Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(7,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.g (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.3 | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.3.g.c.7.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82726 | − | 0.813087i | −0.913632 | − | 0.406543i | ||||
\(3\) | −0.851777 | − | 0.491774i | −0.283926 | − | 0.163925i | 0.351274 | − | 0.936273i | \(-0.385749\pi\) |
−0.635199 | + | 0.772348i | \(0.719082\pi\) | |||||||
\(4\) | 2.67778 | + | 2.97145i | 0.669445 | + | 0.742862i | ||||
\(5\) | 1.71651 | − | 2.97309i | 0.343302 | − | 0.594617i | −0.641741 | − | 0.766921i | \(-0.721788\pi\) |
0.985044 | + | 0.172304i | \(0.0551211\pi\) | |||||||
\(6\) | 1.15657 | + | 1.59117i | 0.192761 | + | 0.265195i | ||||
\(7\) | − | 2.43870i | − | 0.348385i | −0.984712 | − | 0.174193i | \(-0.944268\pi\) | ||
0.984712 | − | 0.174193i | \(-0.0557315\pi\) | |||||||
\(8\) | −2.47697 | − | 7.60688i | −0.309621 | − | 0.950860i | ||||
\(9\) | −4.01632 | − | 6.95647i | −0.446257 | − | 0.772941i | ||||
\(10\) | −5.55390 | + | 4.03694i | −0.555390 | + | 0.403694i | ||||
\(11\) | − | 7.76499i | − | 0.705908i | −0.935641 | − | 0.352954i | \(-0.885177\pi\) | ||
0.935641 | − | 0.352954i | \(-0.114823\pi\) | |||||||
\(12\) | −0.819592 | − | 3.84787i | −0.0682994 | − | 0.320656i | ||||
\(13\) | −4.63516 | − | 8.02833i | −0.356551 | − | 0.617564i | 0.630832 | − | 0.775920i | \(-0.282714\pi\) |
−0.987382 | + | 0.158356i | \(0.949381\pi\) | |||||||
\(14\) | −1.98287 | + | 4.45614i | −0.141634 | + | 0.318296i | ||||
\(15\) | −2.92417 | + | 1.68827i | −0.194945 | + | 0.112551i | ||||
\(16\) | −1.65899 | + | 15.9138i | −0.103687 | + | 0.994610i | ||||
\(17\) | 8.87198 | − | 15.3667i | 0.521881 | − | 0.903924i | −0.477795 | − | 0.878471i | \(-0.658564\pi\) |
0.999676 | − | 0.0254531i | \(-0.00810285\pi\) | |||||||
\(18\) | 1.68266 | + | 15.9769i | 0.0934810 | + | 0.887606i | ||||
\(19\) | 6.84864 | + | 17.7228i | 0.360455 | + | 0.932777i | ||||
\(20\) | 13.4308 | − | 2.86075i | 0.671540 | − | 0.143037i | ||||
\(21\) | −1.19929 | + | 2.07722i | −0.0571089 | + | 0.0989155i | ||||
\(22\) | −6.31361 | + | 14.1887i | −0.286982 | + | 0.644940i | ||||
\(23\) | 10.0507 | − | 5.80275i | 0.436985 | − | 0.252293i | −0.265333 | − | 0.964157i | \(-0.585482\pi\) |
0.702318 | + | 0.711863i | \(0.252148\pi\) | |||||||
\(24\) | −1.63104 | + | 7.69747i | −0.0679601 | + | 0.320728i | ||||
\(25\) | 6.60717 | + | 11.4440i | 0.264287 | + | 0.457758i | ||||
\(26\) | 1.94192 | + | 18.4387i | 0.0746894 | + | 0.709179i | ||||
\(27\) | 16.7524i | 0.620459i | ||||||||
\(28\) | 7.24645 | − | 6.53029i | 0.258802 | − | 0.233225i | ||||
\(29\) | 2.64340 | + | 4.57851i | 0.0911519 | + | 0.157880i | 0.907996 | − | 0.418979i | \(-0.137612\pi\) |
−0.816844 | + | 0.576858i | \(0.804278\pi\) | |||||||
\(30\) | 6.71594 | − | 0.707310i | 0.223865 | − | 0.0235770i | ||||
\(31\) | 10.2531i | 0.330744i | 0.986231 | + | 0.165372i | \(0.0528825\pi\) | ||||
−0.986231 | + | 0.165372i | \(0.947117\pi\) | |||||||
\(32\) | 15.9707 | − | 27.7297i | 0.499083 | − | 0.866554i | ||||
\(33\) | −3.81862 | + | 6.61404i | −0.115716 | + | 0.200425i | ||||
\(34\) | −28.7059 | + | 20.8653i | −0.844291 | + | 0.613687i | ||||
\(35\) | −7.25045 | − | 4.18605i | −0.207156 | − | 0.119601i | ||||
\(36\) | 9.91595 | − | 30.5622i | 0.275443 | − | 0.848949i | ||||
\(37\) | −7.71952 | −0.208636 | −0.104318 | − | 0.994544i | \(-0.533266\pi\) | ||||
−0.104318 | + | 0.994544i | \(0.533266\pi\) | |||||||
\(38\) | 1.89587 | − | 37.9527i | 0.0498912 | − | 0.998755i | ||||
\(39\) | 9.11779i | 0.233790i | ||||||||
\(40\) | −26.8677 | − | 5.69307i | −0.671691 | − | 0.142327i | ||||
\(41\) | −25.2287 | + | 43.6973i | −0.615333 | + | 1.06579i | 0.374992 | + | 0.927028i | \(0.377645\pi\) |
−0.990326 | + | 0.138761i | \(0.955688\pi\) | |||||||
\(42\) | 3.88038 | − | 2.82051i | 0.0923899 | − | 0.0671551i | ||||
\(43\) | −43.2661 | − | 24.9797i | −1.00619 | − | 0.580923i | −0.0961149 | − | 0.995370i | \(-0.530642\pi\) |
−0.910073 | + | 0.414447i | \(0.863975\pi\) | |||||||
\(44\) | 23.0733 | − | 20.7929i | 0.524392 | − | 0.472567i | ||||
\(45\) | −27.5762 | −0.612805 | ||||||||
\(46\) | −23.0833 | + | 2.43109i | −0.501812 | + | 0.0528499i | ||||
\(47\) | 74.9827 | − | 43.2913i | 1.59538 | − | 0.921091i | 0.603015 | − | 0.797730i | \(-0.293966\pi\) |
0.992362 | − | 0.123361i | \(-0.0393674\pi\) | |||||||
\(48\) | 9.23906 | − | 12.7391i | 0.192480 | − | 0.265399i | ||||
\(49\) | 43.0528 | 0.878628 | ||||||||
\(50\) | −2.76811 | − | 26.2833i | −0.0553622 | − | 0.525667i | ||||
\(51\) | −15.1139 | + | 8.72601i | −0.296351 | + | 0.171098i | ||||
\(52\) | 11.4438 | − | 35.2712i | 0.220073 | − | 0.678293i | ||||
\(53\) | 17.3665 | + | 30.0797i | 0.327671 | + | 0.567542i | 0.982049 | − | 0.188625i | \(-0.0604030\pi\) |
−0.654379 | + | 0.756167i | \(0.727070\pi\) | |||||||
\(54\) | 13.6212 | − | 30.6110i | 0.252244 | − | 0.566871i | ||||
\(55\) | −23.0860 | − | 13.3287i | −0.419745 | − | 0.242340i | ||||
\(56\) | −18.5509 | + | 6.04056i | −0.331265 | + | 0.107867i | ||||
\(57\) | 2.88207 | − | 18.4638i | 0.0505626 | − | 0.323927i | ||||
\(58\) | −1.10747 | − | 10.5155i | −0.0190943 | − | 0.181301i | ||||
\(59\) | −63.9961 | − | 36.9482i | −1.08468 | − | 0.626240i | −0.152525 | − | 0.988300i | \(-0.548741\pi\) |
−0.932155 | + | 0.362059i | \(0.882074\pi\) | |||||||
\(60\) | −12.8469 | − | 4.16820i | −0.214115 | − | 0.0694700i | ||||
\(61\) | 40.4426 | + | 70.0487i | 0.662994 | + | 1.14834i | 0.979825 | + | 0.199857i | \(0.0640477\pi\) |
−0.316831 | + | 0.948482i | \(0.602619\pi\) | |||||||
\(62\) | 8.33664 | − | 18.7351i | 0.134462 | − | 0.302179i | ||||
\(63\) | −16.9647 | + | 9.79458i | −0.269281 | + | 0.155469i | ||||
\(64\) | −51.7293 | + | 37.6840i | −0.808270 | + | 0.588812i | ||||
\(65\) | −31.8252 | −0.489619 | ||||||||
\(66\) | 12.3554 | − | 8.98072i | 0.187203 | − | 0.136072i | ||||
\(67\) | −14.8972 | + | 8.60089i | −0.222346 | + | 0.128371i | −0.607036 | − | 0.794674i | \(-0.707642\pi\) |
0.384690 | + | 0.923046i | \(0.374308\pi\) | |||||||
\(68\) | 69.4186 | − | 14.7861i | 1.02086 | − | 0.217442i | ||||
\(69\) | −11.4146 | −0.165428 | ||||||||
\(70\) | 9.84486 | + | 13.5443i | 0.140641 | + | 0.193489i | ||||
\(71\) | 47.9333 | + | 27.6743i | 0.675117 | + | 0.389779i | 0.798013 | − | 0.602640i | \(-0.205885\pi\) |
−0.122896 | + | 0.992420i | \(0.539218\pi\) | |||||||
\(72\) | −42.9687 | + | 47.7826i | −0.596788 | + | 0.663647i | ||||
\(73\) | 27.9468 | − | 48.4053i | 0.382833 | − | 0.663087i | −0.608633 | − | 0.793452i | \(-0.708282\pi\) |
0.991466 | + | 0.130365i | \(0.0416150\pi\) | |||||||
\(74\) | 14.1056 | + | 6.27664i | 0.190616 | + | 0.0848195i | ||||
\(75\) | − | 12.9969i | − | 0.173292i | ||||||
\(76\) | −34.3231 | + | 67.8080i | −0.451619 | + | 0.892211i | ||||
\(77\) | −18.9364 | −0.245928 | ||||||||
\(78\) | 7.41356 | − | 16.6606i | 0.0950456 | − | 0.213598i | ||||
\(79\) | 95.2318 | + | 54.9821i | 1.20547 | + | 0.695976i | 0.961765 | − | 0.273874i | \(-0.0883052\pi\) |
0.243701 | + | 0.969850i | \(0.421639\pi\) | |||||||
\(80\) | 44.4653 | + | 32.2485i | 0.555816 | + | 0.403106i | ||||
\(81\) | −27.9085 | + | 48.3389i | −0.344549 | + | 0.596776i | ||||
\(82\) | 81.6291 | − | 59.3334i | 0.995477 | − | 0.723578i | ||||
\(83\) | 31.3464i | 0.377667i | 0.982009 | + | 0.188834i | \(0.0604707\pi\) | ||||
−0.982009 | + | 0.188834i | \(0.939529\pi\) | |||||||
\(84\) | −9.38379 | + | 1.99874i | −0.111712 | + | 0.0237945i | ||||
\(85\) | −30.4577 | − | 52.7543i | −0.358326 | − | 0.620639i | ||||
\(86\) | 58.7479 | + | 80.8236i | 0.683115 | + | 0.939809i | ||||
\(87\) | − | 5.19983i | − | 0.0597681i | ||||||
\(88\) | −59.0674 | + | 19.2336i | −0.671220 | + | 0.218564i | ||||
\(89\) | −5.29483 | − | 9.17091i | −0.0594925 | − | 0.103044i | 0.834745 | − | 0.550636i | \(-0.185615\pi\) |
−0.894238 | + | 0.447592i | \(0.852282\pi\) | |||||||
\(90\) | 50.3890 | + | 22.4219i | 0.559878 | + | 0.249132i | ||||
\(91\) | −19.5786 | + | 11.3037i | −0.215150 | + | 0.124217i | ||||
\(92\) | 44.1560 | + | 14.3265i | 0.479957 | + | 0.155723i | ||||
\(93\) | 5.04219 | − | 8.73334i | 0.0542171 | − | 0.0939068i | ||||
\(94\) | −172.213 | + | 18.1371i | −1.83205 | + | 0.192948i | ||||
\(95\) | 64.4471 | + | 10.0597i | 0.678390 | + | 0.105892i | ||||
\(96\) | −27.2402 | + | 15.7656i | −0.283752 | + | 0.164225i | ||||
\(97\) | 65.4893 | − | 113.431i | 0.675148 | − | 1.16939i | −0.301278 | − | 0.953536i | \(-0.597413\pi\) |
0.976426 | − | 0.215854i | \(-0.0692535\pi\) | |||||||
\(98\) | −78.6687 | − | 35.0056i | −0.802742 | − | 0.357200i | ||||
\(99\) | −54.0169 | + | 31.1867i | −0.545625 | + | 0.315017i | ||||
\(100\) | −16.3126 | + | 50.2773i | −0.163126 | + | 0.502773i | ||||
\(101\) | −43.6489 | − | 75.6021i | −0.432167 | − | 0.748536i | 0.564892 | − | 0.825165i | \(-0.308918\pi\) |
−0.997060 | + | 0.0766289i | \(0.975584\pi\) | |||||||
\(102\) | 34.7121 | − | 3.65581i | 0.340314 | − | 0.0358413i | ||||
\(103\) | 95.9601i | 0.931651i | 0.884877 | + | 0.465826i | \(0.154243\pi\) | ||||
−0.884877 | + | 0.465826i | \(0.845757\pi\) | |||||||
\(104\) | −49.5894 | + | 55.1450i | −0.476821 | + | 0.530240i | ||||
\(105\) | 4.11718 | + | 7.13116i | 0.0392112 | + | 0.0679158i | ||||
\(106\) | −7.27581 | − | 69.0841i | −0.0686397 | − | 0.651737i | ||||
\(107\) | − | 87.4042i | − | 0.816861i | −0.912789 | − | 0.408431i | \(-0.866076\pi\) | ||
0.912789 | − | 0.408431i | \(-0.133924\pi\) | |||||||
\(108\) | −49.7789 | + | 44.8593i | −0.460915 | + | 0.415363i | ||||
\(109\) | 93.5748 | − | 162.076i | 0.858485 | − | 1.48694i | −0.0148892 | − | 0.999889i | \(-0.504740\pi\) |
0.873374 | − | 0.487050i | \(-0.161927\pi\) | |||||||
\(110\) | 31.3468 | + | 43.1259i | 0.284971 | + | 0.392054i | ||||
\(111\) | 6.57531 | + | 3.79626i | 0.0592370 | + | 0.0342005i | ||||
\(112\) | 38.8088 | + | 4.04576i | 0.346507 | + | 0.0361229i | ||||
\(113\) | −181.373 | −1.60507 | −0.802534 | − | 0.596606i | \(-0.796516\pi\) | ||||
−0.802534 | + | 0.596606i | \(0.796516\pi\) | |||||||
