Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(188,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.188");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 188.8 | ||
Character | \(\chi\) | \(=\) | 231.188 |
Dual form | 231.2.e.a.188.22 |
$q$-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 \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.68989i | − | 1.19493i | −0.801894 | − | 0.597467i | \(-0.796174\pi\) | ||
0.801894 | − | 0.597467i | \(-0.203826\pi\) | |||||||
\(3\) | 1.02930 | − | 1.39303i | 0.594265 | − | 0.804269i | ||||
\(4\) | −0.855732 | −0.427866 | ||||||||
\(5\) | 1.45819 | 0.652123 | 0.326062 | − | 0.945349i | \(-0.394278\pi\) | ||||
0.326062 | + | 0.945349i | \(0.394278\pi\) | |||||||
\(6\) | −2.35408 | − | 1.73940i | −0.961048 | − | 0.710108i | ||||
\(7\) | 0.366782 | + | 2.62020i | 0.138630 | + | 0.990344i | ||||
\(8\) | − | 1.93369i | − | 0.683662i | ||||||
\(9\) | −0.881093 | − | 2.86770i | −0.293698 | − | 0.955898i | ||||
\(10\) | − | 2.46419i | − | 0.779244i | ||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | −0.880803 | + | 1.19207i | −0.254266 | + | 0.344120i | ||||
\(13\) | 3.51679i | 0.975381i | 0.873017 | + | 0.487691i | \(0.162161\pi\) | ||||
−0.873017 | + | 0.487691i | \(0.837839\pi\) | |||||||
\(14\) | 4.42786 | − | 0.619821i | 1.18340 | − | 0.165654i | ||||
\(15\) | 1.50091 | − | 2.03131i | 0.387534 | − | 0.524483i | ||||
\(16\) | −4.97919 | −1.24480 | ||||||||
\(17\) | −2.75133 | −0.667295 | −0.333647 | − | 0.942698i | \(-0.608280\pi\) | ||||
−0.333647 | + | 0.942698i | \(0.608280\pi\) | |||||||
\(18\) | −4.84609 | + | 1.48895i | −1.14224 | + | 0.350949i | ||||
\(19\) | 4.07921i | 0.935834i | 0.883772 | + | 0.467917i | \(0.154995\pi\) | ||||
−0.883772 | + | 0.467917i | \(0.845005\pi\) | |||||||
\(20\) | −1.24782 | −0.279022 | ||||||||
\(21\) | 4.02756 | + | 2.18603i | 0.878886 | + | 0.477031i | ||||
\(22\) | −1.68989 | −0.360286 | ||||||||
\(23\) | 4.35116i | 0.907280i | 0.891185 | + | 0.453640i | \(0.149875\pi\) | ||||
−0.891185 | + | 0.453640i | \(0.850125\pi\) | |||||||
\(24\) | −2.69369 | − | 1.99034i | −0.549848 | − | 0.406277i | ||||
\(25\) | −2.87368 | −0.574735 | ||||||||
\(26\) | 5.94299 | 1.16552 | ||||||||
\(27\) | −4.90171 | − | 1.72432i | −0.943334 | − | 0.331845i | ||||
\(28\) | −0.313867 | − | 2.24219i | −0.0593153 | − | 0.423735i | ||||
\(29\) | 1.86171i | 0.345712i | 0.984947 | + | 0.172856i | \(0.0552995\pi\) | ||||
−0.984947 | + | 0.172856i | \(0.944701\pi\) | |||||||
\(30\) | −3.43270 | − | 2.53638i | −0.626722 | − | 0.463078i | ||||
\(31\) | − | 5.81906i | − | 1.04513i | −0.852598 | − | 0.522567i | \(-0.824974\pi\) | ||
0.852598 | − | 0.522567i | \(-0.175026\pi\) | |||||||
\(32\) | 4.54691i | 0.803788i | ||||||||
\(33\) | −1.39303 | − | 1.02930i | −0.242496 | − | 0.179178i | ||||
\(34\) | 4.64944i | 0.797373i | ||||||||
\(35\) | 0.534838 | + | 3.82076i | 0.0904041 | + | 0.645827i | ||||
\(36\) | 0.753980 | + | 2.45398i | 0.125663 | + | 0.408997i | ||||
\(37\) | 7.59266 | 1.24823 | 0.624113 | − | 0.781334i | \(-0.285461\pi\) | ||||
0.624113 | + | 0.781334i | \(0.285461\pi\) | |||||||
\(38\) | 6.89341 | 1.11826 | ||||||||
\(39\) | 4.89901 | + | 3.61982i | 0.784469 | + | 0.579635i | ||||
\(40\) | − | 2.81969i | − | 0.445832i | ||||||
\(41\) | −0.863985 | −0.134932 | −0.0674659 | − | 0.997722i | \(-0.521491\pi\) | ||||
−0.0674659 | + | 0.997722i | \(0.521491\pi\) | |||||||
\(42\) | 3.69415 | − | 6.80614i | 0.570020 | − | 1.05021i | ||||
\(43\) | 2.11779 | 0.322960 | 0.161480 | − | 0.986876i | \(-0.448373\pi\) | ||||
0.161480 | + | 0.986876i | \(0.448373\pi\) | |||||||
\(44\) | 0.855732i | 0.129007i | ||||||||
\(45\) | −1.28480 | − | 4.18165i | −0.191527 | − | 0.623364i | ||||
\(46\) | 7.35299 | 1.08414 | ||||||||
\(47\) | −0.483798 | −0.0705692 | −0.0352846 | − | 0.999377i | \(-0.511234\pi\) | ||||
−0.0352846 | + | 0.999377i | \(0.511234\pi\) | |||||||
\(48\) | −5.12507 | + | 6.93618i | −0.739739 | + | 1.00115i | ||||
\(49\) | −6.73094 | + | 1.92209i | −0.961563 | + | 0.274584i | ||||
\(50\) | 4.85620i | 0.686770i | ||||||||
\(51\) | −2.83193 | + | 3.83270i | −0.396550 | + | 0.536685i | ||||
\(52\) | − | 3.00943i | − | 0.417333i | ||||||
\(53\) | − | 13.8100i | − | 1.89695i | −0.316857 | − | 0.948473i | \(-0.602628\pi\) | ||
0.316857 | − | 0.948473i | \(-0.397372\pi\) | |||||||
\(54\) | −2.91391 | + | 8.28335i | −0.396533 | + | 1.12722i | ||||
\(55\) | − | 1.45819i | − | 0.196623i | ||||||
\(56\) | 5.06666 | − | 0.709241i | 0.677061 | − | 0.0947763i | ||||
\(57\) | 5.68248 | + | 4.19872i | 0.752662 | + | 0.556134i | ||||
\(58\) | 3.14609 | 0.413102 | ||||||||
\(59\) | 5.87555 | 0.764932 | 0.382466 | − | 0.923970i | \(-0.375075\pi\) | ||||
0.382466 | + | 0.923970i | \(0.375075\pi\) | |||||||
\(60\) | −1.28438 | + | 1.73826i | −0.165813 | + | 0.224408i | ||||
\(61\) | 5.37692i | 0.688444i | 0.938888 | + | 0.344222i | \(0.111857\pi\) | ||||
−0.938888 | + | 0.344222i | \(0.888143\pi\) | |||||||
\(62\) | −9.83358 | −1.24887 | ||||||||
\(63\) | 7.19078 | − | 3.36046i | 0.905953 | − | 0.423378i | ||||
\(64\) | −2.27459 | −0.284324 | ||||||||
\(65\) | 5.12815i | 0.636069i | ||||||||
\(66\) | −1.73940 | + | 2.35408i | −0.214105 | + | 0.289767i | ||||
\(67\) | 12.5438 | 1.53246 | 0.766232 | − | 0.642564i | \(-0.222129\pi\) | ||||
0.766232 | + | 0.642564i | \(0.222129\pi\) | |||||||
\(68\) | 2.35440 | 0.285513 | ||||||||
\(69\) | 6.06132 | + | 4.47864i | 0.729697 | + | 0.539165i | ||||
\(70\) | 6.45667 | − | 0.903818i | 0.771720 | − | 0.108027i | ||||
\(71\) | 10.0663i | 1.19465i | 0.802000 | + | 0.597324i | \(0.203769\pi\) | ||||
−0.802000 | + | 0.597324i | \(0.796231\pi\) | |||||||
\(72\) | −5.54523 | + | 1.70376i | −0.653511 | + | 0.200790i | ||||
\(73\) | − | 12.0605i | − | 1.41157i | −0.708425 | − | 0.705786i | \(-0.750594\pi\) | ||
0.708425 | − | 0.705786i | \(-0.249406\pi\) | |||||||
\(74\) | − | 12.8308i | − | 1.49155i | ||||||
\(75\) | −2.95787 | + | 4.00313i | −0.341545 | + | 0.462242i | ||||
\(76\) | − | 3.49071i | − | 0.400412i | ||||||
\(77\) | 2.62020 | − | 0.366782i | 0.298600 | − | 0.0417986i | ||||
\(78\) | 6.11710 | − | 8.27879i | 0.692626 | − | 0.937388i | ||||
\(79\) | 8.75956 | 0.985528 | 0.492764 | − | 0.870163i | \(-0.335987\pi\) | ||||
0.492764 | + | 0.870163i | \(0.335987\pi\) | |||||||
\(80\) | −7.26061 | −0.811761 | ||||||||
\(81\) | −7.44735 | + | 5.05341i | −0.827483 | + | 0.561490i | ||||
\(82\) | 1.46004i | 0.161234i | ||||||||
\(83\) | −7.13853 | −0.783555 | −0.391777 | − | 0.920060i | \(-0.628140\pi\) | ||||
−0.391777 | + | 0.920060i | \(0.628140\pi\) | |||||||
\(84\) | −3.44652 | − | 1.87066i | −0.376046 | − | 0.204105i | ||||
\(85\) | −4.01196 | −0.435159 | ||||||||
\(86\) | − | 3.57884i | − | 0.385916i | ||||||
\(87\) | 2.59343 | + | 1.91626i | 0.278045 | + | 0.205444i | ||||
\(88\) | −1.93369 | −0.206132 | ||||||||
\(89\) | −15.2657 | −1.61817 | −0.809083 | − | 0.587695i | \(-0.800036\pi\) | ||||
−0.809083 | + | 0.587695i | \(0.800036\pi\) | |||||||
\(90\) | −7.06653 | + | 2.17118i | −0.744878 | + | 0.228862i | ||||
\(91\) | −9.21470 | + | 1.28989i | −0.965963 | + | 0.135217i | ||||
\(92\) | − | 3.72343i | − | 0.388194i | ||||||
\(93\) | −8.10615 | − | 5.98954i | −0.840569 | − | 0.621087i | ||||
\(94\) | 0.817566i | 0.0843255i | ||||||||
\(95\) | 5.94826i | 0.610279i | ||||||||
\(96\) | 6.33400 | + | 4.68012i | 0.646461 | + | 0.477663i | ||||
\(97\) | 11.7571i | 1.19375i | 0.802335 | + | 0.596874i | \(0.203591\pi\) | ||||
−0.802335 | + | 0.596874i | \(0.796409\pi\) | |||||||
\(98\) | 3.24812 | + | 11.3746i | 0.328109 | + | 1.14900i | ||||
\(99\) | −2.86770 | + | 0.881093i | −0.288214 | + | 0.0885532i | ||||
\(100\) | 2.45910 | 0.245910 | ||||||||
\(101\) | 6.38633 | 0.635464 | 0.317732 | − | 0.948181i | \(-0.397079\pi\) | ||||
0.317732 | + | 0.948181i | \(0.397079\pi\) | |||||||
\(102\) | 6.47684 | + | 4.78566i | 0.641303 | + | 0.473851i | ||||
\(103\) | − | 16.9062i | − | 1.66581i | −0.553413 | − | 0.832907i | \(-0.686675\pi\) | ||
0.553413 | − | 0.832907i | \(-0.313325\pi\) | |||||||
\(104\) | 6.80037 | 0.666831 | ||||||||
\(105\) | 5.87296 | + | 3.18765i | 0.573142 | + | 0.311083i | ||||
\(106\) | −23.3374 | −2.26673 | ||||||||
\(107\) | 5.41669i | 0.523651i | 0.965115 | + | 0.261825i | \(0.0843245\pi\) | ||||
−0.965115 | + | 0.261825i | \(0.915676\pi\) | |||||||
\(108\) | 4.19455 | + | 1.47556i | 0.403621 | + | 0.141985i | ||||
\(109\) | −20.0350 | −1.91901 | −0.959504 | − | 0.281694i | \(-0.909104\pi\) | ||||
−0.959504 | + | 0.281694i | \(0.909104\pi\) | |||||||
\(110\) | −2.46419 | −0.234951 | ||||||||
\(111\) | 7.81510 | − | 10.5768i | 0.741777 | − | 1.00391i | ||||
\(112\) | −1.82627 | − | 13.0465i | −0.172567 | − | 1.23278i | ||||
\(113\) | − | 11.5983i | − | 1.09108i | −0.838085 | − | 0.545539i | \(-0.816325\pi\) | ||
