Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(136,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 145.4 | ||
Character | \(\chi\) | \(=\) | 819.145 |
Dual form | 819.2.et.c.514.4 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.430820 | + | 0.430820i | −0.304636 | + | 0.304636i | −0.842824 | − | 0.538189i | \(-0.819109\pi\) |
0.538189 | + | 0.842824i | \(0.319109\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.62879i | 0.814394i | ||||||||
\(5\) | −1.97745 | + | 0.529856i | −0.884342 | + | 0.236959i | −0.672279 | − | 0.740297i | \(-0.734685\pi\) |
−0.212062 | + | 0.977256i | \(0.568018\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.23433 | + | 2.34018i | −0.466534 | + | 0.884503i | ||||
\(8\) | −1.56335 | − | 1.56335i | −0.552729 | − | 0.552729i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.623652 | − | 1.08020i | 0.197216 | − | 0.341588i | ||||
\(11\) | 0.0981532 | − | 0.0263001i | 0.0295943 | − | 0.00792977i | −0.243992 | − | 0.969777i | \(-0.578457\pi\) |
0.273586 | + | 0.961848i | \(0.411790\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.09469 | + | 1.85010i | 0.858313 | + | 0.513126i | ||||
\(14\) | −0.476419 | − | 1.53997i | −0.127328 | − | 0.411574i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.91053 | −0.477632 | ||||||||
\(17\) | −3.63007 | −0.880422 | −0.440211 | − | 0.897894i | \(-0.645096\pi\) | ||||
−0.440211 | + | 0.897894i | \(0.645096\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.374251 | − | 1.39672i | 0.0858590 | − | 0.320430i | −0.909616 | − | 0.415449i | \(-0.863624\pi\) |
0.995475 | + | 0.0950189i | \(0.0302911\pi\) | |||||||
\(20\) | −0.863023 | − | 3.22084i | −0.192978 | − | 0.720203i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0309558 | + | 0.0536170i | −0.00659979 | + | 0.0114312i | ||||
\(23\) | 4.80660i | 1.00224i | 0.865376 | + | 0.501122i | \(0.167079\pi\) | ||||
−0.865376 | + | 0.501122i | \(0.832921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.700572 | + | 0.404476i | −0.140114 | + | 0.0808951i | ||||
\(26\) | −2.13032 | + | 0.536194i | −0.417790 | + | 0.105156i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.81165 | − | 2.01047i | −0.720334 | − | 0.379943i | ||||
\(29\) | −3.79375 | − | 6.57097i | −0.704482 | − | 1.22020i | −0.966878 | − | 0.255238i | \(-0.917846\pi\) |
0.262397 | − | 0.964960i | \(-0.415487\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73499 | − | 6.47506i | 0.311613 | − | 1.16296i | −0.615489 | − | 0.788146i | \(-0.711041\pi\) |
0.927102 | − | 0.374810i | \(-0.122292\pi\) | |||||||
\(32\) | 3.94980 | − | 3.94980i | 0.698233 | − | 0.698233i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.56391 | − | 1.56391i | 0.268208 | − | 0.268208i | ||||
\(35\) | 1.20088 | − | 5.28159i | 0.202985 | − | 0.892752i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.15422 | − | 2.15422i | −0.354152 | − | 0.354152i | 0.507500 | − | 0.861652i | \(-0.330570\pi\) |
−0.861652 | + | 0.507500i | \(0.830570\pi\) | |||||||
\(38\) | 0.440501 | + | 0.762971i | 0.0714588 | + | 0.123770i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.91981 | + | 2.26310i | 0.619776 | + | 0.357828i | ||||
\(41\) | 0.872020 | − | 3.25442i | 0.136187 | − | 0.508256i | −0.863804 | − | 0.503829i | \(-0.831924\pi\) |
0.999990 | − | 0.00442675i | \(-0.00140908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.21579 | − | 4.16604i | −1.10040 | − | 0.635315i | −0.164073 | − | 0.986448i | \(-0.552463\pi\) |
−0.936326 | + | 0.351133i | \(0.885796\pi\) | |||||||
\(44\) | 0.0428372 | + | 0.159871i | 0.00645796 | + | 0.0241014i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.07078 | − | 2.07078i | −0.305320 | − | 0.305320i | ||||
\(47\) | 0.529965 | + | 1.97786i | 0.0773034 | + | 0.288500i | 0.993746 | − | 0.111667i | \(-0.0356189\pi\) |
−0.916442 | + | 0.400167i | \(0.868952\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.95284 | − | 5.77711i | −0.564692 | − | 0.825302i | ||||
\(50\) | 0.127564 | − | 0.476077i | 0.0180403 | − | 0.0673275i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.01343 | + | 5.04060i | −0.417887 | + | 0.699005i | ||||
\(53\) | 5.27832 | + | 9.14232i | 0.725033 | + | 1.25579i | 0.958960 | + | 0.283540i | \(0.0915089\pi\) |
−0.233927 | + | 0.972254i | \(0.575158\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.180158 | + | 0.104014i | −0.0242924 | + | 0.0140252i | ||||
\(56\) | 5.58823 | − | 1.72882i | 0.746758 | − | 0.231024i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.46533 | + | 1.19648i | 0.586326 | + | 0.157106i | ||||
\(59\) | 1.58843 | − | 1.58843i | 0.206796 | − | 0.206796i | −0.596108 | − | 0.802904i | \(-0.703287\pi\) |
0.802904 | + | 0.596108i | \(0.203287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.15531 | + | 2.97642i | −0.660070 | + | 0.381091i | −0.792303 | − | 0.610127i | \(-0.791118\pi\) |
0.132234 | + | 0.991219i | \(0.457785\pi\) | |||||||
\(62\) | 2.04212 | + | 3.53706i | 0.259349 | + | 0.449206i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 0.417744i | − | 0.0522180i | ||||||
\(65\) | −7.09988 | − | 2.01874i | −0.880632 | − | 0.250394i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62200 | − | 6.05338i | −0.198158 | − | 0.739537i | −0.991427 | − | 0.130665i | \(-0.958289\pi\) |
0.793268 | − | 0.608872i | \(-0.208378\pi\) | |||||||
\(68\) | − | 5.91262i | − | 0.717011i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.75806 | + | 2.79278i | 0.210128 | + | 0.333801i | ||||
\(71\) | 0.0733605 | + | 0.273785i | 0.00870629 | + | 0.0324923i | 0.970142 | − | 0.242536i | \(-0.0779793\pi\) |
−0.961436 | + | 0.275029i | \(0.911313\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.17396 | + | 1.11841i | 0.488525 | + | 0.130900i | 0.494669 | − | 0.869081i | \(-0.335289\pi\) |
−0.00614434 | + | 0.999981i | \(0.501956\pi\) | |||||||
\(74\) | 1.85616 | 0.215775 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.27496 | + | 0.609575i | 0.260956 | + | 0.0699230i | ||||
\(77\) | −0.0596070 | + | 0.262159i | −0.00679285 | + | 0.0298758i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.01725 | + | 8.69014i | −0.564485 | + | 0.977717i | 0.432612 | + | 0.901580i | \(0.357592\pi\) |
−0.997097 | + | 0.0761370i | \(0.975741\pi\) | |||||||
\(80\) | 3.77797 | − | 1.01230i | 0.422390 | − | 0.113179i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.02639 | + | 1.77775i | 0.113346 | + | 0.196320i | ||||
\(83\) | −3.74842 | − | 3.74842i | −0.411442 | − | 0.411442i | 0.470798 | − | 0.882241i | \(-0.343966\pi\) |
−0.882241 | + | 0.470798i | \(0.843966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.17828 | − | 1.92342i | 0.778594 | − | 0.208624i | ||||
\(86\) | 4.90352 | − | 1.31389i | 0.528760 | − | 0.141681i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.194565 | − | 0.112332i | −0.0207407 | − | 0.0119746i | ||||
\(89\) | −5.75005 | + | 5.75005i | −0.609504 | + | 0.609504i | −0.942817 | − | 0.333312i | \(-0.891834\pi\) |
0.333312 | + | 0.942817i | \(0.391834\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.14945 | + | 4.95848i | −0.854294 | + | 0.519790i | ||||
\(92\) | −7.82893 | −0.816222 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.08042 | − | 0.623781i | −0.111437 | − | 0.0643381i | ||||
\(95\) | 2.96025i | 0.303715i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5697 | − | 4.43983i | 1.68239 | − | 0.450796i | 0.713985 | − | 0.700161i | \(-0.246889\pi\) |
0.968410 | + | 0.249365i | \(0.0802219\pi\) | |||||||
\(98\) | 4.19186 | + | 0.785934i | 0.423442 | + | 0.0793913i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.658805 | − | 1.14108i | −0.0658805 | − | 0.114108i | ||||
\(101\) | −9.40508 | + | 16.2901i | −0.935840 | + | 1.62092i | −0.162711 | + | 0.986674i | \(0.552024\pi\) |
−0.773129 | + | 0.634249i | \(0.781309\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.800311 | − | 1.38618i | 0.0788569 | − | 0.136584i | −0.823900 | − | 0.566735i | \(-0.808206\pi\) |
0.902757 | + | 0.430151i | \(0.141540\pi\) | |||||||
\(104\) | −1.94574 | − | 7.73047i | −0.190795 | − | 0.758035i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.21270 | − | 1.66469i | −0.603431 | − | 0.161689i | ||||
\(107\) | −18.1365 | −1.75333 | −0.876663 | − | 0.481105i | \(-0.840236\pi\) | ||||
−0.876663 | + | 0.481105i | \(0.840236\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.6210 | − | 3.11385i | −1.11309 | − | 0.298252i | −0.345008 | − | 0.938600i | \(-0.612124\pi\) |
−0.768085 | + | 0.640347i | \(0.778790\pi\) | |||||||
\(110\) | 0.0328042 | − | 0.122427i | 0.00312776 | − | 0.0116729i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.35823 | − | 4.47097i | 0.222832 | − | 0.422467i | ||||
\(113\) | −5.06433 | + | 8.77167i | −0.476412 | + | 0.825170i | −0.999635 | − | 0.0270263i | \(-0.991396\pi\) |
