Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(299,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 299.5 | ||
Character | \(\chi\) | \(=\) | 525.299 |
Dual form | 525.2.q.g.374.5 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.846473 | + | 1.46613i | −0.598547 | + | 1.03671i | 0.394489 | + | 0.918901i | \(0.370922\pi\) |
−0.993036 | + | 0.117813i | \(0.962412\pi\) | |||||||
\(3\) | −1.53466 | − | 0.803015i | −0.886034 | − | 0.463621i | ||||
\(4\) | −0.433034 | − | 0.750036i | −0.216517 | − | 0.375018i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.47637 | − | 1.57028i | 1.01097 | − | 0.641064i | ||||
\(7\) | 2.01688 | − | 1.71236i | 0.762310 | − | 0.647212i | ||||
\(8\) | −1.91969 | −0.678712 | ||||||||
\(9\) | 1.71033 | + | 2.46470i | 0.570111 | + | 0.821567i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.399511 | + | 0.230658i | −0.120457 | + | 0.0695460i | −0.559018 | − | 0.829156i | \(-0.688822\pi\) |
0.438561 | + | 0.898702i | \(0.355488\pi\) | |||||||
\(12\) | 0.0622670 | + | 1.49878i | 0.0179749 | + | 0.432660i | ||||
\(13\) | −3.38501 | −0.938834 | −0.469417 | − | 0.882977i | \(-0.655536\pi\) | ||||
−0.469417 | + | 0.882977i | \(0.655536\pi\) | |||||||
\(14\) | 0.803314 | + | 4.40649i | 0.214695 | + | 1.17768i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49103 | − | 4.31459i | 0.622758 | − | 1.07865i | ||||
\(17\) | −4.76601 | + | 2.75166i | −1.15593 | + | 0.667374i | −0.950324 | − | 0.311261i | \(-0.899249\pi\) |
−0.205602 | + | 0.978636i | \(0.565915\pi\) | |||||||
\(18\) | −5.06134 | + | 0.421275i | −1.19297 | + | 0.0992955i | ||||
\(19\) | −3.49334 | − | 2.01688i | −0.801428 | − | 0.462705i | 0.0425421 | − | 0.999095i | \(-0.486454\pi\) |
−0.843970 | + | 0.536390i | \(0.819788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.47027 | + | 1.00830i | −0.975493 | + | 0.220028i | ||||
\(22\) | − | 0.780983i | − | 0.166506i | ||||||
\(23\) | 2.25223 | − | 3.90097i | 0.469622 | − | 0.813409i | −0.529775 | − | 0.848138i | \(-0.677724\pi\) |
0.999397 | + | 0.0347292i | \(0.0110569\pi\) | |||||||
\(24\) | 2.94606 | + | 1.54154i | 0.601362 | + | 0.314665i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.86532 | − | 4.96289i | 0.561936 | − | 0.973302i | ||||
\(27\) | −0.645580 | − | 5.15589i | −0.124242 | − | 0.992252i | ||||
\(28\) | −2.15771 | − | 0.771225i | −0.407769 | − | 0.145748i | ||||
\(29\) | − | 7.71756i | − | 1.43311i | −0.697528 | − | 0.716557i | \(-0.745717\pi\) | ||
0.697528 | − | 0.716557i | \(-0.254283\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.01611 | + | 1.74135i | −0.541710 | + | 0.312756i | −0.745772 | − | 0.666202i | \(-0.767919\pi\) |
0.204062 | + | 0.978958i | \(0.434586\pi\) | |||||||
\(32\) | 2.29749 | + | 3.97938i | 0.406143 | + | 0.703461i | ||||
\(33\) | 0.798334 | − | 0.0331669i | 0.138972 | − | 0.00577362i | ||||
\(34\) | − | 9.31681i | − | 1.59782i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.10798 | − | 2.35011i | 0.184664 | − | 0.391685i | ||||
\(37\) | 5.02232 | + | 2.89964i | 0.825665 | + | 0.476698i | 0.852366 | − | 0.522946i | \(-0.175167\pi\) |
−0.0267011 | + | 0.999643i | \(0.508500\pi\) | |||||||
\(38\) | 5.91404 | − | 3.41448i | 0.959385 | − | 0.553901i | ||||
\(39\) | 5.19483 | + | 2.71822i | 0.831839 | + | 0.435263i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.25727 | −0.977221 | −0.488610 | − | 0.872502i | \(-0.662496\pi\) | ||||
−0.488610 | + | 0.872502i | \(0.662496\pi\) | |||||||
\(42\) | 2.30567 | − | 7.40752i | 0.355772 | − | 1.14300i | ||||
\(43\) | − | 8.35453i | − | 1.27405i | −0.770842 | − | 0.637027i | \(-0.780164\pi\) | ||
0.770842 | − | 0.637027i | \(-0.219836\pi\) | |||||||
\(44\) | 0.346004 | + | 0.199765i | 0.0521620 | + | 0.0301157i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.81290 | + | 6.60414i | 0.562182 | + | 0.973727i | ||||
\(47\) | 2.73630 | + | 1.57980i | 0.399130 | + | 0.230438i | 0.686109 | − | 0.727499i | \(-0.259317\pi\) |
−0.286978 | + | 0.957937i | \(0.592651\pi\) | |||||||
\(48\) | −7.28756 | + | 4.62108i | −1.05187 | + | 0.666995i | ||||
\(49\) | 1.13564 | − | 6.90727i | 0.162234 | − | 0.986752i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.52380 | − | 0.395668i | 1.33360 | − | 0.0554046i | ||||
\(52\) | 1.46582 | + | 2.53888i | 0.203273 | + | 0.352080i | ||||
\(53\) | −5.78238 | − | 10.0154i | −0.794271 | − | 1.37572i | −0.923301 | − | 0.384078i | \(-0.874519\pi\) |
0.129029 | − | 0.991641i | \(-0.458814\pi\) | |||||||
\(54\) | 8.10570 | + | 3.41782i | 1.10305 | + | 0.465106i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.87179 | + | 3.28720i | −0.517389 | + | 0.439270i | ||||
\(57\) | 3.74149 | + | 5.90043i | 0.495573 | + | 0.781531i | ||||
\(58\) | 11.3150 | + | 6.53271i | 1.48573 | + | 0.857786i | ||||
\(59\) | −4.88061 | − | 8.45346i | −0.635401 | − | 1.10055i | −0.986430 | − | 0.164183i | \(-0.947501\pi\) |
0.351029 | − | 0.936365i | \(-0.385832\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.90647 | − | 3.98746i | −0.884283 | − | 0.510541i | −0.0122151 | − | 0.999925i | \(-0.503888\pi\) |
−0.872068 | + | 0.489384i | \(0.837222\pi\) | |||||||
\(62\) | − | 5.89604i | − | 0.748798i | ||||||
\(63\) | 7.67001 | + | 2.04231i | 0.966330 | + | 0.257307i | ||||
\(64\) | 2.18506 | 0.273132 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.627141 | + | 1.19854i | −0.0771957 | + | 0.147530i | ||||
\(67\) | 0.793481 | − | 0.458116i | 0.0969391 | − | 0.0559678i | −0.450747 | − | 0.892652i | \(-0.648842\pi\) |
0.547686 | + | 0.836684i | \(0.315509\pi\) | |||||||
\(68\) | 4.12768 | + | 2.38312i | 0.500555 | + | 0.288995i | ||||
\(69\) | −6.58893 | + | 4.17808i | −0.793214 | + | 0.502981i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.52593i | − | 0.181094i | −0.995892 | − | 0.0905471i | \(-0.971138\pi\) | ||
0.995892 | − | 0.0905471i | \(-0.0288616\pi\) | |||||||
\(72\) | −3.28331 | − | 4.73146i | −0.386941 | − | 0.557608i | ||||
\(73\) | 3.89906 | + | 6.75338i | 0.456351 | + | 0.790423i | 0.998765 | − | 0.0496883i | \(-0.0158228\pi\) |
−0.542414 | + | 0.840112i | \(0.682489\pi\) | |||||||
\(74\) | −8.50252 | + | 4.90893i | −0.988398 | + | 0.570652i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.49351i | 0.400733i | ||||||||
\(77\) | −0.410798 | + | 1.14932i | −0.0468148 | + | 0.130977i | ||||
\(78\) | −8.38256 | + | 5.31542i | −0.949138 | + | 0.601853i | ||||
\(79\) | −3.58521 | + | 6.20977i | −0.403368 | + | 0.698654i | −0.994130 | − | 0.108192i | \(-0.965494\pi\) |
0.590762 | + | 0.806846i | \(0.298827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.14952 | + | 8.43093i | −0.349946 | + | 0.936770i | ||||
\(82\) | 5.29661 | − | 9.17399i | 0.584912 | − | 1.01310i | ||||
\(83\) | 17.5632i | 1.92781i | 0.266250 | + | 0.963904i | \(0.414215\pi\) | ||||
−0.266250 | + | 0.963904i | \(0.585785\pi\) | |||||||
\(84\) | 2.69204 | + | 2.91624i | 0.293725 | + | 0.318188i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.2489 | + | 7.07188i | 1.32083 | + | 0.762581i | ||||
\(87\) | −6.19732 | + | 11.8438i | −0.664422 | + | 1.26979i | ||||
\(88\) | 0.766937 | − | 0.442791i | 0.0817558 | − | 0.0472017i | ||||
\(89\) | 1.35247 | − | 2.34254i | 0.143361 | − | 0.248309i | −0.785399 | − | 0.618990i | \(-0.787542\pi\) |
0.928760 | + | 0.370681i | \(0.120876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.82718 | + | 5.79637i | −0.715683 | + | 0.607625i | ||||
\(92\) | −3.90116 | −0.406724 | ||||||||
\(93\) | 6.02703 | − | 0.250394i | 0.624974 | − | 0.0259646i | ||||
\(94\) | −4.63241 | + | 2.67452i | −0.477796 | + | 0.275856i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.330363 | − | 7.95189i | −0.0337175 | − | 0.811587i | ||||
\(97\) | −4.44253 | −0.451070 | −0.225535 | − | 0.974235i | \(-0.572413\pi\) | ||||
−0.225535 | + | 0.974235i | \(0.572413\pi\) | |||||||
\(98\) | 9.16569 | + | 7.51181i | 0.925875 | + | 0.758808i | ||||
\(99\) | −1.25180 | − | 0.590174i | −0.125811 | − | 0.0593148i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.36822 | − | 2.36982i | −0.136143 | − | 0.235806i | 0.789891 | − | 0.613248i | \(-0.210137\pi\) |
−0.926033 | + | 0.377442i | \(0.876804\pi\) | |||||||
\(102\) | −7.48154 | + | 14.2981i | −0.740782 | + | 1.41572i | ||||
\(103\) | 9.21552 | − | 15.9618i | 0.908033 | − | 1.57276i | 0.0912387 | − | 0.995829i | \(-0.470917\pi\) |
0.816794 | − | 0.576930i | \(-0.195749\pi\) | |||||||
\(104\) | 6.49817 | 0.637198 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.5785 | 1.90163 | ||||||||
\(107\) | −3.32647 | + | 5.76162i | −0.321582 | + | 0.556997i | −0.980815 | − | 0.194942i | \(-0.937548\pi\) |
0.659232 | + | 0.751939i | \(0.270881\pi\) | |||||||
\(108\) | −3.58755 | + | 2.71688i | −0.345212 | + | 0.261432i | ||||
\(109\) | −3.91662 | − | 6.78379i | −0.375144 | − | 0.649769i | 0.615204 | − | 0.788368i | \(-0.289073\pi\) |
−0.990349 | + | 0.138599i | \(0.955740\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.37908 | − | 8.48295i | −0.510560 | − | 0.805166i | ||||
\(112\) | −2.36402 | − | 12.9676i | −0.223379 | − | 1.22532i | ||||
\(113\) | −17.3914 | −1.63604 | −0.818022 | − | 0.575187i | \(-0.804929\pi\) | ||||
−0.818022 | + | 0.575187i | \(0.804929\pi\) | |||||||
\(114\) | −11.8179 | + | 0.490976i | −1.10685 | + | 0.0459842i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.78845 | + | 3.34196i | −0.537444 | + | 0.310293i | ||||
