Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,2,Mod(199,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.c (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: | \(3.95259490005\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.6 | ||
Root | \(0.403032 + 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.199 |
Dual form | 495.2.c.d.199.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(397\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.67513i | 1.89160i | 0.324745 | + | 0.945802i | \(0.394721\pi\) | ||||
−0.324745 | + | 0.945802i | \(0.605279\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.15633 | −2.57816 | ||||||||
\(5\) | 1.48119 | − | 1.67513i | 0.662410 | − | 0.749141i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.80606i | − | 1.06059i | −0.847812 | − | 0.530296i | \(-0.822081\pi\) | ||
0.847812 | − | 0.530296i | \(-0.177919\pi\) | |||||||
\(8\) | − | 8.44358i | − | 2.98526i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.48119 | + | 3.96239i | 1.41708 | + | 1.25302i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.11871i | − | 1.41968i | −0.704365 | − | 0.709838i | \(-0.748768\pi\) | ||
0.704365 | − | 0.709838i | \(-0.251232\pi\) | |||||||
\(14\) | 7.50659 | 2.00622 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.2750 | 3.06876 | ||||||||
\(17\) | 4.54420i | 1.10213i | 0.834462 | + | 0.551065i | \(0.185778\pi\) | ||||
−0.834462 | + | 0.551065i | \(0.814222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.57452 | 1.04947 | 0.524733 | − | 0.851267i | \(-0.324165\pi\) | ||||
0.524733 | + | 0.851267i | \(0.324165\pi\) | |||||||
\(20\) | −7.63752 | + | 8.63752i | −1.70780 | + | 1.93141i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.67513i | 0.570340i | ||||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.612127 | − | 4.96239i | −0.122425 | − | 0.992478i | ||||
\(26\) | 13.6932 | 2.68546 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 14.4690i | 2.73438i | ||||||||
\(29\) | −2.38787 | −0.443417 | −0.221708 | − | 0.975113i | \(-0.571163\pi\) | ||||
−0.221708 | + | 0.975113i | \(0.571163\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.962389 | −0.172850 | −0.0864250 | − | 0.996258i | \(-0.527544\pi\) | ||||
−0.0864250 | + | 0.996258i | \(0.527544\pi\) | |||||||
\(32\) | 15.9502i | 2.81962i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.1563 | −2.08479 | ||||||||
\(35\) | −4.70052 | − | 4.15633i | −0.794533 | − | 0.702547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.61213i | − | 0.265032i | −0.991181 | − | 0.132516i | \(-0.957694\pi\) | ||
0.991181 | − | 0.132516i | \(-0.0423056\pi\) | |||||||
\(38\) | 12.2374i | 1.98517i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −14.1441 | − | 12.5066i | −2.23638 | − | 1.97747i | ||||
\(41\) | 2.38787 | 0.372923 | 0.186462 | − | 0.982462i | \(-0.440298\pi\) | ||||
0.186462 | + | 0.982462i | \(0.440298\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.80606i | 0.427921i | 0.976842 | + | 0.213960i | \(0.0686363\pi\) | ||||
−0.976842 | + | 0.213960i | \(0.931364\pi\) | |||||||
\(44\) | −5.15633 | −0.777345 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.7005 | 1.57771 | ||||||||
\(47\) | − | 4.31265i | − | 0.629065i | −0.949247 | − | 0.314532i | \(-0.898152\pi\) | ||
0.949247 | − | 0.314532i | \(-0.101848\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.873992 | −0.124856 | ||||||||
\(50\) | 13.2750 | − | 1.63752i | 1.87737 | − | 0.231580i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 26.3938i | 3.66015i | ||||||||
\(53\) | 6.57452i | 0.903079i | 0.892251 | + | 0.451540i | \(0.149125\pi\) | ||||
−0.892251 | + | 0.451540i | \(0.850875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.48119 | − | 1.67513i | 0.199724 | − | 0.225875i | ||||
\(56\) | −23.6932 | −3.16614 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 6.38787i | − | 0.838769i | ||||||
\(59\) | −13.2750 | −1.72826 | −0.864131 | − | 0.503266i | \(-0.832132\pi\) | ||||
−0.864131 | + | 0.503266i | \(0.832132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.92478 | 1.01466 | 0.507332 | − | 0.861751i | \(-0.330632\pi\) | ||||
0.507332 | + | 0.861751i | \(0.330632\pi\) | |||||||
\(62\) | − | 2.57452i | − | 0.326964i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −18.1187 | −2.26484 | ||||||||
\(65\) | −8.57452 | − | 7.58181i | −1.06354 | − | 0.940408i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.7005i | − | 1.30728i | −0.756807 | − | 0.653639i | \(-0.773242\pi\) | ||
0.756807 | − | 0.653639i | \(-0.226758\pi\) | |||||||
\(68\) | − | 23.4314i | − | 2.84147i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.1187 | − | 12.5745i | 1.32894 | − | 1.50294i | ||||
\(71\) | 7.35026 | 0.872316 | 0.436158 | − | 0.899870i | \(-0.356339\pi\) | ||||
0.436158 | + | 0.899870i | \(0.356339\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.41819i | 0.751192i | 0.926783 | + | 0.375596i | \(0.122562\pi\) | ||||
−0.926783 | + | 0.375596i | \(0.877438\pi\) | |||||||
\(74\) | 4.31265 | 0.501335 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −23.5877 | −2.70569 | ||||||||
\(77\) | − | 2.80606i | − | 0.319781i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.35026 | −0.151916 | −0.0759582 | − | 0.997111i | \(-0.524202\pi\) | ||||
−0.0759582 | + | 0.997111i | \(0.524202\pi\) | |||||||
\(80\) | 18.1817 | − | 20.5623i | 2.03278 | − | 2.29893i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.38787i | 0.705423i | ||||||||
\(83\) | 0.806063i | 0.0884770i | 0.999021 | + | 0.0442385i | \(0.0140861\pi\) | ||||
−0.999021 | + | 0.0442385i | \(0.985914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.61213 | + | 6.73084i | 0.825651 | + | 0.730062i | ||||
