Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (of order \(4\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.1 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.a.533.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −1.49908 | − | 0.867616i | −0.865494 | − | 0.500919i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.850241 | − | 2.06811i | −0.380239 | − | 0.924888i | ||||
\(6\) | 1.67351 | − | 0.446512i | 0.683207 | − | 0.182288i | ||||
\(7\) | 0.811234 | + | 0.811234i | 0.306618 | + | 0.306618i | 0.843596 | − | 0.536978i | \(-0.180434\pi\) |
−0.536978 | + | 0.843596i | \(0.680434\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 1.49448 | + | 2.60125i | 0.498161 | + | 0.867084i | ||||
\(10\) | 2.06359 | + | 0.861165i | 0.652564 | + | 0.272324i | ||||
\(11\) | 1.25204i | 0.377504i | 0.982025 | + | 0.188752i | \(0.0604442\pi\) | ||||
−0.982025 | + | 0.188752i | \(0.939556\pi\) | |||||||
\(12\) | −0.867616 | + | 1.49908i | −0.250459 | + | 0.432747i | ||||
\(13\) | 3.40609 | − | 3.40609i | 0.944678 | − | 0.944678i | −0.0538698 | − | 0.998548i | \(-0.517156\pi\) |
0.998548 | + | 0.0538698i | \(0.0171556\pi\) | |||||||
\(14\) | −1.14726 | −0.306618 | ||||||||
\(15\) | −0.519749 | + | 3.83795i | −0.134199 | + | 0.990954i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.04078 | − | 3.04078i | 0.737498 | − | 0.737498i | −0.234595 | − | 0.972093i | \(-0.575376\pi\) |
0.972093 | + | 0.234595i | \(0.0753763\pi\) | |||||||
\(18\) | −2.89612 | − | 0.782605i | −0.682623 | − | 0.184462i | ||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | −2.06811 | + | 0.850241i | −0.462444 | + | 0.190120i | ||||
\(21\) | −0.512265 | − | 1.91995i | −0.111785 | − | 0.418966i | ||||
\(22\) | −0.885325 | − | 0.885325i | −0.188752 | − | 0.188752i | ||||
\(23\) | −5.51574 | − | 5.51574i | −1.15011 | − | 1.15011i | −0.986530 | − | 0.163581i | \(-0.947696\pi\) |
−0.163581 | − | 0.986530i | \(-0.552304\pi\) | |||||||
\(24\) | −0.446512 | − | 1.67351i | −0.0911439 | − | 0.341603i | ||||
\(25\) | −3.55418 | + | 3.51679i | −0.710836 | + | 0.703358i | ||||
\(26\) | 4.81693i | 0.944678i | ||||||||
\(27\) | 0.0165399 | − | 5.19613i | 0.00318310 | − | 0.999995i | ||||
\(28\) | 0.811234 | − | 0.811234i | 0.153309 | − | 0.153309i | ||||
\(29\) | −5.49893 | −1.02113 | −0.510563 | − | 0.859840i | \(-0.670563\pi\) | ||||
−0.510563 | + | 0.859840i | \(0.670563\pi\) | |||||||
\(30\) | −2.34632 | − | 3.08136i | −0.428378 | − | 0.562577i | ||||
\(31\) | −5.80986 | −1.04348 | −0.521741 | − | 0.853104i | \(-0.674717\pi\) | ||||
−0.521741 | + | 0.853104i | \(0.674717\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 1.08629 | − | 1.87691i | 0.189099 | − | 0.326728i | ||||
\(34\) | 4.30032i | 0.737498i | ||||||||
\(35\) | 0.987979 | − | 2.36747i | 0.166999 | − | 0.400175i | ||||
\(36\) | 2.60125 | − | 1.49448i | 0.433542 | − | 0.249081i | ||||
\(37\) | −7.08962 | − | 7.08962i | −1.16553 | − | 1.16553i | −0.983247 | − | 0.182280i | \(-0.941652\pi\) |
−0.182280 | − | 0.983247i | \(-0.558348\pi\) | |||||||
\(38\) | −0.707107 | − | 0.707107i | −0.114708 | − | 0.114708i | ||||
\(39\) | −8.06117 | + | 2.15082i | −1.29082 | + | 0.344407i | ||||
\(40\) | 0.861165 | − | 2.06359i | 0.136162 | − | 0.326282i | ||||
\(41\) | − | 0.259187i | − | 0.0404782i | −0.999795 | − | 0.0202391i | \(-0.993557\pi\) | ||
0.999795 | − | 0.0202391i | \(-0.00644274\pi\) | |||||||
\(42\) | 1.71983 | + | 0.995380i | 0.265376 | + | 0.153591i | ||||
\(43\) | 5.60388 | − | 5.60388i | 0.854584 | − | 0.854584i | −0.136109 | − | 0.990694i | \(-0.543460\pi\) |
0.990694 | + | 0.136109i | \(0.0434599\pi\) | |||||||
\(44\) | 1.25204 | 0.188752 | ||||||||
\(45\) | 4.10901 | − | 5.30245i | 0.612536 | − | 0.790443i | ||||
\(46\) | 7.80043 | 1.15011 | ||||||||
\(47\) | −6.12099 | + | 6.12099i | −0.892838 | + | 0.892838i | −0.994789 | − | 0.101951i | \(-0.967491\pi\) |
0.101951 | + | 0.994789i | \(0.467491\pi\) | |||||||
\(48\) | 1.49908 | + | 0.867616i | 0.216374 | + | 0.125230i | ||||
\(49\) | − | 5.68380i | − | 0.811971i | ||||||
\(50\) | 0.0264390 | − | 4.99993i | 0.00373904 | − | 0.707097i | ||||
\(51\) | −7.19661 | + | 1.92015i | −1.00773 | + | 0.268874i | ||||
\(52\) | −3.40609 | − | 3.40609i | −0.472339 | − | 0.472339i | ||||
\(53\) | 0.465266 | + | 0.465266i | 0.0639091 | + | 0.0639091i | 0.738339 | − | 0.674430i | \(-0.235610\pi\) |
−0.674430 | + | 0.738339i | \(0.735610\pi\) | |||||||
\(54\) | 3.66252 | + | 3.68591i | 0.498406 | + | 0.501589i | ||||
\(55\) | 2.58936 | − | 1.06454i | 0.349149 | − | 0.143542i | ||||
\(56\) | 1.14726i | 0.153309i | ||||||||
\(57\) | 0.867616 | − | 1.49908i | 0.114919 | − | 0.198558i | ||||
\(58\) | 3.88833 | − | 3.88833i | 0.510563 | − | 0.510563i | ||||
\(59\) | 9.08034 | 1.18216 | 0.591080 | − | 0.806613i | \(-0.298702\pi\) | ||||
0.591080 | + | 0.806613i | \(0.298702\pi\) | |||||||
\(60\) | 3.83795 | + | 0.519749i | 0.495477 | + | 0.0670993i | ||||
\(61\) | 6.32624 | 0.809992 | 0.404996 | − | 0.914318i | \(-0.367273\pi\) | ||||
0.404996 | + | 0.914318i | \(0.367273\pi\) | |||||||
\(62\) | 4.10819 | − | 4.10819i | 0.521741 | − | 0.521741i | ||||
\(63\) | −0.897850 | + | 3.32260i | −0.113118 | + | 0.418609i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −9.94016 | − | 4.14817i | −1.23293 | − | 0.514518i | ||||
\(66\) | 0.559051 | + | 2.09530i | 0.0688144 | + | 0.257913i | ||||
\(67\) | −2.40925 | − | 2.40925i | −0.294336 | − | 0.294336i | 0.544454 | − | 0.838791i | \(-0.316737\pi\) |
−0.838791 | + | 0.544454i | \(0.816737\pi\) | |||||||
\(68\) | −3.04078 | − | 3.04078i | −0.368749 | − | 0.368749i | ||||
\(69\) | 3.48299 | + | 13.0541i | 0.419303 | + | 1.57153i | ||||
\(70\) | 0.975447 | + | 2.37266i | 0.116588 | + | 0.283587i | ||||
\(71\) | − | 0.747767i | − | 0.0887437i | −0.999015 | − | 0.0443718i | \(-0.985871\pi\) | ||
0.999015 | − | 0.0443718i | \(-0.0141286\pi\) | |||||||
\(72\) | −0.782605 | + | 2.89612i | −0.0922308 | + | 0.341311i | ||||
\(73\) | 5.45994 | − | 5.45994i | 0.639038 | − | 0.639038i | −0.311280 | − | 0.950318i | \(-0.600758\pi\) |
0.950318 | + | 0.311280i | \(0.100758\pi\) | |||||||
\(74\) | 10.0262 | 1.16553 | ||||||||
\(75\) | 8.37922 | − | 2.18828i | 0.967550 | − | 0.252681i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −1.01570 | + | 1.01570i | −0.115749 | + | 0.115749i | ||||
\(78\) | 4.17925 | − | 7.22097i | 0.473207 | − | 0.817614i | ||||
\(79\) | 4.84381i | 0.544971i | 0.962160 | + | 0.272485i | \(0.0878457\pi\) | ||||
−0.962160 | + | 0.272485i | \(0.912154\pi\) | |||||||
\(80\) | 0.850241 | + | 2.06811i | 0.0950599 | + | 0.231222i | ||||
\(81\) | −4.53304 | + | 7.77506i | −0.503671 | + | 0.863896i | ||||
\(82\) | 0.183273 | + | 0.183273i | 0.0202391 | + | 0.0202391i | ||||
\(83\) | 4.22891 | + | 4.22891i | 0.464183 | + | 0.464183i | 0.900024 | − | 0.435841i | \(-0.143549\pi\) |
−0.435841 | + | 0.900024i | \(0.643549\pi\) | |||||||
\(84\) | −1.91995 | + | 0.512265i | −0.209483 | + | 0.0558927i | ||||
\(85\) | −8.87408 | − | 3.70328i | −0.962530 | − | 0.401678i | ||||
\(86\) | 7.92509i | 0.854584i | ||||||||
\(87\) | 8.24334 | + | 4.77097i | 0.883779 | + | 0.511501i | ||||
\(88\) | −0.885325 | + | 0.885325i | −0.0943760 | + | 0.0943760i | ||||
\(89\) | −12.7982 | −1.35660 | −0.678302 | − | 0.734784i | \(-0.737284\pi\) | ||||
−0.678302 | + | 0.734784i | \(0.737284\pi\) | |||||||
\(90\) | 0.843889 | + | 6.65491i | 0.0889537 | + | 0.701489i | ||||
\(91\) | 5.52627 | 0.579310 | ||||||||
\(92\) | −5.51574 | + | 5.51574i | −0.575055 | + | 0.575055i | ||||
\(93\) | 8.70945 | + | 5.04073i | 0.903128 | + | 0.522699i | ||||
\(94\) | − | 8.65639i | − | 0.892838i | ||||||
\(95\) | 2.06811 | − | 0.850241i | 0.212184 | − | 0.0872329i | ||||
\(96\) | −1.67351 | + | 0.446512i | −0.170802 | + | 0.0455720i | ||||
\(97\) | −12.5537 | − | 12.5537i | −1.27463 | − | 1.27463i | −0.943629 | − | 0.331005i | \(-0.892612\pi\) |
−0.331005 | − | 0.943629i | \(-0.607388\pi\) | |||||||
\(98\) | 4.01905 | + | 4.01905i | 0.405986 | + | 0.405986i | ||||
\(99\) | −3.25687 | + | 1.87115i | −0.327328 | + | 0.188058i | ||||
\(100\) | 3.51679 | + | 3.55418i | 0.351679 | + | 0.355418i | ||||
\(101\) | 3.55522i | 0.353758i | 0.984233 | + | 0.176879i | \(0.0566001\pi\) | ||||
−0.984233 | + | 0.176879i | \(0.943400\pi\) | |||||||
\(102\) | 3.73103 | − | 6.44652i | 0.369427 | − | 0.638301i | ||||
\(103\) | −8.68610 | + | 8.68610i | −0.855867 | + | 0.855867i | −0.990848 | − | 0.134981i | \(-0.956903\pi\) |
0.134981 | + | 0.990848i | \(0.456903\pi\) | |||||||
\(104\) | 4.81693 | 0.472339 | ||||||||
\(105\) | −3.53511 | + | 2.69184i | −0.344992 | + | 0.262697i | ||||
\(106\) | −0.657985 | −0.0639091 | ||||||||
\(107\) | −5.27680 | + | 5.27680i | −0.510128 | + | 0.510128i | −0.914566 | − | 0.404438i | \(-0.867467\pi\) |
0.404438 | + | 0.914566i | \(0.367467\pi\) | |||||||
\(108\) | −5.19613 | − | 0.0165399i | −0.499997 | − | 0.00159155i | ||||
\(109\) | − | 19.4996i | − | 1.86773i | −0.357632 | − | 0.933863i | \(-0.616416\pi\) | ||
0.357632 | − | 0.933863i | \(-0.383584\pi\) | |||||||
\(110\) | −1.07821 | + | 2.58369i | −0.102804 | + | 0.246345i | ||||
\(111\) | 4.47684 | + | 16.7790i | 0.424923 | + | 1.59259i | ||||
\(112\) | −0.811234 | − | 0.811234i | −0.0766544 | − | 0.0766544i | ||||
\(113\) | 3.30686 | + | 3.30686i | 0.311083 | + | 0.311083i | 0.845329 | − | 0.534246i | \(-0.179404\pi\) |
−0.534246 | + | 0.845329i | \(0.679404\pi\) | |||||||
\(114\) | 0.446512 | + | 1.67351i | 0.0418197 | + | 0.156738i | ||||
\(115\) | −6.71746 | + | 16.0969i | −0.626406 | + | 1.50104i | ||||
\(116\) | 5.49893i | 0.510563i | ||||||||
\(117\) | 13.9504 | + | 3.76975i | 1.28972 | + | 0.348514i | ||||
\(118\) | −6.42077 | + | 6.42077i | −0.591080 | + | 0.591080i | ||||