0.523223 | + | 0.852196i | \(0.324730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.54680 | − | 9.50480i | −0.237491 | − | 0.886327i | ||||
\(116\) | 10.7027 | − | 6.17921i | 0.993722 | − | 0.573726i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.36865i | 0.125995i | ||||||||
\(119\) | 4.48072 | − | 8.49501i | 0.410747 | − | 0.778736i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.51734 | + | 5.49484i | −0.865212 | + | 0.499531i | ||||
\(122\) | 0.938710 | − | 3.50331i | 0.0849868 | − | 0.317175i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.5465 | + | 2.82593i | 0.947104 | + | 0.253776i | ||||
\(125\) | 8.40900 | − | 8.40900i | 0.752123 | − | 0.752123i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.73205 | − | 4.46410i | 0.686108 | − | 0.396125i | −0.116044 | − | 0.993244i | \(-0.537021\pi\) |
0.802152 | + | 0.597119i | \(0.203688\pi\) | |||||||
\(128\) | 8.07958 | + | 8.07958i | 0.714141 | + | 0.714141i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.92849 | − | 2.18906i | 0.344551 | − | 0.191993i | ||||
\(131\) | 16.4911 | + | 9.52114i | 1.44083 | + | 0.831866i | 0.997905 | − | 0.0646904i | \(-0.0206060\pi\) |
0.442929 | + | 0.896557i | \(0.353939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.80663 | + | 2.59983i | 0.243365 | + | 0.225434i | ||||
\(134\) | 3.30670 | + | 1.90913i | 0.285656 | + | 0.164923i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.67509 | + | 5.67509i | 0.486635 | + | 0.486635i | ||||
\(137\) | −2.60936 | − | 2.60936i | −0.222933 | − | 0.222933i | 0.586800 | − | 0.809732i | \(-0.300388\pi\) |
−0.809732 | + | 0.586800i | \(0.800388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.25815 | − | 1.88110i | −0.276353 | − | 0.159552i | 0.355418 | − | 0.934707i | \(-0.384338\pi\) |
−0.631771 | + | 0.775155i | \(0.717672\pi\) | |||||||
\(140\) | 8.60260 | + | 1.95597i | 0.727052 | + | 0.165310i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.149557 | − | 0.0863470i | −0.0125506 | − | 0.00724608i | ||||
\(143\) | 0.352412 | + | 0.100203i | 0.0294701 | + | 0.00837938i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.9836 | + | 10.9836i | 0.912139 | + | 0.912139i | ||||
\(146\) | −2.28006 | + | 1.31639i | −0.188699 | + | 0.108945i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.50877 | − | 3.50877i | 0.288419 | − | 0.288419i | ||||
\(149\) | −14.7434 | − | 3.95049i | −1.20783 | − | 0.323636i | −0.401918 | − | 0.915676i | \(-0.631656\pi\) |
−0.805909 | + | 0.592039i | \(0.798323\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.29330 | + | 12.2908i | −0.268005 | + | 1.00021i | 0.692380 | + | 0.721533i | \(0.256562\pi\) |
−0.960385 | + | 0.278676i | \(0.910105\pi\) | |||||||
\(152\) | −2.76866 | + | 1.59849i | −0.224568 | + | 0.129654i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0872633 | − | 0.138623i | −0.00703188 | − | 0.0111706i | ||||
\(155\) | 13.7234i | 1.10229i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3520 | − | 8.86346i | 1.22522 | − | 0.707381i | 0.259194 | − | 0.965825i | \(-0.416543\pi\) |
0.966026 | + | 0.258444i | \(0.0832096\pi\) | |||||||
\(158\) | −1.58235 | − | 5.90542i | −0.125885 | − | 0.469810i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.71771 | + | 9.90336i | −0.452024 | + | 0.782929i | ||||
\(161\) | −11.2483 | − | 5.93295i | −0.886489 | − | 0.467582i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.17370 | + | 23.0406i | −0.483562 | + | 1.80468i | 0.102891 | + | 0.994693i | \(0.467191\pi\) |
−0.586452 | + | 0.809984i | \(0.699476\pi\) | |||||||
\(164\) | 5.30077 | + | 1.42034i | 0.413920 | + | 0.110910i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.22979 | 0.250680 | ||||||||
\(167\) | −6.81217 | − | 1.82532i | −0.527141 | − | 0.141247i | −0.0145735 | − | 0.999894i | \(-0.504639\pi\) |
−0.512568 | + | 0.858647i | \(0.671306\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.15424 | + | 11.4510i | 0.473403 | + | 0.880846i | ||||
\(170\) | −2.26390 | + | 3.92119i | −0.173633 | + | 0.300742i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.78560 | − | 11.7530i | 0.517397 | − | 0.896158i | ||||
\(173\) | 11.1650 | + | 19.3383i | 0.848859 | + | 1.47027i | 0.882227 | + | 0.470824i | \(0.156043\pi\) |
−0.0333684 | + | 0.999443i | \(0.510623\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0818039 | − | 2.13872i | −0.00618379 | − | 0.161672i | ||||
\(176\) | −0.187524 | + | 0.0502470i | −0.0141352 | + | 0.00378751i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 4.95448i | − | 0.371354i | ||||||
\(179\) | −8.47154 | − | 4.89104i | −0.633192 | − | 0.365574i | 0.148795 | − | 0.988868i | \(-0.452461\pi\) |
−0.781987 | + | 0.623294i | \(0.785794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1944 | −1.05506 | −0.527530 | − | 0.849536i | \(-0.676882\pi\) | ||||
−0.527530 | + | 0.849536i | \(0.676882\pi\) | |||||||
\(182\) | 1.37473 | − | 5.64716i | 0.101902 | − | 0.418595i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.51442 | − | 7.51442i | 0.553970 | − | 0.553970i | ||||
\(185\) | 5.40128 | + | 3.11843i | 0.397110 | + | 0.229272i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.356303 | + | 0.0954712i | −0.0260555 | + | 0.00698154i | ||||
\(188\) | −3.22151 | + | 0.863201i | −0.234953 | + | 0.0629554i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.27533 | − | 1.27533i | −0.0925224 | − | 0.0925224i | ||||
\(191\) | −2.33347 | − | 4.04168i | −0.168844 | − | 0.292446i | 0.769170 | − | 0.639044i | \(-0.220670\pi\) |
−0.938014 | + | 0.346598i | \(0.887337\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.08020 | + | 1.36124i | −0.365681 | + | 0.0979839i | −0.436980 | − | 0.899471i | \(-0.643952\pi\) |
0.0712994 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(194\) | −5.22578 | + | 9.05131i | −0.375189 | + | 0.649846i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.40969 | − | 6.43834i | 0.672121 | − | 0.459881i | ||||
\(197\) | 11.0378 | + | 2.95757i | 0.786411 | + | 0.210718i | 0.629609 | − | 0.776912i | \(-0.283215\pi\) |
0.156802 | + | 0.987630i | \(0.449882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.97182 | −0.494219 | −0.247110 | − | 0.968987i | \(-0.579481\pi\) | ||||
−0.247110 | + | 0.968987i | \(0.579481\pi\) | |||||||
\(200\) | 1.72758 | + | 0.462904i | 0.122159 | + | 0.0327323i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.96619 | − | 11.0700i | −0.208701 | − | 0.778881i | ||||
\(203\) | 20.0600 | − | 0.767273i | 1.40793 | − | 0.0538520i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.89750i | 0.481742i | ||||||||
\(206\) | 0.252404 | + | 0.941984i | 0.0175858 | + | 0.0656311i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.91249 | − | 3.53467i | −0.409958 | − | 0.245085i | ||||
\(209\) | − | 0.146936i | − | 0.0101637i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.94886 | + | 6.83963i | 0.271851 | + | 0.470860i | 0.969336 | − | 0.245740i | \(-0.0790309\pi\) |
−0.697485 | + | 0.716600i | \(0.745698\pi\) | |||||||
\(212\) | −14.8909 | + | 8.59727i | −1.02271 | + | 0.590463i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.81359 | − | 7.81359i | 0.534126 | − | 0.534126i | ||||
\(215\) | 16.4763 | + | 4.41480i | 1.12367 | + | 0.301087i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.0112 | + | 12.0526i | 0.883260 | + | 0.818181i | ||||
\(218\) | 6.34808 | − | 3.66507i | 0.429946 | − | 0.248230i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.169417 | − | 0.293439i | −0.0114221 | − | 0.0197836i | ||||
\(221\) | −11.2340 | − | 6.71601i | −0.755678 | − | 0.451768i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.02363 | + | 11.2843i | −0.202477 | + | 0.755654i | 0.787727 | + | 0.616025i | \(0.211258\pi\) |
−0.990204 | + | 0.139630i | \(0.955409\pi\) | |||||||
\(224\) | 4.36786 | + | 14.1186i | 0.291840 | + | 0.943339i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.59720 | − | 5.96083i | −0.106244 | − | 0.396508i | ||||
\(227\) | −7.36360 | − | 7.36360i | −0.488739 | − | 0.488739i | 0.419169 | − | 0.907908i | \(-0.362322\pi\) |
−0.907908 | + | 0.419169i | \(0.862322\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.194192 | − | 0.724734i | −0.0128326 | − | 0.0478918i | 0.959213 | − | 0.282685i | \(-0.0912252\pi\) |
−0.972045 | + | 0.234794i | \(0.924559\pi\) | |||||||
\(230\) | 5.19207 | + | 2.99764i | 0.342355 | + | 0.197659i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.34178 | + | 16.2037i | −0.285052 | + | 1.06383i | ||||
\(233\) | 22.2901 | + | 12.8692i | 1.46028 | + | 0.843091i | 0.999024 | − | 0.0441785i | \(-0.0140670\pi\) |
0.461252 | + | 0.887269i | \(0.347400\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.09596 | − | 3.63031i | −0.136725 | − | 0.236815i | ||||
\(236\) | 2.58721 | + | 2.58721i | 0.168413 | + | 0.168413i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.72944 | + | 5.59021i | 0.112103 | + | 0.362359i | ||||
