Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(100,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.h (of order \(8\), degree \(4\), 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: | \(1.49320251780\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 100.2 | ||
Character | \(\chi\) | \(=\) | 187.100 |
Dual form | 187.2.h.a.144.2 |
$q$-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 \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45974 | − | 1.45974i | −1.03219 | − | 1.03219i | −0.999464 | − | 0.0327267i | \(-0.989581\pi\) |
−0.0327267 | − | 0.999464i | \(-0.510419\pi\) | |||||||
\(3\) | −1.02130 | − | 2.46565i | −0.589650 | − | 1.42354i | −0.883838 | − | 0.467794i | \(-0.845049\pi\) |
0.294188 | − | 0.955748i | \(-0.404951\pi\) | |||||||
\(4\) | 2.26167i | 1.13084i | ||||||||
\(5\) | −1.65483 | + | 0.685451i | −0.740061 | + | 0.306543i | −0.720679 | − | 0.693269i | \(-0.756170\pi\) |
−0.0193818 | + | 0.999812i | \(0.506170\pi\) | |||||||
\(6\) | −2.10836 | + | 5.09004i | −0.860735 | + | 2.07800i | ||||
\(7\) | −0.400229 | − | 0.165780i | −0.151272 | − | 0.0626590i | 0.305763 | − | 0.952108i | \(-0.401089\pi\) |
−0.457035 | + | 0.889449i | \(0.651089\pi\) | |||||||
\(8\) | 0.381975 | − | 0.381975i | 0.135049 | − | 0.135049i | ||||
\(9\) | −2.91503 | + | 2.91503i | −0.971676 | + | 0.971676i | ||||
\(10\) | 3.41619 | + | 1.41503i | 1.08030 | + | 0.447473i | ||||
\(11\) | −0.382683 | + | 0.923880i | −0.115383 | + | 0.278560i | ||||
\(12\) | 5.57649 | − | 2.30986i | 1.60979 | − | 0.666798i | ||||
\(13\) | − | 4.97018i | − | 1.37848i | −0.724533 | − | 0.689241i | \(-0.757944\pi\) | ||
0.724533 | − | 0.689241i | \(-0.242056\pi\) | |||||||
\(14\) | 0.342234 | + | 0.826225i | 0.0914658 | + | 0.220818i | ||||
\(15\) | 3.38016 | + | 3.38016i | 0.872754 | + | 0.872754i | ||||
\(16\) | 3.40818 | 0.852045 | ||||||||
\(17\) | −1.96041 | + | 3.62723i | −0.475469 | + | 0.879732i | ||||
\(18\) | 8.51035 | 2.00591 | ||||||||
\(19\) | 0.0504966 | + | 0.0504966i | 0.0115847 | + | 0.0115847i | 0.712875 | − | 0.701291i | \(-0.247392\pi\) |
−0.701291 | + | 0.712875i | \(0.747392\pi\) | |||||||
\(20\) | −1.55027 | − | 3.74268i | −0.346650 | − | 0.836888i | ||||
\(21\) | 1.15613i | 0.252289i | ||||||||
\(22\) | 1.90724 | − | 0.790005i | 0.406625 | − | 0.168430i | ||||
\(23\) | 1.15112 | − | 2.77906i | 0.240026 | − | 0.579473i | −0.757259 | − | 0.653115i | \(-0.773462\pi\) |
0.997285 | + | 0.0736413i | \(0.0234620\pi\) | |||||||
\(24\) | −1.33193 | − | 0.551703i | −0.271879 | − | 0.112616i | ||||
\(25\) | −1.26693 | + | 1.26693i | −0.253386 | + | 0.253386i | ||||
\(26\) | −7.25517 | + | 7.25517i | −1.42286 | + | 1.42286i | ||||
\(27\) | 2.76761 | + | 1.14638i | 0.532628 | + | 0.220622i | ||||
\(28\) | 0.374941 | − | 0.905187i | 0.0708571 | − | 0.171064i | ||||
\(29\) | −7.19936 | + | 2.98207i | −1.33689 | + | 0.553757i | −0.932612 | − | 0.360880i | \(-0.882477\pi\) |
−0.404276 | + | 0.914637i | \(0.632477\pi\) | |||||||
\(30\) | − | 9.86830i | − | 1.80170i | ||||||
\(31\) | 2.29702 | + | 5.54550i | 0.412557 | + | 0.996002i | 0.984449 | + | 0.175672i | \(0.0562099\pi\) |
−0.571891 | + | 0.820329i | \(0.693790\pi\) | |||||||
\(32\) | −5.73900 | − | 5.73900i | −1.01452 | − | 1.01452i | ||||
\(33\) | 2.66880 | 0.464578 | ||||||||
\(34\) | 8.15649 | − | 2.43312i | 1.39883 | − | 0.417277i | ||||
\(35\) | 0.775944 | 0.131158 | ||||||||
\(36\) | −6.59284 | − | 6.59284i | −1.09881 | − | 1.09881i | ||||
\(37\) | −2.62706 | − | 6.34228i | −0.431886 | − | 1.04266i | −0.978679 | − | 0.205396i | \(-0.934152\pi\) |
0.546793 | − | 0.837268i | \(-0.315848\pi\) | |||||||
\(38\) | − | 0.147424i | − | 0.0239153i | ||||||
\(39\) | −12.2547 | + | 5.07607i | −1.96232 | + | 0.812822i | ||||
\(40\) | −0.370277 | + | 0.893928i | −0.0585460 | + | 0.141342i | ||||
\(41\) | −7.19622 | − | 2.98077i | −1.12386 | − | 0.465518i | −0.258171 | − | 0.966099i | \(-0.583120\pi\) |
−0.865690 | + | 0.500581i | \(0.833120\pi\) | |||||||
\(42\) | 1.68765 | − | 1.68765i | 0.260411 | − | 0.260411i | ||||
\(43\) | −2.52664 | + | 2.52664i | −0.385309 | + | 0.385309i | −0.873010 | − | 0.487702i | \(-0.837835\pi\) |
0.487702 | + | 0.873010i | \(0.337835\pi\) | |||||||
\(44\) | −2.08951 | − | 0.865505i | −0.315006 | − | 0.130480i | ||||
\(45\) | 2.82575 | − | 6.82197i | 0.421238 | − | 1.01696i | ||||
\(46\) | −5.73703 | + | 2.37636i | −0.845880 | + | 0.350375i | ||||
\(47\) | 1.33656i | 0.194957i | 0.995238 | + | 0.0974786i | \(0.0310778\pi\) | ||||
−0.995238 | + | 0.0974786i | \(0.968922\pi\) | |||||||
\(48\) | −3.48079 | − | 8.40336i | −0.502408 | − | 1.21292i | ||||
\(49\) | −4.81705 | − | 4.81705i | −0.688150 | − | 0.688150i | ||||
\(50\) | 3.69877 | 0.523085 | ||||||||
\(51\) | 10.9456 | + | 1.12917i | 1.53270 | + | 0.158116i | ||||
\(52\) | 11.2409 | 1.55884 | ||||||||
\(53\) | 1.43933 | + | 1.43933i | 0.197707 | + | 0.197707i | 0.799016 | − | 0.601309i | \(-0.205354\pi\) |
−0.601309 | + | 0.799016i | \(0.705354\pi\) | |||||||
\(54\) | −2.36657 | − | 5.71341i | −0.322050 | − | 0.777497i | ||||
\(55\) | − | 1.79117i | − | 0.241521i | ||||||
\(56\) | −0.216201 | + | 0.0895536i | −0.0288911 | + | 0.0119671i | ||||
\(57\) | 0.0729344 | − | 0.176079i | 0.00966040 | − | 0.0233223i | ||||
\(58\) | 14.8622 | + | 6.15614i | 1.95151 | + | 0.808341i | ||||
\(59\) | 5.94972 | − | 5.94972i | 0.774588 | − | 0.774588i | −0.204317 | − | 0.978905i | \(-0.565497\pi\) |
0.978905 | + | 0.204317i | \(0.0654973\pi\) | |||||||
\(60\) | −7.64482 | + | 7.64482i | −0.986942 | + | 0.986942i | ||||
\(61\) | −6.64758 | − | 2.75352i | −0.851136 | − | 0.352552i | −0.0859013 | − | 0.996304i | \(-0.527377\pi\) |
−0.765234 | + | 0.643752i | \(0.777377\pi\) | |||||||
\(62\) | 4.74193 | − | 11.4480i | 0.602226 | − | 1.45390i | ||||
\(63\) | 1.64993 | − | 0.683424i | 0.207872 | − | 0.0861033i | ||||
\(64\) | 9.93853i | 1.24232i | ||||||||
\(65\) | 3.40682 | + | 8.22479i | 0.422564 | + | 1.02016i | ||||
\(66\) | −3.89574 | − | 3.89574i | −0.479533 | − | 0.479533i | ||||
\(67\) | 8.63417 | 1.05483 | 0.527416 | − | 0.849607i | \(-0.323161\pi\) | ||||
0.527416 | + | 0.849607i | \(0.323161\pi\) | |||||||
\(68\) | −8.20361 | − | 4.43381i | −0.994834 | − | 0.537678i | ||||
\(69\) | −8.02781 | −0.966435 | ||||||||
\(70\) | −1.13267 | − | 1.13267i | −0.135381 | − | 0.135381i | ||||
\(71\) | 0.171987 | + | 0.415214i | 0.0204111 | + | 0.0492768i | 0.933757 | − | 0.357909i | \(-0.116510\pi\) |
−0.913345 | + | 0.407186i | \(0.866510\pi\) | |||||||
\(72\) | 2.22694i | 0.262447i | ||||||||
\(73\) | −6.55147 | + | 2.71371i | −0.766792 | + | 0.317616i | −0.731572 | − | 0.681764i | \(-0.761213\pi\) |
−0.0352196 | + | 0.999380i | \(0.511213\pi\) | |||||||
\(74\) | −5.42325 | + | 13.0929i | −0.630440 | + | 1.52202i | ||||
\(75\) | 4.41771 | + | 1.82988i | 0.510114 | + | 0.211296i | ||||
\(76\) | −0.114207 | + | 0.114207i | −0.0131004 | + | 0.0131004i | ||||
\(77\) | 0.306322 | − | 0.306322i | 0.0349086 | − | 0.0349086i | ||||
\(78\) | 25.2984 | + | 10.4789i | 2.86448 | + | 1.18651i | ||||
