Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(151,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 301.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.301 |
Dual form | 450.2.e.n.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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.72474 | − | 0.158919i | −0.995782 | − | 0.0917517i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.724745 | − | 1.57313i | −0.295876 | − | 0.642229i | ||||
\(7\) | 0.224745 | + | 0.389270i | 0.0849456 | + | 0.147130i | 0.905368 | − | 0.424628i | \(-0.139595\pi\) |
−0.820422 | + | 0.571758i | \(0.806262\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.94949 | + | 0.548188i | 0.983163 | + | 0.182729i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.72474 | + | 2.98735i | 0.520030 | + | 0.900719i | 0.999729 | + | 0.0232854i | \(0.00741263\pi\) |
−0.479699 | + | 0.877433i | \(0.659254\pi\) | |||||||
\(12\) | 1.00000 | − | 1.41421i | 0.288675 | − | 0.408248i | ||||
\(13\) | −1.22474 | + | 2.12132i | −0.339683 | + | 0.588348i | −0.984373 | − | 0.176096i | \(-0.943653\pi\) |
0.644690 | + | 0.764444i | \(0.276986\pi\) | |||||||
\(14\) | −0.224745 | + | 0.389270i | −0.0600656 | + | 0.104037i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −5.89898 | −1.43071 | −0.715356 | − | 0.698760i | \(-0.753736\pi\) | ||||
−0.715356 | + | 0.698760i | \(0.753736\pi\) | |||||||
\(18\) | 1.00000 | + | 2.82843i | 0.235702 | + | 0.666667i | ||||
\(19\) | −5.44949 | −1.25020 | −0.625099 | − | 0.780545i | \(-0.714942\pi\) | ||||
−0.625099 | + | 0.780545i | \(0.714942\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.325765 | − | 0.707107i | −0.0710878 | − | 0.154303i | ||||
\(22\) | −1.72474 | + | 2.98735i | −0.367717 | + | 0.636904i | ||||
\(23\) | −3.44949 | + | 5.97469i | −0.719268 | + | 1.24581i | 0.242022 | + | 0.970271i | \(0.422189\pi\) |
−0.961290 | + | 0.275538i | \(0.911144\pi\) | |||||||
\(24\) | 1.72474 | + | 0.158919i | 0.352062 | + | 0.0324391i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.44949 | −0.480384 | ||||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | −0.449490 | −0.0849456 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.775255 | + | 1.34278i | −0.139240 | + | 0.241171i | −0.927209 | − | 0.374544i | \(-0.877799\pi\) |
0.787969 | + | 0.615715i | \(0.211133\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −2.50000 | − | 5.42650i | −0.435194 | − | 0.944633i | ||||
\(34\) | −2.94949 | − | 5.10867i | −0.505833 | − | 0.876129i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.94949 | + | 2.28024i | −0.324915 | + | 0.380040i | ||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | −2.72474 | − | 4.71940i | −0.442012 | − | 0.765587i | ||||
\(39\) | 2.44949 | − | 3.46410i | 0.392232 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.500000 | − | 0.866025i | 0.0780869 | − | 0.135250i | −0.824338 | − | 0.566099i | \(-0.808452\pi\) |
0.902424 | + | 0.430848i | \(0.141786\pi\) | |||||||
\(42\) | 0.449490 | − | 0.635674i | 0.0693578 | − | 0.0980867i | ||||
\(43\) | −1.27526 | − | 2.20881i | −0.194475 | − | 0.336840i | 0.752254 | − | 0.658874i | \(-0.228967\pi\) |
−0.946728 | + | 0.322034i | \(0.895634\pi\) | |||||||
\(44\) | −3.44949 | −0.520030 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.89898 | −1.01720 | ||||||||
\(47\) | 2.22474 | + | 3.85337i | 0.324512 | + | 0.562072i | 0.981414 | − | 0.191905i | \(-0.0614665\pi\) |
−0.656901 | + | 0.753977i | \(0.728133\pi\) | |||||||
\(48\) | 0.724745 | + | 1.57313i | 0.104608 | + | 0.227062i | ||||
\(49\) | 3.39898 | − | 5.88721i | 0.485568 | − | 0.841029i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.1742 | + | 0.937458i | 1.42468 | + | 0.131270i | ||||
\(52\) | −1.22474 | − | 2.12132i | −0.169842 | − | 0.294174i | ||||
\(53\) | 3.55051 | 0.487700 | 0.243850 | − | 0.969813i | \(-0.421590\pi\) | ||||
0.243850 | + | 0.969813i | \(0.421590\pi\) | |||||||
\(54\) | −1.27526 | − | 5.03723i | −0.173540 | − | 0.685481i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.224745 | − | 0.389270i | −0.0300328 | − | 0.0520183i | ||||
\(57\) | 9.39898 | + | 0.866025i | 1.24493 | + | 0.114708i | ||||
\(58\) | −3.00000 | + | 5.19615i | −0.393919 | + | 0.682288i | ||||
\(59\) | −6.62372 | + | 11.4726i | −0.862335 | + | 1.49361i | 0.00733331 | + | 0.999973i | \(0.497666\pi\) |
−0.869669 | + | 0.493636i | \(0.835668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.22474 | − | 3.85337i | −0.284849 | − | 0.493374i | 0.687723 | − | 0.725973i | \(-0.258610\pi\) |
−0.972573 | + | 0.232599i | \(0.925277\pi\) | |||||||
\(62\) | −1.55051 | −0.196915 | ||||||||
\(63\) | 0.449490 | + | 1.27135i | 0.0566304 | + | 0.160175i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.44949 | − | 4.87832i | 0.424603 | − | 0.600479i | ||||
\(67\) | −2.27526 | + | 3.94086i | −0.277967 | + | 0.481452i | −0.970879 | − | 0.239569i | \(-0.922994\pi\) |
0.692913 | + | 0.721022i | \(0.256327\pi\) | |||||||
\(68\) | 2.94949 | − | 5.10867i | 0.357678 | − | 0.619517i | ||||
\(69\) | 6.89898 | − | 9.75663i | 0.830540 | − | 1.17456i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.44949 | −0.290701 | −0.145350 | − | 0.989380i | \(-0.546431\pi\) | ||||
−0.145350 | + | 0.989380i | \(0.546431\pi\) | |||||||
\(72\) | −2.94949 | − | 0.548188i | −0.347601 | − | 0.0646046i | ||||
\(73\) | 14.7980 | 1.73197 | 0.865985 | − | 0.500070i | \(-0.166692\pi\) | ||||
0.865985 | + | 0.500070i | \(0.166692\pi\) | |||||||
\(74\) | 4.00000 | + | 6.92820i | 0.464991 | + | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.72474 | − | 4.71940i | 0.312550 | − | 0.541352i | ||||
\(77\) | −0.775255 | + | 1.34278i | −0.0883485 | + | 0.153024i | ||||
\(78\) | 4.22474 | + | 0.389270i | 0.478358 | + | 0.0440761i | ||||
\(79\) | −3.67423 | − | 6.36396i | −0.413384 | − | 0.716002i | 0.581874 | − | 0.813279i | \(-0.302320\pi\) |
−0.995257 | + | 0.0972777i | \(0.968987\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.39898 | + | 3.23375i | 0.933220 | + | 0.359306i | ||||
\(82\) | 1.00000 | 0.110432 | ||||||||
\(83\) | 2.00000 | + | 3.46410i | 0.219529 | + | 0.380235i | 0.954664 | − | 0.297686i | \(-0.0962148\pi\) |
−0.735135 | + | 0.677920i | \(0.762881\pi\) | |||||||
\(84\) | 0.775255 | + | 0.0714323i | 0.0845873 | + | 0.00779390i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.27526 | − | 2.20881i | 0.137514 | − | 0.238182i | ||||
\(87\) | −4.34847 | − | 9.43879i | −0.466205 | − | 1.01194i | ||||
\(88\) | −1.72474 | − | 2.98735i | −0.183858 | − | 0.318452i | ||||
\(89\) | 3.10102 | 0.328708 | 0.164354 | − | 0.986401i | \(-0.447446\pi\) | ||||
0.164354 | + | 0.986401i | \(0.447446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10102 | −0.115418 | ||||||||
\(92\) | −3.44949 | − | 5.97469i | −0.359634 | − | 0.622905i | ||||
\(93\) | 1.55051 | − | 2.19275i | 0.160780 | − | 0.227378i | ||||
\(94\) | −2.22474 | + | 3.85337i | −0.229465 | + | 0.397445i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | + | 1.41421i | −0.102062 | + | 0.144338i | ||||
\(97\) | −6.50000 | − | 11.2583i | −0.659975 | − | 1.14311i | −0.980622 | − | 0.195911i | \(-0.937234\pi\) |
0.320647 | − | 0.947199i | \(-0.396100\pi\) | |||||||
\(98\) | 6.79796 | 0.686698 | ||||||||
\(99\) | 3.44949 | + | 9.75663i | 0.346687 | + | 0.980578i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.00000 | + | 6.92820i | 0.398015 | + | 0.689382i | 0.993481 | − | 0.113998i | \(-0.0363659\pi\) |
−0.595466 | + | 0.803380i | \(0.703033\pi\) | |||||||
\(102\) | 4.27526 | + | 9.27987i | 0.423313 | + | 0.918844i | ||||
\(103\) | 7.12372 | − | 12.3387i | 0.701921 | − | 1.21576i | −0.265870 | − | 0.964009i | \(-0.585659\pi\) |
0.967791 | − | 0.251755i | \(-0.0810076\pi\) | |||||||
\(104\) | 1.22474 | − | 2.12132i | 0.120096 | − | 0.208013i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.77526 | + | 3.07483i | 0.172428 | + | 0.298654i | ||||
\(107\) | 16.3485 | 1.58047 | 0.790233 | − | 0.612806i | \(-0.209959\pi\) | ||||
0.790233 | + | 0.612806i | \(0.209959\pi\) | |||||||
\(108\) | 3.72474 | − | 3.62302i | 0.358414 | − | 0.348625i | ||||
\(109\) | −8.00000 | −0.766261 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.7980 | − | 1.27135i | −1.30964 | − | 0.120671i | ||||
\(112\) | 0.224745 | − | 0.389270i | 0.0212364 | − | 0.0367825i | ||||
\(113\) | 2.44949 | − | 4.24264i | 0.230429 | − | 0.399114i | −0.727506 | − | 0.686102i | \(-0.759321\pi\) |
0.957934 | + | 0.286988i | \(0.0926538\pi\) | |||||||
\(114\) | 3.94949 | + | 8.57277i | 0.369904 | + | 0.802913i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | −4.77526 | + | 5.58542i | −0.441472 | + | 0.516372i | ||||
\(118\) | −13.2474 | −1.21953 | ||||||||
\(119\) | −1.32577 | − | 2.29629i | −0.121533 | − | 0.210501i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.449490 | + | 0.778539i | −0.0408627 | + | 0.0707763i | ||||
