Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(459,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 459.9 | ||
Character | \(\chi\) | \(=\) | 460.459 |
Dual form | 460.2.g.c.459.11 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20833 | − | 0.734800i | −0.854420 | − | 0.519582i | ||||
\(3\) | −1.77158 | −1.02282 | −0.511412 | − | 0.859336i | \(-0.670877\pi\) | ||||
−0.511412 | + | 0.859336i | \(0.670877\pi\) | |||||||
\(4\) | 0.920137 | + | 1.77577i | 0.460069 | + | 0.887883i | ||||
\(5\) | −1.90499 | − | 1.17090i | −0.851937 | − | 0.523644i | ||||
\(6\) | 2.14066 | + | 1.30176i | 0.873922 | + | 0.531441i | ||||
\(7\) | 1.27817i | 0.483102i | 0.970388 | + | 0.241551i | \(0.0776561\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(8\) | 0.193001 | − | 2.82183i | 0.0682362 | − | 0.997669i | ||||
\(9\) | 0.138505 | 0.0461684 | ||||||||
\(10\) | 1.44148 | + | 2.81463i | 0.455837 | + | 0.890063i | ||||
\(11\) | −2.00757 | −0.605305 | −0.302653 | − | 0.953101i | \(-0.597872\pi\) | ||||
−0.302653 | + | 0.953101i | \(0.597872\pi\) | |||||||
\(12\) | −1.63010 | − | 3.14592i | −0.470569 | − | 0.908148i | ||||
\(13\) | 2.02460i | 0.561524i | 0.959777 | + | 0.280762i | \(0.0905871\pi\) | ||||
−0.959777 | + | 0.280762i | \(0.909413\pi\) | |||||||
\(14\) | 0.939197 | − | 1.54445i | 0.251011 | − | 0.412772i | ||||
\(15\) | 3.37485 | + | 2.07435i | 0.871382 | + | 0.535595i | ||||
\(16\) | −2.30669 | + | 3.26790i | −0.576674 | + | 0.816975i | ||||
\(17\) | 3.14239 | 0.762143 | 0.381071 | − | 0.924546i | \(-0.375555\pi\) | ||||
0.381071 | + | 0.924546i | \(0.375555\pi\) | |||||||
\(18\) | −0.167360 | − | 0.101774i | −0.0394472 | − | 0.0239883i | ||||
\(19\) | −1.66004 | −0.380838 | −0.190419 | − | 0.981703i | \(-0.560985\pi\) | ||||
−0.190419 | + | 0.981703i | \(0.560985\pi\) | |||||||
\(20\) | 0.326397 | − | 4.46021i | 0.0729846 | − | 0.997333i | ||||
\(21\) | − | 2.26438i | − | 0.494128i | ||||||
\(22\) | 2.42581 | + | 1.47516i | 0.517185 | + | 0.314506i | ||||
\(23\) | 1.99168 | − | 4.36271i | 0.415294 | − | 0.909687i | ||||
\(24\) | −0.341917 | + | 4.99911i | −0.0697936 | + | 1.02044i | ||||
\(25\) | 2.25797 | + | 4.46112i | 0.451595 | + | 0.892223i | ||||
\(26\) | 1.48768 | − | 2.44639i | 0.291758 | − | 0.479777i | ||||
\(27\) | 5.06937 | 0.975602 | ||||||||
\(28\) | −2.26973 | + | 1.17609i | −0.428938 | + | 0.222260i | ||||
\(29\) | 3.92182 | 0.728263 | 0.364131 | − | 0.931348i | \(-0.381366\pi\) | ||||
0.364131 | + | 0.931348i | \(0.381366\pi\) | |||||||
\(30\) | −2.55371 | − | 4.98634i | −0.466241 | − | 0.910378i | ||||
\(31\) | − | 0.284658i | − | 0.0511261i | −0.999673 | − | 0.0255630i | \(-0.991862\pi\) | ||
0.999673 | − | 0.0255630i | \(-0.00813785\pi\) | |||||||
\(32\) | 5.18851 | − | 2.25375i | 0.917207 | − | 0.398411i | ||||
\(33\) | 3.55658 | 0.619121 | ||||||||
\(34\) | −3.79706 | − | 2.30903i | −0.651190 | − | 0.395996i | ||||
\(35\) | 1.49661 | − | 2.43490i | 0.252973 | − | 0.411572i | ||||
\(36\) | 0.127444 | + | 0.245953i | 0.0212406 | + | 0.0409921i | ||||
\(37\) | 4.55939 | 0.749559 | 0.374780 | − | 0.927114i | \(-0.377718\pi\) | ||||
0.374780 | + | 0.927114i | \(0.377718\pi\) | |||||||
\(38\) | 2.00588 | + | 1.21979i | 0.325396 | + | 0.197877i | ||||
\(39\) | − | 3.58675i | − | 0.574340i | ||||||
\(40\) | −3.67176 | + | 5.14958i | −0.580556 | + | 0.814220i | ||||
\(41\) | 6.34849 | 0.991467 | 0.495733 | − | 0.868475i | \(-0.334899\pi\) | ||||
0.495733 | + | 0.868475i | \(0.334899\pi\) | |||||||
\(42\) | −1.66387 | + | 2.73612i | −0.256740 | + | 0.422193i | ||||
\(43\) | − | 10.3623i | − | 1.58023i | −0.612957 | − | 0.790116i | \(-0.710020\pi\) | ||
0.612957 | − | 0.790116i | \(-0.289980\pi\) | |||||||
\(44\) | −1.84724 | − | 3.56498i | −0.278482 | − | 0.537440i | ||||
\(45\) | −0.263851 | − | 0.162176i | −0.0393326 | − | 0.0241758i | ||||
\(46\) | −5.61233 | + | 3.80812i | −0.827493 | + | 0.561476i | ||||
\(47\) | 7.17707 | 1.04688 | 0.523442 | − | 0.852061i | \(-0.324648\pi\) | ||||
0.523442 | + | 0.852061i | \(0.324648\pi\) | |||||||
\(48\) | 4.08650 | − | 5.78935i | 0.589835 | − | 0.835621i | ||||
\(49\) | 5.36629 | 0.766613 | ||||||||
\(50\) | 0.549644 | − | 7.04967i | 0.0777314 | − | 0.996974i | ||||
\(51\) | −5.56701 | −0.779538 | ||||||||
\(52\) | −3.59522 | + | 1.86291i | −0.498567 | + | 0.258339i | ||||
\(53\) | −9.11216 | −1.25165 | −0.625826 | − | 0.779963i | \(-0.715238\pi\) | ||||
−0.625826 | + | 0.779963i | \(0.715238\pi\) | |||||||
\(54\) | −6.12549 | − | 3.72498i | −0.833574 | − | 0.506905i | ||||
\(55\) | 3.82440 | + | 2.35067i | 0.515682 | + | 0.316964i | ||||
\(56\) | 3.60678 | + | 0.246688i | 0.481976 | + | 0.0329650i | ||||
\(57\) | 2.94089 | 0.389530 | ||||||||
\(58\) | −4.73886 | − | 2.88175i | −0.622243 | − | 0.378392i | ||||
\(59\) | − | 0.407679i | − | 0.0530753i | −0.999648 | − | 0.0265377i | \(-0.991552\pi\) | ||
0.999648 | − | 0.0265377i | \(-0.00844819\pi\) | |||||||
\(60\) | −0.578239 | + | 7.90163i | −0.0746504 | + | 1.02010i | ||||
\(61\) | − | 1.31896i | − | 0.168875i | −0.996429 | − | 0.0844377i | \(-0.973091\pi\) | ||
0.996429 | − | 0.0844377i | \(-0.0269094\pi\) | |||||||
\(62\) | −0.209167 | + | 0.343961i | −0.0265642 | + | 0.0436831i | ||||
\(63\) | 0.177033i | 0.0223040i | ||||||||
\(64\) | −7.92550 | − | 1.08923i | −0.990688 | − | 0.136154i | ||||
\(65\) | 2.37061 | − | 3.85685i | 0.294038 | − | 0.478383i | ||||
\(66\) | −4.29753 | − | 2.61337i | −0.528989 | − | 0.321684i | ||||
\(67\) | 3.80009i | 0.464255i | 0.972685 | + | 0.232127i | \(0.0745686\pi\) | ||||
−0.972685 | + | 0.232127i | \(0.925431\pi\) | |||||||
\(68\) | 2.89144 | + | 5.58016i | 0.350638 | + | 0.676694i | ||||
\(69\) | −3.52842 | + | 7.72890i | −0.424772 | + | 0.930450i | ||||
\(70\) | −3.59756 | + | 1.84246i | −0.429991 | + | 0.220216i | ||||
\(71\) | 7.51415i | 0.891766i | 0.895091 | + | 0.445883i | \(0.147110\pi\) | ||||
−0.895091 | + | 0.445883i | \(0.852890\pi\) | |||||||
\(72\) | 0.0267316 | − | 0.390839i | 0.00315035 | − | 0.0460608i | ||||
\(73\) | 13.3491i | 1.56239i | 0.624288 | + | 0.781194i | \(0.285389\pi\) | ||||
−0.624288 | + | 0.781194i | \(0.714611\pi\) | |||||||
\(74\) | −5.50926 | − | 3.35024i | −0.640439 | − | 0.389457i | ||||
\(75\) | −4.00019 | − | 7.90324i | −0.461902 | − | 0.912587i | ||||
\(76\) | −1.52746 | − | 2.94784i | −0.175212 | − | 0.338140i | ||||
\(77\) | − | 2.56601i | − | 0.292424i | ||||||
\(78\) | −2.63554 | + | 4.33399i | −0.298417 | + | 0.490728i | ||||
\(79\) | 14.7610 | 1.66074 | 0.830369 | − | 0.557214i | \(-0.188130\pi\) | ||||
0.830369 | + | 0.557214i | \(0.188130\pi\) | |||||||
\(80\) | 8.22062 | − | 3.52440i | 0.919093 | − | 0.394040i | ||||
\(81\) | −9.39633 | −1.04404 | ||||||||
\(82\) | −7.67108 | − | 4.66487i | −0.847130 | − | 0.515149i | ||||
\(83\) | 1.17696i | 0.129188i | 0.997912 | + | 0.0645938i | \(0.0205752\pi\) | ||||
−0.997912 | + | 0.0645938i | \(0.979425\pi\) | |||||||
\(84\) | 4.02101 | − | 2.08354i | 0.438728 | − | 0.227333i | ||||
\(85\) | −5.98623 | − | 3.67944i | −0.649298 | − | 0.399091i | ||||
\(86\) | −7.61420 | + | 12.5211i | −0.821060 | + | 1.35018i | ||||
\(87\) | −6.94782 | −0.744885 | ||||||||
\(88\) | −0.387463 | + | 5.66503i | −0.0413037 | + | 0.603894i | ||||
\(89\) | − | 12.7290i | − | 1.34927i | −0.738151 | − | 0.674636i | \(-0.764301\pi\) | ||
0.738151 | − | 0.674636i | \(-0.235699\pi\) | |||||||
\(90\) | 0.199653 | + | 0.389840i | 0.0210453 | + | 0.0410928i | ||||
\(91\) | −2.58778 | −0.271273 | ||||||||
\(92\) | 9.57977 | − | 0.477535i | 0.998760 | − | 0.0497864i | ||||
\(93\) | 0.504295i | 0.0522929i | ||||||||
\(94\) | −8.67229 | − | 5.27371i | −0.894479 | − | 0.543942i | ||||
\(95\) | 3.16235 | + | 1.94374i | 0.324450 | + | 0.199423i | ||||
\(96\) | −9.19187 | + | 3.99271i | −0.938141 | + | 0.407504i | ||||
\(97\) | 7.31027 | 0.742245 | 0.371123 | − | 0.928584i | \(-0.378973\pi\) | ||||
0.371123 | + | 0.928584i | \(0.378973\pi\) | |||||||
\(98\) | −6.48426 | − | 3.94315i | −0.655010 | − | 0.398318i | ||||
\(99\) | −0.278059 | −0.0279460 | ||||||||
\(100\) | −5.84425 | + | 8.11447i | −0.584425 | + | 0.811447i | ||||
\(101\) | 2.90934 | 0.289490 | 0.144745 | − | 0.989469i | \(-0.453764\pi\) | ||||
0.144745 | + | 0.989469i | \(0.453764\pi\) | |||||||
\(102\) | 6.72680 | + | 4.09064i | 0.666053 | + | 0.405034i | ||||
\(103\) | 4.11531i | 0.405493i | 0.979231 | + | 0.202747i | \(0.0649868\pi\) | ||||
−0.979231 | + | 0.202747i | \(0.935013\pi\) | |||||||
\(104\) | 5.71309 | + | 0.390750i | 0.560215 | + | 0.0383162i | ||||
\(105\) | −2.65137 | + | 4.31362i | −0.258747 | + | 0.420966i | ||||
\(106\) | 11.0105 | + | 6.69562i | 1.06944 | + | 0.650336i | ||||
\(107\) | 13.8494i | 1.33888i | 0.742868 | + | 0.669438i | \(0.233465\pi\) | ||||
−0.742868 | + | 0.669438i | \(0.766535\pi\) | |||||||
\(108\) | 4.66452 | + | 9.00203i | 0.448844 | + | 0.866220i | ||||
\(109\) | 12.2651i | 1.17478i | 0.809303 | + | 0.587392i | \(0.199845\pi\) | ||||
−0.809303 | + | 0.587392i | \(0.800155\pi\) | |||||||
\(110\) | −2.89388 | − | 5.65056i | −0.275920 | − | 0.538760i | ||||
\(111\) | −8.07734 | −0.766667 | ||||||||
\(112\) | −4.17692 | − | 2.94834i | −0.394682 | − | 0.278592i | ||||
\(113\) | −15.1939 | −1.42932 | −0.714660 | − | 0.699472i | \(-0.753419\pi\) | ||||
−0.714660 | + | 0.699472i | \(0.753419\pi\) | |||||||
\(114\) | −3.55357 | − | 2.16097i | −0.332823 | − | 0.202393i | ||||
\(115\) | −8.90243 | + | 5.97885i | −0.830156 | + | 0.557531i | ||||