0.838085 | − | 0.545539i | \(-0.183675\pi\) | |||||||
\(114\) | 7.09537 | − | 9.60277i | 0.664543 | − | 0.899381i | ||||
\(115\) | 6.34483i | 0.591658i | ||||||||
\(116\) | − | 1.59313i | − | 0.147918i | ||||||
\(117\) | 10.0851 | − | 3.09862i | 0.932365 | − | 0.286467i | ||||
\(118\) | − | 9.92905i | − | 0.914043i | ||||||
\(119\) | −1.00914 | − | 7.20904i | −0.0925074 | − | 0.660852i | ||||
\(120\) | −3.92792 | − | 2.90230i | −0.358569 | − | 0.264942i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 9.08641 | 0.822645 | ||||||||
\(123\) | −0.889297 | + | 1.20356i | −0.0801852 | + | 0.108521i | ||||
\(124\) | 4.97956i | 0.447177i | ||||||||
\(125\) | −11.4813 | −1.02692 | ||||||||
\(126\) | −5.67881 | − | 12.1516i | −0.505909 | − | 1.08255i | ||||
\(127\) | 3.27840 | 0.290911 | 0.145456 | − | 0.989365i | \(-0.453535\pi\) | ||||
0.145456 | + | 0.989365i | \(0.453535\pi\) | |||||||
\(128\) | 12.9376i | 1.14354i | ||||||||
\(129\) | 2.17984 | − | 2.95016i | 0.191924 | − | 0.259747i | ||||
\(130\) | 8.66602 | 0.760060 | ||||||||
\(131\) | −12.5297 | −1.09473 | −0.547364 | − | 0.836894i | \(-0.684369\pi\) | ||||
−0.547364 | + | 0.836894i | \(0.684369\pi\) | |||||||
\(132\) | 1.19207 | + | 0.880803i | 0.103756 | + | 0.0766641i | ||||
\(133\) | −10.6884 | + | 1.49618i | −0.926798 | + | 0.129735i | ||||
\(134\) | − | 21.1976i | − | 1.83119i | ||||||
\(135\) | −7.14763 | − | 2.51439i | −0.615170 | − | 0.216404i | ||||
\(136\) | 5.32021i | 0.456204i | ||||||||
\(137\) | 0.178787i | 0.0152748i | 0.999971 | + | 0.00763740i | \(0.00243108\pi\) | ||||
−0.999971 | + | 0.00763740i | \(0.997569\pi\) | |||||||
\(138\) | 7.56841 | − | 10.2430i | 0.644266 | − | 0.871939i | ||||
\(139\) | 9.62340i | 0.816246i | 0.912927 | + | 0.408123i | \(0.133817\pi\) | ||||
−0.912927 | + | 0.408123i | \(0.866183\pi\) | |||||||
\(140\) | −0.457678 | − | 3.26955i | −0.0386809 | − | 0.276327i | ||||
\(141\) | −0.497972 | + | 0.673948i | −0.0419368 | + | 0.0567566i | ||||
\(142\) | 17.0109 | 1.42752 | ||||||||
\(143\) | 3.51679 | 0.294089 | ||||||||
\(144\) | 4.38713 | + | 14.2788i | 0.365594 | + | 1.18990i | ||||
\(145\) | 2.71474i | 0.225447i | ||||||||
\(146\) | −20.3809 | −1.68673 | ||||||||
\(147\) | −4.25061 | + | 11.3548i | −0.350585 | + | 0.936531i | ||||
\(148\) | −6.49728 | −0.534073 | ||||||||
\(149\) | − | 12.3604i | − | 1.01260i | −0.862356 | − | 0.506302i | \(-0.831012\pi\) | ||
0.862356 | − | 0.506302i | \(-0.168988\pi\) | |||||||
\(150\) | 6.76486 | + | 4.99848i | 0.552348 | + | 0.408124i | ||||
\(151\) | −4.94666 | −0.402553 | −0.201277 | − | 0.979534i | \(-0.564509\pi\) | ||||
−0.201277 | + | 0.979534i | \(0.564509\pi\) | |||||||
\(152\) | 7.88791 | 0.639794 | ||||||||
\(153\) | 2.42417 | + | 7.88997i | 0.195983 | + | 0.637866i | ||||
\(154\) | −0.619821 | − | 4.42786i | −0.0499466 | − | 0.356807i | ||||
\(155\) | − | 8.48531i | − | 0.681556i | ||||||
\(156\) | −4.19224 | − | 3.09760i | −0.335648 | − | 0.248006i | ||||
\(157\) | 1.59035i | 0.126924i | 0.997984 | + | 0.0634620i | \(0.0202142\pi\) | ||||
−0.997984 | + | 0.0634620i | \(0.979786\pi\) | |||||||
\(158\) | − | 14.8027i | − | 1.17764i | ||||||
\(159\) | −19.2378 | − | 14.2146i | −1.52566 | − | 1.12729i | ||||
\(160\) | 6.63027i | 0.524169i | ||||||||
\(161\) | −11.4009 | + | 1.59593i | −0.898519 | + | 0.125777i | ||||
\(162\) | 8.53971 | + | 12.5852i | 0.670943 | + | 0.988788i | ||||
\(163\) | 17.0776 | 1.33762 | 0.668812 | − | 0.743432i | \(-0.266803\pi\) | ||||
0.668812 | + | 0.743432i | \(0.266803\pi\) | |||||||
\(164\) | 0.739340 | 0.0577327 | ||||||||
\(165\) | −2.03131 | − | 1.50091i | −0.158137 | − | 0.116846i | ||||
\(166\) | 12.0633i | 0.936296i | ||||||||
\(167\) | 19.4712 | 1.50673 | 0.753364 | − | 0.657604i | \(-0.228430\pi\) | ||||
0.753364 | + | 0.657604i | \(0.228430\pi\) | |||||||
\(168\) | 4.22710 | − | 7.78805i | 0.326128 | − | 0.600861i | ||||
\(169\) | 0.632207 | 0.0486313 | ||||||||
\(170\) | 6.77978i | 0.519986i | ||||||||
\(171\) | 11.6979 | − | 3.59416i | 0.894562 | − | 0.274852i | ||||
\(172\) | −1.81226 | −0.138184 | ||||||||
\(173\) | −23.0744 | −1.75431 | −0.877156 | − | 0.480206i | \(-0.840562\pi\) | ||||
−0.877156 | + | 0.480206i | \(0.840562\pi\) | |||||||
\(174\) | 3.23827 | − | 4.38262i | 0.245492 | − | 0.332246i | ||||
\(175\) | −1.05401 | − | 7.52962i | −0.0796758 | − | 0.569186i | ||||
\(176\) | 4.97919i | 0.375320i | ||||||||
\(177\) | 6.04769 | − | 8.18485i | 0.454573 | − | 0.615211i | ||||
\(178\) | 25.7974i | 1.93360i | ||||||||
\(179\) | 3.07484i | 0.229824i | 0.993376 | + | 0.114912i | \(0.0366586\pi\) | ||||
−0.993376 | + | 0.114912i | \(0.963341\pi\) | |||||||
\(180\) | 1.09945 | + | 3.57837i | 0.0819479 | + | 0.266716i | ||||
\(181\) | 11.3295i | 0.842113i | 0.907034 | + | 0.421057i | \(0.138341\pi\) | ||||
−0.907034 | + | 0.421057i | \(0.861659\pi\) | |||||||
\(182\) | 2.17978 | + | 15.5718i | 0.161576 | + | 1.15426i | ||||
\(183\) | 7.49024 | + | 5.53445i | 0.553694 | + | 0.409118i | ||||
\(184\) | 8.41379 | 0.620272 | ||||||||
\(185\) | 11.0716 | 0.813997 | ||||||||
\(186\) | −10.1217 | + | 13.6985i | −0.742157 | + | 1.00442i | ||||
\(187\) | 2.75133i | 0.201197i | ||||||||
\(188\) | 0.414002 | 0.0301942 | ||||||||
\(189\) | 2.72021 | − | 13.4759i | 0.197866 | − | 0.980229i | ||||
\(190\) | 10.0519 | 0.729243 | ||||||||
\(191\) | 11.0831i | 0.801944i | 0.916090 | + | 0.400972i | \(0.131328\pi\) | ||||
−0.916090 | + | 0.400972i | \(0.868672\pi\) | |||||||
\(192\) | −2.34123 | + | 3.16859i | −0.168964 | + | 0.228673i | ||||
\(193\) | 1.41790 | 0.102063 | 0.0510313 | − | 0.998697i | \(-0.483749\pi\) | ||||
0.0510313 | + | 0.998697i | \(0.483749\pi\) | |||||||
\(194\) | 19.8681 | 1.42645 | ||||||||
\(195\) | 7.14369 | + | 5.27839i | 0.511571 | + | 0.377994i | ||||
\(196\) | 5.75989 | − | 1.64479i | 0.411420 | − | 0.117485i | ||||
\(197\) | − | 12.3840i | − | 0.882322i | −0.897428 | − | 0.441161i | \(-0.854567\pi\) | ||
0.897428 | − | 0.441161i | \(-0.145433\pi\) | |||||||
\(198\) | 1.48895 | + | 4.84609i | 0.105815 | + | 0.344397i | ||||
\(199\) | 15.3346i | 1.08704i | 0.839396 | + | 0.543521i | \(0.182909\pi\) | ||||
−0.839396 | + | 0.543521i | \(0.817091\pi\) | |||||||
\(200\) | 5.55679i | 0.392925i | ||||||||
\(201\) | 12.9113 | − | 17.4739i | 0.910691 | − | 1.23251i | ||||
\(202\) | − | 10.7922i | − | 0.759337i | ||||||
\(203\) | −4.87807 | + | 0.682842i | −0.342374 | + | 0.0479261i | ||||
\(204\) | 2.42338 | − | 3.27976i | 0.169670 | − | 0.229629i | ||||
\(205\) | −1.25986 | −0.0879921 | ||||||||
\(206\) | −28.5696 | −1.99054 | ||||||||
\(207\) | 12.4778 | − | 3.83378i | 0.867267 | − | 0.266466i | ||||
\(208\) | − | 17.5107i | − | 1.21415i | ||||||
\(209\) | 4.07921 | 0.282165 | ||||||||
\(210\) | 5.38679 | − | 9.92467i | 0.371724 | − | 0.684867i | ||||
\(211\) | −1.20919 | −0.0832442 | −0.0416221 | − | 0.999133i | \(-0.513253\pi\) | ||||
−0.0416221 | + | 0.999133i | \(0.513253\pi\) | |||||||
\(212\) | 11.8176i | 0.811639i | ||||||||
\(213\) | 14.0227 | + | 10.3612i | 0.960818 | + | 0.709938i | ||||
\(214\) | 9.15361 | 0.625728 | ||||||||
\(215\) | 3.08815 | 0.210610 | ||||||||
\(216\) | −3.33429 | + | 9.47837i | −0.226870 | + | 0.644921i | ||||
\(217\) | 15.2471 | − | 2.13432i | 1.03504 | − | 0.144887i | ||||
\(218\) | 33.8570i | 2.29309i | ||||||||
\(219\) | −16.8007 | − | 12.4138i | −1.13528 | − | 0.838848i | ||||
\(220\) | 1.24782i | 0.0841282i | ||||||||
\(221\) | − | 9.67583i | − | 0.650867i | ||||||
\(222\) | −17.8737 | − | 13.2067i | −1.19960 | − | 0.886374i | ||||
\(223\) | − | 1.60414i | − | 0.107421i | −0.998557 | − | 0.0537106i | \(-0.982895\pi\) | ||
0.998557 | − | 0.0537106i | \(-0.0171048\pi\) | |||||||
\(224\) | −11.9138 | + | 1.66772i | −0.796026 | + | 0.111429i | ||||
\(225\) | 2.53197 | + | 8.24083i | 0.168798 | + | 0.549388i | ||||
\(226\) | −19.5999 | −1.30377 | ||||||||
\(227\) | −15.1868 | −1.00798 | −0.503992 | − | 0.863708i | \(-0.668136\pi\) | ||||
−0.503992 | + | 0.863708i | \(0.668136\pi\) | |||||||
\(228\) | −4.86268 | − | 3.59298i | −0.322039 | − | 0.237951i | ||||
\(229\) | − | 21.7042i | − | 1.43426i | −0.696942 | − | 0.717128i | \(-0.745456\pi\) | ||
0.696942 | − | 0.717128i | \(-0.254544\pi\) | |||||||
\(230\) | 10.7221 | 0.706992 | ||||||||
\(231\) | 2.18603 | − | 4.02756i | 0.143830 | − | 0.264994i | ||||
\(232\) | 3.59997 | 0.236350 | ||||||||
\(233\) | − | 0.456992i | − | 0.0299385i | −0.999888 | − | 0.0149693i | \(-0.995235\pi\) | ||
0.999888 | − | 0.0149693i | \(-0.00476504\pi\) | |||||||
\(234\) | −5.23632 | − | 17.0427i | −0.342309 | − | 1.11411i | ||||
\(235\) | −0.705471 | −0.0460198 | ||||||||
\(236\) | −5.02790 | −0.327289 | ||||||||
\(237\) | 9.01620 | − | 12.2024i | 0.585665 | − | 0.792630i | ||||
\(238\) | −12.1825 | + | 1.70533i | −0.789674 | + | 0.110540i | ||||
