | + | 0.567943i | \(0.807739\pi\) | |||||||
\(480\) | −27.2422 | −1.24343 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −45.0355 | −2.05131 | ||||||||
\(483\) | −2.27748 | − | 3.94471i | −0.103629 | − | 0.179490i | ||||
\(484\) | −14.7201 | − | 25.4960i | −0.669097 | − | 1.15891i | ||||
\(485\) | 27.0722 | − | 46.8904i | 1.22928 | − | 2.12918i | ||||
\(486\) | −2.04892 | −0.0929408 | ||||||||
\(487\) | −6.42394 | + | 11.1266i | −0.291096 | + | 0.504194i | −0.974069 | − | 0.226250i | \(-0.927353\pi\) |
0.682973 | + | 0.730444i | \(0.260687\pi\) | |||||||
\(488\) | −0.746684 | + | 1.29329i | −0.0338008 | + | 0.0585447i | ||||
\(489\) | −11.0465 | −0.499541 | ||||||||
\(490\) | −6.70978 | + | 11.6217i | −0.303117 | + | 0.525014i | ||||
\(491\) | −14.3354 | − | 24.8297i | −0.646948 | − | 1.12055i | −0.983848 | − | 0.179007i | \(-0.942712\pi\) |
0.336899 | − | 0.941541i | \(-0.390622\pi\) | |||||||
\(492\) | −7.62618 | − | 13.2089i | −0.343815 | − | 0.595504i | ||||
\(493\) | −3.59179 | −0.161766 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.5797 | 0.745203 | ||||||||
\(496\) | 15.7363 | + | 27.2560i | 0.706580 | + | 1.22383i | ||||
\(497\) | −2.67241 | − | 4.62874i | −0.119874 | − | 0.207628i | ||||
\(498\) | −2.36443 | + | 4.09531i | −0.105953 | + | 0.183515i | ||||
\(499\) | 33.5555 | 1.50215 | 0.751076 | − | 0.660215i | \(-0.229535\pi\) | ||||
0.751076 | + | 0.660215i | \(0.229535\pi\) | |||||||
\(500\) | 4.68084 | − | 8.10745i | 0.209334 | − | 0.362576i | ||||
\(501\) | −4.05496 | + | 7.02339i | −0.181162 | + | 0.313782i | ||||
\(502\) | 54.5907 | 2.43650 | ||||||||
\(503\) | −10.7817 | + | 18.6744i | −0.480730 | + | 0.832650i | −0.999756 | − | 0.0221094i | \(-0.992962\pi\) |
0.519025 | + | 0.854759i | \(0.326295\pi\) | |||||||
\(504\) | 0.455927 | + | 0.789689i | 0.0203086 | + | 0.0351755i | ||||
\(505\) | −16.6984 | − | 28.9224i | −0.743067 | − | 1.28703i | ||||
\(506\) | −20.5139 | −0.911955 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.3588 | 1.34695 | ||||||||
\(509\) | −4.44504 | − | 7.69904i | −0.197023 | − | 0.341254i | 0.750539 | − | 0.660826i | \(-0.229794\pi\) |
−0.947562 | + | 0.319572i | \(0.896461\pi\) | |||||||
\(510\) | −3.13587 | − | 5.43148i | −0.138859 | − | 0.240510i | ||||
\(511\) | −8.32640 | + | 14.4217i | −0.368338 | + | 0.637980i | ||||
\(512\) | 31.8213 | 1.40632 | ||||||||
\(513\) | 1.90097 | − | 3.29257i | 0.0839298 | − | 0.145371i | ||||
\(514\) | −23.7104 | + | 41.0677i | −1.04582 | + | 1.81142i | ||||
\(515\) | 36.8853 | 1.62536 | ||||||||
\(516\) | −2.51261 | + | 4.35198i | −0.110612 | + | 0.191585i | ||||
\(517\) | −9.38889 | − | 16.2620i | −0.412923 | − | 0.715203i | ||||
\(518\) | −20.2615 | − | 35.0940i | −0.890240 | − | 1.54194i | ||||
\(519\) | 18.0562 | 0.792580 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.3478 | 0.847642 | 0.423821 | − | 0.905746i | \(-0.360688\pi\) | ||||
0.423821 | + | 0.905746i | \(0.360688\pi\) | |||||||
\(522\) | 4.03534 | + | 6.98942i | 0.176622 | + | 0.305919i | ||||
\(523\) | 6.29739 | + | 10.9074i | 0.275366 | + | 0.476947i | 0.970227 | − | 0.242196i | \(-0.0778678\pi\) |
−0.694862 | + | 0.719143i | \(0.744534\pi\) | |||||||
\(524\) | −3.29118 | + | 5.70050i | −0.143776 | + | 0.249027i | ||||
\(525\) | 14.0858 | 0.614753 | ||||||||
\(526\) | 18.9816 | − | 32.8771i | 0.827636 | − | 1.43351i | ||||
\(527\) | −4.02542 | + | 6.97223i | −0.175350 | + | 0.303715i | ||||
\(528\) | −17.6058 | −0.766194 | ||||||||
\(529\) | 9.44534 | − | 16.3598i | 0.410667 | − | 0.711296i | ||||
\(530\) | 1.86695 | + | 3.23366i | 0.0810953 | + | 0.140461i | ||||
\(531\) | −2.35690 | − | 4.08226i | −0.102281 | − | 0.177155i | ||||
\(532\) | −18.7778 | −0.814120 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −20.6093 | −0.891850 | ||||||||
\(535\) | −16.5707 | − | 28.7013i | −0.716413 | − | 1.24086i | ||||
\(536\) | −0.308643 | − | 0.534585i | −0.0133313 | − | 0.0230905i | ||||
\(537\) | −9.93512 | + | 17.2081i | −0.428732 | + | 0.742585i | ||||
\(538\) | 19.9941 | 0.862009 | ||||||||
\(539\) | −4.81820 | + | 8.34537i | −0.207535 | + | 0.359460i | ||||
\(540\) | −3.68933 | + | 6.39011i | −0.158764 | + | 0.274987i | ||||
\(541\) | −29.0019 | −1.24689 | −0.623445 | − | 0.781867i | \(-0.714267\pi\) | ||||
−0.623445 | + | 0.781867i | \(0.714267\pi\) | |||||||
\(542\) | −23.3596 | + | 40.4601i | −1.00338 | + | 1.73791i | ||||
\(543\) | −5.04138 | − | 8.73193i | −0.216347 | − | 0.374723i | ||||
\(544\) | 3.69998 | + | 6.40856i | 0.158635 | + | 0.274765i | ||||
\(545\) | 67.9590 | 2.91104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.7006 | 1.18439 | 0.592197 | − | 0.805793i | \(-0.298261\pi\) | ||||
0.592197 | + | 0.805793i | \(0.298261\pi\) | |||||||
\(548\) | 25.2990 | + | 43.8192i | 1.08072 | + | 1.87186i | ||||