\(116\) | 3.60861 | + | 6.96423i | 0.335051 | + | 0.646612i | ||||
\(117\) | 0.280418i | 0.0259246i | ||||||||
\(118\) | −0.299563 | + | 0.492612i | −0.0275770 | + | 0.0453486i | ||||
\(119\) | 4.01651i | 0.368192i | ||||||||
\(120\) | 6.50482 | − | 9.12291i | 0.593806 | − | 0.832804i | ||||
\(121\) | −6.96966 | −0.633606 | ||||||||
\(122\) | −0.969171 | + | 1.59374i | −0.0877447 | + | 0.144291i | ||||
\(123\) | −11.2469 | −1.01410 | ||||||||
\(124\) | 0.505486 | − | 0.261924i | 0.0453940 | − | 0.0235215i | ||||
\(125\) | 0.922114 | − | 11.1422i | 0.0824764 | − | 0.996593i | ||||
\(126\) | 0.130084 | − | 0.213915i | 0.0115888 | − | 0.0190570i | ||||
\(127\) | 0.743250 | 0.0659528 | 0.0329764 | − | 0.999456i | \(-0.489501\pi\) | ||||
0.0329764 | + | 0.999456i | \(0.489501\pi\) | |||||||
\(128\) | 8.77628 | + | 7.13982i | 0.775720 | + | 0.631077i | ||||
\(129\) | 18.3576i | 1.61630i | ||||||||
\(130\) | −5.69850 | + | 2.91843i | −0.499792 | + | 0.255963i | ||||
\(131\) | − | 3.64274i | − | 0.318268i | −0.987257 | − | 0.159134i | \(-0.949130\pi\) | ||
0.987257 | − | 0.159134i | \(-0.0508702\pi\) | |||||||
\(132\) | 3.27254 | + | 6.31565i | 0.284838 | + | 0.549707i | ||||
\(133\) | − | 2.12180i | − | 0.183984i | ||||||
\(134\) | 2.79231 | − | 4.59177i | 0.241218 | − | 0.396669i | ||||
\(135\) | −9.65711 | − | 5.93574i | −0.831152 | − | 0.510868i | ||||
\(136\) | 0.606485 | − | 8.86732i | 0.0520057 | − | 0.760366i | ||||
\(137\) | 0.996193 | 0.0851105 | 0.0425553 | − | 0.999094i | \(-0.486450\pi\) | ||||
0.0425553 | + | 0.999094i | \(0.486450\pi\) | |||||||
\(138\) | 9.94270 | − | 6.74640i | 0.846379 | − | 0.574291i | ||||
\(139\) | − | 11.4907i | − | 0.974631i | −0.873226 | − | 0.487316i | \(-0.837976\pi\) | ||
0.873226 | − | 0.487316i | \(-0.162024\pi\) | |||||||
\(140\) | 5.70089 | + | 0.417190i | 0.481813 | + | 0.0352590i | ||||
\(141\) | −12.7148 | −1.07078 | ||||||||
\(142\) | 5.52140 | − | 9.07960i | 0.463346 | − | 0.761943i | ||||
\(143\) | − | 4.06453i | − | 0.339893i | ||||||
\(144\) | −0.319489 | + | 0.452621i | −0.0266241 | + | 0.0377184i | ||||
\(145\) | −7.47102 | − | 4.59206i | −0.620434 | − | 0.381350i | ||||
\(146\) | 9.80889 | − | 16.1301i | 0.811789 | − | 1.33494i | ||||
\(147\) | −9.50682 | −0.784110 | ||||||||
\(148\) | 4.19527 | + | 8.09641i | 0.344849 | + | 0.665521i | ||||
\(149\) | 21.5503i | 1.76547i | 0.469870 | + | 0.882735i | \(0.344301\pi\) | ||||
−0.469870 | + | 0.882735i | \(0.655699\pi\) | |||||||
\(150\) | −0.973739 | + | 12.4891i | −0.0795055 | + | 1.01973i | ||||
\(151\) | − | 7.10647i | − | 0.578317i | −0.957281 | − | 0.289158i | \(-0.906625\pi\) | ||
0.957281 | − | 0.289158i | \(-0.0933754\pi\) | |||||||
\(152\) | −0.320389 | + | 4.68435i | −0.0259869 | + | 0.379951i | ||||
\(153\) | 0.435238 | 0.0351869 | ||||||||
\(154\) | −1.88550 | + | 3.10059i | −0.151938 | + | 0.249853i | ||||
\(155\) | −0.333307 | + | 0.542270i | −0.0267718 | + | 0.0435562i | ||||
\(156\) | 6.36923 | − | 3.30030i | 0.509947 | − | 0.264236i | ||||
\(157\) | 19.0039 | 1.51667 | 0.758337 | − | 0.651863i | \(-0.226012\pi\) | ||||
0.758337 | + | 0.651863i | \(0.226012\pi\) | |||||||
\(158\) | −17.8362 | − | 10.8464i | −1.41897 | − | 0.862890i | ||||
\(159\) | 16.1429 | 1.28022 | ||||||||
\(160\) | −12.5230 | − | 1.78186i | −0.990028 | − | 0.140869i | ||||
\(161\) | 5.57627 | + | 2.54570i | 0.439472 | + | 0.200629i | ||||
\(162\) | 11.3539 | + | 6.90443i | 0.892046 | + | 0.542463i | ||||
\(163\) | −3.65003 | −0.285892 | −0.142946 | − | 0.989730i | \(-0.545658\pi\) | ||||
−0.142946 | + | 0.989730i | \(0.545658\pi\) | |||||||
\(164\) | 5.84148 | + | 11.2734i | 0.456143 | + | 0.880307i | ||||
\(165\) | −6.77524 | − | 4.16440i | −0.527452 | − | 0.324198i | ||||
\(166\) | 0.864827 | − | 1.42215i | 0.0671236 | − | 0.110381i | ||||
\(167\) | 4.78902 | 0.370586 | 0.185293 | − | 0.982683i | \(-0.440677\pi\) | ||||
0.185293 | + | 0.982683i | \(0.440677\pi\) | |||||||
\(168\) | −6.38970 | − | 0.437027i | −0.492976 | − | 0.0337174i | ||||
\(169\) | 8.90099 | 0.684691 | ||||||||
\(170\) | 4.52971 | + | 8.84467i | 0.347413 | + | 0.678355i | ||||
\(171\) | −0.229923 | −0.0175827 | ||||||||
\(172\) | 18.4010 | − | 9.53472i | 1.40306 | − | 0.727015i | ||||
\(173\) | − | 9.16554i | − | 0.696843i | −0.937338 | − | 0.348421i | \(-0.886718\pi\) | ||
0.937338 | − | 0.348421i | \(-0.113282\pi\) | |||||||
\(174\) | 8.39528 | + | 5.10526i | 0.636445 | + | 0.387029i | ||||
\(175\) | −5.70205 | + | 2.88607i | −0.431035 | + | 0.218166i | ||||
\(176\) | 4.63085 | − | 6.56054i | 0.349063 | − | 0.494519i | ||||
\(177\) | 0.722238i | 0.0542867i | ||||||||
\(178\) | −9.35327 | + | 15.3809i | −0.701058 | + | 1.15285i | ||||
\(179\) | − | 3.74110i | − | 0.279623i | −0.990178 | − | 0.139812i | \(-0.955350\pi\) | ||
0.990178 | − | 0.139812i | \(-0.0446497\pi\) | |||||||
\(180\) | 0.0452077 | − | 0.617762i | 0.00336958 | − | 0.0460453i | ||||
\(181\) | − | 24.0543i | − | 1.78794i | −0.448127 | − | 0.893970i | \(-0.647909\pi\) | ||
0.448127 | − | 0.893970i | \(-0.352091\pi\) | |||||||
\(182\) | 3.12690 | + | 1.90150i | 0.231781 | + | 0.140949i | ||||
\(183\) | 2.33665i | 0.172730i | ||||||||
\(184\) | −11.9264 | − | 6.46219i | −0.879229 | − | 0.476399i | ||||
\(185\) | −8.68559 | − | 5.33860i | −0.638577 | − | 0.392502i | ||||
\(186\) | 0.370556 | − | 0.609356i | 0.0271705 | − | 0.0446802i | ||||
\(187\) | −6.30858 | −0.461329 | ||||||||
\(188\) | 6.60389 | + | 12.7448i | 0.481638 | + | 0.929510i | ||||
\(189\) | 6.47951i | 0.471315i | ||||||||
\(190\) | −2.39291 | − | 4.67238i | −0.173600 | − | 0.338970i | ||||
\(191\) | 12.2497 | 0.886355 | 0.443177 | − | 0.896434i | \(-0.353851\pi\) | ||||
0.443177 | + | 0.896434i | \(0.353851\pi\) | |||||||
\(192\) | 14.0407 | + | 1.92967i | 1.01330 | + | 0.139262i | ||||
\(193\) | − | 2.06172i | − | 0.148406i | −0.997243 | − | 0.0742028i | \(-0.976359\pi\) | ||
0.997243 | − | 0.0742028i | \(-0.0236412\pi\) | |||||||
\(194\) | −8.83324 | − | 5.37159i | −0.634190 | − | 0.385657i | ||||
\(195\) | −4.19973 | + | 6.83272i | −0.300749 | + | 0.489301i | ||||
\(196\) | 4.93772 | + | 9.52928i | 0.352695 | + | 0.680663i | ||||
\(197\) | − | 23.9037i | − | 1.70307i | −0.524300 | − | 0.851534i | \(-0.675673\pi\) | ||
0.524300 | − | 0.851534i | \(-0.324327\pi\) | |||||||
\(198\) | 0.335988 | + | 0.204318i | 0.0238776 | + | 0.0145202i | ||||
\(199\) | 4.81160 | 0.341085 | 0.170543 | − | 0.985350i | \(-0.445448\pi\) | ||||
0.170543 | + | 0.985350i | \(0.445448\pi\) | |||||||
\(200\) | 13.0243 | − | 5.51063i | 0.920959 | − | 0.389660i | ||||
\(201\) | − | 6.73217i | − | 0.474851i | ||||||
\(202\) | −3.51545 | − | 2.13778i | −0.247346 | − | 0.150414i | ||||
\(203\) | 5.01274i | 0.351825i | ||||||||
\(204\) | −5.12242 | − | 9.88571i | −0.358641 | − | 0.692138i | ||||
\(205\) | −12.0938 | − | 7.43346i | −0.844668 | − | 0.519175i | ||||
\(206\) | 3.02393 | − | 4.97266i | 0.210687 | − | 0.346462i | ||||
\(207\) | 0.275858 | − | 0.604258i | 0.0191734 | − | 0.0419988i | ||||
\(208\) | −6.61619 | − | 4.67014i | −0.458751 | − | 0.323816i | ||||
\(209\) | 3.33264 | 0.230523 | ||||||||
\(210\) | 6.37338 | − | 3.26406i | 0.439805 | − | 0.225242i | ||||
\(211\) | 3.78230i | 0.260385i | 0.991489 | + | 0.130192i | \(0.0415595\pi\) | ||||
−0.991489 | + | 0.130192i | \(0.958441\pi\) | |||||||
\(212\) | −8.38444 | − | 16.1811i | −0.575846 | − | 1.11132i | ||||
\(213\) | − | 13.3119i | − | 0.912119i | ||||||
\(214\) | 10.1766 | − | 16.7347i | 0.695656 | − | 1.14396i | ||||
\(215\) | −12.1332 | + | 19.7400i | −0.827478 | + | 1.34626i | ||||
\(216\) | 0.978395 | − | 14.3049i | 0.0665713 | − | 0.973328i | ||||
\(217\) | 0.363840 | 0.0246991 | ||||||||
\(218\) | 9.01240 | − | 14.8203i | 0.610397 | − | 1.00376i | ||||
\(219\) | − | 23.6490i | − | 1.59805i | ||||||
\(220\) | −0.655265 | + | 8.95418i | −0.0441780 | + | 0.603691i | ||||
\(221\) | 6.36210i | 0.427961i | ||||||||
\(222\) | 9.76011 | + | 5.93523i | 0.655056 | + | 0.398346i | ||||
\(223\) | 14.8969 | 0.997570 | 0.498785 | − | 0.866726i | \(-0.333780\pi\) | ||||
0.498785 | + | 0.866726i | \(0.333780\pi\) | |||||||
\(224\) | 2.88067 | + | 6.63178i | 0.192473 | + | 0.443104i | ||||
\(225\) | 0.312741 | + | 0.617888i | 0.0208494 | + | 0.0411925i | ||||
\(226\) | 18.3593 | + | 11.1645i | 1.22124 | + | 0.742650i | ||||
\(227\) | − | 16.3331i | − | 1.08407i | −0.840357 | − | 0.542033i | \(-0.817655\pi\) | ||
0.840357 | − | 0.542033i | \(-0.182345\pi\) | |||||||
\(228\) | 2.70602 | + | 5.22233i | 0.179211 | + | 0.345858i | ||||
\(229\) | 2.40444i | 0.158890i | 0.996839 | + | 0.0794449i | \(0.0253148\pi\) | ||||
−0.996839 | + | 0.0794449i | \(0.974685\pi\) | |||||||
\(230\) | 15.1504 | − | 0.682936i | 0.998986 | − | 0.0450315i | ||||
\(231\) | 4.54590i | 0.299098i | ||||||||
\(232\) | 0.756915 | − | 11.0667i | 0.0496939 | − | 0.726565i | ||||
\(233\) | − | 13.7561i | − | 0.901195i | −0.892727 | − | 0.450598i | \(-0.851211\pi\) | ||
0.892727 | − | 0.450598i | \(-0.148789\pi\) | |||||||
\(234\) | 0.206051 | − | 0.338838i | 0.0134700 | − | 0.0221505i | ||||
\(235\) | −13.6722 | − | 8.40365i | −0.891879 | − | 0.548194i | ||||
\(236\) | 0.723943 | − | 0.375121i | 0.0471247 | − | 0.0244183i | ||||
\(237\) | −26.1503 | −1.69864 | ||||||||
\(238\) | 2.95133 | − | 4.85328i | 0.191306 | − | 0.314591i | ||||
\(239\) | 27.4657i | 1.77661i | 0.459258 | + | 0.888303i | \(0.348115\pi\) | ||||
−0.459258 | + | 0.888303i | \(0.651885\pi\) | |||||||
\(240\) | −14.5635 | + | 6.24377i | −0.940070 | + | 0.403033i | ||||
