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 | 7.13 | ||
Character | \(\chi\) | \(=\) | 76.7 |
Dual form | 76.3.g.c.11.13 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61779 | − | 1.17591i | 0.808893 | − | 0.587956i | ||||
\(3\) | 0.851777 | − | 0.491774i | 0.283926 | − | 0.163925i | −0.351274 | − | 0.936273i | \(-0.614251\pi\) |
0.635199 | + | 0.772348i | \(0.280918\pi\) | |||||||
\(4\) | 1.23446 | − | 3.80475i | 0.308614 | − | 0.951187i | ||||
\(5\) | 1.71651 | + | 2.97309i | 0.343302 | + | 0.594617i | 0.985044 | − | 0.172304i | \(-0.0551211\pi\) |
−0.641741 | + | 0.766921i | \(0.721788\pi\) | |||||||
\(6\) | 0.799709 | − | 1.79720i | 0.133285 | − | 0.299533i | ||||
\(7\) | − | 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 | ||||
\(10\) | 6.27304 | + | 2.79135i | 0.627304 | + | 0.279135i | ||||
\(11\) | − | 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 | −0.987382 | − | 0.158356i | \(-0.949381\pi\) |
0.630832 | + | 0.775920i | \(0.282714\pi\) | |||||||
\(14\) | −2.86769 | − | 3.94529i | −0.204835 | − | 0.281806i | ||||
\(15\) | 2.92417 | + | 1.68827i | 0.194945 | + | 0.112551i | ||||
\(16\) | −12.9522 | − | 9.39360i | −0.809514 | − | 0.587100i | ||||
\(17\) | 8.87198 | + | 15.3667i | 0.521881 | + | 0.903924i | 0.999676 | + | 0.0254531i | \(0.00810285\pi\) |
−0.477795 | + | 0.878471i | \(0.658564\pi\) | |||||||
\(18\) | 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 | ||||
\(22\) | −9.13095 | − | 12.5621i | −0.415043 | − | 0.571004i | ||||
\(23\) | −10.0507 | − | 5.80275i | −0.436985 | − | 0.252293i | 0.265333 | − | 0.964157i | \(-0.414518\pi\) |
−0.702318 | + | 0.711863i | \(0.747852\pi\) | |||||||
\(24\) | −5.85069 | − | 5.26126i | −0.243779 | − | 0.219219i | ||||
\(25\) | 6.60717 | − | 11.4440i | 0.264287 | − | 0.457758i | ||||
\(26\) | 1.94192 | + | 18.4387i | 0.0746894 | + | 0.709179i | ||||
\(27\) | 16.7524i | 0.620459i | ||||||||
\(28\) | −9.27862 | − | 3.01047i | −0.331379 | − | 0.107517i | ||||
\(29\) | 2.64340 | − | 4.57851i | 0.0911519 | − | 0.157880i | −0.816844 | − | 0.576858i | \(-0.804278\pi\) |
0.907996 | + | 0.418979i | \(0.137612\pi\) | |||||||
\(30\) | 6.71594 | − | 0.707310i | 0.223865 | − | 0.0235770i | ||||
\(31\) | 10.2531i | 0.330744i | 0.986231 | + | 0.165372i | \(0.0528825\pi\) | ||||
−0.986231 | + | 0.165372i | \(0.947117\pi\) | |||||||
\(32\) | −32.0000 | + | 0.0338554i | −0.999999 | + | 0.00105798i | ||||
\(33\) | −3.81862 | − | 6.61404i | −0.115716 | − | 0.200425i | ||||
\(34\) | 32.4229 | + | 14.4274i | 0.953614 | + | 0.424335i | ||||
\(35\) | 7.25045 | − | 4.18605i | 0.207156 | − | 0.119601i | ||||
\(36\) | 21.5096 | + | 23.8685i | 0.597490 | + | 0.663015i | ||||
\(37\) | −7.71952 | −0.208636 | −0.104318 | − | 0.994544i | \(-0.533266\pi\) | ||||
−0.104318 | + | 0.994544i | \(0.533266\pi\) | |||||||
\(38\) | 9.76078 | + | 36.7250i | 0.256863 | + | 0.966448i | ||||
\(39\) | 9.11779i | 0.233790i | ||||||||
\(40\) | 18.3642 | − | 20.4215i | 0.459104 | − | 0.510538i | ||||
\(41\) | −25.2287 | − | 43.6973i | −0.615333 | − | 1.06579i | −0.990326 | − | 0.138761i | \(-0.955688\pi\) |
0.374992 | − | 0.927028i | \(-0.377645\pi\) | |||||||
\(42\) | −4.38282 | − | 1.95025i | −0.104353 | − | 0.0464345i | ||||
\(43\) | 43.2661 | − | 24.9797i | 1.00619 | − | 0.580923i | 0.0961149 | − | 0.995370i | \(-0.469358\pi\) |
0.910073 | + | 0.414447i | \(0.136025\pi\) | |||||||
\(44\) | −29.5438 | − | 9.58555i | −0.671451 | − | 0.217854i | ||||
\(45\) | −27.5762 | −0.612805 | ||||||||
\(46\) | −23.0833 | + | 2.43109i | −0.501812 | + | 0.0528499i | ||||
\(47\) | −74.9827 | − | 43.2913i | −1.59538 | − | 0.921091i | −0.992362 | − | 0.123361i | \(-0.960633\pi\) |
−0.603015 | − | 0.797730i | \(-0.706034\pi\) | |||||||
\(48\) | −15.6519 | − | 1.63169i | −0.326082 | − | 0.0339936i | ||||
\(49\) | 43.0528 | 0.878628 | ||||||||
\(50\) | −2.76811 | − | 26.2833i | −0.0553622 | − | 0.525667i | ||||
\(51\) | 15.1139 | + | 8.72601i | 0.296351 | + | 0.171098i | ||||
\(52\) | 24.8239 | + | 27.5462i | 0.477382 | + | 0.529735i | ||||
\(53\) | 17.3665 | − | 30.0797i | 0.327671 | − | 0.567542i | −0.654379 | − | 0.756167i | \(-0.727070\pi\) |
0.982049 | + | 0.188625i | \(0.0604030\pi\) | |||||||
\(54\) | 19.6994 | + | 27.1018i | 0.364803 | + | 0.501885i | ||||
\(55\) | 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 | \(-0.451259\pi\) |
0.932155 | + | 0.362059i | \(0.117926\pi\) | |||||||
\(60\) | 10.0332 | − | 9.04164i | 0.167220 | − | 0.150694i | ||||
\(61\) | 40.4426 | − | 70.0487i | 0.662994 | − | 1.14834i | −0.316831 | − | 0.948482i | \(-0.602619\pi\) |
0.979825 | − | 0.199857i | \(-0.0640477\pi\) | |||||||
\(62\) | 12.0567 | + | 16.5873i | 0.194463 | + | 0.267537i | ||||
\(63\) | 16.9647 | + | 9.79458i | 0.269281 | + | 0.155469i | ||||
\(64\) | −51.7293 | + | 37.6840i | −0.808270 | + | 0.588812i | ||||
\(65\) | −31.8252 | −0.489619 | ||||||||
\(66\) | −13.9552 | − | 6.20973i | −0.211443 | − | 0.0940869i | ||||
\(67\) | 14.8972 | + | 8.60089i | 0.222346 | + | 0.128371i | 0.607036 | − | 0.794674i | \(-0.292358\pi\) |
−0.384690 | + | 0.923046i | \(0.625692\pi\) | |||||||
\(68\) | 69.4186 | − | 14.7861i | 1.02086 | − | 0.217442i | ||||
\(69\) | −11.4146 | −0.165428 | ||||||||
\(70\) | 6.80724 | − | 15.2980i | 0.0972463 | − | 0.218543i | ||||
\(71\) | −47.9333 | + | 27.6743i | −0.675117 | + | 0.389779i | −0.798013 | − | 0.602640i | \(-0.794115\pi\) |
0.122896 | + | 0.992420i | \(0.460782\pi\) | |||||||
\(72\) | 62.8653 | + | 13.3207i | 0.873129 | + | 0.185010i | ||||
\(73\) | 27.9468 | + | 48.4053i | 0.382833 | + | 0.663087i | 0.991466 | − | 0.130365i | \(-0.0416150\pi\) |
−0.608633 | + | 0.793452i | \(0.708282\pi\) | |||||||
\(74\) | −12.4885 | + | 9.07749i | −0.168764 | + | 0.122669i | ||||
\(75\) | − | 12.9969i | − | 0.173292i | ||||||
\(76\) | 58.9763 | + | 47.9354i | 0.776004 | + | 0.630728i | ||||
\(77\) | −18.9364 | −0.245928 | ||||||||
\(78\) | 10.7217 | + | 14.7506i | 0.137458 | + | 0.189111i | ||||
\(79\) | −95.2318 | + | 54.9821i | −1.20547 | + | 0.695976i | −0.961765 | − | 0.273874i | \(-0.911695\pi\) |
−0.243701 | + | 0.969850i | \(0.578361\pi\) | |||||||
\(80\) | 5.69534 | − | 54.6323i | 0.0711918 | − | 0.682904i | ||||
\(81\) | −27.9085 | − | 48.3389i | −0.344549 | − | 0.596776i | ||||
\(82\) | −92.1988 | − | 41.0262i | −1.12438 | − | 0.500319i | ||||
\(83\) | 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 | ||||
\(86\) | 40.6213 | − | 91.2889i | 0.472341 | − | 1.06150i | ||||
\(87\) | − | 5.19983i | − | 0.0597681i | ||||||
\(88\) | −59.0674 | + | 19.2336i | −0.671220 | + | 0.218564i | ||||
\(89\) | −5.29483 | + | 9.17091i | −0.0594925 | + | 0.103044i | −0.894238 | − | 0.447592i | \(-0.852282\pi\) |
0.834745 | + | 0.550636i | \(0.185615\pi\) | |||||||
\(90\) | −44.6124 | + | 32.4272i | −0.495693 | + | 0.360303i | ||||
\(91\) | 19.5786 | + | 11.3037i | 0.215150 | + | 0.124217i | ||||
\(92\) | −34.4851 | + | 31.0770i | −0.374838 | + | 0.337793i | ||||
\(93\) | 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 | 0.976426 | + | 0.215854i | \(0.0692535\pi\) |
−0.301278 | + | 0.953536i | \(0.597413\pi\) | |||||||
\(98\) | 69.6501 | − | 50.6263i | 0.710716 | − | 0.516595i | ||||
\(99\) | 54.0169 | + | 31.1867i | 0.545625 | + | 0.315017i | ||||
\(100\) | −35.3851 | − | 39.2657i | −0.353851 | − | 0.392657i | ||||
\(101\) | −43.6489 | + | 75.6021i | −0.432167 | + | 0.748536i | −0.997060 | − | 0.0766289i | \(-0.975584\pi\) |
0.564892 | + | 0.825165i | \(0.308918\pi\) | |||||||
\(102\) | 34.7121 | − | 3.65581i | 0.340314 | − | 0.0358413i | ||||
\(103\) | 95.9601i | 0.931651i | 0.884877 | + | 0.465826i | \(0.154243\pi\) | ||||
−0.884877 | + | 0.465826i | \(0.845757\pi\) | |||||||
\(104\) | 72.5517 | + | 15.3732i | 0.697612 | + | 0.147819i | ||||
\(105\) | 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 | \(-0.133924\pi\) | |||||||
\(108\) | 63.7387 | + | 20.6801i | 0.590173 | + | 0.191483i | ||||
\(109\) | 93.5748 | + | 162.076i | 0.858485 | + | 1.48694i | 0.873374 | + | 0.487050i | \(0.161927\pi\) |
−0.0148892 | + | 0.999889i | \(0.504740\pi\) | |||||||
\(110\) | 21.6748 | − | 48.7101i | 0.197043 | − | 0.442819i | ||||
\(111\) | −6.57531 | + | 3.79626i | −0.0592370 | + | 0.0342005i | ||||
\(112\) | −22.9081 | + | 31.5865i | −0.204537 | + | 0.282023i | ||||
\(113\) | −181.373 | −1.60507 | −0.802534 | − | 0.596606i | \(-0.796516\pi\) | ||||