\(119\) | 4.93358 | 0.452260 | ||||||||
\(120\) | −3.08136 | + | 2.34632i | −0.281288 | + | 0.214189i | ||||
\(121\) | 9.43240 | 0.857491 | ||||||||
\(122\) | −4.47333 | + | 4.47333i | −0.404996 | + | 0.404996i | ||||
\(123\) | −0.224875 | + | 0.388542i | −0.0202763 | + | 0.0350336i | ||||
\(124\) | 5.80986i | 0.521741i | ||||||||
\(125\) | 10.2950 | + | 4.36032i | 0.920815 | + | 0.389999i | ||||
\(126\) | −1.71456 | − | 2.98431i | −0.152745 | − | 0.265864i | ||||
\(127\) | −5.40945 | − | 5.40945i | −0.480011 | − | 0.480011i | 0.425124 | − | 0.905135i | \(-0.360231\pi\) |
−0.905135 | + | 0.425124i | \(0.860231\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −13.2627 | + | 3.53865i | −1.16772 | + | 0.311561i | ||||
\(130\) | 9.96196 | − | 4.09555i | 0.873722 | − | 0.359204i | ||||
\(131\) | − | 21.4587i | − | 1.87485i | −0.348185 | − | 0.937426i | \(-0.613202\pi\) | ||
0.348185 | − | 0.937426i | \(-0.386798\pi\) | |||||||
\(132\) | −1.87691 | − | 1.08629i | −0.163364 | − | 0.0945494i | ||||
\(133\) | −0.811234 | + | 0.811234i | −0.0703429 | + | 0.0703429i | ||||
\(134\) | 3.40719 | 0.294336 | ||||||||
\(135\) | −10.7602 | + | 4.38375i | −0.926094 | + | 0.377294i | ||||
\(136\) | 4.30032 | 0.368749 | ||||||||
\(137\) | 13.6290 | − | 13.6290i | 1.16440 | − | 1.16440i | 0.180902 | − | 0.983501i | \(-0.442098\pi\) |
0.983501 | − | 0.180902i | \(-0.0579018\pi\) | |||||||
\(138\) | −11.6935 | − | 6.76778i | −0.995414 | − | 0.576112i | ||||
\(139\) | 10.5758i | 0.897030i | 0.893775 | + | 0.448515i | \(0.148047\pi\) | ||||
−0.893775 | + | 0.448515i | \(0.851953\pi\) | |||||||
\(140\) | −2.36747 | − | 0.987979i | −0.200088 | − | 0.0834995i | ||||
\(141\) | 14.4865 | − | 3.86518i | 1.21999 | − | 0.325507i | ||||
\(142\) | 0.528751 | + | 0.528751i | 0.0443718 | + | 0.0443718i | ||||
\(143\) | 4.26455 | + | 4.26455i | 0.356620 | + | 0.356620i | ||||
\(144\) | −1.49448 | − | 2.60125i | −0.124540 | − | 0.216771i | ||||
\(145\) | 4.67542 | + | 11.3724i | 0.388273 | + | 0.944428i | ||||
\(146\) | 7.72152i | 0.639038i | ||||||||
\(147\) | −4.93136 | + | 8.52047i | −0.406731 | + | 0.702756i | ||||
\(148\) | −7.08962 | + | 7.08962i | −0.582763 | + | 0.582763i | ||||
\(149\) | 0.688172 | 0.0563772 | 0.0281886 | − | 0.999603i | \(-0.491026\pi\) | ||||
0.0281886 | + | 0.999603i | \(0.491026\pi\) | |||||||
\(150\) | −4.37766 | + | 7.47236i | −0.357434 | + | 0.610115i | ||||
\(151\) | −7.78234 | −0.633318 | −0.316659 | − | 0.948539i | \(-0.602561\pi\) | ||||
−0.316659 | + | 0.948539i | \(0.602561\pi\) | |||||||
\(152\) | −0.707107 | + | 0.707107i | −0.0573539 | + | 0.0573539i | ||||
\(153\) | 12.4543 | + | 3.36545i | 1.00687 | + | 0.272080i | ||||
\(154\) | − | 1.43641i | − | 0.115749i | ||||||
\(155\) | 4.93978 | + | 12.0154i | 0.396773 | + | 0.965104i | ||||
\(156\) | 2.15082 | + | 8.06117i | 0.172203 | + | 0.645410i | ||||
\(157\) | 4.92864 | + | 4.92864i | 0.393348 | + | 0.393348i | 0.875879 | − | 0.482531i | \(-0.160282\pi\) |
−0.482531 | + | 0.875879i | \(0.660282\pi\) | |||||||
\(158\) | −3.42509 | − | 3.42509i | −0.272485 | − | 0.272485i | ||||
\(159\) | −0.293798 | − | 1.10114i | −0.0232997 | − | 0.0873263i | ||||
\(160\) | −2.06359 | − | 0.861165i | −0.163141 | − | 0.0680811i | ||||
\(161\) | − | 8.94911i | − | 0.705289i | ||||||
\(162\) | −2.29245 | − | 8.70314i | −0.180112 | − | 0.683783i | ||||
\(163\) | −0.293352 | + | 0.293352i | −0.0229771 | + | 0.0229771i | −0.718502 | − | 0.695525i | \(-0.755172\pi\) |
0.695525 | + | 0.718502i | \(0.255172\pi\) | |||||||
\(164\) | −0.259187 | −0.0202391 | ||||||||
\(165\) | −4.80526 | − | 0.650746i | −0.374089 | − | 0.0506605i | ||||
\(166\) | −5.98058 | −0.464183 | ||||||||
\(167\) | 4.29057 | − | 4.29057i | 0.332015 | − | 0.332015i | −0.521337 | − | 0.853351i | \(-0.674566\pi\) |
0.853351 | + | 0.521337i | \(0.174566\pi\) | |||||||
\(168\) | 0.995380 | − | 1.71983i | 0.0767953 | − | 0.132688i | ||||
\(169\) | − | 10.2028i | − | 0.784834i | ||||||
\(170\) | 8.89354 | − | 3.65631i | 0.682104 | − | 0.280426i | ||||
\(171\) | −2.60125 | + | 1.49448i | −0.198923 | + | 0.114286i | ||||
\(172\) | −5.60388 | − | 5.60388i | −0.427292 | − | 0.427292i | ||||
\(173\) | 3.16382 | + | 3.16382i | 0.240541 | + | 0.240541i | 0.817074 | − | 0.576533i | \(-0.195595\pi\) |
−0.576533 | + | 0.817074i | \(0.695595\pi\) | |||||||
\(174\) | −9.20251 | + | 2.45534i | −0.697640 | + | 0.186139i | ||||
\(175\) | −5.73621 | − | 0.0303324i | −0.433617 | − | 0.00229291i | ||||
\(176\) | − | 1.25204i | − | 0.0943760i | ||||||
\(177\) | −13.6122 | − | 7.87825i | −1.02315 | − | 0.592166i | ||||
\(178\) | 9.04967 | − | 9.04967i | 0.678302 | − | 0.678302i | ||||
\(179\) | −3.82605 | −0.285973 | −0.142986 | − | 0.989725i | \(-0.545670\pi\) | ||||
−0.142986 | + | 0.989725i | \(0.545670\pi\) | |||||||
\(180\) | −5.30245 | − | 4.10901i | −0.395221 | − | 0.306268i | ||||
\(181\) | 11.7262 | 0.871603 | 0.435801 | − | 0.900043i | \(-0.356465\pi\) | ||||
0.435801 | + | 0.900043i | \(0.356465\pi\) | |||||||
\(182\) | −3.90766 | + | 3.90766i | −0.289655 | + | 0.289655i | ||||
\(183\) | −9.48354 | − | 5.48875i | −0.701044 | − | 0.405740i | ||||
\(184\) | − | 7.80043i | − | 0.575055i | ||||||
\(185\) | −8.63425 | + | 20.6900i | −0.634803 | + | 1.52116i | ||||
\(186\) | −9.72284 | + | 2.59417i | −0.712913 | + | 0.190214i | ||||
\(187\) | 3.80718 | + | 3.80718i | 0.278409 | + | 0.278409i | ||||
\(188\) | 6.12099 | + | 6.12099i | 0.446419 | + | 0.446419i | ||||
\(189\) | 4.22869 | − | 4.20186i | 0.307592 | − | 0.305640i | ||||
\(190\) | −0.861165 | + | 2.06359i | −0.0624755 | + | 0.149708i | ||||
\(191\) | 11.0228i | 0.797579i | 0.917042 | + | 0.398790i | \(0.130570\pi\) | ||||
−0.917042 | + | 0.398790i | \(0.869430\pi\) | |||||||
\(192\) | 0.867616 | − | 1.49908i | 0.0626148 | − | 0.108187i | ||||
\(193\) | 6.75179 | − | 6.75179i | 0.486004 | − | 0.486004i | −0.421039 | − | 0.907043i | \(-0.638334\pi\) |
0.907043 | + | 0.421039i | \(0.138334\pi\) | |||||||
\(194\) | 17.7536 | 1.27463 | ||||||||
\(195\) | 11.3021 | + | 14.8427i | 0.809359 | + | 1.06291i | ||||
\(196\) | −5.68380 | −0.405986 | ||||||||
\(197\) | 7.05740 | − | 7.05740i | 0.502819 | − | 0.502819i | −0.409494 | − | 0.912313i | \(-0.634295\pi\) |
0.912313 | + | 0.409494i | \(0.134295\pi\) | |||||||
\(198\) | 0.979852 | − | 3.62606i | 0.0696350 | − | 0.257693i | ||||
\(199\) | 23.7718i | 1.68514i | 0.538588 | + | 0.842569i | \(0.318958\pi\) | ||||
−0.538588 | + | 0.842569i | \(0.681042\pi\) | |||||||
\(200\) | −4.99993 | − | 0.0264390i | −0.353548 | − | 0.00186952i | ||||
\(201\) | 1.52135 | + | 5.70196i | 0.107308 | + | 0.402185i | ||||
\(202\) | −2.51392 | − | 2.51392i | −0.176879 | − | 0.176879i | ||||
\(203\) | −4.46092 | − | 4.46092i | −0.313096 | − | 0.313096i | ||||
\(204\) | 1.92015 | + | 7.19661i | 0.134437 | + | 0.503864i | ||||
\(205\) | −0.536027 | + | 0.220371i | −0.0374378 | + | 0.0153914i | ||||
\(206\) | − | 12.2840i | − | 0.855867i | ||||||
\(207\) | 6.10465 | − | 22.5910i | 0.424303 | − | 1.57018i | ||||
\(208\) | −3.40609 | + | 3.40609i | −0.236170 | + | 0.236170i | ||||
\(209\) | −1.25204 | −0.0866054 | ||||||||
\(210\) | 0.596286 | − | 4.40312i | 0.0411477 | − | 0.303844i | ||||
\(211\) | 16.9279 | 1.16536 | 0.582682 | − | 0.812700i | \(-0.302003\pi\) | ||||
0.582682 | + | 0.812700i | \(0.302003\pi\) | |||||||
\(212\) | 0.465266 | − | 0.465266i | 0.0319546 | − | 0.0319546i | ||||
\(213\) | −0.648775 | + | 1.12096i | −0.0444534 | + | 0.0768071i | ||||
\(214\) | − | 7.46253i | − | 0.510128i | ||||||
\(215\) | −16.3541 | − | 6.82481i | −1.11534 | − | 0.465448i | ||||
\(216\) | 3.68591 | − | 3.66252i | 0.250795 | − | 0.249203i | ||||
\(217\) | −4.71316 | − | 4.71316i | −0.319950 | − | 0.319950i | ||||
\(218\) | 13.7883 | + | 13.7883i | 0.933863 | + | 0.933863i | ||||
\(219\) | −12.9220 | + | 3.44776i | −0.873190 | + | 0.232978i | ||||
\(220\) | −1.06454 | − | 2.58936i | −0.0717710 | − | 0.174574i | ||||
\(221\) | − | 20.7143i | − | 1.39340i | ||||||
\(222\) | −15.0301 | − | 8.69893i | −1.00876 | − | 0.583834i | ||||
\(223\) | −13.0760 | + | 13.0760i | −0.875634 | + | 0.875634i | −0.993079 | − | 0.117446i | \(-0.962529\pi\) |
0.117446 | + | 0.993079i | \(0.462529\pi\) | |||||||
\(224\) | 1.14726 | 0.0766544 | ||||||||
\(225\) | −14.4597 | − | 3.98954i | −0.963982 | − | 0.265969i | ||||
\(226\) | −4.67660 | −0.311083 | ||||||||
\(227\) | 18.5524 | − | 18.5524i | 1.23136 | − | 1.23136i | 0.267923 | − | 0.963440i | \(-0.413663\pi\) |
0.963440 | − | 0.267923i | \(-0.0863373\pi\) | |||||||
\(228\) | −1.49908 | − | 0.867616i | −0.0992790 | − | 0.0574593i | ||||
\(229\) | 2.63822i | 0.174338i | 0.996194 | + | 0.0871692i | \(0.0277821\pi\) | ||||
−0.996194 | + | 0.0871692i | \(0.972218\pi\) | |||||||
\(230\) | −6.63225 | − | 16.1322i | −0.437317 | − | 1.06372i | ||||
\(231\) | 2.40385 | − | 0.641376i | 0.158162 | − | 0.0421994i | ||||
\(232\) | −3.88833 | − | 3.88833i | −0.255282 | − | 0.255282i | ||||
\(233\) | 13.3570 | + | 13.3570i | 0.875046 | + | 0.875046i | 0.993017 | − | 0.117971i | \(-0.0376389\pi\) |
−0.117971 | + | 0.993017i | \(0.537639\pi\) | |||||||
\(234\) | −12.5301 | + | 7.19883i | −0.819116 | + | 0.470602i | ||||
\(235\) | 17.8632 | + | 7.45458i | 1.16527 | + | 0.486283i | ||||
\(236\) | − | 9.08034i | − | 0.591080i | ||||||
\(237\) | 4.20257 | − | 7.26126i | 0.272986 | − | 0.471669i | ||||
\(238\) | −3.48857 | + | 3.48857i | −0.226130 | + | 0.226130i | ||||
\(239\) | −0.359134 | −0.0232304 | −0.0116152 | − | 0.999933i | \(-0.503697\pi\) | ||||
−0.0116152 | + | 0.999933i | \(0.503697\pi\) | |||||||
\(240\) | 0.519749 | − | 3.83795i | 0.0335496 | − | 0.247739i | ||||
\(241\) | 5.42354 | 0.349361 | 0.174681 | − | 0.984625i | \(-0.444111\pi\) | ||||
0.174681 | + | 0.984625i | \(0.444111\pi\) | |||||||