\(241\) | 13.2834i | 0.855657i | 0.903860 | + | 0.427829i | \(0.140721\pi\) | ||||
−0.903860 | + | 0.427829i | \(0.859279\pi\) | |||||||
\(242\) | 8.42167 | + | 5.12131i | 0.541366 | + | 0.329210i | ||||
\(243\) | 1.43825 | 0.0922641 | ||||||||
\(244\) | 2.34216 | − | 1.21362i | 0.149942 | − | 0.0776943i | ||||
\(245\) | −10.2227 | − | 6.28340i | −0.653106 | − | 0.401432i | ||||
\(246\) | 13.5900 | + | 8.26420i | 0.866464 | + | 0.526906i | ||||
\(247\) | − | 3.36091i | − | 0.213850i | ||||||
\(248\) | −0.803257 | − | 0.0549393i | −0.0510069 | − | 0.00348865i | ||||
\(249\) | − | 2.08507i | − | 0.132136i | ||||||
\(250\) | −9.30155 | + | 12.7860i | −0.588281 | + | 0.808656i | ||||
\(251\) | 24.6282 | 1.55452 | 0.777259 | − | 0.629181i | \(-0.216610\pi\) | ||||
0.777259 | + | 0.629181i | \(0.216610\pi\) | |||||||
\(252\) | −0.314369 | + | 0.162894i | −0.0198034 | + | 0.0102614i | ||||
\(253\) | −3.99843 | + | 8.75844i | −0.251379 | + | 0.550638i | ||||
\(254\) | −0.898093 | − | 0.546140i | −0.0563514 | − | 0.0342679i | ||||
\(255\) | 10.6051 | + | 6.51843i | 0.664117 | + | 0.408200i | ||||
\(256\) | −5.35833 | − | 15.0761i | −0.334895 | − | 0.942255i | ||||
\(257\) | − | 19.9497i | − | 1.24443i | −0.782847 | − | 0.622214i | \(-0.786233\pi\) | ||
0.782847 | − | 0.622214i | \(-0.213767\pi\) | |||||||
\(258\) | 13.4892 | − | 22.1821i | 0.839800 | − | 1.38100i | ||||
\(259\) | 5.82766i | 0.362113i | ||||||||
\(260\) | 9.03015 | + | 0.660824i | 0.560026 | + | 0.0409826i | ||||
\(261\) | 0.543192 | 0.0336227 | ||||||||
\(262\) | −2.67669 | + | 4.40165i | −0.165366 | + | 0.271935i | ||||
\(263\) | − | 11.6844i | − | 0.720490i | −0.932858 | − | 0.360245i | \(-0.882693\pi\) | ||
0.932858 | − | 0.360245i | \(-0.117307\pi\) | |||||||
\(264\) | 0.686423 | − | 10.0361i | 0.0422464 | − | 0.617677i | ||||
\(265\) | 17.3586 | + | 10.6695i | 1.06633 | + | 0.655419i | ||||
\(266\) | −1.55910 | + | 2.56384i | −0.0955946 | + | 0.157199i | ||||
\(267\) | 22.5505i | 1.38007i | ||||||||
\(268\) | −6.74807 | + | 3.49660i | −0.412204 | + | 0.213589i | ||||
\(269\) | 6.07560 | 0.370436 | 0.185218 | − | 0.982697i | \(-0.440701\pi\) | ||||
0.185218 | + | 0.982697i | \(0.440701\pi\) | |||||||
\(270\) | 7.30742 | + | 14.2684i | 0.444715 | + | 0.868347i | ||||
\(271\) | 18.4847i | 1.12287i | 0.827521 | + | 0.561434i | \(0.189750\pi\) | ||||
−0.827521 | + | 0.561434i | \(0.810250\pi\) | |||||||
\(272\) | −7.24854 | + | 10.2690i | −0.439507 | + | 0.622651i | ||||
\(273\) | 4.58447 | 0.277464 | ||||||||
\(274\) | −1.20373 | − | 0.732003i | −0.0727202 | − | 0.0442219i | ||||
\(275\) | −4.53304 | − | 8.95600i | −0.273353 | − | 0.540067i | ||||
\(276\) | −16.9714 | + | 0.845992i | −1.02156 | + | 0.0509227i | ||||
\(277\) | 5.09369i | 0.306050i | 0.988222 | + | 0.153025i | \(0.0489015\pi\) | ||||
−0.988222 | + | 0.153025i | \(0.951098\pi\) | |||||||
\(278\) | −8.44339 | + | 13.8846i | −0.506401 | + | 0.832745i | ||||
\(279\) | − | 0.0394266i | − | 0.00236041i | ||||||
\(280\) | −6.58203 | − | 4.69312i | −0.393351 | − | 0.280468i | ||||
\(281\) | 2.02480i | 0.120789i | 0.998175 | + | 0.0603947i | \(0.0192359\pi\) | ||||
−0.998175 | + | 0.0603947i | \(0.980764\pi\) | |||||||
\(282\) | 15.3637 | + | 9.34282i | 0.914894 | + | 0.556357i | ||||
\(283\) | 25.5315i | 1.51769i | 0.651270 | + | 0.758846i | \(0.274236\pi\) | ||||
−0.651270 | + | 0.758846i | \(0.725764\pi\) | |||||||
\(284\) | −13.3434 | + | 6.91405i | −0.791784 | + | 0.410274i | ||||
\(285\) | −5.60237 | − | 3.44350i | −0.331856 | − | 0.203975i | ||||
\(286\) | −2.98662 | + | 4.91131i | −0.176602 | + | 0.290412i | ||||
\(287\) | 8.11443i | 0.478979i | ||||||||
\(288\) | 0.718635 | − | 0.312156i | 0.0423460 | − | 0.0183940i | ||||
\(289\) | −7.12536 | −0.419139 | ||||||||
\(290\) | 5.65323 | + | 11.0384i | 0.331969 | + | 0.648200i | ||||
\(291\) | −12.9507 | −0.759186 | ||||||||
\(292\) | −23.7048 | + | 12.2830i | −1.38722 | + | 0.718806i | ||||
\(293\) | 7.43188 | 0.434175 | 0.217087 | − | 0.976152i | \(-0.430344\pi\) | ||||
0.217087 | + | 0.976152i | \(0.430344\pi\) | |||||||
\(294\) | 11.4874 | + | 6.98562i | 0.669959 | + | 0.407409i | ||||
\(295\) | −0.477353 | + | 0.776625i | −0.0277925 | + | 0.0452169i | ||||
\(296\) | 0.879967 | − | 12.8658i | 0.0511470 | − | 0.747812i | ||||
\(297\) | −10.1771 | −0.590537 | ||||||||
\(298\) | 15.8352 | − | 26.0400i | 0.917307 | − | 1.50845i | ||||
\(299\) | 8.83275 | + | 4.03236i | 0.510811 | + | 0.233197i | ||||
\(300\) | 10.3536 | − | 14.3755i | 0.597764 | − | 0.829968i | ||||
\(301\) | 13.2447 | 0.763413 | ||||||||
\(302\) | −5.22184 | + | 8.58699i | −0.300483 | + | 0.494125i | ||||
\(303\) | −5.15414 | −0.296098 | ||||||||
\(304\) | 3.82919 | − | 5.42483i | 0.219619 | − | 0.311135i | ||||
\(305\) | −1.54437 | + | 2.51260i | −0.0884305 | + | 0.143871i | ||||
\(306\) | −0.525912 | − | 0.319813i | −0.0300644 | − | 0.0182825i | ||||
\(307\) | 20.7426 | 1.18384 | 0.591921 | − | 0.805996i | \(-0.298370\pi\) | ||||
0.591921 | + | 0.805996i | \(0.298370\pi\) | |||||||
\(308\) | 4.55664 | − | 2.36108i | 0.259638 | − | 0.134535i | ||||
\(309\) | − | 7.29061i | − | 0.414748i | ||||||
\(310\) | 0.801206 | − | 0.410329i | 0.0455054 | − | 0.0233051i | ||||
\(311\) | 14.0598i | 0.797256i | 0.917113 | + | 0.398628i | \(0.130513\pi\) | ||||
−0.917113 | + | 0.398628i | \(0.869487\pi\) | |||||||
\(312\) | −10.1212 | − | 0.692247i | −0.573001 | − | 0.0391907i | ||||
\(313\) | 21.8115 | 1.23286 | 0.616429 | − | 0.787410i | \(-0.288579\pi\) | ||||
0.616429 | + | 0.787410i | \(0.288579\pi\) | |||||||
\(314\) | −22.9630 | − | 13.9640i | −1.29588 | − | 0.788037i | ||||
\(315\) | 0.207288 | − | 0.337246i | 0.0116794 | − | 0.0190016i | ||||
\(316\) | 13.5821 | + | 26.2120i | 0.764054 | + | 1.47454i | ||||
\(317\) | 20.9689i | 1.17773i | 0.808231 | + | 0.588866i | \(0.200425\pi\) | ||||
−0.808231 | + | 0.588866i | \(0.799575\pi\) | |||||||
\(318\) | −19.5061 | − | 11.8618i | −1.09385 | − | 0.665179i | ||||
\(319\) | −7.87332 | −0.440821 | ||||||||
\(320\) | 13.8226 | + | 11.3550i | 0.772708 | + | 0.634762i | ||||
\(321\) | − | 24.5354i | − | 1.36943i | ||||||
\(322\) | −4.86741 | − | 7.17349i | −0.271250 | − | 0.399763i | ||||
\(323\) | −5.21649 | −0.290253 | ||||||||
\(324\) | −8.64592 | − | 16.6857i | −0.480329 | − | 0.926983i | ||||
\(325\) | −9.03198 | + | 4.57150i | −0.501004 | + | 0.253581i | ||||
\(326\) | 4.41045 | + | 2.68204i | 0.244272 | + | 0.148545i | ||||
\(327\) | − | 21.7286i | − | 1.20160i | ||||||
\(328\) | 1.22526 | − | 17.9144i | 0.0676539 | − | 0.989156i | ||||
\(329\) | 9.17350i | 0.505751i | ||||||||
\(330\) | 5.12674 | + | 10.0104i | 0.282218 | + | 0.551056i | ||||
\(331\) | − | 32.7363i | − | 1.79935i | −0.436560 | − | 0.899675i | \(-0.643803\pi\) | ||
0.436560 | − | 0.899675i | \(-0.356197\pi\) | |||||||
\(332\) | −2.09000 | + | 1.08296i | −0.114704 | + | 0.0594352i | ||||
\(333\) | 0.631499 | 0.0346059 | ||||||||
\(334\) | −5.78673 | − | 3.51897i | −0.316636 | − | 0.192550i | ||||
\(335\) | 4.44953 | − | 7.23913i | 0.243104 | − | 0.395516i | ||||
\(336\) | 7.39976 | + | 5.22323i | 0.403690 | + | 0.284950i | ||||
\(337\) | −28.2019 | −1.53625 | −0.768127 | − | 0.640298i | \(-0.778811\pi\) | ||||
−0.768127 | + | 0.640298i | \(0.778811\pi\) | |||||||
\(338\) | −10.7554 | − | 6.54045i | −0.585014 | − | 0.355753i | ||||
\(339\) | 26.9172 | 1.46194 | ||||||||
\(340\) | 1.02567 | − | 14.0157i | 0.0556247 | − | 0.760110i | ||||
\(341\) | 0.571471i | 0.0309469i | ||||||||
\(342\) | 0.277824 | + | 0.168948i | 0.0150230 | + | 0.00913565i | ||||
\(343\) | 15.8062i | 0.853454i | ||||||||
\(344\) | −29.2406 | − | 1.99993i | −1.57655 | − | 0.107829i | ||||
\(345\) | 15.7714 | − | 10.5920i | 0.849103 | − | 0.570256i | ||||
\(346\) | −6.73484 | + | 11.0750i | −0.362067 | + | 0.595397i | ||||
\(347\) | −19.8612 | −1.06620 | −0.533102 | − | 0.846051i | \(-0.678974\pi\) | ||||
−0.533102 | + | 0.846051i | \(0.678974\pi\) | |||||||
\(348\) | −6.39295 | − | 12.3377i | −0.342698 | − | 0.661371i | ||||
\(349\) | 26.5042 | 1.41874 | 0.709369 | − | 0.704838i | \(-0.248980\pi\) | ||||
0.709369 | + | 0.704838i | \(0.248980\pi\) | |||||||
\(350\) | 9.01066 | + | 0.702536i | 0.481640 | + | 0.0375522i | ||||
\(351\) | 10.2635i | 0.547823i | ||||||||
\(352\) | −10.4163 | + | 4.52456i | −0.555190 | + | 0.241160i | ||||
\(353\) | − | 8.81853i | − | 0.469363i | −0.972072 | − | 0.234681i | \(-0.924595\pi\) | ||
0.972072 | − | 0.234681i | \(-0.0754047\pi\) | |||||||
\(354\) | 0.530700 | − | 0.872703i | 0.0282064 | − | 0.0463837i | ||||
\(355\) | 8.79834 | − | 14.3144i | 0.466967 | − | 0.759729i | ||||
\(356\) | 22.6037 | − | 11.7124i | 1.19800 | − | 0.620758i | ||||
\(357\) | − | 7.11557i | − | 0.376596i | ||||||
\(358\) | −2.74896 | + | 4.52050i | −0.145287 | + | 0.238916i | ||||
\(359\) | −16.6623 | −0.879401 | −0.439700 | − | 0.898145i | \(-0.644915\pi\) | ||||
−0.439700 | + | 0.898145i | \(0.644915\pi\) | |||||||
\(360\) | −0.508558 | + | 0.713244i | −0.0268033 | + | 0.0375912i | ||||
\(361\) | −16.2443 | −0.854962 | ||||||||
\(362\) | −17.6751 | + | 29.0656i | −0.928982 | + | 1.52765i | ||||
\(363\) | 12.3473 | 0.648067 | ||||||||
\(364\) | −2.38111 | − | 4.59529i | −0.124804 | − | 0.240859i | ||||
\(365\) | 15.6304 | − | 25.4298i | 0.818135 | − | 1.33106i | ||||
\(366\) | 1.71697 | − | 2.82345i | 0.0897473 | − | 0.147584i | ||||
\(367\) | − | 31.1423i | − | 1.62562i | −0.582531 | − | 0.812808i | \(-0.697938\pi\) | ||