\(117\) | −5.78951 | − | 8.34305i | −0.535240 | − | 0.771316i | ||||
\(118\) | 16.5252 | 1.52127 | ||||||||
\(119\) | −4.90065 | + | 13.7109i | −0.449242 | + | 1.25688i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.39359 | + | 9.34198i | −0.490327 | + | 0.849271i | ||||
\(122\) | 11.6923 | − | 6.75055i | 1.05857 | − | 0.611166i | ||||
\(123\) | 9.60275 | + | 5.02468i | 0.865850 | + | 0.453060i | ||||
\(124\) | 2.61216 | + | 1.50813i | 0.234579 | + | 0.135434i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.48675 | + | 9.51650i | −0.845147 | + | 0.847797i | ||||
\(127\) | 12.5556i | 1.11413i | 0.830469 | + | 0.557065i | \(0.188073\pi\) | ||||
−0.830469 | + | 0.557065i | \(0.811927\pi\) | |||||||
\(128\) | −6.44458 | + | 11.1623i | −0.569626 | + | 0.986621i | ||||
\(129\) | −6.70881 | + | 12.8213i | −0.590678 | + | 1.12885i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.36275 | − | 5.82446i | 0.293805 | − | 0.508886i | −0.680901 | − | 0.732375i | \(-0.738412\pi\) |
0.974706 | + | 0.223490i | \(0.0717450\pi\) | |||||||
\(132\) | −0.370582 | − | 0.584417i | −0.0322550 | − | 0.0508670i | ||||
\(133\) | −10.4993 | + | 1.91405i | −0.910405 | + | 0.165969i | ||||
\(134\) | 1.55113i | 0.133997i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.14924 | − | 5.28232i | 0.784541 | − | 0.452955i | ||||
\(137\) | −10.1734 | − | 17.6208i | −0.869171 | − | 1.50545i | −0.862845 | − | 0.505468i | \(-0.831320\pi\) |
−0.00632592 | − | 0.999980i | \(-0.502014\pi\) | |||||||
\(138\) | −0.548267 | − | 13.1969i | −0.0466716 | − | 1.12339i | ||||
\(139\) | 9.79157i | 0.830510i | 0.909705 | + | 0.415255i | \(0.136308\pi\) | ||||
−0.909705 | + | 0.415255i | \(0.863692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.93067 | − | 4.62174i | −0.246807 | − | 0.389221i | ||||
\(142\) | 2.23721 | + | 1.29166i | 0.187743 | + | 0.108393i | ||||
\(143\) | 1.35235 | − | 0.780781i | 0.113089 | − | 0.0652922i | ||||
\(144\) | 14.8947 | − | 1.23974i | 1.24122 | − | 0.103312i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.2018 | −1.09259 | ||||||||
\(147\) | −7.28945 | + | 9.68834i | −0.601224 | + | 0.799081i | ||||
\(148\) | − | 5.02257i | − | 0.412852i | ||||||
\(149\) | 14.1195 | + | 8.15190i | 1.15671 | + | 0.667830i | 0.950514 | − | 0.310680i | \(-0.100557\pi\) |
0.206200 | + | 0.978510i | \(0.433890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.54351 | + | 13.0657i | 0.613882 | + | 1.06328i | 0.990580 | + | 0.136939i | \(0.0437263\pi\) |
−0.376697 | + | 0.926336i | \(0.622940\pi\) | |||||||
\(152\) | 6.70613 | + | 3.87179i | 0.543939 | + | 0.314043i | ||||
\(153\) | −14.9335 | − | 7.04054i | −1.20730 | − | 0.569194i | ||||
\(154\) | −1.33733 | − | 1.57515i | −0.107765 | − | 0.126929i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.210775 | − | 5.07339i | −0.0168755 | − | 0.406196i | ||||
\(157\) | −6.22562 | − | 10.7831i | −0.496858 | − | 0.860584i | 0.503135 | − | 0.864208i | \(-0.332180\pi\) |
−0.999993 | + | 0.00362372i | \(0.998847\pi\) | |||||||
\(158\) | −6.06958 | − | 10.5128i | −0.482869 | − | 0.836354i | ||||
\(159\) | 0.831464 | + | 20.0135i | 0.0659394 | + | 1.58717i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.13739 | − | 11.7244i | −0.168450 | − | 0.924015i | ||||
\(162\) | −9.69489 | − | 11.7542i | −0.761703 | − | 0.923495i | ||||
\(163\) | 4.76649 | + | 2.75193i | 0.373340 | + | 0.215548i | 0.674917 | − | 0.737894i | \(-0.264180\pi\) |
−0.301577 | + | 0.953442i | \(0.597513\pi\) | |||||||
\(164\) | 2.70961 | + | 4.69317i | 0.211585 | + | 0.366475i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.7500 | − | 14.8667i | −1.99858 | − | 1.15388i | ||||
\(167\) | − | 0.799023i | − | 0.0618302i | −0.999522 | − | 0.0309151i | \(-0.990158\pi\) | ||
0.999522 | − | 0.0309151i | \(-0.00984216\pi\) | |||||||
\(168\) | 8.58153 | − | 1.93562i | 0.662079 | − | 0.149336i | ||||
\(169\) | −1.54168 | −0.118590 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00377 | − | 12.0596i | −0.0767601 | − | 0.922221i | ||||
\(172\) | −6.26620 | + | 3.61779i | −0.477793 | + | 0.275854i | ||||
\(173\) | 12.5737 | + | 7.25944i | 0.955962 | + | 0.551925i | 0.894928 | − | 0.446211i | \(-0.147227\pi\) |
0.0610338 | + | 0.998136i | \(0.480560\pi\) | |||||||
\(174\) | −12.1187 | − | 19.1116i | −0.918719 | − | 1.44884i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.29830i | 0.173241i | ||||||||
\(177\) | 0.701796 | + | 16.8924i | 0.0527502 | + | 1.26971i | ||||
\(178\) | 2.28965 | + | 3.96579i | 0.171617 | + | 0.297249i | ||||
\(179\) | 2.04442 | − | 1.18035i | 0.152807 | − | 0.0882234i | −0.421647 | − | 0.906760i | \(-0.638548\pi\) |
0.574454 | + | 0.818537i | \(0.305214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.70696i | 0.721513i | 0.932660 | + | 0.360756i | \(0.117481\pi\) | ||||
−0.932660 | + | 0.360756i | \(0.882519\pi\) | |||||||
\(182\) | −2.71923 | − | 14.9160i | −0.201563 | − | 1.10565i | ||||
\(183\) | 7.39707 | + | 11.6654i | 0.546807 | + | 0.862329i | ||||
\(184\) | −4.32357 | + | 7.48865i | −0.318738 | + | 0.552071i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.73461 | + | 9.04839i | −0.347158 | + | 0.663460i | ||||
\(187\) | 1.26938 | − | 2.19863i | 0.0928264 | − | 0.160780i | ||||
\(188\) | − | 2.73643i | − | 0.199575i | ||||||
\(189\) | −10.1308 | − | 9.29337i | −0.736908 | − | 0.675993i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.37389 | + | 2.52527i | 0.316484 | + | 0.182722i | 0.649824 | − | 0.760085i | \(-0.274843\pi\) |
−0.333341 | + | 0.942807i | \(0.608176\pi\) | |||||||
\(192\) | −3.35331 | − | 1.75463i | −0.242004 | − | 0.126630i | ||||
\(193\) | −11.3481 | + | 6.55182i | −0.816853 | + | 0.471610i | −0.849330 | − | 0.527862i | \(-0.822994\pi\) |
0.0324769 | + | 0.999472i | \(0.489660\pi\) | |||||||
\(194\) | 3.76048 | − | 6.51334i | 0.269987 | − | 0.467631i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.67247 | + | 2.13931i | −0.405176 | + | 0.152808i | ||||
\(197\) | 21.2925 | 1.51703 | 0.758516 | − | 0.651655i | \(-0.225925\pi\) | ||||
0.758516 | + | 0.651655i | \(0.225925\pi\) | |||||||
\(198\) | 1.92489 | − | 1.33574i | 0.136796 | − | 0.0949270i | ||||
\(199\) | 5.78974 | − | 3.34271i | 0.410424 | − | 0.236958i | −0.280548 | − | 0.959840i | \(-0.590516\pi\) |
0.690972 | + | 0.722882i | \(0.257183\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.58559 | + | 0.0658738i | −0.111839 | + | 0.00464638i | ||||
\(202\) | 4.63263 | 0.325951 | ||||||||
\(203\) | −13.2153 | − | 15.5654i | −0.927529 | − | 1.09248i | ||||
\(204\) | −4.42089 | − | 6.97185i | −0.309524 | − | 0.488127i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.6014 | + | 27.0224i | 1.08700 | + | 1.88274i | ||||
\(207\) | 13.4668 | − | 1.12090i | 0.936007 | − | 0.0779076i | ||||
\(208\) | −8.43218 | + | 14.6050i | −0.584666 | + | 1.01267i | ||||
\(209\) | 1.86084 | 0.128717 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.72156 | 0.393889 | 0.196944 | − | 0.980415i | \(-0.436898\pi\) | ||||
0.196944 | + | 0.980415i | \(0.436898\pi\) | |||||||
\(212\) | −5.00793 | + | 8.67399i | −0.343946 | + | 0.595732i | ||||
\(213\) | −1.22534 | + | 2.34177i | −0.0839591 | + | 0.160456i | ||||
\(214\) | −5.63154 | − | 9.75412i | −0.384964 | − | 0.666778i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.23931 | + | 9.89770i | 0.0843245 | + | 0.673453i | ||||
\(217\) | −3.10132 | + | 8.67678i | −0.210531 | + | 0.589019i | ||||
\(218\) | 13.2613 | 0.898166 | ||||||||
\(219\) | −0.560657 | − | 13.4951i | −0.0378857 | − | 0.911915i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.1330 | − | 9.31439i | 1.08522 | − | 0.626554i | ||||
\(222\) | 16.9904 | − | 0.705869i | 1.14032 | − | 0.0473748i | ||||
\(223\) | −5.83493 | −0.390736 | −0.195368 | − | 0.980730i | \(-0.562590\pi\) | ||||
−0.195368 | + | 0.980730i | \(0.562590\pi\) | |||||||
\(224\) | 11.4479 | + | 4.09180i | 0.764896 | + | 0.273395i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.7213 | − | 25.4981i | 0.979249 | − | 1.69611i | ||||
\(227\) | 9.88387 | − | 5.70646i | 0.656016 | − | 0.378751i | −0.134741 | − | 0.990881i | \(-0.543020\pi\) |
0.790757 | + | 0.612130i | \(0.209687\pi\) | |||||||
\(228\) | 2.80534 | − | 5.36134i | 0.185788 | − | 0.355063i | ||||
\(229\) | −0.910719 | − | 0.525804i | −0.0601820 | − | 0.0347461i | 0.469607 | − | 0.882876i | \(-0.344396\pi\) |
−0.529789 | + | 0.848129i | \(0.677729\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.55335 | − | 1.43393i | 0.102203 | − | 0.0943457i | ||||
\(232\) | 14.8153i | 0.972672i | ||||||||
\(233\) | −1.94244 | + | 3.36441i | −0.127254 | + | 0.220410i | −0.922612 | − | 0.385730i | \(-0.873950\pi\) |
0.795358 | + | 0.606140i | \(0.207283\pi\) | |||||||
\(234\) | 17.1327 | − | 1.42602i | 1.12000 | − | 0.0932220i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.22694 | + | 7.32127i | −0.275150 | + | 0.476574i | ||||
\(237\) | 10.4886 | − | 6.65088i | 0.681308 | − | 0.432021i | ||||
\(238\) | −15.9537 | − | 18.7909i | −1.03413 | − | 1.21803i | ||||
\(239\) | − | 6.40306i | − | 0.414180i | −0.978322 | − | 0.207090i | \(-0.933601\pi\) | ||
0.978322 | − | 0.207090i | \(-0.0663993\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.96093 | − | 1.13215i | 0.126315 | − | 0.0729279i | −0.435511 | − | 0.900183i | \(-0.643432\pi\) |
0.561826 | + | 0.827255i | \(0.310099\pi\) | |||||||