\(86\) | −7.50659 | −0.809456 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 8.44358i | − | 0.900089i | ||||||
\(89\) | −2.96239 | −0.314013 | −0.157006 | − | 0.987598i | \(-0.550184\pi\) | ||||
−0.157006 | + | 0.987598i | \(0.550184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.3634 | −1.50570 | ||||||||
\(92\) | 20.6253i | 2.15034i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.5369 | 1.18994 | ||||||||
\(95\) | 6.77575 | − | 7.66291i | 0.695177 | − | 0.786198i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.92478i | 1.00771i | 0.863789 | + | 0.503854i | \(0.168085\pi\) | ||||
−0.863789 | + | 0.503854i | \(0.831915\pi\) | |||||||
\(98\) | − | 2.33804i | − | 0.236178i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.15633 | + | 25.5877i | 0.315633 | + | 2.55877i | ||||
\(101\) | 13.6121 | 1.35446 | 0.677229 | − | 0.735773i | \(-0.263181\pi\) | ||||
0.677229 | + | 0.735773i | \(0.263181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.3127i | 1.60733i | 0.595080 | + | 0.803667i | \(0.297120\pi\) | ||||
−0.595080 | + | 0.803667i | \(0.702880\pi\) | |||||||
\(104\) | −43.2203 | −4.23810 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.5877 | −1.70827 | ||||||||
\(107\) | − | 9.43136i | − | 0.911764i | −0.890040 | − | 0.455882i | \(-0.849324\pi\) | ||
0.890040 | − | 0.455882i | \(-0.150676\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4010 | 1.47515 | 0.737576 | − | 0.675264i | \(-0.235970\pi\) | ||||
0.737576 | + | 0.675264i | \(0.235970\pi\) | |||||||
\(110\) | 4.48119 | + | 3.96239i | 0.427265 | + | 0.377799i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 34.4445i | − | 3.25470i | ||||||
\(113\) | 13.7381i | 1.29238i | 0.763179 | + | 0.646188i | \(0.223638\pi\) | ||||
−0.763179 | + | 0.646188i | \(0.776362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.70052 | − | 5.92478i | −0.624827 | − | 0.552488i | ||||
\(116\) | 12.3127 | 1.14320 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 35.5125i | − | 3.26919i | ||||||
\(119\) | 12.7513 | 1.16891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 21.1998i | 1.91934i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.96239 | 0.445636 | ||||||||
\(125\) | −9.21933 | − | 6.32487i | −0.824602 | − | 0.565713i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.4182i | − | 1.10194i | −0.834526 | − | 0.550968i | \(-0.814259\pi\) | ||
0.834526 | − | 0.550968i | \(-0.185741\pi\) | |||||||
\(128\) | − | 16.5696i | − | 1.46456i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 20.2823 | − | 22.9380i | 1.77888 | − | 2.01179i | ||||
\(131\) | −5.92478 | −0.517650 | −0.258825 | − | 0.965924i | \(-0.583335\pi\) | ||||
−0.258825 | + | 0.965924i | \(0.583335\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 12.8364i | − | 1.11306i | ||||||
\(134\) | 28.6253 | 2.47285 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 38.3693 | 3.29014 | ||||||||
\(137\) | 9.79877i | 0.837165i | 0.908179 | + | 0.418583i | \(0.137473\pi\) | ||||
−0.908179 | + | 0.418583i | \(0.862527\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.12601 | 0.180326 | 0.0901628 | − | 0.995927i | \(-0.471261\pi\) | ||||
0.0901628 | + | 0.995927i | \(0.471261\pi\) | |||||||
\(140\) | 24.2374 | + | 21.4314i | 2.04844 | + | 1.81128i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.6629i | 1.65007i | ||||||||
\(143\) | − | 5.11871i | − | 0.428048i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.53690 | + | 4.00000i | −0.293724 | + | 0.332182i | ||||
\(146\) | −17.1695 | −1.42096 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.31265i | 0.683296i | ||||||||
\(149\) | 8.31265 | 0.680999 | 0.340499 | − | 0.940245i | \(-0.389404\pi\) | ||||
0.340499 | + | 0.940245i | \(0.389404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2750 | −1.24307 | −0.621533 | − | 0.783388i | \(-0.713490\pi\) | ||||
−0.621533 | + | 0.783388i | \(0.713490\pi\) | |||||||
\(152\) | − | 38.6253i | − | 3.13293i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.50659 | 0.604898 | ||||||||
\(155\) | −1.42548 | + | 1.61213i | −0.114498 | + | 0.129489i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.01317i | − | 0.559712i | −0.960042 | − | 0.279856i | \(-0.909713\pi\) | ||
0.960042 | − | 0.279856i | \(-0.0902868\pi\) | |||||||
\(158\) | − | 3.61213i | − | 0.287365i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 26.7186 | + | 23.6253i | 2.11229 | + | 1.86774i | ||||
\(161\) | −11.2243 | −0.884595 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.76116i | 0.529575i | 0.964307 | + | 0.264787i | \(0.0853018\pi\) | ||||
−0.964307 | + | 0.264787i | \(0.914698\pi\) | |||||||
\(164\) | −12.3127 | −0.961456 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.15633 | −0.167363 | ||||||||
\(167\) | − | 11.8192i | − | 0.914600i | −0.889312 | − | 0.457300i | \(-0.848817\pi\) | ||
0.889312 | − | 0.457300i | \(-0.151183\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.2012 | −1.01548 | ||||||||
\(170\) | −18.0059 | + | 20.3634i | −1.38099 | + | 1.56180i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 14.4690i | − | 1.10325i | ||||||
\(173\) | − | 6.99271i | − | 0.531646i | −0.964022 | − | 0.265823i | \(-0.914356\pi\) | ||
0.964022 | − | 0.265823i | \(-0.0856436\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.9248 | + | 1.71767i | −1.05261 | + | 0.129843i | ||||
\(176\) | 12.2750 | 0.925266 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 7.92478i | − | 0.593987i | ||||||
\(179\) | −2.70052 | −0.201847 | −0.100923 | − | 0.994894i | \(-0.532180\pi\) | ||||
−0.100923 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.1998 | −1.57577 | −0.787885 | − | 0.615822i | \(-0.788824\pi\) | ||||
−0.787885 | + | 0.615822i | \(0.788824\pi\) | |||||||
\(182\) | − | 38.4241i | − | 2.84818i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −33.7743 | −2.48988 | ||||||||