\(114\) | −20.2790 | + | 31.3949i | −0.177886 | + | 0.275394i | ||||
\(115\) | − | 39.8420i | − | 0.346452i | ||||||
\(116\) | −6.52634 | + | 20.1150i | −0.0562616 | + | 0.173405i | ||||
\(117\) | −37.2325 | + | 64.4886i | −0.318227 | + | 0.551185i | ||||
\(118\) | 86.8957 | + | 119.548i | 0.736404 | + | 1.01312i | ||||
\(119\) | −37.4747 | − | 21.6361i | −0.314914 | − | 0.181816i | ||||
\(120\) | 20.0855 | + | 18.0620i | 0.167380 | + | 0.150517i | ||||
\(121\) | 60.7049 | 0.501694 | ||||||||
\(122\) | −16.9437 | − | 160.881i | −0.138882 | − | 1.31869i | ||||
\(123\) | 42.9784 | − | 24.8136i | 0.349418 | − | 0.201737i | ||||
\(124\) | −30.4665 | + | 27.4555i | −0.245697 | + | 0.221415i | ||||
\(125\) | 131.191 | 1.04953 | ||||||||
\(126\) | 38.9628 | − | 4.10349i | 0.309229 | − | 0.0325674i | ||||
\(127\) | 141.699 | − | 81.8097i | 1.11574 | − | 0.644171i | 0.175428 | − | 0.984492i | \(-0.443869\pi\) |
0.940309 | + | 0.340321i | \(0.110536\pi\) | |||||||
\(128\) | 125.163 | − | 26.7981i | 0.977839 | − | 0.209360i | ||||
\(129\) | 24.5687 | + | 42.5543i | 0.190455 | + | 0.329878i | ||||
\(130\) | 58.1530 | + | 25.8767i | 0.447331 | + | 0.199051i | ||||
\(131\) | −179.080 | − | 103.392i | −1.36702 | − | 0.789250i | −0.376475 | − | 0.926427i | \(-0.622864\pi\) |
−0.990547 | + | 0.137177i | \(0.956197\pi\) | |||||||
\(132\) | −29.8787 | + | 6.36413i | −0.226354 | + | 0.0482131i | ||||
\(133\) | 43.2204 | − | 16.7018i | 0.324965 | − | 0.125577i | ||||
\(134\) | 34.2143 | − | 3.60339i | 0.255331 | − | 0.0268910i | ||||
\(135\) | 49.8063 | + | 28.7557i | 0.368936 | + | 0.213005i | ||||
\(136\) | −138.868 | − | 29.4253i | −1.02109 | − | 0.216362i | ||||
\(137\) | 70.8332 | + | 122.687i | 0.517031 | + | 0.895524i | 0.999804 | + | 0.0197784i | \(0.00629607\pi\) |
−0.482774 | + | 0.875745i | \(0.660371\pi\) | |||||||
\(138\) | 20.8574 | + | 9.28103i | 0.151141 | + | 0.0672538i | ||||
\(139\) | −140.060 | + | 80.8637i | −1.00763 | + | 0.581753i | −0.910496 | − | 0.413519i | \(-0.864300\pi\) |
−0.0971300 | + | 0.995272i | \(0.530966\pi\) | |||||||
\(140\) | −6.97649 | − | 32.7536i | −0.0498321 | − | 0.233955i | ||||
\(141\) | −85.1581 | −0.603958 | ||||||||
\(142\) | −65.0852 | − | 89.5422i | −0.458346 | − | 0.630579i | ||||
\(143\) | −62.3399 | + | 35.9920i | −0.435943 | + | 0.251692i | ||||
\(144\) | 117.367 | − | 52.3740i | 0.815045 | − | 0.363709i | ||||
\(145\) | 18.1497 | 0.125171 | ||||||||
\(146\) | −90.4239 | + | 65.7261i | −0.619342 | + | 0.450179i | ||||
\(147\) | −36.6714 | − | 21.1722i | −0.249465 | − | 0.144029i | ||||
\(148\) | −20.6712 | − | 22.9381i | −0.139670 | − | 0.154987i | ||||
\(149\) | −3.94728 | + | 6.83690i | −0.0264918 | + | 0.0458852i | −0.878967 | − | 0.476882i | \(-0.841767\pi\) |
0.852476 | + | 0.522767i | \(0.175100\pi\) | |||||||
\(150\) | −10.5676 | + | 23.7488i | −0.0704509 | + | 0.158325i | ||||
\(151\) | − | 214.335i | − | 1.41944i | −0.704484 | − | 0.709719i | \(-0.748822\pi\) | ||
0.704484 | − | 0.709719i | \(-0.251178\pi\) | |||||||
\(152\) | 117.851 | − | 95.9955i | 0.775336 | − | 0.631549i | ||||
\(153\) | −142.531 | −0.931573 | ||||||||
\(154\) | 34.6019 | + | 15.3970i | 0.224687 | + | 0.0999803i | ||||
\(155\) | 30.4833 | + | 17.5995i | 0.196666 | + | 0.113545i | ||||
\(156\) | −27.0930 | + | 24.4154i | −0.173673 | + | 0.156509i | ||||
\(157\) | −5.93576 | + | 10.2810i | −0.0378074 | + | 0.0654844i | −0.884310 | − | 0.466900i | \(-0.845371\pi\) |
0.846503 | + | 0.532385i | \(0.178704\pi\) | |||||||
\(158\) | −129.308 | − | 177.899i | −0.818407 | − | 1.12594i | ||||
\(159\) | − | 34.1616i | − | 0.214853i | ||||||
\(160\) | −55.0290 | − | 95.0806i | −0.343931 | − | 0.594254i | ||||
\(161\) | −14.1511 | − | 24.5105i | −0.0878953 | − | 0.152239i | ||||
\(162\) | 90.2998 | − | 65.6358i | 0.557406 | − | 0.405160i | ||||
\(163\) | 309.533i | 1.89897i | 0.313807 | + | 0.949487i | \(0.398396\pi\) | ||||
−0.313807 | + | 0.949487i | \(0.601604\pi\) | |||||||
\(164\) | −197.401 | + | 42.0462i | −1.20367 | + | 0.256379i | ||||
\(165\) | 13.1094 | + | 22.7062i | 0.0794509 | + | 0.137613i | ||||
\(166\) | 25.4873 | − | 57.2781i | 0.153538 | − | 0.345049i | ||||
\(167\) | 133.887 | − | 77.2997i | 0.801719 | − | 0.462872i | −0.0423532 | − | 0.999103i | \(-0.513485\pi\) |
0.844072 | + | 0.536230i | \(0.180152\pi\) | |||||||
\(168\) | 18.7718 | + | 3.97761i | 0.111737 | + | 0.0236763i | ||||
\(169\) | 41.5306 | − | 71.9332i | 0.245743 | − | 0.425640i | ||||
\(170\) | 12.7604 | + | 121.161i | 0.0750613 | + | 0.712710i | ||||
\(171\) | 95.7814 | − | 118.823i | 0.560125 | − | 0.694869i | ||||
\(172\) | −41.6313 | − | 195.453i | −0.242042 | − | 1.13635i | ||||
\(173\) | −120.328 | + | 208.413i | −0.695535 | + | 1.20470i | 0.274465 | + | 0.961597i | \(0.411499\pi\) |
−0.970000 | + | 0.243105i | \(0.921834\pi\) | |||||||
\(174\) | −4.22791 | + | 9.50145i | −0.0242983 | + | 0.0546060i | ||||
\(175\) | 27.9083 | − | 16.1129i | 0.159476 | − | 0.0920736i | ||||
\(176\) | 123.570 | + | 12.8820i | 0.702103 | + | 0.0731933i | ||||
\(177\) | 36.3403 | + | 62.9432i | 0.205312 | + | 0.355611i | ||||
\(178\) | 2.21830 | + | 21.0628i | 0.0124623 | + | 0.118330i | ||||
\(179\) | 261.566i | 1.46126i | 0.682772 | + | 0.730632i | \(0.260774\pi\) | ||||
−0.682772 | + | 0.730632i | \(0.739226\pi\) | |||||||
\(180\) | −73.8431 | − | 81.9413i | −0.410239 | − | 0.455229i | ||||
\(181\) | 57.7654 | + | 100.053i | 0.319146 | + | 0.552777i | 0.980310 | − | 0.197464i | \(-0.0632706\pi\) |
−0.661164 | + | 0.750241i | \(0.729937\pi\) | |||||||
\(182\) | 44.9663 | − | 4.73576i | 0.247067 | − | 0.0260207i | ||||
\(183\) | − | 79.5545i | − | 0.434724i | ||||||
\(184\) | −69.0360 | − | 62.0810i | −0.375195 | − | 0.337396i | ||||
\(185\) | −13.2507 | + | 22.9508i | −0.0716252 | + | 0.124058i | ||||
\(186\) | −16.3144 | + | 11.8584i | −0.0877117 | + | 0.0637546i | ||||
\(187\) | −119.322 | − | 68.8908i | −0.638088 | − | 0.368400i | ||||
\(188\) | 329.425 | + | 106.883i | 1.75226 | + | 0.568524i | ||||
\(189\) | 40.8540 | 0.216159 | ||||||||
\(190\) | −109.582 | − | 70.7828i | −0.576749 | − | 0.372541i | ||||
\(191\) | 359.726i | 1.88338i | 0.336482 | + | 0.941690i | \(0.390763\pi\) | ||||
−0.336482 | + | 0.941690i | \(0.609237\pi\) | |||||||
\(192\) | 62.5938 | − | 6.65923i | 0.326009 | − | 0.0346835i | ||||
\(193\) | −123.197 | + | 213.383i | −0.638325 | + | 1.10561i | 0.347475 | + | 0.937689i | \(0.387039\pi\) |
−0.985800 | + | 0.167922i | \(0.946294\pi\) | |||||||
\(194\) | −211.895 | + | 154.020i | −1.09224 | + | 0.793915i | ||||
\(195\) | 27.1080 | + | 15.6508i | 0.139015 | + | 0.0802605i | ||||
\(196\) | 115.286 | + | 127.929i | 0.588193 | + | 0.652699i | ||||
\(197\) | −69.4731 | −0.352655 | −0.176328 | − | 0.984332i | \(-0.556422\pi\) | ||||
−0.176328 | + | 0.984332i | \(0.556422\pi\) | |||||||
\(198\) | 124.061 | − | 13.0658i | 0.626568 | − | 0.0659890i | ||||
\(199\) | 119.714 | − | 69.1172i | 0.601580 | − | 0.347322i | −0.168083 | − | 0.985773i | \(-0.553758\pi\) |
0.769663 | + | 0.638450i | \(0.220424\pi\) | |||||||
\(200\) | 70.6871 | − | 78.6063i | 0.353436 | − | 0.393031i | ||||
\(201\) | 16.9188 | 0.0841730 | ||||||||
\(202\) | 18.2869 | + | 173.635i | 0.0905294 | + | 0.859580i | ||||
\(203\) | 11.1656 | − | 6.44646i | 0.0550029 | − | 0.0317560i | ||||
\(204\) | −66.4006 | − | 21.5438i | −0.325493 | − | 0.105607i | ||||
\(205\) | 86.6106 | + | 150.014i | 0.422491 | + | 0.731776i | ||||
\(206\) | 78.0239 | − | 175.344i | 0.378757 | − | 0.851186i | ||||
\(207\) | −80.7333 | − | 46.6114i | −0.390016 | − | 0.225176i | ||||
\(208\) | 135.451 | − | 60.4439i | 0.651205 | − | 0.290596i | ||||
\(209\) | 137.617 | − | 53.1796i | 0.658455 | − | 0.254448i | ||||
\(210\) | −1.72491 | − | 16.3781i | −0.00821388 | − | 0.0779911i | ||||
\(211\) | 83.2015 | + | 48.0364i | 0.394320 | + | 0.227661i | 0.684030 | − | 0.729454i | \(-0.260226\pi\) |
−0.289710 | + | 0.957114i | \(0.593559\pi\) | |||||||
\(212\) | −42.8765 | + | 132.151i | −0.202248 | + | 0.623352i | ||||
\(213\) | −27.2190 | − | 47.1447i | −0.127789 | − | 0.221337i | ||||
\(214\) | −71.0672 | + | 159.710i | −0.332090 | + | 0.746310i | ||||
\(215\) | −148.534 | + | 85.7559i | −0.690854 | + | 0.398865i | ||||
\(216\) | 127.434 | − | 41.4951i | 0.589970 | − | 0.192107i | ||||
\(217\) | 25.0041 | 0.115226 | ||||||||
\(218\) | −302.768 | + | 220.072i | −1.38884 | + | 1.00950i | ||||
\(219\) | −47.6089 | + | 27.4870i | −0.217392 | + | 0.125512i | ||||
\(220\) | −22.2137 | − | 104.290i | −0.100971 | − | 0.474046i | ||||
\(221\) | −164.492 | −0.744308 | ||||||||
\(222\) | −8.92814 | − | 12.2831i | −0.0402168 | − | 0.0553291i | ||||
\(223\) | −118.020 | − | 68.1387i | −0.529236 | − | 0.305555i | 0.211469 | − | 0.977385i | \(-0.432175\pi\) |
−0.740705 | + | 0.671830i | \(0.765509\pi\) | |||||||
\(224\) | −67.6244 | − | 38.9476i | −0.301894 | − | 0.173873i | ||||
\(225\) | 53.0730 | − | 91.9252i | 0.235880 | − | 0.408556i | ||||
\(226\) | 331.416 | + | 147.472i | 1.46644 | + | 0.652530i | ||||
\(227\) | − | 237.981i | − | 1.04838i | −0.851602 | − | 0.524188i | \(-0.824369\pi\) | ||
0.851602 | − | 0.524188i | \(-0.175631\pi\) | |||||||
\(228\) | 62.5818 | − | 40.8781i | 0.274482 | − | 0.179290i | ||||
\(229\) | 162.743 | 0.710668 | 0.355334 | − | 0.934739i | \(-0.384367\pi\) | ||||
0.355334 | + | 0.934739i | \(0.384367\pi\) | |||||||
\(230\) | −32.3950 | + | 72.8017i | −0.140848 | + | 0.316529i | ||||
\(231\) | 16.1296 | + | 9.31245i | 0.0698252 | + | 0.0403136i | ||||
\(232\) | 28.2806 | − | 31.4489i | 0.121899 | − | 0.135556i | ||||
\(233\) | −2.50814 | + | 4.34423i | −0.0107646 | + | 0.0186448i | −0.871358 | − | 0.490649i | \(-0.836760\pi\) |
0.860593 | + | 0.509293i | \(0.170093\pi\) | |||||||
\(234\) | 120.468 | − | 87.5644i | 0.514822 | − | 0.374207i | ||||
\(235\) | − | 297.240i | − | 1.26485i | ||||||
\(236\) | −61.5780 | − | 289.100i | −0.260924 | − | 1.22500i | ||||
\(237\) | −54.0775 | − | 93.6650i | −0.228175 | − | 0.395211i | ||||
\(238\) | 50.8842 | + | 70.0050i | 0.213799 | + | 0.294139i | ||||
\(239\) | 324.149i | 1.35627i | 0.734936 | + | 0.678137i | \(0.237212\pi\) | ||||
