Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(133,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 9x^{8} + 6x^{7} + 59x^{6} + 2x^{5} + 47x^{4} - 26x^{3} + 38x^{2} - 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 133.3 | ||
Root | \(0.194431 + 0.336764i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.133 |
Dual form | 572.2.i.c.529.3 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.194431 | + | 0.336764i | 0.112255 | + | 0.194431i | 0.916679 | − | 0.399624i | \(-0.130859\pi\) |
−0.804424 | + | 0.594055i | \(0.797526\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23435 | 0.999232 | 0.499616 | − | 0.866247i | \(-0.333475\pi\) | ||||
0.499616 | + | 0.866247i | \(0.333475\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.258355 | − | 0.447484i | 0.0976491 | − | 0.169133i | −0.813062 | − | 0.582177i | \(-0.802201\pi\) |
0.910711 | + | 0.413044i | \(0.135534\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.42439 | − | 2.46712i | 0.474798 | − | 0.822374i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.353971 | − | 3.58813i | 0.0981738 | − | 0.995169i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.434426 | + | 0.752448i | 0.112168 | + | 0.194281i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.907221 | − | 1.57135i | 0.220033 | − | 0.381109i | −0.734784 | − | 0.678301i | \(-0.762717\pi\) |
0.954818 | + | 0.297192i | \(0.0960500\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.34714 | + | 2.33331i | −0.309055 | + | 0.535298i | −0.978156 | − | 0.207873i | \(-0.933346\pi\) |
0.669101 | + | 0.743171i | \(0.266679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.200929 | 0.0438463 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.70596 | + | 4.68686i | 0.564231 | + | 0.977277i | 0.997121 | + | 0.0758300i | \(0.0241606\pi\) |
−0.432890 | + | 0.901447i | \(0.642506\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.00768164 | −0.00153633 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.27437 | 0.437702 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.181561 | + | 0.314473i | 0.0337150 | + | 0.0583962i | 0.882391 | − | 0.470518i | \(-0.155933\pi\) |
−0.848676 | + | 0.528914i | \(0.822599\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.11656 | 0.739356 | 0.369678 | − | 0.929160i | \(-0.379468\pi\) | ||||
0.369678 | + | 0.929160i | \(0.379468\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.194431 | − | 0.336764i | 0.0338460 | − | 0.0586231i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.577256 | − | 0.999837i | 0.0975741 | − | 0.169003i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.813255 | − | 1.40860i | −0.133698 | − | 0.231572i | 0.791401 | − | 0.611297i | \(-0.209352\pi\) |
−0.925099 | + | 0.379725i | \(0.876019\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.27718 | − | 0.578439i | 0.204512 | − | 0.0926243i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.518360 | − | 0.897825i | −0.0809542 | − | 0.140217i | 0.822706 | − | 0.568467i | \(-0.192463\pi\) |
−0.903660 | + | 0.428251i | \(0.859130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.382825 | + | 0.663073i | −0.0583803 | + | 0.101118i | −0.893738 | − | 0.448588i | \(-0.851927\pi\) |
0.835358 | + | 0.549706i | \(0.185260\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.18259 | − | 5.51241i | 0.474433 | − | 0.821742i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.64218 | −0.239537 | −0.119769 | − | 0.992802i | \(-0.538215\pi\) | ||||
−0.119769 | + | 0.992802i | \(0.538215\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.36651 | + | 5.83096i | 0.480929 | + | 0.832994i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.705567 | 0.0987991 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.30304 | 0.316347 | 0.158173 | − | 0.987411i | \(-0.449440\pi\) | ||||
0.158173 | + | 0.987411i | \(0.449440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.11717 | − | 1.93500i | −0.150640 | − | 0.260916i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.04770 | −0.138771 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.37434 | − | 2.38043i | 0.178924 | − | 0.309906i | −0.762588 | − | 0.646884i | \(-0.776072\pi\) |
0.941512 | + | 0.336979i | \(0.109405\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.688394 | − | 1.19233i | 0.0881399 | − | 0.152663i | −0.818585 | − | 0.574385i | \(-0.805241\pi\) |
0.906725 | + | 0.421723i | \(0.138574\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.735999 | − | 1.27479i | −0.0927272 | − | 0.160608i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.790895 | − | 8.01715i | 0.0980984 | − | 0.994405i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.08267 | + | 8.80345i | 0.620948 | + | 1.07551i | 0.989310 | + | 0.145830i | \(0.0465853\pi\) |
−0.368362 | + | 0.929682i | \(0.620081\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.05224 | + | 1.82254i | −0.126675 | + | 0.219408i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.80642 | + | 6.59292i | −0.451739 | + | 0.782435i | −0.998494 | − | 0.0548575i | \(-0.982530\pi\) |
0.546755 | + | 0.837293i | \(0.315863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.43120 | −0.167509 | −0.0837546 | − | 0.996486i | \(-0.526691\pi\) | ||||
−0.0837546 | + | 0.996486i | \(0.526691\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.00149355 | − | 0.00258690i | −0.000172460 | − | 0.000298709i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.516710 | −0.0588846 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.23605 | −1.03914 | −0.519569 | − | 0.854429i | \(-0.673907\pi\) | ||||
−0.519569 | + | 0.854429i | \(0.673907\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.83097 | − | 6.63544i | −0.425664 | − | 0.737271i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.93754 | −0.322437 | −0.161219 | − | 0.986919i | \(-0.551542\pi\) | ||||
−0.161219 | + | 0.986919i | \(0.551542\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.02705 | − | 3.51095i | 0.219864 | − | 0.380816i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0706021 | + | 0.122286i | −0.00756934 | + | 0.0131105i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.59232 | + | 2.75797i | 0.168785 | + | 0.292345i | 0.937993 | − | 0.346654i | \(-0.112682\pi\) |
−0.769208 | + | 0.638999i | \(0.779349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.51418 | − | 1.08541i | −0.158730 | − | 0.113782i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.800385 | + | 1.38631i | 0.0829961 | + | 0.143753i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00998 | + | 5.21343i | −0.308817 | + | 0.534887i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.14142 | + | 10.6372i | −0.623566 | + | 1.08005i | 0.365250 | + | 0.930909i | \(0.380983\pi\) |
−0.988816 | + | 0.149139i | \(0.952350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.84879 | −0.286314 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.61553 | + | 2.79817i | 0.160751 | + | 0.278429i | 0.935138 | − | 0.354283i | \(-0.115275\pi\) |
−0.774387 | + | 0.632712i | \(0.781942\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.88299 | −0.678201 | −0.339101 | − | 0.940750i | \(-0.610123\pi\) | ||||
−0.339101 | + | 0.940750i | \(0.610123\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.448945 | 0.0438126 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.36815 | − | 5.83381i | −0.325612 | − | 0.563976i | 0.656024 | − | 0.754740i | \(-0.272237\pi\) |
−0.981636 | + | 0.190764i | \(0.938904\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7754 | −1.12788 | −0.563940 | − | 0.825816i | \(-0.690715\pi\) | ||||