0.582531 | − | 0.812808i | \(-0.302062\pi\) | |||||||
\(368\) | 9.66269 | + | 16.5720i | 0.503703 | + | 0.863877i | ||||
\(369\) | 0.879298 | 0.0457744 | ||||||||
\(370\) | 6.57228 | + | 12.8330i | 0.341677 | + | 0.667155i | ||||
\(371\) | − | 11.6469i | − | 0.604675i | ||||||
\(372\) | −0.895510 | + | 0.464021i | −0.0464300 | + | 0.0240583i | ||||
\(373\) | 24.0915 | 1.24741 | 0.623705 | − | 0.781660i | \(-0.285627\pi\) | ||||
0.623705 | + | 0.781660i | \(0.285627\pi\) | |||||||
\(374\) | 7.62286 | + | 4.63554i | 0.394169 | + | 0.239698i | ||||
\(375\) | −1.63360 | + | 19.7394i | −0.0843588 | + | 1.01934i | ||||
\(376\) | 1.38518 | − | 20.2525i | 0.0714353 | − | 1.04444i | ||||
\(377\) | 7.94012i | 0.408937i | ||||||||
\(378\) | 4.76114 | − | 7.82940i | 0.244887 | − | 0.402701i | ||||
\(379\) | −12.3451 | −0.634127 | −0.317063 | − | 0.948404i | \(-0.602697\pi\) | ||||
−0.317063 | + | 0.948404i | \(0.602697\pi\) | |||||||
\(380\) | −0.541831 | + | 7.40410i | −0.0277953 | + | 0.379823i | ||||
\(381\) | −1.31673 | −0.0674580 | ||||||||
\(382\) | −14.8017 | − | 9.00106i | −0.757320 | − | 0.460534i | ||||
\(383\) | 10.4177i | 0.532320i | 0.963929 | + | 0.266160i | \(0.0857550\pi\) | ||||
−0.963929 | + | 0.266160i | \(0.914245\pi\) | |||||||
\(384\) | −15.5479 | − | 12.6488i | −0.793425 | − | 0.645480i | ||||
\(385\) | −3.00455 | + | 4.88822i | −0.153126 | + | 0.249127i | ||||
\(386\) | −1.51495 | + | 2.49124i | −0.0771089 | + | 0.126801i | ||||
\(387\) | − | 1.43523i | − | 0.0729568i | ||||||
\(388\) | 6.72645 | + | 12.9813i | 0.341484 | + | 0.659027i | ||||
\(389\) | 10.5916i | 0.537015i | 0.963278 | + | 0.268508i | \(0.0865305\pi\) | ||||
−0.963278 | + | 0.268508i | \(0.913470\pi\) | |||||||
\(390\) | 10.0954 | − | 5.17024i | 0.511199 | − | 0.261805i | ||||
\(391\) | 6.25864 | − | 13.7093i | 0.316513 | − | 0.693312i | ||||
\(392\) | 1.03570 | − | 15.1428i | 0.0523107 | − | 0.764826i | ||||
\(393\) | 6.45342i | 0.325532i | ||||||||
\(394\) | −17.5644 | + | 28.8836i | −0.884884 | + | 1.45514i | ||||
\(395\) | −28.1195 | − | 17.2837i | −1.41485 | − | 0.869635i | ||||
\(396\) | −0.255852 | − | 0.493768i | −0.0128571 | − | 0.0248128i | ||||
\(397\) | 37.4766i | 1.88090i | 0.339935 | + | 0.940449i | \(0.389595\pi\) | ||||
−0.339935 | + | 0.940449i | \(0.610405\pi\) | |||||||
\(398\) | −5.81402 | − | 3.53556i | −0.291430 | − | 0.177222i | ||||
\(399\) | 3.75895i | 0.188183i | ||||||||
\(400\) | −19.7869 | − | 2.91160i | −0.989346 | − | 0.145580i | ||||
\(401\) | 8.87101i | 0.442997i | 0.975161 | + | 0.221499i | \(0.0710948\pi\) | ||||
−0.975161 | + | 0.221499i | \(0.928905\pi\) | |||||||
\(402\) | −4.94680 | + | 8.13470i | −0.246724 | + | 0.405722i | ||||
\(403\) | 0.576319 | 0.0287085 | ||||||||
\(404\) | 2.67699 | + | 5.16631i | 0.133185 | + | 0.257034i | ||||
\(405\) | 17.8999 | + | 11.0022i | 0.889454 | + | 0.546703i | ||||
\(406\) | 3.68336 | − | 6.05705i | 0.182802 | − | 0.300607i | ||||
\(407\) | −9.15329 | −0.453712 | ||||||||
\(408\) | −1.07444 | + | 15.7092i | −0.0531927 | + | 0.777721i | ||||
\(409\) | −2.79046 | −0.137979 | −0.0689896 | − | 0.997617i | \(-0.521978\pi\) | ||||
−0.0689896 | + | 0.997617i | \(0.521978\pi\) | |||||||
\(410\) | 9.15123 | + | 17.8686i | 0.451947 | + | 0.882468i | ||||
\(411\) | −1.76484 | −0.0870531 | ||||||||
\(412\) | −7.30782 | + | 3.78665i | −0.360031 | + | 0.186555i | ||||
\(413\) | 0.521082 | 0.0256408 | ||||||||
\(414\) | −0.777337 | + | 0.527444i | −0.0382040 | + | 0.0259225i | ||||
\(415\) | 1.37810 | − | 2.24209i | 0.0676483 | − | 0.110060i | ||||
\(416\) | 4.56295 | + | 10.5047i | 0.223717 | + | 0.515033i | ||||
\(417\) | 20.3568i | 0.996876i | ||||||||
\(418\) | −4.02694 | − | 2.44882i | −0.196964 | − | 0.119776i | ||||
\(419\) | −37.8916 | −1.85113 | −0.925563 | − | 0.378593i | \(-0.876408\pi\) | ||||
−0.925563 | + | 0.378593i | \(0.876408\pi\) | |||||||
\(420\) | −10.0996 | − | 0.739086i | −0.492810 | − | 0.0360637i | ||||
\(421\) | 4.54929i | 0.221719i | 0.993836 | + | 0.110859i | \(0.0353603\pi\) | ||||
−0.993836 | + | 0.110859i | \(0.964640\pi\) | |||||||
\(422\) | 2.77924 | − | 4.57028i | 0.135291 | − | 0.222478i | ||||
\(423\) | 0.994061 | 0.0483329 | ||||||||
\(424\) | −1.75866 | + | 25.7130i | −0.0854079 | + | 1.24873i | ||||
\(425\) | 7.09545 | + | 14.0186i | 0.344180 | + | 0.680001i | ||||
\(426\) | −9.78162 | + | 16.0853i | −0.473921 | + | 0.779333i | ||||
\(427\) | 1.68585 | 0.0815840 | ||||||||
\(428\) | −24.5934 | + | 12.7434i | −1.18877 | + | 0.615975i | ||||
\(429\) | 7.20065i | 0.347651i | ||||||||
\(430\) | 29.1659 | − | 14.9370i | 1.40651 | − | 0.720328i | ||||
\(431\) | 30.1685 | 1.45316 | 0.726582 | − | 0.687079i | \(-0.241108\pi\) | ||||
0.726582 | + | 0.687079i | \(0.241108\pi\) | |||||||
\(432\) | −11.6935 | + | 16.5662i | −0.562604 | + | 0.797042i | ||||
\(433\) | 8.39490 | 0.403433 | 0.201717 | − | 0.979444i | \(-0.435348\pi\) | ||||
0.201717 | + | 0.979444i | \(0.435348\pi\) | |||||||
\(434\) | −0.439640 | − | 0.267350i | −0.0211034 | − | 0.0128332i | ||||
\(435\) | 13.2355 | + | 8.13522i | 0.634595 | + | 0.390054i | ||||
\(436\) | −21.7800 | + | 11.2856i | −1.04307 | + | 0.540481i | ||||
\(437\) | −3.30626 | + | 7.24225i | −0.158160 | + | 0.346444i | ||||
\(438\) | −17.3773 | + | 28.5758i | −0.830317 | + | 1.36541i | ||||
\(439\) | − | 13.8344i | − | 0.660278i | −0.943932 | − | 0.330139i | \(-0.892904\pi\) | ||
0.943932 | − | 0.330139i | \(-0.107096\pi\) | |||||||
\(440\) | 7.37131 | − | 10.3381i | 0.351414 | − | 0.492852i | ||||
\(441\) | 0.743259 | 0.0353933 | ||||||||
\(442\) | 4.67487 | − | 7.68753i | 0.222361 | − | 0.365659i | ||||
\(443\) | 4.14183 | 0.196784 | 0.0983922 | − | 0.995148i | \(-0.468630\pi\) | ||||
0.0983922 | + | 0.995148i | \(0.468630\pi\) | |||||||
\(444\) | −7.43226 | − | 14.3435i | −0.352719 | − | 0.680711i | ||||
\(445\) | −14.9044 | + | 24.2486i | −0.706537 | + | 1.14950i | ||||
\(446\) | −18.0004 | − | 10.9462i | −0.852344 | − | 0.518320i | ||||
\(447\) | − | 38.1782i | − | 1.80577i | ||||||
\(448\) | 1.39222 | − | 10.1301i | 0.0657764 | − | 0.478603i | ||||
\(449\) | −37.8144 | −1.78457 | −0.892286 | − | 0.451470i | \(-0.850900\pi\) | ||||
−0.892286 | + | 0.451470i | \(0.850900\pi\) | |||||||
\(450\) | 0.0761285 | − | 0.976416i | 0.00358873 | − | 0.0460287i | ||||
\(451\) | −12.7450 | −0.600140 | ||||||||
\(452\) | −13.9805 | − | 26.9808i | −0.657586 | − | 1.26907i | ||||
\(453\) | 12.5897i | 0.591516i | ||||||||
\(454\) | −12.0016 | + | 19.7358i | −0.563262 | + | 0.926249i | ||||
\(455\) | 4.92969 | + | 3.03004i | 0.231108 | + | 0.142050i | ||||
\(456\) | 0.567595 | − | 8.29870i | 0.0265801 | − | 0.388622i | ||||
\(457\) | 12.8189 | 0.599642 | 0.299821 | − | 0.953996i | \(-0.403073\pi\) | ||||
0.299821 | + | 0.953996i | \(0.403073\pi\) | |||||||
\(458\) | 1.76678 | − | 2.90536i | 0.0825563 | − | 0.135759i | ||||
\(459\) | 15.9300 | 0.743548 | ||||||||
\(460\) | −18.8085 | − | 10.3073i | −0.876951 | − | 0.480579i | ||||
\(461\) | −8.34863 | −0.388834 | −0.194417 | − | 0.980919i | \(-0.562282\pi\) | ||||
−0.194417 | + | 0.980919i | \(0.562282\pi\) | |||||||
\(462\) | 3.34033 | − | 5.49296i | 0.155406 | − | 0.255556i | ||||
\(463\) | 20.8027 | 0.966786 | 0.483393 | − | 0.875404i | \(-0.339404\pi\) | ||||
0.483393 | + | 0.875404i | \(0.339404\pi\) | |||||||
\(464\) | −9.04643 | + | 12.8161i | −0.419970 | + | 0.594972i | ||||
\(465\) | 0.590480 | − | 0.960677i | 0.0273829 | − | 0.0445503i | ||||
\(466\) | −10.1080 | + | 16.6220i | −0.468245 | + | 0.770000i | ||||
\(467\) | 38.7967i | 1.79530i | 0.440713 | + | 0.897648i | \(0.354726\pi\) | ||||
−0.440713 | + | 0.897648i | \(0.645274\pi\) | |||||||
\(468\) | −0.497957 | + | 0.258023i | −0.0230181 | + | 0.0119271i | ||||
\(469\) | −4.85715 | −0.224282 | ||||||||
\(470\) | 10.3456 | + | 20.2008i | 0.477208 | + | 0.931792i | ||||
\(471\) | −33.6669 | −1.55129 | ||||||||
\(472\) | −1.15040 | − | 0.0786825i | −0.0529516 | − | 0.00362166i | ||||
\(473\) | 20.8030i | 0.956523i | ||||||||
\(474\) | 31.5982 | + | 19.2152i | 1.45136 | + | 0.882584i | ||||
\(475\) | −3.74832 | − | 7.40561i | −0.171985 | − | 0.339793i | ||||
\(476\) | −7.13238 | + | 3.69574i | −0.326912 | + | 0.169394i | ||||
\(477\) | −1.26208 | −0.0577867 | ||||||||
\(478\) | 20.1818 | − | 33.1877i | 0.923093 | − | 1.51797i | ||||
\(479\) | −4.32999 | −0.197842 | −0.0989212 | − | 0.995095i | \(-0.531539\pi\) | ||||
−0.0989212 | + | 0.995095i | \(0.531539\pi\) | |||||||
\(480\) | 22.1855 | + | 3.15672i | 1.01262 | + | 0.144084i | ||||
\(481\) | 9.23095i | 0.420895i | ||||||||
\(482\) | 9.76062 | − | 16.0507i | 0.444584 | − | 0.731091i | ||||
\(483\) | −9.87882 | − | 4.50991i | −0.449502 | − | 0.205208i | ||||
\(484\) | −6.41305 | − | 12.3765i | −0.291502 | − | 0.562568i | ||||
\(485\) | −13.9260 | − | 8.55961i | −0.632347 | − | 0.388672i | ||||
\(486\) | −1.73789 | − | 1.05683i | −0.0788323 | − | 0.0479388i | ||||
\(487\) | 24.4278 | 1.10693 | 0.553465 | − | 0.832872i | \(-0.313305\pi\) | ||||
0.553465 | + | 0.832872i | \(0.313305\pi\) | |||||||
\(488\) | −3.72188 | − | 0.254560i | −0.168482 | − | 0.0115234i | ||||
\(489\) | 6.46633 | 0.292417 | ||||||||
\(490\) | 7.73541 | + | 15.1041i | 0.349450 | + | 0.682334i | ||||
\(491\) | − | 27.9260i | − | 1.26028i | −0.776480 | − | 0.630142i | \(-0.782997\pi\) | ||
0.776480 | − | 0.630142i | \(-0.217003\pi\) | |||||||
\(492\) | −10.3487 | − | 19.9718i | −0.466554 | − | 0.900399i | ||||
\(493\) | 12.3239 | 0.555040 | ||||||||
