Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1223810289.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.1 | ||
Root | \(1.31686 + 2.28087i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.2.e.c.151.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31686 | − | 2.28087i | −0.931162 | − | 1.61282i | −0.781339 | − | 0.624107i | \(-0.785463\pi\) |
−0.149823 | − | 0.988713i | \(-0.547870\pi\) | |||||||
\(3\) | −1.71558 | + | 0.238330i | −0.990488 | + | 0.137600i | ||||
\(4\) | −2.46825 | + | 4.27513i | −1.23412 | + | 2.13757i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.80278 | + | 3.59916i | 1.14423 | + | 1.46935i | ||||
\(7\) | 0.898714 | + | 1.55662i | 0.339682 | + | 0.588346i | 0.984373 | − | 0.176097i | \(-0.0563473\pi\) |
−0.644691 | + | 0.764443i | \(0.723014\pi\) | |||||||
\(8\) | 7.73393 | 2.73436 | ||||||||
\(9\) | 2.88640 | − | 0.817746i | 0.962133 | − | 0.272582i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.904062 | − | 1.56588i | −0.272585 | − | 0.472131i | 0.696938 | − | 0.717131i | \(-0.254545\pi\) |
−0.969523 | + | 0.245000i | \(0.921212\pi\) | |||||||
\(12\) | 3.21558 | − | 7.92257i | 0.928257 | − | 2.28705i | ||||
\(13\) | −0.985914 | + | 1.70765i | −0.273443 | + | 0.473618i | −0.969741 | − | 0.244135i | \(-0.921496\pi\) |
0.696298 | + | 0.717753i | \(0.254829\pi\) | |||||||
\(14\) | 2.36696 | − | 4.09970i | 0.632598 | − | 1.09569i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.24801 | − | 9.08982i | −1.31200 | − | 2.27246i | ||||
\(17\) | 4.80812 | 1.16614 | 0.583071 | − | 0.812421i | \(-0.301851\pi\) | ||||
0.583071 | + | 0.812421i | \(0.301851\pi\) | |||||||
\(18\) | −5.66616 | − | 5.50664i | −1.33553 | − | 1.29793i | ||||
\(19\) | 2.96467 | 0.680142 | 0.340071 | − | 0.940400i | \(-0.389549\pi\) | ||||
0.340071 | + | 0.940400i | \(0.389549\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.91280 | − | 2.45630i | −0.417407 | − | 0.536010i | ||||
\(22\) | −2.38105 | + | 4.12410i | −0.507641 | + | 0.879261i | ||||
\(23\) | 0.866963 | − | 1.50162i | 0.180774 | − | 0.313110i | −0.761370 | − | 0.648317i | \(-0.775473\pi\) |
0.942144 | + | 0.335207i | \(0.108806\pi\) | |||||||
\(24\) | −13.2681 | + | 1.84323i | −2.70835 | + | 0.376247i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.19325 | 1.01848 | ||||||||
\(27\) | −4.75694 | + | 2.09082i | −0.915473 | + | 0.402379i | ||||
\(28\) | −8.87300 | −1.67684 | ||||||||
\(29\) | 3.68382 | + | 6.38057i | 0.684069 | + | 1.18484i | 0.973728 | + | 0.227713i | \(0.0731247\pi\) |
−0.289659 | + | 0.957130i | \(0.593542\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.31151 | − | 2.27161i | 0.235555 | − | 0.407993i | −0.723879 | − | 0.689927i | \(-0.757643\pi\) |
0.959434 | + | 0.281934i | \(0.0909760\pi\) | |||||||
\(32\) | −6.08789 | + | 10.5445i | −1.07620 | + | 1.86403i | ||||
\(33\) | 1.92418 | + | 2.47092i | 0.334957 | + | 0.430132i | ||||
\(34\) | −6.33163 | − | 10.9667i | −1.08587 | − | 1.88078i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.62838 | + | 14.3581i | −0.604729 | + | 2.39302i | ||||
\(37\) | 11.6351 | 1.91280 | 0.956399 | − | 0.292063i | \(-0.0943417\pi\) | ||||
0.956399 | + | 0.292063i | \(0.0943417\pi\) | |||||||
\(38\) | −3.90406 | − | 6.76203i | −0.633322 | − | 1.09695i | ||||
\(39\) | 1.28442 | − | 3.16458i | 0.205673 | − | 0.506738i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.23324 | − | 2.13603i | 0.192600 | − | 0.333592i | −0.753511 | − | 0.657435i | \(-0.771641\pi\) |
0.946111 | + | 0.323842i | \(0.104975\pi\) | |||||||
\(42\) | −3.08362 | + | 7.59746i | −0.475813 | + | 1.17231i | ||||
\(43\) | 3.63907 | + | 6.30306i | 0.554953 | + | 0.961207i | 0.997907 | + | 0.0646628i | \(0.0205972\pi\) |
−0.442954 | + | 0.896544i | \(0.646069\pi\) | |||||||
\(44\) | 8.92580 | 1.34562 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.56668 | −0.673321 | ||||||||
\(47\) | −3.14604 | − | 5.44910i | −0.458897 | − | 0.794833i | 0.540006 | − | 0.841661i | \(-0.318422\pi\) |
−0.998903 | + | 0.0468283i | \(0.985089\pi\) | |||||||
\(48\) | 11.1697 | + | 14.3435i | 1.61221 | + | 2.07031i | ||||
\(49\) | 1.88463 | − | 3.26427i | 0.269233 | − | 0.466324i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.24870 | + | 1.14592i | −1.15505 | + | 0.160461i | ||||
\(52\) | −4.86696 | − | 8.42983i | −0.674926 | − | 1.16901i | ||||
\(53\) | 1.72540 | 0.237001 | 0.118501 | − | 0.992954i | \(-0.462191\pi\) | ||||
0.118501 | + | 0.992954i | \(0.462191\pi\) | |||||||
\(54\) | 11.0331 | + | 8.09664i | 1.50142 | + | 1.10181i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.95059 | + | 12.0388i | 0.928811 | + | 1.60875i | ||||
\(57\) | −5.08612 | + | 0.706570i | −0.673673 | + | 0.0935875i | ||||
\(58\) | 9.70218 | − | 16.8047i | 1.27396 | − | 2.20656i | ||||
\(59\) | −5.51300 | + | 9.54880i | −0.717732 | + | 1.24315i | 0.244165 | + | 0.969734i | \(0.421486\pi\) |
−0.961896 | + | 0.273414i | \(0.911847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.33521 | + | 10.9729i | 0.811141 | + | 1.40494i | 0.912066 | + | 0.410043i | \(0.134486\pi\) |
−0.100925 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(62\) | −6.90833 | −0.877358 | ||||||||
\(63\) | 3.86696 | + | 3.75810i | 0.487192 | + | 0.473476i | ||||
\(64\) | 11.0756 | 1.38445 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.10197 | − | 7.64268i | 0.381826 | − | 0.940748i | ||||
\(67\) | −4.55187 | + | 7.88407i | −0.556100 | + | 0.963193i | 0.441717 | + | 0.897154i | \(0.354369\pi\) |
−0.997817 | + | 0.0660386i | \(0.978964\pi\) | |||||||
\(68\) | −11.8676 | + | 20.5554i | −1.43916 | + | 2.49271i | ||||
\(69\) | −1.12946 | + | 2.78277i | −0.135971 | + | 0.335006i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.27460 | 0.151268 | 0.0756338 | − | 0.997136i | \(-0.475902\pi\) | ||||
0.0756338 | + | 0.997136i | \(0.475902\pi\) | |||||||
\(72\) | 22.3232 | − | 6.32439i | 2.63081 | − | 0.745336i | ||||
\(73\) | −3.58770 | −0.419908 | −0.209954 | − | 0.977711i | \(-0.567331\pi\) | ||||
−0.209954 | + | 0.977711i | \(0.567331\pi\) | |||||||
\(74\) | −15.3218 | − | 26.5382i | −1.78112 | − | 3.08500i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.31755 | + | 12.6744i | −0.839380 | + | 1.45385i | ||||
\(77\) | 1.62499 | − | 2.81456i | 0.185184 | − | 0.320749i | ||||
\(78\) | −8.90941 | + | 1.23771i | −1.00879 | + | 0.140143i | ||||
\(79\) | −1.05545 | − | 1.82809i | −0.118747 | − | 0.205676i | 0.800524 | − | 0.599300i | \(-0.204555\pi\) |
−0.919272 | + | 0.393624i | \(0.871221\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.66258 | − | 4.72068i | 0.851398 | − | 0.524520i | ||||
\(82\) | −6.49602 | −0.717366 | ||||||||
\(83\) | −0.549415 | − | 0.951614i | −0.0603061 | − | 0.104453i | 0.834296 | − | 0.551317i | \(-0.185874\pi\) |
−0.894602 | + | 0.446863i | \(0.852541\pi\) | |||||||
\(84\) | 15.2223 | − | 2.11470i | 1.66089 | − | 0.230733i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.58431 | − | 16.6005i | 1.03350 | − | 1.79008i | ||||
\(87\) | −7.84056 | − | 10.0684i | −0.840596 | − | 1.07944i | ||||
\(88\) | −6.99195 | − | 12.1104i | −0.745344 | − | 1.29097i | ||||
\(89\) | −13.2935 | −1.40910 | −0.704552 | − | 0.709653i | \(-0.748852\pi\) | ||||
−0.704552 | + | 0.709653i | \(0.748852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.54422 | −0.371535 | ||||||||
\(92\) | 4.27976 | + | 7.41277i | 0.446196 | + | 0.772834i | ||||
\(93\) | −1.70861 | + | 4.20969i | −0.177174 | + | 0.436524i | ||||
\(94\) | −8.28580 | + | 14.3514i | −0.854615 | + | 1.48024i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.93115 | − | 19.5409i | 0.809470 | − | 1.99438i | ||||
\(97\) | 1.91638 | + | 3.31926i | 0.194579 | + | 0.337020i | 0.946762 | − | 0.321933i | \(-0.104333\pi\) |
−0.752184 | + | 0.658954i | \(0.770999\pi\) | |||||||
\(98\) | −9.92718 | −1.00280 | ||||||||
\(99\) | −3.88998 | − | 3.78046i | −0.390957 | − | 0.379951i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.27618 | − | 5.67452i | −0.325993 | − | 0.564636i | 0.655720 | − | 0.755004i | \(-0.272365\pi\) |
−0.981713 | + | 0.190368i | \(0.939032\pi\) | |||||||
\(102\) | 13.4761 | + | 17.3052i | 1.33433 | + | 1.71347i | ||||
\(103\) | 4.03779 | − | 6.99365i | 0.397855 | − | 0.689105i | −0.595606 | − | 0.803277i | \(-0.703088\pi\) |
0.993461 | + | 0.114172i | \(0.0364214\pi\) | |||||||
\(104\) | −7.62499 | + | 13.2069i | −0.747691 | + | 1.29504i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.27211 | − | 3.93541i | −0.220687 | − | 0.382241i | ||||
\(107\) | −8.97674 | −0.867814 | −0.433907 | − | 0.900958i | \(-0.642865\pi\) | ||||
−0.433907 | + | 0.900958i | \(0.642865\pi\) | |||||||
\(108\) | 2.80278 | − | 25.4972i | 0.269697 | − | 2.45347i | ||||
\(109\) | −6.34164 | −0.607419 | −0.303710 | − | 0.952765i | \(-0.598225\pi\) | ||||
−0.303710 | + | 0.952765i | \(0.598225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.9609 | + | 2.77299i | −1.89460 | + | 0.263201i | ||||
\(112\) | 9.43292 | − | 16.3383i | 0.891327 | − | 1.54382i | ||||
\(113\) | 7.45127 | − | 12.9060i | 0.700957 | − | 1.21409i | −0.267174 | − | 0.963648i | \(-0.586090\pi\) |
0.968131 | − | 0.250444i | \(-0.0805767\pi\) | |||||||
\(114\) | 8.30931 | + | 10.6703i | 0.778238 | + | 0.999367i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −36.3704 | −3.37691 | ||||||||