−0.734936 | + | 0.678137i | \(0.762788\pi\) | |||||||
\(240\) | −22.0156 | − | 49.3354i | −0.0917316 | − | 0.205564i | ||||
\(241\) | −115.832 | − | 200.626i | −0.480629 | − | 0.832474i | 0.519124 | − | 0.854699i | \(-0.326258\pi\) |
−0.999753 | + | 0.0222253i | \(0.992925\pi\) | |||||||
\(242\) | −110.924 | − | 49.3584i | −0.458363 | − | 0.203960i | ||||
\(243\) | 178.116 | − | 102.835i | 0.732986 | − | 0.423190i | ||||
\(244\) | −99.8494 | + | 307.748i | −0.409219 | + | 1.26126i | ||||
\(245\) | 73.9006 | − | 128.000i | 0.301635 | − | 0.522447i | ||||
\(246\) | −98.7084 | + | 10.3958i | −0.401254 | + | 0.0422593i | ||||
\(247\) | 110.540 | − | 137.131i | 0.447529 | − | 0.555186i | ||||
\(248\) | 77.9939 | − | 25.3965i | 0.314492 | − | 0.102405i | ||||
\(249\) | 15.4153 | − | 26.7001i | 0.0619089 | − | 0.107229i | ||||
\(250\) | −239.720 | − | 106.669i | −0.958880 | − | 0.426678i | ||||
\(251\) | 29.0811 | − | 16.7900i | 0.115861 | − | 0.0668923i | −0.440950 | − | 0.897532i | \(-0.645358\pi\) |
0.556810 | + | 0.830640i | \(0.312025\pi\) | |||||||
\(252\) | −74.5318 | − | 24.1820i | −0.295761 | − | 0.0959602i | ||||
\(253\) | −45.0583 | − | 78.0433i | −0.178096 | − | 0.308471i | ||||
\(254\) | −325.439 | + | 34.2746i | −1.28126 | + | 0.134940i | ||||
\(255\) | 59.9132i | 0.234954i | ||||||||
\(256\) | −250.496 | − | 52.8014i | −0.978498 | − | 0.206256i | ||||
\(257\) | −68.8685 | − | 119.284i | −0.267971 | − | 0.464139i | 0.700367 | − | 0.713783i | \(-0.253020\pi\) |
−0.968338 | + | 0.249644i | \(0.919686\pi\) | |||||||
\(258\) | −10.2932 | − | 97.7343i | −0.0398961 | − | 0.378815i | ||||
\(259\) | 18.8256i | 0.0726856i | ||||||||
\(260\) | −85.2209 | − | 94.5669i | −0.327773 | − | 0.363719i | ||||
\(261\) | 21.2335 | − | 36.7775i | 0.0813544 | − | 0.140910i | ||||
\(262\) | 243.159 | + | 334.531i | 0.928089 | + | 1.27684i | ||||
\(263\) | −312.128 | − | 180.207i | −1.18680 | − | 0.685198i | −0.229220 | − | 0.973375i | \(-0.573618\pi\) |
−0.957577 | + | 0.288177i | \(0.906951\pi\) | |||||||
\(264\) | 59.7708 | + | 12.6650i | 0.226405 | + | 0.0479736i | ||||
\(265\) | 119.240 | 0.449960 | ||||||||
\(266\) | −92.5550 | − | 4.62344i | −0.347951 | − | 0.0173814i | ||||
\(267\) | 10.4154i | 0.0390091i | ||||||||
\(268\) | −65.4485 | − | 21.2349i | −0.244211 | − | 0.0792346i | ||||
\(269\) | 183.963 | − | 318.633i | 0.683876 | − | 1.18451i | −0.289913 | − | 0.957053i | \(-0.593626\pi\) |
0.973789 | − | 0.227455i | \(-0.0730404\pi\) | |||||||
\(270\) | −67.6284 | − | 93.0411i | −0.250476 | − | 0.344597i | ||||
\(271\) | 18.4102 | + | 10.6292i | 0.0679345 | + | 0.0392220i | 0.533583 | − | 0.845748i | \(-0.320845\pi\) |
−0.465648 | + | 0.884970i | \(0.654179\pi\) | |||||||
\(272\) | 229.824 | + | 166.680i | 0.844940 | + | 0.612793i | ||||
\(273\) | 22.2355 | 0.0814488 | ||||||||
\(274\) | −29.6760 | − | 281.774i | −0.108306 | − | 1.02837i | ||||
\(275\) | 88.8622 | − | 51.3046i | 0.323135 | − | 0.186562i | ||||
\(276\) | −30.5657 | − | 33.9178i | −0.110745 | − | 0.122890i | ||||
\(277\) | −221.207 | −0.798581 | −0.399290 | − | 0.916825i | \(-0.630743\pi\) | ||||
−0.399290 | + | 0.916825i | \(0.630743\pi\) | |||||||
\(278\) | 321.676 | − | 33.8783i | 1.15711 | − | 0.121864i | ||||
\(279\) | 71.3252 | − | 41.1796i | 0.255646 | − | 0.147597i | ||||
\(280\) | −13.8837 | + | 65.5220i | −0.0495845 | + | 0.234007i | ||||
\(281\) | −56.6252 | − | 98.0777i | −0.201513 | − | 0.349031i | 0.747503 | − | 0.664258i | \(-0.231253\pi\) |
−0.949016 | + | 0.315227i | \(0.897919\pi\) | |||||||
\(282\) | 155.606 | + | 69.2409i | 0.551795 | + | 0.245535i | ||||
\(283\) | −136.312 | − | 78.7000i | −0.481669 | − | 0.278092i | 0.239443 | − | 0.970911i | \(-0.423035\pi\) |
−0.721112 | + | 0.692819i | \(0.756369\pi\) | |||||||
\(284\) | 46.1222 | + | 216.537i | 0.162402 | + | 0.762454i | ||||
\(285\) | −49.9474 | − | 40.2620i | −0.175254 | − | 0.141270i | ||||
\(286\) | 143.176 | − | 15.0790i | 0.500615 | − | 0.0527239i | ||||
\(287\) | 106.565 | + | 61.5250i | 0.371305 | + | 0.214373i | ||||
\(288\) | −257.044 | + | 0.271948i | −0.892514 | + | 0.000944264i | ||||
\(289\) | −12.9240 | − | 22.3850i | −0.0447196 | − | 0.0774567i | ||||
\(290\) | −33.1644 | − | 14.7573i | −0.114360 | − | 0.0508873i | ||||
\(291\) | −111.565 | + | 64.4119i | −0.383384 | + | 0.221347i | ||||
\(292\) | 218.669 | − | 46.5763i | 0.748868 | − | 0.159508i | ||||
\(293\) | −206.366 | −0.704322 | −0.352161 | − | 0.935939i | \(-0.614553\pi\) | ||||
−0.352161 | + | 0.935939i | \(0.614553\pi\) | |||||||
\(294\) | 49.7934 | + | 68.5042i | 0.169365 | + | 0.233007i | ||||
\(295\) | −219.700 | + | 126.844i | −0.744747 | + | 0.429980i | ||||
\(296\) | 19.1210 | + | 58.7215i | 0.0645979 | + | 0.198383i | ||||
\(297\) | 130.082 | 0.437987 | ||||||||
\(298\) | 12.7717 | − | 9.28333i | 0.0428581 | − | 0.0311521i | ||||
\(299\) | −93.1728 | − | 53.7933i | −0.311615 | − | 0.179911i | ||||
\(300\) | 38.6197 | − | 34.8029i | 0.128732 | − | 0.116010i | ||||
\(301\) | −60.9179 | + | 105.513i | −0.202385 | + | 0.350541i | ||||
\(302\) | −174.273 | + | 391.647i | −0.577063 | + | 1.29684i | ||||
\(303\) | 85.8615i | 0.283371i | ||||||||
\(304\) | −293.398 | + | 79.5858i | −0.965123 | + | 0.261796i | ||||
\(305\) | 277.681 | 0.910429 | ||||||||
\(306\) | 260.441 | + | 115.890i | 0.851115 | + | 0.378725i | ||||
\(307\) | 475.527 | + | 274.546i | 1.54895 | + | 0.894285i | 0.998222 | + | 0.0595984i | \(0.0189820\pi\) |
0.550725 | + | 0.834687i | \(0.314351\pi\) | |||||||
\(308\) | −50.7076 | − | 56.2686i | −0.164635 | − | 0.182690i | ||||
\(309\) | 47.1906 | − | 81.7366i | 0.152721 | − | 0.264520i | ||||
\(310\) | −41.3910 | − | 56.9445i | −0.133519 | − | 0.183692i | ||||
\(311\) | − | 189.205i | − | 0.608375i | −0.952612 | − | 0.304188i | \(-0.901615\pi\) | ||
0.952612 | − | 0.304188i | \(-0.0983850\pi\) | |||||||
\(312\) | 69.3580 | − | 22.5845i | 0.222301 | − | 0.0723861i | ||||
\(313\) | 44.4599 | + | 77.0067i | 0.142044 | + | 0.246028i | 0.928266 | − | 0.371916i | \(-0.121299\pi\) |
−0.786222 | + | 0.617944i | \(0.787966\pi\) | |||||||
\(314\) | 19.2056 | − | 13.9599i | 0.0611643 | − | 0.0444582i | ||||
\(315\) | 67.2500i | 0.213492i | ||||||||
\(316\) | 91.6335 | + | 430.206i | 0.289979 | + | 1.36141i | ||||
\(317\) | 175.632 | + | 304.204i | 0.554045 | + | 0.959634i | 0.997977 | + | 0.0635735i | \(0.0202497\pi\) |
−0.443932 | + | 0.896060i | \(0.646417\pi\) | |||||||
\(318\) | −27.7764 | + | 62.4223i | −0.0873471 | + | 0.196297i | ||||
\(319\) | 35.5521 | − | 20.5260i | 0.111449 | − | 0.0643449i | ||||
\(320\) | 23.2437 | + | 218.481i | 0.0726366 | + | 0.682752i | ||||
\(321\) | −42.9831 | + | 74.4489i | −0.133904 | + | 0.231928i | ||||
\(322\) | 5.92870 | + | 56.2932i | 0.0184121 | + | 0.174824i | ||||
\(323\) | 333.102 | + | 51.9948i | 1.03127 | + | 0.160974i | ||||
\(324\) | −218.369 | + | 46.5124i | −0.673979 | + | 0.143557i | ||||
\(325\) | 61.2506 | − | 106.089i | 0.188463 | − | 0.326428i | ||||
\(326\) | 251.677 | − | 565.598i | 0.772015 | − | 1.73496i | ||||
\(327\) | −159.410 | + | 92.0353i | −0.487492 | + | 0.281453i | ||||
\(328\) | 394.891 | + | 83.6747i | 1.20394 | + | 0.255106i | ||||
\(329\) | −105.574 | − | 182.860i | −0.320894 | − | 0.555805i | ||||
\(330\) | −5.49226 | − | 52.1492i | −0.0166432 | − | 0.158028i | ||||
\(331\) | 428.498i | 1.29456i | 0.762254 | + | 0.647278i | \(0.224093\pi\) | ||||
−0.762254 | + | 0.647278i | \(0.775907\pi\) | |||||||
\(332\) | −93.1441 | + | 83.9387i | −0.280555 | + | 0.252828i | ||||
\(333\) | 31.0041 | + | 53.7006i | 0.0931053 | + | 0.161263i | ||||
\(334\) | −307.498 | + | 32.3851i | −0.920653 | + | 0.0969615i | ||||
\(335\) | 59.0541i | 0.176281i | ||||||||
\(336\) | −31.0669 | − | 22.5312i | −0.0924609 | − | 0.0670573i | ||||
\(337\) | −145.765 | + | 252.472i | −0.432537 | + | 0.749176i | −0.997091 | − | 0.0762204i | \(-0.975715\pi\) |
0.564554 | + | 0.825396i | \(0.309048\pi\) | |||||||
\(338\) | −134.375 | + | 97.6728i | −0.397560 | + | 0.288973i | ||||
\(339\) | 154.489 | + | 89.1943i | 0.455720 | + | 0.263110i | ||||
\(340\) | 75.1975 | − | 231.768i | 0.221169 | − | 0.681670i | ||||
\(341\) | 79.6150 | 0.233475 | ||||||||
\(342\) | −271.631 | + | 139.241i | −0.794242 | + | 0.407139i | ||||
\(343\) | − | 224.489i | − | 0.654486i | ||||||
\(344\) | −82.8489 | + | 390.994i | −0.240840 | + | 1.13661i | ||||
\(345\) | −19.5932 | + | 33.9365i | −0.0567920 | + | 0.0983666i | ||||
\(346\) | 389.328 | − | 282.989i | 1.12523 | − | 0.817889i | ||||
\(347\) | −243.463 | − | 140.563i | −0.701622 | − | 0.405082i | 0.106329 | − | 0.994331i | \(-0.466090\pi\) |
−0.807951 | + | 0.589249i | \(0.799424\pi\) | |||||||
\(348\) | 15.4510 | − | 13.9240i | 0.0443994 | − | 0.0400115i | ||||
\(349\) | −18.0923 | −0.0518403 | −0.0259202 | − | 0.999664i | \(-0.508252\pi\) | ||||
−0.0259202 | + | 0.999664i | \(0.508252\pi\) | |||||||
\(350\) | −64.0970 | + | 6.75058i | −0.183134 | + | 0.0192874i | ||||
\(351\) | 134.494 | − | 77.6500i | 0.383173 | − | 0.221225i | ||||
\(352\) | −215.321 | − | 124.012i | −0.611708 | − | 0.352307i | ||||
\(353\) | −258.038 | −0.730985 | −0.365492 | − | 0.930814i | \(-0.619099\pi\) | ||||
−0.365492 | + | 0.930814i | \(0.619099\pi\) | |||||||
\(354\) | −15.2250 | − | 144.562i | −0.0430084 | − | 0.408366i | ||||
\(355\) | 164.556 | − | 95.0066i | 0.463539 | − | 0.267624i | ||||
\(356\) | 13.0725 | − | 40.2910i | 0.0367205 | − | 0.113177i | ||||
\(357\) | 21.2801 | + | 36.8582i | 0.0596081 | + | 0.103244i | ||||
\(358\) | 212.676 | − | 477.950i | 0.594067 | − | 1.33506i | ||||
\(359\) | −237.555 | − | 137.153i | −0.661714 | − | 0.382041i | 0.131216 | − | 0.991354i | \(-0.458112\pi\) |
−0.792930 | + | 0.609313i | \(0.791445\pi\) | |||||||
\(360\) | 68.3054 | + | 209.769i | 0.189737 | + | 0.582692i | ||||
\(361\) | −267.192 | + | 242.754i | −0.740145 | + | 0.672448i | ||||
\(362\) | −24.2012 | − | 229.791i | −0.0668540 | − | 0.634781i | ||||
\(363\) | −51.7071 | − | 29.8531i | −0.142444 | − | 0.0822399i | ||||
\(364\) | −86.0158 | − | 27.9080i | −0.236307 | − | 0.0766703i | ||||