\(242\) | −6.66971 | + | 6.66971i | −0.428745 | + | 0.428745i | ||||
\(243\) | 13.5412 | − | 7.72250i | 0.868666 | − | 0.495399i | ||||
\(244\) | − | 6.32624i | − | 0.404996i | ||||||
\(245\) | −11.7547 | + | 4.83260i | −0.750982 | + | 0.308743i | ||||
\(246\) | −0.115730 | − | 0.433751i | −0.00737868 | − | 0.0276549i | ||||
\(247\) | 3.40609 | + | 3.40609i | 0.216724 | + | 0.216724i | ||||
\(248\) | −4.10819 | − | 4.10819i | −0.260870 | − | 0.260870i | ||||
\(249\) | −2.67040 | − | 10.0085i | −0.169230 | − | 0.634265i | ||||
\(250\) | −10.3629 | + | 4.19647i | −0.655407 | + | 0.265408i | ||||
\(251\) | − | 13.3902i | − | 0.845179i | −0.906321 | − | 0.422590i | \(-0.861121\pi\) | ||
0.906321 | − | 0.422590i | \(-0.138879\pi\) | |||||||
\(252\) | 3.32260 | + | 0.897850i | 0.209304 | + | 0.0565592i | ||||
\(253\) | 6.90592 | − | 6.90592i | 0.434171 | − | 0.434171i | ||||
\(254\) | 7.65012 | 0.480011 | ||||||||
\(255\) | 10.0899 | + | 13.2508i | 0.631856 | + | 0.829799i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.2263 | + | 16.2263i | −1.01217 | + | 1.01217i | −0.0122435 | + | 0.999925i | \(0.503897\pi\) |
−0.999925 | + | 0.0122435i | \(0.996103\pi\) | |||||||
\(258\) | 6.87594 | − | 11.8803i | 0.428077 | − | 0.739638i | ||||
\(259\) | − | 11.5027i | − | 0.714742i | ||||||
\(260\) | −4.14817 | + | 9.94016i | −0.257259 | + | 0.616463i | ||||
\(261\) | −8.21807 | − | 14.3041i | −0.508686 | − | 0.885403i | ||||
\(262\) | 15.1736 | + | 15.1736i | 0.937426 | + | 0.937426i | ||||
\(263\) | 3.46688 | + | 3.46688i | 0.213777 | + | 0.213777i | 0.805870 | − | 0.592093i | \(-0.201698\pi\) |
−0.592093 | + | 0.805870i | \(0.701698\pi\) | |||||||
\(264\) | 2.09530 | − | 0.559051i | 0.128957 | − | 0.0344072i | ||||
\(265\) | 0.566634 | − | 1.35781i | 0.0348080 | − | 0.0834096i | ||||
\(266\) | − | 1.14726i | − | 0.0703429i | ||||||
\(267\) | 19.1855 | + | 11.1039i | 1.17413 | + | 0.679548i | ||||
\(268\) | −2.40925 | + | 2.40925i | −0.147168 | + | 0.147168i | ||||
\(269\) | −4.91421 | −0.299625 | −0.149812 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149812 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(270\) | 4.50885 | − | 10.7084i | 0.274400 | − | 0.651694i | ||||
\(271\) | 6.09935 | 0.370509 | 0.185255 | − | 0.982691i | \(-0.440689\pi\) | ||||
0.185255 | + | 0.982691i | \(0.440689\pi\) | |||||||
\(272\) | −3.04078 | + | 3.04078i | −0.184375 | + | 0.184375i | ||||
\(273\) | −8.28432 | − | 4.79468i | −0.501390 | − | 0.290187i | ||||
\(274\) | 19.2743i | 1.16440i | ||||||||
\(275\) | −4.40316 | − | 4.44997i | −0.265520 | − | 0.268343i | ||||
\(276\) | 13.0541 | − | 3.48299i | 0.785763 | − | 0.209651i | ||||
\(277\) | −11.4817 | − | 11.4817i | −0.689866 | − | 0.689866i | 0.272336 | − | 0.962202i | \(-0.412204\pi\) |
−0.962202 | + | 0.272336i | \(0.912204\pi\) | |||||||
\(278\) | −7.47824 | − | 7.47824i | −0.448515 | − | 0.448515i | ||||
\(279\) | −8.68274 | − | 15.1129i | −0.519822 | − | 0.904787i | ||||
\(280\) | 2.37266 | − | 0.975447i | 0.141794 | − | 0.0582941i | ||||
\(281\) | − | 19.8457i | − | 1.18389i | −0.805977 | − | 0.591947i | \(-0.798359\pi\) | ||
0.805977 | − | 0.591947i | \(-0.201641\pi\) | |||||||
\(282\) | −7.51042 | + | 12.9766i | −0.447239 | + | 0.772746i | ||||
\(283\) | 13.5529 | − | 13.5529i | 0.805635 | − | 0.805635i | −0.178335 | − | 0.983970i | \(-0.557071\pi\) |
0.983970 | + | 0.178335i | \(0.0570711\pi\) | |||||||
\(284\) | −0.747767 | −0.0443718 | ||||||||
\(285\) | −3.83795 | − | 0.519749i | −0.227341 | − | 0.0307873i | ||||
\(286\) | −6.03099 | −0.356620 | ||||||||
\(287\) | 0.210261 | − | 0.210261i | 0.0124113 | − | 0.0124113i | ||||
\(288\) | 2.89612 | + | 0.782605i | 0.170656 | + | 0.0461154i | ||||
\(289\) | − | 1.49273i | − | 0.0878079i | ||||||
\(290\) | −11.3475 | − | 4.73549i | −0.666350 | − | 0.278078i | ||||
\(291\) | 7.92720 | + | 29.7108i | 0.464701 | + | 1.74168i | ||||
\(292\) | −5.45994 | − | 5.45994i | −0.319519 | − | 0.319519i | ||||
\(293\) | 4.72321 | + | 4.72321i | 0.275933 | + | 0.275933i | 0.831483 | − | 0.555550i | \(-0.187492\pi\) |
−0.555550 | + | 0.831483i | \(0.687492\pi\) | |||||||
\(294\) | −2.53789 | − | 9.51188i | −0.148013 | − | 0.554744i | ||||
\(295\) | −7.72048 | − | 18.7792i | −0.449504 | − | 1.09336i | ||||
\(296\) | − | 10.0262i | − | 0.582763i | ||||||
\(297\) | 6.50575 | + | 0.0207086i | 0.377502 | + | 0.00120163i | ||||
\(298\) | −0.486611 | + | 0.486611i | −0.0281886 | + | 0.0281886i | ||||
\(299\) | −37.5741 | −2.17297 | ||||||||
\(300\) | −2.18828 | − | 8.37922i | −0.126341 | − | 0.483775i | ||||
\(301\) | 9.09213 | 0.524062 | ||||||||
\(302\) | 5.50294 | − | 5.50294i | 0.316659 | − | 0.316659i | ||||
\(303\) | 3.08457 | − | 5.32956i | 0.177204 | − | 0.306175i | ||||
\(304\) | − | 1.00000i | − | 0.0573539i | ||||||
\(305\) | −5.37883 | − | 13.0834i | −0.307991 | − | 0.749152i | ||||
\(306\) | −11.1862 | + | 6.42675i | −0.639473 | + | 0.367393i | ||||
\(307\) | 10.8953 | + | 10.8953i | 0.621830 | + | 0.621830i | 0.945999 | − | 0.324169i | \(-0.105085\pi\) |
−0.324169 | + | 0.945999i | \(0.605085\pi\) | |||||||
\(308\) | 1.01570 | + | 1.01570i | 0.0578747 | + | 0.0578747i | ||||
\(309\) | 20.5574 | − | 5.48496i | 1.16947 | − | 0.312028i | ||||
\(310\) | −11.9892 | − | 5.00325i | −0.680938 | − | 0.284165i | ||||
\(311\) | − | 18.6727i | − | 1.05883i | −0.848363 | − | 0.529415i | \(-0.822412\pi\) | ||
0.848363 | − | 0.529415i | \(-0.177588\pi\) | |||||||
\(312\) | −7.22097 | − | 4.17925i | −0.408807 | − | 0.236603i | ||||
\(313\) | −5.71317 | + | 5.71317i | −0.322928 | + | 0.322928i | −0.849889 | − | 0.526961i | \(-0.823331\pi\) |
0.526961 | + | 0.849889i | \(0.323331\pi\) | |||||||
\(314\) | −6.97014 | −0.393348 | ||||||||
\(315\) | 7.63490 | − | 0.968159i | 0.430178 | − | 0.0545496i | ||||
\(316\) | 4.84381 | 0.272485 | ||||||||
\(317\) | −11.0822 | + | 11.0822i | −0.622438 | + | 0.622438i | −0.946154 | − | 0.323716i | \(-0.895068\pi\) |
0.323716 | + | 0.946154i | \(0.395068\pi\) | |||||||
\(318\) | 0.986372 | + | 0.570878i | 0.0553130 | + | 0.0320133i | ||||
\(319\) | − | 6.88488i | − | 0.385479i | ||||||
\(320\) | 2.06811 | − | 0.850241i | 0.115611 | − | 0.0475299i | ||||
\(321\) | 12.4886 | − | 3.33211i | 0.697045 | − | 0.185980i | ||||
\(322\) | 6.32798 | + | 6.32798i | 0.352644 | + | 0.352644i | ||||
\(323\) | 3.04078 | + | 3.04078i | 0.169194 | + | 0.169194i | ||||
\(324\) | 7.77506 | + | 4.53304i | 0.431948 | + | 0.251836i | ||||
\(325\) | −0.127355 | + | 24.0843i | −0.00706438 | + | 1.33596i | ||||
\(326\) | − | 0.414863i | − | 0.0229771i | ||||||
\(327\) | −16.9182 | + | 29.2315i | −0.935578 | + | 1.61651i | ||||
\(328\) | 0.183273 | − | 0.183273i | 0.0101195 | − | 0.0101195i | ||||
\(329\) | −9.93112 | −0.547520 | ||||||||
\(330\) | 3.85798 | − | 2.93769i | 0.212375 | − | 0.161714i | ||||
\(331\) | 20.0068 | 1.09967 | 0.549837 | − | 0.835272i | \(-0.314690\pi\) | ||||
0.549837 | + | 0.835272i | \(0.314690\pi\) | |||||||
\(332\) | 4.22891 | − | 4.22891i | 0.232091 | − | 0.232091i | ||||
\(333\) | 7.84658 | − | 29.0372i | 0.429990 | − | 1.59123i | ||||
\(334\) | 6.06779i | 0.332015i | ||||||||
\(335\) | −2.93415 | + | 7.03103i | −0.160310 | + | 0.384146i | ||||
\(336\) | 0.512265 | + | 1.91995i | 0.0279464 | + | 0.104742i | ||||
\(337\) | 8.69484 | + | 8.69484i | 0.473638 | + | 0.473638i | 0.903090 | − | 0.429452i | \(-0.141293\pi\) |
−0.429452 | + | 0.903090i | \(0.641293\pi\) | |||||||
\(338\) | 7.21450 | + | 7.21450i | 0.392417 | + | 0.392417i | ||||
\(339\) | −2.08816 | − | 7.82632i | −0.113413 | − | 0.425068i | ||||
\(340\) | −3.70328 | + | 8.87408i | −0.200839 | + | 0.481265i | ||||
\(341\) | − | 7.27417i | − | 0.393919i | ||||||
\(342\) | 0.782605 | − | 2.89612i | 0.0423184 | − | 0.156604i | ||||
\(343\) | 10.2895 | − | 10.2895i | 0.555583 | − | 0.555583i | ||||
\(344\) | 7.92509 | 0.427292 | ||||||||
\(345\) | 24.0359 | − | 18.3023i | 1.29405 | − | 0.985364i | ||||
\(346\) | −4.47431 | −0.240541 | ||||||||
\(347\) | 5.08826 | − | 5.08826i | 0.273152 | − | 0.273152i | −0.557216 | − | 0.830368i | \(-0.688130\pi\) |
0.830368 | + | 0.557216i | \(0.188130\pi\) | |||||||
\(348\) | 4.77097 | − | 8.24334i | 0.255751 | − | 0.441890i | ||||
\(349\) | 21.6797i | 1.16049i | 0.814442 | + | 0.580244i | \(0.197043\pi\) | ||||
−0.814442 | + | 0.580244i | \(0.802957\pi\) | |||||||
\(350\) | 4.07756 | − | 4.03467i | 0.217955 | − | 0.215662i | ||||
\(351\) | −17.6421 | − | 17.7548i | −0.941666 | − | 0.947680i | ||||
\(352\) | 0.885325 | + | 0.885325i | 0.0471880 | + | 0.0471880i | ||||
\(353\) | 7.11922 | + | 7.11922i | 0.378918 | + | 0.378918i | 0.870712 | − | 0.491794i | \(-0.163659\pi\) |
−0.491794 | + | 0.870712i | \(0.663659\pi\) | |||||||
\(354\) | 15.1960 | − | 4.05448i | 0.807659 | − | 0.215493i | ||||
\(355\) | −1.54647 | + | 0.635783i | −0.0820780 | + | 0.0337438i | ||||
\(356\) | 12.7982i | 0.678302i | ||||||||
\(357\) | −7.39583 | − | 4.28045i | −0.391429 | − | 0.226546i | ||||
\(358\) | 2.70543 | − | 2.70543i | 0.142986 | − | 0.142986i | ||||
\(359\) | 24.6824 | 1.30269 | 0.651343 | − | 0.758783i | \(-0.274206\pi\) | ||||
0.651343 | + | 0.758783i | \(0.274206\pi\) | |||||||
\(360\) | 6.65491 | − | 0.843889i | 0.350745 | − | 0.0444768i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −8.29169 | + | 8.29169i | −0.435801 | + | 0.435801i | ||||
\(363\) | −14.1399 | − | 8.18370i | −0.742153 | − | 0.429533i | ||||
\(364\) | − | 5.52627i | − | 0.289655i | ||||||
\(365\) | −15.9340 | − | 6.64951i | −0.834026 | − | 0.348051i | ||||
\(366\) | 10.5870 | − | 2.82474i | 0.553392 | − | 0.147652i | ||||
\(367\) | −1.59834 | − | 1.59834i | −0.0834327 | − | 0.0834327i | 0.664159 | − | 0.747591i | \(-0.268790\pi\) |
−0.747591 | + | 0.664159i | \(0.768790\pi\) | |||||||