\(242\) | −9.13106 | − | 15.8155i | −0.586967 | − | 1.01666i | ||||
\(243\) | 11.6036 | − | 10.4095i | 0.744370 | − | 0.667767i | ||||
\(244\) | 6.90681i | 0.442163i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.4953 | + | 9.82566i | −0.987945 | + | 0.626461i | ||||
\(247\) | 11.8250 | + | 6.82718i | 0.752408 | + | 0.434403i | ||||
\(248\) | 5.79000 | − | 3.34286i | 0.367665 | − | 0.212272i | ||||
\(249\) | 14.1035 | − | 26.9534i | 0.893772 | − | 1.70810i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3221 | 0.840886 | 0.420443 | − | 0.907319i | \(-0.361875\pi\) | ||||
0.420443 | + | 0.907319i | \(0.361875\pi\) | |||||||
\(252\) | −1.78957 | − | 6.63717i | −0.112732 | − | 0.418102i | ||||
\(253\) | 2.07798i | 0.130641i | ||||||||
\(254\) | −18.4082 | − | 10.6280i | −1.15503 | − | 0.666859i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.72527 | − | 15.1126i | −0.545329 | − | 0.944538i | ||||
\(257\) | 16.9680 | + | 9.79648i | 1.05844 | + | 0.611088i | 0.924999 | − | 0.379969i | \(-0.124066\pi\) |
0.133436 | + | 0.991057i | \(0.457399\pi\) | |||||||
\(258\) | −13.1190 | − | 20.6889i | −0.816750 | − | 1.28804i | ||||
\(259\) | 15.0947 | − | 2.75180i | 0.937937 | − | 0.170988i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.0215 | − | 13.1996i | 1.17740 | − | 0.817035i | ||||
\(262\) | 5.69296 | + | 9.86050i | 0.351712 | + | 0.609184i | ||||
\(263\) | 8.38678 | + | 14.5263i | 0.517151 | + | 0.895732i | 0.999802 | + | 0.0199186i | \(0.00634072\pi\) |
−0.482651 | + | 0.875813i | \(0.660326\pi\) | |||||||
\(264\) | −1.53255 | + | 0.0636701i | −0.0943220 | + | 0.00391863i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.08112 | − | 17.0136i | 0.372858 | − | 1.04317i | ||||
\(267\) | −3.95666 | + | 2.50894i | −0.242144 | + | 0.153545i | ||||
\(268\) | −0.687207 | − | 0.396759i | −0.0419779 | − | 0.0242359i | ||||
\(269\) | −14.6703 | − | 25.4097i | −0.894465 | − | 1.54926i | −0.834466 | − | 0.551060i | \(-0.814224\pi\) |
−0.0599988 | − | 0.998198i | \(-0.519110\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.57129 | + | 1.48454i | 0.156195 | + | 0.0901792i | 0.576060 | − | 0.817407i | \(-0.304589\pi\) |
−0.419865 | + | 0.907586i | \(0.637923\pi\) | |||||||
\(272\) | 27.4178i | 1.66245i | ||||||||
\(273\) | 15.1319 | − | 3.41310i | 0.915827 | − | 0.206570i | ||||
\(274\) | 34.4460 | 2.08096 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.98694 | + | 3.13269i | 0.360371 | + | 0.188566i | ||||
\(277\) | −11.2803 | + | 6.51269i | −0.677768 | + | 0.391309i | −0.799014 | − | 0.601313i | \(-0.794644\pi\) |
0.121246 | + | 0.992623i | \(0.461311\pi\) | |||||||
\(278\) | −14.3558 | − | 8.28830i | −0.861001 | − | 0.497099i | ||||
\(279\) | −9.45048 | − | 4.45553i | −0.565786 | − | 0.266745i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.4404i | 1.15972i | 0.814717 | + | 0.579859i | \(0.196892\pi\) | ||||
−0.814717 | + | 0.579859i | \(0.803108\pi\) | |||||||
\(282\) | 9.25683 | − | 0.384577i | 0.551236 | − | 0.0229012i | ||||
\(283\) | −2.81977 | − | 4.88399i | −0.167618 | − | 0.290323i | 0.769964 | − | 0.638088i | \(-0.220274\pi\) |
−0.937582 | + | 0.347764i | \(0.886941\pi\) | |||||||
\(284\) | −1.14450 | + | 0.660778i | −0.0679136 | + | 0.0392099i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.64364i | 0.156322i | ||||||||
\(287\) | −12.6202 | + | 10.7147i | −0.744945 | + | 0.632469i | ||||
\(288\) | −5.87850 | + | 12.4687i | −0.346394 | + | 0.734725i | ||||
\(289\) | 6.64321 | − | 11.5064i | 0.390777 | − | 0.676846i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.81775 | + | 3.56741i | 0.399663 | + | 0.209126i | ||||
\(292\) | 3.37685 | − | 5.84888i | 0.197615 | − | 0.342280i | ||||
\(293\) | − | 21.5754i | − | 1.26045i | −0.776412 | − | 0.630226i | \(-0.782962\pi\) | ||
0.776412 | − | 0.630226i | \(-0.217038\pi\) | |||||||
\(294\) | −8.03409 | − | 18.8882i | −0.468557 | − | 1.10158i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.64129 | − | 5.56640i | −0.560389 | − | 0.323541i | ||||
\(297\) | 1.44716 | + | 1.91093i | 0.0839730 | + | 0.110883i | ||||
\(298\) | −23.9036 | + | 13.8007i | −1.38470 | + | 0.799455i | ||||
\(299\) | −7.62382 | + | 13.2049i | −0.440897 | + | 0.763656i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3060 | − | 16.8501i | −0.824582 | − | 0.971224i | ||||
\(302\) | −25.5415 | −1.46975 | ||||||||
\(303\) | 0.196739 | + | 4.73555i | 0.0113024 | + | 0.272050i | ||||
\(304\) | −17.4041 | + | 10.0482i | −0.998191 | + | 0.576306i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 22.9632 | − | 15.9349i | 1.31272 | − | 0.910935i | ||||
\(307\) | −22.9288 | −1.30861 | −0.654307 | − | 0.756229i | \(-0.727040\pi\) | ||||
−0.654307 | + | 0.756229i | \(0.727040\pi\) | |||||||
\(308\) | 1.03992 | − | 0.189580i | 0.0592549 | − | 0.0108023i | ||||
\(309\) | −26.9602 | + | 17.0956i | −1.53371 | + | 0.972534i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.799023 | − | 1.38395i | −0.0453084 | − | 0.0784765i | 0.842482 | − | 0.538725i | \(-0.181094\pi\) |
−0.887790 | + | 0.460248i | \(0.847760\pi\) | |||||||
\(312\) | −9.97245 | − | 5.21813i | −0.564579 | − | 0.295418i | ||||
\(313\) | −14.4421 | + | 25.0145i | −0.816318 | + | 1.41390i | 0.0920593 | + | 0.995754i | \(0.470655\pi\) |
−0.908378 | + | 0.418151i | \(0.862678\pi\) | |||||||
\(314\) | 21.0793 | 1.18957 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.21007 | 0.349344 | ||||||||
\(317\) | 3.28018 | − | 5.68143i | 0.184233 | − | 0.319101i | −0.759085 | − | 0.650992i | \(-0.774353\pi\) |
0.943318 | + | 0.331891i | \(0.107687\pi\) | |||||||
\(318\) | −30.0463 | − | 15.7219i | −1.68491 | − | 0.881638i | ||||
\(319\) | 1.78012 | + | 3.08325i | 0.0996674 | + | 0.172629i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.73166 | − | 6.17090i | 0.543168 | − | 0.344426i | ||||
\(322\) | 18.9988 | + | 6.79071i | 1.05876 | + | 0.378432i | ||||
\(323\) | 22.1991 | 1.23519 | ||||||||
\(324\) | 7.68735 | − | 1.28862i | 0.427075 | − | 0.0715903i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.06940 | + | 4.65887i | −0.446923 | + | 0.258031i | ||||
\(327\) | 0.563181 | + | 13.5559i | 0.0311440 | + | 0.749642i | ||||
\(328\) | 12.0120 | 0.663251 | ||||||||
\(329\) | 8.22399 | − | 1.49925i | 0.453403 | − | 0.0826566i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.76497 | − | 11.7173i | 0.371836 | − | 0.644040i | −0.618012 | − | 0.786169i | \(-0.712062\pi\) |
0.989848 | + | 0.142129i | \(0.0453949\pi\) | |||||||
\(332\) | 13.1730 | − | 7.60544i | 0.722963 | − | 0.417403i | ||||
\(333\) | 1.44310 | + | 17.3379i | 0.0790815 | + | 0.950110i | ||||
\(334\) | 1.17147 | + | 0.676351i | 0.0641002 | + | 0.0370083i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.78520 | + | 21.7991i | −0.370163 | + | 1.18924i | ||||
\(337\) | − | 30.7122i | − | 1.67300i | −0.547966 | − | 0.836501i | \(-0.684598\pi\) | ||
0.547966 | − | 0.836501i | \(-0.315402\pi\) | |||||||
\(338\) | 1.30499 | − | 2.26030i | 0.0709819 | − | 0.122944i | ||||
\(339\) | 26.6898 | + | 13.9655i | 1.44959 | + | 0.758504i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.803314 | − | 1.39138i | 0.0435019 | − | 0.0753475i | ||||
\(342\) | 18.5307 | + | 8.73647i | 1.00202 | + | 0.472414i | ||||
\(343\) | −9.53729 | − | 15.8758i | −0.514965 | − | 0.857211i | ||||
\(344\) | 16.0381i | 0.864715i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.2866 | + | 12.2898i | −1.14438 | + | 0.660706i | ||||
\(347\) | −3.91036 | − | 6.77295i | −0.209919 | − | 0.363591i | 0.741770 | − | 0.670655i | \(-0.233987\pi\) |
−0.951689 | + | 0.307064i | \(0.900653\pi\) | |||||||
\(348\) | 11.5669 | − | 0.480550i | 0.620052 | − | 0.0257602i | ||||
\(349\) | 25.1501i | 1.34625i | 0.739526 | + | 0.673127i | \(0.235049\pi\) | ||||
−0.739526 | + | 0.673127i | \(0.764951\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.18530 | + | 17.4528i | 0.116643 | + | 0.931560i | ||||
\(352\) | −1.83575 | − | 1.05987i | −0.0978458 | − | 0.0564913i | ||||
\(353\) | −10.6252 | + | 6.13445i | −0.565521 | + | 0.326504i | −0.755359 | − | 0.655312i | \(-0.772537\pi\) |
0.189837 | + | 0.981816i | \(0.439204\pi\) | |||||||
\(354\) | −25.3605 | − | 13.2700i | −1.34790 | − | 0.705292i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.34265 | −0.124160 | ||||||||
\(357\) | 18.5309 | − | 17.1062i | 0.980757 | − | 0.905356i | ||||
\(358\) | 3.99653i | 0.211223i | ||||||||
\(359\) | 7.11574 | + | 4.10828i | 0.375555 | + | 0.216827i | 0.675882 | − | 0.737010i | \(-0.263763\pi\) |
−0.300328 | + | 0.953836i | \(0.597096\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.36436 | − | 2.36315i | −0.0718086 | − | 0.124376i | ||||
\(362\) | −14.2317 | − | 8.21668i | −0.748002 | − | 0.431859i | ||||
\(363\) | 15.7791 | − | 10.0056i | 0.828186 | − | 0.525157i | ||||
\(364\) | 7.30388 | + | 2.61061i | 0.382827 | + | 0.136833i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −23.3644 | + | 0.970679i | −1.22128 | + | 0.0507382i | ||||
\(367\) | −13.9526 | − | 24.1666i | −0.728320 | − | 1.26149i | −0.957593 | − | 0.288125i | \(-0.906968\pi\) |
0.229273 | − | 0.973362i | \(-0.426365\pi\) | |||||||
\(368\) | −11.2207 | − | 19.4349i | −0.584921 | − | 1.01311i | ||||
\(369\) | −10.7020 | − | 15.4223i | −0.557125 | − | 0.802853i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.8123 | − | 10.2983i | −1.49586 | − | 0.534663i | ||||
