Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), 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: | \(7.42608738798\) |
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 | 491.11 | ||
Character | \(\chi\) | \(=\) | 930.491 |
Dual form | 930.2.o.e.161.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.67328 | + | 0.447368i | −0.966068 | + | 0.258288i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | −0.447368 | − | 1.67328i | −0.182637 | − | 0.683113i | ||||
\(7\) | −1.32225 | + | 2.29021i | −0.499764 | + | 0.865617i | −1.00000 | 0.000271954i | \(-0.999913\pi\) | |
0.500236 | + | 0.865889i | \(0.333247\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.59972 | − | 1.49714i | 0.866574 | − | 0.499048i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −1.35563 | − | 2.34802i | −0.408738 | − | 0.707955i | 0.586011 | − | 0.810303i | \(-0.300698\pi\) |
−0.994749 | + | 0.102348i | \(0.967364\pi\) | |||||||
\(12\) | 1.67328 | − | 0.447368i | 0.483034 | − | 0.129144i | ||||
\(13\) | 3.49868 | − | 2.01996i | 0.970359 | − | 0.560237i | 0.0710136 | − | 0.997475i | \(-0.477377\pi\) |
0.899346 | + | 0.437238i | \(0.144043\pi\) | |||||||
\(14\) | −2.29021 | − | 1.32225i | −0.612084 | − | 0.353387i | ||||
\(15\) | −1.22542 | + | 1.22407i | −0.316401 | + | 0.316054i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.370882 | − | 0.642386i | 0.0899521 | − | 0.155802i | −0.817539 | − | 0.575874i | \(-0.804662\pi\) |
0.907491 | + | 0.420072i | \(0.137995\pi\) | |||||||
\(18\) | 1.49714 | + | 2.59972i | 0.352880 | + | 0.612761i | ||||
\(19\) | 1.17674 | − | 2.03818i | 0.269963 | − | 0.467590i | −0.698889 | − | 0.715230i | \(-0.746322\pi\) |
0.968852 | + | 0.247641i | \(0.0796552\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | 1.18793 | − | 4.42369i | 0.259228 | − | 0.965329i | ||||
\(22\) | 2.34802 | − | 1.35563i | 0.500600 | − | 0.289021i | ||||
\(23\) | −3.17723 | −0.662498 | −0.331249 | − | 0.943543i | \(-0.607470\pi\) | ||||
−0.331249 | + | 0.943543i | \(0.607470\pi\) | |||||||
\(24\) | 0.447368 | + | 1.67328i | 0.0913187 | + | 0.341557i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 2.01996 | + | 3.49868i | 0.396148 | + | 0.686148i | ||||
\(27\) | −3.68029 | + | 3.66817i | −0.708271 | + | 0.705940i | ||||
\(28\) | 1.32225 | − | 2.29021i | 0.249882 | − | 0.432809i | ||||
\(29\) | 1.11630 | 0.207292 | 0.103646 | − | 0.994614i | \(-0.466949\pi\) | ||||
0.103646 | + | 0.994614i | \(0.466949\pi\) | |||||||
\(30\) | −1.22407 | − | 1.22542i | −0.223484 | − | 0.223730i | ||||
\(31\) | 4.10522 | − | 3.76128i | 0.737319 | − | 0.675545i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 3.31878 | + | 3.32243i | 0.577725 | + | 0.578360i | ||||
\(34\) | 0.642386 | + | 0.370882i | 0.110168 | + | 0.0636057i | ||||
\(35\) | 2.64450i | 0.447003i | ||||||||
\(36\) | −2.59972 | + | 1.49714i | −0.433287 | + | 0.249524i | ||||
\(37\) | 8.66260 | + | 5.00135i | 1.42412 | + | 0.822218i | 0.996648 | − | 0.0818097i | \(-0.0260700\pi\) |
0.427475 | + | 0.904027i | \(0.359403\pi\) | |||||||
\(38\) | 2.03818 | + | 1.17674i | 0.330636 | + | 0.190893i | ||||
\(39\) | −4.95060 | + | 4.94516i | −0.792730 | + | 0.791860i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | 4.56104 | − | 2.63332i | 0.712315 | − | 0.411255i | −0.0996025 | − | 0.995027i | \(-0.531757\pi\) |
0.811918 | + | 0.583772i | \(0.198424\pi\) | |||||||
\(42\) | 4.42369 | + | 1.18793i | 0.682590 | + | 0.183302i | ||||
\(43\) | 4.20794 | + | 2.42945i | 0.641704 | + | 0.370488i | 0.785271 | − | 0.619153i | \(-0.212524\pi\) |
−0.143567 | + | 0.989641i | \(0.545857\pi\) | |||||||
\(44\) | 1.35563 | + | 2.34802i | 0.204369 | + | 0.353978i | ||||
\(45\) | 1.50285 | − | 2.59643i | 0.224032 | − | 0.387052i | ||||
\(46\) | − | 3.17723i | − | 0.468457i | ||||||
\(47\) | 3.29156i | 0.480123i | 0.970758 | + | 0.240061i | \(0.0771676\pi\) | ||||
−0.970758 | + | 0.240061i | \(0.922832\pi\) | |||||||
\(48\) | −1.67328 | + | 0.447368i | −0.241517 | + | 0.0645721i | ||||
\(49\) | 0.00329675 | + | 0.00571013i | 0.000470964 | + | 0.000815734i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | −0.333205 | + | 1.24081i | −0.0466581 | + | 0.173748i | ||||
\(52\) | −3.49868 | + | 2.01996i | −0.485180 | + | 0.280119i | ||||
\(53\) | 0.432136 | + | 0.748481i | 0.0593584 | + | 0.102812i | 0.894178 | − | 0.447712i | \(-0.147761\pi\) |
−0.834819 | + | 0.550524i | \(0.814428\pi\) | |||||||
\(54\) | −3.66817 | − | 3.68029i | −0.499175 | − | 0.500824i | ||||
\(55\) | −2.34802 | − | 1.35563i | −0.316607 | − | 0.182793i | ||||
\(56\) | 2.29021 | + | 1.32225i | 0.306042 | + | 0.176693i | ||||
\(57\) | −1.05720 | + | 3.93687i | −0.140030 | + | 0.521452i | ||||
\(58\) | 1.11630i | 0.146577i | ||||||||
\(59\) | −0.0673682 | − | 0.0388951i | −0.00877060 | − | 0.00506371i | 0.495608 | − | 0.868546i | \(-0.334945\pi\) |
−0.504379 | + | 0.863482i | \(0.668279\pi\) | |||||||
\(60\) | 1.22542 | − | 1.22407i | 0.158201 | − | 0.158027i | ||||
\(61\) | 8.21375i | 1.05166i | 0.850589 | + | 0.525832i | \(0.176246\pi\) | ||||
−0.850589 | + | 0.525832i | \(0.823754\pi\) | |||||||
\(62\) | 3.76128 | + | 4.10522i | 0.477682 | + | 0.521363i | ||||
\(63\) | −0.00871827 | + | 7.93351i | −0.00109840 | + | 0.999528i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.01996 | − | 3.49868i | 0.250546 | − | 0.433958i | ||||
\(66\) | −3.32243 | + | 3.31878i | −0.408963 | + | 0.408513i | ||||
\(67\) | 4.09060 | + | 7.08512i | 0.499746 | + | 0.865586i | 1.00000 | 0.000293150i | \(-9.33126e-5\pi\) | |
−0.500254 | + | 0.865879i | \(0.666760\pi\) | |||||||
\(68\) | −0.370882 | + | 0.642386i | −0.0449760 | + | 0.0779008i | ||||
\(69\) | 5.31639 | − | 1.42139i | 0.640018 | − | 0.171115i | ||||
\(70\) | −2.64450 | −0.316079 | ||||||||
\(71\) | 11.6252 | − | 6.71183i | 1.37966 | − | 0.796548i | 0.387543 | − | 0.921852i | \(-0.373324\pi\) |
0.992118 | + | 0.125304i | \(0.0399906\pi\) | |||||||
\(72\) | −1.49714 | − | 2.59972i | −0.176440 | − | 0.306380i | ||||
\(73\) | 9.24020 | − | 5.33483i | 1.08148 | − | 0.624395i | 0.150188 | − | 0.988657i | \(-0.452012\pi\) |
0.931296 | + | 0.364262i | \(0.118679\pi\) | |||||||
\(74\) | −5.00135 | + | 8.66260i | −0.581396 | + | 1.00701i | ||||
\(75\) | −0.449207 | + | 1.67279i | −0.0518699 | + | 0.193157i | ||||
\(76\) | −1.17674 | + | 2.03818i | −0.134982 | + | 0.233795i | ||||
\(77\) | 7.16994 | 0.817091 | ||||||||
\(78\) | −4.94516 | − | 4.95060i | −0.559929 | − | 0.560545i | ||||
\(79\) | −10.5492 | − | 6.09057i | −1.18688 | − | 0.685243i | −0.229280 | − | 0.973360i | \(-0.573637\pi\) |
−0.957595 | + | 0.288118i | \(0.906971\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | 4.51712 | − | 7.78432i | 0.501902 | − | 0.864924i | ||||
\(82\) | 2.63332 | + | 4.56104i | 0.290801 | + | 0.503683i | ||||
\(83\) | −2.44932 | − | 4.24235i | −0.268848 | − | 0.465659i | 0.699716 | − | 0.714421i | \(-0.253310\pi\) |
−0.968565 | + | 0.248762i | \(0.919976\pi\) | |||||||
\(84\) | −1.18793 | + | 4.42369i | −0.129614 | + | 0.482664i | ||||
\(85\) | − | 0.741764i | − | 0.0804556i | ||||||
\(86\) | −2.42945 | + | 4.20794i | −0.261975 | + | 0.453753i | ||||
\(87\) | −1.86788 | + | 0.499398i | −0.200258 | + | 0.0535410i | ||||
\(88\) | −2.34802 | + | 1.35563i | −0.250300 | + | 0.144511i | ||||
\(89\) | −17.1663 | −1.81962 | −0.909811 | − | 0.415022i | \(-0.863774\pi\) | ||||
−0.909811 | + | 0.415022i | \(0.863774\pi\) | |||||||
\(90\) | 2.59643 | + | 1.50285i | 0.273687 | + | 0.158415i | ||||
\(91\) | 10.6836i | 1.11995i | ||||||||
\(92\) | 3.17723 | 0.331249 | ||||||||
\(93\) | −5.18650 | + | 8.13021i | −0.537815 | + | 0.843063i | ||||
\(94\) | −3.29156 | −0.339498 | ||||||||
\(95\) | − | 2.35348i | − | 0.241462i | ||||||
\(96\) | −0.447368 | − | 1.67328i | −0.0456593 | − | 0.170778i | ||||
\(97\) | 12.4034 | 1.25938 | 0.629689 | − | 0.776847i | \(-0.283182\pi\) | ||||
0.629689 | + | 0.776847i | \(0.283182\pi\) | |||||||
\(98\) | −0.00571013 | + | 0.00329675i | −0.000576811 | + | 0.000333022i | ||||
\(99\) | −7.03959 | − | 4.07463i | −0.707505 | − | 0.409516i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 0.291018i | 0.0289574i | 0.999895 | + | 0.0144787i | \(0.00460888\pi\) | ||||
−0.999895 | + | 0.0144787i | \(0.995391\pi\) | |||||||
\(102\) | −1.24081 | − | 0.333205i | −0.122859 | − | 0.0329923i | ||||
\(103\) | 3.02724 | + | 5.24333i | 0.298283 | + | 0.516641i | 0.975743 | − | 0.218918i | \(-0.0702528\pi\) |
−0.677460 | + | 0.735559i | \(0.736919\pi\) | |||||||
\(104\) | −2.01996 | − | 3.49868i | −0.198074 | − | 0.343074i | ||||
\(105\) | −1.18307 | − | 4.42499i | −0.115456 | − | 0.431835i | ||||
\(106\) | −0.748481 | + | 0.432136i | −0.0726989 | + | 0.0419727i | ||||
\(107\) | 4.83678 | + | 2.79252i | 0.467590 | + | 0.269963i | 0.715230 | − | 0.698889i | \(-0.246322\pi\) |
−0.247641 | + | 0.968852i | \(0.579655\pi\) | |||||||
\(108\) | 3.68029 | − | 3.66817i | 0.354136 | − | 0.352970i | ||||
\(109\) | 7.74239 | 0.741587 | 0.370793 | − | 0.928715i | \(-0.379086\pi\) | ||||
0.370793 | + | 0.928715i | \(0.379086\pi\) | |||||||
\(110\) | 1.35563 | − | 2.34802i | 0.129254 | − | 0.223875i | ||||
\(111\) | −16.7324 | − | 4.49329i | −1.58817 | − | 0.426484i | ||||
\(112\) | −1.32225 | + | 2.29021i | −0.124941 | + | 0.216404i | ||||
\(113\) | −5.97390 | + | 3.44903i | −0.561978 | + | 0.324458i | −0.753939 | − | 0.656945i | \(-0.771849\pi\) |
0.191961 | + | 0.981402i | \(0.438515\pi\) | |||||||
\(114\) | −3.93687 | − | 1.05720i | −0.368722 | − | 0.0990159i | ||||
\(115\) | −2.75156 | + | 1.58861i | −0.256584 | + | 0.148139i | ||||
\(116\) | −1.11630 | −0.103646 | ||||||||
\(117\) | 6.07142 | − | 10.4894i | 0.561303 | − | 0.969743i | ||||
\(118\) | 0.0388951 | − | 0.0673682i | 0.00358058 | − | 0.00620175i | ||||
\(119\) | 0.980799 | + | 1.69879i | 0.0899097 | + | 0.155728i | ||||
\(120\) | 1.22407 | + | 1.22542i | 0.111742 | + | 0.111865i | ||||