\(494\) | −2.46960 | + | 4.06110i | −0.111112 | + | 0.182718i | ||||
\(495\) | 0.529699 | + | 0.325580i | 0.0238082 | + | 0.0146337i | ||||
\(496\) | 0.930233 | + | 0.656619i | 0.0417687 | + | 0.0294830i | ||||
\(497\) | −9.60434 | −0.430814 | ||||||||
\(498\) | −1.53211 | + | 2.51946i | −0.0686556 | + | 0.112900i | ||||
\(499\) | − | 31.1413i | − | 1.39408i | −0.717034 | − | 0.697038i | \(-0.754501\pi\) | ||
0.717034 | − | 0.697038i | \(-0.245499\pi\) | |||||||
\(500\) | 20.6345 | − | 8.61494i | 0.922803 | − | 0.385272i | ||||
\(501\) | −8.48415 | −0.379044 | ||||||||
\(502\) | −29.7590 | − | 18.0968i | −1.32821 | − | 0.807699i | ||||
\(503\) | − | 22.8311i | − | 1.01799i | −0.860771 | − | 0.508993i | \(-0.830018\pi\) | ||
0.860771 | − | 0.508993i | \(-0.169982\pi\) | |||||||
\(504\) | 0.499557 | + | 0.0341675i | 0.0222520 | + | 0.00152194i | ||||
\(505\) | −5.54227 | − | 3.40656i | −0.246628 | − | 0.151590i | ||||
\(506\) | 11.2671 | − | 7.64506i | 0.500886 | − | 0.339865i | ||||
\(507\) | −15.7688 | −0.700318 | ||||||||
\(508\) | 0.683892 | + | 1.31984i | 0.0303428 | + | 0.0585584i | ||||
\(509\) | 35.6570 | 1.58047 | 0.790235 | − | 0.612804i | \(-0.209958\pi\) | ||||
0.790235 | + | 0.612804i | \(0.209958\pi\) | |||||||
\(510\) | −8.02475 | − | 15.6691i | −0.355342 | − | 0.693838i | ||||
\(511\) | −17.0623 | −0.754793 | ||||||||
\(512\) | −4.60327 | + | 22.1542i | −0.203438 | + | 0.979088i | ||||
\(513\) | −8.41534 | −0.371546 | ||||||||
\(514\) | −14.6590 | + | 24.1059i | −0.646582 | + | 1.06326i | ||||
\(515\) | 4.81862 | − | 7.83962i | 0.212334 | − | 0.345455i | ||||
\(516\) | −32.5989 | + | 16.8915i | −1.43508 | + | 0.743609i | ||||
\(517\) | −14.4085 | −0.633684 | ||||||||
\(518\) | 4.28217 | − | 7.04176i | 0.188148 | − | 0.309397i | ||||
\(519\) | 16.2375i | 0.712747i | ||||||||
\(520\) | −10.4259 | − | 7.43385i | −0.457204 | − | 0.325996i | ||||
\(521\) | − | 5.01032i | − | 0.219506i | −0.993959 | − | 0.109753i | \(-0.964994\pi\) | ||
0.993959 | − | 0.109753i | \(-0.0350060\pi\) | |||||||
\(522\) | −0.656357 | − | 0.399137i | −0.0287279 | − | 0.0174698i | ||||
\(523\) | 1.23284i | 0.0539085i | 0.999637 | + | 0.0269542i | \(0.00858084\pi\) | ||||
−0.999637 | + | 0.0269542i | \(0.991419\pi\) | |||||||
\(524\) | 6.46866 | − | 3.35182i | 0.282585 | − | 0.146425i | ||||
\(525\) | 10.1017 | − | 5.11291i | 0.440872 | − | 0.223146i | ||||
\(526\) | −8.58568 | + | 14.1186i | −0.374354 | + | 0.615601i | ||||
\(527\) | − | 0.894507i | − | 0.0389653i | ||||||
\(528\) | −8.20393 | + | 11.6225i | −0.357030 | + | 0.505806i | ||||
\(529\) | −15.0664 | − | 17.3782i | −0.655062 | − | 0.755575i | ||||
\(530\) | −13.1350 | − | 25.6473i | −0.570549 | − | 1.11405i | ||||
\(531\) | − | 0.0564657i | − | 0.00245040i | ||||||
\(532\) | 3.76783 | − | 1.95235i | 0.163356 | − | 0.0846451i | ||||
\(533\) | 12.8532i | 0.556732i | ||||||||
\(534\) | 16.5701 | − | 27.2485i | 0.717058 | − | 1.17916i | ||||
\(535\) | 16.2163 | − | 26.3830i | 0.701094 | − | 1.14064i | ||||
\(536\) | 10.7232 | + | 0.733421i | 0.463173 | + | 0.0316790i | ||||
\(537\) | 6.62767i | 0.286005i | ||||||||
\(538\) | −7.34134 | − | 4.46435i | −0.316508 | − | 0.192472i | ||||
\(539\) | −10.7732 | −0.464035 | ||||||||
\(540\) | 1.65463 | − | 22.6105i | 0.0712039 | − | 0.973000i | ||||
\(541\) | 23.8421 | 1.02505 | 0.512526 | − | 0.858672i | \(-0.328710\pi\) | ||||
0.512526 | + | 0.858672i | \(0.328710\pi\) | |||||||
\(542\) | 13.5826 | − | 22.3357i | 0.583422 | − | 0.959402i | ||||
\(543\) | 42.6141i | 1.82875i | ||||||||
\(544\) | 16.3043 | − | 7.08218i | 0.699043 | − | 0.303646i | ||||
\(545\) | 14.3612 | − | 23.3649i | 0.615168 | − | 1.00084i | ||||
\(546\) | −5.53956 | − | 3.36867i | −0.237071 | − | 0.144166i | ||||
\(547\) | 4.14950 | 0.177420 | 0.0887099 | − | 0.996058i | \(-0.471726\pi\) | ||||
0.0887099 | + | 0.996058i | \(0.471726\pi\) | |||||||
\(548\) | 0.916635 | + | 1.76901i | 0.0391567 | + | 0.0755682i | ||||
\(549\) | − | 0.182683i | − | 0.00779671i | ||||||
\(550\) | −1.10345 | + | 14.1527i | −0.0470512 | + | 0.603474i | ||||
\(551\) | −6.51035 | −0.277350 | ||||||||
\(552\) | 21.1287 | + | 11.4483i | 0.899296 | + | 0.487272i | ||||
\(553\) | 18.8670i | 0.802306i | ||||||||
\(554\) | 3.74284 | − | 6.15487i | 0.159018 | − | 0.261495i | ||||
\(555\) | 15.3872 | + | 9.45777i | 0.653152 | + | 0.401460i | ||||
\(556\) | 20.4049 | − | 10.5731i | 0.865359 | − | 0.448397i | ||||
\(557\) | 25.9135 | 1.09799 | 0.548996 | − | 0.835825i | \(-0.315010\pi\) | ||||
0.548996 | + | 0.835825i | \(0.315010\pi\) | |||||||
\(558\) | −0.0289707 | + | 0.0476404i | −0.00122643 | + | 0.00201678i | ||||
\(559\) | 20.9795 | 0.887338 | ||||||||
\(560\) | 4.50477 | + | 10.5073i | 0.190361 | + | 0.444016i | ||||
\(561\) | 11.1762 | 0.471858 | ||||||||
\(562\) | 1.48782 | − | 2.44663i | 0.0627600 | − | 0.103205i | ||||
\(563\) | 2.41729i | 0.101877i | 0.998702 | + | 0.0509384i | \(0.0162212\pi\) | ||||
−0.998702 | + | 0.0509384i | \(0.983779\pi\) | |||||||
\(564\) | −11.6993 | − | 22.5785i | −0.492631 | − | 0.950725i | ||||
\(565\) | 28.9442 | + | 17.7906i | 1.21769 | + | 0.748455i | ||||
\(566\) | 18.7606 | − | 30.8506i | 0.788565 | − | 1.29675i | ||||
\(567\) | − | 12.0101i | − | 0.504376i | ||||||
\(568\) | 21.2037 | + | 1.45024i | 0.889687 | + | 0.0608507i | ||||
\(569\) | − | 34.2149i | − | 1.43436i | −0.696886 | − | 0.717182i | \(-0.745432\pi\) | ||
0.696886 | − | 0.717182i | \(-0.254568\pi\) | |||||||
\(570\) | 4.23924 | + | 8.27751i | 0.177562 | + | 0.346707i | ||||
\(571\) | −45.1587 | −1.88983 | −0.944917 | − | 0.327309i | \(-0.893858\pi\) | ||||
−0.944917 | + | 0.327309i | \(0.893858\pi\) | |||||||
\(572\) | 7.21766 | − | 3.73993i | 0.301785 | − | 0.156374i | ||||
\(573\) | −21.7013 | −0.906585 | ||||||||
\(574\) | 5.96248 | − | 9.80493i | 0.248869 | − | 0.409250i | ||||
\(575\) | 23.9597 | − | 0.965773i | 0.999189 | − | 0.0402755i | ||||
\(576\) | −1.09772 | − | 0.150865i | −0.0457385 | − | 0.00628602i | ||||
\(577\) | − | 10.7803i | − | 0.448791i | −0.974498 | − | 0.224395i | \(-0.927959\pi\) | ||
0.974498 | − | 0.224395i | \(-0.0720407\pi\) | |||||||
\(578\) | 8.60980 | + | 5.23571i | 0.358121 | + | 0.217777i | ||||
\(579\) | 3.65250i | 0.151793i | ||||||||
\(580\) | 1.28007 | − | 17.4921i | 0.0531520 | − | 0.726321i | ||||
\(581\) | −1.50435 | −0.0624108 | ||||||||
\(582\) | 15.6488 | + | 9.51621i | 0.648664 | + | 0.394460i | ||||
\(583\) | 18.2933 | 0.757631 | ||||||||
\(584\) | 37.6688 | + | 2.57638i | 1.55875 | + | 0.106611i | ||||
\(585\) | 0.328342 | − | 0.534193i | 0.0135753 | − | 0.0220862i | ||||
\(586\) | −8.98018 | − | 5.46094i | −0.370968 | − | 0.225589i | ||||
\(587\) | 20.1830 | 0.833040 | 0.416520 | − | 0.909127i | \(-0.363250\pi\) | ||||
0.416520 | + | 0.909127i | \(0.363250\pi\) | |||||||
\(588\) | −8.74759 | − | 16.8819i | −0.360744 | − | 0.696198i | ||||
\(589\) | 0.472542i | 0.0194708i | ||||||||
\(590\) | 1.14747 | − | 0.587663i | 0.0472404 | − | 0.0241937i | ||||
\(591\) | 42.3474i | 1.74194i | ||||||||
\(592\) | −10.5171 | + | 14.8996i | −0.432251 | + | 0.612371i | ||||
\(593\) | − | 27.1614i | − | 1.11538i | −0.830048 | − | 0.557692i | \(-0.811687\pi\) | ||
0.830048 | − | 0.557692i | \(-0.188313\pi\) | |||||||
\(594\) | 12.2974 | + | 7.47815i | 0.504567 | + | 0.306832i | ||||
\(595\) | 4.70294 | − | 7.65140i | 0.192802 | − | 0.313677i | ||||
\(596\) | −38.2683 | + | 19.8293i | −1.56753 | + | 0.812238i | ||||
\(597\) | −8.52415 | −0.348870 | ||||||||
\(598\) | −7.70992 | − | 11.3627i | −0.315282 | − | 0.464657i | ||||
\(599\) | − | 29.2766i | − | 1.19621i | −0.801418 | − | 0.598105i | \(-0.795921\pi\) | ||
0.801418 | − | 0.598105i | \(-0.204079\pi\) | |||||||
\(600\) | −23.0737 | + | 9.76254i | −0.941978 | + | 0.398554i | ||||
\(601\) | 17.8309 | 0.727338 | 0.363669 | − | 0.931528i | \(-0.381524\pi\) | ||||
0.363669 | + | 0.931528i | \(0.381524\pi\) | |||||||
\(602\) | −16.0040 | − | 9.73222i | −0.652276 | − | 0.396656i | ||||
\(603\) | 0.526332i | 0.0214339i | ||||||||
\(604\) | 12.6194 | − | 6.53893i | 0.513478 | − | 0.266065i | ||||
\(605\) | 13.2771 | + | 8.16080i | 0.539792 | + | 0.331784i | ||||
\(606\) | 6.22792 | + | 3.78726i | 0.252992 | + | 0.153847i | ||||
\(607\) | −8.00797 | −0.325033 | −0.162517 | − | 0.986706i | \(-0.551961\pi\) | ||||
−0.162517 | + | 0.986706i | \(0.551961\pi\) | |||||||
\(608\) | −8.61310 | + | 3.74131i | −0.349308 | + | 0.151730i | ||||
\(609\) | − | 8.88048i | − | 0.359855i | ||||||
\(610\) | 3.71238 | − | 1.90126i | 0.150310 | − | 0.0769797i | ||||
\(611\) | 14.5307i | 0.587850i | ||||||||
\(612\) | 0.400479 | + | 0.772881i | 0.0161884 | + | 0.0312419i | ||||
\(613\) | −13.3191 | −0.537952 | −0.268976 | − | 0.963147i | \(-0.586685\pi\) | ||||
−0.268976 | + | 0.963147i | \(0.586685\pi\) | |||||||
\(614\) | −25.0639 | − | 15.2416i | −1.01150 | − | 0.615103i | ||||
\(615\) | 21.4252 | + | 13.1690i | 0.863946 | + | 0.531025i | ||||
\(616\) | −7.24086 | − | 0.495243i | −0.291742 | − | 0.0199539i | ||||
\(617\) | −12.7250 | −0.512290 | −0.256145 | − | 0.966638i | \(-0.582452\pi\) | ||||
−0.256145 | + | 0.966638i | \(0.582452\pi\) | |||||||
\(618\) | −5.35714 | + | 8.80948i | −0.215496 | + | 0.354369i | ||||
\(619\) | 12.1732 | 0.489283 | 0.244641 | − | 0.969614i | \(-0.421330\pi\) | ||||
0.244641 | + | 0.969614i | \(0.421330\pi\) | |||||||
\(620\) | −1.26963 | − | 0.0929115i | −0.0509897 | − | 0.00373141i | ||||
\(621\) | 10.0966 | − | 22.1162i | 0.405161 | − | 0.887492i | ||||
