Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(131,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("572.131");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.e (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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 131.8 | ||
Character | \(\chi\) | \(=\) | 572.131 |
Dual form | 572.2.e.b.131.7 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33395 | + | 0.469670i | −0.943242 | + | 0.332107i | ||||
\(3\) | − | 3.04863i | − | 1.76013i | −0.474853 | − | 0.880065i | \(-0.657499\pi\) | ||
0.474853 | − | 0.880065i | \(-0.342501\pi\) | |||||||
\(4\) | 1.55882 | − | 1.25303i | 0.779410 | − | 0.626514i | ||||
\(5\) | −2.77923 | −1.24291 | −0.621455 | − | 0.783450i | \(-0.713458\pi\) | ||||
−0.621455 | + | 0.783450i | \(0.713458\pi\) | |||||||
\(6\) | 1.43185 | + | 4.06671i | 0.584551 | + | 1.66023i | ||||
\(7\) | −0.398342 | −0.150559 | −0.0752795 | − | 0.997162i | \(-0.523985\pi\) | ||||
−0.0752795 | + | 0.997162i | \(0.523985\pi\) | |||||||
\(8\) | −1.49087 | + | 2.40360i | −0.527103 | + | 0.849801i | ||||
\(9\) | −6.29417 | −2.09806 | ||||||||
\(10\) | 3.70734 | − | 1.30532i | 1.17237 | − | 0.412779i | ||||
\(11\) | 1.84401 | + | 2.75674i | 0.555990 | + | 0.831189i | ||||
\(12\) | −3.82002 | − | 4.75227i | −1.10275 | − | 1.37186i | ||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0.531366 | − | 0.187089i | 0.142014 | − | 0.0500017i | ||||
\(15\) | 8.47286i | 2.18768i | ||||||||
\(16\) | 0.859843 | − | 3.90649i | 0.214961 | − | 0.976623i | ||||
\(17\) | 4.37142i | 1.06023i | 0.847927 | + | 0.530113i | \(0.177850\pi\) | ||||
−0.847927 | + | 0.530113i | \(0.822150\pi\) | |||||||
\(18\) | 8.39608 | − | 2.95618i | 1.97898 | − | 0.696779i | ||||
\(19\) | −5.64036 | −1.29399 | −0.646994 | − | 0.762495i | \(-0.723974\pi\) | ||||
−0.646994 | + | 0.762495i | \(0.723974\pi\) | |||||||
\(20\) | −4.33232 | + | 3.48245i | −0.968737 | + | 0.778701i | ||||
\(21\) | 1.21440i | 0.265004i | ||||||||
\(22\) | −3.75457 | − | 2.81127i | −0.800477 | − | 0.599364i | ||||
\(23\) | − | 0.542331i | − | 0.113084i | −0.998400 | − | 0.0565419i | \(-0.981993\pi\) | ||
0.998400 | − | 0.0565419i | \(-0.0180074\pi\) | |||||||
\(24\) | 7.32770 | + | 4.54512i | 1.49576 | + | 0.927770i | ||||
\(25\) | 2.72413 | 0.544826 | ||||||||
\(26\) | −0.469670 | − | 1.33395i | −0.0921098 | − | 0.261608i | ||||
\(27\) | 10.0427i | 1.93272i | ||||||||
\(28\) | −0.620944 | + | 0.499134i | −0.117347 | + | 0.0943274i | ||||
\(29\) | − | 2.16310i | − | 0.401678i | −0.979624 | − | 0.200839i | \(-0.935633\pi\) | ||
0.979624 | − | 0.200839i | \(-0.0643667\pi\) | |||||||
\(30\) | −3.97945 | − | 11.3023i | −0.726544 | − | 2.06351i | ||||
\(31\) | − | 3.59359i | − | 0.645429i | −0.946496 | − | 0.322714i | \(-0.895405\pi\) | ||
0.946496 | − | 0.322714i | \(-0.104595\pi\) | |||||||
\(32\) | 0.687778 | + | 5.61489i | 0.121583 | + | 0.992581i | ||||
\(33\) | 8.40430 | − | 5.62172i | 1.46300 | − | 0.978615i | ||||
\(34\) | −2.05312 | − | 5.83124i | −0.352108 | − | 1.00005i | ||||
\(35\) | 1.10708 | 0.187131 | ||||||||
\(36\) | −9.81149 | + | 7.88677i | −1.63525 | + | 1.31446i | ||||
\(37\) | 10.6214 | 1.74615 | 0.873074 | − | 0.487588i | \(-0.162123\pi\) | ||||
0.873074 | + | 0.487588i | \(0.162123\pi\) | |||||||
\(38\) | 7.52394 | − | 2.64911i | 1.22054 | − | 0.429742i | ||||
\(39\) | 3.04863 | 0.488172 | ||||||||
\(40\) | 4.14348 | − | 6.68017i | 0.655142 | − | 1.05623i | ||||
\(41\) | 10.6003i | 1.65550i | 0.561100 | + | 0.827748i | \(0.310378\pi\) | ||||
−0.561100 | + | 0.827748i | \(0.689622\pi\) | |||||||
\(42\) | −0.570367 | − | 1.61994i | −0.0880095 | − | 0.249962i | ||||
\(43\) | 1.79968 | 0.274448 | 0.137224 | − | 0.990540i | \(-0.456182\pi\) | ||||
0.137224 | + | 0.990540i | \(0.456182\pi\) | |||||||
\(44\) | 6.32876 | + | 1.98667i | 0.954096 | + | 0.299501i | ||||
\(45\) | 17.4930 | 2.60770 | ||||||||
\(46\) | 0.254716 | + | 0.723440i | 0.0375559 | + | 0.106665i | ||||
\(47\) | 3.13709i | 0.457592i | 0.973474 | + | 0.228796i | \(0.0734789\pi\) | ||||
−0.973474 | + | 0.228796i | \(0.926521\pi\) | |||||||
\(48\) | −11.9095 | − | 2.62135i | −1.71898 | − | 0.378359i | ||||
\(49\) | −6.84132 | −0.977332 | ||||||||
\(50\) | −3.63384 | + | 1.27944i | −0.513903 | + | 0.180940i | ||||
\(51\) | 13.3269 | 1.86613 | ||||||||
\(52\) | 1.25303 | + | 1.55882i | 0.173764 | + | 0.216170i | ||||
\(53\) | −2.00293 | −0.275124 | −0.137562 | − | 0.990493i | \(-0.543927\pi\) | ||||
−0.137562 | + | 0.990493i | \(0.543927\pi\) | |||||||
\(54\) | −4.71677 | − | 13.3965i | −0.641871 | − | 1.82303i | ||||
\(55\) | −5.12494 | − | 7.66162i | −0.691046 | − | 1.03309i | ||||
\(56\) | 0.593877 | − | 0.957455i | 0.0793601 | − | 0.127945i | ||||
\(57\) | 17.1954i | 2.27759i | ||||||||
\(58\) | 1.01594 | + | 2.88546i | 0.133400 | + | 0.378879i | ||||
\(59\) | 3.35411i | 0.436668i | 0.975874 | + | 0.218334i | \(0.0700622\pi\) | ||||
−0.975874 | + | 0.218334i | \(0.929938\pi\) | |||||||
\(60\) | 10.6167 | + | 13.2077i | 1.37061 | + | 1.70510i | ||||
\(61\) | − | 5.99977i | − | 0.768192i | −0.923293 | − | 0.384096i | \(-0.874513\pi\) | ||
0.923293 | − | 0.384096i | \(-0.125487\pi\) | |||||||
\(62\) | 1.68780 | + | 4.79366i | 0.214351 | + | 0.608795i | ||||
\(63\) | 2.50723 | 0.315882 | ||||||||
\(64\) | −3.55460 | − | 7.16692i | −0.444325 | − | 0.895866i | ||||
\(65\) | − | 2.77923i | − | 0.344721i | ||||||
\(66\) | −8.57052 | + | 11.4463i | −1.05496 | + | 1.40894i | ||||
\(67\) | 1.31372i | 0.160496i | 0.996775 | + | 0.0802481i | \(0.0255713\pi\) | ||||
−0.996775 | + | 0.0802481i | \(0.974429\pi\) | |||||||
\(68\) | 5.47751 | + | 6.81426i | 0.664246 | + | 0.826350i | ||||
\(69\) | −1.65337 | −0.199042 | ||||||||
\(70\) | −1.47679 | + | 0.519964i | −0.176510 | + | 0.0621476i | ||||
\(71\) | 2.74132i | 0.325334i | 0.986681 | + | 0.162667i | \(0.0520097\pi\) | ||||
−0.986681 | + | 0.162667i | \(0.947990\pi\) | |||||||
\(72\) | 9.38381 | − | 15.1287i | 1.10589 | − | 1.78293i | ||||
\(73\) | 11.0605i | 1.29454i | 0.762263 | + | 0.647268i | \(0.224089\pi\) | ||||
−0.762263 | + | 0.647268i | \(0.775911\pi\) | |||||||
\(74\) | −14.1684 | + | 4.98855i | −1.64704 | + | 0.579907i | ||||
\(75\) | − | 8.30488i | − | 0.958965i | ||||||
\(76\) | −8.79231 | + | 7.06753i | −1.00855 | + | 0.810701i | ||||
\(77\) | −0.734547 | − | 1.09813i | −0.0837094 | − | 0.125143i | ||||
\(78\) | −4.06671 | + | 1.43185i | −0.460464 | + | 0.162125i | ||||
\(79\) | −15.8741 | −1.78598 | −0.892990 | − | 0.450076i | \(-0.851397\pi\) | ||||
−0.892990 | + | 0.450076i | \(0.851397\pi\) | |||||||
\(80\) | −2.38970 | + | 10.8570i | −0.267177 | + | 1.21385i | ||||
\(81\) | 11.7341 | 1.30379 | ||||||||
\(82\) | −4.97866 | − | 14.1403i | −0.549801 | − | 1.56153i | ||||
\(83\) | −12.6524 | −1.38878 | −0.694391 | − | 0.719598i | \(-0.744326\pi\) | ||||
−0.694391 | + | 0.719598i | \(0.744326\pi\) | |||||||
\(84\) | 1.52168 | + | 1.89303i | 0.166028 | + | 0.206547i | ||||
\(85\) | − | 12.1492i | − | 1.31776i | ||||||
\(86\) | −2.40067 | + | 0.845253i | −0.258871 | + | 0.0911460i | ||||
\(87\) | −6.59450 | −0.707005 | ||||||||
\(88\) | −9.37529 | + | 0.322321i | −0.999410 | + | 0.0343595i | ||||
\(89\) | −10.5207 | −1.11519 | −0.557595 | − | 0.830113i | \(-0.688276\pi\) | ||||
−0.557595 | + | 0.830113i | \(0.688276\pi\) | |||||||
\(90\) | −23.3347 | + | 8.21592i | −2.45969 | + | 0.866034i | ||||
\(91\) | − | 0.398342i | − | 0.0417576i | ||||||
\(92\) | −0.679555 | − | 0.845396i | −0.0708486 | − | 0.0881387i | ||||
\(93\) | −10.9556 | −1.13604 | ||||||||
\(94\) | −1.47340 | − | 4.18471i | −0.151969 | − | 0.431620i | ||||
\(95\) | 15.6759 | 1.60831 | ||||||||
\(96\) | 17.1177 | − | 2.09678i | 1.74707 | − | 0.214002i | ||||
\(97\) | 12.5793 | 1.27724 | 0.638619 | − | 0.769523i | \(-0.279506\pi\) | ||||
0.638619 | + | 0.769523i | \(0.279506\pi\) | |||||||
\(98\) | 9.12595 | − | 3.21316i | 0.921860 | − | 0.324579i | ||||
\(99\) | −11.6065 | − | 17.3514i | −1.16650 | − | 1.74388i | ||||
\(100\) | 4.24643 | − | 3.41341i | 0.424643 | − | 0.341341i | ||||
\(101\) | 9.24664i | 0.920075i | 0.887899 | + | 0.460038i | \(0.152164\pi\) | ||||
−0.887899 | + | 0.460038i | \(0.847836\pi\) | |||||||
\(102\) | −17.7773 | + | 6.25923i | −1.76022 | + | 0.619756i | ||||
\(103\) | 16.2399i | 1.60017i | 0.599887 | + | 0.800084i | \(0.295212\pi\) | ||||
−0.599887 | + | 0.800084i | \(0.704788\pi\) | |||||||
\(104\) | −2.40360 | − | 1.49087i | −0.235693 | − | 0.146192i | ||||
\(105\) | − | 3.37510i | − | 0.329376i | ||||||
\(106\) | 2.67180 | − | 0.940717i | 0.259508 | − | 0.0913705i | ||||
\(107\) | 3.19262 | 0.308642 | 0.154321 | − | 0.988021i | \(-0.450681\pi\) | ||||
0.154321 | + | 0.988021i | \(0.450681\pi\) | |||||||
\(108\) | 12.5838 | + | 15.6548i | 1.21088 | + | 1.50638i | ||||
\(109\) | 1.52765i | 0.146323i | 0.997320 | + | 0.0731614i | \(0.0233088\pi\) | ||||
−0.997320 | + | 0.0731614i | \(0.976691\pi\) | |||||||
\(110\) | 10.4348 | + | 7.81316i | 0.994921 | + | 0.744955i | ||||
\(111\) | − | 32.3808i | − | 3.07345i | ||||||
\(112\) | −0.342511 | + | 1.55612i | −0.0323643 | + | 0.147039i | ||||
\(113\) | 4.50879 | 0.424151 | 0.212076 | − | 0.977253i | \(-0.431978\pi\) | ||||