\(79\) | −3.49368 | + | 8.43448i | −0.393069 | + | 0.948953i | 0.596198 | + | 0.802837i | \(0.296677\pi\) |
−0.989267 | + | 0.146116i | \(0.953323\pi\) | |||||||
\(80\) | −5.63995 | + | 2.33614i | −0.630565 | + | 0.261189i | ||||
\(81\) | 4.37265i | 0.485850i | ||||||||
\(82\) | 6.15345 | + | 14.8557i | 0.679535 | + | 1.64054i | ||||
\(83\) | −11.5538 | − | 11.5538i | −1.26820 | − | 1.26820i | −0.947018 | − | 0.321182i | \(-0.895920\pi\) |
−0.321182 | − | 0.947018i | \(-0.604080\pi\) | |||||||
\(84\) | −2.61480 | −0.285298 | ||||||||
\(85\) | 0.757847 | − | 7.34620i | 0.0822000 | − | 0.796807i | ||||
\(86\) | 7.37646 | 0.795424 | ||||||||
\(87\) | 14.7055 | + | 14.7055i | 1.57659 | + | 1.57659i | ||||
\(88\) | 0.206723 | + | 0.499075i | 0.0220368 | + | 0.0532015i | ||||
\(89\) | − | 17.2300i | − | 1.82638i | −0.407532 | − | 0.913191i | \(-0.633611\pi\) | ||
0.407532 | − | 0.913191i | \(-0.366389\pi\) | |||||||
\(90\) | −14.0832 | + | 5.83344i | −1.48450 | + | 0.614898i | ||||
\(91\) | −0.823958 | + | 1.98921i | −0.0863743 | + | 0.208526i | ||||
\(92\) | 6.28532 | + | 2.60346i | 0.655290 | + | 0.271430i | ||||
\(93\) | 11.3273 | − | 11.3273i | 1.17458 | − | 1.17458i | ||||
\(94\) | 1.95103 | − | 1.95103i | 0.201233 | − | 0.201233i | ||||
\(95\) | −0.118176 | − | 0.0489502i | −0.0121246 | − | 0.00502218i | ||||
\(96\) | −8.28908 | + | 20.0116i | −0.846001 | + | 2.04243i | ||||
\(97\) | 9.20938 | − | 3.81465i | 0.935071 | − | 0.387319i | 0.137471 | − | 0.990506i | \(-0.456103\pi\) |
0.797600 | + | 0.603187i | \(0.206103\pi\) | |||||||
\(98\) | 14.0633i | 1.42060i | ||||||||
\(99\) | −1.57760 | − | 3.80867i | −0.158555 | − | 0.382785i | ||||
\(100\) | −2.86538 | − | 2.86538i | −0.286538 | − | 0.286538i | ||||
\(101\) | 16.7302 | 1.66472 | 0.832360 | − | 0.554235i | \(-0.186989\pi\) | ||||
0.832360 | + | 0.554235i | \(0.186989\pi\) | |||||||
\(102\) | −14.3295 | − | 17.6261i | −1.41883 | − | 1.74524i | ||||
\(103\) | 2.27820 | 0.224478 | 0.112239 | − | 0.993681i | \(-0.464198\pi\) | ||||
0.112239 | + | 0.993681i | \(0.464198\pi\) | |||||||
\(104\) | −1.89849 | − | 1.89849i | −0.186162 | − | 0.186162i | ||||
\(105\) | −0.792474 | − | 1.91320i | −0.0773376 | − | 0.186709i | ||||
\(106\) | − | 4.20208i | − | 0.408143i | ||||||
\(107\) | −10.8020 | + | 4.47432i | −1.04427 | + | 0.432549i | −0.837841 | − | 0.545914i | \(-0.816183\pi\) |
−0.206424 | + | 0.978463i | \(0.566183\pi\) | |||||||
\(108\) | −2.59275 | + | 6.25944i | −0.249487 | + | 0.602315i | ||||
\(109\) | −4.82614 | − | 1.99905i | −0.462260 | − | 0.191475i | 0.139384 | − | 0.990238i | \(-0.455488\pi\) |
−0.601645 | + | 0.798764i | \(0.705488\pi\) | |||||||
\(110\) | −2.61464 | + | 2.61464i | −0.249296 | + | 0.249296i | ||||
\(111\) | −12.9548 | + | 12.9548i | −1.22961 | + | 1.22961i | ||||
\(112\) | −1.36405 | − | 0.565009i | −0.128891 | − | 0.0533883i | ||||
\(113\) | 1.04409 | − | 2.52067i | 0.0982201 | − | 0.237124i | −0.867130 | − | 0.498081i | \(-0.834038\pi\) |
0.965350 | + | 0.260957i | \(0.0840381\pi\) | |||||||
\(114\) | −0.363495 | + | 0.150564i | −0.0340444 | + | 0.0141017i | ||||
\(115\) | 5.38789i | 0.502424i | ||||||||
\(116\) | −6.74448 | − | 16.2826i | −0.626209 | − | 1.51180i | ||||
\(117\) | 14.4882 | + | 14.4882i | 1.33944 | + | 1.33944i | ||||
\(118\) | −17.3701 | −1.59905 | ||||||||
\(119\) | 1.38594 | − | 1.12673i | 0.127048 | − | 0.103287i | ||||
\(120\) | 2.58228 | 0.235728 | ||||||||
\(121\) | −0.707107 | − | 0.707107i | −0.0642824 | − | 0.0642824i | ||||
\(122\) | 5.68432 | + | 13.7232i | 0.514634 | + | 1.24244i | ||||
\(123\) | 20.7876i | 1.87435i | ||||||||
\(124\) | −12.5421 | + | 5.19512i | −1.12632 | + | 0.466535i | ||||
\(125\) | 4.65539 | − | 11.2391i | 0.416390 | − | 1.00526i | ||||
\(126\) | −3.40609 | − | 1.41085i | −0.303439 | − | 0.125688i | ||||
\(127\) | 10.7867 | − | 10.7867i | 0.957167 | − | 0.957167i | −0.0419525 | − | 0.999120i | \(-0.513358\pi\) |
0.999120 | + | 0.0419525i | \(0.0133578\pi\) | |||||||
\(128\) | 3.02965 | − | 3.02965i | 0.267785 | − | 0.267785i | ||||
\(129\) | 8.81026 | + | 3.64933i | 0.775700 | + | 0.321306i | ||||
\(130\) | 7.03298 | − | 16.9791i | 0.616833 | − | 1.48917i | ||||
\(131\) | 17.3396 | − | 7.18231i | 1.51497 | − | 0.627522i | 0.538395 | − | 0.842693i | \(-0.319031\pi\) |
0.976576 | + | 0.215171i | \(0.0690309\pi\) | |||||||
\(132\) | 6.03595i | 0.525362i | ||||||||
\(133\) | −0.0118389 | − | 0.0285816i | −0.00102656 | − | 0.00247833i | ||||
\(134\) | −12.6036 | − | 12.6036i | −1.08879 | − | 1.08879i | ||||
\(135\) | −5.36571 | −0.461807 | ||||||||
\(136\) | 0.636684 | + | 2.13434i | 0.0545952 | + | 0.183018i | ||||
\(137\) | −13.0800 | −1.11750 | −0.558748 | − | 0.829337i | \(-0.688718\pi\) | ||||
−0.558748 | + | 0.829337i | \(0.688718\pi\) | |||||||
\(138\) | 11.7185 | + | 11.7185i | 0.997546 | + | 0.997546i | ||||
\(139\) | −7.43974 | − | 17.9611i | −0.631031 | − | 1.52344i | −0.838329 | − | 0.545165i | \(-0.816467\pi\) |
0.207298 | − | 0.978278i | \(-0.433533\pi\) | |||||||
\(140\) | 1.75493i | 0.148319i | ||||||||
\(141\) | 3.29548 | − | 1.36503i | 0.277530 | − | 0.114957i | ||||
\(142\) | 0.355047 | − | 0.857160i | 0.0297949 | − | 0.0719313i | ||||
\(143\) | 4.59185 | + | 1.90201i | 0.383990 | + | 0.159054i | ||||
\(144\) | −9.93493 | + | 9.93493i | −0.827911 | + | 0.827911i | ||||
\(145\) | 9.86963 | − | 9.86963i | 0.819628 | − | 0.819628i | ||||
\(146\) | 13.5247 | + | 5.60213i | 1.11932 | + | 0.463636i | ||||
\(147\) | −6.95746 | + | 16.7968i | −0.573842 | + | 1.38538i | ||||
\(148\) | 14.3442 | − | 5.94155i | 1.17908 | − | 0.488392i | ||||
\(149\) | − | 7.74406i | − | 0.634418i | −0.948356 | − | 0.317209i | \(-0.897254\pi\) | ||
0.948356 | − | 0.317209i | \(-0.102746\pi\) | |||||||
\(150\) | −3.77756 | − | 9.11985i | −0.308437 | − | 0.744632i | ||||
\(151\) | 3.94357 | + | 3.94357i | 0.320923 | + | 0.320923i | 0.849121 | − | 0.528198i | \(-0.177132\pi\) |
−0.528198 | + | 0.849121i | \(0.677132\pi\) | |||||||
\(152\) | 0.0385769 | 0.00312900 | ||||||||
\(153\) | −4.85883 | − | 16.2881i | −0.392813 | − | 1.31682i | ||||
\(154\) | −0.894300 | −0.0720647 | ||||||||
\(155\) | −7.60235 | − | 7.60235i | −0.610635 | − | 0.610635i | ||||
\(156\) | −11.4804 | − | 27.7162i | −0.919169 | − | 2.21907i | ||||
\(157\) | 13.2252i | 1.05549i | 0.849404 | + | 0.527743i | \(0.176961\pi\) | ||||
−0.849404 | + | 0.527743i | \(0.823039\pi\) | |||||||
\(158\) | 17.4120 | − | 7.21228i | 1.38522 | − | 0.573778i | ||||
\(159\) | 2.07888 | − | 5.01886i | 0.164866 | − | 0.398022i | ||||
\(160\) | 13.4309 | + | 5.56324i | 1.06180 | + | 0.439813i | ||||
\(161\) | −0.921425 | + | 0.921425i | −0.0726185 | + | 0.0726185i | ||||
\(162\) | 6.38292 | − | 6.38292i | 0.501490 | − | 0.501490i | ||||
\(163\) | −20.5516 | − | 8.51277i | −1.60973 | − | 0.666772i | −0.616980 | − | 0.786978i | \(-0.711644\pi\) |
−0.992749 | + | 0.120207i | \(0.961644\pi\) | |||||||
\(164\) | 6.74153 | − | 16.2755i | 0.526425 | − | 1.27090i | ||||
\(165\) | −4.41639 | + | 1.82933i | −0.343816 | + | 0.142413i | ||||
\(166\) | 33.7312i | 2.61805i | ||||||||
