Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(218,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.r (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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 218.22 | ||
Character | \(\chi\) | \(=\) | 403.218 |
Dual form | 403.2.r.a.342.22 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.720477 | − | 0.415968i | 0.509454 | − | 0.294134i | −0.223155 | − | 0.974783i | \(-0.571636\pi\) |
0.732609 | + | 0.680649i | \(0.238302\pi\) | |||||||
\(3\) | −1.53222 | − | 2.65388i | −0.884627 | − | 1.53222i | −0.846141 | − | 0.532959i | \(-0.821080\pi\) |
−0.0384860 | − | 0.999259i | \(-0.512253\pi\) | |||||||
\(4\) | −0.653942 | + | 1.13266i | −0.326971 | + | 0.566330i | ||||
\(5\) | 1.49771i | 0.669796i | 0.942254 | + | 0.334898i | \(0.108702\pi\) | ||||
−0.942254 | + | 0.334898i | \(0.891298\pi\) | |||||||
\(6\) | −2.20786 | − | 1.27471i | −0.901354 | − | 0.520397i | ||||
\(7\) | 1.75030 | + | 1.01053i | 0.661550 | + | 0.381946i | 0.792867 | − | 0.609394i | \(-0.208587\pi\) |
−0.131317 | + | 0.991340i | \(0.541921\pi\) | |||||||
\(8\) | 2.75195i | 0.972960i | ||||||||
\(9\) | −3.19539 | + | 5.53457i | −1.06513 | + | 1.84486i | ||||
\(10\) | 0.622999 | + | 1.07907i | 0.197010 | + | 0.341231i | ||||
\(11\) | −4.84342 | + | 2.79635i | −1.46035 | + | 0.843131i | −0.999027 | − | 0.0441027i | \(-0.985957\pi\) |
−0.461319 | + | 0.887234i | \(0.652624\pi\) | |||||||
\(12\) | 4.00793 | 1.15699 | ||||||||
\(13\) | −3.59428 | + | 0.284818i | −0.996875 | + | 0.0789943i | ||||
\(14\) | 1.68140 | 0.449373 | ||||||||
\(15\) | 3.97474 | − | 2.29482i | 1.02627 | − | 0.592519i | ||||
\(16\) | −0.163162 | − | 0.282605i | −0.0407905 | − | 0.0706513i | ||||
\(17\) | 0.509189 | − | 0.881941i | 0.123496 | − | 0.213902i | −0.797648 | − | 0.603124i | \(-0.793923\pi\) |
0.921144 | + | 0.389221i | \(0.127256\pi\) | |||||||
\(18\) | 5.31671i | 1.25316i | ||||||||
\(19\) | 5.64316 | + | 3.25808i | 1.29463 | + | 0.747455i | 0.979471 | − | 0.201585i | \(-0.0646091\pi\) |
0.315158 | + | 0.949039i | \(0.397942\pi\) | |||||||
\(20\) | −1.69640 | − | 0.979414i | −0.379326 | − | 0.219004i | ||||
\(21\) | − | 6.19344i | − | 1.35152i | ||||||
\(22\) | −2.32638 | + | 4.02941i | −0.495987 | + | 0.859074i | ||||
\(23\) | 1.35457 | + | 2.34619i | 0.282448 | + | 0.489214i | 0.971987 | − | 0.235034i | \(-0.0755202\pi\) |
−0.689539 | + | 0.724248i | \(0.742187\pi\) | |||||||
\(24\) | 7.30334 | − | 4.21658i | 1.49079 | − | 0.860706i | ||||
\(25\) | 2.75687 | 0.551373 | ||||||||
\(26\) | −2.47113 | + | 1.70031i | −0.484628 | + | 0.333459i | ||||
\(27\) | 10.3908 | 1.99971 | ||||||||
\(28\) | −2.28918 | + | 1.32166i | −0.432615 | + | 0.249770i | ||||
\(29\) | −1.95518 | − | 3.38647i | −0.363068 | − | 0.628852i | 0.625396 | − | 0.780307i | \(-0.284937\pi\) |
−0.988464 | + | 0.151455i | \(0.951604\pi\) | |||||||
\(30\) | 1.90914 | − | 3.30673i | 0.348560 | − | 0.603723i | ||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | −5.00162 | − | 2.88769i | −0.884170 | − | 0.510476i | ||||
\(33\) | 14.8424 | + | 8.56924i | 2.58372 | + | 1.49171i | ||||
\(34\) | − | 0.847225i | − | 0.145298i | ||||||
\(35\) | −1.51349 | + | 2.62143i | −0.255826 | + | 0.443103i | ||||
\(36\) | −4.17919 | − | 7.23857i | −0.696532 | − | 1.20643i | ||||
\(37\) | −9.35653 | + | 5.40200i | −1.53820 | + | 0.888083i | −0.539260 | + | 0.842139i | \(0.681296\pi\) |
−0.998944 | + | 0.0459436i | \(0.985371\pi\) | |||||||
\(38\) | 5.42102 | 0.879406 | ||||||||
\(39\) | 6.26310 | + | 9.10240i | 1.00290 | + | 1.45755i | ||||
\(40\) | −4.12162 | −0.651685 | ||||||||
\(41\) | −1.13050 | + | 0.652697i | −0.176555 | + | 0.101934i | −0.585673 | − | 0.810547i | \(-0.699170\pi\) |
0.409118 | + | 0.912481i | \(0.365836\pi\) | |||||||
\(42\) | −2.57627 | − | 4.46223i | −0.397527 | − | 0.688537i | ||||
\(43\) | −0.725927 | + | 1.25734i | −0.110703 | + | 0.191743i | −0.916054 | − | 0.401055i | \(-0.868644\pi\) |
0.805351 | + | 0.592798i | \(0.201977\pi\) | |||||||
\(44\) | − | 7.31460i | − | 1.10272i | ||||||
\(45\) | −8.28918 | − | 4.78576i | −1.23568 | − | 0.713419i | ||||
\(46\) | 1.95188 | + | 1.12692i | 0.287789 | + | 0.166155i | ||||
\(47\) | 8.81641i | 1.28601i | 0.765864 | + | 0.643003i | \(0.222312\pi\) | ||||
−0.765864 | + | 0.643003i | \(0.777688\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −1.45764 | − | 2.52471i | −0.208235 | − | 0.360673i | ||||
\(50\) | 1.98626 | − | 1.14677i | 0.280900 | − | 0.162177i | ||||
\(51\) | −3.12076 | −0.436993 | ||||||||
\(52\) | 2.02785 | − | 4.25736i | 0.281212 | − | 0.590389i | ||||
\(53\) | −3.69910 | −0.508111 | −0.254056 | − | 0.967190i | \(-0.581765\pi\) | ||||
−0.254056 | + | 0.967190i | \(0.581765\pi\) | |||||||
\(54\) | 7.48635 | − | 4.32225i | 1.01876 | − | 0.588183i | ||||
\(55\) | −4.18812 | − | 7.25404i | −0.564726 | − | 0.978134i | ||||
\(56\) | −2.78093 | + | 4.81672i | −0.371618 | + | 0.643661i | ||||
\(57\) | − | 19.9684i | − | 2.64487i | ||||||
\(58\) | −2.81733 | − | 1.62658i | −0.369933 | − | 0.213581i | ||||
\(59\) | 1.50669 | + | 0.869889i | 0.196155 | + | 0.113250i | 0.594861 | − | 0.803829i | \(-0.297207\pi\) |
−0.398706 | + | 0.917079i | \(0.630541\pi\) | |||||||
\(60\) | 6.00271i | 0.774946i | ||||||||
\(61\) | 5.78061 | − | 10.0123i | 0.740131 | − | 1.28195i | −0.212304 | − | 0.977204i | \(-0.568097\pi\) |
0.952435 | − | 0.304742i | \(-0.0985701\pi\) | |||||||
\(62\) | −0.415968 | − | 0.720477i | −0.0528280 | − | 0.0915007i | ||||
\(63\) | −11.1857 | + | 6.45809i | −1.40927 | + | 0.813643i | ||||
\(64\) | −4.15209 | −0.519011 | ||||||||
\(65\) | −0.426575 | − | 5.38319i | −0.0529101 | − | 0.667703i | ||||
\(66\) | 14.2581 | 1.75505 | ||||||||
\(67\) | 2.51865 | − | 1.45415i | 0.307703 | − | 0.177652i | −0.338195 | − | 0.941076i | \(-0.609816\pi\) |
0.645898 | + | 0.763424i | \(0.276483\pi\) | |||||||
\(68\) | 0.665960 | + | 1.15348i | 0.0807595 | + | 0.139880i | ||||
\(69\) | 4.15100 | − | 7.18975i | 0.499722 | − | 0.865544i | ||||
\(70\) | 2.51825i | 0.300988i | ||||||||
\(71\) | −3.05994 | − | 1.76666i | −0.363149 | − | 0.209664i | 0.307313 | − | 0.951609i | \(-0.400570\pi\) |
−0.670461 | + | 0.741945i | \(0.733904\pi\) | |||||||
\(72\) | −15.2308 | − | 8.79353i | −1.79497 | − | 1.03633i | ||||
\(73\) | 11.6544i | 1.36404i | 0.731333 | + | 0.682021i | \(0.238899\pi\) | ||||
−0.731333 | + | 0.682021i | \(0.761101\pi\) | |||||||
\(74\) | −4.49411 | + | 7.78403i | −0.522430 | + | 0.904875i | ||||
\(75\) | −4.22412 | − | 7.31639i | −0.487760 | − | 0.844824i | ||||
\(76\) | −7.38059 | + | 4.26119i | −0.846612 | + | 0.488792i | ||||
\(77\) | −11.3032 | −1.28812 | ||||||||
\(78\) | 8.29873 | + | 3.95282i | 0.939646 | + | 0.447569i | ||||
\(79\) | 14.5978 | 1.64238 | 0.821188 | − | 0.570658i | \(-0.193312\pi\) | ||||
0.821188 | + | 0.570658i | \(0.193312\pi\) | |||||||
\(80\) | 0.423260 | − | 0.244369i | 0.0473219 | − | 0.0273213i | ||||
\(81\) | −6.33484 | − | 10.9723i | −0.703871 | − | 1.21914i | ||||
\(82\) | −0.543002 | + | 0.940507i | −0.0599645 | + | 0.103862i | ||||
\(83\) | 15.3384i | 1.68361i | 0.539779 | + | 0.841807i | \(0.318508\pi\) | ||||
−0.539779 | + | 0.841807i | \(0.681492\pi\) | |||||||
\(84\) | 7.01506 | + | 4.05014i | 0.765405 | + | 0.441907i | ||||
\(85\) | 1.32089 | + | 0.762617i | 0.143271 | + | 0.0827174i | ||||
\(86\) | 1.20785i | 0.130246i | ||||||||
\(87\) | −5.99153 | + | 10.3776i | −0.642359 | + | 1.11260i | ||||
\(88\) | −7.69541 | − | 13.3288i | −0.820333 | − | 1.42086i | ||||
\(89\) | 0.250158 | − | 0.144429i | 0.0265166 | − | 0.0153094i | −0.486683 | − | 0.873579i | \(-0.661793\pi\) |
0.513200 | + | 0.858269i | \(0.328460\pi\) | |||||||
\(90\) | −7.96289 | −0.839362 | ||||||||
\(91\) | −6.57888 | − | 3.13363i | −0.689654 | − | 0.328494i | ||||
\(92\) | −3.54325 | −0.369409 | ||||||||
\(93\) | −2.65388 | + | 1.53222i | −0.275195 | + | 0.158884i | ||||
\(94\) | 3.66734 | + | 6.35203i | 0.378258 | + | 0.655162i | ||||
\(95\) | −4.87966 | + | 8.45181i | −0.500642 | + | 0.867138i | ||||
\(96\) | 17.6983i | 1.80632i | ||||||||
\(97\) | −9.34768 | − | 5.39688i | −0.949113 | − | 0.547971i | −0.0563077 | − | 0.998413i | \(-0.517933\pi\) |
−0.892805 | + | 0.450443i | \(0.851266\pi\) | |||||||
\(98\) | −2.10040 | − | 1.21266i | −0.212172 | − | 0.122498i | ||||
\(99\) | − | 35.7417i | − | 3.59218i | ||||||
\(100\) | −1.80283 | + | 3.12259i | −0.180283 | + | 0.312259i | ||||
\(101\) | −3.39785 | − | 5.88524i | −0.338098 | − | 0.585604i | 0.645977 | − | 0.763357i | \(-0.276450\pi\) |
−0.984075 | + | 0.177754i | \(0.943117\pi\) | |||||||
\(102\) | −2.24843 | + | 1.29813i | −0.222628 | + | 0.128534i | ||||
\(103\) | 3.57498 | 0.352253 | 0.176126 | − | 0.984368i | \(-0.443643\pi\) | ||||
0.176126 | + | 0.984368i | \(0.443643\pi\) | |||||||
\(104\) | −0.783804 | − | 9.89128i | −0.0768583 | − | 0.969919i | ||||
\(105\) | 9.27597 | 0.905242 | ||||||||
\(106\) | −2.66512 | + | 1.53871i | −0.258859 | + | 0.149453i | ||||
\(107\) | 7.86970 | + | 13.6307i | 0.760793 | + | 1.31773i | 0.942442 | + | 0.334369i | \(0.108523\pi\) |
−0.181649 | + | 0.983363i | \(0.558144\pi\) | |||||||
\(108\) | −6.79499 | + | 11.7693i | −0.653848 | + | 1.13250i | ||||
\(109\) | 4.63222i | 0.443687i | 0.975082 | + | 0.221843i | \(0.0712074\pi\) | ||||
−0.975082 | + | 0.221843i | \(0.928793\pi\) | |||||||
\(110\) | −6.03489 | − | 3.48425i | −0.575404 | − | 0.332210i | ||||
\(111\) | 28.6725 | + | 16.5541i | 2.72147 | + | 1.57124i | ||||
\(112\) | − | 0.659523i | − | 0.0623191i | ||||||
\(113\) | 6.68385 | − | 11.5768i | 0.628764 | − | 1.08905i | −0.359036 | − | 0.933324i | \(-0.616895\pi\) |