\(122\) | 2.22474 | − | 3.85337i | 0.201419 | − | 0.348868i | ||||
\(123\) | −1.00000 | + | 1.41421i | −0.0901670 | + | 0.127515i | ||||
\(124\) | −0.775255 | − | 1.34278i | −0.0696200 | − | 0.120585i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.876276 | + | 1.02494i | −0.0780648 | + | 0.0913093i | ||||
\(127\) | 6.89898 | 0.612185 | 0.306093 | − | 0.952002i | \(-0.400978\pi\) | ||||
0.306093 | + | 0.952002i | \(0.400978\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 1.84847 | + | 4.01229i | 0.162749 | + | 0.353262i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.44949 | + | 4.24264i | −0.214013 | + | 0.370681i | −0.952967 | − | 0.303075i | \(-0.901987\pi\) |
0.738954 | + | 0.673756i | \(0.235320\pi\) | |||||||
\(132\) | 5.94949 | + | 0.548188i | 0.517837 | + | 0.0477137i | ||||
\(133\) | −1.22474 | − | 2.12132i | −0.106199 | − | 0.183942i | ||||
\(134\) | −4.55051 | −0.393104 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.89898 | 0.505833 | ||||||||
\(137\) | −1.50000 | − | 2.59808i | −0.128154 | − | 0.221969i | 0.794808 | − | 0.606861i | \(-0.207572\pi\) |
−0.922961 | + | 0.384893i | \(0.874238\pi\) | |||||||
\(138\) | 11.8990 | + | 1.09638i | 1.01291 | + | 0.0933298i | ||||
\(139\) | −6.62372 | + | 11.4726i | −0.561817 | + | 0.973096i | 0.435521 | + | 0.900179i | \(0.356564\pi\) |
−0.997338 | + | 0.0729170i | \(0.976769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.22474 | − | 6.99964i | −0.271573 | − | 0.589476i | ||||
\(142\) | −1.22474 | − | 2.12132i | −0.102778 | − | 0.178017i | ||||
\(143\) | −8.44949 | −0.706582 | ||||||||
\(144\) | −1.00000 | − | 2.82843i | −0.0833333 | − | 0.235702i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.39898 | + | 12.8154i | 0.612344 | + | 1.06061i | ||||
\(147\) | −6.79796 | + | 9.61377i | −0.560686 | + | 0.792930i | ||||
\(148\) | −4.00000 | + | 6.92820i | −0.328798 | + | 0.569495i | ||||
\(149\) | 4.12372 | − | 7.14250i | 0.337829 | − | 0.585136i | −0.646195 | − | 0.763172i | \(-0.723641\pi\) |
0.984024 | + | 0.178036i | \(0.0569742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.44949 | − | 2.51059i | −0.117958 | − | 0.204309i | 0.801000 | − | 0.598664i | \(-0.204301\pi\) |
−0.918958 | + | 0.394355i | \(0.870968\pi\) | |||||||
\(152\) | 5.44949 | 0.442012 | ||||||||
\(153\) | −17.3990 | − | 3.23375i | −1.40662 | − | 0.261433i | ||||
\(154\) | −1.55051 | −0.124944 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.77526 | + | 3.85337i | 0.142134 | + | 0.308517i | ||||
\(157\) | −8.00000 | + | 13.8564i | −0.638470 | + | 1.10586i | 0.347299 | + | 0.937754i | \(0.387099\pi\) |
−0.985769 | + | 0.168107i | \(0.946235\pi\) | |||||||
\(158\) | 3.67423 | − | 6.36396i | 0.292306 | − | 0.506290i | ||||
\(159\) | −6.12372 | − | 0.564242i | −0.485643 | − | 0.0447473i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.10102 | −0.244395 | ||||||||
\(162\) | 1.39898 | + | 8.89060i | 0.109914 | + | 0.698512i | ||||
\(163\) | 8.89898 | 0.697022 | 0.348511 | − | 0.937305i | \(-0.386687\pi\) | ||||
0.348511 | + | 0.937305i | \(0.386687\pi\) | |||||||
\(164\) | 0.500000 | + | 0.866025i | 0.0390434 | + | 0.0676252i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | + | 3.46410i | −0.155230 | + | 0.268866i | ||||
\(167\) | −0.123724 | + | 0.214297i | −0.00957408 | + | 0.0165828i | −0.870773 | − | 0.491686i | \(-0.836381\pi\) |
0.861199 | + | 0.508268i | \(0.169714\pi\) | |||||||
\(168\) | 0.325765 | + | 0.707107i | 0.0251333 | + | 0.0545545i | ||||
\(169\) | 3.50000 | + | 6.06218i | 0.269231 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.0732 | − | 2.98735i | −1.22915 | − | 0.228448i | ||||
\(172\) | 2.55051 | 0.194475 | ||||||||
\(173\) | 5.89898 | + | 10.2173i | 0.448491 | + | 0.776809i | 0.998288 | − | 0.0584890i | \(-0.0186282\pi\) |
−0.549797 | + | 0.835298i | \(0.685295\pi\) | |||||||
\(174\) | 6.00000 | − | 8.48528i | 0.454859 | − | 0.643268i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.72474 | − | 2.98735i | 0.130008 | − | 0.225180i | ||||
\(177\) | 13.2474 | − | 18.7347i | 0.995739 | − | 1.40819i | ||||
\(178\) | 1.55051 | + | 2.68556i | 0.116216 | + | 0.201291i | ||||
\(179\) | −0.898979 | −0.0671929 | −0.0335964 | − | 0.999435i | \(-0.510696\pi\) | ||||
−0.0335964 | + | 0.999435i | \(0.510696\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.55051 | 0.412566 | 0.206283 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206283 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(182\) | −0.550510 | − | 0.953512i | −0.0408065 | − | 0.0706790i | ||||
\(183\) | 3.22474 | + | 6.99964i | 0.238380 | + | 0.517428i | ||||
\(184\) | 3.44949 | − | 5.97469i | 0.254300 | − | 0.440460i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.67423 | + | 0.246405i | 0.196084 | + | 0.0180673i | ||||
\(187\) | −10.1742 | − | 17.6223i | −0.744014 | − | 1.28867i | ||||
\(188\) | −4.44949 | −0.324512 | ||||||||
\(189\) | −0.573214 | − | 2.26418i | −0.0416952 | − | 0.164695i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.12372 | − | 15.8028i | −0.660170 | − | 1.14345i | −0.980571 | − | 0.196165i | \(-0.937151\pi\) |
0.320401 | − | 0.947282i | \(-0.396182\pi\) | |||||||
\(192\) | −1.72474 | − | 0.158919i | −0.124473 | − | 0.0114690i | ||||
\(193\) | −6.84847 | + | 11.8619i | −0.492964 | + | 0.853838i | −0.999967 | − | 0.00810596i | \(-0.997420\pi\) |
0.507004 | + | 0.861944i | \(0.330753\pi\) | |||||||
\(194\) | 6.50000 | − | 11.2583i | 0.466673 | − | 0.808301i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.39898 | + | 5.88721i | 0.242784 | + | 0.420515i | ||||
\(197\) | −8.00000 | −0.569976 | −0.284988 | − | 0.958531i | \(-0.591990\pi\) | ||||
−0.284988 | + | 0.958531i | \(0.591990\pi\) | |||||||
\(198\) | −6.72474 | + | 7.86566i | −0.477907 | + | 0.558988i | ||||
\(199\) | 15.5505 | 1.10235 | 0.551173 | − | 0.834391i | \(-0.314180\pi\) | ||||
0.551173 | + | 0.834391i | \(0.314180\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.55051 | − | 6.43539i | 0.320968 | − | 0.453918i | ||||
\(202\) | −4.00000 | + | 6.92820i | −0.281439 | + | 0.487467i | ||||
\(203\) | −1.34847 | + | 2.33562i | −0.0946440 | + | 0.163928i | ||||
\(204\) | −5.89898 | + | 8.34242i | −0.413011 | + | 0.584086i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.2474 | 0.992667 | ||||||||
\(207\) | −13.4495 | + | 15.7313i | −0.934804 | + | 1.09340i | ||||
\(208\) | 2.44949 | 0.169842 | ||||||||
\(209\) | −9.39898 | − | 16.2795i | −0.650141 | − | 1.12608i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.89898 | + | 3.28913i | −0.130731 | + | 0.226433i | −0.923959 | − | 0.382492i | \(-0.875066\pi\) |
0.793227 | + | 0.608925i | \(0.208399\pi\) | |||||||
\(212\) | −1.77526 | + | 3.07483i | −0.121925 | + | 0.211180i | ||||
\(213\) | 4.22474 | + | 0.389270i | 0.289475 | + | 0.0266723i | ||||
\(214\) | 8.17423 | + | 14.1582i | 0.558779 | + | 0.967834i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00000 | + | 1.41421i | 0.340207 | + | 0.0962250i | ||||
\(217\) | −0.696938 | −0.0473113 | ||||||||
\(218\) | −4.00000 | − | 6.92820i | −0.270914 | − | 0.469237i | ||||
\(219\) | −25.5227 | − | 2.35167i | −1.72466 | − | 0.158911i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.22474 | − | 12.5136i | 0.485989 | − | 0.841758i | ||||
\(222\) | −5.79796 | − | 12.5851i | −0.389134 | − | 0.844654i | ||||
\(223\) | −4.55051 | − | 7.88171i | −0.304725 | − | 0.527799i | 0.672475 | − | 0.740120i | \(-0.265231\pi\) |
−0.977200 | + | 0.212321i | \(0.931898\pi\) | |||||||
\(224\) | 0.449490 | 0.0300328 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.89898 | 0.325875 | ||||||||
\(227\) | 1.72474 | + | 2.98735i | 0.114475 | + | 0.198277i | 0.917570 | − | 0.397574i | \(-0.130148\pi\) |
−0.803095 | + | 0.595852i | \(0.796815\pi\) | |||||||
\(228\) | −5.44949 | + | 7.70674i | −0.360901 | + | 0.510391i | ||||
\(229\) | 9.22474 | − | 15.9777i | 0.609588 | − | 1.05584i | −0.381720 | − | 0.924278i | \(-0.624668\pi\) |
0.991308 | − | 0.131560i | \(-0.0419986\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.55051 | − | 2.19275i | 0.102016 | − | 0.144273i | ||||
\(232\) | −3.00000 | − | 5.19615i | −0.196960 | − | 0.341144i | ||||
\(233\) | −13.6969 | −0.897316 | −0.448658 | − | 0.893703i | \(-0.648098\pi\) | ||||
−0.448658 | + | 0.893703i | \(0.648098\pi\) | |||||||
\(234\) | −7.22474 | − | 1.34278i | −0.472296 | − | 0.0877804i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.62372 | − | 11.4726i | −0.431168 | − | 0.746804i | ||||
\(237\) | 5.32577 | + | 11.5601i | 0.345946 | + | 0.750910i | ||||
\(238\) | 1.32577 | − | 2.29629i | 0.0859366 | − | 0.148847i | ||||
\(239\) | 0.348469 | − | 0.603566i | 0.0225406 | − | 0.0390415i | −0.854535 | − | 0.519394i | \(-0.826158\pi\) |