−0.563940 | + | 0.825816i | \(0.690715\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.316243 | − | 0.547750i | 0.0300165 | − | 0.0519901i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.21962 | − | 3.84450i | 0.208805 | − | 0.361660i | −0.742534 | − | 0.669809i | \(-0.766376\pi\) |
0.951338 | + | 0.308149i | \(0.0997094\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.04605 | + | 10.4721i | 0.563797 | + | 0.976526i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.34817 | − | 5.98420i | −0.771789 | − | 0.553240i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.468771 | − | 0.811935i | −0.0429721 | − | 0.0744299i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.201570 | − | 0.349130i | 0.0181750 | − | 0.0314800i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1889 | −1.00077 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.46834 | + | 9.47144i | 0.485236 | + | 0.840454i | 0.999856 | − | 0.0169644i | \(-0.00540021\pi\) |
−0.514620 | + | 0.857419i | \(0.672067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.297732 | −0.0262138 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.6173 | −1.62660 | −0.813300 | − | 0.581845i | \(-0.802331\pi\) | ||||
−0.813300 | + | 0.581845i | \(0.802331\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.696080 | + | 1.20565i | 0.0603578 | + | 0.104543i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.08173 | 0.437366 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.29343 | − | 3.97233i | 0.195941 | − | 0.339379i | −0.751268 | − | 0.659997i | \(-0.770557\pi\) |
0.947208 | + | 0.320618i | \(0.103891\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.746677 | + | 1.29328i | −0.0633323 | + | 0.109695i | −0.895953 | − | 0.444149i | \(-0.853506\pi\) |
0.832621 | + | 0.553844i | \(0.186839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.319291 | − | 0.553028i | −0.0268892 | − | 0.0465734i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.28440 | + | 1.48752i | −0.274655 | + | 0.124393i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.405671 | + | 0.702643i | 0.0336891 | + | 0.0583513i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.30910 | + | 2.26743i | −0.107973 | + | 0.187015i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.91287 | + | 3.31318i | −0.156708 | + | 0.271427i | −0.933680 | − | 0.358109i | \(-0.883422\pi\) |
0.776972 | + | 0.629536i | \(0.216755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0221 | −1.38524 | −0.692621 | − | 0.721302i | \(-0.743544\pi\) | ||||
−0.692621 | + | 0.721302i | \(0.743544\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.58448 | − | 4.47645i | −0.208943 | − | 0.361900i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.19783 | 0.738787 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.27783 | 0.660643 | 0.330321 | − | 0.943869i | \(-0.392843\pi\) | ||||
0.330321 | + | 0.943869i | \(0.392843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.447781 | + | 0.775580i | 0.0355114 | + | 0.0615075i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.79639 | 0.220387 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.881566 | + | 1.52692i | −0.0690496 | + | 0.119597i | −0.898483 | − | 0.439008i | \(-0.855330\pi\) |
0.829434 | + | 0.558605i | \(0.188663\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.434426 | − | 0.752448i | 0.0338200 | − | 0.0585780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.51983 | + | 4.36447i | 0.194990 | + | 0.337733i | 0.946897 | − | 0.321536i | \(-0.104199\pi\) |
−0.751907 | + | 0.659269i | \(0.770866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7494 | − | 2.54019i | −0.980724 | − | 0.195399i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.83771 | + | 6.64710i | 0.293477 | + | 0.508317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.91292 | − | 10.2415i | 0.449551 | − | 0.778645i | −0.548806 | − | 0.835950i | \(-0.684917\pi\) |
0.998357 | + | 0.0573046i | \(0.0182506\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.00198459 | + | 0.00343741i | −0.000150021 | + | 0.000259844i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.06886 | 0.0803403 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.81122 | + | 3.13712i | 0.135377 | + | 0.234479i | 0.925741 | − | 0.378158i | \(-0.123442\pi\) |
−0.790365 | + | 0.612637i | \(0.790109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6433 | 0.865442 | 0.432721 | − | 0.901528i | \(-0.357554\pi\) | ||||
0.432721 | + | 0.901528i | \(0.357554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.535380 | 0.0395764 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.81710 | − | 3.14730i | −0.133596 | − | 0.231394i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.81444 | −0.132685 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.587595 | − | 1.01774i | 0.0427412 | − | 0.0740300i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8990 | − | 20.6096i | 0.860979 | − | 1.49126i | −0.0100051 | − | 0.999950i | \(-0.503185\pi\) |
0.870985 | − | 0.491310i | \(-0.163482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2989 | + | 23.0344i | 0.957275 | + | 1.65805i | 0.729074 | + | 0.684435i | \(0.239951\pi\) |
0.228201 | + | 0.973614i | \(0.426716\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.85366 | − | 1.29243i | 0.204355 | − | 0.0925532i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.6856 | − | 21.9721i | −0.903809 | − | 1.56544i | −0.822508 | − | 0.568754i | \(-0.807426\pi\) |
−0.0813019 | − | 0.996690i | \(-0.525908\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1939 | + | 17.6564i | −0.722629 | + | 1.25163i | 0.237313 | + | 0.971433i | \(0.423733\pi\) |
−0.959942 | + | 0.280197i | \(0.909600\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.97646 | + | 3.42332i | −0.139408 | + | 0.241463i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.187629 | 0.0131690 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.15820 | − | 2.00606i | −0.0808920 | − | 0.140109i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.4174 | 1.07158 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.69427 | 0.186367 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.03811 | + | 5.26217i | 0.209152 | + | 0.362263i | 0.951448 | − | 0.307810i | \(-0.0995962\pi\) |
−0.742295 | + | 0.670073i | \(0.766263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.96034 | −0.202839 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.855365 | + | 1.48154i | −0.0583354 | + | 0.101040i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.06353 | − | 1.84210i | 0.0721974 | − | 0.125050i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.278269 | − | 0.481976i | −0.0188037 | − | 0.0325689i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.31710 | − | 3.81144i | −0.357667 | − | 0.256385i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.63685 | + | 11.4954i | 0.444436 | + | 0.769786i | 0.998013 | − | 0.0630122i | \(-0.0200707\pi\) |
−0.553577 | + | 0.832798i | \(0.686737\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0109417 | + | 0.0189515i | −0.000729445 | + | 0.00126344i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.12824 | + | 3.68622i | −0.141256 | + | 0.244663i | −0.927970 | − | 0.372655i | \(-0.878447\pi\) |
0.786714 | + | 0.617318i | \(0.211781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.8472 | −1.64195 | −0.820974 | − | 0.570965i | \(-0.806569\pi\) | ||||
−0.820974 | + | 0.570965i | \(0.806569\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.100464 | − | 0.174009i | −0.00661007 | − | 0.0114490i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.9835 | 1.63672 | 0.818362 | − | 0.574703i | \(-0.194883\pi\) | ||||
0.818362 | + | 0.574703i | \(0.194883\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.66921 | −0.239353 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.79577 | − | 3.11037i | −0.116648 | − | 0.202040i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.2408 | −1.05053 | −0.525265 | − | 0.850939i | \(-0.676034\pi\) | ||||