\(365\) | −95.9421 | − | 166.177i | −0.262855 | − | 0.455279i | ||||
\(366\) | −64.6847 | + | 145.367i | −0.176734 | + | 0.397177i | ||||
\(367\) | −523.494 | + | 302.240i | −1.42642 | + | 0.823541i | −0.996836 | − | 0.0794877i | \(-0.974672\pi\) |
−0.429580 | + | 0.903029i | \(0.641338\pi\) | |||||||
\(368\) | 75.6697 | + | 169.570i | 0.205624 | + | 0.460789i | ||||
\(369\) | 405.305 | 1.09839 | ||||||||
\(370\) | 42.8734 | − | 31.1632i | 0.115874 | − | 0.0842249i | ||||
\(371\) | 73.3553 | − | 42.3517i | 0.197723 | − | 0.114156i | ||||
\(372\) | 39.4525 | − | 8.40334i | 0.106055 | − | 0.0225896i | ||||
\(373\) | −277.069 | −0.742813 | −0.371406 | − | 0.928470i | \(-0.621124\pi\) | ||||
−0.371406 | + | 0.928470i | \(0.621124\pi\) | |||||||
\(374\) | 162.019 | + | 222.901i | 0.433206 | + | 0.595992i | ||||
\(375\) | −111.745 | − | 64.5162i | −0.297987 | − | 0.172043i | ||||
\(376\) | −515.041 | − | 463.154i | −1.36979 | − | 1.23179i | ||||
\(377\) | 24.5052 | − | 42.4442i | 0.0650005 | − | 0.112584i | ||||
\(378\) | −74.6510 | − | 33.2179i | −0.197489 | − | 0.0878779i | ||||
\(379\) | − | 335.762i | − | 0.885915i | −0.896543 | − | 0.442958i | \(-0.853929\pi\) | ||
0.896543 | − | 0.442958i | \(-0.146071\pi\) | |||||||
\(380\) | 142.683 | + | 218.439i | 0.375482 | + | 0.574839i | ||||
\(381\) | −160.927 | −0.422382 | ||||||||
\(382\) | 292.488 | − | 657.313i | 0.765675 | − | 1.72071i | ||||
\(383\) | 256.524 | + | 148.104i | 0.669775 | + | 0.386695i | 0.795991 | − | 0.605308i | \(-0.206950\pi\) |
−0.126216 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(384\) | −119.790 | − | 38.7260i | −0.311953 | − | 0.100849i | ||||
\(385\) | −32.5046 | + | 56.2997i | −0.0844276 | + | 0.146233i | ||||
\(386\) | 398.612 | − | 289.737i | 1.03267 | − | 0.750615i | ||||
\(387\) | 401.305i | 1.03697i | ||||||||
\(388\) | 512.420 | − | 109.145i | 1.32067 | − | 0.281301i | ||||
\(389\) | 352.122 | + | 609.894i | 0.905199 | + | 1.56785i | 0.820650 | + | 0.571432i | \(0.193612\pi\) |
0.0845496 | + | 0.996419i | \(0.473055\pi\) | |||||||
\(390\) | −36.8080 | − | 50.6393i | −0.0943794 | − | 0.129844i | ||||
\(391\) | − | 205.927i | − | 0.526669i | ||||||
\(392\) | −106.640 | − | 327.497i | −0.272041 | − | 0.835452i | ||||
\(393\) | 101.691 | + | 176.133i | 0.258755 | + | 0.448177i | ||||
\(394\) | 126.946 | + | 56.4876i | 0.322197 | + | 0.143370i | ||||
\(395\) | 326.933 | − | 188.755i | 0.827679 | − | 0.477861i | ||||
\(396\) | −237.315 | − | 76.9973i | −0.599280 | − | 0.194438i | ||||
\(397\) | −159.646 | + | 276.514i | −0.402130 | + | 0.696510i | −0.993983 | − | 0.109536i | \(-0.965063\pi\) |
0.591853 | + | 0.806046i | \(0.298397\pi\) | |||||||
\(398\) | −274.948 | + | 28.9570i | −0.690824 | + | 0.0727563i | ||||
\(399\) | −45.0276 | − | 7.02849i | −0.112851 | − | 0.0176153i | ||||
\(400\) | −193.078 | + | 86.1596i | −0.482694 | + | 0.215399i | ||||
\(401\) | −142.641 | + | 247.061i | −0.355712 | + | 0.616111i | −0.987240 | − | 0.159242i | \(-0.949095\pi\) |
0.631528 | + | 0.775353i | \(0.282428\pi\) | |||||||
\(402\) | −30.9150 | − | 13.7564i | −0.0769031 | − | 0.0342200i | ||||
\(403\) | 82.3151 | − | 47.5246i | 0.204256 | − | 0.117927i | ||||
\(404\) | 107.765 | − | 332.146i | 0.266746 | − | 0.822144i | ||||
\(405\) | 95.8104 | + | 165.949i | 0.236569 | + | 0.409749i | ||||
\(406\) | −25.6440 | + | 2.70078i | −0.0631626 | + | 0.00665217i | ||||
\(407\) | 59.9420i | 0.147278i | ||||||||
\(408\) | 103.814 | + | 93.3556i | 0.254447 | + | 0.228813i | ||||
\(409\) | 9.38811 | + | 16.2607i | 0.0229538 | + | 0.0397572i | 0.877274 | − | 0.479990i | \(-0.159360\pi\) |
−0.854320 | + | 0.519747i | \(0.826026\pi\) | |||||||
\(410\) | −36.2860 | − | 344.537i | −0.0885025 | − | 0.840334i | ||||
\(411\) | − | 139.336i | − | 0.339016i | ||||||
\(412\) | −285.140 | + | 256.960i | −0.692088 | + | 0.623689i | ||||
\(413\) | −90.1054 | + | 156.067i | −0.218173 | + | 0.377886i | ||||
\(414\) | 109.622 | + | 150.814i | 0.264787 | + | 0.364286i | ||||
\(415\) | 93.1955 | + | 53.8064i | 0.224567 | + | 0.129654i | ||||
\(416\) | −296.650 | + | 0.313850i | −0.713101 | + | 0.000754447i | ||||
\(417\) | 159.066 | 0.381454 | ||||||||
\(418\) | −294.702 | − | 14.7214i | −0.705029 | − | 0.0352186i | ||||
\(419\) | 147.770i | 0.352674i | 0.984330 | + | 0.176337i | \(0.0564248\pi\) | ||||
−0.984330 | + | 0.176337i | \(0.943575\pi\) | |||||||
\(420\) | −10.1650 | + | 31.3297i | −0.0242023 | + | 0.0745944i | ||||
\(421\) | 172.053 | − | 298.005i | 0.408678 | − | 0.707851i | −0.586064 | − | 0.810265i | \(-0.699323\pi\) |
0.994742 | + | 0.102414i | \(0.0326567\pi\) | |||||||
\(422\) | −112.973 | − | 155.425i | −0.267709 | − | 0.368306i | ||||
\(423\) | −602.309 | − | 347.743i | −1.42390 | − | 0.822088i | ||||
\(424\) | 185.797 | − | 206.612i | 0.438200 | − | 0.487292i | ||||
\(425\) | 234.475 | 0.551705 | ||||||||
\(426\) | 11.4036 | + | 108.277i | 0.0267689 | + | 0.254172i | ||||
\(427\) | 170.827 | − | 98.6272i | 0.400064 | − | 0.230977i | ||||
\(428\) | 259.717 | − | 234.049i | 0.606815 | − | 0.546844i | ||||
\(429\) | 70.7996 | 0.165034 | ||||||||
\(430\) | 341.137 | − | 35.9279i | 0.793341 | − | 0.0835533i | ||||
\(431\) | −283.031 | + | 163.408i | −0.656686 | + | 0.379138i | −0.791013 | − | 0.611799i | \(-0.790446\pi\) |
0.134327 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(432\) | −266.594 | − | 27.7920i | −0.617115 | − | 0.0643334i | ||||
\(433\) | −258.077 | − | 447.003i | −0.596022 | − | 1.03234i | −0.993402 | − | 0.114686i | \(-0.963414\pi\) |
0.397380 | − | 0.917654i | \(-0.369920\pi\) | |||||||
\(434\) | −45.6891 | − | 20.3305i | −0.105274 | − | 0.0468445i | ||||
\(435\) | −15.4595 | − | 8.92557i | −0.0355392 | − | 0.0205185i | ||||
\(436\) | 732.174 | − | 155.952i | 1.67930 | − | 0.357689i | ||||
\(437\) | 171.674 | + | 138.384i | 0.392847 | + | 0.316669i | ||||
\(438\) | 109.343 | − | 11.5158i | 0.249642 | − | 0.0262919i | ||||
\(439\) | −741.197 | − | 427.930i | −1.68838 | − | 0.974784i | −0.955763 | − | 0.294137i | \(-0.904968\pi\) |
−0.732612 | − | 0.680646i | \(-0.761699\pi\) | |||||||
\(440\) | −44.2067 | + | 208.627i | −0.100470 | + | 0.474152i | ||||
\(441\) | −172.914 | − | 299.495i | −0.392094 | − | 0.679127i | ||||
\(442\) | 300.570 | + | 133.746i | 0.680023 | + | 0.302593i | ||||
\(443\) | 276.161 | − | 159.442i | 0.623389 | − | 0.359914i | −0.154798 | − | 0.987946i | \(-0.549473\pi\) |
0.778187 | + | 0.628032i | \(0.216139\pi\) | |||||||
\(444\) | 6.32686 | + | 29.7037i | 0.0142497 | + | 0.0669003i | ||||
\(445\) | −36.3545 | −0.0816956 | ||||||||
\(446\) | 160.250 | + | 220.468i | 0.359306 | + | 0.494322i | ||||
\(447\) | 6.72441 | − | 3.88234i | 0.0150434 | − | 0.00868533i | ||||
\(448\) | 91.8997 | + | 126.152i | 0.205133 | + | 0.281589i | ||||
\(449\) | 671.176 | 1.49482 | 0.747412 | − | 0.664361i | \(-0.231296\pi\) | ||||
0.747412 | + | 0.664361i | \(0.231296\pi\) | |||||||
\(450\) | −171.721 | + | 124.818i | −0.381603 | + | 0.277374i | ||||
\(451\) | 339.309 | + | 195.900i | 0.752349 | + | 0.434369i | ||||
\(452\) | −485.676 | − | 538.939i | −1.07451 | − | 1.19234i | ||||
\(453\) | −105.404 | + | 182.566i | −0.232681 | + | 0.403015i | ||||
\(454\) | −193.500 | + | 434.855i | −0.426210 | + | 0.957830i | ||||
\(455\) | 77.6120i | 0.170576i | ||||||||
\(456\) | −147.591 | + | 23.8107i | −0.323664 | + | 0.0522164i | ||||
\(457\) | −557.508 | −1.21993 | −0.609965 | − | 0.792429i | \(-0.708816\pi\) | ||||
−0.609965 | + | 0.792429i | \(0.708816\pi\) | |||||||
\(458\) | −297.374 | − | 132.324i | −0.649288 | − | 0.288917i | ||||
\(459\) | 257.429 | + | 148.627i | 0.560848 | + | 0.323806i | ||||
\(460\) | 118.388 | − | 106.688i | 0.257366 | − | 0.231930i | ||||
\(461\) | 289.697 | − | 501.770i | 0.628410 | − | 1.08844i | −0.359460 | − | 0.933160i | \(-0.617039\pi\) |
0.987871 | − | 0.155278i | \(-0.0496274\pi\) | |||||||
\(462\) | −21.9013 | − | 30.1311i | −0.0474053 | − | 0.0652188i | ||||
\(463\) | 338.056i | 0.730142i | 0.930980 | + | 0.365071i | \(0.118955\pi\) | ||||
−0.930980 | + | 0.365071i | \(0.881045\pi\) | |||||||
\(464\) | −77.2467 | + | 34.4708i | −0.166480 | + | 0.0742906i | ||||
\(465\) | −17.3100 | − | 29.9817i | −0.0372257 | − | 0.0644769i | ||||
\(466\) | 8.11528 | − | 5.89872i | 0.0174148 | − | 0.0126582i | ||||
\(467\) | − | 297.175i | − | 0.636349i | −0.948032 | − | 0.318175i | \(-0.896930\pi\) | ||
0.948032 | − | 0.318175i | \(-0.103070\pi\) | |||||||
\(468\) | −291.325 | + | 62.0519i | −0.622489 | + | 0.132590i | ||||
\(469\) | 20.9750 | + | 36.3297i | 0.0447227 | + | 0.0774620i | ||||
\(470\) | −241.682 | + | 543.136i | −0.514217 | + | 1.15561i | ||||
\(471\) | 10.1119 | − | 5.83810i | 0.0214690 | − | 0.0123951i | ||||
\(472\) | −122.544 | + | 578.330i | −0.259628 | + | 1.22528i | ||||
\(473\) | −193.967 | + | 335.961i | −0.410078 | + | 0.710277i | ||||
\(474\) | 22.6561 | + | 215.120i | 0.0477976 | + | 0.453840i | ||||
\(475\) | −157.568 | + | 195.473i | −0.331723 | + | 0.411522i | ||||
\(476\) | −36.0588 | − | 169.291i | −0.0757537 | − | 0.355653i | ||||
\(477\) | 139.499 | − | 241.620i | 0.292451 | − | 0.506540i | ||||
\(478\) | 263.562 | − | 592.306i | 0.551384 | − | 1.23913i | ||||
\(479\) | 271.879 | − | 156.970i | 0.567597 | − | 0.327703i | −0.188592 | − | 0.982056i | \(-0.560392\pi\) |
0.756189 | + | 0.654353i | \(0.227059\pi\) | |||||||
\(480\) | 0.114314 | + | 108.049i | 0.000238154 | + | 0.225103i | ||||
\(481\) | 35.7812 | + | 61.9749i | 0.0743892 | + | 0.128846i | ||||
\(482\) | 48.5283 | + | 460.778i | 0.100681 | + | 0.955971i | ||||
\(483\) | 27.8366i | 0.0576328i | ||||||||
\(484\) | 162.554 | + | 180.381i | 0.335856 | + | 0.372689i | ||||
\(485\) | −224.826 | − | 389.411i | −0.463560 | − | 0.802909i | ||||
\(486\) | −409.078 | + | 43.0833i | −0.841724 | + | 0.0886489i | ||||
\(487\) | 94.5905i | 0.194231i | 0.995273 | + | 0.0971155i | \(0.0309616\pi\) | ||||
−0.995273 | + | 0.0971155i | \(0.969038\pi\) | |||||||
\(488\) | 432.677 | − | 481.150i | 0.886633 | − | 0.985964i | ||||
\(489\) | 152.220 | − | 263.653i | 0.311288 | − | 0.539167i | ||||
\(490\) | −239.111 | + | 173.801i | −0.487981 | + | 0.354697i | ||||