−0.802534 | + | 0.596606i | \(0.796516\pi\) | |||||||
\(114\) | 26.3744 | + | 26.4814i | 0.231354 | + | 0.232293i | ||||
\(115\) | − | 39.8420i | − | 0.346452i | ||||||
\(116\) | −14.1569 | − | 15.7095i | −0.122042 | − | 0.135426i | ||||
\(117\) | −37.2325 | − | 64.4886i | −0.318227 | − | 0.551185i | ||||
\(118\) | 60.0842 | − | 135.028i | 0.509188 | − | 1.14431i | ||||
\(119\) | 37.4747 | − | 21.6361i | 0.314914 | − | 0.181816i | ||||
\(120\) | 5.59941 | − | 26.4256i | 0.0466617 | − | 0.220213i | ||||
\(121\) | 60.7049 | 0.501694 | ||||||||
\(122\) | −16.9437 | − | 160.881i | −0.138882 | − | 1.31869i | ||||
\(123\) | −42.9784 | − | 24.8136i | −0.349418 | − | 0.201737i | ||||
\(124\) | 39.0104 | + | 12.6570i | 0.314600 | + | 0.102073i | ||||
\(125\) | 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 | \(-0.556131\pi\) |
−0.940309 | + | 0.340321i | \(0.889464\pi\) | |||||||
\(128\) | −39.3738 | + | 121.794i | −0.307608 | + | 0.951513i | ||||
\(129\) | 24.5687 | − | 42.5543i | 0.190455 | − | 0.329878i | ||||
\(130\) | −51.4864 | + | 37.4237i | −0.396049 | + | 0.287874i | ||||
\(131\) | 179.080 | − | 103.392i | 1.36702 | − | 0.789250i | 0.376475 | − | 0.926427i | \(-0.377136\pi\) |
0.990547 | + | 0.137177i | \(0.0438028\pi\) | |||||||
\(132\) | −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 | ||||
\(136\) | 94.9172 | − | 105.551i | 0.697921 | − | 0.776110i | ||||
\(137\) | 70.8332 | − | 122.687i | 0.517031 | − | 0.895524i | −0.482774 | − | 0.875745i | \(-0.660371\pi\) |
0.999804 | − | 0.0197784i | \(-0.00629607\pi\) | |||||||
\(138\) | −18.4663 | + | 13.4225i | −0.133814 | + | 0.0972647i | ||||
\(139\) | 140.060 | + | 80.8637i | 1.00763 | + | 0.581753i | 0.910496 | − | 0.413519i | \(-0.135700\pi\) |
0.0971300 | + | 0.995272i | \(0.469034\pi\) | |||||||
\(140\) | −6.97649 | − | 32.7536i | −0.0498321 | − | 0.233955i | ||||
\(141\) | −85.1581 | −0.603958 | ||||||||
\(142\) | −45.0032 | + | 101.137i | −0.316924 | + | 0.712229i | ||||
\(143\) | 62.3399 | + | 35.9920i | 0.435943 | + | 0.251692i | ||||
\(144\) | 117.367 | − | 52.3740i | 0.815045 | − | 0.363709i | ||||
\(145\) | 18.1497 | 0.125171 | ||||||||
\(146\) | 102.132 | + | 45.4464i | 0.699537 | + | 0.311277i | ||||
\(147\) | 36.6714 | − | 21.1722i | 0.249465 | − | 0.144029i | ||||
\(148\) | −9.52943 | + | 29.3708i | −0.0643880 | + | 0.198452i | ||||
\(149\) | −3.94728 | − | 6.83690i | −0.0264918 | − | 0.0458852i | 0.852476 | − | 0.522767i | \(-0.175100\pi\) |
−0.878967 | + | 0.476882i | \(0.841767\pi\) | |||||||
\(150\) | −15.2833 | − | 21.0263i | −0.101888 | − | 0.140175i | ||||
\(151\) | − | 214.335i | − | 1.41944i | −0.704484 | − | 0.709719i | \(-0.748822\pi\) | ||
0.704484 | − | 0.709719i | \(-0.251178\pi\) | |||||||
\(152\) | 151.779 | + | 8.19816i | 0.998544 | + | 0.0539353i | ||||
\(153\) | −142.531 | −0.931573 | ||||||||
\(154\) | −30.6351 | + | 22.2676i | −0.198929 | + | 0.144595i | ||||
\(155\) | −30.4833 | + | 17.5995i | −0.196666 | + | 0.113545i | ||||
\(156\) | 34.6909 | + | 11.2555i | 0.222378 | + | 0.0721508i | ||||
\(157\) | −5.93576 | − | 10.2810i | −0.0378074 | − | 0.0654844i | 0.846503 | − | 0.532385i | \(-0.178704\pi\) |
−0.884310 | + | 0.466900i | \(0.845371\pi\) | |||||||
\(158\) | −89.4105 | + | 200.934i | −0.565889 | + | 1.27173i | ||||
\(159\) | − | 34.1616i | − | 0.214853i | ||||||
\(160\) | −55.0290 | − | 95.0806i | −0.343931 | − | 0.594254i | ||||
\(161\) | −14.1511 | + | 24.5105i | −0.0878953 | + | 0.152239i | ||||
\(162\) | −101.992 | − | 45.3840i | −0.629582 | − | 0.280148i | ||||
\(163\) | 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 | ||||
\(166\) | 36.8606 | + | 50.7117i | 0.222052 | + | 0.305492i | ||||
\(167\) | −133.887 | − | 77.2997i | −0.801719 | − | 0.462872i | 0.0423532 | − | 0.999103i | \(-0.486515\pi\) |
−0.844072 | + | 0.536230i | \(0.819848\pi\) | |||||||
\(168\) | −12.8306 | + | 14.2680i | −0.0763727 | + | 0.0849288i | ||||
\(169\) | 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 | −0.970000 | − | 0.243105i | \(-0.921834\pi\) |
0.274465 | − | 0.961597i | \(-0.411499\pi\) | |||||||
\(174\) | −6.11454 | − | 8.41220i | −0.0351411 | − | 0.0483460i | ||||
\(175\) | −27.9083 | − | 16.1129i | −0.159476 | − | 0.0920736i | ||||
\(176\) | −72.9413 | + | 100.574i | −0.414439 | + | 0.571443i | ||||
\(177\) | 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 | \(0.739226\pi\) | |||||||
\(180\) | −34.0417 | + | 104.921i | −0.189121 | + | 0.582892i | ||||
\(181\) | 57.7654 | − | 100.053i | 0.319146 | − | 0.552777i | −0.661164 | − | 0.750241i | \(-0.729937\pi\) |
0.980310 | + | 0.197464i | \(0.0632706\pi\) | |||||||
\(182\) | 44.9663 | − | 4.73576i | 0.247067 | − | 0.0260207i | ||||
\(183\) | − | 79.5545i | − | 0.434724i | ||||||
\(184\) | −19.2457 | + | 90.8274i | −0.104596 | + | 0.493627i | ||||
\(185\) | −13.2507 | − | 22.9508i | −0.0716252 | − | 0.124058i | ||||
\(186\) | 18.4268 | + | 8.19948i | 0.0990690 | + | 0.0440832i | ||||
\(187\) | 119.322 | − | 68.8908i | 0.638088 | − | 0.368400i | ||||
\(188\) | −257.275 | + | 231.849i | −1.36849 | + | 1.23324i | ||||
\(189\) | 40.8540 | 0.216159 | ||||||||
\(190\) | −92.4321 | + | 92.0586i | −0.486485 | + | 0.484519i | ||||
\(191\) | 359.726i | 1.88338i | 0.336482 | + | 0.941690i | \(0.390763\pi\) | ||||
−0.336482 | + | 0.941690i | \(0.609237\pi\) | |||||||
\(192\) | −25.5298 | + | 57.5374i | −0.132968 | + | 0.299674i | ||||
\(193\) | −123.197 | − | 213.383i | −0.638325 | − | 1.10561i | −0.985800 | − | 0.167922i | \(-0.946294\pi\) |
0.347475 | − | 0.937689i | \(-0.387039\pi\) | |||||||
\(194\) | 239.332 | + | 106.497i | 1.23367 | + | 0.548954i | ||||
\(195\) | −27.1080 | + | 15.6508i | −0.139015 | + | 0.0802605i | ||||
\(196\) | 53.1468 | − | 163.805i | 0.271157 | − | 0.835740i | ||||
\(197\) | −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 | \(-0.446242\pi\) |
−0.769663 | + | 0.638450i | \(0.779576\pi\) | |||||||
\(200\) | −103.419 | − | 21.9137i | −0.517093 | − | 0.109568i | ||||
\(201\) | 16.9188 | 0.0841730 | ||||||||
\(202\) | 18.2869 | + | 173.635i | 0.0905294 | + | 0.859580i | ||||
\(203\) | −11.1656 | − | 6.44646i | −0.0550029 | − | 0.0317560i | ||||
\(204\) | 51.8577 | − | 46.7327i | 0.254205 | − | 0.229082i | ||||
\(205\) | 86.6106 | − | 150.014i | 0.422491 | − | 0.731776i | ||||
\(206\) | 112.841 | + | 155.243i | 0.547770 | + | 0.753606i | ||||
\(207\) | 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 | \(-0.739774\pi\) |
0.289710 | + | 0.957114i | \(0.406441\pi\) | |||||||
\(212\) | −93.0076 | − | 103.207i | −0.438715 | − | 0.486828i | ||||
\(213\) | −27.2190 | + | 47.1447i | −0.127789 | + | 0.221337i | ||||
\(214\) | −102.780 | − | 141.401i | −0.480279 | − | 0.660753i | ||||
\(215\) | 148.534 | + | 85.7559i | 0.690854 | + | 0.398865i | ||||
\(216\) | 127.434 | − | 41.4951i | 0.589970 | − | 0.192107i | ||||
\(217\) | 25.0041 | 0.115226 | ||||||||
\(218\) | 341.972 | + | 152.169i | 1.56868 | + | 0.698023i | ||||
\(219\) | 47.6089 | + | 27.4870i | 0.217392 | + | 0.125512i | ||||
\(220\) | −22.2137 | − | 104.290i | −0.100971 | − | 0.474046i | ||||
\(221\) | −164.492 | −0.744308 | ||||||||
\(222\) | −6.17337 | + | 13.8735i | −0.0278080 | + | 0.0624934i | ||||
\(223\) | 118.020 | − | 68.1387i | 0.529236 | − | 0.305555i | −0.211469 | − | 0.977385i | \(-0.567825\pi\) |
0.740705 | + | 0.671830i | \(0.234491\pi\) | |||||||
\(224\) | 0.0825630 | + | 78.0382i | 0.000368585 | + | 0.348385i | ||||
\(225\) | 53.0730 | + | 91.9252i | 0.235880 | + | 0.408556i | ||||
\(226\) | −293.422 | + | 213.279i | −1.29833 | + | 0.943710i | ||||
\(227\) | − | 237.981i | − | 1.04838i | −0.851602 | − | 0.524188i | \(-0.824369\pi\) | ||
0.851602 | − | 0.524188i | \(-0.175631\pi\) | |||||||
\(228\) | 73.8080 | + | 11.8273i | 0.323719 | + | 0.0518739i | ||||
\(229\) | 162.743 | 0.710668 | 0.355334 | − | 0.934739i | \(-0.384367\pi\) | ||||
0.355334 | + | 0.934739i | \(0.384367\pi\) | |||||||
\(230\) | −46.8507 | − | 64.4557i | −0.203699 | − | 0.280242i | ||||
\(231\) | −16.1296 | + | 9.31245i | −0.0698252 | + | 0.0403136i | ||||
\(232\) | −41.3758 | − | 8.76725i | −0.178344 | − | 0.0377899i | ||||
\(233\) | −2.50814 | − | 4.34423i | −0.0107646 | − | 0.0186448i | 0.860593 | − | 0.509293i | \(-0.170093\pi\) |
−0.871358 | + | 0.490649i | \(0.836760\pi\) | |||||||
\(234\) | −136.067 | − | 60.5465i | −0.581484 | − | 0.258746i | ||||
