Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(4,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.g (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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 4.18 | ||
Character | \(\chi\) | \(=\) | 63.4 |
Dual form | 63.4.g.a.16.18 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.68671 | − | 2.92146i | 0.596341 | − | 1.03289i | −0.397015 | − | 0.917812i | \(-0.629954\pi\) |
0.993356 | − | 0.115081i | \(-0.0367128\pi\) | |||||||
\(3\) | 0.0520064 | − | 5.19589i | 0.0100086 | − | 0.999950i | ||||
\(4\) | −1.68996 | − | 2.92710i | −0.211246 | − | 0.365888i | ||||
\(5\) | −9.74532 | −0.871648 | −0.435824 | − | 0.900032i | \(-0.643543\pi\) | ||||
−0.435824 | + | 0.900032i | \(0.643543\pi\) | |||||||
\(6\) | −15.0919 | − | 8.91589i | −1.02687 | − | 0.606649i | ||||
\(7\) | 0.158327 | − | 18.5196i | 0.00854886 | − | 0.999963i | ||||
\(8\) | 15.5854 | 0.688785 | ||||||||
\(9\) | −26.9946 | − | 0.540440i | −0.999800 | − | 0.0200163i | ||||
\(10\) | −16.4375 | + | 28.4706i | −0.519800 | + | 0.900319i | ||||
\(11\) | 38.9123 | 1.06659 | 0.533296 | − | 0.845929i | \(-0.320953\pi\) | ||||
0.533296 | + | 0.845929i | \(0.320953\pi\) | |||||||
\(12\) | −15.2968 | + | 8.62865i | −0.367984 | + | 0.207573i | ||||
\(13\) | −31.2817 | + | 54.1816i | −0.667384 | + | 1.15594i | 0.311249 | + | 0.950328i | \(0.399253\pi\) |
−0.978633 | + | 0.205615i | \(0.934081\pi\) | |||||||
\(14\) | −53.8372 | − | 31.6997i | −1.02776 | − | 0.605149i | ||||
\(15\) | −0.506819 | + | 50.6356i | −0.00872401 | + | 0.871604i | ||||
\(16\) | 39.8078 | − | 68.9491i | 0.621996 | − | 1.07733i | ||||
\(17\) | 63.3614 | − | 109.745i | 0.903964 | − | 1.56571i | 0.0816621 | − | 0.996660i | \(-0.473977\pi\) |
0.822302 | − | 0.569051i | \(-0.192689\pi\) | |||||||
\(18\) | −47.1109 | + | 77.9521i | −0.616896 | + | 1.02075i | ||||
\(19\) | 22.7332 | + | 39.3751i | 0.274493 | + | 0.475435i | 0.970007 | − | 0.243077i | \(-0.0781568\pi\) |
−0.695514 | + | 0.718512i | \(0.744823\pi\) | |||||||
\(20\) | 16.4692 | + | 28.5256i | 0.184132 | + | 0.318926i | ||||
\(21\) | −96.2175 | − | 1.78579i | −0.999828 | − | 0.0185567i | ||||
\(22\) | 65.6337 | − | 113.681i | 0.636052 | − | 1.10167i | ||||
\(23\) | 153.865 | 1.39491 | 0.697457 | − | 0.716627i | \(-0.254315\pi\) | ||||
0.697457 | + | 0.716627i | \(0.254315\pi\) | |||||||
\(24\) | 0.810542 | − | 80.9801i | 0.00689380 | − | 0.688750i | ||||
\(25\) | −30.0287 | −0.240230 | ||||||||
\(26\) | 105.526 | + | 182.777i | 0.795977 | + | 1.37867i | ||||
\(27\) | −4.21196 | + | 140.233i | −0.0300219 | + | 0.999549i | ||||
\(28\) | −54.4763 | + | 30.8340i | −0.367681 | + | 0.208110i | ||||
\(29\) | 27.4655 | + | 47.5716i | 0.175869 | + | 0.304615i | 0.940462 | − | 0.339899i | \(-0.110393\pi\) |
−0.764592 | + | 0.644514i | \(0.777060\pi\) | |||||||
\(30\) | 147.075 | + | 86.8882i | 0.895072 | + | 0.528785i | ||||
\(31\) | −54.8509 | − | 95.0045i | −0.317791 | − | 0.550430i | 0.662236 | − | 0.749295i | \(-0.269608\pi\) |
−0.980027 | + | 0.198866i | \(0.936274\pi\) | |||||||
\(32\) | −71.9464 | − | 124.615i | −0.397452 | − | 0.688406i | ||||
\(33\) | 2.02369 | − | 202.184i | 0.0106751 | − | 1.06654i | ||||
\(34\) | −213.744 | − | 370.216i | −1.07814 | − | 1.86740i | ||||
\(35\) | −1.54295 | + | 180.479i | −0.00745159 | + | 0.871616i | ||||
\(36\) | 44.0380 | + | 79.9293i | 0.203880 | + | 0.370043i | ||||
\(37\) | 144.482 | + | 250.249i | 0.641962 | + | 1.11191i | 0.984994 | + | 0.172588i | \(0.0552129\pi\) |
−0.343032 | + | 0.939324i | \(0.611454\pi\) | |||||||
\(38\) | 153.377 | 0.654765 | ||||||||
\(39\) | 279.895 | + | 165.354i | 1.14921 | + | 0.678920i | ||||
\(40\) | −151.885 | −0.600378 | ||||||||
\(41\) | −11.3009 | + | 19.5738i | −0.0430465 | + | 0.0745587i | −0.886746 | − | 0.462257i | \(-0.847040\pi\) |
0.843699 | + | 0.536816i | \(0.180373\pi\) | |||||||
\(42\) | −167.508 | + | 278.084i | −0.615406 | + | 1.02165i | ||||
\(43\) | 23.9450 | + | 41.4740i | 0.0849204 | + | 0.147086i | 0.905357 | − | 0.424651i | \(-0.139603\pi\) |
−0.820437 | + | 0.571737i | \(0.806270\pi\) | |||||||
\(44\) | −65.7604 | − | 113.900i | −0.225313 | − | 0.390253i | ||||
\(45\) | 263.071 | + | 5.26676i | 0.871473 | + | 0.0174472i | ||||
\(46\) | 259.525 | − | 449.510i | 0.831845 | − | 1.44080i | ||||
\(47\) | −193.385 | + | 334.953i | −0.600173 | + | 1.03953i | 0.392622 | + | 0.919700i | \(0.371568\pi\) |
−0.992794 | + | 0.119830i | \(0.961765\pi\) | |||||||
\(48\) | −356.182 | − | 210.423i | −1.07105 | − | 0.632748i | ||||
\(49\) | −342.950 | − | 5.86430i | −0.999854 | − | 0.0170971i | ||||
\(50\) | −50.6496 | + | 87.7278i | −0.143259 | + | 0.248132i | ||||
\(51\) | −566.929 | − | 334.926i | −1.55659 | − | 0.919589i | ||||
\(52\) | 211.460 | 0.563928 | ||||||||
\(53\) | −133.617 | + | 231.431i | −0.346296 | + | 0.599802i | −0.985588 | − | 0.169162i | \(-0.945894\pi\) |
0.639293 | + | 0.768964i | \(0.279227\pi\) | |||||||
\(54\) | 402.581 | + | 248.837i | 1.01452 | + | 0.627082i | ||||
\(55\) | −379.213 | −0.929692 | ||||||||
\(56\) | 2.46759 | − | 288.635i | 0.00588832 | − | 0.688759i | ||||
\(57\) | 205.771 | − | 116.072i | 0.478159 | − | 0.269720i | ||||
\(58\) | 185.305 | 0.419513 | ||||||||
\(59\) | −193.371 | − | 334.929i | −0.426691 | − | 0.739051i | 0.569886 | − | 0.821724i | \(-0.306987\pi\) |
−0.996577 | + | 0.0826735i | \(0.973654\pi\) | |||||||
\(60\) | 149.072 | − | 84.0889i | 0.320753 | − | 0.180931i | ||||
\(61\) | −17.8409 | + | 30.9013i | −0.0374473 | + | 0.0648607i | −0.884142 | − | 0.467219i | \(-0.845256\pi\) |
0.846694 | + | 0.532080i | \(0.178589\pi\) | |||||||
\(62\) | −370.070 | −0.758047 | ||||||||
\(63\) | −14.2827 | + | 499.843i | −0.0285627 | + | 0.999592i | ||||
\(64\) | 151.514 | 0.295925 | ||||||||
\(65\) | 304.851 | − | 528.017i | 0.581724 | − | 1.00758i | ||||
\(66\) | −587.260 | − | 346.938i | −1.09525 | − | 0.647047i | ||||
\(67\) | −17.8513 | − | 30.9194i | −0.0325506 | − | 0.0563792i | 0.849291 | − | 0.527925i | \(-0.177030\pi\) |
−0.881842 | + | 0.471545i | \(0.843696\pi\) | |||||||
\(68\) | −428.314 | −0.763834 | ||||||||
\(69\) | 8.00195 | − | 799.465i | 0.0139612 | − | 1.39484i | ||||
\(70\) | 524.661 | + | 308.923i | 0.895843 | + | 0.527477i | ||||
\(71\) | −146.355 | −0.244636 | −0.122318 | − | 0.992491i | \(-0.539033\pi\) | ||||
−0.122318 | + | 0.992491i | \(0.539033\pi\) | |||||||
\(72\) | −420.722 | − | 8.42297i | −0.688647 | − | 0.0137869i | ||||
\(73\) | −364.856 | + | 631.948i | −0.584974 | + | 1.01320i | 0.409905 | + | 0.912128i | \(0.365562\pi\) |
−0.994879 | + | 0.101076i | \(0.967771\pi\) | |||||||
\(74\) | 974.792 | 1.53131 | ||||||||
\(75\) | −1.56169 | + | 156.026i | −0.00240437 | + | 0.240218i | ||||
\(76\) | 76.8367 | − | 133.085i | 0.115971 | − | 0.200867i | ||||
\(77\) | 6.16087 | − | 720.640i | 0.00911814 | − | 1.06655i | ||||
\(78\) | 955.177 | − | 538.798i | 1.38657 | − | 0.782139i | ||||
\(79\) | −250.675 | + | 434.183i | −0.357002 | + | 0.618346i | −0.987459 | − | 0.157879i | \(-0.949535\pi\) |
0.630456 | + | 0.776225i | \(0.282868\pi\) | |||||||
\(80\) | −387.939 | + | 671.931i | −0.542162 | + | 0.939052i | ||||
\(81\) | 728.416 | + | 29.1779i | 0.999199 | + | 0.0400245i | ||||
\(82\) | 38.1227 | + | 66.0304i | 0.0513408 | + | 0.0889249i | ||||
\(83\) | 169.622 | + | 293.794i | 0.224319 | + | 0.388532i | 0.956115 | − | 0.292992i | \(-0.0946510\pi\) |
−0.731796 | + | 0.681524i | \(0.761318\pi\) | |||||||
\(84\) | 157.377 | + | 284.657i | 0.204420 | + | 0.369745i | ||||
\(85\) | −617.477 | + | 1069.50i | −0.787938 | + | 1.36475i | ||||
\(86\) | 161.553 | 0.202566 | ||||||||
\(87\) | 248.605 | − | 140.234i | 0.306360 | − | 0.172812i | ||||
\(88\) | 606.465 | 0.734652 | ||||||||
\(89\) | −104.209 | − | 180.495i | −0.124113 | − | 0.214971i | 0.797273 | − | 0.603619i | \(-0.206275\pi\) |
−0.921386 | + | 0.388649i | \(0.872942\pi\) | |||||||
\(90\) | 459.110 | − | 759.669i | 0.537717 | − | 0.889735i | ||||
\(91\) | 998.467 | + | 587.903i | 1.15020 | + | 0.677242i | ||||
\(92\) | −260.026 | − | 450.378i | −0.294669 | − | 0.510382i | ||||
\(93\) | −496.486 | + | 280.058i | −0.553583 | + | 0.312266i | ||||
\(94\) | 652.368 | + | 1129.94i | 0.715816 | + | 1.23983i | ||||
\(95\) | −221.543 | − | 383.723i | −0.239261 | − | 0.414412i | ||||
\(96\) | −651.227 | + | 367.345i | −0.692350 | + | 0.390542i | ||||
\(97\) | −56.7013 | − | 98.2095i | −0.0593520 | − | 0.102801i | 0.834823 | − | 0.550519i | \(-0.185570\pi\) |
−0.894175 | + | 0.447718i | \(0.852237\pi\) | |||||||
\(98\) | −595.588 | + | 992.024i | −0.613913 | + | 1.02255i | ||||
\(99\) | −1050.42 | − | 21.0297i | −1.06638 | − | 0.0213492i | ||||
\(100\) | 50.7475 | + | 87.8972i | 0.0507475 | + | 0.0878972i | ||||
\(101\) | 1078.01 | 1.06204 | 0.531019 | − | 0.847360i | \(-0.321809\pi\) | ||||
0.531019 | + | 0.847360i | \(0.321809\pi\) | |||||||
\(102\) | −1934.72 | + | 1091.34i | −1.87809 | + | 1.05940i | ||||
\(103\) | 1710.37 | 1.63619 | 0.818097 | − | 0.575080i | \(-0.195029\pi\) | ||||
0.818097 | + | 0.575080i | \(0.195029\pi\) | |||||||
\(104\) | −487.539 | + | 844.442i | −0.459684 | + | 0.796196i | ||||
\(105\) | 937.671 | + | 17.4031i | 0.871498 | + | 0.0161749i | ||||
\(106\) | 450.745 | + | 780.713i | 0.413021 | + | 0.715373i | ||||
\(107\) | −410.398 | − | 710.830i | −0.370791 | − | 0.642229i | 0.618896 | − | 0.785473i | \(-0.287580\pi\) |
−0.989687 | + | 0.143244i | \(0.954247\pi\) | |||||||
\(108\) | 417.594 | − | 224.660i | 0.372065 | − | 0.200166i | ||||
\(109\) | 1064.55 | − | 1843.85i | 0.935460 | − | 1.62026i | 0.161648 | − | 0.986848i | \(-0.448319\pi\) |
0.773812 | − | 0.633416i | \(-0.218348\pi\) | |||||||
\(110\) | −639.621 | + | 1107.86i | −0.554414 | + | 0.960273i | ||||
\(111\) | 1307.78 | − | 737.696i | 1.11828 | − | 0.630802i | ||||
\(112\) | −1270.61 | − | 748.140i | −1.07197 | − | 0.631183i | ||||
\(113\) | 203.179 | − | 351.917i | 0.169146 | − | 0.292970i | −0.768974 | − | 0.639280i | \(-0.779232\pi\) |
0.938120 | + | 0.346311i | \(0.112566\pi\) | |||||||