\(121\) | 1.82453 | − | 3.16018i | 0.165866 | − | 0.287289i | ||||
\(122\) | −8.21375 | −0.743638 | ||||||||
\(123\) | −6.45383 | + | 6.44674i | −0.581922 | + | 0.581283i | ||||
\(124\) | −4.10522 | + | 3.76128i | −0.368659 | + | 0.337772i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −7.93351 | − | 0.00871827i | −0.706773 | − | 0.000776685i | ||||
\(127\) | 6.24347 | + | 3.60467i | 0.554019 | + | 0.319863i | 0.750741 | − | 0.660596i | \(-0.229696\pi\) |
−0.196723 | + | 0.980459i | \(0.563030\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −8.12791 | − | 2.18265i | −0.715623 | − | 0.192172i | ||||
\(130\) | 3.49868 | + | 2.01996i | 0.306855 | + | 0.177163i | ||||
\(131\) | 13.4418 | + | 7.76065i | 1.17442 | + | 0.678051i | 0.954717 | − | 0.297516i | \(-0.0961580\pi\) |
0.219702 | + | 0.975567i | \(0.429491\pi\) | |||||||
\(132\) | −3.31878 | − | 3.32243i | −0.288863 | − | 0.289180i | ||||
\(133\) | 3.11190 | + | 5.38997i | 0.269836 | + | 0.467369i | ||||
\(134\) | −7.08512 | + | 4.09060i | −0.612061 | + | 0.353374i | ||||
\(135\) | −1.35313 | + | 5.01687i | −0.116459 | + | 0.431784i | ||||
\(136\) | −0.642386 | − | 0.370882i | −0.0550842 | − | 0.0318029i | ||||
\(137\) | −9.07490 | − | 15.7182i | −0.775321 | − | 1.34290i | −0.934614 | − | 0.355664i | \(-0.884255\pi\) |
0.159293 | − | 0.987231i | \(-0.449079\pi\) | |||||||
\(138\) | 1.42139 | + | 5.31639i | 0.120997 | + | 0.452561i | ||||
\(139\) | − | 20.3716i | − | 1.72789i | −0.503583 | − | 0.863947i | \(-0.667985\pi\) | ||
0.503583 | − | 0.863947i | \(-0.332015\pi\) | |||||||
\(140\) | − | 2.64450i | − | 0.223501i | ||||||
\(141\) | −1.47254 | − | 5.50769i | −0.124010 | − | 0.463831i | ||||
\(142\) | 6.71183 | + | 11.6252i | 0.563244 | + | 0.975568i | ||||
\(143\) | −9.48584 | − | 5.47665i | −0.793246 | − | 0.457981i | ||||
\(144\) | 2.59972 | − | 1.49714i | 0.216644 | − | 0.124762i | ||||
\(145\) | 0.966745 | − | 0.558150i | 0.0802838 | − | 0.0463519i | ||||
\(146\) | 5.33483 | + | 9.24020i | 0.441514 | + | 0.764725i | ||||
\(147\) | −0.00807091 | − | 0.00807979i | −0.000665678 | − | 0.000666410i | ||||
\(148\) | −8.66260 | − | 5.00135i | −0.712061 | − | 0.411109i | ||||
\(149\) | −6.93481 | − | 4.00381i | −0.568122 | − | 0.328005i | 0.188277 | − | 0.982116i | \(-0.439710\pi\) |
−0.756399 | + | 0.654111i | \(0.773043\pi\) | |||||||
\(150\) | −1.67279 | − | 0.449207i | −0.136582 | − | 0.0366776i | ||||
\(151\) | 7.40096i | 0.602282i | 0.953580 | + | 0.301141i | \(0.0973674\pi\) | ||||
−0.953580 | + | 0.301141i | \(0.902633\pi\) | |||||||
\(152\) | −2.03818 | − | 1.17674i | −0.165318 | − | 0.0954463i | ||||
\(153\) | 0.00244541 | − | 2.22529i | 0.000197700 | − | 0.179904i | ||||
\(154\) | 7.16994i | 0.577771i | ||||||||
\(155\) | 1.67459 | − | 5.30997i | 0.134506 | − | 0.426507i | ||||
\(156\) | 4.95060 | − | 4.94516i | 0.396365 | − | 0.395930i | ||||
\(157\) | 2.41698 | 0.192896 | 0.0964482 | − | 0.995338i | \(-0.469252\pi\) | ||||
0.0964482 | + | 0.995338i | \(0.469252\pi\) | |||||||
\(158\) | 6.09057 | − | 10.5492i | 0.484540 | − | 0.839247i | ||||
\(159\) | −1.05793 | − | 1.05909i | −0.0838993 | − | 0.0839916i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 4.20110 | − | 7.27652i | 0.331093 | − | 0.573470i | ||||
\(162\) | 7.78432 | + | 4.51712i | 0.611594 | + | 0.354898i | ||||
\(163\) | −25.1648 | −1.97106 | −0.985532 | − | 0.169492i | \(-0.945787\pi\) | ||||
−0.985532 | + | 0.169492i | \(0.945787\pi\) | |||||||
\(164\) | −4.56104 | + | 2.63332i | −0.356158 | + | 0.205628i | ||||
\(165\) | 4.53536 | + | 1.21792i | 0.353077 | + | 0.0948147i | ||||
\(166\) | 4.24235 | − | 2.44932i | 0.329270 | − | 0.190104i | ||||
\(167\) | 11.2639 | − | 19.5096i | 0.871624 | − | 1.50970i | 0.0113086 | − | 0.999936i | \(-0.496400\pi\) |
0.860316 | − | 0.509762i | \(-0.170266\pi\) | |||||||
\(168\) | −4.42369 | − | 1.18793i | −0.341295 | − | 0.0916508i | ||||
\(169\) | 1.66051 | − | 2.87609i | 0.127731 | − | 0.221237i | ||||
\(170\) | 0.741764 | 0.0568907 | ||||||||
\(171\) | 0.00775884 | − | 7.06044i | 0.000593333 | − | 0.539926i | ||||
\(172\) | −4.20794 | − | 2.42945i | −0.320852 | − | 0.185244i | ||||
\(173\) | −7.33403 | + | 4.23431i | −0.557596 | + | 0.321928i | −0.752180 | − | 0.658958i | \(-0.770998\pi\) |
0.194584 | + | 0.980886i | \(0.437664\pi\) | |||||||
\(174\) | −0.499398 | − | 1.86788i | −0.0378592 | − | 0.141604i | ||||
\(175\) | 1.32225 | + | 2.29021i | 0.0999529 | + | 0.173123i | ||||
\(176\) | −1.35563 | − | 2.34802i | −0.102185 | − | 0.176989i | ||||
\(177\) | 0.130126 | + | 0.0349439i | 0.00978089 | + | 0.00262654i | ||||
\(178\) | − | 17.1663i | − | 1.28667i | ||||||
\(179\) | 8.32290 | − | 14.4157i | 0.622083 | − | 1.07748i | −0.367014 | − | 0.930215i | \(-0.619620\pi\) |
0.989097 | − | 0.147264i | \(-0.0470466\pi\) | |||||||
\(180\) | −1.50285 | + | 2.59643i | −0.112016 | + | 0.193526i | ||||
\(181\) | −2.86960 | + | 1.65676i | −0.213296 | + | 0.123146i | −0.602842 | − | 0.797861i | \(-0.705965\pi\) |
0.389547 | + | 0.921007i | \(0.372632\pi\) | |||||||
\(182\) | −10.6836 | −0.791922 | ||||||||
\(183\) | −3.67457 | − | 13.7439i | −0.271632 | − | 1.01598i | ||||
\(184\) | 3.17723i | 0.234228i | ||||||||
\(185\) | 10.0027 | 0.735414 | ||||||||
\(186\) | −8.13021 | − | 5.18650i | −0.596136 | − | 0.380292i | ||||
\(187\) | −2.01112 | −0.147067 | ||||||||
\(188\) | − | 3.29156i | − | 0.240061i | ||||||
\(189\) | −3.53461 | − | 13.2789i | −0.257105 | − | 0.965896i | ||||
\(190\) | 2.35348 | 0.170740 | ||||||||
\(191\) | 2.56932 | − | 1.48340i | 0.185909 | − | 0.107335i | −0.404157 | − | 0.914690i | \(-0.632435\pi\) |
0.590066 | + | 0.807355i | \(0.299102\pi\) | |||||||
\(192\) | 1.67328 | − | 0.447368i | 0.120758 | − | 0.0322860i | ||||
\(193\) | 6.42312 | − | 11.1252i | 0.462346 | − | 0.800807i | −0.536731 | − | 0.843753i | \(-0.680341\pi\) |
0.999077 | + | 0.0429465i | \(0.0136745\pi\) | |||||||
\(194\) | 12.4034i | 0.890515i | ||||||||
\(195\) | −1.81476 | + | 6.75794i | −0.129958 | + | 0.483946i | ||||
\(196\) | −0.00329675 | − | 0.00571013i | −0.000235482 | − | 0.000407867i | ||||
\(197\) | −6.44071 | − | 11.1556i | −0.458881 | − | 0.794806i | 0.540021 | − | 0.841652i | \(-0.318416\pi\) |
−0.998902 | + | 0.0468458i | \(0.985083\pi\) | |||||||
\(198\) | 4.07463 | − | 7.03959i | 0.289571 | − | 0.500282i | ||||
\(199\) | 8.97201 | − | 5.17999i | 0.636009 | − | 0.367200i | −0.147067 | − | 0.989127i | \(-0.546983\pi\) |
0.783075 | + | 0.621927i | \(0.213650\pi\) | |||||||
\(200\) | −0.866025 | − | 0.500000i | −0.0612372 | − | 0.0353553i | ||||
\(201\) | −10.0144 | − | 10.0254i | −0.706359 | − | 0.707136i | ||||
\(202\) | −0.291018 | −0.0204760 | ||||||||
\(203\) | −1.47603 | + | 2.55656i | −0.103597 | + | 0.179435i | ||||
\(204\) | 0.333205 | − | 1.24081i | 0.0233290 | − | 0.0868742i | ||||
\(205\) | 2.63332 | − | 4.56104i | 0.183919 | − | 0.318557i | ||||
\(206\) | −5.24333 | + | 3.02724i | −0.365320 | + | 0.210918i | ||||
\(207\) | −8.25991 | + | 4.75677i | −0.574104 | + | 0.330618i | ||||
\(208\) | 3.49868 | − | 2.01996i | 0.242590 | − | 0.140059i | ||||
\(209\) | −6.38091 | −0.441377 | ||||||||
\(210\) | 4.42499 | − | 1.18307i | 0.305354 | − | 0.0816394i | ||||
\(211\) | 2.42025 | − | 4.19199i | 0.166617 | − | 0.288588i | −0.770612 | − | 0.637305i | \(-0.780049\pi\) |
0.937228 | + | 0.348717i | \(0.113382\pi\) | |||||||
\(212\) | −0.432136 | − | 0.748481i | −0.0296792 | − | 0.0514059i | ||||
\(213\) | −16.4496 | + | 16.4315i | −1.12711 | + | 1.12587i | ||||
\(214\) | −2.79252 | + | 4.83678i | −0.190893 | + | 0.330636i | ||||
\(215\) | 4.85891 | 0.331375 | ||||||||
\(216\) | 3.66817 | + | 3.68029i | 0.249588 | + | 0.250412i | ||||
\(217\) | 3.18597 | + | 14.3752i | 0.216278 | + | 0.975849i | ||||
\(218\) | 7.74239i | 0.524381i | ||||||||
\(219\) | −13.0748 | + | 13.0604i | −0.883513 | + | 0.882543i | ||||
\(220\) | 2.34802 | + | 1.35563i | 0.158304 | + | 0.0913966i | ||||
\(221\) | − | 2.99667i | − | 0.201578i | ||||||
\(222\) | 4.49329 | − | 16.7324i | 0.301570 | − | 1.12300i | ||||
\(223\) | 7.55204 | + | 4.36017i | 0.505722 | + | 0.291979i | 0.731073 | − | 0.682299i | \(-0.239020\pi\) |
−0.225351 | + | 0.974278i | \(0.572353\pi\) | |||||||
\(224\) | −2.29021 | − | 1.32225i | −0.153021 | − | 0.0883467i | ||||
\(225\) | 0.00329675 | − | 3.00000i | 0.000219783 | − | 0.200000i | ||||
\(226\) | −3.44903 | − | 5.97390i | −0.229426 | − | 0.397378i | ||||
\(227\) | −11.0216 | + | 6.36331i | −0.731528 | + | 0.422348i | −0.818981 | − | 0.573821i | \(-0.805461\pi\) |
0.0874527 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(228\) | 1.05720 | − | 3.93687i | 0.0700148 | − | 0.260726i | ||||
\(229\) | −0.300311 | − | 0.173385i | −0.0198451 | − | 0.0114576i | 0.490045 | − | 0.871697i | \(-0.336980\pi\) |
−0.509890 | + | 0.860240i | \(0.670314\pi\) | |||||||
\(230\) | −1.58861 | − | 2.75156i | −0.104750 | − | 0.181433i | ||||
\(231\) | −11.9973 | + | 3.20761i | −0.789365 | + | 0.211045i | ||||
\(232\) | − | 1.11630i | − | 0.0732887i | ||||||
\(233\) | 3.05182i | 0.199931i | 0.994991 | + | 0.0999657i | \(0.0318733\pi\) | ||||
−0.994991 | + | 0.0999657i | \(0.968127\pi\) | |||||||
\(234\) | 10.4894 | + | 6.07142i | 0.685712 | + | 0.396901i | ||||
\(235\) | 1.64578 | + | 2.85057i | 0.107359 | + | 0.185951i | ||||
\(236\) | 0.0673682 | + | 0.0388951i | 0.00438530 | + | 0.00253185i | ||||
\(237\) | 20.3764 | + | 5.47185i | 1.32359 | + | 0.355435i | ||||
\(238\) | −1.69879 | + | 0.980799i | −0.110116 | + | 0.0635758i | ||||
\(239\) | 6.34019 | + | 10.9815i | 0.410113 | + | 0.710336i | 0.994902 | − | 0.100850i | \(-0.0321561\pi\) |
−0.584789 | + | 0.811185i | \(0.698823\pi\) | |||||||
\(240\) | −1.22542 | + | 1.22407i | −0.0791004 | + | 0.0790135i | ||||
\(241\) | −17.6091 | − | 10.1666i | −1.13430 | − | 0.654890i | −0.189289 | − | 0.981921i | \(-0.560618\pi\) |
−0.945013 | + | 0.327032i | \(0.893952\pi\) | |||||||
\(242\) | 3.16018 | + | 1.82453i | 0.203144 | + | 0.117285i | ||||