\(235\) | − | 297.240i | − | 1.26485i | ||||||
\(236\) | −61.5780 | − | 289.100i | −0.260924 | − | 1.22500i | ||||
\(237\) | −54.0775 | + | 93.6650i | −0.228175 | + | 0.395211i | ||||
\(238\) | 35.1840 | − | 79.0695i | 0.147832 | − | 0.332225i | ||||
\(239\) | 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 | −0.999753 | − | 0.0222253i | \(-0.992925\pi\) |
0.519124 | + | 0.854699i | \(0.326258\pi\) | |||||||
\(242\) | 98.2075 | − | 71.3837i | 0.405816 | − | 0.294974i | ||||
\(243\) | −178.116 | − | 102.835i | −0.732986 | − | 0.423190i | ||||
\(244\) | −216.593 | − | 240.346i | −0.887676 | − | 0.985025i | ||||
\(245\) | 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 | ||||
\(250\) | 212.238 | − | 154.269i | 0.848954 | − | 0.617076i | ||||
\(251\) | −29.0811 | − | 16.7900i | −0.115861 | − | 0.0668923i | 0.440950 | − | 0.897532i | \(-0.354642\pi\) |
−0.556810 | + | 0.830640i | \(0.687975\pi\) | |||||||
\(252\) | 58.2081 | − | 52.4554i | 0.230985 | − | 0.208157i | ||||
\(253\) | −45.0583 | + | 78.0433i | −0.178096 | + | 0.308471i | ||||
\(254\) | −325.439 | + | 34.2746i | −1.28126 | + | 0.134940i | ||||
\(255\) | 59.9132i | 0.234954i | ||||||||
\(256\) | 79.5204 | + | 243.336i | 0.310626 | + | 0.950532i | ||||
\(257\) | −68.8685 | + | 119.284i | −0.267971 | + | 0.464139i | −0.968338 | − | 0.249644i | \(-0.919686\pi\) |
0.700367 | + | 0.713783i | \(0.253020\pi\) | |||||||
\(258\) | −10.2932 | − | 97.7343i | −0.0398961 | − | 0.378815i | ||||
\(259\) | 18.8256i | 0.0726856i | ||||||||
\(260\) | −39.2869 | + | 121.087i | −0.151103 | + | 0.465719i | ||||
\(261\) | 21.2335 | + | 36.7775i | 0.0813544 | + | 0.140910i | ||||
\(262\) | 168.133 | − | 377.848i | 0.641729 | − | 1.44217i | ||||
\(263\) | 312.128 | − | 180.207i | 1.18680 | − | 0.685198i | 0.229220 | − | 0.973375i | \(-0.426382\pi\) |
0.957577 | + | 0.288177i | \(0.0930491\pi\) | |||||||
\(264\) | −40.8536 | + | 45.4305i | −0.154749 | + | 0.172085i | ||||
\(265\) | 119.240 | 0.449960 | ||||||||
\(266\) | 89.5611 | − | 23.8036i | 0.336696 | − | 0.0894871i | ||||
\(267\) | 10.4154i | 0.0390091i | ||||||||
\(268\) | 51.1142 | − | 46.0626i | 0.190725 | − | 0.171875i | ||||
\(269\) | 183.963 | + | 318.633i | 0.683876 | + | 1.18451i | 0.973789 | + | 0.227455i | \(0.0730404\pi\) |
−0.289913 | + | 0.957053i | \(0.593626\pi\) | |||||||
\(270\) | −46.7617 | + | 105.088i | −0.173192 | + | 0.389216i | ||||
\(271\) | −18.4102 | + | 10.6292i | −0.0679345 | + | 0.0392220i | −0.533583 | − | 0.845748i | \(-0.679155\pi\) |
0.465648 | + | 0.884970i | \(0.345821\pi\) | |||||||
\(272\) | 29.4370 | − | 282.373i | 0.108224 | − | 1.03814i | ||||
\(273\) | 22.2355 | 0.0814488 | ||||||||
\(274\) | −29.6760 | − | 281.774i | −0.108306 | − | 1.02837i | ||||
\(275\) | −88.8622 | − | 51.3046i | −0.323135 | − | 0.186562i | ||||
\(276\) | −14.0908 | + | 43.4295i | −0.0510536 | + | 0.157353i | ||||
\(277\) | −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 | ||||
\(280\) | −49.8019 | − | 44.7846i | −0.177864 | − | 0.159945i | ||||
\(281\) | −56.6252 | + | 98.0777i | −0.201513 | + | 0.349031i | −0.949016 | − | 0.315227i | \(-0.897919\pi\) |
0.747503 | + | 0.664258i | \(0.231253\pi\) | |||||||
\(282\) | −137.767 | + | 100.138i | −0.488537 | + | 0.355101i | ||||
\(283\) | 136.312 | − | 78.7000i | 0.481669 | − | 0.278092i | −0.239443 | − | 0.970911i | \(-0.576965\pi\) |
0.721112 | + | 0.692819i | \(0.243631\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | 128.287 | − | 222.743i | 0.445439 | − | 0.773412i | ||||
\(289\) | −12.9240 | + | 22.3850i | −0.0447196 | + | 0.0774567i | ||||
\(290\) | 29.3624 | − | 21.3425i | 0.101250 | − | 0.0735949i | ||||
\(291\) | 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 | \(0.614553\pi\) | |||||||
\(294\) | 34.4297 | − | 77.3744i | 0.117108 | − | 0.263178i | ||||
\(295\) | 219.700 | + | 126.844i | 0.744747 | + | 0.429980i | ||||
\(296\) | 19.1210 | + | 58.7215i | 0.0645979 | + | 0.198383i | ||||
\(297\) | 130.082 | 0.437987 | ||||||||
\(298\) | −14.4255 | − | 6.41897i | −0.0484076 | − | 0.0215402i | ||||
\(299\) | 93.1728 | − | 53.7933i | 0.311615 | − | 0.179911i | ||||
\(300\) | −49.4501 | − | 16.0442i | −0.164834 | − | 0.0534806i | ||||
\(301\) | −60.9179 | − | 105.513i | −0.202385 | − | 0.350541i | ||||
\(302\) | −252.040 | − | 346.748i | −0.834568 | − | 1.14817i | ||||
\(303\) | 85.8615i | 0.283371i | ||||||||
\(304\) | 255.186 | − | 165.216i | 0.839427 | − | 0.543473i | ||||
\(305\) | 277.681 | 0.910429 | ||||||||
\(306\) | −230.584 | + | 167.604i | −0.753543 | + | 0.547724i | ||||
\(307\) | −475.527 | + | 274.546i | −1.54895 | + | 0.894285i | −0.550725 | + | 0.834687i | \(0.685649\pi\) |
−0.998222 | + | 0.0595984i | \(0.981018\pi\) | |||||||
\(308\) | −23.3762 | + | 72.0484i | −0.0758969 | + | 0.233923i | ||||
\(309\) | 47.1906 | + | 81.7366i | 0.152721 | + | 0.264520i | ||||
\(310\) | −28.6199 | + | 64.3179i | −0.0923222 | + | 0.207477i | ||||
\(311\) | − | 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 | −0.786222 | − | 0.617944i | \(-0.787966\pi\) |
0.928266 | + | 0.371916i | \(0.121299\pi\) | |||||||
\(314\) | −21.6924 | − | 9.65258i | −0.0690841 | − | 0.0307407i | ||||
\(315\) | 67.2500i | 0.213492i | ||||||||
\(316\) | 91.6335 | + | 430.206i | 0.289979 | + | 1.36141i | ||||
\(317\) | 175.632 | − | 304.204i | 0.554045 | − | 0.959634i | −0.443932 | − | 0.896060i | \(-0.646417\pi\) |
0.997977 | − | 0.0635735i | \(-0.0202497\pi\) | |||||||
\(318\) | −40.1711 | − | 55.2662i | −0.126324 | − | 0.173793i | ||||
\(319\) | −35.5521 | − | 20.5260i | −0.111449 | − | 0.0643449i | ||||
\(320\) | −200.832 | − | 89.1106i | −0.627599 | − | 0.278471i | ||||
\(321\) | −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 | ||||
\(326\) | 363.984 | + | 500.757i | 1.11651 | + | 1.53607i | ||||
\(327\) | 159.410 | + | 92.0353i | 0.487492 | + | 0.281453i | ||||
\(328\) | −269.910 | + | 300.148i | −0.822896 | + | 0.915086i | ||||
\(329\) | −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 | \(0.775907\pi\) | |||||||
\(332\) | 119.265 | + | 38.6958i | 0.359232 | + | 0.116554i | ||||
\(333\) | 31.0041 | − | 53.7006i | 0.0931053 | − | 0.161263i | ||||
\(334\) | −307.498 | + | 32.3851i | −0.920653 | + | 0.0969615i | ||||
\(335\) | 59.0541i | 0.176281i | ||||||||
\(336\) | −3.97920 | + | 38.1703i | −0.0118429 | + | 0.113602i | ||||
\(337\) | −145.765 | − | 252.472i | −0.432537 | − | 0.749176i | 0.564554 | − | 0.825396i | \(-0.309048\pi\) |
−0.997091 | + | 0.0762204i | \(0.975715\pi\) | |||||||
\(338\) | 151.775 | + | 67.5360i | 0.449038 | + | 0.199811i | ||||
\(339\) | −154.489 | + | 89.1943i | −0.455720 | + | 0.263110i | ||||
\(340\) | 163.118 | + | 181.007i | 0.479759 | + | 0.532373i | ||||
\(341\) | 79.6150 | 0.233475 | ||||||||
\(342\) | −294.679 | − | 79.5988i | −0.861634 | − | 0.232745i | ||||
\(343\) | − | 224.489i | − | 0.654486i | ||||||
\(344\) | −297.186 | − | 267.246i | −0.863913 | − | 0.776879i | ||||
\(345\) | −19.5932 | − | 33.9365i | −0.0567920 | − | 0.0983666i | ||||
\(346\) | −439.740 | − | 195.673i | −1.27093 | − | 0.565530i | ||||
\(347\) | 243.463 | − | 140.563i | 0.701622 | − | 0.405082i | −0.106329 | − | 0.994331i | \(-0.533910\pi\) |
0.807951 | + | 0.589249i | \(0.200576\pi\) | |||||||
\(348\) | −19.7840 | − | 6.41897i | −0.0568507 | − | 0.0184453i | ||||
\(349\) | −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 | ||||
\(352\) | 0.262887 | + | 248.480i | 0.000746837 | + | 0.705908i | ||||
\(353\) | −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 | ||||
\(356\) | 28.3568 | + | 31.4666i | 0.0796539 | + | 0.0883893i | ||||
\(357\) | 21.2801 | − | 36.8582i | 0.0596081 | − | 0.103244i | ||||
\(358\) | 307.579 | + | 423.158i | 0.859159 | + | 1.18201i | ||||
\(359\) | 237.555 | − | 137.153i | 0.661714 | − | 0.382041i | −0.131216 | − | 0.991354i | \(-0.541888\pi\) |
0.792930 | + | 0.609313i | \(0.208555\pi\) | |||||||
\(360\) | 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 | ||||
\(364\) | 67.1769 | − | 60.5378i | 0.184552 | − | 0.166313i | ||||
\(365\) | −95.9421 | + | 166.177i | −0.262855 | + | 0.455279i | ||||
\(366\) | −93.5491 | − | 128.702i | −0.255599 | − | 0.351645i | ||||
\(367\) | 523.494 | + | 302.240i | 1.42642 | + | 0.823541i | 0.996836 | − | 0.0794877i | \(-0.0253284\pi\) |
0.429580 | + | 0.903029i | \(0.358662\pi\) | |||||||
\(368\) | 75.6697 | + | 169.570i | 0.205624 | + | 0.460789i | ||||