\(239\) | 22.8862i | 1.48038i | 0.672396 | + | 0.740192i | \(0.265265\pi\) | ||||
−0.672396 | + | 0.740192i | \(0.734735\pi\) | |||||||
\(240\) | −7.47333 | + | 10.1143i | −0.482401 | + | 0.652874i | ||||
\(241\) | − | 19.8304i | − | 1.27739i | −0.769461 | − | 0.638693i | \(-0.779475\pi\) | ||
0.769461 | − | 0.638693i | \(-0.220525\pi\) | |||||||
\(242\) | 1.68989i | 0.108630i | ||||||||
\(243\) | −0.625963 | + | 15.5759i | −0.0401556 | + | 0.999193i | ||||
\(244\) | − | 4.60120i | − | 0.294562i | ||||||
\(245\) | −9.81501 | + | 2.80277i | −0.627058 | + | 0.179062i | ||||
\(246\) | 2.03389 | + | 1.50282i | 0.129676 | + | 0.0958160i | ||||
\(247\) | −14.3457 | −0.912795 | ||||||||
\(248\) | −11.2522 | −0.714518 | ||||||||
\(249\) | −7.34767 | + | 9.94422i | −0.465640 | + | 0.630189i | ||||
\(250\) | 19.4022i | 1.22710i | ||||||||
\(251\) | −0.885000 | −0.0558607 | −0.0279304 | − | 0.999610i | \(-0.508892\pi\) | ||||
−0.0279304 | + | 0.999610i | \(0.508892\pi\) | |||||||
\(252\) | −6.15338 | + | 2.87566i | −0.387627 | + | 0.181149i | ||||
\(253\) | 4.35116 | 0.273555 | ||||||||
\(254\) | − | 5.54014i | − | 0.347619i | ||||||
\(255\) | −4.12951 | + | 5.58881i | −0.258600 | + | 0.349985i | ||||
\(256\) | 17.3140 | 1.08213 | ||||||||
\(257\) | 19.1067 | 1.19184 | 0.595921 | − | 0.803043i | \(-0.296787\pi\) | ||||
0.595921 | + | 0.803043i | \(0.296787\pi\) | |||||||
\(258\) | −4.98545 | − | 3.68369i | −0.310381 | − | 0.229337i | ||||
\(259\) | 2.78485 | + | 19.8943i | 0.173042 | + | 1.23617i | ||||
\(260\) | − | 4.38833i | − | 0.272152i | ||||||
\(261\) | 5.33883 | − | 1.64034i | 0.330465 | − | 0.101535i | ||||
\(262\) | 21.1739i | 1.30813i | ||||||||
\(263\) | − | 21.0776i | − | 1.29970i | −0.760061 | − | 0.649851i | \(-0.774831\pi\) | ||
0.760061 | − | 0.649851i | \(-0.225169\pi\) | |||||||
\(264\) | −1.99034 | + | 2.69369i | −0.122497 | + | 0.165785i | ||||
\(265\) | − | 20.1376i | − | 1.23704i | ||||||
\(266\) | 2.52838 | + | 18.0622i | 0.155025 | + | 1.10746i | ||||
\(267\) | −15.7130 | + | 21.2657i | −0.961620 | + | 1.30144i | ||||
\(268\) | −10.7341 | −0.655690 | ||||||||
\(269\) | 19.5822 | 1.19395 | 0.596974 | − | 0.802261i | \(-0.296370\pi\) | ||||
0.596974 | + | 0.802261i | \(0.296370\pi\) | |||||||
\(270\) | −4.24904 | + | 12.0787i | −0.258588 | + | 0.735087i | ||||
\(271\) | 8.26071i | 0.501803i | 0.968013 | + | 0.250901i | \(0.0807270\pi\) | ||||
−0.968013 | + | 0.250901i | \(0.919273\pi\) | |||||||
\(272\) | 13.6994 | 0.830647 | ||||||||
\(273\) | −7.68781 | + | 14.1641i | −0.465287 | + | 0.857249i | ||||
\(274\) | 0.302130 | 0.0182524 | ||||||||
\(275\) | 2.87368i | 0.173289i | ||||||||
\(276\) | −5.18687 | − | 3.83252i | −0.312213 | − | 0.230690i | ||||
\(277\) | −8.38977 | −0.504092 | −0.252046 | − | 0.967715i | \(-0.581103\pi\) | ||||
−0.252046 | + | 0.967715i | \(0.581103\pi\) | |||||||
\(278\) | 16.2625 | 0.975360 | ||||||||
\(279\) | −16.6873 | + | 5.12713i | −0.999042 | + | 0.306953i | ||||
\(280\) | 7.38816 | − | 1.03421i | 0.441527 | − | 0.0618058i | ||||
\(281\) | − | 24.9821i | − | 1.49031i | −0.666892 | − | 0.745154i | \(-0.732376\pi\) | ||
0.666892 | − | 0.745154i | \(-0.267624\pi\) | |||||||
\(282\) | 1.13890 | + | 0.841519i | 0.0678204 | + | 0.0501117i | ||||
\(283\) | − | 12.2954i | − | 0.730888i | −0.930833 | − | 0.365444i | \(-0.880917\pi\) | ||
0.930833 | − | 0.365444i | \(-0.119083\pi\) | |||||||
\(284\) | − | 8.61404i | − | 0.511149i | ||||||
\(285\) | 8.28614 | + | 6.12253i | 0.490829 | + | 0.362668i | ||||
\(286\) | − | 5.94299i | − | 0.351416i | ||||||
\(287\) | −0.316894 | − | 2.26382i | −0.0187056 | − | 0.133629i | ||||
\(288\) | 13.0391 | − | 4.00625i | 0.768339 | − | 0.236070i | ||||
\(289\) | −9.43020 | −0.554717 | ||||||||
\(290\) | 4.58761 | 0.269394 | ||||||||
\(291\) | 16.3780 | + | 12.1015i | 0.960095 | + | 0.709403i | ||||
\(292\) | 10.3205i | 0.603964i | ||||||||
\(293\) | 9.65664 | 0.564147 | 0.282074 | − | 0.959393i | \(-0.408978\pi\) | ||||
0.282074 | + | 0.959393i | \(0.408978\pi\) | |||||||
\(294\) | 19.1884 | + | 7.18307i | 1.11909 | + | 0.418925i | ||||
\(295\) | 8.56769 | 0.498830 | ||||||||
\(296\) | − | 14.6818i | − | 0.853364i | ||||||
\(297\) | −1.72432 | + | 4.90171i | −0.100055 | + | 0.284426i | ||||
\(298\) | −20.8878 | −1.21000 | ||||||||
\(299\) | −15.3021 | −0.884944 | ||||||||
\(300\) | 2.53114 | − | 3.42561i | 0.146136 | − | 0.197778i | ||||
\(301\) | 0.776767 | + | 5.54905i | 0.0447721 | + | 0.319842i | ||||
\(302\) | 8.35932i | 0.481025i | ||||||||
\(303\) | 6.57344 | − | 8.89639i | 0.377634 | − | 0.511084i | ||||
\(304\) | − | 20.3111i | − | 1.16492i | ||||||
\(305\) | 7.84058i | 0.448950i | ||||||||
\(306\) | 13.3332 | − | 4.09659i | 0.762208 | − | 0.234187i | ||||
\(307\) | − | 5.92838i | − | 0.338350i | −0.985586 | − | 0.169175i | \(-0.945890\pi\) | ||
0.985586 | − | 0.169175i | \(-0.0541104\pi\) | |||||||
\(308\) | −2.24219 | + | 0.313867i | −0.127761 | + | 0.0178842i | ||||
\(309\) | −23.5509 | − | 17.4015i | −1.33976 | − | 0.989936i | ||||
\(310\) | −14.3392 | −0.814414 | ||||||||
\(311\) | 3.45749 | 0.196056 | 0.0980281 | − | 0.995184i | \(-0.468746\pi\) | ||||
0.0980281 | + | 0.995184i | \(0.468746\pi\) | |||||||
\(312\) | 6.99960 | − | 9.47315i | 0.396275 | − | 0.536312i | ||||
\(313\) | − | 8.41263i | − | 0.475510i | −0.971325 | − | 0.237755i | \(-0.923588\pi\) | ||
0.971325 | − | 0.237755i | \(-0.0764115\pi\) | |||||||
\(314\) | 2.68753 | 0.151666 | ||||||||
\(315\) | 10.4855 | − | 4.90020i | 0.590793 | − | 0.276095i | ||||
\(316\) | −7.49584 | −0.421674 | ||||||||
\(317\) | 14.8191i | 0.832325i | 0.909290 | + | 0.416162i | \(0.136625\pi\) | ||||
−0.909290 | + | 0.416162i | \(0.863375\pi\) | |||||||
\(318\) | −24.0211 | + | 32.5098i | −1.34704 | + | 1.82306i | ||||
\(319\) | 1.86171 | 0.104236 | ||||||||
\(320\) | −3.31679 | −0.185414 | ||||||||
\(321\) | 7.54563 | + | 5.57538i | 0.421156 | + | 0.311188i | ||||
\(322\) | 2.69694 | + | 19.2663i | 0.150295 | + | 1.07367i | ||||
\(323\) | − | 11.2232i | − | 0.624477i | ||||||
\(324\) | 6.37294 | − | 4.32437i | 0.354052 | − | 0.240243i | ||||
\(325\) | − | 10.1061i | − | 0.560586i | ||||||
\(326\) | − | 28.8593i | − | 1.59837i | ||||||
\(327\) | −20.6220 | + | 27.9095i | −1.14040 | + | 1.54340i | ||||
\(328\) | 1.67068i | 0.0922477i | ||||||||
\(329\) | −0.177448 | − | 1.26765i | −0.00978304 | − | 0.0698878i | ||||
\(330\) | −2.53638 | + | 3.43270i | −0.139623 | + | 0.188964i | ||||
\(331\) | −3.46613 | −0.190516 | −0.0952580 | − | 0.995453i | \(-0.530368\pi\) | ||||
−0.0952580 | + | 0.995453i | \(0.530368\pi\) | |||||||
\(332\) | 6.10867 | 0.335257 | ||||||||
\(333\) | −6.68983 | − | 21.7734i | −0.366601 | − | 1.19318i | ||||
\(334\) | − | 32.9042i | − | 1.80044i | ||||||
\(335\) | 18.2912 | 0.999356 | ||||||||
\(336\) | −20.0540 | − | 10.8847i | −1.09403 | − | 0.593807i | ||||
\(337\) | 26.1356 | 1.42370 | 0.711849 | − | 0.702332i | \(-0.247858\pi\) | ||||
0.711849 | + | 0.702332i | \(0.247858\pi\) | |||||||
\(338\) | − | 1.06836i | − | 0.0581112i | ||||||
\(339\) | −16.1569 | − | 11.9381i | −0.877520 | − | 0.648390i | ||||
\(340\) | 3.43317 | 0.186190 | ||||||||
\(341\) | −5.81906 | −0.315120 | ||||||||
\(342\) | −6.07374 | − | 19.7682i | −0.328430 | − | 1.06894i | ||||
\(343\) | −7.50504 | − | 16.9315i | −0.405234 | − | 0.914213i | ||||
\(344\) | − | 4.09515i | − | 0.220796i | ||||||
\(345\) | 8.83857 | + | 6.53072i | 0.475852 | + | 0.351602i | ||||
\(346\) | 38.9932i | 2.09629i | ||||||||
\(347\) | 6.04785i | 0.324665i | 0.986736 | + | 0.162333i | \(0.0519018\pi\) | ||||
−0.986736 | + | 0.162333i | \(0.948098\pi\) | |||||||
\(348\) | −2.21928 | − | 1.63980i | −0.118966 | − | 0.0879027i | ||||
\(349\) | − | 33.6712i | − | 1.80238i | −0.433424 | − | 0.901190i | \(-0.642695\pi\) | ||
0.433424 | − | 0.901190i | \(-0.357305\pi\) | |||||||
\(350\) | −12.7242 | + | 1.78116i | −0.680139 | + | 0.0952072i | ||||
\(351\) | 6.06406 | − | 17.2383i | 0.323676 | − | 0.920110i | ||||
\(352\) | 4.54691 | 0.242351 | ||||||||
\(353\) | −26.7944 | −1.42612 | −0.713061 | − | 0.701102i | \(-0.752692\pi\) | ||||
−0.713061 | + | 0.701102i | \(0.752692\pi\) | |||||||
\(354\) | −13.8315 | − | 10.2199i | −0.735137 | − | 0.543184i | ||||
\(355\) | 14.6786i | 0.779058i | ||||||||
\(356\) | 13.0634 | 0.692358 | ||||||||
\(357\) | −11.0811 | − | 6.01449i | −0.586476 | − | 0.318320i | ||||
\(358\) | 5.19614 | 0.274625 | ||||||||
\(359\) | − | 11.6784i | − | 0.616364i | −0.951327 | − | 0.308182i | \(-0.900279\pi\) | ||
0.951327 | − | 0.308182i | \(-0.0997206\pi\) | |||||||
\(360\) | −8.08601 | + | 2.48441i | −0.426170 | + | 0.130940i | ||||
\(361\) | 2.36008 | 0.124215 | ||||||||
\(362\) | 19.1456 | 1.00627 | ||||||||
\(363\) | −1.02930 | + | 1.39303i | −0.0540241 | + | 0.0731154i | ||||