\(243\) | −4.07594 | + | 15.0462i | −0.261472 | + | 0.965211i | ||||
\(244\) | − | 8.21375i | − | 0.525832i | ||||||
\(245\) | 0.00571013 | + | 0.00329675i | 0.000364807 | + | 0.000210621i | ||||
\(246\) | −6.44674 | − | 6.45383i | −0.411029 | − | 0.411481i | ||||
\(247\) | − | 9.50790i | − | 0.604973i | ||||||
\(248\) | −3.76128 | − | 4.10522i | −0.238841 | − | 0.260682i | ||||
\(249\) | 5.99630 | + | 6.00289i | 0.380000 | + | 0.380418i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 8.05449 | − | 13.9508i | 0.508395 | − | 0.880565i | −0.491558 | − | 0.870845i | \(-0.663572\pi\) |
0.999953 | − | 0.00972062i | \(-0.00309422\pi\) | |||||||
\(252\) | 0.00871827 | − | 7.93351i | 0.000549199 | − | 0.499764i | ||||
\(253\) | 4.30715 | + | 7.46020i | 0.270788 | + | 0.469019i | ||||
\(254\) | −3.60467 | + | 6.24347i | −0.226177 | + | 0.391750i | ||||
\(255\) | 0.331842 | + | 1.24118i | 0.0207807 | + | 0.0777255i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.9053 | − | 10.3376i | 1.11690 | − | 0.644843i | 0.176293 | − | 0.984338i | \(-0.443589\pi\) |
0.940608 | + | 0.339494i | \(0.110256\pi\) | |||||||
\(258\) | 2.18265 | − | 8.12791i | 0.135886 | − | 0.506022i | ||||
\(259\) | −22.9083 | + | 13.2261i | −1.42345 | + | 0.821830i | ||||
\(260\) | −2.01996 | + | 3.49868i | −0.125273 | + | 0.216979i | ||||
\(261\) | 2.90207 | − | 1.67126i | 0.179634 | − | 0.103449i | ||||
\(262\) | −7.76065 | + | 13.4418i | −0.479455 | + | 0.830440i | ||||
\(263\) | 16.8210 | 1.03723 | 0.518613 | − | 0.855009i | \(-0.326449\pi\) | ||||
0.518613 | + | 0.855009i | \(0.326449\pi\) | |||||||
\(264\) | 3.32243 | − | 3.31878i | 0.204481 | − | 0.204257i | ||||
\(265\) | 0.748481 | + | 0.432136i | 0.0459788 | + | 0.0265459i | ||||
\(266\) | −5.38997 | + | 3.11190i | −0.330480 | + | 0.190803i | ||||
\(267\) | 28.7240 | − | 7.67965i | 1.75788 | − | 0.469987i | ||||
\(268\) | −4.09060 | − | 7.08512i | −0.249873 | − | 0.432793i | ||||
\(269\) | −3.65752 | − | 6.33501i | −0.223003 | − | 0.386252i | 0.732716 | − | 0.680535i | \(-0.238253\pi\) |
−0.955718 | + | 0.294283i | \(0.904919\pi\) | |||||||
\(270\) | −5.01687 | − | 1.35313i | −0.305317 | − | 0.0823492i | ||||
\(271\) | 4.32372i | 0.262647i | 0.991340 | + | 0.131324i | \(0.0419227\pi\) | ||||
−0.991340 | + | 0.131324i | \(0.958077\pi\) | |||||||
\(272\) | 0.370882 | − | 0.642386i | 0.0224880 | − | 0.0389504i | ||||
\(273\) | −4.77951 | − | 17.8767i | −0.289269 | − | 1.08194i | ||||
\(274\) | 15.7182 | − | 9.07490i | 0.949570 | − | 0.548235i | ||||
\(275\) | −2.71126 | −0.163495 | ||||||||
\(276\) | −5.31639 | + | 1.42139i | −0.320009 | + | 0.0855577i | ||||
\(277\) | 12.3568i | 0.742447i | 0.928544 | + | 0.371223i | \(0.121062\pi\) | ||||
−0.928544 | + | 0.371223i | \(0.878938\pi\) | |||||||
\(278\) | 20.3716 | 1.22181 | ||||||||
\(279\) | 5.04126 | − | 15.9244i | 0.301812 | − | 0.953367i | ||||
\(280\) | 2.64450 | 0.158039 | ||||||||
\(281\) | − | 2.26737i | − | 0.135260i | −0.997710 | − | 0.0676300i | \(-0.978456\pi\) | ||
0.997710 | − | 0.0676300i | \(-0.0215437\pi\) | |||||||
\(282\) | 5.50769 | − | 1.47254i | 0.327978 | − | 0.0876884i | ||||
\(283\) | 4.78042 | 0.284166 | 0.142083 | − | 0.989855i | \(-0.454620\pi\) | ||||
0.142083 | + | 0.989855i | \(0.454620\pi\) | |||||||
\(284\) | −11.6252 | + | 6.71183i | −0.689831 | + | 0.398274i | ||||
\(285\) | 1.05287 | + | 3.93803i | 0.0623669 | + | 0.233269i | ||||
\(286\) | 5.47665 | − | 9.48584i | 0.323841 | − | 0.560909i | ||||
\(287\) | 13.9277i | 0.822123i | ||||||||
\(288\) | 1.49714 | + | 2.59972i | 0.0882201 | + | 0.153190i | ||||
\(289\) | 8.22489 | + | 14.2459i | 0.483817 | + | 0.837996i | ||||
\(290\) | 0.558150 | + | 0.966745i | 0.0327757 | + | 0.0567692i | ||||
\(291\) | −20.7544 | + | 5.54891i | −1.21665 | + | 0.325283i | ||||
\(292\) | −9.24020 | + | 5.33483i | −0.540742 | + | 0.312198i | ||||
\(293\) | 16.4722 | + | 9.51024i | 0.962318 | + | 0.555594i | 0.896886 | − | 0.442263i | \(-0.145824\pi\) |
0.0654320 | + | 0.997857i | \(0.479157\pi\) | |||||||
\(294\) | 0.00807979 | − | 0.00807091i | 0.000471223 | − | 0.000470705i | ||||
\(295\) | −0.0777901 | −0.00452912 | ||||||||
\(296\) | 5.00135 | − | 8.66260i | 0.290698 | − | 0.503503i | ||||
\(297\) | 13.6021 | + | 3.66870i | 0.789271 | + | 0.212880i | ||||
\(298\) | 4.00381 | − | 6.93481i | 0.231935 | − | 0.401723i | ||||
\(299\) | −11.1161 | + | 6.41789i | −0.642861 | + | 0.371156i | ||||
\(300\) | 0.449207 | − | 1.67279i | 0.0259350 | − | 0.0965783i | ||||
\(301\) | −11.1279 | + | 6.42470i | −0.641402 | + | 0.370314i | ||||
\(302\) | −7.40096 | −0.425877 | ||||||||
\(303\) | −0.130192 | − | 0.486955i | −0.00747936 | − | 0.0279748i | ||||
\(304\) | 1.17674 | − | 2.03818i | 0.0674908 | − | 0.116897i | ||||
\(305\) | 4.10688 | + | 7.11332i | 0.235159 | + | 0.407308i | ||||
\(306\) | 2.22529 | + | 0.00244541i | 0.127211 | + | 0.000139795i | ||||
\(307\) | −14.0713 | + | 24.3721i | −0.803089 | + | 1.39099i | 0.114485 | + | 0.993425i | \(0.463478\pi\) |
−0.917574 | + | 0.397566i | \(0.869855\pi\) | |||||||
\(308\) | −7.16994 | −0.408546 | ||||||||
\(309\) | −7.41112 | − | 7.41927i | −0.421604 | − | 0.422067i | ||||
\(310\) | 5.30997 | + | 1.67459i | 0.301586 | + | 0.0951100i | ||||
\(311\) | 34.7697i | 1.97161i | 0.167895 | + | 0.985805i | \(0.446303\pi\) | ||||
−0.167895 | + | 0.985805i | \(0.553697\pi\) | |||||||
\(312\) | 4.94516 | + | 4.95060i | 0.279965 | + | 0.280272i | ||||
\(313\) | −13.4245 | − | 7.75065i | −0.758799 | − | 0.438093i | 0.0700654 | − | 0.997542i | \(-0.477679\pi\) |
−0.828864 | + | 0.559450i | \(0.811013\pi\) | |||||||
\(314\) | 2.41698i | 0.136398i | ||||||||
\(315\) | 3.95920 | + | 6.87498i | 0.223076 | + | 0.387361i | ||||
\(316\) | 10.5492 | + | 6.09057i | 0.593438 | + | 0.342621i | ||||
\(317\) | −4.29014 | − | 2.47691i | −0.240958 | − | 0.139117i | 0.374659 | − | 0.927163i | \(-0.377760\pi\) |
−0.615617 | + | 0.788045i | \(0.711093\pi\) | |||||||
\(318\) | 1.05909 | − | 1.05793i | 0.0593910 | − | 0.0593258i | ||||
\(319\) | −1.51329 | − | 2.62110i | −0.0847281 | − | 0.146753i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | −9.34257 | − | 2.50884i | −0.521452 | − | 0.140030i | ||||
\(322\) | 7.27652 | + | 4.20110i | 0.405504 | + | 0.234118i | ||||
\(323\) | −0.872864 | − | 1.51185i | −0.0485675 | − | 0.0841213i | ||||
\(324\) | −4.51712 | + | 7.78432i | −0.250951 | + | 0.432462i | ||||
\(325\) | − | 4.03993i | − | 0.224095i | ||||||
\(326\) | − | 25.1648i | − | 1.39375i | ||||||
\(327\) | −12.9552 | + | 3.46370i | −0.716423 | + | 0.191543i | ||||
\(328\) | −2.63332 | − | 4.56104i | −0.145401 | − | 0.251841i | ||||
\(329\) | −7.53835 | − | 4.35227i | −0.415603 | − | 0.239948i | ||||
\(330\) | −1.21792 | + | 4.53536i | −0.0670442 | + | 0.249663i | ||||
\(331\) | −1.63849 | + | 0.945983i | −0.0900596 | + | 0.0519959i | −0.544353 | − | 0.838856i | \(-0.683225\pi\) |
0.454294 | + | 0.890852i | \(0.349892\pi\) | |||||||
\(332\) | 2.44932 | + | 4.24235i | 0.134424 | + | 0.232829i | ||||
\(333\) | 30.0081 | + | 0.0329764i | 1.64443 | + | 0.00180710i | ||||
\(334\) | 19.5096 | + | 11.2639i | 1.06752 | + | 0.616331i | ||||
\(335\) | 7.08512 | + | 4.09060i | 0.387102 | + | 0.223493i | ||||
\(336\) | 1.18793 | − | 4.42369i | 0.0648069 | − | 0.241332i | ||||
\(337\) | − | 27.5245i | − | 1.49936i | −0.661802 | − | 0.749678i | \(-0.730208\pi\) | ||
0.661802 | − | 0.749678i | \(-0.269792\pi\) | |||||||
\(338\) | 2.87609 | + | 1.66051i | 0.156438 | + | 0.0903198i | ||||
\(339\) | 8.45302 | − | 8.44373i | 0.459105 | − | 0.458601i | ||||
\(340\) | 0.741764i | 0.0402278i | ||||||||
\(341\) | −14.3967 | − | 4.54024i | −0.779626 | − | 0.245868i | ||||
\(342\) | 7.06044 | + | 0.00775884i | 0.381785 | + | 0.000419550i | ||||
\(343\) | −18.5290 | −1.00047 | ||||||||
\(344\) | 2.42945 | − | 4.20794i | 0.130987 | − | 0.226877i | ||||
\(345\) | 3.89343 | − | 3.88916i | 0.209615 | − | 0.209385i | ||||
\(346\) | −4.23431 | − | 7.33403i | −0.227638 | − | 0.394280i | ||||
\(347\) | −12.1983 | + | 21.1281i | −0.654841 | + | 1.13422i | 0.327092 | + | 0.944992i | \(0.393931\pi\) |
−0.981934 | + | 0.189226i | \(0.939402\pi\) | |||||||
\(348\) | 1.86788 | − | 0.499398i | 0.100129 | − | 0.0267705i | ||||
\(349\) | −7.97476 | −0.426879 | −0.213440 | − | 0.976956i | \(-0.568467\pi\) | ||||
−0.213440 | + | 0.976956i | \(0.568467\pi\) | |||||||
\(350\) | −2.29021 | + | 1.32225i | −0.122417 | + | 0.0706774i | ||||
\(351\) | −5.46657 | + | 20.2678i | −0.291784 | + | 1.08182i | ||||
\(352\) | 2.34802 | − | 1.35563i | 0.125150 | − | 0.0722554i | ||||
\(353\) | −17.7462 | + | 30.7372i | −0.944533 | + | 1.63598i | −0.187848 | + | 0.982198i | \(0.560151\pi\) |
−0.756684 | + | 0.653781i | \(0.773182\pi\) | |||||||
\(354\) | −0.0349439 | + | 0.130126i | −0.00185725 | + | 0.00691613i | ||||
\(355\) | 6.71183 | − | 11.6252i | 0.356227 | − | 0.617003i | ||||
\(356\) | 17.1663 | 0.909811 | ||||||||
\(357\) | −2.40114 | − | 2.40378i | −0.127082 | − | 0.127221i | ||||
\(358\) | 14.4157 | + | 8.32290i | 0.761893 | + | 0.439879i | ||||
\(359\) | 8.61779 | − | 4.97548i | 0.454830 | − | 0.262596i | −0.255038 | − | 0.966931i | \(-0.582088\pi\) |
0.709868 | + | 0.704335i | \(0.248755\pi\) | |||||||
\(360\) | −2.59643 | − | 1.50285i | −0.136844 | − | 0.0792074i | ||||
\(361\) | 6.73056 | + | 11.6577i | 0.354240 | + | 0.613562i | ||||
\(362\) | −1.65676 | − | 2.86960i | −0.0870775 | − | 0.150823i | ||||
\(363\) | −1.63918 | + | 6.10410i | −0.0860348 | + | 0.320382i | ||||
\(364\) | − | 10.6836i | − | 0.559973i | ||||||
\(365\) | 5.33483 | − | 9.24020i | 0.279238 | − | 0.483654i | ||||
\(366\) | 13.7439 | − | 3.67457i | 0.718405 | − | 0.192073i | ||||
\(367\) | 4.15155 | − | 2.39690i | 0.216709 | − | 0.125117i | −0.387716 | − | 0.921779i | \(-0.626736\pi\) |
0.604426 | + | 0.796662i | \(0.293403\pi\) | |||||||
\(368\) | −3.17723 | −0.165624 | ||||||||