\(369\) | 405.305 | 1.09839 | ||||||||
\(370\) | −48.4249 | − | 21.5479i | −0.130878 | − | 0.0582375i | ||||
\(371\) | −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 | \(0.621124\pi\) | |||||||
\(374\) | 112.028 | − | 251.763i | 0.299541 | − | 0.673164i | ||||
\(375\) | 111.745 | − | 64.5162i | 0.297987 | − | 0.172043i | ||||
\(376\) | −143.582 | + | 677.616i | −0.381867 | + | 1.80217i | ||||
\(377\) | 24.5052 | + | 42.4442i | 0.0650005 | + | 0.112584i | ||||
\(378\) | 66.0930 | − | 48.0408i | 0.174849 | − | 0.127092i | ||||
\(379\) | − | 335.762i | − | 0.885915i | −0.896543 | − | 0.442958i | \(-0.853929\pi\) | ||
0.896543 | − | 0.442958i | \(-0.146071\pi\) | |||||||
\(380\) | −41.2825 | + | 257.623i | −0.108638 | + | 0.677956i | ||||
\(381\) | −160.927 | −0.422382 | ||||||||
\(382\) | 423.006 | + | 581.959i | 1.10735 | + | 1.52345i | ||||
\(383\) | −256.524 | + | 148.104i | −0.669775 | + | 0.386695i | −0.795991 | − | 0.605308i | \(-0.793050\pi\) |
0.126216 | + | 0.992003i | \(0.459717\pi\) | |||||||
\(384\) | 26.3572 | + | 123.104i | 0.0686386 | + | 0.320584i | ||||
\(385\) | −32.5046 | − | 56.2997i | −0.0844276 | − | 0.146233i | ||||
\(386\) | −450.226 | − | 200.339i | −1.16639 | − | 0.519014i | ||||
\(387\) | 401.305i | 1.03697i | ||||||||
\(388\) | 512.420 | − | 109.145i | 1.32067 | − | 0.281301i | ||||
\(389\) | 352.122 | − | 609.894i | 0.905199 | − | 1.56785i | 0.0845496 | − | 0.996419i | \(-0.473055\pi\) |
0.820650 | − | 0.571432i | \(-0.193612\pi\) | |||||||
\(390\) | −25.4509 | + | 57.1963i | −0.0652588 | + | 0.146657i | ||||
\(391\) | − | 205.927i | − | 0.526669i | ||||||
\(392\) | −106.640 | − | 327.497i | −0.272041 | − | 0.835452i | ||||
\(393\) | 101.691 | − | 176.133i | 0.258755 | − | 0.448177i | ||||
\(394\) | −112.393 | + | 81.6943i | −0.285260 | + | 0.207346i | ||||
\(395\) | −326.933 | − | 188.755i | −0.827679 | − | 0.477861i | ||||
\(396\) | 185.339 | − | 167.022i | 0.468028 | − | 0.421773i | ||||
\(397\) | −159.646 | − | 276.514i | −0.402130 | − | 0.696510i | 0.591853 | − | 0.806046i | \(-0.298397\pi\) |
−0.993983 | + | 0.109536i | \(0.965063\pi\) | |||||||
\(398\) | −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 | 0.631528 | − | 0.775353i | \(-0.282428\pi\) |
−0.987240 | + | 0.159242i | \(0.949095\pi\) | |||||||
\(402\) | 27.3709 | − | 19.8950i | 0.0680869 | − | 0.0494900i | ||||
\(403\) | −82.3151 | − | 47.5246i | −0.204256 | − | 0.117927i | ||||
\(404\) | 233.764 | + | 259.401i | 0.578624 | + | 0.642081i | ||||
\(405\) | 95.8104 | − | 165.949i | 0.236569 | − | 0.409749i | ||||
\(406\) | −25.6440 | + | 2.70078i | −0.0631626 | + | 0.00665217i | ||||
\(407\) | 59.9420i | 0.147278i | ||||||||
\(408\) | 28.9411 | − | 136.584i | 0.0709342 | − | 0.334764i | ||||
\(409\) | 9.38811 | − | 16.2607i | 0.0229538 | − | 0.0397572i | −0.854320 | − | 0.519747i | \(-0.826026\pi\) |
0.877274 | + | 0.479990i | \(0.159360\pi\) | |||||||
\(410\) | −36.2860 | − | 344.537i | −0.0885025 | − | 0.840334i | ||||
\(411\) | − | 139.336i | − | 0.339016i | ||||||
\(412\) | 365.104 | + | 118.459i | 0.886175 | + | 0.287521i | ||||
\(413\) | −90.1054 | − | 156.067i | −0.218173 | − | 0.377886i | ||||
\(414\) | 75.7982 | − | 170.342i | 0.183087 | − | 0.411455i | ||||
\(415\) | −93.1955 | + | 53.8064i | −0.224567 | + | 0.129654i | ||||
\(416\) | 148.053 | − | 257.063i | 0.355897 | − | 0.617941i | ||||
\(417\) | 159.066 | 0.381454 | ||||||||
\(418\) | 285.169 | − | 75.7924i | 0.682224 | − | 0.181322i | ||||
\(419\) | 147.770i | 0.352674i | 0.984330 | + | 0.176337i | \(0.0564248\pi\) | ||||
−0.984330 | + | 0.176337i | \(0.943575\pi\) | |||||||
\(420\) | −22.0498 | − | 24.4679i | −0.0524995 | − | 0.0582570i | ||||
\(421\) | 172.053 | + | 298.005i | 0.408678 | + | 0.707851i | 0.994742 | − | 0.102414i | \(-0.0326567\pi\) |
−0.586064 | + | 0.810265i | \(0.699323\pi\) | |||||||
\(422\) | −78.1155 | + | 175.550i | −0.185108 | + | 0.415996i | ||||
\(423\) | 602.309 | − | 347.743i | 1.42390 | − | 0.822088i | ||||
\(424\) | −271.829 | − | 57.5988i | −0.641107 | − | 0.135846i | ||||
\(425\) | 234.475 | 0.551705 | ||||||||
\(426\) | 11.4036 | + | 108.277i | 0.0267689 | + | 0.254172i | ||||
\(427\) | −170.827 | − | 98.6272i | −0.400064 | − | 0.230977i | ||||
\(428\) | −332.551 | − | 107.897i | −0.776988 | − | 0.252095i | ||||
\(429\) | 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 | \(-0.209554\pi\) |
−0.134327 | + | 0.990937i | \(0.542887\pi\) | |||||||
\(432\) | 157.365 | − | 216.981i | 0.364272 | − | 0.502271i | ||||
\(433\) | −258.077 | + | 447.003i | −0.596022 | + | 1.03234i | 0.397380 | + | 0.917654i | \(0.369920\pi\) |
−0.993402 | + | 0.114686i | \(0.963414\pi\) | |||||||
\(434\) | 40.4513 | − | 29.4027i | 0.0932058 | − | 0.0677481i | ||||
\(435\) | 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 | 0.732612 | − | 0.680646i | \(-0.238301\pi\) |
0.955763 | − | 0.294137i | \(-0.0950323\pi\) | |||||||
\(440\) | −158.573 | − | 142.598i | −0.360393 | − | 0.324085i | ||||
\(441\) | −172.914 | + | 299.495i | −0.392094 | + | 0.679127i | ||||
\(442\) | −266.113 | + | 193.428i | −0.602065 | + | 0.437621i | ||||
\(443\) | −276.161 | − | 159.442i | −0.623389 | − | 0.359914i | 0.154798 | − | 0.987946i | \(-0.450527\pi\) |
−0.778187 | + | 0.628032i | \(0.783861\pi\) | |||||||
\(444\) | 6.32686 | + | 29.7037i | 0.0142497 | + | 0.0669003i | ||||
\(445\) | −36.3545 | −0.0816956 | ||||||||
\(446\) | 110.805 | − | 249.015i | 0.248442 | − | 0.558329i | ||||
\(447\) | −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 | \(0.231296\pi\) | |||||||
\(450\) | 193.957 | + | 86.3059i | 0.431015 | + | 0.191791i | ||||
\(451\) | −339.309 | + | 195.900i | −0.752349 | + | 0.434369i | ||||
\(452\) | −223.897 | + | 690.078i | −0.495347 | + | 1.52672i | ||||
\(453\) | −105.404 | − | 182.566i | −0.232681 | − | 0.403015i | ||||
\(454\) | −279.845 | − | 385.003i | −0.616400 | − | 0.848024i | ||||
\(455\) | 77.6120i | 0.170576i | ||||||||
\(456\) | 133.313 | − | 67.6578i | 0.292354 | − | 0.148372i | ||||
\(457\) | −557.508 | −1.21993 | −0.609965 | − | 0.792429i | \(-0.708816\pi\) | ||||
−0.609965 | + | 0.792429i | \(0.708816\pi\) | |||||||
\(458\) | 263.283 | − | 191.371i | 0.574854 | − | 0.417842i | ||||
\(459\) | −257.429 | + | 148.627i | −0.560848 | + | 0.323806i | ||||
\(460\) | −151.589 | − | 49.1832i | −0.329541 | − | 0.106920i | ||||
\(461\) | 289.697 | + | 501.770i | 0.628410 | + | 1.08844i | 0.987871 | + | 0.155278i | \(0.0496274\pi\) |
−0.359460 | + | 0.933160i | \(0.617039\pi\) | |||||||
\(462\) | −15.1437 | + | 34.0326i | −0.0327785 | + | 0.0736636i | ||||
\(463\) | 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 | ||||
\(466\) | −9.16608 | − | 4.07868i | −0.0196697 | − | 0.00875253i | ||||
\(467\) | − | 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 | ||||
\(470\) | −349.528 | − | 480.870i | −0.743677 | − | 1.02313i | ||||
\(471\) | −10.1119 | − | 5.83810i | −0.0214690 | − | 0.0123951i | ||||
\(472\) | −439.577 | − | 395.292i | −0.931307 | − | 0.837482i | ||||
\(473\) | −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 | ||||
\(478\) | 381.171 | + | 524.404i | 0.797430 | + | 1.09708i | ||||
\(479\) | −271.879 | − | 156.970i | −0.567597 | − | 0.327703i | 0.188592 | − | 0.982056i | \(-0.439608\pi\) |
−0.756189 | + | 0.654353i | \(0.772941\pi\) | |||||||
\(480\) | −93.6306 | − | 53.9256i | −0.195064 | − | 0.112345i | ||||
\(481\) | 35.7812 | − | 61.9749i | 0.0743892 | − | 0.128846i | ||||
\(482\) | 48.5283 | + | 460.778i | 0.100681 | + | 0.955971i | ||||
\(483\) | 27.8366i | 0.0576328i | ||||||||
\(484\) | 74.9377 | − | 230.967i | 0.154830 | − | 0.477205i | ||||
\(485\) | −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 | \(0.969038\pi\) | |||||||
\(488\) | −633.027 | − | 134.134i | −1.29719 | − | 0.274865i | ||||
\(489\) | 152.220 | + | 263.653i | 0.311288 | + | 0.539167i | ||||
\(490\) | 270.072 | + | 120.175i | 0.551167 | + | 0.245255i | ||||
\(491\) | 292.034 | − | 168.606i | 0.594774 | − | 0.343393i | −0.172209 | − | 0.985060i | \(-0.555090\pi\) |
0.766983 | + | 0.641668i | \(0.221757\pi\) | |||||||
\(492\) | −147.465 | + | 132.891i | −0.299725 | + | 0.270103i | ||||
\(493\) | 93.8089 | 0.190282 | ||||||||
\(494\) | −340.083 | − | 91.8635i | −0.688428 | − | 0.185958i | ||||
\(495\) | 214.129i | 0.432584i | ||||||||