\(114\) | 7.97660 | − | 796.932i | 0.00655331 | − | 0.654732i | ||||
\(115\) | −1499.46 | −1.21587 | ||||||||
\(116\) | 92.8314 | − | 160.789i | 0.0743033 | − | 0.128697i | ||||
\(117\) | 873.719 | − | 1445.70i | 0.690388 | − | 1.14235i | ||||
\(118\) | −1304.64 | −1.01781 | ||||||||
\(119\) | −2022.40 | − | 1190.80i | −1.55793 | − | 0.917316i | ||||
\(120\) | −7.89899 | + | 789.178i | −0.00600897 | + | 0.600348i | ||||
\(121\) | 183.168 | 0.137617 | ||||||||
\(122\) | 60.1846 | + | 104.243i | 0.0446628 | + | 0.0773582i | ||||
\(123\) | 101.115 | + | 59.7363i | 0.0741242 | + | 0.0437906i | ||||
\(124\) | −185.392 | + | 321.109i | −0.134264 | + | 0.232552i | ||||
\(125\) | 1510.80 | 1.08104 | ||||||||
\(126\) | 1436.18 | + | 884.815i | 1.01544 | + | 0.625600i | ||||
\(127\) | −2300.05 | −1.60706 | −0.803529 | − | 0.595266i | \(-0.797047\pi\) | ||||
−0.803529 | + | 0.595266i | \(0.797047\pi\) | |||||||
\(128\) | 831.131 | − | 1439.56i | 0.573924 | − | 0.994066i | ||||
\(129\) | 216.739 | − | 122.259i | 0.147929 | − | 0.0834440i | ||||
\(130\) | −1028.39 | − | 1781.22i | −0.693812 | − | 1.20172i | ||||
\(131\) | −583.702 | −0.389300 | −0.194650 | − | 0.980873i | \(-0.562357\pi\) | ||||
−0.194650 | + | 0.980873i | \(0.562357\pi\) | |||||||
\(132\) | −595.234 | + | 335.761i | −0.392489 | + | 0.221395i | ||||
\(133\) | 732.810 | − | 414.776i | 0.477764 | − | 0.270418i | ||||
\(134\) | −120.440 | −0.0776449 | ||||||||
\(135\) | 41.0469 | − | 1366.61i | 0.0261685 | − | 0.871255i | ||||
\(136\) | 987.513 | − | 1710.42i | 0.622636 | − | 1.07844i | ||||
\(137\) | −168.798 | −0.105266 | −0.0526328 | − | 0.998614i | \(-0.516761\pi\) | ||||
−0.0526328 | + | 0.998614i | \(0.516761\pi\) | |||||||
\(138\) | −2322.11 | − | 1371.84i | −1.43240 | − | 0.846223i | ||||
\(139\) | 671.306 | − | 1162.74i | 0.409636 | − | 0.709511i | −0.585213 | − | 0.810880i | \(-0.698989\pi\) |
0.994849 | + | 0.101369i | \(0.0323223\pi\) | |||||||
\(140\) | 530.889 | − | 300.487i | 0.320488 | − | 0.181399i | ||||
\(141\) | 1730.32 | + | 1022.23i | 1.03347 | + | 0.610547i | ||||
\(142\) | −246.858 | + | 427.571i | −0.145887 | + | 0.252683i | ||||
\(143\) | −1217.24 | + | 2108.33i | −0.711826 | + | 1.23292i | ||||
\(144\) | −1111.86 | + | 1839.74i | −0.643436 | + | 1.06466i | ||||
\(145\) | −267.660 | − | 463.601i | −0.153296 | − | 0.265517i | ||||
\(146\) | 1230.81 | + | 2131.82i | 0.697688 | + | 1.20843i | ||||
\(147\) | −48.3059 | + | 1781.63i | −0.0271034 | + | 0.999633i | ||||
\(148\) | 488.337 | − | 845.825i | 0.271223 | − | 0.469773i | ||||
\(149\) | −721.359 | −0.396618 | −0.198309 | − | 0.980140i | \(-0.563545\pi\) | ||||
−0.198309 | + | 0.980140i | \(0.563545\pi\) | |||||||
\(150\) | 453.190 | + | 267.733i | 0.246685 | + | 0.145735i | ||||
\(151\) | −2867.01 | −1.54513 | −0.772563 | − | 0.634938i | \(-0.781026\pi\) | ||||
−0.772563 | + | 0.634938i | \(0.781026\pi\) | |||||||
\(152\) | 354.307 | + | 613.677i | 0.189066 | + | 0.327472i | ||||
\(153\) | −1769.72 | + | 2928.28i | −0.935123 | + | 1.54730i | ||||
\(154\) | −2094.93 | − | 1233.51i | −1.09620 | − | 0.645447i | ||||
\(155\) | 534.540 | + | 925.850i | 0.277002 | + | 0.479781i | ||||
\(156\) | 10.9973 | − | 1098.72i | 0.00564415 | − | 0.563899i | ||||
\(157\) | 375.097 | + | 649.686i | 0.190675 | + | 0.330259i | 0.945474 | − | 0.325697i | \(-0.105599\pi\) |
−0.754799 | + | 0.655956i | \(0.772266\pi\) | |||||||
\(158\) | 845.632 | + | 1464.68i | 0.425790 | + | 0.737491i | ||||
\(159\) | 1195.54 | + | 706.294i | 0.596306 | + | 0.352282i | ||||
\(160\) | 701.141 | + | 1214.41i | 0.346438 | + | 0.600048i | ||||
\(161\) | 24.3610 | − | 2849.51i | 0.0119249 | − | 1.39486i | ||||
\(162\) | 1313.87 | − | 2078.83i | 0.637204 | − | 1.00820i | ||||
\(163\) | 1400.06 | + | 2424.98i | 0.672769 | + | 1.16527i | 0.977116 | + | 0.212709i | \(0.0682285\pi\) |
−0.304347 | + | 0.952561i | \(0.598438\pi\) | |||||||
\(164\) | 76.3926 | 0.0363735 | ||||||||
\(165\) | −19.7215 | + | 1970.35i | −0.00930495 | + | 0.929646i | ||||
\(166\) | 1144.41 | 0.535082 | ||||||||
\(167\) | −0.0790177 | + | 0.136863i | −3.66142e−5 | + | 6.34176e-5i | −0.866044 | − | 0.499968i | \(-0.833345\pi\) |
0.866007 | + | 0.500032i | \(0.166678\pi\) | |||||||
\(168\) | −1499.59 | − | 27.8322i | −0.688666 | − | 0.0127816i | ||||
\(169\) | −858.594 | − | 1487.13i | −0.390803 | − | 0.676890i | ||||
\(170\) | 2083.01 | + | 3607.87i | 0.939760 | + | 1.62771i | ||||
\(171\) | −592.394 | − | 1075.20i | −0.264921 | − | 0.480834i | ||||
\(172\) | 80.9324 | − | 140.179i | 0.0358781 | − | 0.0621427i | ||||
\(173\) | −631.310 | + | 1093.46i | −0.277443 | + | 0.480545i | −0.970748 | − | 0.240099i | \(-0.922820\pi\) |
0.693306 | + | 0.720644i | \(0.256154\pi\) | |||||||
\(174\) | 9.63705 | − | 962.825i | 0.00419875 | − | 0.419492i | ||||
\(175\) | −4.75436 | + | 556.119i | −0.00205369 | + | 0.240221i | ||||
\(176\) | 1549.01 | − | 2682.97i | 0.663416 | − | 1.14907i | ||||
\(177\) | −1750.31 | + | 987.317i | −0.743284 | + | 0.419273i | ||||
\(178\) | −703.078 | −0.296056 | ||||||||
\(179\) | 1457.18 | − | 2523.91i | 0.608462 | − | 1.05389i | −0.383032 | − | 0.923735i | \(-0.625120\pi\) |
0.991494 | − | 0.130152i | \(-0.0415465\pi\) | |||||||
\(180\) | −429.164 | − | 778.937i | −0.177711 | − | 0.322547i | ||||
\(181\) | 870.971 | 0.357673 | 0.178836 | − | 0.983879i | \(-0.442767\pi\) | ||||
0.178836 | + | 0.983879i | \(0.442767\pi\) | |||||||
\(182\) | 3401.66 | − | 1925.36i | 1.38543 | − | 0.784162i | ||||
\(183\) | 159.632 | + | 94.3062i | 0.0644827 | + | 0.0380946i | ||||
\(184\) | 2398.05 | 0.960795 | ||||||||
\(185\) | −1408.02 | − | 2438.76i | −0.559565 | − | 0.969196i | ||||
\(186\) | −19.2460 | + | 1922.84i | −0.00758702 | + | 0.758009i | ||||
\(187\) | 2465.54 | − | 4270.44i | 0.964160 | − | 1.66997i | ||||
\(188\) | 1307.26 | 0.507135 | ||||||||
\(189\) | 2596.39 | + | 100.206i | 0.999256 | + | 0.0385658i | ||||
\(190\) | −1494.71 | −0.570725 | ||||||||
\(191\) | −1588.84 | + | 2751.95i | −0.601907 | + | 1.04253i | 0.390625 | + | 0.920550i | \(0.372259\pi\) |
−0.992532 | + | 0.121983i | \(0.961075\pi\) | |||||||
\(192\) | 7.87969 | − | 787.249i | 0.00296181 | − | 0.295911i | ||||
\(193\) | 851.492 | + | 1474.83i | 0.317574 | + | 0.550054i | 0.979981 | − | 0.199090i | \(-0.0637985\pi\) |
−0.662407 | + | 0.749144i | \(0.730465\pi\) | |||||||
\(194\) | −382.554 | −0.141576 | ||||||||
\(195\) | −2727.66 | − | 1611.43i | −1.00170 | − | 0.591779i | ||||
\(196\) | 562.408 | + | 1013.76i | 0.204959 | + | 0.369446i | ||||
\(197\) | 254.870 | 0.0921763 | 0.0460881 | − | 0.998937i | \(-0.485324\pi\) | ||||
0.0460881 | + | 0.998937i | \(0.485324\pi\) | |||||||
\(198\) | −1833.19 | + | 3033.30i | −0.657976 | + | 1.08872i | ||||
\(199\) | −386.703 | + | 669.790i | −0.137752 | + | 0.238594i | −0.926645 | − | 0.375937i | \(-0.877321\pi\) |
0.788893 | + | 0.614530i | \(0.210654\pi\) | |||||||
\(200\) | −468.010 | −0.165466 | ||||||||
\(201\) | −161.582 | + | 91.1456i | −0.0567022 | + | 0.0319846i | ||||
\(202\) | 1818.28 | − | 3149.36i | 0.633337 | − | 1.09697i | ||||
\(203\) | 885.355 | − | 501.118i | 0.306107 | − | 0.173259i | ||||
\(204\) | −22.2751 | + | 2225.47i | −0.00764494 | + | 0.763795i | ||||
\(205\) | 110.131 | − | 190.753i | 0.0375214 | − | 0.0649890i | ||||
\(206\) | 2884.90 | − | 4996.79i | 0.975730 | − | 1.69001i | ||||
\(207\) | −4153.52 | − | 83.1546i | −1.39463 | − | 0.0279210i | ||||
\(208\) | 2490.51 | + | 4313.69i | 0.830221 | + | 1.43798i | ||||
\(209\) | 884.602 | + | 1532.18i | 0.292771 | + | 0.507095i | ||||
\(210\) | 1632.42 | − | 2710.02i | 0.536417 | − | 0.890519i | ||||
\(211\) | −1834.55 | + | 3177.54i | −0.598558 | + | 1.03673i | 0.394476 | + | 0.918906i | \(0.370926\pi\) |
−0.993034 | + | 0.117827i | \(0.962407\pi\) | |||||||
\(212\) | 903.230 | 0.292614 | ||||||||
\(213\) | −7.61141 | + | 760.445i | −0.00244847 | + | 0.244624i | ||||
\(214\) | −2768.88 | −0.884472 | ||||||||
\(215\) | −233.352 | − | 404.177i | −0.0740207 | − | 0.128208i | ||||
\(216\) | −65.6451 | + | 2185.59i | −0.0206786 | + | 0.688474i | ||||
\(217\) | −1768.13 | + | 1000.77i | −0.553126 | + | 0.313074i | ||||
\(218\) | −3591.16 | − | 6220.07i | −1.11571 | − | 1.93246i | ||||
\(219\) | 3264.56 | + | 1928.62i | 1.00730 | + | 0.595086i | ||||
\(220\) | 640.857 | + | 1110.00i | 0.196393 | + | 0.340163i | ||||
\(221\) | 3964.11 | + | 6866.03i | 1.20658 | + | 2.08986i | ||||
\(222\) | 50.6955 | − | 5064.91i | 0.0153264 | − | 1.53124i | ||||
\(223\) | 1002.18 | + | 1735.83i | 0.300947 | + | 0.521256i | 0.976351 | − | 0.216192i | \(-0.0693639\pi\) |
−0.675404 | + | 0.737448i | \(0.736031\pi\) | |||||||
\(224\) | −2319.21 | + | 1312.69i | −0.691779 | + | 0.391552i | ||||
\(225\) | 810.613 | + | 16.2287i | 0.240182 | + | 0.00480850i | ||||
\(226\) | −685.409 | − | 1187.16i | −0.201738 | − | 0.349420i | ||||
\(227\) | −3396.02 | −0.992958 | −0.496479 | − | 0.868049i | \(-0.665374\pi\) | ||||
−0.496479 | + | 0.868049i | \(0.665374\pi\) | |||||||
\(228\) | −687.500 | − | 406.157i | −0.199696 | − | 0.117975i | ||||
\(229\) | −5153.79 | −1.48721 | −0.743606 | − | 0.668618i | \(-0.766886\pi\) | ||||
−0.743606 | + | 0.668618i | \(0.766886\pi\) | |||||||
\(230\) | −2529.15 | + | 4380.62i | −0.725076 | + | 1.25587i | ||||
\(231\) | −3744.05 | − | 69.4891i | −1.06641 | − | 0.0197924i | ||||
\(232\) | 428.061 | + | 741.424i | 0.121136 | + | 0.209814i | ||||
\(233\) | −3053.12 | − | 5288.16i | −0.858441 | − | 1.48686i | −0.873416 | − | 0.486976i | \(-0.838100\pi\) |
0.0149746 | − | 0.999888i | \(-0.495233\pi\) | |||||||
\(234\) | −2749.86 | − | 4991.02i | −0.768222 | − | 1.39433i | ||||
\(235\) | 1884.60 | − | 3264.22i | 0.523139 | − | 0.906104i | ||||
\(236\) | −653.581 | + | 1132.03i | −0.180273 | + | 0.312242i | ||||
\(237\) | 2242.93 | + | 1325.06i | 0.614742 | + | 0.363173i | ||||
\(238\) | −6890.08 | + | 3899.84i | −1.87655 | + | 1.06214i | ||||
\(239\) | −1301.70 | + | 2254.62i | −0.352302 | + | 0.610205i | −0.986652 | − | 0.162840i | \(-0.947934\pi\) |