\(372\) | −2.79771 | − | 4.41206i | −0.145054 | − | 0.228755i | ||||
\(373\) | −15.6612 | − | 9.04199i | −0.810905 | − | 0.468176i | 0.0363650 | − | 0.999339i | \(-0.488422\pi\) |
−0.847270 | + | 0.531162i | \(0.821755\pi\) | |||||||
\(374\) | 2.14900 | + | 3.72217i | 0.111122 | + | 0.192469i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.25284 | − | 3.03273i | −0.270895 | − | 0.156401i | ||||
\(377\) | 26.1241i | 1.34546i | ||||||||
\(378\) | 22.2008 | − | 6.98655i | 1.14189 | − | 0.359349i | ||||
\(379\) | −24.7450 | −1.27107 | −0.635534 | − | 0.772073i | \(-0.719220\pi\) | ||||
−0.635534 | + | 0.772073i | \(0.719220\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.0823 | − | 19.2685i | 0.516534 | − | 0.987157i | ||||
\(382\) | −7.40476 | + | 4.27514i | −0.378861 | + | 0.218735i | ||||
\(383\) | 11.1972 | + | 6.46470i | 0.572150 | + | 0.330331i | 0.758008 | − | 0.652246i | \(-0.226173\pi\) |
−0.185858 | + | 0.982577i | \(0.559506\pi\) | |||||||
\(384\) | 18.8537 | − | 11.9552i | 0.962126 | − | 0.610089i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 22.1838i | − | 1.12912i | ||||||
\(387\) | 20.5914 | − | 14.2890i | 1.04672 | − | 0.726352i | ||||
\(388\) | 1.92376 | + | 3.33205i | 0.0976642 | + | 0.169159i | ||||
\(389\) | −16.4024 | + | 9.46992i | −0.831634 | + | 0.480144i | −0.854412 | − | 0.519596i | \(-0.826082\pi\) |
0.0227777 | + | 0.999741i | \(0.492749\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.7894i | 1.25365i | ||||||||
\(392\) | −2.18007 | + | 13.2598i | −0.110110 | + | 0.669721i | ||||
\(393\) | −9.83780 | + | 6.23820i | −0.496251 | + | 0.314675i | ||||
\(394\) | −18.0236 | + | 31.2177i | −0.908014 | + | 1.57273i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0994198 | + | 1.19446i | 0.00499603 | + | 0.0600239i | ||||
\(397\) | 3.64333 | − | 6.31044i | 0.182854 | − | 0.316712i | −0.759998 | − | 0.649926i | \(-0.774800\pi\) |
0.942851 | + | 0.333214i | \(0.108133\pi\) | |||||||
\(398\) | 11.3181i | 0.567323i | ||||||||
\(399\) | 17.6498 | + | 5.49369i | 0.883596 | + | 0.275028i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.7394 | − | 7.93243i | −0.686111 | − | 0.396126i | 0.116042 | − | 0.993244i | \(-0.462979\pi\) |
−0.802154 | + | 0.597118i | \(0.796312\pi\) | |||||||
\(402\) | 1.24558 | − | 2.38045i | 0.0621240 | − | 0.118726i | ||||
\(403\) | 10.2096 | − | 5.89451i | 0.508576 | − | 0.293626i | ||||
\(404\) | −1.18497 | + | 2.05242i | −0.0589543 | + | 0.102112i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.0073 | − | 6.19963i | 1.68776 | − | 0.307682i | ||||
\(407\) | −2.67530 | −0.132610 | ||||||||
\(408\) | −18.2827 | + | 0.759558i | −0.905129 | + | 0.0376037i | ||||
\(409\) | 22.8109 | − | 13.1699i | 1.12793 | − | 0.651209i | 0.184515 | − | 0.982830i | \(-0.440929\pi\) |
0.943413 | + | 0.331620i | \(0.107595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.46286 | + | 35.2113i | 0.0721575 | + | 1.73684i | ||||
\(412\) | −15.9625 | −0.786417 | ||||||||
\(413\) | −24.3190 | − | 8.69228i | −1.19666 | − | 0.427719i | ||||
\(414\) | −9.75590 | + | 20.6929i | −0.479476 | + | 1.01700i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.77705 | − | 13.4702i | −0.381301 | − | 0.660433i | ||||
\(417\) | 7.86278 | − | 15.0267i | 0.385042 | − | 0.735860i | ||||
\(418\) | −1.57515 | + | 2.72824i | −0.0770432 | + | 0.133443i | ||||
\(419\) | 14.3499 | 0.701039 | 0.350519 | − | 0.936555i | \(-0.386005\pi\) | ||||
0.350519 | + | 0.936555i | \(0.386005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0679 | −0.490682 | −0.245341 | − | 0.969437i | \(-0.578900\pi\) | ||||
−0.245341 | + | 0.969437i | \(0.578900\pi\) | |||||||
\(422\) | −4.84315 | + | 8.38858i | −0.235761 | + | 0.408350i | ||||
\(423\) | 0.786241 | + | 9.44616i | 0.0382284 | + | 0.459288i | ||||
\(424\) | 11.1004 | + | 19.2264i | 0.539082 | + | 0.933717i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.39613 | − | 3.77876i | −0.116093 | − | 0.183082i | ||||
\(427\) | −20.7575 | + | 3.78415i | −1.00453 | + | 0.183128i | ||||
\(428\) | 5.76190 | 0.278512 | ||||||||
\(429\) | −2.70237 | + | 0.112271i | −0.130472 | + | 0.00542047i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.13983 | + | 4.12218i | −0.343914 | + | 0.198559i | −0.662001 | − | 0.749503i | \(-0.730293\pi\) |
0.318088 | + | 0.948061i | \(0.396959\pi\) | |||||||
\(432\) | −23.8537 | − | 10.0581i | −1.14766 | − | 0.483919i | ||||
\(433\) | 10.7241 | 0.515367 | 0.257683 | − | 0.966229i | \(-0.417041\pi\) | ||||
0.257683 | + | 0.966229i | \(0.417041\pi\) | |||||||
\(434\) | −10.0961 | − | 11.8916i | −0.484631 | − | 0.570816i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.39206 | + | 5.87521i | −0.162450 | + | 0.281372i | ||||
\(437\) | −15.7356 | + | 9.08496i | −0.752737 | + | 0.434593i | ||||
\(438\) | 20.2602 | + | 10.6013i | 0.968071 | + | 0.506548i | ||||
\(439\) | 2.74233 | + | 1.58329i | 0.130884 | + | 0.0755661i | 0.564013 | − | 0.825766i | \(-0.309257\pi\) |
−0.433128 | + | 0.901332i | \(0.642590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.9667 | − | 9.01472i | 0.903175 | − | 0.429273i | ||||
\(442\) | 31.5375i | 1.50009i | ||||||||
\(443\) | −8.72667 | + | 15.1150i | −0.414617 | + | 0.718137i | −0.995388 | − | 0.0959297i | \(-0.969418\pi\) |
0.580772 | + | 0.814067i | \(0.302751\pi\) | |||||||
\(444\) | −4.03319 | + | 7.70791i | −0.191407 | + | 0.365801i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.93911 | − | 8.55480i | 0.233874 | − | 0.405081i | ||||
\(447\) | −15.1225 | − | 23.8485i | −0.715268 | − | 1.12800i | ||||
\(448\) | 4.40700 | − | 3.74161i | 0.208211 | − | 0.176774i | ||||
\(449\) | 12.2873i | 0.579876i | 0.957046 | + | 0.289938i | \(0.0936346\pi\) | ||||
−0.957046 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.49985 | − | 1.44329i | 0.117713 | − | 0.0679618i | ||||
\(452\) | 7.53105 | + | 13.0442i | 0.354231 | + | 0.613546i | ||||
\(453\) | −1.08470 | − | 26.1090i | −0.0509637 | − | 1.22671i | ||||
\(454\) | 19.3215i | 0.906801i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.18250 | − | 11.3270i | −0.336351 | − | 0.530434i | ||||
\(457\) | −4.23430 | − | 2.44467i | −0.198072 | − | 0.114357i | 0.397684 | − | 0.917523i | \(-0.369814\pi\) |
−0.595756 | + | 0.803165i | \(0.703147\pi\) | |||||||
\(458\) | 1.54180 | − | 0.890158i | 0.0720435 | − | 0.0415943i | ||||
\(459\) | 17.2641 | + | 22.7966i | 0.805818 | + | 1.06405i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.12746 | 0.238810 | 0.119405 | − | 0.992846i | \(-0.461901\pi\) | ||||
0.119405 | + | 0.992846i | \(0.461901\pi\) | |||||||
\(462\) | 0.787463 | + | 3.49121i | 0.0366361 | + | 0.162426i | ||||
\(463\) | − | 39.9073i | − | 1.85465i | −0.374257 | − | 0.927325i | \(-0.622102\pi\) | ||
0.374257 | − | 0.927325i | \(-0.377898\pi\) | |||||||
\(464\) | −33.2981 | − | 19.2247i | −1.54583 | − | 0.892483i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.28845 | − | 5.69577i | −0.152335 | − | 0.263851i | ||||
\(467\) | −7.90350 | − | 4.56309i | −0.365730 | − | 0.211155i | 0.305861 | − | 0.952076i | \(-0.401056\pi\) |
−0.671592 | + | 0.740922i | \(0.734389\pi\) | |||||||
\(468\) | −3.75054 | + | 7.95516i | −0.173369 | + | 0.367727i | ||||
\(469\) | 0.815897 | − | 2.28269i | 0.0376746 | − | 0.105405i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.895198 | + | 21.5476i | 0.0412486 | + | 0.992860i | ||||
\(472\) | 9.36925 | + | 16.2280i | 0.431254 | + | 0.746955i | ||||
\(473\) | 1.92704 | + | 3.33773i | 0.0886053 | + | 0.153469i | ||||
\(474\) | 0.872760 | + | 21.0075i | 0.0400872 | + | 0.964907i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.4058 | − | 2.26161i | 0.568619 | − | 0.103661i | ||||
\(477\) | 14.7951 | − | 31.3815i | 0.677422 | − | 1.43686i | ||||
\(478\) | 9.38775 | + | 5.42002i | 0.429386 | + | 0.247906i | ||||
\(479\) | −6.20210 | − | 10.7424i | −0.283381 | − | 0.490831i | 0.688834 | − | 0.724919i | \(-0.258123\pi\) |
−0.972215 | + | 0.234088i | \(0.924790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.0006 | − | 9.81532i | −0.775162 | − | 0.447540i | ||||
\(482\) | 3.83332i | 0.174603i | ||||||||
\(483\) | −6.13473 | + | 19.7093i | −0.279140 | + | 0.896805i | ||||
\(484\) | 9.34243 | 0.424656 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.43955 | + | 25.8237i | 0.246743 | + | 1.17139i | ||||
\(487\) | 12.2665 | − | 7.08208i | 0.555849 | − | 0.320920i | −0.195628 | − | 0.980678i | \(-0.562675\pi\) |
0.751478 | + | 0.659758i | \(0.229341\pi\) | |||||||
\(488\) | 13.2583 | + | 7.65467i | 0.600174 | + | 0.346511i | ||||
\(489\) | −5.10507 | − | 8.05083i | −0.230859 | − | 0.364071i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1216i | 1.44963i | 0.688946 | + | 0.724813i | \(0.258074\pi\) | ||||
−0.688946 | + | 0.724813i | \(0.741926\pi\) | |||||||
\(492\) | −0.389621 | − | 9.37826i | −0.0175655 | − | 0.422805i | ||||
\(493\) | 21.2361 | + | 36.7819i | 0.956424 | + | 1.65658i | ||||
\(494\) | −20.0191 | + | 11.5580i | −0.900703 | + | 0.520021i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.3511i | 0.779086i | ||||||||
\(497\) | −2.61294 | − | 3.07762i | −0.117206 | − | 0.138050i | ||||
\(498\) | 27.5791 | + | 43.4929i | 1.23585 | + | 1.94897i | ||||
\(499\) | 13.3589 | − | 23.1383i | 0.598027 | − | 1.03581i | −0.395085 | − | 0.918644i | \(-0.629285\pi\) |