\(496\) | 96.3134 | − | 132.800i | 0.194180 | − | 0.267742i | ||||
\(497\) | 67.4892 | + | 116.895i | 0.135793 | + | 0.235201i | ||||
\(498\) | 56.3357 | + | 25.0680i | 0.113124 | + | 0.0503373i | ||||
\(499\) | −617.010 | + | 356.231i | −1.23649 | + | 0.713890i | −0.968376 | − | 0.249496i | \(-0.919735\pi\) |
−0.268118 | + | 0.963386i | \(0.586402\pi\) | |||||||
\(500\) | 161.949 | − | 499.148i | 0.323899 | − | 0.998296i | ||||
\(501\) | −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 | \(-0.394193\pi\) |
−0.655463 | + | 0.755227i | \(0.727526\pi\) | |||||||
\(504\) | 32.4852 | − | 153.309i | 0.0644548 | − | 0.304185i | ||||
\(505\) | −299.695 | −0.593456 | ||||||||
\(506\) | 18.8774 | + | 179.242i | 0.0373072 | + | 0.354233i | ||||
\(507\) | 70.7497 | + | 40.8473i | 0.139546 | + | 0.0805668i | ||||
\(508\) | −486.186 | + | 438.137i | −0.957060 | + | 0.862474i | ||||
\(509\) | −300.486 | + | 520.456i | −0.590345 | + | 1.02251i | 0.403841 | + | 0.914829i | \(0.367675\pi\) |
−0.994186 | + | 0.107678i | \(0.965658\pi\) | |||||||
\(510\) | 70.4527 | + | 96.9267i | 0.138143 | + | 0.190052i | ||||
\(511\) | 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 | ||||
\(516\) | −131.579 | − | 146.009i | −0.254998 | − | 0.282964i | ||||
\(517\) | −336.156 | + | 582.240i | −0.650206 | + | 1.12619i | ||||
\(518\) | 22.1372 | + | 30.4557i | 0.0427360 | + | 0.0587948i | ||||
\(519\) | −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 | \(0.479857\pi\) | |||||||
\(522\) | 77.5984 | + | 34.5294i | 0.148656 | + | 0.0661482i | ||||
\(523\) | −210.412 | − | 121.482i | −0.402318 | − | 0.232278i | 0.285166 | − | 0.958478i | \(-0.407951\pi\) |
−0.687484 | + | 0.726200i | \(0.741285\pi\) | |||||||
\(524\) | −172.313 | − | 808.986i | −0.328842 | − | 1.54387i | ||||
\(525\) | −31.6956 | −0.0603725 | ||||||||
\(526\) | 293.048 | − | 658.571i | 0.557125 | − | 1.25204i | ||||
\(527\) | −157.556 | + | 90.9651i | −0.298968 | + | 0.172609i | ||||
\(528\) | −12.6701 | + | 121.537i | −0.0239964 | + | 0.230184i | ||||
\(529\) | −197.156 | − | 341.485i | −0.372696 | − | 0.645528i | ||||
\(530\) | 192.904 | − | 140.215i | 0.363970 | − | 0.264557i | ||||
\(531\) | 593.583i | 1.11786i | ||||||||
\(532\) | 116.900 | − | 143.825i | 0.219736 | − | 0.270348i | ||||
\(533\) | 467.755 | 0.877590 | ||||||||
\(534\) | 12.2476 | + | 16.8499i | 0.0229356 | + | 0.0315542i | ||||
\(535\) | 259.860 | − | 150.030i | 0.485720 | − | 0.280430i | ||||
\(536\) | 28.5262 | − | 134.625i | 0.0532204 | − | 0.251166i | ||||
\(537\) | 128.631 | + | 222.796i | 0.239537 | + | 0.414890i | ||||
\(538\) | 672.296 | + | 299.155i | 1.24962 | + | 0.556050i | ||||
\(539\) | − | 334.304i | − | 0.620231i | ||||||
\(540\) | 47.9244 | + | 224.998i | 0.0887489 | + | 0.416663i | ||||
\(541\) | 176.484 | − | 305.680i | 0.326219 | − | 0.565028i | −0.655539 | − | 0.755161i | \(-0.727559\pi\) |
0.981758 | + | 0.190133i | \(0.0608920\pi\) | |||||||
\(542\) | −17.2849 | + | 38.8445i | −0.0318909 | + | 0.0716689i | ||||
\(543\) | − | 113.630i | − | 0.209264i | ||||||
\(544\) | −284.423 | − | 491.434i | −0.522837 | − | 0.903372i | ||||
\(545\) | −321.245 | + | 556.412i | −0.589440 | + | 1.02094i | ||||
\(546\) | 35.9723 | − | 26.1470i | 0.0658833 | − | 0.0478883i | ||||
\(547\) | 795.788 | + | 459.449i | 1.45482 | + | 0.839943i | 0.998749 | − | 0.0499992i | \(-0.0159219\pi\) |
0.456074 | + | 0.889942i | \(0.349255\pi\) | |||||||
\(548\) | −379.352 | − | 420.954i | −0.692247 | − | 0.768165i | ||||
\(549\) | 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 | ||||
\(554\) | −357.865 | + | 260.120i | −0.645966 | + | 0.469531i | ||||
\(555\) | −22.5732 | − | 13.0326i | −0.0406724 | − | 0.0234822i | ||||
\(556\) | 480.564 | − | 433.070i | 0.864324 | − | 0.778903i | ||||
\(557\) | 271.529 | − | 470.301i | 0.487484 | − | 0.844347i | −0.512413 | − | 0.858739i | \(-0.671248\pi\) |
0.999896 | + | 0.0143926i | \(0.00458146\pi\) | |||||||
\(558\) | −163.812 | + | 17.2524i | −0.293571 | + | 0.0309183i | ||||
\(559\) | 463.139i | 0.828514i | ||||||||
\(560\) | −133.232 | − | 13.8892i | −0.237914 | − | 0.0248021i | ||||
\(561\) | 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 | \(0.982841\pi\) | |||||||
\(564\) | −105.124 | + | 324.005i | −0.186390 | + | 0.574477i | ||||
\(565\) | −311.328 | − | 539.237i | −0.551024 | − | 0.954401i | ||||
\(566\) | 127.980 | − | 287.611i | 0.226113 | − | 0.508147i | ||||
\(567\) | −117.884 | + | 68.0602i | −0.207908 | + | 0.120036i | ||||
\(568\) | 329.244 | + | 296.075i | 0.579656 | + | 0.521258i | ||||
\(569\) | 527.240 | 0.926609 | 0.463304 | − | 0.886199i | \(-0.346664\pi\) | ||||
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(570\) | −33.4596 | + | 123.869i | −0.0587010 | + | 0.217314i | ||||
\(571\) | − | 470.688i | − | 0.824322i | −0.911111 | − | 0.412161i | \(-0.864774\pi\) | ||
0.911111 | − | 0.412161i | \(-0.135226\pi\) | |||||||
\(572\) | 213.896 | − | 192.757i | 0.373945 | − | 0.336988i | ||||
\(573\) | 176.904 | + | 306.406i | 0.308732 | + | 0.534740i | ||||
\(574\) | −100.050 | + | 224.845i | −0.174304 | + | 0.391716i | ||||
\(575\) | −132.813 | + | 76.6796i | −0.230979 | + | 0.133356i | ||||
\(576\) | −54.3859 | − | 511.204i | −0.0944201 | − | 0.887507i | ||||
\(577\) | 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 | ||||
\(580\) | 22.4051 | − | 69.0552i | 0.0386295 | − | 0.119061i | ||||
\(581\) | 76.4443 | 0.131574 | ||||||||
\(582\) | 256.230 | − | 26.9857i | 0.440258 | − | 0.0463672i | ||||
\(583\) | −233.569 | − | 134.851i | −0.400633 | − | 0.231305i | ||||
\(584\) | 298.990 | − | 332.487i | 0.511970 | − | 0.569326i | ||||
\(585\) | 127.820 | − | 221.391i | 0.218496 | − | 0.378446i | ||||
\(586\) | −333.857 | + | 242.669i | −0.569721 | + | 0.414111i | ||||
\(587\) | 329.898 | − | 190.467i | 0.562008 | − | 0.324475i | −0.191943 | − | 0.981406i | \(-0.561479\pi\) |
0.753951 | + | 0.656931i | \(0.228146\pi\) | |||||||
\(588\) | −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 | ||||
\(592\) | 99.9850 | + | 72.5141i | 0.168894 | + | 0.122490i | ||||
\(593\) | 182.978 | − | 316.927i | 0.308563 | − | 0.534446i | −0.669486 | − | 0.742825i | \(-0.733485\pi\) |
0.978048 | + | 0.208379i | \(0.0668187\pi\) | |||||||
\(594\) | 210.445 | − | 152.965i | 0.354285 | − | 0.257517i | ||||
\(595\) | 128.652 | + | 74.2771i | 0.216221 | + | 0.124835i | ||||
\(596\) | −30.8854 | + | 6.57856i | −0.0518212 | + | 0.0110379i | ||||
\(597\) | −135.960 | −0.227739 | ||||||||
\(598\) | 87.4773 | − | 196.589i | 0.146283 | − | 0.328744i | ||||
\(599\) | −114.625 | − | 66.1790i | −0.191361 | − | 0.110483i | 0.401258 | − | 0.915965i | \(-0.368573\pi\) |
−0.592620 | + | 0.805482i | \(0.701906\pi\) | |||||||
\(600\) | −98.8662 | + | 32.1930i | −0.164777 | + | 0.0536549i | ||||
\(601\) | 30.0876 | 0.0500626 | 0.0250313 | − | 0.999687i | \(-0.492031\pi\) | ||||
0.0250313 | + | 0.999687i | \(0.492031\pi\) | |||||||
\(602\) | −222.626 | − | 99.0630i | −0.369810 | − | 0.164556i | ||||
\(603\) | −119.664 | + | 69.0878i | −0.198447 | + | 0.114573i | ||||
\(604\) | −815.492 | − | 264.588i | −1.35015 | − | 0.438059i | ||||
\(605\) | 104.201 | + | 180.481i | 0.172233 | + | 0.298316i | ||||
\(606\) | 100.966 | + | 138.905i | 0.166610 | + | 0.229217i | ||||
\(607\) | − | 25.4139i | − | 0.0418681i | −0.999781 | − | 0.0209340i | \(-0.993336\pi\) | ||
0.999781 | − | 0.0209340i | \(-0.00666400\pi\) | |||||||
\(608\) | 218.556 | − | 567.360i | 0.359468 | − | 0.933157i | ||||
\(609\) | −12.6808 | −0.0208223 | ||||||||
\(610\) | 449.228 | − | 326.529i | 0.736439 | − | 0.535293i | ||||
\(611\) | 695.113 | − | 401.324i | 1.13766 | − | 0.656831i | ||||
\(612\) | −175.948 | + | 542.294i | −0.287497 | + | 0.886101i | ||||
\(613\) | −536.454 | − | 929.165i | −0.875128 | − | 1.51577i | −0.856626 | − | 0.515938i | \(-0.827443\pi\) |
−0.0185025 | − | 0.999829i | \(-0.505890\pi\) | |||||||
\(614\) | −446.459 | + | 1003.33i | −0.727131 | + | 1.63409i | ||||
\(615\) | − | 170.371i | − | 0.277027i | ||||||
\(616\) | 46.9049 | + | 144.047i | 0.0761444 | + | 0.233843i | ||||
\(617\) | −304.579 | + | 527.546i | −0.493645 | + | 0.855018i | −0.999973 | − | 0.00732287i | \(-0.997669\pi\) |
0.506328 | + | 0.862341i | \(0.331002\pi\) | |||||||
\(618\) | 172.459 | + | 76.7402i | 0.279061 | + | 0.124175i | ||||
\(619\) | − | 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 | ||||