0.634350 | + | 0.773046i | \(0.281268\pi\) | |||||||
\(240\) | 3471.10 | + | 2050.64i | 0.933578 | + | 0.551533i | ||||
\(241\) | 2322.27 | 0.620707 | 0.310354 | − | 0.950621i | \(-0.399553\pi\) | ||||
0.310354 | + | 0.950621i | \(0.399553\pi\) | |||||||
\(242\) | 308.950 | − | 535.118i | 0.0820665 | − | 0.142143i | ||||
\(243\) | 189.487 | − | 3783.25i | 0.0500232 | − | 0.998748i | ||||
\(244\) | 120.602 | 0.0316423 | ||||||||
\(245\) | 3342.16 | + | 57.1495i | 0.871521 | + | 0.0149026i | ||||
\(246\) | 345.070 | − | 194.647i | 0.0894343 | − | 0.0504482i | ||||
\(247\) | −2844.54 | −0.732768 | ||||||||
\(248\) | −854.874 | − | 1480.69i | −0.218889 | − | 0.379127i | ||||
\(249\) | 1535.35 | − | 866.060i | 0.390757 | − | 0.220419i | ||||
\(250\) | 2548.29 | − | 4413.76i | 0.644671 | − | 1.11660i | ||||
\(251\) | −476.889 | −0.119924 | −0.0599621 | − | 0.998201i | \(-0.519098\pi\) | ||||
−0.0599621 | + | 0.998201i | \(0.519098\pi\) | |||||||
\(252\) | 1487.23 | − | 802.910i | 0.371773 | − | 0.200709i | ||||
\(253\) | 5987.23 | 1.48780 | ||||||||
\(254\) | −3879.51 | + | 6719.51i | −0.958354 | + | 1.65992i | ||||
\(255\) | 5524.90 | + | 3263.96i | 1.35679 | + | 0.801558i | ||||
\(256\) | −2197.69 | − | 3806.52i | −0.536546 | − | 0.929326i | ||||
\(257\) | 3736.85 | 0.906997 | 0.453499 | − | 0.891257i | \(-0.350176\pi\) | ||||
0.453499 | + | 0.891257i | \(0.350176\pi\) | |||||||
\(258\) | 8.40179 | − | 839.411i | 0.00202741 | − | 0.202556i | ||||
\(259\) | 4657.39 | − | 2636.12i | 1.11736 | − | 0.632433i | ||||
\(260\) | −2060.75 | −0.491546 | ||||||||
\(261\) | −715.710 | − | 1299.02i | −0.169737 | − | 0.308074i | ||||
\(262\) | −984.535 | + | 1705.26i | −0.232156 | + | 0.402105i | ||||
\(263\) | 1009.13 | 0.236600 | 0.118300 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118300 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(264\) | 31.5400 | − | 3151.12i | 0.00735286 | − | 0.734615i | ||||
\(265\) | 1302.14 | − | 2255.37i | 0.301848 | − | 0.522816i | ||||
\(266\) | 24.2838 | − | 2840.48i | 0.00559749 | − | 0.654741i | ||||
\(267\) | −943.251 | + | 532.070i | −0.216202 | + | 0.121956i | ||||
\(268\) | −60.3362 | + | 104.505i | −0.0137523 | + | 0.0238197i | ||||
\(269\) | −4069.36 | + | 7048.33i | −0.922354 | + | 1.59756i | −0.126591 | + | 0.991955i | \(0.540403\pi\) |
−0.795763 | + | 0.605608i | \(0.792930\pi\) | |||||||
\(270\) | −3923.28 | − | 2425.00i | −0.884308 | − | 0.546595i | ||||
\(271\) | 3384.69 | + | 5862.46i | 0.758692 | + | 1.31409i | 0.943518 | + | 0.331321i | \(0.107494\pi\) |
−0.184826 | + | 0.982771i | \(0.559172\pi\) | |||||||
\(272\) | −5044.55 | − | 8737.41i | −1.12452 | − | 1.94773i | ||||
\(273\) | 3106.61 | − | 5157.35i | 0.688720 | − | 1.14336i | ||||
\(274\) | −284.713 | + | 493.137i | −0.0627742 | + | 0.108728i | ||||
\(275\) | −1168.49 | −0.256227 | ||||||||
\(276\) | −2353.64 | + | 1327.64i | −0.513306 | + | 0.289546i | ||||
\(277\) | −6519.00 | −1.41404 | −0.707019 | − | 0.707194i | \(-0.749961\pi\) | ||||
−0.707019 | + | 0.707194i | \(0.749961\pi\) | |||||||
\(278\) | −2264.59 | − | 3922.39i | −0.488566 | − | 0.846221i | ||||
\(279\) | 1429.33 | + | 2594.25i | 0.306709 | + | 0.556680i | ||||
\(280\) | −24.0475 | + | 2812.84i | −0.00513254 | + | 0.600356i | ||||
\(281\) | −3138.53 | − | 5436.10i | −0.666296 | − | 1.15406i | −0.978932 | − | 0.204185i | \(-0.934545\pi\) |
0.312636 | − | 0.949873i | \(-0.398788\pi\) | |||||||
\(282\) | 5904.95 | − | 3330.87i | 1.24693 | − | 0.703371i | ||||
\(283\) | −403.166 | − | 698.304i | −0.0846845 | − | 0.146678i | 0.820572 | − | 0.571543i | \(-0.193655\pi\) |
−0.905257 | + | 0.424865i | \(0.860322\pi\) | |||||||
\(284\) | 247.335 | + | 428.397i | 0.0516783 | + | 0.0895094i | ||||
\(285\) | −2005.31 | + | 1131.16i | −0.416786 | + | 0.235101i | ||||
\(286\) | 4106.27 | + | 7112.27i | 0.848982 | + | 1.47048i | ||||
\(287\) | 360.709 | + | 212.387i | 0.0741880 | + | 0.0436823i | ||||
\(288\) | 1874.82 | + | 3402.81i | 0.383593 | + | 0.696224i | ||||
\(289\) | −5572.82 | − | 9652.42i | −1.13430 | − | 1.96467i | ||||
\(290\) | −1805.86 | −0.365668 | ||||||||
\(291\) | −513.235 | + | 289.506i | −0.103390 | + | 0.0583201i | ||||
\(292\) | 2466.37 | 0.494293 | ||||||||
\(293\) | 3084.92 | − | 5343.24i | 0.615095 | − | 1.06538i | −0.375272 | − | 0.926915i | \(-0.622451\pi\) |
0.990368 | − | 0.138462i | \(-0.0442158\pi\) | |||||||
\(294\) | 5123.48 | + | 3146.21i | 1.01635 | + | 0.624117i | ||||
\(295\) | 1884.46 | + | 3263.99i | 0.371924 | + | 0.644192i | ||||
\(296\) | 2251.80 | + | 3900.24i | 0.442174 | + | 0.765868i | ||||
\(297\) | −163.897 | + | 5456.78i | −0.0320211 | + | 1.06611i | ||||
\(298\) | −1216.72 | + | 2107.42i | −0.236519 | + | 0.409664i | ||||
\(299\) | −4813.16 | + | 8336.63i | −0.930943 | + | 1.61244i | ||||
\(300\) | 459.343 | − | 259.107i | 0.0884007 | − | 0.0498652i | ||||
\(301\) | 771.871 | − | 436.885i | 0.147807 | − | 0.0836599i | ||||
\(302\) | −4835.81 | + | 8375.87i | −0.921423 | + | 1.59595i | ||||
\(303\) | 56.0633 | − | 5601.21i | 0.0106296 | − | 1.06198i | ||||
\(304\) | 3619.84 | 0.682933 | ||||||||
\(305\) | 173.865 | − | 301.143i | 0.0326409 | − | 0.0565357i | ||||
\(306\) | 5569.86 | + | 10109.3i | 1.04055 | + | 1.88860i | ||||
\(307\) | 4381.77 | 0.814596 | 0.407298 | − | 0.913295i | \(-0.366471\pi\) | ||||
0.407298 | + | 0.913295i | \(0.366471\pi\) | |||||||
\(308\) | −2119.80 | + | 1199.82i | −0.392165 | + | 0.221968i | ||||
\(309\) | 88.9504 | − | 8886.91i | 0.0163761 | − | 1.63611i | ||||
\(310\) | 3606.45 | 0.660750 | ||||||||
\(311\) | 4231.30 | + | 7328.83i | 0.771495 | + | 1.33627i | 0.936743 | + | 0.350017i | \(0.113824\pi\) |
−0.165248 | + | 0.986252i | \(0.552843\pi\) | |||||||
\(312\) | 4362.27 | + | 2577.12i | 0.791555 | + | 0.467630i | ||||
\(313\) | −2910.23 | + | 5040.67i | −0.525547 | + | 0.910273i | 0.474011 | + | 0.880519i | \(0.342806\pi\) |
−0.999557 | + | 0.0297543i | \(0.990528\pi\) | |||||||
\(314\) | 2530.71 | 0.454829 | ||||||||
\(315\) | 139.189 | − | 4871.13i | 0.0248966 | − | 0.871292i | ||||
\(316\) | 1694.53 | 0.301661 | ||||||||
\(317\) | 3207.59 | − | 5555.71i | 0.568316 | − | 0.984353i | −0.428416 | − | 0.903582i | \(-0.640928\pi\) |
0.996733 | − | 0.0807714i | \(-0.0257384\pi\) | |||||||
\(318\) | 4079.94 | − | 2301.42i | 0.719471 | − | 0.405840i | ||||
\(319\) | 1068.75 | + | 1851.12i | 0.187581 | + | 0.324900i | ||||
\(320\) | −1476.55 | −0.257943 | ||||||||
\(321\) | −3714.74 | + | 2095.41i | −0.645908 | + | 0.364345i | ||||
\(322\) | −8283.65 | − | 4877.46i | −1.43363 | − | 0.844131i | ||||
\(323\) | 5761.63 | 0.992526 | ||||||||
\(324\) | −1145.59 | − | 2181.46i | −0.196432 | − | 0.374050i | ||||
\(325\) | 939.350 | − | 1627.00i | 0.160325 | − | 0.277692i | ||||
\(326\) | 9445.98 | 1.60480 | ||||||||
\(327\) | −9525.08 | − | 5627.16i | −1.61082 | − | 0.951630i | ||||
\(328\) | −176.130 | + | 305.065i | −0.0296498 | + | 0.0513549i | ||||
\(329\) | 6172.57 | + | 3634.44i | 1.03436 | + | 0.609038i | ||||
\(330\) | 5723.04 | + | 3381.02i | 0.954676 | + | 0.563997i | ||||
\(331\) | 414.418 | − | 717.794i | 0.0688172 | − | 0.119195i | −0.829564 | − | 0.558412i | \(-0.811411\pi\) |
0.898381 | + | 0.439217i | \(0.144744\pi\) | |||||||
\(332\) | 573.311 | − | 993.004i | 0.0947727 | − | 0.164151i | ||||
\(333\) | −3764.97 | − | 6833.46i | −0.619578 | − | 1.12454i | ||||
\(334\) | 0.266559 | + | 0.461694i | 4.36691e−5 | + | 7.56371e-5i | ||||
\(335\) | 173.967 | + | 301.320i | 0.0283726 | + | 0.0491428i | ||||
\(336\) | −3953.33 | + | 6563.02i | −0.641881 | + | 1.06560i | ||||
\(337\) | −2906.88 | + | 5034.86i | −0.469875 | + | 0.813847i | −0.999407 | − | 0.0344432i | \(-0.989034\pi\) |
0.529532 | + | 0.848290i | \(0.322368\pi\) | |||||||
\(338\) | −5792.79 | −0.932207 | ||||||||
\(339\) | −1817.96 | − | 1074.00i | −0.291262 | − | 0.172070i | ||||
\(340\) | 4174.06 | 0.665794 | ||||||||
\(341\) | −2134.37 | − | 3696.85i | −0.338953 | − | 0.587083i | ||||
\(342\) | −4140.36 | − | 82.8911i | −0.654634 | − | 0.0131060i | ||||
\(343\) | −162.903 | + | 6350.36i | −0.0256441 | + | 0.999671i | ||||
\(344\) | 373.193 | + | 646.389i | 0.0584919 | + | 0.101311i | ||||
\(345\) | −77.9816 | + | 7791.04i | −0.0121692 | + | 1.21581i | ||||
\(346\) | 2129.67 | + | 3688.70i | 0.330901 | + | 0.573137i | ||||
\(347\) | −1661.46 | − | 2877.74i | −0.257038 | − | 0.445202i | 0.708409 | − | 0.705802i | \(-0.249413\pi\) |
−0.965447 | + | 0.260600i | \(0.916080\pi\) | |||||||
\(348\) | −830.613 | − | 490.704i | −0.127947 | − | 0.0755877i | ||||
\(349\) | −376.201 | − | 651.599i | −0.0577008 | − | 0.0999407i | 0.835732 | − | 0.549137i | \(-0.185044\pi\) |
−0.893433 | + | 0.449197i | \(0.851710\pi\) | |||||||
\(350\) | 1616.66 | + | 951.900i | 0.246898 | + | 0.145375i | ||||
\(351\) | −7466.28 | − | 4614.94i | −1.13539 | − | 0.701787i | ||||
\(352\) | −2799.60 | − | 4849.05i | −0.423918 | − | 0.734248i | ||||
\(353\) | −2213.65 | −0.333770 | −0.166885 | − | 0.985976i | \(-0.553371\pi\) | ||||
−0.166885 | + | 0.985976i | \(0.553371\pi\) | |||||||
\(354\) | −67.8498 | + | 6778.78i | −0.0101869 | + | 1.01776i | ||||
\(355\) | 1426.28 | 0.213236 | ||||||||
\(356\) | −352.218 | + | 610.060i | −0.0524368 | + | 0.0908233i | ||||
\(357\) | −6292.45 | + | 10446.3i | −0.932863 | + | 1.54867i | ||||
\(358\) | −4915.67 | − | 8514.19i | −0.725702 | − | 1.25695i | ||||
\(359\) | −435.090 | − | 753.599i | −0.0639643 | − | 0.110789i | 0.832270 | − | 0.554371i | \(-0.187041\pi\) |
−0.896234 | + | 0.443581i | \(0.853708\pi\) | |||||||
\(360\) | 4100.07 | + | 82.0846i | 0.600257 | + | 0.0120173i | ||||
\(361\) | 2395.90 | − | 4149.82i | 0.349308 | − | 0.605018i | ||||
\(362\) | 1469.07 | − | 2544.51i | 0.213295 | − | 0.369438i | ||||
\(363\) | 9.52590 | − | 951.720i | 0.00137736 | − | 0.137610i | ||||
\(364\) | 33.4799 | − | 3916.15i | 0.00482094 | − | 0.563907i | ||||
\(365\) | 3555.63 | − | 6158.54i | 0.509892 | − | 0.883158i | ||||
\(366\) | 544.764 | − | 307.292i | 0.0778014 | − | 0.0438863i | ||||