\(369\) | 7.91499 | − | 13.6744i | 0.412038 | − | 0.711863i | ||||
\(370\) | 10.0027i | 0.520016i | ||||||||
\(371\) | −2.28557 | −0.118661 | ||||||||
\(372\) | 5.18650 | − | 8.13021i | 0.268907 | − | 0.421532i | ||||
\(373\) | −23.1098 | −1.19658 | −0.598289 | − | 0.801280i | \(-0.704153\pi\) | ||||
−0.598289 | + | 0.801280i | \(0.704153\pi\) | |||||||
\(374\) | − | 2.01112i | − | 0.103992i | ||||||
\(375\) | 0.447368 | + | 1.67328i | 0.0231020 | + | 0.0864077i | ||||
\(376\) | 3.29156 | 0.169749 | ||||||||
\(377\) | 3.90558 | − | 2.25489i | 0.201148 | − | 0.116133i | ||||
\(378\) | 13.2789 | − | 3.53461i | 0.682992 | − | 0.181801i | ||||
\(379\) | −0.565702 | + | 0.979824i | −0.0290582 | + | 0.0503302i | −0.880189 | − | 0.474624i | \(-0.842584\pi\) |
0.851131 | + | 0.524954i | \(0.175917\pi\) | |||||||
\(380\) | 2.35348i | 0.120731i | ||||||||
\(381\) | −12.0597 | − | 3.23849i | −0.617837 | − | 0.165913i | ||||
\(382\) | 1.48340 | + | 2.56932i | 0.0758971 | + | 0.131458i | ||||
\(383\) | −1.85664 | − | 3.21579i | −0.0948697 | − | 0.164319i | 0.814685 | − | 0.579904i | \(-0.196910\pi\) |
−0.909554 | + | 0.415585i | \(0.863577\pi\) | |||||||
\(384\) | 0.447368 | + | 1.67328i | 0.0228297 | + | 0.0853891i | ||||
\(385\) | 6.20935 | − | 3.58497i | 0.316458 | − | 0.182707i | ||||
\(386\) | 11.1252 | + | 6.42312i | 0.566256 | + | 0.326928i | ||||
\(387\) | 14.5767 | + | 0.0160186i | 0.740976 | + | 0.000814271i | ||||
\(388\) | −12.4034 | −0.629689 | ||||||||
\(389\) | −4.87542 | + | 8.44448i | −0.247194 | + | 0.428152i | −0.962746 | − | 0.270407i | \(-0.912842\pi\) |
0.715552 | + | 0.698559i | \(0.246175\pi\) | |||||||
\(390\) | −6.75794 | − | 1.81476i | −0.342201 | − | 0.0918941i | ||||
\(391\) | −1.17838 | + | 2.04101i | −0.0595931 | + | 0.103218i | ||||
\(392\) | 0.00571013 | − | 0.00329675i | 0.000288405 | − | 0.000166511i | ||||
\(393\) | −25.9638 | − | 6.97228i | −1.30970 | − | 0.351705i | ||||
\(394\) | 11.1556 | − | 6.44071i | 0.562013 | − | 0.324478i | ||||
\(395\) | −12.1811 | −0.612900 | ||||||||
\(396\) | 7.03959 | + | 4.07463i | 0.353753 | + | 0.204758i | ||||
\(397\) | −5.53921 | + | 9.59420i | −0.278005 | + | 0.481519i | −0.970889 | − | 0.239530i | \(-0.923007\pi\) |
0.692884 | + | 0.721049i | \(0.256340\pi\) | |||||||
\(398\) | 5.17999 | + | 8.97201i | 0.259650 | + | 0.449726i | ||||
\(399\) | −7.61837 | − | 7.62675i | −0.381396 | − | 0.381815i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −0.963613 | −0.0481205 | −0.0240603 | − | 0.999711i | \(-0.507659\pi\) | ||||
−0.0240603 | + | 0.999711i | \(0.507659\pi\) | |||||||
\(402\) | 10.0254 | − | 10.0144i | 0.500021 | − | 0.499471i | ||||
\(403\) | 6.76520 | − | 21.4519i | 0.336999 | − | 1.06859i | ||||
\(404\) | − | 0.291018i | − | 0.0144787i | ||||||
\(405\) | 0.0197805 | − | 8.99998i | 0.000982900 | − | 0.447213i | ||||
\(406\) | −2.55656 | − | 1.47603i | −0.126880 | − | 0.0732542i | ||||
\(407\) | − | 27.1200i | − | 1.34429i | ||||||
\(408\) | 1.24081 | + | 0.333205i | 0.0614294 | + | 0.0164961i | ||||
\(409\) | −3.39020 | − | 1.95733i | −0.167635 | − | 0.0967838i | 0.413835 | − | 0.910352i | \(-0.364189\pi\) |
−0.581470 | + | 0.813568i | \(0.697522\pi\) | |||||||
\(410\) | 4.56104 | + | 2.63332i | 0.225254 | + | 0.130050i | ||||
\(411\) | 22.2167 | + | 22.2411i | 1.09587 | + | 1.09707i | ||||
\(412\) | −3.02724 | − | 5.24333i | −0.149141 | − | 0.258321i | ||||
\(413\) | 0.178156 | − | 0.102858i | 0.00876647 | − | 0.00506132i | ||||
\(414\) | −4.75677 | − | 8.25991i | −0.233782 | − | 0.405953i | ||||
\(415\) | −4.24235 | − | 2.44932i | −0.208249 | − | 0.120233i | ||||
\(416\) | 2.01996 | + | 3.49868i | 0.0990369 | + | 0.171537i | ||||
\(417\) | 9.11360 | + | 34.0873i | 0.446295 | + | 1.66926i | ||||
\(418\) | − | 6.38091i | − | 0.312100i | ||||||
\(419\) | 6.12859i | 0.299401i | 0.988731 | + | 0.149701i | \(0.0478310\pi\) | ||||
−0.988731 | + | 0.149701i | \(0.952169\pi\) | |||||||
\(420\) | 1.18307 | + | 4.42499i | 0.0577278 | + | 0.215918i | ||||
\(421\) | −6.31725 | − | 10.9418i | −0.307884 | − | 0.533271i | 0.670015 | − | 0.742347i | \(-0.266288\pi\) |
−0.977899 | + | 0.209077i | \(0.932954\pi\) | |||||||
\(422\) | 4.19199 | + | 2.42025i | 0.204063 | + | 0.117816i | ||||
\(423\) | 4.92794 | + | 8.55714i | 0.239604 | + | 0.416062i | ||||
\(424\) | 0.748481 | − | 0.432136i | 0.0363495 | − | 0.0209864i | ||||
\(425\) | −0.370882 | − | 0.642386i | −0.0179904 | − | 0.0311603i | ||||
\(426\) | −16.4315 | − | 16.4496i | −0.796110 | − | 0.796985i | ||||
\(427\) | −18.8112 | − | 10.8607i | −0.910338 | − | 0.525584i | ||||
\(428\) | −4.83678 | − | 2.79252i | −0.233795 | − | 0.134982i | ||||
\(429\) | 18.3225 | + | 4.92030i | 0.884620 | + | 0.237554i | ||||
\(430\) | 4.85891i | 0.234317i | ||||||||
\(431\) | −24.8975 | − | 14.3746i | −1.19927 | − | 0.692399i | −0.238878 | − | 0.971050i | \(-0.576780\pi\) |
−0.960393 | + | 0.278650i | \(0.910113\pi\) | |||||||
\(432\) | −3.68029 | + | 3.66817i | −0.177068 | + | 0.176485i | ||||
\(433\) | 7.12270i | 0.342295i | 0.985245 | + | 0.171148i | \(0.0547475\pi\) | ||||
−0.985245 | + | 0.171148i | \(0.945252\pi\) | |||||||
\(434\) | −14.3752 | + | 3.18597i | −0.690030 | + | 0.152931i | ||||
\(435\) | −1.36793 | + | 1.36643i | −0.0655874 | + | 0.0655154i | ||||
\(436\) | −7.74239 | −0.370793 | ||||||||
\(437\) | −3.73878 | + | 6.47575i | −0.178850 | + | 0.309777i | ||||
\(438\) | −13.0604 | − | 13.0748i | −0.624052 | − | 0.624738i | ||||
\(439\) | 16.5785 | + | 28.7148i | 0.791248 | + | 1.37048i | 0.925194 | + | 0.379494i | \(0.123902\pi\) |
−0.133946 | + | 0.990989i | \(0.542765\pi\) | |||||||
\(440\) | −1.35563 | + | 2.34802i | −0.0646272 | + | 0.111938i | ||||
\(441\) | 0.0171195 | + | 0.00990906i | 0.000815215 | + | 0.000471860i | ||||
\(442\) | 2.99667 | 0.142537 | ||||||||
\(443\) | −23.1960 | + | 13.3922i | −1.10207 | + | 0.636283i | −0.936765 | − | 0.349959i | \(-0.886196\pi\) |
−0.165310 | + | 0.986242i | \(0.552862\pi\) | |||||||
\(444\) | 16.7324 | + | 4.49329i | 0.794084 | + | 0.213242i | ||||
\(445\) | −14.8664 | + | 8.58314i | −0.704737 | + | 0.406880i | ||||
\(446\) | −4.36017 | + | 7.55204i | −0.206460 | + | 0.357599i | ||||
\(447\) | 13.3951 | + | 3.59708i | 0.633564 | + | 0.170136i | ||||
\(448\) | 1.32225 | − | 2.29021i | 0.0624706 | − | 0.108202i | ||||
\(449\) | 24.5175 | 1.15705 | 0.578527 | − | 0.815663i | \(-0.303628\pi\) | ||||
0.578527 | + | 0.815663i | \(0.303628\pi\) | |||||||
\(450\) | 3.00000 | + | 0.00329675i | 0.141421 | + | 0.000155410i | ||||
\(451\) | −12.3662 | − | 7.13962i | −0.582301 | − | 0.336191i | ||||
\(452\) | 5.97390 | − | 3.44903i | 0.280989 | − | 0.162229i | ||||
\(453\) | −3.31096 | − | 12.3839i | −0.155562 | − | 0.581845i | ||||
\(454\) | −6.36331 | − | 11.0216i | −0.298645 | − | 0.517269i | ||||
\(455\) | 5.34180 | + | 9.25228i | 0.250428 | + | 0.433753i | ||||
\(456\) | 3.93687 | + | 1.05720i | 0.184361 | + | 0.0495080i | ||||
\(457\) | − | 8.46145i | − | 0.395810i | −0.980221 | − | 0.197905i | \(-0.936586\pi\) | ||
0.980221 | − | 0.197905i | \(-0.0634137\pi\) | |||||||
\(458\) | 0.173385 | − | 0.300311i | 0.00810174 | − | 0.0140326i | ||||
\(459\) | 0.991433 | + | 3.72462i | 0.0462761 | + | 0.173851i | ||||
\(460\) | 2.75156 | − | 1.58861i | 0.128292 | − | 0.0740695i | ||||
\(461\) | −10.2584 | −0.477779 | −0.238890 | − | 0.971047i | \(-0.576783\pi\) | ||||
−0.238890 | + | 0.971047i | \(0.576783\pi\) | |||||||
\(462\) | −3.20761 | − | 11.9973i | −0.149231 | − | 0.558166i | ||||
\(463\) | − | 16.4580i | − | 0.764870i | −0.923982 | − | 0.382435i | \(-0.875086\pi\) | ||
0.923982 | − | 0.382435i | \(-0.124914\pi\) | |||||||
\(464\) | 1.11630 | 0.0518230 | ||||||||
\(465\) | −0.426535 | + | 9.63421i | −0.0197801 | + | 0.446776i | ||||
\(466\) | −3.05182 | −0.141373 | ||||||||
\(467\) | 21.7403i | 1.00602i | 0.864281 | + | 0.503010i | \(0.167774\pi\) | ||||
−0.864281 | + | 0.503010i | \(0.832226\pi\) | |||||||
\(468\) | −6.07142 | + | 10.4894i | −0.280652 | + | 0.484872i | ||||
\(469\) | −21.6352 | −0.999021 | ||||||||
\(470\) | −2.85057 | + | 1.64578i | −0.131487 | + | 0.0759141i | ||||
\(471\) | −4.04429 | + | 1.08128i | −0.186351 | + | 0.0498229i | ||||
\(472\) | −0.0388951 | + | 0.0673682i | −0.00179029 | + | 0.00310087i | ||||
\(473\) | − | 13.1738i | − | 0.605730i | ||||||
\(474\) | −5.47185 | + | 20.3764i | −0.251331 | + | 0.935921i | ||||
\(475\) | −1.17674 | − | 2.03818i | −0.0539926 | − | 0.0935179i | ||||
\(476\) | −0.980799 | − | 1.69879i | −0.0449548 | − | 0.0778641i | ||||
\(477\) | 2.24402 | + | 1.29887i | 0.102747 | + | 0.0594714i | ||||
\(478\) | −10.9815 | + | 6.34019i | −0.502283 | + | 0.289993i | ||||
\(479\) | −16.4488 | − | 9.49670i | −0.751563 | − | 0.433915i | 0.0746954 | − | 0.997206i | \(-0.476202\pi\) |
−0.826258 | + | 0.563291i | \(0.809535\pi\) | |||||||
\(480\) | −1.22407 | − | 1.22542i | −0.0558710 | − | 0.0559324i | ||||
\(481\) | 40.4102 | 1.84255 | ||||||||
\(482\) | 10.1666 | − | 17.6091i | 0.463077 | − | 0.802073i | ||||
\(483\) | −3.77432 | + | 14.0551i | −0.171738 | + | 0.639528i | ||||
\(484\) | −1.82453 | + | 3.16018i | −0.0829332 | + | 0.143645i | ||||
\(485\) | 10.7417 | − | 6.20172i | 0.487755 | − | 0.281606i | ||||
\(486\) | −15.0462 | − | 4.07594i | −0.682507 | − | 0.184888i | ||||
\(487\) | 21.3554 | − | 12.3295i | 0.967704 | − | 0.558704i | 0.0691683 | − | 0.997605i | \(-0.477965\pi\) |
0.898535 | + | 0.438901i | \(0.144632\pi\) | |||||||
\(488\) | 8.21375 | 0.371819 | ||||||||
\(489\) | 42.1078 | − | 11.2580i | 1.90418 | − | 0.509102i | ||||
\(490\) | −0.00329675 | + | 0.00571013i | −0.000148932 | + | 0.000257958i | ||||
\(491\) | 13.0832 | + | 22.6608i | 0.590438 | + | 1.02267i | 0.994173 | + | 0.107793i | \(0.0343784\pi\) |
−0.403735 | + | 0.914876i | \(0.632288\pi\) | |||||||
\(492\) | 6.45383 | − | 6.44674i | 0.290961 | − | 0.290642i | ||||
\(493\) | 0.414016 | − | 0.717096i | 0.0186463 | − | 0.0322964i | ||||
\(494\) | 9.50790 | 0.427781 | ||||||||