\(368\) | 5.51574 | + | 5.51574i | 0.287528 | + | 0.287528i | ||||
\(369\) | 0.674210 | − | 0.387350i | 0.0350980 | − | 0.0201647i | ||||
\(370\) | −8.52472 | − | 20.7354i | −0.443179 | − | 1.07798i | ||||
\(371\) | 0.754879i | 0.0391914i | ||||||||
\(372\) | 5.04073 | − | 8.70945i | 0.261350 | − | 0.451564i | ||||
\(373\) | −20.6849 | + | 20.6849i | −1.07102 | + | 1.07102i | −0.0737477 | + | 0.997277i | \(0.523496\pi\) |
−0.997277 | + | 0.0737477i | \(0.976504\pi\) | |||||||
\(374\) | −5.38417 | −0.278409 | ||||||||
\(375\) | −11.6500 | − | 15.4686i | −0.601602 | − | 0.798796i | ||||
\(376\) | −8.65639 | −0.446419 | ||||||||
\(377\) | −18.7298 | + | 18.7298i | −0.964636 | + | 0.964636i | ||||
\(378\) | −0.0189755 | + | 5.96130i | −0.000975995 | + | 0.306616i | ||||
\(379\) | 19.2862i | 0.990668i | 0.868703 | + | 0.495334i | \(0.164954\pi\) | ||||
−0.868703 | + | 0.495334i | \(0.835046\pi\) | |||||||
\(380\) | −0.850241 | − | 2.06811i | −0.0436165 | − | 0.106092i | ||||
\(381\) | 3.41587 | + | 12.8025i | 0.175001 | + | 0.655894i | ||||
\(382\) | −7.79427 | − | 7.79427i | −0.398790 | − | 0.398790i | ||||
\(383\) | −22.7437 | − | 22.7437i | −1.16215 | − | 1.16215i | −0.984004 | − | 0.178146i | \(-0.942990\pi\) |
−0.178146 | − | 0.984004i | \(-0.557010\pi\) | |||||||
\(384\) | 0.446512 | + | 1.67351i | 0.0227860 | + | 0.0854008i | ||||
\(385\) | 2.96416 | + | 1.23699i | 0.151068 | + | 0.0630428i | ||||
\(386\) | 9.54847i | 0.486004i | ||||||||
\(387\) | 22.9520 | + | 6.20221i | 1.16672 | + | 0.315276i | ||||
\(388\) | −12.5537 | + | 12.5537i | −0.637317 | + | 0.637317i | ||||
\(389\) | 20.2169 | 1.02504 | 0.512519 | − | 0.858676i | \(-0.328713\pi\) | ||||
0.512519 | + | 0.858676i | \(0.328713\pi\) | |||||||
\(390\) | −18.4871 | − | 2.50359i | −0.936133 | − | 0.126774i | ||||
\(391\) | −33.5443 | −1.69641 | ||||||||
\(392\) | 4.01905 | − | 4.01905i | 0.202993 | − | 0.202993i | ||||
\(393\) | −18.6179 | + | 32.1683i | −0.939148 | + | 1.62267i | ||||
\(394\) | 9.98068i | 0.502819i | ||||||||
\(395\) | 10.0175 | − | 4.11841i | 0.504037 | − | 0.207219i | ||||
\(396\) | 1.87115 | + | 3.25687i | 0.0940289 | + | 0.163664i | ||||
\(397\) | 0.250592 | + | 0.250592i | 0.0125768 | + | 0.0125768i | 0.713367 | − | 0.700790i | \(-0.247169\pi\) |
−0.700790 | + | 0.713367i | \(0.747169\pi\) | |||||||
\(398\) | −16.8092 | − | 16.8092i | −0.842569 | − | 0.842569i | ||||
\(399\) | 1.91995 | − | 0.512265i | 0.0961175 | − | 0.0256453i | ||||
\(400\) | 3.55418 | − | 3.51679i | 0.177709 | − | 0.175839i | ||||
\(401\) | 21.6861i | 1.08295i | 0.840716 | + | 0.541476i | \(0.182134\pi\) | ||||
−0.840716 | + | 0.541476i | \(0.817866\pi\) | |||||||
\(402\) | −5.10765 | − | 2.95613i | −0.254746 | − | 0.147439i | ||||
\(403\) | −19.7889 | + | 19.7889i | −0.985754 | + | 0.985754i | ||||
\(404\) | 3.55522 | 0.176879 | ||||||||
\(405\) | 19.9339 | + | 2.76416i | 0.990522 | + | 0.137352i | ||||
\(406\) | 6.30870 | 0.313096 | ||||||||
\(407\) | 8.87649 | − | 8.87649i | 0.439991 | − | 0.439991i | ||||
\(408\) | −6.44652 | − | 3.73103i | −0.319150 | − | 0.184713i | ||||
\(409\) | − | 5.94808i | − | 0.294114i | −0.989128 | − | 0.147057i | \(-0.953020\pi\) | ||
0.989128 | − | 0.147057i | \(-0.0469800\pi\) | |||||||
\(410\) | 0.223203 | − | 0.534855i | 0.0110232 | − | 0.0264146i | ||||
\(411\) | −32.2557 | + | 8.60622i | −1.59106 | + | 0.424513i | ||||
\(412\) | 8.68610 | + | 8.68610i | 0.427933 | + | 0.427933i | ||||
\(413\) | 7.36628 | + | 7.36628i | 0.362471 | + | 0.362471i | ||||
\(414\) | 11.6576 | + | 20.2909i | 0.572940 | + | 0.997243i | ||||
\(415\) | 5.15026 | − | 12.3414i | 0.252817 | − | 0.605818i | ||||
\(416\) | − | 4.81693i | − | 0.236170i | ||||||
\(417\) | 9.17576 | − | 15.8540i | 0.449339 | − | 0.776375i | ||||
\(418\) | 0.885325 | − | 0.885325i | 0.0433027 | − | 0.0433027i | ||||
\(419\) | −35.8879 | −1.75324 | −0.876620 | − | 0.481184i | \(-0.840207\pi\) | ||||
−0.876620 | + | 0.481184i | \(0.840207\pi\) | |||||||
\(420\) | 2.69184 | + | 3.53511i | 0.131348 | + | 0.172496i | ||||
\(421\) | −13.5450 | −0.660145 | −0.330073 | − | 0.943956i | \(-0.607073\pi\) | ||||
−0.330073 | + | 0.943956i | \(0.607073\pi\) | |||||||
\(422\) | −11.9698 | + | 11.9698i | −0.582682 | + | 0.582682i | ||||
\(423\) | −25.0700 | − | 6.77453i | −1.21894 | − | 0.329389i | ||||
\(424\) | 0.657985i | 0.0319546i | ||||||||
\(425\) | −0.113696 | + | 21.5013i | −0.00551507 | + | 1.04297i | ||||
\(426\) | −0.333887 | − | 1.25139i | −0.0161769 | − | 0.0606302i | ||||
\(427\) | 5.13206 | + | 5.13206i | 0.248358 | + | 0.248358i | ||||
\(428\) | 5.27680 | + | 5.27680i | 0.255064 | + | 0.255064i | ||||
\(429\) | −2.69291 | − | 10.0929i | −0.130015 | − | 0.487290i | ||||
\(430\) | 16.3900 | − | 6.73824i | 0.790395 | − | 0.324947i | ||||
\(431\) | 0.445342i | 0.0214514i | 0.999942 | + | 0.0107257i | \(0.00341416\pi\) | ||||
−0.999942 | + | 0.0107257i | \(0.996586\pi\) | |||||||
\(432\) | −0.0165399 | + | 5.19613i | −0.000795775 | + | 0.249999i | ||||
\(433\) | 20.9273 | − | 20.9273i | 1.00570 | − | 1.00570i | 0.00571854 | − | 0.999984i | \(-0.498180\pi\) |
0.999984 | − | 0.00571854i | \(-0.00182028\pi\) | |||||||
\(434\) | 6.66541 | 0.319950 | ||||||||
\(435\) | 2.85806 | − | 21.1046i | 0.137034 | − | 1.01189i | ||||
\(436\) | −19.4996 | −0.933863 | ||||||||
\(437\) | 5.51574 | − | 5.51574i | 0.263854 | − | 0.263854i | ||||
\(438\) | 6.69932 | − | 11.5752i | 0.320106 | − | 0.553084i | ||||
\(439\) | − | 0.487999i | − | 0.0232909i | −0.999932 | − | 0.0116455i | \(-0.996293\pi\) | ||
0.999932 | − | 0.0116455i | \(-0.00370695\pi\) | |||||||
\(440\) | 2.58369 | + | 1.07821i | 0.123173 | + | 0.0514018i | ||||
\(441\) | 14.7850 | − | 8.49434i | 0.704048 | − | 0.404492i | ||||
\(442\) | 14.6473 | + | 14.6473i | 0.696699 | + | 0.696699i | ||||
\(443\) | −5.91639 | − | 5.91639i | −0.281096 | − | 0.281096i | 0.552450 | − | 0.833546i | \(-0.313693\pi\) |
−0.833546 | + | 0.552450i | \(0.813693\pi\) | |||||||
\(444\) | 16.7790 | − | 4.47684i | 0.796295 | − | 0.212461i | ||||
\(445\) | 10.8815 | + | 26.4681i | 0.515834 | + | 1.25471i | ||||
\(446\) | − | 18.4923i | − | 0.875634i | ||||||
\(447\) | −1.03162 | − | 0.597069i | −0.0487942 | − | 0.0282404i | ||||
\(448\) | −0.811234 | + | 0.811234i | −0.0383272 | + | 0.0383272i | ||||
\(449\) | 16.3599 | 0.772074 | 0.386037 | − | 0.922483i | \(-0.373844\pi\) | ||||
0.386037 | + | 0.922483i | \(0.373844\pi\) | |||||||
\(450\) | 13.0456 | − | 7.40354i | 0.614975 | − | 0.349006i | ||||
\(451\) | 0.324512 | 0.0152807 | ||||||||
\(452\) | 3.30686 | − | 3.30686i | 0.155541 | − | 0.155541i | ||||
\(453\) | 11.6664 | + | 6.75209i | 0.548133 | + | 0.317241i | ||||
\(454\) | 26.2370i | 1.23136i | ||||||||
\(455\) | −4.69866 | − | 11.4289i | −0.220277 | − | 0.535797i | ||||
\(456\) | 1.67351 | − | 0.446512i | 0.0783692 | − | 0.0209099i | ||||
\(457\) | −22.9810 | − | 22.9810i | −1.07501 | − | 1.07501i | −0.996949 | − | 0.0780586i | \(-0.975128\pi\) |
−0.0780586 | − | 0.996949i | \(-0.524872\pi\) | |||||||
\(458\) | −1.86550 | − | 1.86550i | −0.0871692 | − | 0.0871692i | ||||
\(459\) | −15.7500 | − | 15.8506i | −0.735147 | − | 0.739842i | ||||
\(460\) | 16.0969 | + | 6.71746i | 0.750521 | + | 0.313203i | ||||
\(461\) | − | 16.8678i | − | 0.785612i | −0.919621 | − | 0.392806i | \(-0.871504\pi\) | ||
0.919621 | − | 0.392806i | \(-0.128496\pi\) | |||||||
\(462\) | −1.24626 | + | 2.15330i | −0.0579811 | + | 0.100180i | ||||
\(463\) | −17.7793 | + | 17.7793i | −0.826272 | + | 0.826272i | −0.986999 | − | 0.160727i | \(-0.948616\pi\) |
0.160727 | + | 0.986999i | \(0.448616\pi\) | |||||||
\(464\) | 5.49893 | 0.255282 | ||||||||
\(465\) | 3.01967 | − | 22.2980i | 0.140034 | − | 1.03404i | ||||
\(466\) | −18.8897 | −0.875046 | ||||||||
\(467\) | −12.4366 | + | 12.4366i | −0.575497 | + | 0.575497i | −0.933659 | − | 0.358162i | \(-0.883404\pi\) |
0.358162 | + | 0.933659i | \(0.383404\pi\) | |||||||
\(468\) | 3.76975 | − | 13.9504i | 0.174257 | − | 0.644859i | ||||
\(469\) | − | 3.90893i | − | 0.180497i | ||||||
\(470\) | −17.9024 | + | 7.36002i | −0.825775 | + | 0.339492i | ||||
\(471\) | −3.11225 | − | 11.6646i | −0.143405 | − | 0.537476i | ||||
\(472\) | 6.42077 | + | 6.42077i | 0.295540 | + | 0.295540i | ||||
\(473\) | 7.01628 | + | 7.01628i | 0.322609 | + | 0.322609i | ||||
\(474\) | 2.16282 | + | 8.10615i | 0.0993416 | + | 0.372328i | ||||
\(475\) | −3.51679 | − | 3.55418i | −0.161361 | − | 0.163077i | ||||
\(476\) | − | 4.93358i | − | 0.226130i | ||||||
\(477\) | −0.514942 | + | 1.90561i | −0.0235776 | + | 0.0872517i | ||||
\(478\) | 0.253946 | − | 0.253946i | 0.0116152 | − | 0.0116152i | ||||
\(479\) | 37.6990 | 1.72251 | 0.861256 | − | 0.508172i | \(-0.169679\pi\) | ||||
0.861256 | + | 0.508172i | \(0.169679\pi\) | |||||||
\(480\) | 2.34632 | + | 3.08136i | 0.107094 | + | 0.140644i | ||||
\(481\) | −48.2957 | −2.20210 | ||||||||
\(482\) | −3.83502 | + | 3.83502i | −0.174681 | + | 0.174681i | ||||
\(483\) | −7.76440 | + | 13.4154i | −0.353292 | + | 0.610423i | ||||
\(484\) | − | 9.43240i | − | 0.428745i | ||||||
\(485\) | −15.2888 | + | 36.6361i | −0.694228 | + | 1.66356i | ||||
\(486\) | −4.11441 | + | 15.0357i | −0.186634 | + | 0.682032i | ||||
\(487\) | 1.14616 | + | 1.14616i | 0.0519376 | + | 0.0519376i | 0.732599 | − | 0.680661i | \(-0.238307\pi\) |
−0.680661 | + | 0.732599i | \(0.738307\pi\) | |||||||
\(488\) | 4.47333 | + | 4.47333i | 0.202498 | + | 0.202498i | ||||
\(489\) | 0.694276 | − | 0.185241i | 0.0313963 | − | 0.00837691i | ||||
\(490\) | 4.89469 | − | 11.7290i | 0.221119 | − | 0.529863i | ||||
\(491\) | − | 11.1351i | − | 0.502519i | −0.967920 | − | 0.251260i | \(-0.919155\pi\) | ||
0.967920 | − | 0.251260i | \(-0.0808448\pi\) | |||||||
\(492\) | 0.388542 | + | 0.224875i | 0.0175168 | + | 0.0101381i | ||||