\(239\) | 8.82009 | − | 8.82009i | 0.570524 | − | 0.570524i | −0.361751 | − | 0.932275i | \(-0.617821\pi\) |
0.932275 | + | 0.361751i | \(0.117821\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.8684 | + | 20.8684i | −1.34425 | + | 1.34425i | −0.452474 | + | 0.891777i | \(0.649459\pi\) |
−0.891777 | + | 0.452474i | \(0.850541\pi\) | |||||||
\(242\) | 1.73297 | − | 6.46755i | 0.111400 | − | 0.415750i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.84796 | − | 8.39690i | −0.310359 | − | 0.537557i | ||||
\(245\) | 10.8776 | + | 9.32951i | 0.694943 | + | 0.596040i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.74227 | − | 3.63002i | 0.238115 | − | 0.230973i | ||||
\(248\) | −12.8352 | + | 7.41042i | −0.815038 | + | 0.470562i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.24553i | 0.458247i | ||||||||
\(251\) | 3.38771 | − | 5.86769i | 0.213831 | − | 0.370365i | −0.739080 | − | 0.673618i | \(-0.764739\pi\) |
0.952910 | + | 0.303253i | \(0.0980726\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.126414 | + | 0.471783i | 0.00794757 | + | 0.0296607i | ||||
\(254\) | −1.40790 | + | 5.25435i | −0.0883394 | + | 0.329687i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.12620 | −0.382888 | ||||||||
\(257\) | 12.9504 | 0.807822 | 0.403911 | − | 0.914798i | \(-0.367651\pi\) | ||||
0.403911 | + | 0.914798i | \(0.367651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.70028 | − | 2.38223i | 0.478472 | − | 0.148024i | ||||
\(260\) | 3.28810 | − | 11.5642i | 0.203919 | − | 0.717181i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.2066 | + | 3.00280i | −0.692346 | + | 0.185514i | ||||
\(263\) | −2.76188 | + | 4.78372i | −0.170305 | + | 0.294977i | −0.938526 | − | 0.345207i | \(-0.887809\pi\) |
0.768222 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.2817 | − | 15.2817i | −0.938748 | − | 0.938748i | ||||
\(266\) | −2.32921 | + | 0.0890900i | −0.142813 | + | 0.00546246i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.85967 | − | 2.64189i | 0.602275 | − | 0.161379i | ||||
\(269\) | − | 12.1333i | − | 0.739778i | −0.929076 | − | 0.369889i | \(-0.879396\pi\) | ||
0.929076 | − | 0.369889i | \(-0.120604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.61558 | + | 1.61558i | −0.0981395 | + | 0.0981395i | −0.754472 | − | 0.656332i | \(-0.772107\pi\) |
0.656332 | + | 0.754472i | \(0.272107\pi\) | |||||||
\(272\) | 6.93535 | 0.420518 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.24833 | 0.135827 | ||||||||
\(275\) | −0.0581257 | + | 0.0581257i | −0.00350511 | + | 0.00350511i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.18421i | 0.311489i | 0.987797 | + | 0.155745i | \(0.0497777\pi\) | ||||
−0.987797 | + | 0.155745i | \(0.950222\pi\) | |||||||
\(278\) | 2.21409 | − | 0.593264i | 0.132792 | − | 0.0355816i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.1344 | + | 6.37961i | −0.605646 | + | 0.381255i | ||||
\(281\) | −13.5499 | − | 13.5499i | −0.808321 | − | 0.808321i | 0.176059 | − | 0.984380i | \(-0.443665\pi\) |
−0.984380 | + | 0.176059i | \(0.943665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.84696 | − | 11.8593i | 0.407009 | − | 0.704961i | −0.587544 | − | 0.809192i | \(-0.699905\pi\) |
0.994553 | + | 0.104232i | \(0.0332383\pi\) | |||||||
\(284\) | −0.445938 | + | 0.119489i | −0.0264615 | + | 0.00709035i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.194995 | + | 0.108657i | −0.0115303 | + | 0.00642500i | ||||
\(287\) | 6.53956 | + | 6.05772i | 0.386018 | + | 0.357576i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.82256 | −0.224857 | ||||||||
\(290\) | −9.46392 | −0.555740 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.82165 | + | 6.79850i | −0.106604 | + | 0.397852i | ||||
\(293\) | 5.35275 | + | 19.9768i | 0.312711 | + | 1.16705i | 0.926102 | + | 0.377274i | \(0.123139\pi\) |
−0.613390 | + | 0.789780i | \(0.710195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.29940 | + | 3.98267i | −0.133876 | + | 0.231880i | ||||
\(296\) | 6.73562i | 0.391500i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.05371 | − | 4.64981i | 0.466539 | − | 0.269356i | ||||
\(299\) | −8.89270 | + | 14.8749i | −0.514278 | + | 0.860240i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.6560 | − | 11.7439i | 1.07531 | − | 0.676909i | ||||
\(302\) | −3.87629 | − | 6.71393i | −0.223055 | − | 0.386343i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.715016 | + | 2.66848i | −0.0410090 | + | 0.153048i | ||||
\(305\) | 8.61728 | − | 8.61728i | 0.493424 | − | 0.493424i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7621 | − | 12.7621i | 0.728370 | − | 0.728370i | −0.241925 | − | 0.970295i | \(-0.577779\pi\) |
0.970295 | + | 0.241925i | \(0.0777788\pi\) | |||||||
\(308\) | −0.427001 | − | 0.0970872i | −0.0243306 | − | 0.00553206i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.91232 | − | 5.91232i | −0.335797 | − | 0.335797i | ||||
\(311\) | 3.99213 | + | 6.91458i | 0.226373 | + | 0.392090i | 0.956731 | − | 0.290975i | \(-0.0939798\pi\) |
−0.730357 | + | 0.683065i | \(0.760646\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.6125 | − | 9.59123i | −0.938994 | − | 0.542129i | −0.0493493 | − | 0.998782i | \(-0.515715\pi\) |
−0.889645 | + | 0.456653i | \(0.849048\pi\) | |||||||
\(314\) | −2.79538 | + | 10.4325i | −0.157752 | + | 0.588740i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.1544 | − | 8.17204i | −0.796247 | − | 0.459713i | ||||
\(317\) | −6.86941 | − | 25.6370i | −0.385824 | − | 1.43992i | −0.836864 | − | 0.547412i | \(-0.815613\pi\) |
0.451039 | − | 0.892504i | \(-0.351053\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.545185 | − | 0.545185i | −0.0305245 | − | 0.0305245i | ||||
\(320\) | 0.221344 | + | 0.826067i | 0.0123735 | + | 0.0461785i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.40202 | − | 2.28995i | 0.412498 | − | 0.127614i | ||||
\(323\) | −1.35856 | + | 5.07021i | −0.0755922 | + | 0.282114i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.91638 | − | 0.0444031i | −0.161772 | − | 0.00246304i | ||||
\(326\) | −7.26659 | − | 12.5861i | −0.402459 | − | 0.697079i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.45110 | + | 3.72454i | −0.356202 | + | 0.205653i | ||||
\(329\) | −5.28269 | − | 1.20112i | −0.291244 | − | 0.0662201i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.6825 | − | 8.75726i | −1.79639 | − | 0.481343i | −0.802989 | − | 0.595994i | \(-0.796758\pi\) |
−0.993406 | + | 0.114651i | \(0.963425\pi\) | |||||||
\(332\) | 6.10538 | − | 6.10538i | 0.335076 | − | 0.335076i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.72120 | − | 2.14844i | 0.203615 | − | 0.117557i | ||||
\(335\) | 6.41483 | + | 11.1108i | 0.350480 | + | 0.607049i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.82368i | − | 0.262763i | −0.991332 | − | 0.131381i | \(-0.958059\pi\) | ||
0.991332 | − | 0.131381i | \(-0.0419412\pi\) | |||||||
\(338\) | −7.58469 | − | 2.28195i | −0.412553 | − | 0.124122i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.13284 | + | 11.6919i | 0.169902 | + | 0.634082i | ||||
\(341\) | − | 0.681178i | − | 0.0368879i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3986 | − | 2.11945i | 0.993430 | − | 0.114440i | ||||
\(344\) | 4.76785 | + | 17.7938i | 0.257065 | + | 0.959380i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.1415 | − | 3.52124i | −0.706489 | − | 0.189303i | ||||
\(347\) | −30.0530 | −1.61333 | −0.806664 | − | 0.591010i | \(-0.798729\pi\) | ||||
−0.806664 | + | 0.591010i | \(0.798729\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.5463 | + | 7.91691i | 1.58158 | + | 0.423782i | 0.939414 | − | 0.342785i | \(-0.111370\pi\) |
0.642164 | + | 0.766567i | \(0.278037\pi\) | |||||||
\(350\) | 0.956647 | + | 0.886161i | 0.0511349 | + | 0.0473673i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.283806 | − | 0.491566i | 0.0151269 | − | 0.0262005i | ||||
\(353\) | −30.1693 | + | 8.08384i | −1.60575 | + | 0.430260i | −0.946773 | − | 0.321903i | \(-0.895678\pi\) |
−0.658978 | + | 0.752162i | \(0.729011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.290133 | − | 0.502525i | −0.0153987 | − | 0.0266713i | ||||
\(356\) | −9.36562 | − | 9.36562i | −0.496377 | − | 0.496377i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.75687 | − | 1.54255i | 0.304260 | − | 0.0815262i | ||||
\(359\) | −12.8721 | + | 3.44908i | −0.679366 | + | 0.182035i | −0.581970 | − | 0.813210i | \(-0.697718\pi\) |
−0.0973957 | + | 0.995246i | \(0.531051\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6437 | + | 8.45455i | 0.770722 | + | 0.444976i | ||||
\(362\) | 6.11523 | − | 6.11523i | 0.321409 | − | 0.321409i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.07631 | − | 13.2737i | −0.423314 | − | 0.695732i | ||||
\(365\) | −8.84639 | −0.463041 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.0733 | − | 11.5893i | −1.04782 | − | 0.604957i | −0.125779 | − | 0.992058i | \(-0.540143\pi\) |