\(549\) | −1.83997 | − | 3.18692i | −0.0785280 | − | 0.136014i | ||||
\(550\) | 31.7186 | − | 54.9383i | 1.35249 | − | 2.34258i | ||||
\(551\) | −14.9758 | −0.637992 | ||||||||
\(552\) | 0.411322 | − | 0.712430i | 0.0175070 | − | 0.0303230i | ||||
\(553\) | −4.20291 | + | 7.27965i | −0.178726 | + | 0.309562i | ||||
\(554\) | −49.1135 | −2.08663 | ||||||||
\(555\) | 14.7736 | − | 25.5886i | 0.627104 | − | 1.08618i | ||||
\(556\) | −1.07984 | − | 1.87034i | −0.0457956 | − | 0.0793203i | ||||
\(557\) | 3.40485 | + | 5.89738i | 0.144268 | + | 0.249880i | 0.929100 | − | 0.369829i | \(-0.120584\pi\) |
−0.784831 | + | 0.619709i | \(0.787251\pi\) | |||||||
\(558\) | 18.0901 | 0.765814 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −26.8877 | −1.13621 | ||||||||
\(561\) | −2.25182 | − | 3.90027i | −0.0950721 | − | 0.164670i | ||||
\(562\) | −4.22587 | − | 7.31943i | −0.178258 | − | 0.308751i | ||||
\(563\) | 9.62618 | − | 16.6730i | 0.405695 | − | 0.702684i | −0.588707 | − | 0.808346i | \(-0.700363\pi\) |
0.994402 | + | 0.105662i | \(0.0336962\pi\) | |||||||
\(564\) | 8.35690 | 0.351889 | ||||||||
\(565\) | 16.2676 | − | 28.1762i | 0.684381 | − | 1.18538i | ||||
\(566\) | 16.0387 | − | 27.7798i | 0.674157 | − | 1.16767i | ||||
\(567\) | −2.24698 | −0.0943643 | ||||||||
\(568\) | 0.482647 | − | 0.835969i | 0.0202514 | − | 0.0350765i | ||||
\(569\) | −3.92423 | − | 6.79697i | −0.164512 | − | 0.284944i | 0.771970 | − | 0.635659i | \(-0.219272\pi\) |
−0.936482 | + | 0.350716i | \(0.885938\pi\) | |||||||
\(570\) | −13.0749 | − | 22.6463i | −0.547646 | − | 0.948551i | ||||
\(571\) | 29.8568 | 1.24947 | 0.624735 | − | 0.780837i | \(-0.285207\pi\) | ||||
0.624735 | + | 0.780837i | \(0.285207\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.58748 | 0.275196 | ||||||||
\(574\) | −15.9731 | − | 27.6663i | −0.666706 | − | 1.15477i | ||||
\(575\) | −6.35384 | − | 11.0052i | −0.264973 | − | 0.458947i | ||||
\(576\) | 4.74914 | − | 8.22574i | 0.197881 | − | 0.342739i | ||||
\(577\) | −8.97823 | −0.373769 | −0.186884 | − | 0.982382i | \(-0.559839\pi\) | ||||
−0.186884 | + | 0.982382i | \(0.559839\pi\) | |||||||
\(578\) | 16.5640 | − | 28.6897i | 0.688971 | − | 1.19333i | ||||
\(579\) | −5.43362 | + | 9.41131i | −0.225814 | + | 0.391121i | ||||
\(580\) | 29.0646 | 1.20684 | ||||||||
\(581\) | −2.59299 | + | 4.49119i | −0.107575 | + | 0.186326i | ||||
\(582\) | 16.5238 | + | 28.6201i | 0.684933 | + | 1.18634i | ||||
\(583\) | 1.34063 | + | 2.32205i | 0.0555234 | + | 0.0961693i | ||||
\(584\) | −3.00756 | −0.124454 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46.2948 | −1.91242 | ||||||||
\(587\) | 11.9269 | + | 20.6580i | 0.492277 | + | 0.852648i | 0.999960 | − | 0.00889531i | \(-0.00283150\pi\) |
−0.507684 | + | 0.861543i | \(0.669498\pi\) | |||||||
\(588\) | −2.14430 | − | 3.71404i | −0.0884295 | − | 0.153164i | ||||
\(589\) | −16.7838 | + | 29.0704i | −0.691565 | + | 1.19783i | ||||
\(590\) | −32.4215 | −1.33477 | ||||||||
\(591\) | −4.62080 | + | 8.00346i | −0.190074 | + | 0.329218i | ||||
\(592\) | −15.6879 | + | 27.1722i | −0.644769 | + | 1.11677i | ||||
\(593\) | −11.9866 | −0.492230 | −0.246115 | − | 0.969241i | \(-0.579154\pi\) | ||||
−0.246115 | + | 0.969241i | \(0.579154\pi\) | |||||||
\(594\) | −5.05980 | + | 8.76383i | −0.207606 | + | 0.359585i | ||||
\(595\) | −3.43900 | − | 5.95652i | −0.140985 | − | 0.244194i | ||||
\(596\) | 11.2750 | + | 19.5289i | 0.461843 | + | 0.799936i | ||||
\(597\) | 1.56465 | 0.0640367 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.1142 | 1.18958 | 0.594788 | − | 0.803883i | \(-0.297236\pi\) | ||||
0.594788 | + | 0.803883i | \(0.297236\pi\) | |||||||
\(600\) | 1.27197 | + | 2.20312i | 0.0519280 | + | 0.0899419i | ||||
\(601\) | −18.5683 | − | 32.1612i | −0.757417 | − | 1.31188i | −0.944164 | − | 0.329476i | \(-0.893128\pi\) |
0.186747 | − | 0.982408i | \(-0.440205\pi\) | |||||||
\(602\) | −5.26271 | + | 9.11528i | −0.214492 | + | 0.371511i | ||||
\(603\) | 1.52111 | 0.0619442 | ||||||||
\(604\) | −22.1658 | + | 38.3924i | −0.901915 | + | 1.56216i | ||||
\(605\) | 22.4807 | − | 38.9377i | 0.913970 | − | 1.58304i | ||||
\(606\) | 20.3840 | 0.828045 | ||||||||
\(607\) | 7.11625 | − | 12.3257i | 0.288840 | − | 0.500285i | −0.684693 | − | 0.728831i | \(-0.740064\pi\) |
0.973533 | + | 0.228546i | \(0.0733972\pi\) | |||||||
\(608\) | 15.4269 | + | 26.7202i | 0.625644 | + | 1.08365i | ||||
\(609\) | 4.42543 | + | 7.66507i | 0.179327 | + | 0.310604i | ||||
\(610\) | −25.3106 | −1.02480 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.00431 | 0.0810195 | ||||||||
\(613\) | 15.1570 | + | 26.2526i | 0.612184 | + | 1.06033i | 0.990872 | + | 0.134810i | \(0.0430423\pi\) |
−0.378687 | + | 0.925525i | \(0.623624\pi\) | |||||||
\(614\) | −6.71528 | − | 11.6312i | −0.271007 | − | 0.469398i | ||||