\(622\) | −222.488 | − | 306.092i | −0.357698 | − | 0.492110i | ||||
\(623\) | 22.3651 | + | 12.9125i | 0.0358990 | + | 0.0207263i | ||||
\(624\) | 85.6489 | − | 118.096i | 0.137258 | − | 0.189256i | ||||
\(625\) | 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 | ||||
\(630\) | 79.0802 | + | 108.796i | 0.125524 | + | 0.172692i | ||||
\(631\) | −340.675 | − | 196.689i | −0.539897 | − | 0.311710i | 0.205140 | − | 0.978733i | \(-0.434235\pi\) |
−0.745037 | + | 0.667023i | \(0.767568\pi\) | |||||||
\(632\) | 654.128 | + | 588.228i | 1.03501 | + | 0.930741i | ||||
\(633\) | −47.2461 | + | 81.8326i | −0.0746384 | + | 0.129277i | ||||
\(634\) | −73.5821 | − | 698.665i | −0.116060 | − | 1.10199i | ||||
\(635\) | − | 561.710i | − | 0.884582i | ||||||
\(636\) | −129.976 | − | 42.1711i | −0.204365 | − | 0.0663068i | ||||
\(637\) | −199.556 | + | 345.642i | −0.313275 | + | 0.542609i | ||||
\(638\) | −81.6525 | + | 8.59949i | −0.127982 | + | 0.0134788i | ||||
\(639\) | − | 444.595i | − | 0.695767i | ||||||
\(640\) | −429.689 | + | 91.9986i | −0.671389 | + | 0.143748i | ||||
\(641\) | −348.127 | − | 602.973i | −0.543100 | − | 0.940676i | −0.998724 | − | 0.0505039i | \(-0.983917\pi\) |
0.455624 | − | 0.890172i | \(-0.349416\pi\) | |||||||
\(642\) | −157.083 | − | 69.8979i | −0.244677 | − | 0.108875i | ||||
\(643\) | 187.039 | − | 107.987i | 0.290886 | − | 0.167943i | −0.347456 | − | 0.937696i | \(-0.612954\pi\) |
0.638341 | + | 0.769754i | \(0.279621\pi\) | |||||||
\(644\) | 75.7873 | + | 84.0987i | 0.117682 | + | 0.130588i | ||||
\(645\) | 168.690 | 0.261535 | ||||||||
\(646\) | −477.745 | + | 475.815i | −0.739544 | + | 0.736555i | ||||
\(647\) | 664.315i | 1.02676i | 0.858161 | + | 0.513381i | \(0.171607\pi\) | ||||
−0.858161 | + | 0.513381i | \(0.828393\pi\) | |||||||
\(648\) | −298.580 | + | 332.030i | −0.460771 | + | 0.512392i | ||||
\(649\) | −286.902 | − | 496.929i | −0.442068 | − | 0.765685i | ||||
\(650\) | 223.842 | + | 99.6041i | 0.344372 | + | 0.153237i | ||||
\(651\) | 21.2979 | − | 12.2964i | 0.0327157 | − | 0.0188884i | ||||
\(652\) | 1177.69 | + | 382.105i | 1.80628 | + | 0.586051i | ||||
\(653\) | −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 | ||||
\(656\) | −83.7081 | + | 802.966i | −0.127604 | + | 1.22403i | ||||
\(657\) | −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 | \(-0.325769\pi\) |
−0.479280 | + | 0.877662i | \(0.659102\pi\) | |||||||
\(660\) | −70.2082 | − | 77.9078i | −0.106376 | − | 0.118042i | ||||
\(661\) | 308.493 | − | 534.326i | 0.466707 | − | 0.808360i | −0.532570 | − | 0.846386i | \(-0.678774\pi\) |
0.999277 | + | 0.0380258i | \(0.0121069\pi\) | |||||||
\(662\) | 503.877 | + | 693.218i | 0.761143 | + | 1.04716i | ||||
\(663\) | −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 | ||||
\(668\) | −459.384 | + | 413.983i | −0.687700 | + | 0.619735i | ||||
\(669\) | 67.0176 | − | 116.078i | 0.100176 | − | 0.173510i | ||||
\(670\) | 69.4425 | + | 95.5369i | 0.103646 | + | 0.142592i | ||||
\(671\) | −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 | \(0.367271\pi\) | |||||||
\(674\) | −532.701 | − | 237.039i | −0.790358 | − | 0.351690i | ||||
\(675\) | 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 | \(0.442698\pi\) | |||||||
\(678\) | −145.045 | + | 325.963i | −0.213931 | + | 0.480771i | ||||
\(679\) | 276.623 | − | 159.709i | 0.407398 | − | 0.235211i | ||||
\(680\) | 476.738 | + | 101.018i | 0.701086 | + | 0.148555i | ||||
\(681\) | −117.033 | − | 202.707i | −0.171855 | − | 0.297661i | ||||
\(682\) | 128.800 | − | 93.6204i | 0.188856 | − | 0.137273i | ||||
\(683\) | 408.747i | 0.598459i | 0.954181 | + | 0.299229i | \(0.0967296\pi\) | ||||
−0.954181 | + | 0.299229i | \(0.903270\pi\) | |||||||
\(684\) | −570.328 | + | 217.743i | −0.833813 | + | 0.318337i | ||||
\(685\) | 486.344 | 0.709992 | ||||||||
\(686\) | −263.979 | − | 363.174i | −0.384809 | − | 0.529409i | ||||
\(687\) | 138.621 | − | 80.0327i | 0.201777 | − | 0.116496i | ||||
\(688\) | −795.042 | − | 82.8820i | −1.15558 | − | 0.120468i | ||||
\(689\) | 160.993 | + | 278.849i | 0.233662 | + | 0.404715i | ||||
\(690\) | −71.6040 | − | 31.8620i | −0.103774 | − | 0.0461768i | ||||
\(691\) | 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 | ||||
\(694\) | 228.580 | − | 513.693i | 0.329367 | − | 0.740191i | ||||
\(695\) | 555.214i | 0.798869i | ||||||||
\(696\) | −39.5545 | + | 12.8798i | −0.0568311 | + | 0.0185054i | ||||
\(697\) | 447.656 | − | 775.364i | 0.642262 | − | 1.11243i | ||||
\(698\) | −29.2694 | + | 21.2749i | −0.0419332 | + | 0.0304798i | ||||
\(699\) | −4.27276 | − | 2.46688i | −0.00611267 | − | 0.00352915i | ||||
\(700\) | −95.7572 | + | 86.2935i | −0.136796 | + | 0.123276i | ||||
\(701\) | −469.659 | − | 813.474i | −0.669985 | − | 1.16045i | −0.977908 | − | 0.209037i | \(-0.932967\pi\) |
0.307923 | − | 0.951411i | \(-0.400366\pi\) | |||||||
\(702\) | −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 | ||||
\(706\) | −417.449 | + | 303.430i | −0.591288 | + | 0.429787i | ||||
\(707\) | 184.371 | + | 106.446i | 0.260779 | + | 0.150561i | ||||
\(708\) | −194.623 | − | 215.966i | −0.274891 | − | 0.305037i | ||||
\(709\) | −149.306 | + | 258.606i | −0.210587 | + | 0.364747i | −0.951898 | − | 0.306414i | \(-0.900871\pi\) |
0.741312 | + | 0.671161i | \(0.234204\pi\) | |||||||
\(710\) | −377.936 | + | 39.8035i | −0.532304 | + | 0.0560613i | ||||
\(711\) | − | 883.303i | − | 1.24234i | ||||||
\(712\) | 82.8771 | + | 17.5611i | 0.116400 | + | 0.0246645i | ||||
\(713\) | 59.4960 | − | 103.050i | 0.0834447 | − | 0.144530i | ||||
\(714\) | −8.91541 | − | 84.6521i | −0.0124866 | − | 0.118560i | ||||
\(715\) | 247.122i | 0.345626i | ||||||||
\(716\) | 995.193 | + | 322.892i | 1.38993 | + | 0.450967i | ||||
\(717\) | 159.408 | + | 276.103i | 0.222327 | + | 0.385081i | ||||
\(718\) | 223.034 | − | 501.228i | 0.310632 | − | 0.698089i | ||||
\(719\) | −1030.58 | + | 595.008i | −1.43336 | + | 0.827549i | −0.997375 | − | 0.0724069i | \(-0.976932\pi\) |
−0.435981 | + | 0.899956i | \(0.643599\pi\) | |||||||
\(720\) | 357.174 | + | 259.040i | 0.496074 | + | 0.359778i | ||||
\(721\) | 234.017 | 0.324573 | ||||||||
\(722\) | −717.717 | − | 78.5285i | −0.994067 | − | 0.108765i | ||||
\(723\) | 227.852i | 0.315147i | ||||||||
\(724\) | −309.366 | − | 343.294i | −0.427302 | − | 0.474163i | ||||
\(725\) | −34.9309 | − | 60.5020i | −0.0481805 | − | 0.0834511i | ||||
\(726\) | 48.5463 | − | 109.099i | 0.0668682 | − | 0.150274i | ||||
\(727\) | −702.834 | + | 405.781i | −0.966759 | + | 0.558159i | −0.898247 | − | 0.439491i | \(-0.855159\pi\) |
−0.0685127 | + | 0.997650i | \(0.521825\pi\) | |||||||
\(728\) | 37.4906 | − | 176.931i | 0.0514980 | − | 0.243038i | ||||
\(729\) | 300.066 | 0.411613 | ||||||||
\(730\) | 40.1955 | + | 381.658i | 0.0550623 | + | 0.522819i | ||||
\(731\) | 767.712 | + | 443.239i | 1.05022 | + | 0.606345i | ||||
\(732\) | −302.685 | − | 98.2066i | −0.413504 | − | 0.134162i | ||||
\(733\) | 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 | ||||
\(736\) | 321.817 | + | 185.348i | 0.437252 | + | 0.251831i | ||||
\(737\) | 66.7858 | − | 115.676i | 0.0906185 | − | 0.156956i | ||||
\(738\) | 655.697 | − | 476.604i | 0.888478 | − | 0.645805i | ||||
\(739\) | −1168.02 | + | 674.356i | −1.58054 | + | 0.912525i | −0.585760 | + | 0.810485i | \(0.699204\pi\) |
−0.994780 | + | 0.102041i | \(0.967463\pi\) | |||||||
\(740\) | −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 | \(-0.746968\pi\) |
0.268008 | + | 0.963417i | \(0.413635\pi\) | |||||||
\(744\) | 53.9441 | − | 59.9875i | 0.0725055 | − | 0.0806284i | ||||
\(745\) | 13.5511 | − | 23.4712i | 0.0181894 | − | 0.0315050i | ||||
\(746\) | −448.238 | + | 325.809i | −0.600856 | + | 0.436742i | ||||
\(747\) | −218.060 | − | 125.897i | −0.291914 | − | 0.168537i | ||||
\(748\) | −114.814 | − | 539.035i | −0.153494 | − | 0.720634i | ||||
\(749\) | −213.152 | −0.284582 | ||||||||
\(750\) | 104.914 | − | 235.776i | 0.139886 | − | 0.314368i | ||||
\(751\) | −257.836 | − | 148.862i | −0.343324 | − | 0.198218i | 0.318417 | − | 0.947951i | \(-0.396849\pi\) |
−0.661741 | + | 0.749733i | \(0.730182\pi\) | |||||||
\(752\) | 564.532 | + | 1265.08i | 0.750707 | + | 1.68228i | ||||
\(753\) | −33.0274 | −0.0438611 | ||||||||
\(754\) | 89.5549 | + | 39.8497i | 0.118773 | + | 0.0528510i | ||||
\(755\) | 637.237 | − | 367.909i | 0.844023 | − | 0.487297i | ||||