\(495\) | −8.13378 | − | 0.00893835i | −0.365586 | − | 0.000401749i | ||||
\(496\) | 4.10522 | − | 3.76128i | 0.184330 | − | 0.168886i | ||||
\(497\) | 35.4989i | 1.59235i | ||||||||
\(498\) | −6.00289 | + | 5.99630i | −0.268996 | + | 0.268700i | ||||
\(499\) | −25.4093 | − | 14.6701i | −1.13748 | − | 0.656722i | −0.191672 | − | 0.981459i | \(-0.561391\pi\) |
−0.945804 | + | 0.324737i | \(0.894724\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | −10.1196 | + | 37.6841i | −0.452111 | + | 1.68360i | ||||
\(502\) | 13.9508 | + | 8.05449i | 0.622654 | + | 0.359489i | ||||
\(503\) | −6.14219 | − | 3.54620i | −0.273867 | − | 0.158117i | 0.356777 | − | 0.934190i | \(-0.383876\pi\) |
−0.630644 | + | 0.776073i | \(0.717209\pi\) | |||||||
\(504\) | 7.93351 | + | 0.00871827i | 0.353387 | + | 0.000388342i | ||||
\(505\) | 0.145509 | + | 0.252029i | 0.00647508 | + | 0.0112152i | ||||
\(506\) | −7.46020 | + | 4.30715i | −0.331646 | + | 0.191476i | ||||
\(507\) | −1.49182 | + | 5.55535i | −0.0662543 | + | 0.246722i | ||||
\(508\) | −6.24347 | − | 3.60467i | −0.277009 | − | 0.159931i | ||||
\(509\) | 11.2332 | + | 19.4565i | 0.497903 | + | 0.862393i | 0.999997 | − | 0.00241974i | \(-0.000770229\pi\) |
−0.502094 | + | 0.864813i | \(0.667437\pi\) | |||||||
\(510\) | −1.24118 | + | 0.331842i | −0.0549603 | + | 0.0146942i | ||||
\(511\) | 28.2160i | 1.24820i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.14564 | + | 11.8176i | 0.138883 | + | 0.521758i | ||||
\(514\) | 10.3376 | + | 17.9053i | 0.455973 | + | 0.789769i | ||||
\(515\) | 5.24333 | + | 3.02724i | 0.231049 | + | 0.133396i | ||||
\(516\) | 8.12791 | + | 2.18265i | 0.357811 | + | 0.0960860i | ||||
\(517\) | 7.72865 | − | 4.46214i | 0.339905 | − | 0.196245i | ||||
\(518\) | −13.2261 | − | 22.9083i | −0.581122 | − | 1.00653i | ||||
\(519\) | 10.3776 | − | 10.3662i | 0.455525 | − | 0.455025i | ||||
\(520\) | −3.49868 | − | 2.01996i | −0.153427 | − | 0.0885813i | ||||
\(521\) | 24.2738 | + | 14.0145i | 1.06346 | + | 0.613986i | 0.926386 | − | 0.376575i | \(-0.122898\pi\) |
0.137069 | + | 0.990561i | \(0.456232\pi\) | |||||||
\(522\) | 1.67126 | + | 2.90207i | 0.0731492 | + | 0.127020i | ||||
\(523\) | 22.8974i | 1.00123i | 0.865669 | + | 0.500617i | \(0.166893\pi\) | ||||
−0.865669 | + | 0.500617i | \(0.833107\pi\) | |||||||
\(524\) | −13.4418 | − | 7.76065i | −0.587210 | − | 0.339026i | ||||
\(525\) | −3.23706 | − | 3.24062i | −0.141277 | − | 0.141432i | ||||
\(526\) | 16.8210i | 0.733429i | ||||||||
\(527\) | −0.893641 | − | 4.03212i | −0.0389276 | − | 0.175642i | ||||
\(528\) | 3.31878 | + | 3.32243i | 0.144431 | + | 0.144590i | ||||
\(529\) | −12.9052 | −0.561097 | ||||||||
\(530\) | −0.432136 | + | 0.748481i | −0.0187708 | + | 0.0325119i | ||||
\(531\) | −0.233370 | 0.000256455i | −0.0101274 | 1.11292e-5i | ||||||
\(532\) | −3.11190 | − | 5.38997i | −0.134918 | − | 0.233685i | ||||
\(533\) | 10.6384 | − | 18.4263i | 0.460801 | − | 0.798131i | ||||
\(534\) | 7.67965 | + | 28.7240i | 0.332331 | + | 1.24301i | ||||
\(535\) | 5.58504 | 0.241462 | ||||||||
\(536\) | 7.08512 | − | 4.09060i | 0.306031 | − | 0.176687i | ||||
\(537\) | −7.47741 | + | 27.8449i | −0.322674 | + | 1.20159i | ||||
\(538\) | 6.33501 | − | 3.65752i | 0.273122 | − | 0.157687i | ||||
\(539\) | 0.00893835 | − | 0.0154817i | 0.000385002 | − | 0.000666843i | ||||
\(540\) | 1.35313 | − | 5.01687i | 0.0582296 | − | 0.215892i | ||||
\(541\) | −6.55194 | + | 11.3483i | −0.281690 | + | 0.487901i | −0.971801 | − | 0.235802i | \(-0.924228\pi\) |
0.690111 | + | 0.723703i | \(0.257562\pi\) | |||||||
\(542\) | −4.32372 | −0.185720 | ||||||||
\(543\) | 4.06045 | − | 4.05599i | 0.174251 | − | 0.174059i | ||||
\(544\) | 0.642386 | + | 0.370882i | 0.0275421 | + | 0.0159014i | ||||
\(545\) | 6.70511 | − | 3.87120i | 0.287215 | − | 0.165824i | ||||
\(546\) | 17.8767 | − | 4.77951i | 0.765050 | − | 0.204544i | ||||
\(547\) | −23.1238 | − | 40.0517i | −0.988704 | − | 1.71249i | −0.624153 | − | 0.781302i | \(-0.714556\pi\) |
−0.364552 | − | 0.931183i | \(-0.618778\pi\) | |||||||
\(548\) | 9.07490 | + | 15.7182i | 0.387661 | + | 0.671448i | ||||
\(549\) | 12.2972 | + | 21.3535i | 0.524831 | + | 0.911345i | ||||
\(550\) | − | 2.71126i | − | 0.115609i | ||||||
\(551\) | 1.31360 | − | 2.27522i | 0.0559611 | − | 0.0969275i | ||||
\(552\) | −1.42139 | − | 5.31639i | −0.0604984 | − | 0.226281i | ||||
\(553\) | 27.8974 | − | 16.1065i | 1.18632 | − | 0.684920i | ||||
\(554\) | −12.3568 | −0.524989 | ||||||||
\(555\) | −16.7373 | + | 4.47490i | −0.710460 | + | 0.189949i | ||||
\(556\) | 20.3716i | 0.863947i | ||||||||
\(557\) | −36.3726 | −1.54116 | −0.770579 | − | 0.637345i | \(-0.780033\pi\) | ||||
−0.770579 | + | 0.637345i | \(0.780033\pi\) | |||||||
\(558\) | 15.9244 | + | 5.04126i | 0.674133 | + | 0.213413i | ||||
\(559\) | 19.6296 | 0.830245 | ||||||||
\(560\) | 2.64450i | 0.111751i | ||||||||
\(561\) | 3.36516 | − | 0.899710i | 0.142077 | − | 0.0379858i | ||||
\(562\) | 2.26737 | 0.0956432 | ||||||||
\(563\) | −19.8508 | + | 11.4609i | −0.836613 | + | 0.483019i | −0.856112 | − | 0.516791i | \(-0.827126\pi\) |
0.0194982 | + | 0.999810i | \(0.493793\pi\) | |||||||
\(564\) | 1.47254 | + | 5.50769i | 0.0620051 | + | 0.231916i | ||||
\(565\) | −3.44903 | + | 5.97390i | −0.145102 | + | 0.251324i | ||||
\(566\) | 4.78042i | 0.200936i | ||||||||
\(567\) | 11.8549 | + | 20.6380i | 0.497861 | + | 0.866714i | ||||
\(568\) | −6.71183 | − | 11.6252i | −0.281622 | − | 0.487784i | ||||
\(569\) | 6.04836 | + | 10.4761i | 0.253561 | + | 0.439180i | 0.964504 | − | 0.264070i | \(-0.0850649\pi\) |
−0.710943 | + | 0.703250i | \(0.751732\pi\) | |||||||
\(570\) | −3.93803 | + | 1.05287i | −0.164946 | + | 0.0441000i | ||||
\(571\) | 32.0896 | − | 18.5270i | 1.34291 | − | 0.775329i | 0.355676 | − | 0.934609i | \(-0.384251\pi\) |
0.987233 | + | 0.159281i | \(0.0509175\pi\) | |||||||
\(572\) | 9.48584 | + | 5.47665i | 0.396623 | + | 0.228990i | ||||
\(573\) | −3.63556 | + | 3.63157i | −0.151878 | + | 0.151711i | ||||
\(574\) | −13.9277 | −0.581329 | ||||||||
\(575\) | −1.58861 | + | 2.75156i | −0.0662498 | + | 0.114748i | ||||
\(576\) | −2.59972 | + | 1.49714i | −0.108322 | + | 0.0623810i | ||||
\(577\) | 10.8409 | − | 18.7769i | 0.451311 | − | 0.781693i | −0.547157 | − | 0.837030i | \(-0.684290\pi\) |
0.998468 | + | 0.0553370i | \(0.0176233\pi\) | |||||||
\(578\) | −14.2459 | + | 8.22489i | −0.592553 | + | 0.342110i | ||||
\(579\) | −5.77062 | + | 21.4890i | −0.239819 | + | 0.893052i | ||||
\(580\) | −0.966745 | + | 0.558150i | −0.0401419 | + | 0.0231759i | ||||
\(581\) | 12.9545 | 0.537443 | ||||||||
\(582\) | −5.54891 | − | 20.7544i | −0.230010 | − | 0.860298i | ||||
\(583\) | 1.17163 | − | 2.02933i | 0.0485241 | − | 0.0840462i | ||||
\(584\) | −5.33483 | − | 9.24020i | −0.220757 | − | 0.382362i | ||||
\(585\) | 0.0133186 | − | 12.1198i | 0.000550657 | − | 0.501091i | ||||
\(586\) | −9.51024 | + | 16.4722i | −0.392864 | + | 0.680461i | ||||
\(587\) | 34.2190 | 1.41237 | 0.706185 | − | 0.708027i | \(-0.250415\pi\) | ||||
0.706185 | + | 0.708027i | \(0.250415\pi\) | |||||||
\(588\) | 0.00807091 | + | 0.00807979i | 0.000332839 | + | 0.000333205i | ||||
\(589\) | −2.83536 | − | 12.7932i | −0.116829 | − | 0.527135i | ||||
\(590\) | − | 0.0777901i | − | 0.00320257i | ||||||
\(591\) | 15.7678 | + | 15.7851i | 0.648600 | + | 0.649313i | ||||
\(592\) | 8.66260 | + | 5.00135i | 0.356031 | + | 0.205554i | ||||
\(593\) | 22.8931i | 0.940105i | 0.882638 | + | 0.470053i | \(0.155765\pi\) | ||||
−0.882638 | + | 0.470053i | \(0.844235\pi\) | |||||||
\(594\) | −3.66870 | + | 13.6021i | −0.150529 | + | 0.558099i | ||||
\(595\) | 1.69879 | + | 0.980799i | 0.0696437 | + | 0.0402088i | ||||
\(596\) | 6.93481 | + | 4.00381i | 0.284061 | + | 0.164003i | ||||
\(597\) | −12.6953 | + | 12.6814i | −0.519584 | + | 0.519014i | ||||
\(598\) | −6.41789 | − | 11.1161i | −0.262447 | − | 0.454571i | ||||
\(599\) | 34.1667 | − | 19.7261i | 1.39601 | − | 0.805988i | 0.402041 | − | 0.915622i | \(-0.368301\pi\) |
0.993972 | + | 0.109634i | \(0.0349677\pi\) | |||||||
\(600\) | 1.67279 | + | 0.449207i | 0.0682912 | + | 0.0183388i | ||||
\(601\) | 28.0179 | + | 16.1761i | 1.14287 | + | 0.659838i | 0.947140 | − | 0.320820i | \(-0.103958\pi\) |
0.195732 | + | 0.980657i | \(0.437292\pi\) | |||||||
\(602\) | −6.42470 | − | 11.1279i | −0.261851 | − | 0.453540i | ||||
\(603\) | 21.2419 | + | 12.2951i | 0.865036 | + | 0.500697i | ||||
\(604\) | − | 7.40096i | − | 0.301141i | ||||||
\(605\) | − | 3.64906i | − | 0.148355i | ||||||
\(606\) | 0.486955 | − | 0.130192i | 0.0197812 | − | 0.00528871i | ||||
\(607\) | −7.33156 | − | 12.6986i | −0.297579 | − | 0.515422i | 0.678002 | − | 0.735060i | \(-0.262846\pi\) |
−0.975582 | + | 0.219638i | \(0.929513\pi\) | |||||||
\(608\) | 2.03818 | + | 1.17674i | 0.0826590 | + | 0.0477232i | ||||
\(609\) | 1.32609 | − | 4.93817i | 0.0537358 | − | 0.200105i | ||||
\(610\) | −7.11332 | + | 4.10688i | −0.288010 | + | 0.166283i | ||||
\(611\) | 6.64883 | + | 11.5161i | 0.268983 | + | 0.465892i | ||||
\(612\) | −0.00244541 | + | 2.22529i | −9.88498e−5 | + | 0.0899520i | ||||
\(613\) | −9.31317 | − | 5.37696i | −0.376155 | − | 0.217173i | 0.299989 | − | 0.953943i | \(-0.403017\pi\) |
−0.676144 | + | 0.736769i | \(0.736350\pi\) | |||||||
\(614\) | −24.3721 | − | 14.0713i | −0.983579 | − | 0.567870i | ||||
\(615\) | −2.36581 | + | 8.80996i | −0.0953987 | + | 0.355252i | ||||
\(616\) | − | 7.16994i | − | 0.288885i | ||||||
\(617\) | −38.3757 | − | 22.1562i | −1.54495 | − | 0.891975i | −0.998515 | − | 0.0544716i | \(-0.982653\pi\) |
−0.546431 | − | 0.837504i | \(-0.684014\pi\) | |||||||
\(618\) | 7.41927 | − | 7.41112i | 0.298447 | − | 0.298119i | ||||
\(619\) | − | 31.8706i | − | 1.28099i | −0.767963 | − | 0.640495i | \(-0.778729\pi\) | ||
0.767963 | − | 0.640495i | \(-0.221271\pi\) | |||||||
\(620\) | −1.67459 | + | 5.30997i | −0.0672530 | + | 0.213253i | ||||