\(615\) | 11.6468 | − | 20.1728i | 0.469642 | − | 0.813444i | ||||
\(616\) | 4.50365 | 0.181457 | ||||||||
\(617\) | −12.4819 | + | 21.6192i | −0.502501 | + | 0.870358i | 0.497494 | + | 0.867467i | \(0.334254\pi\) |
−0.999996 | + | 0.00289086i | \(0.999080\pi\) | |||||||
\(618\) | −11.2567 | + | 19.4971i | −0.452810 | + | 0.784289i | ||||
\(619\) | −35.6122 | −1.43138 | −0.715688 | − | 0.698420i | \(-0.753887\pi\) | ||||
−0.715688 | + | 0.698420i | \(0.753887\pi\) | |||||||
\(620\) | 32.5734 | − | 56.4188i | 1.30818 | − | 2.26584i | ||||
\(621\) | 1.01357 | + | 1.75556i | 0.0406733 | + | 0.0704482i | ||||
\(622\) | 12.3337 | + | 21.3626i | 0.494536 | + | 0.856561i | ||||
\(623\) | −22.6015 | −0.905509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0465 | −0.681861 | ||||||||
\(626\) | 34.7240 | + | 60.1438i | 1.38785 | + | 2.40383i | ||||
\(627\) | −9.38889 | − | 16.2620i | −0.374956 | − | 0.649443i | ||||
\(628\) | −11.4721 | + | 19.8702i | −0.457785 | + | 0.792907i | ||||
\(629\) | −8.02608 | −0.320021 | ||||||||
\(630\) | −7.72737 | + | 13.3842i | −0.307866 | + | 0.533239i | ||||
\(631\) | 11.9415 | − | 20.6832i | 0.475382 | − | 0.823385i | −0.524221 | − | 0.851582i | \(-0.675643\pi\) |
0.999602 | + | 0.0281972i | \(0.00897663\pi\) | |||||||
\(632\) | −1.51812 | −0.0603877 | ||||||||
\(633\) | 11.6223 | − | 20.1304i | 0.461945 | − | 0.800112i | ||||
\(634\) | −4.60829 | − | 7.98180i | −0.183019 | − | 0.316998i | ||||
\(635\) | 23.1821 | + | 40.1526i | 0.919953 | + | 1.59341i | ||||
\(636\) | −1.19328 | −0.0473165 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 39.8611 | 1.57812 | ||||||||
\(639\) | 1.18933 | + | 2.05999i | 0.0470493 | + | 0.0814918i | ||||
\(640\) | −5.42237 | − | 9.39182i | −0.214338 | − | 0.371244i | ||||
\(641\) | 12.3288 | − | 21.3542i | 0.486960 | − | 0.843440i | −0.512927 | − | 0.858432i | \(-0.671439\pi\) |
0.999888 | + | 0.0149922i | \(0.00477233\pi\) | |||||||
\(642\) | 20.2282 | 0.798343 | ||||||||
\(643\) | 23.9083 | − | 41.4103i | 0.942850 | − | 1.63306i | 0.182850 | − | 0.983141i | \(-0.441468\pi\) |
0.760000 | − | 0.649923i | \(-0.225199\pi\) | |||||||
\(644\) | 5.00604 | − | 8.67072i | 0.197266 | − | 0.341674i | ||||
\(645\) | −7.67456 | −0.302186 | ||||||||
\(646\) | −3.55161 | + | 6.15156i | −0.139736 | + | 0.242030i | ||||
\(647\) | 2.69471 | + | 4.66737i | 0.105940 | + | 0.183493i | 0.914122 | − | 0.405440i | \(-0.132882\pi\) |
−0.808182 | + | 0.588933i | \(0.799548\pi\) | |||||||
\(648\) | −0.202907 | − | 0.351445i | −0.00797092 | − | 0.0138060i | ||||
\(649\) | −23.2814 | −0.913876 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.8388 | 0.777543 | ||||||||
\(652\) | −12.1405 | − | 21.0279i | −0.475458 | − | 0.823517i | ||||
\(653\) | 2.51895 | + | 4.36295i | 0.0985741 | + | 0.170735i | 0.911095 | − | 0.412197i | \(-0.135239\pi\) |
−0.812521 | + | 0.582933i | \(0.801905\pi\) | |||||||
\(654\) | −20.7397 | + | 35.9223i | −0.810988 | + | 1.40467i | ||||
\(655\) | −10.0526 | −0.392789 | ||||||||
\(656\) | −12.3675 | + | 21.4212i | −0.482871 | + | 0.836358i | ||||
\(657\) | 3.70560 | − | 6.41828i | 0.144569 | − | 0.250401i | ||||
\(658\) | 17.5036 | 0.682363 | ||||||||
\(659\) | 21.9906 | − | 38.0888i | 0.856632 | − | 1.48373i | −0.0184899 | − | 0.999829i | \(-0.505886\pi\) |
0.875122 | − | 0.483902i | \(-0.160781\pi\) | |||||||
\(660\) | 18.2216 | + | 31.5608i | 0.709276 | + | 1.22850i | ||||
\(661\) | −19.1097 | − | 33.0989i | −0.743280 | − | 1.28740i | −0.950994 | − | 0.309210i | \(-0.899936\pi\) |
0.207714 | − | 0.978190i | \(-0.433398\pi\) | |||||||
\(662\) | 22.9748 | 0.892940 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.936608 | −0.0363474 | ||||||||
\(665\) | −14.3388 | − | 24.8355i | −0.556034 | − | 0.963079i | ||||
\(666\) | 9.01722 | + | 15.6183i | 0.349410 | + | 0.605196i | ||||
\(667\) | 3.99247 | − | 6.91516i | 0.154589 | − | 0.267756i | ||||
\(668\) | −17.8261 | −0.689713 | ||||||||
\(669\) | −5.36927 | + | 9.29985i | −0.207588 | + | 0.359553i | ||||
\(670\) | 5.23109 | − | 9.06051i | 0.202094 | − | 0.350038i | ||||
\(671\) | −18.1752 | −0.701647 | ||||||||
\(672\) | 9.11745 | − | 15.7919i | 0.351713 | − | 0.609185i | ||||
\(673\) | 3.33244 | + | 5.77195i | 0.128456 | + | 0.222492i | 0.923079 | − | 0.384611i | \(-0.125665\pi\) |
−0.794623 | + | 0.607104i | \(0.792331\pi\) | |||||||
\(674\) | −7.22132 | − | 12.5077i | −0.278155 | − | 0.481779i | ||||
\(675\) | −6.26875 | −0.241284 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.80194 | 0.184553 | 0.0922767 | − | 0.995733i | \(-0.470586\pi\) | ||||
0.0922767 | + | 0.995733i | \(0.470586\pi\) | |||||||
\(678\) | 9.92908 | + | 17.1977i | 0.381324 | + | 0.660472i | ||||
\(679\) | 18.1211 | + | 31.3867i | 0.695424 | + | 1.20451i | ||||
\(680\) | 0.621097 | − | 1.07577i | 0.0238180 | − | 0.0412539i | ||||
\(681\) | −6.97584 | −0.267315 | ||||||||