\(117\) | −1.44931 | + | 5.73519i | −0.133989 | + | 0.530219i | ||||
\(118\) | 29.0394 | 2.67330 | ||||||||
\(119\) | 4.32113 | + | 7.48441i | 0.396117 | + | 0.686095i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.86534 | − | 6.69497i | 0.351395 | − | 0.608634i | ||||
\(122\) | 16.6852 | − | 28.8996i | 1.51061 | − | 2.61645i | ||||
\(123\) | −1.60663 | + | 3.95845i | −0.144865 | + | 0.356921i | ||||
\(124\) | 6.47428 | + | 11.2138i | 0.581408 | + | 1.00703i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.47948 | − | 13.7689i | 0.309977 | − | 1.22663i | ||||
\(127\) | 3.62303 | 0.321492 | 0.160746 | − | 0.986996i | \(-0.448610\pi\) | ||||
0.160746 | + | 0.986996i | \(0.448610\pi\) | |||||||
\(128\) | −2.40922 | − | 4.17289i | −0.212947 | − | 0.368835i | ||||
\(129\) | −7.74531 | − | 9.94607i | −0.681936 | − | 0.875703i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.64673 | + | 6.31631i | −0.318616 | + | 0.551859i | −0.980200 | − | 0.198012i | \(-0.936551\pi\) |
0.661584 | + | 0.749871i | \(0.269885\pi\) | |||||||
\(132\) | −15.3129 | + | 2.12729i | −1.33282 | + | 0.185157i | ||||
\(133\) | 2.66439 | + | 4.61486i | 0.231032 | + | 0.400159i | ||||
\(134\) | 23.9767 | 2.07127 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 37.1857 | 3.18865 | ||||||||
\(137\) | 3.56310 | + | 6.17148i | 0.304417 | + | 0.527265i | 0.977131 | − | 0.212637i | \(-0.0682052\pi\) |
−0.672715 | + | 0.739902i | \(0.734872\pi\) | |||||||
\(138\) | 7.83449 | − | 1.08838i | 0.666916 | − | 0.0926488i | ||||
\(139\) | 7.35533 | − | 12.7398i | 0.623871 | − | 1.08058i | −0.364887 | − | 0.931052i | \(-0.618892\pi\) |
0.988758 | − | 0.149525i | \(-0.0477744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.69595 | + | 8.59855i | 0.563901 | + | 0.724128i | ||||
\(142\) | −1.67848 | − | 2.90721i | −0.140855 | − | 0.243967i | ||||
\(143\) | 3.56531 | 0.298146 | ||||||||
\(144\) | −22.5810 | − | 21.9453i | −1.88175 | − | 1.82878i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.72450 | + | 8.18308i | 0.391003 | + | 0.677236i | ||||
\(147\) | −2.45525 | + | 6.04927i | −0.202505 | + | 0.498935i | ||||
\(148\) | −28.7183 | + | 49.7416i | −2.36063 | + | 4.08873i | ||||
\(149\) | 0.282655 | − | 0.489572i | 0.0231560 | − | 0.0401073i | −0.854215 | − | 0.519920i | \(-0.825962\pi\) |
0.877371 | + | 0.479812i | \(0.159295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0766925 | − | 0.132835i | −0.00624115 | − | 0.0108100i | 0.862888 | − | 0.505395i | \(-0.168653\pi\) |
−0.869129 | + | 0.494585i | \(0.835320\pi\) | |||||||
\(152\) | 22.9285 | 1.85975 | ||||||||
\(153\) | 13.8782 | − | 3.93183i | 1.12198 | − | 0.317869i | ||||
\(154\) | −8.55953 | −0.689746 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.3587 | + | 13.3021i | 0.829362 | + | 1.06502i | ||||
\(157\) | 5.73035 | − | 9.92525i | 0.457332 | − | 0.792121i | −0.541487 | − | 0.840709i | \(-0.682139\pi\) |
0.998819 | + | 0.0485874i | \(0.0154719\pi\) | |||||||
\(158\) | −2.77976 | + | 4.81469i | −0.221146 | + | 0.383036i | ||||
\(159\) | −2.96005 | + | 0.411214i | −0.234747 | + | 0.0326114i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.11661 | 0.245623 | ||||||||
\(162\) | −20.8578 | − | 11.2609i | −1.63875 | − | 0.884738i | ||||
\(163\) | −22.0595 | −1.72783 | −0.863915 | − | 0.503637i | \(-0.831995\pi\) | ||||
−0.863915 | + | 0.503637i | \(0.831995\pi\) | |||||||
\(164\) | 6.08789 | + | 10.5445i | 0.475384 | + | 0.823389i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.44701 | + | 2.50629i | −0.112310 | + | 0.194526i | ||||
\(167\) | −8.53421 | + | 14.7817i | −0.660397 | + | 1.14384i | 0.320115 | + | 0.947379i | \(0.396279\pi\) |
−0.980511 | + | 0.196462i | \(0.937055\pi\) | |||||||
\(168\) | −14.7935 | − | 18.9969i | −1.14134 | − | 1.46564i | ||||
\(169\) | 4.55595 | + | 7.89113i | 0.350457 | + | 0.607010i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.55722 | − | 2.42435i | 0.654387 | − | 0.185395i | ||||
\(172\) | −35.9285 | −2.73953 | ||||||||
\(173\) | −5.97233 | − | 10.3444i | −0.454067 | − | 0.786468i | 0.544567 | − | 0.838718i | \(-0.316694\pi\) |
−0.998634 | + | 0.0522497i | \(0.983361\pi\) | |||||||
\(174\) | −12.6398 | + | 31.1420i | −0.958218 | + | 2.36087i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.48906 | + | 16.4355i | −0.715265 | + | 1.23887i | ||||
\(177\) | 7.18221 | − | 17.6956i | 0.539848 | − | 1.33008i | ||||
\(178\) | 17.5056 | + | 30.3207i | 1.31210 | + | 2.27263i | ||||
\(179\) | 8.54921 | 0.638998 | 0.319499 | − | 0.947587i | \(-0.396485\pi\) | ||||
0.319499 | + | 0.947587i | \(0.396485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5524 | −0.784351 | −0.392176 | − | 0.919890i | \(-0.628277\pi\) | ||||
−0.392176 | + | 0.919890i | \(0.628277\pi\) | |||||||
\(182\) | 4.66724 | + | 8.08390i | 0.345959 | + | 0.599219i | ||||
\(183\) | −13.4837 | − | 17.3150i | −0.996744 | − | 1.27996i | ||||
\(184\) | 6.70503 | − | 11.6135i | 0.494301 | − | 0.856155i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.8518 | − | 1.64646i | 0.869013 | − | 0.120724i | ||||
\(187\) | −4.34684 | − | 7.52895i | −0.317873 | − | 0.550571i | ||||
\(188\) | 31.0608 | 2.26534 | ||||||||
\(189\) | −7.52973 | − | 5.52569i | −0.547708 | − | 0.401935i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.66862 | + | 15.0145i | 0.627239 | + | 1.08641i | 0.988103 | + | 0.153792i | \(0.0491485\pi\) |
−0.360864 | + | 0.932618i | \(0.617518\pi\) | |||||||
\(192\) | −19.0010 | + | 2.63964i | −1.37128 | + | 0.190500i | ||||
\(193\) | −0.779763 | + | 1.35059i | −0.0561286 | + | 0.0972175i | −0.892724 | − | 0.450603i | \(-0.851209\pi\) |
0.836596 | + | 0.547821i | \(0.184542\pi\) | |||||||
\(194\) | 5.04721 | − | 8.74202i | 0.362369 | − | 0.627641i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.30346 | + | 16.1141i | 0.664533 | + | 1.15100i | ||||
\(197\) | 17.9767 | 1.28079 | 0.640395 | − | 0.768046i | \(-0.278771\pi\) | ||||
0.640395 | + | 0.768046i | \(0.278771\pi\) | |||||||
\(198\) | −3.50019 | + | 13.8509i | −0.248748 | + | 0.984339i | ||||
\(199\) | 11.0225 | 0.781362 | 0.390681 | − | 0.920526i | \(-0.372240\pi\) | ||||
0.390681 | + | 0.920526i | \(0.372240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.93007 | − | 14.6106i | 0.418275 | − | 1.03055i | ||||
\(202\) | −8.62856 | + | 14.9451i | −0.607104 | + | 1.05153i | ||||
\(203\) | −6.62141 | + | 11.4686i | −0.464732 | + | 0.804939i | ||||
\(204\) | 15.4609 | − | 38.0927i | 1.08248 | − | 2.66702i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21.2688 | −1.48187 | ||||||||
\(207\) | 1.27445 | − | 5.04324i | 0.0885806 | − | 0.350529i | ||||
\(208\) | 20.6964 | 1.43503 | ||||||||
\(209\) | −2.68025 | − | 4.64232i | −0.185397 | − | 0.321116i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9643 | − | 20.7227i | 0.823655 | − | 1.42661i | −0.0792886 | − | 0.996852i | \(-0.525265\pi\) |
0.902943 | − | 0.429760i | \(-0.141402\pi\) | |||||||
\(212\) | −4.25871 | + | 7.37630i | −0.292489 | + | 0.506606i | ||||
\(213\) | −2.18668 | + | 0.303776i | −0.149829 | + | 0.0208144i | ||||
\(214\) | 11.8211 | + | 20.4748i | 0.808076 | + | 1.39963i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −36.7898 | + | 16.1703i | −2.50323 | + | 1.10025i | ||||
\(217\) | 4.71470 | 0.320055 | ||||||||
\(218\) | 8.35107 | + | 14.4645i | 0.565606 | + | 0.979658i | ||||
\(219\) | 6.15497 | − | 0.855056i | 0.415914 | − | 0.0577793i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.74040 | + | 8.21061i | −0.318874 | + | 0.552305i | ||||
\(222\) | 32.6106 | + | 41.8766i | 2.18868 | + | 2.81057i | ||||
\(223\) | −10.8553 | − | 18.8020i | −0.726927 | − | 1.25907i | −0.958176 | − | 0.286180i | \(-0.907615\pi\) |
0.231249 | − | 0.972895i | \(-0.425719\pi\) | |||||||
\(224\) | −21.8851 | −1.46226 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −39.2492 | −2.61082 | ||||||||
\(227\) | −7.05010 | − | 12.2111i | −0.467932 | − | 0.810481i | 0.531397 | − | 0.847123i | \(-0.321667\pi\) |
−0.999328 | + | 0.0366416i | \(0.988334\pi\) | |||||||
\(228\) | 9.53312 | − | 23.4878i | 0.631347 | − | 1.55552i | ||||
\(229\) | −1.83879 | + | 3.18488i | −0.121511 | + | 0.210463i | −0.920364 | − | 0.391064i | \(-0.872107\pi\) |
0.798853 | + | 0.601526i | \(0.205441\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.11699 | + | 5.21587i | −0.139288 | + | 0.343179i | ||||
\(232\) | 28.4904 | + | 49.3469i | 1.87049 | + | 3.23978i | ||||
\(233\) | −5.34164 | −0.349943 | −0.174971 | − | 0.984574i | \(-0.555983\pi\) | ||||
−0.174971 | + | 0.984574i | \(0.555983\pi\) | |||||||
\(234\) | 14.9898 | − | 4.24676i | 0.979913 | − | 0.277619i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −27.2149 | − | 47.1376i | −1.77154 | − | 3.06840i | ||||
\(237\) | 2.24639 | + | 2.88469i | 0.145919 | + | 0.187380i | ||||
\(238\) | 11.3807 | − | 19.7119i | 0.737698 | − | 1.27773i | ||||
\(239\) | 11.0167 | − | 19.0815i | 0.712613 | − | 1.23428i | −0.251260 | − | 0.967920i | \(-0.580845\pi\) |
0.963873 | − | 0.266362i | \(-0.0858218\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.32358 | + | 16.1489i | 0.600585 | + | 1.04024i | 0.992733 | + | 0.120341i | \(0.0383988\pi\) |
−0.392148 | + | 0.919902i | \(0.628268\pi\) | |||||||