\(493\) | −16.7211 | + | 16.7211i | −0.753079 | + | 0.753079i | ||||
\(494\) | −4.81693 | −0.216724 | ||||||||
\(495\) | 6.63888 | + | 5.14465i | 0.298395 | + | 0.231235i | ||||
\(496\) | 5.80986 | 0.260870 | ||||||||
\(497\) | 0.606615 | − | 0.606615i | 0.0272104 | − | 0.0272104i | ||||
\(498\) | 8.96537 | + | 5.18885i | 0.401748 | + | 0.232518i | ||||
\(499\) | 2.14480i | 0.0960142i | 0.998847 | + | 0.0480071i | \(0.0152870\pi\) | ||||
−0.998847 | + | 0.0480071i | \(0.984713\pi\) | |||||||
\(500\) | 4.36032 | − | 10.2950i | 0.195000 | − | 0.460408i | ||||
\(501\) | −10.1545 | + | 2.70934i | −0.453669 | + | 0.121044i | ||||
\(502\) | 9.46827 | + | 9.46827i | 0.422590 | + | 0.422590i | ||||
\(503\) | 22.0328 | + | 22.0328i | 0.982393 | + | 0.982393i | 0.999848 | − | 0.0174544i | \(-0.00555619\pi\) |
−0.0174544 | + | 0.999848i | \(0.505556\pi\) | |||||||
\(504\) | −2.98431 | + | 1.71456i | −0.132932 | + | 0.0763725i | ||||
\(505\) | 7.35260 | − | 3.02280i | 0.327186 | − | 0.134513i | ||||
\(506\) | 9.76645i | 0.434171i | ||||||||
\(507\) | −8.85215 | + | 15.2949i | −0.393138 | + | 0.679269i | ||||
\(508\) | −5.40945 | + | 5.40945i | −0.240006 | + | 0.240006i | ||||
\(509\) | 44.4681 | 1.97101 | 0.985507 | − | 0.169634i | \(-0.0542586\pi\) | ||||
0.985507 | + | 0.169634i | \(0.0542586\pi\) | |||||||
\(510\) | −16.5044 | − | 2.23508i | −0.730827 | − | 0.0989712i | ||||
\(511\) | 8.85858 | 0.391881 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 5.19613 | + | 0.0165399i | 0.229415 | + | 0.000730253i | ||||
\(514\) | − | 22.9474i | − | 1.01217i | ||||||
\(515\) | 25.3491 | + | 10.5785i | 1.11702 | + | 0.466147i | ||||
\(516\) | 3.53865 | + | 13.2627i | 0.155780 | + | 0.583858i | ||||
\(517\) | −7.66372 | − | 7.66372i | −0.337050 | − | 0.337050i | ||||
\(518\) | 8.13363 | + | 8.13363i | 0.357371 | + | 0.357371i | ||||
\(519\) | −1.99784 | − | 7.48780i | −0.0876953 | − | 0.328678i | ||||
\(520\) | −4.09555 | − | 9.96196i | −0.179602 | − | 0.436861i | ||||
\(521\) | 24.7771i | 1.08551i | 0.839892 | + | 0.542753i | \(0.182618\pi\) | ||||
−0.839892 | + | 0.542753i | \(0.817382\pi\) | |||||||
\(522\) | 15.9256 | + | 4.30349i | 0.697044 | + | 0.188359i | ||||
\(523\) | −15.2015 | + | 15.2015i | −0.664717 | + | 0.664717i | −0.956488 | − | 0.291771i | \(-0.905755\pi\) |
0.291771 | + | 0.956488i | \(0.405755\pi\) | |||||||
\(524\) | −21.4587 | −0.937426 | ||||||||
\(525\) | 8.57273 | + | 5.02230i | 0.374144 | + | 0.219191i | ||||
\(526\) | −4.90290 | −0.213777 | ||||||||
\(527\) | −17.6665 | + | 17.6665i | −0.769566 | + | 0.769566i | ||||
\(528\) | −1.08629 | + | 1.87691i | −0.0472747 | + | 0.0816819i | ||||
\(529\) | 37.8467i | 1.64551i | ||||||||
\(530\) | 0.559446 | + | 1.36079i | 0.0243008 | + | 0.0591088i | ||||
\(531\) | 13.5704 | + | 23.6203i | 0.588906 | + | 1.02503i | ||||
\(532\) | 0.811234 | + | 0.811234i | 0.0351715 | + | 0.0351715i | ||||
\(533\) | −0.882812 | − | 0.882812i | −0.0382388 | − | 0.0382388i | ||||
\(534\) | −21.4178 | + | 5.71454i | −0.926840 | + | 0.247292i | ||||
\(535\) | 15.3996 | + | 6.42647i | 0.665782 | + | 0.277840i | ||||
\(536\) | − | 3.40719i | − | 0.147168i | ||||||
\(537\) | 5.73556 | + | 3.31955i | 0.247508 | + | 0.143249i | ||||
\(538\) | 3.47487 | − | 3.47487i | 0.149812 | − | 0.149812i | ||||
\(539\) | 7.11634 | 0.306522 | ||||||||
\(540\) | 4.38375 | + | 10.7602i | 0.188647 | + | 0.463047i | ||||
\(541\) | 30.5234 | 1.31231 | 0.656153 | − | 0.754628i | \(-0.272183\pi\) | ||||
0.656153 | + | 0.754628i | \(0.272183\pi\) | |||||||
\(542\) | −4.31289 | + | 4.31289i | −0.185255 | + | 0.185255i | ||||
\(543\) | −17.5785 | − | 10.1739i | −0.754367 | − | 0.436602i | ||||
\(544\) | − | 4.30032i | − | 0.184375i | ||||||
\(545\) | −40.3274 | + | 16.5794i | −1.72744 | + | 0.710183i | ||||
\(546\) | 9.24825 | − | 2.46755i | 0.395788 | − | 0.105601i | ||||
\(547\) | 2.58026 | + | 2.58026i | 0.110324 | + | 0.110324i | 0.760114 | − | 0.649790i | \(-0.225143\pi\) |
−0.649790 | + | 0.760114i | \(0.725143\pi\) | |||||||
\(548\) | −13.6290 | − | 13.6290i | −0.582202 | − | 0.582202i | ||||
\(549\) | 9.45446 | + | 16.4562i | 0.403507 | + | 0.702332i | ||||
\(550\) | 6.26011 | + | 0.0331027i | 0.266932 | + | 0.00141150i | ||||
\(551\) | − | 5.49893i | − | 0.234263i | ||||||
\(552\) | −6.76778 | + | 11.6935i | −0.288056 | + | 0.497707i | ||||
\(553\) | −3.92946 | + | 3.92946i | −0.167098 | + | 0.167098i | ||||
\(554\) | 16.2375 | 0.689866 | ||||||||
\(555\) | 30.8944 | − | 23.5248i | 1.31140 | − | 0.998572i | ||||
\(556\) | 10.5758 | 0.448515 | ||||||||
\(557\) | −23.0216 | + | 23.0216i | −0.975455 | + | 0.975455i | −0.999706 | − | 0.0242514i | \(-0.992280\pi\) |
0.0242514 | + | 0.999706i | \(0.492280\pi\) | |||||||
\(558\) | 16.8261 | + | 4.54682i | 0.712304 | + | 0.192482i | ||||
\(559\) | − | 38.1746i | − | 1.61461i | ||||||
\(560\) | −0.987979 | + | 2.36747i | −0.0417497 | + | 0.100044i | ||||
\(561\) | −2.40410 | − | 9.01044i | −0.101501 | − | 0.380421i | ||||
\(562\) | 14.0330 | + | 14.0330i | 0.591947 | + | 0.591947i | ||||
\(563\) | 29.0925 | + | 29.0925i | 1.22610 | + | 1.22610i | 0.965426 | + | 0.260676i | \(0.0839453\pi\) |
0.260676 | + | 0.965426i | \(0.416055\pi\) | |||||||
\(564\) | −3.86518 | − | 14.4865i | −0.162754 | − | 0.609993i | ||||
\(565\) | 4.02732 | − | 9.65057i | 0.169431 | − | 0.406003i | ||||
\(566\) | 19.1667i | 0.805635i | ||||||||
\(567\) | −9.98475 | + | 2.63004i | −0.419320 | + | 0.110451i | ||||
\(568\) | 0.528751 | − | 0.528751i | 0.0221859 | − | 0.0221859i | ||||
\(569\) | 31.9886 | 1.34103 | 0.670515 | − | 0.741896i | \(-0.266073\pi\) | ||||
0.670515 | + | 0.741896i | \(0.266073\pi\) | |||||||
\(570\) | 3.08136 | − | 2.34632i | 0.129064 | − | 0.0982766i | ||||
\(571\) | −19.7915 | −0.828248 | −0.414124 | − | 0.910220i | \(-0.635912\pi\) | ||||
−0.414124 | + | 0.910220i | \(0.635912\pi\) | |||||||
\(572\) | 4.26455 | − | 4.26455i | 0.178310 | − | 0.178310i | ||||
\(573\) | 9.56353 | − | 16.5240i | 0.399522 | − | 0.690300i | ||||
\(574\) | 0.297354i | 0.0124113i | ||||||||
\(575\) | 39.0016 | + | 0.206236i | 1.62648 | + | 0.00860062i | ||||
\(576\) | −2.60125 | + | 1.49448i | −0.108386 | + | 0.0622701i | ||||
\(577\) | 21.8776 | + | 21.8776i | 0.910777 | + | 0.910777i | 0.996333 | − | 0.0855565i | \(-0.0272668\pi\) |
−0.0855565 | + | 0.996333i | \(0.527267\pi\) | |||||||
\(578\) | 1.05552 | + | 1.05552i | 0.0439040 | + | 0.0439040i | ||||
\(579\) | −15.9794 | + | 4.26351i | −0.664082 | + | 0.177185i | ||||
\(580\) | 11.3724 | − | 4.67542i | 0.472214 | − | 0.194136i | ||||
\(581\) | 6.86127i | 0.284653i | ||||||||
\(582\) | −26.6141 | − | 15.4033i | −1.10319 | − | 0.638488i | ||||
\(583\) | −0.582531 | + | 0.582531i | −0.0241260 | + | 0.0241260i | ||||
\(584\) | 7.72152 | 0.319519 | ||||||||
\(585\) | −4.06496 | − | 32.0563i | −0.168065 | − | 1.32536i | ||||
\(586\) | −6.67963 | −0.275933 | ||||||||
\(587\) | 19.3270 | − | 19.3270i | 0.797710 | − | 0.797710i | −0.185024 | − | 0.982734i | \(-0.559236\pi\) |
0.982734 | + | 0.185024i | \(0.0592363\pi\) | |||||||
\(588\) | 8.52047 | + | 4.93136i | 0.351378 | + | 0.203366i | ||||
\(589\) | − | 5.80986i | − | 0.239391i | ||||||
\(590\) | 18.7381 | + | 7.81967i | 0.771434 | + | 0.321931i | ||||
\(591\) | −16.7027 | + | 4.45649i | −0.687059 | + | 0.183316i | ||||
\(592\) | 7.08962 | + | 7.08962i | 0.291382 | + | 0.291382i | ||||
\(593\) | −4.82260 | − | 4.82260i | −0.198040 | − | 0.198040i | 0.601119 | − | 0.799159i | \(-0.294722\pi\) |
−0.799159 | + | 0.601119i | \(0.794722\pi\) | |||||||
\(594\) | −4.61491 | + | 4.58562i | −0.189352 | + | 0.188150i | ||||
\(595\) | −4.19473 | − | 10.2032i | −0.171967 | − | 0.418290i | ||||
\(596\) | − | 0.688172i | − | 0.0281886i | ||||||
\(597\) | 20.6248 | − | 35.6358i | 0.844117 | − | 1.45848i | ||||
\(598\) | 26.5689 | − | 26.5689i | 1.08648 | − | 1.08648i | ||||
\(599\) | 12.4755 | 0.509735 | 0.254868 | − | 0.966976i | \(-0.417968\pi\) | ||||
0.254868 | + | 0.966976i | \(0.417968\pi\) | |||||||
\(600\) | 7.47236 | + | 4.37766i | 0.305058 | + | 0.178717i | ||||
\(601\) | 33.9363 | 1.38429 | 0.692145 | − | 0.721758i | \(-0.256666\pi\) | ||||
0.692145 | + | 0.721758i | \(0.256666\pi\) | |||||||
\(602\) | −6.42911 | + | 6.42911i | −0.262031 | + | 0.262031i | ||||
\(603\) | 2.66648 | − | 9.86764i | 0.108588 | − | 0.401841i | ||||
\(604\) | 7.78234i | 0.316659i | ||||||||
\(605\) | −8.01981 | − | 19.5073i | −0.326052 | − | 0.793083i | ||||
\(606\) | 1.58745 | + | 5.94969i | 0.0644858 | + | 0.241690i | ||||
\(607\) | 9.17452 | + | 9.17452i | 0.372382 | + | 0.372382i | 0.868344 | − | 0.495962i | \(-0.165185\pi\) |
−0.495962 | + | 0.868344i | \(0.665185\pi\) | |||||||
\(608\) | 0.707107 | + | 0.707107i | 0.0286770 | + | 0.0286770i | ||||
\(609\) | 2.81691 | + | 10.5577i | 0.114147 | + | 0.427818i | ||||
\(610\) | 13.0548 | + | 5.44794i | 0.528571 | + | 0.220581i | ||||
\(611\) | 41.6972i | 1.68689i | ||||||||
\(612\) | 3.36545 | − | 12.4543i | 0.136040 | − | 0.503433i | ||||
\(613\) | −9.18173 | + | 9.18173i | −0.370847 | + | 0.370847i | −0.867786 | − | 0.496939i | \(-0.834457\pi\) |
0.496939 | + | 0.867786i | \(0.334457\pi\) | |||||||
\(614\) | −15.4083 | −0.621830 | ||||||||
\(615\) | 0.994746 | + | 0.134712i | 0.0401120 | + | 0.00543211i | ||||
\(616\) | −1.43641 | −0.0578747 | ||||||||
\(617\) | −22.1031 | + | 22.1031i | −0.889839 | + | 0.889839i | −0.994507 | − | 0.104668i | \(-0.966622\pi\) |
0.104668 | + | 0.994507i | \(0.466622\pi\) | |||||||
\(618\) | −10.6578 | + | 18.4147i | −0.428720 | + | 0.740748i | ||||
\(619\) | − | 45.0921i | − | 1.81240i | −0.422844 | − | 0.906202i | \(-0.638968\pi\) | ||
0.422844 | − | 0.906202i | \(-0.361032\pi\) | |||||||
\(620\) | 12.0154 | − | 4.93978i | 0.482552 | − | 0.198386i | ||||