\(682\) | 44.6734 | − | 77.3766i | 1.71063 | − | 2.96290i | ||||
\(683\) | 5.62953 | − | 9.75063i | 0.215408 | − | 0.373098i | −0.737991 | − | 0.674811i | \(-0.764225\pi\) |
0.953399 | + | 0.301713i | \(0.0975585\pi\) | |||||||
\(684\) | 8.35690 | 0.319534 | ||||||||
\(685\) | −38.6368 | + | 66.9209i | −1.47624 | + | 2.55692i | ||||
\(686\) | −20.6048 | − | 35.6886i | −0.786696 | − | 1.36260i | ||||
\(687\) | 8.40246 | + | 14.5535i | 0.320574 | + | 0.555250i | ||||
\(688\) | 8.14952 | 0.310698 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 13.9427 | 0.530790 | ||||||||
\(691\) | −12.3572 | − | 21.4033i | −0.470090 | − | 0.814219i | 0.529325 | − | 0.848419i | \(-0.322445\pi\) |
−0.999415 | + | 0.0341997i | \(0.989112\pi\) | |||||||
\(692\) | 19.8443 | + | 34.3714i | 0.754369 | + | 1.30660i | ||||
\(693\) | −5.54892 | + | 9.61101i | −0.210786 | + | 0.365092i | ||||
\(694\) | −5.54048 | −0.210314 | ||||||||
\(695\) | 1.64914 | − | 2.85640i | 0.0625556 | − | 0.108350i | ||||
\(696\) | −0.799249 | + | 1.38434i | −0.0302955 | + | 0.0524733i | ||||
\(697\) | −6.32736 | −0.239666 | ||||||||
\(698\) | −0.425665 | + | 0.737273i | −0.0161116 | + | 0.0279062i | ||||
\(699\) | 4.34601 | + | 7.52751i | 0.164381 | + | 0.284717i | ||||
\(700\) | 15.4807 | + | 26.8133i | 0.585115 | + | 1.01345i | ||||
\(701\) | 25.8920 | 0.977927 | 0.488964 | − | 0.872304i | \(-0.337375\pi\) | ||||
0.488964 | + | 0.872304i | \(0.337375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.4644 | −1.26213 | ||||||||
\(704\) | −23.4560 | − | 40.6270i | −0.884031 | − | 1.53119i | ||||
\(705\) | 6.38135 | + | 11.0528i | 0.240336 | + | 0.416274i | ||||
\(706\) | −32.9540 | + | 57.0779i | −1.24024 | + | 2.14816i | ||||
\(707\) | 22.3545 | 0.840728 | ||||||||
\(708\) | 5.18060 | − | 8.97307i | 0.194699 | − | 0.337229i | ||||
\(709\) | 0.0425810 | − | 0.0737525i | 0.00159916 | − | 0.00276983i | −0.865225 | − | 0.501384i | \(-0.832824\pi\) |
0.866824 | + | 0.498614i | \(0.166158\pi\) | |||||||
\(710\) | 16.3605 | 0.613998 | ||||||||
\(711\) | 1.87047 | − | 3.23975i | 0.0701481 | − | 0.121500i | ||||
\(712\) | −2.04096 | − | 3.53504i | −0.0764881 | − | 0.132481i | ||||
\(713\) | −8.94893 | − | 15.5000i | −0.335140 | − | 0.580479i | ||||
\(714\) | 4.19806 | 0.157109 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −43.6760 | −1.63225 | ||||||||
\(717\) | 11.4596 | + | 19.8486i | 0.427966 | + | 0.741258i | ||||
\(718\) | 22.8988 | + | 39.6619i | 0.854576 | + | 1.48017i | ||||
\(719\) | −13.5254 | + | 23.4267i | −0.504413 | + | 0.873669i | 0.495574 | + | 0.868566i | \(0.334958\pi\) |
−0.999987 | + | 0.00510319i | \(0.998376\pi\) | |||||||
\(720\) | 11.9661 | 0.445952 | ||||||||
\(721\) | −12.3448 | + | 21.3818i | −0.459745 | + | 0.796302i | ||||
\(722\) | 4.65644 | − | 8.06519i | 0.173295 | − | 0.300155i | ||||
\(723\) | 21.9801 | 0.817451 | ||||||||
\(724\) | 11.0813 | − | 19.1933i | 0.411832 | − | 0.713315i | ||||
\(725\) | 12.3463 | + | 21.3844i | 0.458530 | + | 0.794198i | ||||
\(726\) | 13.7213 | + | 23.7660i | 0.509246 | + | 0.882040i | ||||
\(727\) | −47.1584 | −1.74901 | −0.874503 | − | 0.485019i | \(-0.838813\pi\) | ||||
−0.874503 | + | 0.485019i | \(0.838813\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −25.4871 | − | 44.1449i | −0.943320 | − | 1.63388i | ||||
\(731\) | 1.04234 | + | 1.80539i | 0.0385525 | + | 0.0667749i | ||||
\(732\) | 4.04437 | − | 7.00505i | 0.149484 | − | 0.258914i | ||||
\(733\) | 9.68186 | 0.357608 | 0.178804 | − | 0.983885i | \(-0.442777\pi\) | ||||
0.178804 | + | 0.983885i | \(0.442777\pi\) | |||||||
\(734\) | 2.35892 | − | 4.08577i | 0.0870693 | − | 0.150809i | ||||
\(735\) | 3.27479 | − | 5.67210i | 0.120792 | − | 0.209219i | ||||
\(736\) | −16.4509 | −0.606388 | ||||||||
\(737\) | 3.75637 | − | 6.50623i | 0.138368 | − | 0.239660i | ||||
\(738\) | 7.10872 | + | 12.3127i | 0.261676 | + | 0.453235i | ||||
\(739\) | 18.1570 | + | 31.4488i | 0.667915 | + | 1.15686i | 0.978486 | + | 0.206313i | \(0.0661464\pi\) |
−0.310571 | + | 0.950550i | \(0.600520\pi\) | |||||||
\(740\) | 64.9466 | 2.38748 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.49934 | −0.0917535 | ||||||||
\(743\) | −20.8768 | − | 36.1597i | −0.765896 | − | 1.32657i | −0.939772 | − | 0.341803i | \(-0.888963\pi\) |
0.173876 | − | 0.984768i | \(-0.444371\pi\) | |||||||
\(744\) | 1.79148 | + | 3.10293i | 0.0656788 | + | 0.113759i | ||||
\(745\) | −17.2193 | + | 29.8247i | −0.630866 | + | 1.09269i | ||||
\(746\) | −39.4950 | −1.44602 | ||||||||
\(747\) | 1.15399 | − | 1.99877i | 0.0422223 | − | 0.0731311i | ||||
\(748\) | 4.94965 | − | 8.57304i | 0.180977 | − | 0.313462i | ||||
\(749\) | 22.1836 | 0.810571 | ||||||||
\(750\) | −4.36323 | + | 7.55734i | −0.159323 | + | 0.275955i | ||||
\(751\) | 11.0963 | + | 19.2194i | 0.404911 | + | 0.701327i | 0.994311 | − | 0.106515i | \(-0.0339691\pi\) |