−0.525265 | + | 0.850939i | \(0.676034\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.58793 | − | 2.75038i | 0.102288 | − | 0.177167i | −0.810339 | − | 0.585961i | \(-0.800717\pi\) |
0.912627 | + | 0.408794i | \(0.134050\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.90127 | − | 8.48925i | 0.314417 | − | 0.544585i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.52195 | + | 13.0284i | 0.480560 | + | 0.832354i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.89538 | + | 5.65963i | 0.502371 | + | 0.360114i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.571148 | − | 0.989258i | −0.0361951 | − | 0.0626917i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.05217 | − | 13.9468i | 0.508249 | − | 0.880312i | −0.491706 | − | 0.870761i | \(-0.663626\pi\) |
0.999954 | − | 0.00955091i | \(-0.00304020\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.70596 | − | 4.68686i | 0.170122 | − | 0.294660i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.57648 | 0.0987232 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.40142 | − | 11.0876i | −0.399310 | − | 0.691624i | 0.594331 | − | 0.804220i | \(-0.297417\pi\) |
−0.993641 | + | 0.112596i | \(0.964083\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.840435 | −0.0522221 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.03446 | 0.0640313 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.52370 | − | 16.4955i | −0.587256 | − | 1.01716i | −0.994590 | − | 0.103878i | \(-0.966875\pi\) |
0.407334 | − | 0.913279i | \(-0.366459\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.14579 | 0.316104 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.619191 | + | 1.07247i | −0.0378939 | + | 0.0656341i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.93239 | − | 8.54314i | 0.300733 | − | 0.520885i | −0.675569 | − | 0.737297i | \(-0.736102\pi\) |
0.976302 | + | 0.216412i | \(0.0694354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.11184 | − | 5.38986i | −0.189031 | − | 0.327410i | 0.755897 | − | 0.654691i | \(-0.227201\pi\) |
−0.944927 | + | 0.327280i | \(0.893868\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0711229 | − | 0.720959i | 0.00430456 | − | 0.0436344i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.00384082 | + | 0.00665249i | 0.000231610 | + | 0.000401160i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.38118 | + | 11.0525i | −0.383408 | + | 0.664082i | −0.991547 | − | 0.129749i | \(-0.958583\pi\) |
0.608139 | + | 0.793830i | \(0.291916\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.86360 | − | 10.1560i | 0.351044 | − | 0.608027i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4506 | 1.33929 | 0.669644 | − | 0.742682i | \(-0.266447\pi\) | ||||
0.669644 | + | 0.742682i | \(0.266447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.85309 | + | 13.6019i | 0.466818 | + | 0.808552i | 0.999282 | − | 0.0379008i | \(-0.0120671\pi\) |
−0.532464 | + | 0.846453i | \(0.678734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.34093 | −0.138665 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.535684 | −0.0316204 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.85390 | + | 11.8713i | 0.403171 | + | 0.698312i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.77632 | −0.279993 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.99766 | − | 5.19209i | 0.175125 | − | 0.303325i | −0.765080 | − | 0.643936i | \(-0.777300\pi\) |
0.940205 | + | 0.340610i | \(0.110634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.07076 | − | 5.31872i | 0.178787 | − | 0.309668i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.13718 | − | 1.96966i | −0.0659861 | − | 0.114291i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.7749 | − | 8.05033i | 1.02795 | − | 0.465562i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.197810 | + | 0.342617i | 0.0114016 | + | 0.0197481i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.628216 | + | 1.08810i | −0.0360900 | + | 0.0625098i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.53811 | − | 2.66409i | 0.0880721 | − | 0.152545i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.1887 | −0.809793 | −0.404896 | − | 0.914363i | \(-0.632692\pi\) | ||||
−0.404896 | + | 0.914363i | \(0.632692\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.33826 | − | 2.31794i | −0.0761312 | − | 0.131863i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.0732 | 1.87541 | 0.937706 | − | 0.347430i | \(-0.112946\pi\) | ||||
0.937706 | + | 0.347430i | \(0.112946\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.3433 | 1.09335 | 0.546673 | − | 0.837346i | \(-0.315894\pi\) | ||||
0.546673 | + | 0.837346i | \(0.315894\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.64448 | − | 2.84832i | −0.0926559 | − | 0.160485i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.3583 | −0.581779 | −0.290890 | − | 0.956757i | \(-0.593951\pi\) | ||||
−0.290890 | + | 0.956757i | \(0.593951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.181561 | − | 0.314473i | 0.0101655 | − | 0.0176071i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.30975 | − | 2.26855i | 0.0731029 | − | 0.126618i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.44430 | + | 4.23366i | 0.136005 | + | 0.235567i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.00271908 | + | 0.0275627i | −0.000150827 | + | 0.00152891i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.28950 | − | 3.96553i | −0.126610 | − | 0.219294i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.424267 | + | 0.734852i | −0.0233906 | + | 0.0405137i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.34652 | − | 14.4566i | 0.458766 | − | 0.794607i | −0.540130 | − | 0.841582i | \(-0.681625\pi\) |
0.998896 | + | 0.0469751i | \(0.0149581\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.63358 | −0.253919 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3565 | + | 19.6700i | 0.620470 | + | 1.07469i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.4301 | 1.76658 | 0.883291 | − | 0.468826i | \(-0.155323\pi\) | ||||
0.883291 | + | 0.468826i | \(0.155323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.72625 | 0.0937572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.05828 | − | 3.56504i | −0.111462 | − | 0.193058i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.09599 | 0.383147 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.35108 | + | 4.07219i | −0.126578 | + | 0.219239i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4773 | − | 26.8074i | 0.830863 | − | 1.43910i | −0.0664919 | − | 0.997787i | \(-0.521181\pi\) |
0.897355 | − | 0.441310i | \(-0.145486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.75013 | + | 4.76336i | 0.147211 | + | 0.254977i | 0.930196 | − | 0.367064i | \(-0.119637\pi\) |
−0.782985 | + | 0.622041i | \(0.786304\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.805060 | − | 8.16074i | 0.0429709 | − | 0.435588i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.2458 | + | 17.7462i | 0.545329 | + | 0.944537i | 0.998586 | + | 0.0531573i | \(0.0169285\pi\) |
−0.453257 | + | 0.891380i | \(0.649738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.50488 | + | 14.7309i | −0.451392 | + | 0.781834i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.182287 | − | 0.315730i | 0.00964764 | − | 0.0167102i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.0381 | −1.16313 | −0.581564 | − | 0.813501i | \(-0.697559\pi\) | ||||