\(367\) | −2528.67 | −0.359660 | −0.179830 | − | 0.983698i | \(-0.557555\pi\) | ||||
−0.179830 | + | 0.983698i | \(0.557555\pi\) | |||||||
\(368\) | 6125.01 | − | 10608.8i | 0.867631 | − | 1.50278i | ||||
\(369\) | 315.642 | − | 522.278i | 0.0445303 | − | 0.0736822i | ||||
\(370\) | −9499.66 | −1.33477 | ||||||||
\(371\) | 4264.85 | + | 2511.17i | 0.596819 | + | 0.351411i | ||||
\(372\) | 1658.80 | + | 979.977i | 0.231196 | + | 0.136585i | ||||
\(373\) | 5370.58 | 0.745518 | 0.372759 | − | 0.927928i | \(-0.378412\pi\) | ||||
0.372759 | + | 0.927928i | \(0.378412\pi\) | |||||||
\(374\) | −8317.28 | − | 14406.0i | −1.14994 | − | 1.99175i | ||||
\(375\) | 78.5715 | − | 7849.98i | 0.0108198 | − | 1.08099i | ||||
\(376\) | −3013.99 | + | 5220.38i | −0.413390 | + | 0.716012i | ||||
\(377\) | −3436.67 | −0.469490 | ||||||||
\(378\) | 4672.10 | − | 7416.23i | 0.635732 | − | 1.00913i | ||||
\(379\) | −9923.53 | −1.34495 | −0.672477 | − | 0.740118i | \(-0.734770\pi\) | ||||
−0.672477 | + | 0.740118i | \(0.734770\pi\) | |||||||
\(380\) | −748.798 | + | 1296.96i | −0.101086 | + | 0.175085i | ||||
\(381\) | −119.617 | + | 11950.8i | −0.0160845 | + | 1.60698i | ||||
\(382\) | 5359.81 | + | 9283.46i | 0.717884 | + | 1.24341i | ||||
\(383\) | 11187.6 | 1.49259 | 0.746295 | − | 0.665616i | \(-0.231831\pi\) | ||||
0.746295 | + | 0.665616i | \(0.231831\pi\) | |||||||
\(384\) | −7436.58 | − | 4393.33i | −0.988272 | − | 0.583845i | ||||
\(385\) | −60.0397 | + | 7022.87i | −0.00794781 | + | 0.929658i | ||||
\(386\) | 5744.87 | 0.757529 | ||||||||
\(387\) | −623.971 | − | 1132.51i | −0.0819593 | − | 0.148757i | ||||
\(388\) | −191.646 | + | 331.941i | −0.0250757 | + | 0.0434324i | ||||
\(389\) | −1683.37 | −0.219410 | −0.109705 | − | 0.993964i | \(-0.534991\pi\) | ||||
−0.109705 | + | 0.993964i | \(0.534991\pi\) | |||||||
\(390\) | −9308.51 | + | 5250.76i | −1.20860 | + | 0.681750i | ||||
\(391\) | 9749.08 | − | 16885.9i | 1.26095 | − | 2.18403i | ||||
\(392\) | −5345.02 | − | 91.3976i | −0.688684 | − | 0.0117762i | ||||
\(393\) | −30.3563 | + | 3032.85i | −0.00389636 | + | 0.389280i | ||||
\(394\) | 429.891 | − | 744.593i | 0.0549685 | − | 0.0952083i | ||||
\(395\) | 2442.91 | − | 4231.25i | 0.311180 | − | 0.538980i | ||||
\(396\) | 1713.62 | + | 3110.23i | 0.217456 | + | 0.394685i | ||||
\(397\) | −1775.41 | − | 3075.09i | −0.224446 | − | 0.388752i | 0.731707 | − | 0.681619i | \(-0.238724\pi\) |
−0.956153 | + | 0.292867i | \(0.905391\pi\) | |||||||
\(398\) | 1304.51 | + | 2259.48i | 0.164295 | + | 0.284566i | ||||
\(399\) | −2117.02 | − | 3829.17i | −0.265623 | − | 0.480447i | ||||
\(400\) | −1195.38 | + | 2070.45i | −0.149422 | + | 0.258806i | ||||
\(401\) | −3801.66 | −0.473431 | −0.236716 | − | 0.971579i | \(-0.576071\pi\) | ||||
−0.236716 | + | 0.971579i | \(0.576071\pi\) | |||||||
\(402\) | −6.26365 | + | 625.793i | −0.000777120 | + | 0.0776411i | ||||
\(403\) | 6863.32 | 0.848354 | ||||||||
\(404\) | −1821.80 | − | 3155.44i | −0.224351 | − | 0.388587i | ||||
\(405\) | −7098.65 | − | 284.348i | −0.870950 | − | 0.0348873i | ||||
\(406\) | 29.3388 | − | 3431.77i | 0.00358636 | − | 0.419498i | ||||
\(407\) | 5622.11 | + | 9737.78i | 0.684712 | + | 1.18596i | ||||
\(408\) | −8835.82 | − | 5219.97i | −1.07215 | − | 0.633399i | ||||
\(409\) | −6622.39 | − | 11470.3i | −0.800626 | − | 1.38673i | −0.919204 | − | 0.393781i | \(-0.871167\pi\) |
0.118578 | − | 0.992945i | \(-0.462166\pi\) | |||||||
\(410\) | −371.518 | − | 643.488i | −0.0447511 | − | 0.0775112i | ||||
\(411\) | −8.77858 | + | 877.056i | −0.00105357 | + | 0.105260i | ||||
\(412\) | −2890.47 | − | 5006.44i | −0.345639 | − | 0.598664i | ||||
\(413\) | −6233.35 | + | 3528.12i | −0.742671 | + | 0.420357i | ||||
\(414\) | −7248.70 | + | 11994.1i | −0.860517 | + | 1.42386i | ||||
\(415\) | −1653.02 | − | 2863.12i | −0.195527 | − | 0.338663i | ||||
\(416\) | 9002.44 | 1.06101 | ||||||||
\(417\) | −6006.54 | − | 3548.50i | −0.705376 | − | 0.416717i | ||||
\(418\) | 5968.26 | 0.698367 | ||||||||
\(419\) | 1435.52 | − | 2486.39i | 0.167374 | − | 0.289900i | −0.770122 | − | 0.637897i | \(-0.779805\pi\) |
0.937496 | + | 0.347997i | \(0.113138\pi\) | |||||||
\(420\) | −1533.69 | − | 2774.07i | −0.178182 | − | 0.322288i | ||||
\(421\) | −441.098 | − | 764.004i | −0.0510637 | − | 0.0884449i | 0.839364 | − | 0.543570i | \(-0.182928\pi\) |
−0.890427 | + | 0.455125i | \(0.849594\pi\) | |||||||
\(422\) | 6188.70 | + | 10719.1i | 0.713890 | + | 1.23649i | ||||
\(423\) | 5401.37 | − | 8937.40i | 0.620860 | − | 1.02731i | ||||
\(424\) | −2082.47 | + | 3606.95i | −0.238523 | + | 0.413134i | ||||
\(425\) | −1902.66 | + | 3295.50i | −0.217159 | + | 0.376130i | ||||
\(426\) | 2208.77 | + | 1304.89i | 0.251210 | + | 0.148408i | ||||
\(427\) | 569.454 | + | 335.298i | 0.0645382 | + | 0.0380005i | ||||
\(428\) | −1387.12 | + | 2402.55i | −0.156656 | + | 0.271336i | ||||
\(429\) | 10891.3 | + | 6434.32i | 1.22573 | + | 0.724130i | ||||
\(430\) | −1574.38 | −0.176566 | ||||||||
\(431\) | −4337.40 | + | 7512.59i | −0.484745 | + | 0.839603i | −0.999846 | − | 0.0175265i | \(-0.994421\pi\) |
0.515102 | + | 0.857129i | \(0.327754\pi\) | |||||||
\(432\) | 9501.26 | + | 5872.77i | 1.05817 | + | 0.654059i | ||||
\(433\) | −10521.0 | −1.16769 | −0.583843 | − | 0.811866i | \(-0.698452\pi\) | ||||
−0.583843 | + | 0.811866i | \(0.698452\pi\) | |||||||
\(434\) | −58.5920 | + | 6853.54i | −0.00648043 | + | 0.758019i | ||||
\(435\) | −2422.74 | + | 1366.62i | −0.267038 | + | 0.150631i | ||||
\(436\) | −7196.19 | −0.790447 | ||||||||
\(437\) | 3497.84 | + | 6058.44i | 0.382894 | + | 0.663191i | ||||
\(438\) | 11140.7 | − | 6284.28i | 1.21535 | − | 0.685559i | ||||
\(439\) | 5603.51 | − | 9705.56i | 0.609205 | − | 1.05517i | −0.382167 | − | 0.924093i | \(-0.624822\pi\) |
0.991372 | − | 0.131080i | \(-0.0418445\pi\) | |||||||
\(440\) | −5910.19 | −0.640358 | ||||||||
\(441\) | 9254.62 | + | 343.648i | 0.999311 | + | 0.0371070i | ||||
\(442\) | 26745.2 | 2.87814 | ||||||||
\(443\) | 1280.39 | − | 2217.70i | 0.137321 | − | 0.237847i | −0.789161 | − | 0.614187i | \(-0.789484\pi\) |
0.926482 | + | 0.376340i | \(0.122817\pi\) | |||||||
\(444\) | −4369.42 | − | 2581.34i | −0.467035 | − | 0.275912i | ||||
\(445\) | 1015.55 | + | 1758.98i | 0.108183 | + | 0.187379i | ||||
\(446\) | 6761.57 | 0.717869 | ||||||||
\(447\) | −37.5153 | + | 3748.10i | −0.00396960 | + | 0.396598i | ||||
\(448\) | 23.9887 | − | 2805.97i | 0.00252982 | − | 0.295915i | ||||
\(449\) | 10296.7 | 1.08225 | 0.541126 | − | 0.840941i | \(-0.317998\pi\) | ||||
0.541126 | + | 0.840941i | \(0.317998\pi\) | |||||||
\(450\) | 1414.68 | − | 2340.80i | 0.148197 | − | 0.245214i | ||||
\(451\) | −439.745 | + | 761.660i | −0.0459130 | + | 0.0795237i | ||||
\(452\) | −1373.46 | −0.142926 | ||||||||
\(453\) | −149.103 | + | 14896.7i | −0.0154646 | + | 1.54505i | ||||
\(454\) | −5728.08 | + | 9921.33i | −0.592142 | + | 1.02562i | ||||
\(455\) | −9730.38 | − | 5729.30i | −1.00257 | − | 0.590316i | ||||
\(456\) | 3207.03 | − | 1809.02i | 0.329348 | − | 0.185779i | ||||
\(457\) | −7182.41 | + | 12440.3i | −0.735184 | + | 1.27338i | 0.219459 | + | 0.975622i | \(0.429571\pi\) |
−0.954643 | + | 0.297754i | \(0.903762\pi\) | |||||||
\(458\) | −8692.93 | + | 15056.6i | −0.886886 | + | 1.53613i | ||||
\(459\) | 15123.0 | + | 9347.59i | 1.53787 | + | 0.950562i | ||||
\(460\) | 2534.04 | + | 4389.08i | 0.256848 | + | 0.444874i | ||||
\(461\) | −2747.56 | − | 4758.92i | −0.277585 | − | 0.480792i | 0.693199 | − | 0.720746i | \(-0.256201\pi\) |
−0.970784 | + | 0.239955i | \(0.922867\pi\) | |||||||
\(462\) | −6518.12 | + | 10820.9i | −0.656386 | + | 1.08968i | ||||
\(463\) | 3667.94 | − | 6353.05i | 0.368172 | − | 0.637692i | −0.621108 | − | 0.783725i | \(-0.713317\pi\) |
0.989280 | + | 0.146033i | \(0.0466506\pi\) | |||||||
\(464\) | 4373.36 | 0.437561 | ||||||||
\(465\) | 4838.42 | − | 2729.26i | 0.482529 | − | 0.272186i | ||||
\(466\) | −20598.9 | −2.04769 | ||||||||
\(467\) | 1503.29 | + | 2603.77i | 0.148959 | + | 0.258004i | 0.930843 | − | 0.365420i | \(-0.119074\pi\) |
−0.781884 | + | 0.623424i | \(0.785741\pi\) | |||||||
\(468\) | −5708.28 | − | 114.281i | −0.563815 | − | 0.0112877i | ||||
\(469\) | −575.441 | + | 325.704i | −0.0566554 | + | 0.0320674i | ||||
\(470\) | −6357.54 | − | 11011.6i | −0.623939 | − | 1.08069i | ||||
\(471\) | 3395.21 | − | 1915.17i | 0.332151 | − | 0.187360i | ||||
\(472\) | −3013.77 | − | 5220.00i | −0.293898 | − | 0.509047i | ||||
\(473\) | 931.755 | + | 1613.85i | 0.0905754 | + | 0.156881i | ||||
\(474\) | 7654.29 | − | 4317.64i | 0.741715 | − | 0.418388i | ||||
\(475\) | −682.649 | − | 1182.38i | −0.0659413 | − | 0.114214i | ||||
\(476\) | −67.8137 | + | 7932.19i | −0.00652990 | + | 0.763806i | ||||
\(477\) | 3732.00 | − | 6175.17i | 0.358232 | − | 0.592750i | ||||
\(478\) | 4391.19 | + | 7605.76i | 0.420185 | + | 0.727781i | ||||
\(479\) | 10603.8 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331219\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331219\pi\) | |||||||
\(480\) | 6346.42 | − | 3579.90i | 0.603485 | − | 0.340415i | ||||
\(481\) | −18078.5 | −1.71374 | ||||||||
\(482\) | 3916.99 | − | 6784.42i | 0.370153 | − | 0.641124i | ||||
\(483\) | −14804.5 | − | 274.770i | −1.39467 | − | 0.0258850i | ||||
\(484\) | −309.547 | − | 536.151i | −0.0290709 | − | 0.0503523i | ||||
\(485\) | 552.572 | + | 957.083i | 0.0517340 | + | 0.0896060i | ||||
\(486\) | −10733.0 | − | 6934.82i | −1.00177 | − | 0.647263i | ||||
\(487\) | 7160.77 | − | 12402.8i | 0.666294 | − | 1.15406i | −0.312638 | − | 0.949872i | \(-0.601213\pi\) |
0.978933 | − | 0.204183i | \(-0.0654538\pi\) | |||||||
\(488\) | −278.057 | + | 481.609i | −0.0257932 | + | 0.0446751i | ||||
\(489\) | 12672.7 | − | 7148.46i | 1.17194 | − | 0.661072i | ||||
\(490\) | 5804.20 | − | 9667.59i | 0.535116 | − | 0.891301i | ||||
\(491\) | −2111.73 | + | 3657.62i | −0.194096 | + | 0.336184i | −0.946604 | − | 0.322399i | \(-0.895511\pi\) |