\(167\) | −5.42837 | − | 13.1052i | −0.420060 | − | 1.01411i | −0.982329 | − | 0.187160i | \(-0.940072\pi\) |
0.562270 | − | 0.826954i | \(-0.309928\pi\) | |||||||
\(168\) | 0.441615 | + | 0.441615i | 0.0340713 | + | 0.0340713i | ||||
\(169\) | −11.7027 | −0.900211 | ||||||||
\(170\) | −11.8298 | + | 9.61727i | −0.907304 | + | 0.737611i | ||||
\(171\) | −0.294398 | −0.0225132 | ||||||||
\(172\) | −5.71443 | − | 5.71443i | −0.435721 | − | 0.435721i | ||||
\(173\) | 5.01564 | + | 12.1088i | 0.381332 | + | 0.920617i | 0.991709 | + | 0.128506i | \(0.0410181\pi\) |
−0.610377 | + | 0.792111i | \(0.708982\pi\) | |||||||
\(174\) | − | 42.9323i | − | 3.25469i | ||||||
\(175\) | 0.717093 | − | 0.297029i | 0.0542071 | − | 0.0224533i | ||||
\(176\) | −1.30425 | + | 3.14875i | −0.0983118 | + | 0.237346i | ||||
\(177\) | −20.7464 | − | 8.59343i | −1.55939 | − | 0.645922i | ||||
\(178\) | −25.1514 | + | 25.1514i | −1.88517 | + | 1.88517i | ||||
\(179\) | 7.83859 | − | 7.83859i | 0.585884 | − | 0.585884i | −0.350630 | − | 0.936514i | \(-0.614033\pi\) |
0.936514 | + | 0.350630i | \(0.114033\pi\) | |||||||
\(180\) | 15.4291 | + | 6.39093i | 1.15002 | + | 0.476352i | ||||
\(181\) | 1.70622 | − | 4.11918i | 0.126822 | − | 0.306176i | −0.847697 | − | 0.530481i | \(-0.822011\pi\) |
0.974519 | + | 0.224305i | \(0.0720112\pi\) | |||||||
\(182\) | 4.10649 | − | 1.70097i | 0.304393 | − | 0.126084i | ||||
\(183\) | 19.2028i | 1.41951i | ||||||||
\(184\) | −0.621830 | − | 1.50123i | −0.0458419 | − | 0.110672i | ||||
\(185\) | 8.69465 | + | 8.69465i | 0.639243 | + | 0.639243i | ||||
\(186\) | −33.0698 | −2.42479 | ||||||||
\(187\) | −2.60091 | − | 3.19926i | −0.190197 | − | 0.233953i | ||||
\(188\) | −3.02286 | −0.220465 | ||||||||
\(189\) | −0.917632 | − | 0.917632i | −0.0667479 | − | 0.0667479i | ||||
\(190\) | 0.101052 | + | 0.243961i | 0.00733107 | + | 0.0176988i | ||||
\(191\) | 23.5043i | 1.70071i | 0.526208 | + | 0.850356i | \(0.323613\pi\) | ||||
−0.526208 | + | 0.850356i | \(0.676387\pi\) | |||||||
\(192\) | 24.5049 | − | 10.1503i | 1.76849 | − | 0.732532i | ||||
\(193\) | −5.11360 | + | 12.3453i | −0.368085 | + | 0.888636i | 0.625979 | + | 0.779840i | \(0.284700\pi\) |
−0.994064 | + | 0.108796i | \(0.965300\pi\) | |||||||
\(194\) | −19.0117 | − | 7.87490i | −1.36496 | − | 0.565385i | ||||
\(195\) | 16.8000 | − | 16.8000i | 1.20307 | − | 1.20307i | ||||
\(196\) | 10.8946 | − | 10.8946i | 0.778185 | − | 0.778185i | ||||
\(197\) | 7.53664 | + | 3.12178i | 0.536963 | + | 0.222418i | 0.634650 | − | 0.772800i | \(-0.281144\pi\) |
−0.0976866 | + | 0.995217i | \(0.531144\pi\) | |||||||
\(198\) | −3.25677 | + | 7.86254i | −0.231449 | + | 0.558767i | ||||
\(199\) | −19.7071 | + | 8.16295i | −1.39700 | + | 0.578656i | −0.948971 | − | 0.315363i | \(-0.897874\pi\) |
−0.448029 | + | 0.894019i | \(0.647874\pi\) | |||||||
\(200\) | 0.967870i | 0.0684387i | ||||||||
\(201\) | −8.81811 | − | 21.2888i | −0.621982 | − | 1.50160i | ||||
\(202\) | −24.4218 | − | 24.4218i | −1.71831 | − | 1.71831i | ||||
\(203\) | 3.37576 | 0.236932 | ||||||||
\(204\) | −2.55382 | + | 24.7555i | −0.178803 | + | 1.73323i | ||||
\(205\) | 13.9517 | 0.974427 | ||||||||
\(206\) | −3.32558 | − | 3.32558i | −0.231704 | − | 0.231704i | ||||
\(207\) | 4.74547 | + | 11.4566i | 0.329833 | + | 0.796287i | ||||
\(208\) | − | 16.9393i | − | 1.17453i | ||||||
\(209\) | −0.0659770 | + | 0.0273286i | −0.00456373 | + | 0.00189036i | ||||
\(210\) | −1.63597 | + | 3.94958i | −0.112893 | + | 0.272547i | ||||
\(211\) | 1.55187 | + | 0.642806i | 0.106835 | + | 0.0442526i | 0.435461 | − | 0.900208i | \(-0.356585\pi\) |
−0.328626 | + | 0.944460i | \(0.606585\pi\) | |||||||
\(212\) | −3.25529 | + | 3.25529i | −0.223574 | + | 0.223574i | ||||
\(213\) | 0.848119 | − | 0.848119i | 0.0581121 | − | 0.0581121i | ||||
\(214\) | 22.2994 | + | 9.23671i | 1.52435 | + | 0.631408i | ||||
\(215\) | 2.44926 | − | 5.91303i | 0.167038 | − | 0.403266i | ||||
\(216\) | 1.49505 | − | 0.619270i | 0.101725 | − | 0.0421360i | ||||
\(217\) | − | 2.60027i | − | 0.176518i | ||||||
\(218\) | 4.12681 | + | 9.96300i | 0.279503 | + | 0.674779i | ||||
\(219\) | 13.3821 | + | 13.3821i | 0.904278 | + | 0.904278i | ||||
\(220\) | 4.05104 | 0.273121 | ||||||||
\(221\) | 18.0280 | + | 9.74360i | 1.21269 | + | 0.655425i | ||||
\(222\) | 37.8212 | 2.53839 | ||||||||
\(223\) | 13.7198 | + | 13.7198i | 0.918749 | + | 0.918749i | 0.996939 | − | 0.0781896i | \(-0.0249139\pi\) |
−0.0781896 | + | 0.996939i | \(0.524914\pi\) | |||||||
\(224\) | 1.34550 | + | 3.24833i | 0.0899001 | + | 0.217038i | ||||
\(225\) | − | 7.38626i | − | 0.492417i | ||||||
\(226\) | −5.20362 | + | 2.15541i | −0.346139 | + | 0.143376i | ||||
\(227\) | 2.05527 | − | 4.96186i | 0.136413 | − | 0.329330i | −0.840880 | − | 0.541221i | \(-0.817962\pi\) |
0.977293 | + | 0.211891i | \(0.0679622\pi\) | |||||||
\(228\) | 0.398234 | + | 0.164954i | 0.0263737 | + | 0.0109243i | ||||
\(229\) | −8.58698 | + | 8.58698i | −0.567444 | + | 0.567444i | −0.931412 | − | 0.363968i | \(-0.881422\pi\) |
0.363968 | + | 0.931412i | \(0.381422\pi\) | |||||||
\(230\) | 7.86492 | − | 7.86492i | 0.518597 | − | 0.518597i | ||||
\(231\) | −1.06813 | − | 0.442434i | −0.0702777 | − | 0.0291100i | ||||
\(232\) | −1.61090 | + | 3.88906i | −0.105761 | + | 0.255329i | ||||
\(233\) | −9.37899 | + | 3.88490i | −0.614438 | + | 0.254508i | −0.668125 | − | 0.744049i | \(-0.732903\pi\) |
0.0536868 | + | 0.998558i | \(0.482903\pi\) | |||||||
\(234\) | − | 42.2980i | − | 2.76511i | ||||||
\(235\) | −0.916147 | − | 2.21177i | −0.0597628 | − | 0.144280i | ||||
\(236\) | 13.4563 | + | 13.4563i | 0.875933 | + | 0.875933i | ||||
\(237\) | 24.3645 | 1.58265 | ||||||||
\(238\) | −3.66783 | − | 0.378379i | −0.237750 | − | 0.0245267i | ||||
\(239\) | −5.36807 | −0.347232 | −0.173616 | − | 0.984813i | \(-0.555545\pi\) | ||||
−0.173616 | + | 0.984813i | \(0.555545\pi\) | |||||||
\(240\) | 11.5202 | + | 11.5202i | 0.743625 | + | 0.743625i | ||||
\(241\) | 0.336088 | + | 0.811387i | 0.0216493 | + | 0.0522660i | 0.934335 | − | 0.356397i | \(-0.115995\pi\) |
−0.912685 | + | 0.408663i | \(0.865995\pi\) | |||||||
\(242\) | 2.06438i | 0.132704i | ||||||||
\(243\) | 19.0842 | − | 7.90495i | 1.22425 | − | 0.507103i | ||||
\(244\) | 6.22756 | − | 15.0347i | 0.398679 | − | 0.962496i | ||||
\(245\) | 11.2732 | + | 4.66952i | 0.720220 | + | 0.298325i | ||||
\(246\) | 30.3445 | − | 30.3445i | 1.93469 | − | 1.93469i | ||||
\(247\) | 0.250978 | − | 0.250978i | 0.0159693 | − | 0.0159693i | ||||
\(248\) | 2.99565 | + | 1.24084i | 0.190224 | + | 0.0787934i | ||||
\(249\) | −16.6877 | + | 40.2877i | −1.05754 | + | 2.55313i | ||||
\(250\) | −23.2018 | + | 9.61049i | −1.46741 | + | 0.607821i | ||||
\(251\) | 26.8734i | 1.69624i | 0.529808 | + | 0.848118i | \(0.322264\pi\) | ||||
−0.529808 | + | 0.848118i | \(0.677736\pi\) | |||||||
\(252\) | 1.54568 | + | 3.73161i | 0.0973688 | + | 0.235069i | ||||
\(253\) | 2.12700 | + | 2.12700i | 0.133723 | + | 0.133723i | ||||
\(254\) | −31.4916 | −1.97596 | ||||||||
\(255\) | −18.8871 | + | 5.63412i | −1.18276 | + | 0.352822i | ||||
\(256\) | 11.0321 | 0.689504 | ||||||||