−0.581564 | + | 0.813501i | \(0.697559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.87044 | + | 10.1679i | 0.308971 | + | 0.535153i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.388861 | −0.0204099 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.19780 | −0.167380 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.77866 | − | 13.4730i | −0.406043 | − | 0.703286i | 0.588400 | − | 0.808570i | \(-0.299758\pi\) |
−0.994442 | + | 0.105284i | \(0.966425\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.95339 | −0.153747 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.595002 | − | 1.03057i | 0.0308910 | − | 0.0535047i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3568 | − | 19.6705i | 0.588032 | − | 1.01850i | −0.406458 | − | 0.913669i | \(-0.633236\pi\) |
0.994490 | − | 0.104831i | \(-0.0334303\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.17547 | − | 3.76802i | −0.112341 | − | 0.194580i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.19264 | − | 0.540151i | 0.0614240 | − | 0.0278192i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.478525 | + | 0.828830i | 0.0245802 | + | 0.0425741i | 0.878054 | − | 0.478562i | \(-0.158842\pi\) |
−0.853474 | + | 0.521136i | \(0.825508\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.12643 | + | 3.68308i | −0.108940 | + | 0.188690i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.72112 | − | 8.17722i | 0.241238 | − | 0.417836i | −0.719829 | − | 0.694151i | \(-0.755780\pi\) |
0.961067 | + | 0.276315i | \(0.0891133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.15451 | −0.0588394 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.09059 | + | 1.88895i | 0.0554377 | + | 0.0960209i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.8869 | −1.46463 | −0.732313 | − | 0.680969i | \(-0.761559\pi\) | ||||
−0.732313 | + | 0.680969i | \(0.761559\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.81961 | 0.496599 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.61977 | − | 6.26963i | −0.182593 | − | 0.316261i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.6366 | −1.03834 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.03473 | + | 3.52426i | −0.102120 | + | 0.176878i | −0.912558 | − | 0.408947i | \(-0.865896\pi\) |
0.810438 | + | 0.585825i | \(0.199229\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.270679 | + | 0.468829i | −0.0135509 | + | 0.0234708i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.2458 | + | 24.6745i | 0.711402 | + | 1.23218i | 0.964331 | + | 0.264699i | \(0.0852726\pi\) |
−0.252930 | + | 0.967485i | \(0.581394\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.45714 | − | 14.7708i | 0.0725854 | − | 0.735784i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.55973 | − | 14.8259i | −0.425337 | − | 0.736705i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.813255 | + | 1.40860i | −0.0403115 | + | 0.0698216i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.3256 | + | 31.7408i | −0.906141 | + | 1.56948i | −0.0867621 | + | 0.996229i | \(0.527652\pi\) |
−0.819379 | + | 0.573253i | \(0.805681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.78365 | 0.0879809 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.710137 | − | 1.22999i | −0.0349436 | − | 0.0605240i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.56349 | −0.322189 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.580708 | −0.0284374 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.453737 | + | 0.785896i | 0.0221665 | + | 0.0383935i | 0.876896 | − | 0.480680i | \(-0.159610\pi\) |
−0.854729 | + | 0.519074i | \(0.826277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.35823 | −0.212407 | −0.106204 | − | 0.994344i | \(-0.533870\pi\) | ||||
−0.106204 | + | 0.994344i | \(0.533870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.33912 | + | 4.05147i | −0.113732 | + | 0.196989i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.00696894 | + | 0.0120706i | −0.000338043 | + | 0.000585508i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.355701 | − | 0.616092i | −0.0172136 | − | 0.0298148i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.13953 | − | 0.816848i | −0.0550171 | − | 0.0394378i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.65437 | − | 9.79365i | −0.272361 | − | 0.471743i | 0.697105 | − | 0.716969i | \(-0.254471\pi\) |
−0.969466 | + | 0.245226i | \(0.921138\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2332 | + | 24.6527i | −0.684006 | + | 1.18473i | 0.289742 | + | 0.957105i | \(0.406430\pi\) |
−0.973748 | + | 0.227628i | \(0.926903\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.157750 | + | 0.273231i | −0.00756352 | + | 0.0131004i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.5812 | −0.697513 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.9359 | − | 27.6018i | −0.760579 | − | 1.31736i | −0.942552 | − | 0.334058i | \(-0.891582\pi\) |
0.181973 | − | 0.983303i | \(-0.441752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.1809 | 0.913377 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.12755 | 0.433663 | 0.216832 | − | 0.976209i | \(-0.430428\pi\) | ||||
0.216832 | + | 0.976209i | \(0.430428\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.55779 | + | 6.16228i | 0.168656 | + | 0.292120i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.48768 | −0.0703649 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.93863 | + | 13.7501i | −0.374647 | + | 0.648908i | −0.990274 | − | 0.139130i | \(-0.955569\pi\) |
0.615627 | + | 0.788038i | \(0.288903\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.518360 | + | 0.897825i | −0.0244086 | + | 0.0422769i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.30962 | − | 5.73244i | −0.155500 | − | 0.269333i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.38322 | − | 2.42518i | −0.158608 | − | 0.113694i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.2126 | + | 17.6888i | 0.477727 | + | 0.827448i | 0.999674 | − | 0.0255301i | \(-0.00812736\pi\) |
−0.521947 | + | 0.852978i | \(0.674794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.06335 | − | 3.57383i | 0.0963091 | − | 0.166812i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7928 | + | 32.5500i | −0.875267 | + | 1.51601i | −0.0187889 | + | 0.999823i | \(0.505981\pi\) |
−0.856478 | + | 0.516183i | \(0.827352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.12816 | −0.0524301 | −0.0262150 | − | 0.999656i | \(-0.508345\pi\) | ||||
−0.0262150 | + | 0.999656i | \(0.508345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.78834 | + | 3.09750i | 0.0829323 | + | 0.143643i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.8091 | −0.777833 | −0.388916 | − | 0.921273i | \(-0.627150\pi\) | ||||
−0.388916 | + | 0.921273i | \(0.627150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.25254 | 0.242540 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.60946 | + | 2.78767i | 0.0741602 | + | 0.128449i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.765650 | 0.0352046 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0103482 | − | 0.0179236i | 0.000474809 | − | 0.000822393i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.28043 | − | 5.68188i | 0.150201 | − | 0.260155i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.5359 | + | 19.9807i | 0.527086 | + | 0.912941i | 0.999502 | + | 0.0315645i | \(0.0100490\pi\) |
−0.472415 | + | 0.881376i | \(0.656618\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.34211 | + | 2.41946i | −0.243579 | + | 0.110318i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.543705 | + | 0.941724i | 0.0247394 | + | 0.0428499i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.7221 | + | 23.7673i | −0.623087 | + | 1.07922i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.03355 | − | 8.71837i | 0.228092 | − | 0.395067i | −0.729151 | − | 0.684353i | \(-0.760085\pi\) |