0.987800 | − | 0.155727i | \(-0.0497721\pi\) | |||||||
\(114\) | −8.30619 | − | 14.3868i | −0.777946 | − | 1.34744i | ||||
\(115\) | −3.51391 | + | 2.02876i | −0.327674 | + | 0.189183i | ||||
\(116\) | 5.11429 | 0.474850 | ||||||||
\(117\) | 9.90878 | − | 20.8029i | 0.916067 | − | 1.92323i | ||||
\(118\) | 1.44738 | 0.133242 | ||||||||
\(119\) | 1.78246 | − | 1.02911i | 0.163398 | − | 0.0943380i | ||||
\(120\) | 6.31522 | + | 10.9383i | 0.576498 | + | 0.998523i | ||||
\(121\) | 10.1392 | − | 17.5615i | 0.921741 | − | 1.59650i | ||||
\(122\) | − | 9.61819i | − | 0.870790i | ||||||
\(123\) | 3.46436 | + | 2.00015i | 0.312371 | + | 0.180347i | ||||
\(124\) | 1.13266 | + | 0.653942i | 0.101716 | + | 0.0587257i | ||||
\(125\) | 11.6175i | 1.03910i | ||||||||
\(126\) | −5.37272 | + | 9.30582i | −0.478640 | + | 0.829029i | ||||
\(127\) | 0.237217 | + | 0.410872i | 0.0210496 | + | 0.0364590i | 0.876358 | − | 0.481660i | \(-0.159966\pi\) |
−0.855309 | + | 0.518119i | \(0.826633\pi\) | |||||||
\(128\) | 7.01175 | − | 4.04824i | 0.619757 | − | 0.357817i | ||||
\(129\) | 4.44912 | 0.391723 | ||||||||
\(130\) | −2.54657 | − | 3.70103i | −0.223349 | − | 0.324602i | ||||
\(131\) | −8.54543 | −0.746618 | −0.373309 | − | 0.927707i | \(-0.621777\pi\) | ||||
−0.373309 | + | 0.927707i | \(0.621777\pi\) | |||||||
\(132\) | −19.4121 | + | 11.2076i | −1.68960 | + | 0.975493i | ||||
\(133\) | 6.58480 | + | 11.4052i | 0.570974 | + | 0.988957i | ||||
\(134\) | 1.20976 | − | 2.09536i | 0.104507 | − | 0.181011i | ||||
\(135\) | 15.5624i | 1.33940i | ||||||||
\(136\) | 2.42705 | + | 1.40126i | 0.208118 | + | 0.120157i | ||||
\(137\) | 3.86960 | + | 2.23411i | 0.330602 | + | 0.190873i | 0.656108 | − | 0.754667i | \(-0.272201\pi\) |
−0.325506 | + | 0.945540i | \(0.605535\pi\) | |||||||
\(138\) | − | 6.90674i | − | 0.587940i | ||||||
\(139\) | 6.64590 | − | 11.5110i | 0.563698 | − | 0.976354i | −0.433471 | − | 0.901167i | \(-0.642712\pi\) |
0.997170 | − | 0.0751863i | \(-0.0239552\pi\) | |||||||
\(140\) | −1.97946 | − | 3.42853i | −0.167295 | − | 0.289764i | ||||
\(141\) | 23.3977 | − | 13.5087i | 1.97044 | − | 1.13764i | ||||
\(142\) | −2.93949 | −0.246677 | ||||||||
\(143\) | 16.6122 | − | 11.4304i | 1.38918 | − | 0.955856i | ||||
\(144\) | 2.08546 | 0.173789 | ||||||||
\(145\) | 5.07195 | − | 2.92829i | 0.421203 | − | 0.243181i | ||||
\(146\) | 4.84785 | + | 8.39672i | 0.401211 | + | 0.694917i | ||||
\(147\) | −4.46685 | + | 7.73682i | −0.368420 | + | 0.638122i | ||||
\(148\) | − | 14.1304i | − | 1.16151i | ||||||
\(149\) | −3.64875 | − | 2.10661i | −0.298918 | − | 0.172580i | 0.343039 | − | 0.939321i | \(-0.388544\pi\) |
−0.641956 | + | 0.766741i | \(0.721877\pi\) | |||||||
\(150\) | −6.08677 | − | 3.51420i | −0.496983 | − | 0.286933i | ||||
\(151\) | − | 5.35318i | − | 0.435635i | −0.975989 | − | 0.217818i | \(-0.930106\pi\) | ||
0.975989 | − | 0.217818i | \(-0.0698938\pi\) | |||||||
\(152\) | −8.96606 | + | 15.5297i | −0.727243 | + | 1.25962i | ||||
\(153\) | 3.25411 | + | 5.63629i | 0.263079 | + | 0.455667i | ||||
\(154\) | −8.14372 | + | 4.70178i | −0.656240 | + | 0.378880i | ||||
\(155\) | 1.49771 | 0.120299 | ||||||||
\(156\) | −14.4056 | + | 1.14153i | −1.15337 | + | 0.0913955i | ||||
\(157\) | 22.7079 | 1.81229 | 0.906145 | − | 0.422968i | \(-0.139012\pi\) | ||||
0.906145 | + | 0.422968i | \(0.139012\pi\) | |||||||
\(158\) | 10.5174 | − | 6.07220i | 0.836716 | − | 0.483078i | ||||
\(159\) | 5.66784 | + | 9.81698i | 0.449489 | + | 0.778537i | ||||
\(160\) | 4.32491 | − | 7.49097i | 0.341915 | − | 0.592213i | ||||
\(161\) | 5.47537i | 0.431519i | ||||||||
\(162\) | −9.12822 | − | 5.27018i | −0.717180 | − | 0.414064i | ||||
\(163\) | 0.665811 | + | 0.384406i | 0.0521503 | + | 0.0301090i | 0.525848 | − | 0.850578i | \(-0.323748\pi\) |
−0.473698 | + | 0.880687i | \(0.657081\pi\) | |||||||
\(164\) | − | 1.70730i | − | 0.133318i | ||||||
\(165\) | −12.8342 | + | 22.2295i | −0.999144 | + | 1.73057i | ||||
\(166\) | 6.38030 | + | 11.0510i | 0.495207 | + | 0.857724i | ||||
\(167\) | 5.93541 | − | 3.42681i | 0.459296 | − | 0.265175i | −0.252452 | − | 0.967609i | \(-0.581237\pi\) |
0.711748 | + | 0.702435i | \(0.247904\pi\) | |||||||
\(168\) | 17.0440 | 1.31497 | ||||||||
\(169\) | 12.8378 | − | 2.04743i | 0.987520 | − | 0.157495i | ||||
\(170\) | 1.26890 | 0.0973200 | ||||||||
\(171\) | −36.0642 | + | 20.8216i | −2.75789 | + | 1.59227i | ||||
\(172\) | −0.949428 | − | 1.64446i | −0.0723932 | − | 0.125389i | ||||
\(173\) | 1.76070 | − | 3.04963i | 0.133864 | − | 0.231859i | −0.791299 | − | 0.611429i | \(-0.790595\pi\) |
0.925163 | + | 0.379571i | \(0.123928\pi\) | |||||||
\(174\) | 9.96913i | 0.755758i | ||||||||
\(175\) | 4.82533 | + | 2.78591i | 0.364761 | + | 0.210595i | ||||
\(176\) | 1.58053 | + | 0.912517i | 0.119137 | + | 0.0687835i | ||||
\(177\) | − | 5.33144i | − | 0.400736i | ||||||
\(178\) | 0.120155 | − | 0.208115i | 0.00900602 | − | 0.0155989i | ||||
\(179\) | −11.0673 | − | 19.1691i | −0.827208 | − | 1.43277i | −0.900220 | − | 0.435436i | \(-0.856594\pi\) |
0.0730116 | − | 0.997331i | \(-0.476739\pi\) | |||||||
\(180\) | 10.8413 | − | 6.25922i | 0.808061 | − | 0.466534i | ||||
\(181\) | 4.41482 | 0.328151 | 0.164075 | − | 0.986448i | \(-0.447536\pi\) | ||||
0.164075 | + | 0.986448i | \(0.447536\pi\) | |||||||
\(182\) | −6.04342 | + | 0.478893i | −0.447968 | + | 0.0354979i | ||||
\(183\) | −35.4286 | −2.61896 | ||||||||
\(184\) | −6.45659 | + | 3.72771i | −0.475986 | + | 0.274811i | ||||
\(185\) | −8.09062 | − | 14.0134i | −0.594834 | − | 1.03028i | ||||
\(186\) | −1.27471 | + | 2.20786i | −0.0934661 | + | 0.161888i | ||||
\(187\) | 5.69548i | 0.416495i | ||||||||
\(188\) | −9.98600 | − | 5.76542i | −0.728304 | − | 0.420486i | ||||
\(189\) | 18.1870 | + | 10.5003i | 1.32291 | + | 0.763782i | ||||
\(190\) | 8.11912i | 0.589023i | ||||||||
\(191\) | 4.36959 | − | 7.56835i | 0.316172 | − | 0.547627i | −0.663514 | − | 0.748164i | \(-0.730936\pi\) |
0.979686 | + | 0.200538i | \(0.0642689\pi\) | |||||||
\(192\) | 6.36191 | + | 11.0192i | 0.459131 | + | 0.795239i | ||||
\(193\) | −12.7744 | + | 7.37532i | −0.919524 | + | 0.530887i | −0.883483 | − | 0.468463i | \(-0.844808\pi\) |
−0.0360409 | + | 0.999350i | \(0.511475\pi\) | |||||||
\(194\) | −8.97972 | −0.644706 | ||||||||
\(195\) | −13.6327 | + | 9.38031i | −0.976261 | + | 0.671738i | ||||
\(196\) | 3.81285 | 0.272347 | ||||||||
\(197\) | −1.73925 | + | 1.00416i | −0.123916 | + | 0.0715431i | −0.560677 | − | 0.828035i | \(-0.689459\pi\) |
0.436761 | + | 0.899578i | \(0.356126\pi\) | |||||||
\(198\) | −14.8674 | − | 25.7511i | −1.05658 | − | 1.83005i | ||||
\(199\) | −7.14092 | + | 12.3684i | −0.506206 | + | 0.876775i | 0.493768 | + | 0.869594i | \(0.335619\pi\) |
−0.999974 | + | 0.00718137i | \(0.997714\pi\) | |||||||
\(200\) | 7.58675i | 0.536464i | ||||||||
\(201\) | −7.71826 | − | 4.45614i | −0.544404 | − | 0.314312i | ||||
\(202\) | −4.89614 | − | 2.82679i | −0.344492 | − | 0.198892i | ||||
\(203\) | − | 7.90310i | − | 0.554689i | ||||||
\(204\) | 2.04079 | − | 3.53475i | 0.142884 | − | 0.247482i | ||||
\(205\) | −0.977551 | − | 1.69317i | −0.0682751 | − | 0.118256i | ||||
\(206\) | 2.57569 | − | 1.48708i | 0.179457 | − | 0.103609i | ||||
\(207\) | −17.3135 | −1.20337 | ||||||||
\(208\) | 0.666942 | + | 0.969291i | 0.0462441 | + | 0.0672083i | ||||
\(209\) | −36.4429 | −2.52081 | ||||||||
\(210\) | 6.68312 | − | 3.85850i | 0.461179 | − | 0.266262i | ||||
\(211\) | −1.88634 | − | 3.26723i | −0.129861 | − | 0.224926i | 0.793762 | − | 0.608229i | \(-0.208120\pi\) |
−0.923623 | + | 0.383303i | \(0.874786\pi\) | |||||||
\(212\) | 2.41900 | − | 4.18983i | 0.166137 | − | 0.287758i | ||||
\(213\) | 10.8276i | 0.741897i | ||||||||
\(214\) | 11.3399 | + | 6.54709i | 0.775179 | + | 0.447550i | ||||
\(215\) | −1.88313 | − | 1.08723i | −0.128429 | − | 0.0741483i | ||||
\(216\) | 28.5950i | 1.94564i | ||||||||
\(217\) | 1.01053 | − | 1.75030i | 0.0685995 | − | 0.118818i | ||||
\(218\) | 1.92686 | + | 3.33741i | 0.130503 | + | 0.226038i | ||||
\(219\) | 30.9293 | − | 17.8571i | 2.09001 | − | 1.20667i | ||||
\(220\) | 10.9551 | 0.738596 | ||||||||
\(221\) | −1.57898 | + | 3.31497i | −0.106214 | + | 0.222989i | ||||
\(222\) | 27.5439 | 1.84862 | ||||||||
\(223\) | 24.6060 | − | 14.2063i | 1.64774 | − | 0.951324i | 0.669775 | − | 0.742564i | \(-0.266391\pi\) |
0.977967 | − | 0.208760i | \(-0.0669428\pi\) | |||||||
\(224\) | −5.83621 | − | 10.1086i | −0.389948 | − | 0.675410i | ||||
\(225\) | −8.80926 | + | 15.2581i | −0.587284 | + | 1.01721i | ||||
\(226\) | − | 11.1211i | − | 0.739762i | ||||||
\(227\) | −10.7151 | − | 6.18635i | −0.711185 | − | 0.410603i | 0.100315 | − | 0.994956i | \(-0.468015\pi\) |
−0.811500 | + | 0.584353i | \(0.801348\pi\) | |||||||
\(228\) | 22.6174 | + | 13.0581i | 1.49787 | + | 0.864796i | ||||
\(229\) | 26.4190i | 1.74582i | 0.487883 | + | 0.872909i | \(0.337769\pi\) | ||||
−0.487883 | + | 0.872909i | \(0.662231\pi\) | |||||||
\(230\) | −1.68779 | + | 2.92335i | −0.111290 | + | 0.192760i | ||||
\(231\) | 17.3190 | + | 29.9974i | 1.13951 | + | 1.97369i | ||||
\(232\) | 9.31939 | − | 5.38055i | 0.611848 | − | 0.353250i | ||||
\(233\) | −17.2631 | −1.13094 | −0.565472 | − | 0.824768i | \(-0.691306\pi\) | ||||
−0.565472 | + | 0.824768i | \(0.691306\pi\) | |||||||
\(234\) | −1.51430 | − | 19.1098i | −0.0989926 | − | 1.24925i | ||||
\(235\) | −13.2044 | −0.861362 | ||||||||
\(236\) | −1.97058 | + | 1.13771i | −0.128274 | + | 0.0740588i | ||||
\(237\) | −22.3670 | − | 38.7407i | −1.45289 | − | 2.51648i | ||||
\(238\) | 0.856150 | − | 1.48289i | 0.0554959 | − | 0.0961218i | ||||