\(185\) | −2.70052 | − | 2.38787i | −0.198546 | − | 0.175560i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.54420i | 0.332305i | ||||||||
\(188\) | 22.2374i | 1.62183i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 20.4993 | + | 18.1260i | 1.48717 | + | 1.31500i | ||||
\(191\) | −13.1490 | −0.951430 | −0.475715 | − | 0.879599i | \(-0.657811\pi\) | ||||
−0.475715 | + | 0.879599i | \(0.657811\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.89446i | 0.424293i | 0.977238 | + | 0.212146i | \(0.0680453\pi\) | ||||
−0.977238 | + | 0.212146i | \(0.931955\pi\) | |||||||
\(194\) | −26.5501 | −1.90618 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.50659 | 0.321899 | ||||||||
\(197\) | 20.3938i | 1.45299i | 0.687169 | + | 0.726497i | \(0.258853\pi\) | ||||
−0.687169 | + | 0.726497i | \(0.741147\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.4010 | −1.23353 | −0.616764 | − | 0.787148i | \(-0.711557\pi\) | ||||
−0.616764 | + | 0.787148i | \(0.711557\pi\) | |||||||
\(200\) | −41.9003 | + | 5.16854i | −2.96280 | + | 0.365471i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 36.4142i | 2.56210i | ||||||||
\(203\) | 6.70052i | 0.470285i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.53690 | − | 4.00000i | 0.247028 | − | 0.279372i | ||||
\(206\) | −43.6385 | −3.04044 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 62.8324i | − | 4.35664i | ||||||
\(209\) | 4.57452 | 0.316426 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1260 | 1.24785 | 0.623923 | − | 0.781486i | \(-0.285538\pi\) | ||||
0.623923 | + | 0.781486i | \(0.285538\pi\) | |||||||
\(212\) | − | 33.9003i | − | 2.32828i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.2301 | 1.72470 | ||||||||
\(215\) | 4.70052 | + | 4.15633i | 0.320573 | + | 0.283459i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.70052i | 0.183323i | ||||||||
\(218\) | 41.1998i | 2.79040i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.63752 | + | 8.63752i | −0.514921 | + | 0.582341i | ||||
\(221\) | 23.2605 | 1.56467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6385i | 1.58295i | 0.611202 | + | 0.791475i | \(0.290686\pi\) | ||||
−0.611202 | + | 0.791475i | \(0.709314\pi\) | |||||||
\(224\) | 44.7572 | 2.99047 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −36.7513 | −2.44466 | ||||||||
\(227\) | − | 1.26916i | − | 0.0842371i | −0.999113 | − | 0.0421185i | \(-0.986589\pi\) | ||
0.999113 | − | 0.0421185i | \(-0.0134107\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1768 | −1.06899 | −0.534496 | − | 0.845171i | \(-0.679499\pi\) | ||||
−0.534496 | + | 0.845171i | \(0.679499\pi\) | |||||||
\(230\) | 15.8496 | − | 17.9248i | 1.04509 | − | 1.18192i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.1622i | 1.32371i | ||||||||
\(233\) | 18.4690i | 1.20994i | 0.796247 | + | 0.604971i | \(0.206815\pi\) | ||||
−0.796247 | + | 0.604971i | \(0.793185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.22425 | − | 6.38787i | −0.471258 | − | 0.416699i | ||||
\(236\) | 68.4504 | 4.45574 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 34.1114i | 2.21111i | ||||||||
\(239\) | 19.3258 | 1.25008 | 0.625042 | − | 0.780591i | \(-0.285082\pi\) | ||||
0.625042 | + | 0.780591i | \(0.285082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.5501 | 1.83907 | 0.919536 | − | 0.393006i | \(-0.128565\pi\) | ||||
0.919536 | + | 0.393006i | \(0.128565\pi\) | |||||||
\(242\) | 2.67513i | 0.171964i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −40.8627 | −2.61597 | ||||||||
\(245\) | −1.29455 | + | 1.46405i | −0.0827059 | + | 0.0935348i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 23.4156i | − | 1.48990i | ||||||
\(248\) | 8.12601i | 0.516002i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.9199 | − | 24.6629i | 1.07011 | − | 1.55982i | ||||
\(251\) | −23.1998 | −1.46436 | −0.732180 | − | 0.681112i | \(-0.761497\pi\) | ||||
−0.732180 | + | 0.681112i | \(0.761497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.00000i | − | 0.251478i | ||||||
\(254\) | 33.2203 | 2.08443 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.08840 | 0.505525 | ||||||||
\(257\) | − | 10.8872i | − | 0.679123i | −0.940584 | − | 0.339561i | \(-0.889721\pi\) | ||
0.940584 | − | 0.339561i | \(-0.110279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.52373 | −0.281091 | ||||||||
\(260\) | 44.2130 | + | 39.0943i | 2.74197 | + | 2.42452i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 15.8496i | − | 0.979189i | ||||||
\(263\) | − | 9.11871i | − | 0.562284i | −0.959666 | − | 0.281142i | \(-0.909287\pi\) | ||
0.959666 | − | 0.281142i | \(-0.0907132\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0132 | + | 9.73813i | 0.676534 | + | 0.598209i | ||||
\(266\) | 34.3390 | 2.10546 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 55.1754i | 3.37037i | ||||||||
\(269\) | −11.2995 | −0.688941 | −0.344471 | − | 0.938797i | \(-0.611942\pi\) | ||||
−0.344471 | + | 0.938797i | \(0.611942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.1998 | 1.53078 | 0.765390 | − | 0.643567i | \(-0.222546\pi\) | ||||
0.765390 | + | 0.643567i | \(0.222546\pi\) | |||||||
\(272\) | 55.7802i | 3.38217i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.2130 | −1.58358 | ||||||||
\(275\) | −0.612127 | − | 4.96239i | −0.0369126 | − | 0.299243i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.41819i | 0.145295i | 0.997358 | + | 0.0726475i | \(0.0231448\pi\) | ||||
−0.997358 | + | 0.0726475i | \(0.976855\pi\) | |||||||
\(278\) | 5.68735i | 0.341105i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −35.0943 | + | 39.6893i | −2.09728 | + | 2.37189i | ||||
\(281\) | −30.4894 | −1.81885 | −0.909424 | − | 0.415870i | \(-0.863477\pi\) | ||||