\(257\) | −10.7866 | − | 10.7866i | −0.672852 | − | 0.672852i | 0.285520 | − | 0.958373i | \(-0.407834\pi\) |
−0.958373 | + | 0.285520i | \(0.907834\pi\) | |||||||
\(258\) | −7.53361 | − | 18.1877i | −0.469022 | − | 1.13232i | ||||
\(259\) | 2.97388i | 0.184788i | ||||||||
\(260\) | −18.6018 | + | 7.70512i | −1.15363 | + | 0.477851i | ||||
\(261\) | 12.2935 | − | 29.6792i | 0.760949 | − | 1.83709i | ||||
\(262\) | −35.7956 | − | 14.8270i | −2.21146 | − | 0.916018i | ||||
\(263\) | 0.819101 | − | 0.819101i | 0.0505079 | − | 0.0505079i | −0.681402 | − | 0.731910i | \(-0.738629\pi\) |
0.731910 | + | 0.681402i | \(0.238629\pi\) | |||||||
\(264\) | 1.01941 | − | 1.01941i | 0.0627406 | − | 0.0627406i | ||||
\(265\) | −3.36843 | − | 1.39525i | −0.206921 | − | 0.0857094i | ||||
\(266\) | −0.0244399 | + | 0.0590032i | −0.00149851 | + | 0.00361772i | ||||
\(267\) | −42.4832 | + | 17.5971i | −2.59993 | + | 1.07693i | ||||
\(268\) | 19.5277i | 1.19284i | ||||||||
\(269\) | 12.0872 | + | 29.1810i | 0.736967 | + | 1.77920i | 0.617819 | + | 0.786320i | \(0.288016\pi\) |
0.119148 | + | 0.992876i | \(0.461984\pi\) | |||||||
\(270\) | 7.83254 | + | 7.83254i | 0.476673 | + | 0.476673i | ||||
\(271\) | 20.5379 | 1.24759 | 0.623794 | − | 0.781589i | \(-0.285591\pi\) | ||||
0.623794 | + | 0.781589i | \(0.285591\pi\) | |||||||
\(272\) | −6.68143 | + | 12.3622i | −0.405121 | + | 0.749572i | ||||
\(273\) | 5.74620 | 0.347776 | ||||||||
\(274\) | 19.0933 | + | 19.0933i | 1.15347 | + | 1.15347i | ||||
\(275\) | −0.685656 | − | 1.65532i | −0.0413466 | − | 0.0998196i | ||||
\(276\) | − | 18.1563i | − | 1.09288i | ||||||
\(277\) | −16.1157 | + | 6.67535i | −0.968300 | + | 0.401083i | −0.810079 | − | 0.586321i | \(-0.800576\pi\) |
−0.158221 | + | 0.987404i | \(0.550576\pi\) | |||||||
\(278\) | −15.3585 | + | 37.0786i | −0.921140 | + | 2.22383i | ||||
\(279\) | −22.8612 | − | 9.46941i | −1.36866 | − | 0.566919i | ||||
\(280\) | 0.296391 | − | 0.296391i | 0.0177128 | − | 0.0177128i | ||||
\(281\) | −3.66525 | + | 3.66525i | −0.218650 | + | 0.218650i | −0.807930 | − | 0.589279i | \(-0.799412\pi\) |
0.589279 | + | 0.807930i | \(0.299412\pi\) | |||||||
\(282\) | −6.80313 | − | 2.81795i | −0.405121 | − | 0.167807i | ||||
\(283\) | 8.62565 | − | 20.8242i | 0.512742 | − | 1.23787i | −0.429540 | − | 0.903048i | \(-0.641324\pi\) |
0.942282 | − | 0.334820i | \(-0.108676\pi\) | |||||||
\(284\) | −0.939078 | + | 0.388979i | −0.0557240 | + | 0.0230816i | ||||
\(285\) | 0.341373i | 0.0202212i | ||||||||
\(286\) | −3.92647 | − | 9.47934i | −0.232177 | − | 0.560525i | ||||
\(287\) | 2.38598 | + | 2.38598i | 0.140840 | + | 0.140840i | ||||
\(288\) | 33.4587 | 1.97157 | ||||||||
\(289\) | −9.31359 | − | 14.2217i | −0.547858 | − | 0.836571i | ||||
\(290\) | −28.8142 | −1.69203 | ||||||||
\(291\) | −18.8112 | − | 18.8112i | −1.10273 | − | 1.10273i | ||||
\(292\) | −6.13752 | − | 14.8173i | −0.359171 | − | 0.867116i | ||||
\(293\) | − | 5.00079i | − | 0.292150i | −0.989274 | − | 0.146075i | \(-0.953336\pi\) | ||
0.989274 | − | 0.146075i | \(-0.0466640\pi\) | |||||||
\(294\) | 34.6750 | − | 14.3629i | 2.02229 | − | 0.837659i | ||||
\(295\) | −5.76751 | + | 13.9240i | −0.335797 | + | 0.810687i | ||||
\(296\) | −3.42606 | − | 1.41912i | −0.199136 | − | 0.0824848i | ||||
\(297\) | −2.11824 | + | 2.11824i | −0.122913 | + | 0.122913i | ||||
\(298\) | −11.3043 | + | 11.3043i | −0.654840 | + | 0.654840i | ||||
\(299\) | −13.8124 | − | 5.72129i | −0.798793 | − | 0.330871i | ||||
\(300\) | −4.13858 | + | 9.99142i | −0.238941 | + | 0.576855i | ||||
\(301\) | 1.43010 | − | 0.592367i | 0.0824296 | − | 0.0341435i | ||||
\(302\) | − | 11.5132i | − | 0.662508i | ||||||
\(303\) | −17.0867 | − | 41.2508i | −0.981603 | − | 2.36980i | ||||
\(304\) | 0.172102 | + | 0.172102i | 0.00987070 | + | 0.00987070i | ||||
\(305\) | 12.8880 | 0.737965 | ||||||||
\(306\) | −16.6838 | + | 30.8690i | −0.953748 | + | 1.76466i | ||||
\(307\) | 3.65731 | 0.208734 | 0.104367 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(308\) | 0.692800 | + | 0.692800i | 0.0394760 | + | 0.0394760i | ||||
\(309\) | −2.32674 | − | 5.61725i | −0.132364 | − | 0.319554i | ||||
\(310\) | 22.1949i | 1.26058i | ||||||||
\(311\) | 17.8568 | − | 7.39652i | 1.01257 | − | 0.419418i | 0.186175 | − | 0.982517i | \(-0.440391\pi\) |
0.826390 | + | 0.563098i | \(0.190391\pi\) | |||||||
\(312\) | −2.74206 | + | 6.61993i | −0.155239 | + | 0.374780i | ||||
\(313\) | −27.2753 | − | 11.2978i | −1.54169 | − | 0.638588i | −0.559899 | − | 0.828561i | \(-0.689160\pi\) |
−0.981789 | + | 0.189973i | \(0.939160\pi\) | |||||||
\(314\) | 19.3053 | − | 19.3053i | 1.08946 | − | 1.08946i | ||||
\(315\) | −2.26190 | + | 2.26190i | −0.127443 | + | 0.127443i | ||||
\(316\) | −19.0760 | − | 7.90156i | −1.07311 | − | 0.444497i | ||||
\(317\) | 3.12888 | − | 7.55377i | 0.175735 | − | 0.424262i | −0.811329 | − | 0.584590i | \(-0.801255\pi\) |
0.987064 | + | 0.160328i | \(0.0512552\pi\) | |||||||
\(318\) | −10.3609 | + | 4.29161i | −0.581008 | + | 0.240661i | ||||
\(319\) | − | 7.79254i | − | 0.436298i | ||||||
\(320\) | −6.81238 | − | 16.4465i | −0.380823 | − | 0.919389i | ||||
\(321\) | 22.0642 | + | 22.0642i | 1.23150 | + | 1.23150i | ||||
\(322\) | 2.69008 | 0.149912 | ||||||||
\(323\) | −0.282157 | + | 0.0841688i | −0.0156996 | + | 0.00468328i | ||||
\(324\) | −9.88950 | −0.549417 | ||||||||
\(325\) | 6.29686 | + | 6.29686i | 0.349287 | + | 0.349287i | ||||
\(326\) | 17.5736 | + | 42.4265i | 0.973312 | + | 2.34978i | ||||
\(327\) | 13.9412i | 0.770950i | ||||||||
\(328\) | −3.88736 | + | 1.61020i | −0.214643 | + | 0.0889082i | ||||
\(329\) | 0.221575 | − | 0.534930i | 0.0122158 | − | 0.0294916i | ||||
\(330\) | 9.11712 | + | 3.77644i | 0.501881 | + | 0.207886i | ||||
\(331\) | 8.65499 | − | 8.65499i | 0.475721 | − | 0.475721i | −0.428039 | − | 0.903760i | \(-0.640795\pi\) |
0.903760 | + | 0.428039i | \(0.140795\pi\) | |||||||
\(332\) | 26.1310 | − | 26.1310i | 1.43413 | − | 1.43413i | ||||
\(333\) | 26.1459 | + | 10.8300i | 1.43278 | + | 0.593479i | ||||
\(334\) | −11.2062 | + | 27.0542i | −0.613177 | + | 1.48034i | ||||
\(335\) | −14.2881 | + | 5.91831i | −0.780640 | + | 0.323352i | ||||
\(336\) | 3.94031i | 0.214962i | ||||||||
\(337\) | 5.29877 | + | 12.7924i | 0.288643 | + | 0.696845i | 0.999982 | − | 0.00600377i | \(-0.00191107\pi\) |
−0.711339 | + | 0.702849i | \(0.751911\pi\) | |||||||
\(338\) | 17.0829 | + | 17.0829i | 0.929189 | + | 0.929189i | ||||
\(339\) | −7.28141 | −0.395472 | ||||||||
\(340\) | 16.6147 | + | 1.71400i | 0.901059 | + | 0.0929548i | ||||
\(341\) | −6.00241 | −0.325049 | ||||||||
\(342\) | 0.429744 | + | 0.429744i | 0.0232379 | + | 0.0232379i | ||||
\(343\) | 2.28981 | + | 5.52809i | 0.123638 | + | 0.298489i | ||||
\(344\) | 1.93023i | 0.104071i | ||||||||
\(345\) | 13.2846 | − | 5.50268i | 0.715221 | − | 0.296254i | ||||
\(346\) | 10.3542 | − | 24.9973i | 0.556645 | − | 1.34386i | ||||
\(347\) | 15.7283 | + | 6.51489i | 0.844341 | + | 0.349738i | 0.762564 | − | 0.646913i | \(-0.223940\pi\) |
0.0817775 | + | 0.996651i | \(0.473940\pi\) | |||||||