\(239\) | 19.6451i | 1.27074i | 0.772210 | + | 0.635368i | \(0.219151\pi\) | ||||
−0.772210 | + | 0.635368i | \(0.780849\pi\) | |||||||
\(240\) | −1.29705 | − | 0.748855i | −0.0837245 | − | 0.0483384i | ||||
\(241\) | 16.0493 | + | 9.26606i | 1.03383 | + | 0.596879i | 0.918078 | − | 0.396400i | \(-0.129740\pi\) |
0.115747 | + | 0.993279i | \(0.463074\pi\) | |||||||
\(242\) | − | 16.8702i | − | 1.08446i | ||||||
\(243\) | −3.82649 | + | 6.62768i | −0.245469 | + | 0.425166i | ||||
\(244\) | 7.56036 | + | 13.0949i | 0.484003 | + | 0.838317i | ||||
\(245\) | 3.78128 | − | 2.18312i | 0.241577 | − | 0.139475i | ||||
\(246\) | 3.32799 | 0.212185 | ||||||||
\(247\) | −21.2111 | − | 10.1032i | −1.34963 | − | 0.642850i | ||||
\(248\) | 2.75195 | 0.174749 | ||||||||
\(249\) | 40.7064 | − | 23.5019i | 2.57966 | − | 1.48937i | ||||
\(250\) | 4.83252 | + | 8.37017i | 0.305635 | + | 0.529376i | ||||
\(251\) | −8.11034 | + | 14.0475i | −0.511920 | + | 0.886671i | 0.487985 | + | 0.872852i | \(0.337732\pi\) |
−0.999905 | + | 0.0138191i | \(0.995601\pi\) | |||||||
\(252\) | − | 16.8929i | − | 1.06415i | ||||||
\(253\) | −13.1215 | − | 7.57572i | −0.824944 | − | 0.476282i | ||||
\(254\) | 0.341819 | + | 0.197350i | 0.0214477 | + | 0.0123828i | ||||
\(255\) | − | 4.67398i | − | 0.292696i | ||||||
\(256\) | 7.51996 | − | 13.0250i | 0.469998 | − | 0.814060i | ||||
\(257\) | 0.918472 | + | 1.59084i | 0.0572927 | + | 0.0992339i | 0.893249 | − | 0.449562i | \(-0.148420\pi\) |
−0.835957 | + | 0.548796i | \(0.815087\pi\) | |||||||
\(258\) | 3.20549 | − | 1.85069i | 0.199565 | − | 0.115219i | ||||
\(259\) | −21.8356 | −1.35680 | ||||||||
\(260\) | 6.37628 | + | 3.03713i | 0.395440 | + | 0.188355i | ||||
\(261\) | 24.9902 | 1.54686 | ||||||||
\(262\) | −6.15679 | + | 3.55463i | −0.380368 | + | 0.219605i | ||||
\(263\) | 15.4862 | + | 26.8228i | 0.954918 | + | 1.65397i | 0.734556 | + | 0.678548i | \(0.237390\pi\) |
0.220362 | + | 0.975418i | \(0.429276\pi\) | |||||||
\(264\) | −23.5821 | + | 40.8454i | −1.45138 | + | 2.51386i | ||||
\(265\) | − | 5.54018i | − | 0.340331i | ||||||
\(266\) | 9.48840 | + | 5.47813i | 0.581771 | + | 0.335886i | ||||
\(267\) | −0.766592 | − | 0.442592i | −0.0469147 | − | 0.0270862i | ||||
\(268\) | 3.80371i | 0.232348i | ||||||||
\(269\) | −10.4643 | + | 18.1247i | −0.638021 | + | 1.10509i | 0.347845 | + | 0.937552i | \(0.386914\pi\) |
−0.985866 | + | 0.167533i | \(0.946420\pi\) | |||||||
\(270\) | 6.47347 | + | 11.2124i | 0.393963 | + | 0.682363i | ||||
\(271\) | 18.0501 | − | 10.4212i | 1.09646 | − | 0.633044i | 0.161174 | − | 0.986926i | \(-0.448472\pi\) |
0.935290 | + | 0.353882i | \(0.115138\pi\) | |||||||
\(272\) | −0.332321 | −0.0201499 | ||||||||
\(273\) | 1.76400 | + | 22.2610i | 0.106762 | + | 1.34729i | ||||
\(274\) | 3.71728 | 0.224569 | ||||||||
\(275\) | −13.3527 | + | 7.70917i | −0.805196 | + | 0.464880i | ||||
\(276\) | 5.42903 | + | 9.40335i | 0.326789 | + | 0.566015i | ||||
\(277\) | 6.49340 | − | 11.2469i | 0.390151 | − | 0.675761i | −0.602318 | − | 0.798256i | \(-0.705756\pi\) |
0.992469 | + | 0.122495i | \(0.0390896\pi\) | |||||||
\(278\) | − | 11.0579i | − | 0.663210i | ||||||
\(279\) | 5.53457 | + | 3.19539i | 0.331346 | + | 0.191303i | ||||
\(280\) | −7.21405 | − | 4.16503i | −0.431122 | − | 0.248908i | ||||
\(281\) | − | 5.18043i | − | 0.309038i | −0.987990 | − | 0.154519i | \(-0.950617\pi\) | ||
0.987990 | − | 0.154519i | \(-0.0493828\pi\) | |||||||
\(282\) | 11.2383 | − | 19.4654i | 0.669234 | − | 1.15915i | ||||
\(283\) | 14.1912 | + | 24.5798i | 0.843577 | + | 1.46112i | 0.886851 | + | 0.462055i | \(0.152888\pi\) |
−0.0432745 | + | 0.999063i | \(0.513779\pi\) | |||||||
\(284\) | 4.00205 | − | 2.31058i | 0.237478 | − | 0.137108i | ||||
\(285\) | 29.9068 | 1.77153 | ||||||||
\(286\) | 7.21403 | − | 15.1455i | 0.426575 | − | 0.895570i | ||||
\(287\) | −2.63829 | −0.155733 | ||||||||
\(288\) | 31.9642 | − | 18.4546i | 1.88351 | − | 1.08744i | ||||
\(289\) | 7.98145 | + | 13.8243i | 0.469497 | + | 0.813193i | ||||
\(290\) | 2.43615 | − | 4.21954i | 0.143056 | − | 0.247780i | ||||
\(291\) | 33.0768i | 1.93900i | ||||||||
\(292\) | −13.2004 | − | 7.62128i | −0.772498 | − | 0.446002i | ||||
\(293\) | −9.48668 | − | 5.47714i | −0.554218 | − | 0.319978i | 0.196604 | − | 0.980483i | \(-0.437009\pi\) |
−0.750821 | + | 0.660505i | \(0.770342\pi\) | |||||||
\(294\) | 7.43227i | 0.433459i | ||||||||
\(295\) | −1.30284 | + | 2.25659i | −0.0758543 | + | 0.131384i | ||||
\(296\) | −14.8660 | − | 25.7487i | −0.864069 | − | 1.49661i | ||||
\(297\) | −50.3271 | + | 29.0564i | −2.92027 | + | 1.68602i | ||||
\(298\) | −3.50513 | −0.203046 | ||||||||
\(299\) | −5.53696 | − | 8.04706i | −0.320210 | − | 0.465374i | ||||
\(300\) | 11.0493 | 0.637933 | ||||||||
\(301\) | −2.54118 | + | 1.46715i | −0.146471 | + | 0.0845650i | ||||
\(302\) | −2.22675 | − | 3.85684i | −0.128135 | − | 0.221936i | ||||
\(303\) | −10.4125 | + | 18.0350i | −0.598182 | + | 1.03608i | ||||
\(304\) | − | 2.12638i | − | 0.121956i | ||||||
\(305\) | 14.9955 | + | 8.65768i | 0.858642 | + | 0.495737i | ||||
\(306\) | 4.68903 | + | 2.70721i | 0.268054 | + | 0.154761i | ||||
\(307\) | − | 20.4028i | − | 1.16445i | −0.813028 | − | 0.582224i | \(-0.802183\pi\) | ||
0.813028 | − | 0.582224i | \(-0.197817\pi\) | |||||||
\(308\) | 7.39165 | − | 12.8027i | 0.421178 | − | 0.729502i | ||||
\(309\) | −5.47765 | − | 9.48756i | −0.311612 | − | 0.539728i | ||||
\(310\) | 1.07907 | − | 0.622999i | 0.0612868 | − | 0.0353840i | ||||
\(311\) | 9.75439 | 0.553121 | 0.276560 | − | 0.960997i | \(-0.410805\pi\) | ||||
0.276560 | + | 0.960997i | \(0.410805\pi\) | |||||||
\(312\) | −25.0493 | + | 17.2357i | −1.41814 | + | 0.975780i | ||||
\(313\) | −17.9950 | −1.01714 | −0.508568 | − | 0.861022i | \(-0.669825\pi\) | ||||
−0.508568 | + | 0.861022i | \(0.669825\pi\) | |||||||
\(314\) | 16.3605 | − | 9.44576i | 0.923279 | − | 0.533055i | ||||
\(315\) | −9.67235 | − | 16.7530i | −0.544975 | − | 0.943925i | ||||
\(316\) | −9.54608 | + | 16.5343i | −0.537009 | + | 0.930127i | ||||
\(317\) | − | 22.7973i | − | 1.28043i | −0.768198 | − | 0.640213i | \(-0.778846\pi\) | ||
0.768198 | − | 0.640213i | \(-0.221154\pi\) | |||||||
\(318\) | 8.16710 | + | 4.71527i | 0.457988 | + | 0.264419i | ||||
\(319\) | 18.9395 | + | 10.9347i | 1.06041 | + | 0.612228i | ||||
\(320\) | − | 6.21862i | − | 0.347632i | ||||||
\(321\) | 24.1162 | − | 41.7705i | 1.34604 | − | 2.33140i | ||||
\(322\) | 2.27758 | + | 3.94488i | 0.126924 | + | 0.219839i | ||||
\(323\) | 5.74687 | − | 3.31796i | 0.319764 | − | 0.184616i | ||||
\(324\) | 16.5705 | 0.920581 | ||||||||
\(325\) | −9.90896 | + | 0.785206i | −0.549650 | + | 0.0435554i | ||||
\(326\) | 0.639602 | 0.0354243 | ||||||||
\(327\) | 12.2934 | − | 7.09758i | 0.679825 | − | 0.392497i | ||||
\(328\) | −1.79619 | − | 3.11109i | −0.0991778 | − | 0.171781i | ||||
\(329\) | −8.90929 | + | 15.4313i | −0.491185 | + | 0.850757i | ||||
\(330\) | 21.3545i | 1.17553i | ||||||||
\(331\) | −1.52038 | − | 0.877792i | −0.0835677 | − | 0.0482478i | 0.457634 | − | 0.889141i | \(-0.348697\pi\) |
−0.541202 | + | 0.840893i | \(0.682030\pi\) | |||||||
\(332\) | −17.3732 | − | 10.0304i | −0.953481 | − | 0.550492i | ||||
\(333\) | − | 69.0459i | − | 3.78369i | ||||||
\(334\) | 2.85089 | − | 4.93788i | 0.155994 | − | 0.270189i | ||||
\(335\) | 2.17789 | + | 3.77221i | 0.118991 | + | 0.206098i | ||||
\(336\) | −1.75030 | + | 1.01053i | −0.0954865 | + | 0.0551291i | ||||
\(337\) | 9.12206 | 0.496910 | 0.248455 | − | 0.968643i | \(-0.420077\pi\) | ||||
0.248455 | + | 0.968643i | \(0.420077\pi\) | |||||||
\(338\) | 8.39765 | − | 6.81522i | 0.456772 | − | 0.370699i | ||||
\(339\) | −40.9645 | −2.22489 | ||||||||
\(340\) | −1.72757 | + | 0.997414i | −0.0936907 | + | 0.0540924i | ||||
\(341\) | 2.79635 | + | 4.84342i | 0.151431 | + | 0.262286i | ||||
\(342\) | −17.3223 | + | 30.0031i | −0.936681 | + | 1.62238i | ||||
\(343\) | − | 20.0395i | − | 1.08203i | ||||||
\(344\) | −3.46014 | − | 1.99771i | −0.186558 | − | 0.107709i | ||||
\(345\) | 10.7682 | + | 6.21700i | 0.579738 | + | 0.334712i | ||||
\(346\) | − | 2.92958i | − | 0.157495i | ||||||
\(347\) | −15.7978 | + | 27.3626i | −0.848071 | + | 1.46890i | 0.0348570 | + | 0.999392i | \(0.488902\pi\) |
−0.882928 | + | 0.469509i | \(0.844431\pi\) | |||||||
\(348\) | −7.83622 | − | 13.5727i | −0.420065 | − | 0.727574i | ||||
\(349\) | −3.47285 | + | 2.00505i | −0.185898 | + | 0.107328i | −0.590061 | − | 0.807359i | \(-0.700896\pi\) |
0.404163 | + | 0.914687i | \(0.367563\pi\) | |||||||
\(350\) | 4.63539 | 0.247772 | ||||||||
\(351\) | −37.3475 | + | 2.95949i | −1.99346 | + | 0.157966i | ||||
\(352\) | 32.2999 | 1.72159 | ||||||||
\(353\) | −6.23031 | + | 3.59707i | −0.331606 | + | 0.191453i | −0.656554 | − | 0.754279i | \(-0.727987\pi\) |
0.324948 | + | 0.945732i | \(0.394653\pi\) | |||||||
\(354\) | −2.21771 | − | 3.84118i | −0.117870 | − | 0.204157i | ||||
\(355\) | 2.64594 | − | 4.58291i | 0.140432 | − | 0.243235i | ||||
\(356\) | 0.377791i | 0.0200229i | ||||||||
\(357\) | −5.46225 | − | 3.15363i | −0.289093 | − | 0.166908i | ||||
\(358\) | −15.9475 | − | 9.20728i | −0.842850 | − | 0.486620i | ||||
\(359\) | − | 11.3596i | − | 0.599539i | −0.954012 | − | 0.299769i | \(-0.903090\pi\) | ||
0.954012 | − | 0.299769i | \(-0.0969098\pi\) | |||||||
\(360\) | 13.1702 | − | 22.8114i | 0.694128 | − | 1.20227i | ||||
\(361\) | 11.7302 | + | 20.3172i | 0.617377 | + | 1.06933i | ||||
\(362\) | 3.18078 | − | 1.83642i | 0.167178 | − | 0.0965202i | ||||
\(363\) | −62.1416 | −3.26159 | ||||||||
\(364\) | 7.85154 | − | 5.40242i | 0.411533 | − | 0.283164i | ||||