0.212076 | + | 0.977253i | \(0.431978\pi\) | |||||||
\(114\) | −8.07616 | − | 22.9377i | −0.756402 | − | 2.14832i | ||||
\(115\) | 1.50726i | 0.140553i | ||||||||
\(116\) | −2.71042 | − | 3.37188i | −0.251657 | − | 0.313072i | ||||
\(117\) | − | 6.29417i | − | 0.581896i | ||||||
\(118\) | −1.57532 | − | 4.47420i | −0.145020 | − | 0.411883i | ||||
\(119\) | − | 1.74132i | − | 0.159627i | ||||||
\(120\) | −20.3654 | − | 12.6320i | −1.85910 | − | 1.15313i | ||||
\(121\) | −4.19924 | + | 10.1669i | −0.381749 | + | 0.924266i | ||||
\(122\) | 2.81791 | + | 8.00337i | 0.255122 | + | 0.724591i | ||||
\(123\) | 32.3166 | 2.91389 | ||||||||
\(124\) | −4.50287 | − | 5.60177i | −0.404370 | − | 0.503054i | ||||
\(125\) | 6.32517 | 0.565740 | ||||||||
\(126\) | −3.34451 | + | 1.17757i | −0.297953 | + | 0.104906i | ||||
\(127\) | 3.98567 | 0.353671 | 0.176835 | − | 0.984240i | \(-0.443414\pi\) | ||||
0.176835 | + | 0.984240i | \(0.443414\pi\) | |||||||
\(128\) | 8.10773 | + | 7.89080i | 0.716629 | + | 0.697455i | ||||
\(129\) | − | 5.48655i | − | 0.483064i | ||||||
\(130\) | 1.30532 | + | 3.70734i | 0.114484 | + | 0.325156i | ||||
\(131\) | −10.5958 | −0.925755 | −0.462878 | − | 0.886422i | \(-0.653183\pi\) | ||||
−0.462878 | + | 0.886422i | \(0.653183\pi\) | |||||||
\(132\) | 6.05662 | − | 19.2941i | 0.527161 | − | 1.67933i | ||||
\(133\) | 2.24679 | 0.194822 | ||||||||
\(134\) | −0.617013 | − | 1.75243i | −0.0533018 | − | 0.151387i | ||||
\(135\) | − | 27.9111i | − | 2.40220i | ||||||
\(136\) | −10.5072 | − | 6.51723i | −0.900981 | − | 0.558848i | ||||
\(137\) | −20.2489 | −1.72998 | −0.864992 | − | 0.501786i | \(-0.832677\pi\) | ||||
−0.864992 | + | 0.501786i | \(0.832677\pi\) | |||||||
\(138\) | 2.20550 | − | 0.776537i | 0.187745 | − | 0.0661032i | ||||
\(139\) | 2.34340 | 0.198765 | 0.0993823 | − | 0.995049i | \(-0.468313\pi\) | ||||
0.0993823 | + | 0.995049i | \(0.468313\pi\) | |||||||
\(140\) | 1.72575 | − | 1.38721i | 0.145852 | − | 0.117240i | ||||
\(141\) | 9.56385 | 0.805422 | ||||||||
\(142\) | −1.28751 | − | 3.65677i | −0.108046 | − | 0.306869i | ||||
\(143\) | −2.75674 | + | 1.84401i | −0.230530 | + | 0.154204i | ||||
\(144\) | −5.41200 | + | 24.5881i | −0.451000 | + | 2.04901i | ||||
\(145\) | 6.01176i | 0.499249i | ||||||||
\(146\) | −5.19479 | − | 14.7541i | −0.429924 | − | 1.22106i | ||||
\(147\) | 20.8567i | 1.72023i | ||||||||
\(148\) | 16.5569 | − | 13.3089i | 1.36097 | − | 1.09399i | ||||
\(149\) | − | 20.6774i | − | 1.69396i | −0.531625 | − | 0.846980i | \(-0.678418\pi\) | ||
0.531625 | − | 0.846980i | \(-0.321582\pi\) | |||||||
\(150\) | 3.90055 | + | 11.0783i | 0.318479 | + | 0.904536i | ||||
\(151\) | −22.6843 | −1.84602 | −0.923009 | − | 0.384778i | \(-0.874278\pi\) | ||||
−0.923009 | + | 0.384778i | \(0.874278\pi\) | |||||||
\(152\) | 8.40906 | − | 13.5572i | 0.682065 | − | 1.09963i | ||||
\(153\) | − | 27.5145i | − | 2.22441i | ||||||
\(154\) | 1.49560 | + | 1.11984i | 0.120519 | + | 0.0902397i | ||||
\(155\) | 9.98743i | 0.802210i | ||||||||
\(156\) | 4.75227 | − | 3.82002i | 0.380486 | − | 0.305847i | ||||
\(157\) | 20.0985 | 1.60403 | 0.802016 | − | 0.597303i | \(-0.203761\pi\) | ||||
0.802016 | + | 0.597303i | \(0.203761\pi\) | |||||||
\(158\) | 21.1752 | − | 7.45560i | 1.68461 | − | 0.593136i | ||||
\(159\) | 6.10621i | 0.484254i | ||||||||
\(160\) | −1.91149 | − | 15.6051i | −0.151117 | − | 1.23369i | ||||
\(161\) | 0.216033i | 0.0170258i | ||||||||
\(162\) | −15.6526 | + | 5.51115i | −1.22979 | + | 0.432997i | ||||
\(163\) | 7.36228i | 0.576658i | 0.957531 | + | 0.288329i | \(0.0930998\pi\) | ||||
−0.957531 | + | 0.288329i | \(0.906900\pi\) | |||||||
\(164\) | 13.2825 | + | 16.5240i | 1.03719 | + | 1.29031i | ||||
\(165\) | −23.3575 | + | 15.6241i | −1.81838 | + | 1.21633i | ||||
\(166\) | 16.8776 | − | 5.94245i | 1.30996 | − | 0.461224i | ||||
\(167\) | −20.9937 | −1.62454 | −0.812271 | − | 0.583280i | \(-0.801769\pi\) | ||||
−0.812271 | + | 0.583280i | \(0.801769\pi\) | |||||||
\(168\) | −2.91893 | − | 1.81051i | −0.225200 | − | 0.139684i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 5.70611 | + | 16.2064i | 0.437639 | + | 1.24297i | ||||
\(171\) | 35.5014 | 2.71486 | ||||||||
\(172\) | 2.80537 | − | 2.25504i | 0.213908 | − | 0.171945i | ||||
\(173\) | − | 18.2803i | − | 1.38982i | −0.719095 | − | 0.694912i | \(-0.755443\pi\) | ||
0.719095 | − | 0.694912i | \(-0.244557\pi\) | |||||||
\(174\) | 8.79670 | − | 3.09724i | 0.666876 | − | 0.234801i | ||||
\(175\) | −1.08514 | −0.0820285 | ||||||||
\(176\) | 12.3547 | − | 4.83325i | 0.931274 | − | 0.364320i | ||||
\(177\) | 10.2255 | 0.768592 | ||||||||
\(178\) | 14.0340 | − | 4.94124i | 1.05189 | − | 0.370362i | ||||
\(179\) | 14.0224i | 1.04808i | 0.851692 | + | 0.524042i | \(0.175577\pi\) | ||||
−0.851692 | + | 0.524042i | \(0.824423\pi\) | |||||||
\(180\) | 27.2684 | − | 21.9192i | 2.03247 | − | 1.63376i | ||||
\(181\) | −8.16756 | −0.607090 | −0.303545 | − | 0.952817i | \(-0.598170\pi\) | ||||
−0.303545 | + | 0.952817i | \(0.598170\pi\) | |||||||
\(182\) | 0.187089 | + | 0.531366i | 0.0138680 | + | 0.0393875i | ||||
\(183\) | −18.2911 | −1.35212 | ||||||||
\(184\) | 1.30355 | + | 0.808546i | 0.0960988 | + | 0.0596068i | ||||
\(185\) | −29.5193 | −2.17030 | ||||||||
\(186\) | 14.6141 | − | 5.14549i | 1.07156 | − | 0.377286i | ||||
\(187\) | −12.0509 | + | 8.06095i | −0.881247 | + | 0.589475i | ||||
\(188\) | 3.93087 | + | 4.89017i | 0.286688 | + | 0.356652i | ||||
\(189\) | − | 4.00044i | − | 0.290989i | ||||||
\(190\) | −20.9108 | + | 7.36249i | −1.51703 | + | 0.534131i | ||||
\(191\) | − | 13.3593i | − | 0.966648i | −0.875441 | − | 0.483324i | \(-0.839429\pi\) | ||
0.875441 | − | 0.483324i | \(-0.160571\pi\) | |||||||
\(192\) | −21.8493 | + | 10.8367i | −1.57684 | + | 0.782070i | ||||
\(193\) | − | 18.5956i | − | 1.33854i | −0.743018 | − | 0.669271i | \(-0.766607\pi\) | ||
0.743018 | − | 0.669271i | \(-0.233393\pi\) | |||||||
\(194\) | −16.7802 | + | 5.90814i | −1.20474 | + | 0.424180i | ||||
\(195\) | −8.47286 | −0.606754 | ||||||||
\(196\) | −10.6644 | + | 8.57237i | −0.761743 | + | 0.612312i | ||||
\(197\) | 2.33017i | 0.166018i | 0.996549 | + | 0.0830090i | \(0.0264530\pi\) | ||||
−0.996549 | + | 0.0830090i | \(0.973547\pi\) | |||||||
\(198\) | 23.6319 | + | 17.6946i | 1.67945 | + | 1.25750i | ||||
\(199\) | − | 10.2603i | − | 0.727331i | −0.931530 | − | 0.363665i | \(-0.881525\pi\) | ||
0.931530 | − | 0.363665i | \(-0.118475\pi\) | |||||||
\(200\) | −4.06133 | + | 6.54772i | −0.287179 | + | 0.462994i | ||||
\(201\) | 4.00504 | 0.282494 | ||||||||
\(202\) | −4.34287 | − | 12.3345i | −0.305563 | − | 0.867853i | ||||
\(203\) | 0.861653i | 0.0604762i | ||||||||
\(204\) | 20.7742 | − | 16.6989i | 1.45448 | − | 1.16916i | ||||
\(205\) | − | 29.4608i | − | 2.05763i | ||||||
\(206\) | −7.62741 | − | 21.6632i | −0.531427 | − | 1.50935i | ||||
\(207\) | 3.41352i | 0.237256i | ||||||||
\(208\) | 3.90649 | + | 0.859843i | 0.270866 | + | 0.0596194i | ||||
\(209\) | −10.4009 | − | 15.5490i | −0.719445 | − | 1.07555i | ||||
\(210\) | 1.58518 | + | 4.50219i | 0.109388 | + | 0.310681i | ||||
\(211\) | 26.2772 | 1.80899 | 0.904497 | − | 0.426479i | \(-0.140246\pi\) | ||||
0.904497 | + | 0.426479i | \(0.140246\pi\) | |||||||
\(212\) | −3.12221 | + | 2.50973i | −0.214434 | + | 0.172369i | ||||
\(213\) | 8.35727 | 0.572631 | ||||||||
\(214\) | −4.25878 | + | 1.49948i | −0.291124 | + | 0.102502i | ||||
\(215\) | −5.00172 | −0.341114 | ||||||||
\(216\) | −24.1387 | − | 14.9724i | −1.64243 | − | 1.01874i | ||||
\(217\) | 1.43148i | 0.0971752i | ||||||||
\(218\) | −0.717493 | − | 2.03781i | −0.0485948 | − | 0.138018i | ||||
\(219\) | 33.7195 | 2.27855 | ||||||||
\(220\) | −17.5891 | − | 5.52141i | −1.18586 | − | 0.372253i | ||||
\(221\) | −4.37142 | −0.294054 | ||||||||
\(222\) | 15.2083 | + | 43.1942i | 1.02071 | + | 2.89900i | ||||
\(223\) | 23.7985i | 1.59366i | 0.604202 | + | 0.796831i | \(0.293492\pi\) | ||||
−0.604202 | + | 0.796831i | \(0.706508\pi\) | |||||||
\(224\) | −0.273971 | − | 2.23665i | −0.0183054 | − | 0.149442i | ||||
\(225\) | −17.1461 | −1.14308 | ||||||||
\(226\) | −6.01448 | + | 2.11764i | −0.400077 | + | 0.140864i | ||||
\(227\) | −13.8822 | −0.921397 | −0.460699 | − | 0.887557i | \(-0.652401\pi\) | ||||
−0.460699 | + | 0.887557i | \(0.652401\pi\) | |||||||
\(228\) | 21.5463 | + | 26.8045i | 1.42694 | + | 1.77517i | ||||
\(229\) | −25.6686 | −1.69623 | −0.848113 | − | 0.529815i | \(-0.822261\pi\) | ||||
−0.848113 | + | 0.529815i | \(0.822261\pi\) | |||||||
\(230\) | −0.707916 | − | 2.01061i | −0.0466786 | − | 0.132575i | ||||
\(231\) | −3.34778 | + | 2.23937i | −0.220268 | + | 0.147339i | ||||
\(232\) | 5.19923 | + | 3.22491i | 0.341346 | + | 0.211725i | ||||
\(233\) | 8.23801i | 0.539690i | 0.962904 | + | 0.269845i | \(0.0869725\pi\) | ||||
−0.962904 | + | 0.269845i | \(0.913027\pi\) | |||||||
\(234\) | 2.95618 | + | 8.39608i | 0.193252 | + | 0.548869i | ||||
\(235\) | − | 8.71871i | − | 0.568746i | ||||||
\(236\) | 4.20279 | + | 5.22845i | 0.273578 | + | 0.340343i | ||||
\(237\) | 48.3945i | 3.14356i | ||||||||
\(238\) | 0.817845 | + | 2.32283i | 0.0530130 | + | 0.150566i | ||||