0.957243 | + | 0.289286i | \(0.0934180\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.685614 | −0.0310046 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.96903 | + | 8.60662i | 0.224249 | + | 0.388411i | 0.956094 | − | 0.293060i | \(-0.0946736\pi\) |
−0.731845 | + | 0.681472i | \(0.761340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.658864 | 0.0296738 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.36519 | −0.286094 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.96682 | + | 3.40663i | 0.0882238 | + | 0.152808i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.7183 | −1.33037 | −0.665187 | − | 0.746677i | \(-0.731648\pi\) | ||||
−0.665187 | + | 0.746677i | \(0.731648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.979865 | + | 1.69718i | −0.0437771 | + | 0.0758242i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.0862 | − | 17.4698i | 0.449721 | − | 0.778939i | −0.548647 | − | 0.836054i | \(-0.684857\pi\) |
0.998368 | + | 0.0571150i | \(0.0181902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.60965 | + | 6.25210i | 0.160627 | + | 0.278215i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.62343 | − | 4.78743i | −0.0720992 | − | 0.212617i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.2621 | − | 19.5065i | −0.499184 | − | 0.864612i | 0.500816 | − | 0.865554i | \(-0.333033\pi\) |
−1.00000 | 0.000942237i | \(0.999700\pi\) | ||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.369758 | + | 0.640439i | −0.0163571 | + | 0.0283314i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.06389 | + | 5.30681i | −0.135274 | + | 0.234301i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.3790 | −0.677680 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.821092 | + | 1.42217i | 0.0361116 | + | 0.0625471i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.59861 | 0.201857 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.26684 | 0.186934 | 0.0934668 | − | 0.995622i | \(-0.470205\pi\) | ||||
0.0934668 | + | 0.995622i | \(0.470205\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.7236 | − | 20.3059i | −0.512638 | − | 0.887916i | −0.999893 | − | 0.0146554i | \(-0.995335\pi\) |
0.487254 | − | 0.873260i | \(-0.337998\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.00154346 | −6.73622e−5 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.73463 | − | 6.46857i | 0.162683 | − | 0.281775i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.14441 | + | 5.44627i | −0.136713 | + | 0.236795i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.91521 | − | 6.78134i | −0.169906 | − | 0.294285i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.40500 | + | 1.54214i | −0.147487 | + | 0.0667975i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.52563 | − | 13.0348i | −0.325362 | − | 0.563543i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.704312 | + | 1.21990i | −0.0303933 | + | 0.0526427i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.36651 | − | 5.83096i | 0.145006 | − | 0.251157i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4042 | −1.22119 | −0.610597 | − | 0.791941i | \(-0.709070\pi\) | ||||
−0.610597 | + | 0.791941i | \(0.709070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.26382 | + | 3.92105i | 0.0971499 | + | 0.168269i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.3104 | −1.12701 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.2484 | −0.438192 | −0.219096 | − | 0.975703i | \(-0.570311\pi\) | ||||
−0.219096 | + | 0.975703i | \(0.570311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.96109 | − | 3.39671i | −0.0836972 | − | 0.144968i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.978351 | −0.0416792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.38618 | + | 4.13299i | −0.101471 | + | 0.175753i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.706598 | − | 1.22386i | 0.0299934 | − | 0.0519502i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.47914 | − | 16.4184i | −0.401644 | − | 0.695668i | 0.592280 | − | 0.805732i | \(-0.298228\pi\) |
−0.993925 | + | 0.110064i | \(0.964894\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.24368 | + | 1.60834i | 0.0948977 | + | 0.0680254i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.352783 | − | 0.611039i | −0.0148945 | − | 0.0257981i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.63085 | − | 16.6811i | 0.405892 | − | 0.703025i | −0.588533 | − | 0.808473i | \(-0.700294\pi\) |
0.994425 | + | 0.105448i | \(0.0336276\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.95942 | − | 8.58996i | 0.208644 | − | 0.361382i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.95901 | −0.166263 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.09062 | + | 8.81720i | 0.213410 | + | 0.369636i | 0.952779 | − | 0.303663i | \(-0.0982098\pi\) |
−0.739370 | + | 0.673300i | \(0.764876\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0131 | 0.586430 | 0.293215 | − | 0.956047i | \(-0.405275\pi\) | ||||
0.293215 | + | 0.956047i | \(0.405275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.25410 | 0.386596 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0207862 | − | 0.0360027i | −0.000866844 | − | 0.00150142i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.0742 | 0.960592 | 0.480296 | − | 0.877106i | \(-0.340529\pi\) | ||||
0.480296 | + | 0.877106i | \(0.340529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.17143 | + | 8.95717i | −0.214917 | + | 0.372247i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.758929 | + | 1.31450i | −0.0314857 | + | 0.0545348i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.15152 | − | 1.99449i | −0.0476911 | − | 0.0826033i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.6527 | − | 13.3708i | −0.771195 | − | 0.552815i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.2669 | + | 29.9071i | 0.712680 | + | 1.23440i | 0.963847 | + | 0.266455i | \(0.0858523\pi\) |
−0.251167 | + | 0.967944i | \(0.580814\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.54557 | + | 9.60521i | −0.228501 | + | 0.395776i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.93293 | − | 8.54408i | 0.202914 | − | 0.351457i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.7576 | 0.688152 | 0.344076 | − | 0.938942i | \(-0.388192\pi\) | ||||
0.344076 | + | 0.938942i | \(0.388192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.04740 | − | 1.81415i | −0.0429391 | − | 0.0743727i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.92806 | −0.324474 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.8452 | −0.647417 | −0.323709 | − | 0.946157i | \(-0.604930\pi\) | ||||
−0.323709 | + | 0.946157i | \(0.604930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.2788 | + | 28.1957i | 0.664027 | + | 1.15013i | 0.979548 | + | 0.201210i | \(0.0644872\pi\) |
−0.315522 | + | 0.948918i | \(0.602179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.9589 | 1.17930 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.11717 | + | 1.93500i | −0.0454196 | + | 0.0786691i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2599 | + | 19.5026i | −0.457024 | + | 0.791588i | −0.998802 | − | 0.0489333i | \(-0.984418\pi\) |
0.541779 | + | 0.840521i | \(0.317751\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0364808 | + | 0.0631867i | 0.00147828 | + | 0.00256045i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.581285 | + | 5.89238i | −0.0235163 | + | 0.238380i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.2788 | − | 22.9995i | −0.536324 | − | 0.928940i | −0.999098 | − | 0.0424639i | \(-0.986479\pi\) |
0.462774 | − | 0.886476i | \(-0.346854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.450378 | − | 0.780078i | 0.0181610 | − | 0.0314558i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.6034 | + | 23.5618i | −0.547653 | + | 0.948562i | 0.450782 | + | 0.892634i | \(0.351145\pi\) |