\(756\) | 50.4326 | − | 155.439i | 0.0667097 | − | 0.205607i | ||||
\(757\) | 365.069 | + | 632.318i | 0.482257 | + | 0.835294i | 0.999793 | − | 0.0203675i | \(-0.00648363\pi\) |
−0.517535 | + | 0.855662i | \(0.673150\pi\) | |||||||
\(758\) | −394.827 | − | 543.191i | −0.520880 | − | 0.716610i | ||||
\(759\) | 88.6339i | 0.116777i | ||||||||
\(760\) | 236.156 | + | 465.323i | 0.310732 | + | 0.612268i | ||||
\(761\) | −629.518 | −0.827225 | −0.413612 | − | 0.910453i | \(-0.635733\pi\) | ||||
−0.413612 | + | 0.910453i | \(0.635733\pi\) | |||||||
\(762\) | −260.346 | + | 189.237i | −0.341662 | + | 0.248342i | ||||
\(763\) | 395.255 | − | 228.201i | 0.518027 | − | 0.299083i | ||||
\(764\) | 1368.67 | + | 444.066i | 1.79145 | + | 0.581238i | ||||
\(765\) | −244.656 | − | 423.756i | −0.319811 | − | 0.553929i | ||||
\(766\) | −240.843 | + | 541.250i | −0.314416 | + | 0.706593i | ||||
\(767\) | 685.043i | 0.893146i | ||||||||
\(768\) | 187.400 | + | 168.162i | 0.244010 | + | 0.218961i | ||||
\(769\) | −431.124 | + | 746.729i | −0.560630 | + | 0.971039i | 0.436812 | + | 0.899553i | \(0.356108\pi\) |
−0.997442 | + | 0.0714863i | \(0.977226\pi\) | |||||||
\(770\) | −118.789 | − | 52.8582i | −0.154271 | − | 0.0686470i | ||||
\(771\) | 135.471i | 0.175708i | ||||||||
\(772\) | −963.950 | + | 205.320i | −1.24864 | + | 0.265959i | ||||
\(773\) | −596.731 | + | 1033.57i | −0.771967 | + | 1.33709i | 0.164516 | + | 0.986374i | \(0.447394\pi\) |
−0.936483 | + | 0.350712i | \(0.885940\pi\) | |||||||
\(774\) | 471.900 | + | 649.226i | 0.609690 | + | 0.838793i | ||||
\(775\) | 117.336 | + | 67.7439i | 0.151401 | + | 0.0874114i | ||||
\(776\) | 700.640 | − | 779.134i | 0.902887 | − | 1.00404i | ||||
\(777\) | 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 | ||||
\(782\) | −242.153 | − | 333.146i | −0.309658 | − | 0.426018i | ||||
\(783\) | 76.7011 | + | 44.2834i | 0.0979579 | + | 0.0565560i | ||||
\(784\) | −557.629 | − | 404.421i | −0.711262 | − | 0.515843i | ||||
\(785\) | 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 | \(-0.122043\pi\) | |||||||
\(788\) | −85.7616 | + | 264.328i | −0.108834 | + | 0.335441i | ||||
\(789\) | 177.242 | − | 306.992i | 0.224641 | − | 0.389090i | ||||
\(790\) | −750.867 | + | 79.0799i | −0.950464 | + | 0.100101i | ||||
\(791\) | 442.313i | 0.559182i | ||||||||
\(792\) | 103.435 | − | 488.148i | 0.130600 | − | 0.616349i | ||||
\(793\) | 374.916 | + | 649.373i | 0.472781 | + | 0.818882i | ||||
\(794\) | −583.429 | − | 259.612i | −0.734798 | − | 0.326967i | ||||
\(795\) | 101.565 | − | 58.6389i | 0.127755 | − | 0.0737596i | ||||
\(796\) | −410.756 | + | 370.161i | −0.516025 | + | 0.465027i | ||||
\(797\) | −860.660 | −1.07987 | −0.539937 | − | 0.841705i | \(-0.681552\pi\) | ||||
−0.539937 | + | 0.841705i | \(0.681552\pi\) | |||||||
\(798\) | 64.5801 | − | 64.3192i | 0.0809275 | − | 0.0806004i | ||||
\(799\) | − | 1536.32i | − | 1.92280i | ||||||
\(800\) | −211.042 | + | 366.430i | −0.263803 | + | 0.458038i | ||||
\(801\) | −42.5314 | − | 73.6666i | −0.0530979 | − | 0.0919683i | ||||
\(802\) | −521.284 | − | 231.958i | −0.649979 | − | 0.289225i | ||||
\(803\) | 375.867 | − | 217.007i | 0.468078 | − | 0.270245i | ||||
\(804\) | 20.8855 | − | 64.3717i | 0.0259770 | − | 0.0800642i | ||||
\(805\) | −97.1624 | −0.120699 | ||||||||
\(806\) | −189.053 | + | 19.9107i | −0.234557 | + | 0.0247031i | ||||
\(807\) | 313.390 | + | 180.936i | 0.388340 | + | 0.224208i | ||||
\(808\) | 683.213 | + | 144.768i | 0.845561 | + | 0.179169i | ||||
\(809\) | 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 | \(-0.410865\pi\) |
−0.694103 | + | 0.719876i | \(0.744199\pi\) | |||||||
\(812\) | −38.3106 | + | 34.5244i | −0.0471806 | + | 0.0425177i | ||||
\(813\) | −10.4543 | + | 18.1074i | −0.0128589 | + | 0.0222723i | ||||
\(814\) | 70.4866 | + | 96.9733i | 0.0865929 | + | 0.119132i | ||||
\(815\) | −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 | ||||
\(820\) | −463.848 | − | 514.718i | −0.565669 | − | 0.627704i | ||||
\(821\) | 362.567 | − | 627.984i | 0.441616 | − | 0.764902i | −0.556193 | − | 0.831053i | \(-0.687739\pi\) |
0.997810 | + | 0.0661512i | \(0.0210720\pi\) | |||||||
\(822\) | −163.847 | − | 225.415i | −0.199327 | − | 0.274228i | ||||
\(823\) | −907.175 | − | 523.758i | −1.10228 | − | 0.636401i | −0.165460 | − | 0.986217i | \(-0.552911\pi\) |
−0.936819 | + | 0.349816i | \(0.886244\pi\) | |||||||
\(824\) | 729.957 | − | 237.690i | 0.885870 | − | 0.288458i | ||||
\(825\) | −100.921 | −0.122329 | ||||||||
\(826\) | −329.292 | − | 146.527i | −0.398659 | − | 0.177393i | ||||
\(827\) | −102.476 | − | 59.1644i | −0.123913 | − | 0.0715410i | 0.436763 | − | 0.899577i | \(-0.356125\pi\) |
−0.560675 | + | 0.828036i | \(0.689458\pi\) | |||||||
\(828\) | −77.6827 | − | 364.710i | −0.0938197 | − | 0.440471i | ||||
\(829\) | −565.539 | −0.682194 | −0.341097 | − | 0.940028i | \(-0.610799\pi\) | ||||
−0.341097 | + | 0.940028i | \(0.610799\pi\) | |||||||
\(830\) | −87.4986 | + | 196.637i | −0.105420 | + | 0.236912i | ||||
\(831\) | −188.419 | + | 108.784i | −0.226738 | + | 0.130907i | ||||
\(832\) | −62.7658 | − | 589.971i | −0.0754397 | − | 0.709099i | ||||
\(833\) | 381.963 | + | 661.580i | 0.458539 | + | 0.794213i | ||||
\(834\) | 257.335 | − | 187.048i | 0.308556 | − | 0.224279i | ||||
\(835\) | − | 530.743i | − | 0.635621i | ||||||
\(836\) | 372.218 | − | 457.950i | 0.445236 | − | 0.547787i | ||||
\(837\) | −171.764 | −0.205213 | ||||||||
\(838\) | 173.765 | + | 239.061i | 0.207357 | + | 0.285275i | ||||
\(839\) | 573.840 | − | 331.306i | 0.683957 | − | 0.394883i | −0.117387 | − | 0.993086i | \(-0.537452\pi\) |
0.801344 | + | 0.598204i | \(0.204119\pi\) | |||||||
\(840\) | −64.4440 | − | 13.6552i | −0.0767191 | − | 0.0162562i | ||||
\(841\) | 406.525 | + | 704.122i | 0.483383 | + | 0.837243i | ||||
\(842\) | 628.773 | + | 279.789i | 0.746762 | + | 0.332290i | ||||
\(843\) | 111.387i | 0.132132i | ||||||||
\(844\) | 80.0577 | + | 375.860i | 0.0948551 | + | 0.445331i | ||||
\(845\) | −142.576 | + | 246.948i | −0.168729 | + | 0.292247i | ||||
\(846\) | 565.490 | − | 1270.84i | 0.668428 | − | 1.50217i | ||||
\(847\) | − | 148.041i | − | 0.174783i | ||||||
\(848\) | −507.493 | + | 226.465i | −0.598458 | + | 0.267058i | ||||
\(849\) | 77.4052 | − | 134.070i | 0.0911722 | − | 0.157915i | ||||
\(850\) | 379.330 | − | 275.722i | 0.446270 | − | 0.324379i | ||||
\(851\) | 77.5863 | + | 44.7945i | 0.0911707 | + | 0.0526374i | ||||
\(852\) | 145.773 | + | 161.760i | 0.171095 | + | 0.189859i | ||||
\(853\) | 640.005 | + | 1108.52i | 0.750298 | + | 1.29955i | 0.947678 | + | 0.319228i | \(0.103424\pi\) |
−0.197380 | + | 0.980327i | \(0.563243\pi\) | |||||||
\(854\) | −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 | 0.883698 | − | 0.468058i | \(-0.155046\pi\) |
−0.847199 | + | 0.531276i | \(0.821713\pi\) | |||||||
\(858\) | 114.539 | − | 83.2541i | 0.133495 | − | 0.0970328i | ||||
\(859\) | 954.077 | + | 550.837i | 1.11068 | + | 0.641253i | 0.939006 | − | 0.343900i | \(-0.111748\pi\) |
0.171677 | + | 0.985153i | \(0.445081\pi\) | |||||||
\(860\) | 509.638 | − | 459.271i | 0.592602 | − | 0.534036i | ||||
\(861\) | −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 | \(-0.329072\pi\) | |||||||
\(864\) | −0.567159 | − | 536.077i | −0.000656434 | − | 0.620459i | ||||
\(865\) | 413.087 | − | 715.488i | 0.477558 | − | 0.827154i | ||||
\(866\) | 108.123 | + | 1026.63i | 0.124853 | + | 1.18549i | ||||
\(867\) | 25.4227i | 0.0293226i | ||||||||
\(868\) | 30.8666 | − | 95.1344i | 0.0355605 | − | 0.109602i | ||||
\(869\) | 426.936 | + | 739.474i | 0.491295 | + | 0.850948i | ||||
\(870\) | 14.5145 | − | 32.6187i | 0.0166834 | − | 0.0374928i | ||||
\(871\) | −138.102 | + | 79.7330i | −0.158555 | + | 0.0915419i | ||||
\(872\) | 1001.11 | − | 1113.27i | 1.14807 | − | 1.27669i | ||||
\(873\) | −1052.10 | −1.20516 | ||||||||
\(874\) | 115.004 | − | 425.750i | 0.131583 | − | 0.487128i | ||||
\(875\) | − | 319.934i | − | 0.365639i | ||||||
\(876\) | 163.352 | − | 147.208i | 0.186475 | − | 0.168046i | ||||
\(877\) | 177.007 | + | 306.585i | 0.201832 | + | 0.349583i | 0.949119 | − | 0.314918i | \(-0.101977\pi\) |
−0.747287 | + | 0.664502i | \(0.768644\pi\) | |||||||
\(878\) | 695.889 | − | 1563.88i | 0.792584 | − | 1.78119i | ||||
\(879\) | −175.778 | + | 101.486i | −0.199975 | + | 0.115456i | ||||