\(622\) | 10.3311 | − | 16.9889i | 0.414240 | − | 0.681192i | ||||
\(623\) | 16.2698 | 0.651836 | ||||||||
\(624\) | 11.7211 | + | 8.27353i | 0.469221 | + | 0.331206i | ||||
\(625\) | −14.8031 | + | 20.1462i | −0.592124 | + | 0.805847i | ||||
\(626\) | −26.3555 | − | 16.0271i | −1.05338 | − | 0.640571i | ||||
\(627\) | −5.90404 | −0.235785 | ||||||||
\(628\) | 17.4862 | + | 33.7464i | 0.697774 | + | 1.34663i | ||||
\(629\) | 14.3274 | 0.571271 | ||||||||
\(630\) | −0.498281 | + | 0.255190i | −0.0198520 | + | 0.0101670i | ||||
\(631\) | 35.3099 | 1.40566 | 0.702832 | − | 0.711356i | \(-0.251919\pi\) | ||||
0.702832 | + | 0.711356i | \(0.251919\pi\) | |||||||
\(632\) | 2.84888 | − | 41.6530i | 0.113322 | − | 1.65687i | ||||
\(633\) | − | 6.70066i | − | 0.266327i | ||||||
\(634\) | 15.4080 | − | 25.3374i | 0.611928 | − | 1.00628i | ||||
\(635\) | −1.41588 | − | 0.870273i | −0.0561876 | − | 0.0345357i | ||||
\(636\) | 14.8537 | + | 28.6661i | 0.588989 | + | 1.13668i | ||||
\(637\) | 10.8646i | 0.430471i | ||||||||
\(638\) | 9.51359 | + | 5.78532i | 0.376647 | + | 0.229043i | ||||
\(639\) | 1.04075i | 0.0411714i | ||||||||
\(640\) | −8.35869 | − | 23.8774i | −0.330406 | − | 0.943839i | ||||
\(641\) | 18.1190i | 0.715656i | 0.933788 | + | 0.357828i | \(0.116483\pi\) | ||||
−0.933788 | + | 0.357828i | \(0.883517\pi\) | |||||||
\(642\) | −18.0286 | + | 29.6470i | −0.711534 | + | 1.17007i | ||||
\(643\) | − | 40.3890i | − | 1.59279i | −0.604778 | − | 0.796394i | \(-0.706738\pi\) | ||
0.604778 | − | 0.796394i | \(-0.293262\pi\) | |||||||
\(644\) | 0.610369 | + | 12.2445i | 0.0240519 | + | 0.482503i | ||||
\(645\) | 21.4950 | − | 34.9711i | 0.846364 | − | 1.37699i | ||||
\(646\) | 6.30325 | + | 3.83307i | 0.247998 | + | 0.150810i | ||||
\(647\) | −39.1470 | −1.53903 | −0.769514 | − | 0.638630i | \(-0.779502\pi\) | ||||
−0.769514 | + | 0.638630i | \(0.779502\pi\) | |||||||
\(648\) | −1.81350 | + | 26.5149i | −0.0712411 | + | 1.04160i | ||||
\(649\) | 0.818445i | 0.0321268i | ||||||||
\(650\) | 14.2728 | + | 1.11281i | 0.559825 | + | 0.0436480i | ||||
\(651\) | −0.644573 | −0.0252628 | ||||||||
\(652\) | −3.35853 | − | 6.48160i | −0.131530 | − | 0.253839i | ||||
\(653\) | 30.4895i | 1.19315i | 0.802558 | + | 0.596574i | \(0.203472\pi\) | ||||
−0.802558 | + | 0.596574i | \(0.796528\pi\) | |||||||
\(654\) | −15.9662 | + | 26.2554i | −0.624328 | + | 1.02667i | ||||
\(655\) | −4.26530 | + | 6.93939i | −0.166659 | + | 0.271144i | ||||
\(656\) | −14.6440 | + | 20.7462i | −0.571753 | + | 0.810003i | ||||
\(657\) | 1.84891i | 0.0721330i | ||||||||
\(658\) | 6.74069 | − | 11.0846i | 0.262779 | − | 0.432124i | ||||
\(659\) | 17.9308 | 0.698487 | 0.349243 | − | 0.937032i | \(-0.386439\pi\) | ||||
0.349243 | + | 0.937032i | \(0.386439\pi\) | |||||||
\(660\) | 1.16086 | − | 15.8631i | 0.0451863 | − | 0.617469i | ||||
\(661\) | − | 35.5572i | − | 1.38301i | −0.722370 | − | 0.691507i | \(-0.756947\pi\) | ||
0.722370 | − | 0.691507i | \(-0.243053\pi\) | |||||||
\(662\) | −24.0546 | + | 39.5564i | −0.934910 | + | 1.53740i | ||||
\(663\) | − | 11.2710i | − | 0.437729i | ||||||
\(664\) | 3.32117 | + | 0.227154i | 0.128886 | + | 0.00881527i | ||||
\(665\) | −2.48442 | + | 4.04201i | −0.0963418 | + | 0.156743i | ||||
\(666\) | −0.763061 | − | 0.464026i | −0.0295680 | − | 0.0179806i | ||||
\(667\) | 7.81100 | − | 17.1097i | 0.302443 | − | 0.662492i | ||||
\(668\) | 4.40656 | + | 8.50419i | 0.170495 | + | 0.329037i | ||||
\(669\) | −26.3911 | −1.02034 | ||||||||
\(670\) | −10.6958 | + | 5.47776i | −0.413216 | + | 0.211624i | ||||
\(671\) | 2.64790i | 0.102221i | ||||||||
\(672\) | −5.10335 | − | 11.7487i | −0.196866 | − | 0.453218i | ||||
\(673\) | − | 49.8311i | − | 1.92085i | −0.278543 | − | 0.960424i | \(-0.589852\pi\) | ||
0.278543 | − | 0.960424i | \(-0.410148\pi\) | |||||||
\(674\) | 34.0773 | + | 20.7227i | 1.31261 | + | 0.798210i | ||||
\(675\) | 11.4465 | + | 22.6151i | 0.440577 | + | 0.870454i | ||||
\(676\) | 8.19013 | + | 15.8061i | 0.315005 | + | 0.607926i | ||||
\(677\) | −24.1638 | −0.928688 | −0.464344 | − | 0.885655i | \(-0.653710\pi\) | ||||
−0.464344 | + | 0.885655i | \(0.653710\pi\) | |||||||
\(678\) | −32.5250 | − | 19.7788i | −1.24911 | − | 0.759600i | ||||
\(679\) | 9.34374i | 0.358580i | ||||||||
\(680\) | −11.5381 | + | 16.1820i | −0.442467 | + | 0.620552i | ||||
\(681\) | 28.9355i | 1.10881i | ||||||||
\(682\) | 0.419917 | − | 0.690527i | 0.0160794 | − | 0.0264416i | ||||
\(683\) | −33.5547 | −1.28394 | −0.641968 | − | 0.766732i | \(-0.721882\pi\) | ||||
−0.641968 | + | 0.766732i | \(0.721882\pi\) | |||||||
\(684\) | −0.211561 | − | 0.408290i | −0.00808924 | − | 0.0156114i | ||||
\(685\) | −1.89774 | − | 1.16645i | −0.0725088 | − | 0.0445676i | ||||
\(686\) | 11.6144 | − | 19.0991i | 0.443439 | − | 0.729208i | ||||
\(687\) | − | 4.25966i | − | 0.162516i | ||||||
\(688\) | 33.8629 | + | 23.9026i | 1.29101 | + | 0.911278i | ||||
\(689\) | − | 18.4485i | − | 0.702832i | ||||||
\(690\) | −26.8401 | + | 1.20988i | −1.02179 | + | 0.0460593i | ||||
\(691\) | 51.0577i | 1.94233i | 0.238415 | + | 0.971163i | \(0.423372\pi\) | ||||
−0.238415 | + | 0.971163i | \(0.576628\pi\) | |||||||
\(692\) | 16.2759 | − | 8.43355i | 0.618715 | − | 0.320596i | ||||
\(693\) | − | 0.355406i | − | 0.0135007i | ||||||
\(694\) | 23.9989 | + | 14.5940i | 0.910986 | + | 0.553980i | ||||
\(695\) | −13.4545 | + | 21.8897i | −0.510359 | + | 0.830325i | ||||
\(696\) | −1.34094 | + | 19.6056i | −0.0508281 | + | 0.743148i | ||||
\(697\) | 19.9494 | 0.755639 | ||||||||
\(698\) | −32.0259 | − | 19.4753i | −1.21220 | − | 0.737151i | ||||
\(699\) | 24.3702i | 0.921764i | ||||||||
\(700\) | −10.3717 | − | 7.46993i | −0.392012 | − | 0.282337i | ||||
\(701\) | 27.2145i | 1.02788i | 0.857827 | + | 0.513939i | \(0.171814\pi\) | ||||
−0.857827 | + | 0.513939i | \(0.828186\pi\) | |||||||
\(702\) | 7.54160 | − | 12.4017i | 0.284639 | − | 0.468071i | ||||
\(703\) | −7.56875 | −0.285461 | ||||||||
\(704\) | 15.9110 | + | 2.18671i | 0.599668 | + | 0.0824149i | ||||
\(705\) | 24.2215 | + | 14.8878i | 0.912235 | + | 0.560706i | ||||
\(706\) | −6.47986 | + | 10.6557i | −0.243873 | + | 0.401033i | ||||
\(707\) | 3.71862i | 0.139853i | ||||||||
\(708\) | −1.28253 | + | 0.664558i | −0.0482003 | + | 0.0249756i | ||||
\(709\) | 16.0965i | 0.604518i | 0.953226 | + | 0.302259i | \(0.0977407\pi\) | ||||
−0.953226 | + | 0.302259i | \(0.902259\pi\) | |||||||
\(710\) | −21.1495 | + | 10.8315i | −0.793728 | + | 0.406500i | ||||
\(711\) | 2.04447 | 0.0766736 | ||||||||
\(712\) | −35.9191 | − | 2.45671i | −1.34613 | − | 0.0920691i | ||||
\(713\) | −1.24188 | − | 0.566947i | −0.0465087 | − | 0.0212323i | ||||
\(714\) | −5.22852 | + | 8.59798i | −0.195673 | + | 0.321771i | ||||
\(715\) | −4.75917 | + | 7.74289i | −0.177983 | + | 0.289568i | ||||
\(716\) | 6.64333 | − | 3.44233i | 0.248273 | − | 0.128646i | ||||
\(717\) | − | 48.6577i | − | 1.81715i | ||||||
\(718\) | 20.1336 | + | 12.2434i | 0.751378 | + | 0.456921i | ||||
\(719\) | 39.4635i | 1.47174i | 0.677122 | + | 0.735870i | \(0.263227\pi\) | ||||
−0.677122 | + | 0.735870i | \(0.736773\pi\) | |||||||
\(720\) | 1.13860 | − | 0.488148i | 0.0424331 | − | 0.0181922i | ||||
\(721\) | −5.26005 | −0.195894 | ||||||||
\(722\) | 19.6285 | + | 11.9363i | 0.730497 | + | 0.444223i | ||||
\(723\) | − | 23.5326i | − | 0.875186i | ||||||
\(724\) | 42.7148 | − | 22.1332i | 1.58748 | − | 0.822575i | ||||
\(725\) | 8.85536 | + | 17.4957i | 0.328880 | + | 0.649773i | ||||
\(726\) | −14.9197 | − | 9.07282i | −0.553722 | − | 0.336724i | ||||
\(727\) | 12.8559i | 0.476798i | 0.971167 | + | 0.238399i | \(0.0766226\pi\) | ||||
−0.971167 | + | 0.238399i | \(0.923377\pi\) | |||||||
\(728\) | −0.499444 | + | 7.30229i | −0.0185106 | + | 0.270641i | ||||
\(729\) | 25.6410 | 0.949667 | ||||||||
\(730\) | −37.5726 | + | 19.2424i | −1.39062 | + | 0.712194i | ||||
\(731\) | − | 32.5624i | − | 1.20436i | ||||||
\(732\) | −4.14934 | + | 2.15003i | −0.153364 | + | 0.0794676i | ||||
\(733\) | 31.2706 | 1.15501 | 0.577503 | − | 0.816388i | \(-0.304027\pi\) | ||||
0.577503 | + | 0.816388i | \(0.304027\pi\) | |||||||
\(734\) | −22.8834 | + | 37.6303i | −0.844642 | + | 1.38896i | ||||
\(735\) | 18.1104 | + | 11.1316i | 0.668012 | + | 0.410594i | ||||
\(736\) | 0.501381 | − | 27.1247i | 0.0184812 | − | 0.999829i | ||||
\(737\) | − | 7.62894i | − | 0.281016i | ||||||
\(738\) | −1.06248 | − | 0.646108i | −0.0391106 | − | 0.0237836i | ||||
\(739\) | 14.1135i | 0.519174i | 0.965720 | + | 0.259587i | \(0.0835864\pi\) | ||||
−0.965720 | + | 0.259587i | \(0.916414\pi\) | |||||||
\(740\) | 1.48817 | − | 20.3358i | 0.0547063 | − | 0.747560i | ||||
\(741\) | 5.95413i | 0.218730i | ||||||||
\(742\) | −8.55812 | + | 14.0733i | −0.314178 | + | 0.516647i | ||||
\(743\) | 15.2288i | 0.558691i | 0.960191 | + | 0.279345i | \(0.0901175\pi\) | ||||
−0.960191 | + | 0.279345i | \(0.909883\pi\) | |||||||
\(744\) | 1.42304 | + | 0.0973294i | 0.0521711 | + | 0.00356827i | ||||
\(745\) | 25.2333 | − | 41.0531i | 0.924477 | − | 1.50407i | ||||
\(746\) | −29.1105 | − | 17.7024i | −1.06581 | − | 0.648132i | ||||
\(747\) | 0.163014i | 0.00596438i | ||||||||
\(748\) | −5.80476 | − | 11.2026i | −0.212243 | − | 0.409606i | ||||
\(749\) | −17.7019 | −0.646813 | ||||||||
\(750\) | 16.4785 | − | 22.6514i | 0.601708 | − | 0.827113i | ||||
\(751\) | 19.8242 | 0.723396 | 0.361698 | − | 0.932295i | \(-0.382197\pi\) | ||||
0.361698 | + | 0.932295i | \(0.382197\pi\) | |||||||
\(752\) | −16.5553 | + | 23.4539i | −0.603710 | + | 0.855277i | ||||