\(348\) | −33.2590 | + | 33.2590i | −1.78287 | + | 1.78287i | ||||
\(349\) | 7.87592 | − | 7.87592i | 0.421588 | − | 0.421588i | −0.464162 | − | 0.885750i | \(-0.653644\pi\) |
0.885750 | + | 0.464162i | \(0.153644\pi\) | |||||||
\(350\) | −1.48035 | − | 0.613182i | −0.0791282 | − | 0.0327760i | ||||
\(351\) | 5.69774 | − | 13.7556i | 0.304123 | − | 0.734217i | ||||
\(352\) | 7.49837 | − | 3.10593i | 0.399664 | − | 0.165546i | ||||
\(353\) | − | 26.9051i | − | 1.43201i | −0.698094 | − | 0.716006i | \(-0.745968\pi\) | ||
0.698094 | − | 0.716006i | \(-0.254032\pi\) | |||||||
\(354\) | 17.7401 | + | 42.8285i | 0.942877 | + | 2.27631i | ||||
\(355\) | −0.569218 | − | 0.569218i | −0.0302109 | − | 0.0302109i | ||||
\(356\) | 38.9687 | 2.06534 | ||||||||
\(357\) | −4.19357 | − | 2.26650i | −0.221947 | − | 0.119956i | ||||
\(358\) | −22.8846 | −1.20949 | ||||||||
\(359\) | −5.09233 | − | 5.09233i | −0.268763 | − | 0.268763i | 0.559839 | − | 0.828602i | \(-0.310863\pi\) |
−0.828602 | + | 0.559839i | \(0.810863\pi\) | |||||||
\(360\) | −1.52646 | − | 3.68519i | −0.0804513 | − | 0.194227i | ||||
\(361\) | − | 18.9949i | − | 0.999732i | ||||||
\(362\) | −8.50356 | + | 3.52229i | −0.446937 | + | 0.185127i | ||||
\(363\) | −1.02130 | + | 2.46565i | −0.0536046 | + | 0.129413i | ||||
\(364\) | −4.49895 | − | 1.86353i | −0.235809 | − | 0.0976753i | ||||
\(365\) | 8.98143 | − | 8.98143i | 0.470110 | − | 0.470110i | ||||
\(366\) | 28.0310 | − | 28.0310i | 1.46520 | − | 1.46520i | ||||
\(367\) | −4.81934 | − | 1.99624i | −0.251567 | − | 0.104203i | 0.253336 | − | 0.967378i | \(-0.418472\pi\) |
−0.504904 | + | 0.863176i | \(0.668472\pi\) | |||||||
\(368\) | 3.92323 | − | 9.47152i | 0.204513 | − | 0.493737i | ||||
\(369\) | 29.6662 | − | 12.2881i | 1.54436 | − | 0.639695i | ||||
\(370\) | − | 25.3838i | − | 1.31964i | ||||||
\(371\) | −0.337448 | − | 0.814673i | −0.0175195 | − | 0.0422957i | ||||
\(372\) | 25.6186 | + | 25.6186i | 1.32826 | + | 1.32826i | ||||
\(373\) | −24.9667 | −1.29273 | −0.646363 | − | 0.763030i | \(-0.723711\pi\) | ||||
−0.646363 | + | 0.763030i | \(0.723711\pi\) | |||||||
\(374\) | −0.873443 | + | 8.46673i | −0.0451646 | + | 0.437804i | ||||
\(375\) | −32.4662 | −1.67655 | ||||||||
\(376\) | 0.510533 | + | 0.510533i | 0.0263287 | + | 0.0263287i | ||||
\(377\) | 14.8215 | + | 35.7822i | 0.763344 | + | 1.84288i | ||||
\(378\) | 2.67900i | 0.137793i | ||||||||
\(379\) | 11.2662 | − | 4.66663i | 0.578708 | − | 0.239709i | −0.0740763 | − | 0.997253i | \(-0.523601\pi\) |
0.652784 | + | 0.757544i | \(0.273601\pi\) | |||||||
\(380\) | 0.110709 | − | 0.267276i | 0.00567927 | − | 0.0137110i | ||||
\(381\) | −37.6128 | − | 15.5797i | −1.92696 | − | 0.798173i | ||||
\(382\) | 34.3101 | − | 34.3101i | 1.75546 | − | 1.75546i | ||||
\(383\) | −6.49211 | + | 6.49211i | −0.331731 | + | 0.331731i | −0.853244 | − | 0.521512i | \(-0.825368\pi\) |
0.521512 | + | 0.853244i | \(0.325368\pi\) | |||||||
\(384\) | −10.5642 | − | 4.37585i | −0.539103 | − | 0.223304i | ||||
\(385\) | −0.296941 | + | 0.716878i | −0.0151335 | + | 0.0365355i | ||||
\(386\) | 25.4855 | − | 10.5564i | 1.29718 | − | 0.537308i | ||||
\(387\) | − | 14.7304i | − | 0.748790i | ||||||
\(388\) | 8.62749 | + | 20.8286i | 0.437995 | + | 1.05741i | ||||
\(389\) | −3.96805 | − | 3.96805i | −0.201188 | − | 0.201188i | 0.599321 | − | 0.800509i | \(-0.295437\pi\) |
−0.800509 | + | 0.599321i | \(0.795437\pi\) | |||||||
\(390\) | −49.0473 | −2.48361 | ||||||||
\(391\) | 7.82360 | + | 9.62347i | 0.395657 | + | 0.486680i | ||||
\(392\) | −3.67999 | −0.185867 | ||||||||
\(393\) | −35.4181 | − | 35.4181i | −1.78661 | − | 1.78661i | ||||
\(394\) | −6.44454 | − | 15.5585i | −0.324671 | − | 0.783826i | ||||
\(395\) | − | 16.3523i | − | 0.822776i | ||||||
\(396\) | 8.61396 | − | 3.56802i | 0.432868 | − | 0.179300i | ||||
\(397\) | −1.34262 | + | 3.24137i | −0.0673841 | + | 0.162680i | −0.953984 | − | 0.299858i | \(-0.903061\pi\) |
0.886600 | + | 0.462537i | \(0.153061\pi\) | |||||||
\(398\) | 40.6830 | + | 16.8514i | 2.03925 | + | 0.844687i | ||||
\(399\) | −0.0583809 | + | 0.0583809i | −0.00292270 | + | 0.00292270i | ||||
\(400\) | −4.31792 | + | 4.31792i | −0.215896 | + | 0.215896i | ||||
\(401\) | −10.9940 | − | 4.55388i | −0.549016 | − | 0.227410i | 0.0908930 | − | 0.995861i | \(-0.471028\pi\) |
−0.639909 | + | 0.768451i | \(0.721028\pi\) | |||||||
\(402\) | −18.2040 | + | 43.9482i | −0.907931 | + | 2.19194i | ||||
\(403\) | 27.5622 | − | 11.4166i | 1.37297 | − | 0.568703i | ||||
\(404\) | 37.8383i | 1.88253i | ||||||||
\(405\) | −2.99724 | − | 7.23597i | −0.148934 | − | 0.359558i | ||||
\(406\) | −4.92773 | − | 4.92773i | −0.244559 | − | 0.244559i | ||||
\(407\) | 6.86483 | 0.340277 | ||||||||
\(408\) | 4.61228 | − | 3.74965i | 0.228342 | − | 0.185635i | ||||
\(409\) | 20.3531 | 1.00640 | 0.503198 | − | 0.864171i | \(-0.332157\pi\) | ||||
0.503198 | + | 0.864171i | \(0.332157\pi\) | |||||||
\(410\) | −20.3658 | − | 20.3658i | −1.00579 | − | 1.00579i | ||||
\(411\) | 13.3586 | + | 32.2505i | 0.658932 | + | 1.59080i | ||||
\(412\) | 5.15256i | 0.253848i | ||||||||
\(413\) | −3.36760 | + | 1.39490i | −0.165709 | + | 0.0686388i | ||||
\(414\) | 9.79646 | − | 23.6508i | 0.481470 | − | 1.16237i | ||||
\(415\) | 27.0392 | + | 11.2000i | 1.32730 | + | 0.549787i | ||||
\(416\) | −28.5239 | + | 28.5239i | −1.39850 | + | 1.39850i | ||||
\(417\) | −36.6875 | + | 36.6875i | −1.79660 | + | 1.79660i | ||||
\(418\) | 0.136202 | + | 0.0564166i | 0.00666185 | + | 0.00275943i | ||||
\(419\) | 12.9586 | − | 31.2849i | 0.633071 | − | 1.52837i | −0.202671 | − | 0.979247i | \(-0.564962\pi\) |
0.835742 | − | 0.549122i | \(-0.185038\pi\) | |||||||
\(420\) | 4.32704 | − | 1.79232i | 0.211138 | − | 0.0874562i | ||||
\(421\) | − | 13.1999i | − | 0.643325i | −0.946854 | − | 0.321663i | \(-0.895758\pi\) | ||
0.946854 | − | 0.321663i | \(-0.104242\pi\) | |||||||
\(422\) | −1.32700 | − | 3.20366i | −0.0645972 | − | 0.155952i | ||||
\(423\) | −3.89611 | − | 3.89611i | −0.189435 | − | 0.189435i | ||||
\(424\) | 1.09958 | 0.0534001 | ||||||||
\(425\) | −2.11174 | − | 7.07913i | −0.102434 | − | 0.343388i | ||||
\(426\) | −2.47606 | −0.119966 | ||||||||
\(427\) | 2.20408 | + | 2.20408i | 0.106663 | + | 0.106663i | ||||
\(428\) | −10.1195 | − | 24.4305i | −0.489142 | − | 1.18089i | ||||
\(429\) | − | 13.2644i | − | 0.640412i | ||||||
\(430\) | −12.2068 | + | 5.05621i | −0.588662 | + | 0.243832i | ||||
\(431\) | 3.64331 | − | 8.79572i | 0.175492 | − | 0.423675i | −0.811519 | − | 0.584325i | \(-0.801359\pi\) |
0.987011 | + | 0.160650i | \(0.0513592\pi\) | |||||||
\(432\) | 9.43253 | + | 3.90708i | 0.453823 | + | 0.187980i | ||||
\(433\) | −12.3445 | + | 12.3445i | −0.593241 | + | 0.593241i | −0.938505 | − | 0.345264i | \(-0.887789\pi\) |
0.345264 | + | 0.938505i | \(0.387789\pi\) | |||||||
\(434\) | −3.79572 | + | 3.79572i | −0.182200 | + | 0.182200i | ||||
\(435\) | −34.4149 | − | 14.2551i | −1.65007 | − | 0.683481i | ||||
\(436\) | 4.52120 | − | 10.9152i | 0.216526 | − | 0.522741i | ||||