\(491\) | −292.034 | − | 168.606i | −0.594774 | − | 0.343393i | 0.172209 | − | 0.985060i | \(-0.444910\pi\) |
−0.766983 | + | 0.641668i | \(0.778243\pi\) | |||||||
\(492\) | 188.819 | + | 61.2627i | 0.383778 | + | 0.124518i | ||||
\(493\) | 93.8089 | 0.190282 | ||||||||
\(494\) | −313.484 | + | 160.696i | −0.634583 | + | 0.325296i | ||||
\(495\) | 214.129i | 0.432584i | ||||||||
\(496\) | −163.165 | − | 17.0097i | −0.328962 | − | 0.0342938i | ||||
\(497\) | 67.4892 | − | 116.895i | 0.135793 | − | 0.235201i | ||||
\(498\) | −49.8774 | + | 36.2542i | −0.100155 | + | 0.0727995i | ||||
\(499\) | 617.010 | + | 356.231i | 1.23649 | + | 0.713890i | 0.968376 | − | 0.249496i | \(-0.0802650\pi\) |
0.268118 | + | 0.963386i | \(0.413598\pi\) | |||||||
\(500\) | 351.300 | + | 389.826i | 0.702600 | + | 0.779653i | ||||
\(501\) | −152.056 | −0.303505 | ||||||||
\(502\) | −66.7904 | + | 7.03425i | −0.133049 | + | 0.0140124i | ||||
\(503\) | 165.562 | − | 95.5870i | 0.329148 | − | 0.190034i | −0.326315 | − | 0.945261i | \(-0.605807\pi\) |
0.655463 | + | 0.755227i | \(0.272474\pi\) | |||||||
\(504\) | 116.527 | + | 104.788i | 0.231205 | + | 0.207912i | ||||
\(505\) | −299.695 | −0.593456 | ||||||||
\(506\) | 18.8774 | + | 179.242i | 0.0373072 | + | 0.354233i | ||||
\(507\) | −70.7497 | + | 40.8473i | −0.139546 | + | 0.0805668i | ||||
\(508\) | 622.531 | + | 201.981i | 1.22545 | + | 0.397601i | ||||
\(509\) | −300.486 | − | 520.456i | −0.590345 | − | 1.02251i | −0.994186 | − | 0.107678i | \(-0.965658\pi\) |
0.403841 | − | 0.914829i | \(-0.367675\pi\) | |||||||
\(510\) | 48.7146 | − | 109.477i | 0.0955189 | − | 0.214661i | ||||
\(511\) | −118.046 | − | 68.1538i | −0.231010 | − | 0.133373i | ||||
\(512\) | 414.789 | + | 300.157i | 0.810135 | + | 0.586244i | ||||
\(513\) | −296.899 | + | 114.731i | −0.578750 | + | 0.223648i | ||||
\(514\) | 28.8529 | + | 273.959i | 0.0561340 | + | 0.532994i | ||||
\(515\) | 285.298 | + | 164.717i | 0.553976 | + | 0.319838i | ||||
\(516\) | −60.6581 | + | 186.956i | −0.117554 | + | 0.362317i | ||||
\(517\) | −336.156 | − | 582.240i | −0.650206 | − | 1.12619i | ||||
\(518\) | 15.3068 | − | 34.3993i | 0.0295498 | − | 0.0664078i | ||||
\(519\) | 204.984 | − | 118.348i | 0.394960 | − | 0.228031i | ||||
\(520\) | 78.8299 | + | 242.091i | 0.151596 | + | 0.465559i | ||||
\(521\) | 65.8959 | 0.126480 | 0.0632398 | − | 0.997998i | \(-0.479857\pi\) | ||||
0.0632398 | + | 0.997998i | \(0.479857\pi\) | |||||||
\(522\) | −68.7025 | + | 49.9375i | −0.131614 | + | 0.0956657i | ||||
\(523\) | 210.412 | − | 121.482i | 0.402318 | − | 0.232278i | −0.285166 | − | 0.958478i | \(-0.592049\pi\) |
0.687484 | + | 0.726200i | \(0.258715\pi\) | |||||||
\(524\) | −172.313 | − | 808.986i | −0.328842 | − | 1.54387i | ||||
\(525\) | −31.6956 | −0.0603725 | ||||||||
\(526\) | 423.815 | + | 583.072i | 0.805733 | + | 1.10850i | ||||
\(527\) | 157.556 | + | 90.9651i | 0.298968 | + | 0.172609i | ||||
\(528\) | −98.9192 | − | 71.7412i | −0.187347 | − | 0.135873i | ||||
\(529\) | −197.156 | + | 341.485i | −0.372696 | + | 0.645528i | ||||
\(530\) | −217.882 | − | 96.9521i | −0.411098 | − | 0.182928i | ||||
\(531\) | 593.583i | 1.11786i | ||||||||
\(532\) | 165.363 | + | 83.7035i | 0.310833 | + | 0.157337i | ||||
\(533\) | 467.755 | 0.877590 | ||||||||
\(534\) | 8.46865 | − | 19.0317i | 0.0158589 | − | 0.0356399i | ||||
\(535\) | −259.860 | − | 150.030i | −0.485720 | − | 0.280430i | ||||
\(536\) | 102.326 | + | 92.0170i | 0.190906 | + | 0.171673i | ||||
\(537\) | 128.631 | − | 222.796i | 0.239537 | − | 0.414890i | ||||
\(538\) | −595.224 | + | 432.648i | −1.10636 | + | 0.804178i | ||||
\(539\) | − | 334.304i | − | 0.620231i | ||||||
\(540\) | 47.9244 | + | 224.998i | 0.0887489 | + | 0.416663i | ||||
\(541\) | 176.484 | + | 305.680i | 0.326219 | + | 0.565028i | 0.981758 | − | 0.190133i | \(-0.0608920\pi\) |
−0.655539 | + | 0.755161i | \(0.727559\pi\) | |||||||
\(542\) | −24.9979 | − | 34.3914i | −0.0461217 | − | 0.0634528i | ||||
\(543\) | − | 113.630i | − | 0.209264i | ||||||
\(544\) | −284.423 | − | 491.434i | −0.522837 | − | 0.903372i | ||||
\(545\) | −321.245 | − | 556.412i | −0.589440 | − | 1.02094i | ||||
\(546\) | −40.6301 | − | 18.0794i | −0.0744142 | − | 0.0331125i | ||||
\(547\) | −795.788 | + | 459.449i | −1.45482 | + | 0.839943i | −0.998749 | − | 0.0499992i | \(-0.984078\pi\) |
−0.456074 | + | 0.889942i | \(0.650745\pi\) | |||||||
\(548\) | −174.881 | + | 539.005i | −0.319126 | + | 0.983586i | ||||
\(549\) | 324.861 | − | 562.675i | 0.591732 | − | 1.02491i | ||||
\(550\) | −204.090 | + | 21.4944i | −0.371072 | + | 0.0390807i | ||||
\(551\) | −63.0401 | + | 78.2050i | −0.114410 | + | 0.141933i | ||||
\(552\) | 28.2735 | + | 86.8292i | 0.0512200 | + | 0.157299i | ||||
\(553\) | 134.085 | − | 232.241i | 0.242468 | − | 0.419966i | ||||
\(554\) | 404.203 | + | 179.860i | 0.729608 | + | 0.324658i | ||||
\(555\) | 22.5732 | − | 13.0326i | 0.0406724 | − | 0.0234822i | ||||
\(556\) | −615.332 | − | 199.646i | −1.10671 | − | 0.359075i | ||||
\(557\) | 271.529 | + | 470.301i | 0.487484 | + | 0.844347i | 0.999896 | − | 0.0143926i | \(-0.00458146\pi\) |
−0.512413 | + | 0.858739i | \(0.671248\pi\) | |||||||
\(558\) | −163.812 | + | 17.2524i | −0.293571 | + | 0.0309183i | ||||
\(559\) | 463.139i | 0.828514i | ||||||||
\(560\) | 78.6442 | − | 108.437i | 0.140436 | − | 0.193638i | ||||
\(561\) | 67.7574 | + | 117.359i | 0.120780 | + | 0.209196i | ||||
\(562\) | 23.7234 | + | 225.255i | 0.0422125 | + | 0.400809i | ||||
\(563\) | 60.6683i | 0.107759i | 0.998547 | + | 0.0538795i | \(0.0171587\pi\) | ||||
−0.998547 | + | 0.0538795i | \(0.982841\pi\) | |||||||
\(564\) | −228.035 | − | 253.043i | −0.404317 | − | 0.448657i | ||||
\(565\) | −311.328 | + | 539.237i | −0.551024 | + | 0.954401i | ||||
\(566\) | 185.089 | + | 254.639i | 0.327012 | + | 0.449893i | ||||
\(567\) | 117.884 | + | 68.0602i | 0.207908 | + | 0.120036i | ||||
\(568\) | 91.7861 | − | 433.171i | 0.161595 | − | 0.762626i | ||||
\(569\) | 527.240 | 0.926609 | 0.463304 | − | 0.886199i | \(-0.346664\pi\) | ||||
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(570\) | 58.5306 | + | 114.181i | 0.102685 | + | 0.200317i | ||||
\(571\) | − | 470.688i | − | 0.824322i | −0.911111 | − | 0.412161i | \(-0.864774\pi\) | ||
0.911111 | − | 0.412161i | \(-0.135226\pi\) | |||||||
\(572\) | −273.881 | − | 88.8611i | −0.478812 | − | 0.155352i | ||||
\(573\) | 176.904 | − | 306.406i | 0.308732 | − | 0.534740i | ||||
\(574\) | −144.696 | − | 199.069i | −0.252084 | − | 0.346809i | ||||
\(575\) | 132.813 | + | 76.6796i | 0.230979 | + | 0.133356i | ||||
\(576\) | 469.908 | + | 208.502i | 0.815813 | + | 0.361983i | ||||
\(577\) | 302.670 | 0.524558 | 0.262279 | − | 0.964992i | \(-0.415526\pi\) | ||||
0.262279 | + | 0.964992i | \(0.415526\pi\) | |||||||
\(578\) | 5.41457 | + | 51.4116i | 0.00936777 | + | 0.0889474i | ||||
\(579\) | 209.872 | − | 121.170i | 0.362474 | − | 0.209274i | ||||
\(580\) | 48.6010 | + | 53.9310i | 0.0837949 | + | 0.0929845i | ||||
\(581\) | 76.4443 | 0.131574 | ||||||||
\(582\) | 256.230 | − | 26.9857i | 0.440258 | − | 0.0463672i | ||||
\(583\) | 233.569 | − | 134.851i | 0.400633 | − | 0.231305i | ||||
\(584\) | −437.437 | − | 92.6899i | −0.749036 | − | 0.158716i | ||||
\(585\) | 127.820 | + | 221.391i | 0.218496 | + | 0.378446i | ||||
\(586\) | 377.086 | + | 167.794i | 0.643491 | + | 0.286338i | ||||
\(587\) | −329.898 | − | 190.467i | −0.562008 | − | 0.324475i | 0.191943 | − | 0.981406i | \(-0.438521\pi\) |
−0.753951 | + | 0.656931i | \(0.771854\pi\) | |||||||
\(588\) | −35.2857 | − | 165.662i | −0.0600097 | − | 0.281737i | ||||
\(589\) | −181.713 | + | 70.2197i | −0.308511 | + | 0.119218i | ||||
\(590\) | 504.585 | − | 53.1420i | 0.855229 | − | 0.0900712i | ||||
\(591\) | 59.1756 | + | 34.1650i | 0.100128 | + | 0.0578088i | ||||
\(592\) | 12.8066 | − | 122.847i | 0.0216327 | − | 0.207511i | ||||
\(593\) | 182.978 | + | 316.927i | 0.308563 | + | 0.534446i | 0.978048 | − | 0.208379i | \(-0.0668187\pi\) |
−0.669486 | + | 0.742825i | \(0.733485\pi\) | |||||||
\(594\) | −237.694 | − | 105.768i | −0.400159 | − | 0.178061i | ||||
\(595\) | −128.652 | + | 74.2771i | −0.216221 | + | 0.124835i | ||||
\(596\) | −30.8854 | + | 6.57856i | −0.0518212 | + | 0.0110379i | ||||
\(597\) | −135.960 | −0.227739 | ||||||||
\(598\) | 126.513 | + | 174.052i | 0.211559 | + | 0.291057i | ||||
\(599\) | 114.625 | − | 66.1790i | 0.191361 | − | 0.110483i | −0.401258 | − | 0.915965i | \(-0.631427\pi\) |
0.592620 | + | 0.805482i | \(0.298094\pi\) | |||||||
\(600\) | −98.8662 | + | 32.1930i | −0.164777 | + | 0.0536549i | ||||
\(601\) | 30.0876 | 0.0500626 | 0.0250313 | − | 0.999687i | \(-0.492031\pi\) | ||||
0.0250313 | + | 0.999687i | \(0.492031\pi\) | |||||||
\(602\) | 197.104 | − | 143.268i | 0.327415 | − | 0.237987i | ||||
\(603\) | 119.664 | + | 69.0878i | 0.198447 | + | 0.114573i | ||||
\(604\) | 636.886 | − | 573.943i | 1.05445 | − | 0.950236i | ||||
\(605\) | 104.201 | − | 180.481i | 0.172233 | − | 0.298316i | ||||
\(606\) | 69.8128 | − | 156.892i | 0.115203 | − | 0.258897i | ||||
\(607\) | − | 25.4139i | − | 0.0418681i | −0.999781 | − | 0.0209340i | \(-0.993336\pi\) | ||
0.999781 | − | 0.0209340i | \(-0.00666400\pi\) | |||||||
\(608\) | 600.825 | + | 93.1333i | 0.988198 | + | 0.153180i | ||||
\(609\) | −12.6808 | −0.0208223 | ||||||||
\(610\) | −507.396 | − | 225.779i | −0.831797 | − | 0.370129i | ||||
\(611\) | −695.113 | − | 401.324i | −1.13766 | − | 0.656831i | ||||
\(612\) | −381.666 | − | 423.522i | −0.623637 | − | 0.692030i | ||||
\(613\) | −536.454 | + | 929.165i | −0.875128 | + | 1.51577i | −0.0185025 | + | 0.999829i | \(0.505890\pi\) |
−0.856626 | + | 0.515938i | \(0.827443\pi\) | |||||||
\(614\) | −645.683 | − | 888.311i | −1.05160 | − | 1.44676i | ||||
\(615\) | − | 170.371i | − | 0.277027i | ||||||
\(616\) | 46.9049 | + | 144.047i | 0.0761444 | + | 0.233843i | ||||
\(617\) | −304.579 | − | 527.546i | −0.493645 | − | 0.855018i | 0.506328 | − | 0.862341i | \(-0.331002\pi\) |
−0.999973 | + | 0.00732287i | \(0.997669\pi\) | |||||||
\(618\) | −152.689 | + | 110.984i | −0.247069 | + | 0.179586i | ||||