\(621\) | −28.7517 | + | 28.5692i | −1.15377 | + | 1.14644i | ||||
\(622\) | 13.2036 | + | 13.2036i | 0.529415 | + | 0.529415i | ||||
\(623\) | −10.3823 | − | 10.3823i | −0.415959 | − | 0.415959i | ||||
\(624\) | 8.06117 | − | 2.15082i | 0.322705 | − | 0.0861017i | ||||
\(625\) | 0.264386 | − | 24.9986i | 0.0105755 | − | 0.999944i | ||||
\(626\) | − | 8.07965i | − | 0.322928i | ||||||
\(627\) | 1.87691 | + | 1.08629i | 0.0749565 | + | 0.0433822i | ||||
\(628\) | 4.92864 | − | 4.92864i | 0.196674 | − | 0.196674i | ||||
\(629\) | −43.1160 | −1.71915 | ||||||||
\(630\) | −4.71410 | + | 6.08328i | −0.187814 | + | 0.242364i | ||||
\(631\) | −10.9260 | −0.434958 | −0.217479 | − | 0.976065i | \(-0.569783\pi\) | ||||
−0.217479 | + | 0.976065i | \(0.569783\pi\) | |||||||
\(632\) | −3.42509 | + | 3.42509i | −0.136243 | + | 0.136243i | ||||
\(633\) | −25.3763 | − | 14.6869i | −1.00862 | − | 0.583752i | ||||
\(634\) | − | 15.6726i | − | 0.622438i | ||||||
\(635\) | −6.58802 | + | 15.7867i | −0.261438 | + | 0.626476i | ||||
\(636\) | −1.10114 | + | 0.293798i | −0.0436631 | + | 0.0116499i | ||||
\(637\) | −19.3595 | − | 19.3595i | −0.767051 | − | 0.767051i | ||||
\(638\) | 4.86835 | + | 4.86835i | 0.192740 | + | 0.192740i | ||||
\(639\) | 1.94513 | − | 1.11753i | 0.0769483 | − | 0.0442086i | ||||
\(640\) | −0.861165 | + | 2.06359i | −0.0340405 | + | 0.0815705i | ||||
\(641\) | − | 26.0023i | − | 1.02703i | −0.858081 | − | 0.513515i | \(-0.828343\pi\) | ||
0.858081 | − | 0.513515i | \(-0.171657\pi\) | |||||||
\(642\) | −6.47461 | + | 11.1869i | −0.255533 | + | 0.441513i | ||||
\(643\) | 9.72854 | − | 9.72854i | 0.383656 | − | 0.383656i | −0.488761 | − | 0.872418i | \(-0.662551\pi\) |
0.872418 | + | 0.488761i | \(0.162551\pi\) | |||||||
\(644\) | −8.94911 | −0.352644 | ||||||||
\(645\) | 18.5948 | + | 24.4200i | 0.732170 | + | 0.961538i | ||||
\(646\) | −4.30032 | −0.169194 | ||||||||
\(647\) | 27.1481 | − | 27.1481i | 1.06730 | − | 1.06730i | 0.0697360 | − | 0.997565i | \(-0.477784\pi\) |
0.997565 | − | 0.0697360i | \(-0.0222157\pi\) | |||||||
\(648\) | −8.70314 | + | 2.29245i | −0.341892 | + | 0.0900561i | ||||
\(649\) | 11.3689i | 0.446270i | ||||||||
\(650\) | −16.9401 | − | 17.1202i | −0.664447 | − | 0.671511i | ||||
\(651\) | 2.97619 | + | 11.1546i | 0.116646 | + | 0.437184i | ||||
\(652\) | 0.293352 | + | 0.293352i | 0.0114886 | + | 0.0114886i | ||||
\(653\) | −14.8598 | − | 14.8598i | −0.581507 | − | 0.581507i | 0.353810 | − | 0.935317i | \(-0.384886\pi\) |
−0.935317 | + | 0.353810i | \(0.884886\pi\) | |||||||
\(654\) | −8.70682 | − | 32.6328i | −0.340464 | − | 1.27604i | ||||
\(655\) | −44.3789 | + | 18.2450i | −1.73403 | + | 0.712893i | ||||
\(656\) | 0.259187i | 0.0101195i | ||||||||
\(657\) | 22.3625 | + | 6.04290i | 0.872444 | + | 0.235756i | ||||
\(658\) | 7.02236 | − | 7.02236i | 0.273760 | − | 0.273760i | ||||
\(659\) | 3.67408 | 0.143122 | 0.0715609 | − | 0.997436i | \(-0.477202\pi\) | ||||
0.0715609 | + | 0.997436i | \(0.477202\pi\) | |||||||
\(660\) | −0.650746 | + | 4.80526i | −0.0253302 | + | 0.187045i | ||||
\(661\) | 5.30895 | 0.206494 | 0.103247 | − | 0.994656i | \(-0.467077\pi\) | ||||
0.103247 | + | 0.994656i | \(0.467077\pi\) | |||||||
\(662\) | −14.1470 | + | 14.1470i | −0.549837 | + | 0.549837i | ||||
\(663\) | −17.9721 | + | 31.0525i | −0.697979 | + | 1.20598i | ||||
\(664\) | 5.98058i | 0.232091i | ||||||||
\(665\) | 2.36747 | + | 0.987979i | 0.0918065 | + | 0.0383122i | ||||
\(666\) | 14.9840 | + | 26.0808i | 0.580620 | + | 1.01061i | ||||
\(667\) | 30.3307 | + | 30.3307i | 1.17441 | + | 1.17441i | ||||
\(668\) | −4.29057 | − | 4.29057i | −0.166007 | − | 0.166007i | ||||
\(669\) | 30.9469 | − | 8.25702i | 1.19648 | − | 0.319235i | ||||
\(670\) | −2.89693 | − | 7.04645i | −0.111918 | − | 0.272228i | ||||
\(671\) | 7.92070i | 0.305775i | ||||||||
\(672\) | −1.71983 | − | 0.995380i | −0.0663440 | − | 0.0383976i | ||||
\(673\) | 25.8750 | − | 25.8750i | 0.997409 | − | 0.997409i | −0.00258791 | − | 0.999997i | \(-0.500824\pi\) |
0.999997 | + | 0.00258791i | \(0.000823758\pi\) | |||||||
\(674\) | −12.2964 | −0.473638 | ||||||||
\(675\) | 18.2149 | + | 18.5261i | 0.701092 | + | 0.713071i | ||||
\(676\) | −10.2028 | −0.392417 | ||||||||
\(677\) | 19.1276 | − | 19.1276i | 0.735134 | − | 0.735134i | −0.236498 | − | 0.971632i | \(-0.576000\pi\) |
0.971632 | + | 0.236498i | \(0.0759996\pi\) | |||||||
\(678\) | 7.01060 | + | 4.05749i | 0.269240 | + | 0.155827i | ||||
\(679\) | − | 20.3680i | − | 0.781651i | ||||||
\(680\) | −3.65631 | − | 8.89354i | −0.140213 | − | 0.341052i | ||||
\(681\) | −43.9078 | + | 11.7151i | −1.68255 | + | 0.448925i | ||||
\(682\) | 5.14362 | + | 5.14362i | 0.196959 | + | 0.196959i | ||||
\(683\) | −3.97993 | − | 3.97993i | −0.152288 | − | 0.152288i | 0.626851 | − | 0.779139i | \(-0.284343\pi\) |
−0.779139 | + | 0.626851i | \(0.784343\pi\) | |||||||
\(684\) | 1.49448 | + | 2.60125i | 0.0571430 | + | 0.0994614i | ||||
\(685\) | −39.7742 | − | 16.5984i | −1.51970 | − | 0.634191i | ||||
\(686\) | 14.5516i | 0.555583i | ||||||||
\(687\) | 2.28896 | − | 3.95490i | 0.0873293 | − | 0.150889i | ||||
\(688\) | −5.60388 | + | 5.60388i | −0.213646 | + | 0.213646i | ||||
\(689\) | 3.16947 | 0.120747 | ||||||||
\(690\) | −4.05426 | + | 29.9377i | −0.154343 | + | 1.13971i | ||||
\(691\) | −15.6719 | −0.596186 | −0.298093 | − | 0.954537i | \(-0.596351\pi\) | ||||
−0.298093 | + | 0.954537i | \(0.596351\pi\) | |||||||
\(692\) | 3.16382 | − | 3.16382i | 0.120270 | − | 0.120270i | ||||
\(693\) | −4.16003 | − | 1.12414i | −0.158026 | − | 0.0427027i | ||||
\(694\) | 7.19589i | 0.273152i | ||||||||
\(695\) | 21.8720 | − | 8.99201i | 0.829653 | − | 0.341086i | ||||
\(696\) | 2.45534 | + | 9.20251i | 0.0930695 | + | 0.348820i | ||||
\(697\) | −0.788131 | − | 0.788131i | −0.0298526 | − | 0.0298526i | ||||
\(698\) | −15.3299 | − | 15.3299i | −0.580244 | − | 0.580244i | ||||
\(699\) | −8.43446 | − | 31.6120i | −0.319021 | − | 1.19567i | ||||
\(700\) | −0.0303324 | + | 5.73621i | −0.00114646 | + | 0.216808i | ||||
\(701\) | − | 43.9609i | − | 1.66038i | −0.557480 | − | 0.830191i | \(-0.688232\pi\) | ||
0.557480 | − | 0.830191i | \(-0.311768\pi\) | |||||||
\(702\) | 25.0294 | + | 0.0796715i | 0.944673 | + | 0.00300701i | ||||
\(703\) | 7.08962 | − | 7.08962i | 0.267390 | − | 0.267390i | ||||
\(704\) | −1.25204 | −0.0471880 | ||||||||
\(705\) | −20.3107 | − | 26.6734i | −0.764944 | − | 1.00458i | ||||
\(706\) | −10.0681 | −0.378918 | ||||||||
\(707\) | −2.88412 | + | 2.88412i | −0.108468 | + | 0.108468i | ||||
\(708\) | −7.87825 | + | 13.6122i | −0.296083 | + | 0.511576i | ||||
\(709\) | − | 25.0308i | − | 0.940050i | −0.882653 | − | 0.470025i | \(-0.844245\pi\) | ||
0.882653 | − | 0.470025i | \(-0.155755\pi\) | |||||||
\(710\) | 0.643951 | − | 1.54308i | 0.0241671 | − | 0.0579109i | ||||
\(711\) | −12.6000 | + | 7.23899i | −0.472536 | + | 0.271483i | ||||
\(712\) | −9.04967 | − | 9.04967i | −0.339151 | − | 0.339151i | ||||
\(713\) | 32.0457 | + | 32.0457i | 1.20012 | + | 1.20012i | ||||
\(714\) | 8.25638 | − | 2.20290i | 0.308987 | − | 0.0824416i | ||||
\(715\) | 5.19368 | − | 12.4455i | 0.194233 | − | 0.465434i | ||||
\(716\) | 3.82605i | 0.142986i | ||||||||
\(717\) | 0.538370 | + | 0.311590i | 0.0201058 | + | 0.0116366i | ||||
\(718\) | −17.4531 | + | 17.4531i | −0.651343 | + | 0.651343i | ||||
\(719\) | −22.3343 | −0.832930 | −0.416465 | − | 0.909152i | \(-0.636731\pi\) | ||||
−0.416465 | + | 0.909152i | \(0.636731\pi\) | |||||||
\(720\) | −4.10901 | + | 5.30245i | −0.153134 | + | 0.197611i | ||||
\(721\) | −14.0929 | −0.524848 | ||||||||
\(722\) | 0.707107 | − | 0.707107i | 0.0263158 | − | 0.0263158i | ||||
\(723\) | −8.13033 | − | 4.70555i | −0.302370 | − | 0.175001i | ||||
\(724\) | − | 11.7262i | − | 0.435801i | ||||||
\(725\) | 19.5442 | − | 19.3386i | 0.725853 | − | 0.718217i | ||||
\(726\) | 15.7852 | − | 4.21168i | 0.585843 | − | 0.156310i | ||||
\(727\) | −27.5404 | − | 27.5404i | −1.02142 | − | 1.02142i | −0.999766 | − | 0.0216511i | \(-0.993108\pi\) |
−0.0216511 | − | 0.999766i | \(-0.506892\pi\) | |||||||
\(728\) | 3.90766 | + | 3.90766i | 0.144828 | + | 0.144828i | ||||
\(729\) | −26.9995 | − | 0.171887i | −0.999980 | − | 0.00636617i | ||||
\(730\) | 15.9690 | − | 6.56516i | 0.591038 | − | 0.242987i | ||||
\(731\) | − | 34.0804i | − | 1.26051i | ||||||
\(732\) | −5.48875 | + | 9.48354i | −0.202870 | + | 0.350522i | ||||
\(733\) | −28.9159 | + | 28.9159i | −1.06803 | + | 1.06803i | −0.0705243 | + | 0.997510i | \(0.522467\pi\) |
−0.997510 | + | 0.0705243i | \(0.977533\pi\) | |||||||
\(734\) | 2.26039 | 0.0834327 | ||||||||
\(735\) | 21.8141 | + | 2.95415i | 0.804626 | + | 0.108965i | ||||
\(736\) | −7.80043 | −0.287528 | ||||||||
\(737\) | 3.01647 | − | 3.01647i | 0.111113 | − | 0.111113i | ||||
\(738\) | −0.202841 | + | 0.750637i | −0.00746667 | + | 0.0276313i | ||||
\(739\) | 20.1578i | 0.741515i | 0.928730 | + | 0.370758i | \(0.120902\pi\) | ||||
−0.928730 | + | 0.370758i | \(0.879098\pi\) | |||||||
\(740\) | 20.6900 | + | 8.63425i | 0.760581 | + | 0.317401i | ||||
\(741\) | −2.15082 | − | 8.06117i | −0.0790123 | − | 0.296135i | ||||
\(742\) | −0.533780 | − | 0.533780i | −0.0195957 | − | 0.0195957i | ||||
\(743\) | −26.7472 | − | 26.7472i | −0.981260 | − | 0.981260i | 0.0185673 | − | 0.999828i | \(-0.494090\pi\) |
−0.999828 | + | 0.0185673i | \(0.994090\pi\) | |||||||
\(744\) | 2.59417 | + | 9.72284i | 0.0951070 | + | 0.356457i | ||||
\(745\) | −0.585112 | − | 1.42322i | −0.0214369 | − | 0.0521426i | ||||
\(746\) | − | 29.2529i | − | 1.07102i | ||||||
\(747\) | −4.68043 | + | 17.3205i | −0.171248 | + | 0.633724i | ||||
\(748\) | 3.80718 | − | 3.80718i | 0.139204 | − | 0.139204i | ||||
\(749\) | −8.56145 | −0.312828 | ||||||||