−0.909424 | + | 0.415870i | \(0.863477\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.35756i | 0.496805i | 0.968657 | + | 0.248403i | \(0.0799056\pi\) | ||||
−0.968657 | + | 0.248403i | \(0.920094\pi\) | |||||||
\(284\) | −37.9003 | −2.24897 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.6932 | 0.809698 | ||||||||
\(287\) | − | 6.70052i | − | 0.395519i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.64974 | −0.214690 | ||||||||
\(290\) | −10.7005 | − | 9.46168i | −0.628356 | − | 0.555609i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 33.0943i | − | 1.93670i | ||||||
\(293\) | 23.0943i | 1.34918i | 0.738192 | + | 0.674591i | \(0.235680\pi\) | ||||
−0.738192 | + | 0.674591i | \(0.764320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.6629 | + | 22.2374i | −1.14482 | + | 1.29471i | ||||
\(296\) | −13.6121 | −0.791189 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.2374i | 1.28818i | ||||||||
\(299\) | −20.4749 | −1.18409 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.87399 | 0.453849 | ||||||||
\(302\) | − | 40.8627i | − | 2.35139i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 56.1524 | 3.22056 | ||||||||
\(305\) | 11.7381 | − | 13.2750i | 0.672124 | − | 0.760127i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.65562i | − | 0.151564i | −0.997124 | − | 0.0757821i | \(-0.975855\pi\) | ||
0.997124 | − | 0.0757821i | \(-0.0241453\pi\) | |||||||
\(308\) | 14.4690i | 0.824446i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.31265 | − | 3.81336i | −0.244942 | − | 0.216584i | ||||
\(311\) | 15.9756 | 0.905891 | 0.452946 | − | 0.891538i | \(-0.350373\pi\) | ||||
0.452946 | + | 0.891538i | \(0.350373\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 0.0606343i | − | 0.00342726i | −0.999999 | − | 0.00171363i | \(-0.999455\pi\) | ||
0.999999 | − | 0.00171363i | \(-0.000545465\pi\) | |||||||
\(314\) | 18.7612 | 1.05875 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.96239 | 0.391665 | ||||||||
\(317\) | 3.81336i | 0.214180i | 0.994249 | + | 0.107090i | \(0.0341532\pi\) | ||||
−0.994249 | + | 0.107090i | \(0.965847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.38787 | −0.133695 | ||||||||
\(320\) | −26.8373 | + | 30.3512i | −1.50025 | + | 1.69668i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 30.0263i | − | 1.67330i | ||||||
\(323\) | 20.7875i | 1.15665i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.4010 | + | 3.13330i | −1.40900 | + | 0.173804i | ||||
\(326\) | −18.0870 | −1.00175 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 20.1622i | − | 1.11327i | ||||||
\(329\) | −12.1016 | −0.667181 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2882 | 1.33500 | 0.667500 | − | 0.744609i | \(-0.267364\pi\) | ||||
0.667500 | + | 0.744609i | \(0.267364\pi\) | |||||||
\(332\) | − | 4.15633i | − | 0.228108i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 31.6180 | 1.73006 | ||||||||
\(335\) | −17.9248 | − | 15.8496i | −0.979335 | − | 0.865954i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.5804i | 1.23003i | 0.788514 | + | 0.615016i | \(0.210851\pi\) | ||||
−0.788514 | + | 0.615016i | \(0.789149\pi\) | |||||||
\(338\) | − | 35.3150i | − | 1.92088i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −39.2506 | − | 34.7064i | −2.12866 | − | 1.88222i | ||||
\(341\) | −0.962389 | −0.0521163 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.1900i | − | 0.928171i | ||||||
\(344\) | 23.6932 | 1.27745 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.7064 | 1.00566 | ||||||||
\(347\) | 20.1925i | 1.08399i | 0.840381 | + | 0.541996i | \(0.182331\pi\) | ||||
−0.840381 | + | 0.541996i | \(0.817669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2506 | 1.45869 | 0.729346 | − | 0.684145i | \(-0.239825\pi\) | ||||
0.729346 | + | 0.684145i | \(0.239825\pi\) | |||||||
\(350\) | −4.59498 | − | 37.2506i | −0.245612 | − | 1.99113i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.9502i | 0.850147i | ||||||||
\(353\) | − | 5.02302i | − | 0.267349i | −0.991025 | − | 0.133674i | \(-0.957322\pi\) | ||
0.991025 | − | 0.133674i | \(-0.0426776\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8872 | − | 12.3127i | 0.577831 | − | 0.653488i | ||||
\(356\) | 15.2750 | 0.809575 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 7.22425i | − | 0.381814i | ||||||
\(359\) | −18.1768 | −0.959334 | −0.479667 | − | 0.877450i | \(-0.659243\pi\) | ||||
−0.479667 | + | 0.877450i | \(0.659243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.92619 | 0.101379 | ||||||||
\(362\) | − | 56.7123i | − | 2.98073i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 74.0625 | 3.88193 | ||||||||
\(365\) | 10.7513 | + | 9.50659i | 0.562749 | + | 0.497598i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.56467i | 0.447072i | 0.974696 | + | 0.223536i | \(0.0717600\pi\) | ||||
−0.974696 | + | 0.223536i | \(0.928240\pi\) | |||||||
\(368\) | − | 49.1002i | − | 2.55952i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.38787 | − | 7.22425i | 0.332090 | − | 0.375571i | ||||
\(371\) | 18.4485 | 0.957799 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.81924i | 0.404865i | 0.979296 | + | 0.202432i | \(0.0648846\pi\) | ||||
−0.979296 | + | 0.202432i | \(0.935115\pi\) | |||||||
\(374\) | −12.1563 | −0.628589 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −36.4142 | −1.87792 | ||||||||
\(377\) | 12.2228i | 0.629508i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.14903 | −0.0590218 | −0.0295109 | − | 0.999564i | \(-0.509395\pi\) | ||||
−0.0295109 | + | 0.999564i | \(0.509395\pi\) | |||||||
\(380\) | −34.9380 | + | 39.5125i | −1.79228 | + | 2.02695i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 35.1754i | − | 1.79973i | ||||||