0.752508 | + | 0.658583i | \(0.228844\pi\) | |||||||
\(492\) | 3.97291 | − | 396.928i | 0.000364050 | − | 0.0363717i | ||||
\(493\) | 6961.01 | 0.635919 | ||||||||
\(494\) | −4797.91 | + | 8310.22i | −0.436980 | + | 0.756871i | ||||
\(495\) | 10236.7 | + | 204.942i | 0.929506 | + | 0.0186090i | ||||
\(496\) | −8733.96 | −0.790658 | ||||||||
\(497\) | −23.1720 | + | 2710.44i | −0.00209136 | + | 0.244627i | ||||
\(498\) | 59.5168 | − | 5946.25i | 0.00535545 | − | 0.535055i | ||||
\(499\) | 18697.4 | 1.67738 | 0.838690 | − | 0.544610i | \(-0.183322\pi\) | ||||
0.838690 | + | 0.544610i | \(0.183322\pi\) | |||||||
\(500\) | −2553.21 | − | 4422.28i | −0.228366 | − | 0.395541i | ||||
\(501\) | 0.707014 | + | 0.417685i | 6.30480e−5 | + | 3.72471e-5i | ||||
\(502\) | −804.372 | + | 1393.21i | −0.0715157 | + | 0.123869i | ||||
\(503\) | −7096.25 | −0.629038 | −0.314519 | − | 0.949251i | \(-0.601843\pi\) | ||||
−0.314519 | + | 0.949251i | \(0.601843\pi\) | |||||||
\(504\) | −222.602 | + | 7790.26i | −0.0196735 | + | 0.688504i | ||||
\(505\) | −10505.5 | −0.925723 | ||||||||
\(506\) | 10098.7 | − | 17491.5i | 0.887238 | − | 1.53674i | ||||
\(507\) | −7771.61 | + | 4383.82i | −0.680768 | + | 0.384008i | ||||
\(508\) | 3887.00 | + | 6732.48i | 0.339484 | + | 0.588003i | ||||
\(509\) | −6419.73 | −0.559037 | −0.279518 | − | 0.960140i | \(-0.590175\pi\) | ||||
−0.279518 | + | 0.960140i | \(0.590175\pi\) | |||||||
\(510\) | 18854.4 | − | 10635.4i | 1.63704 | − | 0.923422i | ||||
\(511\) | 11645.7 | + | 6857.03i | 1.00817 | + | 0.593614i | ||||
\(512\) | −1529.38 | −0.132011 | ||||||||
\(513\) | −5617.44 | + | 3022.10i | −0.483462 | + | 0.260095i | ||||
\(514\) | 6302.97 | − | 10917.1i | 0.540880 | − | 0.936831i | ||||
\(515\) | −16668.1 | −1.42619 | ||||||||
\(516\) | −724.146 | − | 427.806i | −0.0617805 | − | 0.0364983i | ||||
\(517\) | −7525.06 | + | 13033.8i | −0.640139 | + | 1.10875i | ||||
\(518\) | 154.336 | − | 18052.7i | 0.0130910 | − | 1.53126i | ||||
\(519\) | 5648.67 | + | 3337.08i | 0.477744 | + | 0.282238i | ||||
\(520\) | 4751.22 | − | 8229.36i | 0.400682 | − | 0.694002i | ||||
\(521\) | 4877.13 | − | 8447.45i | 0.410117 | − | 0.710344i | −0.584785 | − | 0.811188i | \(-0.698821\pi\) |
0.994902 | + | 0.100844i | \(0.0321544\pi\) | |||||||
\(522\) | −5002.23 | − | 100.146i | −0.419429 | − | 0.00839709i | ||||
\(523\) | −2134.28 | − | 3696.68i | −0.178443 | − | 0.309072i | 0.762905 | − | 0.646511i | \(-0.223773\pi\) |
−0.941347 | + | 0.337439i | \(0.890439\pi\) | |||||||
\(524\) | 986.436 | + | 1708.56i | 0.0822379 | + | 0.142440i | ||||
\(525\) | 2889.29 | + | 53.6249i | 0.240188 | + | 0.00445787i | ||||
\(526\) | 1702.11 | − | 2948.15i | 0.141094 | − | 0.244383i | ||||
\(527\) | −13901.7 | −1.14909 | ||||||||
\(528\) | −13859.8 | − | 8188.03i | −1.14237 | − | 0.674883i | ||||
\(529\) | 11507.4 | 0.945784 | ||||||||
\(530\) | −4392.65 | − | 7608.30i | −0.360009 | − | 0.623553i | ||||
\(531\) | 5038.96 | + | 9145.76i | 0.411813 | + | 0.747443i | ||||
\(532\) | −2452.51 | − | 1444.05i | −0.199868 | − | 0.117684i | ||||
\(533\) | −707.025 | − | 1224.60i | −0.0574571 | − | 0.0995186i | ||||
\(534\) | −36.5646 | + | 3653.12i | −0.00296312 | + | 0.296041i | ||||
\(535\) | 3999.46 | + | 6927.26i | 0.323199 | + | 0.559798i | ||||
\(536\) | −278.220 | − | 481.892i | −0.0224203 | − | 0.0388331i | ||||
\(537\) | −13038.2 | − | 7702.60i | −1.04774 | − | 0.618979i | ||||
\(538\) | 13727.6 | + | 23777.0i | 1.10007 | + | 1.90539i | ||||
\(539\) | −13345.0 | − | 228.194i | −1.06644 | − | 0.0182356i | ||||
\(540\) | −4069.59 | + | 2189.38i | −0.324310 | + | 0.174474i | ||||
\(541\) | 10185.3 | + | 17641.4i | 0.809426 | + | 1.40197i | 0.913262 | + | 0.407373i | \(0.133555\pi\) |
−0.103836 | + | 0.994594i | \(0.533112\pi\) | |||||||
\(542\) | 22835.9 | 1.80976 | ||||||||
\(543\) | 45.2961 | − | 4525.47i | 0.00357982 | − | 0.357655i | ||||
\(544\) | −18234.5 | −1.43713 | ||||||||
\(545\) | −10374.4 | + | 17968.9i | −0.815392 | + | 1.41230i | ||||
\(546\) | −9827.08 | − | 17774.8i | −0.770256 | − | 1.39321i | ||||
\(547\) | −1046.82 | − | 1813.14i | −0.0818258 | − | 0.141726i | 0.822208 | − | 0.569187i | \(-0.192742\pi\) |
−0.904034 | + | 0.427460i | \(0.859408\pi\) | |||||||
\(548\) | 285.263 | + | 494.089i | 0.0222369 | + | 0.0385154i | ||||
\(549\) | 498.307 | − | 824.525i | 0.0387381 | − | 0.0640981i | ||||
\(550\) | −1970.89 | + | 3413.69i | −0.152799 | + | 0.264655i | ||||
\(551\) | −1248.76 | + | 2162.91i | −0.0965498 | + | 0.167229i | ||||
\(552\) | 124.714 | − | 12460.0i | 0.00961625 | − | 0.960747i | ||||
\(553\) | 8001.19 | + | 4711.15i | 0.615272 | + | 0.362275i | ||||
\(554\) | −10995.6 | + | 19045.0i | −0.843249 | + | 1.46055i | ||||
\(555\) | −12744.8 | + | 7189.08i | −0.974748 | + | 0.549837i | ||||
\(556\) | −4537.94 | −0.346135 | ||||||||
\(557\) | 844.740 | − | 1463.13i | 0.0642599 | − | 0.111301i | −0.832106 | − | 0.554617i | \(-0.812865\pi\) |
0.896365 | + | 0.443316i | \(0.146198\pi\) | |||||||
\(558\) | 9989.88 | + | 200.000i | 0.757895 | + | 0.0151733i | ||||
\(559\) | −2996.16 | −0.226698 | ||||||||
\(560\) | 12382.5 | + | 7290.86i | 0.934383 | + | 0.550170i | ||||
\(561\) | −22060.5 | − | 13032.8i | −1.66024 | − | 0.980826i | ||||
\(562\) | −21175.1 | −1.58936 | ||||||||
\(563\) | −6454.60 | − | 11179.7i | −0.483178 | − | 0.836888i | 0.516636 | − | 0.856205i | \(-0.327184\pi\) |
−0.999813 | + | 0.0193169i | \(0.993851\pi\) | |||||||
\(564\) | 67.9857 | − | 6792.36i | 0.00507574 | − | 0.507110i | ||||
\(565\) | −1980.05 | + | 3429.55i | −0.147436 | + | 0.255367i | ||||
\(566\) | −2720.09 | −0.202004 | ||||||||
\(567\) | 655.690 | − | 13485.3i | 0.0485651 | − | 0.998820i | ||||
\(568\) | −2281.01 | −0.168501 | ||||||||
\(569\) | 13211.4 | − | 22882.8i | 0.973377 | − | 1.68594i | 0.288185 | − | 0.957575i | \(-0.406948\pi\) |
0.685191 | − | 0.728363i | \(-0.259719\pi\) | |||||||
\(570\) | −77.7345 | + | 7766.35i | −0.00571218 | + | 0.570696i | ||||
\(571\) | 6392.78 | + | 11072.6i | 0.468528 | + | 0.811515i | 0.999353 | − | 0.0359669i | \(-0.0114511\pi\) |
−0.530825 | + | 0.847482i | \(0.678118\pi\) | |||||||
\(572\) | 8228.40 | 0.601480 | ||||||||
\(573\) | 14216.2 | + | 8398.54i | 1.03646 | + | 0.612311i | ||||
\(574\) | 1228.89 | − | 695.562i | 0.0893606 | − | 0.0505787i | ||||
\(575\) | −4620.36 | −0.335100 | ||||||||
\(576\) | −4090.05 | − | 81.8841i | −0.295866 | − | 0.00592333i | ||||
\(577\) | −2294.12 | + | 3973.54i | −0.165521 | + | 0.286691i | −0.936840 | − | 0.349758i | \(-0.886264\pi\) |
0.771319 | + | 0.636449i | \(0.219597\pi\) | |||||||
\(578\) | −37598.9 | −2.70572 | ||||||||
\(579\) | 7707.33 | − | 4347.56i | 0.553205 | − | 0.312053i | ||||
\(580\) | −904.672 | + | 1566.94i | −0.0647663 | + | 0.112179i | ||||
\(581\) | 5467.81 | − | 3094.82i | 0.390435 | − | 0.220989i | ||||
\(582\) | −19.8953 | + | 1987.71i | −0.00141698 | + | 0.141569i | ||||
\(583\) | −5199.34 | + | 9005.52i | −0.369356 | + | 0.639743i | ||||
\(584\) | −5686.43 | + | 9849.18i | −0.402921 | + | 0.697880i | ||||
\(585\) | −8514.68 | + | 14088.8i | −0.601775 | + | 0.995730i | ||||
\(586\) | −10406.7 | − | 18025.0i | −0.733613 | − | 1.27066i | ||||
\(587\) | 10298.2 | + | 17837.0i | 0.724111 | + | 1.25420i | 0.959339 | + | 0.282256i | \(0.0910829\pi\) |
−0.235228 | + | 0.971940i | \(0.575584\pi\) | |||||||
\(588\) | 5296.64 | − | 2869.49i | 0.371479 | − | 0.201251i | ||||
\(589\) | 2493.88 | − | 4319.52i | 0.174462 | − | 0.302178i | ||||
\(590\) | 12714.2 | 0.887175 | ||||||||
\(591\) | 13.2549 | − | 1324.28i | 0.000922559 | − | 0.0921717i | ||||
\(592\) | 23005.9 | 1.59719 | ||||||||
\(593\) | −3894.55 | − | 6745.56i | −0.269697 | − | 0.467128i | 0.699087 | − | 0.715037i | \(-0.253590\pi\) |
−0.968783 | + | 0.247909i | \(0.920257\pi\) | |||||||
\(594\) | 15665.3 | + | 9682.82i | 1.08208 | + | 0.668840i | ||||
\(595\) | 19709.0 | + | 11604.7i | 1.35796 | + | 0.799577i | ||||
\(596\) | 1219.07 | + | 2111.49i | 0.0837837 | + | 0.145118i | ||||
\(597\) | 3460.04 | + | 2044.10i | 0.237203 | + | 0.140133i | ||||
\(598\) | 16236.8 | + | 28122.9i | 1.11032 | + | 1.92313i | ||||
\(599\) | −10937.0 | − | 18943.4i | −0.746031 | − | 1.29216i | −0.949712 | − | 0.313126i | \(-0.898624\pi\) |
0.203681 | − | 0.979037i | \(-0.434709\pi\) | |||||||
\(600\) | −24.3395 | + | 2431.73i | −0.00165609 | + | 0.165458i | ||||
\(601\) | −13992.6 | − | 24235.9i | −0.949702 | − | 1.64493i | −0.746052 | − | 0.665888i | \(-0.768053\pi\) |
−0.203650 | − | 0.979044i | \(-0.565281\pi\) | |||||||
\(602\) | 25.5782 | − | 2991.89i | 0.00173171 | − | 0.202559i | ||||
\(603\) | 465.179 | + | 844.304i | 0.0314155 | + | 0.0570195i | ||||
\(604\) | 4845.15 | + | 8392.04i | 0.326401 | + | 0.565343i | ||||
\(605\) | −1785.03 | −0.119953 | ||||||||
\(606\) | −16269.2 | − | 9611.40i | −1.09058 | − | 0.644284i | ||||
\(607\) | −4683.46 | −0.313172 | −0.156586 | − | 0.987664i | \(-0.550049\pi\) | ||||
−0.156586 | + | 0.987664i | \(0.550049\pi\) | |||||||
\(608\) | 3271.15 | − | 5665.80i | 0.218195 | − | 0.377925i | ||||
\(609\) | −2557.71 | − | 4626.27i | −0.170187 | − | 0.307826i | ||||
\(610\) | −586.518 | − | 1015.88i | −0.0389302 | − | 0.0674291i | ||||
\(611\) | −12098.8 | − | 20955.8i | −0.801091 | − | 1.38753i | ||||
\(612\) | 11562.2 | + | 231.478i | 0.763681 | + | 0.0152891i | ||||
\(613\) | −13144.7 | + | 22767.2i | −0.866082 | + | 1.50010i | −0.000113990 | 1.00000i | \(0.500036\pi\) | |
−0.865968 | + | 0.500099i | \(0.833297\pi\) | |||||||
\(614\) | 7390.77 | − | 12801.2i | 0.485777 | − | 0.841391i | ||||
\(615\) | −985.403 | − | 582.150i | −0.0646102 | − | 0.0381700i | ||||
\(616\) | 96.0197 | − | 11231.5i | 0.00628043 | − | 0.734625i | ||||
\(617\) | −215.459 | + | 373.186i | −0.0140584 | + | 0.0243499i | −0.872969 | − | 0.487776i | \(-0.837808\pi\) |
0.858911 | + | 0.512126i | \(0.171142\pi\) | |||||||
\(618\) | −25812.8 | − | 15249.5i | −1.68016 | − | 0.992596i | ||||
\(619\) | −17378.1 | −1.12841 | −0.564205 | − | 0.825635i | \(-0.690817\pi\) | ||||