\(753\) | −43.6309 | −1.59000 | ||||||||
\(754\) | 5.83440 | − | 9.59431i | 0.212476 | − | 0.349404i | ||||
\(755\) | −8.32099 | + | 13.5378i | −0.302832 | + | 0.492689i | ||||
\(756\) | −11.5061 | + | 5.96204i | −0.418473 | + | 0.216837i | ||||
\(757\) | −5.98547 | −0.217545 | −0.108773 | − | 0.994067i | \(-0.534692\pi\) | ||||
−0.108773 | + | 0.994067i | \(0.534692\pi\) | |||||||
\(758\) | 14.9170 | + | 9.07121i | 0.541811 | + | 0.329481i | ||||
\(759\) | 7.08356 | − | 15.5163i | 0.257117 | − | 0.563206i | ||||
\(760\) | 6.09525 | − | 8.54849i | 0.221098 | − | 0.310086i | ||||
\(761\) | 6.47102 | 0.234574 | 0.117287 | − | 0.993098i | \(-0.462580\pi\) | ||||
0.117287 | + | 0.993098i | \(0.462580\pi\) | |||||||
\(762\) | 1.59105 | + | 0.967532i | 0.0576375 | + | 0.0350500i | ||||
\(763\) | −15.6768 | −0.567540 | ||||||||
\(764\) | 11.2714 | + | 21.7526i | 0.407784 | + | 0.786980i | ||||
\(765\) | −0.829124 | − | 0.509621i | −0.0299770 | − | 0.0184254i | ||||
\(766\) | 7.65494 | − | 12.5881i | 0.276584 | − | 0.454825i | ||||
\(767\) | 0.825388 | 0.0298030 | ||||||||
\(768\) | 9.49272 | + | 26.7085i | 0.342539 | + | 0.963761i | ||||
\(769\) | − | 22.1852i | − | 0.800017i | −0.916511 | − | 0.400009i | \(-0.869007\pi\) | ||
0.916511 | − | 0.400009i | \(-0.130993\pi\) | |||||||
\(770\) | 7.22236 | − | 3.69886i | 0.260276 | − | 0.133298i | ||||
\(771\) | 35.3425i | 1.27283i | ||||||||
\(772\) | 3.66113 | − | 1.89706i | 0.131767 | − | 0.0682767i | ||||
\(773\) | −20.9231 | −0.752551 | −0.376276 | − | 0.926508i | \(-0.622795\pi\) | ||||
−0.376276 | + | 0.926508i | \(0.622795\pi\) | |||||||
\(774\) | −1.05461 | + | 1.73423i | −0.0379070 | + | 0.0623358i | ||||
\(775\) | 1.26989 | − | 0.642750i | 0.0456158 | − | 0.0230883i | ||||
\(776\) | 1.41089 | − | 20.6284i | 0.0506480 | − | 0.740515i | ||||
\(777\) | − | 10.3242i | − | 0.370378i | ||||||
\(778\) | 7.78271 | − | 12.7982i | 0.279024 | − | 0.458837i | ||||
\(779\) | −10.5387 | −0.377588 | ||||||||
\(780\) | −15.9977 | − | 1.17070i | −0.572808 | − | 0.0419179i | ||||
\(781\) | − | 15.0852i | − | 0.539790i | ||||||
\(782\) | −17.6362 | + | 11.9666i | −0.630668 | + | 0.427925i | ||||
\(783\) | 19.8812 | 0.710494 | ||||||||
\(784\) | −12.3784 | + | 17.5365i | −0.442085 | + | 0.626303i | ||||
\(785\) | −36.2022 | − | 22.2517i | −1.29211 | − | 0.794196i | ||||
\(786\) | 4.74198 | − | 7.79788i | 0.169141 | − | 0.278141i | ||||
\(787\) | 38.9650i | 1.38895i | 0.719515 | + | 0.694476i | \(0.244364\pi\) | ||||
−0.719515 | + | 0.694476i | \(0.755636\pi\) | |||||||
\(788\) | 42.4474 | − | 21.9947i | 1.51213 | − | 0.783528i | ||||
\(789\) | 20.6998i | 0.736934i | ||||||||
\(790\) | 21.2777 | + | 41.5466i | 0.757026 | + | 1.47816i | ||||
\(791\) | − | 19.4203i | − | 0.690507i | ||||||
\(792\) | −0.0536657 | + | 0.784636i | −0.00190693 | + | 0.0278808i | ||||
\(793\) | 2.67037 | 0.0948275 | ||||||||
\(794\) | 27.5378 | − | 45.2842i | 0.977281 | − | 1.60708i | ||||
\(795\) | −30.7521 | − | 18.9018i | −1.09067 | − | 0.670378i | ||||
\(796\) | 4.42733 | + | 8.54428i | 0.156923 | + | 0.302844i | ||||
\(797\) | −0.230952 | −0.00818073 | −0.00409036 | − | 0.999992i | \(-0.501302\pi\) | ||||
−0.00409036 | + | 0.999992i | \(0.501302\pi\) | |||||||
\(798\) | 2.76208 | − | 4.54206i | 0.0977764 | − | 0.160787i | ||||
\(799\) | 22.5532 | 0.797875 | ||||||||
\(800\) | 21.7698 | + | 18.0576i | 0.769677 | + | 0.638433i | ||||
\(801\) | − | 1.76303i | − | 0.0622937i | ||||||
\(802\) | 6.51842 | − | 10.7191i | 0.230173 | − | 0.378506i | ||||
\(803\) | − | 26.7992i | − | 0.945722i | ||||||
\(804\) | 11.9548 | − | 6.19452i | 0.421612 | − | 0.218464i | ||||
\(805\) | −7.64197 | − | 11.3788i | −0.269344 | − | 0.401050i | ||||
\(806\) | −0.696385 | − | 0.423479i | −0.0245291 | − | 0.0149164i | ||||
\(807\) | −10.7634 | −0.378890 | ||||||||
\(808\) | 0.561506 | − | 8.20968i | 0.0197537 | − | 0.288816i | ||||
\(809\) | −18.7034 | −0.657576 | −0.328788 | − | 0.944404i | \(-0.606640\pi\) | ||||
−0.328788 | + | 0.944404i | \(0.606640\pi\) | |||||||
\(810\) | −13.5447 | − | 26.4472i | −0.475911 | − | 0.929259i | ||||
\(811\) | − | 7.83804i | − | 0.275231i | −0.990486 | − | 0.137615i | \(-0.956056\pi\) | ||
0.990486 | − | 0.137615i | \(-0.0439438\pi\) | |||||||
\(812\) | −8.90145 | + | 4.61241i | −0.312380 | + | 0.161864i | ||||
\(813\) | − | 32.7473i | − | 1.14850i | ||||||
\(814\) | 11.0602 | + | 6.72584i | 0.387661 | + | 0.235741i | ||||
\(815\) | 6.95327 | + | 4.27383i | 0.243562 | + | 0.149706i | ||||
\(816\) | 12.8414 | − | 18.1924i | 0.449539 | − | 0.636863i | ||||
\(817\) | 17.2017i | 0.601813i | ||||||||
\(818\) | 3.37180 | + | 2.05043i | 0.117892 | + | 0.0716915i | ||||
\(819\) | −0.358421 | −0.0125242 | ||||||||
\(820\) | 2.07213 | − | 28.3156i | 0.0723618 | − | 0.988823i | ||||
\(821\) | −10.5077 | −0.366720 | −0.183360 | − | 0.983046i | \(-0.558697\pi\) | ||||
−0.183360 | + | 0.983046i | \(0.558697\pi\) | |||||||
\(822\) | 2.13251 | + | 1.29680i | 0.0743799 | + | 0.0452312i | ||||
\(823\) | −46.7259 | −1.62876 | −0.814381 | − | 0.580330i | \(-0.802924\pi\) | ||||
−0.814381 | + | 0.580330i | \(0.802924\pi\) | |||||||
\(824\) | 11.6127 | + | 0.794258i | 0.404548 | + | 0.0276693i | ||||
\(825\) | 8.03066 | + | 15.8663i | 0.279592 | + | 0.552394i | ||||
\(826\) | −0.629641 | − | 0.382891i | −0.0219080 | − | 0.0133225i | ||||
\(827\) | 12.6771i | 0.440826i | 0.975407 | + | 0.220413i | \(0.0707405\pi\) | ||||
−0.975407 | + | 0.220413i | \(0.929259\pi\) | |||||||
\(828\) | 1.32685 | − | 0.0661410i | 0.0461111 | − | 0.00229856i | ||||
\(829\) | 27.8620 | 0.967686 | 0.483843 | − | 0.875155i | \(-0.339241\pi\) | ||||
0.483843 | + | 0.875155i | \(0.339241\pi\) | |||||||
\(830\) | −3.31269 | + | 1.69656i | −0.114985 | + | 0.0588885i | ||||
\(831\) | − | 9.02389i | − | 0.313035i | ||||||
\(832\) | 2.20527 | − | 16.0460i | 0.0764538 | − | 0.556294i | ||||
\(833\) | 16.8630 | 0.584268 | ||||||||
\(834\) | 14.9582 | − | 24.5978i | 0.517959 | − | 0.851751i | ||||
\(835\) | −9.12304 | − | 5.60748i | −0.315716 | − | 0.194055i | ||||
\(836\) | 3.06648 | + | 5.91799i | 0.106057 | + | 0.204678i | ||||
\(837\) | − | 1.44304i | − | 0.0498787i | ||||||
\(838\) | 45.7857 | + | 27.8428i | 1.58164 | + | 0.961812i | ||||
\(839\) | −41.6414 | −1.43762 | −0.718810 | − | 0.695206i | \(-0.755313\pi\) | ||||
−0.718810 | + | 0.695206i | \(0.755313\pi\) | |||||||
\(840\) | 11.6606 | + | 8.31425i | 0.402329 | + | 0.286869i | ||||
\(841\) | −13.6194 | −0.469633 | ||||||||
\(842\) | 3.34282 | − | 5.49706i | 0.115201 | − | 0.189441i | ||||
\(843\) | − | 3.58710i | − | 0.123546i | ||||||
\(844\) | −6.71649 | + | 3.48024i | −0.231191 | + | 0.119795i | ||||
\(845\) | −16.9563 | − | 10.4222i | −0.583314 | − | 0.358534i | ||||
\(846\) | −1.20116 | − | 0.730437i | −0.0412966 | − | 0.0251129i | ||||
\(847\) | − | 8.90839i | − | 0.306096i | ||||||
\(848\) | 21.0190 | − | 29.7776i | 0.721794 | − | 1.02257i | ||||
\(849\) | − | 45.2312i | − | 1.55233i | ||||||
\(850\) | 1.72720 | − | 22.1529i | 0.0592424 | − | 0.759837i | ||||
\(851\) | 9.08084 | − | 19.8913i | 0.311287 | − | 0.681864i | ||||
\(852\) | 23.6389 | − | 12.2488i | 0.809855 | − | 0.419638i | ||||
\(853\) | 1.29526i | 0.0443489i | 0.999754 | + | 0.0221744i | \(0.00705892\pi\) | ||||
−0.999754 | + | 0.0221744i | \(0.992941\pi\) | |||||||
\(854\) | −2.03707 | − | 1.23876i | −0.0697070 | − | 0.0423896i | ||||
\(855\) | 0.438002 | + | 0.269218i | 0.0149793 | + | 0.00920706i | ||||
\(856\) | 39.0808 | + | 2.67296i | 1.33576 | + | 0.0913598i | ||||
\(857\) | 3.79939i | 0.129785i | 0.997892 | + | 0.0648924i | \(0.0206704\pi\) | ||||
−0.997892 | + | 0.0648924i | \(0.979330\pi\) | |||||||
\(858\) | 5.29104 | − | 8.70079i | 0.180633 | − | 0.297040i | ||||
\(859\) | − | 33.2447i | − | 1.13430i | −0.823616 | − | 0.567148i | \(-0.808047\pi\) | ||
0.823616 | − | 0.567148i | \(-0.191953\pi\) | |||||||
\(860\) | −46.2179 | − | 3.38222i | −1.57602 | − | 0.115333i | ||||
\(861\) | − | 14.3754i | − | 0.489911i | ||||||
\(862\) | −36.4536 | − | 22.1678i | −1.24161 | − | 0.755038i | ||||
\(863\) | −14.8617 | −0.505898 | −0.252949 | − | 0.967480i | \(-0.581400\pi\) | ||||
−0.252949 | + | 0.967480i | \(0.581400\pi\) | |||||||
\(864\) | 26.3025 | − | 11.4251i | 0.894829 | − | 0.388690i | ||||
\(865\) | −10.7319 | + | 17.4603i | −0.364897 | + | 0.593666i | ||||
\(866\) | −10.1438 | − | 6.16858i | −0.344702 | − | 0.209617i | ||||
\(867\) | 12.6232 | 0.428705 | ||||||||
\(868\) | 0.334783 | + | 0.646095i | 0.0113633 | + | 0.0219299i | ||||
\(869\) | −29.6337 | −1.00525 | ||||||||
\(870\) | −10.0152 | − | 19.5555i | −0.339546 | − | 0.662994i | ||||
\(871\) | −7.69367 | −0.260690 | ||||||||
\(872\) | 34.6101 | + | 2.36718i | 1.17205 | + | 0.0801627i | ||||
\(873\) | 1.01251 | 0.0342683 | ||||||||
\(874\) | 9.31666 | − | 6.32161i | 0.315141 | − | 0.213832i | ||||
\(875\) | 14.2417 | + | 1.17862i | 0.481456 | + | 0.0398445i | ||||
\(876\) | 41.9950 | − | 21.7603i | 1.41888 | − | 0.735212i | ||||
\(877\) | 11.1811i | 0.377558i | 0.982020 | + | 0.188779i | \(0.0604529\pi\) | ||||
−0.982020 | + | 0.188779i | \(0.939547\pi\) | |||||||
\(878\) | −10.1655 | + | 16.7165i | −0.343069 | + | 0.564155i | ||||
\(879\) | −13.1662 | −0.444084 | ||||||||
\(880\) | −16.5035 | + | 7.07548i | −0.556332 | + | 0.238514i | ||||
\(881\) | 46.4474i | 1.56485i | 0.622743 | + | 0.782426i | \(0.286018\pi\) | ||||
−0.622743 | + | 0.782426i | \(0.713982\pi\) | |||||||