0.877076 | + | 0.480352i | \(0.159491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | − | 0.866025i | −0.0322078 | − | 0.0557856i | 0.849472 | − | 0.527633i | \(-0.176921\pi\) |
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(242\) | −0.898979 | −0.0577886 | ||||||||
\(243\) | −13.9722 | − | 6.91215i | −0.896317 | − | 0.443415i | ||||
\(244\) | 4.44949 | 0.284849 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.72474 | − | 0.158919i | −0.109966 | − | 0.0101323i | ||||
\(247\) | 6.67423 | − | 11.5601i | 0.424671 | − | 0.735552i | ||||
\(248\) | 0.775255 | − | 1.34278i | 0.0492287 | − | 0.0852667i | ||||
\(249\) | −2.89898 | − | 6.29253i | −0.183715 | − | 0.398773i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.55051 | 0.413465 | 0.206732 | − | 0.978398i | \(-0.433717\pi\) | ||||
0.206732 | + | 0.978398i | \(0.433717\pi\) | |||||||
\(252\) | −1.32577 | − | 0.246405i | −0.0835154 | − | 0.0155221i | ||||
\(253\) | −23.7980 | −1.49616 | ||||||||
\(254\) | 3.44949 | + | 5.97469i | 0.216440 | + | 0.374885i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.05051 | + | 8.74774i | −0.315042 | + | 0.545669i | −0.979446 | − | 0.201704i | \(-0.935352\pi\) |
0.664404 | + | 0.747373i | \(0.268685\pi\) | |||||||
\(258\) | −2.55051 | + | 3.60697i | −0.158788 | + | 0.224560i | ||||
\(259\) | 1.79796 | + | 3.11416i | 0.111720 | + | 0.193504i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | + | 16.9706i | 0.371391 | + | 1.05045i | ||||
\(262\) | −4.89898 | −0.302660 | ||||||||
\(263\) | 6.22474 | + | 10.7816i | 0.383834 | + | 0.664820i | 0.991607 | − | 0.129291i | \(-0.0412701\pi\) |
−0.607773 | + | 0.794111i | \(0.707937\pi\) | |||||||
\(264\) | 2.50000 | + | 5.42650i | 0.153864 | + | 0.333978i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.22474 | − | 2.12132i | 0.0750939 | − | 0.130066i | ||||
\(267\) | −5.34847 | − | 0.492810i | −0.327321 | − | 0.0301595i | ||||
\(268\) | −2.27526 | − | 3.94086i | −0.138983 | − | 0.240726i | ||||
\(269\) | 16.0454 | 0.978306 | 0.489153 | − | 0.872198i | \(-0.337306\pi\) | ||||
0.489153 | + | 0.872198i | \(0.337306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5959 | −0.947385 | −0.473692 | − | 0.880690i | \(-0.657079\pi\) | ||||
−0.473692 | + | 0.880690i | \(0.657079\pi\) | |||||||
\(272\) | 2.94949 | + | 5.10867i | 0.178839 | + | 0.309758i | ||||
\(273\) | 1.89898 | + | 0.174973i | 0.114931 | + | 0.0105898i | ||||
\(274\) | 1.50000 | − | 2.59808i | 0.0906183 | − | 0.156956i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.00000 | + | 10.8530i | 0.300965 | + | 0.653274i | ||||
\(277\) | 14.7980 | + | 25.6308i | 0.889123 | + | 1.54001i | 0.840914 | + | 0.541169i | \(0.182018\pi\) |
0.0482095 | + | 0.998837i | \(0.484648\pi\) | |||||||
\(278\) | −13.2474 | −0.794529 | ||||||||
\(279\) | −3.02270 | + | 3.53553i | −0.180965 | + | 0.211667i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | − | 10.3923i | −0.357930 | − | 0.619953i | 0.629685 | − | 0.776851i | \(-0.283184\pi\) |
−0.987615 | + | 0.156898i | \(0.949851\pi\) | |||||||
\(282\) | 4.44949 | − | 6.29253i | 0.264963 | − | 0.374715i | ||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 1.22474 | − | 2.12132i | 0.0726752 | − | 0.125877i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.22474 | − | 7.31747i | −0.249814 | − | 0.432691i | ||||
\(287\) | 0.449490 | 0.0265325 | ||||||||
\(288\) | 1.94949 | − | 2.28024i | 0.114875 | − | 0.134364i | ||||
\(289\) | 17.7980 | 1.04694 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.42168 | + | 20.4507i | 0.552309 | + | 1.19884i | ||||
\(292\) | −7.39898 | + | 12.8154i | −0.432993 | + | 0.749965i | ||||
\(293\) | −9.00000 | + | 15.5885i | −0.525786 | + | 0.910687i | 0.473763 | + | 0.880652i | \(0.342895\pi\) |
−0.999549 | + | 0.0300351i | \(0.990438\pi\) | |||||||
\(294\) | −11.7247 | − | 1.08032i | −0.683801 | − | 0.0630057i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | −4.39898 | − | 17.3759i | −0.255255 | − | 1.00825i | ||||
\(298\) | 8.24745 | 0.477762 | ||||||||
\(299\) | −8.44949 | − | 14.6349i | −0.488647 | − | 0.846361i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.573214 | − | 0.992836i | 0.0330395 | − | 0.0572261i | ||||
\(302\) | 1.44949 | − | 2.51059i | 0.0834088 | − | 0.144468i | ||||
\(303\) | −5.79796 | − | 12.5851i | −0.333084 | − | 0.722993i | ||||
\(304\) | 2.72474 | + | 4.71940i | 0.156275 | + | 0.270676i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.89898 | − | 16.6848i | −0.337222 | − | 0.953808i | ||||
\(307\) | 29.9444 | 1.70902 | 0.854508 | − | 0.519438i | \(-0.173859\pi\) | ||||
0.854508 | + | 0.519438i | \(0.173859\pi\) | |||||||
\(308\) | −0.775255 | − | 1.34278i | −0.0441743 | − | 0.0765121i | ||||
\(309\) | −14.2474 | + | 20.1489i | −0.810509 | + | 1.14623i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.55051 | + | 11.3458i | −0.371445 | + | 0.643362i | −0.989788 | − | 0.142546i | \(-0.954471\pi\) |
0.618343 | + | 0.785909i | \(0.287804\pi\) | |||||||
\(312\) | −2.44949 | + | 3.46410i | −0.138675 | + | 0.196116i | ||||
\(313\) | 10.8485 | + | 18.7901i | 0.613192 | + | 1.06208i | 0.990699 | + | 0.136073i | \(0.0434480\pi\) |
−0.377507 | + | 0.926007i | \(0.623219\pi\) | |||||||
\(314\) | −16.0000 | −0.902932 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.34847 | 0.413384 | ||||||||
\(317\) | −11.4722 | − | 19.8704i | −0.644343 | − | 1.11603i | −0.984453 | − | 0.175649i | \(-0.943798\pi\) |
0.340110 | − | 0.940386i | \(-0.389536\pi\) | |||||||
\(318\) | −2.57321 | − | 5.58542i | −0.144299 | − | 0.313215i | ||||
\(319\) | −10.3485 | + | 17.9241i | −0.579403 | + | 1.00356i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.1969 | − | 2.59808i | −1.57380 | − | 0.145010i | ||||
\(322\) | −1.55051 | − | 2.68556i | −0.0864066 | − | 0.149661i | ||||
\(323\) | 32.1464 | 1.78868 | ||||||||
\(324\) | −7.00000 | + | 5.65685i | −0.388889 | + | 0.314270i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.44949 | + | 7.70674i | 0.246434 | + | 0.426837i | ||||
\(327\) | 13.7980 | + | 1.27135i | 0.763029 | + | 0.0703058i | ||||
\(328\) | −0.500000 | + | 0.866025i | −0.0276079 | + | 0.0478183i | ||||
\(329\) | −1.00000 | + | 1.73205i | −0.0551318 | + | 0.0954911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6969 | + | 21.9917i | 0.697887 | + | 1.20878i | 0.969198 | + | 0.246284i | \(0.0792095\pi\) |
−0.271311 | + | 0.962492i | \(0.587457\pi\) | |||||||
\(332\) | −4.00000 | −0.219529 | ||||||||
\(333\) | 23.5959 | + | 4.38551i | 1.29305 | + | 0.240324i | ||||
\(334\) | −0.247449 | −0.0135398 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.449490 | + | 0.635674i | −0.0245217 | + | 0.0346789i | ||||
\(337\) | −9.29796 | + | 16.1045i | −0.506492 | + | 0.877270i | 0.493480 | + | 0.869757i | \(0.335725\pi\) |
−0.999972 | + | 0.00751272i | \(0.997609\pi\) | |||||||
\(338\) | −3.50000 | + | 6.06218i | −0.190375 | + | 0.329739i | ||||
\(339\) | −4.89898 | + | 6.92820i | −0.266076 | + | 0.376288i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.34847 | −0.289636 | ||||||||
\(342\) | −5.44949 | − | 15.4135i | −0.294675 | − | 0.833466i | ||||
\(343\) | 6.20204 | 0.334879 | ||||||||
\(344\) | 1.27526 | + | 2.20881i | 0.0687571 | + | 0.119091i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.89898 | + | 10.2173i | −0.317131 | + | 0.549287i | ||||
\(347\) | −4.62372 | + | 8.00853i | −0.248215 | + | 0.429920i | −0.963030 | − | 0.269392i | \(-0.913177\pi\) |
0.714816 | + | 0.699313i | \(0.246510\pi\) | |||||||
\(348\) | 10.3485 | + | 0.953512i | 0.554736 | + | 0.0511136i | ||||
\(349\) | 13.7980 | + | 23.8988i | 0.738588 | + | 1.27927i | 0.953131 | + | 0.302557i | \(0.0978403\pi\) |
−0.214543 | + | 0.976714i | \(0.568826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.12372 | − | 8.87455i | 0.486988 | − | 0.473688i | ||||
\(352\) | 3.44949 | 0.183858 | ||||||||
\(353\) | −16.2980 | − | 28.2289i | −0.867453 | − | 1.50247i | −0.864591 | − | 0.502476i | \(-0.832422\pi\) |
−0.00286194 | − | 0.999996i | \(-0.500911\pi\) | |||||||
\(354\) | 22.8485 | + | 2.10527i | 1.21438 | + | 0.111894i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.55051 | + | 2.68556i | −0.0821769 | + | 0.142335i | ||||
\(357\) | 1.92168 | + | 4.17121i | 0.101706 | + | 0.220764i | ||||
\(358\) | −0.449490 | − | 0.778539i | −0.0237563 | − | 0.0411471i | ||||
\(359\) | 3.55051 | 0.187389 | 0.0936944 | − | 0.995601i | \(-0.470132\pi\) | ||||
0.0936944 | + | 0.995601i | \(0.470132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6969 | 0.562997 | ||||||||
\(362\) | 2.77526 | + | 4.80688i | 0.145864 | + | 0.252644i | ||||
\(363\) | 0.898979 | − | 1.27135i | 0.0471842 | − | 0.0667285i | ||||
\(364\) | 0.550510 | − | 0.953512i | 0.0288546 | − | 0.0499776i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.44949 | + | 6.29253i | −0.232579 | + | 0.328916i | ||||