\(750\) | 19.1757 | + | 2.70018i | 0.700199 | + | 0.0985966i | ||||
\(751\) | −30.8503 | −1.12574 | −0.562871 | − | 0.826545i | \(-0.690303\pi\) | ||||
−0.562871 | + | 0.826545i | \(0.690303\pi\) | |||||||
\(752\) | 6.12099 | − | 6.12099i | 0.223210 | − | 0.223210i | ||||
\(753\) | −11.6175 | + | 20.0729i | −0.423366 | + | 0.731498i | ||||
\(754\) | − | 26.4880i | − | 0.964636i | ||||||
\(755\) | 6.61687 | + | 16.0948i | 0.240812 | + | 0.585748i | ||||
\(756\) | −4.20186 | − | 4.22869i | −0.152820 | − | 0.153796i | ||||
\(757\) | 25.2568 | + | 25.2568i | 0.917975 | + | 0.917975i | 0.996882 | − | 0.0789067i | \(-0.0251429\pi\) |
−0.0789067 | + | 0.996882i | \(0.525143\pi\) | |||||||
\(758\) | −13.6374 | − | 13.6374i | −0.495334 | − | 0.495334i | ||||
\(759\) | −16.3442 | + | 4.36084i | −0.593258 | + | 0.158288i | ||||
\(760\) | 2.06359 | + | 0.861165i | 0.0748542 | + | 0.0312377i | ||||
\(761\) | − | 7.51765i | − | 0.272514i | −0.990673 | − | 0.136257i | \(-0.956493\pi\) | ||
0.990673 | − | 0.136257i | \(-0.0435074\pi\) | |||||||
\(762\) | −11.4681 | − | 6.63737i | −0.415447 | − | 0.240447i | ||||
\(763\) | 15.8188 | − | 15.8188i | 0.572678 | − | 0.572678i | ||||
\(764\) | 11.0228 | 0.398790 | ||||||||
\(765\) | −3.62899 | − | 28.6182i | −0.131206 | − | 1.03469i | ||||
\(766\) | 32.1645 | 1.16215 | ||||||||
\(767\) | 30.9284 | − | 30.9284i | 1.11676 | − | 1.11676i | ||||
\(768\) | −1.49908 | − | 0.867616i | −0.0540934 | − | 0.0313074i | ||||
\(769\) | 45.1162i | 1.62693i | 0.581611 | + | 0.813467i | \(0.302422\pi\) | ||||
−0.581611 | + | 0.813467i | \(0.697578\pi\) | |||||||
\(770\) | −2.97066 | + | 1.22130i | −0.107055 | + | 0.0440125i | ||||
\(771\) | 38.4027 | − | 10.2463i | 1.38304 | − | 0.369012i | ||||
\(772\) | −6.75179 | − | 6.75179i | −0.243002 | − | 0.243002i | ||||
\(773\) | −25.7371 | − | 25.7371i | −0.925698 | − | 0.925698i | 0.0717268 | − | 0.997424i | \(-0.477149\pi\) |
−0.997424 | + | 0.0717268i | \(0.977149\pi\) | |||||||
\(774\) | −20.6152 | + | 11.8439i | −0.740997 | + | 0.425721i | ||||
\(775\) | 20.6493 | − | 20.4321i | 0.741744 | − | 0.733941i | ||||
\(776\) | − | 17.7536i | − | 0.637317i | ||||||
\(777\) | −9.97992 | + | 17.2435i | −0.358028 | + | 0.618606i | ||||
\(778\) | −14.2955 | + | 14.2955i | −0.512519 | + | 0.512519i | ||||
\(779\) | 0.259187 | 0.00928633 | ||||||||
\(780\) | 14.8427 | − | 11.3021i | 0.531454 | − | 0.404679i | ||||
\(781\) | 0.936234 | 0.0335011 | ||||||||
\(782\) | 23.7194 | − | 23.7194i | 0.848205 | − | 0.848205i | ||||
\(783\) | −0.0909517 | + | 28.5732i | −0.00325035 | + | 1.02112i | ||||
\(784\) | 5.68380i | 0.202993i | ||||||||
\(785\) | 6.00244 | − | 14.3835i | 0.214236 | − | 0.513369i | ||||
\(786\) | −9.58156 | − | 35.9112i | −0.341763 | − | 1.28091i | ||||
\(787\) | −23.2941 | − | 23.2941i | −0.830343 | − | 0.830343i | 0.157220 | − | 0.987564i | \(-0.449747\pi\) |
−0.987564 | + | 0.157220i | \(0.949747\pi\) | |||||||
\(788\) | −7.05740 | − | 7.05740i | −0.251410 | − | 0.251410i | ||||
\(789\) | −2.18921 | − | 8.20505i | −0.0779378 | − | 0.292107i | ||||
\(790\) | −4.17132 | + | 9.99562i | −0.148409 | + | 0.355628i | ||||
\(791\) | 5.36527i | 0.190767i | ||||||||
\(792\) | −3.62606 | − | 0.979852i | −0.128846 | − | 0.0348175i | ||||
\(793\) | 21.5477 | − | 21.5477i | 0.765182 | − | 0.765182i | ||||
\(794\) | −0.354390 | −0.0125768 | ||||||||
\(795\) | −2.02749 | + | 1.54384i | −0.0719076 | + | 0.0547545i | ||||
\(796\) | 23.7718 | 0.842569 | ||||||||
\(797\) | −16.2849 | + | 16.2849i | −0.576840 | + | 0.576840i | −0.934031 | − | 0.357192i | \(-0.883734\pi\) |
0.357192 | + | 0.934031i | \(0.383734\pi\) | |||||||
\(798\) | −0.995380 | + | 1.71983i | −0.0352361 | + | 0.0608814i | ||||
\(799\) | 37.2252i | 1.31693i | ||||||||
\(800\) | −0.0264390 | + | 4.99993i | −0.000934760 | + | 0.176774i | ||||
\(801\) | −19.1267 | − | 33.2913i | −0.675807 | − | 1.17629i | ||||
\(802\) | −15.3344 | − | 15.3344i | −0.541476 | − | 0.541476i | ||||
\(803\) | 6.83606 | + | 6.83606i | 0.241239 | + | 0.241239i | ||||
\(804\) | 5.70196 | − | 1.52135i | 0.201092 | − | 0.0536539i | ||||
\(805\) | −18.5078 | + | 7.60890i | −0.652313 | + | 0.268179i | ||||
\(806\) | − | 27.9857i | − | 0.985754i | ||||||
\(807\) | 7.36680 | + | 4.26365i | 0.259323 | + | 0.150088i | ||||
\(808\) | −2.51392 | + | 2.51392i | −0.0884394 | + | 0.0884394i | ||||
\(809\) | −20.3523 | −0.715549 | −0.357775 | − | 0.933808i | \(-0.616464\pi\) | ||||
−0.357775 | + | 0.933808i | \(0.616464\pi\) | |||||||
\(810\) | −16.0499 | + | 12.1408i | −0.563937 | + | 0.426585i | ||||
\(811\) | 32.7529 | 1.15011 | 0.575056 | − | 0.818114i | \(-0.304980\pi\) | ||||
0.575056 | + | 0.818114i | \(0.304980\pi\) | |||||||
\(812\) | −4.46092 | + | 4.46092i | −0.156548 | + | 0.156548i | ||||
\(813\) | −9.14342 | − | 5.29190i | −0.320674 | − | 0.185595i | ||||
\(814\) | 12.5532i | 0.439991i | ||||||||
\(815\) | 0.856106 | + | 0.357266i | 0.0299881 | + | 0.0125145i | ||||
\(816\) | 7.19661 | − | 1.92015i | 0.251932 | − | 0.0672185i | ||||
\(817\) | 5.60388 | + | 5.60388i | 0.196055 | + | 0.196055i | ||||
\(818\) | 4.20593 | + | 4.20593i | 0.147057 | + | 0.147057i | ||||
\(819\) | 8.25891 | + | 14.3752i | 0.288590 | + | 0.502311i | ||||
\(820\) | 0.220371 | + | 0.536027i | 0.00769570 | + | 0.0187189i | ||||
\(821\) | 15.1106i | 0.527363i | 0.964610 | + | 0.263681i | \(0.0849367\pi\) | ||||
−0.964610 | + | 0.263681i | \(0.915063\pi\) | |||||||
\(822\) | 16.7227 | − | 28.8937i | 0.583271 | − | 1.00778i | ||||
\(823\) | 38.5308 | − | 38.5308i | 1.34310 | − | 1.34310i | 0.450139 | − | 0.892958i | \(-0.351374\pi\) |
0.892958 | − | 0.450139i | \(-0.148626\pi\) | |||||||
\(824\) | −12.2840 | −0.427933 | ||||||||
\(825\) | 2.73982 | + | 10.4911i | 0.0953882 | + | 0.365254i | ||||
\(826\) | −10.4175 | −0.362471 | ||||||||
\(827\) | −7.31829 | + | 7.31829i | −0.254482 | + | 0.254482i | −0.822805 | − | 0.568323i | \(-0.807592\pi\) |
0.568323 | + | 0.822805i | \(0.307592\pi\) | |||||||
\(828\) | −22.5910 | − | 6.10465i | −0.785092 | − | 0.212151i | ||||
\(829\) | − | 0.579874i | − | 0.0201399i | −0.999949 | − | 0.0100699i | \(-0.996795\pi\) | ||
0.999949 | − | 0.0100699i | \(-0.00320541\pi\) | |||||||
\(830\) | 5.08493 | + | 12.3685i | 0.176501 | + | 0.429317i | ||||
\(831\) | 7.25025 | + | 27.1736i | 0.251509 | + | 0.942642i | ||||
\(832\) | 3.40609 | + | 3.40609i | 0.118085 | + | 0.118085i | ||||
\(833\) | −17.2832 | − | 17.2832i | −0.598827 | − | 0.598827i | ||||
\(834\) | 4.72224 | + | 17.6987i | 0.163518 | + | 0.612857i | ||||
\(835\) | −12.5214 | − | 5.22537i | −0.433321 | − | 0.180831i | ||||
\(836\) | 1.25204i | 0.0433027i | ||||||||
\(837\) | −0.0960944 | + | 30.1888i | −0.00332151 | + | 1.04348i | ||||
\(838\) | 25.3766 | − | 25.3766i | 0.876620 | − | 0.876620i | ||||
\(839\) | −14.3633 | −0.495878 | −0.247939 | − | 0.968776i | \(-0.579753\pi\) | ||||
−0.247939 | + | 0.968776i | \(0.579753\pi\) | |||||||
\(840\) | −4.40312 | − | 0.596286i | −0.151922 | − | 0.0205738i | ||||
\(841\) | 1.23828 | 0.0426995 | ||||||||
\(842\) | 9.57779 | − | 9.57779i | 0.330073 | − | 0.330073i | ||||
\(843\) | −17.2184 | + | 29.7503i | −0.593035 | + | 1.02465i | ||||
\(844\) | − | 16.9279i | − | 0.582682i | ||||||
\(845\) | −21.1006 | + | 8.67487i | −0.725883 | + | 0.298425i | ||||
\(846\) | 22.5175 | − | 12.9368i | 0.774166 | − | 0.444777i | ||||
\(847\) | 7.65188 | + | 7.65188i | 0.262922 | + | 0.262922i | ||||
\(848\) | −0.465266 | − | 0.465266i | −0.0159773 | − | 0.0159773i | ||||
\(849\) | −32.0755 | + | 8.55815i | −1.10083 | + | 0.293715i | ||||
\(850\) | −15.1233 | − | 15.2841i | −0.518725 | − | 0.524240i | ||||
\(851\) | 78.2090i | 2.68097i | ||||||||
\(852\) | 1.12096 | + | 0.648775i | 0.0384036 | + | 0.0222267i | ||||
\(853\) | −28.0005 | + | 28.0005i | −0.958719 | + | 0.958719i | −0.999181 | − | 0.0404617i | \(-0.987117\pi\) |
0.0404617 | + | 0.999181i | \(0.487117\pi\) | |||||||
\(854\) | −7.25783 | −0.248358 | ||||||||
\(855\) | 5.30245 | + | 4.10901i | 0.181340 | + | 0.140525i | ||||
\(856\) | −7.46253 | −0.255064 | ||||||||
\(857\) | −32.1199 | + | 32.1199i | −1.09720 | + | 1.09720i | −0.102459 | + | 0.994737i | \(0.532671\pi\) |
−0.994737 | + | 0.102459i | \(0.967329\pi\) | |||||||
\(858\) | 9.04094 | + | 5.23259i | 0.308652 | + | 0.178638i | ||||
\(859\) | − | 18.3812i | − | 0.627159i | −0.949562 | − | 0.313579i | \(-0.898472\pi\) | ||
0.949562 | − | 0.313579i | \(-0.101528\pi\) | |||||||
\(860\) | −6.82481 | + | 16.3541i | −0.232724 | + | 0.557671i | ||||
\(861\) | −0.497624 | + | 0.132772i | −0.0169590 | + | 0.00452487i | ||||
\(862\) | −0.314904 | − | 0.314904i | −0.0107257 | − | 0.0107257i | ||||
\(863\) | −11.6814 | − | 11.6814i | −0.397638 | − | 0.397638i | 0.479761 | − | 0.877399i | \(-0.340723\pi\) |
−0.877399 | + | 0.479761i | \(0.840723\pi\) | |||||||
\(864\) | −3.66252 | − | 3.68591i | −0.124601 | − | 0.125397i | ||||
\(865\) | 3.85312 | − | 9.23314i | 0.131010 | − | 0.313936i | ||||
\(866\) | 29.5957i | 1.00570i | ||||||||
\(867\) | −1.29512 | + | 2.23773i | −0.0439846 | + | 0.0759973i | ||||
\(868\) | −4.71316 | + | 4.71316i | −0.159975 | + | 0.159975i | ||||
\(869\) | −6.06464 | −0.205729 | ||||||||
\(870\) | 12.9023 | + | 16.9442i | 0.437428 | + | 0.574462i | ||||
\(871\) | −16.4122 | −0.556106 | ||||||||
\(872\) | 13.7883 | − | 13.7883i | 0.466931 | − | 0.466931i | ||||
\(873\) | 13.8940 | − | 51.4166i | 0.470242 | − | 1.74019i | ||||
\(874\) | 7.80043i | 0.263854i | ||||||||
\(875\) | 4.81443 | + | 11.8889i | 0.162758 | + | 0.401919i | ||||
\(876\) | 3.44776 | + | 12.9220i | 0.116489 | + | 0.436595i | ||||
\(877\) | −14.5905 | − | 14.5905i | −0.492685 | − | 0.492685i | 0.416466 | − | 0.909151i | \(-0.363268\pi\) |
−0.909151 | + | 0.416466i | \(0.863268\pi\) | |||||||