\(364\) | 7.88532 | − | 1.10380i | 0.413303 | − | 0.0578550i | ||||
\(365\) | − | 17.5865i | − | 0.920519i | ||||||
\(366\) | 9.35262 | − | 12.6577i | 0.488869 | − | 0.661628i | ||||
\(367\) | − | 11.9966i | − | 0.626217i | −0.949717 | − | 0.313109i | \(-0.898630\pi\) | ||
0.949717 | − | 0.313109i | \(-0.101370\pi\) | |||||||
\(368\) | − | 21.6652i | − | 1.12938i | ||||||
\(369\) | 0.761251 | + | 2.47764i | 0.0396291 | + | 0.128981i | ||||
\(370\) | − | 18.7097i | − | 0.972672i | ||||||
\(371\) | 36.1850 | − | 5.06525i | 1.87863 | − | 0.262974i | ||||
\(372\) | 6.93670 | + | 5.12545i | 0.359651 | + | 0.265742i | ||||
\(373\) | −11.1248 | −0.576019 | −0.288009 | − | 0.957628i | \(-0.592993\pi\) | ||||
−0.288009 | + | 0.957628i | \(0.592993\pi\) | |||||||
\(374\) | 4.64944 | 0.240417 | ||||||||
\(375\) | −11.8177 | + | 15.9939i | −0.610264 | + | 0.825921i | ||||
\(376\) | 0.935515i | 0.0482455i | ||||||||
\(377\) | −6.54725 | −0.337201 | ||||||||
\(378\) | −22.7728 | − | 4.59686i | −1.17131 | − | 0.236437i | ||||
\(379\) | −0.528289 | −0.0271364 | −0.0135682 | − | 0.999908i | \(-0.504319\pi\) | ||||
−0.0135682 | + | 0.999908i | \(0.504319\pi\) | |||||||
\(380\) | − | 5.09012i | − | 0.261118i | ||||||
\(381\) | 3.37445 | − | 4.56693i | 0.172878 | − | 0.233971i | ||||
\(382\) | 18.7292 | 0.958270 | ||||||||
\(383\) | 15.9107 | 0.812998 | 0.406499 | − | 0.913651i | \(-0.366749\pi\) | ||||
0.406499 | + | 0.913651i | \(0.366749\pi\) | |||||||
\(384\) | 18.0226 | + | 13.3167i | 0.919711 | + | 0.679564i | ||||
\(385\) | 3.82076 | − | 0.534838i | 0.194724 | − | 0.0272579i | ||||
\(386\) | − | 2.39610i | − | 0.121958i | ||||||
\(387\) | −1.86597 | − | 6.07319i | −0.0948527 | − | 0.308717i | ||||
\(388\) | − | 10.0609i | − | 0.510765i | ||||||
\(389\) | 21.7159i | 1.10104i | 0.834822 | + | 0.550520i | \(0.185570\pi\) | ||||
−0.834822 | + | 0.550520i | \(0.814430\pi\) | |||||||
\(390\) | 8.91991 | − | 12.0721i | 0.451677 | − | 0.611293i | ||||
\(391\) | − | 11.9715i | − | 0.605423i | ||||||
\(392\) | 3.71671 | + | 13.0155i | 0.187722 | + | 0.657384i | ||||
\(393\) | −12.8968 | + | 17.4544i | −0.650559 | + | 0.880457i | ||||
\(394\) | −20.9276 | −1.05432 | ||||||||
\(395\) | 12.7731 | 0.642686 | ||||||||
\(396\) | 2.45398 | − | 0.753980i | 0.123317 | − | 0.0378889i | ||||
\(397\) | 15.2832i | 0.767043i | 0.923532 | + | 0.383522i | \(0.125289\pi\) | ||||
−0.923532 | + | 0.383522i | \(0.874711\pi\) | |||||||
\(398\) | 25.9138 | 1.29894 | ||||||||
\(399\) | −8.91727 | + | 16.4293i | −0.446422 | + | 0.822492i | ||||
\(400\) | 14.3086 | 0.715428 | ||||||||
\(401\) | 20.2500i | 1.01124i | 0.862758 | + | 0.505618i | \(0.168735\pi\) | ||||
−0.862758 | + | 0.505618i | \(0.831265\pi\) | |||||||
\(402\) | −29.5290 | − | 21.8186i | −1.47277 | − | 1.08821i | ||||
\(403\) | 20.4644 | 1.01940 | ||||||||
\(404\) | −5.46499 | −0.271894 | ||||||||
\(405\) | −10.8597 | + | 7.36884i | −0.539621 | + | 0.366161i | ||||
\(406\) | 1.15393 | + | 8.24341i | 0.0572686 | + | 0.409114i | ||||
\(407\) | − | 7.59266i | − | 0.376354i | ||||||
\(408\) | 7.41124 | + | 5.47608i | 0.366911 | + | 0.271106i | ||||
\(409\) | 0.450101i | 0.0222561i | 0.999938 | + | 0.0111280i | \(0.00354224\pi\) | ||||
−0.999938 | + | 0.0111280i | \(0.996458\pi\) | |||||||
\(410\) | 2.12902i | 0.105145i | ||||||||
\(411\) | 0.249056 | + | 0.184025i | 0.0122850 | + | 0.00907728i | ||||
\(412\) | 14.4672i | 0.712746i | ||||||||
\(413\) | 2.15504 | + | 15.3952i | 0.106043 | + | 0.757546i | ||||
\(414\) | −6.47866 | − | 21.0861i | −0.318409 | − | 1.03633i | ||||
\(415\) | −10.4093 | −0.510974 | ||||||||
\(416\) | −15.9905 | −0.783999 | ||||||||
\(417\) | 13.4057 | + | 9.90534i | 0.656481 | + | 0.485067i | ||||
\(418\) | − | 6.89341i | − | 0.337168i | ||||||
\(419\) | 39.4106 | 1.92533 | 0.962667 | − | 0.270689i | \(-0.0872515\pi\) | ||||
0.962667 | + | 0.270689i | \(0.0872515\pi\) | |||||||
\(420\) | −5.02568 | − | 2.72778i | −0.245228 | − | 0.133102i | ||||
\(421\) | −17.0494 | −0.830937 | −0.415468 | − | 0.909608i | \(-0.636382\pi\) | ||||
−0.415468 | + | 0.909608i | \(0.636382\pi\) | |||||||
\(422\) | 2.04340i | 0.0994713i | ||||||||
\(423\) | 0.426271 | + | 1.38739i | 0.0207260 | + | 0.0674570i | ||||
\(424\) | −26.7042 | −1.29687 | ||||||||
\(425\) | 7.90642 | 0.383518 | ||||||||
\(426\) | 17.5093 | − | 23.6968i | 0.848328 | − | 1.14811i | ||||
\(427\) | −14.0886 | + | 1.97215i | −0.681796 | + | 0.0954393i | ||||
\(428\) | − | 4.63523i | − | 0.224053i | ||||||
\(429\) | 3.61982 | − | 4.89901i | 0.174767 | − | 0.236526i | ||||
\(430\) | − | 5.21864i | − | 0.251665i | ||||||
\(431\) | 31.4958i | 1.51710i | 0.651616 | + | 0.758549i | \(0.274091\pi\) | ||||
−0.651616 | + | 0.758549i | \(0.725909\pi\) | |||||||
\(432\) | 24.4065 | + | 8.58571i | 1.17426 | + | 0.413080i | ||||
\(433\) | 18.0607i | 0.867943i | 0.900927 | + | 0.433971i | \(0.142888\pi\) | ||||
−0.900927 | + | 0.433971i | \(0.857112\pi\) | |||||||
\(434\) | −3.60677 | − | 25.7660i | −0.173131 | − | 1.23681i | ||||
\(435\) | 3.78172 | + | 2.79427i | 0.181320 | + | 0.133975i | ||||
\(436\) | 17.1446 | 0.821079 | ||||||||
\(437\) | −17.7493 | −0.849063 | ||||||||
\(438\) | −20.9780 | + | 28.3913i | −1.00237 | + | 1.35659i | ||||
\(439\) | 11.4461i | 0.546294i | 0.961972 | + | 0.273147i | \(0.0880645\pi\) | ||||
−0.961972 | + | 0.273147i | \(0.911935\pi\) | |||||||
\(440\) | −2.81969 | −0.134423 | ||||||||
\(441\) | 11.4425 | + | 17.6088i | 0.544883 | + | 0.838512i | ||||
\(442\) | −16.3511 | −0.777743 | ||||||||
\(443\) | 10.3278i | 0.490690i | 0.969436 | + | 0.245345i | \(0.0789012\pi\) | ||||
−0.969436 | + | 0.245345i | \(0.921099\pi\) | |||||||
\(444\) | −6.68764 | + | 9.05094i | −0.317381 | + | 0.429539i | ||||
\(445\) | −22.2604 | −1.05524 | ||||||||
\(446\) | −2.71082 | −0.128361 | ||||||||
\(447\) | −17.2185 | − | 12.7225i | −0.814407 | − | 0.601756i | ||||
\(448\) | −0.834279 | − | 5.95990i | −0.0394160 | − | 0.281579i | ||||
\(449\) | 15.4000i | 0.726770i | 0.931639 | + | 0.363385i | \(0.118379\pi\) | ||||
−0.931639 | + | 0.363385i | \(0.881621\pi\) | |||||||
\(450\) | 13.9261 | − | 4.27876i | 0.656483 | − | 0.201703i | ||||
\(451\) | 0.863985i | 0.0406834i | ||||||||
\(452\) | 9.92506i | 0.466835i | ||||||||
\(453\) | −5.09158 | + | 6.89087i | −0.239224 | + | 0.323761i | ||||
\(454\) | 25.6641i | 1.20447i | ||||||||
\(455\) | −13.4368 | + | 1.88091i | −0.629927 | + | 0.0881785i | ||||
\(456\) | 8.11901 | − | 10.9881i | 0.380207 | − | 0.514567i | ||||
\(457\) | 18.0431 | 0.844020 | 0.422010 | − | 0.906591i | \(-0.361325\pi\) | ||||
0.422010 | + | 0.906591i | \(0.361325\pi\) | |||||||
\(458\) | −36.6778 | −1.71384 | ||||||||
\(459\) | 13.4862 | + | 4.74417i | 0.629482 | + | 0.221439i | ||||
\(460\) | − | 5.42947i | − | 0.253151i | ||||||
\(461\) | −41.0255 | −1.91075 | −0.955374 | − | 0.295399i | \(-0.904547\pi\) | ||||
−0.955374 | + | 0.295399i | \(0.904547\pi\) | |||||||
\(462\) | −6.80614 | − | 3.69415i | −0.316651 | − | 0.171868i | ||||
\(463\) | 8.69880 | 0.404267 | 0.202134 | − | 0.979358i | \(-0.435212\pi\) | ||||
0.202134 | + | 0.979358i | \(0.435212\pi\) | |||||||
\(464\) | − | 9.26982i | − | 0.430341i | ||||||
\(465\) | −11.8203 | − | 8.73390i | −0.548155 | − | 0.405025i | ||||
\(466\) | −0.772267 | −0.0357746 | ||||||||
\(467\) | −2.83763 | −0.131310 | −0.0656549 | − | 0.997842i | \(-0.520914\pi\) | ||||
−0.0656549 | + | 0.997842i | \(0.520914\pi\) | |||||||
\(468\) | −8.63012 | + | 2.65159i | −0.398928 | + | 0.122570i | ||||
\(469\) | 4.60082 | + | 32.8672i | 0.212446 | + | 1.51767i | ||||
\(470\) | 1.19217i | 0.0549906i | ||||||||
\(471\) | 2.21542 | + | 1.63695i | 0.102081 | + | 0.0754266i | ||||
\(472\) | − | 11.3615i | − | 0.522955i | ||||||
\(473\) | − | 2.11779i | − | 0.0973762i | ||||||
\(474\) | −20.6207 | − | 15.2364i | −0.947140 | − | 0.699831i | ||||
\(475\) | − | 11.7223i | − | 0.537857i | ||||||
\(476\) | 0.863551 | + | 6.16901i | 0.0395808 | + | 0.282756i | ||||
\(477\) | −39.6028 | + | 12.1679i | −1.81329 | + | 0.557129i | ||||
\(478\) | 38.6751 | 1.76896 | ||||||||
\(479\) | −2.89906 | −0.132461 | −0.0662307 | − | 0.997804i | \(-0.521097\pi\) | ||||
−0.0662307 | + | 0.997804i | \(0.521097\pi\) | |||||||
\(480\) | 9.23619 | + | 6.82452i | 0.421573 | + | 0.311495i | ||||
\(481\) | 26.7018i | 1.21750i | ||||||||
\(482\) | −33.5112 | −1.52639 | ||||||||
\(483\) | −9.51177 | + | 17.5246i | −0.432801 | + | 0.797396i | ||||
\(484\) | 0.855732 | 0.0388969 | ||||||||
\(485\) | 17.1440i | 0.778471i | ||||||||
\(486\) | 26.3216 | + | 1.05781i | 1.19397 | + | 0.0479832i | ||||
\(487\) | −13.7638 | −0.623698 | −0.311849 | − | 0.950132i | \(-0.600948\pi\) | ||||
−0.311849 | + | 0.950132i | \(0.600948\pi\) | |||||||
\(488\) | 10.3973 | 0.470663 | ||||||||
\(489\) | 17.5780 | − | 23.7897i | 0.794903 | − | 1.07581i | ||||