\(619\) | − | 546.890i | − | 0.883505i | −0.897137 | − | 0.441753i | \(-0.854357\pi\) | ||
0.897137 | − | 0.441753i | \(-0.145643\pi\) | |||||||
\(620\) | 29.3315 | + | 137.707i | 0.0473088 | + | 0.222108i | ||||
\(621\) | 97.2100 | + | 168.373i | 0.156538 | + | 0.271132i | ||||
\(622\) | −153.840 | + | 345.727i | −0.247331 | + | 0.555831i | ||||
\(623\) | −22.3651 | + | 12.9125i | −0.0358990 | + | 0.0207263i | ||||
\(624\) | −145.098 | − | 15.1263i | −0.232529 | − | 0.0242409i | ||||
\(625\) | 60.0112 | − | 103.942i | 0.0960179 | − | 0.166308i | ||||
\(626\) | −18.6267 | − | 176.861i | −0.0297551 | − | 0.282526i | ||||
\(627\) | −143.371 | − | 22.3792i | −0.228662 | − | 0.0356926i | ||||
\(628\) | −46.4442 | + | 9.89257i | −0.0739558 | + | 0.0157525i | ||||
\(629\) | −68.4874 | + | 118.624i | −0.108883 | + | 0.188591i | ||||
\(630\) | 54.6801 | − | 122.883i | 0.0867938 | − | 0.195053i | ||||
\(631\) | 340.675 | − | 196.689i | 0.539897 | − | 0.311710i | −0.205140 | − | 0.978733i | \(-0.565765\pi\) |
0.745037 | + | 0.667023i | \(0.232432\pi\) | |||||||
\(632\) | 182.357 | − | 860.606i | 0.288539 | − | 1.36172i | ||||
\(633\) | −47.2461 | − | 81.8326i | −0.0746384 | − | 0.129277i | ||||
\(634\) | −73.5821 | − | 698.665i | −0.116060 | − | 1.10199i | ||||
\(635\) | − | 561.710i | − | 0.884582i | ||||||
\(636\) | 101.509 | − | 91.4773i | 0.159606 | − | 0.143832i | ||||
\(637\) | −199.556 | − | 345.642i | −0.313275 | − | 0.542609i | ||||
\(638\) | −81.6525 | + | 8.59949i | −0.127982 | + | 0.0134788i | ||||
\(639\) | − | 444.595i | − | 0.695767i | ||||||
\(640\) | 135.171 | − | 418.121i | 0.211205 | − | 0.653313i | ||||
\(641\) | −348.127 | + | 602.973i | −0.543100 | + | 0.940676i | 0.455624 | + | 0.890172i | \(0.349416\pi\) |
−0.998724 | + | 0.0505039i | \(0.983917\pi\) | |||||||
\(642\) | 139.075 | − | 101.089i | 0.216627 | − | 0.157459i | ||||
\(643\) | −187.039 | − | 107.987i | −0.290886 | − | 0.167943i | 0.347456 | − | 0.937696i | \(-0.387046\pi\) |
−0.638341 | + | 0.769754i | \(0.720379\pi\) | |||||||
\(644\) | 34.9380 | − | 107.683i | 0.0542515 | − | 0.167210i | ||||
\(645\) | 168.690 | 0.261535 | ||||||||
\(646\) | −566.388 | − | 365.849i | −0.876762 | − | 0.566329i | ||||
\(647\) | 664.315i | 1.02676i | 0.858161 | + | 0.513381i | \(0.171607\pi\) | ||||
−0.858161 | + | 0.513381i | \(0.828393\pi\) | |||||||
\(648\) | 436.836 | + | 92.5627i | 0.674130 | + | 0.142844i | ||||
\(649\) | −286.902 | + | 496.929i | −0.442068 | + | 0.765685i | ||||
\(650\) | −198.181 | + | 144.051i | −0.304893 | + | 0.221616i | ||||
\(651\) | −21.2979 | − | 12.2964i | −0.0327157 | − | 0.0188884i | ||||
\(652\) | −919.760 | + | 828.861i | −1.41067 | + | 1.27126i | ||||
\(653\) | −709.962 | −1.08723 | −0.543616 | − | 0.839334i | \(-0.682945\pi\) | ||||
−0.543616 | + | 0.839334i | \(0.682945\pi\) | |||||||
\(654\) | 366.116 | − | 38.5587i | 0.559811 | − | 0.0589583i | ||||
\(655\) | −614.785 | + | 354.946i | −0.938603 | + | 0.541903i | ||||
\(656\) | −653.535 | − | 473.976i | −0.996242 | − | 0.722525i | ||||
\(657\) | −448.973 | −0.683369 | ||||||||
\(658\) | 44.2309 | + | 419.974i | 0.0672203 | + | 0.638259i | ||||
\(659\) | −27.1231 | + | 15.6595i | −0.0411580 | + | 0.0237626i | −0.520438 | − | 0.853900i | \(-0.674231\pi\) |
0.479280 | + | 0.877662i | \(0.340898\pi\) | |||||||
\(660\) | −32.3660 | + | 99.7560i | −0.0490394 | + | 0.151145i | ||||
\(661\) | 308.493 | + | 534.326i | 0.466707 | + | 0.808360i | 0.999277 | − | 0.0380258i | \(-0.0121069\pi\) |
−0.532570 | + | 0.846386i | \(0.678774\pi\) | |||||||
\(662\) | 348.406 | − | 782.979i | 0.526293 | − | 1.18275i | ||||
\(663\) | 140.111 | + | 80.8929i | 0.211328 | + | 0.122010i | ||||
\(664\) | 238.448 | − | 77.6439i | 0.359109 | − | 0.116934i | ||||
\(665\) | 24.5326 | − | 157.167i | 0.0368911 | − | 0.236341i | ||||
\(666\) | −12.9893 | − | 123.334i | −0.0195035 | − | 0.185186i | ||||
\(667\) | 53.1359 | + | 30.6780i | 0.0796640 | + | 0.0459941i | ||||
\(668\) | 588.212 | + | 190.846i | 0.880557 | + | 0.285698i | ||||
\(669\) | 67.0176 | + | 116.078i | 0.100176 | + | 0.173510i | ||||
\(670\) | 48.0161 | − | 107.907i | 0.0716658 | − | 0.161056i | ||||
\(671\) | 543.927 | − | 314.037i | 0.810622 | − | 0.468013i | ||||
\(672\) | 38.4475 | + | 66.4306i | 0.0572135 | + | 0.0988550i | ||||
\(673\) | 545.130 | 0.810000 | 0.405000 | − | 0.914317i | \(-0.367271\pi\) | ||||
0.405000 | + | 0.914317i | \(0.367271\pi\) | |||||||
\(674\) | 471.632 | − | 342.814i | 0.699751 | − | 0.508625i | ||||
\(675\) | −191.714 | + | 110.686i | −0.284021 | + | 0.163979i | ||||
\(676\) | 324.955 | − | 69.2152i | 0.480703 | − | 0.102389i | ||||
\(677\) | 242.431 | 0.358096 | 0.179048 | − | 0.983840i | \(-0.442698\pi\) | ||||
0.179048 | + | 0.983840i | \(0.442698\pi\) | |||||||
\(678\) | −209.770 | − | 288.595i | −0.309395 | − | 0.425656i | ||||
\(679\) | −276.623 | − | 159.709i | −0.407398 | − | 0.235211i | ||||
\(680\) | −325.853 | + | 362.359i | −0.479196 | + | 0.532881i | ||||
\(681\) | −117.033 | + | 202.707i | −0.171855 | + | 0.297661i | ||||
\(682\) | −145.478 | − | 64.7339i | −0.213310 | − | 0.0949178i | ||||
\(683\) | 408.747i | 0.598459i | 0.954181 | + | 0.299229i | \(0.0967296\pi\) | ||||
−0.954181 | + | 0.299229i | \(0.903270\pi\) | |||||||
\(684\) | 609.556 | − | 33.5713i | 0.891164 | − | 0.0490809i | ||||
\(685\) | 486.344 | 0.709992 | ||||||||
\(686\) | −182.529 | + | 410.200i | −0.266077 | + | 0.597959i | ||||
\(687\) | −138.621 | − | 80.0327i | −0.201777 | − | 0.116496i | ||||
\(688\) | 469.299 | − | 647.085i | 0.682120 | − | 0.940531i | ||||
\(689\) | 160.993 | − | 278.849i | 0.233662 | − | 0.404715i | ||||
\(690\) | 63.3953 | − | 46.0799i | 0.0918772 | − | 0.0667824i | ||||
\(691\) | 236.274i | 0.341931i | 0.985277 | + | 0.170965i | \(0.0546886\pi\) | ||||
−0.985277 | + | 0.170965i | \(0.945311\pi\) | |||||||
\(692\) | −941.500 | + | 200.538i | −1.36055 | + | 0.289796i | ||||
\(693\) | 76.0548 | + | 131.731i | 0.109747 | + | 0.190088i | ||||
\(694\) | 330.581 | + | 454.803i | 0.476341 | + | 0.655335i | ||||
\(695\) | 555.214i | 0.798869i | ||||||||
\(696\) | −39.5545 | + | 12.8798i | −0.0568311 | + | 0.0185054i | ||||
\(697\) | 447.656 | + | 775.364i | 0.642262 | + | 1.11243i | ||||
\(698\) | 33.0593 | + | 14.7106i | 0.0473629 | + | 0.0210753i | ||||
\(699\) | 4.27276 | − | 2.46688i | 0.00611267 | − | 0.00352915i | ||||
\(700\) | 122.611 | + | 39.7814i | 0.175159 | + | 0.0568305i | ||||
\(701\) | −469.659 | + | 813.474i | −0.669985 | + | 1.16045i | 0.307923 | + | 0.951411i | \(0.400366\pi\) |
−0.977908 | + | 0.209037i | \(0.932967\pi\) | |||||||
\(702\) | −308.892 | + | 32.5319i | −0.440017 | + | 0.0463418i | ||||
\(703\) | −52.8683 | − | 136.811i | −0.0752038 | − | 0.194611i | ||||
\(704\) | 292.616 | + | 401.677i | 0.415647 | + | 0.570565i | ||||
\(705\) | −146.175 | + | 253.182i | −0.207340 | + | 0.359124i | ||||
\(706\) | 471.503 | + | 209.807i | 0.667851 | + | 0.297177i | ||||
\(707\) | −184.371 | + | 106.446i | −0.260779 | + | 0.150561i | ||||
\(708\) | −89.7211 | + | 276.531i | −0.126725 | + | 0.390581i | ||||
\(709\) | −149.306 | − | 258.606i | −0.210587 | − | 0.364747i | 0.741312 | − | 0.671161i | \(-0.234204\pi\) |
−0.951898 | + | 0.306414i | \(0.900871\pi\) | |||||||
\(710\) | −377.936 | + | 39.8035i | −0.532304 | + | 0.0560613i | ||||
\(711\) | − | 883.303i | − | 1.24234i | ||||||
\(712\) | −56.6469 | + | 62.9932i | −0.0795603 | + | 0.0884735i | ||||
\(713\) | 59.4960 | + | 103.050i | 0.0834447 | + | 0.144530i | ||||
\(714\) | −8.91541 | − | 84.6521i | −0.0124866 | − | 0.118560i | ||||
\(715\) | 247.122i | 0.345626i | ||||||||
\(716\) | −777.230 | + | 700.417i | −1.08552 | + | 0.978235i | ||||
\(717\) | 159.408 | − | 276.103i | 0.222327 | − | 0.385081i | ||||
\(718\) | 322.559 | + | 443.767i | 0.449246 | + | 0.618060i | ||||
\(719\) | 1030.58 | + | 595.008i | 1.43336 | + | 0.827549i | 0.997375 | − | 0.0724069i | \(-0.0230680\pi\) |
0.435981 | + | 0.899956i | \(0.356401\pi\) | |||||||
\(720\) | 45.7486 | − | 438.841i | 0.0635397 | − | 0.609502i | ||||
\(721\) | 234.017 | 0.324573 | ||||||||
\(722\) | 685.610 | − | 226.324i | 0.949599 | − | 0.313469i | ||||
\(723\) | 227.852i | 0.315147i | ||||||||
\(724\) | −142.618 | + | 439.566i | −0.196986 | + | 0.607135i | ||||
\(725\) | −34.9309 | + | 60.5020i | −0.0481805 | + | 0.0834511i | ||||
\(726\) | 70.2092 | + | 96.5918i | 0.0967070 | + | 0.133046i | ||||
\(727\) | 702.834 | + | 405.781i | 0.966759 | + | 0.558159i | 0.898247 | − | 0.439491i | \(-0.144841\pi\) |
0.0685127 | + | 0.997650i | \(0.478175\pi\) | |||||||
\(728\) | 134.482 | + | 120.933i | 0.184728 | + | 0.166117i | ||||
\(729\) | 300.066 | 0.411613 | ||||||||
\(730\) | 40.1955 | + | 381.658i | 0.0550623 | + | 0.522819i | ||||
\(731\) | −767.712 | + | 443.239i | −1.05022 | + | 0.606345i | ||||
\(732\) | 236.392 | − | 213.029i | 0.322940 | − | 0.291024i | ||||
\(733\) | 452.401 | 0.617191 | 0.308596 | − | 0.951193i | \(-0.400141\pi\) | ||||
0.308596 | + | 0.951193i | \(0.400141\pi\) | |||||||
\(734\) | 1202.31 | − | 126.625i | 1.63802 | − | 0.172514i | ||||
\(735\) | −125.894 | + | 72.6847i | −0.171284 | + | 0.0988908i | ||||
\(736\) | −0.392909 | − | 371.376i | −0.000533843 | − | 0.504587i | ||||
\(737\) | 66.7858 | + | 115.676i | 0.0906185 | + | 0.156956i | ||||
\(738\) | −740.600 | − | 329.548i | −1.00352 | − | 0.446543i | ||||
\(739\) | 1168.02 | + | 674.356i | 1.58054 | + | 0.912525i | 0.994780 | + | 0.102041i | \(0.0325372\pi\) |
0.585760 | + | 0.810485i | \(0.300796\pi\) | |||||||
\(740\) | −103.679 | + | 22.0836i | −0.140107 | + | 0.0298427i | ||||
\(741\) | −161.592 | + | 62.4445i | −0.218073 | + | 0.0842706i | ||||
\(742\) | −168.475 | + | 17.7435i | −0.227055 | + | 0.0239131i | ||||
\(743\) | 321.223 | + | 185.458i | 0.432332 | + | 0.249607i | 0.700340 | − | 0.713810i | \(-0.253032\pi\) |
−0.268008 | + | 0.963417i | \(0.586365\pi\) | |||||||
\(744\) | −78.9228 | − | 16.7232i | −0.106079 | − | 0.0224774i | ||||
\(745\) | 13.5511 | + | 23.4712i | 0.0181894 | + | 0.0315050i | ||||
\(746\) | 506.278 | + | 225.281i | 0.678657 | + | 0.301986i | ||||