−0.922037 | + | 0.387101i | \(0.873476\pi\) | |||||||
\(368\) | − | 9.18313i | − | 0.478704i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.67047 | + | 0.983498i | −0.190818 | + | 0.0511296i | ||||
\(371\) | −27.9098 | + | 1.06752i | −1.44901 | + | 0.0554230i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.724254 | − | 1.25444i | −0.0375004 | − | 0.0649527i | 0.846666 | − | 0.532125i | \(-0.178606\pi\) |
−0.884166 | + | 0.467172i | \(0.845273\pi\) | |||||||
\(374\) | 0.112372 | − | 0.194634i | 0.00581060 | − | 0.0100643i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.26357 | − | 3.92062i | 0.116735 | − | 0.202190i | ||||
\(377\) | 0.416476 | − | 27.3539i | 0.0214496 | − | 1.40880i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.31805 | − | 0.621121i | −0.119070 | − | 0.0319048i | 0.198792 | − | 0.980042i | \(-0.436298\pi\) |
−0.317862 | + | 0.948137i | \(0.602965\pi\) | |||||||
\(380\) | −4.82161 | −0.247343 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.74654 | + | 0.735934i | 0.140525 | + | 0.0376537i | ||||
\(383\) | 7.48482 | − | 27.9337i | 0.382456 | − | 1.42735i | −0.459681 | − | 0.888084i | \(-0.652036\pi\) |
0.842137 | − | 0.539263i | \(-0.181297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0210365 | − | 0.549988i | −0.00107212 | − | 0.0280300i | ||||
\(386\) | 1.60221 | − | 2.77510i | 0.0815501 | − | 0.141249i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.23154 | + | 26.9885i | 0.367126 | + | 1.37013i | ||||
\(389\) | 26.2815 | − | 15.1736i | 1.33252 | − | 0.769332i | 0.346837 | − | 0.937925i | \(-0.387256\pi\) |
0.985686 | + | 0.168593i | \(0.0539223\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.4483i | − | 0.882399i | ||||||
\(392\) | −2.85199 | + | 15.2114i | −0.144047 | + | 0.768290i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.02949 | + | 3.48113i | −0.303761 | + | 0.175377i | ||||
\(395\) | 5.31684 | − | 19.8427i | 0.267519 | − | 0.998396i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6187 | + | 4.45296i | 0.834068 | + | 0.223488i | 0.650488 | − | 0.759517i | \(-0.274565\pi\) |
0.183580 | + | 0.983005i | \(0.441231\pi\) | |||||||
\(398\) | 3.00360 | − | 3.00360i | 0.150557 | − | 0.150557i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.33846 | − | 0.772762i | 0.0669231 | − | 0.0386381i | ||||
\(401\) | 10.6544 | + | 10.6544i | 0.532056 | + | 0.532056i | 0.921184 | − | 0.389128i | \(-0.127224\pi\) |
−0.389128 | + | 0.921184i | \(0.627224\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.3488 | − | 16.8284i | 0.864205 | − | 0.838283i | ||||
\(404\) | −26.5331 | − | 15.3189i | −1.32007 | − | 0.762143i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.31168 | + | 8.97279i | −0.412502 | + | 0.445312i | ||||
\(407\) | −0.268100 | − | 0.154787i | −0.0132892 | − | 0.00767253i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7272 | + | 12.7272i | 0.629320 | + | 0.629320i | 0.947897 | − | 0.318577i | \(-0.103205\pi\) |
−0.318577 | + | 0.947897i | \(0.603205\pi\) | |||||||
\(410\) | −2.97158 | − | 2.97158i | −0.146756 | − | 0.146756i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.25779 | + | 1.30354i | 0.111233 | + | 0.0642206i | ||||
\(413\) | 1.75655 | + | 5.67785i | 0.0864341 | + | 0.279389i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.39842 | + | 5.42618i | 0.461351 | + | 0.266361i | ||||
\(416\) | 19.5310 | − | 4.91588i | 0.957584 | − | 0.241021i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0633028 | + | 0.0633028i | 0.00309624 | + | 0.00309624i | ||||
\(419\) | −13.0716 | + | 7.54692i | −0.638592 | + | 0.368691i | −0.784072 | − | 0.620670i | \(-0.786861\pi\) |
0.145480 | + | 0.989361i | \(0.453527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.2298 | + | 13.2298i | −0.644780 | + | 0.644780i | −0.951727 | − | 0.306947i | \(-0.900693\pi\) |
0.306947 | + | 0.951727i | \(0.400693\pi\) | |||||||
\(422\) | −4.64790 | − | 1.24540i | −0.226256 | − | 0.0606252i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.04080 | − | 22.5446i | 0.293367 | − | 1.09486i | ||||
\(425\) | 2.54313 | − | 1.46828i | 0.123360 | − | 0.0712219i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.601971 | − | 15.7382i | −0.0291314 | − | 0.761626i | ||||
\(428\) | − | 29.5406i | − | 1.42790i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.00029 | + | 5.19632i | −0.434032 | + | 0.250589i | ||||
\(431\) | −10.5271 | − | 39.2876i | −0.507072 | − | 1.89242i | −0.447701 | − | 0.894183i | \(-0.647757\pi\) |
−0.0593708 | − | 0.998236i | \(-0.518909\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.94157 | + | 3.36289i | −0.0933058 | + | 0.161610i | −0.908900 | − | 0.417014i | \(-0.863077\pi\) |
0.815594 | + | 0.578624i | \(0.196410\pi\) | |||||||
\(434\) | −10.7980 | + | 0.413012i | −0.518320 | + | 0.0198252i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.07180 | − | 18.9282i | 0.242895 | − | 0.906496i | ||||
\(437\) | 6.71348 | + | 1.79887i | 0.321149 | + | 0.0860517i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.3601 | −1.11491 | −0.557457 | − | 0.830206i | \(-0.688223\pi\) | ||||
−0.557457 | + | 0.830206i | \(0.688223\pi\) | |||||||
\(440\) | 0.444261 | + | 0.119039i | 0.0211793 | + | 0.00567498i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.73321 | − | 1.94642i | 0.367831 | − | 0.0925820i | ||||
\(443\) | 7.62370 | − | 13.2046i | 0.362213 | − | 0.627371i | −0.626112 | − | 0.779733i | \(-0.715355\pi\) |
0.988325 | + | 0.152362i | \(0.0486880\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.32374 | − | 14.4171i | 0.394583 | − | 0.683438i | ||||
\(446\) | −3.55888 | − | 6.16415i | −0.168518 | − | 0.291881i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.977594 | + | 0.515635i | 0.0461870 | + | 0.0243615i | ||||
\(449\) | −22.2529 | + | 5.96266i | −1.05018 | + | 0.281395i | −0.742327 | − | 0.670038i | \(-0.766278\pi\) |
−0.307855 | + | 0.951433i | \(0.599611\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.342366i | − | 0.0161214i | ||||||
\(452\) | −14.2872 | − | 8.24872i | −0.672013 | − | 0.387987i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.34478 | 0.297775 | ||||||||
\(455\) | 13.4878 | − | 14.1232i | 0.632319 | − | 0.662104i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.86607 | + | 2.86607i | −0.134069 | + | 0.134069i | −0.770957 | − | 0.636887i | \(-0.780222\pi\) |
0.636887 | + | 0.770957i | \(0.280222\pi\) | |||||||
\(458\) | 0.395892 | + | 0.228568i | 0.0184988 | + | 0.0106803i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.4813 | − | 4.14820i | 0.721819 | − | 0.193411i | ||||
\(461\) | 14.2239 | − | 3.81128i | 0.662473 | − | 0.177509i | 0.0881113 | − | 0.996111i | \(-0.471917\pi\) |
0.574362 | + | 0.818601i | \(0.305250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.88913 | + | 3.88913i | 0.180743 | + | 0.180743i | 0.791680 | − | 0.610936i | \(-0.209207\pi\) |
−0.610936 | + | 0.791680i | \(0.709207\pi\) | |||||||
\(464\) | 7.24806 | + | 12.5540i | 0.336483 | + | 0.582805i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.1474 | + | 4.05872i | −0.701688 | + | 0.188017i | ||||
\(467\) | −2.18755 | + | 3.78894i | −0.101228 | + | 0.175331i | −0.912191 | − | 0.409766i | \(-0.865610\pi\) |
0.810963 | + | 0.585097i | \(0.198944\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.1680 | + | 3.67613i | 0.746571 | + | 0.169748i | ||||
\(470\) | 2.46699 | + | 0.661028i | 0.113794 | + | 0.0304909i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.96655 | −0.228604 | ||||||||
\(473\) | −0.817820 | − | 0.219134i | −0.0376034 | − | 0.0100758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.302751 | + | 1.12988i | 0.0138912 | + | 0.0518425i | ||||
\(476\) | 13.8366 | + | 7.29815i | 0.634198 | + | 0.334510i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.59974i | 0.347604i | ||||||||
\(479\) | −8.19394 | − | 30.5802i | −0.374391 | − | 1.39724i | −0.854233 | − | 0.519890i | \(-0.825973\pi\) |
0.479843 | − | 0.877355i | \(-0.340694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.68112 | − | 10.6522i | −0.122249 | − | 0.485697i | ||||
\(482\) | − | 17.9811i | − | 0.819015i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.94993 | − | 15.5017i | −0.406815 | − | 0.704624i | ||||
\(485\) | −30.4132 | + | 17.5591i | −1.38099 | + | 0.797316i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.4600 | + | 22.4600i | −1.01776 | + | 1.01776i | −0.0179183 | + | 0.999839i | \(0.505704\pi\) |
−0.999839 | + | 0.0179183i | \(0.994296\pi\) | |||||||
\(488\) | 12.7128 | + | 3.40638i | 0.575480 | + | 0.154199i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.70562 | + | 0.666938i | −0.393280 | + | 0.0301292i | ||||
\(491\) | −3.19371 | + | 1.84389i | −0.144130 | + | 0.0832136i | −0.570331 | − | 0.821415i | \(-0.693185\pi\) |