\(367\) | −13.7980 | − | 23.8988i | −0.720248 | − | 1.24751i | −0.960900 | − | 0.276894i | \(-0.910695\pi\) |
0.240653 | − | 0.970611i | \(-0.422638\pi\) | |||||||
\(368\) | 6.89898 | 0.359634 | ||||||||
\(369\) | 1.94949 | − | 2.28024i | 0.101486 | − | 0.118704i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.797959 | + | 1.38211i | 0.0414280 | + | 0.0717553i | ||||
\(372\) | 1.12372 | + | 2.43916i | 0.0582624 | + | 0.126464i | ||||
\(373\) | 6.79796 | − | 11.7744i | 0.351985 | − | 0.609656i | −0.634612 | − | 0.772831i | \(-0.718840\pi\) |
0.986597 | + | 0.163175i | \(0.0521735\pi\) | |||||||
\(374\) | 10.1742 | − | 17.6223i | 0.526097 | − | 0.911227i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.22474 | − | 3.85337i | −0.114732 | − | 0.198722i | ||||
\(377\) | −14.6969 | −0.756931 | ||||||||
\(378\) | 1.67423 | − | 1.62851i | 0.0861133 | − | 0.0837615i | ||||
\(379\) | 4.14643 | 0.212988 | 0.106494 | − | 0.994313i | \(-0.466038\pi\) | ||||
0.106494 | + | 0.994313i | \(0.466038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.8990 | − | 1.09638i | −0.609603 | − | 0.0561691i | ||||
\(382\) | 9.12372 | − | 15.8028i | 0.466810 | − | 0.808539i | ||||
\(383\) | 8.89898 | − | 15.4135i | 0.454717 | − | 0.787592i | −0.543955 | − | 0.839114i | \(-0.683074\pi\) |
0.998672 | + | 0.0515220i | \(0.0164072\pi\) | |||||||
\(384\) | −0.724745 | − | 1.57313i | −0.0369845 | − | 0.0802786i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.6969 | −0.697156 | ||||||||
\(387\) | −2.55051 | − | 7.21393i | −0.129650 | − | 0.366705i | ||||
\(388\) | 13.0000 | 0.659975 | ||||||||
\(389\) | −8.77526 | − | 15.1992i | −0.444923 | − | 0.770629i | 0.553124 | − | 0.833099i | \(-0.313436\pi\) |
−0.998047 | + | 0.0624697i | \(0.980102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.3485 | − | 35.2446i | 1.02907 | − | 1.78240i | ||||
\(392\) | −3.39898 | + | 5.88721i | −0.171674 | + | 0.297349i | ||||
\(393\) | 4.89898 | − | 6.92820i | 0.247121 | − | 0.349482i | ||||
\(394\) | −4.00000 | − | 6.92820i | −0.201517 | − | 0.349038i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.1742 | − | 1.89097i | −0.511275 | − | 0.0950248i | ||||
\(397\) | −1.79796 | −0.0902370 | −0.0451185 | − | 0.998982i | \(-0.514367\pi\) | ||||
−0.0451185 | + | 0.998982i | \(0.514367\pi\) | |||||||
\(398\) | 7.77526 | + | 13.4671i | 0.389738 | + | 0.675047i | ||||
\(399\) | 1.77526 | + | 3.85337i | 0.0888739 | + | 0.192910i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.60102 | + | 7.96920i | −0.229764 | + | 0.397963i | −0.957738 | − | 0.287642i | \(-0.907129\pi\) |
0.727974 | + | 0.685605i | \(0.240462\pi\) | |||||||
\(402\) | 7.84847 | + | 0.723161i | 0.391446 | + | 0.0360680i | ||||
\(403\) | −1.89898 | − | 3.28913i | −0.0945949 | − | 0.163843i | ||||
\(404\) | −8.00000 | −0.398015 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.69694 | −0.133847 | ||||||||
\(407\) | 13.7980 | + | 23.8988i | 0.683939 | + | 1.18462i | ||||
\(408\) | −10.1742 | − | 0.937458i | −0.503700 | − | 0.0464111i | ||||
\(409\) | −7.94949 | + | 13.7689i | −0.393077 | + | 0.680829i | −0.992854 | − | 0.119338i | \(-0.961923\pi\) |
0.599777 | + | 0.800167i | \(0.295256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.17423 | + | 4.71940i | 0.107247 | + | 0.232791i | ||||
\(412\) | 7.12372 | + | 12.3387i | 0.350961 | + | 0.607882i | ||||
\(413\) | −5.95459 | −0.293006 | ||||||||
\(414\) | −20.3485 | − | 3.78194i | −1.00007 | − | 0.185872i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.22474 | + | 2.12132i | 0.0600481 | + | 0.104006i | ||||
\(417\) | 13.2474 | − | 18.7347i | 0.648730 | − | 0.917443i | ||||
\(418\) | 9.39898 | − | 16.2795i | 0.459719 | − | 0.796257i | ||||
\(419\) | 4.44949 | − | 7.70674i | 0.217372 | − | 0.376499i | −0.736632 | − | 0.676294i | \(-0.763585\pi\) |
0.954004 | + | 0.299795i | \(0.0969183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.77526 | + | 10.0030i | 0.281469 | + | 0.487518i | 0.971747 | − | 0.236026i | \(-0.0758451\pi\) |
−0.690278 | + | 0.723544i | \(0.742512\pi\) | |||||||
\(422\) | −3.79796 | −0.184882 | ||||||||
\(423\) | 4.44949 | + | 12.5851i | 0.216342 | + | 0.611906i | ||||
\(424\) | −3.55051 | −0.172428 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.77526 | + | 3.85337i | 0.0860114 | + | 0.186696i | ||||
\(427\) | 1.00000 | − | 1.73205i | 0.0483934 | − | 0.0838198i | ||||
\(428\) | −8.17423 | + | 14.1582i | −0.395117 | + | 0.684362i | ||||
\(429\) | 14.5732 | + | 1.34278i | 0.703601 | + | 0.0648301i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.2474 | 1.84231 | 0.921157 | − | 0.389190i | \(-0.127245\pi\) | ||||
0.921157 | + | 0.389190i | \(0.127245\pi\) | |||||||
\(432\) | 1.27526 | + | 5.03723i | 0.0613557 | + | 0.242354i | ||||
\(433\) | 23.0000 | 1.10531 | 0.552655 | − | 0.833410i | \(-0.313615\pi\) | ||||
0.552655 | + | 0.833410i | \(0.313615\pi\) | |||||||
\(434\) | −0.348469 | − | 0.603566i | −0.0167271 | − | 0.0289721i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.00000 | − | 6.92820i | 0.191565 | − | 0.331801i | ||||
\(437\) | 18.7980 | − | 32.5590i | 0.899228 | − | 1.55751i | ||||
\(438\) | −10.7247 | − | 23.2791i | −0.512448 | − | 1.11232i | ||||
\(439\) | −11.0227 | − | 19.0919i | −0.526085 | − | 0.911206i | −0.999538 | − | 0.0303869i | \(-0.990326\pi\) |
0.473453 | − | 0.880819i | \(-0.343007\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.2526 | − | 15.5010i | 0.631074 | − | 0.738141i | ||||
\(442\) | 14.4495 | 0.687292 | ||||||||
\(443\) | −10.6237 | − | 18.4008i | −0.504748 | − | 0.874250i | −0.999985 | − | 0.00549166i | \(-0.998252\pi\) |
0.495237 | − | 0.868758i | \(-0.335081\pi\) | |||||||
\(444\) | 8.00000 | − | 11.3137i | 0.379663 | − | 0.536925i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.55051 | − | 7.88171i | 0.215473 | − | 0.373210i | ||||
\(447\) | −8.24745 | + | 11.6637i | −0.390091 | + | 0.551672i | ||||
\(448\) | 0.224745 | + | 0.389270i | 0.0106182 | + | 0.0183913i | ||||
\(449\) | 18.7980 | 0.887131 | 0.443565 | − | 0.896242i | \(-0.353713\pi\) | ||||
0.443565 | + | 0.896242i | \(0.353713\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.44949 | 0.162430 | ||||||||
\(452\) | 2.44949 | + | 4.24264i | 0.115214 | + | 0.199557i | ||||
\(453\) | 2.10102 | + | 4.56048i | 0.0987146 | + | 0.214270i | ||||
\(454\) | −1.72474 | + | 2.98735i | −0.0809463 | + | 0.140203i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.39898 | − | 0.866025i | −0.440148 | − | 0.0405554i | ||||
\(457\) | 8.94949 | + | 15.5010i | 0.418639 | + | 0.725105i | 0.995803 | − | 0.0915238i | \(-0.0291738\pi\) |
−0.577163 | + | 0.816629i | \(0.695840\pi\) | |||||||
\(458\) | 18.4495 | 0.862088 | ||||||||
\(459\) | 29.4949 | + | 8.34242i | 1.37670 | + | 0.389391i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.22474 | + | 2.12132i | 0.0570421 | + | 0.0987997i | 0.893136 | − | 0.449786i | \(-0.148500\pi\) |
−0.836094 | + | 0.548586i | \(0.815166\pi\) | |||||||
\(462\) | 2.67423 | + | 0.246405i | 0.124417 | + | 0.0114638i | ||||
\(463\) | −12.0000 | + | 20.7846i | −0.557687 | + | 0.965943i | 0.440002 | + | 0.897997i | \(0.354978\pi\) |
−0.997689 | + | 0.0679458i | \(0.978356\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.84847 | − | 11.8619i | −0.317249 | − | 0.549492i | ||||
\(467\) | −10.3485 | −0.478870 | −0.239435 | − | 0.970912i | \(-0.576962\pi\) | ||||
−0.239435 | + | 0.970912i | \(0.576962\pi\) | |||||||
\(468\) | −2.44949 | − | 6.92820i | −0.113228 | − | 0.320256i | ||||
\(469\) | −2.04541 | −0.0944482 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0000 | − | 22.6274i | 0.737241 | − | 1.04262i | ||||
\(472\) | 6.62372 | − | 11.4726i | 0.304882 | − | 0.528070i | ||||
\(473\) | 4.39898 | − | 7.61926i | 0.202265 | − | 0.350334i | ||||
\(474\) | −7.34847 | + | 10.3923i | −0.337526 | + | 0.477334i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.65153 | 0.121533 | ||||||||
\(477\) | 10.4722 | + | 1.94635i | 0.479489 | + | 0.0891171i | ||||
\(478\) | 0.696938 | 0.0318772 | ||||||||
\(479\) | −8.34847 | − | 14.4600i | −0.381451 | − | 0.660693i | 0.609819 | − | 0.792541i | \(-0.291242\pi\) |
−0.991270 | + | 0.131848i | \(0.957909\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.79796 | + | 16.9706i | −0.446748 | + | 0.773791i | ||||
\(482\) | 0.500000 | − | 0.866025i | 0.0227744 | − | 0.0394464i | ||||
\(483\) | 5.34847 | + | 0.492810i | 0.243364 | + | 0.0224236i | ||||
\(484\) | −0.449490 | − | 0.778539i | −0.0204314 | − | 0.0353881i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | − | 15.5563i | −0.0453609 | − | 0.705650i | ||||
\(487\) | −25.1010 | −1.13744 | −0.568718 | − | 0.822533i | \(-0.692560\pi\) | ||||
−0.568718 | + | 0.822533i | \(0.692560\pi\) | |||||||
\(488\) | 2.22474 | + | 3.85337i | 0.100709 | + | 0.174434i | ||||