\(490\) | 4.73638 | + | 16.5863i | 0.213968 | + | 0.749292i | ||||
\(491\) | 8.92839i | 0.402933i | 0.979495 | + | 0.201466i | \(0.0645707\pi\) | ||||
−0.979495 | + | 0.201466i | \(0.935429\pi\) | |||||||
\(492\) | 0.761001 | − | 1.02993i | 0.0343086 | − | 0.0464327i | ||||
\(493\) | − | 5.12219i | − | 0.230692i | ||||||
\(494\) | 24.2427i | 1.09073i | ||||||||
\(495\) | −4.18165 | + | 1.28480i | −0.187951 | + | 0.0577476i | ||||
\(496\) | 28.9742i | 1.30098i | ||||||||
\(497\) | −26.3757 | + | 3.69213i | −1.18311 | + | 0.165614i | ||||
\(498\) | 16.8046 | + | 12.4168i | 0.753034 | + | 0.556408i | ||||
\(499\) | −37.9058 | −1.69689 | −0.848447 | − | 0.529280i | \(-0.822462\pi\) | ||||
−0.848447 | + | 0.529280i | \(0.822462\pi\) | |||||||
\(500\) | 9.82495 | 0.439385 | ||||||||
\(501\) | 20.0417 | − | 27.1241i | 0.895396 | − | 1.21181i | ||||
\(502\) | 1.49555i | 0.0667498i | ||||||||
\(503\) | 38.2037 | 1.70342 | 0.851709 | − | 0.524016i | \(-0.175567\pi\) | ||||
0.851709 | + | 0.524016i | \(0.175567\pi\) | |||||||
\(504\) | −6.49808 | − | 13.9047i | −0.289448 | − | 0.619366i | ||||
\(505\) | 9.31250 | 0.414401 | ||||||||
\(506\) | − | 7.35299i | − | 0.326880i | ||||||
\(507\) | 0.650729 | − | 0.880686i | 0.0288999 | − | 0.0391126i | ||||
\(508\) | −2.80543 | −0.124471 | ||||||||
\(509\) | 36.4703 | 1.61652 | 0.808259 | − | 0.588827i | \(-0.200410\pi\) | ||||
0.808259 | + | 0.588827i | \(0.200410\pi\) | |||||||
\(510\) | 9.44447 | + | 6.97841i | 0.418208 | + | 0.309009i | ||||
\(511\) | 31.6009 | − | 4.42356i | 1.39794 | − | 0.195687i | ||||
\(512\) | − | 3.38352i | − | 0.149532i | ||||||
\(513\) | 7.03385 | − | 19.9951i | 0.310552 | − | 0.882804i | ||||
\(514\) | − | 32.2882i | − | 1.42417i | ||||||
\(515\) | − | 24.6524i | − | 1.08632i | ||||||
\(516\) | −1.86536 | + | 2.52455i | −0.0821179 | + | 0.111137i | ||||
\(517\) | 0.483798i | 0.0212774i | ||||||||
\(518\) | 33.6192 | − | 4.70609i | 1.47714 | − | 0.206774i | ||||
\(519\) | −23.7504 | + | 32.1434i | −1.04253 | + | 1.41094i | ||||
\(520\) | 9.91624 | 0.434856 | ||||||||
\(521\) | 10.7999 | 0.473151 | 0.236576 | − | 0.971613i | \(-0.423975\pi\) | ||||
0.236576 | + | 0.971613i | \(0.423975\pi\) | |||||||
\(522\) | −2.77200 | − | 9.02204i | −0.121327 | − | 0.394884i | ||||
\(523\) | 16.5059i | 0.721751i | 0.932614 | + | 0.360875i | \(0.117522\pi\) | ||||
−0.932614 | + | 0.360875i | \(0.882478\pi\) | |||||||
\(524\) | 10.7221 | 0.468397 | ||||||||
\(525\) | −11.5739 | − | 6.28194i | −0.505127 | − | 0.274167i | ||||
\(526\) | −35.6189 | −1.55306 | ||||||||
\(527\) | 16.0101i | 0.697413i | ||||||||
\(528\) | 6.93618 | + | 5.12507i | 0.301859 | + | 0.223040i | ||||
\(529\) | 4.06741 | 0.176844 | ||||||||
\(530\) | −34.0304 | −1.47818 | ||||||||
\(531\) | −5.17691 | − | 16.8493i | −0.224659 | − | 0.731197i | ||||
\(532\) | 9.14637 | − | 1.28033i | 0.396545 | − | 0.0555092i | ||||
\(533\) | − | 3.03845i | − | 0.131610i | ||||||
\(534\) | 35.9367 | + | 26.5533i | 1.55514 | + | 1.14907i | ||||
\(535\) | 7.89857i | 0.341485i | ||||||||
\(536\) | − | 24.2557i | − | 1.04769i | ||||||
\(537\) | 4.28336 | + | 3.16492i | 0.184840 | + | 0.136577i | ||||
\(538\) | − | 33.0918i | − | 1.42669i | ||||||
\(539\) | 1.92209 | + | 6.73094i | 0.0827901 | + | 0.289922i | ||||
\(540\) | 6.11646 | + | 2.15164i | 0.263210 | + | 0.0925920i | ||||
\(541\) | 43.4115 | 1.86641 | 0.933203 | − | 0.359349i | \(-0.117001\pi\) | ||||
0.933203 | + | 0.359349i | \(0.117001\pi\) | |||||||
\(542\) | 13.9597 | 0.599621 | ||||||||
\(543\) | 15.7824 | + | 11.6614i | 0.677286 | + | 0.500439i | ||||
\(544\) | − | 12.5100i | − | 0.536363i | ||||||
\(545\) | −29.2149 | −1.25143 | ||||||||
\(546\) | 23.9358 | + | 12.9916i | 1.02436 | + | 0.555987i | ||||
\(547\) | 1.13100 | 0.0483579 | 0.0241789 | − | 0.999708i | \(-0.492303\pi\) | ||||
0.0241789 | + | 0.999708i | \(0.492303\pi\) | |||||||
\(548\) | − | 0.152994i | − | 0.00653557i | ||||||
\(549\) | 15.4194 | − | 4.73756i | 0.658082 | − | 0.202194i | ||||
\(550\) | 4.85620 | 0.207069 | ||||||||
\(551\) | −7.59432 | −0.323529 | ||||||||
\(552\) | 8.66029 | − | 11.7207i | 0.368606 | − | 0.498866i | ||||
\(553\) | 3.21285 | + | 22.9519i | 0.136624 | + | 0.976012i | ||||
\(554\) | 14.1778i | 0.602357i | ||||||||
\(555\) | 11.3959 | − | 15.4231i | 0.483730 | − | 0.654672i | ||||
\(556\) | − | 8.23505i | − | 0.349244i | ||||||
\(557\) | 2.69594i | 0.114230i | 0.998368 | + | 0.0571152i | \(0.0181902\pi\) | ||||
−0.998368 | + | 0.0571152i | \(0.981810\pi\) | |||||||
\(558\) | 8.66429 | + | 28.1997i | 0.366789 | + | 1.19379i | ||||
\(559\) | 7.44783i | 0.315010i | ||||||||
\(560\) | −2.66306 | − | 19.0243i | −0.112535 | − | 0.803923i | ||||
\(561\) | 3.83270 | + | 2.83193i | 0.161817 | + | 0.119564i | ||||
\(562\) | −42.2171 | −1.78082 | ||||||||
\(563\) | 1.54693 | 0.0651951 | 0.0325976 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325976 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(564\) | 0.426131 | − | 0.576719i | 0.0179434 | − | 0.0242843i | ||||
\(565\) | − | 16.9126i | − | 0.711517i | ||||||
\(566\) | −20.7780 | −0.873363 | ||||||||
\(567\) | −15.9725 | − | 17.6601i | −0.670783 | − | 0.741654i | ||||
\(568\) | 19.4650 | 0.816735 | ||||||||
\(569\) | 20.8296i | 0.873222i | 0.899650 | + | 0.436611i | \(0.143821\pi\) | ||||
−0.899650 | + | 0.436611i | \(0.856179\pi\) | |||||||
\(570\) | 10.3464 | − | 14.0027i | 0.433364 | − | 0.586508i | ||||
\(571\) | 42.0434 | 1.75946 | 0.879731 | − | 0.475472i | \(-0.157723\pi\) | ||||
0.879731 | + | 0.475472i | \(0.157723\pi\) | |||||||
\(572\) | −3.00943 | −0.125831 | ||||||||
\(573\) | 15.4391 | + | 11.4078i | 0.644979 | + | 0.476568i | ||||
\(574\) | −3.82560 | + | 0.535516i | −0.159678 | + | 0.0223520i | ||||
\(575\) | − | 12.5038i | − | 0.521446i | ||||||
\(576\) | 2.00413 | + | 6.52284i | 0.0835053 | + | 0.271785i | ||||
\(577\) | 45.5882i | 1.89786i | 0.315487 | + | 0.948930i | \(0.397832\pi\) | ||||
−0.315487 | + | 0.948930i | \(0.602168\pi\) | |||||||
\(578\) | 15.9360i | 0.662851i | ||||||||
\(579\) | 1.45944 | − | 1.97518i | 0.0606523 | − | 0.0820858i | ||||
\(580\) | − | 2.32309i | − | 0.0964610i | ||||||
\(581\) | −2.61828 | − | 18.7044i | −0.108625 | − | 0.775989i | ||||
\(582\) | 20.4502 | − | 27.6770i | 0.847690 | − | 1.14725i | ||||
\(583\) | −13.8100 | −0.571951 | ||||||||
\(584\) | −23.3212 | −0.965038 | ||||||||
\(585\) | 14.7060 | − | 4.51838i | 0.608017 | − | 0.186812i | ||||
\(586\) | − | 16.3187i | − | 0.674118i | ||||||
\(587\) | −17.4054 | −0.718397 | −0.359199 | − | 0.933261i | \(-0.616950\pi\) | ||||
−0.359199 | + | 0.933261i | \(0.616950\pi\) | |||||||
\(588\) | 3.63739 | − | 9.71670i | 0.150003 | − | 0.400710i | ||||
\(589\) | 23.7371 | 0.978072 | ||||||||
\(590\) | − | 14.4785i | − | 0.596069i | ||||||
\(591\) | −17.2513 | − | 12.7468i | −0.709624 | − | 0.524333i | ||||
\(592\) | −37.8053 | −1.55379 | ||||||||
\(593\) | 1.16298 | 0.0477580 | 0.0238790 | − | 0.999715i | \(-0.492398\pi\) | ||||
0.0238790 | + | 0.999715i | \(0.492398\pi\) | |||||||
\(594\) | 8.28335 | + | 2.91391i | 0.339870 | + | 0.119559i | ||||
\(595\) | −1.47151 | − | 10.5122i | −0.0603262 | − | 0.430957i | ||||
\(596\) | 10.5772i | 0.433259i | ||||||||
\(597\) | 21.3617 | + | 15.7839i | 0.874274 | + | 0.645991i | ||||
\(598\) | 25.8589i | 1.05745i | ||||||||
\(599\) | − | 34.7781i | − | 1.42099i | −0.703700 | − | 0.710497i | \(-0.748470\pi\) | ||
0.703700 | − | 0.710497i | \(-0.251530\pi\) | |||||||
\(600\) | 7.74081 | + | 5.71959i | 0.316017 | + | 0.233501i | ||||
\(601\) | 16.1517i | 0.658841i | 0.944183 | + | 0.329420i | \(0.106853\pi\) | ||||
−0.944183 | + | 0.329420i | \(0.893147\pi\) | |||||||
\(602\) | 9.37729 | − | 1.31265i | 0.382190 | − | 0.0534997i | ||||
\(603\) | −11.0522 | − | 35.9717i | −0.450081 | − | 1.46488i | ||||
\(604\) | 4.23302 | 0.172239 | ||||||||
\(605\) | −1.45819 | −0.0592839 | ||||||||
\(606\) | −15.0339 | − | 11.1084i | −0.610711 | − | 0.451248i | ||||
\(607\) | − | 0.757029i | − | 0.0307269i | −0.999882 | − | 0.0153634i | \(-0.995109\pi\) | ||
0.999882 | − | 0.0153634i | \(-0.00489053\pi\) | |||||||
\(608\) | −18.5478 | −0.752212 | ||||||||
\(609\) | −4.06976 | + | 7.49817i | −0.164915 | + | 0.303841i | ||||
\(610\) | 13.2497 | 0.536466 | ||||||||
\(611\) | − | 1.70142i | − | 0.0688319i | ||||||
\(612\) | −2.07444 | − | 6.75170i | −0.0838545 | − | 0.272921i | ||||
\(613\) | −18.2996 | −0.739112 | −0.369556 | − | 0.929208i | \(-0.620490\pi\) | ||||
−0.369556 | + | 0.929208i | \(0.620490\pi\) | |||||||
\(614\) | −10.0183 | −0.404306 | ||||||||
\(615\) | −1.29677 | + | 1.75502i | −0.0522907 | + | 0.0707694i | ||||
\(616\) | −0.709241 | − | 5.06666i | −0.0285761 | − | 0.204141i | ||||
\(617\) | 48.9521i | 1.97074i | 0.170439 | + | 0.985368i | \(0.445482\pi\) | ||||
−0.170439 | + | 0.985368i | \(0.554518\pi\) | |||||||