0.993112 | − | 0.117168i | \(-0.0373817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.641627 | + | 1.22622i | −0.0286658 | + | 0.0547837i | ||||
\(502\) | −11.2768 | + | 19.5320i | −0.503310 | + | 0.871758i | ||||
\(503\) | − | 9.55539i | − | 0.426054i | −0.977046 | − | 0.213027i | \(-0.931668\pi\) | ||
0.977046 | − | 0.213027i | \(-0.0683322\pi\) | |||||||
\(504\) | −14.7240 | − | 3.92059i | −0.655860 | − | 0.174637i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.04659 | − | 1.75895i | −0.135438 | − | 0.0781950i | ||||
\(507\) | 2.36594 | + | 1.23799i | 0.105075 | + | 0.0549810i | ||||
\(508\) | 9.41716 | − | 5.43700i | 0.417819 | − | 0.241228i | ||||
\(509\) | 9.10071 | − | 15.7629i | 0.403382 | − | 0.698678i | −0.590750 | − | 0.806855i | \(-0.701168\pi\) |
0.994132 | + | 0.108177i | \(0.0345013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.4282 | + | 6.94417i | 0.859452 | + | 0.307192i | ||||
\(512\) | 3.76451 | 0.166369 | ||||||||
\(513\) | −8.14360 | + | 19.3134i | −0.359549 | + | 0.852706i | ||||
\(514\) | −28.7259 | + | 16.5849i | −1.26705 | + | 0.731530i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.5216 | − | 0.520212i | 0.551232 | − | 0.0229010i | ||||
\(517\) | −1.45758 | −0.0641042 | ||||||||
\(518\) | −8.74273 | + | 24.4601i | −0.384133 | + | 1.07472i | ||||
\(519\) | −13.4669 | − | 21.2376i | −0.591130 | − | 0.932228i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.93741 | − | 3.35569i | −0.0848794 | − | 0.147015i | 0.820460 | − | 0.571703i | \(-0.193717\pi\) |
−0.905340 | + | 0.424688i | \(0.860384\pi\) | |||||||
\(522\) | 3.25122 | + | 39.0612i | 0.142302 | + | 1.70966i | ||||
\(523\) | −9.42099 | + | 16.3176i | −0.411951 | + | 0.713520i | −0.995103 | − | 0.0988429i | \(-0.968486\pi\) |
0.583152 | + | 0.812363i | \(0.301819\pi\) | |||||||
\(524\) | −5.82474 | −0.254455 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.3967 | −1.23816 | ||||||||
\(527\) | 9.58321 | − | 16.5986i | 0.417451 | − | 0.723047i | ||||
\(528\) | 1.84557 | − | 3.52711i | 0.0803183 | − | 0.153498i | ||||
\(529\) | 1.35494 | + | 2.34682i | 0.0589104 | + | 0.102036i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.4878 | − | 26.4875i | 0.541924 | − | 1.14946i | ||||
\(532\) | 5.98216 | + | 7.04601i | 0.259359 | + | 0.305483i | ||||
\(533\) | 21.1809 | 0.917448 | ||||||||
\(534\) | −0.329235 | − | 7.92475i | −0.0142474 | − | 0.342937i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.52324 | + | 0.879440i | −0.0657937 | + | 0.0379860i | ||||
\(537\) | −4.08532 | + | 0.169725i | −0.176295 | + | 0.00732419i | ||||
\(538\) | 49.6721 | 2.14152 | ||||||||
\(539\) | 1.13952 | + | 3.02147i | 0.0490824 | + | 0.130144i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0977 | + | 19.2218i | −0.477128 | + | 0.826410i | −0.999656 | − | 0.0262117i | \(-0.991656\pi\) |
0.522528 | + | 0.852622i | \(0.324989\pi\) | |||||||
\(542\) | −4.35306 | + | 2.51324i | −0.186980 | + | 0.107953i | ||||
\(543\) | 7.79483 | − | 14.8968i | 0.334508 | − | 0.639285i | ||||
\(544\) | −21.8997 | − | 12.6438i | −0.938944 | − | 0.542099i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.80472 | + | 25.0746i | −0.334011 | + | 1.07309i | ||||
\(547\) | − | 1.23468i | − | 0.0527911i | −0.999652 | − | 0.0263956i | \(-0.991597\pi\) | ||
0.999652 | − | 0.0263956i | \(-0.00840295\pi\) | |||||||
\(548\) | −8.81083 | + | 15.2608i | −0.376380 | + | 0.651910i | ||||
\(549\) | −1.98449 | − | 23.8423i | −0.0846959 | − | 1.01756i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.5654 | + | 26.9601i | −0.663109 | + | 1.14854i | ||||
\(552\) | 12.6487 | − | 8.02060i | 0.538364 | − | 0.341379i | ||||
\(553\) | 3.40242 | + | 18.6636i | 0.144685 | + | 0.793656i | ||||
\(554\) | − | 22.0513i | − | 0.936868i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.34403 | − | 4.24008i | 0.311456 | − | 0.179819i | ||||
\(557\) | −1.15681 | − | 2.00365i | −0.0490155 | − | 0.0848973i | 0.840477 | − | 0.541848i | \(-0.182275\pi\) |
−0.889492 | + | 0.456950i | \(0.848942\pi\) | |||||||
\(558\) | 14.5320 | − | 10.0842i | 0.615188 | − | 0.426898i | ||||
\(559\) | 28.2802i | 1.19612i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.71360 | + | 2.35481i | −0.156788 | + | 0.0994203i | ||||
\(562\) | −28.5023 | − | 16.4558i | −1.20230 | − | 0.694146i | ||||
\(563\) | 15.7239 | − | 9.07818i | 0.662682 | − | 0.382600i | −0.130616 | − | 0.991433i | \(-0.541696\pi\) |
0.793298 | + | 0.608833i | \(0.208362\pi\) | |||||||
\(564\) | −2.19740 | + | 4.19948i | −0.0925270 | + | 0.176830i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.54745 | 0.401309 | ||||||||
\(567\) | 8.08459 | + | 22.3973i | 0.339521 | + | 0.940599i | ||||
\(568\) | 2.92930i | 0.122911i | ||||||||
\(569\) | 12.9811 | + | 7.49465i | 0.544197 | + | 0.314192i | 0.746778 | − | 0.665073i | \(-0.231600\pi\) |
−0.202581 | + | 0.979265i | \(0.564933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.6375 | − | 20.1568i | −0.487015 | − | 0.843535i | 0.512873 | − | 0.858464i | \(-0.328581\pi\) |
−0.999889 | + | 0.0149293i | \(0.995248\pi\) | |||||||
\(572\) | −1.17123 | − | 0.676208i | −0.0489715 | − | 0.0282737i | ||||
\(573\) | −4.68459 | − | 7.38771i | −0.195701 | − | 0.308626i | ||||
\(574\) | −5.02655 | − | 27.5726i | −0.209804 | − | 1.15086i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.73718 | + | 5.38551i | 0.155716 | + | 0.224396i | ||||
\(577\) | 13.3341 | + | 23.0953i | 0.555105 | + | 0.961471i | 0.997895 | + | 0.0648455i | \(0.0206554\pi\) |
−0.442790 | + | 0.896625i | \(0.646011\pi\) | |||||||
\(578\) | 11.2466 | + | 19.4797i | 0.467797 | + | 0.810248i | ||||
\(579\) | 22.6766 | − | 0.942104i | 0.942408 | − | 0.0391525i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0745 | + | 35.4229i | 1.24770 | + | 1.46959i | ||||
\(582\) | −11.0013 | + | 6.97601i | −0.456021 | + | 0.289165i | ||||
\(583\) | 4.62026 | + | 2.66751i | 0.191351 | + | 0.110477i | ||||
\(584\) | −7.48499 | − | 12.9644i | −0.309731 | − | 0.536470i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.6325 | + | 18.2630i | 1.30673 | + | 0.754439i | ||||
\(587\) | − | 45.9722i | − | 1.89748i | −0.316065 | − | 0.948738i | \(-0.602362\pi\) | ||
0.316065 | − | 0.948738i | \(-0.397638\pi\) | |||||||
\(588\) | 10.4232 | + | 1.27197i | 0.429845 | + | 0.0524553i | ||||
\(589\) | 14.0484 | 0.578856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.6767 | − | 17.0982i | −1.34414 | − | 0.703327i | ||||
\(592\) | 25.0215 | − | 14.4462i | 1.02838 | − | 0.593735i | ||||
\(593\) | −2.68984 | − | 1.55298i | −0.110458 | − | 0.0637732i | 0.443753 | − | 0.896149i | \(-0.353647\pi\) |
−0.554211 | + | 0.832376i | \(0.686980\pi\) | |||||||
\(594\) | −4.02666 | + | 0.504187i | −0.165216 | + | 0.0206871i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 14.1202i | − | 0.578385i | ||||||
\(597\) | −11.5695 | + | 0.480657i | −0.473508 | + | 0.0196720i | ||||
\(598\) | −12.9067 | − | 22.3551i | −0.527795 | − | 0.914168i | ||||
\(599\) | −7.34708 | + | 4.24184i | −0.300193 | + | 0.173317i | −0.642530 | − | 0.766261i | \(-0.722115\pi\) |
0.342336 | + | 0.939577i | \(0.388782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.63388i | − | 0.107438i | −0.998556 | − | 0.0537191i | \(-0.982892\pi\) | ||
0.998556 | − | 0.0537191i | \(-0.0171076\pi\) | |||||||
\(602\) | 36.8141 | − | 6.71131i | 1.50043 | − | 0.273533i | ||||
\(603\) | 2.48624 | + | 1.17216i | 0.101247 | + | 0.0477341i | ||||
\(604\) | 6.53319 | − | 11.3158i | 0.265832 | − | 0.460434i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.10949 | − | 3.72007i | −0.288803 | − | 0.151118i | ||||
\(607\) | 15.1355 | − | 26.2154i | 0.614330 | − | 1.06405i | −0.376171 | − | 0.926550i | \(-0.622760\pi\) |
0.990502 | − | 0.137501i | \(-0.0439070\pi\) | |||||||
\(608\) | − | 18.5351i | − | 0.751698i | ||||||
\(609\) | 7.78159 | + | 34.4996i | 0.315326 | + | 1.39799i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.26241 | − | 5.34766i | −0.374717 | − | 0.216343i | ||||
\(612\) | 1.18604 | + | 14.2494i | 0.0479427 | + | 0.575999i | ||||
\(613\) | −15.6207 | + | 9.01861i | −0.630914 | + | 0.364258i | −0.781106 | − | 0.624399i | \(-0.785344\pi\) |
0.150192 | + | 0.988657i | \(0.452011\pi\) | |||||||
\(614\) | 19.4086 | − | 33.6167i | 0.783267 | − | 1.35666i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.788604 | − | 2.20633i | 0.0317738 | − | 0.0888956i | ||||
\(617\) | 11.2586 | 0.453254 | 0.226627 | − | 0.973982i | \(-0.427230\pi\) | ||||
0.226627 | + | 0.973982i | \(0.427230\pi\) | |||||||
\(618\) | −2.24336 | − | 53.9982i | −0.0902414 | − | 2.17213i | ||||
\(619\) | 5.23950 | − | 3.02503i | 0.210593 | − | 0.121586i | −0.390994 | − | 0.920393i | \(-0.627869\pi\) |
0.601587 | + | 0.798807i | \(0.294535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.5670 | − | 9.09385i | −0.865454 | − | 0.364924i | ||||
\(622\) | 2.70540 | 0.108477 | ||||||||
\(623\) | −1.28351 | − | 7.04054i | −0.0514227 | − | 0.282073i | ||||
\(624\) | 24.6685 | − | 15.6424i | 0.987530 | − | 0.626198i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −24.4498 | − | 42.3482i | −0.977209 | − | 1.69258i | ||||
\(627\) | −2.85575 | − | 1.49428i | −0.114048 | − | 0.0596759i | ||||
\(628\) | −5.39180 | + | 9.33888i | −0.215156 | + | 0.372662i | ||||
\(629\) | −31.9152 | −1.27254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.3970 | 1.88684 | 0.943422 | − | 0.331594i | \(-0.107586\pi\) | ||||