\(489\) | −15.3485 | − | 1.41421i | −0.694082 | − | 0.0639529i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.27526 | + | 16.0652i | −0.418586 | + | 0.725013i | −0.995798 | − | 0.0915820i | \(-0.970808\pi\) |
0.577211 | + | 0.816595i | \(0.304141\pi\) | |||||||
\(492\) | −0.724745 | − | 1.57313i | −0.0326740 | − | 0.0709223i | ||||
\(493\) | −17.6969 | − | 30.6520i | −0.797030 | − | 1.38050i | ||||
\(494\) | 13.3485 | 0.600576 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.55051 | 0.0696200 | ||||||||
\(497\) | −0.550510 | − | 0.953512i | −0.0246938 | − | 0.0427708i | ||||
\(498\) | 4.00000 | − | 5.65685i | 0.179244 | − | 0.253490i | ||||
\(499\) | 10.6237 | − | 18.4008i | 0.475583 | − | 0.823734i | −0.524026 | − | 0.851703i | \(-0.675570\pi\) |
0.999609 | + | 0.0279682i | \(0.00890372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.247449 | − | 0.349945i | 0.0110552 | − | 0.0156344i | ||||
\(502\) | 3.27526 | + | 5.67291i | 0.146182 | + | 0.253194i | ||||
\(503\) | 14.4495 | 0.644271 | 0.322135 | − | 0.946694i | \(-0.395599\pi\) | ||||
0.322135 | + | 0.946694i | \(0.395599\pi\) | |||||||
\(504\) | −0.449490 | − | 1.27135i | −0.0200219 | − | 0.0566304i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.8990 | − | 20.6096i | −0.528974 | − | 0.916210i | ||||
\(507\) | −5.07321 | − | 11.0119i | −0.225309 | − | 0.489057i | ||||
\(508\) | −3.44949 | + | 5.97469i | −0.153046 | + | 0.265084i | ||||
\(509\) | −15.7980 | + | 27.3629i | −0.700232 | + | 1.21284i | 0.268153 | + | 0.963376i | \(0.413587\pi\) |
−0.968385 | + | 0.249461i | \(0.919746\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.32577 | + | 5.76039i | 0.147123 | + | 0.254825i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 27.2474 | + | 7.70674i | 1.20300 | + | 0.340261i | ||||
\(514\) | −10.1010 | −0.445537 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.39898 | − | 0.405324i | −0.193654 | − | 0.0178434i | ||||
\(517\) | −7.67423 | + | 13.2922i | −0.337512 | + | 0.584589i | ||||
\(518\) | −1.79796 | + | 3.11416i | −0.0789978 | + | 0.136828i | ||||
\(519\) | −8.55051 | − | 18.5597i | −0.375326 | − | 0.814683i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.6969 | 0.950560 | 0.475280 | − | 0.879835i | \(-0.342347\pi\) | ||||
0.475280 | + | 0.879835i | \(0.342347\pi\) | |||||||
\(522\) | −11.6969 | + | 13.6814i | −0.511961 | + | 0.598820i | ||||
\(523\) | −10.2020 | −0.446104 | −0.223052 | − | 0.974807i | \(-0.571602\pi\) | ||||
−0.223052 | + | 0.974807i | \(0.571602\pi\) | |||||||
\(524\) | −2.44949 | − | 4.24264i | −0.107006 | − | 0.185341i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.22474 | + | 10.7816i | −0.271412 | + | 0.470099i | ||||
\(527\) | 4.57321 | − | 7.92104i | 0.199212 | − | 0.345046i | ||||
\(528\) | −3.44949 | + | 4.87832i | −0.150120 | + | 0.212301i | ||||
\(529\) | −12.2980 | − | 21.3007i | −0.534694 | − | 0.926117i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.8258 | + | 30.2073i | −1.12074 | + | 1.31089i | ||||
\(532\) | 2.44949 | 0.106199 | ||||||||
\(533\) | 1.22474 | + | 2.12132i | 0.0530496 | + | 0.0918846i | ||||
\(534\) | −2.24745 | − | 4.87832i | −0.0972566 | − | 0.211105i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.27526 | − | 3.94086i | 0.0982761 | − | 0.170219i | ||||
\(537\) | 1.55051 | + | 0.142865i | 0.0669095 | + | 0.00616506i | ||||
\(538\) | 8.02270 | + | 13.8957i | 0.345883 | + | 0.599087i | ||||
\(539\) | 23.4495 | 1.01004 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.404082 | −0.0173728 | −0.00868642 | − | 0.999962i | \(-0.502765\pi\) | ||||
−0.00868642 | + | 0.999962i | \(0.502765\pi\) | |||||||
\(542\) | −7.79796 | − | 13.5065i | −0.334951 | − | 0.580152i | ||||
\(543\) | −9.57321 | − | 0.882079i | −0.410826 | − | 0.0378537i | ||||
\(544\) | −2.94949 | + | 5.10867i | −0.126458 | + | 0.219032i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.797959 | + | 1.73205i | 0.0341495 | + | 0.0741249i | ||||
\(547\) | −8.62372 | − | 14.9367i | −0.368724 | − | 0.638648i | 0.620642 | − | 0.784094i | \(-0.286872\pi\) |
−0.989366 | + | 0.145445i | \(0.953539\pi\) | |||||||
\(548\) | 3.00000 | 0.128154 | ||||||||
\(549\) | −4.44949 | − | 12.5851i | −0.189900 | − | 0.537117i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.3485 | − | 28.3164i | −0.696468 | − | 1.20632i | ||||
\(552\) | −6.89898 | + | 9.75663i | −0.293640 | + | 0.415270i | ||||
\(553\) | 1.65153 | − | 2.86054i | 0.0702302 | − | 0.121642i | ||||
\(554\) | −14.7980 | + | 25.6308i | −0.628705 | + | 1.08895i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.62372 | − | 11.4726i | −0.280908 | − | 0.486548i | ||||
\(557\) | 14.9444 | 0.633214 | 0.316607 | − | 0.948557i | \(-0.397456\pi\) | ||||
0.316607 | + | 0.948557i | \(0.397456\pi\) | |||||||
\(558\) | −4.57321 | − | 0.849971i | −0.193600 | − | 0.0359822i | ||||
\(559\) | 6.24745 | 0.264239 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.7474 | + | 32.0108i | 0.622638 | + | 1.35150i | ||||
\(562\) | 6.00000 | − | 10.3923i | 0.253095 | − | 0.438373i | ||||
\(563\) | −0.926786 | + | 1.60524i | −0.0390594 | + | 0.0676528i | −0.884894 | − | 0.465792i | \(-0.845769\pi\) |
0.845835 | + | 0.533445i | \(0.179103\pi\) | |||||||
\(564\) | 7.67423 | + | 0.707107i | 0.323144 | + | 0.0297746i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0.628827 | + | 3.99624i | 0.0264082 | + | 0.167826i | ||||
\(568\) | 2.44949 | 0.102778 | ||||||||
\(569\) | 15.7474 | + | 27.2754i | 0.660167 | + | 1.14344i | 0.980571 | + | 0.196162i | \(0.0628480\pi\) |
−0.320404 | + | 0.947281i | \(0.603819\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.6237 | + | 32.2572i | −0.779379 | + | 1.34992i | 0.152922 | + | 0.988238i | \(0.451132\pi\) |
−0.932300 | + | 0.361685i | \(0.882202\pi\) | |||||||
\(572\) | 4.22474 | − | 7.31747i | 0.176645 | − | 0.305959i | ||||
\(573\) | 13.2247 | + | 28.7056i | 0.552472 | + | 1.19920i | ||||
\(574\) | 0.224745 | + | 0.389270i | 0.00938067 | + | 0.0162478i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.94949 | + | 0.548188i | 0.122895 | + | 0.0228412i | ||||
\(577\) | −15.6969 | −0.653472 | −0.326736 | − | 0.945116i | \(-0.605949\pi\) | ||||
−0.326736 | + | 0.945116i | \(0.605949\pi\) | |||||||
\(578\) | 8.89898 | + | 15.4135i | 0.370149 | + | 0.641116i | ||||
\(579\) | 13.6969 | − | 19.3704i | 0.569225 | − | 0.805006i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.898979 | + | 1.55708i | −0.0372960 | + | 0.0645985i | ||||
\(582\) | −13.0000 | + | 18.3848i | −0.538867 | + | 0.762073i | ||||
\(583\) | 6.12372 | + | 10.6066i | 0.253619 | + | 0.439281i | ||||
\(584\) | −14.7980 | −0.612344 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 11.9722 | + | 20.7364i | 0.494145 | + | 0.855885i | 0.999977 | − | 0.00674727i | \(-0.00214774\pi\) |
−0.505832 | + | 0.862632i | \(0.668814\pi\) | |||||||
\(588\) | −4.92679 | − | 10.6941i | −0.203177 | − | 0.441017i | ||||
\(589\) | 4.22474 | − | 7.31747i | 0.174078 | − | 0.301511i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.7980 | + | 1.27135i | 0.567572 | + | 0.0522963i | ||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | −17.3939 | −0.714281 | −0.357140 | − | 0.934051i | \(-0.616248\pi\) | ||||
−0.357140 | + | 0.934051i | \(0.616248\pi\) | |||||||
\(594\) | 12.8485 | − | 12.4976i | 0.527179 | − | 0.512782i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.12372 | + | 7.14250i | 0.168914 | + | 0.292568i | ||||
\(597\) | −26.8207 | − | 2.47127i | −1.09770 | − | 0.101142i | ||||
\(598\) | 8.44949 | − | 14.6349i | 0.345525 | − | 0.598467i | ||||
\(599\) | −16.8990 | + | 29.2699i | −0.690474 | + | 1.19594i | 0.281209 | + | 0.959646i | \(0.409264\pi\) |
−0.971683 | + | 0.236289i | \(0.924069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.3990 | − | 33.6000i | −0.791301 | − | 1.37057i | −0.925162 | − | 0.379573i | \(-0.876071\pi\) |
0.133861 | − | 0.991000i | \(-0.457262\pi\) | |||||||
\(602\) | 1.14643 | 0.0467249 | ||||||||
\(603\) | −8.87117 | + | 10.3763i | −0.361262 | + | 0.422554i | ||||
\(604\) | 2.89898 | 0.117958 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.00000 | − | 11.3137i | 0.324978 | − | 0.459588i | ||||
\(607\) | 13.7980 | − | 23.8988i | 0.560042 | − | 0.970021i | −0.437450 | − | 0.899243i | \(-0.644118\pi\) |
0.997492 | − | 0.0707783i | \(-0.0225483\pi\) | |||||||
\(608\) | −2.72474 | + | 4.71940i | −0.110503 | + | 0.191397i | ||||
\(609\) | 2.69694 | − | 3.81405i | 0.109285 | − | 0.154553i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.8990 | −0.440926 | ||||||||
\(612\) | 11.5000 | − | 13.4511i | 0.464860 | − | 0.543728i | ||||
\(613\) | −36.9444 | −1.49217 | −0.746085 | − | 0.665851i | \(-0.768069\pi\) | ||||
−0.746085 | + | 0.665851i | \(0.768069\pi\) | |||||||
\(614\) | 14.9722 | + | 25.9326i | 0.604229 | + | 1.04655i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.775255 | − | 1.34278i | 0.0312359 | − | 0.0541022i | ||||