0.426201 | + | 0.904629i | \(0.359852\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.7716 | + | 23.8531i | 0.620241 | + | 1.07429i | ||||
\(494\) | −0.0483580 | + | 3.17613i | −0.00217573 | + | 0.142901i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.31474 | + | 12.3708i | −0.148836 | + | 0.555464i | ||||
\(497\) | −0.731257 | − | 0.166266i | −0.0328013 | − | 0.00745804i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.61668 | − | 28.4258i | −0.340969 | − | 1.27252i | −0.897251 | − | 0.441521i | \(-0.854439\pi\) |
0.556281 | − | 0.830994i | \(-0.312228\pi\) | |||||||
\(500\) | 13.6965 | + | 13.6965i | 0.612525 | + | 0.612525i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.06842 | + | 3.98741i | 0.0476861 | + | 0.177967i | ||||
\(503\) | 12.1149 | + | 6.99455i | 0.540178 | + | 0.311872i | 0.745151 | − | 0.666896i | \(-0.232377\pi\) |
−0.204973 | + | 0.978768i | \(0.565711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.96667 | − | 37.1961i | 0.443511 | − | 1.65520i | ||||
\(506\) | −0.257715 | − | 0.148792i | −0.0114568 | − | 0.00661461i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.27107 | + | 12.5939i | 0.322602 | + | 0.558763i | ||||
\(509\) | 26.6190 | + | 26.6190i | 1.17987 | + | 1.17987i | 0.979777 | + | 0.200090i | \(0.0641235\pi\) |
0.200090 | + | 0.979777i | \(0.435877\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.76933 | + | 8.38731i | −0.343695 | + | 0.371033i | ||||
\(512\) | −13.5199 | + | 13.5199i | −0.597499 | + | 0.597499i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.57928 | + | 5.57928i | −0.246092 | + | 0.246092i | ||||
\(515\) | −0.848098 | + | 3.16515i | −0.0373717 | + | 0.139473i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.104036 | + | 0.180195i | 0.00457548 | + | 0.00792496i | ||||
\(518\) | −2.29112 | + | 4.34375i | −0.100666 | + | 0.190853i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.94362 | + | 14.2556i | 0.348351 | + | 0.625151i | ||||
\(521\) | 6.79737 | − | 3.92446i | 0.297798 | − | 0.171934i | −0.343655 | − | 0.939096i | \(-0.611665\pi\) |
0.641453 | + | 0.767162i | \(0.278332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.2423i | 0.579043i | 0.957171 | + | 0.289522i | \(0.0934962\pi\) | ||||
−0.957171 | + | 0.289522i | \(0.906504\pi\) | |||||||
\(524\) | −15.5079 | + | 26.8605i | −0.677467 | + | 1.17341i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.871048 | − | 3.25079i | −0.0379795 | − | 0.141741i | ||||
\(527\) | −6.29813 | + | 23.5050i | −0.274351 | + | 1.02389i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.103385 | −0.00449500 | ||||||||
\(530\) | 13.1673 | 0.571953 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.23458 | + | 4.57140i | −0.183592 | + | 0.198195i | ||||
\(533\) | 8.71965 | − | 8.45811i | 0.377690 | − | 0.366362i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.8641 | − | 9.60975i | 1.55054 | − | 0.415466i | ||||
\(536\) | −6.92782 | + | 11.9993i | −0.299236 | + | 0.518292i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.22726 | + | 5.22726i | 0.225363 | + | 0.225363i | ||||
\(539\) | −0.539922 | − | 0.463082i | −0.0232561 | − | 0.0199464i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.6349 | − | 6.33296i | 1.01614 | − | 0.272275i | 0.287950 | − | 0.957645i | \(-0.407026\pi\) |
0.728195 | + | 0.685370i | \(0.240360\pi\) | |||||||
\(542\) | − | 1.39205i | − | 0.0597936i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.3381 | + | 14.3381i | −0.614740 | + | 0.614740i | ||||
\(545\) | 24.6299 | 1.05503 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.7857 | −1.70111 | −0.850557 | − | 0.525883i | \(-0.823735\pi\) | ||||
−0.850557 | + | 0.525883i | \(0.823735\pi\) | |||||||
\(548\) | 4.25009 | − | 4.25009i | 0.181555 | − | 0.181555i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 0.0500834i | − | 0.00213556i | ||||||
\(551\) | −10.5976 | + | 2.83963i | −0.451474 | + | 0.120972i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.1435 | − | 22.4678i | −0.601442 | − | 0.955428i | ||||
\(554\) | −2.23346 | − | 2.23346i | −0.0948908 | − | 0.0948908i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.06391 | − | 5.30684i | 0.129939 | − | 0.225060i | ||||
\(557\) | 0.380110 | − | 0.101850i | 0.0161058 | − | 0.00431553i | −0.250757 | − | 0.968050i | \(-0.580680\pi\) |
0.266863 | + | 0.963734i | \(0.414013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6231 | − | 26.2426i | −0.618489 | − | 1.10994i | ||||
\(560\) | −2.29431 | + | 10.0906i | −0.0969521 | + | 0.426407i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.6752 | 0.492487 | ||||||||
\(563\) | −27.7772 | −1.17067 | −0.585335 | − | 0.810792i | \(-0.699037\pi\) | ||||
−0.585335 | + | 0.810792i | \(0.699037\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.36673 | − | 20.0289i | 0.225780 | − | 0.842622i | ||||
\(566\) | 2.15941 | + | 8.05902i | 0.0907667 | + | 0.338746i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.313335 | − | 0.542712i | 0.0131472 | − | 0.0227717i | ||||
\(569\) | − | 0.573198i | − | 0.0240297i | −0.999928 | − | 0.0120149i | \(-0.996175\pi\) | ||
0.999928 | − | 0.0120149i | \(-0.00382454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.2481 | − | 15.1543i | 1.09845 | − | 0.634189i | 0.162635 | − | 0.986686i | \(-0.448001\pi\) |
0.935813 | + | 0.352497i | \(0.114667\pi\) | |||||||
\(572\) | −0.163209 | + | 0.574004i | −0.00682412 | + | 0.0240003i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.42716 | + | 0.207583i | −0.226525 | + | 0.00866437i | ||||
\(575\) | −1.94415 | − | 3.36737i | −0.0810768 | − | 0.140429i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1337 | + | 37.8193i | −0.421870 | + | 1.57444i | 0.348795 | + | 0.937199i | \(0.386591\pi\) |
−0.770665 | + | 0.637240i | \(0.780076\pi\) | |||||||
\(578\) | 1.64684 | − | 1.64684i | 0.0684994 | − | 0.0684994i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.8900 | + | 17.8900i | −0.742841 | + | 0.742841i | ||||
\(581\) | 13.3988 | − | 4.14516i | 0.555874 | − | 0.171970i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.758528 | + | 0.758528i | 0.0314150 | + | 0.0314150i | ||||
\(584\) | −4.77691 | − | 8.27385i | −0.197670 | − | 0.342374i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.9125 | − | 6.30031i | −0.450790 | − | 0.260264i | ||||
\(587\) | −4.30312 | + | 16.0595i | −0.177609 | + | 0.662845i | 0.818484 | + | 0.574530i | \(0.194815\pi\) |
−0.996093 | + | 0.0883156i | \(0.971852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.39455 | − | 4.84659i | −0.345891 | − | 0.199700i | ||||
\(590\) | −0.725188 | − | 2.70644i | −0.0298555 | − | 0.111422i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.11569 | + | 4.11569i | 0.169154 | + | 0.169154i | ||||
\(593\) | 1.93471 | + | 7.22043i | 0.0794489 | + | 0.296507i | 0.994205 | − | 0.107499i | \(-0.0342841\pi\) |
−0.914756 | + | 0.404006i | \(0.867617\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.35927 | + | 19.1726i | −0.178713 | + | 0.785999i | ||||
\(596\) | 6.43450 | − | 24.0139i | 0.263568 | − | 0.983647i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.57727 | − | 10.2396i | −0.105392 | − | 0.418727i | ||||
\(599\) | −2.38287 | − | 4.12725i | −0.0973613 | − | 0.168635i | 0.813230 | − | 0.581942i | \(-0.197707\pi\) |
−0.910592 | + | 0.413307i | \(0.864374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.7639 | + | 9.10131i | −0.643024 | + | 0.371250i | −0.785778 | − | 0.618508i | \(-0.787737\pi\) |
0.142754 | + | 0.989758i | \(0.454404\pi\) | |||||||
\(602\) | −2.97784 | + | 13.0969i | −0.121368 | + | 0.533789i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.0191 | − | 5.36409i | −0.814564 | − | 0.218262i | ||||
\(605\) | 15.9086 | − | 15.9086i | 0.646775 | − | 0.646775i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.1421 | + | 14.5158i | −1.02048 | + | 0.589177i | −0.914244 | − | 0.405163i | \(-0.867215\pi\) |
−0.106240 | + | 0.994340i | \(0.533881\pi\) | |||||||
\(608\) | −4.03856 | − | 6.99499i | −0.163785 | − | 0.283685i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.42500i | 0.300629i | ||||||||
\(611\) | −2.01916 | + | 7.10135i | −0.0816865 | + | 0.287290i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.94070 | + | 10.9749i | 0.118774 | + | 0.443270i | 0.999542 | − | 0.0302784i | \(-0.00963940\pi\) |
−0.880768 | + | 0.473549i | \(0.842973\pi\) | |||||||
\(614\) | 10.9963i | 0.443775i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.503034 | − | 0.316660i | 0.0202678 | − | 0.0127586i | ||||
\(617\) | 5.32917 | + | 19.8887i | 0.214544 | + | 0.800690i | 0.986327 | + | 0.164803i | \(0.0526988\pi\) |
−0.771782 | + | 0.635887i | \(0.780635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.198576 | − | 0.0532082i | −0.00798143 | − | 0.00213862i | 0.254826 | − | 0.966987i | \(-0.417982\pi\) |
−0.262808 | + | 0.964848i | \(0.584648\pi\) | |||||||