\(242\) | −20.3605 | −1.30882 | ||||||||
\(243\) | −12.0207 | + | 9.92491i | −0.771126 | + | 0.636683i | ||||
\(244\) | −62.5475 | −4.00420 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.1444 | − | 1.54820i | 0.710542 | − | 0.0987095i | ||||
\(247\) | −2.92291 | + | 5.06263i | −0.185980 | + | 0.322127i | ||||
\(248\) | 10.1431 | − | 17.5684i | 0.644091 | − | 1.11560i | ||||
\(249\) | 1.16936 | + | 1.50162i | 0.0741052 | + | 0.0951616i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6929 | 0.927407 | 0.463704 | − | 0.885990i | \(-0.346520\pi\) | ||||
0.463704 | + | 0.885990i | \(0.346520\pi\) | |||||||
\(252\) | −25.6110 | + | 7.25586i | −1.61334 | + | 0.457076i | ||||
\(253\) | −3.13515 | −0.197105 | ||||||||
\(254\) | −4.77103 | − | 8.26366i | −0.299361 | − | 0.518508i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.73035 | − | 8.19320i | 0.295647 | − | 0.512075i | ||||
\(257\) | −11.1045 | + | 19.2335i | −0.692678 | + | 1.19975i | 0.278280 | + | 0.960500i | \(0.410236\pi\) |
−0.970957 | + | 0.239253i | \(0.923098\pi\) | |||||||
\(258\) | −12.4862 | + | 30.7637i | −0.777357 | + | 1.91526i | ||||
\(259\) | 10.4566 | + | 18.1114i | 0.649743 | + | 1.12539i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.8507 | + | 15.4044i | 0.981132 | + | 0.953510i | ||||
\(262\) | 19.2089 | 1.18673 | ||||||||
\(263\) | −2.87001 | − | 4.97100i | −0.176972 | − | 0.306525i | 0.763870 | − | 0.645370i | \(-0.223297\pi\) |
−0.940842 | + | 0.338846i | \(0.889964\pi\) | |||||||
\(264\) | 14.8815 | + | 19.1099i | 0.915892 | + | 1.17613i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.01727 | − | 12.1543i | 0.430256 | − | 0.745226i | ||||
\(267\) | 22.8059 | − | 3.16823i | 1.39570 | − | 0.193892i | ||||
\(268\) | −22.4703 | − | 38.9197i | −1.37259 | − | 2.37740i | ||||
\(269\) | −15.6162 | −0.952139 | −0.476070 | − | 0.879408i | \(-0.657939\pi\) | ||||
−0.476070 | + | 0.879408i | \(0.657939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.75315 | −0.410225 | −0.205112 | − | 0.978738i | \(-0.565756\pi\) | ||||
−0.205112 | + | 0.978738i | \(0.565756\pi\) | |||||||
\(272\) | −25.2331 | − | 43.7050i | −1.52998 | − | 2.65000i | ||||
\(273\) | 6.08037 | − | 0.844693i | 0.368001 | − | 0.0511232i | ||||
\(274\) | 9.38423 | − | 16.2540i | 0.566922 | − | 0.981938i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.10894 | − | 11.6972i | −0.548294 | − | 0.704087i | ||||
\(277\) | −15.1483 | − | 26.2376i | −0.910172 | − | 1.57646i | −0.813820 | − | 0.581118i | \(-0.802616\pi\) |
−0.0963529 | − | 0.995347i | \(-0.530718\pi\) | |||||||
\(278\) | −38.7438 | −2.32370 | ||||||||
\(279\) | 1.92795 | − | 7.62925i | 0.115423 | − | 0.456751i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.31755 | − | 16.1385i | −0.555838 | − | 0.962740i | −0.997838 | − | 0.0657249i | \(-0.979064\pi\) |
0.441999 | − | 0.897015i | \(-0.354269\pi\) | |||||||
\(282\) | 10.7945 | − | 26.5957i | 0.642805 | − | 1.58375i | ||||
\(283\) | 2.83683 | − | 4.91354i | 0.168632 | − | 0.292079i | −0.769307 | − | 0.638879i | \(-0.779398\pi\) |
0.937939 | + | 0.346800i | \(0.112732\pi\) | |||||||
\(284\) | −3.14604 | + | 5.44910i | −0.186683 | + | 0.323345i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.69502 | − | 8.13201i | −0.277622 | − | 0.480856i | ||||
\(287\) | 4.43332 | 0.261690 | ||||||||
\(288\) | −8.94931 | + | 35.4141i | −0.527343 | + | 2.08679i | ||||
\(289\) | 6.11806 | 0.359886 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.07877 | − | 5.23772i | −0.239102 | − | 0.307040i | ||||
\(292\) | 8.85533 | − | 15.3379i | 0.518219 | − | 0.897582i | ||||
\(293\) | −9.13867 | + | 15.8286i | −0.533887 | + | 0.924720i | 0.465329 | + | 0.885138i | \(0.345936\pi\) |
−0.999216 | + | 0.0395819i | \(0.987397\pi\) | |||||||
\(294\) | 17.0308 | − | 2.36594i | 0.993257 | − | 0.137985i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 89.9850 | 5.23027 | ||||||||
\(297\) | 7.57454 | + | 5.55857i | 0.439520 | + | 0.322541i | ||||
\(298\) | −1.48887 | −0.0862478 | ||||||||
\(299\) | 1.70950 | + | 2.96094i | 0.0988631 | + | 0.171236i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.54097 | + | 11.3293i | −0.377015 | + | 0.653009i | ||||
\(302\) | −0.201987 | + | 0.349852i | −0.0116230 | + | 0.0201317i | ||||
\(303\) | 6.97295 | + | 8.95425i | 0.400585 | + | 0.514408i | ||||
\(304\) | −15.5586 | − | 26.9483i | −0.892349 | − | 1.54559i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −27.2436 | − | 26.4766i | −1.55741 | − | 1.51357i | ||||
\(307\) | −15.5050 | −0.884915 | −0.442458 | − | 0.896789i | \(-0.645893\pi\) | ||||
−0.442458 | + | 0.896789i | \(0.645893\pi\) | |||||||
\(308\) | 8.02174 | + | 13.8941i | 0.457081 | + | 0.791688i | ||||
\(309\) | −5.26033 | + | 12.9605i | −0.299250 | + | 0.737295i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.2232 | + | 26.3673i | −0.863228 | + | 1.49515i | 0.00556798 | + | 0.999984i | \(0.498228\pi\) |
−0.868796 | + | 0.495170i | \(0.835106\pi\) | |||||||
\(312\) | 9.93365 | − | 24.4746i | 0.562382 | − | 1.38560i | ||||
\(313\) | 3.47468 | + | 6.01832i | 0.196401 | + | 0.340176i | 0.947359 | − | 0.320174i | \(-0.103741\pi\) |
−0.750958 | + | 0.660350i | \(0.770408\pi\) | |||||||
\(314\) | −30.1843 | −1.70340 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4205 | 0.586196 | ||||||||
\(317\) | 8.07253 | + | 13.9820i | 0.453398 | + | 0.785309i | 0.998595 | − | 0.0529995i | \(-0.0168782\pi\) |
−0.545196 | + | 0.838308i | \(0.683545\pi\) | |||||||
\(318\) | 4.83590 | + | 6.20998i | 0.271184 | + | 0.348238i | ||||
\(319\) | 6.66081 | − | 11.5369i | 0.372934 | − | 0.645940i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.4003 | − | 2.13943i | 0.859560 | − | 0.119411i | ||||
\(322\) | −4.10414 | − | 7.10858i | −0.228715 | − | 0.396146i | ||||
\(323\) | 14.2545 | 0.793142 | ||||||||
\(324\) | 1.26838 | + | 44.4104i | 0.0704655 | + | 2.46724i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.0493 | + | 50.3148i | 1.60889 | + | 2.78668i | ||||
\(327\) | 10.8796 | − | 1.51140i | 0.601642 | − | 0.0835808i | ||||
\(328\) | 9.53779 | − | 16.5199i | 0.526636 | − | 0.912160i | ||||
\(329\) | 5.65478 | − | 9.79436i | 0.311758 | − | 0.539981i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.31112 | − | 10.9312i | −0.346890 | − | 0.600832i | 0.638805 | − | 0.769369i | \(-0.279429\pi\) |
−0.985695 | + | 0.168537i | \(0.946096\pi\) | |||||||
\(332\) | 5.42437 | 0.297701 | ||||||||
\(333\) | 33.5835 | − | 9.51456i | 1.84037 | − | 0.521394i | ||||
\(334\) | 44.9535 | 2.45975 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.2890 | + | 30.2777i | −0.670419 | + | 1.65179i | ||||
\(337\) | 3.46020 | − | 5.99324i | 0.188489 | − | 0.326473i | −0.756258 | − | 0.654274i | \(-0.772974\pi\) |
0.944747 | + | 0.327801i | \(0.106308\pi\) | |||||||
\(338\) | 11.9991 | − | 20.7831i | 0.652665 | − | 1.13045i | ||||
\(339\) | −9.70734 | + | 23.9170i | −0.527230 | + | 1.29900i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.74276 | −0.256835 | ||||||||
\(342\) | −16.7983 | − | 16.3254i | −0.908348 | − | 0.882776i | ||||
\(343\) | 19.3570 | 1.04518 | ||||||||
\(344\) | 28.1443 | + | 48.7474i | 1.51744 | + | 2.62828i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.7295 | + | 27.2442i | −0.845621 | + | 1.46466i | ||||
\(347\) | −6.90317 | + | 11.9566i | −0.370581 | + | 0.641866i | −0.989655 | − | 0.143467i | \(-0.954175\pi\) |
0.619074 | + | 0.785333i | \(0.287508\pi\) | |||||||
\(348\) | 62.3962 | − | 8.66816i | 3.34479 | − | 0.464662i | ||||
\(349\) | −3.28384 | − | 5.68778i | −0.175780 | − | 0.304460i | 0.764651 | − | 0.644445i | \(-0.222911\pi\) |
−0.940431 | + | 0.339985i | \(0.889578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.11954 | − | 10.1846i | 0.0597564 | − | 0.543612i | ||||
\(352\) | 22.0153 | 1.17342 | ||||||||
\(353\) | 1.76250 | + | 3.05273i | 0.0938082 | + | 0.162481i | 0.909111 | − | 0.416555i | \(-0.136763\pi\) |
−0.815302 | + | 0.579035i | \(0.803429\pi\) | |||||||
\(354\) | −49.8194 | + | 6.92097i | −2.64787 | + | 0.367846i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 32.8116 | − | 56.8313i | 1.73901 | − | 3.01205i | ||||
\(357\) | −9.19698 | − | 11.8102i | −0.486756 | − | 0.625063i | ||||
\(358\) | −11.2581 | − | 19.4996i | −0.595010 | − | 1.03059i | ||||
\(359\) | 22.9285 | 1.21012 | 0.605061 | − | 0.796179i | \(-0.293149\pi\) | ||||
0.605061 | + | 0.796179i | \(0.293149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.2107 | −0.537407 | ||||||||
\(362\) | 13.8960 | + | 24.0686i | 0.730358 | + | 1.26502i | ||||
\(363\) | −5.03568 | + | 12.4070i | −0.264304 | + | 0.651196i | ||||
\(364\) | 8.74801 | − | 15.1520i | 0.458520 | − | 0.794181i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −21.7371 | + | 53.5560i | −1.13621 | + | 2.79942i | ||||
\(367\) | −2.08966 | − | 3.61939i | −0.109079 | − | 0.188931i | 0.806318 | − | 0.591482i | \(-0.201457\pi\) |
−0.915397 | + | 0.402551i | \(0.868124\pi\) | |||||||
\(368\) | −18.1993 | −0.948706 | ||||||||
\(369\) | 1.81289 | − | 7.17392i | 0.0943751 | − | 0.373459i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.55064 | + | 2.68578i | 0.0805051 | + | 0.139439i | ||||
\(372\) | −13.7797 | − | 17.6951i | −0.714444 | − | 0.917447i | ||||