−0.998435 | + | 0.0559282i | \(0.982188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.2049 | −1.29442 | −0.647211 | − | 0.762311i | \(-0.724065\pi\) | ||||
−0.647211 | + | 0.762311i | \(0.724065\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.15434 | + | 10.6596i | 0.246965 | + | 0.427756i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.64553 | 0.0659269 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9615 | −0.998461 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.523850 | + | 0.907335i | 0.0209205 | + | 0.0362355i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.95121 | −0.117672 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.3407 | − | 36.9631i | 0.849558 | − | 1.47148i | −0.0320452 | − | 0.999486i | \(-0.510202\pi\) |
0.881603 | − | 0.471991i | \(-0.156465\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.18141 | + | 2.04625i | −0.0469566 | + | 0.0813313i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.2182 | + | 21.1625i | 0.484864 | + | 0.839808i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.1139 | − | 10.0155i | 0.876185 | − | 0.396828i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.8437 | + | 18.7818i | 0.428969 | + | 0.742997i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.25454 | − | 10.8332i | 0.247039 | − | 0.427885i | −0.715664 | − | 0.698445i | \(-0.753876\pi\) |
0.962703 | + | 0.270560i | \(0.0872090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.97199 | − | 15.5399i | 0.353821 | − | 0.612836i | −0.633095 | − | 0.774074i | \(-0.718216\pi\) |
0.986915 | + | 0.161239i | \(0.0515489\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.665237 | −0.0261937 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5920 | + | 33.9343i | 0.770241 | + | 1.33410i | 0.937431 | + | 0.348172i | \(0.113198\pi\) |
−0.167189 | + | 0.985925i | \(0.553469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.74869 | −0.107895 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.827135 | 0.0324180 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.8620 | − | 24.0097i | −0.542463 | − | 0.939573i | −0.998762 | − | 0.0497463i | \(-0.984159\pi\) |
0.456299 | − | 0.889826i | \(-0.349175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.5975 | −1.62535 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.03859 | + | 3.53094i | −0.0795330 | + | 0.137755i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.7045 | + | 25.4689i | −0.572805 | + | 0.992127i | 0.423472 | + | 0.905909i | \(0.360811\pi\) |
−0.996276 | + | 0.0862173i | \(0.972522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.02132 | + | 1.76898i | 0.0397249 | + | 0.0688055i | 0.885204 | − | 0.465203i | \(-0.154019\pi\) |
−0.845479 | + | 0.534008i | \(0.820685\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.249750 | − | 2.53167i | 0.00969949 | − | 0.0983218i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.55529 | + | 2.69383i | 0.0603114 | + | 0.104462i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.982593 | + | 1.70190i | −0.0380462 | + | 0.0658979i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.58081 | + | 4.47010i | −0.0997801 | + | 0.172824i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.37679 | −0.0531503 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.7194 | − | 18.5666i | −0.413204 | − | 0.715690i | 0.582034 | − | 0.813164i | \(-0.302257\pi\) |
−0.995238 | + | 0.0974740i | \(0.968924\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0174709 | −0.000672454 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.0759 | 0.425681 | 0.212840 | − | 0.977087i | \(-0.431729\pi\) | ||||
0.212840 | + | 0.977087i | \(0.431729\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.17333 | + | 5.49637i | 0.121781 | + | 0.210931i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.65518 | −0.0634267 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.1937 | − | 19.3880i | 0.428315 | − | 0.741863i | −0.568409 | − | 0.822746i | \(-0.692441\pi\) |
0.996724 | + | 0.0808835i | \(0.0257742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.12431 | − | 8.87557i | 0.195790 | − | 0.339118i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.83106 | − | 8.36764i | −0.184316 | − | 0.319245i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.815208 | − | 8.26361i | 0.0310570 | − | 0.314818i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.1528 | − | 27.9774i | −0.614480 | − | 1.06431i | −0.990475 | − | 0.137689i | \(-0.956033\pi\) |
0.375995 | − | 0.926622i | \(-0.377301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.735999 | + | 1.27479i | −0.0279583 | + | 0.0484252i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.66834 | + | 2.88965i | −0.0632837 | + | 0.109610i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.88107 | −0.0712505 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.85756 | + | 8.41354i | 0.183730 | + | 0.318229i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.5048 | −1.11438 | −0.557190 | − | 0.830385i | \(-0.688120\pi\) | ||||
−0.557190 | + | 0.830385i | \(0.688120\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.38226 | 0.165280 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.713408 | − | 1.23566i | −0.0268685 | − | 0.0465376i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.66952 | 0.0627887 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.87231 | − | 17.0994i | 0.370763 | − | 0.642180i | −0.618921 | − | 0.785454i | \(-0.712430\pi\) |
0.989683 | + | 0.143274i | \(0.0457630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.1558 | + | 22.7865i | −0.493380 | + | 0.854559i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.1392 | + | 19.2937i | 0.417167 | + | 0.722555i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.33850 | + | 3.32364i | −0.274444 | + | 0.124297i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.15771 | − | 5.46931i | −0.117927 | − | 0.204255i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.28734 | − | 9.15793i | 0.197184 | − | 0.341533i | −0.750430 | − | 0.660950i | \(-0.770154\pi\) |
0.947614 | + | 0.319417i | \(0.103487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.77826 | + | 3.08003i | −0.0662257 | + | 0.114706i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.23497 | 0.0459290 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.00139469 | − | 0.00241567i | −5.17974e−5 | − | 8.97157e-5i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.1291 | 0.598195 | 0.299097 | − | 0.954223i | \(-0.403314\pi\) | ||||
0.299097 | + | 0.954223i | \(0.403314\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.1740 | −0.710149 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.694614 | + | 1.20311i | 0.0256912 | + | 0.0444985i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.4144 | 1.67742 | 0.838709 | − | 0.544580i | \(-0.183311\pi\) | ||||
0.838709 | + | 0.544580i | \(0.183311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.92500 | + | 5.06624i | −0.107890 | + | 0.186871i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.08267 | − | 8.80345i | 0.187223 | − | 0.324279i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.06507 | − | 13.9691i | −0.296678 | − | 0.513862i | 0.678696 | − | 0.734420i | \(-0.262546\pi\) |
−0.975374 | + | 0.220558i | \(0.929212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.370855 | + | 3.75929i | −0.0136237 | + | 0.138101i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.0939 | + | 38.2678i | 0.810548 | + | 1.40391i | 0.912481 | + | 0.409119i | \(0.134164\pi\) |