\(239\) | 4.50382 | 0.291328 | 0.145664 | − | 0.989334i | \(-0.453468\pi\) | ||||
0.145664 | + | 0.989334i | \(0.453468\pi\) | |||||||
\(240\) | 33.0992 | + | 7.28533i | 2.13654 | + | 0.470266i | ||||
\(241\) | 26.5414i | 1.70968i | 0.518892 | + | 0.854840i | \(0.326345\pi\) | ||||
−0.518892 | + | 0.854840i | \(0.673655\pi\) | |||||||
\(242\) | 0.826463 | − | 15.5344i | 0.0531271 | − | 0.998588i | ||||
\(243\) | − | 5.64477i | − | 0.362112i | ||||||
\(244\) | −7.51788 | − | 9.35257i | −0.481283 | − | 0.598737i | ||||
\(245\) | 19.0136 | 1.21474 | ||||||||
\(246\) | −43.1085 | + | 15.1781i | −2.74850 | + | 0.967722i | ||||
\(247\) | − | 5.64036i | − | 0.358888i | ||||||
\(248\) | 8.63757 | + | 5.35759i | 0.548486 | + | 0.340207i | ||||
\(249\) | 38.5726i | 2.44444i | ||||||||
\(250\) | −8.43743 | + | 2.97074i | −0.533630 | + | 0.187886i | ||||
\(251\) | 24.5386i | 1.54886i | 0.632660 | + | 0.774430i | \(0.281963\pi\) | ||||
−0.632660 | + | 0.774430i | \(0.718037\pi\) | |||||||
\(252\) | 3.90833 | − | 3.14163i | 0.246201 | − | 0.197904i | ||||
\(253\) | 1.49507 | − | 1.00006i | 0.0939940 | − | 0.0628735i | ||||
\(254\) | −5.31666 | + | 1.87195i | −0.333597 | + | 0.117456i | ||||
\(255\) | −37.0384 | −2.31944 | ||||||||
\(256\) | −14.5213 | − | 6.71794i | −0.907584 | − | 0.419871i | ||||
\(257\) | −7.69395 | −0.479935 | −0.239968 | − | 0.970781i | \(-0.577137\pi\) | ||||
−0.239968 | + | 0.970781i | \(0.577137\pi\) | |||||||
\(258\) | 2.57687 | + | 7.31876i | 0.160429 | + | 0.455646i | ||||
\(259\) | −4.23095 | −0.262898 | ||||||||
\(260\) | −3.48245 | − | 4.33232i | −0.215973 | − | 0.268679i | ||||
\(261\) | 13.6149i | 0.842743i | ||||||||
\(262\) | 14.1342 | − | 4.97651i | 0.873211 | − | 0.307450i | ||||
\(263\) | 20.1790 | 1.24429 | 0.622147 | − | 0.782901i | \(-0.286261\pi\) | ||||
0.622147 | + | 0.782901i | \(0.286261\pi\) | |||||||
\(264\) | 0.982638 | + | 28.5818i | 0.0604772 | + | 1.75909i | ||||
\(265\) | 5.56661 | 0.341954 | ||||||||
\(266\) | −2.99710 | + | 1.05525i | −0.183764 | + | 0.0647016i | ||||
\(267\) | 32.0737i | 1.96288i | ||||||||
\(268\) | 1.64612 | + | 2.04785i | 0.100553 | + | 0.125092i | ||||
\(269\) | 9.03850 | 0.551087 | 0.275544 | − | 0.961289i | \(-0.411142\pi\) | ||||
0.275544 | + | 0.961289i | \(0.411142\pi\) | |||||||
\(270\) | 13.1090 | + | 37.2318i | 0.797788 | + | 2.26586i | ||||
\(271\) | −9.82055 | −0.596556 | −0.298278 | − | 0.954479i | \(-0.596412\pi\) | ||||
−0.298278 | + | 0.954479i | \(0.596412\pi\) | |||||||
\(272\) | 17.0769 | + | 3.75873i | 1.03544 | + | 0.227907i | ||||
\(273\) | −1.21440 | −0.0734988 | ||||||||
\(274\) | 27.0110 | − | 9.51032i | 1.63179 | − | 0.574539i | ||||
\(275\) | 5.02333 | + | 7.50972i | 0.302918 | + | 0.452853i | ||||
\(276\) | −2.57730 | + | 2.07172i | −0.155135 | + | 0.124703i | ||||
\(277\) | − | 10.0070i | − | 0.601265i | −0.953740 | − | 0.300632i | \(-0.902802\pi\) | ||
0.953740 | − | 0.300632i | \(-0.0971978\pi\) | |||||||
\(278\) | −3.12597 | + | 1.10062i | −0.187483 | + | 0.0660110i | ||||
\(279\) | 22.6187i | 1.35415i | ||||||||
\(280\) | −1.65052 | + | 2.66099i | −0.0986375 | + | 0.159025i | ||||
\(281\) | − | 10.9285i | − | 0.651937i | −0.945381 | − | 0.325968i | \(-0.894310\pi\) | ||
0.945381 | − | 0.325968i | \(-0.105690\pi\) | |||||||
\(282\) | −12.7577 | + | 4.49185i | −0.759708 | + | 0.267486i | ||||
\(283\) | 9.99728 | 0.594277 | 0.297138 | − | 0.954834i | \(-0.403968\pi\) | ||||
0.297138 | + | 0.954834i | \(0.403968\pi\) | |||||||
\(284\) | 3.43495 | + | 4.27322i | 0.203827 | + | 0.253569i | ||||
\(285\) | − | 47.7900i | − | 2.83084i | ||||||
\(286\) | 2.81127 | − | 3.75457i | 0.166234 | − | 0.222012i | ||||
\(287\) | − | 4.22256i | − | 0.249250i | ||||||
\(288\) | −4.32899 | − | 35.3411i | −0.255088 | − | 2.08249i | ||||
\(289\) | −2.10931 | −0.124077 | ||||||||
\(290\) | −2.82354 | − | 8.01935i | −0.165804 | − | 0.470913i | ||||
\(291\) | − | 38.3498i | − | 2.24811i | ||||||
\(292\) | 13.8591 | + | 17.2414i | 0.811045 | + | 1.00897i | ||||
\(293\) | − | 8.30235i | − | 0.485029i | −0.970148 | − | 0.242514i | \(-0.922028\pi\) | ||
0.970148 | − | 0.242514i | \(-0.0779721\pi\) | |||||||
\(294\) | −9.79576 | − | 27.8217i | −0.571300 | − | 1.62259i | ||||
\(295\) | − | 9.32185i | − | 0.542739i | ||||||
\(296\) | −15.8351 | + | 25.5296i | −0.920399 | + | 1.48388i | ||||
\(297\) | −27.6852 | + | 18.5189i | −1.60646 | + | 1.07458i | ||||
\(298\) | 9.71156 | + | 27.5825i | 0.562575 | + | 1.59781i | ||||
\(299\) | 0.542331 | 0.0313638 | ||||||||
\(300\) | −10.4062 | − | 12.9458i | −0.600805 | − | 0.747427i | ||||
\(301\) | −0.716886 | −0.0413206 | ||||||||
\(302\) | 30.2596 | − | 10.6541i | 1.74124 | − | 0.613075i | ||||
\(303\) | 28.1896 | 1.61945 | ||||||||
\(304\) | −4.84982 | + | 22.0340i | −0.278157 | + | 1.26374i | ||||
\(305\) | 16.6748i | 0.954794i | ||||||||
\(306\) | 12.9227 | + | 36.7028i | 0.738743 | + | 2.09816i | ||||
\(307\) | −14.5500 | −0.830412 | −0.415206 | − | 0.909727i | \(-0.636290\pi\) | ||||
−0.415206 | + | 0.909727i | \(0.636290\pi\) | |||||||
\(308\) | −2.52101 | − | 0.791373i | −0.143648 | − | 0.0450926i | ||||
\(309\) | 49.5096 | 2.81651 | ||||||||
\(310\) | −4.69080 | − | 13.3227i | −0.266419 | − | 0.756678i | ||||
\(311\) | − | 6.87576i | − | 0.389889i | −0.980814 | − | 0.194944i | \(-0.937547\pi\) | ||
0.980814 | − | 0.194944i | \(-0.0624526\pi\) | |||||||
\(312\) | −4.54512 | + | 7.32770i | −0.257317 | + | 0.414849i | ||||
\(313\) | −11.2456 | −0.635637 | −0.317819 | − | 0.948152i | \(-0.602950\pi\) | ||||
−0.317819 | + | 0.948152i | \(0.602950\pi\) | |||||||
\(314\) | −26.8102 | + | 9.43964i | −1.51299 | + | 0.532710i | ||||
\(315\) | −6.96818 | −0.392613 | ||||||||
\(316\) | −24.7449 | + | 19.8907i | −1.39201 | + | 1.11894i | ||||
\(317\) | 12.1388 | 0.681784 | 0.340892 | − | 0.940102i | \(-0.389271\pi\) | ||||
0.340892 | + | 0.940102i | \(0.389271\pi\) | |||||||
\(318\) | −2.86790 | − | 8.14535i | −0.160824 | − | 0.456769i | ||||
\(319\) | 5.96311 | − | 3.98878i | 0.333870 | − | 0.223329i | ||||
\(320\) | 9.87906 | + | 19.9185i | 0.552256 | + | 1.11348i | ||||
\(321\) | − | 9.73313i | − | 0.543250i | ||||||
\(322\) | −0.101464 | − | 0.288176i | −0.00565438 | − | 0.0160594i | ||||
\(323\) | − | 24.6564i | − | 1.37192i | ||||||
\(324\) | 18.2913 | − | 14.7031i | 1.01619 | − | 0.816841i | ||||
\(325\) | 2.72413i | 0.151108i | ||||||||
\(326\) | −3.45784 | − | 9.82088i | −0.191512 | − | 0.543928i | ||||
\(327\) | 4.65726 | 0.257547 | ||||||||
\(328\) | −25.4790 | − | 15.8038i | −1.40684 | − | 0.872616i | ||||
\(329\) | − | 1.24964i | − | 0.0688947i | ||||||
\(330\) | 23.8195 | − | 31.8119i | 1.31122 | − | 1.75119i | ||||
\(331\) | − | 32.4843i | − | 1.78550i | −0.450556 | − | 0.892748i | \(-0.648774\pi\) | ||
0.450556 | − | 0.892748i | \(-0.351226\pi\) | |||||||
\(332\) | −19.7228 | + | 15.8538i | −1.08243 | + | 0.870091i | ||||
\(333\) | −66.8529 | −3.66352 | ||||||||
\(334\) | 28.0045 | − | 9.86011i | 1.53234 | − | 0.539521i | ||||
\(335\) | − | 3.65113i | − | 0.199482i | ||||||
\(336\) | 4.74404 | + | 1.04419i | 0.258809 | + | 0.0569654i | ||||
\(337\) | 17.7181i | 0.965164i | 0.875851 | + | 0.482582i | \(0.160301\pi\) | ||||
−0.875851 | + | 0.482582i | \(0.839699\pi\) | |||||||
\(338\) | 1.33395 | − | 0.469670i | 0.0725571 | − | 0.0255467i | ||||
\(339\) | − | 13.7457i | − | 0.746562i | ||||||
\(340\) | −15.2233 | − | 18.9384i | −0.825598 | − | 1.02708i | ||||
\(341\) | 9.90661 | − | 6.62663i | 0.536473 | − | 0.358852i | ||||
\(342\) | −47.3569 | + | 16.6739i | −2.56077 | + | 0.901624i | ||||
\(343\) | 5.51358 | 0.297705 | ||||||||
\(344\) | −2.68309 | + | 4.32570i | −0.144662 | + | 0.233226i | ||||
\(345\) | 4.59509 | 0.247392 | ||||||||
\(346\) | 8.58570 | + | 24.3849i | 0.461570 | + | 1.31094i | ||||
\(347\) | −3.14912 | −0.169054 | −0.0845269 | − | 0.996421i | \(-0.526938\pi\) | ||||
−0.0845269 | + | 0.996421i | \(0.526938\pi\) | |||||||
\(348\) | −10.2796 | + | 8.26309i | −0.551047 | + | 0.442948i | ||||
\(349\) | 18.5071i | 0.990663i | 0.868704 | + | 0.495332i | \(0.164953\pi\) | ||||
−0.868704 | + | 0.495332i | \(0.835047\pi\) | |||||||
\(350\) | 1.44751 | − | 0.509655i | 0.0773727 | − | 0.0272422i | ||||
\(351\) | −10.0427 | −0.536041 | ||||||||
\(352\) | −14.2105 | + | 12.2499i | −0.757423 | + | 0.652924i | ||||
\(353\) | −17.3977 | −0.925987 | −0.462994 | − | 0.886362i | \(-0.653225\pi\) | ||||
−0.462994 | + | 0.886362i | \(0.653225\pi\) | |||||||
\(354\) | −13.6402 | + | 4.80259i | −0.724968 | + | 0.255255i | ||||
\(355\) | − | 7.61876i | − | 0.404362i | ||||||
\(356\) | −16.3998 | + | 13.1827i | −0.869190 | + | 0.698682i | ||||
\(357\) | −5.30865 | −0.280963 | ||||||||
\(358\) | −6.58591 | − | 18.7051i | −0.348076 | − | 0.988597i | ||||
\(359\) | 30.6959 | 1.62007 | 0.810033 | − | 0.586384i | \(-0.199449\pi\) | ||||
0.810033 | + | 0.586384i | \(0.199449\pi\) | |||||||
\(360\) | −26.0798 | + | 42.0461i | −1.37452 | + | 2.21603i | ||||
\(361\) | 12.8137 | 0.674405 | ||||||||
\(362\) | 10.8951 | − | 3.83606i | 0.572633 | − | 0.201619i | ||||
\(363\) | 30.9952 | + | 12.8020i | 1.62683 | + | 0.671929i | ||||