\(617\) | −4.15153 | + | 7.19066i | −0.167134 | + | 0.289485i | −0.937411 | − | 0.348224i | \(-0.886785\pi\) |
0.770277 | + | 0.637710i | \(0.220118\pi\) | |||||||
\(618\) | −24.5732 | − | 2.26418i | −0.988480 | − | 0.0910789i | ||||
\(619\) | 14.2753 | + | 24.7255i | 0.573771 | + | 0.993800i | 0.996174 | + | 0.0873923i | \(0.0278534\pi\) |
−0.422403 | + | 0.906408i | \(0.638813\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.6969 | − | 24.9951i | 1.03118 | − | 1.00302i | ||||
\(622\) | −13.1010 | −0.525303 | ||||||||
\(623\) | 0.696938 | + | 1.20713i | 0.0279222 | + | 0.0483628i | ||||
\(624\) | −4.22474 | − | 0.389270i | −0.169125 | − | 0.0155833i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.8485 | + | 18.7901i | −0.433592 | + | 0.751003i | ||||
\(627\) | 13.6237 | + | 29.5717i | 0.544079 | + | 1.18098i | ||||
\(628\) | −8.00000 | − | 13.8564i | −0.319235 | − | 0.552931i | ||||
\(629\) | −47.1918 | −1.88166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.3485 | −0.451775 | −0.225888 | − | 0.974153i | \(-0.572528\pi\) | ||||
−0.225888 | + | 0.974153i | \(0.572528\pi\) | |||||||
\(632\) | 3.67423 | + | 6.36396i | 0.146153 | + | 0.253145i | ||||
\(633\) | 3.79796 | − | 5.37113i | 0.150955 | − | 0.213483i | ||||
\(634\) | 11.4722 | − | 19.8704i | 0.455619 | − | 0.789155i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.55051 | − | 5.02118i | 0.140787 | − | 0.199103i | ||||
\(637\) | 8.32577 | + | 14.4206i | 0.329879 | + | 0.571367i | ||||
\(638\) | −20.6969 | −0.819400 | ||||||||
\(639\) | −7.22474 | − | 1.34278i | −0.285806 | − | 0.0531196i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.5000 | + | 32.0429i | 0.730706 | + | 1.26562i | 0.956582 | + | 0.291464i | \(0.0941423\pi\) |
−0.225876 | + | 0.974156i | \(0.572524\pi\) | |||||||
\(642\) | −11.8485 | − | 25.7183i | −0.467622 | − | 1.01502i | ||||
\(643\) | −7.62372 | + | 13.2047i | −0.300650 | + | 0.520742i | −0.976283 | − | 0.216496i | \(-0.930537\pi\) |
0.675633 | + | 0.737238i | \(0.263870\pi\) | |||||||
\(644\) | 1.55051 | − | 2.68556i | 0.0610987 | − | 0.105826i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.0732 | + | 27.8396i | 0.632392 | + | 1.09534i | ||||
\(647\) | 34.8990 | 1.37202 | 0.686010 | − | 0.727592i | \(-0.259361\pi\) | ||||
0.686010 | + | 0.727592i | \(0.259361\pi\) | |||||||
\(648\) | −8.39898 | − | 3.23375i | −0.329943 | − | 0.127034i | ||||
\(649\) | −45.6969 | −1.79376 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.20204 | + | 0.110756i | 0.0471117 | + | 0.00434089i | ||||
\(652\) | −4.44949 | + | 7.70674i | −0.174255 | + | 0.301819i | ||||
\(653\) | 17.0000 | − | 29.4449i | 0.665261 | − | 1.15227i | −0.313953 | − | 0.949439i | \(-0.601653\pi\) |
0.979214 | − | 0.202828i | \(-0.0650132\pi\) | |||||||
\(654\) | 5.79796 | + | 12.5851i | 0.226718 | + | 0.492115i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | 43.6464 | + | 8.11207i | 1.70281 | + | 0.316482i | ||||
\(658\) | −2.00000 | −0.0779681 | ||||||||
\(659\) | 17.8990 | + | 31.0019i | 0.697245 | + | 1.20766i | 0.969418 | + | 0.245416i | \(0.0789245\pi\) |
−0.272173 | + | 0.962248i | \(0.587742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.89898 | + | 5.02118i | −0.112757 | + | 0.195301i | −0.916881 | − | 0.399161i | \(-0.869302\pi\) |
0.804124 | + | 0.594462i | \(0.202635\pi\) | |||||||
\(662\) | −12.6969 | + | 21.9917i | −0.493481 | + | 0.854733i | ||||
\(663\) | −14.4495 | + | 20.4347i | −0.561172 | + | 0.793617i | ||||
\(664\) | −2.00000 | − | 3.46410i | −0.0776151 | − | 0.134433i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.00000 | + | 22.6274i | 0.309994 | + | 0.876795i | ||||
\(667\) | −41.3939 | −1.60278 | ||||||||
\(668\) | −0.123724 | − | 0.214297i | −0.00478704 | − | 0.00829139i | ||||
\(669\) | 6.59592 | + | 14.3171i | 0.255013 | + | 0.553531i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.67423 | − | 13.2922i | 0.296261 | − | 0.513138i | ||||
\(672\) | −0.775255 | − | 0.0714323i | −0.0299061 | − | 0.00275556i | ||||
\(673\) | 14.4495 | + | 25.0273i | 0.556987 | + | 0.964730i | 0.997746 | + | 0.0671042i | \(0.0213760\pi\) |
−0.440759 | + | 0.897625i | \(0.645291\pi\) | |||||||
\(674\) | −18.5959 | −0.716288 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | −19.7980 | − | 34.2911i | −0.760897 | − | 1.31791i | −0.942389 | − | 0.334520i | \(-0.891426\pi\) |
0.181491 | − | 0.983393i | \(-0.441908\pi\) | |||||||
\(678\) | −8.44949 | − | 0.778539i | −0.324501 | − | 0.0298996i | ||||
\(679\) | 2.92168 | − | 5.06050i | 0.112124 | − | 0.194204i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.50000 | − | 5.42650i | −0.0958002 | − | 0.207944i | ||||
\(682\) | −2.67423 | − | 4.63191i | −0.102402 | − | 0.177365i | ||||
\(683\) | −45.4495 | −1.73908 | −0.869538 | − | 0.493866i | \(-0.835583\pi\) | ||||
−0.869538 | + | 0.493866i | \(0.835583\pi\) | |||||||
\(684\) | 10.6237 | − | 12.4261i | 0.406208 | − | 0.475125i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.10102 | + | 5.37113i | 0.118398 | + | 0.205071i | ||||
\(687\) | −18.4495 | + | 26.0915i | −0.703892 | + | 0.995454i | ||||
\(688\) | −1.27526 | + | 2.20881i | −0.0486186 | + | 0.0842100i | ||||
\(689\) | −4.34847 | + | 7.53177i | −0.165663 | + | 0.286938i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.79796 | − | 15.2385i | −0.334690 | − | 0.579700i | 0.648735 | − | 0.761014i | \(-0.275298\pi\) |
−0.983425 | + | 0.181314i | \(0.941965\pi\) | |||||||
\(692\) | −11.7980 | −0.448491 | ||||||||
\(693\) | −3.02270 | + | 3.53553i | −0.114823 | + | 0.134304i | ||||
\(694\) | −9.24745 | −0.351028 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.34847 | + | 9.43879i | 0.164828 | + | 0.357777i | ||||
\(697\) | −2.94949 | + | 5.10867i | −0.111720 | + | 0.193505i | ||||
\(698\) | −13.7980 | + | 23.8988i | −0.522260 | + | 0.904582i | ||||
\(699\) | 23.6237 | + | 2.17670i | 0.893531 | + | 0.0823303i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.3939 | −1.48789 | −0.743943 | − | 0.668243i | \(-0.767047\pi\) | ||||
−0.743943 | + | 0.668243i | \(0.767047\pi\) | |||||||
\(702\) | 12.2474 | + | 3.46410i | 0.462250 | + | 0.130744i | ||||
\(703\) | −43.5959 | −1.64425 | ||||||||
\(704\) | 1.72474 | + | 2.98735i | 0.0650038 | + | 0.112590i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.2980 | − | 28.2289i | 0.613382 | − | 1.06241i | ||||
\(707\) | −1.79796 | + | 3.11416i | −0.0676192 | + | 0.117120i | ||||
\(708\) | 9.60102 | + | 20.8400i | 0.360828 | + | 0.783215i | ||||
\(709\) | −18.6742 | − | 32.3447i | −0.701326 | − | 1.21473i | −0.968001 | − | 0.250945i | \(-0.919259\pi\) |
0.266676 | − | 0.963786i | \(-0.414075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.34847 | − | 20.7846i | −0.275589 | − | 0.779484i | ||||
\(712\) | −3.10102 | −0.116216 | ||||||||
\(713\) | −5.34847 | − | 9.26382i | −0.200302 | − | 0.346933i | ||||
\(714\) | −2.65153 | + | 3.74983i | −0.0992310 | + | 0.140334i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.449490 | − | 0.778539i | 0.0167982 | − | 0.0290954i | ||||
\(717\) | −0.696938 | + | 0.985620i | −0.0260276 | + | 0.0368086i | ||||
\(718\) | 1.77526 | + | 3.07483i | 0.0662519 | + | 0.114752i | ||||
\(719\) | 41.7980 | 1.55880 | 0.779400 | − | 0.626526i | \(-0.215524\pi\) | ||||
0.779400 | + | 0.626526i | \(0.215524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.40408 | 0.238500 | ||||||||
\(722\) | 5.34847 | + | 9.26382i | 0.199049 | + | 0.344764i | ||||
\(723\) | 0.724745 | + | 1.57313i | 0.0269536 | + | 0.0585054i | ||||
\(724\) | −2.77526 | + | 4.80688i | −0.103142 | + | 0.178646i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.55051 | + | 0.142865i | 0.0575448 | + | 0.00530220i | ||||
\(727\) | 12.6742 | + | 21.9524i | 0.470061 | + | 0.814170i | 0.999414 | − | 0.0342318i | \(-0.0108985\pi\) |
−0.529353 | + | 0.848402i | \(0.677565\pi\) | |||||||
\(728\) | 1.10102 | 0.0408065 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.52270 | + | 13.0297i | 0.278237 | + | 0.481921i | ||||
\(732\) | −7.67423 | − | 0.707107i | −0.283648 | − | 0.0261354i | ||||
\(733\) | −10.5732 | + | 18.3133i | −0.390531 | + | 0.676419i | −0.992520 | − | 0.122086i | \(-0.961042\pi\) |
0.601989 | + | 0.798504i | \(0.294375\pi\) | |||||||
\(734\) | 13.7980 | − | 23.8988i | 0.509292 | − | 0.882120i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.44949 | + | 5.97469i | 0.127150 | + | 0.220230i | ||||
\(737\) | −15.6969 | −0.578204 | ||||||||
\(738\) | 2.94949 | + | 0.548188i | 0.108572 | + | 0.0201791i | ||||
\(739\) | −17.2474 | −0.634458 | −0.317229 | − | 0.948349i | \(-0.602752\pi\) | ||||
−0.317229 | + | 0.948349i | \(0.602752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.3485 | + | 18.8776i | −0.490368 | + | 0.693485i | ||||
\(742\) | −0.797959 | + | 1.38211i | −0.0292940 | + | 0.0507387i | ||||