\(373\) | −3.42045 | + | 5.92440i | −0.177104 | + | 0.306754i | −0.940888 | − | 0.338719i | \(-0.890006\pi\) |
0.763783 | + | 0.645473i | \(0.223340\pi\) | |||||||
\(374\) | −11.4484 | + | 19.8292i | −0.591982 | + | 1.02534i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.3312 | − | 42.1429i | −1.25479 | − | 2.17336i | ||||
\(377\) | −14.5277 | −0.748217 | ||||||||
\(378\) | −2.68776 | + | 24.4509i | −0.138244 | + | 1.25762i | ||||
\(379\) | −12.7764 | −0.656280 | −0.328140 | − | 0.944629i | \(-0.606422\pi\) | ||||
−0.328140 | + | 0.944629i | \(0.606422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.21558 | + | 0.863476i | −0.318434 | + | 0.0442372i | ||||
\(382\) | 22.8307 | − | 39.5440i | 1.16812 | − | 2.02325i | ||||
\(383\) | −3.76730 | + | 6.52515i | −0.192500 | + | 0.333420i | −0.946078 | − | 0.323939i | \(-0.894993\pi\) |
0.753578 | + | 0.657358i | \(0.228326\pi\) | |||||||
\(384\) | 5.12773 | + | 6.58472i | 0.261673 | + | 0.336025i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.10736 | 0.209059 | ||||||||
\(387\) | 15.6581 | + | 15.2173i | 0.795946 | + | 0.773538i | ||||
\(388\) | −18.9204 | −0.960538 | ||||||||
\(389\) | −2.72588 | − | 4.72135i | −0.138207 | − | 0.239382i | 0.788611 | − | 0.614893i | \(-0.210801\pi\) |
−0.926818 | + | 0.375511i | \(0.877467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.16847 | − | 7.22000i | 0.210808 | − | 0.365131i | ||||
\(392\) | 14.5756 | − | 25.2456i | 0.736177 | − | 1.27510i | ||||
\(393\) | 4.75087 | − | 11.7052i | 0.239649 | − | 0.590451i | ||||
\(394\) | −23.6729 | − | 41.0026i | −1.19262 | − | 2.06568i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 25.7634 | − | 7.29904i | 1.29466 | − | 0.366791i | ||||
\(397\) | −5.64549 | −0.283339 | −0.141670 | − | 0.989914i | \(-0.545247\pi\) | ||||
−0.141670 | + | 0.989914i | \(0.545247\pi\) | |||||||
\(398\) | −14.5151 | − | 25.1408i | −0.727574 | − | 1.26020i | ||||
\(399\) | −5.67082 | − | 7.28214i | −0.283896 | − | 0.364563i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.75209 | − | 4.76676i | 0.137433 | − | 0.238040i | −0.789091 | − | 0.614276i | \(-0.789448\pi\) |
0.926524 | + | 0.376235i | \(0.122782\pi\) | |||||||
\(402\) | −41.1339 | + | 5.71438i | −2.05157 | + | 0.285007i | ||||
\(403\) | 2.58608 | + | 4.47922i | 0.128822 | + | 0.223126i | ||||
\(404\) | 32.3458 | 1.60926 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.8779 | 1.73096 | ||||||||
\(407\) | −10.5188 | − | 18.2192i | −0.521400 | − | 0.903091i | ||||
\(408\) | −63.7948 | + | 8.86246i | −3.15831 | + | 0.438757i | ||||
\(409\) | −16.4265 | + | 28.4515i | −0.812238 | + | 1.40684i | 0.0990570 | + | 0.995082i | \(0.468417\pi\) |
−0.911295 | + | 0.411755i | \(0.864916\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.58362 | − | 9.73844i | −0.374072 | − | 0.480362i | ||||
\(412\) | 19.9325 | + | 34.5241i | 0.982005 | + | 1.70088i | ||||
\(413\) | −19.8184 | −0.975202 | ||||||||
\(414\) | −13.1813 | + | 3.73439i | −0.647824 | + | 0.183535i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.0043 | − | 20.7920i | −0.588558 | − | 1.01941i | ||||
\(417\) | −9.58235 | + | 23.6091i | −0.469250 | + | 1.15614i | ||||
\(418\) | −7.05903 | + | 12.2266i | −0.345268 | + | 0.598022i | ||||
\(419\) | −11.4295 | + | 19.7965i | −0.558369 | + | 0.967124i | 0.439264 | + | 0.898358i | \(0.355239\pi\) |
−0.997633 | + | 0.0687656i | \(0.978094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.97071 | − | 15.5377i | −0.437205 | − | 0.757262i | 0.560267 | − | 0.828312i | \(-0.310698\pi\) |
−0.997473 | + | 0.0710498i | \(0.977365\pi\) | |||||||
\(422\) | −63.0212 | −3.06782 | ||||||||
\(423\) | −13.5367 | − | 13.1556i | −0.658177 | − | 0.639648i | ||||
\(424\) | 13.3441 | 0.648046 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.57243 | + | 4.58750i | 0.173085 | + | 0.222265i | ||||
\(427\) | −11.3871 | + | 19.7230i | −0.551060 | + | 0.954463i | ||||
\(428\) | 22.1568 | − | 38.3768i | 1.07099 | − | 1.85501i | ||||
\(429\) | −6.11656 | + | 0.849720i | −0.295310 | + | 0.0410249i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.18871 | −0.298100 | −0.149050 | − | 0.988830i | \(-0.547622\pi\) | ||||
−0.149050 | + | 0.988830i | \(0.547622\pi\) | |||||||
\(432\) | 43.9697 | + | 32.2671i | 2.11549 | + | 1.55245i | ||||
\(433\) | −3.11806 | −0.149844 | −0.0749221 | − | 0.997189i | \(-0.523871\pi\) | ||||
−0.0749221 | + | 0.997189i | \(0.523871\pi\) | |||||||
\(434\) | −6.20861 | − | 10.7536i | −0.298023 | − | 0.516190i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.6528 | − | 27.1114i | 0.749631 | − | 1.29840i | ||||
\(437\) | 2.57026 | − | 4.45182i | 0.122952 | − | 0.212960i | ||||
\(438\) | −10.0555 | − | 12.9127i | −0.480471 | − | 0.616992i | ||||
\(439\) | −6.75494 | − | 11.6999i | −0.322396 | − | 0.558406i | 0.658586 | − | 0.752505i | \(-0.271155\pi\) |
−0.980982 | + | 0.194100i | \(0.937822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.77044 | − | 10.9631i | 0.131926 | − | 0.522054i | ||||
\(442\) | 24.9698 | 1.18769 | ||||||||
\(443\) | 12.1387 | + | 21.0248i | 0.576726 | + | 0.998918i | 0.995852 | + | 0.0909904i | \(0.0290032\pi\) |
−0.419126 | + | 0.907928i | \(0.637663\pi\) | |||||||
\(444\) | 37.4135 | − | 92.1799i | 1.77557 | − | 4.37466i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −28.5899 | + | 49.5192i | −1.35377 | + | 2.34480i | ||||
\(447\) | −0.368236 | + | 0.907263i | −0.0174169 | + | 0.0429121i | ||||
\(448\) | 9.95377 | + | 17.2404i | 0.470271 | + | 0.814534i | ||||
\(449\) | −24.1437 | −1.13941 | −0.569705 | − | 0.821849i | \(-0.692943\pi\) | ||||
−0.569705 | + | 0.821849i | \(0.692943\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.45970 | −0.209999 | ||||||||
\(452\) | 36.7832 | + | 63.7104i | 1.73014 | + | 2.99668i | ||||
\(453\) | 0.163230 | + | 0.209611i | 0.00766924 | + | 0.00984838i | ||||
\(454\) | −18.5680 | + | 32.1607i | −0.871440 | + | 1.50938i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −39.3357 | + | 5.46456i | −1.84206 | + | 0.255902i | ||||
\(457\) | 1.41078 | + | 2.44355i | 0.0659937 | + | 0.114304i | 0.897134 | − | 0.441758i | \(-0.145645\pi\) |
−0.831141 | + | 0.556062i | \(0.812312\pi\) | |||||||
\(458\) | 9.68573 | 0.452585 | ||||||||
\(459\) | −22.8720 | + | 10.0529i | −1.06757 | + | 0.469230i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.7286 | − | 18.5825i | −0.499681 | − | 0.865474i | 0.500318 | − | 0.865841i | \(-0.333216\pi\) |
−1.00000 | 0.000367761i | \(0.999883\pi\) | ||||||||
\(462\) | 14.6845 | − | 2.03999i | 0.683185 | − | 0.0949090i | ||||
\(463\) | 9.90167 | − | 17.1502i | 0.460170 | − | 0.797037i | −0.538799 | − | 0.842434i | \(-0.681122\pi\) |
0.998969 | + | 0.0453970i | \(0.0144553\pi\) | |||||||
\(464\) | 38.6655 | − | 66.9706i | 1.79500 | − | 3.10903i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.03421 | + | 12.1836i | 0.325853 | + | 0.564395i | ||||
\(467\) | 22.7210 | 1.05140 | 0.525701 | − | 0.850669i | \(-0.323803\pi\) | ||||
0.525701 | + | 0.850669i | \(0.323803\pi\) | |||||||
\(468\) | −20.9415 | − | 20.3519i | −0.968019 | − | 0.940767i | ||||
\(469\) | −16.3633 | −0.755588 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.46536 | + | 18.3932i | −0.343986 | + | 0.847516i | ||||
\(472\) | −42.6372 | + | 73.8497i | −1.96253 | + | 3.39921i | ||||
\(473\) | 6.57989 | − | 11.3967i | 0.302544 | − | 0.524021i | ||||
\(474\) | 3.62141 | − | 8.92247i | 0.166337 | − | 0.409822i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −42.6625 | −1.95543 | ||||||||
\(477\) | 4.98018 | − | 1.41094i | 0.228027 | − | 0.0646023i | ||||
\(478\) | −58.0300 | −2.65423 | ||||||||
\(479\) | −10.6440 | − | 18.4359i | −0.486336 | − | 0.842359i | 0.513541 | − | 0.858065i | \(-0.328334\pi\) |
−0.999877 | + | 0.0157065i | \(0.995000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4712 | + | 19.8687i | −0.523042 | + | 0.905935i | ||||
\(482\) | 24.5557 | − | 42.5318i | 1.11848 | − | 1.93727i | ||||
\(483\) | −5.34677 | + | 0.742781i | −0.243287 | + | 0.0337977i | ||||
\(484\) | 19.0813 | + | 33.0497i | 0.867330 | + | 1.50226i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 38.4670 | + | 14.3478i | 1.74490 | + | 0.650831i | ||||
\(487\) | −9.58690 | −0.434424 | −0.217212 | − | 0.976124i | \(-0.569696\pi\) | ||||
−0.217212 | + | 0.976124i | \(0.569696\pi\) | |||||||
\(488\) | 48.9961 | + | 84.8637i | 2.21795 | + | 3.84160i | ||||
\(489\) | 37.8447 | − | 5.25743i | 1.71140 | − | 0.237749i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.9222 | − | 32.7742i | 0.853945 | − | 1.47908i | −0.0236745 | − | 0.999720i | \(-0.507537\pi\) |
0.877620 | − | 0.479357i | \(-0.159130\pi\) | |||||||
\(492\) | −12.9573 | − | 16.6390i | −0.584160 | − | 0.750144i | ||||
\(493\) | 17.7123 | + | 30.6786i | 0.797721 | + | 1.38169i | ||||
\(494\) | 15.3963 | 0.692711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −27.5314 | −1.23619 | ||||||||
\(497\) | 1.14550 | + | 1.98407i | 0.0513829 | + | 0.0889977i | ||||
\(498\) | 1.88513 | − | 4.64459i | 0.0844745 | − | 0.208129i | ||||
\(499\) | −8.46266 | + | 14.6577i | −0.378840 | + | 0.656171i | −0.990894 | − | 0.134646i | \(-0.957010\pi\) |
0.612053 | + | 0.790816i | \(0.290344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.1182 | − | 27.3930i | 0.496723 | − | 1.22383i | ||||