\(364\) | −0.499134 | − | 0.620944i | −0.0261617 | − | 0.0325463i | ||||
\(365\) | − | 30.7398i | − | 1.60899i | ||||||
\(366\) | 24.3994 | − | 8.59079i | 1.27537 | − | 0.449048i | ||||
\(367\) | − | 1.67921i | − | 0.0876542i | −0.999039 | − | 0.0438271i | \(-0.986045\pi\) | ||
0.999039 | − | 0.0438271i | \(-0.0139551\pi\) | |||||||
\(368\) | −2.11861 | − | 0.466319i | −0.110440 | − | 0.0243086i | ||||
\(369\) | − | 66.7204i | − | 3.47332i | ||||||
\(370\) | 39.3772 | − | 13.8643i | 2.04712 | − | 0.720773i | ||||
\(371\) | 0.797852 | 0.0414224 | ||||||||
\(372\) | −17.0777 | + | 13.7276i | −0.885440 | + | 0.711744i | ||||
\(373\) | 9.13778i | 0.473136i | 0.971615 | + | 0.236568i | \(0.0760226\pi\) | ||||
−0.971615 | + | 0.236568i | \(0.923977\pi\) | |||||||
\(374\) | 12.2892 | − | 16.4128i | 0.635461 | − | 0.848686i | ||||
\(375\) | − | 19.2831i | − | 0.995776i | ||||||
\(376\) | −7.54032 | − | 4.67701i | −0.388863 | − | 0.241198i | ||||
\(377\) | 2.16310 | 0.111405 | ||||||||
\(378\) | 1.87889 | + | 5.33637i | 0.0966395 | + | 0.274473i | ||||
\(379\) | − | 5.76958i | − | 0.296363i | −0.988960 | − | 0.148182i | \(-0.952658\pi\) | ||
0.988960 | − | 0.148182i | \(-0.0473420\pi\) | |||||||
\(380\) | 24.4359 | − | 19.6423i | 1.25353 | − | 1.00763i | ||||
\(381\) | − | 12.1508i | − | 0.622507i | ||||||
\(382\) | 6.27448 | + | 17.8206i | 0.321030 | + | 0.911783i | ||||
\(383\) | − | 13.1633i | − | 0.672615i | −0.941752 | − | 0.336308i | \(-0.890822\pi\) | ||
0.941752 | − | 0.336308i | \(-0.109178\pi\) | |||||||
\(384\) | 24.0562 | − | 24.7175i | 1.22761 | − | 1.26136i | ||||
\(385\) | 2.04148 | + | 3.05195i | 0.104043 | + | 0.155542i | ||||
\(386\) | 8.73380 | + | 24.8055i | 0.444539 | + | 1.26257i | ||||
\(387\) | −11.3275 | −0.575808 | ||||||||
\(388\) | 19.6089 | − | 15.7623i | 0.995493 | − | 0.800208i | ||||
\(389\) | −25.5589 | −1.29589 | −0.647943 | − | 0.761688i | \(-0.724371\pi\) | ||||
−0.647943 | + | 0.761688i | \(0.724371\pi\) | |||||||
\(390\) | 11.3023 | − | 3.97945i | 0.572316 | − | 0.201507i | ||||
\(391\) | 2.37076 | 0.119894 | ||||||||
\(392\) | 10.1995 | − | 16.4438i | 0.515154 | − | 0.830538i | ||||
\(393\) | 32.3026i | 1.62945i | ||||||||
\(394\) | −1.09441 | − | 3.10832i | −0.0551357 | − | 0.156595i | ||||
\(395\) | 44.1179 | 2.21981 | ||||||||
\(396\) | −39.8343 | − | 12.5044i | −2.00175 | − | 0.628371i | ||||
\(397\) | −5.52154 | −0.277118 | −0.138559 | − | 0.990354i | \(-0.544247\pi\) | ||||
−0.138559 | + | 0.990354i | \(0.544247\pi\) | |||||||
\(398\) | 4.81894 | + | 13.6866i | 0.241551 | + | 0.686049i | ||||
\(399\) | − | 6.84965i | − | 0.342911i | ||||||
\(400\) | 2.34232 | − | 10.6418i | 0.117116 | − | 0.532090i | ||||
\(401\) | −18.2270 | −0.910214 | −0.455107 | − | 0.890437i | \(-0.650399\pi\) | ||||
−0.455107 | + | 0.890437i | \(0.650399\pi\) | |||||||
\(402\) | −5.34251 | + | 1.88105i | −0.266460 | + | 0.0938182i | ||||
\(403\) | 3.59359 | 0.179010 | ||||||||
\(404\) | 11.5863 | + | 14.4139i | 0.576440 | + | 0.717116i | ||||
\(405\) | −32.6118 | −1.62049 | ||||||||
\(406\) | −0.404693 | − | 1.14940i | −0.0200846 | − | 0.0570437i | ||||
\(407\) | 19.5860 | + | 29.2804i | 0.970841 | + | 1.45138i | ||||
\(408\) | −19.8686 | + | 32.0325i | −0.983645 | + | 1.58584i | ||||
\(409\) | − | 24.0118i | − | 1.18730i | −0.804722 | − | 0.593652i | \(-0.797685\pi\) | ||
0.804722 | − | 0.593652i | \(-0.202315\pi\) | |||||||
\(410\) | 13.8369 | + | 39.2991i | 0.683354 | + | 1.94084i | ||||
\(411\) | 61.7316i | 3.04500i | ||||||||
\(412\) | 20.3491 | + | 25.3152i | 1.00253 | + | 1.24719i | ||||
\(413\) | − | 1.33608i | − | 0.0657443i | ||||||
\(414\) | −1.60323 | − | 4.55345i | −0.0787944 | − | 0.223790i | ||||
\(415\) | 35.1640 | 1.72613 | ||||||||
\(416\) | −5.61489 | + | 0.687778i | −0.275293 | + | 0.0337211i | ||||
\(417\) | − | 7.14417i | − | 0.349851i | ||||||
\(418\) | 21.1771 | + | 15.8566i | 1.03581 | + | 0.775570i | ||||
\(419\) | − | 19.6547i | − | 0.960195i | −0.877215 | − | 0.480098i | \(-0.840601\pi\) | ||
0.877215 | − | 0.480098i | \(-0.159399\pi\) | |||||||
\(420\) | −4.22909 | − | 5.26117i | −0.206358 | − | 0.256719i | ||||
\(421\) | 15.0542 | 0.733699 | 0.366849 | − | 0.930280i | \(-0.380436\pi\) | ||||
0.366849 | + | 0.930280i | \(0.380436\pi\) | |||||||
\(422\) | −35.0523 | + | 12.3416i | −1.70632 | + | 0.600779i | ||||
\(423\) | − | 19.7454i | − | 0.960055i | ||||||
\(424\) | 2.98612 | − | 4.81425i | 0.145019 | − | 0.233801i | ||||
\(425\) | 11.9083i | 0.577638i | ||||||||
\(426\) | −11.1481 | + | 3.92516i | −0.540129 | + | 0.190175i | ||||
\(427\) | 2.38996i | 0.115658i | ||||||||
\(428\) | 4.97672 | − | 4.00044i | 0.240559 | − | 0.193369i | ||||
\(429\) | 5.62172 | + | 8.40430i | 0.271419 | + | 0.405763i | ||||
\(430\) | 6.67202 | − | 2.34916i | 0.321753 | − | 0.113286i | ||||
\(431\) | −24.4855 | −1.17942 | −0.589711 | − | 0.807614i | \(-0.700759\pi\) | ||||
−0.589711 | + | 0.807614i | \(0.700759\pi\) | |||||||
\(432\) | 39.2318 | + | 8.63517i | 1.88754 | + | 0.415460i | ||||
\(433\) | 18.6992 | 0.898627 | 0.449313 | − | 0.893374i | \(-0.351669\pi\) | ||||
0.449313 | + | 0.893374i | \(0.351669\pi\) | |||||||
\(434\) | −0.672323 | − | 1.90952i | −0.0322725 | − | 0.0916597i | ||||
\(435\) | 18.3276 | 0.878743 | ||||||||
\(436\) | 1.91419 | + | 2.38134i | 0.0916732 | + | 0.114045i | ||||
\(437\) | 3.05894i | 0.146329i | ||||||||
\(438\) | −44.9799 | + | 15.8370i | −2.14923 | + | 0.756722i | ||||
\(439\) | 12.8816 | 0.614806 | 0.307403 | − | 0.951579i | \(-0.400540\pi\) | ||||
0.307403 | + | 0.951579i | \(0.400540\pi\) | |||||||
\(440\) | 26.0561 | − | 0.895804i | 1.24218 | − | 0.0427058i | ||||
\(441\) | 43.0605 | 2.05050 | ||||||||
\(442\) | 5.83124 | − | 2.05312i | 0.277364 | − | 0.0976572i | ||||
\(443\) | − | 21.8314i | − | 1.03724i | −0.855005 | − | 0.518620i | \(-0.826446\pi\) | ||
0.855005 | − | 0.518620i | \(-0.173554\pi\) | |||||||
\(444\) | −40.5740 | − | 50.4758i | −1.92556 | − | 2.39548i | ||||
\(445\) | 29.2394 | 1.38608 | ||||||||
\(446\) | −11.1774 | − | 31.7458i | −0.529266 | − | 1.50321i | ||||
\(447\) | −63.0379 | −2.98159 | ||||||||
\(448\) | 1.41595 | + | 2.85489i | 0.0668972 | + | 0.134881i | ||||
\(449\) | 23.8044 | 1.12340 | 0.561699 | − | 0.827341i | \(-0.310148\pi\) | ||||
0.561699 | + | 0.827341i | \(0.310148\pi\) | |||||||
\(450\) | 22.8720 | − | 8.05303i | 1.07820 | − | 0.379623i | ||||
\(451\) | −29.2224 | + | 19.5472i | −1.37603 | + | 0.920440i | ||||
\(452\) | 7.02840 | − | 5.64964i | 0.330588 | − | 0.265737i | ||||
\(453\) | 69.1560i | 3.24923i | ||||||||
\(454\) | 18.5182 | − | 6.52007i | 0.869100 | − | 0.306002i | ||||
\(455\) | 1.10708i | 0.0519009i | ||||||||
\(456\) | −41.3309 | − | 25.6361i | −1.93550 | − | 1.20052i | ||||
\(457\) | − | 31.0035i | − | 1.45028i | −0.688599 | − | 0.725142i | \(-0.741774\pi\) | ||
0.688599 | − | 0.725142i | \(-0.258226\pi\) | |||||||
\(458\) | 34.2405 | − | 12.0558i | 1.59995 | − | 0.563328i | ||||
\(459\) | −43.9010 | −2.04912 | ||||||||
\(460\) | 1.88864 | + | 2.34955i | 0.0880584 | + | 0.109548i | ||||
\(461\) | 6.53832i | 0.304520i | 0.988340 | + | 0.152260i | \(0.0486551\pi\) | ||||
−0.988340 | + | 0.152260i | \(0.951345\pi\) | |||||||
\(462\) | 3.41400 | − | 4.55954i | 0.158834 | − | 0.212129i | ||||
\(463\) | 4.13457i | 0.192150i | 0.995374 | + | 0.0960750i | \(0.0306289\pi\) | ||||
−0.995374 | + | 0.0960750i | \(0.969371\pi\) | |||||||
\(464\) | −8.45013 | − | 1.85993i | −0.392287 | − | 0.0863449i | ||||
\(465\) | 30.4480 | 1.41199 | ||||||||
\(466\) | −3.86915 | − | 10.9891i | −0.179235 | − | 0.509058i | ||||
\(467\) | 18.9956i | 0.879014i | 0.898239 | + | 0.439507i | \(0.144847\pi\) | ||||
−0.898239 | + | 0.439507i | \(0.855153\pi\) | |||||||
\(468\) | −7.88677 | − | 9.81149i | −0.364566 | − | 0.453536i | ||||
\(469\) | − | 0.523309i | − | 0.0241642i | ||||||
\(470\) | 4.09492 | + | 11.6303i | 0.188884 | + | 0.536465i | ||||
\(471\) | − | 61.2729i | − | 2.82330i | ||||||
\(472\) | −8.06194 | − | 5.00055i | −0.371081 | − | 0.230169i | ||||
\(473\) | 3.31862 | + | 4.96124i | 0.152590 | + | 0.228118i | ||||
\(474\) | −22.7294 | − | 64.5556i | −1.04400 | − | 2.96513i | ||||
\(475\) | −15.3651 | −0.704998 | ||||||||
\(476\) | −2.18192 | − | 2.71441i | −0.100008 | − | 0.124415i | ||||
\(477\) | 12.6068 | 0.577226 | ||||||||
\(478\) | −6.00784 | + | 2.11531i | −0.274792 | + | 0.0967519i | ||||
\(479\) | −13.2771 | −0.606644 | −0.303322 | − | 0.952888i | \(-0.598096\pi\) | ||||
−0.303322 | + | 0.952888i | \(0.598096\pi\) | |||||||
\(480\) | −47.5742 | + | 5.82745i | −2.17145 | + | 0.265985i | ||||
\(481\) | 10.6214i | 0.484294i | ||||||||
\(482\) | −12.4657 | − | 35.4047i | −0.567796 | − | 1.61264i | ||||
\(483\) | 0.658606 | 0.0299676 | ||||||||
\(484\) | 6.19357 | + | 21.1102i | 0.281526 | + | 0.959554i | ||||
\(485\) | −34.9609 | −1.58749 | ||||||||
\(486\) | 2.65118 | + | 7.52981i | 0.120260 | + | 0.341559i | ||||
\(487\) | 21.6937i | 0.983036i | 0.870867 | + | 0.491518i | \(0.163558\pi\) | ||||
−0.870867 | + | 0.491518i | \(0.836442\pi\) | |||||||
\(488\) | 14.4211 | + | 8.94490i | 0.652811 | + | 0.404916i | ||||
\(489\) | 22.4449 | 1.01499 | ||||||||