\(437\) | 0.198461 | − | 0.0822052i | 0.00949367 | − | 0.00393241i | ||||
\(438\) | − | 39.0687i | − | 1.86677i | ||||||
\(439\) | 4.90118 | + | 11.8325i | 0.233920 | + | 0.564734i | 0.996632 | − | 0.0820051i | \(-0.0261324\pi\) |
−0.762712 | + | 0.646739i | \(0.776132\pi\) | |||||||
\(440\) | −0.684183 | − | 0.684183i | −0.0326171 | − | 0.0326171i | ||||
\(441\) | 28.0836 | 1.33732 | ||||||||
\(442\) | −12.0931 | − | 40.5393i | −0.575209 | − | 1.92826i | ||||
\(443\) | −7.14043 | −0.339252 | −0.169626 | − | 0.985509i | \(-0.554256\pi\) | ||||
−0.169626 | + | 0.985509i | \(0.554256\pi\) | |||||||
\(444\) | −29.2995 | − | 29.2995i | −1.39049 | − | 1.39049i | ||||
\(445\) | 11.8104 | + | 28.5127i | 0.559865 | + | 1.35163i | ||||
\(446\) | − | 40.0548i | − | 1.89665i | ||||||
\(447\) | −19.0941 | + | 7.90903i | −0.903120 | + | 0.374085i | ||||
\(448\) | 1.64761 | − | 3.97769i | 0.0778423 | − | 0.187928i | ||||
\(449\) | −2.51520 | − | 1.04183i | −0.118700 | − | 0.0491671i | 0.322543 | − | 0.946555i | \(-0.395462\pi\) |
−0.441243 | + | 0.897388i | \(0.645462\pi\) | |||||||
\(450\) | −10.7820 | + | 10.7820i | −0.508268 | + | 0.508268i | ||||
\(451\) | 5.50775 | − | 5.50775i | 0.259350 | − | 0.259350i | ||||
\(452\) | 5.70092 | + | 2.36140i | 0.268149 | + | 0.111071i | ||||
\(453\) | 5.69586 | − | 13.7510i | 0.267615 | − | 0.646080i | ||||
\(454\) | −10.2432 | + | 4.24286i | −0.480736 | + | 0.199127i | ||||
\(455\) | − | 3.85658i | − | 0.180799i | ||||||
\(456\) | −0.0393988 | − | 0.0951170i | −0.00184502 | − | 0.00445426i | ||||
\(457\) | 10.2949 | + | 10.2949i | 0.481577 | + | 0.481577i | 0.905635 | − | 0.424058i | \(-0.139395\pi\) |
−0.424058 | + | 0.905635i | \(0.639395\pi\) | |||||||
\(458\) | 25.0695 | 1.17142 | ||||||||
\(459\) | −9.58385 | + | 7.79139i | −0.447336 | + | 0.363671i | ||||
\(460\) | −12.1857 | −0.568159 | ||||||||
\(461\) | −18.4490 | − | 18.4490i | −0.859255 | − | 0.859255i | 0.131995 | − | 0.991250i | \(-0.457862\pi\) |
−0.991250 | + | 0.131995i | \(0.957862\pi\) | |||||||
\(462\) | 0.913352 | + | 2.20503i | 0.0424930 | + | 0.102587i | ||||
\(463\) | 2.84672i | 0.132298i | 0.997810 | + | 0.0661490i | \(0.0210713\pi\) | ||||
−0.997810 | + | 0.0661490i | \(0.978929\pi\) | |||||||
\(464\) | −24.5367 | + | 10.1634i | −1.13909 | + | 0.471826i | ||||
\(465\) | −10.9804 | + | 26.5090i | −0.509203 | + | 1.22933i | ||||
\(466\) | 19.3618 | + | 8.01993i | 0.896919 | + | 0.371516i | ||||
\(467\) | 13.2555 | − | 13.2555i | 0.613393 | − | 0.613393i | −0.330435 | − | 0.943829i | \(-0.607196\pi\) |
0.943829 | + | 0.330435i | \(0.107196\pi\) | |||||||
\(468\) | −32.7676 | + | 32.7676i | −1.51468 | + | 1.51468i | ||||
\(469\) | −3.45565 | − | 1.43138i | −0.159567 | − | 0.0660948i | ||||
\(470\) | −1.89128 | + | 4.56595i | −0.0872381 | + | 0.210611i | ||||
\(471\) | 32.6086 | − | 13.5069i | 1.50253 | − | 0.622367i | ||||
\(472\) | − | 4.54529i | − | 0.209214i | ||||||
\(473\) | −1.36741 | − | 3.30121i | −0.0628734 | − | 0.151790i | ||||
\(474\) | −35.5659 | − | 35.5659i | −1.63359 | − | 1.63359i | ||||
\(475\) | −0.127951 | −0.00587080 | ||||||||
\(476\) | 2.54828 | + | 3.13453i | 0.116800 | + | 0.143671i | ||||
\(477\) | −8.39136 | −0.384214 | ||||||||
\(478\) | 7.83598 | + | 7.83598i | 0.358409 | + | 0.358409i | ||||
\(479\) | 3.10860 | + | 7.50483i | 0.142036 | + | 0.342904i | 0.978849 | − | 0.204584i | \(-0.0655841\pi\) |
−0.836813 | + | 0.547488i | \(0.815584\pi\) | |||||||
\(480\) | − | 38.7975i | − | 1.77086i | ||||||
\(481\) | −31.5223 | + | 13.0570i | −1.43729 | + | 0.595346i | ||||
\(482\) | 0.693813 | − | 1.67501i | 0.0316023 | − | 0.0762948i | ||||
\(483\) | 3.21296 | + | 1.33085i | 0.146195 | + | 0.0605559i | ||||
\(484\) | 1.59924 | − | 1.59924i | 0.0726929 | − | 0.0726929i | ||||
\(485\) | −12.6252 | + | 12.6252i | −0.573279 | + | 0.573279i | ||||
\(486\) | −39.3972 | − | 16.3188i | −1.78709 | − | 0.740238i | ||||
\(487\) | −0.272834 | + | 0.658679i | −0.0123633 | + | 0.0298476i | −0.929941 | − | 0.367710i | \(-0.880142\pi\) |
0.917577 | + | 0.397557i | \(0.130142\pi\) | |||||||
\(488\) | −3.59099 | + | 1.48744i | −0.162556 | + | 0.0673331i | ||||
\(489\) | 59.3672i | 2.68468i | ||||||||
\(490\) | −9.63968 | − | 23.2723i | −0.435476 | − | 1.05133i | ||||
\(491\) | −11.9282 | − | 11.9282i | −0.538314 | − | 0.538314i | 0.384719 | − | 0.923034i | \(-0.374298\pi\) |
−0.923034 | + | 0.384719i | \(0.874298\pi\) | |||||||
\(492\) | −47.0148 | −2.11959 | ||||||||
\(493\) | 3.29703 | − | 31.9598i | 0.148491 | − | 1.43940i | ||||
\(494\) | −0.732723 | −0.0329668 | ||||||||
\(495\) | 5.22131 | + | 5.22131i | 0.234681 | + | 0.234681i | ||||
\(496\) | 7.82866 | + | 18.9001i | 0.351517 | + | 0.848638i | ||||
\(497\) | − | 0.194693i | − | 0.00873316i | ||||||
\(498\) | 83.1692 | − | 34.4498i | 3.72690 | − | 1.54373i | ||||
\(499\) | −1.64451 | + | 3.97021i | −0.0736185 | + | 0.177731i | −0.956405 | − | 0.292044i | \(-0.905665\pi\) |
0.882786 | + | 0.469774i | \(0.155665\pi\) | |||||||
\(500\) | 25.4192 | + | 10.5290i | 1.13678 | + | 0.470870i | ||||
\(501\) | −26.7689 | + | 26.7689i | −1.19594 | + | 1.19594i | ||||
\(502\) | 39.2282 | − | 39.2282i | 1.75084 | − | 1.75084i | ||||
\(503\) | 7.17119 | + | 2.97040i | 0.319748 | + | 0.132444i | 0.536784 | − | 0.843720i | \(-0.319639\pi\) |
−0.217036 | + | 0.976164i | \(0.569639\pi\) | |||||||
\(504\) | 0.369182 | − | 0.891284i | 0.0164447 | − | 0.0397010i | ||||
\(505\) | −27.6856 | + | 11.4678i | −1.23199 | + | 0.510309i | ||||
\(506\) | − | 6.20972i | − | 0.276056i | ||||||
\(507\) | 11.9521 | + | 28.8548i | 0.530809 | + | 1.28149i | ||||
\(508\) | 24.3961 | + | 24.3961i | 1.08240 | + | 1.08240i | ||||
\(509\) | 6.80086 | 0.301443 | 0.150721 | − | 0.988576i | \(-0.451840\pi\) | ||||
0.150721 | + | 0.988576i | \(0.451840\pi\) | |||||||
\(510\) | 35.7946 | + | 19.3459i | 1.58501 | + | 0.856651i | ||||
\(511\) | 3.07197 | 0.135896 | ||||||||
\(512\) | −22.1632 | − | 22.1632i | −0.979486 | − | 0.979486i | ||||
\(513\) | 0.0818667 | + | 0.197644i | 0.00361450 | + | 0.00872618i | ||||
\(514\) | 31.4914i | 1.38902i | ||||||||
\(515\) | −3.77003 | + | 1.56160i | −0.166127 | + | 0.0688123i | ||||
\(516\) | −8.25359 | + | 19.9259i | −0.363344 | + | 0.877190i | ||||
\(517\) | −1.23482 | − | 0.511479i | −0.0543073 | − | 0.0224948i | ||||
\(518\) | 4.34108 | − | 4.34108i | 0.190736 | − | 0.190736i | ||||
\(519\) | 24.7336 | − | 24.7336i | 1.08568 | − | 1.08568i | ||||
\(520\) | 4.44299 | + | 1.84035i | 0.194838 | + | 0.0807045i | ||||
\(521\) | −8.39270 | + | 20.2618i | −0.367691 | + | 0.887684i | 0.626437 | + | 0.779472i | \(0.284513\pi\) |
−0.994128 | + | 0.108212i | \(0.965487\pi\) | |||||||
\(522\) | −61.2691 | + | 25.3785i | −2.68168 | + | 1.11079i | ||||
\(523\) | 39.9420i | 1.74654i | 0.487237 | + | 0.873270i | \(0.338005\pi\) | ||||
−0.487237 | + | 0.873270i | \(0.661995\pi\) | |||||||
\(524\) | 16.2440 | + | 39.2166i | 0.709625 | + | 1.71319i | ||||
\(525\) | −1.46474 | − | 1.46474i | −0.0639264 | − | 0.0639264i | ||||
\(526\) | −2.39135 | −0.104268 | ||||||||
\(527\) | −24.6179 | − | 2.53963i | −1.07237 | − | 0.110628i | ||||