−0.589400 | + | 0.807841i | \(0.700636\pi\) | |||||||
\(752\) | −6.77628 | − | 11.7369i | −0.247106 | − | 0.427999i | ||||
\(753\) | −26.6437 | −0.970950 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −67.7036 | −2.46399 | ||||||||
\(756\) | −2.46950 | − | 4.27730i | −0.0898149 | − | 0.155564i | ||||
\(757\) | −4.61865 | − | 7.99973i | −0.167868 | − | 0.290755i | 0.769802 | − | 0.638282i | \(-0.220355\pi\) |
−0.937670 | + | 0.347527i | \(0.887021\pi\) | |||||||
\(758\) | −7.51895 | + | 13.0232i | −0.273101 | + | 0.473024i | ||||
\(759\) | 10.0121 | 0.363416 | ||||||||
\(760\) | 2.58964 | − | 4.48538i | 0.0939360 | − | 0.162702i | ||||
\(761\) | −3.75086 | + | 6.49669i | −0.135969 | + | 0.235505i | −0.925967 | − | 0.377604i | \(-0.876748\pi\) |
0.789998 | + | 0.613109i | \(0.210081\pi\) | |||||||
\(762\) | −28.2989 | −1.02516 | ||||||||
\(763\) | −22.7446 | + | 39.3948i | −0.823409 | + | 1.42619i | ||||
\(764\) | 7.23985 | + | 12.5398i | 0.261929 | + | 0.453673i | ||||
\(765\) | 1.53050 | + | 2.65090i | 0.0553353 | + | 0.0958436i | ||||
\(766\) | −39.1140 | −1.41325 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12.3773 | −0.446629 | ||||||||
\(769\) | 2.57002 | + | 4.45141i | 0.0926774 | + | 0.160522i | 0.908637 | − | 0.417587i | \(-0.137124\pi\) |
−0.815959 | + | 0.578109i | \(0.803791\pi\) | |||||||
\(770\) | 38.1655 | + | 66.1045i | 1.37539 | + | 2.38224i | ||||
\(771\) | 11.5722 | − | 20.0436i | 0.416762 | − | 0.721853i | ||||
\(772\) | −23.8869 | −0.859708 | ||||||||
\(773\) | −4.25086 | + | 7.36271i | −0.152893 | + | 0.264818i | −0.932290 | − | 0.361712i | \(-0.882192\pi\) |
0.779397 | + | 0.626531i | \(0.215526\pi\) | |||||||
\(774\) | 2.34213 | − | 4.05668i | 0.0841860 | − | 0.145814i | ||||
\(775\) | 55.3473 | 1.98813 | ||||||||
\(776\) | −3.27274 | + | 5.66855i | −0.117485 | + | 0.203489i | ||||
\(777\) | 9.88889 | + | 17.1281i | 0.354762 | + | 0.614466i | ||||
\(778\) | 24.5746 | + | 42.5645i | 0.881043 | + | 1.52601i | ||||
\(779\) | −26.3817 | −0.945221 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7482 | 0.420385 | ||||||||
\(782\) | −1.89367 | − | 3.27994i | −0.0677176 | − | 0.117290i | ||||
\(783\) | −1.96950 | − | 3.41127i | −0.0703842 | − | 0.121909i | ||||
\(784\) | −3.47746 | + | 6.02314i | −0.124195 | + | 0.215112i | ||||
\(785\) | −35.0404 | −1.25065 | ||||||||
\(786\) | 3.06787 | − | 5.31370i | 0.109427 | − | 0.189533i | ||||
\(787\) | −3.89277 | + | 6.74248i | −0.138762 | + | 0.240343i | −0.927028 | − | 0.374991i | \(-0.877646\pi\) |
0.788266 | + | 0.615335i | \(0.210979\pi\) | |||||||
\(788\) | −20.3136 | −0.723643 | ||||||||
\(789\) | −9.26420 | + | 16.0461i | −0.329814 | + | 0.571255i | ||||
\(790\) | −12.8651 | − | 22.2830i | −0.457719 | − | 0.792793i | ||||
\(791\) | 10.8889 | + | 18.8601i | 0.387164 | + | 0.670588i | ||||
\(792\) | −2.00431 | −0.0712201 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.05190 | 0.321240 | ||||||||
\(795\) | −0.911190 | − | 1.57823i | −0.0323166 | − | 0.0559740i | ||||
\(796\) | 1.71960 | + | 2.97843i | 0.0609494 | + | 0.105568i | ||||
\(797\) | −10.6920 | + | 18.5191i | −0.378731 | + | 0.655981i | −0.990878 | − | 0.134763i | \(-0.956973\pi\) |
0.612147 | + | 0.790744i | \(0.290306\pi\) | |||||||
\(798\) | 17.5036 | 0.619622 | ||||||||
\(799\) | 1.73341 | − | 3.00235i | 0.0613235 | − | 0.106215i | ||||
\(800\) | 25.4364 | − | 44.0571i | 0.899312 | − | 1.55765i | ||||
\(801\) | 10.0586 | 0.355403 | ||||||||
\(802\) | −20.9080 | + | 36.2137i | −0.738286 | + | 1.27875i | ||||
\(803\) | −18.3019 | − | 31.6999i | −0.645861 | − | 1.11866i | ||||
\(804\) | 1.67174 | + | 2.89554i | 0.0589578 | + | 0.102118i | ||||
\(805\) | 15.2905 | 0.538920 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.75840 | −0.343512 | ||||||||
\(808\) | 2.01865 | + | 3.49641i | 0.0710160 | + | 0.123003i | ||||
\(809\) | −1.14310 | − | 1.97991i | −0.0401894 | − | 0.0696101i | 0.845231 | − | 0.534401i | \(-0.179463\pi\) |
−0.885420 | + | 0.464791i | \(0.846129\pi\) | |||||||
\(810\) | 3.43900 | − | 5.95652i | 0.120834 | − | 0.209291i | ||||
\(811\) | −17.8079 | −0.625320 | −0.312660 | − | 0.949865i | \(-0.601220\pi\) | ||||
−0.312660 | + | 0.949865i | \(0.601220\pi\) | |||||||
\(812\) | −9.72737 | + | 16.8483i | −0.341364 | + | 0.591259i | ||||
\(813\) | 11.4010 | − | 19.7471i | 0.399849 | − | 0.692560i | ||||
\(814\) | 89.0721 | 3.12198 | ||||||||
\(815\) | 18.5410 | − | 32.1140i | 0.649463 | − | 1.12490i | ||||
\(816\) | −1.62522 | − | 2.81496i | −0.0568940 | − | 0.0985434i | ||||
\(817\) | 4.34601 | + | 7.52751i | 0.152048 | + | 0.263354i | ||||
\(818\) | 45.3818 | 1.58674 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 51.2006 | 1.78800 | ||||||||
\(821\) | 6.95271 | + | 12.0424i | 0.242651 | + | 0.420284i | 0.961469 | − | 0.274915i | \(-0.0886496\pi\) |