−0.564205 | + | 0.825635i | \(0.690817\pi\) | |||||||
\(620\) | 1806.71 | − | 3129.31i | 0.117031 | − | 0.202703i | ||||
\(621\) | −648.072 | + | 21576.9i | −0.0418780 | + | 1.39428i | ||||
\(622\) | 28547.9 | 1.84030 | ||||||||
\(623\) | −3359.19 | + | 1901.32i | −0.216024 | + | 0.122271i | ||||
\(624\) | 22543.0 | − | 12716.1i | 1.44622 | − | 0.815787i | ||||
\(625\) | −10969.7 | −0.702060 | ||||||||
\(626\) | 9817.42 | + | 17004.3i | 0.626810 | + | 1.08567i | ||||
\(627\) | 8007.03 | − | 4516.62i | 0.510000 | − | 0.287681i | ||||
\(628\) | 1267.80 | − | 2195.89i | 0.0805585 | − | 0.139531i | ||||
\(629\) | 36618.2 | 2.32124 | ||||||||
\(630\) | −13996.1 | − | 8622.81i | −0.885105 | − | 0.545303i | ||||
\(631\) | −176.931 | −0.0111625 | −0.00558123 | − | 0.999984i | \(-0.501777\pi\) | ||||
−0.00558123 | + | 0.999984i | \(0.501777\pi\) | |||||||
\(632\) | −3906.88 | + | 6766.92i | −0.245898 | + | 0.425907i | ||||
\(633\) | 16414.7 | + | 9697.38i | 1.03069 | + | 0.608904i | ||||
\(634\) | −10820.5 | − | 18741.7i | −0.677821 | − | 1.17402i | ||||
\(635\) | 22414.7 | 1.40079 | ||||||||
\(636\) | 46.9738 | − | 4693.09i | 0.00292867 | − | 0.292599i | ||||
\(637\) | 11045.8 | − | 18398.1i | 0.687050 | − | 1.14436i | ||||
\(638\) | 7210.65 | 0.447449 | ||||||||
\(639\) | 3950.80 | + | 79.0961i | 0.244587 | + | 0.00489670i | ||||
\(640\) | −8099.64 | + | 14029.0i | −0.500260 | + | 0.866475i | ||||
\(641\) | −21029.9 | −1.29583 | −0.647917 | − | 0.761711i | \(-0.724360\pi\) | ||||
−0.647917 | + | 0.761711i | \(0.724360\pi\) | |||||||
\(642\) | −144.000 | + | 14386.8i | −0.00885236 | + | 0.884428i | ||||
\(643\) | −6304.53 | + | 10919.8i | −0.386666 | + | 0.669725i | −0.991999 | − | 0.126247i | \(-0.959707\pi\) |
0.605333 | + | 0.795973i | \(0.293040\pi\) | |||||||
\(644\) | −8381.99 | + | 4744.27i | −0.512883 | + | 0.290295i | ||||
\(645\) | −2112.20 | + | 1191.45i | −0.128942 | + | 0.0727338i | ||||
\(646\) | 9718.19 | − | 16832.4i | 0.591884 | − | 1.02517i | ||||
\(647\) | −5084.38 | + | 8806.41i | −0.308945 | + | 0.535109i | −0.978132 | − | 0.207985i | \(-0.933309\pi\) |
0.669187 | + | 0.743094i | \(0.266643\pi\) | |||||||
\(648\) | 11352.7 | + | 454.750i | 0.688233 | + | 0.0275683i | ||||
\(649\) | −7524.52 | − | 13032.8i | −0.455105 | − | 0.788265i | ||||
\(650\) | −3168.82 | − | 5488.55i | −0.191217 | − | 0.331198i | ||||
\(651\) | 5107.96 | + | 9239.05i | 0.307522 | + | 0.556232i | ||||
\(652\) | 4732.11 | − | 8196.26i | 0.284239 | − | 0.492316i | ||||
\(653\) | 17327.5 | 1.03841 | 0.519203 | − | 0.854651i | \(-0.326229\pi\) | ||||
0.519203 | + | 0.854651i | \(0.326229\pi\) | |||||||
\(654\) | −32505.6 | + | 18335.8i | −1.94353 | + | 1.09631i | ||||
\(655\) | 5688.36 | 0.339333 | ||||||||
\(656\) | 899.728 | + | 1558.38i | 0.0535495 | + | 0.0927505i | ||||
\(657\) | 10190.7 | − | 16862.0i | 0.605137 | − | 1.00129i | ||||
\(658\) | 21029.2 | − | 11902.7i | 1.24590 | − | 0.705190i | ||||
\(659\) | 7431.15 | + | 12871.1i | 0.439266 | + | 0.760831i | 0.997633 | − | 0.0687629i | \(-0.0219052\pi\) |
−0.558367 | + | 0.829594i | \(0.688572\pi\) | |||||||
\(660\) | 5800.75 | − | 3272.09i | 0.342112 | − | 0.192979i | ||||
\(661\) | −15644.7 | − | 27097.4i | −0.920588 | − | 1.59451i | −0.798507 | − | 0.601985i | \(-0.794377\pi\) |
−0.122081 | − | 0.992520i | \(-0.538957\pi\) | |||||||
\(662\) | −1398.01 | − | 2421.42i | −0.0820771 | − | 0.142162i | ||||
\(663\) | 35881.3 | − | 20240.0i | 2.10183 | − | 1.18561i | ||||
\(664\) | 2643.63 | + | 4578.91i | 0.154507 | + | 0.267615i | ||||
\(665\) | −7141.47 | + | 4042.12i | −0.416442 | + | 0.235709i | ||||
\(666\) | −26314.1 | − | 526.816i | −1.53101 | − | 0.0306512i | ||||
\(667\) | 4225.97 | + | 7319.60i | 0.245323 | + | 0.424911i | ||||
\(668\) | 0.534148 | 3.09383e−5 | ||||||||
\(669\) | 9071.33 | − | 5116.97i | 0.524242 | − | 0.295715i | ||||
\(670\) | 1173.73 | 0.0676791 | ||||||||
\(671\) | −694.229 | + | 1202.44i | −0.0399410 | + | 0.0691798i | ||||
\(672\) | 6699.97 | + | 12118.6i | 0.384609 | + | 0.695663i | ||||
\(673\) | 2162.02 | + | 3744.73i | 0.123833 | + | 0.214485i | 0.921276 | − | 0.388909i | \(-0.127148\pi\) |
−0.797443 | + | 0.603394i | \(0.793815\pi\) | |||||||
\(674\) | 9806.11 | + | 16984.7i | 0.560411 | + | 0.970661i | ||||
\(675\) | 126.480 | − | 4211.01i | 0.00721215 | − | 0.240121i | ||||
\(676\) | −2901.99 | + | 5026.39i | −0.165111 | + | 0.285980i | ||||
\(677\) | 2404.70 | − | 4165.07i | 0.136514 | − | 0.236450i | −0.789661 | − | 0.613544i | \(-0.789743\pi\) |
0.926175 | + | 0.377094i | \(0.123077\pi\) | |||||||
\(678\) | −6204.02 | + | 3499.57i | −0.351421 | + | 0.198230i | ||||
\(679\) | −1827.78 | + | 1034.53i | −0.103304 | + | 0.0584710i | ||||
\(680\) | −9623.63 | + | 16668.6i | −0.542720 | + | 0.940018i | ||||
\(681\) | −176.615 | + | 17645.3i | −0.00993816 | + | 0.992908i | ||||
\(682\) | −14400.3 | −0.808526 | ||||||||
\(683\) | −13158.2 | + | 22790.8i | −0.737169 | + | 1.27681i | 0.216596 | + | 0.976261i | \(0.430504\pi\) |
−0.953765 | + | 0.300553i | \(0.902829\pi\) | |||||||
\(684\) | −2146.10 | + | 3551.05i | −0.119968 | + | 0.198506i | ||||
\(685\) | 1644.99 | 0.0917545 | ||||||||
\(686\) | 18277.6 | + | 11187.1i | 1.01726 | + | 0.622633i | ||||
\(687\) | −268.030 | + | 26778.5i | −0.0148850 | + | 1.48714i | ||||
\(688\) | 3812.79 | 0.211281 | ||||||||
\(689\) | −8359.53 | − | 14479.1i | −0.462224 | − | 0.800596i | ||||
\(690\) | 22629.7 | + | 13369.0i | 1.24855 | + | 0.737609i | ||||
\(691\) | −1095.59 | + | 1897.63i | −0.0603161 | + | 0.104470i | −0.894607 | − | 0.446854i | \(-0.852544\pi\) |
0.834291 | + | 0.551325i | \(0.185878\pi\) | |||||||
\(692\) | 4267.56 | 0.234434 | ||||||||
\(693\) | −555.772 | + | 19450.0i | −0.0304647 | + | 1.06616i | ||||
\(694\) | −11209.6 | −0.613128 | ||||||||
\(695\) | −6542.10 | + | 11331.2i | −0.357059 | + | 0.618444i | ||||
\(696\) | 3874.62 | − | 2185.60i | 0.211016 | − | 0.119030i | ||||
\(697\) | 1432.08 | + | 2480.44i | 0.0778250 | + | 0.134797i | ||||
\(698\) | −2538.16 | −0.137637 | ||||||||
\(699\) | −27635.5 | + | 15588.7i | −1.49538 | + | 0.843517i | ||||
\(700\) | 1635.85 | − | 925.905i | 0.0883278 | − | 0.0499942i | ||||
\(701\) | 7938.38 | 0.427715 | 0.213858 | − | 0.976865i | \(-0.431397\pi\) | ||||
0.213858 | + | 0.976865i | \(0.431397\pi\) | |||||||
\(702\) | −26075.8 | + | 14028.4i | −1.40195 | + | 0.754228i | ||||
\(703\) | −6569.06 | + | 11377.9i | −0.352428 | + | 0.610423i | ||||
\(704\) | 5895.75 | 0.315631 | ||||||||
\(705\) | −16862.5 | − | 9961.94i | −0.900823 | − | 0.532182i | ||||
\(706\) | −3733.79 | + | 6467.11i | −0.199041 | + | 0.344749i | ||||
\(707\) | 170.678 | − | 19964.3i | 0.00907921 | − | 1.06200i | ||||
\(708\) | 5847.94 | + | 3454.81i | 0.310422 | + | 0.183389i | ||||
\(709\) | −11439.3 | + | 19813.4i | −0.605940 | + | 1.04952i | 0.385962 | + | 0.922515i | \(0.373870\pi\) |
−0.991902 | + | 0.127004i | \(0.959464\pi\) | |||||||
\(710\) | 2405.71 | − | 4166.82i | 0.127162 | − | 0.220251i | ||||
\(711\) | 7001.53 | − | 11585.1i | 0.369308 | − | 0.611077i | ||||
\(712\) | −1624.14 | − | 2813.09i | −0.0854875 | − | 0.148069i | ||||
\(713\) | −8439.62 | − | 14617.8i | −0.443291 | − | 0.767802i | ||||
\(714\) | 19904.8 | + | 36002.9i | 1.04330 | + | 1.88708i | ||||
\(715\) | 11862.4 | − | 20546.3i | 0.620462 | − | 1.07467i | ||||
\(716\) | −9850.32 | −0.514139 | ||||||||
\(717\) | 11647.1 | + | 6880.77i | 0.606649 | + | 0.358392i | ||||
\(718\) | −2935.48 | −0.152578 | ||||||||
\(719\) | −5773.81 | − | 10000.5i | −0.299481 | − | 0.518716i | 0.676536 | − | 0.736409i | \(-0.263480\pi\) |
−0.976017 | + | 0.217693i | \(0.930147\pi\) | |||||||
\(720\) | 10835.4 | − | 17928.8i | 0.560849 | − | 0.928012i | ||||
\(721\) | 270.798 | − | 31675.4i | 0.0139876 | − | 1.63613i | ||||
\(722\) | −8082.37 | − | 13999.1i | −0.416613 | − | 0.721595i | ||||
\(723\) | 120.773 | − | 12066.3i | 0.00621244 | − | 0.620676i | ||||
\(724\) | −1471.91 | − | 2549.42i | −0.0755568 | − | 0.130868i | ||||
\(725\) | −824.753 | − | 1428.51i | −0.0422491 | − | 0.0731775i | ||||
\(726\) | −2764.35 | − | 1633.10i | −0.141315 | − | 0.0834850i | ||||
\(727\) | −9053.60 | − | 15681.3i | −0.461870 | − | 0.799982i | 0.537184 | − | 0.843465i | \(-0.319488\pi\) |
−0.999054 | + | 0.0434827i | \(0.986155\pi\) | |||||||
\(728\) | 15561.5 | + | 9162.71i | 0.792237 | + | 0.466474i | ||||
\(729\) | −19647.5 | − | 1181.31i | −0.998197 | − | 0.0600168i | ||||
\(730\) | −11994.6 | − | 20775.3i | −0.608139 | − | 1.05333i | ||||
\(731\) | 6068.75 | 0.307060 | ||||||||
\(732\) | 6.27206 | − | 626.633i | 0.000316697 | − | 0.0316408i | ||||
\(733\) | 23101.1 | 1.16406 | 0.582032 | − | 0.813166i | \(-0.302258\pi\) | ||||
0.582032 | + | 0.813166i | \(0.302258\pi\) | |||||||
\(734\) | −4265.12 | + | 7387.41i | −0.214480 | + | 0.371491i | ||||
\(735\) | 470.756 | − | 17362.5i | 0.0236246 | − | 0.871328i | ||||
\(736\) | −11070.0 | − | 19173.8i | −0.554411 | − | 0.960267i | ||||
\(737\) | −694.636 | − | 1203.15i | −0.0347181 | − | 0.0601336i | ||||
\(738\) | −993.421 | − | 1803.07i | −0.0495506 | − | 0.0899347i | ||||
\(739\) | −5479.70 | + | 9491.12i | −0.272766 | + | 0.472444i | −0.969569 | − | 0.244818i | \(-0.921272\pi\) |
0.696803 | + | 0.717262i | \(0.254605\pi\) | |||||||
\(740\) | −4759.00 | + | 8242.84i | −0.236411 | + | 0.409477i | ||||
\(741\) | −147.934 | + | 14779.9i | −0.00733401 | + | 0.732731i | ||||
\(742\) | 14529.8 | − | 8224.00i | 0.718878 | − | 0.406890i | ||||
\(743\) | −2774.77 | + | 4806.05i | −0.137008 | + | 0.237304i | −0.926363 | − | 0.376633i | \(-0.877082\pi\) |
0.789355 | + | 0.613937i | \(0.210415\pi\) | |||||||
\(744\) | −7737.94 | + | 4364.83i | −0.381299 | + | 0.215084i | ||||
\(745\) | 7029.87 | 0.345711 | ||||||||
\(746\) | 9058.60 | − | 15690.0i | 0.444583 | − | 0.770040i | ||||
\(747\) | −4420.11 | − | 8022.53i | −0.216497 | − | 0.392944i | ||||
\(748\) | −16666.7 | −0.814698 | ||||||||
\(749\) | −13229.2 | + | 7487.85i | −0.645375 | + | 0.365287i | ||||
\(750\) | −22800.9 | − | 13470.2i | −1.11009 | − | 0.655814i | ||||