\(618\) | −29.4066 | + | 39.7984i | −1.18291 | + | 1.60093i | ||||
\(619\) | − | 37.7204i | − | 1.51611i | −0.652191 | − | 0.758055i | \(-0.726150\pi\) | ||
0.652191 | − | 0.758055i | \(-0.273850\pi\) | |||||||
\(620\) | 7.26115i | 0.291615i | ||||||||
\(621\) | 7.50279 | − | 21.3281i | 0.301077 | − | 0.855868i | ||||
\(622\) | − | 5.84278i | − | 0.234274i | ||||||
\(623\) | −5.59919 | − | 39.9994i | −0.224327 | − | 1.60254i | ||||
\(624\) | −24.3931 | − | 18.0238i | −0.976504 | − | 0.721528i | ||||
\(625\) | −2.37361 | −0.0949443 | ||||||||
\(626\) | −14.2164 | −0.568203 | ||||||||
\(627\) | 4.19872 | − | 5.68248i | 0.167681 | − | 0.226936i | ||||
\(628\) | − | 1.36092i | − | 0.0543065i | ||||||
\(629\) | −20.8899 | −0.832934 | ||||||||
\(630\) | −8.28080 | − | 17.7194i | −0.329915 | − | 0.705958i | ||||
\(631\) | 3.50668 | 0.139599 | 0.0697993 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0697993 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(632\) | − | 16.9383i | − | 0.673768i | ||||||
\(633\) | −1.24462 | + | 1.68445i | −0.0494692 | + | 0.0669508i | ||||
\(634\) | 25.0427 | 0.994573 | ||||||||
\(635\) | 4.78054 | 0.189710 | ||||||||
\(636\) | 16.4624 | + | 12.1639i | 0.652776 | + | 0.482329i | ||||
\(637\) | −6.75956 | − | 23.6713i | −0.267824 | − | 0.937891i | ||||
\(638\) | − | 3.14609i | − | 0.124555i | ||||||
\(639\) | 28.8670 | − | 8.86933i | 1.14196 | − | 0.350865i | ||||
\(640\) | 18.8656i | 0.745726i | ||||||||
\(641\) | 4.33625i | 0.171271i | 0.996327 | + | 0.0856357i | \(0.0272921\pi\) | ||||
−0.996327 | + | 0.0856357i | \(0.972708\pi\) | |||||||
\(642\) | 9.42179 | − | 12.7513i | 0.371848 | − | 0.503254i | ||||
\(643\) | 3.54931i | 0.139971i | 0.997548 | + | 0.0699856i | \(0.0222953\pi\) | ||||
−0.997548 | + | 0.0699856i | \(0.977705\pi\) | |||||||
\(644\) | 9.75614 | − | 1.36568i | 0.384446 | − | 0.0538155i | ||||
\(645\) | 3.17862 | − | 4.30190i | 0.125158 | − | 0.169387i | ||||
\(646\) | −18.9660 | −0.746209 | ||||||||
\(647\) | 25.1464 | 0.988605 | 0.494303 | − | 0.869290i | \(-0.335423\pi\) | ||||
0.494303 | + | 0.869290i | \(0.335423\pi\) | |||||||
\(648\) | 9.77172 | + | 14.4009i | 0.383869 | + | 0.565719i | ||||
\(649\) | − | 5.87555i | − | 0.230636i | ||||||
\(650\) | −17.0782 | −0.669863 | ||||||||
\(651\) | 12.7206 | − | 23.4366i | 0.498561 | − | 0.918554i | ||||
\(652\) | −14.6139 | −0.572324 | ||||||||
\(653\) | − | 22.5809i | − | 0.883657i | −0.897099 | − | 0.441829i | \(-0.854330\pi\) | ||
0.897099 | − | 0.441829i | \(-0.145670\pi\) | |||||||
\(654\) | 47.1640 | + | 34.8490i | 1.84426 | + | 1.36270i | ||||
\(655\) | −18.2708 | −0.713898 | ||||||||
\(656\) | 4.30194 | 0.167963 | ||||||||
\(657\) | −34.5858 | + | 10.6264i | −1.34932 | + | 0.414575i | ||||
\(658\) | −2.14219 | + | 0.299868i | −0.0835113 | + | 0.0116901i | ||||
\(659\) | 31.6426i | 1.23262i | 0.787504 | + | 0.616310i | \(0.211373\pi\) | ||||
−0.787504 | + | 0.616310i | \(0.788627\pi\) | |||||||
\(660\) | 1.73826 | + | 1.28438i | 0.0676617 | + | 0.0499944i | ||||
\(661\) | 6.23184i | 0.242390i | 0.992629 | + | 0.121195i | \(0.0386727\pi\) | ||||
−0.992629 | + | 0.121195i | \(0.961327\pi\) | |||||||
\(662\) | 5.85739i | 0.227654i | ||||||||
\(663\) | −13.4788 | − | 9.95931i | −0.523472 | − | 0.386788i | ||||
\(664\) | 13.8037i | 0.535687i | ||||||||
\(665\) | −15.5857 | + | 2.18171i | −0.604386 | + | 0.0846032i | ||||
\(666\) | −36.7947 | + | 11.3051i | −1.42577 | + | 0.438063i | ||||
\(667\) | −8.10062 | −0.313657 | ||||||||
\(668\) | −16.6622 | −0.644678 | ||||||||
\(669\) | −2.23462 | − | 1.65114i | −0.0863956 | − | 0.0638367i | ||||
\(670\) | − | 30.9102i | − | 1.19416i | ||||||
\(671\) | 5.37692 | 0.207574 | ||||||||
\(672\) | −9.93968 | + | 18.3130i | −0.383432 | + | 0.706438i | ||||
\(673\) | 10.7998 | 0.416301 | 0.208151 | − | 0.978097i | \(-0.433256\pi\) | ||||
0.208151 | + | 0.978097i | \(0.433256\pi\) | |||||||
\(674\) | − | 44.1664i | − | 1.70122i | ||||||
\(675\) | 14.0859 | + | 4.95513i | 0.542167 | + | 0.190723i | ||||
\(676\) | −0.541000 | −0.0208077 | ||||||||
\(677\) | 46.0148 | 1.76849 | 0.884247 | − | 0.467019i | \(-0.154672\pi\) | ||||
0.884247 | + | 0.467019i | \(0.154672\pi\) | |||||||
\(678\) | −20.1741 | + | 27.3033i | −0.774783 | + | 1.04858i | ||||
\(679\) | −30.8059 | + | 4.31227i | −1.18222 | + | 0.165490i | ||||
\(680\) | 7.75789i | 0.297501i | ||||||||
\(681\) | −15.6318 | + | 21.1558i | −0.599010 | + | 0.810691i | ||||
\(682\) | 9.83358i | 0.376547i | ||||||||
\(683\) | − | 20.9248i | − | 0.800665i | −0.916370 | − | 0.400333i | \(-0.868895\pi\) | ||
0.916370 | − | 0.400333i | \(-0.131105\pi\) | |||||||
\(684\) | −10.0103 | + | 3.07564i | −0.382753 | + | 0.117600i | ||||
\(685\) | 0.260706i | 0.00996105i | ||||||||
\(686\) | −28.6123 | + | 12.6827i | −1.09242 | + | 0.484228i | ||||
\(687\) | −30.2347 | − | 22.3401i | −1.15353 | − | 0.852328i | ||||
\(688\) | −10.5449 | −0.402020 | ||||||||
\(689\) | 48.5668 | 1.85025 | ||||||||
\(690\) | 11.0362 | − | 14.9362i | 0.420141 | − | 0.568612i | ||||
\(691\) | − | 24.6653i | − | 0.938313i | −0.883115 | − | 0.469156i | \(-0.844558\pi\) | ||
0.883115 | − | 0.469156i | \(-0.155442\pi\) | |||||||
\(692\) | 19.7455 | 0.750611 | ||||||||
\(693\) | −3.36046 | − | 7.19078i | −0.127653 | − | 0.273155i | ||||
\(694\) | 10.2202 | 0.387954 | ||||||||
\(695\) | 14.0328i | 0.532293i | ||||||||
\(696\) | 3.70545 | − | 5.01489i | 0.140455 | − | 0.190089i | ||||
\(697\) | 2.37710 | 0.0900393 | ||||||||
\(698\) | −56.9007 | −2.15372 | ||||||||
\(699\) | −0.636606 | − | 0.470381i | −0.0240786 | − | 0.0177914i | ||||
\(700\) | 0.901952 | + | 6.44334i | 0.0340906 | + | 0.243535i | ||||
\(701\) | − | 46.1898i | − | 1.74456i | −0.489004 | − | 0.872282i | \(-0.662640\pi\) | ||
0.489004 | − | 0.872282i | \(-0.337360\pi\) | |||||||
\(702\) | −29.1308 | − | 10.2476i | −1.09947 | − | 0.386771i | ||||
\(703\) | 30.9720i | 1.16813i | ||||||||
\(704\) | 2.27459i | 0.0857269i | ||||||||
\(705\) | −0.726139 | + | 0.982745i | −0.0273480 | + | 0.0370123i | ||||
\(706\) | 45.2796i | 1.70412i | ||||||||
\(707\) | 2.34239 | + | 16.7335i | 0.0880946 | + | 0.629328i | ||||
\(708\) | −5.17521 | + | 7.00404i | −0.194496 | + | 0.263228i | ||||
\(709\) | −2.12583 | −0.0798371 | −0.0399185 | − | 0.999203i | \(-0.512710\pi\) | ||||
−0.0399185 | + | 0.999203i | \(0.512710\pi\) | |||||||
\(710\) | 24.8052 | 0.930922 | ||||||||
\(711\) | −7.71799 | − | 25.1198i | −0.289447 | − | 0.942065i | ||||
\(712\) | 29.5192i | 1.10628i | ||||||||
\(713\) | 25.3197 | 0.948229 | ||||||||
\(714\) | −10.1638 | + | 18.7259i | −0.380372 | + | 0.700800i | ||||
\(715\) | 5.12815 | 0.191782 | ||||||||
\(716\) | − | 2.63124i | − | 0.0983340i | ||||||
\(717\) | 31.8812 | + | 23.5567i | 1.19063 | + | 0.879740i | ||||
\(718\) | −19.7353 | −0.736515 | ||||||||
\(719\) | −26.6268 | −0.993013 | −0.496507 | − | 0.868033i | \(-0.665384\pi\) | ||||
−0.496507 | + | 0.868033i | \(0.665384\pi\) | |||||||
\(720\) | 6.39727 | + | 20.8212i | 0.238412 | + | 0.775961i | ||||
\(721\) | 44.2976 | − | 6.20087i | 1.64973 | − | 0.230932i | ||||
\(722\) | − | 3.98828i | − | 0.148429i | ||||||
\(723\) | −27.6244 | − | 20.4114i | −1.02736 | − | 0.759107i | ||||
\(724\) | − | 9.69500i | − | 0.360312i | ||||||
\(725\) | − | 5.34996i | − | 0.198693i | ||||||
\(726\) | 2.35408 | + | 1.73940i | 0.0873680 | + | 0.0645552i | ||||
\(727\) | − | 36.4042i | − | 1.35016i | −0.737745 | − | 0.675079i | \(-0.764110\pi\) | ||
0.737745 | − | 0.675079i | \(-0.235890\pi\) | |||||||
\(728\) | 2.49425 | + | 17.8184i | 0.0924430 | + | 0.660392i | ||||
\(729\) | 21.0534 | + | 16.9042i | 0.779757 | + | 0.626082i | ||||
\(730\) | −29.7192 | −1.09996 | ||||||||
\(731\) | −5.82674 | −0.215510 | ||||||||
\(732\) | −6.40964 | − | 4.73601i | −0.236907 | − | 0.175048i | ||||
\(733\) | − | 16.7068i | − | 0.617078i | −0.951212 | − | 0.308539i | \(-0.900160\pi\) | ||
0.951212 | − | 0.308539i | \(-0.0998400\pi\) | |||||||
\(734\) | −20.2729 | −0.748288 | ||||||||
\(735\) | −6.19821 | + | 16.5575i | −0.228624 | + | 0.610734i | ||||
\(736\) | −19.7843 | −0.729260 | ||||||||
\(737\) | − | 12.5438i | − | 0.462055i | ||||||
\(738\) | 4.18695 | − | 1.28643i | 0.154124 | − | 0.0473542i | ||||
\(739\) | −20.1718 | −0.742032 | −0.371016 | − | 0.928626i | \(-0.620991\pi\) | ||||
−0.371016 | + | 0.928626i | \(0.620991\pi\) | |||||||
\(740\) | −9.47429 | −0.348282 | ||||||||
\(741\) | −14.7660 | + | 19.9841i | −0.542442 | + | 0.734133i | ||||
\(742\) | −8.55971 | − | 61.1487i | −0.314237 | − | 2.24484i | ||||
\(743\) | − | 17.2512i | − | 0.632884i | −0.948612 | − | 0.316442i | \(-0.897512\pi\) | ||
0.948612 | − | 0.316442i | \(-0.102488\pi\) | |||||||
\(744\) | −11.5819 | + | 15.6748i | −0.424613 | + | 0.574665i | ||||
\(745\) | − | 18.0239i | − | 0.660343i | ||||||