−0.718817 | + | 0.695199i | \(0.755316\pi\) | |||||||
\(822\) | −23.5824 | − | 40.8459i | −0.822531 | − | 1.42466i | ||||
\(823\) | 3.62415 | − | 6.27722i | 0.126330 | − | 0.218810i | −0.795922 | − | 0.605399i | \(-0.793013\pi\) |
0.922252 | + | 0.386589i | \(0.126347\pi\) | |||||||
\(824\) | −4.45904 | −0.155338 | ||||||||
\(825\) | −15.4807 | + | 26.8133i | −0.538968 | + | 0.933520i | ||||
\(826\) | 10.8509 | − | 18.7942i | 0.377550 | − | 0.653935i | ||||
\(827\) | −54.1191 | −1.88191 | −0.940953 | − | 0.338536i | \(-0.890068\pi\) | ||||
−0.940953 | + | 0.338536i | \(0.890068\pi\) | |||||||
\(828\) | −2.22790 | + | 3.85883i | −0.0774248 | + | 0.134104i | ||||
\(829\) | 2.89589 | + | 5.01582i | 0.100578 | + | 0.174207i | 0.911923 | − | 0.410361i | \(-0.134597\pi\) |
−0.811345 | + | 0.584568i | \(0.801264\pi\) | |||||||
\(830\) | −7.93714 | − | 13.7475i | −0.275502 | − | 0.477184i | ||||
\(831\) | 23.9705 | 0.831526 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.77910 | −0.0616422 | ||||||||
\(834\) | 1.00657 | + | 1.74344i | 0.0348548 | + | 0.0603703i | ||||
\(835\) | −13.6121 | − | 23.5768i | −0.471065 | − | 0.815909i | ||||
\(836\) | 20.6374 | − | 35.7450i | 0.713758 | − | 1.23627i | ||||
\(837\) | −8.82908 | −0.305178 | ||||||||
\(838\) | −15.1169 | + | 26.1833i | −0.522205 | + | 0.904486i | ||||
\(839\) | −2.64675 | + | 4.58431i | −0.0913760 | + | 0.158268i | −0.908090 | − | 0.418774i | \(-0.862460\pi\) |
0.816714 | + | 0.577042i | \(0.195793\pi\) | |||||||
\(840\) | −3.06100 | −0.105614 | ||||||||
\(841\) | 6.74214 | − | 11.6777i | 0.232487 | − | 0.402680i | ||||
\(842\) | 8.67941 | + | 15.0332i | 0.299112 | + | 0.518077i | ||||
\(843\) | 2.06249 | + | 3.57234i | 0.0710360 | + | 0.123038i | ||||
\(844\) | 51.0930 | 1.75870 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.78986 | −0.267821 | ||||||||
\(847\) | 15.0477 | + | 26.0634i | 0.517046 | + | 0.895550i | ||||
\(848\) | 0.967582 | + | 1.67590i | 0.0332269 | + | 0.0575507i | ||||
\(849\) | −7.82789 | + | 13.5583i | −0.268652 | + | 0.465320i | ||||
\(850\) | 11.7120 | 0.401718 | ||||||||
\(851\) | 8.92141 | − | 15.4523i | 0.305822 | − | 0.529699i | ||||
\(852\) | −2.61423 | + | 4.52798i | −0.0895620 | + | 0.155126i | ||||
\(853\) | 13.5961 | 0.465522 | 0.232761 | − | 0.972534i | \(-0.425224\pi\) | ||||
0.232761 | + | 0.972534i | \(0.425224\pi\) | |||||||
\(854\) | 8.47099 | − | 14.6722i | 0.289871 | − | 0.502072i | ||||
\(855\) | 6.38135 | + | 11.0528i | 0.218238 | + | 0.377999i | ||||
\(856\) | 2.00322 | + | 3.46968i | 0.0684687 | + | 0.118591i | ||||
\(857\) | −23.8323 | −0.814097 | −0.407048 | − | 0.913407i | \(-0.633442\pi\) | ||||
−0.407048 | + | 0.913407i | \(0.633442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.9861 | −0.920754 | −0.460377 | − | 0.887723i | \(-0.652286\pi\) | ||||
−0.460377 | + | 0.887723i | \(0.652286\pi\) | |||||||
\(860\) | −8.43458 | − | 14.6091i | −0.287617 | − | 0.498167i | ||||
\(861\) | 7.79590 | + | 13.5029i | 0.265683 | + | 0.460177i | ||||
\(862\) | 2.45031 | − | 4.24407i | 0.0834580 | − | 0.144553i | ||||
\(863\) | 27.0291 | 0.920080 | 0.460040 | − | 0.887898i | \(-0.347835\pi\) | ||||
0.460040 | + | 0.887898i | \(0.347835\pi\) | |||||||
\(864\) | −4.05765 | + | 7.02805i | −0.138044 | + | 0.239099i | ||||
\(865\) | −30.3064 | + | 52.4922i | −1.03045 | + | 1.78479i | ||||
\(866\) | −21.3674 | −0.726095 | ||||||||
\(867\) | −8.08426 | + | 14.0024i | −0.274556 | + | 0.475545i | ||||
\(868\) | 21.8034 | + | 37.7646i | 0.740057 | + | 1.28182i | ||||
\(869\) | −9.23825 | − | 16.0011i | −0.313386 | − | 0.542801i | ||||
\(870\) | −27.0925 | −0.918520 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.21552 | −0.278213 | ||||||||
\(873\) | −8.06465 | − | 13.9684i | −0.272947 | − | 0.472758i | ||||
\(874\) | −7.89559 | − | 13.6756i | −0.267072 | − | 0.462583i | ||||
\(875\) | −4.78501 | + | 8.28788i | −0.161763 | + | 0.280182i | ||||
\(876\) | 16.2903 | 0.550397 | ||||||||
\(877\) | 20.4390 | − | 35.4014i | 0.690176 | − | 1.19542i | −0.281604 | − | 0.959531i | \(-0.590866\pi\) |
0.971780 | − | 0.235889i | \(-0.0758002\pi\) | |||||||
\(878\) | 33.3463 | − | 57.7575i | 1.12538 | − | 1.94922i | ||||
\(879\) | 22.5948 | 0.762103 | ||||||||
\(880\) | 29.5504 | − | 51.1828i | 0.996144 | − | 1.72537i | ||||
\(881\) | 11.2482 | + | 19.4824i | 0.378961 | + | 0.656379i | 0.990911 | − | 0.134517i | \(-0.0429482\pi\) |
−0.611951 | + | 0.790896i | \(0.709615\pi\) | |||||||
\(882\) | 1.99880 | + | 3.46203i | 0.0673032 | + | 0.116573i | ||||
\(883\) | −4.16315 | −0.140101 | −0.0700505 | − | 0.997543i | \(-0.522316\pi\) | ||||
−0.0700505 | + | 0.997543i | \(0.522316\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.8237 | 0.531908 | ||||||||
\(886\) | −9.81647 | − | 17.0026i | −0.329791 | − | 0.571214i | ||||