−0.101933 | + | 0.994791i | \(0.532503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.27401 | + | 7.40281i | −0.156588 | + | 0.271218i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.18421 | + | 7.24727i | −0.153092 | + | 0.265164i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.48072 | −0.127183 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.30780 | − | 7.46132i | −0.157194 | − | 0.272268i | 0.776662 | − | 0.629918i | \(-0.216911\pi\) |
−0.933856 | + | 0.357650i | \(0.883578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.26236 | 0.228213 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.0334 | −1.38418 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.5725 | + | 40.8288i | 0.856758 | + | 1.48395i | 0.875005 | + | 0.484114i | \(0.160858\pi\) |
−0.0182473 | + | 0.999834i | \(0.505809\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.10448 | 0.0763880 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.91697 | − | 15.4446i | 0.323240 | − | 0.559868i | −0.657915 | − | 0.753093i | \(-0.728561\pi\) |
0.981155 | + | 0.193225i | \(0.0618946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.04224 | + | 5.26931i | −0.110136 | + | 0.190762i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.77463 | − | 10.0020i | −0.208782 | − | 0.361621i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.05483 | − | 5.77393i | −0.290843 | − | 0.208484i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.8605 | + | 22.2751i | 0.463762 | + | 0.803260i | 0.999145 | − | 0.0413500i | \(-0.0131659\pi\) |
−0.535383 | + | 0.844610i | \(0.679833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.48927 | − | 4.31153i | 0.0896487 | − | 0.155276i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.59564 | − | 9.69194i | 0.201261 | − | 0.348595i | −0.747674 | − | 0.664066i | \(-0.768829\pi\) |
0.948935 | + | 0.315471i | \(0.102163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0316219 | −0.00113589 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.163406 | − | 0.283028i | −0.00586217 | − | 0.0101536i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.79321 | 0.100077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.61284 | 0.272409 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.412937 | + | 0.715227i | 0.0147572 | + | 0.0255601i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.4956 | 0.660135 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.2652 | − | 35.1004i | 0.722377 | − | 1.25119i | −0.237668 | − | 0.971347i | \(-0.576383\pi\) |
0.960045 | − | 0.279847i | \(-0.0902837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.70340 | − | 6.41448i | 0.131844 | − | 0.228361i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.14690 | − | 1.98649i | −0.0407792 | − | 0.0706316i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.03458 | − | 2.89210i | −0.143272 | − | 0.102702i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.00050 | + | 1.73292i | 0.0354841 | + | 0.0614602i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.4497 | − | 18.0995i | 0.370148 | − | 0.641116i | −0.619440 | − | 0.785044i | \(-0.712640\pi\) |
0.989588 | + | 0.143929i | \(0.0459735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.48982 | + | 2.58045i | −0.0527062 | + | 0.0912898i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.07234 | 0.320555 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.715599 | + | 1.23945i | 0.0252530 | + | 0.0437394i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.24812 | 0.220217 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.83603 | 0.135035 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.3397 | − | 42.1576i | −0.855738 | − | 1.48218i | −0.875958 | − | 0.482387i | \(-0.839770\pi\) |
0.0202203 | − | 0.999796i | \(-0.493563\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6081 | 1.21526 | 0.607628 | − | 0.794222i | \(-0.292121\pi\) | ||||
0.607628 | + | 0.794222i | \(0.292121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.21007 | − | 2.09591i | 0.0424391 | − | 0.0735067i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.96973 | + | 3.41167i | −0.0689965 | + | 0.119506i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.03144 | − | 1.78650i | −0.0360854 | − | 0.0625017i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.83463 | + | 2.18963i | −0.168936 | + | 0.0765117i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.24753 | + | 7.35694i | 0.148240 | + | 0.256759i | 0.930577 | − | 0.366096i | \(-0.119306\pi\) |
−0.782337 | + | 0.622855i | \(0.785973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.9849 | − | 27.6866i | 0.557197 | − | 0.965094i | −0.440531 | − | 0.897737i | \(-0.645210\pi\) |
0.997729 | − | 0.0673571i | \(-0.0214567\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.00149355 | + | 0.00258690i | −5.19986e−5 | + | 9.00642e-5i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.0984 | 1.29004 | 0.645018 | − | 0.764167i | \(-0.276850\pi\) | ||||
0.645018 | + | 0.764167i | \(0.276850\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.71616 | + | 6.43657i | 0.129067 | + | 0.223551i | 0.923316 | − | 0.384042i | \(-0.125468\pi\) |
−0.794248 | + | 0.607594i | \(0.792135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.96279 | −0.172157 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.2167 | 0.423282 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.63018 | + | 9.75176i | 0.194840 | + | 0.337473i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.36256 | 0.323618 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.94859 | − | 8.57121i | 0.170844 | − | 0.295911i | −0.767871 | − | 0.640604i | \(-0.778684\pi\) |
0.938715 | + | 0.344694i | \(0.112017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4341 | − | 25.0005i | 0.497727 | − | 0.862088i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.36508 | + | 7.56054i | 0.150341 | + | 0.260399i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.4866 | − | 5.67567i | −0.979970 | − | 0.195249i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.258355 | + | 0.447484i | 0.00887719 | + | 0.0153757i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.05376 | + | 5.28927i | −0.104805 | + | 0.181527i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.40127 | − | 7.62322i | 0.150873 | − | 0.261320i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.0693 | 0.858357 | 0.429179 | − | 0.903220i | \(-0.358803\pi\) | ||||
0.429179 | + | 0.903220i | \(0.358803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.57478 | + | 14.8520i | 0.293251 | + | 0.507926i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.3183 | 0.830698 | 0.415349 | − | 0.909662i | \(-0.363659\pi\) | ||||
0.415349 | + | 0.909662i | \(0.363659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0711 | 1.06013 | 0.530066 | − | 0.847957i | \(-0.322167\pi\) | ||||
0.530066 | + | 0.847957i | \(0.322167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.104153 | − | 0.180399i | −0.00354954 | − | 0.00614798i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.2262 | −1.02891 | −0.514456 | − | 0.857517i | \(-0.672006\pi\) | ||||
−0.514456 | + | 0.857517i | \(0.672006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.2115 | − | 22.8831i | 0.449206 | − | 0.778047i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.66522 | + | 4.61629i | −0.0905155 | + | 0.156777i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.61803 | + | 7.99866i | 0.156656 | + | 0.271336i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3871 | − | 15.1212i | 1.13128 | − | 0.512361i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.4956 | + | 30.3032i | 0.592136 | + | 1.02561i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.89071 | + | 5.00686i | −0.0977240 | + | 0.169263i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.37115 | − | 4.10695i | 0.0800679 | − | 0.138682i | −0.823211 | − | 0.567736i | \(-0.807820\pi\) |