\(383\) | − | 34.0870i | − | 1.74176i | −0.491493 | − | 0.870882i | \(-0.663549\pi\) | ||
0.491493 | − | 0.870882i | \(-0.336451\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.70052 | − | 4.15633i | −0.239561 | − | 0.211826i | ||||
\(386\) | −15.7685 | −0.802593 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 51.1754i | − | 2.59804i | ||||||
\(389\) | 23.7743 | 1.20541 | 0.602703 | − | 0.797965i | \(-0.294090\pi\) | ||||
0.602703 | + | 0.797965i | \(0.294090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.1768 | 0.919240 | ||||||||
\(392\) | 7.37962i | 0.372727i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −54.5560 | −2.74849 | ||||||||
\(395\) | −2.00000 | + | 2.26187i | −0.100631 | + | 0.113807i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.15045i | 0.208305i | 0.994561 | + | 0.104152i | \(0.0332130\pi\) | ||||
−0.994561 | + | 0.104152i | \(0.966787\pi\) | |||||||
\(398\) | − | 46.5501i | − | 2.33334i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.51388 | − | 60.9135i | −0.375694 | − | 3.04568i | ||||
\(401\) | 33.9149 | 1.69363 | 0.846815 | − | 0.531887i | \(-0.178517\pi\) | ||||
0.846815 | + | 0.531887i | \(0.178517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.92619i | 0.245391i | ||||||||
\(404\) | −70.1886 | −3.49201 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.9248 | −0.889592 | ||||||||
\(407\) | − | 1.61213i | − | 0.0799102i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.55008 | −0.422774 | −0.211387 | − | 0.977402i | \(-0.567798\pi\) | ||||
−0.211387 | + | 0.977402i | \(0.567798\pi\) | |||||||
\(410\) | 10.7005 | + | 9.46168i | 0.528461 | + | 0.467279i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 84.1133i | − | 4.14397i | ||||||
\(413\) | 37.2506i | 1.83298i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.35026 | + | 1.19394i | 0.0662817 | + | 0.0586080i | ||||
\(416\) | 81.6444 | 4.00294 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.2374i | 0.598552i | ||||||||
\(419\) | 13.2995 | 0.649722 | 0.324861 | − | 0.945762i | \(-0.394682\pi\) | ||||
0.324861 | + | 0.945762i | \(0.394682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.3014 | 1.62301 | 0.811505 | − | 0.584345i | \(-0.198649\pi\) | ||||
0.811505 | + | 0.584345i | \(0.198649\pi\) | |||||||
\(422\) | 48.4894i | 2.36043i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 55.5125 | 2.69592 | ||||||||
\(425\) | 22.5501 | − | 2.78163i | 1.09384 | − | 0.134929i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 22.2374i | − | 1.07614i | ||||||
\(428\) | 48.6312i | 2.35068i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.1187 | + | 12.5745i | −0.536192 | + | 0.606397i | ||||
\(431\) | −2.07522 | −0.0999600 | −0.0499800 | − | 0.998750i | \(-0.515916\pi\) | ||||
−0.0499800 | + | 0.998750i | \(0.515916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 37.4010i | − | 1.79738i | −0.438585 | − | 0.898690i | \(-0.644520\pi\) | ||
0.438585 | − | 0.898690i | \(-0.355480\pi\) | |||||||
\(434\) | −7.22425 | −0.346775 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −79.4128 | −3.80318 | ||||||||
\(437\) | − | 18.2981i | − | 0.875315i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.02444 | 0.287531 | 0.143765 | − | 0.989612i | \(-0.454079\pi\) | ||||
0.143765 | + | 0.989612i | \(0.454079\pi\) | |||||||
\(440\) | −14.1441 | − | 12.5066i | −0.674294 | − | 0.596228i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 62.2247i | 2.95973i | ||||||||
\(443\) | 10.1359i | 0.481569i | 0.970579 | + | 0.240785i | \(0.0774047\pi\) | ||||
−0.970579 | + | 0.240785i | \(0.922595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.38787 | + | 4.96239i | −0.208005 | + | 0.235240i | ||||
\(446\) | −63.2360 | −2.99431 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 50.8423i | 2.40207i | ||||||||
\(449\) | −11.4861 | −0.542063 | −0.271032 | − | 0.962570i | \(-0.587365\pi\) | ||||
−0.271032 | + | 0.962570i | \(0.587365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.38787 | 0.112441 | ||||||||
\(452\) | − | 70.8383i | − | 3.33195i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.39517 | 0.159343 | ||||||||
\(455\) | −21.2750 | + | 24.0606i | −0.997389 | + | 1.12798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0435i | 0.703705i | 0.936055 | + | 0.351852i | \(0.114448\pi\) | ||||
−0.936055 | + | 0.351852i | \(0.885552\pi\) | |||||||
\(458\) | − | 43.2750i | − | 2.02211i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 34.5501 | + | 30.5501i | 1.61091 | + | 1.42440i | ||||
\(461\) | 26.2374 | 1.22200 | 0.610999 | − | 0.791631i | \(-0.290768\pi\) | ||||
0.610999 | + | 0.791631i | \(0.290768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.46168i | − | 0.253826i | −0.991914 | − | 0.126913i | \(-0.959493\pi\) | ||
0.991914 | − | 0.126913i | \(-0.0405069\pi\) | |||||||
\(464\) | −29.3112 | −1.36074 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −49.4069 | −2.28873 | ||||||||
\(467\) | − | 2.70052i | − | 0.124965i | −0.998046 | − | 0.0624827i | \(-0.980098\pi\) | ||
0.998046 | − | 0.0624827i | \(-0.0199018\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0263 | −1.38649 | ||||||||
\(470\) | 17.0884 | − | 19.3258i | 0.788229 | − | 0.891434i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 112.089i | 5.15931i | ||||||||
\(473\) | 2.80606i | 0.129023i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.80018 | − | 22.7005i | −0.128481 | − | 1.04157i | ||||
\(476\) | −65.7499 | −3.01364 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 51.6991i | 2.36466i | ||||||||
\(479\) | 16.7757 | 0.766503 | 0.383252 | − | 0.923644i | \(-0.374804\pi\) | ||||
0.383252 | + | 0.923644i | \(0.374804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.25202 | −0.376260 | ||||||||