\(490\) | −25.3631 | + | 8.93013i | −1.14579 | + | 0.403422i | ||||
\(491\) | 17.5909 | 0.793867 | 0.396933 | − | 0.917847i | \(-0.370074\pi\) | ||||
0.396933 | + | 0.917847i | \(0.370074\pi\) | |||||||
\(492\) | 50.3757 | − | 40.4936i | 2.27111 | − | 1.82559i | ||||
\(493\) | 9.45582 | 0.425869 | ||||||||
\(494\) | 2.64911 | + | 7.52394i | 0.119189 | + | 0.338518i | ||||
\(495\) | 32.2572 | + | 48.2236i | 1.44985 | + | 2.16749i | ||||
\(496\) | −14.0383 | − | 3.08993i | −0.630340 | − | 0.138742i | ||||
\(497\) | − | 1.09198i | − | 0.0489821i | ||||||
\(498\) | −18.1164 | − | 51.4537i | −0.811814 | − | 2.30569i | ||||
\(499\) | 24.1164i | 1.07960i | 0.841794 | + | 0.539799i | \(0.181500\pi\) | ||||
−0.841794 | + | 0.539799i | \(0.818500\pi\) | |||||||
\(500\) | 9.85980 | − | 7.92561i | 0.440944 | − | 0.354444i | ||||
\(501\) | 64.0021i | 2.85940i | ||||||||
\(502\) | −11.5250 | − | 32.7331i | −0.514387 | − | 1.46095i | ||||
\(503\) | 10.6931 | 0.476781 | 0.238390 | − | 0.971169i | \(-0.423380\pi\) | ||||
0.238390 | + | 0.971169i | \(0.423380\pi\) | |||||||
\(504\) | −3.73796 | + | 6.02639i | −0.166502 | + | 0.268437i | ||||
\(505\) | − | 25.6986i | − | 1.14357i | ||||||
\(506\) | −1.52464 | + | 2.03622i | −0.0677783 | + | 0.0905209i | ||||
\(507\) | 3.04863i | 0.135395i | ||||||||
\(508\) | 6.21294 | − | 4.99415i | 0.275655 | − | 0.221580i | ||||
\(509\) | 4.63668 | 0.205517 | 0.102759 | − | 0.994706i | \(-0.467233\pi\) | ||||
0.102759 | + | 0.994706i | \(0.467233\pi\) | |||||||
\(510\) | 49.4073 | − | 17.3958i | 2.18779 | − | 0.770301i | ||||
\(511\) | − | 4.40587i | − | 0.194904i | ||||||
\(512\) | 22.5259 | + | 2.14112i | 0.995513 | + | 0.0946252i | ||||
\(513\) | − | 56.6446i | − | 2.50092i | ||||||
\(514\) | 10.2633 | − | 3.61361i | 0.452695 | − | 0.159390i | ||||
\(515\) | − | 45.1346i | − | 1.98887i | ||||||
\(516\) | −6.87480 | − | 8.55255i | −0.302646 | − | 0.376505i | ||||
\(517\) | −8.64816 | + | 5.78484i | −0.380346 | + | 0.254417i | ||||
\(518\) | 5.64385 | − | 1.98715i | 0.247977 | − | 0.0873103i | ||||
\(519\) | −55.7299 | −2.44627 | ||||||||
\(520\) | 6.68017 | + | 4.14348i | 0.292945 | + | 0.181704i | ||||
\(521\) | 21.2044 | 0.928982 | 0.464491 | − | 0.885578i | \(-0.346237\pi\) | ||||
0.464491 | + | 0.885578i | \(0.346237\pi\) | |||||||
\(522\) | −6.39452 | − | 18.1616i | −0.279880 | − | 0.794910i | ||||
\(523\) | −41.4207 | −1.81120 | −0.905599 | − | 0.424134i | \(-0.860579\pi\) | ||||
−0.905599 | + | 0.424134i | \(0.860579\pi\) | |||||||
\(524\) | −16.5169 | + | 13.2768i | −0.721543 | + | 0.579999i | ||||
\(525\) | 3.30818i | 0.144381i | ||||||||
\(526\) | −26.9177 | + | 9.47749i | −1.17367 | + | 0.413238i | ||||
\(527\) | 15.7091 | 0.684300 | ||||||||
\(528\) | −14.7348 | − | 37.6651i | −0.641250 | − | 1.63916i | ||||
\(529\) | 22.7059 | 0.987212 | ||||||||
\(530\) | −7.42556 | + | 2.61447i | −0.322546 | + | 0.113565i | ||||
\(531\) | − | 21.1113i | − | 0.916154i | ||||||
\(532\) | 3.50235 | − | 2.81529i | 0.151846 | − | 0.122058i | ||||
\(533\) | −10.6003 | −0.459152 | ||||||||
\(534\) | −15.0640 | − | 42.7846i | −0.651885 | − | 1.85147i | ||||
\(535\) | −8.87303 | −0.383614 | ||||||||
\(536\) | −3.15765 | − | 1.95858i | −0.136390 | − | 0.0845980i | ||||
\(537\) | 42.7492 | 1.84477 | ||||||||
\(538\) | −12.0569 | + | 4.24511i | −0.519808 | + | 0.183020i | ||||
\(539\) | −12.6155 | − | 18.8598i | −0.543387 | − | 0.812347i | ||||
\(540\) | −34.9733 | − | 43.5084i | −1.50501 | − | 1.87230i | ||||
\(541\) | − | 27.5097i | − | 1.18274i | −0.806402 | − | 0.591368i | \(-0.798588\pi\) | ||
0.806402 | − | 0.591368i | \(-0.201412\pi\) | |||||||
\(542\) | 13.1001 | − | 4.61242i | 0.562696 | − | 0.198120i | ||||
\(543\) | 24.8999i | 1.06856i | ||||||||
\(544\) | −24.5450 | + | 3.00657i | −1.05236 | + | 0.128905i | ||||
\(545\) | − | 4.24570i | − | 0.181866i | ||||||
\(546\) | 1.61994 | − | 0.570367i | 0.0693271 | − | 0.0244094i | ||||
\(547\) | 0.394737 | 0.0168777 | 0.00843887 | − | 0.999964i | \(-0.497314\pi\) | ||||
0.00843887 | + | 0.999964i | \(0.497314\pi\) | |||||||
\(548\) | −31.5645 | + | 25.3725i | −1.34837 | + | 1.08386i | ||||
\(549\) | 37.7636i | 1.61171i | ||||||||
\(550\) | −10.2279 | − | 7.65825i | −0.436121 | − | 0.326549i | ||||
\(551\) | 12.2007i | 0.519766i | ||||||||
\(552\) | 2.46496 | − | 3.97404i | 0.104916 | − | 0.169146i | ||||
\(553\) | 6.32334 | 0.268896 | ||||||||
\(554\) | 4.70001 | + | 13.3488i | 0.199684 | + | 0.567138i | ||||
\(555\) | 89.9937i | 3.82002i | ||||||||
\(556\) | 3.65294 | − | 2.93634i | 0.154919 | − | 0.124529i | ||||
\(557\) | − | 21.0202i | − | 0.890654i | −0.895368 | − | 0.445327i | \(-0.853087\pi\) | ||
0.895368 | − | 0.445327i | \(-0.146913\pi\) | |||||||
\(558\) | −10.6233 | − | 30.1721i | −0.449721 | − | 1.27729i | ||||
\(559\) | 1.79968i | 0.0761182i | ||||||||
\(560\) | 0.951919 | − | 4.32482i | 0.0402259 | − | 0.182757i | ||||
\(561\) | 24.5749 | + | 36.7387i | 1.03755 | + | 1.55111i | ||||
\(562\) | 5.13276 | + | 14.5780i | 0.216513 | + | 0.614934i | ||||
\(563\) | 24.4448 | 1.03023 | 0.515113 | − | 0.857122i | \(-0.327750\pi\) | ||||
0.515113 | + | 0.857122i | \(0.327750\pi\) | |||||||
\(564\) | 14.9083 | − | 11.9838i | 0.627754 | − | 0.504608i | ||||
\(565\) | −12.5310 | −0.527182 | ||||||||
\(566\) | −13.3358 | + | 4.69542i | −0.560547 | + | 0.197363i | ||||
\(567\) | −4.67418 | −0.196297 | ||||||||
\(568\) | −6.58903 | − | 4.08695i | −0.276470 | − | 0.171485i | ||||
\(569\) | − | 0.868758i | − | 0.0364202i | −0.999834 | − | 0.0182101i | \(-0.994203\pi\) | ||
0.999834 | − | 0.0182101i | \(-0.00579678\pi\) | |||||||
\(570\) | 22.4455 | + | 63.7493i | 0.940140 | + | 2.67016i | ||||
\(571\) | −3.23890 | −0.135544 | −0.0677719 | − | 0.997701i | \(-0.521589\pi\) | ||||
−0.0677719 | + | 0.997701i | \(0.521589\pi\) | |||||||
\(572\) | −1.98667 | + | 6.32876i | −0.0830667 | + | 0.264619i | ||||
\(573\) | −40.7278 | −1.70143 | ||||||||
\(574\) | 1.98321 | + | 5.63267i | 0.0827776 | + | 0.235103i | ||||
\(575\) | − | 1.47738i | − | 0.0616110i | ||||||
\(576\) | 22.3733 | + | 45.1099i | 0.932220 | + | 1.87958i | ||||
\(577\) | 14.9094 | 0.620687 | 0.310344 | − | 0.950624i | \(-0.399556\pi\) | ||||
0.310344 | + | 0.950624i | \(0.399556\pi\) | |||||||
\(578\) | 2.81371 | − | 0.990681i | 0.117035 | − | 0.0412069i | ||||
\(579\) | −56.6912 | −2.35601 | ||||||||
\(580\) | 7.53290 | + | 9.37125i | 0.312787 | + | 0.389120i | ||||
\(581\) | 5.03998 | 0.209094 | ||||||||
\(582\) | 18.0118 | + | 51.1566i | 0.746611 | + | 2.12051i | ||||
\(583\) | −3.69343 | − | 5.52157i | −0.152966 | − | 0.228680i | ||||
\(584\) | −26.5851 | − | 16.4898i | −1.10010 | − | 0.682354i | ||||
\(585\) | 17.4930i | 0.723245i | ||||||||
\(586\) | 3.89936 | + | 11.0749i | 0.161081 | + | 0.457499i | ||||
\(587\) | − | 39.7810i | − | 1.64194i | −0.570974 | − | 0.820968i | \(-0.693434\pi\) | ||
0.570974 | − | 0.820968i | \(-0.306566\pi\) | |||||||
\(588\) | 26.1340 | + | 32.5118i | 1.07775 | + | 1.34077i | ||||
\(589\) | 20.2692i | 0.835177i | ||||||||
\(590\) | 4.37819 | + | 12.4348i | 0.180247 | + | 0.511934i | ||||
\(591\) | 7.10385 | 0.292213 | ||||||||
\(592\) | 9.13273 | − | 41.4924i | 0.375353 | − | 1.70533i | ||||
\(593\) | 19.6509i | 0.806966i | 0.914987 | + | 0.403483i | \(0.132200\pi\) | ||||
−0.914987 | + | 0.403483i | \(0.867800\pi\) | |||||||
\(594\) | 28.2328 | − | 37.7061i | 1.15840 | − | 1.54710i | ||||
\(595\) | 4.83953i | 0.198401i | ||||||||
\(596\) | −25.9094 | − | 32.2324i | −1.06129 | − | 1.32029i | ||||
\(597\) | −31.2798 | −1.28020 | ||||||||
\(598\) | −0.723440 | + | 0.254716i | −0.0295836 | + | 0.0104161i | ||||
\(599\) | 17.3473i | 0.708793i | 0.935095 | + | 0.354397i | \(0.115314\pi\) | ||||
−0.935095 | + | 0.354397i | \(0.884686\pi\) | |||||||
\(600\) | 19.9616 | + | 12.3815i | 0.814930 | + | 0.505473i | ||||
\(601\) | − | 16.1383i | − | 0.658293i | −0.944279 | − | 0.329147i | \(-0.893239\pi\) | ||
0.944279 | − | 0.329147i | \(-0.106761\pi\) | |||||||
\(602\) | 0.956287 | − | 0.336700i | 0.0389754 | − | 0.0137229i | ||||
\(603\) | − | 8.26876i | − | 0.336730i | ||||||
\(604\) | −35.3607 | + | 28.4240i | −1.43881 | + | 1.15656i | ||||
\(605\) | 11.6707 | − | 28.2562i | 0.474480 | − | 1.14878i | ||||
\(606\) | −37.6034 | + | 13.2398i | −1.52753 | + | 0.537831i | ||||
\(607\) | 17.2287 | 0.699291 | 0.349645 | − | 0.936882i | \(-0.386302\pi\) | ||||
0.349645 | + | 0.936882i | \(0.386302\pi\) | |||||||
\(608\) | −3.87932 | − | 31.6700i | −0.157327 | − | 1.28439i | ||||
\(609\) | 2.62687 | 0.106446 | ||||||||
\(610\) | −7.83163 | − | 22.2432i | −0.317094 | − | 0.900602i | ||||
\(611\) | −3.13709 | −0.126913 | ||||||||
\(612\) | −34.4764 | − | 42.8901i | −1.39363 | − | 1.73373i | ||||
\(613\) | − | 4.08340i | − | 0.164927i | −0.996594 | − | 0.0824634i | \(-0.973721\pi\) | ||
0.996594 | − | 0.0824634i | \(-0.0262788\pi\) | |||||||
\(614\) | 19.4089 | − | 6.83369i | 0.783279 | − | 0.275785i | ||||
\(615\) | −89.8153 | −3.62170 | ||||||||
\(616\) | 3.73457 | − | 0.128394i | 0.150470 | − | 0.00517314i | ||||
\(617\) | −15.6375 | −0.629540 | −0.314770 | − | 0.949168i | \(-0.601927\pi\) | ||||
−0.314770 | + | 0.949168i | \(0.601927\pi\) | |||||||