0.943422 | + | 0.331594i | \(0.107586\pi\) | |||||||
\(632\) | 6.88249 | − | 11.9208i | 0.273771 | − | 0.474185i | ||||
\(633\) | −8.78063 | − | 4.59450i | −0.348999 | − | 0.182615i | ||||
\(634\) | 5.55316 | + | 9.61836i | 0.220544 | + | 0.381994i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.6508 | − | 9.29014i | 0.580942 | − | 0.368378i | ||||
\(637\) | −3.84415 | + | 23.3812i | −0.152311 | + | 0.926397i | ||||
\(638\) | −6.02728 | −0.238622 | ||||||||
\(639\) | 3.76096 | − | 2.60984i | 0.148781 | − | 0.103244i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.08690 | − | 1.20488i | 0.0824278 | − | 0.0475897i | −0.458220 | − | 0.888839i | \(-0.651513\pi\) |
0.540647 | + | 0.841249i | \(0.318179\pi\) | |||||||
\(642\) | 0.809774 | + | 19.4914i | 0.0319592 | + | 0.769265i | ||||
\(643\) | 30.1631 | 1.18952 | 0.594759 | − | 0.803904i | \(-0.297247\pi\) | ||||
0.594759 | + | 0.803904i | \(0.297247\pi\) | |||||||
\(644\) | −7.86819 | + | 6.68020i | −0.310050 | + | 0.263237i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.7909 | + | 32.5468i | −0.739319 | + | 1.28054i | ||||
\(647\) | −12.1065 | + | 6.98967i | −0.475954 | + | 0.274792i | −0.718729 | − | 0.695291i | \(-0.755276\pi\) |
0.242775 | + | 0.970083i | \(0.421942\pi\) | |||||||
\(648\) | 6.04609 | − | 16.1847i | 0.237513 | − | 0.635797i | ||||
\(649\) | 3.89972 | + | 2.25150i | 0.153077 | + | 0.0883792i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.7270 | − | 10.8255i | 0.459619 | − | 0.424283i | ||||
\(652\) | − | 4.76671i | − | 0.186679i | ||||||
\(653\) | 3.42169 | − | 5.92653i | 0.133901 | − | 0.231923i | −0.791276 | − | 0.611459i | \(-0.790583\pi\) |
0.925177 | + | 0.379536i | \(0.123916\pi\) | |||||||
\(654\) | −20.3515 | − | 10.6490i | −0.795805 | − | 0.416408i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.5870 | + | 26.9975i | −0.608572 | + | 1.05408i | ||||
\(657\) | −9.97636 | + | 21.1606i | −0.389215 | + | 0.825552i | ||||
\(658\) | −4.76328 | + | 13.3266i | −0.185692 | + | 0.519523i | ||||
\(659\) | 10.0735i | 0.392409i | 0.980563 | + | 0.196204i | \(0.0628616\pi\) | ||||
−0.980563 | + | 0.196204i | \(0.937138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.84503 | + | 5.10668i | −0.344032 | + | 0.198627i | −0.662053 | − | 0.749457i | \(-0.730315\pi\) |
0.318022 | + | 0.948083i | \(0.396981\pi\) | |||||||
\(662\) | 11.4527 | + | 19.8367i | 0.445123 | + | 0.770976i | ||||
\(663\) | −32.2382 | + | 1.33934i | −1.25203 | + | 0.0520157i | ||||
\(664\) | − | 33.7158i | − | 1.30843i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.6412 | − | 12.5603i | −1.03233 | − | 0.486701i | ||||
\(667\) | −30.1060 | − | 17.3817i | −1.16571 | − | 0.673022i | ||||
\(668\) | −0.599296 | + | 0.346004i | −0.0231875 | + | 0.0133873i | ||||
\(669\) | 8.95461 | + | 4.68554i | 0.346205 | + | 0.181153i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.67895 | 0.142024 | ||||||||
\(672\) | −14.2828 | − | 15.4723i | −0.550972 | − | 0.596858i | ||||
\(673\) | − | 19.1004i | − | 0.736266i | −0.929773 | − | 0.368133i | \(-0.879997\pi\) | ||
0.929773 | − | 0.368133i | \(-0.120003\pi\) | |||||||
\(674\) | 45.0282 | + | 25.9971i | 1.73442 | + | 1.00137i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.667597 | + | 1.15631i | 0.0256768 | + | 0.0444735i | ||||
\(677\) | 3.44314 | + | 1.98790i | 0.132331 | + | 0.0764011i | 0.564704 | − | 0.825294i | \(-0.308990\pi\) |
−0.432373 | + | 0.901695i | \(0.642324\pi\) | |||||||
\(678\) | −43.0675 | + | 27.3094i | −1.65400 | + | 1.04881i | ||||
\(679\) | −8.96006 | + | 7.60721i | −0.343855 | + | 0.291938i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.7507 | + | 0.820547i | −0.756849 | + | 0.0314434i | ||||
\(682\) | 1.35997 | + | 2.35553i | 0.0520759 | + | 0.0901981i | ||||
\(683\) | 5.32313 | + | 9.21993i | 0.203684 | + | 0.352791i | 0.949713 | − | 0.313123i | \(-0.101375\pi\) |
−0.746029 | + | 0.665914i | \(0.768042\pi\) | |||||||
\(684\) | −8.61047 | + | 5.97507i | −0.329229 | + | 0.228463i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 31.3491 | − | 0.544533i | 1.19691 | − | 0.0207904i | ||||
\(687\) | 0.975412 | + | 1.53825i | 0.0372143 | + | 0.0586879i | ||||
\(688\) | −36.0464 | − | 20.8114i | −1.37426 | − | 0.793427i | ||||
\(689\) | 19.5735 | + | 33.9022i | 0.745689 | + | 1.29157i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.3020 | + | 8.25729i | 0.544076 | + | 0.314122i | 0.746729 | − | 0.665128i | \(-0.231623\pi\) |
−0.202653 | + | 0.979251i | \(0.564956\pi\) | |||||||
\(692\) | − | 12.5743i | − | 0.478004i | ||||||
\(693\) | −3.53533 | + | 0.953223i | −0.134296 | + | 0.0362099i | ||||
\(694\) | 13.2401 | 0.502586 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.8969 | − | 22.7364i | 0.450951 | − | 0.861820i | ||||
\(697\) | 29.8222 | − | 17.2178i | 1.12960 | − | 0.652172i | ||||
\(698\) | −36.8735 | − | 21.2889i | −1.39568 | − | 0.805797i | ||||
\(699\) | 5.68265 | − | 3.60340i | 0.214938 | − | 0.136293i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.5702i | − | 0.739158i | −0.929199 | − | 0.369579i | \(-0.879502\pi\) | ||
0.929199 | − | 0.369579i | \(-0.120498\pi\) | |||||||
\(702\) | −27.4379 | − | 11.5694i | −1.03558 | − | 0.436657i | ||||
\(703\) | −11.6965 | − | 20.2589i | −0.441141 | − | 0.764078i | ||||
\(704\) | −0.872955 | + | 0.504001i | −0.0329007 | + | 0.0189952i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 20.7706i | − | 0.781712i | ||||||
\(707\) | −6.81752 | − | 2.43677i | −0.256399 | − | 0.0916441i | ||||
\(708\) | 12.3660 | − | 7.84133i | 0.464742 | − | 0.294695i | ||||
\(709\) | 14.1418 | − | 24.4943i | 0.531106 | − | 0.919903i | −0.468235 | − | 0.883604i | \(-0.655110\pi\) |
0.999341 | − | 0.0362991i | \(-0.0115569\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.4372 | + | 1.78430i | −0.803956 | + | 0.0669165i | ||||
\(712\) | −2.59631 | + | 4.49694i | −0.0973009 | + | 0.168530i | ||||
\(713\) | 15.6877i | 0.587509i | ||||||||
\(714\) | 9.39411 | + | 41.6487i | 0.351566 | + | 1.55866i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.77061 | − | 1.02226i | −0.0661707 | − | 0.0382037i | ||||
\(717\) | −5.14176 | + | 9.82650i | −0.192022 | + | 0.366977i | ||||
\(718\) | −12.0466 | + | 6.95509i | −0.449574 | + | 0.259562i | ||||
\(719\) | −9.75873 | + | 16.9026i | −0.363939 | + | 0.630361i | −0.988605 | − | 0.150531i | \(-0.951902\pi\) |
0.624666 | + | 0.780892i | \(0.285235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.74566 | − | 47.9733i | −0.325705 | − | 1.78662i | ||||
\(722\) | 4.61959 | 0.171923 | ||||||||
\(723\) | −3.91849 | + | 0.162794i | −0.145730 | + | 0.00605438i | ||||
\(724\) | 7.28057 | − | 4.20344i | 0.270580 | − | 0.156220i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.31298 | + | 31.6037i | 0.0487293 | + | 1.17292i | ||||
\(727\) | 26.5060 | 0.983052 | 0.491526 | − | 0.870863i | \(-0.336439\pi\) | ||||
0.491526 | + | 0.870863i | \(0.336439\pi\) | |||||||
\(728\) | 13.1061 | − | 11.1272i | 0.485743 | − | 0.412402i | ||||
\(729\) | −26.1665 | + | 6.65709i | −0.969128 | + | 0.246559i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.9888 | + | 39.8177i | 0.850271 | + | 1.47271i | ||||
\(732\) | 5.54627 | − | 10.5996i | 0.204996 | − | 0.391771i | ||||
\(733\) | −0.106580 | + | 0.184602i | −0.00393663 | + | 0.00681844i | −0.867987 | − | 0.496587i | \(-0.834586\pi\) |
0.864050 | + | 0.503405i | \(0.167920\pi\) | |||||||
\(734\) | 47.2420 | 1.74373 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.6979 | 0.762935 | ||||||||
\(737\) | −0.211336 | + | 0.366045i | −0.00778467 | + | 0.0134835i | ||||
\(738\) | 31.6701 | − | 2.63603i | 1.16579 | − | 0.0970337i | ||||
\(739\) | −23.2265 | − | 40.2296i | −0.854402 | − | 1.47987i | −0.877198 | − | 0.480128i | \(-0.840590\pi\) |
0.0227959 | − | 0.999740i | \(-0.492743\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.6650 | − | 19.9730i | −0.465261 | − | 0.733728i | ||||
\(742\) | 39.4876 | − | 33.5255i | 1.44964 | − | 1.23076i | ||||
\(743\) | −28.0937 | −1.03066 | −0.515330 | − | 0.856992i | \(-0.672330\pi\) | ||||
−0.515330 | + | 0.856992i | \(0.672330\pi\) | |||||||
\(744\) | −11.5700 | + | 0.480678i | −0.424177 | + | 0.0176225i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.5135 | − | 15.3076i | 0.970729 | − | 0.560451i | ||||
\(747\) | −43.2880 | + | 30.0389i | −1.58382 | + | 1.09907i | ||||
\(748\) | −2.19874 | −0.0803939 | ||||||||
\(749\) | 3.15687 | + | 17.3166i | 0.115349 | + | 0.632736i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4832 | + | 21.6215i | −0.455518 | + | 0.788981i | −0.998718 | − | 0.0506227i | \(-0.983879\pi\) |
0.543199 | + | 0.839604i | \(0.317213\pi\) | |||||||
\(752\) | 13.6324 | − | 7.87068i | 0.497123 | − | 0.287014i | ||||
\(753\) | −20.4449 | − | 10.6979i | −0.745053 | − | 0.389852i | ||||
\(754\) | −38.3014 | − | 22.1133i | −1.39485 | − | 0.805319i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.58338 | + | 11.6228i | −0.0939566 | + | 0.422718i | ||||
\(757\) | 6.25577i | 0.227370i | 0.993517 | + | 0.113685i | \(0.0362655\pi\) | ||||
−0.993517 | + | 0.113685i | \(0.963735\pi\) | |||||||
\(758\) | 20.9460 | − | 36.2796i | 0.760794 | − | 1.31773i | ||||