\(482\) | 76.3752i | 3.47879i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.15633 | −0.234378 | ||||||||
\(485\) | 16.6253 | + | 14.7005i | 0.754916 | + | 0.667516i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.3996i | 1.55880i | 0.626529 | + | 0.779398i | \(0.284475\pi\) | ||||
−0.626529 | + | 0.779398i | \(0.715525\pi\) | |||||||
\(488\) | − | 66.9135i | − | 3.02903i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.91653 | − | 3.46310i | −0.176931 | − | 0.156447i | ||||
\(491\) | −14.9525 | −0.674799 | −0.337399 | − | 0.941362i | \(-0.609547\pi\) | ||||
−0.337399 | + | 0.941362i | \(0.609547\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 10.8510i | − | 0.488703i | ||||||
\(494\) | 62.6399 | 2.81830 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.8134 | −0.530435 | ||||||||
\(497\) | − | 20.6253i | − | 0.925171i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.85097 | 0.127627 | 0.0638135 | − | 0.997962i | \(-0.479674\pi\) | ||||
0.0638135 | + | 0.997962i | \(0.479674\pi\) | |||||||
\(500\) | 47.5379 | + | 32.6131i | 2.12596 | + | 1.45850i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 62.0625i | − | 2.76999i | ||||||
\(503\) | − | 1.48024i | − | 0.0660006i | −0.999455 | − | 0.0330003i | \(-0.989494\pi\) | ||
0.999455 | − | 0.0330003i | \(-0.0105062\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.1622 | − | 22.8021i | 0.897206 | − | 1.01468i | ||||
\(506\) | 10.7005 | 0.475696 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 64.0322i | 2.84097i | ||||||||
\(509\) | −23.2995 | −1.03273 | −0.516366 | − | 0.856368i | \(-0.672715\pi\) | ||||
−0.516366 | + | 0.856368i | \(0.672715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0098 | 0.796709 | ||||||||
\(512\) | − | 11.5017i | − | 0.508306i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.1246 | 1.28463 | ||||||||
\(515\) | 27.3258 | + | 24.1622i | 1.20412 | + | 1.06471i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.31265i | − | 0.189670i | ||||||
\(518\) | − | 12.1016i | − | 0.531712i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −64.0176 | + | 72.3996i | −2.80736 | + | 3.17493i | ||||
\(521\) | 6.81194 | 0.298437 | 0.149218 | − | 0.988804i | \(-0.452324\pi\) | ||||
0.149218 | + | 0.988804i | \(0.452324\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.0567i | − | 0.702109i | −0.936355 | − | 0.351054i | \(-0.885823\pi\) | ||
0.936355 | − | 0.351054i | \(-0.114177\pi\) | |||||||
\(524\) | 30.5501 | 1.33459 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.3938 | 1.06362 | ||||||||
\(527\) | − | 4.37328i | − | 0.190503i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | −26.0508 | + | 29.4617i | −1.13157 | + | 1.27973i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 66.1886i | 2.86964i | ||||||||
\(533\) | − | 12.2228i | − | 0.529430i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.7988 | − | 13.9697i | −0.683040 | − | 0.603962i | ||||
\(536\) | −90.3508 | −3.90256 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 30.2276i | − | 1.30320i | ||||||
\(539\) | −0.873992 | −0.0376455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.62530 | 0.284844 | 0.142422 | − | 0.989806i | \(-0.454511\pi\) | ||||
0.142422 | + | 0.989806i | \(0.454511\pi\) | |||||||
\(542\) | 67.4128i | 2.89563i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −72.4807 | −3.10759 | ||||||||
\(545\) | 22.8119 | − | 25.7988i | 0.977156 | − | 1.10510i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.75860i | 0.246220i | 0.992393 | + | 0.123110i | \(0.0392868\pi\) | ||||
−0.992393 | + | 0.123110i | \(0.960713\pi\) | |||||||
\(548\) | − | 50.5256i | − | 2.15835i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.2750 | − | 1.63752i | 0.566050 | − | 0.0698241i | ||||
\(551\) | −10.9234 | −0.465351 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.78892i | 0.161121i | ||||||||
\(554\) | −6.46898 | −0.274840 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.9624 | −0.464909 | ||||||||
\(557\) | 19.8700i | 0.841920i | 0.907079 | + | 0.420960i | \(0.138307\pi\) | ||||
−0.907079 | + | 0.420960i | \(0.861693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.3634 | 0.607509 | ||||||||
\(560\) | −57.6991 | − | 51.0191i | −2.43823 | − | 2.15595i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 81.5633i | − | 3.44054i | ||||||
\(563\) | − | 5.83383i | − | 0.245866i | −0.992415 | − | 0.122933i | \(-0.960770\pi\) | ||
0.992415 | − | 0.122933i | \(-0.0392301\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.0132 | + | 20.3488i | 0.968171 | + | 0.856082i | ||||
\(566\) | −22.3576 | −0.939758 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 62.0625i | − | 2.60409i | ||||||
\(569\) | 46.7123 | 1.95828 | 0.979140 | − | 0.203185i | \(-0.0651293\pi\) | ||||
0.979140 | + | 0.203185i | \(0.0651293\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.4241 | −1.02212 | −0.511058 | − | 0.859546i | \(-0.670746\pi\) | ||||
−0.511058 | + | 0.859546i | \(0.670746\pi\) | |||||||
\(572\) | 26.3938i | 1.10358i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.9248 | 0.748166 | ||||||||
\(575\) | −19.8496 | + | 2.44851i | −0.827784 | + | 0.102110i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 16.5647i | − | 0.689596i | −0.938677 | − | 0.344798i | \(-0.887947\pi\) | ||
0.938677 | − | 0.344798i | \(-0.112053\pi\) | |||||||
\(578\) | − | 9.76353i | − | 0.406109i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 18.2374 | − | 20.6253i | 0.757268 | − | 0.856419i | ||||
\(581\) | 2.26187 | 0.0938380 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.57452i | 0.272289i | ||||||||
\(584\) | 54.1925 | 2.24250 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −61.7802 | −2.55212 | ||||||||
\(587\) | 27.3258i | 1.12786i | 0.825823 | + | 0.563929i | \(0.190711\pi\) | ||||