\(618\) | −66.0432 | + | 23.2532i | −2.65665 | + | 0.935380i | ||||
\(619\) | 3.23623i | 0.130075i | 0.997883 | + | 0.0650375i | \(0.0207167\pi\) | ||||
−0.997883 | + | 0.0650375i | \(0.979283\pi\) | |||||||
\(620\) | 12.5145 | + | 15.5686i | 0.502596 | + | 0.625251i | ||||
\(621\) | 5.44648 | 0.218560 | ||||||||
\(622\) | 3.22934 | + | 9.17189i | 0.129485 | + | 0.367759i | ||||
\(623\) | 4.19083 | 0.167902 | ||||||||
\(624\) | 2.62135 | − | 11.9095i | 0.104938 | − | 0.476760i | ||||
\(625\) | −31.1998 | −1.24799 | ||||||||
\(626\) | 15.0010 | − | 5.28170i | 0.599560 | − | 0.211099i | ||||
\(627\) | −47.4033 | + | 31.7085i | −1.89310 | + | 1.26632i | ||||
\(628\) | 31.3299 | − | 25.1839i | 1.25020 | − | 1.00495i | ||||
\(629\) | 46.4306i | 1.85131i | ||||||||
\(630\) | 9.29517 | − | 3.27274i | 0.370329 | − | 0.130389i | ||||
\(631\) | 16.8096i | 0.669178i | 0.942364 | + | 0.334589i | \(0.108598\pi\) | ||||
−0.942364 | + | 0.334589i | \(0.891402\pi\) | |||||||
\(632\) | 23.6663 | − | 38.1551i | 0.941395 | − | 1.51773i | ||||
\(633\) | − | 80.1095i | − | 3.18407i | ||||||
\(634\) | −16.1925 | + | 5.70124i | −0.643087 | + | 0.226425i | ||||
\(635\) | −11.0771 | −0.439581 | ||||||||
\(636\) | 7.65125 | + | 9.51849i | 0.303392 | + | 0.377432i | ||||
\(637\) | − | 6.84132i | − | 0.271063i | ||||||
\(638\) | −6.08105 | + | 8.12151i | −0.240751 | + | 0.321534i | ||||
\(639\) | − | 17.2543i | − | 0.682570i | ||||||
\(640\) | −22.5333 | − | 21.9304i | −0.890706 | − | 0.866873i | ||||
\(641\) | −19.6035 | −0.774292 | −0.387146 | − | 0.922018i | \(-0.626539\pi\) | ||||
−0.387146 | + | 0.922018i | \(0.626539\pi\) | |||||||
\(642\) | 4.57136 | + | 12.9835i | 0.180417 | + | 0.512416i | ||||
\(643\) | − | 30.6343i | − | 1.20810i | −0.796947 | − | 0.604049i | \(-0.793553\pi\) | ||
0.796947 | − | 0.604049i | \(-0.206447\pi\) | |||||||
\(644\) | 0.270695 | + | 0.336757i | 0.0106669 | + | 0.0132701i | ||||
\(645\) | 15.2484i | 0.600405i | ||||||||
\(646\) | 11.5804 | + | 32.8903i | 0.455623 | + | 1.29405i | ||||
\(647\) | − | 5.31737i | − | 0.209047i | −0.994522 | − | 0.104524i | \(-0.966668\pi\) | ||
0.994522 | − | 0.104524i | \(-0.0333318\pi\) | |||||||
\(648\) | −17.4940 | + | 28.2041i | −0.687230 | + | 1.10796i | ||||
\(649\) | −9.24641 | + | 6.18501i | −0.362953 | + | 0.242783i | ||||
\(650\) | −1.27944 | − | 3.63384i | −0.0501838 | − | 0.142531i | ||||
\(651\) | 4.36406 | 0.171041 | ||||||||
\(652\) | 9.22514 | + | 11.4765i | 0.361285 | + | 0.449454i | ||||
\(653\) | −20.2079 | −0.790796 | −0.395398 | − | 0.918510i | \(-0.629393\pi\) | ||||
−0.395398 | + | 0.918510i | \(0.629393\pi\) | |||||||
\(654\) | −6.21253 | + | 2.18737i | −0.242929 | + | 0.0855331i | ||||
\(655\) | 29.4481 | 1.15063 | ||||||||
\(656\) | 41.4101 | + | 9.11463i | 1.61679 | + | 0.355866i | ||||
\(657\) | − | 69.6168i | − | 2.71601i | ||||||
\(658\) | 0.586916 | + | 1.66695i | 0.0228804 | + | 0.0649843i | ||||
\(659\) | −26.7656 | −1.04264 | −0.521320 | − | 0.853361i | \(-0.674560\pi\) | ||||
−0.521320 | + | 0.853361i | \(0.674560\pi\) | |||||||
\(660\) | −16.8328 | + | 53.6227i | −0.655214 | + | 2.08726i | ||||
\(661\) | −26.7508 | −1.04048 | −0.520242 | − | 0.854019i | \(-0.674158\pi\) | ||||
−0.520242 | + | 0.854019i | \(0.674158\pi\) | |||||||
\(662\) | 15.2569 | + | 43.3322i | 0.592975 | + | 1.68415i | ||||
\(663\) | 13.3269i | 0.517572i | ||||||||
\(664\) | 18.8631 | − | 30.4113i | 0.732031 | − | 1.18019i | ||||
\(665\) | −6.24436 | −0.242146 | ||||||||
\(666\) | 89.1781 | − | 31.3988i | 3.45558 | − | 1.21668i | ||||
\(667\) | −1.17312 | −0.0454232 | ||||||||
\(668\) | −32.7254 | + | 26.3057i | −1.26618 | + | 1.01780i | ||||
\(669\) | 72.5528 | 2.80505 | ||||||||
\(670\) | 1.71482 | + | 4.87040i | 0.0662494 | + | 0.188160i | ||||
\(671\) | 16.5398 | − | 11.0637i | 0.638513 | − | 0.427108i | ||||
\(672\) | −6.81871 | + | 0.835236i | −0.263038 | + | 0.0322199i | ||||
\(673\) | − | 1.05814i | − | 0.0407881i | −0.999792 | − | 0.0203941i | \(-0.993508\pi\) | ||
0.999792 | − | 0.0203941i | \(-0.00649208\pi\) | |||||||
\(674\) | −8.32164 | − | 23.6349i | −0.320538 | − | 0.910383i | ||||
\(675\) | 27.3577i | 1.05300i | ||||||||
\(676\) | −1.55882 | + | 1.25303i | −0.0599546 | + | 0.0481934i | ||||
\(677\) | 6.91957i | 0.265941i | 0.991120 | + | 0.132970i | \(0.0424515\pi\) | ||||
−0.991120 | + | 0.132970i | \(0.957548\pi\) | |||||||
\(678\) | 6.45592 | + | 18.3360i | 0.247938 | + | 0.704188i | ||||
\(679\) | −5.01088 | −0.192300 | ||||||||
\(680\) | 29.2018 | + | 18.1129i | 1.11984 | + | 0.694598i | ||||
\(681\) | 42.3219i | 1.62178i | ||||||||
\(682\) | −10.1025 | + | 13.4924i | −0.386847 | + | 0.516651i | ||||
\(683\) | 24.2529i | 0.928010i | 0.885833 | + | 0.464005i | \(0.153588\pi\) | ||||
−0.885833 | + | 0.464005i | \(0.846412\pi\) | |||||||
\(684\) | 55.3403 | − | 44.4843i | 2.11599 | − | 1.70090i | ||||
\(685\) | 56.2765 | 2.15022 | ||||||||
\(686\) | −7.35481 | + | 2.58956i | −0.280808 | + | 0.0988699i | ||||
\(687\) | 78.2541i | 2.98558i | ||||||||
\(688\) | 1.54744 | − | 7.03042i | 0.0589955 | − | 0.268032i | ||||
\(689\) | − | 2.00293i | − | 0.0763057i | ||||||
\(690\) | −6.12960 | + | 2.15818i | −0.233350 | + | 0.0821604i | ||||
\(691\) | − | 3.44537i | − | 0.131068i | −0.997850 | − | 0.0655341i | \(-0.979125\pi\) | ||
0.997850 | − | 0.0655341i | \(-0.0208751\pi\) | |||||||
\(692\) | −22.9057 | − | 28.4957i | −0.870744 | − | 1.08324i | ||||
\(693\) | 4.62337 | + | 6.91179i | 0.175627 | + | 0.262557i | ||||
\(694\) | 4.20076 | − | 1.47905i | 0.159459 | − | 0.0561439i | ||||
\(695\) | −6.51285 | −0.247047 | ||||||||
\(696\) | 9.83156 | − | 15.8506i | 0.372664 | − | 0.600814i | ||||
\(697\) | −46.3386 | −1.75520 | ||||||||
\(698\) | −8.69223 | − | 24.6875i | −0.329006 | − | 0.934435i | ||||
\(699\) | 25.1147 | 0.949925 | ||||||||
\(700\) | −1.69153 | + | 1.35970i | −0.0639339 | + | 0.0513920i | ||||
\(701\) | − | 0.151692i | − | 0.00572934i | −0.999996 | − | 0.00286467i | \(-0.999088\pi\) | ||
0.999996 | − | 0.00286467i | \(-0.000911854\pi\) | |||||||
\(702\) | 13.3965 | − | 4.71677i | 0.505616 | − | 0.178023i | ||||
\(703\) | −59.9085 | −2.25949 | ||||||||
\(704\) | 13.2026 | − | 23.0150i | 0.497593 | − | 0.867411i | ||||
\(705\) | −26.5802 | −1.00107 | ||||||||
\(706\) | 23.2076 | − | 8.17118i | 0.873430 | − | 0.307527i | ||||
\(707\) | − | 3.68332i | − | 0.138526i | ||||||
\(708\) | 15.9396 | − | 12.8128i | 0.599048 | − | 0.481534i | ||||
\(709\) | 47.3746 | 1.77919 | 0.889595 | − | 0.456750i | \(-0.150987\pi\) | ||||
0.889595 | + | 0.456750i | \(0.150987\pi\) | |||||||
\(710\) | 3.57830 | + | 10.1630i | 0.134291 | + | 0.381411i | ||||
\(711\) | 99.9146 | 3.74709 | ||||||||
\(712\) | 15.6850 | − | 25.2875i | 0.587819 | − | 0.947690i | ||||
\(713\) | −1.94892 | −0.0729875 | ||||||||
\(714\) | 7.08145 | − | 2.49331i | 0.265016 | − | 0.0933099i | ||||
\(715\) | 7.66162 | − | 5.12494i | 0.286528 | − | 0.191662i | ||||
\(716\) | 17.5705 | + | 21.8584i | 0.656640 | + | 0.816888i | ||||
\(717\) | − | 13.7305i | − | 0.512774i | ||||||
\(718\) | −40.9466 | + | 14.4169i | −1.52811 | + | 0.538035i | ||||
\(719\) | − | 7.18100i | − | 0.267806i | −0.990994 | − | 0.133903i | \(-0.957249\pi\) | ||
0.990994 | − | 0.133903i | \(-0.0427511\pi\) | |||||||
\(720\) | 15.0412 | − | 68.3361i | 0.560552 | − | 2.54674i | ||||
\(721\) | − | 6.46905i | − | 0.240920i | ||||||
\(722\) | −17.0928 | + | 6.01820i | −0.636127 | + | 0.223974i | ||||
\(723\) | 80.9149 | 3.00926 | ||||||||
\(724\) | −12.7318 | + | 10.2342i | −0.473172 | + | 0.380350i | ||||
\(725\) | − | 5.89257i | − | 0.218844i | ||||||
\(726\) | −47.3586 | − | 2.51958i | −1.75764 | − | 0.0935105i | ||||
\(727\) | − | 4.27355i | − | 0.158497i | −0.996855 | − | 0.0792486i | \(-0.974748\pi\) | ||
0.996855 | − | 0.0792486i | \(-0.0252521\pi\) | |||||||
\(728\) | 0.957455 | + | 0.593877i | 0.0354857 | + | 0.0220105i | ||||
\(729\) | 17.9934 | 0.666423 | ||||||||
\(730\) | 14.4375 | + | 41.0051i | 0.534357 | + | 1.51767i | ||||
\(731\) | 7.86714i | 0.290977i | ||||||||
\(732\) | −28.5126 | + | 22.9193i | −1.05386 | + | 0.847121i | ||||
\(733\) | 18.8094i | 0.694741i | 0.937728 | + | 0.347371i | \(0.112925\pi\) | ||||
−0.937728 | + | 0.347371i | \(0.887075\pi\) | |||||||
\(734\) | 0.788675 | + | 2.23998i | 0.0291105 | + | 0.0826791i | ||||
\(735\) | − | 57.9656i | − | 2.13809i | ||||||
\(736\) | 3.04513 | − | 0.373003i | 0.112245 | − | 0.0137491i | ||||
\(737\) | −3.62158 | + | 2.42251i | −0.133403 | + | 0.0892343i | ||||
\(738\) | 31.3366 | + | 89.0014i | 1.15351 | + | 3.27619i | ||||
\(739\) | 15.2080 | 0.559435 | 0.279718 | − | 0.960082i | \(-0.409759\pi\) | ||||
0.279718 | + | 0.960082i | \(0.409759\pi\) | |||||||
\(740\) | −46.0153 | + | 36.9885i | −1.69156 | + | 1.35973i | ||||
\(741\) | −17.1954 | −0.631689 | ||||||||
\(742\) | −1.06429 | + | 0.374727i | −0.0390714 | + | 0.0137567i | ||||
\(743\) | −7.71852 | −0.283165 | −0.141583 | − | 0.989926i | \(-0.545219\pi\) | ||||
−0.141583 | + | 0.989926i | \(0.545219\pi\) | |||||||
\(744\) | 16.3333 | − | 26.3328i | 0.598809 | − | 0.965407i | ||||
\(745\) | 57.4673i | 2.10544i | ||||||||
\(746\) | −4.29174 | − | 12.1893i | −0.157132 | − | 0.446282i | ||||