\(882\) | −0.898104 | − | 0.546147i | −0.0302407 | − | 0.0183897i | ||||
\(883\) | 16.7375 | 0.563262 | 0.281631 | − | 0.959523i | \(-0.409125\pi\) | ||||
0.281631 | + | 0.959523i | \(0.409125\pi\) | |||||||
\(884\) | −11.2976 | + | 5.85401i | −0.379980 | + | 0.196892i | ||||
\(885\) | 0.845670 | − | 1.37586i | 0.0284269 | − | 0.0462489i | ||||
\(886\) | −5.00471 | − | 3.04342i | −0.168137 | − | 0.102246i | ||||
\(887\) | 42.1114 | 1.41396 | 0.706981 | − | 0.707232i | \(-0.250056\pi\) | ||||
0.706981 | + | 0.707232i | \(0.250056\pi\) | |||||||
\(888\) | −1.55893 | + | 22.7929i | −0.0523144 | + | 0.764880i | ||||
\(889\) | 0.949997i | 0.0318619i | ||||||||
\(890\) | 35.8274 | − | 18.3486i | 1.20094 | − | 0.615048i | ||||
\(891\) | 18.8638 | 0.631961 | ||||||||
\(892\) | 13.7072 | + | 26.4534i | 0.458951 | + | 0.885726i | ||||
\(893\) | −11.9142 | −0.398693 | ||||||||
\(894\) | −28.0533 | + | 46.1319i | −0.938244 | + | 1.54288i | ||||
\(895\) | −4.38047 | + | 7.12676i | −0.146423 | + | 0.238221i | ||||
\(896\) | −9.12588 | + | 11.2175i | −0.304874 | + | 0.374752i | ||||
\(897\) | −15.6479 | − | 7.14365i | −0.522470 | − | 0.238520i | ||||
\(898\) | 45.6924 | + | 27.7860i | 1.52478 | + | 0.927232i | ||||
\(899\) | − | 1.11638i | − | 0.0372332i | ||||||
\(900\) | −0.809459 | + | 1.12390i | −0.0269820 | + | 0.0374632i | ||||
\(901\) | −28.6340 | −0.953937 | ||||||||
\(902\) | 15.4002 | + | 9.36505i | 0.512772 | + | 0.311822i | ||||
\(903\) | −23.4641 | −0.780837 | ||||||||
\(904\) | −2.93244 | + | 42.8746i | −0.0975314 | + | 1.42599i | ||||
\(905\) | −28.1652 | + | 45.8232i | −0.936243 | + | 1.52321i | ||||
\(906\) | 9.25092 | − | 15.2126i | 0.307341 | − | 0.505403i | ||||
\(907\) | 34.7744i | 1.15466i | 0.816509 | + | 0.577332i | \(0.195906\pi\) | ||||
−0.816509 | + | 0.577332i | \(0.804094\pi\) | |||||||
\(908\) | 29.0038 | − | 15.0287i | 0.962525 | − | 0.498745i | ||||
\(909\) | 0.402959 | 0.0133653 | ||||||||
\(910\) | −3.73024 | − | 7.28364i | −0.123656 | − | 0.241450i | ||||
\(911\) | −25.7678 | −0.853724 | −0.426862 | − | 0.904317i | \(-0.640381\pi\) | ||||
−0.426862 | + | 0.904317i | \(0.640381\pi\) | |||||||
\(912\) | −6.78373 | + | 9.61053i | −0.224632 | + | 0.318236i | ||||
\(913\) | − | 2.36282i | − | 0.0781979i | ||||||
\(914\) | −15.4895 | − | 9.41931i | −0.512346 | − | 0.311563i | ||||
\(915\) | 2.73598 | − | 4.45129i | 0.0904488 | − | 0.147155i | ||||
\(916\) | −4.26972 | + | 2.21241i | −0.141076 | + | 0.0731002i | ||||
\(917\) | 4.65604 | 0.153756 | ||||||||
\(918\) | −19.2487 | − | 11.7053i | −0.635302 | − | 0.386334i | ||||
\(919\) | −22.1371 | −0.730237 | −0.365119 | − | 0.930961i | \(-0.618972\pi\) | ||||
−0.365119 | + | 0.930961i | \(0.618972\pi\) | |||||||
\(920\) | 15.1532 | + | 26.2751i | 0.499585 | + | 0.866265i | ||||
\(921\) | −36.7472 | −1.21086 | ||||||||
\(922\) | 10.0879 | + | 6.13457i | 0.332228 | + | 0.202031i | ||||
\(923\) | −15.2132 | −0.500747 | ||||||||
\(924\) | −8.07246 | + | 4.18285i | −0.265564 | + | 0.137606i | ||||
\(925\) | 10.2950 | + | 20.3400i | 0.338497 | + | 0.668774i | ||||
\(926\) | −25.1366 | − | 15.2859i | −0.826041 | − | 0.502325i | ||||
\(927\) | 0.569991i | 0.0187210i | ||||||||
\(928\) | 20.3484 | − | 8.83880i | 0.667968 | − | 0.290148i | ||||
\(929\) | −39.8417 | −1.30717 | −0.653583 | − | 0.756855i | \(-0.726735\pi\) | ||||
−0.653583 | + | 0.756855i | \(0.726735\pi\) | |||||||
\(930\) | −1.41940 | + | 0.726932i | −0.0465440 | + | 0.0238371i | ||||
\(931\) | −8.90823 | −0.291955 | ||||||||
\(932\) | 24.4277 | − | 12.6575i | 0.800156 | − | 0.414612i | ||||
\(933\) | − | 24.9080i | − | 0.815452i | ||||||
\(934\) | 28.5078 | − | 46.8793i | 0.932804 | − | 1.53394i | ||||
\(935\) | 12.0178 | + | 7.38673i | 0.393023 | + | 0.241572i | ||||
\(936\) | 0.791293 | + | 0.0541209i | 0.0258642 | + | 0.00176900i | ||||
\(937\) | −34.8765 | −1.13937 | −0.569683 | − | 0.821865i | \(-0.692934\pi\) | ||||
−0.569683 | + | 0.821865i | \(0.692934\pi\) | |||||||
\(938\) | 5.86905 | + | 3.56903i | 0.191631 | + | 0.116533i | ||||
\(939\) | −38.6409 | −1.26100 | ||||||||
\(940\) | 2.34257 | − | 32.0112i | 0.0764064 | − | 1.04409i | ||||
\(941\) | 35.7740i | 1.16620i | 0.812400 | + | 0.583100i | \(0.198160\pi\) | ||||
−0.812400 | + | 0.583100i | \(0.801840\pi\) | |||||||
\(942\) | 40.6809 | + | 24.7385i | 1.32545 | + | 0.806023i | ||||
\(943\) | 12.6441 | − | 27.6966i | 0.411750 | − | 0.901925i | ||||
\(944\) | 1.33225 | + | 0.940391i | 0.0433612 | + | 0.0306071i | ||||
\(945\) | 7.58687 | − | 12.3434i | 0.246801 | − | 0.401531i | ||||
\(946\) | 15.2860 | − | 25.1369i | 0.496992 | − | 0.817272i | ||||
\(947\) | 39.1911 | 1.27354 | 0.636770 | − | 0.771054i | \(-0.280270\pi\) | ||||
0.636770 | + | 0.771054i | \(0.280270\pi\) | |||||||
\(948\) | −24.0618 | − | 46.4368i | −0.781492 | − | 1.50820i | ||||
\(949\) | −27.0265 | −0.877318 | ||||||||
\(950\) | −0.912428 | + | 11.7027i | −0.0296031 | + | 0.379686i | ||||
\(951\) | − | 37.1482i | − | 1.20461i | ||||||
\(952\) | 11.3339 | + | 0.775190i | 0.367334 | + | 0.0251240i | ||||
\(953\) | −45.4643 | −1.47273 | −0.736366 | − | 0.676583i | \(-0.763460\pi\) | ||||
−0.736366 | + | 0.676583i | \(0.763460\pi\) | |||||||
\(954\) | 1.52501 | + | 0.927377i | 0.0493742 | + | 0.0300250i | ||||
\(955\) | −23.3355 | − | 14.3432i | −0.755119 | − | 0.464134i | ||||
\(956\) | −48.7726 | + | 25.2722i | −1.57742 | + | 0.817361i | ||||
\(957\) | 13.9482 | 0.450882 | ||||||||
\(958\) | 5.23207 | + | 3.18168i | 0.169041 | + | 0.102795i | ||||
\(959\) | 1.27330i | 0.0411170i | ||||||||
\(960\) | −24.4879 | − | 20.1163i | −0.790344 | − | 0.649250i | ||||
\(961\) | 30.9190 | 0.997386 | ||||||||
\(962\) | 6.78290 | − | 11.1541i | 0.218690 | − | 0.359621i | ||||
\(963\) | 1.91822i | 0.0618138i | ||||||||
\(964\) | −23.5882 | + | 12.2225i | −0.759724 | + | 0.393661i | ||||
\(965\) | −2.41407 | + | 3.92755i | −0.0777116 | + | 0.126432i | ||||
\(966\) | 8.62302 | + | 12.7084i | 0.277441 | + | 0.408887i | ||||
\(967\) | −48.2956 | −1.55308 | −0.776541 | − | 0.630067i | \(-0.783028\pi\) | ||||
−0.776541 | + | 0.630067i | \(0.783028\pi\) | |||||||
\(968\) | −1.34515 | + | 19.6672i | −0.0432348 | + | 0.632129i | ||||
\(969\) | 9.24144 | 0.296878 | ||||||||
\(970\) | 10.5376 | + | 20.5757i | 0.338343 | + | 0.660645i | ||||
\(971\) | −15.4880 | −0.497032 | −0.248516 | − | 0.968628i | \(-0.579943\pi\) | ||||
−0.248516 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(972\) | 1.32339 | + | 2.55400i | 0.0424478 | + | 0.0819197i | ||||
\(973\) | 14.6871 | 0.470846 | ||||||||
\(974\) | −29.5170 | − | 17.9496i | −0.945784 | − | 0.575142i | ||||
\(975\) | 16.0009 | − | 8.09879i | 0.512439 | − | 0.259369i | ||||
\(976\) | 4.31022 | + | 3.04244i | 0.137967 | + | 0.0973860i | ||||
\(977\) | 53.6843 | 1.71751 | 0.858756 | − | 0.512385i | \(-0.171238\pi\) | ||||
0.858756 | + | 0.512385i | \(0.171238\pi\) | |||||||
\(978\) | −7.81348 | − | 4.75146i | −0.249847 | − | 0.151935i | ||||
\(979\) | 25.5544i | 0.816721i | ||||||||
\(980\) | 1.75154 | − | 23.9348i | 0.0559509 | − | 0.764568i | ||||
\(981\) | 1.69878i | 0.0542379i | ||||||||
\(982\) | −20.5201 | + | 33.7440i | −0.654821 | + | 1.07681i | ||||
\(983\) | − | 10.7086i | − | 0.341550i | −0.985310 | − | 0.170775i | \(-0.945373\pi\) | ||
0.985310 | − | 0.170775i | \(-0.0546271\pi\) | |||||||
\(984\) | −2.17066 | + | 31.7368i | −0.0691980 | + | 1.01173i | ||||
\(985\) | −27.9889 | + | 45.5363i | −0.891800 | + | 1.45091i | ||||
\(986\) | −14.8914 | − | 9.05560i | −0.474238 | − | 0.288389i | ||||
\(987\) | − | 16.2516i | − | 0.517294i | ||||||
\(988\) | 5.96819 | − | 3.09250i | 0.189874 | − | 0.0983855i | ||||
\(989\) | −45.2076 | − | 20.6383i | −1.43752 | − | 0.656260i | ||||
\(990\) | −0.400817 | − | 0.782632i | −0.0127388 | − | 0.0248737i | ||||
\(991\) | − | 51.1415i | − | 1.62456i | −0.583266 | − | 0.812282i | \(-0.698225\pi\) | ||
0.583266 | − | 0.812282i | \(-0.301775\pi\) | |||||||
\(992\) | −0.641548 | − | 1.47695i | −0.0203692 | − | 0.0468932i | ||||
\(993\) | 57.9951i | 1.84042i | ||||||||
\(994\) | 11.6052 | + | 7.05727i | 0.368096 | + | 0.223843i | ||||
\(995\) | −9.16605 | − | 5.63392i | −0.290583 | − | 0.178607i | ||||
\(996\) | 3.70260 | − | 1.91855i | 0.117321 | − | 0.0607917i | ||||
\(997\) | − | 44.5820i | − | 1.41193i | −0.708249 | − | 0.705963i | \(-0.750514\pi\) | ||
0.708249 | − | 0.705963i | \(-0.249486\pi\) | |||||||
\(998\) | −22.8826 | + | 37.6291i | −0.724337 | + | 1.19113i | ||||
\(999\) | 23.1133 | 0.731271 |
(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 | 460.2.g.c.459.9 | ✓ | 56 | |
4.3 | odd | 2 | inner | 460.2.g.c.459.45 | yes | 56 | |
5.4 | even | 2 | inner | 460.2.g.c.459.48 | yes | 56 | |
20.19 | odd | 2 | inner | 460.2.g.c.459.12 | yes | 56 | |
23.22 | odd | 2 | inner | 460.2.g.c.459.10 | yes | 56 | |
92.91 | even | 2 | inner | 460.2.g.c.459.46 | yes | 56 | |
115.114 | odd | 2 | inner | 460.2.g.c.459.47 | yes | 56 | |
460.459 | even | 2 | inner | 460.2.g.c.459.11 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.g.c.459.9 | ✓ | 56 | 1.1 | even | 1 | trivial | |
460.2.g.c.459.10 | yes | 56 | 23.22 | odd | 2 | inner | |
460.2.g.c.459.11 | yes | 56 | 460.459 | even | 2 | inner | |
460.2.g.c.459.12 | yes | 56 | 20.19 | odd | 2 | inner | |
460.2.g.c.459.45 | yes | 56 | 4.3 | odd | 2 | inner | |
460.2.g.c.459.46 | yes | 56 | 92.91 | even | 2 | inner | |
460.2.g.c.459.47 | yes | 56 | 115.114 | odd | 2 | inner | |
460.2.g.c.459.48 | yes | 56 | 5.4 | even | 2 | inner |