\(621\) | 11.6931 | − | 11.6546i | 0.469228 | − | 0.467684i | ||||
\(622\) | −34.7697 | −1.39414 | ||||||||
\(623\) | 22.6982 | − | 39.3144i | 0.909383 | − | 1.57510i | ||||
\(624\) | −4.95060 | + | 4.94516i | −0.198183 | + | 0.197965i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 7.75065 | − | 13.4245i | 0.309778 | − | 0.536552i | ||||
\(627\) | 10.6770 | − | 2.85462i | 0.426400 | − | 0.114002i | ||||
\(628\) | −2.41698 | −0.0964482 | ||||||||
\(629\) | 6.42560 | − | 3.70982i | 0.256206 | − | 0.147920i | ||||
\(630\) | −6.87498 | + | 3.95920i | −0.273906 | + | 0.157738i | ||||
\(631\) | −30.4987 | + | 17.6084i | −1.21413 | + | 0.700980i | −0.963657 | − | 0.267143i | \(-0.913920\pi\) |
−0.250476 | + | 0.968123i | \(0.580587\pi\) | |||||||
\(632\) | −6.09057 | + | 10.5492i | −0.242270 | + | 0.419624i | ||||
\(633\) | −2.17438 | + | 8.09711i | −0.0864240 | + | 0.321831i | ||||
\(634\) | 2.47691 | − | 4.29014i | 0.0983708 | − | 0.170383i | ||||
\(635\) | 7.20934 | 0.286094 | ||||||||
\(636\) | 1.05793 | + | 1.05909i | 0.0419497 | + | 0.0419958i | ||||
\(637\) | 0.0230685 | + | 0.0133186i | 0.000914009 | + | 0.000527703i | ||||
\(638\) | 2.62110 | − | 1.51329i | 0.103770 | − | 0.0599118i | ||||
\(639\) | 20.1738 | − | 34.8536i | 0.798064 | − | 1.37879i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 2.24960 | + | 3.89643i | 0.0888540 | + | 0.153900i | 0.907027 | − | 0.421073i | \(-0.138346\pi\) |
−0.818173 | + | 0.574972i | \(0.805013\pi\) | |||||||
\(642\) | 2.50884 | − | 9.34257i | 0.0990159 | − | 0.368722i | ||||
\(643\) | − | 7.11918i | − | 0.280753i | −0.990098 | − | 0.140376i | \(-0.955169\pi\) | ||
0.990098 | − | 0.140376i | \(-0.0448313\pi\) | |||||||
\(644\) | −4.20110 | + | 7.27652i | −0.165546 | + | 0.286735i | ||||
\(645\) | −8.13030 | + | 2.17372i | −0.320130 | + | 0.0855902i | ||||
\(646\) | 1.51185 | − | 0.872864i | 0.0594827 | − | 0.0343424i | ||||
\(647\) | −38.1767 | −1.50088 | −0.750441 | − | 0.660937i | \(-0.770159\pi\) | ||||
−0.750441 | + | 0.660937i | \(0.770159\pi\) | |||||||
\(648\) | −7.78432 | − | 4.51712i | −0.305797 | − | 0.177449i | ||||
\(649\) | 0.210909i | 0.00827892i | ||||||||
\(650\) | 4.03993 | 0.158459 | ||||||||
\(651\) | −11.7620 | − | 22.6283i | −0.460989 | − | 0.886875i | ||||
\(652\) | 25.1648 | 0.985532 | ||||||||
\(653\) | − | 31.6623i | − | 1.23904i | −0.784981 | − | 0.619520i | \(-0.787327\pi\) | ||
0.784981 | − | 0.619520i | \(-0.212673\pi\) | |||||||
\(654\) | −3.46370 | − | 12.9552i | −0.135441 | − | 0.506588i | ||||
\(655\) | 15.5213 | 0.606468 | ||||||||
\(656\) | 4.56104 | − | 2.63332i | 0.178079 | − | 0.102814i | ||||
\(657\) | 16.0350 | − | 27.7030i | 0.625583 | − | 1.08080i | ||||
\(658\) | 4.35227 | − | 7.53835i | 0.169669 | − | 0.293876i | ||||
\(659\) | − | 23.6853i | − | 0.922648i | −0.887232 | − | 0.461324i | \(-0.847375\pi\) | ||
0.887232 | − | 0.461324i | \(-0.152625\pi\) | |||||||
\(660\) | −4.53536 | − | 1.21792i | −0.176539 | − | 0.0474074i | ||||
\(661\) | 4.12220 | + | 7.13985i | 0.160335 | + | 0.277708i | 0.934989 | − | 0.354677i | \(-0.115409\pi\) |
−0.774654 | + | 0.632385i | \(0.782076\pi\) | |||||||
\(662\) | −0.945983 | − | 1.63849i | −0.0367667 | − | 0.0636818i | ||||
\(663\) | 1.34062 | + | 5.01427i | 0.0520652 | + | 0.194738i | ||||
\(664\) | −4.24235 | + | 2.44932i | −0.164635 | + | 0.0950522i | ||||
\(665\) | 5.38997 | + | 3.11190i | 0.209014 | + | 0.120674i | ||||
\(666\) | −0.0329764 | + | 30.0081i | −0.00127781 | + | 1.16279i | ||||
\(667\) | −3.54674 | −0.137330 | ||||||||
\(668\) | −11.2639 | + | 19.5096i | −0.435812 | + | 0.754849i | ||||
\(669\) | −14.5873 | − | 3.91724i | −0.563976 | − | 0.151449i | ||||
\(670\) | −4.09060 | + | 7.08512i | −0.158034 | + | 0.273722i | ||||
\(671\) | 19.2861 | − | 11.1348i | 0.744531 | − | 0.429855i | ||||
\(672\) | 4.42369 | + | 1.18793i | 0.170648 | + | 0.0458254i | ||||
\(673\) | 9.26140 | − | 5.34707i | 0.357001 | − | 0.206114i | −0.310764 | − | 0.950487i | \(-0.600585\pi\) |
0.667764 | + | 0.744373i | \(0.267251\pi\) | |||||||
\(674\) | 27.5245 | 1.06021 | ||||||||
\(675\) | 1.33659 | + | 5.02131i | 0.0514453 | + | 0.193270i | ||||
\(676\) | −1.66051 | + | 2.87609i | −0.0638657 | + | 0.110619i | ||||
\(677\) | −7.89992 | − | 13.6831i | −0.303619 | − | 0.525883i | 0.673334 | − | 0.739338i | \(-0.264862\pi\) |
−0.976953 | + | 0.213455i | \(0.931528\pi\) | |||||||
\(678\) | 8.44373 | + | 8.45302i | 0.324280 | + | 0.324636i | ||||
\(679\) | −16.4005 | + | 28.4065i | −0.629393 | + | 1.09014i | ||||
\(680\) | −0.741764 | −0.0284453 | ||||||||
\(681\) | 15.5954 | − | 15.5783i | 0.597618 | − | 0.596962i | ||||
\(682\) | 4.54024 | − | 14.3967i | 0.173855 | − | 0.551279i | ||||
\(683\) | 34.5090i | 1.32045i | 0.751068 | + | 0.660224i | \(0.229539\pi\) | ||||
−0.751068 | + | 0.660224i | \(0.770461\pi\) | |||||||
\(684\) | −0.00775884 | + | 7.06044i | −0.000296667 | + | 0.269963i | ||||
\(685\) | −15.7182 | − | 9.07490i | −0.600561 | − | 0.346734i | ||||
\(686\) | − | 18.5290i | − | 0.707439i | ||||||
\(687\) | 0.580071 | + | 0.155771i | 0.0221311 | + | 0.00594305i | ||||
\(688\) | 4.20794 | + | 2.42945i | 0.160426 | + | 0.0926220i | ||||
\(689\) | 3.02381 | + | 1.74580i | 0.115198 | + | 0.0665096i | ||||
\(690\) | 3.88916 | + | 3.89343i | 0.148058 | + | 0.148220i | ||||
\(691\) | 8.69755 | + | 15.0646i | 0.330870 | + | 0.573084i | 0.982683 | − | 0.185296i | \(-0.0593244\pi\) |
−0.651813 | + | 0.758380i | \(0.725991\pi\) | |||||||
\(692\) | 7.33403 | − | 4.23431i | 0.278798 | − | 0.160964i | ||||
\(693\) | 18.6399 | − | 10.7344i | 0.708070 | − | 0.407768i | ||||
\(694\) | −21.1281 | − | 12.1983i | −0.802013 | − | 0.463043i | ||||
\(695\) | −10.1858 | − | 17.6423i | −0.386369 | − | 0.669210i | ||||
\(696\) | 0.499398 | + | 1.86788i | 0.0189296 | + | 0.0708019i | ||||
\(697\) | − | 3.90660i | − | 0.147973i | ||||||
\(698\) | − | 7.97476i | − | 0.301849i | ||||||
\(699\) | −1.36529 | − | 5.10655i | −0.0516399 | − | 0.193147i | ||||
\(700\) | −1.32225 | − | 2.29021i | −0.0499764 | − | 0.0865617i | ||||
\(701\) | 14.1135 | + | 8.14843i | 0.533060 | + | 0.307762i | 0.742261 | − | 0.670110i | \(-0.233753\pi\) |
−0.209202 | + | 0.977872i | \(0.567087\pi\) | |||||||
\(702\) | −20.2678 | − | 5.46657i | −0.764959 | − | 0.206322i | ||||
\(703\) | 20.3873 | − | 11.7706i | 0.768921 | − | 0.443937i | ||||
\(704\) | 1.35563 | + | 2.34802i | 0.0510923 | + | 0.0884944i | ||||
\(705\) | −4.02910 | − | 4.03353i | −0.151745 | − | 0.151912i | ||||
\(706\) | −30.7372 | − | 17.7462i | −1.15681 | − | 0.667885i | ||||
\(707\) | −0.666493 | − | 0.384800i | −0.0250660 | − | 0.0144719i | ||||
\(708\) | −0.130126 | − | 0.0349439i | −0.00489044 | − | 0.00131327i | ||||
\(709\) | − | 34.3386i | − | 1.28961i | −0.764346 | − | 0.644807i | \(-0.776938\pi\) | ||
0.764346 | − | 0.644807i | \(-0.223062\pi\) | |||||||
\(710\) | 11.6252 | + | 6.71183i | 0.436287 | + | 0.251891i | ||||
\(711\) | −36.5434 | − | 0.0401581i | −1.37048 | − | 0.00150605i | ||||
\(712\) | 17.1663i | 0.643334i | ||||||||
\(713\) | −13.0432 | + | 11.9504i | −0.488472 | + | 0.447547i | ||||
\(714\) | 2.40378 | − | 2.40114i | 0.0899591 | − | 0.0898603i | ||||
\(715\) | −10.9533 | −0.409630 | ||||||||
\(716\) | −8.32290 | + | 14.4157i | −0.311041 | + | 0.538739i | ||||
\(717\) | −15.5217 | − | 15.5388i | −0.579668 | − | 0.580305i | ||||
\(718\) | 4.97548 | + | 8.61779i | 0.185683 | + | 0.321613i | ||||
\(719\) | 12.9598 | − | 22.4470i | 0.483319 | − | 0.837133i | −0.516497 | − | 0.856289i | \(-0.672764\pi\) |
0.999817 | + | 0.0191556i | \(0.00609778\pi\) | |||||||
\(720\) | 1.50285 | − | 2.59643i | 0.0560081 | − | 0.0967631i | ||||
\(721\) | −16.0111 | −0.596285 | ||||||||
\(722\) | −11.6577 | + | 6.73056i | −0.433854 | + | 0.250485i | ||||
\(723\) | 34.0132 | + | 9.13384i | 1.26496 | + | 0.339691i | ||||
\(724\) | 2.86960 | − | 1.65676i | 0.106648 | − | 0.0615731i | ||||
\(725\) | 0.558150 | − | 0.966745i | 0.0207292 | − | 0.0359040i | ||||
\(726\) | −6.10410 | − | 1.63918i | −0.226544 | − | 0.0608358i | ||||
\(727\) | −5.51137 | + | 9.54597i | −0.204405 | + | 0.354040i | −0.949943 | − | 0.312423i | \(-0.898859\pi\) |
0.745538 | + | 0.666463i | \(0.232193\pi\) | |||||||
\(728\) | 10.6836 | 0.395961 | ||||||||
\(729\) | 0.0890120 | − | 26.9999i | 0.00329674 | − | 0.999995i | ||||
\(730\) | 9.24020 | + | 5.33483i | 0.341995 | + | 0.197451i | ||||
\(731\) | 3.12129 | − | 1.80208i | 0.115445 | − | 0.0666523i | ||||
\(732\) | 3.67457 | + | 13.7439i | 0.135816 | + | 0.507989i | ||||
\(733\) | 23.9907 | + | 41.5531i | 0.886116 | + | 1.53480i | 0.844429 | + | 0.535667i | \(0.179940\pi\) |
0.0416867 | + | 0.999131i | \(0.486727\pi\) | |||||||
\(734\) | 2.39690 | + | 4.15155i | 0.0884711 | + | 0.153236i | ||||
\(735\) | −0.0110295 | − | 0.00296184i | −0.000406830 | − | 0.000109249i | ||||
\(736\) | − | 3.17723i | − | 0.117114i | ||||||
\(737\) | 11.0907 | − | 19.2096i | 0.408531 | − | 0.707596i | ||||
\(738\) | 13.6744 | + | 7.91499i | 0.503363 | + | 0.291355i | ||||
\(739\) | 27.7681 | − | 16.0319i | 1.02147 | − | 0.589745i | 0.106939 | − | 0.994266i | \(-0.465895\pi\) |
0.914529 | + | 0.404521i | \(0.132562\pi\) | |||||||
\(740\) | −10.0027 | −0.367707 | ||||||||
\(741\) | 4.25353 | + | 15.9094i | 0.156258 | + | 0.584445i | ||||
\(742\) | − | 2.28557i | − | 0.0839059i | ||||||
\(743\) | 25.3947 | 0.931641 | 0.465821 | − | 0.884879i | \(-0.345759\pi\) | ||||
0.465821 | + | 0.884879i | \(0.345759\pi\) | |||||||
\(744\) | 8.13021 | + | 5.18650i | 0.298068 | + | 0.190146i | ||||
\(745\) | −8.00763 | −0.293377 | ||||||||
\(746\) | − | 23.1098i | − | 0.846109i | ||||||
\(747\) | −12.7190 | − | 7.36195i | −0.465363 | − | 0.269360i | ||||
\(748\) | 2.01112 | 0.0735337 | ||||||||
\(749\) | −12.7909 | + | 7.38483i | −0.467369 | + | 0.269836i | ||||
\(750\) | −1.67328 | + | 0.447368i | −0.0610995 | + | 0.0163356i | ||||