\(887\) | 13.1501 | + | 22.7766i | 0.441537 | + | 0.764765i | 0.997804 | − | 0.0662389i | \(-0.0211000\pi\) |
−0.556266 | + | 0.831004i | \(0.687767\pi\) | |||||||
\(888\) | −1.78597 | + | 3.09339i | −0.0599333 | + | 0.103807i | ||||
\(889\) | −31.0344 | −1.04086 | ||||||||
\(890\) | 34.5916 | − | 59.9143i | 1.15951 | − | 2.00833i | ||||
\(891\) | 2.46950 | − | 4.27730i | 0.0827314 | − | 0.143295i | ||||
\(892\) | −23.6040 | −0.790320 | ||||||||
\(893\) | 7.22737 | − | 12.5182i | 0.241855 | − | 0.418904i | ||||
\(894\) | −10.5100 | − | 18.2038i | −0.351506 | − | 0.608827i | ||||
\(895\) | −33.3512 | − | 57.7659i | −1.11481 | − | 1.93090i | ||||
\(896\) | 7.25906 | 0.242508 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 58.1764 | 1.94137 | ||||||||
\(899\) | 17.3889 | + | 30.1184i | 0.579952 | + | 1.00451i | ||||
\(900\) | −6.88955 | − | 11.9331i | −0.229652 | − | 0.397768i | ||||
\(901\) | −0.247512 | + | 0.428703i | −0.00824582 | + | 0.0142822i | ||||
\(902\) | 70.2199 | 2.33807 | ||||||||
\(903\) | 2.56853 | − | 4.44883i | 0.0854754 | − | 0.148048i | ||||
\(904\) | −1.96658 | + | 3.40621i | −0.0654073 | + | 0.113289i | ||||
\(905\) | 33.8468 | 1.12511 | ||||||||
\(906\) | 20.6618 | − | 35.7873i | 0.686443 | − | 1.18895i | ||||
\(907\) | 28.9557 | + | 50.1527i | 0.961458 | + | 1.66529i | 0.718845 | + | 0.695171i | \(0.244671\pi\) |
0.242613 | + | 0.970123i | \(0.421995\pi\) | |||||||
\(908\) | −7.66666 | − | 13.2790i | −0.254427 | − | 0.440681i | ||||
\(909\) | −9.94869 | −0.329977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.286799 | −0.00950208 | −0.00475104 | − | 0.999989i | \(-0.501512\pi\) | ||||
−0.00475104 | + | 0.999989i | \(0.501512\pi\) | |||||||
\(912\) | −6.77628 | − | 11.7369i | −0.224385 | − | 0.388646i | ||||
\(913\) | −5.69955 | − | 9.87192i | −0.188628 | − | 0.326713i | ||||
\(914\) | 5.11788 | − | 8.86442i | 0.169284 | − | 0.293209i | ||||
\(915\) | 12.3532 | 0.408383 | ||||||||
\(916\) | −18.4691 | + | 31.9895i | −0.610237 | + | 1.05696i | ||||
\(917\) | 3.36443 | − | 5.82736i | 0.111103 | − | 0.192436i | ||||
\(918\) | −1.86831 | −0.0616635 | ||||||||
\(919\) | 15.5620 | − | 26.9541i | 0.513342 | − | 0.889134i | −0.486539 | − | 0.873659i | \(-0.661741\pi\) |
0.999880 | − | 0.0154747i | \(-0.00492596\pi\) | |||||||
\(920\) | 1.38076 | + | 2.39155i | 0.0455224 | + | 0.0788472i | ||||
\(921\) | 3.27748 | + | 5.67676i | 0.107997 | + | 0.187056i | ||||
\(922\) | −2.77133 | −0.0912690 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −24.3937 | −0.802495 | ||||||||
\(925\) | 27.5886 | + | 47.7848i | 0.907107 | + | 1.57115i | ||||
\(926\) | −3.44696 | − | 5.97031i | −0.113274 | − | 0.196197i | ||||
\(927\) | 5.49396 | − | 9.51582i | 0.180445 | − | 0.312540i | ||||
\(928\) | 31.9661 | 1.04934 | ||||||||
\(929\) | 3.81336 | − | 6.60493i | 0.125112 | − | 0.216701i | −0.796665 | − | 0.604422i | \(-0.793404\pi\) |
0.921777 | + | 0.387721i | \(0.126738\pi\) | |||||||
\(930\) | −30.3632 | + | 52.5907i | −0.995650 | + | 1.72452i | ||||
\(931\) | −7.41789 | −0.243112 | ||||||||
\(932\) | −9.55280 | + | 16.5459i | −0.312912 | + | 0.541980i | ||||
\(933\) | −6.01961 | − | 10.4263i | −0.197073 | − | 0.341341i | ||||
\(934\) | −7.07982 | − | 12.2626i | −0.231659 | − | 0.401245i | ||||
\(935\) | 15.1183 | 0.494421 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.67324 | −0.185337 | −0.0926683 | − | 0.995697i | \(-0.529540\pi\) | ||||
−0.0926683 | + | 0.995697i | \(0.529540\pi\) | |||||||
\(938\) | 3.50149 | + | 6.06476i | 0.114328 | + | 0.198021i | ||||
\(939\) | −16.9475 | − | 29.3539i | −0.553061 | − | 0.957929i | ||||
\(940\) | −14.0266 | + | 24.2948i | −0.457498 | + | 0.792409i | ||||
\(941\) | −41.5394 | −1.35415 | −0.677073 | − | 0.735916i | \(-0.736752\pi\) | ||||
−0.677073 | + | 0.735916i | \(0.736752\pi\) | |||||||
\(942\) | 10.6936 | − | 18.5219i | 0.348418 | − | 0.603477i | ||||
\(943\) | 7.03319 | − | 12.1818i | 0.229032 | − | 0.396695i | ||||
\(944\) | −16.8030 | −0.546891 | ||||||||
\(945\) | 3.77144 | − | 6.53232i | 0.122685 | − | 0.212496i | ||||
\(946\) | −11.5678 | − | 20.0360i | −0.376100 | − | 0.651425i | ||||
\(947\) | −23.6555 | − | 40.9725i | −0.768700 | − | 1.33143i | −0.938268 | − | 0.345909i | \(-0.887571\pi\) |
0.169568 | − | 0.985518i | \(-0.445763\pi\) | |||||||
\(948\) | 8.22282 | 0.267065 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 48.8327 | 1.58434 | ||||||||
\(951\) | 2.24914 | + | 3.89562i | 0.0729332 | + | 0.126324i | ||||
\(952\) | 0.415739 | + | 0.720081i | 0.0134742 | + | 0.0233380i | ||||
\(953\) | 17.1717 | − | 29.7423i | 0.556247 | − | 0.963449i | −0.441558 | − | 0.897233i | \(-0.645574\pi\) |
0.997805 | − | 0.0662159i | \(-0.0210926\pi\) | |||||||
\(954\) | 1.11231 | 0.0360123 | ||||||||
\(955\) | −11.0567 | + | 19.1508i | −0.357788 | + | 0.619707i | ||||