\(747\) | 79.6364 | 2.91374 | ||||||||
\(748\) | −8.68456 | + | 27.6657i | −0.317539 | + | 1.01156i | ||||
\(749\) | −1.27175 | −0.0464689 | ||||||||
\(750\) | 9.05670 | + | 25.7226i | 0.330704 | + | 0.939258i | ||||
\(751\) | − | 13.8636i | − | 0.505891i | −0.967481 | − | 0.252945i | \(-0.918601\pi\) | ||
0.967481 | − | 0.252945i | \(-0.0813993\pi\) | |||||||
\(752\) | 12.2550 | + | 2.69741i | 0.446895 | + | 0.0983643i | ||||
\(753\) | 74.8091 | 2.72619 | ||||||||
\(754\) | −2.88546 | + | 1.01594i | −0.105082 | + | 0.0369985i | ||||
\(755\) | 63.0448 | 2.29444 | ||||||||
\(756\) | −5.01266 | − | 6.23597i | −0.182309 | − | 0.226800i | ||||
\(757\) | 13.5309 | 0.491790 | 0.245895 | − | 0.969296i | \(-0.420918\pi\) | ||||
0.245895 | + | 0.969296i | \(0.420918\pi\) | |||||||
\(758\) | 2.70980 | + | 7.69630i | 0.0984243 | + | 0.279542i | ||||
\(759\) | −3.04883 | − | 4.55791i | −0.110666 | − | 0.165442i | ||||
\(760\) | −23.3707 | + | 37.6786i | −0.847745 | + | 1.36674i | ||||
\(761\) | − | 17.1462i | − | 0.621549i | −0.950484 | − | 0.310775i | \(-0.899412\pi\) | ||
0.950484 | − | 0.310775i | \(-0.100588\pi\) | |||||||
\(762\) | 5.70688 | + | 16.2086i | 0.206739 | + | 0.587174i | ||||
\(763\) | − | 0.608529i | − | 0.0220302i | ||||||
\(764\) | −16.7396 | − | 20.8248i | −0.605619 | − | 0.753416i | ||||
\(765\) | 76.4691i | 2.76475i | ||||||||
\(766\) | 6.18242 | + | 17.5592i | 0.223380 | + | 0.634439i | ||||
\(767\) | −3.35411 | −0.121110 | ||||||||
\(768\) | −20.4805 | + | 44.2703i | −0.739027 | + | 1.59747i | ||||
\(769\) | 20.8264i | 0.751018i | 0.926819 | + | 0.375509i | \(0.122532\pi\) | ||||
−0.926819 | + | 0.375509i | \(0.877468\pi\) | |||||||
\(770\) | −4.15663 | − | 3.11231i | −0.149794 | − | 0.112160i | ||||
\(771\) | 23.4560i | 0.844748i | ||||||||
\(772\) | −23.3008 | − | 28.9872i | −0.838615 | − | 1.04327i | ||||
\(773\) | −2.70966 | −0.0974595 | −0.0487298 | − | 0.998812i | \(-0.515517\pi\) | ||||
−0.0487298 | + | 0.998812i | \(0.515517\pi\) | |||||||
\(774\) | 15.1102 | − | 5.32017i | 0.543126 | − | 0.191230i | ||||
\(775\) | − | 9.78942i | − | 0.351646i | ||||||
\(776\) | −18.7542 | + | 30.2357i | −0.673236 | + | 1.08540i | ||||
\(777\) | 12.8986i | 0.462735i | ||||||||
\(778\) | 34.0942 | − | 12.0042i | 1.22233 | − | 0.430373i | ||||
\(779\) | − | 59.7898i | − | 2.14219i | ||||||
\(780\) | −13.2077 | + | 10.6167i | −0.472911 | + | 0.380140i | ||||
\(781\) | −7.55710 | + | 5.05502i | −0.270414 | + | 0.180883i | ||||
\(782\) | −3.16246 | + | 1.11347i | −0.113089 | + | 0.0398177i | ||||
\(783\) | 21.7234 | 0.776332 | ||||||||
\(784\) | −5.88246 | + | 26.7256i | −0.210088 | + | 0.954485i | ||||
\(785\) | −55.8583 | −1.99367 | ||||||||
\(786\) | −15.1715 | − | 43.0899i | −0.541151 | − | 1.53697i | ||||
\(787\) | 11.8080 | 0.420908 | 0.210454 | − | 0.977604i | \(-0.432506\pi\) | ||||
0.210454 | + | 0.977604i | \(0.432506\pi\) | |||||||
\(788\) | 2.91977 | + | 3.63232i | 0.104013 | + | 0.129396i | ||||
\(789\) | − | 61.5185i | − | 2.19012i | ||||||
\(790\) | −58.8509 | + | 20.7209i | −2.09382 | + | 0.737215i | ||||
\(791\) | −1.79604 | −0.0638599 | ||||||||
\(792\) | 59.0097 | − | 2.02874i | 2.09682 | − | 0.0720882i | ||||
\(793\) | 5.99977 | 0.213058 | ||||||||
\(794\) | 7.36544 | − | 2.59330i | 0.261390 | − | 0.0920329i | ||||
\(795\) | − | 16.9706i | − | 0.601884i | ||||||
\(796\) | −12.8564 | − | 15.9939i | −0.455683 | − | 0.566889i | ||||
\(797\) | −8.02123 | −0.284127 | −0.142063 | − | 0.989858i | \(-0.545374\pi\) | ||||
−0.142063 | + | 0.989858i | \(0.545374\pi\) | |||||||
\(798\) | 3.21707 | + | 9.13706i | 0.113883 | + | 0.323448i | ||||
\(799\) | −13.7136 | −0.485151 | ||||||||
\(800\) | 1.87360 | + | 15.2957i | 0.0662416 | + | 0.540784i | ||||
\(801\) | 66.2189 | 2.33973 | ||||||||
\(802\) | 24.3139 | − | 8.56068i | 0.858552 | − | 0.302288i | ||||
\(803\) | −30.4910 | + | 20.3957i | −1.07600 | + | 0.719750i | ||||
\(804\) | 6.24315 | − | 5.01843i | 0.220179 | − | 0.176986i | ||||
\(805\) | − | 0.600406i | − | 0.0211615i | ||||||
\(806\) | −4.79366 | + | 1.68780i | −0.168849 | + | 0.0594503i | ||||
\(807\) | − | 27.5551i | − | 0.969985i | ||||||
\(808\) | −22.2252 | − | 13.7856i | −0.781881 | − | 0.484974i | ||||
\(809\) | 21.2989i | 0.748829i | 0.927262 | + | 0.374414i | \(0.122156\pi\) | ||||
−0.927262 | + | 0.374414i | \(0.877844\pi\) | |||||||
\(810\) | 43.5023 | − | 15.3168i | 1.52852 | − | 0.538176i | ||||
\(811\) | 42.2055 | 1.48203 | 0.741017 | − | 0.671486i | \(-0.234344\pi\) | ||||
0.741017 | + | 0.671486i | \(0.234344\pi\) | |||||||
\(812\) | 1.07968 | + | 1.34316i | 0.0378892 | + | 0.0471358i | ||||
\(813\) | 29.9393i | 1.05002i | ||||||||
\(814\) | −39.8788 | − | 29.8596i | −1.39775 | − | 1.04658i | ||||
\(815\) | − | 20.4615i | − | 0.716735i | ||||||
\(816\) | 11.4590 | − | 52.0613i | 0.401145 | − | 1.82251i | ||||
\(817\) | −10.1508 | −0.355132 | ||||||||
\(818\) | 11.2776 | + | 32.0304i | 0.394312 | + | 1.11992i | ||||
\(819\) | 2.50723i | 0.0876098i | ||||||||
\(820\) | −36.9152 | − | 45.9241i | −1.28914 | − | 1.60374i | ||||
\(821\) | 6.73040i | 0.234893i | 0.993079 | + | 0.117446i | \(0.0374708\pi\) | ||||
−0.993079 | + | 0.117446i | \(0.962529\pi\) | |||||||
\(822\) | −28.9935 | − | 82.3466i | −1.01126 | − | 2.87217i | ||||
\(823\) | − | 3.03370i | − | 0.105748i | −0.998601 | − | 0.0528740i | \(-0.983162\pi\) | ||
0.998601 | − | 0.0528740i | \(-0.0168382\pi\) | |||||||
\(824\) | −39.0343 | − | 24.2117i | −1.35983 | − | 0.843454i | ||||
\(825\) | 22.8944 | − | 15.3143i | 0.797081 | − | 0.533175i | ||||
\(826\) | 0.627517 | + | 1.78226i | 0.0218341 | + | 0.0620128i | ||||
\(827\) | −31.7649 | −1.10457 | −0.552286 | − | 0.833654i | \(-0.686244\pi\) | ||||
−0.552286 | + | 0.833654i | \(0.686244\pi\) | |||||||
\(828\) | 4.27724 | + | 5.32107i | 0.148644 | + | 0.184920i | ||||
\(829\) | −39.2573 | −1.36346 | −0.681732 | − | 0.731602i | \(-0.738773\pi\) | ||||
−0.681732 | + | 0.731602i | \(0.738773\pi\) | |||||||
\(830\) | −46.9068 | + | 16.5155i | −1.62816 | + | 0.573260i | ||||
\(831\) | −30.5078 | −1.05830 | ||||||||
\(832\) | 7.16692 | − | 3.55460i | 0.248468 | − | 0.123234i | ||||
\(833\) | − | 29.9063i | − | 1.03619i | ||||||
\(834\) | 3.35540 | + | 9.52993i | 0.116188 | + | 0.329995i | ||||
\(835\) | 58.3464 | 2.01916 | ||||||||
\(836\) | −35.6965 | − | 11.2055i | −1.23459 | − | 0.387551i | ||||
\(837\) | 36.0895 | 1.24744 | ||||||||
\(838\) | 9.23122 | + | 26.2183i | 0.318887 | + | 0.905696i | ||||
\(839\) | − | 15.8911i | − | 0.548621i | −0.961641 | − | 0.274311i | \(-0.911550\pi\) | ||
0.961641 | − | 0.274311i | \(-0.0884497\pi\) | |||||||
\(840\) | 8.11239 | + | 5.03184i | 0.279904 | + | 0.173615i | ||||
\(841\) | 24.3210 | 0.838655 | ||||||||
\(842\) | −20.0815 | + | 7.07052i | −0.692056 | + | 0.243666i | ||||
\(843\) | −33.3169 | −1.14749 | ||||||||
\(844\) | 40.9614 | − | 32.9260i | 1.40995 | − | 1.13336i | ||||
\(845\) | 2.77923 | 0.0956085 | ||||||||
\(846\) | 9.27382 | + | 26.3393i | 0.318841 | + | 0.905564i | ||||
\(847\) | 1.67273 | − | 4.04991i | 0.0574758 | − | 0.139157i | ||||
\(848\) | −1.72221 | + | 7.82444i | −0.0591408 | + | 0.268692i | ||||
\(849\) | − | 30.4781i | − | 1.04600i | ||||||
\(850\) | −5.59298 | − | 15.8850i | −0.191838 | − | 0.544853i | ||||
\(851\) | − | 5.76031i | − | 0.197461i | ||||||
\(852\) | 13.0275 | − | 10.4719i | 0.446314 | − | 0.358761i | ||||
\(853\) | 38.2952i | 1.31120i | 0.755107 | + | 0.655602i | \(0.227585\pi\) | ||||
−0.755107 | + | 0.655602i | \(0.772415\pi\) | |||||||
\(854\) | −1.12249 | − | 3.18808i | −0.0384109 | − | 0.109094i | ||||
\(855\) | −98.6667 | −3.37433 | ||||||||
\(856\) | −4.75978 | + | 7.67378i | −0.162686 | + | 0.262284i | ||||
\(857\) | − | 34.9983i | − | 1.19552i | −0.801675 | − | 0.597760i | \(-0.796058\pi\) | ||
0.801675 | − | 0.597760i | \(-0.203942\pi\) | |||||||
\(858\) | −11.4463 | − | 8.57052i | −0.390771 | − | 0.292593i | ||||
\(859\) | − | 19.2913i | − | 0.658212i | −0.944293 | − | 0.329106i | \(-0.893253\pi\) | ||
0.944293 | − | 0.329106i | \(-0.106747\pi\) | |||||||
\(860\) | −7.79678 | + | 6.26729i | −0.265868 | + | 0.213713i | ||||
\(861\) | −12.8730 | −0.438712 | ||||||||
\(862\) | 32.6623 | − | 11.5001i | 1.11248 | − | 0.391694i | ||||
\(863\) | 21.2878i | 0.724644i | 0.932053 | + | 0.362322i | \(0.118016\pi\) | ||||
−0.932053 | + | 0.362322i | \(0.881984\pi\) | |||||||
\(864\) | −56.3888 | + | 6.90716i | −1.91839 | + | 0.234986i | ||||
\(865\) | 50.8052i | 1.72743i | ||||||||
\(866\) | −24.9437 | + | 8.78246i | −0.847623 | + | 0.298440i | ||||
\(867\) | 6.43053i | 0.218392i | ||||||||
\(868\) | 1.79368 | + | 2.23142i | 0.0608816 | + | 0.0757393i | ||||
\(869\) | −29.2721 | − | 43.7609i | −0.992988 | − | 1.48449i | ||||
\(870\) | −24.4481 | + | 8.60794i | −0.828868 | + | 0.291837i | ||||
\(871\) | −1.31372 | −0.0445136 | ||||||||
\(872\) | −3.67187 | − | 2.27754i | −0.124345 | − | 0.0771271i | ||||
\(873\) | −79.1766 | −2.67972 | ||||||||
\(874\) | −1.43669 | − | 4.08046i | −0.0485969 | − | 0.138024i | ||||
\(875\) | −2.51958 | −0.0851774 | ||||||||
\(876\) | 52.5626 | − | 42.2514i | 1.77593 | − | 1.42754i | ||||