\(365\) | −17.4549 | −0.913630 | ||||||||
\(366\) | −25.5255 | + | 14.7372i | −1.33424 | + | 0.770324i | ||||
\(367\) | 5.00983 | + | 8.67728i | 0.261511 | + | 0.452950i | 0.966644 | − | 0.256125i | \(-0.0824459\pi\) |
−0.705133 | + | 0.709075i | \(0.749113\pi\) | |||||||
\(368\) | 0.442030 | − | 0.765618i | 0.0230424 | − | 0.0399106i | ||||
\(369\) | − | 8.34248i | − | 0.434292i | ||||||
\(370\) | −11.6582 | − | 6.73088i | −0.606082 | − | 0.349922i | ||||
\(371\) | −6.47453 | − | 3.73807i | −0.336141 | − | 0.194071i | ||||
\(372\) | − | 4.00793i | − | 0.207801i | ||||||
\(373\) | −9.00207 | + | 15.5920i | −0.466109 | + | 0.807325i | −0.999251 | − | 0.0387009i | \(-0.987678\pi\) |
0.533141 | + | 0.846026i | \(0.321011\pi\) | |||||||
\(374\) | 2.36914 | + | 4.10347i | 0.122505 | + | 0.212185i | ||||
\(375\) | 30.8315 | − | 17.8006i | 1.59213 | − | 0.919219i | ||||
\(376\) | −24.2623 | −1.25123 | ||||||||
\(377\) | 7.99200 | + | 11.6151i | 0.411609 | + | 0.598207i | ||||
\(378\) | 17.4711 | 0.898616 | ||||||||
\(379\) | −5.56688 | + | 3.21404i | −0.285952 | + | 0.165094i | −0.636115 | − | 0.771594i | \(-0.719460\pi\) |
0.350163 | + | 0.936689i | \(0.386126\pi\) | |||||||
\(380\) | −6.38202 | − | 11.0540i | −0.327391 | − | 0.567057i | ||||
\(381\) | 0.726937 | − | 1.25909i | 0.0372421 | − | 0.0645053i | ||||
\(382\) | − | 7.27043i | − | 0.371988i | ||||||
\(383\) | 4.33125 | + | 2.50065i | 0.221317 | + | 0.127777i | 0.606560 | − | 0.795038i | \(-0.292549\pi\) |
−0.385243 | + | 0.922815i | \(0.625882\pi\) | |||||||
\(384\) | −21.4871 | − | 12.4056i | −1.09651 | − | 0.633069i | ||||
\(385\) | − | 16.9290i | − | 0.862779i | ||||||
\(386\) | −6.13580 | + | 10.6275i | −0.312304 | + | 0.540926i | ||||
\(387\) | −4.63924 | − | 8.03540i | −0.235826 | − | 0.408462i | ||||
\(388\) | 12.2257 | − | 7.05849i | 0.620664 | − | 0.358341i | ||||
\(389\) | 21.2028 | 1.07502 | 0.537512 | − | 0.843256i | \(-0.319364\pi\) | ||||
0.537512 | + | 0.843256i | \(0.319364\pi\) | |||||||
\(390\) | −5.92018 | + | 12.4291i | −0.299780 | + | 0.629371i | ||||
\(391\) | 2.75893 | 0.139525 | ||||||||
\(392\) | 6.94787 | − | 4.01135i | 0.350920 | − | 0.202604i | ||||
\(393\) | 13.0935 | + | 22.6786i | 0.660478 | + | 1.14398i | ||||
\(394\) | −0.835393 | + | 1.44694i | −0.0420865 | + | 0.0728959i | ||||
\(395\) | 21.8632i | 1.10006i | ||||||||
\(396\) | 40.4832 | + | 23.3730i | 2.03436 | + | 1.17454i | ||||
\(397\) | −2.21384 | − | 1.27816i | −0.111109 | − | 0.0641489i | 0.443416 | − | 0.896316i | \(-0.353767\pi\) |
−0.554525 | + | 0.832167i | \(0.687100\pi\) | |||||||
\(398\) | 11.8816i | 0.595569i | ||||||||
\(399\) | 20.1787 | − | 34.9505i | 1.01020 | − | 1.74972i | ||||
\(400\) | −0.449816 | − | 0.779104i | −0.0224908 | − | 0.0389552i | ||||
\(401\) | −20.8544 | + | 12.0403i | −1.04142 | + | 0.601264i | −0.920235 | − | 0.391366i | \(-0.872003\pi\) |
−0.121184 | + | 0.992630i | \(0.538669\pi\) | |||||||
\(402\) | −7.41444 | −0.369799 | ||||||||
\(403\) | 0.284818 | + | 3.59428i | 0.0141878 | + | 0.179044i | ||||
\(404\) | 8.88797 | 0.442193 | ||||||||
\(405\) | 16.4333 | − | 9.48775i | 0.816575 | − | 0.471450i | ||||
\(406\) | −3.28744 | − | 5.69401i | −0.163153 | − | 0.282589i | ||||
\(407\) | 30.2117 | − | 52.3283i | 1.49754 | − | 2.59382i | ||||
\(408\) | − | 8.58815i | − | 0.425177i | ||||||
\(409\) | 19.7862 | + | 11.4236i | 0.978366 | + | 0.564860i | 0.901776 | − | 0.432203i | \(-0.142264\pi\) |
0.0765893 | + | 0.997063i | \(0.475597\pi\) | |||||||
\(410\) | −1.40861 | − | 0.813259i | −0.0695661 | − | 0.0401640i | ||||
\(411\) | − | 13.6926i | − | 0.675406i | ||||||
\(412\) | −2.33783 | + | 4.04923i | −0.115176 | + | 0.199491i | ||||
\(413\) | 1.75810 | + | 3.04513i | 0.0865107 | + | 0.149841i | ||||
\(414\) | −12.4740 | + | 7.20188i | −0.613064 | + | 0.353953i | ||||
\(415\) | −22.9725 | −1.12768 | ||||||||
\(416\) | 18.7997 | + | 8.95461i | 0.921731 | + | 0.439036i | ||||
\(417\) | −40.7319 | −1.99465 | ||||||||
\(418\) | −26.2563 | + | 15.1591i | −1.28424 | + | 0.741455i | ||||
\(419\) | −8.68199 | − | 15.0376i | −0.424143 | − | 0.734637i | 0.572197 | − | 0.820116i | \(-0.306091\pi\) |
−0.996340 | + | 0.0854792i | \(0.972758\pi\) | |||||||
\(420\) | −6.06594 | + | 10.5065i | −0.295988 | + | 0.512665i | ||||
\(421\) | 3.16733i | 0.154366i | 0.997017 | + | 0.0771832i | \(0.0245926\pi\) | ||||
−0.997017 | + | 0.0771832i | \(0.975407\pi\) | |||||||
\(422\) | −2.71813 | − | 1.56931i | −0.132316 | − | 0.0763929i | ||||
\(423\) | −48.7951 | − | 28.1719i | −2.37250 | − | 1.36976i | ||||
\(424\) | − | 10.1797i | − | 0.494372i | ||||||
\(425\) | 1.40377 | − | 2.43139i | 0.0680927 | − | 0.117940i | ||||
\(426\) | 4.50395 | + | 7.80106i | 0.218217 | + | 0.377963i | ||||
\(427\) | 20.2356 | − | 11.6830i | 0.979268 | − | 0.565380i | ||||
\(428\) | −20.5853 | −0.995028 | ||||||||
\(429\) | −55.7883 | − | 26.5729i | −2.69349 | − | 1.28295i | ||||
\(430\) | −1.80901 | −0.0872381 | ||||||||
\(431\) | 9.69038 | − | 5.59474i | 0.466769 | − | 0.269489i | −0.248117 | − | 0.968730i | \(-0.579812\pi\) |
0.714886 | + | 0.699241i | \(0.246478\pi\) | |||||||
\(432\) | −1.69539 | − | 2.93650i | −0.0815693 | − | 0.141282i | ||||
\(433\) | −15.5991 | + | 27.0183i | −0.749643 | + | 1.29842i | 0.198352 | + | 0.980131i | \(0.436441\pi\) |
−0.947994 | + | 0.318288i | \(0.896892\pi\) | |||||||
\(434\) | − | 1.68140i | − | 0.0807097i | ||||||
\(435\) | −15.5427 | − | 8.97357i | −0.745214 | − | 0.430250i | ||||
\(436\) | −5.24674 | − | 3.02920i | −0.251273 | − | 0.145073i | ||||
\(437\) | 17.6532i | 0.844468i | ||||||||
\(438\) | 14.8559 | − | 25.7312i | 0.709843 | − | 1.22948i | ||||
\(439\) | −3.28051 | − | 5.68202i | −0.156570 | − | 0.271188i | 0.777059 | − | 0.629427i | \(-0.216710\pi\) |
−0.933630 | + | 0.358239i | \(0.883377\pi\) | |||||||
\(440\) | 19.9627 | − | 11.5255i | 0.951685 | − | 0.549456i | ||||
\(441\) | 18.6309 | 0.887187 | ||||||||
\(442\) | 0.241305 | + | 3.04517i | 0.0114777 | + | 0.144844i | ||||
\(443\) | −7.46246 | −0.354552 | −0.177276 | − | 0.984161i | \(-0.556729\pi\) | ||||
−0.177276 | + | 0.984161i | \(0.556729\pi\) | |||||||
\(444\) | −37.5003 | + | 21.6508i | −1.77968 | + | 1.02750i | ||||
\(445\) | 0.216312 | + | 0.374663i | 0.0102542 | + | 0.0177607i | ||||
\(446\) | 11.8187 | − | 20.4706i | 0.559633 | − | 0.969313i | ||||
\(447\) | 12.9111i | 0.610676i | ||||||||
\(448\) | −7.26739 | − | 4.19583i | −0.343352 | − | 0.198234i | ||||
\(449\) | 6.19599 | + | 3.57726i | 0.292407 | + | 0.168821i | 0.639027 | − | 0.769184i | \(-0.279337\pi\) |
−0.346620 | + | 0.938006i | \(0.612671\pi\) | |||||||
\(450\) | 14.6575i | 0.690960i | ||||||||
\(451\) | 3.65034 | − | 6.32257i | 0.171888 | − | 0.297718i | ||||
\(452\) | 8.74169 | + | 15.1411i | 0.411175 | + | 0.712176i | ||||
\(453\) | −14.2067 | + | 8.20224i | −0.667489 | + | 0.385375i | ||||
\(454\) | −10.2933 | −0.483088 | ||||||||
\(455\) | 4.69327 | − | 9.85325i | 0.220024 | − | 0.461927i | ||||
\(456\) | 54.9518 | 2.57336 | ||||||||
\(457\) | 9.15194 | − | 5.28387i | 0.428110 | − | 0.247169i | −0.270431 | − | 0.962739i | \(-0.587166\pi\) |
0.698541 | + | 0.715570i | \(0.253833\pi\) | |||||||
\(458\) | 10.9895 | + | 19.0343i | 0.513504 | + | 0.889415i | ||||
\(459\) | 5.29089 | − | 9.16409i | 0.246958 | − | 0.427743i | ||||
\(460\) | − | 5.30675i | − | 0.247429i | ||||||
\(461\) | 27.4427 | + | 15.8440i | 1.27813 | + | 0.737930i | 0.976505 | − | 0.215495i | \(-0.0691366\pi\) |
0.301628 | + | 0.953426i | \(0.402470\pi\) | |||||||
\(462\) | 24.9559 | + | 14.4083i | 1.16105 | + | 0.670335i | ||||
\(463\) | 37.4935i | 1.74247i | 0.490864 | + | 0.871236i | \(0.336681\pi\) | ||||
−0.490864 | + | 0.871236i | \(0.663319\pi\) | |||||||
\(464\) | −0.638023 | + | 1.10509i | −0.0296195 | + | 0.0513024i | ||||
\(465\) | −2.29482 | − | 3.97474i | −0.106420 | − | 0.184324i | ||||
\(466\) | −12.4377 | + | 7.18090i | −0.576164 | + | 0.332649i | ||||
\(467\) | −7.61460 | −0.352362 | −0.176181 | − | 0.984358i | \(-0.556374\pi\) | ||||
−0.176181 | + | 0.984358i | \(0.556374\pi\) | |||||||
\(468\) | 17.0829 | + | 24.8272i | 0.789657 | + | 1.14764i | ||||
\(469\) | 5.87786 | 0.271414 | ||||||||
\(470\) | −9.51349 | + | 5.49262i | −0.438825 | + | 0.253355i | ||||
\(471\) | −34.7935 | − | 60.2641i | −1.60320 | − | 2.77682i | ||||
\(472\) | −2.39389 | + | 4.14633i | −0.110188 | + | 0.190850i | ||||
\(473\) | − | 8.11979i | − | 0.373348i | ||||||
\(474\) | −32.2298 | − | 18.6079i | −1.48036 | − | 0.854688i | ||||
\(475\) | 15.5574 | + | 8.98209i | 0.713824 | + | 0.412127i | ||||
\(476\) | 2.69190i | 0.123383i | ||||||||
\(477\) | 11.8201 | − | 20.4730i | 0.541204 | − | 0.937393i | ||||
\(478\) | 8.17173 | + | 14.1538i | 0.373766 | + | 0.647382i | ||||
\(479\) | 7.20059 | − | 4.15726i | 0.329003 | − | 0.189950i | −0.326395 | − | 0.945233i | \(-0.605834\pi\) |
0.655398 | + | 0.755283i | \(0.272501\pi\) | |||||||
\(480\) | −26.5069 | −1.20987 | ||||||||
\(481\) | 32.0914 | − | 22.0812i | 1.46324 | − | 1.00682i | ||||
\(482\) | 15.4175 | 0.702249 | ||||||||
\(483\) | 14.5310 | − | 8.38946i | 0.661182 | − | 0.381734i | ||||
\(484\) | 13.2608 | + | 22.9684i | 0.602765 | + | 1.04402i | ||||
\(485\) | 8.08296 | − | 14.0001i | 0.367028 | − | 0.635712i | ||||
\(486\) | 6.36679i | 0.288803i | ||||||||
\(487\) | −2.73749 | − | 1.58049i | −0.124048 | − | 0.0716190i | 0.436692 | − | 0.899611i | \(-0.356150\pi\) |
−0.560740 | + | 0.827992i | \(0.689483\pi\) | |||||||
\(488\) | 27.5533 | + | 15.9079i | 1.24728 | + | 0.720118i | ||||
\(489\) | − | 2.35598i | − | 0.106541i | ||||||
\(490\) | 1.81622 | − | 3.14578i | 0.0820484 | − | 0.142112i | ||||