\(620\) | −22.3525 | −0.897698 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.69883 | − | 1.25905i | −0.188406 | − | 0.0504832i | ||||
\(623\) | −6.35865 | − | 20.5536i | −0.254754 | − | 0.823463i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.1504 | + | 17.5810i | −0.406017 | + | 0.703242i | ||||
\(626\) | 11.2891 | − | 3.02490i | 0.451203 | − | 0.120899i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.4367 | + | 25.0051i | 0.576087 | + | 0.997812i | ||||
\(629\) | 7.81998 | + | 7.81998i | 0.311803 | + | 0.311803i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.5113 | − | 7.63958i | 1.13502 | − | 0.304127i | 0.358071 | − | 0.933694i | \(-0.383435\pi\) |
0.776946 | + | 0.629568i | \(0.216768\pi\) | |||||||
\(632\) | 21.4295 | − | 5.74202i | 0.852421 | − | 0.228405i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0044 | + | 8.08544i | 0.556186 | + | 0.321114i | ||||
\(635\) | −12.9244 | + | 12.9244i | −0.512889 | + | 0.512889i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.54457 | − | 25.1916i | −0.0611982 | − | 0.998126i | ||||
\(638\) | 0.469754 | 0.0185977 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −20.2580 | − | 11.6959i | −0.800766 | − | 0.462323i | ||||
\(641\) | 47.3075i | 1.86853i | 0.356575 | + | 0.934267i | \(0.383944\pi\) | ||||
−0.356575 | + | 0.934267i | \(0.616056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.6736 | − | 5.27154i | 0.775853 | − | 0.207889i | 0.150897 | − | 0.988549i | \(-0.451784\pi\) |
0.624955 | + | 0.780660i | \(0.285117\pi\) | |||||||
\(644\) | 9.66351 | − | 18.3211i | 0.380796 | − | 0.721951i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.59905 | − | 2.76964i | −0.0629139 | − | 0.108970i | ||||
\(647\) | 1.56833 | − | 2.71643i | 0.0616576 | − | 0.106794i | −0.833549 | − | 0.552446i | \(-0.813695\pi\) |
0.895206 | + | 0.445652i | \(0.147028\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.114133 | − | 0.197685i | 0.00448013 | − | 0.00775981i | ||||
\(650\) | 1.27556 | − | 1.23730i | 0.0500317 | − | 0.0485311i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −37.5282 | − | 10.0557i | −1.46972 | − | 0.393810i | ||||
\(653\) | 4.18468 | 0.163759 | 0.0818795 | − | 0.996642i | \(-0.473908\pi\) | ||||
0.0818795 | + | 0.996642i | \(0.473908\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.6551 | − | 10.0897i | −1.47131 | − | 0.394236i | ||||
\(656\) | −1.66602 | + | 6.21766i | −0.0650471 | + | 0.242759i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.79336 | − | 1.75842i | 0.108896 | − | 0.0685503i | ||||
\(659\) | 8.69927 | − | 15.0676i | 0.338875 | − | 0.586949i | −0.645346 | − | 0.763890i | \(-0.723287\pi\) |
0.984221 | + | 0.176941i | \(0.0566202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.68938 | − | 28.6972i | −0.299082 | − | 1.11619i | −0.937921 | − | 0.346849i | \(-0.887252\pi\) |
0.638839 | − | 0.769341i | \(-0.279415\pi\) | |||||||
\(662\) | 17.8531 | − | 10.3075i | 0.693880 | − | 0.400612i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.7202i | 0.454833i | ||||||||
\(665\) | −6.92749 | − | 3.65393i | −0.268637 | − | 0.141693i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.5840 | − | 18.2350i | 1.22294 | − | 0.706063i | ||||
\(668\) | 2.97305 | − | 11.0956i | 0.115031 | − | 0.429301i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.55040 | − | 2.02312i | −0.291697 | − | 0.0781601i | ||||
\(671\) | −0.427730 | + | 0.427730i | −0.0165123 | + | 0.0165123i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.9048 | + | 13.2241i | −0.882917 | + | 0.509752i | −0.871619 | − | 0.490184i | \(-0.836930\pi\) |
−0.0112978 | + | 0.999936i | \(0.503596\pi\) | |||||||
\(674\) | 2.07814 | + | 2.07814i | 0.0800469 | + | 0.0800469i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.6512 | + | 10.0240i | −0.717356 | + | 0.385537i | ||||
\(677\) | 8.72930 | + | 5.03986i | 0.335494 | + | 0.193698i | 0.658278 | − | 0.752775i | \(-0.271285\pi\) |
−0.322783 | + | 0.946473i | \(0.604619\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0625 | + | 44.2561i | −0.386164 | + | 1.69839i | ||||
\(680\) | −14.2292 | − | 8.21522i | −0.545664 | − | 0.315039i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.293465 | + | 0.293465i | 0.0112374 | + | 0.0112374i | ||||
\(683\) | 31.5016 | + | 31.5016i | 1.20537 | + | 1.20537i | 0.972509 | + | 0.232864i | \(0.0748097\pi\) |
0.232864 | + | 0.972509i | \(0.425190\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.54246 | + | 3.77729i | 0.249974 | + | 0.144323i | ||||
\(686\) | −7.01338 | + | 8.83958i | −0.267772 | + | 0.337497i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.7860 | + | 7.95933i | 0.525585 | + | 0.303447i | ||||
\(689\) | −0.579451 | + | 38.0581i | −0.0220753 | + | 1.44990i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.87952 | − | 2.87952i | −0.109542 | − | 0.109542i | 0.650211 | − | 0.759753i | \(-0.274680\pi\) |
−0.759753 | + | 0.650211i | \(0.774680\pi\) | |||||||
\(692\) | −31.4981 | + | 18.1854i | −1.19738 | + | 0.691306i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.9474 | − | 12.9474i | 0.491478 | − | 0.491478i | ||||
\(695\) | 7.43954 | + | 1.99342i | 0.282198 | + | 0.0756146i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.16550 | + | 11.8138i | −0.119902 | + | 0.447479i | ||||
\(698\) | −16.1399 | + | 9.31838i | −0.610905 | + | 0.352706i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.48352 | − | 0.133241i | 0.131665 | − | 0.00503604i | ||||
\(701\) | 19.7829i | 0.747191i | 0.927592 | + | 0.373596i | \(0.121875\pi\) | ||||
−0.927592 | + | 0.373596i | \(0.878125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.81507 | + | 2.20263i | −0.143888 | + | 0.0830737i | ||||
\(704\) | −0.0109867 | − | 0.0410029i | −0.000414076 | − | 0.00154535i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.51487 | − | 16.4802i | 0.358097 | − | 0.620242i | ||||
\(707\) | −26.5126 | − | 42.1169i | −0.997110 | − | 1.58397i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.08628 | + | 4.05405i | −0.0407960 | + | 0.152253i | −0.983319 | − | 0.181888i | \(-0.941779\pi\) |
0.942523 | + | 0.334140i | \(0.108446\pi\) | |||||||
\(710\) | 0.341493 | + | 0.0915029i | 0.0128160 | + | 0.00343404i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.9787 | 0.673782 | ||||||||
\(713\) | 31.1230 | + | 8.33939i | 1.16557 | + | 0.312313i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.749969 | − | 0.0114186i | −0.0280472 | − | 0.000427032i | ||||
\(716\) | 7.96647 | − | 13.7983i | 0.297721 | − | 0.515668i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.05964 | − | 7.03151i | 0.151505 | − | 0.262414i | ||||
\(719\) | −10.3212 | − | 17.8769i | −0.384918 | − | 0.666697i | 0.606840 | − | 0.794824i | \(-0.292437\pi\) |
−0.991758 | + | 0.128127i | \(0.959103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.25605 | + | 3.58387i | 0.0840197 | + | 0.133470i | ||||
\(722\) | −9.95120 | + | 2.66642i | −0.370345 | + | 0.0992337i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 23.1196i | − | 0.859235i | ||||||
\(725\) | 5.31559 | + | 3.06896i | 0.197416 | + | 0.113978i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.8265 | 0.549885 | 0.274942 | − | 0.961461i | \(-0.411341\pi\) | ||||
0.274942 | + | 0.961461i | \(0.411341\pi\) | |||||||
\(728\) | 20.4923 | + | 4.98862i | 0.759497 | + | 0.184890i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.81120 | − | 3.81120i | 0.141059 | − | 0.141059i | ||||
\(731\) | 26.1939 | + | 15.1230i | 0.968815 | + | 0.559346i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.1303 | − | 10.2170i | 1.40838 | − | 0.377373i | 0.527031 | − | 0.849846i | \(-0.323305\pi\) |
0.881345 | + | 0.472473i | \(0.156639\pi\) | |||||||
\(734\) | 13.6409 | − | 3.65506i | 0.503494 | − | 0.134911i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.9851 | + | 18.9851i | 0.699801 | + | 0.699801i | ||||
\(737\) | −0.318408 | − | 0.551499i | −0.0117287 | − | 0.0203147i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3718 | − | 2.77912i | 0.381533 | − | 0.102232i | −0.0629547 | − | 0.998016i | \(-0.520052\pi\) |
0.444488 | + | 0.895785i | \(0.353386\pi\) | |||||||
\(740\) | −5.07927 | + | 8.79755i | −0.186718 | + | 0.323404i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.5642 | − | 12.4840i | 0.424536 | − | 0.458303i | ||||
\(743\) | 23.5602 | + | 6.31294i | 0.864340 | + | 0.231599i | 0.663639 | − | 0.748053i | \(-0.269011\pi\) |
0.200701 | + | 0.979652i | \(0.435678\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.2475 | 1.14482 | ||||||||
\(746\) | 0.852463 | + | 0.228417i | 0.0312109 | + | 0.00836293i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.155502 | − | 0.580343i | −0.00568573 | − | 0.0212194i | ||||
\(749\) | 22.3865 | − | 42.4427i | 0.817987 | − | 1.55082i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.0350i | 1.60686i | 0.595398 | + | 0.803431i | \(0.296994\pi\) | ||||