\(877\) | − | 25.5294i | − | 0.862065i | −0.902336 | − | 0.431033i | \(-0.858149\pi\) | ||
0.902336 | − | 0.431033i | \(-0.141851\pi\) | |||||||
\(878\) | −17.1834 | + | 6.05011i | −0.579911 | + | 0.204181i | ||||
\(879\) | −25.3108 | −0.853713 | ||||||||
\(880\) | −34.3367 | + | 13.4327i | −1.15749 | + | 0.452817i | ||||
\(881\) | −16.6394 | −0.560595 | −0.280297 | − | 0.959913i | \(-0.590433\pi\) | ||||
−0.280297 | + | 0.959913i | \(0.590433\pi\) | |||||||
\(882\) | −57.4403 | + | 20.2242i | −1.93412 | + | 0.680984i | ||||
\(883\) | 23.3708i | 0.786489i | 0.919434 | + | 0.393245i | \(0.128647\pi\) | ||||
−0.919434 | + | 0.393245i | \(0.871353\pi\) | |||||||
\(884\) | −6.81426 | + | 5.47751i | −0.229188 | + | 0.184229i | ||||
\(885\) | −28.4189 | −0.955291 | ||||||||
\(886\) | 10.2535 | + | 29.1218i | 0.344474 | + | 0.978367i | ||||
\(887\) | 24.0995 | 0.809181 | 0.404590 | − | 0.914498i | \(-0.367414\pi\) | ||||
0.404590 | + | 0.914498i | \(0.367414\pi\) | |||||||
\(888\) | 77.8305 | + | 48.2756i | 2.61182 | + | 1.62002i | ||||
\(889\) | −1.58766 | −0.0532484 | ||||||||
\(890\) | −39.0038 | + | 13.7329i | −1.30741 | + | 0.460327i | ||||
\(891\) | 21.6378 | + | 32.3479i | 0.724894 | + | 1.08369i | ||||
\(892\) | 29.8201 | + | 37.0975i | 0.998452 | + | 1.24212i | ||||
\(893\) | − | 17.6943i | − | 0.592119i | ||||||
\(894\) | 84.0891 | − | 29.6070i | 2.81236 | − | 0.990206i | ||||
\(895\) | − | 38.9715i | − | 1.30268i | ||||||
\(896\) | −3.22965 | − | 3.14324i | −0.107895 | − | 0.105008i | ||||
\(897\) | − | 1.65337i | − | 0.0552044i | ||||||
\(898\) | −31.7538 | + | 11.1802i | −1.05964 | + | 0.373088i | ||||
\(899\) | −7.77330 | −0.259254 | ||||||||
\(900\) | −26.7278 | + | 21.4846i | −0.890926 | + | 0.716153i | ||||
\(901\) | − | 8.75566i | − | 0.291693i | ||||||
\(902\) | 29.8004 | − | 39.7997i | 0.992244 | − | 1.32519i | ||||
\(903\) | 2.18552i | 0.0727297i | ||||||||
\(904\) | −6.72203 | + | 10.8373i | −0.223571 | + | 0.360445i | ||||
\(905\) | 22.6996 | 0.754559 | ||||||||
\(906\) | −32.4805 | − | 92.2503i | −1.07909 | − | 3.06481i | ||||
\(907\) | 7.57714i | 0.251595i | 0.992056 | + | 0.125797i | \(0.0401489\pi\) | ||||
−0.992056 | + | 0.125797i | \(0.959851\pi\) | |||||||
\(908\) | −21.6399 | + | 17.3948i | −0.718146 | + | 0.577268i | ||||
\(909\) | − | 58.2000i | − | 1.93037i | ||||||
\(910\) | −0.519964 | − | 1.47679i | −0.0172366 | − | 0.0489551i | ||||
\(911\) | 20.2403i | 0.670592i | 0.942113 | + | 0.335296i | \(0.108836\pi\) | ||||
−0.942113 | + | 0.335296i | \(0.891164\pi\) | |||||||
\(912\) | 67.1737 | + | 14.7853i | 2.22434 | + | 0.489592i | ||||
\(913\) | −23.3312 | − | 34.8794i | −0.772149 | − | 1.15434i | ||||
\(914\) | 14.5614 | + | 41.3570i | 0.481649 | + | 1.36797i | ||||
\(915\) | 50.8353 | 1.68056 | ||||||||
\(916\) | −40.0127 | + | 32.1634i | −1.32206 | + | 1.06271i | ||||
\(917\) | 4.22073 | 0.139381 | ||||||||
\(918\) | 58.5615 | − | 20.6190i | 1.93282 | − | 0.680527i | ||||
\(919\) | −19.8045 | −0.653292 | −0.326646 | − | 0.945147i | \(-0.605918\pi\) | ||||
−0.326646 | + | 0.945147i | \(0.605918\pi\) | |||||||
\(920\) | −3.62286 | − | 2.24714i | −0.119442 | − | 0.0740859i | ||||
\(921\) | 44.3576i | 1.46163i | ||||||||
\(922\) | −3.07085 | − | 8.72176i | −0.101133 | − | 0.287236i | ||||
\(923\) | −2.74132 | −0.0902315 | ||||||||
\(924\) | −2.41261 | + | 7.68564i | −0.0793689 | + | 0.252839i | ||||
\(925\) | 28.9341 | 0.951347 | ||||||||
\(926\) | −1.94188 | − | 5.51529i | −0.0638143 | − | 0.181244i | ||||
\(927\) | − | 102.217i | − | 3.35725i | ||||||
\(928\) | 12.1456 | − | 1.48773i | 0.398698 | − | 0.0488372i | ||||
\(929\) | 29.5708 | 0.970186 | 0.485093 | − | 0.874463i | \(-0.338786\pi\) | ||||
0.485093 | + | 0.874463i | \(0.338786\pi\) | |||||||
\(930\) | −40.6160 | + | 14.3005i | −1.33185 | + | 0.468933i | ||||
\(931\) | 38.5875 | 1.26466 | ||||||||
\(932\) | 10.3225 | + | 12.8416i | 0.338123 | + | 0.420640i | ||||
\(933\) | −20.9617 | −0.686255 | ||||||||
\(934\) | −8.92168 | − | 25.3392i | −0.291926 | − | 0.829123i | ||||
\(935\) | 33.4922 | − | 22.4032i | 1.09531 | − | 0.732665i | ||||
\(936\) | 15.1287 | + | 9.38381i | 0.494496 | + | 0.306719i | ||||
\(937\) | 30.9032i | 1.00956i | 0.863247 | + | 0.504782i | \(0.168427\pi\) | ||||
−0.863247 | + | 0.504782i | \(0.831573\pi\) | |||||||
\(938\) | 0.245782 | + | 0.698065i | 0.00802508 | + | 0.0227926i | ||||
\(939\) | 34.2836i | 1.11880i | ||||||||
\(940\) | −10.9248 | − | 13.5909i | −0.356327 | − | 0.443287i | ||||
\(941\) | − | 7.58140i | − | 0.247147i | −0.992335 | − | 0.123573i | \(-0.960565\pi\) | ||
0.992335 | − | 0.123573i | \(-0.0394354\pi\) | |||||||
\(942\) | 28.7780 | + | 81.7346i | 0.937638 | + | 2.66306i | ||||
\(943\) | 5.74889 | 0.187210 | ||||||||
\(944\) | 13.1028 | + | 2.88401i | 0.426460 | + | 0.0938664i | ||||
\(945\) | 11.1182i | 0.361673i | ||||||||
\(946\) | −6.75701 | − | 5.05937i | −0.219689 | − | 0.164494i | ||||
\(947\) | − | 49.0637i | − | 1.59436i | −0.603744 | − | 0.797178i | \(-0.706325\pi\) | ||
0.603744 | − | 0.797178i | \(-0.293675\pi\) | |||||||
\(948\) | 60.6396 | + | 75.4383i | 1.96948 | + | 2.45012i | ||||
\(949\) | −11.0605 | −0.359040 | ||||||||
\(950\) | 20.4962 | − | 7.21652i | 0.664984 | − | 0.234135i | ||||
\(951\) | − | 37.0068i | − | 1.20003i | ||||||
\(952\) | 4.18544 | + | 2.59609i | 0.135651 | + | 0.0841396i | ||||
\(953\) | 21.8247i | 0.706973i | 0.935440 | + | 0.353486i | \(0.115004\pi\) | ||||
−0.935440 | + | 0.353486i | \(0.884996\pi\) | |||||||
\(954\) | −16.8168 | + | 5.92104i | −0.544464 | + | 0.191701i | ||||
\(955\) | 37.1287i | 1.20146i | ||||||||
\(956\) | 7.02064 | − | 5.64341i | 0.227064 | − | 0.182521i | ||||
\(957\) | −12.1603 | − | 18.1793i | −0.393088 | − | 0.587654i | ||||
\(958\) | 17.7109 | − | 6.23583i | 0.572212 | − | 0.201471i | ||||
\(959\) | 8.06600 | 0.260465 | ||||||||
\(960\) | 60.7244 | − | 30.1176i | 1.95987 | − | 0.972043i | ||||
\(961\) | 18.0861 | 0.583422 | ||||||||
\(962\) | −4.98855 | − | 14.1684i | −0.160837 | − | 0.456806i | ||||
\(963\) | −20.0949 | −0.647549 | ||||||||
\(964\) | 33.2571 | + | 41.3732i | 1.07114 | + | 1.33254i | ||||
\(965\) | 51.6815i | 1.66369i | ||||||||
\(966\) | −0.878544 | + | 0.309327i | −0.0282667 | + | 0.00995244i | ||||
\(967\) | 21.1479 | 0.680071 | 0.340036 | − | 0.940413i | \(-0.389561\pi\) | ||||
0.340036 | + | 0.940413i | \(0.389561\pi\) | |||||||
\(968\) | −18.1767 | − | 25.2509i | −0.584221 | − | 0.811594i | ||||
\(969\) | −75.1683 | −2.41475 | ||||||||
\(970\) | 46.6359 | − | 16.4201i | 1.49739 | − | 0.527217i | ||||
\(971\) | 17.7242i | 0.568798i | 0.958706 | + | 0.284399i | \(0.0917941\pi\) | ||||
−0.958706 | + | 0.284399i | \(0.908206\pi\) | |||||||
\(972\) | −7.07305 | − | 8.79918i | −0.226868 | − | 0.282234i | ||||
\(973\) | −0.933474 | −0.0299258 | ||||||||
\(974\) | −10.1889 | − | 28.9382i | −0.326473 | − | 0.927241i | ||||
\(975\) | 8.30488 | 0.265969 | ||||||||
\(976\) | −23.4381 | − | 5.15886i | −0.750234 | − | 0.165131i | ||||
\(977\) | 47.7847 | 1.52877 | 0.764384 | − | 0.644761i | \(-0.223043\pi\) | ||||
0.764384 | + | 0.644761i | \(0.223043\pi\) | |||||||
\(978\) | −29.9403 | + | 10.5417i | −0.957385 | + | 0.337086i | ||||
\(979\) | −19.4002 | − | 29.0028i | −0.620035 | − | 0.926933i | ||||
\(980\) | 29.6388 | − | 23.8246i | 0.946778 | − | 0.761049i | ||||
\(981\) | − | 9.61532i | − | 0.306993i | ||||||
\(982\) | −23.4653 | + | 8.26192i | −0.748808 | + | 0.263648i | ||||
\(983\) | 16.4652i | 0.525158i | 0.964911 | + | 0.262579i | \(0.0845730\pi\) | ||||
−0.964911 | + | 0.262579i | \(0.915427\pi\) | |||||||
\(984\) | −48.1799 | + | 77.6762i | −1.53592 | + | 2.47623i | ||||
\(985\) | − | 6.47609i | − | 0.206345i | ||||||
\(986\) | −12.6135 | + | 4.44111i | −0.401697 | + | 0.141434i | ||||
\(987\) | −3.80968 | −0.121264 | ||||||||
\(988\) | −7.06753 | − | 8.79231i | −0.224848 | − | 0.279721i | ||||
\(989\) | − | 0.976019i | − | 0.0310356i | ||||||
\(990\) | −65.6785 | − | 49.1774i | −2.08740 | − | 1.56296i | ||||
\(991\) | 20.8552i | 0.662486i | 0.943545 | + | 0.331243i | \(0.107468\pi\) | ||||
−0.943545 | + | 0.331243i | \(0.892532\pi\) | |||||||
\(992\) | 20.1776 | − | 2.47159i | 0.640640 | − | 0.0784732i | ||||
\(993\) | −99.0326 | −3.14271 | ||||||||
\(994\) | 0.512871 | + | 1.45664i | 0.0162673 | + | 0.0462019i | ||||
\(995\) | 28.5157i | 0.904007i | ||||||||
\(996\) | 48.3325 | + | 60.1277i | 1.53147 | + | 1.90522i | ||||
\(997\) | 40.7675i | 1.29112i | 0.763709 | + | 0.645561i | \(0.223376\pi\) | ||||
−0.763709 | + | 0.645561i | \(0.776624\pi\) | |||||||
\(998\) | −11.3267 | − | 32.1700i | −0.358542 | − | 1.01832i | ||||
\(999\) | 106.668i | 3.37482i |
(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.e.b.131.8 | yes | 64 | |
4.3 | odd | 2 | inner | 572.2.e.b.131.58 | yes | 64 | |
11.10 | odd | 2 | inner | 572.2.e.b.131.57 | yes | 64 | |
44.43 | even | 2 | inner | 572.2.e.b.131.7 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.e.b.131.7 | ✓ | 64 | 44.43 | even | 2 | inner | |
572.2.e.b.131.8 | yes | 64 | 1.1 | even | 1 | trivial | |
572.2.e.b.131.57 | yes | 64 | 11.10 | odd | 2 | inner | |
572.2.e.b.131.58 | yes | 64 | 4.3 | odd | 2 | inner |