\(528\) | 9.09573 | 0.395841 | ||||||||
\(529\) | 9.86539 | + | 9.86539i | 0.428930 | + | 0.428930i | ||||
\(530\) | 2.88033 | + | 6.95372i | 0.125113 | + | 0.302050i | ||||
\(531\) | 34.6872i | 1.50530i | ||||||||
\(532\) | 0.0646421 | − | 0.0267757i | 0.00280259 | − | 0.00116087i | ||||
\(533\) | −14.8150 | + | 35.7665i | −0.641708 | + | 1.54922i | ||||
\(534\) | 87.7015 | + | 36.3272i | 3.79522 | + | 1.57203i | ||||
\(535\) | 14.8084 | − | 14.8084i | 0.640225 | − | 0.640225i | ||||
\(536\) | 3.29804 | − | 3.29804i | 0.142454 | − | 0.142454i | ||||
\(537\) | −27.3328 | − | 11.3216i | −1.17950 | − | 0.488564i | ||||
\(538\) | 24.9525 | − | 60.2407i | 1.07578 | − | 2.59716i | ||||
\(539\) | 6.29378 | − | 2.60697i | 0.271092 | − | 0.112290i | ||||
\(540\) | − | 12.1355i | − | 0.522228i | ||||||
\(541\) | 2.62808 | + | 6.34476i | 0.112990 | + | 0.272782i | 0.970252 | − | 0.242099i | \(-0.0778359\pi\) |
−0.857261 | + | 0.514882i | \(0.827836\pi\) | |||||||
\(542\) | −29.9799 | − | 29.9799i | −1.28775 | − | 1.28775i | ||||
\(543\) | −11.8990 | −0.510635 | ||||||||
\(544\) | 32.0675 | − | 9.56589i | 1.37488 | − | 0.410134i | ||||
\(545\) | 9.35668 | 0.400796 | ||||||||
\(546\) | −8.38795 | − | 8.38795i | −0.358971 | − | 0.358971i | ||||
\(547\) | −4.12937 | − | 9.96918i | −0.176559 | − | 0.426251i | 0.810681 | − | 0.585488i | \(-0.199097\pi\) |
−0.987241 | + | 0.159236i | \(0.949097\pi\) | |||||||
\(548\) | − | 29.5826i | − | 1.26371i | ||||||
\(549\) | 27.4045 | − | 11.3513i | 1.16959 | − | 0.484462i | ||||
\(550\) | −1.41546 | + | 3.41721i | −0.0603553 | + | 0.145711i | ||||
\(551\) | −0.514128 | − | 0.212959i | −0.0219026 | − | 0.00907236i | ||||
\(552\) | −3.06643 | + | 3.06643i | −0.130516 | + | 0.130516i | ||||
\(553\) | 2.79654 | − | 2.79654i | 0.118921 | − | 0.118921i | ||||
\(554\) | 33.2690 | + | 13.7805i | 1.41346 | + | 0.585476i | ||||
\(555\) | 12.5580 | − | 30.3178i | 0.533059 | − | 1.28692i | ||||
\(556\) | 40.6222 | − | 16.8263i | 1.72277 | − | 0.713593i | ||||
\(557\) | − | 3.94309i | − | 0.167074i | −0.996505 | − | 0.0835371i | \(-0.973378\pi\) | ||
0.996505 | − | 0.0835371i | \(-0.0266217\pi\) | |||||||
\(558\) | 19.5485 | + | 47.1942i | 0.827553 | + | 1.99789i | ||||
\(559\) | 12.5579 | + | 12.5579i | 0.531141 | + | 0.531141i | ||||
\(560\) | 2.64456 | 0.111753 | ||||||||
\(561\) | −5.23193 | + | 9.68034i | −0.220892 | + | 0.408704i | ||||
\(562\) | 10.7006 | 0.451378 | ||||||||
\(563\) | −3.60886 | − | 3.60886i | −0.152096 | − | 0.152096i | 0.626958 | − | 0.779053i | \(-0.284300\pi\) |
−0.779053 | + | 0.626958i | \(0.784300\pi\) | |||||||
\(564\) | 3.08726 | + | 7.45331i | 0.129997 | + | 0.313841i | ||||
\(565\) | 4.88694i | 0.205595i | ||||||||
\(566\) | −42.9890 | + | 17.8066i | −1.80696 | + | 0.748469i | ||||
\(567\) | 0.724899 | − | 1.75006i | 0.0304429 | − | 0.0734956i | ||||
\(568\) | 0.224296 | + | 0.0929065i | 0.00941126 | + | 0.00389827i | ||||
\(569\) | −7.12268 | + | 7.12268i | −0.298598 | + | 0.298598i | −0.840465 | − | 0.541866i | \(-0.817718\pi\) |
0.541866 | + | 0.840465i | \(0.317718\pi\) | |||||||
\(570\) | 0.498316 | − | 0.498316i | 0.0208722 | − | 0.0208722i | ||||
\(571\) | −0.403574 | − | 0.167166i | −0.0168891 | − | 0.00699568i | 0.374223 | − | 0.927339i | \(-0.377909\pi\) |
−0.391112 | + | 0.920343i | \(0.627909\pi\) | |||||||
\(572\) | −4.30172 | + | 10.3853i | −0.179864 | + | 0.434230i | ||||
\(573\) | 57.9533 | − | 24.0050i | 2.42103 | − | 1.00283i | ||||
\(574\) | − | 6.96582i | − | 0.290748i | ||||||
\(575\) | 2.06247 | + | 4.97925i | 0.0860111 | + | 0.207649i | ||||
\(576\) | −28.9711 | − | 28.9711i | −1.20713 | − | 1.20713i | ||||
\(577\) | −0.679953 | −0.0283068 | −0.0141534 | − | 0.999900i | \(-0.504505\pi\) | ||||
−0.0141534 | + | 0.999900i | \(0.504505\pi\) | |||||||
\(578\) | −7.16457 | + | 34.3554i | −0.298007 | + | 1.42900i | ||||
\(579\) | 35.6617 | 1.48205 | ||||||||
\(580\) | 22.3219 | + | 22.3219i | 0.926866 | + | 0.926866i | ||||
\(581\) | 2.70878 | + | 6.53958i | 0.112379 | + | 0.271308i | ||||
\(582\) | 54.9187i | 2.27645i | ||||||||
\(583\) | −1.88057 | + | 0.778959i | −0.0778853 | + | 0.0322612i | ||||
\(584\) | −1.46593 | + | 3.53907i | −0.0606606 | + | 0.146448i | ||||
\(585\) | −33.9065 | − | 14.0445i | −1.40186 | − | 0.580669i | ||||
\(586\) | −7.29985 | + | 7.29985i | −0.301554 | + | 0.301554i | ||||
\(587\) | 3.21525 | − | 3.21525i | 0.132707 | − | 0.132707i | −0.637633 | − | 0.770340i | \(-0.720086\pi\) |
0.770340 | + | 0.637633i | \(0.220086\pi\) | |||||||
\(588\) | −37.9889 | − | 15.7355i | −1.56664 | − | 0.648922i | ||||
\(589\) | −0.164037 | + | 0.396021i | −0.00675904 | + | 0.0163178i | ||||
\(590\) | 28.7445 | − | 11.9063i | 1.18339 | − | 0.490177i | ||||
\(591\) | − | 21.7710i | − | 0.895538i | ||||||
\(592\) | −8.95348 | − | 21.6156i | −0.367986 | − | 0.888397i | ||||
\(593\) | 1.28643 | + | 1.28643i | 0.0528272 | + | 0.0528272i | 0.733027 | − | 0.680200i | \(-0.238107\pi\) |
−0.680200 | + | 0.733027i | \(0.738107\pi\) | |||||||
\(594\) | 6.18416 | 0.253739 | ||||||||
\(595\) | −1.52117 | + | 2.81453i | −0.0623618 | + | 0.115384i | ||||
\(596\) | 17.5145 | 0.717423 | ||||||||
\(597\) | 40.2539 | + | 40.2539i | 1.64748 | + | 1.64748i | ||||
\(598\) | 11.8109 | + | 28.5141i | 0.482985 | + | 1.16603i | ||||
\(599\) | 13.0472i | 0.533092i | 0.963822 | + | 0.266546i | \(0.0858825\pi\) | ||||
−0.963822 | + | 0.266546i | \(0.914118\pi\) | |||||||
\(600\) | 2.38642 | − | 0.988489i | 0.0974254 | − | 0.0403549i | ||||
\(601\) | −4.82503 | + | 11.6486i | −0.196817 | + | 0.475158i | −0.991218 | − | 0.132235i | \(-0.957785\pi\) |
0.794401 | + | 0.607393i | \(0.207785\pi\) | |||||||
\(602\) | −2.95227 | − | 1.22287i | −0.120326 | − | 0.0498405i | ||||
\(603\) | −25.1688 | + | 25.1688i | −1.02495 | + | 1.02495i | ||||
\(604\) | −8.91907 | + | 8.91907i | −0.362912 | + | 0.362912i | ||||
\(605\) | 1.65483 | + | 0.685451i | 0.0672783 | + | 0.0278676i | ||||
\(606\) | −35.2734 | + | 85.1575i | −1.43288 | + | 3.45929i | ||||
\(607\) | 8.43220 | − | 3.49273i | 0.342252 | − | 0.141766i | −0.204935 | − | 0.978776i | \(-0.565698\pi\) |
0.547188 | + | 0.837010i | \(0.315698\pi\) | |||||||
\(608\) | − | 0.579600i | − | 0.0235059i | ||||||
\(609\) | −3.44768 | − | 8.32343i | −0.139707 | − | 0.337283i | ||||
\(610\) | −18.8131 | − | 18.8131i | −0.761721 | − | 0.761721i | ||||
\(611\) | 6.64295 | 0.268745 | ||||||||
\(612\) | 36.8384 | − | 10.9891i | 1.48910 | − | 0.444207i | ||||
\(613\) | −36.6191 | −1.47903 | −0.739516 | − | 0.673139i | \(-0.764946\pi\) | ||||
−0.739516 | + | 0.673139i | \(0.764946\pi\) | |||||||
\(614\) | −5.33872 | − | 5.33872i | −0.215453 | − | 0.215453i | ||||
\(615\) | −14.2489 | − | 34.3999i | −0.574571 | − | 1.38714i | ||||
\(616\) | − | 0.234015i | − | 0.00942872i | ||||||
\(617\) | 3.10717 | − | 1.28703i | 0.125090 | − | 0.0518140i | −0.319260 | − | 0.947667i | \(-0.603434\pi\) |
0.444351 | + | 0.895853i | \(0.353434\pi\) | |||||||
\(618\) | −4.80328 | + | 11.5961i | −0.193216 | + | 0.466465i | ||||