\(491\) | 17.1620 | + | 29.7255i | 0.774511 | + | 1.34149i | 0.935069 | + | 0.354467i | \(0.115338\pi\) |
−0.160557 | + | 0.987027i | \(0.551329\pi\) | |||||||
\(492\) | −4.53098 | + | 2.61596i | −0.204272 | + | 0.117937i | ||||
\(493\) | −3.98223 | −0.179350 | ||||||||
\(494\) | −19.4847 | + | 1.54401i | −0.876658 | + | 0.0694681i | ||||
\(495\) | 53.5307 | 2.40602 | ||||||||
\(496\) | −0.282605 | + | 0.163162i | −0.0126893 | + | 0.00732619i | ||||
\(497\) | −3.57054 | − | 6.18435i | −0.160161 | − | 0.277406i | ||||
\(498\) | 19.5520 | − | 33.8651i | 0.876147 | − | 1.51753i | ||||
\(499\) | − | 36.5003i | − | 1.63398i | −0.576652 | − | 0.816990i | \(-0.695641\pi\) | ||
0.576652 | − | 0.816990i | \(-0.304359\pi\) | |||||||
\(500\) | −13.1587 | − | 7.59719i | −0.588476 | − | 0.339757i | ||||
\(501\) | −18.1887 | − | 10.5012i | −0.812611 | − | 0.469161i | ||||
\(502\) | 13.4946i | 0.602292i | ||||||||
\(503\) | −2.16613 | + | 3.75185i | −0.0965831 | + | 0.167287i | −0.910268 | − | 0.414019i | \(-0.864125\pi\) |
0.813685 | + | 0.581306i | \(0.197458\pi\) | |||||||
\(504\) | −17.7723 | − | 30.7826i | −0.791642 | − | 1.37116i | ||||
\(505\) | 8.81438 | − | 5.08899i | 0.392235 | − | 0.226457i | ||||
\(506\) | −12.6050 | −0.560362 | ||||||||
\(507\) | −25.1039 | − | 30.9328i | −1.11490 | − | 1.37377i | ||||
\(508\) | −0.620505 | −0.0275305 | ||||||||
\(509\) | −12.4356 | + | 7.17972i | −0.551200 | + | 0.318236i | −0.749606 | − | 0.661884i | \(-0.769757\pi\) |
0.198406 | + | 0.980120i | \(0.436424\pi\) | |||||||
\(510\) | −1.94423 | − | 3.36750i | −0.0860918 | − | 0.149115i | ||||
\(511\) | −11.7771 | + | 20.3986i | −0.520990 | + | 0.902382i | ||||
\(512\) | 3.68070i | 0.162665i | ||||||||
\(513\) | 58.6370 | + | 33.8541i | 2.58889 | + | 1.49469i | ||||
\(514\) | 1.32348 | + | 0.764110i | 0.0583760 | + | 0.0337034i | ||||
\(515\) | 5.35428i | 0.235938i | ||||||||
\(516\) | −2.90946 | + | 5.03934i | −0.128082 | + | 0.221844i | ||||
\(517\) | −24.6538 | − | 42.7016i | −1.08427 | − | 1.87801i | ||||
\(518\) | −15.7321 | + | 9.08291i | −0.691227 | + | 0.399080i | ||||
\(519\) | −10.7911 | −0.473678 | ||||||||
\(520\) | 14.8143 | − | 1.17391i | 0.649648 | − | 0.0514794i | ||||
\(521\) | −12.7273 | −0.557593 | −0.278797 | − | 0.960350i | \(-0.589936\pi\) | ||||
−0.278797 | + | 0.960350i | \(0.589936\pi\) | |||||||
\(522\) | 18.0049 | − | 10.3951i | 0.788053 | − | 0.454983i | ||||
\(523\) | 9.12642 | + | 15.8074i | 0.399071 | + | 0.691211i | 0.993611 | − | 0.112855i | \(-0.0359995\pi\) |
−0.594541 | + | 0.804065i | \(0.702666\pi\) | |||||||
\(524\) | 5.58821 | − | 9.67907i | 0.244122 | − | 0.422832i | ||||
\(525\) | − | 17.0745i | − | 0.745191i | ||||||
\(526\) | 22.3149 | + | 12.8835i | 0.972974 | + | 0.561747i | ||||
\(527\) | −0.881941 | − | 0.509189i | −0.0384180 | − | 0.0221806i | ||||
\(528\) | − | 5.59270i | − | 0.243391i | ||||||
\(529\) | 7.83026 | − | 13.5624i | 0.340446 | − | 0.589670i | ||||
\(530\) | −2.30454 | − | 3.99158i | −0.100103 | − | 0.173383i | ||||
\(531\) | −9.62893 | + | 5.55926i | −0.417860 | + | 0.241251i | ||||
\(532\) | −17.2243 | −0.746768 | ||||||||
\(533\) | 3.87745 | − | 2.66797i | 0.167951 | − | 0.115562i | ||||
\(534\) | −0.736416 | −0.0318678 | ||||||||
\(535\) | −20.4149 | + | 11.7865i | −0.882612 | + | 0.509576i | ||||
\(536\) | 4.00173 | + | 6.93120i | 0.172848 | + | 0.299382i | ||||
\(537\) | −33.9150 | + | 58.7425i | −1.46354 | + | 2.53493i | ||||
\(538\) | 17.4113i | 0.750654i | ||||||||
\(539\) | 14.1200 | + | 8.15216i | 0.608189 | + | 0.351138i | ||||
\(540\) | −17.6269 | − | 10.1769i | −0.758542 | − | 0.437945i | ||||
\(541\) | − | 24.0161i | − | 1.03253i | −0.856428 | − | 0.516267i | \(-0.827321\pi\) | ||
0.856428 | − | 0.516267i | \(-0.172679\pi\) | |||||||
\(542\) | 8.66979 | − | 15.0165i | 0.372399 | − | 0.645014i | ||||
\(543\) | −6.76447 | − | 11.7164i | −0.290291 | − | 0.502799i | ||||
\(544\) | −5.09354 | + | 2.94076i | −0.218384 | + | 0.126084i | ||||
\(545\) | −6.93773 | −0.297180 | ||||||||
\(546\) | 10.5308 | + | 15.3048i | 0.450675 | + | 0.654983i | ||||
\(547\) | 17.8886 | 0.764860 | 0.382430 | − | 0.923984i | \(-0.375087\pi\) | ||||
0.382430 | + | 0.923984i | \(0.375087\pi\) | |||||||
\(548\) | −5.06098 | + | 2.92196i | −0.216194 | + | 0.124820i | ||||
\(549\) | 36.9426 | + | 63.9864i | 1.57667 | + | 2.73087i | ||||
\(550\) | −6.41353 | + | 11.1086i | −0.273474 | + | 0.473671i | ||||
\(551\) | − | 25.4805i | − | 1.08551i | ||||||
\(552\) | 19.7858 | + | 11.4233i | 0.842140 | + | 0.486210i | ||||
\(553\) | 25.5504 | + | 14.7515i | 1.08651 | + | 0.627299i | ||||
\(554\) | − | 10.8042i | − | 0.459026i | ||||||
\(555\) | −24.7932 | + | 42.9431i | −1.05241 | + | 1.82283i | ||||
\(556\) | 8.69206 | + | 15.0551i | 0.368626 | + | 0.638478i | ||||
\(557\) | 7.51808 | − | 4.34057i | 0.318551 | − | 0.183916i | −0.332195 | − | 0.943211i | \(-0.607789\pi\) |
0.650747 | + | 0.759295i | \(0.274456\pi\) | |||||||
\(558\) | 5.31671 | 0.225074 | ||||||||
\(559\) | 2.25108 | − | 4.72601i | 0.0952103 | − | 0.199889i | ||||
\(560\) | 0.987774 | 0.0417411 | ||||||||
\(561\) | 15.1151 | − | 8.72673i | 0.638161 | − | 0.368443i | ||||
\(562\) | −2.15489 | − | 3.73238i | −0.0908986 | − | 0.157441i | ||||
\(563\) | −15.3358 | + | 26.5625i | −0.646329 | + | 1.11947i | 0.337664 | + | 0.941267i | \(0.390363\pi\) |
−0.983993 | + | 0.178208i | \(0.942970\pi\) | |||||||
\(564\) | 35.3355i | 1.48789i | ||||||||
\(565\) | 17.3386 | + | 10.0105i | 0.729442 | + | 0.421143i | ||||
\(566\) | 20.4488 | + | 11.8061i | 0.859528 | + | 0.496249i | ||||
\(567\) | − | 25.6063i | − | 1.07536i | ||||||
\(568\) | 4.86175 | − | 8.42080i | 0.203995 | − | 0.353329i | ||||
\(569\) | 2.22636 | + | 3.85616i | 0.0933337 | + | 0.161659i | 0.908912 | − | 0.416988i | \(-0.136914\pi\) |
−0.815578 | + | 0.578647i | \(0.803581\pi\) | |||||||
\(570\) | 21.5472 | − | 12.4403i | 0.902512 | − | 0.521065i | ||||
\(571\) | −20.9889 | −0.878359 | −0.439179 | − | 0.898399i | \(-0.644731\pi\) | ||||
−0.439179 | + | 0.898399i | \(0.644731\pi\) | |||||||
\(572\) | 2.08333 | + | 26.2907i | 0.0871084 | + | 1.09927i | ||||
\(573\) | −26.7807 | −1.11878 | ||||||||
\(574\) | −1.90083 | + | 1.09744i | −0.0793390 | + | 0.0458064i | ||||
\(575\) | 3.73438 | + | 6.46813i | 0.155734 | + | 0.269740i | ||||
\(576\) | 13.2675 | − | 22.9800i | 0.552814 | − | 0.957502i | ||||
\(577\) | − | 10.6421i | − | 0.443035i | −0.975156 | − | 0.221518i | \(-0.928899\pi\) | ||
0.975156 | − | 0.221518i | \(-0.0711010\pi\) | |||||||
\(578\) | 11.5009 | + | 6.64006i | 0.478375 | + | 0.276190i | ||||
\(579\) | 39.1465 | + | 22.6012i | 1.62687 | + | 0.939275i | ||||
\(580\) | 7.65973i | 0.318053i | ||||||||
\(581\) | −15.5000 | + | 26.8468i | −0.643049 | + | 1.11379i | ||||
\(582\) | 13.7589 | + | 23.8311i | 0.570325 | + | 0.987831i | ||||
\(583\) | 17.9163 | − | 10.3440i | 0.742018 | − | 0.428404i | ||||
\(584\) | −32.0722 | −1.32716 | ||||||||
\(585\) | 31.1567 | + | 14.8405i | 1.28817 | + | 0.613578i | ||||
\(586\) | −9.11325 | −0.376465 | ||||||||
\(587\) | 19.7842 | − | 11.4224i | 0.816580 | − | 0.471452i | −0.0326560 | − | 0.999467i | \(-0.510397\pi\) |
0.849236 | + | 0.528014i | \(0.177063\pi\) | |||||||
\(588\) | −5.84212 | − | 10.1189i | −0.240925 | − | 0.417294i | ||||
\(589\) | 3.25808 | − | 5.64316i | 0.134247 | − | 0.232522i | ||||
\(590\) | 2.16776i | 0.0892452i | ||||||||
\(591\) | 5.32982 | + | 3.07717i | 0.219239 | + | 0.126578i | ||||
\(592\) | 3.05326 | + | 1.76280i | 0.125488 | + | 0.0724507i | ||||
\(593\) | 25.3190i | 1.03973i | 0.854250 | + | 0.519863i | \(0.174017\pi\) | ||||
−0.854250 | + | 0.519863i | \(0.825983\pi\) | |||||||
\(594\) | −24.1730 | + | 41.8689i | −0.991831 | + | 1.71790i | ||||
\(595\) | 1.54130 | + | 2.66961i | 0.0631872 | + | 0.109443i | ||||
\(596\) | 4.77214 | − | 2.75520i | 0.195475 | − | 0.112857i | ||||
\(597\) | 43.7658 | 1.79121 | ||||||||
\(598\) | −7.33657 | − | 3.49453i | −0.300015 | − | 0.142902i | ||||
\(599\) | −12.2836 | −0.501894 | −0.250947 | − | 0.968001i | \(-0.580742\pi\) | ||||
−0.250947 | + | 0.968001i | \(0.580742\pi\) | |||||||
\(600\) | 20.1343 | − | 11.6246i | 0.821980 | − | 0.474571i | ||||
\(601\) | −13.6249 | − | 23.5991i | −0.555773 | − | 0.962627i | −0.997843 | − | 0.0656462i | \(-0.979089\pi\) |
0.442070 | − | 0.896980i | \(-0.354244\pi\) | |||||||
\(602\) | −1.22057 | + | 2.11409i | −0.0497468 | + | 0.0861641i | ||||
\(603\) | 18.5862i | 0.756890i | ||||||||
\(604\) | 6.06333 | + | 3.50066i | 0.246713 | + | 0.142440i | ||||
\(605\) | 26.3021 | + | 15.1855i | 1.06933 | + | 0.617379i | ||||
\(606\) | 17.3250i | 0.703782i | ||||||||
\(607\) | −2.34092 | + | 4.05460i | −0.0950151 | + | 0.164571i | −0.909615 | − | 0.415452i | \(-0.863623\pi\) |
0.814600 | + | 0.580023i | \(0.196957\pi\) | |||||||
\(608\) | −18.8166 | − | 32.5913i | −0.763115 | − | 1.32175i | ||||
\(609\) | −20.9739 | + | 12.1093i | −0.849905 | + | 0.490693i | ||||
\(610\) | 14.4053 | 0.583252 | ||||||||
\(611\) | −2.51107 | − | 31.6887i | −0.101587 | − | 1.28199i | ||||
\(612\) | −8.51200 | −0.344077 | ||||||||
\(613\) | −17.8198 | + | 10.2883i | −0.719736 | + | 0.415540i | −0.814655 | − | 0.579945i | \(-0.803074\pi\) |
0.0949195 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(614\) | −8.48690 | − | 14.6997i | −0.342503 | − | 0.593233i | ||||
\(615\) | −2.99564 | + | 5.18860i | −0.120796 | + | 0.209225i | ||||
\(616\) | − | 31.1059i | − | 1.25329i | ||||||
\(617\) | −22.4196 | − | 12.9440i | −0.902580 | − | 0.521105i | −0.0245439 | − | 0.999699i | \(-0.507813\pi\) |
−0.878036 | + | 0.478594i | \(0.841147\pi\) | |||||||