\(747\) | 218.060 | − | 125.897i | 0.291914 | − | 0.168537i | ||||
\(748\) | −114.814 | − | 539.035i | −0.153494 | − | 0.720634i | ||||
\(749\) | −213.152 | −0.284582 | ||||||||
\(750\) | 151.731 | + | 208.747i | 0.202308 | + | 0.278329i | ||||
\(751\) | 257.836 | − | 148.862i | 0.343324 | − | 0.198218i | −0.318417 | − | 0.947951i | \(-0.603151\pi\) |
0.661741 | + | 0.749733i | \(0.269818\pi\) | |||||||
\(752\) | 564.532 | + | 1265.08i | 0.750707 | + | 1.68228i | ||||
\(753\) | −33.0274 | −0.0438611 | ||||||||
\(754\) | −79.2883 | + | 57.6319i | −0.105157 | + | 0.0764349i | ||||
\(755\) | −637.237 | − | 367.909i | −0.844023 | − | 0.487297i | ||||
\(756\) | 109.398 | + | 121.395i | 0.144706 | + | 0.160576i | ||||
\(757\) | 365.069 | − | 632.318i | 0.482257 | − | 0.835294i | −0.517535 | − | 0.855662i | \(-0.673150\pi\) |
0.999793 | + | 0.0203675i | \(0.00648363\pi\) | |||||||
\(758\) | −273.003 | + | 613.525i | −0.360163 | + | 0.809400i | ||||
\(759\) | 88.6339i | 0.116777i | ||||||||
\(760\) | −83.1100 | − | 515.159i | −0.109355 | − | 0.677840i | ||||
\(761\) | −629.518 | −0.827225 | −0.413612 | − | 0.910453i | \(-0.635733\pi\) | ||||
−0.413612 | + | 0.910453i | \(0.635733\pi\) | |||||||
\(762\) | 294.057 | + | 130.848i | 0.385901 | + | 0.171717i | ||||
\(763\) | −395.255 | − | 228.201i | −0.518027 | − | 0.299083i | ||||
\(764\) | −1068.91 | + | 963.266i | −1.39909 | + | 1.26082i | ||||
\(765\) | −244.656 | + | 423.756i | −0.319811 | + | 0.553929i | ||||
\(766\) | −348.315 | − | 479.201i | −0.454720 | − | 0.625589i | ||||
\(767\) | 685.043i | 0.893146i | ||||||||
\(768\) | 187.400 | + | 168.162i | 0.244010 | + | 0.218961i | ||||
\(769\) | −431.124 | − | 746.729i | −0.560630 | − | 0.971039i | −0.997442 | − | 0.0714863i | \(-0.977226\pi\) |
0.436812 | − | 0.899553i | \(-0.356108\pi\) | |||||||
\(770\) | 105.171 | − | 76.4452i | 0.136586 | − | 0.0992795i | ||||
\(771\) | 135.471i | 0.175708i | ||||||||
\(772\) | −963.950 | + | 205.320i | −1.24864 | + | 0.265959i | ||||
\(773\) | −596.731 | − | 1033.57i | −0.771967 | − | 1.33709i | −0.936483 | − | 0.350712i | \(-0.885940\pi\) |
0.164516 | − | 0.986374i | \(-0.447394\pi\) | |||||||
\(774\) | 326.296 | − | 733.291i | 0.421571 | − | 0.947404i | ||||
\(775\) | −117.336 | + | 67.7439i | −0.151401 | + | 0.0874114i | ||||
\(776\) | −1025.07 | − | 217.205i | −1.32097 | − | 0.279904i | ||||
\(777\) | 9.25792 | − | 16.0352i | 0.0119150 | − | 0.0206373i | ||||
\(778\) | −147.524 | − | 1400.74i | −0.189619 | − | 1.80044i | ||||
\(779\) | −947.219 | − | 147.854i | −1.21594 | − | 0.189800i | ||||
\(780\) | 26.0837 | + | 122.459i | 0.0334406 | + | 0.156999i | ||||
\(781\) | 214.891 | − | 372.202i | 0.275148 | − | 0.476571i | ||||
\(782\) | −167.437 | + | 376.284i | −0.214114 | + | 0.481181i | ||||
\(783\) | −76.7011 | + | 44.2834i | −0.0979579 | + | 0.0565560i | ||||
\(784\) | −71.4240 | + | 685.131i | −0.0911020 | + | 0.873892i | ||||
\(785\) | 20.3776 | + | 35.2951i | 0.0259587 | + | 0.0449619i | ||||
\(786\) | −42.6039 | − | 404.525i | −0.0542034 | − | 0.514663i | ||||
\(787\) | − | 588.811i | − | 0.748172i | −0.927394 | − | 0.374086i | \(-0.877957\pi\) | ||
0.927394 | − | 0.374086i | \(-0.122043\pi\) | |||||||
\(788\) | −186.034 | − | 206.435i | −0.236083 | − | 0.261974i | ||||
\(789\) | 177.242 | + | 306.992i | 0.224641 | + | 0.389090i | ||||
\(790\) | −750.867 | + | 79.0799i | −0.950464 | + | 0.100101i | ||||
\(791\) | 442.313i | 0.559182i | ||||||||
\(792\) | 371.031 | + | 333.652i | 0.468474 | + | 0.421278i | ||||
\(793\) | 374.916 | − | 649.373i | 0.472781 | − | 0.818882i | ||||
\(794\) | 516.545 | − | 375.459i | 0.650560 | − | 0.472870i | ||||
\(795\) | −101.565 | − | 58.6389i | −0.127755 | − | 0.0737596i | ||||
\(796\) | 525.947 | + | 170.644i | 0.660737 | + | 0.214377i | ||||
\(797\) | −860.660 | −1.07987 | −0.539937 | − | 0.841705i | \(-0.681552\pi\) | ||||
−0.539937 | + | 0.841705i | \(0.681552\pi\) | |||||||
\(798\) | 76.5626 | + | 49.4543i | 0.0959431 | + | 0.0619728i | ||||
\(799\) | − | 1536.32i | − | 1.92280i | ||||||
\(800\) | 422.859 | − | 0.447377i | 0.528574 | − | 0.000559221i | ||||
\(801\) | −42.5314 | + | 73.6666i | −0.0530979 | + | 0.0919683i | ||||
\(802\) | 461.523 | − | 335.466i | 0.575466 | − | 0.418286i | ||||
\(803\) | −375.867 | − | 217.007i | −0.468078 | − | 0.270245i | ||||
\(804\) | 45.3047 | + | 50.2732i | 0.0563492 | + | 0.0625289i | ||||
\(805\) | −97.1624 | −0.120699 | ||||||||
\(806\) | −189.053 | + | 19.9107i | −0.234557 | + | 0.0247031i | ||||
\(807\) | −313.390 | + | 180.936i | −0.388340 | + | 0.224208i | ||||
\(808\) | −466.979 | + | 519.296i | −0.577945 | + | 0.642693i | ||||
\(809\) | 64.3915 | 0.0795939 | 0.0397970 | − | 0.999208i | \(-0.487329\pi\) | ||||
0.0397970 | + | 0.999208i | \(0.487329\pi\) | |||||||
\(810\) | −40.1403 | − | 381.134i | −0.0495559 | − | 0.470536i | ||||
\(811\) | 338.774 | − | 195.591i | 0.417724 | − | 0.241173i | −0.276379 | − | 0.961049i | \(-0.589135\pi\) |
0.694103 | + | 0.719876i | \(0.255801\pi\) | |||||||
\(812\) | 49.0543 | + | 15.9158i | 0.0604117 | + | 0.0196007i | ||||
\(813\) | −10.4543 | − | 18.1074i | −0.0128589 | − | 0.0222723i | ||||
\(814\) | 48.7381 | − | 109.530i | 0.0598748 | − | 0.134558i | ||||
\(815\) | 920.267 | + | 531.317i | 1.12916 | + | 0.651922i | ||||
\(816\) | −113.790 | − | 254.995i | −0.139448 | − | 0.312494i | ||||
\(817\) | 146.395 | − | 937.871i | 0.179186 | − | 1.14795i | ||||
\(818\) | −3.93320 | − | 37.3459i | −0.00480831 | − | 0.0456551i | ||||
\(819\) | 157.268 | + | 90.7988i | 0.192025 | + | 0.110865i | ||||
\(820\) | −213.834 | + | 659.063i | −0.260774 | + | 0.803736i | ||||
\(821\) | 362.567 | + | 627.984i | 0.441616 | + | 0.764902i | 0.997810 | − | 0.0661512i | \(-0.0210720\pi\) |
−0.556193 | + | 0.831053i | \(0.687739\pi\) | |||||||
\(822\) | −113.292 | + | 254.603i | −0.137825 | + | 0.309736i | ||||
\(823\) | 907.175 | − | 523.758i | 1.10228 | − | 0.636401i | 0.165460 | − | 0.986217i | \(-0.447089\pi\) |
0.936819 | + | 0.349816i | \(0.113756\pi\) | |||||||
\(824\) | 729.957 | − | 237.690i | 0.885870 | − | 0.288458i | ||||
\(825\) | −100.921 | −0.122329 | ||||||||
\(826\) | 291.542 | − | 211.912i | 0.352957 | − | 0.256552i | ||||
\(827\) | 102.476 | − | 59.1644i | 0.123913 | − | 0.0715410i | −0.436763 | − | 0.899577i | \(-0.643875\pi\) |
0.560675 | + | 0.828036i | \(0.310542\pi\) | |||||||
\(828\) | −77.6827 | − | 364.710i | −0.0938197 | − | 0.440471i | ||||
\(829\) | −565.539 | −0.682194 | −0.341097 | − | 0.940028i | \(-0.610799\pi\) | ||||
−0.341097 | + | 0.940028i | \(0.610799\pi\) | |||||||
\(830\) | −126.543 | − | 174.095i | −0.152462 | − | 0.209752i | ||||
\(831\) | 188.419 | + | 108.784i | 0.226738 | + | 0.130907i | ||||
\(832\) | 542.313 | + | 240.629i | 0.651818 | + | 0.289217i | ||||
\(833\) | 381.963 | − | 661.580i | 0.458539 | − | 0.794213i | ||||
\(834\) | −290.656 | − | 129.335i | −0.348509 | − | 0.155078i | ||||
\(835\) | − | 530.743i | − | 0.635621i | ||||||
\(836\) | 526.529 | + | 266.518i | 0.629819 | + | 0.318802i | ||||
\(837\) | −171.764 | −0.205213 | ||||||||
\(838\) | 120.150 | − | 270.015i | 0.143377 | − | 0.322214i | ||||
\(839\) | −573.840 | − | 331.306i | −0.683957 | − | 0.394883i | 0.117387 | − | 0.993086i | \(-0.462548\pi\) |
−0.801344 | + | 0.598204i | \(0.795881\pi\) | |||||||
\(840\) | 44.0478 | − | 48.9825i | 0.0524379 | − | 0.0583125i | ||||
\(841\) | 406.525 | − | 704.122i | 0.483383 | − | 0.837243i | ||||
\(842\) | −556.691 | + | 404.639i | −0.661153 | + | 0.480569i | ||||
\(843\) | 111.387i | 0.132132i | ||||||||
\(844\) | 80.0577 | + | 375.860i | 0.0948551 | + | 0.445331i | ||||
\(845\) | −142.576 | − | 246.948i | −0.168729 | − | 0.292247i | ||||
\(846\) | 817.831 | + | 1125.15i | 0.966703 | + | 1.32996i | ||||
\(847\) | − | 148.041i | − | 0.174783i | ||||||
\(848\) | −507.493 | + | 226.465i | −0.598458 | + | 0.267058i | ||||
\(849\) | 77.4052 | + | 134.070i | 0.0911722 | + | 0.157915i | ||||
\(850\) | −428.447 | − | 190.648i | −0.504055 | − | 0.224292i | ||||
\(851\) | −77.5863 | + | 44.7945i | −0.0911707 | + | 0.0526374i | ||||
\(852\) | 67.2014 | − | 207.123i | 0.0788749 | − | 0.243102i | ||||
\(853\) | 640.005 | − | 1108.52i | 0.750298 | − | 1.29955i | −0.197380 | − | 0.980327i | \(-0.563243\pi\) |
0.947678 | − | 0.319228i | \(-0.103424\pi\) | |||||||
\(854\) | −392.339 | + | 41.3204i | −0.459413 | + | 0.0483846i | ||||
\(855\) | −188.860 | − | 488.727i | −0.220889 | − | 0.571610i | ||||
\(856\) | −664.873 | + | 216.497i | −0.776721 | + | 0.252917i | ||||
\(857\) | 31.2794 | − | 54.1776i | 0.0364987 | − | 0.0632177i | −0.847199 | − | 0.531276i | \(-0.821713\pi\) |
0.883698 | + | 0.468058i | \(0.155046\pi\) | |||||||
\(858\) | −129.369 | − | 57.5662i | −0.150780 | − | 0.0670935i | ||||
\(859\) | −954.077 | + | 550.837i | −1.11068 | + | 0.641253i | −0.939006 | − | 0.343900i | \(-0.888252\pi\) |
−0.171677 | + | 0.985153i | \(0.554919\pi\) | |||||||
\(860\) | −652.559 | − | 211.724i | −0.758790 | − | 0.246191i | ||||
\(861\) | −60.5128 | − | 104.811i | −0.0702820 | − | 0.121732i | ||||
\(862\) | 650.038 | − | 68.4608i | 0.754104 | − | 0.0794209i | ||||
\(863\) | − | 1483.07i | − | 1.71851i | −0.511549 | − | 0.859254i | \(-0.670928\pi\) | ||
0.511549 | − | 0.859254i | \(-0.329072\pi\) | |||||||
\(864\) | 464.540 | + | 267.547i | 0.537661 | + | 0.309661i | ||||
\(865\) | 413.087 | + | 715.488i | 0.477558 | + | 0.827154i | ||||
\(866\) | 108.123 | + | 1026.63i | 0.124853 | + | 1.18549i | ||||
\(867\) | 25.4227i | 0.0293226i | ||||||||
\(868\) | 66.9556 | + | 74.2984i | 0.0771378 | + | 0.0855973i | ||||
\(869\) | 426.936 | − | 739.474i | 0.491295 | − | 0.850948i | ||||
\(870\) | 20.9914 | + | 28.8793i | 0.0241280 | + | 0.0331946i | ||||
\(871\) | 138.102 | + | 79.7330i | 0.158555 | + | 0.0915419i | ||||
\(872\) | −1464.68 | − | 310.355i | −1.67968 | − | 0.355912i | ||||
\(873\) | −1052.10 | −1.20516 | ||||||||
\(874\) | −201.175 | − | 392.451i | −0.230178 | − | 0.449028i | ||||
\(875\) | − | 319.934i | − | 0.365639i | ||||||
\(876\) | −209.163 | − | 67.8632i | −0.238770 | − | 0.0774694i | ||||