\(880\) | −424.219 | − | 44.2243i | −0.482068 | − | 0.0502549i | ||||
\(881\) | 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 | \(-0.0218254\pi\) |
0.439491 | + | 0.898247i | \(0.355159\pi\) | |||||||
\(884\) | −203.059 | + | 625.851i | −0.229704 | + | 0.707976i | ||||
\(885\) | 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 | \(-0.215170\pi\) |
−0.151789 | + | 0.988413i | \(0.548503\pi\) | |||||||
\(888\) | 45.1645 | + | 40.6144i | 0.0508609 | + | 0.0457370i | ||||
\(889\) | −199.509 | + | 345.560i | −0.224420 | + | 0.388706i | ||||
\(890\) | −58.8138 | + | 42.7498i | −0.0660830 | + | 0.0480335i | ||||
\(891\) | −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 | ||||
\(896\) | 297.018 | + | 96.0208i | 0.331493 | + | 0.107166i | ||||
\(897\) | 52.9083 | − | 91.6398i | 0.0589836 | − | 0.102163i | ||||
\(898\) | 1085.82 | − | 789.244i | 1.20915 | − | 0.878891i | ||||
\(899\) | 46.9438 | + | 27.1030i | 0.0522178 | + | 0.0301480i | ||||
\(900\) | 415.269 | − | 88.4517i | 0.461409 | − | 0.0982797i | ||||
\(901\) | 616.302 | 0.684020 | ||||||||
\(902\) | −318.568 | + | 715.923i | −0.353180 | + | 0.793706i | ||||
\(903\) | −103.777 | − | 59.9156i | −0.114925 | − | 0.0663517i | ||||
\(904\) | 449.254 | + | 1379.68i | 0.496962 | + | 1.52620i | ||||
\(905\) | 396.620 | 0.438254 | ||||||||
\(906\) | −385.203 | − | 171.406i | −0.425169 | − | 0.189190i | ||||
\(907\) | 340.966 | − | 196.857i | 0.375927 | − | 0.217042i | −0.300118 | − | 0.953902i | \(-0.597026\pi\) |
0.676045 | + | 0.736861i | \(0.263693\pi\) | |||||||
\(908\) | −905.460 | − | 293.778i | −0.997202 | − | 0.323544i | ||||
\(909\) | −350.616 | − | 607.284i | −0.385716 | − | 0.668079i | ||||
\(910\) | 91.2649 | + | 125.560i | 0.100291 | + | 0.137978i | ||||
\(911\) | 1032.58i | 1.13346i | 0.823903 | + | 0.566731i | \(0.191792\pi\) | ||||
−0.823903 | + | 0.566731i | \(0.808208\pi\) | |||||||
\(912\) | 136.113 | − | 266.221i | 0.149246 | − | 0.291909i | ||||
\(913\) | 243.404 | 0.266598 | ||||||||
\(914\) | −901.928 | + | 655.580i | −0.986792 | + | 0.717265i | ||||
\(915\) | 236.522 | − | 136.556i | 0.258494 | − | 0.149242i | ||||
\(916\) | 200.899 | − | 619.196i | 0.219322 | − | 0.675978i | ||||
\(917\) | −252.141 | − | 436.721i | −0.274963 | − | 0.476250i | ||||
\(918\) | −241.693 | + | 543.161i | −0.263282 | + | 0.591679i | ||||
\(919\) | − | 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 | ||||
\(922\) | 1058.71 | + | 471.098i | 1.14827 | + | 0.510952i | ||||
\(923\) | − | 513.099i | − | 0.555904i | ||||||
\(924\) | 15.5202 | + | 72.8650i | 0.0167967 | + | 0.0788582i | ||||
\(925\) | −51.0042 | + | 88.3419i | −0.0551397 | + | 0.0955048i | ||||
\(926\) | 397.524 | + | 546.902i | 0.429292 | + | 0.590606i | ||||
\(927\) | −667.543 | − | 385.406i | −0.720111 | − | 0.415756i | ||||
\(928\) | −84.4339 | + | 146.602i | −0.0909848 | + | 0.157976i | ||||
\(929\) | −566.361 | − | 980.965i | −0.609645 | − | 1.05594i | −0.991299 | − | 0.131631i | \(-0.957979\pi\) |
0.381653 | − | 0.924306i | \(-0.375355\pi\) | |||||||
\(930\) | 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 | ||||
\(934\) | −349.452 | − | 480.766i | −0.374146 | − | 0.514738i | ||||
\(935\) | 409.637 | + | 236.504i | 0.438114 | + | 0.252945i | ||||
\(936\) | −398.334 | + | 442.959i | −0.425570 | + | 0.473247i | ||||
\(937\) | 22.4629 | − | 38.9068i | 0.0239732 | − | 0.0415228i | −0.853790 | − | 0.520618i | \(-0.825702\pi\) |
0.877763 | + | 0.479095i | \(0.159035\pi\) | |||||||
\(938\) | −8.78757 | − | 83.4383i | −0.00936842 | − | 0.0889535i | ||||
\(939\) | − | 87.4567i | − | 0.0931382i | ||||||
\(940\) | −1130.92 | − | 366.930i | −1.20311 | − | 0.390351i | ||||
\(941\) | −565.174 | + | 978.911i | −0.600610 | + | 1.04029i | 0.392118 | + | 0.919915i | \(0.371742\pi\) |
−0.992729 | + | 0.120373i | \(0.961591\pi\) | |||||||
\(942\) | −23.2240 | + | 2.44591i | −0.0246539 | + | 0.00259650i | ||||
\(943\) | 585.583i | 0.620978i | ||||||||
\(944\) | −1175.97 | − | 122.593i | −1.24573 | − | 0.129866i | ||||
\(945\) | 70.1264 | + | 121.462i | 0.0742078 | + | 0.128532i | ||||
\(946\) | −708.858 | − | 315.424i | −0.749321 | − | 0.333429i | ||||
\(947\) | −122.275 | + | 70.5956i | −0.129118 | + | 0.0745466i | −0.563168 | − | 0.826342i | \(-0.690418\pi\) |
0.434050 | + | 0.900889i | \(0.357084\pi\) | |||||||
\(948\) | 289.615 | + | 321.377i | 0.305501 | + | 0.339005i | ||||
\(949\) | −518.152 | −0.545998 | ||||||||
\(950\) | 484.771 | + | 130.947i | 0.510285 | + | 0.137838i | ||||
\(951\) | − | 345.485i | − | 0.363286i | ||||||
\(952\) | −257.407 | − | 231.474i | −0.270385 | − | 0.243145i | ||||
\(953\) | −561.043 | − | 971.755i | −0.588712 | − | 1.01968i | −0.994401 | − | 0.105669i | \(-0.966302\pi\) |
0.405689 | − | 0.914011i | \(-0.367032\pi\) | |||||||
\(954\) | 509.803 | + | 226.850i | 0.534385 | + | 0.237788i | ||||
\(955\) | −1069.49 | + | 617.473i | −1.11989 | + | 0.646569i | ||||
\(956\) | 1233.31 | + | 400.149i | 1.29007 | + | 0.418566i | ||||
\(957\) | −40.3766 | −0.0421908 | ||||||||
\(958\) | −624.425 | + | 65.7633i | −0.651800 | + | 0.0686464i | ||||
\(959\) | −299.196 | − | 172.741i | −0.311987 | − | 0.180126i | ||||
\(960\) | −214.886 | + | 22.8613i | −0.223840 | + | 0.0238138i | ||||
\(961\) | 855.874 | 0.890608 | ||||||||
\(962\) | −14.9907 | − | 142.338i | −0.0155829 | − | 0.147960i | ||||
\(963\) | 608.024 | + | 351.043i | 0.631385 | + | 0.364530i | ||||
\(964\) | 620.343 | + | 688.374i | 0.643509 | + | 0.714081i | ||||
\(965\) | 422.937 | − | 732.549i | 0.438277 | − | 0.759118i | ||||
\(966\) | 32.7335 | + | 45.0337i | 0.0338856 | + | 0.0466187i | ||||
\(967\) | −961.049 | + | 554.862i | −0.993845 | + | 0.573797i | −0.906422 | − | 0.422374i | \(-0.861197\pi\) |
−0.0874239 | + | 0.996171i | \(0.527863\pi\) | |||||||
\(968\) | −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 | \(-0.621290\pi\) |
0.617967 | + | 0.786204i | \(0.287957\pi\) | |||||||
\(972\) | −611.138 | + | 550.740i | −0.628743 | + | 0.566605i | ||||
\(973\) | 197.202 | − | 341.564i | 0.202674 | − | 0.351042i | ||||
\(974\) | 111.230 | + | 153.027i | 0.114199 | + | 0.157112i | ||||
\(975\) | 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 | \(0.808281\pi\) | |||||||
\(978\) | 556.292 | + | 247.536i | 0.568806 | + | 0.253104i | ||||
\(979\) | 71.2120 | + | 41.1143i | 0.0727396 | + | 0.0419962i | ||||
\(980\) | 578.233 | − | 123.163i | 0.590034 | − | 0.125677i | ||||
\(981\) | −1503.31 | −1.53242 | ||||||||
\(982\) | 274.182 | − | 616.174i | 0.279208 | − | 0.627469i | ||||
\(983\) | −1506.60 | + | 869.839i | −1.53266 | + | 0.884882i | −0.533422 | + | 0.845849i | \(0.679094\pi\) |
−0.999238 | + | 0.0390327i | \(0.987572\pi\) | |||||||
\(984\) | −82.2980 | + | 388.394i | −0.0836362 | + | 0.394709i | ||||
\(985\) | −119.251 | − | 206.549i | −0.121067 | − | 0.209695i | ||||
\(986\) | 151.763 | − | 110.311i | 0.153918 | − | 0.111877i | ||||
\(987\) | 207.675i | 0.210410i | ||||||||
\(988\) | −658.205 | + | 251.293i | −0.666199 | + | 0.254345i | ||||
\(989\) | −579.804 | −0.586252 | ||||||||
\(990\) | 251.797 | + | 346.415i | 0.254341 | + | 0.349914i | ||||
\(991\) | 259.117 | − | 149.601i | 0.261470 | − | 0.150960i | −0.363535 | − | 0.931581i | \(-0.618430\pi\) |
0.625005 | + | 0.780621i | \(0.285097\pi\) | |||||||
\(992\) | −0.347122 | − | 328.098i | −0.000349921 | − | 0.330744i | ||||
\(993\) | 210.724 | + | 364.985i | 0.212210 | + | 0.367558i | ||||
\(994\) | 246.641 | + | 109.749i | 0.248130 | + | 0.110412i | ||||
\(995\) | − | 474.562i | − | 0.476946i | ||||||
\(996\) | 120.617 | − | 25.6913i | 0.121101 | − | 0.0257944i | ||||
\(997\) | 310.285 | − | 537.429i | 0.311219 | − | 0.539047i | −0.667408 | − | 0.744692i | \(-0.732596\pi\) |
0.978626 | + | 0.205646i | \(0.0659295\pi\) | |||||||
\(998\) | −579.294 | + | 1301.86i | −0.580454 | + | 1.30446i | ||||
\(999\) | − | 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.7.13 | yes | 28 | |
4.3 | odd | 2 | inner | 76.3.g.c.7.3 | ✓ | 28 | |
19.11 | even | 3 | inner | 76.3.g.c.11.3 | yes | 28 | |
76.11 | odd | 6 | inner | 76.3.g.c.11.13 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.c.7.3 | ✓ | 28 | 4.3 | odd | 2 | inner | |
76.3.g.c.7.13 | yes | 28 | 1.1 | even | 1 | trivial | |
76.3.g.c.11.3 | yes | 28 | 19.11 | even | 3 | inner | |
76.3.g.c.11.13 | yes | 28 | 76.11 | odd | 6 | inner |