\(743\) | 11.4495 | − | 19.8311i | 0.420041 | − | 0.727532i | −0.575902 | − | 0.817519i | \(-0.695349\pi\) |
0.995943 | + | 0.0899863i | \(0.0286823\pi\) | |||||||
\(744\) | −1.55051 | + | 2.19275i | −0.0568445 | + | 0.0803902i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.5959 | 0.497782 | ||||||||
\(747\) | 4.00000 | + | 11.3137i | 0.146352 | + | 0.413947i | ||||
\(748\) | 20.3485 | 0.744014 | ||||||||
\(749\) | 3.67423 | + | 6.36396i | 0.134254 | + | 0.232534i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.4949 | − | 45.8905i | 0.966813 | − | 1.67457i | 0.262148 | − | 0.965028i | \(-0.415569\pi\) |
0.704664 | − | 0.709541i | \(-0.251098\pi\) | |||||||
\(752\) | 2.22474 | − | 3.85337i | 0.0811281 | − | 0.140518i | ||||
\(753\) | −11.2980 | − | 1.04100i | −0.411721 | − | 0.0379361i | ||||
\(754\) | −7.34847 | − | 12.7279i | −0.267615 | − | 0.463524i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.24745 | + | 0.635674i | 0.0817389 | + | 0.0231193i | ||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 2.07321 | + | 3.59091i | 0.0753025 | + | 0.130428i | ||||
\(759\) | 41.0454 | + | 3.78194i | 1.48985 | + | 0.137276i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.247449 | + | 0.428594i | −0.00897001 | + | 0.0155365i | −0.870476 | − | 0.492212i | \(-0.836189\pi\) |
0.861506 | + | 0.507748i | \(0.169522\pi\) | |||||||
\(762\) | −5.00000 | − | 10.8530i | −0.181131 | − | 0.393163i | ||||
\(763\) | −1.79796 | − | 3.11416i | −0.0650905 | − | 0.112740i | ||||
\(764\) | 18.2474 | 0.660170 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.7980 | 0.643066 | ||||||||
\(767\) | −16.2247 | − | 28.1021i | −0.585842 | − | 1.01471i | ||||
\(768\) | 1.00000 | − | 1.41421i | 0.0360844 | − | 0.0510310i | ||||
\(769\) | −12.2474 | + | 21.2132i | −0.441654 | + | 0.764968i | −0.997812 | − | 0.0661088i | \(-0.978942\pi\) |
0.556158 | + | 0.831076i | \(0.312275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1010 | − | 14.2850i | 0.363779 | − | 0.514462i | ||||
\(772\) | −6.84847 | − | 11.8619i | −0.246482 | − | 0.426919i | ||||
\(773\) | 35.3939 | 1.27303 | 0.636515 | − | 0.771265i | \(-0.280375\pi\) | ||||
0.636515 | + | 0.771265i | \(0.280375\pi\) | |||||||
\(774\) | 4.97219 | − | 5.81577i | 0.178722 | − | 0.209044i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.50000 | + | 11.2583i | 0.233336 | + | 0.404151i | ||||
\(777\) | −2.60612 | − | 5.65685i | −0.0934941 | − | 0.202939i | ||||
\(778\) | 8.77526 | − | 15.1992i | 0.314608 | − | 0.544917i | ||||
\(779\) | −2.72474 | + | 4.71940i | −0.0976241 | + | 0.169090i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.22474 | − | 7.31747i | −0.151173 | − | 0.261840i | ||||
\(782\) | 40.6969 | 1.45532 | ||||||||
\(783\) | −7.65153 | − | 30.2234i | −0.273443 | − | 1.08010i | ||||
\(784\) | −6.79796 | −0.242784 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.44949 | + | 0.778539i | 0.301383 | + | 0.0277696i | ||||
\(787\) | 25.6969 | − | 44.5084i | 0.915997 | − | 1.58655i | 0.110562 | − | 0.993869i | \(-0.464735\pi\) |
0.805435 | − | 0.592684i | \(-0.201932\pi\) | |||||||
\(788\) | 4.00000 | − | 6.92820i | 0.142494 | − | 0.246807i | ||||
\(789\) | −9.02270 | − | 19.5847i | −0.321217 | − | 0.697234i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.20204 | 0.0782956 | ||||||||
\(792\) | −3.44949 | − | 9.75663i | −0.122572 | − | 0.346687i | ||||
\(793\) | 10.8990 | 0.387034 | ||||||||
\(794\) | −0.898979 | − | 1.55708i | −0.0319036 | − | 0.0552586i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.77526 | + | 13.4671i | −0.275587 | + | 0.477330i | ||||
\(797\) | −1.79796 | + | 3.11416i | −0.0636870 | + | 0.110309i | −0.896111 | − | 0.443830i | \(-0.853619\pi\) |
0.832424 | + | 0.554139i | \(0.186953\pi\) | |||||||
\(798\) | −2.44949 | + | 3.46410i | −0.0867110 | + | 0.122628i | ||||
\(799\) | −13.1237 | − | 22.7310i | −0.464284 | − | 0.804163i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.14643 | + | 1.69994i | 0.323173 | + | 0.0600645i | ||||
\(802\) | −9.20204 | −0.324935 | ||||||||
\(803\) | 25.5227 | + | 44.2066i | 0.900677 | + | 1.56002i | ||||
\(804\) | 3.29796 | + | 7.15855i | 0.116310 | + | 0.252463i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.89898 | − | 3.28913i | 0.0668887 | − | 0.115855i | ||||
\(807\) | −27.6742 | − | 2.54991i | −0.974179 | − | 0.0897612i | ||||
\(808\) | −4.00000 | − | 6.92820i | −0.140720 | − | 0.243733i | ||||
\(809\) | −41.0908 | −1.44468 | −0.722338 | − | 0.691540i | \(-0.756933\pi\) | ||||
−0.722338 | + | 0.691540i | \(0.756933\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.24745 | 0.254492 | 0.127246 | − | 0.991871i | \(-0.459386\pi\) | ||||
0.127246 | + | 0.991871i | \(0.459386\pi\) | |||||||
\(812\) | −1.34847 | − | 2.33562i | −0.0473220 | − | 0.0819641i | ||||
\(813\) | 26.8990 | + | 2.47848i | 0.943388 | + | 0.0869242i | ||||
\(814\) | −13.7980 | + | 23.8988i | −0.483618 | + | 0.837651i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.27526 | − | 9.27987i | −0.149664 | − | 0.324861i | ||||
\(817\) | 6.94949 | + | 12.0369i | 0.243132 | + | 0.421117i | ||||
\(818\) | −15.8990 | −0.555895 | ||||||||
\(819\) | −3.24745 | − | 0.603566i | −0.113475 | − | 0.0210903i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.02270 | − | 1.77138i | −0.0356926 | − | 0.0618214i | 0.847627 | − | 0.530592i | \(-0.178030\pi\) |
−0.883320 | + | 0.468771i | \(0.844697\pi\) | |||||||
\(822\) | −3.00000 | + | 4.24264i | −0.104637 | + | 0.147979i | ||||
\(823\) | 15.7980 | − | 27.3629i | 0.550682 | − | 0.953810i | −0.447543 | − | 0.894262i | \(-0.647701\pi\) |
0.998225 | − | 0.0595473i | \(-0.0189657\pi\) | |||||||
\(824\) | −7.12372 | + | 12.3387i | −0.248167 | + | 0.429837i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.97730 | − | 5.15683i | −0.103593 | − | 0.179429i | ||||
\(827\) | 5.79796 | 0.201615 | 0.100807 | − | 0.994906i | \(-0.467857\pi\) | ||||
0.100807 | + | 0.994906i | \(0.467857\pi\) | |||||||
\(828\) | −6.89898 | − | 19.5133i | −0.239756 | − | 0.678133i | ||||
\(829\) | −26.4495 | −0.918629 | −0.459314 | − | 0.888274i | \(-0.651905\pi\) | ||||
−0.459314 | + | 0.888274i | \(0.651905\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.4495 | − | 46.5583i | −0.744075 | − | 1.61509i | ||||
\(832\) | −1.22474 | + | 2.12132i | −0.0424604 | + | 0.0735436i | ||||
\(833\) | −20.0505 | + | 34.7285i | −0.694709 | + | 1.20327i | ||||
\(834\) | 22.8485 | + | 2.10527i | 0.791178 | + | 0.0728994i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.7980 | 0.650141 | ||||||||
\(837\) | 5.77526 | − | 5.61753i | 0.199622 | − | 0.194170i | ||||
\(838\) | 8.89898 | 0.307410 | ||||||||
\(839\) | −20.1237 | − | 34.8553i | −0.694748 | − | 1.20334i | −0.970266 | − | 0.242043i | \(-0.922183\pi\) |
0.275517 | − | 0.961296i | \(-0.411151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −5.77526 | + | 10.0030i | −0.199028 | + | 0.344727i | ||||
\(843\) | 8.69694 | + | 18.8776i | 0.299538 | + | 0.650179i | ||||
\(844\) | −1.89898 | − | 3.28913i | −0.0653656 | − | 0.113216i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.67423 | + | 10.1459i | −0.298226 | + | 0.348823i | ||||
\(847\) | −0.404082 | −0.0138844 | ||||||||
\(848\) | −1.77526 | − | 3.07483i | −0.0609625 | − | 0.105590i | ||||
\(849\) | 4.00000 | − | 5.65685i | 0.137280 | − | 0.194143i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.5959 | + | 47.7975i | −0.945976 | + | 1.63848i | ||||
\(852\) | −2.44949 | + | 3.46410i | −0.0839181 | + | 0.118678i | ||||
\(853\) | −4.57321 | − | 7.92104i | −0.156584 | − | 0.271211i | 0.777051 | − | 0.629438i | \(-0.216715\pi\) |
−0.933635 | + | 0.358227i | \(0.883381\pi\) | |||||||
\(854\) | 2.00000 | 0.0684386 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.3485 | −0.558779 | ||||||||
\(857\) | −2.69694 | − | 4.67123i | −0.0921257 | − | 0.159566i | 0.816280 | − | 0.577657i | \(-0.196033\pi\) |
−0.908405 | + | 0.418091i | \(0.862699\pi\) | |||||||
\(858\) | 6.12372 | + | 13.2922i | 0.209061 | + | 0.453787i | ||||
\(859\) | 18.8712 | − | 32.6858i | 0.643876 | − | 1.11523i | −0.340684 | − | 0.940178i | \(-0.610659\pi\) |
0.984560 | − | 0.175048i | \(-0.0560081\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.775255 | − | 0.0714323i | −0.0264206 | − | 0.00243441i | ||||
\(862\) | 19.1237 | + | 33.1233i | 0.651357 | + | 1.12818i | ||||
\(863\) | 26.4495 | 0.900351 | 0.450176 | − | 0.892940i | \(-0.351361\pi\) | ||||
0.450176 | + | 0.892940i | \(0.351361\pi\) | |||||||
\(864\) | −3.72474 | + | 3.62302i | −0.126718 | + | 0.123258i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.5000 | + | 19.9186i | 0.390786 | + | 0.676861i | ||||
\(867\) | −30.6969 | − | 2.82843i | −1.04252 | − | 0.0960584i | ||||
\(868\) | 0.348469 | − | 0.603566i | 0.0118278 | − | 0.0204864i | ||||