\(877\) | 177.007 | − | 306.585i | 0.201832 | − | 0.349583i | −0.747287 | − | 0.664502i | \(-0.768644\pi\) |
0.949119 | + | 0.314918i | \(0.101977\pi\) | |||||||
\(878\) | 1006.42 | + | 1384.60i | 1.14626 | + | 1.57699i | ||||
\(879\) | 175.778 | + | 101.486i | 0.199975 | + | 0.115456i | ||||
\(880\) | 250.409 | − | 345.273i | 0.284556 | − | 0.392355i | ||||
\(881\) | 187.993 | 0.213385 | 0.106693 | − | 0.994292i | \(-0.465974\pi\) | ||||
0.106693 | + | 0.994292i | \(0.465974\pi\) | |||||||
\(882\) | 72.4431 | + | 687.850i | 0.0821350 | + | 0.779875i | ||||
\(883\) | −1269.00 | + | 732.655i | −1.43714 | + | 0.829734i | −0.997650 | − | 0.0685129i | \(-0.978175\pi\) |
−0.439491 | + | 0.898247i | \(0.644841\pi\) | |||||||
\(884\) | −440.474 | − | 488.779i | −0.498273 | − | 0.552918i | ||||
\(885\) | 249.514 | 0.281937 | ||||||||
\(886\) | −634.259 | + | 66.7990i | −0.715868 | + | 0.0753939i | ||||
\(887\) | −557.309 | + | 321.762i | −0.628308 | + | 0.362754i | −0.780096 | − | 0.625659i | \(-0.784830\pi\) |
0.151789 | + | 0.988413i | \(0.451497\pi\) | |||||||
\(888\) | 12.5909 | − | 59.4208i | 0.0141789 | − | 0.0669153i | ||||
\(889\) | −199.509 | − | 345.560i | −0.224420 | − | 0.388706i | ||||
\(890\) | 66.4293 | + | 29.5594i | 0.0746397 | + | 0.0332128i | ||||
\(891\) | 375.351 | + | 216.709i | 0.421269 | + | 0.243220i | ||||
\(892\) | −113.560 | − | 533.150i | −0.127310 | − | 0.597701i | ||||
\(893\) | 1280.77 | + | 1032.41i | 1.43423 | + | 1.15612i | ||||
\(894\) | −15.4440 | + | 1.62653i | −0.0172751 | + | 0.00181938i | ||||
\(895\) | 777.659 | + | 448.981i | 0.868892 | + | 0.501655i | ||||
\(896\) | −65.3524 | − | 305.235i | −0.0729380 | − | 0.340664i | ||||
\(897\) | 52.9083 | + | 91.6398i | 0.0589836 | + | 0.102163i | ||||
\(898\) | −1226.41 | − | 545.724i | −1.36572 | − | 0.607711i | ||||
\(899\) | −46.9438 | + | 27.1030i | −0.0522178 | + | 0.0301480i | ||||
\(900\) | 415.269 | − | 88.4517i | 0.461409 | − | 0.0982797i | ||||
\(901\) | 616.302 | 0.684020 | ||||||||
\(902\) | −460.724 | − | 633.850i | −0.510780 | − | 0.702716i | ||||
\(903\) | 103.777 | − | 59.9156i | 0.114925 | − | 0.0663517i | ||||
\(904\) | 449.254 | + | 1379.68i | 0.496962 | + | 1.52620i | ||||
\(905\) | 396.620 | 0.438254 | ||||||||
\(906\) | 341.043 | − | 247.893i | 0.376428 | − | 0.273612i | ||||
\(907\) | −340.966 | − | 196.857i | −0.375927 | − | 0.217042i | 0.300118 | − | 0.953902i | \(-0.402974\pi\) |
−0.676045 | + | 0.736861i | \(0.736307\pi\) | |||||||
\(908\) | 707.149 | − | 637.262i | 0.778798 | − | 0.701830i | ||||
\(909\) | −350.616 | + | 607.284i | −0.385716 | + | 0.668079i | ||||
\(910\) | 63.1053 | − | 141.818i | 0.0693465 | − | 0.155843i | ||||
\(911\) | 1032.58i | 1.13346i | 0.823903 | + | 0.566731i | \(0.191792\pi\) | ||||
−0.823903 | + | 0.566731i | \(0.808208\pi\) | |||||||
\(912\) | 289.047 | + | 76.4958i | 0.316938 | + | 0.0838770i | ||||
\(913\) | 243.404 | 0.266598 | ||||||||
\(914\) | 1018.71 | + | 453.302i | 1.11457 | + | 0.495954i | ||||
\(915\) | −236.522 | − | 136.556i | −0.258494 | − | 0.149242i | ||||
\(916\) | 435.790 | + | 483.582i | 0.475753 | + | 0.527928i | ||||
\(917\) | −252.141 | + | 436.721i | −0.274963 | + | 0.476250i | ||||
\(918\) | −349.545 | − | 480.893i | −0.380768 | − | 0.523849i | ||||
\(919\) | − | 1028.61i | − | 1.11927i | −0.828738 | − | 0.559636i | \(-0.810941\pi\) | ||
0.828738 | − | 0.559636i | \(-0.189059\pi\) | |||||||
\(920\) | −303.073 | + | 98.6871i | −0.329427 | + | 0.107269i | ||||
\(921\) | −270.029 | − | 467.703i | −0.293191 | − | 0.507821i | ||||
\(922\) | −937.336 | + | 681.317i | −1.01663 | + | 0.738956i | ||||
\(923\) | − | 513.099i | − | 0.555904i | ||||||
\(924\) | 15.5202 | + | 72.8650i | 0.0167967 | + | 0.0788582i | ||||
\(925\) | −51.0042 | − | 88.3419i | −0.0551397 | − | 0.0955048i | ||||
\(926\) | 274.869 | − | 617.717i | 0.296834 | − | 0.667081i | ||||
\(927\) | 667.543 | − | 385.406i | 0.720111 | − | 0.415756i | ||||
\(928\) | 169.178 | − | 0.178987i | 0.182304 | − | 0.000192874i | ||||
\(929\) | −566.361 | + | 980.965i | −0.609645 | + | 1.05594i | 0.381653 | + | 0.924306i | \(0.375355\pi\) |
−0.991299 | + | 0.131631i | \(0.957979\pi\) | |||||||
\(930\) | 7.25211 | + | 68.8590i | 0.00779797 | + | 0.0740420i | ||||
\(931\) | 294.853 | + | 763.014i | 0.316706 | + | 0.819564i | ||||
\(932\) | −19.6249 | + | 4.18009i | −0.0210568 | + | 0.00448507i | ||||
\(933\) | −93.0459 | + | 161.160i | −0.0997276 | + | 0.172733i | ||||
\(934\) | −241.629 | + | 543.017i | −0.258704 | + | 0.581389i | ||||
\(935\) | −409.637 | + | 236.504i | −0.438114 | + | 0.252945i | ||||
\(936\) | 582.781 | + | 123.487i | 0.622629 | + | 0.131931i | ||||
\(937\) | 22.4629 | + | 38.9068i | 0.0239732 | + | 0.0415228i | 0.877763 | − | 0.479095i | \(-0.159035\pi\) |
−0.853790 | + | 0.520618i | \(0.825702\pi\) | |||||||
\(938\) | −8.78757 | − | 83.4383i | −0.00936842 | − | 0.0889535i | ||||
\(939\) | − | 87.4567i | − | 0.0931382i | ||||||
\(940\) | 883.233 | − | 795.943i | 0.939609 | − | 0.846748i | ||||
\(941\) | −565.174 | − | 978.911i | −0.600610 | − | 1.04029i | −0.992729 | − | 0.120373i | \(-0.961591\pi\) |
0.392118 | − | 0.919915i | \(-0.371742\pi\) | |||||||
\(942\) | −23.2240 | + | 2.44591i | −0.0246539 | + | 0.00259650i | ||||
\(943\) | 585.583i | 0.620978i | ||||||||
\(944\) | 694.153 | − | 957.123i | 0.735332 | − | 1.01390i | ||||
\(945\) | 70.1264 | − | 121.462i | 0.0742078 | − | 0.128532i | ||||
\(946\) | 627.594 | − | 456.177i | 0.663419 | − | 0.482216i | ||||
\(947\) | 122.275 | + | 70.5956i | 0.129118 | + | 0.0745466i | 0.563168 | − | 0.826342i | \(-0.309582\pi\) |
−0.434050 | + | 0.900889i | \(0.642916\pi\) | |||||||
\(948\) | 133.513 | − | 411.503i | 0.140836 | − | 0.434075i | ||||
\(949\) | −518.152 | −0.545998 | ||||||||
\(950\) | 446.855 | − | 229.064i | 0.470374 | − | 0.241120i | ||||
\(951\) | − | 345.485i | − | 0.363286i | ||||||
\(952\) | −71.7593 | + | 338.658i | −0.0753774 | + | 0.355733i | ||||
\(953\) | −561.043 | + | 971.755i | −0.588712 | + | 1.01968i | 0.405689 | + | 0.914011i | \(0.367032\pi\) |
−0.994401 | + | 0.105669i | \(0.966302\pi\) | |||||||
\(954\) | −451.359 | + | 328.078i | −0.473123 | + | 0.343897i | ||||
\(955\) | 1069.49 | + | 617.473i | 1.11989 | + | 0.646569i | ||||
\(956\) | −963.193 | + | 868.001i | −1.00752 | + | 0.907951i | ||||
\(957\) | −40.3766 | −0.0421908 | ||||||||
\(958\) | −624.425 | + | 65.7633i | −0.651800 | + | 0.0686464i | ||||
\(959\) | 299.196 | − | 172.741i | 0.311987 | − | 0.180126i | ||||
\(960\) | 87.6445 | − | 197.527i | 0.0912964 | − | 0.205758i | ||||
\(961\) | 855.874 | 0.890608 | ||||||||
\(962\) | −14.9907 | − | 142.338i | −0.0155829 | − | 0.147960i | ||||
\(963\) | −608.024 | + | 351.043i | −0.631385 | + | 0.364530i | ||||
\(964\) | 285.978 | − | 881.420i | 0.296658 | − | 0.914336i | ||||
\(965\) | 422.937 | + | 732.549i | 0.438277 | + | 0.759118i | ||||
\(966\) | 22.6336 | − | 50.8649i | 0.0234302 | − | 0.0526551i | ||||
\(967\) | 961.049 | + | 554.862i | 0.993845 | + | 0.573797i | 0.906422 | − | 0.422374i | \(-0.138803\pi\) |
0.0874239 | + | 0.996171i | \(0.472137\pi\) | |||||||
\(968\) | −150.364 | − | 461.775i | −0.155335 | − | 0.477040i | ||||
\(969\) | −258.159 | − | 208.099i | −0.266418 | − | 0.214756i | ||||
\(970\) | 94.1923 | + | 894.359i | 0.0971055 | + | 0.922020i | ||||
\(971\) | −238.941 | − | 137.953i | −0.246077 | − | 0.142073i | 0.371889 | − | 0.928277i | \(-0.378710\pi\) |
−0.617967 | + | 0.786204i | \(0.712043\pi\) | |||||||
\(972\) | 782.524 | + | 253.891i | 0.805065 | + | 0.261205i | ||||
\(973\) | 197.202 | + | 341.564i | 0.202674 | + | 0.351042i | ||||
\(974\) | 76.9102 | − | 172.842i | 0.0789633 | − | 0.177456i | ||||
\(975\) | −104.344 | + | 60.2428i | −0.107019 | + | 0.0617875i | ||||
\(976\) | −1181.83 | + | 527.384i | −1.21089 | + | 0.540353i | ||||
\(977\) | −1610.16 | −1.64807 | −0.824034 | − | 0.566541i | \(-0.808281\pi\) | ||||
−0.824034 | + | 0.566541i | \(0.808281\pi\) | |||||||
\(978\) | −492.519 | + | 357.995i | −0.503598 | + | 0.366048i | ||||
\(979\) | −71.2120 | + | 41.1143i | −0.0727396 | + | 0.0419962i | ||||
\(980\) | 578.233 | − | 123.163i | 0.590034 | − | 0.125677i | ||||
\(981\) | −1503.31 | −1.53242 | ||||||||
\(982\) | 396.532 | + | 545.536i | 0.403800 | + | 0.555536i | ||||
\(983\) | 1506.60 | + | 869.839i | 1.53266 | + | 0.884882i | 0.999238 | + | 0.0390327i | \(0.0124276\pi\) |
0.533422 | + | 0.845849i | \(0.320906\pi\) | |||||||
\(984\) | −295.210 | − | 265.469i | −0.300010 | − | 0.269786i | ||||
\(985\) | −119.251 | + | 206.549i | −0.121067 | + | 0.209695i | ||||
\(986\) | −171.414 | − | 76.2748i | −0.173847 | − | 0.0773578i | ||||
\(987\) | 207.675i | 0.210410i | ||||||||
\(988\) | 703.478 | − | 38.7440i | 0.712022 | − | 0.0392146i | ||||
\(989\) | −579.804 | −0.586252 | ||||||||
\(990\) | 174.106 | − | 391.270i | 0.175864 | − | 0.395222i | ||||
\(991\) | −259.117 | − | 149.601i | −0.261470 | − | 0.150960i | 0.363535 | − | 0.931581i | \(-0.381570\pi\) |
−0.625005 | + | 0.780621i | \(0.714903\pi\) | |||||||
\(992\) | 284.315 | + | 163.749i | 0.286608 | + | 0.165069i | ||||
\(993\) | 210.724 | − | 364.985i | 0.212210 | − | 0.367558i | ||||
\(994\) | −218.366 | + | 158.723i | −0.219684 | + | 0.159681i | ||||
\(995\) | − | 474.562i | − | 0.476946i | ||||||
\(996\) | 120.617 | − | 25.6913i | 0.121101 | − | 0.0257944i | ||||
\(997\) | 310.285 | + | 537.429i | 0.311219 | + | 0.539047i | 0.978626 | − | 0.205646i | \(-0.0659295\pi\) |
−0.667408 | + | 0.744692i | \(0.732596\pi\) | |||||||
\(998\) | −837.793 | − | 1152.61i | −0.839472 | − | 1.15492i | ||||
\(999\) | − | 129.321i | − | 0.129450i |
(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 | 76.3.g.c.11.3 | yes | 28 | |
4.3 | odd | 2 | inner | 76.3.g.c.11.13 | yes | 28 | |
19.7 | even | 3 | inner | 76.3.g.c.7.13 | yes | 28 | |
76.7 | odd | 6 | inner | 76.3.g.c.7.3 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.c.7.3 | ✓ | 28 | 76.7 | odd | 6 | inner | |
76.3.g.c.7.13 | yes | 28 | 19.7 | even | 3 | inner | |
76.3.g.c.11.3 | yes | 28 | 1.1 | even | 1 | trivial | |
76.3.g.c.11.13 | yes | 28 | 4.3 | odd | 2 | inner |