\(878\) | 0.345068 | + | 0.345068i | 0.0116455 | + | 0.0116455i | ||||
\(879\) | −2.98254 | − | 11.1784i | −0.100598 | − | 0.377038i | ||||
\(880\) | −2.58936 | + | 1.06454i | −0.0872872 | + | 0.0358855i | ||||
\(881\) | − | 4.06288i | − | 0.136882i | −0.997655 | − | 0.0684409i | \(-0.978198\pi\) | ||
0.997655 | − | 0.0684409i | \(-0.0218025\pi\) | |||||||
\(882\) | −4.44817 | + | 16.4610i | −0.149778 | + | 0.554270i | ||||
\(883\) | 39.1005 | − | 39.1005i | 1.31584 | − | 1.31584i | 0.398798 | − | 0.917039i | \(-0.369428\pi\) |
0.917039 | − | 0.398798i | \(-0.130572\pi\) | |||||||
\(884\) | −20.7143 | −0.696699 | ||||||||
\(885\) | −4.71949 | + | 34.8499i | −0.158644 | + | 1.17147i | ||||
\(886\) | 8.36703 | 0.281096 | ||||||||
\(887\) | −7.54810 | + | 7.54810i | −0.253440 | + | 0.253440i | −0.822380 | − | 0.568939i | \(-0.807354\pi\) |
0.568939 | + | 0.822380i | \(0.307354\pi\) | |||||||
\(888\) | −8.69893 | + | 15.0301i | −0.291917 | + | 0.504378i | ||||
\(889\) | − | 8.77667i | − | 0.294360i | ||||||
\(890\) | −26.4101 | − | 11.0213i | −0.885270 | − | 0.369436i | ||||
\(891\) | −9.73468 | − | 5.67554i | −0.326124 | − | 0.190138i | ||||
\(892\) | 13.0760 | + | 13.0760i | 0.437817 | + | 0.437817i | ||||
\(893\) | −6.12099 | − | 6.12099i | −0.204831 | − | 0.204831i | ||||
\(894\) | 1.15166 | − | 0.307277i | 0.0385173 | − | 0.0102769i | ||||
\(895\) | 3.25307 | + | 7.91271i | 0.108738 | + | 0.264493i | ||||
\(896\) | − | 1.14726i | − | 0.0383272i | ||||||
\(897\) | 56.3267 | + | 32.5999i | 1.88069 | + | 1.08848i | ||||
\(898\) | −11.5682 | + | 11.5682i | −0.386037 | + | 0.386037i | ||||
\(899\) | 31.9480 | 1.06553 | ||||||||
\(900\) | −3.98954 | + | 14.4597i | −0.132985 | + | 0.481991i | ||||
\(901\) | 2.82954 | 0.0942658 | ||||||||
\(902\) | −0.229465 | + | 0.229465i | −0.00764034 | + | 0.00764034i | ||||
\(903\) | −13.6298 | − | 7.88848i | −0.453572 | − | 0.262512i | ||||
\(904\) | 4.67660i | 0.155541i | ||||||||
\(905\) | −9.97011 | − | 24.2511i | −0.331418 | − | 0.806135i | ||||
\(906\) | −13.0238 | + | 3.47491i | −0.432687 | + | 0.115446i | ||||
\(907\) | −36.9489 | − | 36.9489i | −1.22687 | − | 1.22687i | −0.965143 | − | 0.261724i | \(-0.915709\pi\) |
−0.261724 | − | 0.965143i | \(-0.584291\pi\) | |||||||
\(908\) | −18.5524 | − | 18.5524i | −0.615682 | − | 0.615682i | ||||
\(909\) | −9.24803 | + | 5.31322i | −0.306738 | + | 0.176228i | ||||
\(910\) | 11.4039 | + | 4.75903i | 0.378037 | + | 0.157760i | ||||
\(911\) | − | 17.9950i | − | 0.596200i | −0.954535 | − | 0.298100i | \(-0.903647\pi\) | ||
0.954535 | − | 0.298100i | \(-0.0963529\pi\) | |||||||
\(912\) | −0.867616 | + | 1.49908i | −0.0287297 | + | 0.0496395i | ||||
\(913\) | −5.29476 | + | 5.29476i | −0.175231 | + | 0.175231i | ||||
\(914\) | 32.5001 | 1.07501 | ||||||||
\(915\) | −3.28806 | + | 24.2798i | −0.108700 | + | 0.802665i | ||||
\(916\) | 2.63822 | 0.0871692 | ||||||||
\(917\) | 17.4080 | − | 17.4080i | 0.574863 | − | 0.574863i | ||||
\(918\) | 22.3450 | + | 0.0711267i | 0.737495 | + | 0.00234753i | ||||
\(919\) | − | 7.22194i | − | 0.238230i | −0.992880 | − | 0.119115i | \(-0.961994\pi\) | ||
0.992880 | − | 0.119115i | \(-0.0380057\pi\) | |||||||
\(920\) | −16.1322 | + | 6.63225i | −0.531862 | + | 0.218659i | ||||
\(921\) | −6.88001 | − | 25.7860i | −0.226704 | − | 0.849676i | ||||
\(922\) | 11.9273 | + | 11.9273i | 0.392806 | + | 0.392806i | ||||
\(923\) | −2.54696 | − | 2.54696i | −0.0838342 | − | 0.0838342i | ||||
\(924\) | −0.641376 | − | 2.40385i | −0.0210997 | − | 0.0790808i | ||||
\(925\) | 50.1305 | + | 0.265084i | 1.64828 | + | 0.00871590i | ||||
\(926\) | − | 25.1437i | − | 0.826272i | ||||||
\(927\) | −35.5760 | − | 9.61351i | −1.16847 | − | 0.315749i | ||||
\(928\) | −3.88833 | + | 3.88833i | −0.127641 | + | 0.127641i | ||||
\(929\) | 10.0132 | 0.328523 | 0.164262 | − | 0.986417i | \(-0.447476\pi\) | ||||
0.164262 | + | 0.986417i | \(0.447476\pi\) | |||||||
\(930\) | 13.6318 | + | 17.9023i | 0.447005 | + | 0.587038i | ||||
\(931\) | 5.68380 | 0.186279 | ||||||||
\(932\) | 13.3570 | − | 13.3570i | 0.437523 | − | 0.437523i | ||||
\(933\) | −16.2007 | + | 27.9918i | −0.530387 | + | 0.916411i | ||||
\(934\) | − | 17.5880i | − | 0.575497i | ||||||
\(935\) | 4.63666 | − | 11.1107i | 0.151635 | − | 0.363359i | ||||
\(936\) | 7.19883 | + | 12.5301i | 0.235301 | + | 0.409558i | ||||
\(937\) | 32.1574 | + | 32.1574i | 1.05054 | + | 1.05054i | 0.998653 | + | 0.0518829i | \(0.0165223\pi\) |
0.0518829 | + | 0.998653i | \(0.483478\pi\) | |||||||
\(938\) | 2.76403 | + | 2.76403i | 0.0902487 | + | 0.0902487i | ||||
\(939\) | 13.5213 | − | 3.60766i | 0.441253 | − | 0.117732i | ||||
\(940\) | 7.45458 | − | 17.8632i | 0.243142 | − | 0.582634i | ||||
\(941\) | − | 10.3250i | − | 0.336585i | −0.985737 | − | 0.168292i | \(-0.946175\pi\) | ||
0.985737 | − | 0.168292i | \(-0.0538252\pi\) | |||||||
\(942\) | 10.4488 | + | 6.04741i | 0.340440 | + | 0.197035i | ||||
\(943\) | −1.42961 | + | 1.42961i | −0.0465544 | + | 0.0465544i | ||||
\(944\) | −9.08034 | −0.295540 | ||||||||
\(945\) | −12.2853 | − | 5.17282i | −0.399642 | − | 0.168272i | ||||
\(946\) | −9.92252 | −0.322609 | ||||||||
\(947\) | −7.92954 | + | 7.92954i | −0.257676 | + | 0.257676i | −0.824108 | − | 0.566433i | \(-0.808323\pi\) |
0.566433 | + | 0.824108i | \(0.308323\pi\) | |||||||
\(948\) | −7.26126 | − | 4.20257i | −0.235835 | − | 0.136493i | ||||
\(949\) | − | 37.1941i | − | 1.20737i | ||||||
\(950\) | 4.99993 | + | 0.0264390i | 0.162219 | + | 0.000857795i | ||||
\(951\) | 26.2282 | − | 6.99801i | 0.850508 | − | 0.226926i | ||||
\(952\) | 3.48857 | + | 3.48857i | 0.113065 | + | 0.113065i | ||||
\(953\) | 18.1770 | + | 18.1770i | 0.588812 | + | 0.588812i | 0.937310 | − | 0.348498i | \(-0.113308\pi\) |
−0.348498 | + | 0.937310i | \(0.613308\pi\) | |||||||
\(954\) | −0.983347 | − | 1.71159i | −0.0318370 | − | 0.0554146i | ||||
\(955\) | 22.7963 | − | 9.37201i | 0.737671 | − | 0.303271i | ||||
\(956\) | 0.359134i | 0.0116152i | ||||||||
\(957\) | −5.97344 | + | 10.3210i | −0.193094 | + | 0.333630i | ||||
\(958\) | −26.6572 | + | 26.6572i | −0.861256 | + | 0.861256i | ||||
\(959\) | 22.1126 | 0.714054 | ||||||||
\(960\) | −3.83795 | − | 0.519749i | −0.123869 | − | 0.0167748i | ||||
\(961\) | 2.75447 | 0.0888539 | ||||||||
\(962\) | 34.1502 | − | 34.1502i | 1.10105 | − | 1.10105i | ||||
\(963\) | −21.6124 | − | 5.84021i | −0.696450 | − | 0.188198i | ||||
\(964\) | − | 5.42354i | − | 0.174681i | ||||||
\(965\) | −19.7041 | − | 8.22281i | −0.634297 | − | 0.264701i | ||||
\(966\) | −3.99589 | − | 14.9764i | −0.128566 | − | 0.481858i | ||||
\(967\) | 9.81253 | + | 9.81253i | 0.315550 | + | 0.315550i | 0.847055 | − | 0.531505i | \(-0.178373\pi\) |
−0.531505 | + | 0.847055i | \(0.678373\pi\) | |||||||
\(968\) | 6.66971 | + | 6.66971i | 0.214373 | + | 0.214373i | ||||
\(969\) | −1.92015 | − | 7.19661i | −0.0616839 | − | 0.231189i | ||||
\(970\) | −15.0948 | − | 36.7164i | −0.484666 | − | 1.17889i | ||||
\(971\) | 13.6046i | 0.436594i | 0.975882 | + | 0.218297i | \(0.0700501\pi\) | ||||
−0.975882 | + | 0.218297i | \(0.929950\pi\) | |||||||
\(972\) | −7.72250 | − | 13.5412i | −0.247699 | − | 0.434333i | ||||
\(973\) | −8.57948 | + | 8.57948i | −0.275045 | + | 0.275045i | ||||
\(974\) | −1.62092 | −0.0519376 | ||||||||
\(975\) | 21.0869 | − | 35.9938i | 0.675320 | − | 1.15273i | ||||
\(976\) | −6.32624 | −0.202498 | ||||||||
\(977\) | 1.36368 | − | 1.36368i | 0.0436279 | − | 0.0436279i | −0.684956 | − | 0.728584i | \(-0.740179\pi\) |
0.728584 | + | 0.684956i | \(0.240179\pi\) | |||||||
\(978\) | −0.359942 | + | 0.621913i | −0.0115097 | + | 0.0198866i | ||||
\(979\) | − | 16.0238i | − | 0.512123i | ||||||
\(980\) | 4.83260 | + | 11.7547i | 0.154372 | + | 0.375491i | ||||
\(981\) | 50.7235 | − | 29.1419i | 1.61948 | − | 0.930428i | ||||
\(982\) | 7.87369 | + | 7.87369i | 0.251260 | + | 0.251260i | ||||
\(983\) | 22.8849 | + | 22.8849i | 0.729917 | + | 0.729917i | 0.970603 | − | 0.240686i | \(-0.0773725\pi\) |
−0.240686 | + | 0.970603i | \(0.577373\pi\) | |||||||
\(984\) | −0.433751 | + | 0.115730i | −0.0138275 | + | 0.00368934i | ||||
\(985\) | −20.5960 | − | 8.59501i | −0.656243 | − | 0.273860i | ||||
\(986\) | − | 23.6472i | − | 0.753079i | ||||||
\(987\) | 14.8875 | + | 8.61640i | 0.473876 | + | 0.274263i | ||||
\(988\) | 3.40609 | − | 3.40609i | 0.108362 | − | 0.108362i | ||||
\(989\) | −61.8191 | −1.96573 | ||||||||
\(990\) | −8.33221 | + | 1.05658i | −0.264815 | + | 0.0335804i | ||||
\(991\) | −26.5275 | −0.842673 | −0.421336 | − | 0.906904i | \(-0.638439\pi\) | ||||
−0.421336 | + | 0.906904i | \(0.638439\pi\) | |||||||
\(992\) | −4.10819 | + | 4.10819i | −0.130435 | + | 0.130435i | ||||
\(993\) | −29.9918 | − | 17.3582i | −0.951761 | − | 0.550847i | ||||
\(994\) | 0.857883i | 0.0272104i | ||||||||
\(995\) | 49.1628 | − | 20.2118i | 1.55856 | − | 0.640756i | ||||
\(996\) | −10.0085 | + | 2.67040i | −0.317133 | + | 0.0846149i | ||||
\(997\) | 38.6488 | + | 38.6488i | 1.22402 | + | 1.22402i | 0.966190 | + | 0.257830i | \(0.0830074\pi\) |
0.257830 | + | 0.966190i | \(0.416993\pi\) | |||||||
\(998\) | −1.51660 | − | 1.51660i | −0.0480071 | − | 0.0480071i | ||||
\(999\) | −36.9558 | + | 36.7213i | −1.16923 | + | 1.16181i |
(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 | 570.2.k.a.77.1 | ✓ | 36 | |
3.2 | odd | 2 | inner | 570.2.k.a.77.15 | yes | 36 | |
5.3 | odd | 4 | inner | 570.2.k.a.533.15 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.a.533.1 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.a.77.1 | ✓ | 36 | 1.1 | even | 1 | trivial | |
570.2.k.a.77.15 | yes | 36 | 3.2 | odd | 2 | inner | |
570.2.k.a.533.1 | yes | 36 | 15.8 | even | 4 | inner | |
570.2.k.a.533.15 | yes | 36 | 5.3 | odd | 4 | inner |