\(759\) | 1.66865 | − | 3.18898i | 0.0605680 | − | 0.115753i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.3374 | − | 45.6178i | 0.954731 | − | 1.65364i | 0.219750 | − | 0.975556i | \(-0.429476\pi\) |
0.734982 | − | 0.678087i | \(-0.237191\pi\) | |||||||
\(762\) | 19.7158 | + | 31.0924i | 0.714229 | + | 1.12636i | ||||
\(763\) | −19.5157 | − | 6.97543i | −0.706514 | − | 0.252528i | ||||
\(764\) | − | 4.37410i | − | 0.158249i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.9563 | + | 10.9444i | −0.684917 | + | 0.395437i | ||||
\(767\) | 16.5209 | + | 28.6151i | 0.596536 | + | 1.03323i | ||||
\(768\) | 1.25463 | + | 30.1992i | 0.0452725 | + | 1.08972i | ||||
\(769\) | − | 5.37059i | − | 0.193669i | −0.995301 | − | 0.0968343i | \(-0.969128\pi\) | ||
0.995301 | − | 0.0968343i | \(-0.0308717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.1733 | − | 28.6598i | −0.654496 | − | 1.03216i | ||||
\(772\) | 9.82820 | + | 5.67432i | 0.353725 | + | 0.204223i | ||||
\(773\) | −2.12434 | + | 1.22649i | −0.0764073 | + | 0.0441138i | −0.537717 | − | 0.843125i | \(-0.680713\pi\) |
0.461310 | + | 0.887239i | \(0.347380\pi\) | |||||||
\(774\) | 3.51956 | + | 42.2851i | 0.126508 | + | 1.51991i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.52826 | 0.306147 | ||||||||
\(777\) | −25.3749 | − | 7.89819i | −0.910318 | − | 0.283346i | ||||
\(778\) | − | 32.0641i | − | 1.14956i | ||||||
\(779\) | 21.8588 | + | 12.6202i | 0.783172 | + | 0.452165i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.351967 | + | 0.609625i | 0.0125944 | + | 0.0218141i | ||||
\(782\) | −36.3446 | − | 20.9836i | −1.29968 | − | 0.750371i | ||||
\(783\) | −39.7909 | + | 4.98230i | −1.42201 | + | 0.178053i | ||||
\(784\) | −26.9731 | − | 22.1060i | −0.963326 | − | 0.789501i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.818606 | − | 19.7040i | −0.0291987 | − | 0.702818i | ||||
\(787\) | −20.6048 | − | 35.6885i | −0.734481 | − | 1.27216i | −0.954951 | − | 0.296764i | \(-0.904092\pi\) |
0.220470 | − | 0.975394i | \(-0.429241\pi\) | |||||||
\(788\) | −9.22039 | − | 15.9702i | −0.328463 | − | 0.568914i | ||||
\(789\) | −1.20596 | − | 29.0276i | −0.0429332 | − | 1.03341i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.0764 | + | 29.7803i | −1.24717 | + | 1.05887i | ||||
\(792\) | 2.40307 | + | 1.13295i | 0.0853893 | + | 0.0402576i | ||||
\(793\) | 23.3785 | + | 13.4976i | 0.830196 | + | 0.479314i | ||||
\(794\) | 6.16797 | + | 10.6832i | 0.218893 | + | 0.379134i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.01431 | − | 2.89501i | −0.177727 | − | 0.102611i | ||||
\(797\) | − | 36.9407i | − | 1.30851i | −0.756276 | − | 0.654253i | \(-0.772983\pi\) | ||
0.756276 | − | 0.654253i | \(-0.227017\pi\) | |||||||
\(798\) | −22.9946 | + | 21.2267i | −0.814000 | + | 0.751419i | ||||
\(799\) | −17.3883 | −0.615154 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.08683 | − | 0.673099i | 0.285734 | − | 0.0237828i | ||||
\(802\) | 23.2600 | − | 13.4292i | 0.821339 | − | 0.474200i | ||||
\(803\) | −3.11544 | − | 1.79870i | −0.109942 | − | 0.0634748i | ||||
\(804\) | 0.736023 | + | 1.16073i | 0.0259575 | + | 0.0409357i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.9582i | 0.702997i | ||||||||
\(807\) | 2.10948 | + | 50.7756i | 0.0742573 | + | 1.78739i | ||||
\(808\) | 2.62655 | + | 4.54931i | 0.0924016 | + | 0.160044i | ||||
\(809\) | 45.9461 | − | 26.5270i | 1.61538 | − | 0.932640i | 0.627285 | − | 0.778790i | \(-0.284166\pi\) |
0.988094 | − | 0.153850i | \(-0.0491672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19.0686i | − | 0.669590i | −0.942291 | − | 0.334795i | \(-0.891333\pi\) | ||
0.942291 | − | 0.334795i | \(-0.108667\pi\) | |||||||
\(812\) | −5.95198 | + | 16.6523i | −0.208873 | + | 0.584380i | ||||
\(813\) | −2.75394 | − | 4.34304i | −0.0965850 | − | 0.152317i | ||||
\(814\) | 2.26457 | − | 3.92235i | 0.0793731 | − | 0.137478i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 22.0169 | − | 42.0769i | 0.770747 | − | 1.47299i | ||||
\(817\) | −16.8501 | + | 29.1852i | −0.589511 | + | 1.02106i | ||||
\(818\) | 44.5918i | 1.55912i | ||||||||
\(819\) | −25.9631 | − | 6.91324i | −0.907223 | − | 0.241568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.46302 | − | 5.46348i | −0.330262 | − | 0.190677i | 0.325696 | − | 0.945475i | \(-0.394402\pi\) |
−0.655957 | + | 0.754798i | \(0.727735\pi\) | |||||||
\(822\) | −52.8627 | − | 27.6606i | −1.84380 | − | 0.964776i | ||||
\(823\) | 36.3622 | − | 20.9937i | 1.26750 | − | 0.731794i | 0.292990 | − | 0.956116i | \(-0.405350\pi\) |
0.974515 | + | 0.224321i | \(0.0720165\pi\) | |||||||
\(824\) | −17.6909 | + | 30.6416i | −0.616293 | + | 1.06745i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.3294 | − | 28.2971i | 1.15968 | − | 0.984584i | ||||
\(827\) | −22.1128 | −0.768937 | −0.384468 | − | 0.923138i | \(-0.625615\pi\) | ||||
−0.384468 | + | 0.923138i | \(0.625615\pi\) | |||||||
\(828\) | −6.67229 | − | 9.61520i | −0.231878 | − | 0.334151i | ||||
\(829\) | −27.1141 | + | 15.6543i | −0.941711 | + | 0.543697i | −0.890496 | − | 0.454990i | \(-0.849643\pi\) |
−0.0512148 | + | 0.998688i | \(0.516309\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.5412 | − | 0.936477i | 0.781944 | − | 0.0324860i | ||||
\(832\) | −7.39645 | −0.256426 | ||||||||
\(833\) | 13.5940 | + | 36.0450i | 0.471003 | + | 1.24888i | ||||
\(834\) | 15.3755 | + | 24.2476i | 0.532410 | + | 0.839625i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.805806 | − | 1.39570i | −0.0278694 | − | 0.0482712i | ||||
\(837\) | 10.9254 | + | 14.4266i | 0.377636 | + | 0.498655i | ||||
\(838\) | −12.1468 | + | 21.0389i | −0.419605 | + | 0.726777i | ||||
\(839\) | −8.65688 | −0.298869 | −0.149434 | − | 0.988772i | \(-0.547745\pi\) | ||||
−0.149434 | + | 0.988772i | \(0.547745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.5607 | −1.05382 | ||||||||
\(842\) | 8.52225 | − | 14.7610i | 0.293696 | − | 0.508696i | ||||
\(843\) | 15.6109 | − | 29.8343i | 0.537669 | − | 1.02755i | ||||
\(844\) | −2.47763 | − | 4.29138i | −0.0852835 | − | 0.147715i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −14.5149 | − | 6.84318i | −0.499031 | − | 0.235273i | ||||
\(847\) | 5.11859 | + | 28.0775i | 0.175877 | + | 0.964753i | ||||
\(848\) | −57.6164 | −1.97855 | ||||||||
\(849\) | 0.405463 | + | 9.75956i | 0.0139154 | + | 0.334947i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.6228 | − | 13.0613i | 0.775501 | − | 0.447736i | ||||
\(852\) | 2.28703 | − | 0.0950150i | 0.0783523 | − | 0.00325516i | ||||
\(853\) | −48.3400 | −1.65513 | −0.827565 | − | 0.561370i | \(-0.810274\pi\) | ||||
−0.827565 | + | 0.561370i | \(0.810274\pi\) | |||||||
\(854\) | 12.0226 | − | 33.6365i | 0.411405 | − | 1.15102i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.38579 | − | 11.0605i | 0.218262 | − | 0.378041i | ||||
\(857\) | −29.1362 | + | 16.8218i | −0.995274 | + | 0.574622i | −0.906847 | − | 0.421461i | \(-0.861517\pi\) |
−0.0884274 | + | 0.996083i | \(0.528184\pi\) | |||||||
\(858\) | 2.12288 | − | 4.05708i | 0.0724740 | − | 0.138506i | ||||
\(859\) | −22.6082 | − | 13.0528i | −0.771382 | − | 0.445357i | 0.0619856 | − | 0.998077i | \(-0.480257\pi\) |
−0.833367 | + | 0.552720i | \(0.813590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.9717 | − | 6.30918i | 0.953272 | − | 0.215016i | ||||
\(862\) | − | 13.9573i | − | 0.475387i | ||||||
\(863\) | 19.6742 | − | 34.0767i | 0.669718 | − | 1.15998i | −0.308265 | − | 0.951300i | \(-0.599748\pi\) |
0.977983 | − | 0.208685i | \(-0.0669182\pi\) | |||||||
\(864\) | 19.0340 | − | 14.4146i | 0.647550 | − | 0.490396i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.07765 | + | 15.7230i | −0.308471 | + | 0.534288i | ||||
\(867\) | −19.4348 | + | 12.3237i | −0.660042 | + | 0.418536i | ||||
\(868\) | 7.85088 | − | 1.43124i | 0.266476 | − | 0.0485793i | ||||
\(869\) | − | 3.30783i | − | 0.112211i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.68594 | + | 1.55073i | −0.0910097 | + | 0.0525445i | ||||
\(872\) | 7.51869 | + | 13.0227i | 0.254615 | + | 0.441006i | ||||
\(873\) | −7.59820 | − | 10.9495i | −0.257160 | − | 0.370585i | ||||
\(874\) | − | 30.7607i | − | 1.04050i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.87904 | + | 6.26435i | −0.333782 | + | 0.211653i | ||||
\(877\) | 22.9766 | + | 13.2655i | 0.775864 | + | 0.447945i | 0.834963 | − | 0.550307i | \(-0.185489\pi\) |
−0.0590984 | + | 0.998252i | \(0.518823\pi\) | |||||||
\(878\) | −4.64262 | + | 2.68042i | −0.156681 | + | 0.0904597i | ||||
\(879\) | −17.3254 | + | 33.1109i | −0.584371 | + | 1.11680i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.2055 | 0.444904 | 0.222452 | − | 0.974944i | \(-0.428594\pi\) | ||||
0.222452 | + | 0.974944i | \(0.428594\pi\) | |||||||
\(882\) | −2.83798 | + | 35.4384i | −0.0955598 | + | 1.19327i | ||||
\(883\) | − | 27.3728i | − | 0.921169i | −0.887616 | − | 0.460584i | \(-0.847640\pi\) | ||
0.887616 | − | 0.460584i | \(-0.152360\pi\) | |||||||
\(884\) | −13.9723 | − | 8.06689i | −0.469938 | − | 0.271319i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.7738 | − | 25.5889i | −0.496335 | − | 0.859677i | ||||
\(887\) | 28.5105 | + | 16.4606i | 0.957290 | + | 0.552692i | 0.895338 | − | 0.445387i | \(-0.146934\pi\) |
0.0619524 | + | 0.998079i | \(0.480267\pi\) | |||||||
\(888\) | 10.3262 | + | 16.2846i | 0.346523 | + | 0.546476i | ||||