−0.825823 | + | 0.563929i | \(0.809289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.40246 | −0.181400 | ||||||||
\(590\) | −59.4880 | − | 52.6009i | −2.44908 | − | 2.16554i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 19.7889i | − | 0.813320i | ||||||
\(593\) | 12.6048i | 0.517618i | 0.965928 | + | 0.258809i | \(0.0833301\pi\) | ||||
−0.965928 | + | 0.258809i | \(0.916670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.8872 | − | 21.3601i | 0.774298 | − | 0.875679i | ||||
\(596\) | −42.8627 | −1.75573 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 54.7729i | − | 2.23983i | ||||||
\(599\) | 10.5990 | 0.433061 | 0.216531 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216531 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4749 | −0.916768 | −0.458384 | − | 0.888754i | \(-0.651572\pi\) | ||||
−0.458384 | + | 0.888754i | \(0.651572\pi\) | |||||||
\(602\) | 21.0640i | 0.858503i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 78.7631 | 3.20482 | ||||||||
\(605\) | 1.48119 | − | 1.67513i | 0.0602191 | − | 0.0681038i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 33.5183i | − | 1.36047i | −0.732995 | − | 0.680234i | \(-0.761878\pi\) | ||
0.732995 | − | 0.680234i | \(-0.238122\pi\) | |||||||
\(608\) | 72.9643i | 2.95909i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 35.5125 | + | 31.4010i | 1.43786 | + | 1.27139i | ||||
\(611\) | −22.0752 | −0.893068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5672i | 0.467196i | 0.972333 | + | 0.233598i | \(0.0750499\pi\) | ||||
−0.972333 | + | 0.233598i | \(0.924950\pi\) | |||||||
\(614\) | 7.10413 | 0.286699 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −23.6932 | −0.954627 | ||||||||
\(617\) | − | 33.3357i | − | 1.34204i | −0.741438 | − | 0.671022i | \(-0.765856\pi\) | ||
0.741438 | − | 0.671022i | \(-0.234144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.43866 | −0.178405 | −0.0892024 | − | 0.996014i | \(-0.528432\pi\) | ||||
−0.0892024 | + | 0.996014i | \(0.528432\pi\) | |||||||
\(620\) | 7.35026 | − | 8.31265i | 0.295194 | − | 0.333844i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 42.7367i | 1.71359i | ||||||||
\(623\) | 8.31265i | 0.333039i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | + | 6.07522i | −0.970024 | + | 0.243009i | ||||
\(626\) | 0.162205 | 0.00648301 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.1622i | 1.44303i | ||||||||
\(629\) | 7.32582 | 0.292100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.8496 | −1.58639 | −0.793193 | − | 0.608971i | \(-0.791583\pi\) | ||||
−0.793193 | + | 0.608971i | \(0.791583\pi\) | |||||||
\(632\) | 11.4010i | 0.453509i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.2012 | −0.405143 | ||||||||
\(635\) | −20.8021 | − | 18.3938i | −0.825506 | − | 0.729934i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47371i | 0.177255i | ||||||||
\(638\) | − | 6.38787i | − | 0.252898i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.7562 | − | 24.5428i | −1.09716 | − | 0.970139i | ||||
\(641\) | 3.88858 | 0.153590 | 0.0767948 | − | 0.997047i | \(-0.475531\pi\) | ||||
0.0767948 | + | 0.997047i | \(0.475531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.9380i | 1.61444i | 0.590254 | + | 0.807218i | \(0.299028\pi\) | ||||
−0.590254 | + | 0.807218i | \(0.700972\pi\) | |||||||
\(644\) | 57.8759 | 2.28063 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −55.6093 | −2.18792 | ||||||||
\(647\) | 1.76257i | 0.0692939i | 0.999400 | + | 0.0346469i | \(0.0110307\pi\) | ||||
−0.999400 | + | 0.0346469i | \(0.988969\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.2750 | −0.521091 | ||||||||
\(650\) | −8.38199 | − | 67.9511i | −0.328769 | − | 2.66526i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 34.8627i | − | 1.36533i | ||||||
\(653\) | 7.03761i | 0.275403i | 0.990474 | + | 0.137702i | \(0.0439715\pi\) | ||||
−0.990474 | + | 0.137702i | \(0.956029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.77575 | + | 9.92478i | −0.342897 | + | 0.387793i | ||||
\(656\) | 29.3112 | 1.14441 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 32.3733i | − | 1.26204i | ||||||
\(659\) | −12.6253 | −0.491812 | −0.245906 | − | 0.969294i | \(-0.579085\pi\) | ||||
−0.245906 | + | 0.969294i | \(0.579085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2243 | 0.514364 | 0.257182 | − | 0.966363i | \(-0.417206\pi\) | ||||
0.257182 | + | 0.966363i | \(0.417206\pi\) | |||||||
\(662\) | 64.9741i | 2.52529i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.80606 | 0.264126 | ||||||||
\(665\) | −21.5026 | − | 19.0132i | −0.833836 | − | 0.737299i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.55149i | 0.369835i | ||||||||
\(668\) | 60.9438i | 2.35799i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 42.3996 | − | 47.9511i | 1.63804 | − | 1.85251i | ||||
\(671\) | 7.92478 | 0.305933 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2677i | 0.704170i | 0.935968 | + | 0.352085i | \(0.114527\pi\) | ||||
−0.935968 | + | 0.352085i | \(0.885473\pi\) | |||||||
\(674\) | −60.4055 | −2.32673 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 68.0698 | 2.61807 | ||||||||
\(677\) | − | 33.0191i | − | 1.26903i | −0.772912 | − | 0.634513i | \(-0.781201\pi\) | ||
0.772912 | − | 0.634513i | \(-0.218799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.8496 | 1.06877 | ||||||||
\(680\) | 56.8324 | − | 64.2736i | 2.17942 | − | 2.46478i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 2.57452i | − | 0.0985833i | ||||||
\(683\) | − | 30.8627i | − | 1.18093i | −0.807063 | − | 0.590465i | \(-0.798944\pi\) | ||
0.807063 | − | 0.590465i | \(-0.201056\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.4142 | + | 14.5139i | 0.627155 | + | 0.554547i | ||||