\(869\) | 12.6742 | − | 21.9524i | 0.429944 | − | 0.744685i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.57321 | − | 9.65309i | −0.188841 | − | 0.327082i | ||||
\(872\) | 8.00000 | 0.270914 | ||||||||
\(873\) | −13.0000 | − | 36.7696i | −0.439983 | − | 1.24446i | ||||
\(874\) | 37.5959 | 1.27170 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.7980 | − | 20.9275i | 0.499977 | − | 0.707074i | ||||
\(877\) | 10.4268 | − | 18.0597i | 0.352088 | − | 0.609834i | −0.634527 | − | 0.772900i | \(-0.718805\pi\) |
0.986615 | + | 0.163067i | \(0.0521386\pi\) | |||||||
\(878\) | 11.0227 | − | 19.0919i | 0.371998 | − | 0.644320i | ||||
\(879\) | 18.0000 | − | 25.4558i | 0.607125 | − | 0.858604i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 20.0505 | + | 3.72656i | 0.675136 | + | 0.125480i | ||||
\(883\) | −6.55051 | −0.220442 | −0.110221 | − | 0.993907i | \(-0.535156\pi\) | ||||
−0.110221 | + | 0.993907i | \(0.535156\pi\) | |||||||
\(884\) | 7.22474 | + | 12.5136i | 0.242994 | + | 0.420879i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.6237 | − | 18.4008i | 0.356911 | − | 0.618188i | ||||
\(887\) | −9.67423 | + | 16.7563i | −0.324829 | + | 0.562620i | −0.981478 | − | 0.191576i | \(-0.938640\pi\) |
0.656649 | + | 0.754197i | \(0.271973\pi\) | |||||||
\(888\) | 13.7980 | + | 1.27135i | 0.463029 | + | 0.0426637i | ||||
\(889\) | 1.55051 | + | 2.68556i | 0.0520024 | + | 0.0900709i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.82577 | + | 30.6681i | 0.161669 | + | 1.02742i | ||||
\(892\) | 9.10102 | 0.304725 | ||||||||
\(893\) | −12.1237 | − | 20.9989i | −0.405705 | − | 0.702702i | ||||
\(894\) | −14.2247 | − | 1.31067i | −0.475747 | − | 0.0438355i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.224745 | + | 0.389270i | −0.00750820 | + | 0.0130046i | ||||
\(897\) | 12.2474 | + | 26.5843i | 0.408930 | + | 0.887625i | ||||
\(898\) | 9.39898 | + | 16.2795i | 0.313648 | + | 0.543254i | ||||
\(899\) | −9.30306 | −0.310274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.9444 | −0.697759 | ||||||||
\(902\) | 1.72474 | + | 2.98735i | 0.0574277 | + | 0.0994677i | ||||
\(903\) | −1.14643 | + | 1.62129i | −0.0381507 | + | 0.0539533i | ||||
\(904\) | −2.44949 | + | 4.24264i | −0.0814688 | + | 0.141108i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.89898 | + | 4.09978i | −0.0963121 | + | 0.136206i | ||||
\(907\) | 19.8712 | + | 34.4179i | 0.659811 | + | 1.14283i | 0.980664 | + | 0.195698i | \(0.0626972\pi\) |
−0.320853 | + | 0.947129i | \(0.603969\pi\) | |||||||
\(908\) | −3.44949 | −0.114475 | ||||||||
\(909\) | 8.00000 | + | 22.6274i | 0.265343 | + | 0.750504i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.1237 | − | 20.9989i | −0.401677 | − | 0.695725i | 0.592252 | − | 0.805753i | \(-0.298239\pi\) |
−0.993928 | + | 0.110028i | \(0.964906\pi\) | |||||||
\(912\) | −3.94949 | − | 8.57277i | −0.130781 | − | 0.283873i | ||||
\(913\) | −6.89898 | + | 11.9494i | −0.228323 | + | 0.395467i | ||||
\(914\) | −8.94949 | + | 15.5010i | −0.296023 | + | 0.512727i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.22474 | + | 15.9777i | 0.304794 | + | 0.527919i | ||||
\(917\) | −2.20204 | −0.0727178 | ||||||||
\(918\) | 7.52270 | + | 29.7145i | 0.248286 | + | 0.980726i | ||||
\(919\) | 1.10102 | 0.0363193 | 0.0181597 | − | 0.999835i | \(-0.494219\pi\) | ||||
0.0181597 | + | 0.999835i | \(0.494219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.6464 | − | 4.75872i | −1.70181 | − | 0.156805i | ||||
\(922\) | −1.22474 | + | 2.12132i | −0.0403348 | + | 0.0698620i | ||||
\(923\) | 3.00000 | − | 5.19615i | 0.0987462 | − | 0.171033i | ||||
\(924\) | 1.12372 | + | 2.43916i | 0.0369678 | + | 0.0802424i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24.0000 | −0.788689 | ||||||||
\(927\) | 27.7753 | − | 32.4876i | 0.912259 | − | 1.06703i | ||||
\(928\) | 6.00000 | 0.196960 | ||||||||
\(929\) | 8.20204 | + | 14.2064i | 0.269100 | + | 0.466095i | 0.968630 | − | 0.248508i | \(-0.0799404\pi\) |
−0.699529 | + | 0.714604i | \(0.746607\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.5227 | + | 32.0823i | −0.607057 | + | 1.05145i | ||||
\(932\) | 6.84847 | − | 11.8619i | 0.224329 | − | 0.388549i | ||||
\(933\) | 13.1010 | − | 18.5276i | 0.428908 | − | 0.606568i | ||||
\(934\) | −5.17423 | − | 8.96204i | −0.169306 | − | 0.293247i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.77526 | − | 5.58542i | 0.156084 | − | 0.182565i | ||||
\(937\) | −0.404082 | −0.0132008 | −0.00660039 | − | 0.999978i | \(-0.502101\pi\) | ||||
−0.00660039 | + | 0.999978i | \(0.502101\pi\) | |||||||
\(938\) | −1.02270 | − | 1.77138i | −0.0333925 | − | 0.0578374i | ||||
\(939\) | −15.7247 | − | 34.1322i | −0.513158 | − | 1.11386i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.1010 | − | 26.1557i | 0.492279 | − | 0.852653i | −0.507681 | − | 0.861545i | \(-0.669497\pi\) |
0.999960 | + | 0.00889239i | \(0.00283057\pi\) | |||||||
\(942\) | 27.5959 | + | 2.54270i | 0.899124 | + | 0.0828456i | ||||
\(943\) | 3.44949 | + | 5.97469i | 0.112331 | + | 0.194563i | ||||
\(944\) | 13.2474 | 0.431168 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.79796 | 0.286046 | ||||||||
\(947\) | −1.62372 | − | 2.81237i | −0.0527640 | − | 0.0913898i | 0.838437 | − | 0.544998i | \(-0.183470\pi\) |
−0.891201 | + | 0.453609i | \(0.850136\pi\) | |||||||
\(948\) | −12.6742 | − | 1.16781i | −0.411640 | − | 0.0379287i | ||||
\(949\) | −18.1237 | + | 31.3912i | −0.588321 | + | 1.01900i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.6288 | + | 36.0946i | 0.539227 | + | 1.17045i | ||||
\(952\) | 1.32577 | + | 2.29629i | 0.0429683 | + | 0.0744233i | ||||
\(953\) | −31.2020 | −1.01073 | −0.505367 | − | 0.862905i | \(-0.668643\pi\) | ||||
−0.505367 | + | 0.862905i | \(0.668643\pi\) | |||||||
\(954\) | 3.55051 | + | 10.0424i | 0.114952 | + | 0.325133i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.348469 | + | 0.603566i | 0.0112703 | + | 0.0195207i | ||||
\(957\) | 20.6969 | − | 29.2699i | 0.669037 | − | 0.946161i | ||||
\(958\) | 8.34847 | − | 14.4600i | 0.269727 | − | 0.467181i | ||||
\(959\) | 0.674235 | − | 1.16781i | 0.0217722 | − | 0.0377105i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.2980 | + | 24.7648i | 0.461224 | + | 0.798864i | ||||
\(962\) | −19.5959 | −0.631798 | ||||||||
\(963\) | 48.2196 | + | 8.96204i | 1.55386 | + | 0.288798i | ||||
\(964\) | 1.00000 | 0.0322078 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.24745 | + | 4.87832i | 0.0723105 | + | 0.156957i | ||||
\(967\) | −0.348469 | + | 0.603566i | −0.0112060 | + | 0.0194094i | −0.871574 | − | 0.490264i | \(-0.836900\pi\) |
0.860368 | + | 0.509673i | \(0.170234\pi\) | |||||||
\(968\) | 0.449490 | − | 0.778539i | 0.0144471 | − | 0.0250232i | ||||
\(969\) | −55.4444 | − | 5.10867i | −1.78113 | − | 0.164114i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.3939 | 1.13584 | 0.567922 | − | 0.823083i | \(-0.307748\pi\) | ||||
0.567922 | + | 0.823083i | \(0.307748\pi\) | |||||||
\(972\) | 12.9722 | − | 8.64420i | 0.416083 | − | 0.277263i | ||||
\(973\) | −5.95459 | −0.190895 | ||||||||
\(974\) | −12.5505 | − | 21.7381i | −0.402144 | − | 0.696534i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.22474 | + | 3.85337i | −0.0712123 | + | 0.123343i | ||||
\(977\) | −14.0505 | + | 24.3362i | −0.449516 | + | 0.778584i | −0.998354 | − | 0.0573443i | \(-0.981737\pi\) |
0.548839 | + | 0.835928i | \(0.315070\pi\) | |||||||
\(978\) | −6.44949 | − | 13.9993i | −0.206232 | − | 0.447647i | ||||
\(979\) | 5.34847 | + | 9.26382i | 0.170938 | + | 0.296073i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.5959 | − | 4.38551i | −0.753360 | − | 0.140018i | ||||
\(982\) | −18.5505 | −0.591971 | ||||||||
\(983\) | −10.6969 | − | 18.5276i | −0.341179 | − | 0.590940i | 0.643473 | − | 0.765469i | \(-0.277493\pi\) |
−0.984652 | + | 0.174529i | \(0.944160\pi\) | |||||||
\(984\) | 1.00000 | − | 1.41421i | 0.0318788 | − | 0.0450835i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.6969 | − | 30.6520i | 0.563585 | − | 0.976158i | ||||
\(987\) | 2.00000 | − | 2.82843i | 0.0636607 | − | 0.0900298i | ||||
\(988\) | 6.67423 | + | 11.5601i | 0.212336 | + | 0.367776i | ||||
\(989\) | 17.5959 | 0.559518 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 0.775255 | + | 1.34278i | 0.0246144 | + | 0.0426333i | ||||
\(993\) | −18.4041 | − | 39.9479i | −0.584036 | − | 1.26771i | ||||
\(994\) | 0.550510 | − | 0.953512i | 0.0174611 | − | 0.0302436i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.89898 | + | 0.635674i | 0.218603 | + | 0.0201421i | ||||
\(997\) | −10.4722 | − | 18.1384i | −0.331658 | − | 0.574448i | 0.651179 | − | 0.758924i | \(-0.274275\pi\) |
−0.982837 | + | 0.184476i | \(0.940941\pi\) | |||||||
\(998\) | 21.2474 | 0.672576 | ||||||||
\(999\) | −40.0000 | − | 11.3137i | −1.26554 | − | 0.357950i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))