\(618\) | −7.89304 | − | 4.55705i | −0.317505 | − | 0.183311i | ||||
\(619\) | 13.0268i | 0.523589i | 0.965124 | + | 0.261795i | \(0.0843143\pi\) | ||||
−0.965124 | + | 0.261795i | \(0.915686\pi\) | |||||||
\(620\) | −0.979414 | + | 1.69640i | −0.0393342 | + | 0.0681289i | ||||
\(621\) | 14.0751 | + | 24.3788i | 0.564815 | + | 0.978288i | ||||
\(622\) | 7.02782 | − | 4.05751i | 0.281790 | − | 0.162691i | ||||
\(623\) | 0.583800 | 0.0233894 | ||||||||
\(624\) | 1.55048 | − | 3.25515i | 0.0620690 | − | 0.130310i | ||||
\(625\) | −3.61535 | −0.144614 | ||||||||
\(626\) | −12.9650 | + | 7.48533i | −0.518185 | + | 0.299174i | ||||
\(627\) | 55.8385 | + | 96.7152i | 2.22998 | + | 3.86243i | ||||
\(628\) | −14.8497 | + | 25.7203i | −0.592566 | + | 1.02635i | ||||
\(629\) | 11.0025i | 0.438700i | ||||||||
\(630\) | −13.9374 | − | 8.04677i | −0.555280 | − | 0.320591i | ||||
\(631\) | −14.6600 | − | 8.46393i | −0.583604 | − | 0.336944i | 0.178960 | − | 0.983856i | \(-0.442727\pi\) |
−0.762564 | + | 0.646912i | \(0.776060\pi\) | |||||||
\(632\) | 40.1722i | 1.59797i | ||||||||
\(633\) | −5.78057 | + | 10.0122i | −0.229757 | + | 0.397951i | ||||
\(634\) | −9.48296 | − | 16.4250i | −0.376616 | − | 0.652319i | ||||
\(635\) | −0.615367 | + | 0.355283i | −0.0244201 | + | 0.0140990i | ||||
\(636\) | −14.8257 | −0.587879 | ||||||||
\(637\) | 5.95826 | + | 8.65937i | 0.236075 | + | 0.343097i | ||||
\(638\) | 18.1940 | 0.720307 | ||||||||
\(639\) | 19.5554 | − | 11.2903i | 0.773600 | − | 0.446638i | ||||
\(640\) | 6.06308 | + | 10.5016i | 0.239664 | + | 0.415111i | ||||
\(641\) | 1.11590 | − | 1.93280i | 0.0440755 | − | 0.0763410i | −0.843146 | − | 0.537685i | \(-0.819299\pi\) |
0.887222 | + | 0.461344i | \(0.152632\pi\) | |||||||
\(642\) | − | 40.1263i | − | 1.58366i | ||||||
\(643\) | 12.6232 | + | 7.28802i | 0.497811 | + | 0.287411i | 0.727809 | − | 0.685780i | \(-0.240539\pi\) |
−0.229998 | + | 0.973191i | \(0.573872\pi\) | |||||||
\(644\) | −6.20173 | − | 3.58057i | −0.244382 | − | 0.141094i | ||||
\(645\) | 6.66348i | 0.262374i | ||||||||
\(646\) | 2.76033 | − | 4.78103i | 0.108604 | − | 0.188107i | ||||
\(647\) | −18.4836 | − | 32.0145i | −0.726664 | − | 1.25862i | −0.958285 | − | 0.285813i | \(-0.907736\pi\) |
0.231621 | − | 0.972806i | \(-0.425597\pi\) | |||||||
\(648\) | 30.1951 | − | 17.4331i | 1.18617 | − | 0.684838i | ||||
\(649\) | −9.73006 | −0.381938 | ||||||||
\(650\) | −6.81256 | + | 4.68753i | −0.267211 | + | 0.183860i | ||||
\(651\) | −6.19344 | −0.242740 | ||||||||
\(652\) | −0.870802 | + | 0.502758i | −0.0341033 | + | 0.0196895i | ||||
\(653\) | 0.823360 | + | 1.42610i | 0.0322206 | + | 0.0558076i | 0.881686 | − | 0.471837i | \(-0.156409\pi\) |
−0.849465 | + | 0.527644i | \(0.823075\pi\) | |||||||
\(654\) | 5.90473 | − | 10.2273i | 0.230893 | − | 0.399919i | ||||
\(655\) | − | 12.7986i | − | 0.500082i | ||||||
\(656\) | 0.368911 | + | 0.212991i | 0.0144036 | + | 0.00831589i | ||||
\(657\) | −64.5020 | − | 37.2403i | −2.51646 | − | 1.45288i | ||||
\(658\) | 14.8239i | 0.577896i | ||||||||
\(659\) | 8.92854 | − | 15.4647i | 0.347806 | − | 0.602418i | −0.638053 | − | 0.769992i | \(-0.720260\pi\) |
0.985860 | + | 0.167574i | \(0.0535933\pi\) | |||||||
\(660\) | −16.7857 | − | 29.0736i | −0.653381 | − | 1.13169i | ||||
\(661\) | −26.3168 | + | 15.1940i | −1.02360 | + | 0.590978i | −0.915146 | − | 0.403123i | \(-0.867925\pi\) |
−0.108459 | + | 0.994101i | \(0.534591\pi\) | |||||||
\(662\) | −1.46053 | −0.0567652 | ||||||||
\(663\) | 11.2169 | − | 0.888848i | 0.435628 | − | 0.0345200i | ||||
\(664\) | −42.2106 | −1.63809 | ||||||||
\(665\) | −17.0817 | + | 9.86211i | −0.662399 | + | 0.382436i | ||||
\(666\) | −28.7209 | − | 49.7460i | −1.11291 | − | 1.92762i | ||||
\(667\) | 5.29687 | − | 9.17445i | 0.205096 | − | 0.355236i | ||||
\(668\) | 8.96374i | 0.346817i | ||||||||
\(669\) | −75.4036 | − | 43.5343i | −2.91527 | − | 1.68313i | ||||
\(670\) | 3.13824 | + | 1.81186i | 0.121241 | + | 0.0699984i | ||||
\(671\) | 64.6585i | 2.49611i | ||||||||
\(672\) | −17.8847 | + | 30.9772i | −0.689917 | + | 1.19497i | ||||
\(673\) | −15.0214 | − | 26.0178i | −0.579032 | − | 1.00291i | −0.995591 | − | 0.0938040i | \(-0.970097\pi\) |
0.416559 | − | 0.909109i | \(-0.363236\pi\) | |||||||
\(674\) | 6.57224 | − | 3.79448i | 0.253153 | − | 0.146158i | ||||
\(675\) | 28.6461 | 1.10259 | ||||||||
\(676\) | −6.07610 | + | 15.8797i | −0.233696 | + | 0.610758i | ||||
\(677\) | 14.9123 | 0.573128 | 0.286564 | − | 0.958061i | \(-0.407487\pi\) | ||||
0.286564 | + | 0.958061i | \(0.407487\pi\) | |||||||
\(678\) | −29.5140 | + | 17.0399i | −1.13348 | + | 0.654414i | ||||
\(679\) | −10.9075 | − | 18.8923i | −0.418590 | − | 0.725020i | ||||
\(680\) | −2.09868 | + | 3.63502i | −0.0804808 | + | 0.139397i | ||||
\(681\) | 37.9154i | 1.45292i | ||||||||
\(682\) | 4.02941 | + | 2.32638i | 0.154294 | + | 0.0890818i | ||||
\(683\) | −28.1539 | − | 16.2547i | −1.07728 | − | 0.621967i | −0.147118 | − | 0.989119i | \(-0.547000\pi\) |
−0.930161 | + | 0.367152i | \(0.880333\pi\) | |||||||
\(684\) | − | 54.4646i | − | 2.08250i | ||||||
\(685\) | −3.34605 | + | 5.79553i | −0.127846 | + | 0.221436i | ||||
\(686\) | −8.33577 | − | 14.4380i | −0.318261 | − | 0.551245i | ||||
\(687\) | 70.1129 | − | 40.4797i | 2.67498 | − | 1.54440i | ||||
\(688\) | 0.473775 | 0.0180625 | ||||||||
\(689\) | 13.2956 | − | 1.05357i | 0.506523 | − | 0.0401379i | ||||
\(690\) | 10.3443 | 0.393800 | ||||||||
\(691\) | −10.7982 | + | 6.23432i | −0.410782 | + | 0.237165i | −0.691126 | − | 0.722735i | \(-0.742885\pi\) |
0.280344 | + | 0.959900i | \(0.409552\pi\) | |||||||
\(692\) | 2.30279 | + | 3.98855i | 0.0875390 | + | 0.151622i | ||||
\(693\) | 36.1182 | − | 62.5585i | 1.37202 | − | 2.37640i | ||||
\(694\) | 26.2855i | 0.997785i | ||||||||
\(695\) | 17.2402 | + | 9.95363i | 0.653958 | + | 0.377563i | ||||
\(696\) | −28.5587 | − | 16.4884i | −1.08251 | − | 0.624990i | ||||
\(697\) | 1.32938i | 0.0503540i | ||||||||
\(698\) | −1.66807 | + | 2.88919i | −0.0631375 | + | 0.109357i | ||||
\(699\) | 26.4508 | + | 45.8142i | 1.00046 | + | 1.73285i | ||||
\(700\) | −6.31097 | + | 3.64364i | −0.238532 | + | 0.137717i | ||||
\(701\) | 36.8033 | 1.39004 | 0.695021 | − | 0.718989i | \(-0.255395\pi\) | ||||
0.695021 | + | 0.718989i | \(0.255395\pi\) | |||||||
\(702\) | −25.6770 | + | 17.6676i | −0.969116 | + | 0.666822i | ||||
\(703\) | −70.4005 | −2.65521 | ||||||||
\(704\) | 20.1103 | − | 11.6107i | 0.757936 | − | 0.437595i | ||||
\(705\) | 20.2321 | + | 35.0430i | 0.761984 | + | 1.31979i | ||||
\(706\) | −2.99253 | + | 5.18322i | −0.112625 | + | 0.195073i | ||||
\(707\) | − | 13.7346i | − | 0.516541i | ||||||
\(708\) | 6.03871 | + | 3.48645i | 0.226949 | + | 0.131029i | ||||
\(709\) | −36.5498 | − | 21.1020i | −1.37266 | − | 0.792503i | −0.381393 | − | 0.924413i | \(-0.624556\pi\) |
−0.991262 | + | 0.131910i | \(0.957889\pi\) | |||||||
\(710\) | − | 4.40251i | − | 0.165223i | ||||||
\(711\) | −46.6455 | + | 80.7924i | −1.74934 | + | 3.02995i | ||||
\(712\) | 0.397459 | + | 0.688420i | 0.0148954 | + | 0.0257996i | ||||
\(713\) | 2.34619 | − | 1.35457i | 0.0878655 | − | 0.0507292i | ||||
\(714\) | −5.24723 | −0.196373 | ||||||||
\(715\) | 17.1194 | + | 24.8802i | 0.640228 | + | 0.930467i | ||||
\(716\) | 28.9494 | 1.08189 | ||||||||
\(717\) | 52.1357 | − | 30.1006i | 1.94704 | − | 1.12413i | ||||
\(718\) | −4.72525 | − | 8.18437i | −0.176345 | − | 0.305438i | ||||
\(719\) | −2.03072 | + | 3.51731i | −0.0757331 | + | 0.131174i | −0.901405 | − | 0.432977i | \(-0.857463\pi\) |
0.825672 | + | 0.564151i | \(0.190796\pi\) | |||||||
\(720\) | 3.12342i | 0.116403i | ||||||||
\(721\) | 6.25727 | + | 3.61264i | 0.233033 | + | 0.134542i | ||||
\(722\) | 16.9026 | + | 9.75874i | 0.629051 | + | 0.363183i | ||||
\(723\) | − | 56.7905i | − | 2.11206i | ||||||
\(724\) | −2.88703 | + | 5.00049i | −0.107296 | + | 0.185842i | ||||
\(725\) | −5.39017 | − | 9.33605i | −0.200186 | − | 0.346732i | ||||
\(726\) | −44.7716 | + | 25.8489i | −1.66163 | + | 0.959343i | ||||
\(727\) | 5.61475 | 0.208240 | 0.104120 | − | 0.994565i | \(-0.466797\pi\) | ||||
0.104120 | + | 0.994565i | \(0.466797\pi\) | |||||||
\(728\) | 8.62358 | − | 18.1047i | 0.319611 | − | 0.671006i | ||||
\(729\) | −14.5570 | −0.539146 | ||||||||
\(730\) | −12.5758 | + | 7.26067i | −0.465453 | + | 0.268729i | ||||
\(731\) | 0.739268 | + | 1.28045i | 0.0273428 | + | 0.0473592i | ||||
\(732\) | 23.1683 | − | 40.1286i | 0.856323 | − | 1.48320i | ||||
\(733\) | − | 11.2823i | − | 0.416720i | −0.978052 | − | 0.208360i | \(-0.933187\pi\) | ||
0.978052 | − | 0.208360i | \(-0.0668125\pi\) | |||||||
\(734\) | 7.21894 | + | 4.16785i | 0.266456 | + | 0.153838i | ||||
\(735\) | −11.5875 | − | 6.69005i | −0.427412 | − | 0.246766i | ||||
\(736\) | − | 15.6463i | − | 0.576731i | ||||||
\(737\) | −8.13260 | + | 14.0861i | −0.299568 | + | 0.518868i | ||||
\(738\) | −3.47020 | − | 6.01057i | −0.127740 | − | 0.221252i | ||||
\(739\) | −8.51900 | + | 4.91844i | −0.313376 | + | 0.180928i | −0.648436 | − | 0.761269i | \(-0.724577\pi\) |
0.335060 | + | 0.942197i | \(0.391243\pi\) | |||||||
\(740\) | 21.1632 | 0.777974 | ||||||||
\(741\) | 5.68735 | + | 71.7719i | 0.208930 | + | 2.63661i | ||||
\(742\) | −6.21967 | −0.228331 | ||||||||
\(743\) | 34.1306 | − | 19.7053i | 1.25213 | − | 0.722917i | 0.280597 | − | 0.959826i | \(-0.409468\pi\) |
0.971532 | + | 0.236909i | \(0.0761342\pi\) | |||||||
\(744\) | −4.21658 | − | 7.30334i | −0.154587 | − | 0.267753i | ||||
\(745\) | 3.15509 | − | 5.46477i | 0.115593 | − | 0.200214i | ||||
\(746\) | 14.9783i | 0.548394i | ||||||||