0.903279 | + | 0.429054i | \(0.141153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.33135 | 0.0786344 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.4430 | − | 37.1403i | −0.722432 | − | 1.25129i | −0.960022 | − | 0.279923i | \(-0.909691\pi\) |
0.237591 | − | 0.971365i | \(-0.423642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.96202 | −0.133333 | −0.0666663 | − | 0.997775i | \(-0.521236\pi\) | ||||
−0.0666663 | + | 0.997775i | \(0.521236\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.38820 | 0.0802785 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.42375 | − | 4.19805i | −0.0813815 | − | 0.140957i | 0.822462 | − | 0.568820i | \(-0.192600\pi\) |
−0.903844 | + | 0.427863i | \(0.859267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.65109 | 0.189532 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.83097 | + | 6.63544i | −0.128342 | + | 0.222296i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.21225 | − | 3.83173i | 0.0740301 | − | 0.128224i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.04689 | + | 7.00942i | 0.135273 | + | 0.234299i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.16704 | + | 4.42071i | 0.205912 | + | 0.147603i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.747407 | + | 1.29455i | 0.0249274 | + | 0.0431755i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.08937 | − | 3.61889i | 0.0696069 | − | 0.120563i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.0769206 | + | 0.133230i | −0.00255976 | + | 0.00443363i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.0153 | 0.864777 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.17441 | − | 12.4264i | −0.238222 | − | 0.412613i | 0.721982 | − | 0.691912i | \(-0.243231\pi\) |
−0.960204 | + | 0.279299i | \(0.909898\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.20458 | 0.305297 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.7273 | 0.454807 | 0.227403 | − | 0.973801i | \(-0.426976\pi\) | ||||
0.227403 | + | 0.973801i | \(0.426976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.46877 | + | 2.54399i | 0.0486092 | + | 0.0841936i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.19623 | 0.0395460 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.80987 | + | 8.33094i | −0.158836 | + | 0.275112i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.66632 | + | 8.08230i | −0.153928 | + | 0.266610i | −0.932668 | − | 0.360736i | \(-0.882526\pi\) |
0.778740 | + | 0.627346i | \(0.215859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.75872 | − | 4.77825i | −0.0909030 | − | 0.157449i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.3089 | + | 15.9916i | 0.734306 | + | 0.526372i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.00624713 | + | 0.0108203i | 0.000205404 | + | 0.000355771i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.80408 | + | 16.9812i | −0.322008 | + | 0.557735i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.43829 | + | 5.95529i | −0.112807 | + | 0.195387i | −0.916901 | − | 0.399115i | \(-0.869317\pi\) |
0.804094 | + | 0.594502i | \(0.202651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.1406 | −0.594534 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.43046 | + | 11.1379i | 0.210524 | + | 0.364638i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.05410 | −0.132583 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.9678 | −1.01167 | −0.505837 | − | 0.862629i | \(-0.668816\pi\) | ||||
−0.505837 | + | 0.862629i | \(0.668816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.76093 | + | 6.51412i | 0.122733 | + | 0.212580i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.2992 | 0.661736 | 0.330868 | − | 0.943677i | \(-0.392658\pi\) | ||||
0.330868 | + | 0.943677i | \(0.392658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.80532 | − | 4.85895i | 0.0913537 | − | 0.158229i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.31289 | − | 2.27400i | 0.0427084 | − | 0.0739731i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.03019 | − | 15.6408i | −0.293442 | − | 0.508256i | 0.681179 | − | 0.732117i | \(-0.261467\pi\) |
−0.974621 | + | 0.223860i | \(0.928134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.506603 | + | 5.13533i | −0.0164450 | + | 0.166700i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.01397 | − | 3.48830i | −0.0653074 | − | 0.113116i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.2333 | − | 24.6528i | 0.461061 | − | 0.798581i | −0.537953 | − | 0.842975i | \(-0.680802\pi\) |
0.999014 | + | 0.0443937i | \(0.0141356\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.5865 | − | 46.0491i | 0.860318 | − | 1.49011i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.141204 | 0.00456448 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.18504 | − | 2.05254i | −0.0382668 | − | 0.0662801i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0540 | −0.453353 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.1903 | −0.618399 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.7144 | + | 51.4668i | 0.956539 | + | 1.65677i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.01197 | 0.193332 | 0.0966659 | − | 0.995317i | \(-0.469182\pi\) | ||||
0.0966659 | + | 0.995317i | \(0.469182\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.950495 | + | 1.64631i | −0.0305343 | + | 0.0528870i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.60598 | + | 16.6380i | −0.308271 | + | 0.533940i | −0.977984 | − | 0.208679i | \(-0.933084\pi\) |
0.669714 | + | 0.742620i | \(0.266417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.385816 | + | 0.668253i | 0.0123687 | + | 0.0214232i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.00981081 | + | 0.00444336i | −0.000314197 | + | 0.000142301i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.3874 | − | 45.7044i | −0.844208 | − | 1.46221i | −0.886307 | − | 0.463098i | \(-0.846738\pi\) |
0.0420985 | − | 0.999113i | \(-0.486596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.59232 | − | 2.75797i | 0.0508907 | − | 0.0881452i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.7728 | + | 29.0514i | −0.535515 | + | 0.927538i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.8304 | 1.36608 | 0.683039 | − | 0.730382i | \(-0.260658\pi\) | ||||
0.683039 | + | 0.730382i | \(0.260658\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.3440 | − | 49.0932i | −0.903115 | − | 1.56424i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.329962 | −0.0105028 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.14363 | −0.131760 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.1177 | − | 26.1846i | −0.480229 | − | 0.831781i | 0.519514 | − | 0.854462i | \(-0.326113\pi\) |
−0.999743 | + | 0.0226813i | \(0.992780\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.49128 | 0.205995 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.7768 | + | 39.4506i | −0.722074 | + | 1.25067i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.2386 | − | 19.4658i | 0.355929 | − | 0.616488i | −0.631347 | − | 0.775500i | \(-0.717498\pi\) |
0.987277 | + | 0.159012i | \(0.0508310\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.84964 | − | 3.20367i | −0.0585200 | − | 0.101360i |
(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 | 572.2.i.c.133.3 | ✓ | 10 | |
13.3 | even | 3 | 7436.2.a.r.1.3 | 5 | |||
13.9 | even | 3 | inner | 572.2.i.c.529.3 | yes | 10 | |
13.10 | even | 6 | 7436.2.a.q.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.i.c.133.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
572.2.i.c.529.3 | yes | 10 | 13.9 | even | 3 | inner | |
7436.2.a.q.1.3 | 5 | 13.10 | even | 6 | |||
7436.2.a.r.1.3 | 5 | 13.3 | even | 3 |