\(751\) | 9.23056 | − | 15.9878i | 0.336828 | − | 0.583403i | −0.647006 | − | 0.762485i | \(-0.723979\pi\) |
0.983834 | + | 0.179082i | \(0.0573126\pi\) | |||||||
\(752\) | 3.29156i | 0.120031i | ||||||||
\(753\) | −7.23626 | + | 26.9469i | −0.263704 | + | 0.981998i | ||||
\(754\) | 2.25489 | + | 3.90558i | 0.0821181 | + | 0.142233i | ||||
\(755\) | 3.70048 | + | 6.40942i | 0.134674 | + | 0.233263i | ||||
\(756\) | 3.53461 | + | 13.2789i | 0.128553 | + | 0.482948i | ||||
\(757\) | −36.5554 | + | 21.1053i | −1.32863 | + | 0.767084i | −0.985088 | − | 0.172053i | \(-0.944960\pi\) |
−0.343541 | + | 0.939138i | \(0.611627\pi\) | |||||||
\(758\) | −0.979824 | − | 0.565702i | −0.0355888 | − | 0.0205472i | ||||
\(759\) | −10.5445 | − | 10.5561i | −0.382742 | − | 0.383163i | ||||
\(760\) | −2.35348 | −0.0853698 | ||||||||
\(761\) | 0.562411 | − | 0.974124i | 0.0203874 | − | 0.0353120i | −0.855652 | − | 0.517552i | \(-0.826843\pi\) |
0.876039 | + | 0.482240i | \(0.160177\pi\) | |||||||
\(762\) | 3.23849 | − | 12.0597i | 0.117318 | − | 0.436876i | ||||
\(763\) | −10.2374 | + | 17.7317i | −0.370619 | + | 0.641930i | ||||
\(764\) | −2.56932 | + | 1.48340i | −0.0929546 | + | 0.0536674i | ||||
\(765\) | −1.11053 | − | 1.92838i | −0.0401512 | − | 0.0697207i | ||||
\(766\) | 3.21579 | − | 1.85664i | 0.116191 | − | 0.0670830i | ||||
\(767\) | −0.314267 | −0.0113475 | ||||||||
\(768\) | −1.67328 | + | 0.447368i | −0.0603792 | + | 0.0161430i | ||||
\(769\) | −18.7708 | + | 32.5120i | −0.676892 | + | 1.17241i | 0.299020 | + | 0.954247i | \(0.403340\pi\) |
−0.975912 | + | 0.218165i | \(0.929993\pi\) | |||||||
\(770\) | 3.58497 | + | 6.20935i | 0.129193 | + | 0.223770i | ||||
\(771\) | −25.3358 | + | 25.3080i | −0.912447 | + | 0.911445i | ||||
\(772\) | −6.42312 | + | 11.1252i | −0.231173 | + | 0.400403i | ||||
\(773\) | 13.0451 | 0.469198 | 0.234599 | − | 0.972092i | \(-0.424622\pi\) | ||||
0.234599 | + | 0.972092i | \(0.424622\pi\) | |||||||
\(774\) | −0.0160186 | + | 14.5767i | −0.000575776 | + | 0.523949i | ||||
\(775\) | −1.20475 | − | 5.43586i | −0.0432759 | − | 0.195262i | ||||
\(776\) | − | 12.4034i | − | 0.445258i | ||||||
\(777\) | 32.4150 | − | 32.3794i | 1.16288 | − | 1.16160i | ||||
\(778\) | −8.44448 | − | 4.87542i | −0.302749 | − | 0.174792i | ||||
\(779\) | − | 12.3949i | − | 0.444095i | ||||||
\(780\) | 1.81476 | − | 6.75794i | 0.0649790 | − | 0.241973i | ||||
\(781\) | −31.5190 | − | 18.1975i | −1.12784 | − | 0.651159i | ||||
\(782\) | −2.04101 | − | 1.17838i | −0.0729863 | − | 0.0421387i | ||||
\(783\) | −4.10831 | + | 4.09478i | −0.146819 | + | 0.146336i | ||||
\(784\) | 0.00329675 | + | 0.00571013i | 0.000117741 | + | 0.000203933i | ||||
\(785\) | 2.09317 | − | 1.20849i | 0.0747084 | − | 0.0431329i | ||||
\(786\) | 6.97228 | − | 25.9638i | 0.248693 | − | 0.926099i | ||||
\(787\) | −1.98975 | − | 1.14878i | −0.0709269 | − | 0.0409497i | 0.464117 | − | 0.885774i | \(-0.346372\pi\) |
−0.535044 | + | 0.844824i | \(0.679705\pi\) | |||||||
\(788\) | 6.44071 | + | 11.1556i | 0.229441 | + | 0.397403i | ||||
\(789\) | −28.1462 | + | 7.52517i | −1.00203 | + | 0.267903i | ||||
\(790\) | − | 12.1811i | − | 0.433386i | ||||||
\(791\) | − | 18.2420i | − | 0.648610i | ||||||
\(792\) | −4.07463 | + | 7.03959i | −0.144786 | + | 0.250141i | ||||
\(793\) | 16.5915 | + | 28.7373i | 0.589181 | + | 1.02049i | ||||
\(794\) | −9.59420 | − | 5.53921i | −0.340485 | − | 0.196579i | ||||
\(795\) | −1.44574 | − | 0.388237i | −0.0512752 | − | 0.0137693i | ||||
\(796\) | −8.97201 | + | 5.17999i | −0.318004 | + | 0.183600i | ||||
\(797\) | −5.95313 | − | 10.3111i | −0.210871 | − | 0.365239i | 0.741116 | − | 0.671376i | \(-0.234297\pi\) |
−0.951987 | + | 0.306137i | \(0.900963\pi\) | |||||||
\(798\) | 7.62675 | − | 7.61837i | 0.269984 | − | 0.269688i | ||||
\(799\) | 2.11445 | + | 1.22078i | 0.0748039 | + | 0.0431881i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | −44.6276 | + | 25.7004i | −1.57684 | + | 0.908079i | ||||
\(802\) | − | 0.963613i | − | 0.0340264i | ||||||
\(803\) | −25.0526 | − | 14.4641i | −0.884087 | − | 0.510428i | ||||
\(804\) | 10.0144 | + | 10.0254i | 0.353180 | + | 0.353568i | ||||
\(805\) | − | 8.40220i | − | 0.296138i | ||||||
\(806\) | 21.4519 | + | 6.76520i | 0.755611 | + | 0.238294i | ||||
\(807\) | 8.95413 | + | 8.96398i | 0.315200 | + | 0.315547i | ||||
\(808\) | 0.291018 | 0.0102380 | ||||||||
\(809\) | −11.3601 | + | 19.6762i | −0.399398 | + | 0.691778i | −0.993652 | − | 0.112500i | \(-0.964114\pi\) |
0.594254 | + | 0.804278i | \(0.297448\pi\) | |||||||
\(810\) | 8.99998 | + | 0.0197805i | 0.316227 | + | 0.000695015i | ||||
\(811\) | 7.53102 | + | 13.0441i | 0.264450 | + | 0.458041i | 0.967419 | − | 0.253179i | \(-0.0814763\pi\) |
−0.702969 | + | 0.711220i | \(0.748143\pi\) | |||||||
\(812\) | 1.47603 | − | 2.55656i | 0.0517985 | − | 0.0897177i | ||||
\(813\) | −1.93430 | − | 7.23479i | −0.0678388 | − | 0.253735i | ||||
\(814\) | 27.1200 | 0.950554 | ||||||||
\(815\) | −21.7934 | + | 12.5824i | −0.763389 | + | 0.440743i | ||||
\(816\) | −0.333205 | + | 1.24081i | −0.0116645 | + | 0.0434371i | ||||
\(817\) | 9.90330 | − | 5.71768i | 0.346473 | − | 0.200036i | ||||
\(818\) | 1.95733 | − | 3.39020i | 0.0684365 | − | 0.118535i | ||||
\(819\) | 15.9949 | + | 27.7744i | 0.558907 | + | 0.970517i | ||||
\(820\) | −2.63332 | + | 4.56104i | −0.0919595 | + | 0.159279i | ||||
\(821\) | 56.1246 | 1.95876 | 0.979382 | − | 0.202018i | \(-0.0647500\pi\) | ||||
0.979382 | + | 0.202018i | \(0.0647500\pi\) | |||||||
\(822\) | −22.2411 | + | 22.2167i | −0.775747 | + | 0.774895i | ||||
\(823\) | −32.8353 | − | 18.9575i | −1.14457 | − | 0.660816i | −0.197010 | − | 0.980401i | \(-0.563123\pi\) |
−0.947558 | + | 0.319585i | \(0.896457\pi\) | |||||||
\(824\) | 5.24333 | − | 3.02724i | 0.182660 | − | 0.105459i | ||||
\(825\) | 4.53670 | − | 1.21293i | 0.157947 | − | 0.0422289i | ||||
\(826\) | 0.102858 | + | 0.178156i | 0.00357890 | + | 0.00619883i | ||||
\(827\) | 3.95780 | + | 6.85511i | 0.137626 | + | 0.238375i | 0.926598 | − | 0.376054i | \(-0.122719\pi\) |
−0.788971 | + | 0.614430i | \(0.789386\pi\) | |||||||
\(828\) | 8.25991 | − | 4.75677i | 0.287052 | − | 0.165309i | ||||
\(829\) | 13.2824i | 0.461318i | 0.973035 | + | 0.230659i | \(0.0740881\pi\) | ||||
−0.973035 | + | 0.230659i | \(0.925912\pi\) | |||||||
\(830\) | 2.44932 | − | 4.24235i | 0.0850173 | − | 0.147254i | ||||
\(831\) | −5.52803 | − | 20.6763i | −0.191765 | − | 0.717254i | ||||
\(832\) | −3.49868 | + | 2.01996i | −0.121295 | + | 0.0700297i | ||||
\(833\) | 0.00489082 | 0.000169457 | ||||||||
\(834\) | −34.0873 | + | 9.11360i | −1.18035 | + | 0.315578i | ||||
\(835\) | − | 22.5277i | − | 0.779604i | ||||||
\(836\) | 6.38091 | 0.220688 | ||||||||
\(837\) | −1.31137 | + | 28.9012i | −0.0453275 | + | 0.998972i | ||||
\(838\) | −6.12859 | −0.211709 | ||||||||
\(839\) | − | 40.0948i | − | 1.38423i | −0.721789 | − | 0.692113i | \(-0.756680\pi\) | ||
0.721789 | − | 0.692113i | \(-0.243320\pi\) | |||||||
\(840\) | −4.42499 | + | 1.18307i | −0.152677 | + | 0.0408197i | ||||
\(841\) | −27.7539 | −0.957030 | ||||||||
\(842\) | 10.9418 | − | 6.31725i | 0.377079 | − | 0.217707i | ||||
\(843\) | 1.01435 | + | 3.79394i | 0.0349361 | + | 0.130670i | ||||
\(844\) | −2.42025 | + | 4.19199i | −0.0833083 | + | 0.144294i | ||||
\(845\) | − | 3.32102i | − | 0.114247i | ||||||
\(846\) | −8.55714 | + | 4.92794i | −0.294200 | + | 0.169426i | ||||
\(847\) | 4.82498 | + | 8.35711i | 0.165788 | + | 0.287154i | ||||
\(848\) | 0.432136 | + | 0.748481i | 0.0148396 | + | 0.0257030i | ||||
\(849\) | −7.99897 | + | 2.13861i | −0.274524 | + | 0.0733968i | ||||
\(850\) | 0.642386 | − | 0.370882i | 0.0220337 | − | 0.0127211i | ||||
\(851\) | −27.5231 | − | 15.8904i | −0.943478 | − | 0.544717i | ||||
\(852\) | 16.4496 | − | 16.4315i | 0.563554 | − | 0.562935i | ||||
\(853\) | 8.66750 | 0.296769 | 0.148385 | − | 0.988930i | \(-0.452593\pi\) | ||||
0.148385 | + | 0.988930i | \(0.452593\pi\) | |||||||
\(854\) | 10.8607 | − | 18.8112i | 0.371644 | − | 0.643706i | ||||
\(855\) | −3.52350 | − | 6.11840i | −0.120501 | − | 0.209245i | ||||
\(856\) | 2.79252 | − | 4.83678i | 0.0954463 | − | 0.165318i | ||||
\(857\) | −13.4362 | + | 7.75737i | −0.458970 | + | 0.264987i | −0.711611 | − | 0.702574i | \(-0.752034\pi\) |
0.252641 | + | 0.967560i | \(0.418701\pi\) | |||||||
\(858\) | −4.92030 | + | 18.3225i | −0.167976 | + | 0.625521i | ||||
\(859\) | −31.0933 | + | 17.9517i | −1.06089 | + | 0.612504i | −0.925678 | − | 0.378313i | \(-0.876504\pi\) |
−0.135211 | + | 0.990817i | \(0.543171\pi\) | |||||||
\(860\) | −4.85891 | −0.165687 | ||||||||
\(861\) | −6.23079 | − | 23.3048i | −0.212345 | − | 0.794227i | ||||
\(862\) | 14.3746 | − | 24.8975i | 0.489600 | − | 0.848012i | ||||
\(863\) | −16.5186 | − | 28.6110i | −0.562299 | − | 0.973930i | −0.997295 | − | 0.0734982i | \(-0.976584\pi\) |
0.434996 | − | 0.900432i | \(-0.356750\pi\) | |||||||
\(864\) | −3.66817 | − | 3.68029i | −0.124794 | − | 0.125206i | ||||
\(865\) | −4.23431 | + | 7.33403i | −0.143971 | + | 0.249365i | ||||
\(866\) | −7.12270 | −0.242039 | ||||||||
\(867\) | −20.1357 | − | 20.1579i | −0.683845 | − | 0.684597i | ||||
\(868\) | −3.18597 | − | 14.3752i | −0.108139 | − | 0.487925i | ||||
\(869\) | 33.0263i | 1.12034i | ||||||||
\(870\) | −1.36643 | − | 1.36793i | −0.0463264 | − | 0.0463773i | ||||
\(871\) | 28.6234 | + | 16.5257i | 0.969867 | + | 0.559953i | ||||
\(872\) | − | 7.74239i | − | 0.262191i | ||||||
\(873\) | 32.2455 | − | 18.5697i | 1.09135 | − | 0.628490i | ||||
\(874\) | −6.47575 | − | 3.73878i | −0.219046 | − | 0.126466i | ||||
\(875\) | 2.29021 | + | 1.32225i | 0.0774232 | + | 0.0447003i | ||||
\(876\) | 13.0748 | − | 13.0604i | 0.441757 | − | 0.441271i | ||||
\(877\) | −19.1990 | − | 33.2536i | −0.648303 | − | 1.12289i | −0.983528 | − | 0.180755i | \(-0.942146\pi\) |
0.335225 | − | 0.942138i | \(-0.391188\pi\) | |||||||