\(747\) | −84.8917 | − | 49.0123i | −3.10603 | − | 1.79327i | ||||
\(748\) | −6.45105 | − | 3.72451i | −0.235874 | − | 0.136182i | ||||
\(749\) | 31.8104i | 1.16233i | ||||||||
\(750\) | 14.8090 | − | 25.6499i | 0.540746 | − | 0.936600i | ||||
\(751\) | 0.269911 | + | 0.467500i | 0.00984920 | + | 0.0170593i | 0.870908 | − | 0.491446i | \(-0.163532\pi\) |
−0.861059 | + | 0.508505i | \(0.830198\pi\) | |||||||
\(752\) | 2.49156 | − | 1.43850i | 0.0908579 | − | 0.0524569i | ||||
\(753\) | 49.7072 | 1.81143 | ||||||||
\(754\) | 10.5896 | + | 5.04398i | 0.385649 | + | 0.183691i | ||||
\(755\) | 8.01750 | 0.291787 | ||||||||
\(756\) | −23.7865 | + | 13.7331i | −0.865106 | + | 0.499469i | ||||
\(757\) | 4.69490 | + | 8.13181i | 0.170639 | + | 0.295556i | 0.938644 | − | 0.344889i | \(-0.112083\pi\) |
−0.768004 | + | 0.640445i | \(0.778750\pi\) | |||||||
\(758\) | −2.67388 | + | 4.63129i | −0.0971196 | + | 0.168216i | ||||
\(759\) | 46.4306i | 1.68533i | ||||||||
\(760\) | −23.2589 | − | 13.4285i | −0.843690 | − | 0.487105i | ||||
\(761\) | 2.68784 | + | 1.55183i | 0.0974341 | + | 0.0562536i | 0.547925 | − | 0.836527i | \(-0.315418\pi\) |
−0.450491 | + | 0.892781i | \(0.648751\pi\) | |||||||
\(762\) | − | 1.20953i | − | 0.0438167i | ||||||
\(763\) | −4.68102 | + | 8.10776i | −0.169464 | + | 0.293521i | ||||
\(764\) | 5.71491 | + | 9.89852i | 0.206758 | + | 0.358116i | ||||
\(765\) | −8.44152 | + | 4.87371i | −0.305204 | + | 0.176210i | ||||
\(766\) | 4.16076 | 0.150334 | ||||||||
\(767\) | −5.66324 | − | 2.69749i | −0.204488 | − | 0.0974009i | ||||
\(768\) | −46.0889 | −1.66309 | ||||||||
\(769\) | −16.5943 | + | 9.58071i | −0.598405 | + | 0.345489i | −0.768414 | − | 0.639953i | \(-0.778954\pi\) |
0.170009 | + | 0.985443i | \(0.445620\pi\) | |||||||
\(770\) | −7.04190 | − | 12.1969i | −0.253772 | − | 0.439547i | ||||
\(771\) | 2.81460 | − | 4.87503i | 0.101365 | − | 0.175570i | ||||
\(772\) | − | 19.2921i | − | 0.694339i | ||||||
\(773\) | 22.8771 | + | 13.2081i | 0.822831 | + | 0.475061i | 0.851392 | − | 0.524531i | \(-0.175759\pi\) |
−0.0285611 | + | 0.999592i | \(0.509093\pi\) | |||||||
\(774\) | −6.68493 | − | 3.85955i | −0.240285 | − | 0.138729i | ||||
\(775\) | − | 2.75687i | − | 0.0990296i | ||||||
\(776\) | 14.8519 | − | 25.7243i | 0.533153 | − | 0.923449i | ||||
\(777\) | 33.4569 | + | 57.9491i | 1.20026 | + | 2.07891i | ||||
\(778\) | 15.2761 | − | 8.81968i | 0.547676 | − | 0.316201i | ||||
\(779\) | −8.50615 | −0.304765 | ||||||||
\(780\) | −1.70968 | − | 21.5754i | −0.0612164 | − | 0.772525i | ||||
\(781\) | 19.7608 | 0.707097 | ||||||||
\(782\) | 1.98775 | − | 1.14763i | 0.0710818 | − | 0.0410391i | ||||
\(783\) | −20.3159 | − | 35.1882i | −0.726032 | − | 1.25752i | ||||
\(784\) | −0.475664 | + | 0.823874i | −0.0169880 | + | 0.0294241i | ||||
\(785\) | 34.0099i | 1.21386i | ||||||||
\(786\) | 18.8671 | + | 10.8929i | 0.672967 | + | 0.388538i | ||||
\(787\) | 29.7004 | + | 17.1475i | 1.05870 | + | 0.611243i | 0.925073 | − | 0.379789i | \(-0.124003\pi\) |
0.133630 | + | 0.991031i | \(0.457337\pi\) | |||||||
\(788\) | − | 2.62664i | − | 0.0935700i | ||||||
\(789\) | 47.4564 | − | 82.1969i | 1.68949 | − | 2.92629i | ||||
\(790\) | 9.09439 | + | 15.7519i | 0.323564 | + | 0.560429i | ||||
\(791\) | 23.3974 | − | 13.5085i | 0.831917 | − | 0.480307i | ||||
\(792\) | 98.3592 | 3.49504 | ||||||||
\(793\) | −17.9255 | + | 37.6335i | −0.636552 | + | 1.33641i | ||||
\(794\) | −2.12669 | −0.0754735 | ||||||||
\(795\) | −14.7030 | + | 8.48877i | −0.521461 | + | 0.301066i | ||||
\(796\) | −9.33949 | − | 16.1765i | −0.331029 | − | 0.573360i | ||||
\(797\) | 23.1887 | − | 40.1640i | 0.821385 | − | 1.42268i | −0.0832657 | − | 0.996527i | \(-0.526535\pi\) |
0.904651 | − | 0.426153i | \(-0.140132\pi\) | |||||||
\(798\) | − | 33.5748i | − | 1.18853i | ||||||
\(799\) | 7.77556 | + | 4.48922i | 0.275080 | + | 0.158817i | ||||
\(800\) | −13.7888 | − | 7.96097i | −0.487508 | − | 0.281463i | ||||
\(801\) | 1.84602i | 0.0652259i | ||||||||
\(802\) | −10.0168 | + | 17.3495i | −0.353704 | + | 0.612633i | ||||
\(803\) | −32.5897 | − | 56.4471i | −1.15007 | − | 1.99197i | ||||
\(804\) | 10.0946 | − | 5.82811i | 0.356008 | − | 0.205542i | ||||
\(805\) | −8.20051 | −0.289030 | ||||||||
\(806\) | 1.70031 | + | 2.47113i | 0.0598909 | + | 0.0870417i | ||||
\(807\) | 64.1346 | 2.25764 | ||||||||
\(808\) | 16.1959 | − | 9.35069i | 0.569769 | − | 0.328956i | ||||
\(809\) | −3.50932 | − | 6.07832i | −0.123381 | − | 0.213702i | 0.797718 | − | 0.603031i | \(-0.206040\pi\) |
−0.921099 | + | 0.389328i | \(0.872707\pi\) | |||||||
\(810\) | 7.89320 | − | 13.6714i | 0.277339 | − | 0.480365i | ||||
\(811\) | − | 1.60718i | − | 0.0564356i | −0.999602 | − | 0.0282178i | \(-0.991017\pi\) | ||
0.999602 | − | 0.0282178i | \(-0.00898319\pi\) | |||||||
\(812\) | 8.95153 | + | 5.16817i | 0.314137 | + | 0.181367i | ||||
\(813\) | −55.3134 | − | 31.9352i | −1.93992 | − | 1.12002i | ||||
\(814\) | − | 50.2685i | − | 1.76191i | ||||||
\(815\) | −0.575728 | + | 0.997191i | −0.0201669 | + | 0.0349301i | ||||
\(816\) | 0.509189 | + | 0.881941i | 0.0178252 | + | 0.0308741i | ||||
\(817\) | −8.19305 | + | 4.73026i | −0.286638 | + | 0.165491i | ||||
\(818\) | 19.0074 | 0.664577 | ||||||||
\(819\) | 38.3654 | − | 26.3981i | 1.34059 | − | 0.922425i | ||||
\(820\) | 2.55704 | 0.0892958 | ||||||||
\(821\) | 27.7575 | − | 16.0258i | 0.968745 | − | 0.559305i | 0.0698915 | − | 0.997555i | \(-0.477735\pi\) |
0.898853 | + | 0.438249i | \(0.144401\pi\) | |||||||
\(822\) | −5.69568 | − | 9.86521i | −0.198660 | − | 0.344089i | ||||
\(823\) | 7.89566 | − | 13.6757i | 0.275225 | − | 0.476704i | −0.694967 | − | 0.719042i | \(-0.744581\pi\) |
0.970192 | + | 0.242338i | \(0.0779142\pi\) | |||||||
\(824\) | 9.83814i | 0.342728i | ||||||||
\(825\) | 40.9184 | + | 23.6243i | 1.42460 | + | 0.822491i | ||||
\(826\) | 2.53335 | + | 1.46263i | 0.0881465 | + | 0.0508914i | ||||
\(827\) | 20.7307i | 0.720877i | 0.932783 | + | 0.360439i | \(0.117373\pi\) | ||||
−0.932783 | + | 0.360439i | \(0.882627\pi\) | |||||||
\(828\) | 11.3220 | − | 19.6104i | 0.393468 | − | 0.681507i | ||||
\(829\) | −10.2008 | − | 17.6683i | −0.354289 | − | 0.613646i | 0.632707 | − | 0.774391i | \(-0.281944\pi\) |
−0.986996 | + | 0.160745i | \(0.948610\pi\) | |||||||
\(830\) | −16.5512 | + | 9.55583i | −0.574500 | + | 0.331688i | ||||
\(831\) | −39.7972 | −1.38055 | ||||||||
\(832\) | 14.9238 | − | 1.18259i | 0.517389 | − | 0.0409989i | ||||
\(833\) | −2.96886 | −0.102865 | ||||||||
\(834\) | −29.3464 | + | 16.9432i | −1.01618 | + | 0.586694i | ||||
\(835\) | 5.13237 | + | 8.88952i | 0.177613 | + | 0.307635i | ||||
\(836\) | 23.8315 | − | 41.2774i | 0.824231 | − | 1.42761i | ||||
\(837\) | − | 10.3908i | − | 0.359159i | ||||||
\(838\) | −12.5104 | − | 7.22286i | −0.432163 | − | 0.249509i | ||||
\(839\) | 34.5711 | + | 19.9597i | 1.19353 | + | 0.689084i | 0.959105 | − | 0.283051i | \(-0.0913466\pi\) |
0.234423 | + | 0.972135i | \(0.424680\pi\) | |||||||
\(840\) | 25.5270i | 0.880764i | ||||||||
\(841\) | 6.85454 | − | 11.8724i | 0.236363 | − | 0.409393i | ||||
\(842\) | 1.31751 | + | 2.28199i | 0.0454043 | + | 0.0786426i | ||||
\(843\) | −13.7482 | + | 7.93754i | −0.473514 | + | 0.273384i | ||||
\(844\) | 4.93422 | 0.169843 | ||||||||
\(845\) | 3.06646 | + | 19.2272i | 0.105489 | + | 0.661437i | ||||
\(846\) | −46.8743 | −1.61157 | ||||||||
\(847\) | 35.4930 | − | 20.4919i | 1.21956 | − | 0.704111i | ||||
\(848\) | 0.603553 | + | 1.04539i | 0.0207261 | + | 0.0358987i | ||||
\(849\) | 43.4879 | − | 75.3233i | 1.49250 | − | 2.58509i | ||||
\(850\) | − | 2.33569i | − | 0.0801134i | ||||||
\(851\) | −25.3482 | − | 14.6348i | −0.868925 | − | 0.501674i | ||||
\(852\) | −12.2640 | − | 7.08064i | −0.420159 | − | 0.242579i | ||||
\(853\) | − | 18.6811i | − | 0.639628i | −0.947480 | − | 0.319814i | \(-0.896380\pi\) | ||
0.947480 | − | 0.319814i | \(-0.103620\pi\) | |||||||
\(854\) | 9.71951 | − | 16.8347i | 0.332595 | − | 0.576071i | ||||
\(855\) | −31.1848 | − | 54.0136i | −1.06650 | − | 1.84723i | ||||
\(856\) | −37.5110 | + | 21.6570i | −1.28210 | + | 0.740221i | ||||
\(857\) | 30.2414 | 1.03303 | 0.516514 | − | 0.856279i | \(-0.327229\pi\) | ||||
0.516514 | + | 0.856279i | \(0.327229\pi\) | |||||||
\(858\) | −51.2477 | + | 4.06097i | −1.74957 | + | 0.138639i | ||||
\(859\) | 30.8023 | 1.05096 | 0.525481 | − | 0.850805i | \(-0.323885\pi\) | ||||
0.525481 | + | 0.850805i | \(0.323885\pi\) | |||||||
\(860\) | 2.46292 | − | 1.42197i | 0.0839849 | − | 0.0484887i | ||||
\(861\) | 4.04244 | + | 7.00171i | 0.137766 | + | 0.238618i | ||||
\(862\) | 4.65447 | − | 8.06177i | 0.158532 | − | 0.274585i | ||||
\(863\) | 51.1994i | 1.74285i | 0.490532 | + | 0.871423i | \(0.336803\pi\) | ||||
−0.490532 | + | 0.871423i | \(0.663197\pi\) | |||||||
\(864\) | −51.9709 | − | 30.0054i | −1.76809 | − | 1.02080i | ||||
\(865\) | 4.56745 | + | 2.63702i | 0.155298 | + | 0.0896614i | ||||
\(866\) | 25.9548i | 0.881980i | ||||||||
\(867\) | 24.4587 | − | 42.3636i | 0.830660 | − | 1.43874i | ||||
\(868\) | 1.32166 | + | 2.28918i | 0.0448601 | + | 0.0776999i | ||||
\(869\) | −70.7031 | + | 40.8204i | −2.39844 | + | 1.38474i | ||||
\(870\) | −14.9309 | −0.506204 | ||||||||
\(871\) | −8.63859 | + | 5.94397i | −0.292708 | + | 0.201404i | ||||
\(872\) | −12.7476 | −0.431689 | ||||||||
\(873\) | 59.7389 | − | 34.4903i | 2.02186 | − | 1.16732i | ||||
\(874\) | 7.34317 | + | 12.7187i | 0.248387 | + | 0.430218i | ||||
\(875\) | −11.7399 | + | 20.3341i | −0.396881 | + | 0.687419i | ||||
\(876\) | 46.7099i | 1.57818i | ||||||||
\(877\) | −7.88404 | − | 4.55185i | −0.266225 | − | 0.153705i | 0.360946 | − | 0.932587i | \(-0.382454\pi\) |