−0.595398 | + | 0.803431i | \(0.703006\pi\) | |||||||
\(752\) | −1.01251 | − | 3.77875i | −0.0369225 | − | 0.137797i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.6052 | + | 11.9641i | 0.422637 | + | 0.435705i | ||||
\(755\) | − | 26.0493i | − | 0.948032i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1721 | + | 26.2788i | 0.551438 | + | 0.955119i | 0.998171 | + | 0.0604518i | \(0.0192542\pi\) |
−0.446733 | + | 0.894667i | \(0.647413\pi\) | |||||||
\(758\) | 1.26626 | − | 0.731073i | 0.0459925 | − | 0.0265538i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.62791 | − | 4.62791i | 0.167872 | − | 0.167872i | ||||
\(761\) | −30.3847 | − | 8.14155i | −1.10144 | − | 0.295131i | −0.338092 | − | 0.941113i | \(-0.609781\pi\) |
−0.763353 | + | 0.645982i | \(0.776448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.6312 | − | 23.3517i | 0.783101 | − | 0.845389i | ||||
\(764\) | 6.58305 | − | 3.80072i | 0.238166 | − | 0.137505i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.80980 | + | 15.2590i | 0.318311 | + | 0.551331i | ||||
\(767\) | 7.85445 | − | 1.97694i | 0.283608 | − | 0.0713832i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.01297 | + | 22.4407i | −0.216833 | + | 0.809232i | 0.768680 | + | 0.639633i | \(0.220914\pi\) |
−0.985513 | + | 0.169599i | \(0.945753\pi\) | |||||||
\(770\) | 0.246009 | + | 0.227883i | 0.00886555 | + | 0.00821234i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.21717 | − | 8.27457i | −0.0797975 | − | 0.297808i | ||||
\(773\) | 38.0766 | + | 38.0766i | 1.36952 | + | 1.36952i | 0.861125 | + | 0.508394i | \(0.169761\pi\) |
0.508394 | + | 0.861125i | \(0.330239\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.40352 | + | 5.23801i | 0.0504160 | + | 0.188155i | ||||
\(776\) | −32.8453 | − | 18.9632i | −1.17908 | − | 0.680741i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.78549 | + | 17.8597i | −0.171568 | + | 0.640300i | ||||
\(779\) | −4.21917 | − | 2.43594i | −0.151168 | − | 0.0872766i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0144011 | + | 0.0249435i | 0.000515313 | + | 0.000892548i | ||||
\(782\) | 7.51708 | + | 7.51708i | 0.268810 | + | 0.268810i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.55201 | + | 11.0373i | 0.269715 | + | 0.394190i | ||||
\(785\) | −25.6614 | + | 25.6614i | −0.915894 | + | 0.915894i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.8317 | − | 14.8317i | 0.528695 | − | 0.528695i | −0.391488 | − | 0.920183i | \(-0.628040\pi\) |
0.920183 | + | 0.391488i | \(0.128040\pi\) | |||||||
\(788\) | −4.81726 | + | 17.9783i | −0.171608 | + | 0.640449i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.25804 | + | 10.8392i | 0.222651 | + | 0.385643i | ||||
\(791\) | −14.2762 | − | 22.6786i | −0.507603 | − | 0.806358i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.4608 | − | 0.326750i | −0.762094 | − | 0.0116032i | ||||
\(794\) | −9.07809 | + | 5.24124i | −0.322169 | + | 0.186005i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 11.3556i | − | 0.402489i | ||||||
\(797\) | 9.47306 | − | 16.4078i | 0.335553 | − | 0.581195i | −0.648038 | − | 0.761608i | \(-0.724410\pi\) |
0.983591 | + | 0.180413i | \(0.0577434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.92381 | − | 7.17977i | −0.0680596 | − | 0.254002i | ||||
\(800\) | −1.16952 | + | 4.36472i | −0.0413489 | + | 0.154316i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.18027 | −0.324167 | ||||||||
\(803\) | 0.439102 | 0.0154956 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.3865 | + | 5.77213i | 0.894757 | + | 0.203441i | ||||
\(806\) | −0.224183 | + | 14.7242i | −0.00789650 | + | 0.518639i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 40.1706 | − | 10.7637i | 1.41320 | − | 0.378665i | ||||
\(809\) | −20.9032 | + | 36.2055i | −0.734918 | + | 1.27292i | 0.219841 | + | 0.975536i | \(0.429446\pi\) |
−0.954759 | + | 0.297380i | \(0.903887\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.4161 | − | 16.4161i | −0.576448 | − | 0.576448i | 0.357475 | − | 0.933923i | \(-0.383638\pi\) |
−0.933923 | + | 0.357475i | \(0.883638\pi\) | |||||||
\(812\) | 1.24973 | + | 32.6734i | 0.0438568 | + | 1.14661i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.182188 | − | 0.0488172i | 0.00638570 | − | 0.00171104i | ||||
\(815\) | − | 48.8327i | − | 1.71053i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.51932 | + | 8.51932i | −0.298053 | + | 0.298053i | ||||
\(818\) | −10.9663 | −0.383427 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.2346 | −0.392328 | ||||||||
\(821\) | 28.3759 | − | 28.3759i | 0.990327 | − | 0.990327i | −0.00962644 | − | 0.999954i | \(-0.503064\pi\) |
0.999954 | + | 0.00962644i | \(0.00306424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.5127i | 0.924176i | 0.886834 | + | 0.462088i | \(0.152900\pi\) | ||||
−0.886834 | + | 0.462088i | \(0.847100\pi\) | |||||||
\(824\) | −3.41826 | + | 0.915920i | −0.119081 | + | 0.0319076i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.20289 | − | 1.68937i | −0.111443 | − | 0.0587808i | ||||
\(827\) | 9.55537 | + | 9.55537i | 0.332273 | + | 0.332273i | 0.853449 | − | 0.521176i | \(-0.174507\pi\) |
−0.521176 | + | 0.853449i | \(0.674507\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.75261 | + | 6.49971i | −0.130333 | + | 0.225744i | −0.923805 | − | 0.382863i | \(-0.874938\pi\) |
0.793472 | + | 0.608607i | \(0.208271\pi\) | |||||||
\(830\) | −6.38674 | + | 1.71132i | −0.221687 | + | 0.0594008i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.772869 | − | 1.29279i | 0.0267944 | − | 0.0448194i | ||||
\(833\) | 14.3491 | + | 20.9714i | 0.497167 | + | 0.726614i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.4379 | 0.499643 | ||||||||
\(836\) | 0.239327 | 0.00827729 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.38016 | − | 8.88289i | 0.0822214 | − | 0.306854i | ||||
\(839\) | 3.08672 | + | 11.5198i | 0.106566 | + | 0.397708i | 0.998518 | − | 0.0544211i | \(-0.0173313\pi\) |
−0.891953 | + | 0.452129i | \(0.850665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.2851 | + | 24.7425i | −0.492589 | + | 0.853189i | ||||
\(842\) | − | 11.3993i | − | 0.392846i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.1403 | + | 6.43186i | −0.383465 | + | 0.221394i | ||||
\(845\) | −18.2371 | − | 19.3829i | −0.627374 | − | 0.666792i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.11131 | − | 29.0547i | −0.0381852 | − | 0.998331i | ||||
\(848\) | −10.0844 | − | 17.4666i | −0.346299 | − | 0.599807i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.463068 | + | 1.72819i | −0.0158831 | + | 0.0592766i | ||||
\(851\) | 10.3545 | − | 10.3545i | 0.354947 | − | 0.354947i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.51458 | + | 3.51458i | −0.120337 | + | 0.120337i | −0.764711 | − | 0.644374i | \(-0.777118\pi\) |
0.644374 | + | 0.764711i | \(0.277118\pi\) | |||||||
\(854\) | 7.03968 | + | 6.52100i | 0.240893 | + | 0.223144i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.3539 | + | 28.3539i | 0.969115 | + | 0.969115i | ||||
\(857\) | 27.7599 | + | 48.0815i | 0.948259 | + | 1.64243i | 0.749091 | + | 0.662467i | \(0.230491\pi\) |
0.199168 | + | 0.979965i | \(0.436176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.3968 | + | 13.5082i | 0.798289 | + | 0.460892i | 0.842872 | − | 0.538113i | \(-0.180863\pi\) |
−0.0445837 | + | 0.999006i | \(0.514196\pi\) | |||||||
\(860\) | −7.19077 | + | 26.8363i | −0.245203 | + | 0.915111i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.4612 | + | 12.3906i | 0.730971 | + | 0.422026i | ||||
\(863\) | 0.273598 | + | 1.02108i | 0.00931338 | + | 0.0347580i | 0.970426 | − | 0.241398i | \(-0.0776060\pi\) |
−0.961113 | + | 0.276156i | \(0.910939\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.3247 | − | 32.3247i | −1.09907 | − | 1.09907i | ||||
\(866\) | −0.612336 | − | 2.28527i | −0.0208080 | − | 0.0776566i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −19.6311 | + | 21.1925i | −0.666322 | + | 0.719321i | ||||
\(869\) | −0.263908 | + | 0.984919i | −0.00895247 | + | 0.0334111i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.17978 | − | 21.7342i | 0.209394 | − | 0.736435i | ||||
\(872\) | 13.2998 | + | 23.0358i | 0.450386 | + | 0.780092i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.66729 | + | 2.11731i | −0.124048 | + | 0.0716192i | ||||
\(875\) | 9.29902 | + | 30.0580i | 0.314364 | + | 1.01615i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.6254 | − | 6.33040i | −0.797772 | − | 0.213762i | −0.163167 | − | 0.986599i | \(-0.552171\pi\) |
−0.634606 | + | 0.772836i | \(0.718837\pi\) | |||||||
\(878\) | 10.0640 | − | 10.0640i | 0.339643 | − | 0.339643i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.344196 | − | 0.198722i | 0.0116028 | − | 0.00669890i | ||||