\(878\) | −28.7148 | + | 16.5785i | −0.969077 | + | 0.559497i | ||||
\(879\) | −31.8172 | − | 8.54413i | −1.07317 | − | 0.288186i | ||||
\(880\) | −2.34802 | − | 1.35563i | −0.0791518 | − | 0.0456983i | ||||
\(881\) | −18.3245 | − | 31.7390i | −0.617369 | − | 1.06932i | −0.989964 | − | 0.141321i | \(-0.954865\pi\) |
0.372594 | − | 0.927994i | \(-0.378468\pi\) | |||||||
\(882\) | −0.00990906 | + | 0.0171195i | −0.000333655 | + | 0.000576444i | ||||
\(883\) | 28.7912i | 0.968901i | 0.874819 | + | 0.484451i | \(0.160980\pi\) | ||||
−0.874819 | + | 0.484451i | \(0.839020\pi\) | |||||||
\(884\) | 2.99667i | 0.100789i | ||||||||
\(885\) | 0.130165 | − | 0.0348009i | 0.00437544 | − | 0.00116982i | ||||
\(886\) | −13.3922 | − | 23.1960i | −0.449920 | − | 0.779285i | ||||
\(887\) | −10.4123 | − | 6.01154i | −0.349611 | − | 0.201848i | 0.314903 | − | 0.949124i | \(-0.398028\pi\) |
−0.664514 | + | 0.747276i | \(0.731361\pi\) | |||||||
\(888\) | −4.49329 | + | 16.7324i | −0.150785 | + | 0.561502i | ||||
\(889\) | −16.5109 | + | 9.53257i | −0.553758 | + | 0.319712i | ||||
\(890\) | −8.58314 | − | 14.8664i | −0.287708 | − | 0.498324i | ||||
\(891\) | −24.4013 | − | 0.0536300i | −0.817474 | − | 0.00179667i | ||||
\(892\) | −7.55204 | − | 4.36017i | −0.252861 | − | 0.145989i | ||||
\(893\) | 6.70877 | + | 3.87331i | 0.224501 | + | 0.129615i | ||||
\(894\) | −3.59708 | + | 13.3951i | −0.120304 | + | 0.447998i | ||||
\(895\) | − | 16.6458i | − | 0.556408i | ||||||
\(896\) | 2.29021 | + | 1.32225i | 0.0765105 | + | 0.0441734i | ||||
\(897\) | 15.7292 | − | 15.7119i | 0.525182 | − | 0.524605i | ||||
\(898\) | 24.5175i | 0.818161i | ||||||||
\(899\) | 4.58266 | − | 4.19871i | 0.152840 | − | 0.140035i | ||||
\(900\) | −0.00329675 | + | 3.00000i | −0.000109892 | + | 0.0999999i | ||||
\(901\) | 0.641085 | 0.0213577 | ||||||||
\(902\) | 7.13962 | − | 12.3662i | 0.237723 | − | 0.411749i | ||||
\(903\) | 15.7459 | − | 15.7286i | 0.523990 | − | 0.523415i | ||||
\(904\) | 3.44903 | + | 5.97390i | 0.114713 | + | 0.198689i | ||||
\(905\) | −1.65676 | + | 2.86960i | −0.0550727 | + | 0.0953886i | ||||
\(906\) | 12.3839 | − | 3.31096i | 0.411427 | − | 0.109999i | ||||
\(907\) | −55.4236 | −1.84031 | −0.920155 | − | 0.391554i | \(-0.871938\pi\) | ||||
−0.920155 | + | 0.391554i | \(0.871938\pi\) | |||||||
\(908\) | 11.0216 | − | 6.36331i | 0.365764 | − | 0.211174i | ||||
\(909\) | 0.435697 | + | 0.756567i | 0.0144511 | + | 0.0250938i | ||||
\(910\) | −9.25228 | + | 5.34180i | −0.306710 | + | 0.177079i | ||||
\(911\) | −21.2928 | + | 36.8802i | −0.705462 | + | 1.22190i | 0.261062 | + | 0.965322i | \(0.415927\pi\) |
−0.966524 | + | 0.256574i | \(0.917406\pi\) | |||||||
\(912\) | −1.05720 | + | 3.93687i | −0.0350074 | + | 0.130363i | ||||
\(913\) | −6.64076 | + | 11.5021i | −0.219777 | + | 0.380665i | ||||
\(914\) | 8.46145 | 0.279880 | ||||||||
\(915\) | −10.0542 | − | 10.0653i | −0.332382 | − | 0.332748i | ||||
\(916\) | 0.300311 | + | 0.173385i | 0.00992256 | + | 0.00572880i | ||||
\(917\) | −35.5470 | + | 20.5231i | −1.17387 | + | 0.677732i | ||||
\(918\) | −3.72462 | + | 0.991433i | −0.122931 | + | 0.0327222i | ||||
\(919\) | −1.62944 | − | 2.82227i | −0.0537502 | − | 0.0930980i | 0.837898 | − | 0.545826i | \(-0.183784\pi\) |
−0.891649 | + | 0.452728i | \(0.850451\pi\) | |||||||
\(920\) | 1.58861 | + | 2.75156i | 0.0523751 | + | 0.0907163i | ||||
\(921\) | 12.6418 | − | 47.0764i | 0.416562 | − | 1.55122i | ||||
\(922\) | − | 10.2584i | − | 0.337841i | ||||||
\(923\) | 27.1153 | − | 46.9651i | 0.892512 | − | 1.54588i | ||||
\(924\) | 11.9973 | − | 3.20761i | 0.394683 | − | 0.105523i | ||||
\(925\) | 8.66260 | − | 5.00135i | 0.284825 | − | 0.164444i | ||||
\(926\) | 16.4580 | 0.540845 | ||||||||
\(927\) | 15.7200 | + | 9.09900i | 0.516313 | + | 0.298850i | ||||
\(928\) | 1.11630i | 0.0366444i | ||||||||
\(929\) | −26.9297 | −0.883535 | −0.441767 | − | 0.897130i | \(-0.645648\pi\) | ||||
−0.441767 | + | 0.897130i | \(0.645648\pi\) | |||||||
\(930\) | −9.63421 | − | 0.426535i | −0.315918 | − | 0.0139866i | ||||
\(931\) | 0.0155177 | 0.000508571 | ||||||||
\(932\) | − | 3.05182i | − | 0.0999657i | ||||||
\(933\) | −15.5549 | − | 58.1794i | −0.509244 | − | 1.90471i | ||||
\(934\) | −21.7403 | −0.711363 | ||||||||
\(935\) | −1.74168 | + | 1.00556i | −0.0569589 | + | 0.0328853i | ||||
\(936\) | −10.4894 | − | 6.07142i | −0.342856 | − | 0.198451i | ||||
\(937\) | 21.0825 | − | 36.5160i | 0.688735 | − | 1.19292i | −0.283512 | − | 0.958969i | \(-0.591500\pi\) |
0.972247 | − | 0.233956i | \(-0.0751670\pi\) | |||||||
\(938\) | − | 21.6352i | − | 0.706415i | ||||||
\(939\) | 25.9304 | + | 6.96329i | 0.846205 | + | 0.227238i | ||||
\(940\) | −1.64578 | − | 2.85057i | −0.0536794 | − | 0.0929754i | ||||
\(941\) | 7.15865 | + | 12.3992i | 0.233365 | + | 0.404201i | 0.958796 | − | 0.284094i | \(-0.0916928\pi\) |
−0.725431 | + | 0.688295i | \(0.758359\pi\) | |||||||
\(942\) | −1.08128 | − | 4.04429i | −0.0352301 | − | 0.131770i | ||||
\(943\) | −14.4915 | + | 8.36666i | −0.471907 | + | 0.272456i | ||||
\(944\) | −0.0673682 | − | 0.0388951i | −0.00219265 | − | 0.00126593i | ||||
\(945\) | −9.70050 | − | 9.73253i | −0.315557 | − | 0.316599i | ||||
\(946\) | 13.1738 | 0.428316 | ||||||||
\(947\) | −4.56614 | + | 7.90879i | −0.148380 | + | 0.257001i | −0.930629 | − | 0.365965i | \(-0.880739\pi\) |
0.782249 | + | 0.622966i | \(0.214072\pi\) | |||||||
\(948\) | −20.3764 | − | 5.47185i | −0.661796 | − | 0.177718i | ||||
\(949\) | 21.5523 | − | 37.3298i | 0.699619 | − | 1.21178i | ||||
\(950\) | 2.03818 | − | 1.17674i | 0.0661272 | − | 0.0381785i | ||||
\(951\) | 8.28669 | + | 2.22529i | 0.268714 | + | 0.0721601i | ||||
\(952\) | 1.69879 | − | 0.980799i | 0.0550582 | − | 0.0317879i | ||||
\(953\) | −37.8957 | −1.22756 | −0.613781 | − | 0.789476i | \(-0.710352\pi\) | ||||
−0.613781 | + | 0.789476i | \(0.710352\pi\) | |||||||
\(954\) | −1.29887 | + | 2.24402i | −0.0420526 | + | 0.0726528i | ||||
\(955\) | 1.48340 | − | 2.56932i | 0.0480016 | − | 0.0831412i | ||||
\(956\) | −6.34019 | − | 10.9815i | −0.205056 | − | 0.355168i | ||||
\(957\) | 3.70475 | + | 3.70883i | 0.119758 | + | 0.119889i | ||||
\(958\) | 9.49670 | − | 16.4488i | 0.306824 | − | 0.531435i | ||||
\(959\) | 47.9972 | 1.54991 | ||||||||
\(960\) | 1.22542 | − | 1.22407i | 0.0395502 | − | 0.0395067i | ||||
\(961\) | 2.70562 | − | 30.8817i | 0.0872781 | − | 0.996184i | ||||
\(962\) | 40.4102i | 1.30288i | ||||||||
\(963\) | 16.7551 | + | 0.0184125i | 0.539926 | + | 0.000593333i | ||||
\(964\) | 17.6091 | + | 10.1666i | 0.567151 | + | 0.327445i | ||||
\(965\) | − | 12.8462i | − | 0.413535i | ||||||
\(966\) | −14.0551 | − | 3.77432i | −0.452215 | − | 0.121437i | ||||
\(967\) | −22.3015 | − | 12.8758i | −0.717169 | − | 0.414058i | 0.0965407 | − | 0.995329i | \(-0.469222\pi\) |
−0.813710 | + | 0.581271i | \(0.802556\pi\) | |||||||
\(968\) | −3.16018 | − | 1.82453i | −0.101572 | − | 0.0586426i | ||||
\(969\) | 2.13690 | + | 2.13925i | 0.0686470 | + | 0.0687225i | ||||
\(970\) | 6.20172 | + | 10.7417i | 0.199125 | + | 0.344895i | ||||
\(971\) | −4.80189 | + | 2.77237i | −0.154100 | + | 0.0889697i | −0.575067 | − | 0.818106i | \(-0.695024\pi\) |
0.420967 | + | 0.907076i | \(0.361691\pi\) | |||||||
\(972\) | 4.07594 | − | 15.0462i | 0.130736 | − | 0.482606i | ||||
\(973\) | 46.6551 | + | 26.9364i | 1.49570 | + | 0.863540i | ||||
\(974\) | 12.3295 | + | 21.3554i | 0.395063 | + | 0.684270i | ||||
\(975\) | 1.80734 | + | 6.75993i | 0.0578811 | + | 0.216491i | ||||
\(976\) | 8.21375i | 0.262916i | ||||||||
\(977\) | 12.3135i | 0.393945i | 0.980409 | + | 0.196972i | \(0.0631110\pi\) | ||||
−0.980409 | + | 0.196972i | \(0.936889\pi\) | |||||||
\(978\) | 11.2580 | + | 42.1078i | 0.359990 | + | 1.34646i | ||||
\(979\) | 23.2711 | + | 40.3068i | 0.743749 | + | 1.28821i | ||||
\(980\) | −0.00571013 | − | 0.00329675i | −0.000182404 | − | 0.000105311i | ||||
\(981\) | 20.1281 | − | 11.5915i | 0.642640 | − | 0.370087i | ||||
\(982\) | −22.6608 | + | 13.0832i | −0.723136 | + | 0.417503i | ||||
\(983\) | 14.8812 | + | 25.7750i | 0.474636 | + | 0.822094i | 0.999578 | − | 0.0290441i | \(-0.00924631\pi\) |
−0.524942 | + | 0.851138i | \(0.675913\pi\) | |||||||
\(984\) | 6.44674 | + | 6.45383i | 0.205515 | + | 0.205741i | ||||
\(985\) | −11.1556 | − | 6.44071i | −0.355448 | − | 0.205218i | ||||
\(986\) | 0.717096 | + | 0.414016i | 0.0228370 | + | 0.0131849i | ||||
\(987\) | 14.5608 | + | 3.91014i | 0.463476 | + | 0.124461i | ||||
\(988\) | 9.50790i | 0.302487i | ||||||||
\(989\) | −13.3696 | − | 7.71893i | −0.425128 | − | 0.245448i | ||||
\(990\) | 0.00893835 | − | 8.13378i | 0.000284079 | − | 0.258508i | ||||
\(991\) | 0.499587i | 0.0158699i | 0.999969 | + | 0.00793495i | \(0.00252580\pi\) | ||||
−0.999969 | + | 0.00793495i | \(0.997474\pi\) | |||||||
\(992\) | 3.76128 | + | 4.10522i | 0.119421 | + | 0.130341i | ||||
\(993\) | 2.31845 | − | 2.31590i | 0.0735738 | − | 0.0734930i | ||||
\(994\) | −35.4989 | −1.12596 | ||||||||
\(995\) | 5.17999 | − | 8.97201i | 0.164217 | − | 0.284432i | ||||
\(996\) | −5.99630 | − | 6.00289i | −0.190000 | − | 0.190209i | ||||
\(997\) | 23.2105 | + | 40.2018i | 0.735085 | + | 1.27320i | 0.954686 | + | 0.297615i | \(0.0961910\pi\) |
−0.219601 | + | 0.975590i | \(0.570476\pi\) | |||||||
\(998\) | 14.6701 | − | 25.4093i | 0.464373 | − | 0.804317i | ||||
\(999\) | −50.2267 | + | 13.3695i | −1.58910 | + | 0.422992i |
(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 | 930.2.o.e.491.11 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.491.4 | yes | 40 | |
31.6 | odd | 6 | inner | 930.2.o.e.161.14 | yes | 40 | |
93.68 | even | 6 | inner | 930.2.o.e.161.1 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.1 | ✓ | 40 | 93.68 | even | 6 | inner | |
930.2.o.e.161.14 | yes | 40 | 31.6 | odd | 6 | inner | |
930.2.o.e.491.4 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.491.11 | yes | 40 | 1.1 | even | 1 | trivial |