−0.627171 | + | 0.778882i | \(0.715787\pi\) | |||||||
\(878\) | −4.72707 | − | 2.72918i | −0.159531 | − | 0.0921053i | ||||
\(879\) | 33.5687i | 1.13224i | ||||||||
\(880\) | −1.36668 | + | 2.36717i | −0.0460709 | + | 0.0797972i | ||||
\(881\) | −27.5119 | − | 47.6520i | −0.926899 | − | 1.60544i | −0.788478 | − | 0.615063i | \(-0.789131\pi\) |
−0.138421 | − | 0.990373i | \(-0.544203\pi\) | |||||||
\(882\) | 13.4232 | − | 7.74987i | 0.451981 | − | 0.260952i | ||||
\(883\) | −48.5436 | −1.63362 | −0.816811 | − | 0.576905i | \(-0.804260\pi\) | ||||
−0.816811 | + | 0.576905i | \(0.804260\pi\) | |||||||
\(884\) | −2.72218 | − | 3.95624i | −0.0915568 | − | 0.133063i | ||||
\(885\) | 7.98495 | 0.268411 | ||||||||
\(886\) | −5.37653 | + | 3.10414i | −0.180628 | + | 0.104286i | ||||
\(887\) | 21.5606 | + | 37.3441i | 0.723936 | + | 1.25389i | 0.959411 | + | 0.282013i | \(0.0910021\pi\) |
−0.235475 | + | 0.971880i | \(0.575665\pi\) | |||||||
\(888\) | −45.5559 | + | 78.9052i | −1.52876 | + | 2.64788i | ||||
\(889\) | 0.958864i | 0.0321593i | ||||||||
\(890\) | 0.311696 | + | 0.179958i | 0.0104481 | + | 0.00603219i | ||||
\(891\) | 61.3646 | + | 35.4289i | 2.05579 | + | 1.18691i | ||||
\(892\) | 37.1604i | 1.24422i | ||||||||
\(893\) | −28.7246 | + | 49.7524i | −0.961231 | + | 1.66490i | ||||
\(894\) | 5.37062 | + | 9.30218i | 0.179620 | + | 0.311112i | ||||
\(895\) | 28.7098 | − | 16.5756i | 0.959661 | − | 0.554061i | ||||
\(896\) | 16.3635 | 0.546667 | ||||||||
\(897\) | −12.8721 | + | 27.0243i | −0.429787 | + | 0.902314i | ||||
\(898\) | 5.95210 | 0.198624 | ||||||||
\(899\) | −3.38647 | + | 1.95518i | −0.112945 | + | 0.0652089i | ||||
\(900\) | −11.5215 | − | 19.9558i | −0.384049 | − | 0.665193i | ||||
\(901\) | −1.88354 | + | 3.26239i | −0.0627499 | + | 0.108686i | ||||
\(902\) | − | 6.07370i | − | 0.202232i | ||||||
\(903\) | 7.78727 | + | 4.49598i | 0.259144 | + | 0.149617i | ||||
\(904\) | 31.8586 | + | 18.3936i | 1.05960 | + | 0.611762i | ||||
\(905\) | 6.61212i | 0.219794i | ||||||||
\(906\) | −6.82373 | + | 11.8191i | −0.226703 | + | 0.392662i | ||||
\(907\) | 16.8029 | + | 29.1034i | 0.557930 | + | 0.966364i | 0.997669 | + | 0.0682381i | \(0.0217377\pi\) |
−0.439739 | + | 0.898126i | \(0.644929\pi\) | |||||||
\(908\) | 14.0141 | − | 8.09103i | 0.465073 | − | 0.268510i | ||||
\(909\) | 43.4298 | 1.44047 | ||||||||
\(910\) | −0.717242 | − | 9.05129i | −0.0237763 | − | 0.300047i | ||||
\(911\) | 21.1755 | 0.701576 | 0.350788 | − | 0.936455i | \(-0.385914\pi\) | ||||
0.350788 | + | 0.936455i | \(0.385914\pi\) | |||||||
\(912\) | −5.64316 | + | 3.25808i | −0.186864 | + | 0.107886i | ||||
\(913\) | −42.8917 | − | 74.2906i | −1.41951 | − | 2.45866i | ||||
\(914\) | 4.39584 | − | 7.61382i | 0.145402 | − | 0.251843i | ||||
\(915\) | − | 53.0618i | − | 1.75417i | ||||||
\(916\) | −29.9238 | − | 17.2765i | −0.988709 | − | 0.570832i | ||||
\(917\) | −14.9570 | − | 8.63545i | −0.493925 | − | 0.285168i | ||||
\(918\) | − | 8.80336i | − | 0.290554i | ||||||
\(919\) | −19.2620 | + | 33.3628i | −0.635395 | + | 1.10054i | 0.351036 | + | 0.936362i | \(0.385829\pi\) |
−0.986431 | + | 0.164175i | \(0.947504\pi\) | |||||||
\(920\) | −5.58303 | − | 9.67009i | −0.184067 | − | 0.318813i | ||||
\(921\) | −54.1465 | + | 31.2615i | −1.78419 | + | 1.03010i | ||||
\(922\) | 26.3624 | 0.868201 | ||||||||
\(923\) | 11.5015 | + | 5.47835i | 0.378576 | + | 0.180322i | ||||
\(924\) | −45.3025 | −1.49034 | ||||||||
\(925\) | −25.7947 | + | 14.8926i | −0.848125 | + | 0.489665i | ||||
\(926\) | 15.5961 | + | 27.0132i | 0.512520 | + | 0.887710i | ||||
\(927\) | −11.4234 | + | 19.7860i | −0.375195 | + | 0.649857i | ||||
\(928\) | 22.5838i | 0.741349i | ||||||||
\(929\) | −45.6673 | − | 26.3661i | −1.49830 | − | 0.865042i | −0.498299 | − | 0.867005i | \(-0.666042\pi\) |
−0.999998 | + | 0.00196329i | \(0.999375\pi\) | |||||||
\(930\) | −3.30673 | − | 1.90914i | −0.108432 | − | 0.0626032i | ||||
\(931\) | − | 18.9965i | − | 0.622584i | ||||||
\(932\) | 11.2891 | − | 19.5532i | 0.369785 | − | 0.640487i | ||||
\(933\) | −14.9459 | − | 25.8870i | −0.489305 | − | 0.847502i | ||||
\(934\) | −5.48615 | + | 3.16743i | −0.179512 | + | 0.103641i | ||||
\(935\) | −8.53018 | −0.278967 | ||||||||
\(936\) | 57.2485 | + | 27.2684i | 1.87123 | + | 0.891297i | ||||
\(937\) | −28.5850 | −0.933830 | −0.466915 | − | 0.884302i | \(-0.654635\pi\) | ||||
−0.466915 | + | 0.884302i | \(0.654635\pi\) | |||||||
\(938\) | 4.23486 | − | 2.44500i | 0.138273 | − | 0.0798320i | ||||
\(939\) | 27.5722 | + | 47.7565i | 0.899786 | + | 1.55848i | ||||
\(940\) | 8.63492 | − | 14.9561i | 0.281640 | − | 0.487815i | ||||
\(941\) | − | 44.7743i | − | 1.45960i | −0.683660 | − | 0.729801i | \(-0.739613\pi\) | ||
0.683660 | − | 0.729801i | \(-0.260387\pi\) | |||||||
\(942\) | −50.1359 | − | 28.9459i | −1.63351 | − | 0.943110i | ||||
\(943\) | −3.06270 | − | 1.76825i | −0.0997353 | − | 0.0575822i | ||||
\(944\) | − | 0.567731i | − | 0.0184781i | ||||||
\(945\) | −15.7264 | + | 27.2388i | −0.511578 | + | 0.886080i | ||||
\(946\) | −3.37757 | − | 5.85012i | −0.109814 | − | 0.190204i | ||||
\(947\) | −46.5264 | + | 26.8621i | −1.51191 | + | 0.872899i | −0.512003 | + | 0.858984i | \(0.671096\pi\) |
−0.999903 | + | 0.0139157i | \(0.995570\pi\) | |||||||
\(948\) | 58.5067 | 1.90021 | ||||||||
\(949\) | −3.31938 | − | 41.8892i | −0.107752 | − | 1.35978i | ||||
\(950\) | 14.9450 | 0.484881 | ||||||||
\(951\) | −60.5014 | + | 34.9305i | −1.96189 | + | 1.13270i | ||||
\(952\) | 2.83204 | + | 4.90524i | 0.0917870 | + | 0.158980i | ||||
\(953\) | 7.42269 | − | 12.8565i | 0.240445 | − | 0.416462i | −0.720396 | − | 0.693563i | \(-0.756040\pi\) |
0.960841 | + | 0.277100i | \(0.0893734\pi\) | |||||||
\(954\) | − | 19.6671i | − | 0.636745i | ||||||
\(955\) | 11.3352 | + | 6.54437i | 0.366798 | + | 0.211771i | ||||
\(956\) | −22.2512 | − | 12.8467i | −0.719656 | − | 0.415493i | ||||
\(957\) | − | 67.0176i | − | 2.16637i | ||||||
\(958\) | 3.45857 | − | 5.99043i | 0.111741 | − | 0.193542i | ||||
\(959\) | 4.51529 | + | 7.82072i | 0.145806 | + | 0.252544i | ||||
\(960\) | −16.5035 | + | 9.52829i | −0.532648 | + | 0.307524i | ||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 13.9361 | − | 29.2580i | 0.449317 | − | 0.943317i | ||||
\(963\) | −100.587 | −3.24137 | ||||||||
\(964\) | −20.9906 | + | 12.1189i | −0.676061 | + | 0.390324i | ||||
\(965\) | −11.0461 | − | 19.1324i | −0.355586 | − | 0.615894i | ||||
\(966\) | 6.97949 | − | 12.0888i | 0.224561 | − | 0.388952i | ||||
\(967\) | 0.771974i | 0.0248250i | 0.999923 | + | 0.0124125i | \(0.00395112\pi\) | ||||
−0.999923 | + | 0.0124125i | \(0.996049\pi\) | |||||||
\(968\) | 48.3284 | + | 27.9024i | 1.55333 | + | 0.896817i | ||||
\(969\) | −17.6109 | − | 10.1677i | −0.565744 | − | 0.326633i | ||||
\(970\) | − | 13.4490i | − | 0.431822i | ||||||
\(971\) | 25.5192 | − | 44.2006i | 0.818951 | − | 1.41846i | −0.0875048 | − | 0.996164i | \(-0.527889\pi\) |
0.906456 | − | 0.422301i | \(-0.138777\pi\) | |||||||
\(972\) | −5.00460 | − | 8.66823i | −0.160523 | − | 0.278033i | ||||
\(973\) | 23.2646 | − | 13.4318i | 0.745829 | − | 0.430604i | ||||
\(974\) | −2.62974 | −0.0842622 | ||||||||
\(975\) | 17.2665 | + | 25.0941i | 0.552972 | + | 0.803654i | ||||
\(976\) | −3.77271 | −0.120761 | ||||||||
\(977\) | −18.7545 | + | 10.8279i | −0.600010 | + | 0.346416i | −0.769046 | − | 0.639194i | \(-0.779268\pi\) |
0.169035 | + | 0.985610i | \(0.445935\pi\) | |||||||
\(978\) | −0.980010 | − | 1.69743i | −0.0313373 | − | 0.0542777i | ||||
\(979\) | −0.807745 | + | 1.39906i | −0.0258157 | + | 0.0447140i | ||||
\(980\) | 5.71054i | 0.182417i | ||||||||
\(981\) | −25.6374 | − | 14.8018i | −0.818539 | − | 0.472584i | ||||
\(982\) | 24.7297 | + | 14.2777i | 0.789157 | + | 0.455620i | ||||
\(983\) | 27.0623i | 0.863152i | 0.902077 | + | 0.431576i | \(0.142042\pi\) | ||||
−0.902077 | + | 0.431576i | \(0.857958\pi\) | |||||||
\(984\) | −5.50430 | + | 9.53373i | −0.175471 | + | 0.303924i | ||||
\(985\) | −1.50393 | − | 2.60489i | −0.0479193 | − | 0.0829987i | ||||
\(986\) | −2.86910 | + | 1.65648i | −0.0913709 | + | 0.0527530i | ||||
\(987\) | 54.6039 | 1.73806 | ||||||||
\(988\) | 25.3143 | − | 17.4180i | 0.805355 | − | 0.554142i | ||||
\(989\) | −3.93329 | −0.125071 | ||||||||
\(990\) | 38.5676 | − | 22.2670i | 1.22576 | − | 0.707693i | ||||
\(991\) | −14.7710 | − | 25.5842i | −0.469217 | − | 0.812708i | 0.530163 | − | 0.847896i | \(-0.322131\pi\) |
−0.999381 | + | 0.0351872i | \(0.988797\pi\) | |||||||
\(992\) | −2.88769 | + | 5.00162i | −0.0916841 | + | 0.158802i | ||||
\(993\) | 5.37988i | 0.170725i | ||||||||
\(994\) | −5.14498 | − | 2.97046i | −0.163189 | − | 0.0942172i | ||||
\(995\) | −18.5243 | − | 10.6950i | −0.587260 | − | 0.339055i | ||||
\(996\) | 61.4753i | 1.94792i | ||||||||
\(997\) | −7.40350 | + | 12.8232i | −0.234471 | + | 0.406116i | −0.959119 | − | 0.283003i | \(-0.908669\pi\) |
0.724648 | + | 0.689120i | \(0.242003\pi\) | |||||||
\(998\) | −15.1830 | − | 26.2977i | −0.480608 | − | 0.832438i | ||||
\(999\) | −97.2220 | + | 56.1311i | −3.07597 | + | 1.77591i |
(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 | 403.2.r.a.218.22 | ✓ | 68 | |
13.2 | odd | 12 | 5239.2.a.r.1.22 | 34 | |||
13.4 | even | 6 | inner | 403.2.r.a.342.22 | yes | 68 | |
13.11 | odd | 12 | 5239.2.a.q.1.13 | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.r.a.218.22 | ✓ | 68 | 1.1 | even | 1 | trivial | |
403.2.r.a.342.22 | yes | 68 | 13.4 | even | 6 | inner | |
5239.2.a.q.1.13 | 34 | 13.11 | odd | 12 | |||
5239.2.a.r.1.22 | 34 | 13.2 | odd | 12 |