\(502\) | −19.3485 | − | 33.5126i | −0.863566 | − | 1.49574i | ||||
\(503\) | 40.4168 | 1.80210 | 0.901048 | − | 0.433719i | \(-0.142799\pi\) | ||||
0.901048 | + | 0.433719i | \(0.142799\pi\) | |||||||
\(504\) | 29.9068 | + | 29.0649i | 1.33216 | + | 1.29465i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.12856 | + | 7.15088i | 0.183537 | + | 0.317896i | ||||
\(507\) | −9.69676 | − | 12.4520i | −0.430648 | − | 0.553013i | ||||
\(508\) | −8.94253 | + | 15.4889i | −0.396761 | + | 0.687210i | ||||
\(509\) | 20.7034 | − | 35.8593i | 0.917660 | − | 1.58943i | 0.114701 | − | 0.993400i | \(-0.463409\pi\) |
0.802959 | − | 0.596034i | \(-0.203258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.22431 | − | 5.58467i | −0.142635 | − | 0.247051i | ||||
\(512\) | −34.5537 | −1.52707 | ||||||||
\(513\) | −14.1028 | + | 6.19860i | −0.622652 | + | 0.273675i | ||||
\(514\) | 58.4922 | 2.57998 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 61.6381 | − | 8.56285i | 2.71347 | − | 0.376959i | ||||
\(517\) | −5.68843 | + | 9.85265i | −0.250177 | + | 0.433319i | ||||
\(518\) | 27.5398 | − | 47.7004i | 1.21003 | − | 2.09584i | ||||
\(519\) | 12.7113 | + | 16.3232i | 0.557966 | + | 0.716507i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0301 | −0.746103 | −0.373052 | − | 0.927811i | \(-0.621689\pi\) | ||||
−0.373052 | + | 0.927811i | \(0.621689\pi\) | |||||||
\(522\) | 14.2624 | − | 56.4389i | 0.624248 | − | 2.47026i | ||||
\(523\) | 9.57651 | 0.418751 | 0.209376 | − | 0.977835i | \(-0.432857\pi\) | ||||
0.209376 | + | 0.977835i | \(0.432857\pi\) | |||||||
\(524\) | −18.0021 | − | 31.1805i | −0.786424 | − | 1.36213i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.55880 | + | 13.0922i | −0.329579 | + | 0.570848i | ||||
\(527\) | 6.30592 | − | 10.9222i | 0.274690 | − | 0.475777i | ||||
\(528\) | 12.3621 | − | 30.4579i | 0.537992 | − | 1.32551i | ||||
\(529\) | 9.99675 | + | 17.3149i | 0.434641 | + | 0.752821i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.10422 | + | 32.0699i | −0.351693 | + | 1.39171i | ||||
\(532\) | −26.3055 | −1.14049 | ||||||||
\(533\) | 2.43174 | + | 4.21189i | 0.105330 | + | 0.182437i | ||||
\(534\) | −37.2586 | − | 47.8452i | −1.61234 | − | 2.07047i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −35.2038 | + | 60.9748i | −1.52057 | + | 2.63371i | ||||
\(537\) | −14.6668 | + | 2.03753i | −0.632920 | + | 0.0879260i | ||||
\(538\) | 20.5644 | + | 35.6187i | 0.886596 | + | 1.53563i | ||||
\(539\) | −6.81528 | −0.293555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.833751 | −0.0358458 | −0.0179229 | − | 0.999839i | \(-0.505705\pi\) | ||||
−0.0179229 | + | 0.999839i | \(0.505705\pi\) | |||||||
\(542\) | 8.89297 | + | 15.4031i | 0.381986 | + | 0.661619i | ||||
\(543\) | 18.1034 | − | 2.51495i | 0.776891 | − | 0.107927i | ||||
\(544\) | −29.2713 | + | 50.6994i | −1.25500 | + | 2.17372i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.93365 | − | 12.7562i | −0.425121 | − | 0.545915i | ||||
\(547\) | 14.1635 | + | 24.5319i | 0.605587 | + | 1.04891i | 0.991958 | + | 0.126565i | \(0.0403951\pi\) |
−0.386371 | + | 0.922343i | \(0.626272\pi\) | |||||||
\(548\) | −35.1785 | −1.50275 | ||||||||
\(549\) | 27.2590 | + | 26.4916i | 1.16339 | + | 1.13063i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.9213 | + | 18.9163i | 0.465264 | + | 0.805861i | ||||
\(552\) | −8.73515 | + | 21.5218i | −0.371793 | + | 0.916027i | ||||
\(553\) | 1.89709 | − | 3.28586i | 0.0806727 | − | 0.139729i | ||||
\(554\) | −39.8964 | + | 69.1026i | −1.69504 | + | 2.93589i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.3096 | + | 62.8901i | 1.53987 | + | 2.66713i | ||||
\(557\) | 11.5042 | 0.487448 | 0.243724 | − | 0.969845i | \(-0.421631\pi\) | ||||
0.243724 | + | 0.969845i | \(0.421631\pi\) | |||||||
\(558\) | −19.9402 | + | 5.64926i | −0.844135 | + | 0.239152i | ||||
\(559\) | −14.3512 | −0.606993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.25171 | + | 11.8805i | 0.390608 | + | 0.501595i | ||||
\(562\) | −24.5398 | + | 42.5043i | −1.03515 | + | 1.79293i | ||||
\(563\) | −16.5030 | + | 28.5840i | −0.695517 | + | 1.20467i | 0.274490 | + | 0.961590i | \(0.411491\pi\) |
−0.970006 | + | 0.243080i | \(0.921842\pi\) | |||||||
\(564\) | −53.2872 | + | 7.40273i | −2.24380 | + | 0.311711i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.9429 | −0.628095 | ||||||||
\(567\) | 14.2348 | + | 7.68517i | 0.597804 | + | 0.322747i | ||||
\(568\) | 9.85769 | 0.413619 | ||||||||
\(569\) | 13.5044 | + | 23.3903i | 0.566135 | + | 0.980574i | 0.996943 | + | 0.0781305i | \(0.0248951\pi\) |
−0.430809 | + | 0.902443i | \(0.641772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2122 | − | 21.1521i | 0.511064 | − | 0.885189i | −0.488854 | − | 0.872366i | \(-0.662585\pi\) |
0.999918 | − | 0.0128232i | \(-0.00408185\pi\) | |||||||
\(572\) | −8.80007 | + | 15.2422i | −0.367950 | + | 0.637307i | ||||
\(573\) | −18.4501 | − | 23.6925i | −0.770763 | − | 0.989768i | ||||
\(574\) | −5.83807 | − | 10.1118i | −0.243676 | − | 0.422060i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 31.9685 | − | 9.05701i | 1.33202 | − | 0.377375i | ||||
\(577\) | 14.7976 | 0.616033 | 0.308017 | − | 0.951381i | \(-0.400335\pi\) | ||||
0.308017 | + | 0.951381i | \(0.400335\pi\) | |||||||
\(578\) | −8.05663 | − | 13.9545i | −0.335112 | − | 0.580431i | ||||
\(579\) | 1.01586 | − | 2.50288i | 0.0422175 | − | 0.104016i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.987533 | − | 1.71046i | 0.0409698 | − | 0.0709617i | ||||
\(582\) | −6.57538 | + | 16.2005i | −0.272558 | + | 0.671532i | ||||
\(583\) | −1.55987 | − | 2.70177i | −0.0646030 | − | 0.111896i | ||||
\(584\) | −27.7470 | −1.14818 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 48.1375 | 1.98854 | ||||||||
\(587\) | −15.2890 | − | 26.4813i | −0.631044 | − | 1.09300i | −0.987339 | − | 0.158626i | \(-0.949294\pi\) |
0.356295 | − | 0.934374i | \(-0.384040\pi\) | |||||||
\(588\) | −19.8013 | − | 25.4276i | −0.816590 | − | 1.04862i | ||||
\(589\) | 3.88821 | − | 6.73457i | 0.160211 | − | 0.277493i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.8405 | + | 4.28440i | −1.26861 | + | 0.176237i | ||||
\(592\) | −61.0611 | − | 105.761i | −2.50960 | − | 4.34675i | ||||
\(593\) | −5.09990 | −0.209428 | −0.104714 | − | 0.994502i | \(-0.533393\pi\) | ||||
−0.104714 | + | 0.994502i | \(0.533393\pi\) | |||||||
\(594\) | 2.70376 | − | 24.5964i | 0.110936 | − | 1.00920i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.39532 | + | 2.41677i | 0.0571547 | + | 0.0989949i | ||||
\(597\) | −18.9099 | + | 2.62698i | −0.773929 | + | 0.107515i | ||||
\(598\) | 4.50236 | − | 7.79831i | 0.184115 | − | 0.318897i | ||||
\(599\) | 0.282655 | − | 0.489572i | 0.0115490 | − | 0.0200034i | −0.860193 | − | 0.509968i | \(-0.829657\pi\) |
0.871742 | + | 0.489965i | \(0.162990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50480 | + | 9.53459i | 0.224546 | + | 0.388924i | 0.956183 | − | 0.292770i | \(-0.0945769\pi\) |
−0.731637 | + | 0.681694i | \(0.761244\pi\) | |||||||
\(602\) | 34.4542 | 1.40425 | ||||||||
\(603\) | −6.69134 | + | 26.4788i | −0.272492 | + | 1.07830i | ||||
\(604\) | 0.757185 | 0.0308094 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.2411 | − | 27.6959i | 0.456638 | − | 1.12507i | ||||
\(607\) | 9.54913 | − | 16.5396i | 0.387587 | − | 0.671321i | −0.604537 | − | 0.796577i | \(-0.706642\pi\) |
0.992124 | + | 0.125256i | \(0.0399753\pi\) | |||||||
\(608\) | −18.0486 | + | 31.2611i | −0.731967 | + | 1.26780i | ||||
\(609\) | 8.62621 | − | 21.2534i | 0.349552 | − | 0.861229i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.4069 | 0.501929 | ||||||||
\(612\) | −17.4457 | + | 69.0357i | −0.705200 | + | 2.79060i | ||||
\(613\) | 9.33918 | 0.377206 | 0.188603 | − | 0.982053i | \(-0.439604\pi\) | ||||
0.188603 | + | 0.982053i | \(0.439604\pi\) | |||||||
\(614\) | 20.4179 | + | 35.3648i | 0.823999 | + | 1.42721i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.5675 | − | 21.7676i | 0.506360 | − | 0.877041i | ||||
\(617\) | 12.2077 | − | 21.1444i | 0.491464 | − | 0.851241i | −0.508488 | − | 0.861069i | \(-0.669795\pi\) |
0.999952 | + | 0.00982861i | \(0.00312859\pi\) | |||||||
\(618\) | 36.4883 | − | 5.06900i | 1.46777 | − | 0.203905i | ||||
\(619\) | −19.7431 | − | 34.1961i | −0.793544 | − | 1.37446i | −0.923760 | − | 0.382973i | \(-0.874900\pi\) |
0.130216 | − | 0.991486i | \(-0.458433\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.984464 | + | 8.95580i | −0.0395052 | + | 0.359384i | ||||
\(622\) | 80.1874 | 3.21522 | ||||||||
\(623\) | −11.9470 | − | 20.6928i | −0.478647 | − | 0.829040i | ||||
\(624\) | −35.5062 | + | 4.93256i | −1.42138 | + | 0.197461i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.15135 | − | 15.8506i | 0.365761 | − | 0.633517i | ||||
\(627\) | 5.70457 | + | 7.32547i | 0.227819 | + | 0.292551i | ||||
\(628\) | 28.2879 | + | 48.9960i | 1.12881 | + | 1.95515i | ||||
\(629\) | 55.9430 | 2.23059 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.1634 | 1.67850 | 0.839249 | − | 0.543747i | \(-0.182995\pi\) | ||||
0.839249 | + | 0.543747i | \(0.182995\pi\) | |||||||
\(632\) | −8.16277 | − | 14.1383i | −0.324698 | − | 0.562393i | ||||
\(633\) | −15.5868 | + | 38.4029i | −0.619518 | + | 1.52638i | ||||