\(751\) | −16603.6 | −0.806754 | −0.403377 | − | 0.915034i | \(-0.632164\pi\) | ||||
−0.403377 | + | 0.915034i | \(0.632164\pi\) | |||||||
\(752\) | 15396.5 | + | 26667.4i | 0.746610 | + | 1.29317i | ||||
\(753\) | −24.8013 | + | 2477.86i | −0.00120028 | + | 0.119918i | ||||
\(754\) | −5796.66 | + | 10040.1i | −0.279976 | + | 0.484933i | ||||
\(755\) | 27939.9 | 1.34681 | ||||||||
\(756\) | −4094.49 | − | 7769.24i | −0.196978 | − | 0.373763i | ||||
\(757\) | 2336.31 | 0.112172 | 0.0560862 | − | 0.998426i | \(-0.482138\pi\) | ||||
0.0560862 | + | 0.998426i | \(0.482138\pi\) | |||||||
\(758\) | −16738.1 | + | 28991.2i | −0.802052 | + | 1.38919i | ||||
\(759\) | 311.375 | − | 31109.0i | 0.0148909 | − | 1.48773i | ||||
\(760\) | −3452.83 | − | 5980.48i | −0.164799 | − | 0.285441i | ||||
\(761\) | 10068.8 | 0.479625 | 0.239812 | − | 0.970819i | \(-0.422914\pi\) | ||||
0.239812 | + | 0.970819i | \(0.422914\pi\) | |||||||
\(762\) | 34712.1 | + | 20507.0i | 1.65024 | + | 0.974920i | ||||
\(763\) | −33978.8 | − | 20006.9i | −1.61221 | − | 0.949277i | ||||
\(764\) | 10740.3 | 0.508601 | ||||||||
\(765\) | 17246.5 | − | 28537.0i | 0.815098 | − | 1.34870i | ||||
\(766\) | 18870.3 | − | 32684.3i | 0.890093 | − | 1.54169i | ||||
\(767\) | 24195.9 | 1.13907 | ||||||||
\(768\) | −19892.6 | + | 11221.0i | −0.934649 | + | 0.527218i | ||||
\(769\) | −1220.38 | + | 2113.76i | −0.0572277 | + | 0.0991213i | −0.893220 | − | 0.449620i | \(-0.851559\pi\) |
0.835992 | + | 0.548741i | \(0.184893\pi\) | |||||||
\(770\) | 20415.8 | + | 12020.9i | 0.955498 | + | 0.562603i | ||||
\(771\) | 194.340 | − | 19416.3i | 0.00907781 | − | 0.906952i | ||||
\(772\) | 2877.98 | − | 4984.81i | 0.134172 | − | 0.232393i | ||||
\(773\) | 5436.01 | − | 9415.44i | 0.252936 | − | 0.438098i | −0.711397 | − | 0.702791i | \(-0.751937\pi\) |
0.964333 | + | 0.264692i | \(0.0852704\pi\) | |||||||
\(774\) | −4361.05 | − | 87.3095i | −0.202526 | − | 0.00405462i | ||||
\(775\) | 1647.10 | + | 2852.86i | 0.0763428 | + | 0.132230i | ||||
\(776\) | −883.713 | − | 1530.64i | −0.0408807 | − | 0.0708075i | ||||
\(777\) | −13454.8 | − | 24336.4i | −0.621219 | − | 1.12363i | ||||
\(778\) | −2839.35 | + | 4917.91i | −0.130843 | + | 0.226627i | ||||
\(779\) | −1027.63 | −0.0472638 | ||||||||
\(780\) | −107.172 | + | 10707.4i | −0.00491971 | + | 0.491522i | ||||
\(781\) | −5695.01 | −0.260927 | ||||||||
\(782\) | −32887.7 | − | 56963.2i | −1.50391 | − | 2.60486i | ||||
\(783\) | −6786.79 | + | 3651.20i | −0.309758 | + | 0.166645i | ||||
\(784\) | −14056.4 | + | 23412.6i | −0.640324 | + | 1.06654i | ||||
\(785\) | −3655.44 | − | 6331.40i | −0.166201 | − | 0.287869i | ||||
\(786\) | 8809.17 | + | 5204.22i | 0.399762 | + | 0.236168i | ||||
\(787\) | −9740.91 | − | 16871.7i | −0.441202 | − | 0.764184i | 0.556577 | − | 0.830796i | \(-0.312114\pi\) |
−0.997779 | + | 0.0666120i | \(0.978781\pi\) | |||||||
\(788\) | −430.721 | − | 746.031i | −0.0194718 | − | 0.0337262i | ||||
\(789\) | 52.4814 | − | 5243.35i | 0.00236805 | − | 0.236588i | ||||
\(790\) | −8240.96 | − | 14273.8i | −0.371139 | − | 0.642832i | ||||
\(791\) | −6485.19 | − | 3818.52i | −0.291513 | − | 0.171645i | ||||
\(792\) | −16371.3 | − | 327.757i | −0.734504 | − | 0.0147050i | ||||
\(793\) | −1116.19 | − | 1933.29i | −0.0499835 | − | 0.0865740i | ||||
\(794\) | −11978.4 | −0.535385 | ||||||||
\(795\) | −11650.9 | − | 6883.06i | −0.519769 | − | 0.307066i | ||||
\(796\) | 2614.06 | 0.116398 | ||||||||
\(797\) | 1644.31 | − | 2848.02i | 0.0730794 | − | 0.126577i | −0.827170 | − | 0.561952i | \(-0.810051\pi\) |
0.900249 | + | 0.435374i | \(0.143384\pi\) | |||||||
\(798\) | −14757.6 | − | 273.899i | −0.654652 | − | 0.0121503i | ||||
\(799\) | 24506.3 | + | 42446.1i | 1.08507 | + | 1.87939i | ||||
\(800\) | 2160.46 | + | 3742.02i | 0.0954797 | + | 0.165376i | ||||
\(801\) | 2715.52 | + | 4928.70i | 0.119786 | + | 0.217412i | ||||
\(802\) | −6412.29 | + | 11106.4i | −0.282327 | + | 0.489004i | ||||
\(803\) | −14197.4 | + | 24590.6i | −0.623928 | + | 1.08068i | ||||
\(804\) | 539.861 | + | 318.936i | 0.0236809 | + | 0.0139900i | ||||
\(805\) | −237.405 | + | 27769.4i | −0.0103943 | + | 1.21583i | ||||
\(806\) | 11576.4 | − | 20050.9i | 0.505908 | − | 0.876259i | ||||
\(807\) | 36410.8 | + | 21510.5i | 1.58825 | + | 0.938297i | ||||
\(808\) | 16801.2 | 0.731515 | ||||||||
\(809\) | 14785.3 | − | 25608.8i | 0.642549 | − | 1.11293i | −0.342313 | − | 0.939586i | \(-0.611210\pi\) |
0.984862 | − | 0.173341i | \(-0.0554562\pi\) | |||||||
\(810\) | −12804.1 | + | 20258.8i | −0.555418 | + | 0.878793i | ||||
\(811\) | −1910.74 | −0.0827313 | −0.0413656 | − | 0.999144i | \(-0.513171\pi\) | ||||
−0.0413656 | + | 0.999144i | \(0.513171\pi\) | |||||||
\(812\) | −2963.04 | − | 1744.66i | −0.128057 | − | 0.0754008i | ||||
\(813\) | 30636.7 | − | 17281.6i | 1.32162 | − | 0.745501i | ||||
\(814\) | 37931.4 | 1.63329 | ||||||||
\(815\) | −13644.1 | − | 23632.2i | −0.586418 | − | 1.01571i | ||||
\(816\) | −45661.0 | + | 25756.5i | −1.95889 | + | 1.10497i | ||||
\(817\) | −1088.69 | + | 1885.67i | −0.0466201 | + | 0.0807483i | ||||
\(818\) | −44680.1 | −1.90979 | ||||||||
\(819\) | −26635.5 | − | 16409.8i | −1.13641 | − | 0.700129i | ||||
\(820\) | −744.471 | −0.0317049 | ||||||||
\(821\) | 16782.8 | − | 29068.7i | 0.713428 | − | 1.23569i | −0.250135 | − | 0.968211i | \(-0.580475\pi\) |
0.963563 | − | 0.267482i | \(-0.0861917\pi\) | |||||||
\(822\) | 2547.48 | + | 1504.98i | 0.108094 | + | 0.0638593i | ||||
\(823\) | 19668.3 | + | 34066.5i | 0.833042 | + | 1.44287i | 0.895614 | + | 0.444831i | \(0.146736\pi\) |
−0.0625721 | + | 0.998040i | \(0.519930\pi\) | |||||||
\(824\) | 26656.9 | 1.12699 | ||||||||
\(825\) | −60.7688 | + | 6071.33i | −0.00256448 | + | 0.256214i | ||||
\(826\) | −206.560 | + | 24161.4i | −0.00870114 | + | 1.01778i | ||||
\(827\) | 36017.5 | 1.51445 | 0.757226 | − | 0.653153i | \(-0.226554\pi\) | ||||
0.757226 | + | 0.653153i | \(0.226554\pi\) | |||||||
\(828\) | 6775.89 | + | 12298.3i | 0.284394 | + | 0.516178i | ||||
\(829\) | −1351.86 | + | 2341.49i | −0.0566369 | + | 0.0980980i | −0.892954 | − | 0.450148i | \(-0.851371\pi\) |
0.836317 | + | 0.548246i | \(0.184704\pi\) | |||||||
\(830\) | −11152.7 | −0.466403 | ||||||||
\(831\) | −339.030 | + | 33872.0i | −0.0141526 | + | 1.41397i | ||||
\(832\) | −4739.61 | + | 8209.25i | −0.197496 | + | 0.342073i | ||||
\(833\) | −22373.3 | + | 37265.5i | −0.930601 | + | 1.55003i | ||||
\(834\) | −20498.1 | + | 11562.6i | −0.851069 | + | 0.480072i | ||||
\(835\) | 0.770052 | − | 1.33377i | 3.19147e−5 | − | 5.52779e-5i | ||||
\(836\) | 2989.89 | − | 5178.65i | 0.123693 | − | 0.214243i | ||||
\(837\) | 13553.8 | − | 7291.74i | 0.559722 | − | 0.301123i | ||||
\(838\) | −4842.59 | − | 8387.62i | −0.199624 | − | 0.345758i | ||||
\(839\) | −14788.7 | − | 25614.8i | −0.608537 | − | 1.05402i | −0.991482 | − | 0.130245i | \(-0.958424\pi\) |
0.382945 | − | 0.923771i | \(-0.374910\pi\) | |||||||
\(840\) | 14614.0 | + | 271.234i | 0.600274 | + | 0.0111410i | ||||
\(841\) | 10685.8 | − | 18508.3i | 0.438140 | − | 0.758880i | ||||
\(842\) | −2976.01 | −0.121805 | ||||||||
\(843\) | −28408.6 | + | 16024.8i | −1.16067 | + | 0.654712i | ||||
\(844\) | 12401.3 | 0.505771 | ||||||||
\(845\) | 8367.27 | + | 14492.5i | 0.340642 | + | 0.590010i | ||||
\(846\) | −16999.8 | − | 30854.7i | −0.690855 | − | 1.25391i | ||||
\(847\) | 29.0004 | − | 3392.19i | 0.00117647 | − | 0.137612i | ||||
\(848\) | 10638.0 | + | 18425.5i | 0.430789 | + | 0.746149i | ||||
\(849\) | −3649.28 | + | 2058.49i | −0.147518 | + | 0.0832123i | ||||
\(850\) | 6418.46 | + | 11117.1i | 0.259002 | + | 0.448604i | ||||
\(851\) | 22230.6 | + | 38504.5i | 0.895482 | + | 1.55102i | ||||
\(852\) | 2238.77 | − | 1262.85i | 0.0900221 | − | 0.0507798i | ||||
\(853\) | 1776.98 | + | 3077.82i | 0.0713279 | + | 0.123544i | 0.899484 | − | 0.436955i | \(-0.143943\pi\) |
−0.828156 | + | 0.560498i | \(0.810610\pi\) | |||||||
\(854\) | 1940.06 | − | 1098.09i | 0.0777372 | − | 0.0439998i | ||||
\(855\) | 5773.07 | + | 10478.2i | 0.230918 | + | 0.419118i | ||||
\(856\) | −6396.22 | − | 11078.6i | −0.255395 | − | 0.442357i | ||||
\(857\) | 13277.7 | 0.529237 | 0.264619 | − | 0.964353i | \(-0.414754\pi\) | ||||
0.264619 | + | 0.964353i | \(0.414754\pi\) | |||||||
\(858\) | 37168.1 | − | 20965.9i | 1.47890 | − | 0.834222i | ||||
\(859\) | 36198.1 | 1.43779 | 0.718896 | − | 0.695117i | \(-0.244648\pi\) | ||||
0.718896 | + | 0.695117i | \(0.244648\pi\) | |||||||
\(860\) | −788.712 | + | 1366.09i | −0.0312731 | + | 0.0541666i | ||||
\(861\) | 1122.30 | − | 1863.16i | 0.0444227 | − | 0.0737471i | ||||
\(862\) | 14631.8 | + | 25343.1i | 0.578147 | + | 1.00138i | ||||
\(863\) | 8941.47 | + | 15487.1i | 0.352689 | + | 0.610876i | 0.986720 | − | 0.162432i | \(-0.0519339\pi\) |
−0.634030 | + | 0.773308i | \(0.718601\pi\) | |||||||
\(864\) | 17778.1 | − | 9564.38i | 0.700028 | − | 0.376605i | ||||
\(865\) | 6152.32 | − | 10656.1i | 0.241832 | − | 0.418866i | ||||
\(866\) | −17745.9 | + | 30736.8i | −0.696340 | + | 1.20610i | ||||
\(867\) | −50442.7 | + | 28453.8i | −1.97592 | + | 1.11458i | ||||
\(868\) | 5917.45 | + | 3484.23i | 0.231395 | + | 0.136247i | ||||
\(869\) | −9754.36 | + | 16895.0i | −0.380776 | + | 0.659523i | ||||
\(870\) | −93.9162 | + | 9383.04i | −0.00365984 | + | 0.365649i | ||||
\(871\) | 2233.68 | 0.0868949 | ||||||||
\(872\) | 16591.4 | − | 28737.2i | 0.644330 | − | 1.11601i | ||||
\(873\) | 1477.55 | + | 2681.77i | 0.0572824 | + | 0.103968i | ||||
\(874\) | 23599.3 | 0.913341 | ||||||||
\(875\) | 239.201 | − | 27979.5i | 0.00924169 | − | 1.08100i | ||||
\(876\) | 128.267 | − | 12815.0i | 0.00494720 | − | 0.494268i | ||||
\(877\) | −10938.4 | −0.421166 | −0.210583 | − | 0.977576i | \(-0.567536\pi\) | ||||
−0.210583 | + | 0.977576i | \(0.567536\pi\) | |||||||
\(878\) | −18903.0 | − | 32740.9i | −0.726587 | − | 1.25849i | ||||
\(879\) | −27602.5 | − | 16306.8i | −1.05917 | − | 0.625727i | ||||