\(686\) | 45.9854 | 1.75573 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 34.4445i | 1.31319i | ||||||||
\(689\) | 33.6531 | 1.28208 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.6991 | 1.05372 | 0.526862 | − | 0.849951i | \(-0.323369\pi\) | ||||
0.526862 | + | 0.849951i | \(0.323369\pi\) | |||||||
\(692\) | 36.0567i | 1.37067i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −54.0176 | −2.05048 | ||||||||
\(695\) | 3.14903 | − | 3.56134i | 0.119450 | − | 0.135089i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8510i | 0.411010i | ||||||||
\(698\) | 72.8989i | 2.75927i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 71.8007 | − | 8.85685i | 2.71381 | − | 0.334757i | ||||
\(701\) | 38.9643 | 1.47166 | 0.735831 | − | 0.677166i | \(-0.236792\pi\) | ||||
0.735831 | + | 0.677166i | \(0.236792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.37470i | − | 0.278142i | ||||||
\(704\) | −18.1187 | −0.682875 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.4372 | 0.505717 | ||||||||
\(707\) | − | 38.1965i | − | 1.43653i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.32250 | 0.162335 | 0.0811674 | − | 0.996700i | \(-0.474135\pi\) | ||||
0.0811674 | + | 0.996700i | \(0.474135\pi\) | |||||||
\(710\) | 32.9380 | + | 29.1246i | 1.23614 | + | 1.09303i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 25.0132i | 0.937408i | ||||||||
\(713\) | 3.84955i | 0.144167i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.57452 | − | 7.58181i | −0.320669 | − | 0.283544i | ||||
\(716\) | 13.9248 | 0.520393 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 48.6253i | − | 1.81468i | ||||||
\(719\) | −38.3996 | −1.43206 | −0.716032 | − | 0.698067i | \(-0.754044\pi\) | ||||
−0.716032 | + | 0.698067i | \(0.754044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.7743 | 1.70473 | ||||||||
\(722\) | 5.15282i | 0.191768i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 109.313 | 4.06259 | ||||||||
\(725\) | 1.46168 | + | 11.8496i | 0.0542855 | + | 0.440081i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6728i | 0.803798i | 0.915684 | + | 0.401899i | \(0.131650\pi\) | ||||
−0.915684 | + | 0.401899i | \(0.868350\pi\) | |||||||
\(728\) | 121.279i | 4.49489i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −25.4314 | + | 28.7612i | −0.941257 | + | 1.06450i | ||||
\(731\) | −12.7513 | −0.471624 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.0698i | 0.925976i | 0.886365 | + | 0.462988i | \(0.153223\pi\) | ||||
−0.886365 | + | 0.462988i | \(0.846777\pi\) | |||||||
\(734\) | −22.9116 | −0.845683 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 63.8007 | 2.35172 | ||||||||
\(737\) | − | 10.7005i | − | 0.394159i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.9018 | 0.695312 | 0.347656 | − | 0.937622i | \(-0.386978\pi\) | ||||
0.347656 | + | 0.937622i | \(0.386978\pi\) | |||||||
\(740\) | 13.9248 | + | 12.3127i | 0.511885 | + | 0.452622i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 49.3522i | 1.81178i | ||||||||
\(743\) | − | 43.6688i | − | 1.60205i | −0.598629 | − | 0.801026i | \(-0.704288\pi\) | ||
0.598629 | − | 0.801026i | \(-0.295712\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.3127 | − | 13.9248i | 0.451101 | − | 0.510164i | ||||
\(746\) | −20.9175 | −0.765843 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 23.4314i | − | 0.856736i | ||||||
\(749\) | −26.4650 | −0.967010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.0541 | −1.71703 | −0.858514 | − | 0.512789i | \(-0.828612\pi\) | ||||
−0.858514 | + | 0.512789i | \(0.828612\pi\) | |||||||
\(752\) | − | 52.9380i | − | 1.93045i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −32.6977 | −1.19078 | ||||||||
\(755\) | −22.6253 | + | 25.5877i | −0.823419 | + | 0.931231i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.9116i | 0.978119i | 0.872250 | + | 0.489059i | \(0.162660\pi\) | ||||
−0.872250 | + | 0.489059i | \(0.837340\pi\) | |||||||
\(758\) | − | 3.07381i | − | 0.111646i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −64.7024 | − | 57.2116i | −2.34700 | − | 2.07528i | ||||
\(761\) | −16.6859 | −0.604865 | −0.302432 | − | 0.953171i | \(-0.597799\pi\) | ||||
−0.302432 | + | 0.953171i | \(0.597799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 43.2163i | − | 1.56454i | ||||||
\(764\) | 67.8007 | 2.45294 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 91.1871 | 3.29473 | ||||||||
\(767\) | 67.9511i | 2.45357i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.2995 | −0.840201 | −0.420100 | − | 0.907478i | \(-0.638005\pi\) | ||||
−0.420100 | + | 0.907478i | \(0.638005\pi\) | |||||||
\(770\) | 11.1187 | − | 12.5745i | 0.400691 | − | 0.453154i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 30.3938i | − | 1.09390i | ||||||
\(773\) | 1.63656i | 0.0588631i | 0.999567 | + | 0.0294316i | \(0.00936971\pi\) | ||||
−0.999567 | + | 0.0294316i | \(0.990630\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.589104 | + | 4.77575i | 0.0211612 | + | 0.171550i | ||||
\(776\) | 83.8007 | 3.00827 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 63.5994i | 2.28015i | ||||||||
\(779\) | 10.9234 | 0.391370 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.35026 | 0.263013 | ||||||||
\(782\) | 48.6253i | 1.73884i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.7283 | −0.383153 | ||||||||
\(785\) | −11.7480 | − | 10.3879i | −0.419304 | − | 0.370759i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.09095i | 0.0745344i | 0.999305 | + | 0.0372672i | \(0.0118653\pi\) | ||||
−0.999305 | + | 0.0372672i | \(0.988135\pi\) | |||||||
\(788\) | − | 105.157i | − | 3.74606i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.05079 | − | 5.35026i | −0.215277 | − | 0.190354i |