\(634\) | 21.2608 | − | 36.8248i | 0.844375 | − | 1.46250i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.54814 | − | 13.6696i | 0.219998 | − | 0.542034i | ||||
\(637\) | 3.71616 | + | 6.43658i | 0.147240 | + | 0.255027i | ||||
\(638\) | −35.0855 | −1.38905 | ||||||||
\(639\) | 3.67901 | − | 1.04230i | 0.145539 | − | 0.0412328i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.6577 | − | 30.5841i | −0.697438 | − | 1.20800i | −0.969352 | − | 0.245677i | \(-0.920990\pi\) |
0.271913 | − | 0.962322i | \(-0.412344\pi\) | |||||||
\(642\) | −25.1598 | − | 32.3087i | −0.992978 | − | 1.27512i | ||||
\(643\) | −7.09771 | + | 12.2936i | −0.279906 | + | 0.484812i | −0.971361 | − | 0.237608i | \(-0.923637\pi\) |
0.691455 | + | 0.722420i | \(0.256970\pi\) | |||||||
\(644\) | −7.69256 | + | 13.3239i | −0.303129 | + | 0.525036i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.7712 | − | 32.5127i | −0.738544 | − | 1.27919i | ||||
\(647\) | 17.4897 | 0.687593 | 0.343796 | − | 0.939044i | \(-0.388287\pi\) | ||||
0.343796 | + | 0.939044i | \(0.388287\pi\) | |||||||
\(648\) | 59.2618 | − | 36.5094i | 2.32803 | − | 1.43422i | ||||
\(649\) | 19.9364 | 0.782572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.08842 | + | 1.12365i | −0.317010 | + | 0.0440395i | ||||
\(652\) | 54.4483 | − | 94.3072i | 2.13236 | − | 3.69335i | ||||
\(653\) | 5.48858 | − | 9.50650i | 0.214785 | − | 0.372018i | −0.738421 | − | 0.674340i | \(-0.764428\pi\) |
0.953206 | + | 0.302322i | \(0.0977617\pi\) | |||||||
\(654\) | −17.7742 | − | 22.8246i | −0.695026 | − | 0.892512i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −25.8882 | −1.01077 | ||||||||
\(657\) | −10.3555 | + | 2.93383i | −0.404007 | + | 0.114459i | ||||
\(658\) | −29.7862 | −1.16119 | ||||||||
\(659\) | 7.89381 | + | 13.6725i | 0.307499 | + | 0.532604i | 0.977815 | − | 0.209472i | \(-0.0671746\pi\) |
−0.670316 | + | 0.742076i | \(0.733841\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.9466 | + | 43.2088i | −0.970311 | + | 1.68063i | −0.275697 | + | 0.961245i | \(0.588909\pi\) |
−0.694614 | + | 0.719383i | \(0.744425\pi\) | |||||||
\(662\) | −16.6217 | + | 28.7897i | −0.646022 | + | 1.11894i | ||||
\(663\) | 6.17567 | − | 15.2157i | 0.239843 | − | 0.590929i | ||||
\(664\) | −4.24913 | − | 7.35972i | −0.164898 | − | 0.285612i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −65.9263 | − | 64.0703i | −2.55459 | − | 2.48267i | ||||
\(667\) | 12.7750 | 0.494649 | ||||||||
\(668\) | −42.1291 | − | 72.9698i | −1.63002 | − | 2.82328i | ||||
\(669\) | 23.1042 | + | 29.6691i | 0.893261 | + | 1.14707i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4549 | − | 19.8404i | 0.442210 | − | 0.765929i | ||||
\(672\) | 37.5455 | − | 5.21587i | 1.44835 | − | 0.201207i | ||||
\(673\) | −14.4197 | − | 24.9757i | −0.555840 | − | 0.962743i | −0.997838 | − | 0.0657266i | \(-0.979063\pi\) |
0.441998 | − | 0.897016i | \(-0.354270\pi\) | |||||||
\(674\) | −18.2264 | −0.702055 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −44.9809 | −1.73003 | ||||||||
\(677\) | −5.23181 | − | 9.06176i | −0.201075 | − | 0.348272i | 0.747800 | − | 0.663924i | \(-0.231110\pi\) |
−0.948875 | + | 0.315652i | \(0.897777\pi\) | |||||||
\(678\) | 67.3349 | − | 9.35426i | 2.58598 | − | 0.359248i | ||||
\(679\) | −3.44455 | + | 5.96614i | −0.132190 | + | 0.228959i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.0053 | + | 19.2689i | 0.575003 | + | 0.738385i | ||||
\(682\) | 6.24556 | + | 10.8176i | 0.239155 | + | 0.414228i | ||||
\(683\) | −16.1875 | −0.619396 | −0.309698 | − | 0.950835i | \(-0.600228\pi\) | ||||
−0.309698 | + | 0.950835i | \(0.600228\pi\) | |||||||
\(684\) | −10.7569 | + | 42.5672i | −0.411302 | + | 1.62760i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −25.4904 | − | 44.1507i | −0.973229 | − | 1.68568i | ||||
\(687\) | 2.39553 | − | 5.90214i | 0.0913953 | − | 0.225181i | ||||
\(688\) | 38.1958 | − | 66.1570i | 1.45620 | − | 2.52221i | ||||
\(689\) | −1.70109 | + | 2.94638i | −0.0648065 | + | 0.112248i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.94181 | − | 8.55946i | −0.187995 | − | 0.325617i | 0.756586 | − | 0.653894i | \(-0.226866\pi\) |
−0.944582 | + | 0.328276i | \(0.893532\pi\) | |||||||
\(692\) | 58.9648 | 2.24150 | ||||||||
\(693\) | 2.38876 | − | 9.45276i | 0.0907415 | − | 0.359081i | ||||
\(694\) | 36.3621 | 1.38029 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −60.6383 | − | 77.8682i | −2.29849 | − | 2.95158i | ||||
\(697\) | 5.92957 | − | 10.2703i | 0.224598 | − | 0.389016i | ||||
\(698\) | −8.64872 | + | 14.9800i | −0.327359 | + | 0.567002i | ||||
\(699\) | 9.16399 | − | 1.27307i | 0.346614 | − | 0.0481521i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.9692 | 1.66069 | 0.830346 | − | 0.557248i | \(-0.188143\pi\) | ||||
0.830346 | + | 0.557248i | \(0.188143\pi\) | |||||||
\(702\) | −24.7040 | + | 10.8582i | −0.932391 | + | 0.409815i | ||||
\(703\) | 34.4942 | 1.30097 | ||||||||
\(704\) | −10.0130 | − | 17.3430i | −0.377379 | − | 0.653640i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.64193 | − | 8.04005i | 0.174701 | − | 0.302591i | ||||
\(707\) | 5.88870 | − | 10.1995i | 0.221467 | − | 0.383593i | ||||
\(708\) | 57.9236 | + | 74.3820i | 2.17690 | + | 2.79545i | ||||
\(709\) | −12.6130 | − | 21.8464i | −0.473692 | − | 0.820458i | 0.525855 | − | 0.850574i | \(-0.323746\pi\) |
−0.999546 | + | 0.0301162i | \(0.990412\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.54136 | − | 4.41351i | −0.170314 | − | 0.165520i | ||||
\(712\) | −102.811 | −3.85299 | ||||||||
\(713\) | −2.27407 | − | 3.93880i | −0.0851645 | − | 0.147509i | ||||
\(714\) | −14.8264 | + | 36.5295i | −0.554865 | + | 1.36708i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.1016 | + | 36.5490i | −0.788603 | + | 1.36590i | ||||
\(717\) | −14.3523 | + | 35.3614i | −0.535998 | + | 1.32060i | ||||
\(718\) | −30.1937 | − | 52.2971i | −1.12682 | − | 1.95171i | ||||
\(719\) | −36.8600 | −1.37465 | −0.687323 | − | 0.726352i | \(-0.741214\pi\) | ||||
−0.687323 | + | 0.726352i | \(0.741214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5153 | 0.540576 | ||||||||
\(722\) | 13.4461 | + | 23.2893i | 0.500412 | + | 0.866740i | ||||
\(723\) | −19.8441 | − | 25.4826i | −0.738009 | − | 0.947708i | ||||
\(724\) | 26.0459 | − | 45.1128i | 0.967988 | − | 1.67660i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 34.9300 | − | 4.85252i | 1.29637 | − | 0.180094i | ||||
\(727\) | 19.1226 | + | 33.1213i | 0.709217 | + | 1.22840i | 0.965148 | + | 0.261705i | \(0.0842847\pi\) |
−0.255931 | + | 0.966695i | \(0.582382\pi\) | |||||||
\(728\) | −27.4107 | −1.01591 | ||||||||
\(729\) | 18.2569 | − | 19.8918i | 0.676183 | − | 0.736734i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.4971 | + | 30.3059i | 0.647154 | + | 1.12090i | ||||
\(732\) | 107.305 | − | 14.9070i | 3.96611 | − | 0.550977i | ||||
\(733\) | −19.7916 | + | 34.2801i | −0.731020 | + | 1.26616i | 0.225428 | + | 0.974260i | \(0.427622\pi\) |
−0.956448 | + | 0.291903i | \(0.905711\pi\) | |||||||
\(734\) | −5.50358 | + | 9.53248i | −0.203141 | + | 0.351850i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.5559 | + | 18.2834i | 0.389097 | + | 0.673936i | ||||
\(737\) | 16.4607 | 0.606338 | ||||||||
\(738\) | −18.7501 | + | 5.31210i | −0.690201 | + | 0.195541i | ||||
\(739\) | −8.24773 | −0.303398 | −0.151699 | − | 0.988427i | \(-0.548474\pi\) | ||||
−0.151699 | + | 0.988427i | \(0.548474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.80790 | − | 9.38194i | 0.139887 | − | 0.344654i | ||||
\(742\) | 4.08395 | − | 7.07361i | 0.149927 | − | 0.259680i | ||||
\(743\) | −0.654091 | + | 1.13292i | −0.0239963 | + | 0.0415627i | −0.877774 | − | 0.479075i | \(-0.840972\pi\) |
0.853778 | + | 0.520637i | \(0.174306\pi\) | |||||||
\(744\) | −13.2142 | + | 32.5574i | −0.484458 | + | 1.19361i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.0171 | 0.659651 | ||||||||
\(747\) | −2.36401 | − | 2.29746i | −0.0864946 | − | 0.0840595i | ||||
\(748\) | 42.9164 | 1.56918 | ||||||||
\(749\) | −8.06752 | − | 13.9734i | −0.294781 | − | 0.510575i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.2234 | + | 24.6357i | −0.519020 | + | 0.898969i | 0.480736 | + | 0.876866i | \(0.340370\pi\) |
−0.999756 | + | 0.0221034i | \(0.992964\pi\) | |||||||
\(752\) | −33.0209 | + | 57.1939i | −1.20415 | + | 2.08565i | ||||
\(753\) | −25.2068 | + | 3.50176i | −0.918585 | + | 0.127611i | ||||
\(754\) | 19.1310 | + | 33.1359i | 0.696711 | + | 1.20674i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 42.2083 | − | 18.5518i | 1.53510 | − | 0.674724i | ||||
\(757\) | −38.2012 | −1.38845 | −0.694223 | − | 0.719760i | \(-0.744252\pi\) | ||||
−0.694223 | + | 0.719760i | \(0.744252\pi\) | |||||||
\(758\) | 16.8248 | + | 29.1414i | 0.611103 | + | 1.05846i | ||||
\(759\) | 5.37859 | − | 0.747201i | 0.195231 | − | 0.0271217i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0952 | + | 19.2174i | −0.402200 | + | 0.696632i | −0.993991 | − | 0.109460i | \(-0.965088\pi\) |
0.591791 | + | 0.806092i | \(0.298421\pi\) | |||||||
\(762\) | 10.1545 | + | 13.0398i | 0.367860 | + | 0.472384i | ||||
\(763\) | −5.69932 | − | 9.87152i | −0.206329 | − | 0.357373i | ||||