\(880\) | −15095.6 | + | 26146.4i | −0.578265 | + | 1.00158i | ||||
\(881\) | −16145.8 | −0.617442 | −0.308721 | − | 0.951153i | \(-0.599901\pi\) | ||||
−0.308721 | + | 0.951153i | \(0.599901\pi\) | |||||||
\(882\) | 16613.8 | − | 26457.4i | 0.634258 | − | 1.01005i | ||||
\(883\) | −36343.7 | −1.38512 | −0.692562 | − | 0.721359i | \(-0.743518\pi\) | ||||
−0.692562 | + | 0.721359i | \(0.743518\pi\) | |||||||
\(884\) | 13398.4 | − | 23206.7i | 0.509770 | − | 0.882948i | ||||
\(885\) | 17057.3 | − | 9621.72i | 0.647882 | − | 0.365458i | ||||
\(886\) | −4319.29 | − | 7481.23i | −0.163780 | − | 0.283676i | ||||
\(887\) | 24675.6 | 0.934077 | 0.467038 | − | 0.884237i | \(-0.345321\pi\) | ||||
0.467038 | + | 0.884237i | \(0.345321\pi\) | |||||||
\(888\) | 20382.3 | − | 11497.3i | 0.770255 | − | 0.434486i | ||||
\(889\) | −364.160 | + | 42595.9i | −0.0137385 | + | 1.60700i | ||||
\(890\) | 6851.72 | 0.258057 | ||||||||
\(891\) | 28344.3 | + | 1135.38i | 1.06574 | + | 0.0426898i | ||||
\(892\) | 3387.31 | − | 5867.00i | 0.127148 | − | 0.220226i | ||||
\(893\) | −17585.1 | −0.658972 | ||||||||
\(894\) | 10886.7 | + | 6431.55i | 0.407276 | + | 0.240608i | ||||
\(895\) | −14200.7 | + | 24596.3i | −0.530365 | + | 0.918618i | ||||
\(896\) | −26528.5 | − | 15620.1i | −0.989123 | − | 0.582401i | ||||
\(897\) | 43065.9 | + | 25442.2i | 1.60304 | + | 0.947035i | ||||
\(898\) | 17367.5 | − | 30081.4i | 0.645392 | − | 1.11785i | ||||
\(899\) | 3013.01 | − | 5218.69i | 0.111779 | − | 0.193608i | ||||
\(900\) | −1322.40 | − | 2400.17i | −0.0489779 | − | 0.0888953i | ||||
\(901\) | 16932.3 | + | 29327.6i | 0.626078 | + | 1.08440i | ||||
\(902\) | 1483.44 | + | 2569.40i | 0.0547597 | + | 0.0948465i | ||||
\(903\) | −2229.86 | − | 4033.28i | −0.0821764 | − | 0.148637i | ||||
\(904\) | 3166.64 | − | 5484.78i | 0.116505 | − | 0.201793i | ||||
\(905\) | −8487.89 | −0.311765 | ||||||||
\(906\) | 43268.6 | + | 25561.9i | 1.58665 | + | 0.937350i | ||||
\(907\) | −16901.6 | −0.618753 | −0.309377 | − | 0.950940i | \(-0.600120\pi\) | ||||
−0.309377 | + | 0.950940i | \(0.600120\pi\) | |||||||
\(908\) | 5739.15 | + | 9940.49i | 0.209758 | + | 0.363311i | ||||
\(909\) | −29100.4 | − | 582.598i | −1.06182 | − | 0.0212580i | ||||
\(910\) | −33150.3 | + | 18763.3i | −1.20760 | + | 0.683513i | ||||
\(911\) | −17861.1 | − | 30936.3i | −0.649576 | − | 1.12510i | −0.983224 | − | 0.182401i | \(-0.941613\pi\) |
0.333649 | − | 0.942698i | \(-0.391720\pi\) | |||||||
\(912\) | 188.255 | − | 18808.3i | 0.00683524 | − | 0.682899i | ||||
\(913\) | 6600.39 | + | 11432.2i | 0.239256 | + | 0.414404i | ||||
\(914\) | 24229.3 | + | 41966.3i | 0.876841 | + | 1.51873i | ||||
\(915\) | −1555.66 | − | 919.045i | −0.0562062 | − | 0.0332051i | ||||
\(916\) | 8709.71 | + | 15085.7i | 0.314167 | + | 0.544153i | ||||
\(917\) | −92.4158 | + | 10809.9i | −0.00332807 | + | 0.389286i | ||||
\(918\) | 52816.7 | − | 28414.6i | 1.89892 | − | 1.02159i | ||||
\(919\) | −706.061 | − | 1222.93i | −0.0253436 | − | 0.0438965i | 0.853075 | − | 0.521788i | \(-0.174735\pi\) |
−0.878419 | + | 0.477891i | \(0.841401\pi\) | |||||||
\(920\) | −23369.7 | −0.837475 | ||||||||
\(921\) | 227.880 | − | 22767.2i | 0.00815300 | − | 0.814555i | ||||
\(922\) | −18537.4 | −0.662142 | ||||||||
\(923\) | 4578.24 | − | 7929.75i | 0.163266 | − | 0.282785i | ||||
\(924\) | 6123.90 | + | 11076.6i | 0.218032 | + | 0.394367i | ||||
\(925\) | −4338.59 | − | 7514.66i | −0.154218 | − | 0.267114i | ||||
\(926\) | −12373.5 | − | 21431.5i | −0.439112 | − | 0.760564i | ||||
\(927\) | −46170.8 | − | 924.353i | −1.63587 | − | 0.0327505i | ||||
\(928\) | 3952.09 | − | 6845.22i | 0.139799 | − | 0.242139i | ||||
\(929\) | 6295.72 | − | 10904.5i | 0.222342 | − | 0.385108i | −0.733177 | − | 0.680038i | \(-0.761963\pi\) |
0.955519 | + | 0.294930i | \(0.0952964\pi\) | |||||||
\(930\) | 187.558 | − | 18738.7i | 0.00661321 | − | 0.660717i | ||||
\(931\) | −7565.45 | − | 13637.0i | −0.266324 | − | 0.480059i | ||||
\(932\) | −10319.3 | + | 17873.6i | −0.362684 | + | 0.628187i | ||||
\(933\) | 38299.8 | − | 21604.2i | 1.34392 | − | 0.758082i | ||||
\(934\) | 10142.4 | 0.355321 | ||||||||
\(935\) | −24027.4 | + | 41616.8i | −0.840408 | + | 1.45563i | ||||
\(936\) | 13617.3 | − | 22531.9i | 0.475529 | − | 0.786835i | ||||
\(937\) | 48310.9 | 1.68436 | 0.842182 | − | 0.539193i | \(-0.181271\pi\) | ||||
0.842182 | + | 0.539193i | \(0.181271\pi\) | |||||||
\(938\) | −19.0689 | + | 2230.50i | −0.000663776 | + | 0.0776421i | ||||
\(939\) | 26039.4 | + | 15383.4i | 0.904968 | + | 0.534631i | ||||
\(940\) | −12739.6 | −0.442044 | ||||||||
\(941\) | 10507.2 | + | 18199.0i | 0.364000 | + | 0.630467i | 0.988615 | − | 0.150466i | \(-0.0480773\pi\) |
−0.624615 | + | 0.780933i | \(0.714744\pi\) | |||||||
\(942\) | 131.613 | − | 13149.3i | 0.00455222 | − | 0.454807i | ||||
\(943\) | −1738.81 | + | 3011.71i | −0.0600462 | + | 0.104003i | ||||
\(944\) | −30790.7 | −1.06160 | ||||||||
\(945\) | −25302.6 | − | 976.543i | −0.871000 | − | 0.0336158i | ||||
\(946\) | 6286.39 | 0.216055 | ||||||||
\(947\) | −25990.5 | + | 45016.9i | −0.891845 | + | 1.54472i | −0.0541843 | + | 0.998531i | \(0.517256\pi\) |
−0.837661 | + | 0.546190i | \(0.816077\pi\) | |||||||
\(948\) | 88.1265 | − | 8804.60i | 0.00301921 | − | 0.301646i | ||||
\(949\) | −22826.6 | − | 39536.9i | −0.780805 | − | 1.35239i | ||||
\(950\) | −4605.72 | −0.157294 | ||||||||
\(951\) | −28700.1 | − | 16955.2i | −0.978616 | − | 0.578140i | ||||
\(952\) | −31520.0 | − | 18559.1i | −1.07308 | − | 0.631833i | ||||
\(953\) | −26692.5 | −0.907296 | −0.453648 | − | 0.891181i | \(-0.649878\pi\) | ||||
−0.453648 | + | 0.891181i | \(0.649878\pi\) | |||||||
\(954\) | −11745.7 | − | 21318.6i | −0.398619 | − | 0.723497i | ||||
\(955\) | 15483.7 | − | 26818.6i | 0.524651 | − | 0.908722i | ||||
\(956\) | 8799.33 | 0.297689 | ||||||||
\(957\) | 9673.81 | − | 5456.82i | 0.326761 | − | 0.184320i | ||||
\(958\) | 17885.5 | − | 30978.6i | 0.603187 | − | 1.04475i | ||||
\(959\) | −26.7253 | + | 3126.07i | −0.000899900 | + | 0.105262i | ||||
\(960\) | −76.7901 | + | 7672.00i | −0.00258166 | + | 0.257930i | ||||
\(961\) | 8878.26 | − | 15377.6i | 0.298018 | − | 0.516183i | ||||
\(962\) | −30493.2 | + | 52815.8i | −1.02197 | + | 1.77011i | ||||
\(963\) | 10694.4 | + | 19410.4i | 0.357862 | + | 0.649522i | ||||
\(964\) | −3924.55 | − | 6797.52i | −0.131122 | − | 0.227109i | ||||
\(965\) | −8298.07 | − | 14372.7i | −0.276813 | − | 0.479454i | ||||
\(966\) | −25773.6 | + | 42787.3i | −0.858438 | + | 1.42511i | ||||
\(967\) | −17421.6 | + | 30175.0i | −0.579359 | + | 1.00348i | 0.416194 | + | 0.909276i | \(0.363364\pi\) |
−0.995553 | + | 0.0942029i | \(0.969970\pi\) | |||||||
\(968\) | 2854.75 | 0.0947882 | ||||||||
\(969\) | 299.642 | − | 29936.8i | 0.00993383 | − | 0.992476i | ||||
\(970\) | 3728.11 | 0.123405 | ||||||||
\(971\) | −3963.58 | − | 6865.13i | −0.130996 | − | 0.226892i | 0.793065 | − | 0.609138i | \(-0.208484\pi\) |
−0.924061 | + | 0.382245i | \(0.875151\pi\) | |||||||
\(972\) | −11394.2 | + | 5838.91i | −0.375997 | + | 0.192678i | ||||
\(973\) | −21427.1 | − | 12616.4i | −0.705983 | − | 0.415687i | ||||
\(974\) | −24156.2 | − | 41839.8i | −0.794677 | − | 1.37642i | ||||
\(975\) | −8404.87 | − | 4965.38i | −0.276073 | − | 0.163097i | ||||
\(976\) | 1420.41 | + | 2460.22i | 0.0465842 | + | 0.0806862i | ||||
\(977\) | 3122.04 | + | 5407.52i | 0.102234 | + | 0.177075i | 0.912605 | − | 0.408843i | \(-0.134068\pi\) |
−0.810371 | + | 0.585918i | \(0.800734\pi\) | |||||||
\(978\) | 491.252 | − | 49080.3i | 0.0160619 | − | 1.60472i | ||||
\(979\) | −4055.00 | − | 7023.47i | −0.132378 | − | 0.229286i | ||||
\(980\) | −5480.84 | − | 9879.42i | −0.178652 | − | 0.322027i | ||||
\(981\) | −29733.5 | + | 49198.7i | −0.967704 | + | 1.60122i | ||||
\(982\) | 7123.74 | + | 12338.7i | 0.231495 | + | 0.400961i | ||||
\(983\) | 8380.12 | 0.271907 | 0.135953 | − | 0.990715i | \(-0.456590\pi\) | ||||
0.135953 | + | 0.990715i | \(0.456590\pi\) | |||||||
\(984\) | 1575.93 | + | 931.015i | 0.0510556 | + | 0.0301623i | ||||
\(985\) | −2483.79 | −0.0803453 | ||||||||
\(986\) | 11741.2 | − | 20336.3i | 0.379225 | − | 0.656836i | ||||
\(987\) | 19205.2 | − | 31883.0i | 0.619360 | − | 1.02821i | ||||
\(988\) | 4807.17 | + | 8326.26i | 0.154794 | + | 0.268111i | ||||
\(989\) | 3684.29 | + | 6381.38i | 0.118457 | + | 0.205173i | ||||
\(990\) | 17865.0 | − | 29560.5i | 0.573524 | − | 0.948983i | ||||
\(991\) | 4971.94 | − | 8611.66i | 0.159373 | − | 0.276043i | −0.775269 | − | 0.631631i | \(-0.782386\pi\) |
0.934643 | + | 0.355588i | \(0.115719\pi\) | |||||||
\(992\) | −7892.65 | + | 13670.5i | −0.252613 | + | 0.437538i | ||||
\(993\) | −3708.03 | − | 2190.60i | −0.118500 | − | 0.0700067i | ||||
\(994\) | 7879.35 | + | 4639.41i | 0.251426 | + | 0.148041i | ||||
\(995\) | 3768.55 | − | 6527.32i | 0.120071 | − | 0.207970i | ||||
\(996\) | −5129.73 | − | 3030.51i | −0.163194 | − | 0.0964109i | ||||
\(997\) | 34946.8 | 1.11011 | 0.555053 | − | 0.831815i | \(-0.312698\pi\) | ||||
0.555053 | + | 0.831815i | \(0.312698\pi\) | |||||||
\(998\) | 31537.1 | − | 54623.9i | 1.00029 | − | 1.73255i | ||||
\(999\) | −35701.7 | + | 19207.0i | −1.13068 | + | 0.608291i |
(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 | 63.4.g.a.4.18 | ✓ | 44 | |
3.2 | odd | 2 | 189.4.g.a.172.5 | 44 | |||
7.2 | even | 3 | 63.4.h.a.58.5 | yes | 44 | ||
9.2 | odd | 6 | 189.4.h.a.46.18 | 44 | |||
9.7 | even | 3 | 63.4.h.a.25.5 | yes | 44 | ||
21.2 | odd | 6 | 189.4.h.a.37.18 | 44 | |||
63.2 | odd | 6 | 189.4.g.a.100.5 | 44 | |||
63.16 | even | 3 | inner | 63.4.g.a.16.18 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.g.a.4.18 | ✓ | 44 | 1.1 | even | 1 | trivial | |
63.4.g.a.16.18 | yes | 44 | 63.16 | even | 3 | inner | |
63.4.h.a.25.5 | yes | 44 | 9.7 | even | 3 | ||
63.4.h.a.58.5 | yes | 44 | 7.2 | even | 3 | ||
189.4.g.a.100.5 | 44 | 63.2 | odd | 6 | |||
189.4.g.a.172.5 | 44 | 3.2 | odd | 2 | |||
189.4.h.a.37.18 | 44 | 21.2 | odd | 6 | |||
189.4.h.a.46.18 | 44 | 9.2 | odd | 6 |