\(881\) | −11.6797 | − | 20.2298i | −0.393498 | − | 0.681558i | 0.599411 | − | 0.800442i | \(-0.295402\pi\) |
−0.992908 | + | 0.118884i | \(0.962068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 52.8083i | − | 1.77714i | −0.458739 | − | 0.888571i | \(-0.651699\pi\) | ||
0.458739 | − | 0.888571i | \(-0.348301\pi\) | |||||||
\(884\) | 10.9390 | − | 18.2977i | 0.367917 | − | 0.615420i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.40438 | + | 8.97326i | 0.0807767 | + | 0.301463i | ||||
\(887\) | − | 43.8954i | − | 1.47386i | −0.675966 | − | 0.736932i | \(-0.736274\pi\) | ||
0.675966 | − | 0.736932i | \(-0.263726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.902850 | + | 23.6045i | 0.0302806 | + | 0.791671i | ||||
\(890\) | 2.62516 | + | 9.79722i | 0.0879955 | + | 0.328404i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.3798 | − | 4.92485i | −0.615400 | − | 0.164896i | ||||
\(893\) | 2.96086 | 0.0990813 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.3436 | + | 5.18309i | 0.646584 | + | 0.173252i | ||||
\(896\) | −28.8805 | + | 8.93473i | −0.964831 | + | 0.298489i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.01818 | − | 12.1559i | 0.234200 | − | 0.405646i | ||||
\(899\) | −49.1295 | + | 13.1642i | −1.63856 | + | 0.439051i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.1607 | − | 33.1873i | −0.638335 | − | 1.10563i | ||||
\(902\) | 0.147498 | + | 0.147498i | 0.00491115 | + | 0.00491115i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.6306 | − | 5.79590i | 0.719422 | − | 0.192769i | ||||
\(905\) | 28.0687 | − | 7.52098i | 0.933034 | − | 0.250006i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0797 | + | 9.86098i | 0.567123 | + | 0.327429i | 0.755999 | − | 0.654572i | \(-0.227151\pi\) |
−0.188876 | + | 0.982001i | \(0.560485\pi\) | |||||||
\(908\) | 11.9937 | − | 11.9937i | 0.398026 | − | 0.398026i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.273714 | + | 11.8954i | 0.00907354 | + | 0.394328i | ||||
\(911\) | 32.0257 | 1.06106 | 0.530529 | − | 0.847667i | \(-0.321993\pi\) | ||||
0.530529 | + | 0.847667i | \(0.321993\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.466503 | − | 0.269336i | −0.0154390 | − | 0.00891371i | ||||
\(914\) | − | 2.46953i | − | 0.0816846i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.18044 | − | 0.316297i | 0.0390028 | − | 0.0104508i | ||||
\(917\) | −42.6367 | + | 26.8398i | −1.40799 | + | 0.886329i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8209 | − | 22.2064i | −0.422922 | − | 0.732523i | 0.573302 | − | 0.819344i | \(-0.305662\pi\) |
−0.996224 | + | 0.0868215i | \(0.972329\pi\) | |||||||
\(920\) | −10.8778 | + | 18.8409i | −0.358631 | + | 0.621167i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.48597 | + | 7.76992i | −0.147737 | + | 0.255889i | ||||
\(923\) | −0.279502 | + | 0.983005i | −0.00919993 | + | 0.0323560i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.38052 | + | 0.637858i | 0.0782709 | + | 0.0209726i | ||||
\(926\) | −3.35103 | −0.110122 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40.9386 | − | 10.9695i | −1.34388 | − | 0.360090i | ||||
\(929\) | 4.40197 | − | 16.4284i | 0.144424 | − | 0.538998i | −0.855356 | − | 0.518040i | \(-0.826662\pi\) |
0.999780 | − | 0.0209579i | \(-0.00667159\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.54838 | + | 3.35893i | −0.312935 | + | 0.110085i | ||||
\(932\) | −20.9612 | + | 36.3059i | −0.686608 | + | 1.18924i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.689913 | − | 2.57479i | −0.0225747 | − | 0.0842498i | ||||
\(935\) | 0.653985 | − | 0.377579i | 0.0213876 | − | 0.0123481i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.7513i | 0.775922i | 0.921676 | + | 0.387961i | \(0.126820\pi\) | ||||
−0.921676 | + | 0.387961i | \(0.873180\pi\) | |||||||
\(938\) | −8.54927 | + | 5.38177i | −0.279144 | + | 0.175721i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.91300 | − | 3.41387i | 0.192861 | − | 0.111348i | ||||
\(941\) | 4.82733 | − | 18.0159i | 0.157367 | − | 0.587300i | −0.841525 | − | 0.540219i | \(-0.818341\pi\) |
0.998891 | − | 0.0470811i | \(-0.0149919\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.6427 | + | 4.19145i | 0.509397 | + | 0.136492i | ||||
\(944\) | −3.03473 | + | 3.03473i | −0.0987721 | + | 0.0987721i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.446741 | − | 0.257926i | 0.0145248 | − | 0.00838589i | ||||
\(947\) | −34.1328 | − | 34.1328i | −1.10917 | − | 1.10917i | −0.993260 | − | 0.115906i | \(-0.963023\pi\) |
−0.115906 | − | 0.993260i | \(-0.536977\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.8480 | + | 11.1834i | 0.352139 | + | 0.363028i | ||||
\(950\) | −0.617206 | − | 0.356344i | −0.0200248 | − | 0.0115613i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20.2857 | + | 6.27576i | −0.657462 | + | 0.203398i | ||||
\(953\) | 5.68926 | + | 3.28470i | 0.184293 | + | 0.106402i | 0.589308 | − | 0.807908i | \(-0.299400\pi\) |
−0.405015 | + | 0.914310i | \(0.632734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.75582 | + | 6.75582i | 0.218613 | + | 0.218613i | ||||
\(956\) | 14.3661 | + | 14.3661i | 0.464631 | + | 0.464631i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.7047 | + | 9.64445i | 0.539704 | + | 0.311598i | ||||
\(959\) | 9.32718 | − | 2.88554i | 0.301190 | − | 0.0931789i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.0695 | − | 6.96831i | −0.389338 | − | 0.224784i | ||||
\(962\) | 5.74425 | + | 3.43409i | 0.185202 | + | 0.110720i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −33.9902 | − | 33.9902i | −1.09475 | − | 1.09475i | ||||
\(965\) | 9.32458 | − | 5.38355i | 0.300169 | − | 0.173303i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.29098 | + | 3.29098i | −0.105831 | + | 0.105831i | −0.758039 | − | 0.652209i | \(-0.773843\pi\) |
0.652209 | + | 0.758039i | \(0.273843\pi\) | |||||||
\(968\) | 23.4694 | + | 6.28860i | 0.754334 | + | 0.202123i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.53781 | − | 20.6674i | 0.177809 | − | 0.663590i | ||||
\(971\) | −8.75030 | + | 5.05199i | −0.280811 | + | 0.162126i | −0.633790 | − | 0.773505i | \(-0.718502\pi\) |
0.352980 | + | 0.935631i | \(0.385168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.42374 | − | 5.30275i | 0.270053 | − | 0.169998i | ||||
\(974\) | − | 19.3524i | − | 0.620091i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.84935 | − | 5.68653i | 0.315270 | − | 0.182021i | ||||
\(977\) | 3.55718 | + | 13.2756i | 0.113804 | + | 0.424723i | 0.999195 | − | 0.0401249i | \(-0.0127756\pi\) |
−0.885390 | + | 0.464848i | \(0.846109\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.413159 | + | 0.715613i | −0.0132046 | + | 0.0228711i | ||||
\(980\) | −15.1958 | + | 17.7173i | −0.485412 | + | 0.565957i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.581530 | − | 2.17030i | 0.0185574 | − | 0.0692571i | ||||
\(983\) | −45.8389 | − | 12.2825i | −1.46203 | − | 0.391751i | −0.561842 | − | 0.827244i | \(-0.689907\pi\) |
−0.900192 | + | 0.435494i | \(0.856574\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.3938 | −0.745388 | ||||||||
\(986\) | −16.2095 | − | 4.34332i | −0.516215 | − | 0.138319i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.91254 | + | 6.09537i | 0.188103 | + | 0.193919i | ||||
\(989\) | 20.0245 | − | 34.6834i | 0.636741 | − | 1.10287i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.62262 | − | 8.00661i | 0.146842 | − | 0.254338i | −0.783216 | − | 0.621749i | \(-0.786422\pi\) |
0.930059 | + | 0.367411i | \(0.119756\pi\) | |||||||
\(992\) | −18.7224 | − | 32.4281i | −0.594436 | − | 1.02959i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.386671 | − | 0.243409i | 0.0122644 | − | 0.00772048i | ||||
\(995\) | 13.7864 | − | 3.69406i | 0.437059 | − | 0.117110i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 38.4529i | − | 1.21782i | −0.793241 | − | 0.608908i | \(-0.791608\pi\) | ||
0.793241 | − | 0.608908i | \(-0.208392\pi\) | |||||||
\(998\) | 15.5278 | + | 8.96500i | 0.491525 | + | 0.283782i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.et.c.145.4 | 36 | ||
3.2 | odd | 2 | 273.2.bt.a.145.6 | ✓ | 36 | ||
7.3 | odd | 6 | 819.2.gh.c.262.4 | 36 | |||
13.7 | odd | 12 | 819.2.gh.c.397.4 | 36 | |||
21.17 | even | 6 | 273.2.cg.a.262.6 | yes | 36 | ||
39.20 | even | 12 | 273.2.cg.a.124.6 | yes | 36 | ||
91.59 | even | 12 | inner | 819.2.et.c.514.4 | 36 | ||
273.59 | odd | 12 | 273.2.bt.a.241.6 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bt.a.145.6 | ✓ | 36 | 3.2 | odd | 2 | ||
273.2.bt.a.241.6 | yes | 36 | 273.59 | odd | 12 | ||
273.2.cg.a.124.6 | yes | 36 | 39.20 | even | 12 | ||
273.2.cg.a.262.6 | yes | 36 | 21.17 | even | 6 | ||
819.2.et.c.145.4 | 36 | 1.1 | even | 1 | trivial | ||
819.2.et.c.514.4 | 36 | 91.59 | even | 12 | inner | ||
819.2.gh.c.262.4 | 36 | 7.3 | odd | 6 | |||
819.2.gh.c.397.4 | 36 | 13.7 | odd | 12 |