\(764\) | −85.5852 | −3.09637 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.8440 | 0.716994 | ||||||||
\(767\) | −10.8707 | − | 18.8286i | −0.392518 | − | 0.679861i | ||||
\(768\) | −6.16258 | + | 15.1834i | −0.222373 | + | 0.547885i | ||||
\(769\) | 8.45652 | − | 14.6471i | 0.304950 | − | 0.528189i | −0.672300 | − | 0.740279i | \(-0.734694\pi\) |
0.977250 | + | 0.212090i | \(0.0680270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.4666 | − | 35.6431i | 0.521003 | − | 1.28365i | ||||
\(772\) | −3.84930 | − | 6.66718i | −0.138539 | − | 0.239957i | ||||
\(773\) | −38.6464 | −1.39001 | −0.695007 | − | 0.719003i | \(-0.744599\pi\) | ||||
−0.695007 | + | 0.719003i | \(0.744599\pi\) | |||||||
\(774\) | 14.0891 | − | 55.7532i | 0.506423 | − | 2.00401i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.8211 | + | 25.6709i | 0.532047 | + | 0.921533i | ||||
\(777\) | −22.2556 | − | 28.5793i | −0.798416 | − | 1.02528i | ||||
\(778\) | −7.17920 | + | 12.4347i | −0.257387 | + | 0.445807i | ||||
\(779\) | 3.65615 | − | 6.33264i | 0.130995 | − | 0.226890i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.15232 | − | 1.99588i | −0.0412333 | − | 0.0714181i | ||||
\(782\) | −21.9572 | −0.785187 | ||||||||
\(783\) | −30.8644 | − | 22.6498i | −1.10300 | − | 0.809437i | ||||
\(784\) | −39.5622 | −1.41294 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.9544 | + | 4.57807i | −1.17544 | + | 0.163294i | ||||
\(787\) | −5.45734 | + | 9.45240i | −0.194533 | + | 0.336942i | −0.946747 | − | 0.321977i | \(-0.895653\pi\) |
0.752214 | + | 0.658919i | \(0.228986\pi\) | |||||||
\(788\) | −44.3711 | + | 76.8530i | −1.58065 | + | 2.73777i | ||||
\(789\) | 6.10845 | + | 7.84411i | 0.217467 | + | 0.279258i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.7862 | 0.952409 | ||||||||
\(792\) | −30.0848 | − | 29.2378i | −1.06902 | − | 1.03892i | ||||
\(793\) | −24.9839 | −0.887204 | ||||||||
\(794\) | 7.43433 | + | 12.8766i | 0.263835 | + | 0.456975i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.2062 | + | 47.1225i | −0.964298 | + | 1.67021i | ||||
\(797\) | 1.46275 | − | 2.53356i | 0.0518133 | − | 0.0897432i | −0.838956 | − | 0.544200i | \(-0.816833\pi\) |
0.890769 | + | 0.454457i | \(0.150167\pi\) | |||||||
\(798\) | −9.14193 | + | 22.5240i | −0.323621 | + | 0.797340i | ||||
\(799\) | −15.1265 | − | 26.1999i | −0.535139 | − | 0.926888i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.3702 | + | 10.8707i | −1.35574 | + | 0.384096i | ||||
\(802\) | −14.4965 | −0.511888 | ||||||||
\(803\) | 3.24350 | + | 5.61791i | 0.114461 | + | 0.198252i | ||||
\(804\) | 47.8252 | + | 61.4144i | 1.68667 | + | 2.16592i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.81102 | − | 11.7970i | 0.239908 | − | 0.415532i | ||||
\(807\) | 26.7909 | − | 3.72182i | 0.943083 | − | 0.131014i | ||||
\(808\) | −25.3378 | − | 43.8863i | −0.891380 | − | 1.54391i | ||||
\(809\) | −37.9241 | −1.33334 | −0.666671 | − | 0.745352i | \(-0.732281\pi\) | ||||
−0.666671 | + | 0.745352i | \(0.732281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5050 | 0.684912 | 0.342456 | − | 0.939534i | \(-0.388741\pi\) | ||||
0.342456 | + | 0.939534i | \(0.388741\pi\) | |||||||
\(812\) | −32.6866 | − | 56.6148i | −1.14707 | − | 1.98679i | ||||
\(813\) | 11.5855 | − | 1.60948i | 0.406323 | − | 0.0564469i | ||||
\(814\) | −27.7037 | + | 47.9843i | −0.971016 | + | 1.68185i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 53.7055 | + | 68.9654i | 1.88007 | + | 2.41427i | ||||
\(817\) | 10.7887 | + | 18.6865i | 0.377447 | + | 0.653758i | ||||
\(818\) | 86.5257 | 3.02530 | ||||||||
\(819\) | −10.2300 | + | 2.89827i | −0.357466 | + | 0.101274i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3762 | − | 38.7567i | −0.780934 | − | 1.35262i | −0.931398 | − | 0.364002i | \(-0.881410\pi\) |
0.150464 | − | 0.988615i | \(-0.451923\pi\) | |||||||
\(822\) | −12.2255 | + | 30.1214i | −0.426415 | + | 1.05061i | ||||
\(823\) | 17.9497 | − | 31.0898i | 0.625687 | − | 1.08372i | −0.362721 | − | 0.931898i | \(-0.618152\pi\) |
0.988408 | − | 0.151824i | \(-0.0485146\pi\) | |||||||
\(824\) | 31.2279 | − | 54.0884i | 1.08788 | − | 1.88426i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.0981 | + | 45.2033i | 0.908071 | + | 1.57282i | ||||
\(827\) | −16.2717 | −0.565822 | −0.282911 | − | 0.959146i | \(-0.591300\pi\) | ||||
−0.282911 | + | 0.959146i | \(0.591300\pi\) | |||||||
\(828\) | 18.4149 | + | 17.8964i | 0.639961 | + | 0.621944i | ||||
\(829\) | −20.6592 | −0.717525 | −0.358762 | − | 0.933429i | \(-0.616801\pi\) | ||||
−0.358762 | + | 0.933429i | \(0.616801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.2412 | + | 41.4023i | 1.11844 | + | 1.43623i | ||||
\(832\) | −10.9196 | + | 18.9132i | −0.378568 | + | 0.655698i | ||||
\(833\) | 9.06152 | − | 15.6950i | 0.313963 | − | 0.543800i | ||||
\(834\) | 66.4680 | − | 9.23382i | 2.30160 | − | 0.319741i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.4621 | 0.915210 | ||||||||
\(837\) | −1.48927 | + | 13.5480i | −0.0514765 | + | 0.468289i | ||||
\(838\) | 60.2044 | 2.07973 | ||||||||
\(839\) | 6.11836 | + | 10.5973i | 0.211229 | + | 0.365860i | 0.952100 | − | 0.305788i | \(-0.0989200\pi\) |
−0.740870 | + | 0.671648i | \(0.765587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.6411 | + | 21.8951i | −0.435901 | + | 0.755003i | ||||
\(842\) | −23.6264 | + | 40.9221i | −0.814218 | + | 1.41027i | ||||
\(843\) | 19.8312 | + | 25.4661i | 0.683024 | + | 0.877099i | ||||
\(844\) | 59.0616 | + | 102.298i | 2.03299 | + | 3.52123i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.1803 | + | 48.1996i | −0.418767 | + | 1.65714i | ||||
\(847\) | 13.8953 | 0.477450 | ||||||||
\(848\) | −9.05490 | − | 15.6836i | −0.310947 | − | 0.538575i | ||||
\(849\) | −3.69576 | + | 9.10565i | −0.126838 | + | 0.312505i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.0872 | − | 17.4715i | 0.345785 | − | 0.598917i | ||||
\(852\) | 4.09858 | − | 10.0981i | 0.140415 | − | 0.345956i | ||||
\(853\) | −8.21464 | − | 14.2282i | −0.281264 | − | 0.487164i | 0.690432 | − | 0.723397i | \(-0.257420\pi\) |
−0.971696 | + | 0.236233i | \(0.924087\pi\) | |||||||
\(854\) | 59.9809 | 2.05250 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −69.4255 | −2.37291 | ||||||||
\(857\) | −24.5449 | − | 42.5129i | −0.838436 | − | 1.45221i | −0.891202 | − | 0.453607i | \(-0.850137\pi\) |
0.0527655 | − | 0.998607i | \(-0.483196\pi\) | |||||||
\(858\) | 9.99276 | + | 12.8321i | 0.341147 | + | 0.438081i | ||||
\(859\) | −20.5454 | + | 35.5856i | −0.700999 | + | 1.21417i | 0.267117 | + | 0.963664i | \(0.413929\pi\) |
−0.968116 | + | 0.250502i | \(0.919404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.60569 | + | 1.05659i | −0.259201 | + | 0.0360086i | ||||
\(862\) | 8.14968 | + | 14.1157i | 0.277579 | + | 0.480781i | ||||
\(863\) | 47.8366 | 1.62838 | 0.814188 | − | 0.580601i | \(-0.197183\pi\) | ||||
0.814188 | + | 0.580601i | \(0.197183\pi\) | |||||||
\(864\) | 6.91299 | − | 62.8884i | 0.235185 | − | 2.13951i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.10605 | + | 7.11189i | 0.139529 | + | 0.241672i | ||||
\(867\) | −10.4960 | + | 1.45812i | −0.356462 | + | 0.0495202i | ||||
\(868\) | −11.6371 | + | 20.1560i | −0.394987 | + | 0.684138i | ||||
\(869\) | −1.90838 | + | 3.30542i | −0.0647375 | + | 0.112129i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.97551 | − | 15.5460i | −0.304123 | − | 0.526757i | ||||
\(872\) | −49.0458 | −1.66090 | ||||||||
\(873\) | 8.24574 | + | 8.01361i | 0.279076 | + | 0.271219i | ||||
\(874\) | −13.5387 | −0.457954 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.5365 | + | 28.4238i | −0.389783 | + | 0.960351i | ||||
\(877\) | 5.68859 | − | 9.85292i | 0.192090 | − | 0.332710i | −0.753853 | − | 0.657043i | \(-0.771807\pi\) |
0.945943 | + | 0.324334i | \(0.105140\pi\) | |||||||
\(878\) | −17.7906 | + | 30.8143i | −0.600405 | + | 1.03993i | ||||
\(879\) | 11.9056 | − | 29.3333i | 0.401567 | − | 0.989386i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.9924 | −1.48214 | −0.741071 | − | 0.671426i | \(-0.765682\pi\) | ||||
−0.741071 | + | 0.671426i | \(0.765682\pi\) | |||||||
\(882\) | −28.6538 | + | 8.11791i | −0.964823 | + | 0.273344i | ||||
\(883\) | 37.6820 | 1.26810 | 0.634051 | − | 0.773291i | \(-0.281391\pi\) | ||||
0.634051 | + | 0.773291i | \(0.281391\pi\) | |||||||
\(884\) | −23.4010 | − | 40.5317i | −0.787060 | − | 1.36323i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.9699 | − | 55.3735i | 1.07405 | − | 1.86031i | ||||
\(887\) | 16.6416 | − | 28.8241i | 0.558771 | − | 0.967820i | −0.438828 | − | 0.898571i | \(-0.644606\pi\) |
0.997599 | − | 0.0692492i | \(-0.0220603\pi\) | |||||||
\(888\) | −154.376 | + | 21.4461i | −5.18052 | + | 0.719685i | ||||
\(889\) | 3.25606 | + | 5.63967i | 0.109205 | + | 0.189148i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.3195 | − | 7.73091i | −0.479721 | − | 0.258995i | ||||
\(892\) | 107.175 | 3.58847 | ||||||||
\(893\) | −9.32697 | − | 16.1548i | −0.312115 | − | 0.540599i | ||||
\(894\) | 2.55427 | − | 0.354842i | 0.0854274 | − | 0.0118677i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.33040 | − | 7.50047i | 0.144669 | − | 0.250573i | ||||
\(897\) | −3.63846 | − | 4.67230i | −0.121485 | − | 0.156003i | ||||