\(746\) | 18.7996i | 0.688304i | ||||||||
\(747\) | 6.28970 | + | 20.4711i | 0.230128 | + | 0.748999i | ||||
\(748\) | − | 2.35440i | − | 0.0860854i | ||||||
\(749\) | −14.1928 | + | 1.98674i | −0.518595 | + | 0.0725939i | ||||
\(750\) | 27.0279 | + | 19.9706i | 0.986921 | + | 0.729225i | ||||
\(751\) | −21.4620 | −0.783160 | −0.391580 | − | 0.920144i | \(-0.628071\pi\) | ||||
−0.391580 | + | 0.920144i | \(0.628071\pi\) | |||||||
\(752\) | 2.40892 | 0.0878443 | ||||||||
\(753\) | −0.910928 | + | 1.23284i | −0.0331961 | + | 0.0449270i | ||||
\(754\) | 11.0641i | 0.402932i | ||||||||
\(755\) | −7.21318 | −0.262514 | ||||||||
\(756\) | −2.32777 | + | 11.5318i | −0.0846603 | + | 0.419407i | ||||
\(757\) | −31.1462 | −1.13203 | −0.566014 | − | 0.824395i | \(-0.691515\pi\) | ||||
−0.566014 | + | 0.824395i | \(0.691515\pi\) | |||||||
\(758\) | 0.892750i | 0.0324261i | ||||||||
\(759\) | 4.47864 | − | 6.06132i | 0.162564 | − | 0.220012i | ||||
\(760\) | 11.5021 | 0.417225 | ||||||||
\(761\) | −39.7189 | −1.43981 | −0.719905 | − | 0.694073i | \(-0.755815\pi\) | ||||
−0.719905 | + | 0.694073i | \(0.755815\pi\) | |||||||
\(762\) | −7.71761 | − | 5.70245i | −0.279580 | − | 0.206578i | ||||
\(763\) | −7.34848 | − | 52.4959i | −0.266033 | − | 1.90048i | ||||
\(764\) | − | 9.48416i | − | 0.343125i | ||||||
\(765\) | 3.53491 | + | 11.5051i | 0.127805 | + | 0.415967i | ||||
\(766\) | − | 26.8873i | − | 0.971479i | ||||||
\(767\) | 20.6631i | 0.746100i | ||||||||
\(768\) | 17.8213 | − | 24.1190i | 0.643069 | − | 0.870320i | ||||
\(769\) | 23.5141i | 0.847939i | 0.905677 | + | 0.423969i | \(0.139364\pi\) | ||||
−0.905677 | + | 0.423969i | \(0.860636\pi\) | |||||||
\(770\) | −0.903818 | − | 6.45667i | −0.0325713 | − | 0.232682i | ||||
\(771\) | 19.6665 | − | 26.6163i | 0.708270 | − | 0.958561i | ||||
\(772\) | −1.21334 | −0.0436692 | ||||||||
\(773\) | −11.3070 | −0.406684 | −0.203342 | − | 0.979108i | \(-0.565180\pi\) | ||||
−0.203342 | + | 0.979108i | \(0.565180\pi\) | |||||||
\(774\) | −10.2630 | + | 3.15329i | −0.368897 | + | 0.113343i | ||||
\(775\) | 16.7221i | 0.600675i | ||||||||
\(776\) | 22.7345 | 0.816120 | ||||||||
\(777\) | 30.5799 | + | 16.5978i | 1.09705 | + | 0.595442i | ||||
\(778\) | 36.6975 | 1.31567 | ||||||||
\(779\) | − | 3.52437i | − | 0.126274i | ||||||
\(780\) | −6.11309 | − | 4.51689i | −0.218884 | − | 0.161731i | ||||
\(781\) | 10.0663 | 0.360200 | ||||||||
\(782\) | −20.2305 | −0.723440 | ||||||||
\(783\) | 3.21019 | − | 9.12558i | 0.114723 | − | 0.326122i | ||||
\(784\) | 33.5146 | − | 9.57042i | 1.19695 | − | 0.341801i | ||||
\(785\) | 2.31904i | 0.0827702i | ||||||||
\(786\) | 29.4960 | + | 21.7943i | 1.05209 | + | 0.777375i | ||||
\(787\) | 8.67136i | 0.309100i | 0.987985 | + | 0.154550i | \(0.0493928\pi\) | ||||
−0.987985 | + | 0.154550i | \(0.950607\pi\) | |||||||
\(788\) | 10.5974i | 0.377516i | ||||||||
\(789\) | −29.3619 | − | 21.6952i | −1.04531 | − | 0.772368i | ||||
\(790\) | − | 21.5852i | − | 0.767967i | ||||||
\(791\) | 30.3900 | − | 4.25405i | 1.08054 | − | 0.151257i | ||||
\(792\) | 1.70376 | + | 5.54523i | 0.0605404 | + | 0.197041i | ||||
\(793\) | −18.9095 | −0.671495 | ||||||||
\(794\) | 25.8270 | 0.916566 | ||||||||
\(795\) | −28.0524 | − | 20.7276i | −0.994916 | − | 0.735132i | ||||
\(796\) | − | 13.1223i | − | 0.465109i | ||||||
\(797\) | −5.56607 | −0.197160 | −0.0985801 | − | 0.995129i | \(-0.531430\pi\) | ||||
−0.0985801 | + | 0.995129i | \(0.531430\pi\) | |||||||
\(798\) | 27.7637 | + | 15.0692i | 0.982823 | + | 0.533444i | ||||
\(799\) | 1.33109 | 0.0470905 | ||||||||
\(800\) | − | 13.0663i | − | 0.461965i | ||||||
\(801\) | 13.4505 | + | 43.7775i | 0.475251 | + | 1.54680i | ||||
\(802\) | 34.2203 | 1.20836 | ||||||||
\(803\) | −12.0605 | −0.425605 | ||||||||
\(804\) | −11.0486 | + | 14.9530i | −0.389654 | + | 0.527351i | ||||
\(805\) | −16.6247 | + | 2.32717i | −0.585945 | + | 0.0820218i | ||||
\(806\) | − | 34.5826i | − | 1.21812i | ||||||
\(807\) | 20.1559 | − | 27.2787i | 0.709522 | − | 0.960255i | ||||
\(808\) | − | 12.3492i | − | 0.434442i | ||||||
\(809\) | 16.2308i | 0.570644i | 0.958432 | + | 0.285322i | \(0.0921005\pi\) | ||||
−0.958432 | + | 0.285322i | \(0.907900\pi\) | |||||||
\(810\) | 12.4525 | + | 18.3517i | 0.437538 | + | 0.644812i | ||||
\(811\) | 10.8313i | 0.380340i | 0.981751 | + | 0.190170i | \(0.0609039\pi\) | ||||
−0.981751 | + | 0.190170i | \(0.939096\pi\) | |||||||
\(812\) | 4.17432 | − | 0.584330i | 0.146490 | − | 0.0205060i | ||||
\(813\) | 11.5075 | + | 8.50273i | 0.403584 | + | 0.298204i | ||||
\(814\) | −12.8308 | −0.449718 | ||||||||
\(815\) | 24.9025 | 0.872295 | ||||||||
\(816\) | 14.1007 | − | 19.0837i | 0.493624 | − | 0.668063i | ||||
\(817\) | 8.63891i | 0.302237i | ||||||||
\(818\) | 0.760622 | 0.0265945 | ||||||||
\(819\) | 11.8180 | + | 25.2884i | 0.412955 | + | 0.883650i | ||||
\(820\) | 1.07810 | 0.0376489 | ||||||||
\(821\) | − | 21.3847i | − | 0.746332i | −0.927765 | − | 0.373166i | \(-0.878272\pi\) | ||
0.927765 | − | 0.373166i | \(-0.121728\pi\) | |||||||
\(822\) | 0.310982 | − | 0.420878i | 0.0108467 | − | 0.0146798i | ||||
\(823\) | 22.2162 | 0.774408 | 0.387204 | − | 0.921994i | \(-0.373441\pi\) | ||||
0.387204 | + | 0.921994i | \(0.373441\pi\) | |||||||
\(824\) | −32.6913 | −1.13885 | ||||||||
\(825\) | 4.00313 | + | 2.95787i | 0.139371 | + | 0.102980i | ||||
\(826\) | 26.0161 | − | 3.64179i | 0.905217 | − | 0.126714i | ||||
\(827\) | − | 47.5182i | − | 1.65237i | −0.563400 | − | 0.826184i | \(-0.690507\pi\) | ||
0.563400 | − | 0.826184i | \(-0.309493\pi\) | |||||||
\(828\) | −10.6777 | + | 3.28069i | −0.371074 | + | 0.114012i | ||||
\(829\) | − | 23.6060i | − | 0.819871i | −0.912115 | − | 0.409935i | \(-0.865551\pi\) | ||
0.912115 | − | 0.409935i | \(-0.134449\pi\) | |||||||
\(830\) | 17.5907i | 0.610581i | ||||||||
\(831\) | −8.63557 | + | 11.6872i | −0.299564 | + | 0.405426i | ||||
\(832\) | − | 7.99926i | − | 0.277324i | ||||||
\(833\) | 18.5190 | − | 5.28829i | 0.641646 | − | 0.183228i | ||||
\(834\) | 16.7389 | − | 22.6542i | 0.579622 | − | 0.784452i | ||||
\(835\) | 28.3928 | 0.982573 | ||||||||
\(836\) | −3.49071 | −0.120729 | ||||||||
\(837\) | −10.0339 | + | 28.5233i | −0.346823 | + | 0.985910i | ||||
\(838\) | − | 66.5996i | − | 2.30065i | ||||||
\(839\) | −8.39883 | −0.289960 | −0.144980 | − | 0.989435i | \(-0.546312\pi\) | ||||
−0.144980 | + | 0.989435i | \(0.546312\pi\) | |||||||
\(840\) | 6.16392 | − | 11.3565i | 0.212676 | − | 0.391836i | ||||
\(841\) | 25.5340 | 0.880483 | ||||||||
\(842\) | 28.8116i | 0.992914i | ||||||||
\(843\) | −34.8010 | − | 25.7140i | −1.19861 | − | 0.885638i | ||||
\(844\) | 1.03474 | 0.0356174 | ||||||||
\(845\) | 0.921879 | 0.0317136 | ||||||||
\(846\) | 2.34453 | − | 0.720352i | 0.0806066 | − | 0.0247662i | ||||
\(847\) | −0.366782 | − | 2.62020i | −0.0126028 | − | 0.0900313i | ||||
\(848\) | 68.7625i | 2.36131i | ||||||||
\(849\) | −17.1280 | − | 12.6557i | −0.587831 | − | 0.434342i | ||||
\(850\) | − | 13.3610i | − | 0.458278i | ||||||
\(851\) | 33.0369i | 1.13249i | ||||||||
\(852\) | −11.9997 | − | 8.86641i | −0.411102 | − | 0.303758i | ||||
\(853\) | 33.4361i | 1.14483i | 0.819963 | + | 0.572416i | \(0.193994\pi\) | ||||
−0.819963 | + | 0.572416i | \(0.806006\pi\) | |||||||
\(854\) | 3.33273 | + | 23.8082i | 0.114044 | + | 0.814701i | ||||
\(855\) | 17.0578 | − | 5.24097i | 0.583365 | − | 0.179237i | ||||
\(856\) | 10.4742 | 0.358000 | ||||||||
\(857\) | 17.6528 | 0.603010 | 0.301505 | − | 0.953465i | \(-0.402511\pi\) | ||||
0.301505 | + | 0.953465i | \(0.402511\pi\) | |||||||
\(858\) | −8.27879 | − | 6.11710i | −0.282633 | − | 0.208834i | ||||
\(859\) | 30.3759i | 1.03641i | 0.855255 | + | 0.518207i | \(0.173400\pi\) | ||||
−0.855255 | + | 0.518207i | \(0.826600\pi\) | |||||||
\(860\) | −2.64263 | −0.0901129 | ||||||||
\(861\) | −3.47975 | − | 1.88870i | −0.118590 | − | 0.0643666i | ||||
\(862\) | 53.2244 | 1.81283 | ||||||||
\(863\) | − | 17.3523i | − | 0.590678i | −0.955393 | − | 0.295339i | \(-0.904567\pi\) | ||
0.955393 | − | 0.295339i | \(-0.0954325\pi\) | |||||||
\(864\) | 7.84032 | − | 22.2876i | 0.266733 | − | 0.758240i | ||||
\(865\) | −33.6469 | −1.14403 | ||||||||
\(866\) | 30.5207 | 1.03713 | ||||||||
\(867\) | −9.70648 | + | 13.1366i | −0.329649 | + | 0.446142i | ||||
\(868\) | −13.0475 | + | 1.82641i | −0.442860 | + | 0.0619924i | ||||
\(869\) | − | 8.75956i | − | 0.297148i | ||||||
\(870\) | 4.72202 | − | 6.39070i | 0.160091 | − | 0.216665i | ||||
\(871\) | 44.1137i | 1.49474i | ||||||||
\(872\) | 38.7415i | 1.31195i | ||||||||
\(873\) | 33.7157 | − | 10.3591i | 1.14110 | − | 0.350601i | ||||
\(874\) | 29.9943i | 1.01457i | ||||||||
\(875\) | −4.21114 | − | 30.0834i | −0.142363 | − | 1.01701i | ||||
\(876\) | 14.3769 | + | 10.6229i | 0.485749 | + | 0.358915i | ||||