\(956\) | −25.1889 | + | 43.6284i | −0.814666 | + | 1.41104i | ||||
\(957\) | −19.4547 | −0.628882 | ||||||||
\(958\) | 3.60172 | − | 6.23836i | 0.116366 | − | 0.201552i | ||||
\(959\) | −25.8620 | − | 44.7944i | −0.835129 | − | 1.44649i | ||||
\(960\) | 15.9424 | + | 27.6130i | 0.514537 | + | 0.891205i | ||||
\(961\) | 46.9527 | 1.51460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.87263 | −0.318141 | ||||||||
\(964\) | 24.1569 | + | 41.8409i | 0.778040 | + | 1.34761i | ||||
\(965\) | −18.2401 | − | 31.5928i | −0.587170 | − | 1.01701i | ||||
\(966\) | −4.66637 | + | 8.08238i | −0.150138 | + | 0.260046i | ||||
\(967\) | −48.5096 | −1.55996 | −0.779982 | − | 0.625802i | \(-0.784772\pi\) | ||||
−0.779982 | + | 0.625802i | \(0.784772\pi\) | |||||||
\(968\) | −2.71768 | + | 4.70715i | −0.0873494 | + | 0.151294i | ||||
\(969\) | 1.73341 | − | 3.00235i | 0.0556850 | − | 0.0964493i | ||||
\(970\) | −110.937 | −3.56198 | ||||||||
\(971\) | −20.7325 | + | 35.9098i | −0.665338 | + | 1.15240i | 0.313856 | + | 0.949471i | \(0.398379\pi\) |
−0.979194 | + | 0.202928i | \(0.934954\pi\) | |||||||
\(972\) | 1.09903 | + | 1.90358i | 0.0352514 | + | 0.0610573i | ||||
\(973\) | 1.10388 | + | 1.91197i | 0.0353886 | + | 0.0612949i | ||||
\(974\) | 26.3242 | 0.843483 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.1177 | −0.419887 | ||||||||
\(977\) | −1.04838 | − | 1.81586i | −0.0335408 | − | 0.0580944i | 0.848768 | − | 0.528766i | \(-0.177345\pi\) |
−0.882309 | + | 0.470671i | \(0.844012\pi\) | |||||||
\(978\) | 11.3167 | + | 19.6011i | 0.361868 | + | 0.626774i | ||||
\(979\) | 24.8397 | − | 43.0237i | 0.793881 | − | 1.37504i | ||||
\(980\) | 14.3964 | 0.459876 | ||||||||
\(981\) | 10.1223 | − | 17.5323i | 0.323180 | − | 0.559764i | ||||
\(982\) | −29.3721 | + | 50.8740i | −0.937301 | + | 1.62345i | ||||
\(983\) | −25.2336 | −0.804826 | −0.402413 | − | 0.915458i | \(-0.631828\pi\) | ||||
−0.402413 | + | 0.915458i | \(0.631828\pi\) | |||||||
\(984\) | −1.40797 | + | 2.43867i | −0.0448844 | + | 0.0777421i | ||||
\(985\) | −15.5115 | − | 26.8668i | −0.494239 | − | 0.856047i | ||||
\(986\) | 3.67964 | + | 6.37333i | 0.117184 | + | 0.202968i | ||||
\(987\) | −8.54288 | −0.271923 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.63448 | −0.147368 | ||||||||
\(990\) | −16.9852 | − | 29.4193i | −0.539826 | − | 0.935006i | ||||
\(991\) | −6.02446 | − | 10.4347i | −0.191373 | − | 0.331468i | 0.754332 | − | 0.656493i | \(-0.227961\pi\) |
−0.945706 | + | 0.325025i | \(0.894627\pi\) | |||||||
\(992\) | 35.8253 | − | 62.0512i | 1.13745 | − | 1.97013i | ||||
\(993\) | −11.2131 | −0.355838 | ||||||||
\(994\) | −5.47554 | + | 9.48392i | −0.173674 | + | 0.300812i | ||||
\(995\) | −2.62618 | + | 4.54867i | −0.0832554 | + | 0.144203i | ||||
\(996\) | 5.07308 | 0.160747 | ||||||||
\(997\) | 0.717013 | − | 1.24190i | 0.0227080 | − | 0.0393314i | −0.854448 | − | 0.519537i | \(-0.826105\pi\) |
0.877156 | + | 0.480205i | \(0.159438\pi\) | |||||||
\(998\) | −34.3763 | − | 59.5415i | −1.08816 | − | 1.88475i | ||||
\(999\) | −4.40097 | − | 7.62270i | −0.139240 | − | 0.241172i |
(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.e.l.484.1 | 6 | ||
13.2 | odd | 12 | 507.2.b.f.337.3 | 6 | |||
13.3 | even | 3 | 507.2.a.i.1.3 | ✓ | 3 | ||
13.4 | even | 6 | 507.2.e.i.22.3 | 6 | |||
13.5 | odd | 4 | 507.2.j.i.361.3 | 12 | |||
13.6 | odd | 12 | 507.2.j.i.316.4 | 12 | |||
13.7 | odd | 12 | 507.2.j.i.316.3 | 12 | |||
13.8 | odd | 4 | 507.2.j.i.361.4 | 12 | |||
13.9 | even | 3 | inner | 507.2.e.l.22.1 | 6 | ||
13.10 | even | 6 | 507.2.a.l.1.1 | yes | 3 | ||
13.11 | odd | 12 | 507.2.b.f.337.4 | 6 | |||
13.12 | even | 2 | 507.2.e.i.484.3 | 6 | |||
39.2 | even | 12 | 1521.2.b.k.1351.4 | 6 | |||
39.11 | even | 12 | 1521.2.b.k.1351.3 | 6 | |||
39.23 | odd | 6 | 1521.2.a.n.1.3 | 3 | |||
39.29 | odd | 6 | 1521.2.a.s.1.1 | 3 | |||
52.3 | odd | 6 | 8112.2.a.cg.1.2 | 3 | |||
52.23 | odd | 6 | 8112.2.a.cp.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.3 | ✓ | 3 | 13.3 | even | 3 | ||
507.2.a.l.1.1 | yes | 3 | 13.10 | even | 6 | ||
507.2.b.f.337.3 | 6 | 13.2 | odd | 12 | |||
507.2.b.f.337.4 | 6 | 13.11 | odd | 12 | |||
507.2.e.i.22.3 | 6 | 13.4 | even | 6 | |||
507.2.e.i.484.3 | 6 | 13.12 | even | 2 | |||
507.2.e.l.22.1 | 6 | 13.9 | even | 3 | inner | ||
507.2.e.l.484.1 | 6 | 1.1 | even | 1 | trivial | ||
507.2.j.i.316.3 | 12 | 13.7 | odd | 12 | |||
507.2.j.i.316.4 | 12 | 13.6 | odd | 12 | |||
507.2.j.i.361.3 | 12 | 13.5 | odd | 4 | |||
507.2.j.i.361.4 | 12 | 13.8 | odd | 4 | |||
1521.2.a.n.1.3 | 3 | 39.23 | odd | 6 | |||
1521.2.a.s.1.1 | 3 | 39.29 | odd | 6 | |||
1521.2.b.k.1351.3 | 6 | 39.11 | even | 12 | |||
1521.2.b.k.1351.4 | 6 | 39.2 | even | 12 | |||
8112.2.a.cg.1.2 | 3 | 52.3 | odd | 6 | |||
8112.2.a.cp.1.2 | 3 | 52.23 | odd | 6 |