\(898\) | 31.7939 | + | 55.0686i | 1.06098 | + | 1.83766i | ||||
\(899\) | 19.3255 | 0.644543 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.29592 | 0.276377 | ||||||||
\(902\) | 5.87281 | + | 10.1720i | 0.195543 | + | 0.338691i | ||||
\(903\) | 8.52141 | − | 20.9952i | 0.283575 | − | 0.698675i | ||||
\(904\) | 57.6276 | − | 99.8139i | 1.91667 | − | 3.31976i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.263144 | − | 0.648336i | 0.00874236 | − | 0.0215395i | ||||
\(907\) | 7.03918 | + | 12.1922i | 0.233732 | + | 0.404836i | 0.958903 | − | 0.283733i | \(-0.0915728\pi\) |
−0.725171 | + | 0.688568i | \(0.758239\pi\) | |||||||
\(908\) | 69.6056 | 2.30994 | ||||||||
\(909\) | −14.0967 | − | 13.6998i | −0.467558 | − | 0.454395i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.65761 | − | 6.33517i | −0.121182 | − | 0.209894i | 0.799052 | − | 0.601262i | \(-0.205335\pi\) |
−0.920234 | + | 0.391368i | \(0.872002\pi\) | |||||||
\(912\) | 33.1146 | + | 42.5238i | 1.09653 | + | 1.40810i | ||||
\(913\) | −0.993410 | + | 1.72064i | −0.0328771 | + | 0.0569448i | ||||
\(914\) | 3.71561 | − | 6.43563i | 0.122902 | − | 0.212872i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.07719 | − | 15.7222i | −0.299919 | − | 0.519475i | ||||
\(917\) | −13.1094 | −0.432912 | ||||||||
\(918\) | 53.0486 | + | 38.9297i | 1.75087 | + | 1.28487i | ||||
\(919\) | 4.44684 | 0.146688 | 0.0733438 | − | 0.997307i | \(-0.476633\pi\) | ||||
0.0733438 | + | 0.997307i | \(0.476633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.5999 | − | 3.69530i | 0.876498 | − | 0.121764i | ||||
\(922\) | −28.2562 | + | 48.9412i | −0.930569 | + | 1.61179i | ||||
\(923\) | −1.25665 | + | 2.17658i | −0.0413631 | + | 0.0716430i | ||||
\(924\) | −17.0733 | − | 21.9245i | −0.561669 | − | 0.721263i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −52.1565 | −1.71397 | ||||||||
\(927\) | 5.93562 | − | 23.4883i | 0.194951 | − | 0.771458i | ||||
\(928\) | −89.7068 | −2.94477 | ||||||||
\(929\) | −6.55663 | − | 11.3564i | −0.215116 | − | 0.372592i | 0.738192 | − | 0.674590i | \(-0.235680\pi\) |
−0.953309 | + | 0.301998i | \(0.902346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.58730 | − | 9.67749i | 0.183116 | − | 0.317167i | ||||
\(932\) | 13.1845 | − | 22.8362i | 0.431873 | − | 0.748026i | ||||
\(933\) | 19.8324 | − | 48.8633i | 0.649284 | − | 1.59971i | ||||
\(934\) | −29.9204 | − | 51.8236i | −0.979025 | − | 1.69572i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11.2089 | + | 44.3556i | −0.366374 | + | 1.44981i | ||||
\(937\) | −33.5187 | −1.09501 | −0.547504 | − | 0.836803i | \(-0.684422\pi\) | ||||
−0.547504 | + | 0.836803i | \(0.684422\pi\) | |||||||
\(938\) | 21.5482 | + | 37.3226i | 0.703574 | + | 1.21863i | ||||
\(939\) | −7.39543 | − | 9.49677i | −0.241341 | − | 0.309915i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.895381 | + | 1.55085i | −0.0291886 | + | 0.0505561i | −0.880251 | − | 0.474509i | \(-0.842626\pi\) |
0.851062 | + | 0.525065i | \(0.175959\pi\) | |||||||
\(942\) | 51.7834 | − | 7.19383i | 1.68720 | − | 0.234388i | ||||
\(943\) | −2.13835 | − | 3.70373i | −0.0696342 | − | 0.120610i | ||||
\(944\) | 115.729 | 3.76667 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.6592 | −1.12687 | ||||||||
\(947\) | 26.3175 | + | 45.5832i | 0.855204 | + | 1.48126i | 0.876456 | + | 0.481482i | \(0.159901\pi\) |
−0.0212525 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(948\) | −17.8771 | + | 2.48351i | −0.580620 | + | 0.0806606i | ||||
\(949\) | 3.53716 | − | 6.12654i | 0.114821 | − | 0.198876i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.1814 | − | 22.0633i | −0.557144 | − | 0.715451i | ||||
\(952\) | 33.4193 | + | 57.8839i | 1.08312 | + | 1.87603i | ||||
\(953\) | −18.4072 | −0.596268 | −0.298134 | − | 0.954524i | \(-0.596364\pi\) | ||||
−0.298134 | + | 0.954524i | \(0.596364\pi\) | |||||||
\(954\) | −9.77637 | − | 9.50114i | −0.316522 | − | 0.307611i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 54.3841 | + | 94.1960i | 1.75891 | + | 3.04652i | ||||
\(957\) | −8.67754 | + | 21.3798i | −0.280505 | + | 0.691112i | ||||
\(958\) | −28.0333 | + | 48.5551i | −0.905715 | + | 1.56874i | ||||
\(959\) | −6.40442 | + | 11.0928i | −0.206810 | + | 0.358205i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0599 | + | 20.8883i | 0.389028 | + | 0.673816i | ||||
\(962\) | 60.4240 | 1.94815 | ||||||||
\(963\) | −25.9104 | + | 7.34070i | −0.834952 | + | 0.236551i | ||||
\(964\) | −92.0517 | −2.96479 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.73515 | + | 11.2172i | 0.281049 | + | 0.360906i | ||||
\(967\) | 3.04790 | − | 5.27911i | 0.0980137 | − | 0.169765i | −0.812849 | − | 0.582475i | \(-0.802084\pi\) |
0.910862 | + | 0.412710i | \(0.135418\pi\) | |||||||
\(968\) | 29.8943 | − | 51.7784i | 0.960839 | − | 1.66422i | ||||
\(969\) | −24.4547 | + | 3.39728i | −0.785598 | + | 0.109136i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.1077 | −1.09457 | −0.547283 | − | 0.836947i | \(-0.684338\pi\) | ||||
−0.547283 | + | 0.836947i | \(0.684338\pi\) | |||||||
\(972\) | −12.7603 | − | 75.8871i | −0.409288 | − | 2.43408i | ||||
\(973\) | 26.4414 | 0.847671 | ||||||||
\(974\) | 12.6246 | + | 21.8665i | 0.404519 | + | 0.700648i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 66.4945 | − | 115.172i | 2.12844 | − | 3.68656i | ||||
\(977\) | −24.3957 | + | 42.2546i | −0.780488 | + | 1.35184i | 0.151170 | + | 0.988508i | \(0.451696\pi\) |
−0.931658 | + | 0.363337i | \(0.881637\pi\) | |||||||
\(978\) | −61.8277 | − | 79.3955i | −1.97703 | − | 2.53879i | ||||
\(979\) | 12.0181 | + | 20.8160i | 0.384100 | + | 0.665281i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.3045 | + | 5.18586i | −0.584418 | + | 0.165572i | ||||
\(982\) | −99.6715 | −3.18065 | ||||||||
\(983\) | −16.7086 | − | 28.9402i | −0.532922 | − | 0.923048i | −0.999261 | − | 0.0384416i | \(-0.987761\pi\) |
0.466339 | − | 0.884606i | \(-0.345573\pi\) | |||||||
\(984\) | −12.4256 | + | 30.6143i | −0.396113 | + | 0.975949i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 46.6493 | − | 80.7989i | 1.48562 | − | 2.57316i | ||||
\(987\) | −7.36691 | + | 18.1507i | −0.234491 | + | 0.577742i | ||||
\(988\) | −14.4289 | − | 24.9917i | −0.459046 | − | 0.795091i | ||||
\(989\) | 12.6198 | 0.401285 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3512 | −0.614713 | −0.307356 | − | 0.951595i | \(-0.599444\pi\) | ||||
−0.307356 | + | 0.951595i | \(0.599444\pi\) | |||||||
\(992\) | 15.9687 | + | 27.6586i | 0.507006 | + | 0.878161i | ||||
\(993\) | 13.4324 | + | 17.2491i | 0.426265 | + | 0.547384i | ||||
\(994\) | 3.01694 | − | 5.22549i | 0.0956915 | − | 0.165743i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.30592 | + | 1.29279i | −0.294869 | + | 0.0409636i | ||||
\(997\) | −19.7721 | − | 34.2463i | −0.626189 | − | 1.08459i | −0.988310 | − | 0.152460i | \(-0.951281\pi\) |
0.362121 | − | 0.932131i | \(-0.382053\pi\) | |||||||
\(998\) | 44.5766 | 1.41105 | ||||||||
\(999\) | −55.3474 | + | 24.3269i | −1.75112 | + | 0.769669i |
(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 | 225.2.e.c.76.1 | ✓ | 8 | |
3.2 | odd | 2 | 675.2.e.e.226.4 | 8 | |||
5.2 | odd | 4 | 225.2.k.c.49.8 | 16 | |||
5.3 | odd | 4 | 225.2.k.c.49.1 | 16 | |||
5.4 | even | 2 | 225.2.e.e.76.4 | yes | 8 | ||
9.2 | odd | 6 | 675.2.e.e.451.4 | 8 | |||
9.4 | even | 3 | 2025.2.a.y.1.4 | 4 | |||
9.5 | odd | 6 | 2025.2.a.p.1.1 | 4 | |||
9.7 | even | 3 | inner | 225.2.e.c.151.1 | yes | 8 | |
15.2 | even | 4 | 675.2.k.c.199.1 | 16 | |||
15.8 | even | 4 | 675.2.k.c.199.8 | 16 | |||
15.14 | odd | 2 | 675.2.e.c.226.1 | 8 | |||
45.2 | even | 12 | 675.2.k.c.424.8 | 16 | |||
45.4 | even | 6 | 2025.2.a.q.1.1 | 4 | |||
45.7 | odd | 12 | 225.2.k.c.124.1 | 16 | |||
45.13 | odd | 12 | 2025.2.b.n.649.1 | 8 | |||
45.14 | odd | 6 | 2025.2.a.z.1.4 | 4 | |||
45.22 | odd | 12 | 2025.2.b.n.649.8 | 8 | |||
45.23 | even | 12 | 2025.2.b.o.649.8 | 8 | |||
45.29 | odd | 6 | 675.2.e.c.451.1 | 8 | |||
45.32 | even | 12 | 2025.2.b.o.649.1 | 8 | |||
45.34 | even | 6 | 225.2.e.e.151.4 | yes | 8 | ||
45.38 | even | 12 | 675.2.k.c.424.1 | 16 | |||
45.43 | odd | 12 | 225.2.k.c.124.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
225.2.e.c.151.1 | yes | 8 | 9.7 | even | 3 | inner | |
225.2.e.e.76.4 | yes | 8 | 5.4 | even | 2 | ||
225.2.e.e.151.4 | yes | 8 | 45.34 | even | 6 | ||
225.2.k.c.49.1 | 16 | 5.3 | odd | 4 | |||
225.2.k.c.49.8 | 16 | 5.2 | odd | 4 | |||
225.2.k.c.124.1 | 16 | 45.7 | odd | 12 | |||
225.2.k.c.124.8 | 16 | 45.43 | odd | 12 | |||
675.2.e.c.226.1 | 8 | 15.14 | odd | 2 | |||
675.2.e.c.451.1 | 8 | 45.29 | odd | 6 | |||
675.2.e.e.226.4 | 8 | 3.2 | odd | 2 | |||
675.2.e.e.451.4 | 8 | 9.2 | odd | 6 | |||
675.2.k.c.199.1 | 16 | 15.2 | even | 4 | |||
675.2.k.c.199.8 | 16 | 15.8 | even | 4 | |||
675.2.k.c.424.1 | 16 | 45.38 | even | 12 | |||
675.2.k.c.424.8 | 16 | 45.2 | even | 12 | |||
2025.2.a.p.1.1 | 4 | 9.5 | odd | 6 | |||
2025.2.a.q.1.1 | 4 | 45.4 | even | 6 | |||
2025.2.a.y.1.4 | 4 | 9.4 | even | 3 | |||
2025.2.a.z.1.4 | 4 | 45.14 | odd | 6 | |||
2025.2.b.n.649.1 | 8 | 45.13 | odd | 12 | |||
2025.2.b.n.649.8 | 8 | 45.22 | odd | 12 | |||
2025.2.b.o.649.1 | 8 | 45.32 | even | 12 | |||
2025.2.b.o.649.8 | 8 | 45.23 | even | 12 |