\(889\) | 21.4997 | + | 25.3232i | 0.721078 | + | 0.849313i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.686394 | − | 4.09471i | −0.0229951 | − | 0.137178i | ||||
\(892\) | 2.52672 | + | 4.37641i | 0.0846009 | + | 0.146533i | ||||
\(893\) | −6.37256 | − | 11.0376i | −0.213250 | − | 0.369359i | ||||
\(894\) | 47.7659 | − | 1.98444i | 1.59753 | − | 0.0663697i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.11599 | + | 33.5486i | 0.204321 | + | 1.12078i | ||||
\(897\) | 22.3036 | − | 14.1429i | 0.744697 | − | 0.472216i | ||||
\(898\) | −18.0149 | − | 10.4009i | −0.601165 | − | 0.347083i | ||||
\(899\) | 13.4390 | + | 23.2770i | 0.448216 | + | 0.776333i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.1178 | + | 31.8223i | 1.83624 | + | 1.06015i | ||||
\(902\) | 4.88682i | 0.162713i | ||||||||
\(903\) | 8.42384 | + | 37.3470i | 0.280328 | + | 1.24283i | ||||
\(904\) | 33.3860 | 1.11040 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 39.1974 | + | 20.5102i | 1.30225 | + | 0.681406i | ||||
\(907\) | −18.0335 | + | 10.4117i | −0.598793 | + | 0.345714i | −0.768567 | − | 0.639770i | \(-0.779030\pi\) |
0.169773 | + | 0.985483i | \(0.445696\pi\) | |||||||
\(908\) | −8.56010 | − | 4.94217i | −0.284077 | − | 0.164012i | ||||
\(909\) | 3.50079 | − | 7.42543i | 0.116114 | − | 0.246286i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 50.2293i | − | 1.66417i | −0.554648 | − | 0.832085i | \(-0.687147\pi\) | ||
0.554648 | − | 0.832085i | \(-0.312853\pi\) | |||||||
\(912\) | 34.7781 | − | 1.44486i | 1.15162 | − | 0.0478442i | ||||
\(913\) | −4.05108 | − | 7.01668i | −0.134071 | − | 0.232218i | ||||
\(914\) | 7.16844 | − | 4.13870i | 0.237111 | − | 0.136896i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.910763i | 0.0300925i | ||||||||
\(917\) | −3.19130 | − | 17.5055i | −0.105386 | − | 0.578083i | ||||
\(918\) | −48.0365 | + | 6.01475i | −1.58544 | + | 0.198516i | ||||
\(919\) | −9.88707 | + | 17.1249i | −0.326144 | + | 0.564899i | −0.981743 | − | 0.190211i | \(-0.939083\pi\) |
0.655599 | + | 0.755109i | \(0.272416\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.1878 | + | 18.4121i | 1.15948 | + | 0.606701i | ||||
\(922\) | −4.34026 | + | 7.51755i | −0.142939 | + | 0.247577i | ||||
\(923\) | 5.16529i | 0.170017i | ||||||||
\(924\) | −1.74815 | − | 0.544131i | −0.0575100 | − | 0.0179006i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 58.5095 | + | 33.7805i | 1.92274 | + | 1.11009i | ||||
\(927\) | 55.1026 | − | 4.58641i | 1.80981 | − | 0.150637i | ||||
\(928\) | 30.7111 | − | 17.7310i | 1.00814 | − | 0.582050i | ||||
\(929\) | 1.84133 | − | 3.18927i | 0.0604119 | − | 0.104637i | −0.834238 | − | 0.551405i | \(-0.814092\pi\) |
0.894650 | + | 0.446769i | \(0.147425\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.8983 | + | 21.8390i | −0.586594 | + | 0.715745i | ||||
\(932\) | 3.36457 | 0.110210 | ||||||||
\(933\) | 0.114894 | + | 2.76551i | 0.00376145 | + | 0.0905387i | ||||
\(934\) | 13.3802 | − | 7.72506i | 0.437814 | − | 0.252772i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11.1140 | + | 16.0161i | 0.363274 | + | 0.523501i | ||||
\(937\) | 36.7871 | 1.20178 | 0.600891 | − | 0.799331i | \(-0.294813\pi\) | ||||
0.600891 | + | 0.799331i | \(0.294813\pi\) | |||||||
\(938\) | 2.65610 | + | 3.12845i | 0.0867247 | + | 0.102148i | ||||
\(939\) | 42.2507 | − | 26.7914i | 1.37880 | − | 0.874305i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.1072 | + | 17.5061i | 0.329484 | + | 0.570684i | 0.982410 | − | 0.186739i | \(-0.0597917\pi\) |
−0.652925 | + | 0.757422i | \(0.726458\pi\) | |||||||
\(942\) | −32.3494 | − | 16.9270i | −1.05400 | − | 0.551511i | ||||
\(943\) | −14.0928 | + | 24.4094i | −0.458924 | + | 0.794880i | ||||
\(944\) | −48.6310 | −1.58280 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.52474 | −0.212138 | ||||||||
\(947\) | 4.91182 | − | 8.50752i | 0.159613 | − | 0.276457i | −0.775116 | − | 0.631819i | \(-0.782309\pi\) |
0.934729 | + | 0.355361i | \(0.115642\pi\) | |||||||
\(948\) | −9.53032 | − | 4.98678i | −0.309530 | − | 0.161963i | ||||
\(949\) | −13.1984 | − | 22.8603i | −0.428438 | − | 0.742076i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.59621 | + | 6.08501i | −0.311179 | + | 0.197320i | ||||
\(952\) | 9.40772 | − | 26.3206i | 0.304906 | − | 0.853057i | ||||
\(953\) | 24.7365 | 0.801294 | 0.400647 | − | 0.916232i | \(-0.368785\pi\) | ||||
0.400647 | + | 0.916232i | \(0.368785\pi\) | |||||||
\(954\) | 33.4858 | + | 48.2552i | 1.08414 | + | 1.56232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.80253 | + | 2.77274i | −0.155325 | + | 0.0896769i | ||||
\(957\) | −0.255968 | − | 6.16119i | −0.00827426 | − | 0.199163i | ||||
\(958\) | 20.9996 | 0.678468 | ||||||||
\(959\) | −50.6917 | − | 18.1186i | −1.63692 | − | 0.585081i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.43537 | + | 16.3425i | −0.304367 | + | 0.527179i | ||||
\(962\) | 28.7812 | − | 16.6168i | 0.927942 | − | 0.535748i | ||||
\(963\) | −19.8901 | + | 1.65553i | −0.640948 | + | 0.0533487i | ||||
\(964\) | −1.69830 | − | 0.980514i | −0.0546986 | − | 0.0315802i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −23.7036 | − | 25.6778i | −0.762652 | − | 0.826168i | ||||
\(967\) | 14.0157i | 0.450713i | 0.974276 | + | 0.225357i | \(0.0723547\pi\) | ||||
−0.974276 | + | 0.225357i | \(0.927645\pi\) | |||||||
\(968\) | 10.3540 | − | 17.9337i | 0.332791 | − | 0.576410i | ||||
\(969\) | −34.0679 | − | 17.8262i | −1.09442 | − | 0.572660i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.0308306 | + | 0.0534003i | −0.000989403 | + | 0.00171370i | −0.866520 | − | 0.499143i | \(-0.833648\pi\) |
0.865530 | + | 0.500857i | \(0.166982\pi\) | |||||||
\(972\) | −12.8322 | − | 4.19546i | −0.411593 | − | 0.134569i | ||||
\(973\) | 16.7667 | + | 19.7485i | 0.537516 | + | 0.633106i | ||||
\(974\) | 23.9792i | 0.768342i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.4085 | + | 19.8657i | −1.10139 | + | 0.635887i | ||||
\(977\) | 9.53996 | + | 16.5237i | 0.305210 | + | 0.528640i | 0.977308 | − | 0.211822i | \(-0.0679399\pi\) |
−0.672098 | + | 0.740462i | \(0.734607\pi\) | |||||||
\(978\) | 16.1249 | − | 0.669912i | 0.515617 | − | 0.0214214i | ||||
\(979\) | 1.24783i | 0.0398808i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0213 | − | 21.2558i | 0.319955 | − | 0.678647i | ||||
\(982\) | −47.0945 | − | 27.1900i | −1.50285 | − | 0.867669i | ||||
\(983\) | −7.05465 | + | 4.07300i | −0.225008 | + | 0.129909i | −0.608267 | − | 0.793732i | \(-0.708135\pi\) |
0.383259 | + | 0.923641i | \(0.374802\pi\) | |||||||
\(984\) | −18.4343 | − | 9.64581i | −0.587663 | − | 0.307497i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −71.9030 | −2.28986 | ||||||||
\(987\) | −13.8249 | − | 4.30315i | −0.440052 | − | 0.136971i | ||||
\(988\) | − | 11.8256i | − | 0.376222i | ||||||
\(989\) | −32.5908 | − | 18.8163i | −1.03633 | − | 0.598324i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.21862 | − | 9.03891i | −0.165775 | − | 0.287130i | 0.771155 | − | 0.636647i | \(-0.219679\pi\) |
−0.936930 | + | 0.349517i | \(0.886346\pi\) | |||||||
\(992\) | −13.8590 | − | 8.00150i | −0.440024 | − | 0.254048i | ||||
\(993\) | −19.7910 | + | 12.5496i | −0.628050 | + | 0.398250i | ||||
\(994\) | 6.72398 | − | 1.22580i | 0.213272 | − | 0.0388800i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −26.3233 | + | 1.09361i | −0.834086 | + | 0.0346522i | ||||
\(997\) | 6.74411 | + | 11.6811i | 0.213588 | + | 0.369945i | 0.952835 | − | 0.303489i | \(-0.0981517\pi\) |
−0.739247 | + | 0.673435i | \(0.764818\pi\) | |||||||
\(998\) | 22.6159 | + | 39.1719i | 0.715894 | + | 1.23996i | ||||
\(999\) | 11.7079 | − | 27.7665i | 0.370422 | − | 0.878494i |
(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 | 525.2.q.g.299.5 | 40 | ||
3.2 | odd | 2 | inner | 525.2.q.g.299.15 | 40 | ||
5.2 | odd | 4 | 525.2.t.h.26.3 | ✓ | 20 | ||
5.3 | odd | 4 | 525.2.t.i.26.8 | yes | 20 | ||
5.4 | even | 2 | inner | 525.2.q.g.299.16 | 40 | ||
7.3 | odd | 6 | inner | 525.2.q.g.374.6 | 40 | ||
15.2 | even | 4 | 525.2.t.h.26.8 | yes | 20 | ||
15.8 | even | 4 | 525.2.t.i.26.3 | yes | 20 | ||
15.14 | odd | 2 | inner | 525.2.q.g.299.6 | 40 | ||
21.17 | even | 6 | inner | 525.2.q.g.374.16 | 40 | ||
35.3 | even | 12 | 525.2.t.i.101.3 | yes | 20 | ||
35.17 | even | 12 | 525.2.t.h.101.8 | yes | 20 | ||
35.24 | odd | 6 | inner | 525.2.q.g.374.15 | 40 | ||
105.17 | odd | 12 | 525.2.t.h.101.3 | yes | 20 | ||
105.38 | odd | 12 | 525.2.t.i.101.8 | yes | 20 | ||
105.59 | even | 6 | inner | 525.2.q.g.374.5 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.q.g.299.5 | 40 | 1.1 | even | 1 | trivial | ||
525.2.q.g.299.6 | 40 | 15.14 | odd | 2 | inner | ||
525.2.q.g.299.15 | 40 | 3.2 | odd | 2 | inner | ||
525.2.q.g.299.16 | 40 | 5.4 | even | 2 | inner | ||
525.2.q.g.374.5 | 40 | 105.59 | even | 6 | inner | ||
525.2.q.g.374.6 | 40 | 7.3 | odd | 6 | inner | ||
525.2.q.g.374.15 | 40 | 35.24 | odd | 6 | inner | ||
525.2.q.g.374.16 | 40 | 21.17 | even | 6 | inner | ||
525.2.t.h.26.3 | ✓ | 20 | 5.2 | odd | 4 | ||
525.2.t.h.26.8 | yes | 20 | 15.2 | even | 4 | ||
525.2.t.h.101.3 | yes | 20 | 105.17 | odd | 12 | ||
525.2.t.h.101.8 | yes | 20 | 35.17 | even | 12 | ||
525.2.t.i.26.3 | yes | 20 | 15.8 | even | 4 | ||
525.2.t.i.26.8 | yes | 20 | 5.3 | odd | 4 | ||
525.2.t.i.101.3 | yes | 20 | 35.3 | even | 12 | ||
525.2.t.i.101.8 | yes | 20 | 105.38 | odd | 12 |