\(877\) | 19.0234 | 0.642375 | 0.321187 | − | 0.947016i | \(-0.395918\pi\) | ||||
0.321187 | + | 0.947016i | \(0.395918\pi\) | |||||||
\(878\) | 19.3427 | 0.652785 | ||||||||
\(879\) | 9.93956 | − | 13.4520i | 0.335253 | − | 0.453726i | ||||
\(880\) | 7.26061i | 0.244755i | ||||||||
\(881\) | −25.9732 | −0.875061 | −0.437530 | − | 0.899204i | \(-0.644147\pi\) | ||||
−0.437530 | + | 0.899204i | \(0.644147\pi\) | |||||||
\(882\) | 29.7569 | − | 19.3366i | 1.00197 | − | 0.651099i | ||||
\(883\) | 7.05819 | 0.237527 | 0.118764 | − | 0.992923i | \(-0.462107\pi\) | ||||
0.118764 | + | 0.992923i | \(0.462107\pi\) | |||||||
\(884\) | 8.27992i | 0.278484i | ||||||||
\(885\) | 8.81870 | − | 11.9351i | 0.296437 | − | 0.401194i | ||||
\(886\) | 17.4529 | 0.586342 | ||||||||
\(887\) | 41.3253 | 1.38757 | 0.693785 | − | 0.720183i | \(-0.255942\pi\) | ||||
0.693785 | + | 0.720183i | \(0.255942\pi\) | |||||||
\(888\) | −20.4523 | − | 15.1120i | −0.686334 | − | 0.507125i | ||||
\(889\) | 1.20246 | + | 8.59008i | 0.0403291 | + | 0.288102i | ||||
\(890\) | 37.6176i | 1.26095i | ||||||||
\(891\) | 5.05341 | + | 7.44735i | 0.169296 | + | 0.249496i | ||||
\(892\) | 1.37272i | 0.0459619i | ||||||||
\(893\) | − | 1.97351i | − | 0.0660411i | ||||||
\(894\) | −21.4997 | + | 29.0974i | −0.719058 | + | 0.973162i | ||||
\(895\) | 4.48370i | 0.149874i | ||||||||
\(896\) | −33.8992 | + | 4.74528i | −1.13249 | + | 0.158529i | ||||
\(897\) | −15.7504 | + | 21.3164i | −0.525891 | + | 0.711733i | ||||
\(898\) | 26.0243 | 0.868442 | ||||||||
\(899\) | 10.8334 | 0.361315 | ||||||||
\(900\) | −2.16669 | − | 7.05194i | −0.0722231 | − | 0.235065i | ||||
\(901\) | 37.9958i | 1.26582i | ||||||||
\(902\) | 1.46004 | 0.0486140 | ||||||||
\(903\) | 8.52955 | + | 4.62956i | 0.283846 | + | 0.154062i | ||||
\(904\) | −22.4275 | −0.745928 | ||||||||
\(905\) | 16.5206i | 0.549162i | ||||||||
\(906\) | 11.6448 | + | 8.60422i | 0.386873 | + | 0.285856i | ||||
\(907\) | −42.9161 | −1.42500 | −0.712502 | − | 0.701670i | \(-0.752438\pi\) | ||||
−0.712502 | + | 0.701670i | \(0.752438\pi\) | |||||||
\(908\) | 12.9959 | 0.431282 | ||||||||
\(909\) | −5.62695 | − | 18.3141i | −0.186634 | − | 0.607439i | ||||
\(910\) | 3.17854 | + | 22.7067i | 0.105367 | + | 0.752721i | ||||
\(911\) | 19.6193i | 0.650018i | 0.945711 | + | 0.325009i | \(0.105367\pi\) | ||||
−0.945711 | + | 0.325009i | \(0.894633\pi\) | |||||||
\(912\) | −28.2941 | − | 20.9062i | −0.936912 | − | 0.692273i | ||||
\(913\) | 7.13853i | 0.236251i | ||||||||
\(914\) | − | 30.4908i | − | 1.00855i | ||||||
\(915\) | 10.9222 | + | 8.07029i | 0.361077 | + | 0.266796i | ||||
\(916\) | 18.5730i | 0.613670i | ||||||||
\(917\) | −4.59568 | − | 32.8305i | −0.151763 | − | 1.08416i | ||||
\(918\) | 8.01712 | − | 22.7902i | 0.264605 | − | 0.752189i | ||||
\(919\) | −6.36026 | −0.209806 | −0.104903 | − | 0.994482i | \(-0.533453\pi\) | ||||
−0.104903 | + | 0.994482i | \(0.533453\pi\) | |||||||
\(920\) | 12.2689 | 0.404494 | ||||||||
\(921\) | −8.25844 | − | 6.10206i | −0.272125 | − | 0.201070i | ||||
\(922\) | 69.3286i | 2.28322i | ||||||||
\(923\) | −35.4010 | −1.16524 | ||||||||
\(924\) | −1.87066 | + | 3.44652i | −0.0615401 | + | 0.113382i | ||||
\(925\) | −21.8188 | −0.717399 | ||||||||
\(926\) | − | 14.7000i | − | 0.483073i | ||||||
\(927\) | −48.4817 | + | 14.8959i | −1.59235 | + | 0.489246i | ||||
\(928\) | −8.46505 | −0.277879 | ||||||||
\(929\) | −11.9445 | −0.391885 | −0.195942 | − | 0.980615i | \(-0.562777\pi\) | ||||
−0.195942 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(930\) | −14.7593 | + | 19.9751i | −0.483978 | + | 0.655008i | ||||
\(931\) | −7.84058 | − | 27.4569i | −0.256965 | − | 0.899863i | ||||
\(932\) | 0.391063i | 0.0128097i | ||||||||
\(933\) | 3.55879 | − | 4.81640i | 0.116509 | − | 0.157682i | ||||
\(934\) | 4.79529i | 0.156907i | ||||||||
\(935\) | 4.01196i | 0.131205i | ||||||||
\(936\) | −5.99176 | − | 19.5014i | −0.195847 | − | 0.637423i | ||||
\(937\) | − | 46.7121i | − | 1.52602i | −0.646388 | − | 0.763009i | \(-0.723721\pi\) | ||
0.646388 | − | 0.763009i | \(-0.276279\pi\) | |||||||
\(938\) | 55.5420 | − | 7.77489i | 1.81351 | − | 0.253859i | ||||
\(939\) | −11.7191 | − | 8.65910i | −0.382438 | − | 0.282579i | ||||
\(940\) | 0.603694 | 0.0196903 | ||||||||
\(941\) | −49.6376 | −1.61814 | −0.809070 | − | 0.587712i | \(-0.800029\pi\) | ||||
−0.809070 | + | 0.587712i | \(0.800029\pi\) | |||||||
\(942\) | 2.76626 | − | 3.74382i | 0.0901298 | − | 0.121980i | ||||
\(943\) | − | 3.75934i | − | 0.122421i | ||||||
\(944\) | −29.2555 | −0.952185 | ||||||||
\(945\) | 3.96659 | − | 19.6505i | 0.129033 | − | 0.639230i | ||||
\(946\) | −3.57884 | −0.116358 | ||||||||
\(947\) | 6.58429i | 0.213961i | 0.994261 | + | 0.106980i | \(0.0341182\pi\) | ||||
−0.994261 | + | 0.106980i | \(0.965882\pi\) | |||||||
\(948\) | −7.71545 | + | 10.4420i | −0.250586 | + | 0.339139i | ||||
\(949\) | 42.4141 | 1.37682 | ||||||||
\(950\) | −19.8094 | −0.642703 | ||||||||
\(951\) | 20.6436 | + | 15.2533i | 0.669413 | + | 0.494622i | ||||
\(952\) | −13.9400 | + | 1.95135i | −0.451799 | + | 0.0632438i | ||||
\(953\) | 14.5012i | 0.469741i | 0.972027 | + | 0.234871i | \(0.0754667\pi\) | ||||
−0.972027 | + | 0.234871i | \(0.924533\pi\) | |||||||
\(954\) | 20.5624 | + | 66.9244i | 0.665732 | + | 2.16676i | ||||
\(955\) | 16.1613i | 0.522967i | ||||||||
\(956\) | − | 19.5844i | − | 0.633406i | ||||||
\(957\) | 1.91626 | − | 2.59343i | 0.0619438 | − | 0.0838338i | ||||
\(958\) | 4.89909i | 0.158282i | ||||||||
\(959\) | −0.468458 | + | 0.0655757i | −0.0151273 | + | 0.00211755i | ||||
\(960\) | −3.41397 | + | 4.62041i | −0.110185 | + | 0.149123i | ||||
\(961\) | −2.86145 | −0.0923048 | ||||||||
\(962\) | 45.1231 | 1.45483 | ||||||||
\(963\) | 15.5334 | − | 4.77260i | 0.500557 | − | 0.153795i | ||||
\(964\) | 16.9695i | 0.546551i | ||||||||
\(965\) | 2.06757 | 0.0665574 | ||||||||
\(966\) | 29.6146 | + | 16.0739i | 0.952835 | + | 0.517168i | ||||
\(967\) | −3.74566 | −0.120452 | −0.0602262 | − | 0.998185i | \(-0.519182\pi\) | ||||
−0.0602262 | + | 0.998185i | \(0.519182\pi\) | |||||||
\(968\) | 1.93369i | 0.0621511i | ||||||||
\(969\) | −15.6344 | − | 11.5520i | −0.502248 | − | 0.371105i | ||||
\(970\) | 28.9716 | 0.930221 | ||||||||
\(971\) | −12.8433 | −0.412162 | −0.206081 | − | 0.978535i | \(-0.566071\pi\) | ||||
−0.206081 | + | 0.978535i | \(0.566071\pi\) | |||||||
\(972\) | 0.535657 | − | 13.3288i | 0.0171812 | − | 0.427521i | ||||
\(973\) | −25.2153 | + | 3.52968i | −0.808364 | + | 0.113156i | ||||
\(974\) | 23.2594i | 0.745278i | ||||||||
\(975\) | −14.0782 | − | 10.4022i | −0.450862 | − | 0.333137i | ||||
\(976\) | − | 26.7727i | − | 0.856973i | ||||||
\(977\) | 21.0624i | 0.673845i | 0.941532 | + | 0.336923i | \(0.109386\pi\) | ||||
−0.941532 | + | 0.336923i | \(0.890614\pi\) | |||||||
\(978\) | −40.2021 | − | 29.7048i | −1.28552 | − | 0.949856i | ||||
\(979\) | 15.2657i | 0.487895i | ||||||||
\(980\) | 8.39902 | − | 2.39842i | 0.268297 | − | 0.0766147i | ||||
\(981\) | 17.6527 | + | 57.4544i | 0.563608 | + | 1.83438i | ||||
\(982\) | 15.0880 | 0.481478 | ||||||||
\(983\) | 8.69359 | 0.277282 | 0.138641 | − | 0.990343i | \(-0.455727\pi\) | ||||
0.138641 | + | 0.990343i | \(0.455727\pi\) | |||||||
\(984\) | 2.32731 | + | 1.71962i | 0.0741920 | + | 0.0548196i | ||||
\(985\) | − | 18.0582i | − | 0.575383i | ||||||
\(986\) | −8.65594 | −0.275661 | ||||||||
\(987\) | −1.94853 | − | 1.05760i | −0.0620223 | − | 0.0336637i | ||||
\(988\) | 12.2761 | 0.390554 | ||||||||
\(989\) | 9.21486i | 0.293015i | ||||||||
\(990\) | 2.17118 | + | 7.06653i | 0.0690045 | + | 0.224589i | ||||
\(991\) | −3.59873 | −0.114318 | −0.0571588 | − | 0.998365i | \(-0.518204\pi\) | ||||
−0.0571588 | + | 0.998365i | \(0.518204\pi\) | |||||||
\(992\) | 26.4587 | 0.840066 | ||||||||
\(993\) | −3.56768 | + | 4.82845i | −0.113217 | + | 0.153226i | ||||
\(994\) | 6.23929 | + | 44.5721i | 0.197898 | + | 1.41374i | ||||
\(995\) | 22.3608i | 0.708885i | ||||||||
\(996\) | 6.28764 | − | 8.50959i | 0.199231 | − | 0.269637i | ||||
\(997\) | 3.11530i | 0.0986626i | 0.998782 | + | 0.0493313i | \(0.0157090\pi\) | ||||
−0.998782 | + | 0.0493313i | \(0.984291\pi\) | |||||||
\(998\) | 64.0566i | 2.02768i | ||||||||
\(999\) | −37.2170 | − | 13.0922i | −1.17749 | − | 0.414218i |
(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 | 231.2.e.a.188.8 | yes | 28 | |
3.2 | odd | 2 | inner | 231.2.e.a.188.21 | yes | 28 | |
7.6 | odd | 2 | inner | 231.2.e.a.188.7 | ✓ | 28 | |
21.20 | even | 2 | inner | 231.2.e.a.188.22 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.e.a.188.7 | ✓ | 28 | 7.6 | odd | 2 | inner | |
231.2.e.a.188.8 | yes | 28 | 1.1 | even | 1 | trivial | |
231.2.e.a.188.21 | yes | 28 | 3.2 | odd | 2 | inner | |
231.2.e.a.188.22 | yes | 28 | 21.20 | even | 2 | inner |