\(619\) | −13.4475 | − | 5.57016i | −0.540502 | − | 0.223883i | 0.0956936 | − | 0.995411i | \(-0.469493\pi\) |
−0.636196 | + | 0.771527i | \(0.719493\pi\) | |||||||
\(620\) | 17.1940 | − | 17.1940i | 0.690529 | − | 0.690529i | ||||
\(621\) | 6.37173 | − | 6.37173i | 0.255689 | − | 0.255689i | ||||
\(622\) | −36.8632 | − | 15.2693i | −1.47808 | − | 0.612241i | ||||
\(623\) | −2.85640 | + | 6.89596i | −0.114439 | + | 0.276281i | ||||
\(624\) | −41.7663 | + | 17.3002i | −1.67199 | + | 0.692560i | ||||
\(625\) | 12.8313i | 0.513250i | ||||||||
\(626\) | 23.3229 | + | 56.3065i | 0.932172 | + | 2.25046i | ||||
\(627\) | 0.134765 | + | 0.134765i | 0.00538200 | + | 0.00538200i | ||||
\(628\) | −29.9111 | −1.19358 | ||||||||
\(629\) | 28.1550 | + | 2.90452i | 1.12261 | + | 0.115811i | ||||
\(630\) | 6.60356 | 0.263092 | ||||||||
\(631\) | 3.47009 | + | 3.47009i | 0.138142 | + | 0.138142i | 0.772796 | − | 0.634654i | \(-0.218857\pi\) |
−0.634654 | + | 0.772796i | \(0.718857\pi\) | |||||||
\(632\) | 1.88726 | + | 4.55626i | 0.0750714 | + | 0.181238i | ||||
\(633\) | − | 4.48287i | − | 0.178178i | ||||||
\(634\) | −15.5939 | + | 6.45919i | −0.619312 | + | 0.256527i | ||||
\(635\) | −10.4564 | + | 25.2439i | −0.414949 | + | 1.00178i | ||||
\(636\) | 11.3510 | + | 4.70175i | 0.450098 | + | 0.186437i | ||||
\(637\) | −23.9416 | + | 23.9416i | −0.948601 | + | 0.948601i | ||||
\(638\) | −11.3751 | + | 11.3751i | −0.450343 | + | 0.450343i | ||||
\(639\) | −1.71171 | − | 0.709012i | −0.0677141 | − | 0.0280481i | ||||
\(640\) | −2.93686 | + | 7.09021i | −0.116090 | + | 0.280265i | ||||
\(641\) | 4.83567 | − | 2.00300i | 0.190997 | − | 0.0791137i | −0.285135 | − | 0.958487i | \(-0.592038\pi\) |
0.476132 | + | 0.879374i | \(0.342038\pi\) | |||||||
\(642\) | − | 64.4159i | − | 2.54229i | ||||||
\(643\) | −6.19776 | − | 14.9627i | −0.244416 | − | 0.590072i | 0.753296 | − | 0.657682i | \(-0.228463\pi\) |
−0.997712 | + | 0.0676096i | \(0.978463\pi\) | |||||||
\(644\) | −2.08396 | − | 2.08396i | −0.0821197 | − | 0.0821197i | ||||
\(645\) | −17.0809 | −0.672559 | ||||||||
\(646\) | 0.534740 | + | 0.289011i | 0.0210391 | + | 0.0113710i | ||||
\(647\) | −23.3703 | −0.918780 | −0.459390 | − | 0.888235i | \(-0.651932\pi\) | ||||
−0.459390 | + | 0.888235i | \(0.651932\pi\) | |||||||
\(648\) | 1.67024 | + | 1.67024i | 0.0656134 | + | 0.0656134i | ||||
\(649\) | 3.21997 | + | 7.77369i | 0.126395 | + | 0.305144i | ||||
\(650\) | − | 18.3836i | − | 0.721062i | ||||||
\(651\) | −6.41135 | + | 2.65567i | −0.251281 | + | 0.104084i | ||||
\(652\) | 19.2531 | − | 46.4811i | 0.754010 | − | 1.82034i | ||||
\(653\) | 6.70988 | + | 2.77933i | 0.262578 | + | 0.108763i | 0.510089 | − | 0.860122i | \(-0.329613\pi\) |
−0.247511 | + | 0.968885i | \(0.579613\pi\) | |||||||
\(654\) | 20.3505 | − | 20.3505i | 0.795767 | − | 0.795767i | ||||
\(655\) | −23.7710 | + | 23.7710i | −0.928808 | + | 0.928808i | ||||
\(656\) | −24.5260 | − | 10.1590i | −0.957580 | − | 0.396642i | ||||
\(657\) | 11.1872 | − | 27.0082i | 0.436454 | − | 1.05369i | ||||
\(658\) | −1.10430 | + | 0.457416i | −0.0430501 | + | 0.0178319i | ||||
\(659\) | − | 45.6467i | − | 1.77814i | −0.457768 | − | 0.889072i | \(-0.651351\pi\) | ||
0.457768 | − | 0.889072i | \(-0.348649\pi\) | |||||||
\(660\) | −4.13735 | − | 9.98844i | −0.161046 | − | 0.388800i | ||||
\(661\) | −34.9161 | − | 34.9161i | −1.35808 | − | 1.35808i | −0.876283 | − | 0.481797i | \(-0.839984\pi\) |
−0.481797 | − | 0.876283i | \(-0.660016\pi\) | |||||||
\(662\) | −25.2680 | −0.982070 | ||||||||
\(663\) | 5.61219 | − | 54.4018i | 0.217959 | − | 2.11279i | ||||
\(664\) | −8.82656 | −0.342537 | ||||||||
\(665\) | 0.0391825 | + | 0.0391825i | 0.00151943 | + | 0.00151943i | ||||
\(666\) | −22.3572 | − | 53.9750i | −0.866324 | − | 2.09149i | ||||
\(667\) | 23.4402i | 0.907607i | ||||||||
\(668\) | 29.6398 | − | 12.2772i | 1.14680 | − | 0.475019i | ||||
\(669\) | 19.8161 | − | 47.8404i | 0.766137 | − | 1.84962i | ||||
\(670\) | 29.4960 | + | 12.2176i | 1.13953 | + | 0.472009i | ||||
\(671\) | 5.08784 | − | 5.08784i | 0.196414 | − | 0.196414i | ||||
\(672\) | 6.63506 | − | 6.63506i | 0.255953 | − | 0.255953i | ||||
\(673\) | 30.7723 | + | 12.7463i | 1.18619 | + | 0.491334i | 0.886511 | − | 0.462708i | \(-0.153122\pi\) |
0.299674 | + | 0.954042i | \(0.403122\pi\) | |||||||
\(674\) | 10.9387 | − | 26.4083i | 0.421343 | − | 1.01721i | ||||
\(675\) | −4.95875 | + | 2.05398i | −0.190862 | + | 0.0790578i | ||||
\(676\) | − | 26.4678i | − | 1.01799i | ||||||
\(677\) | −16.1252 | − | 38.9297i | −0.619742 | − | 1.49619i | −0.852004 | − | 0.523536i | \(-0.824613\pi\) |
0.232262 | − | 0.972653i | \(-0.425387\pi\) | |||||||
\(678\) | 10.6289 | + | 10.6289i | 0.408202 | + | 0.408202i | ||||
\(679\) | −4.31825 | −0.165719 | ||||||||
\(680\) | −2.51659 | − | 3.09555i | −0.0965067 | − | 0.118709i | ||||
\(681\) | −14.3332 | −0.549251 | ||||||||
\(682\) | 8.76195 | + | 8.76195i | 0.335512 | + | 0.335512i | ||||
\(683\) | −2.39371 | − | 5.77892i | −0.0915927 | − | 0.221124i | 0.871444 | − | 0.490495i | \(-0.163184\pi\) |
−0.963036 | + | 0.269371i | \(0.913184\pi\) | |||||||
\(684\) | − | 0.665832i | − | 0.0254587i | ||||||
\(685\) | 21.6451 | − | 8.96568i | 0.827015 | − | 0.342561i | ||||
\(686\) | 4.72705 | − | 11.4121i | 0.180479 | − | 0.435716i | ||||
\(687\) | 29.9424 | + | 12.4025i | 1.14237 | + | 0.473186i | ||||
\(688\) | −8.61124 | + | 8.61124i | −0.328300 | + | 0.328300i | ||||
\(689\) | 7.15372 | − | 7.15372i | 0.272535 | − | 0.272535i | ||||
\(690\) | −27.4246 | − | 11.3596i | −1.04404 | − | 0.432454i | ||||
\(691\) | −13.8772 | + | 33.5026i | −0.527914 | + | 1.27450i | 0.404973 | + | 0.914329i | \(0.367281\pi\) |
−0.932887 | + | 0.360169i | \(0.882719\pi\) | |||||||
\(692\) | −27.3862 | + | 11.3437i | −1.04107 | + | 0.431224i | ||||
\(693\) | 1.78587i | 0.0678397i | ||||||||
\(694\) | −13.4492 | − | 32.4693i | −0.510526 | − | 1.23252i | ||||
\(695\) | 24.6230 | + | 24.6230i | 0.934002 | + | 0.934002i | ||||
\(696\) | 11.2343 | 0.425833 | ||||||||
\(697\) | 24.9195 | − | 20.2588i | 0.943892 | − | 0.767357i | ||||
\(698\) | −22.9936 | −0.870319 | ||||||||
\(699\) | 19.1576 | + | 19.1576i | 0.724607 | + | 0.724607i | ||||
\(700\) | 0.671784 | + | 1.62183i | 0.0253910 | + | 0.0612994i | ||||
\(701\) | 43.1404i | 1.62939i | 0.579889 | + | 0.814695i | \(0.303096\pi\) | ||||
−0.579889 | + | 0.814695i | \(0.696904\pi\) | |||||||
\(702\) | −28.3967 | + | 11.7623i | −1.07177 | + | 0.443940i | ||||
\(703\) | 0.187606 | − | 0.452921i | 0.00707570 | − | 0.0170822i | ||||
\(704\) | −9.18200 | − | 3.80331i | −0.346060 | − | 0.143343i | ||||
\(705\) | −4.51779 | + | 4.51779i | −0.170150 | + | 0.170150i | ||||
\(706\) | −39.2743 | + | 39.2743i | −1.47811 | + | 1.47811i | ||||
\(707\) | −6.69592 | − | 2.77354i | −0.251826 | − | 0.104310i | ||||
\(708\) | 19.4355 | − | 46.9216i | 0.730432 | − | 1.76342i | ||||
\(709\) | 16.8634 | − | 6.98503i | 0.633317 | − | 0.262328i | −0.0428447 | − | 0.999082i | \(-0.513642\pi\) |
0.676162 | + | 0.736753i | \(0.263642\pi\) | |||||||
\(710\) | 1.66182i | 0.0623669i | ||||||||
\(711\) | −14.4026 | − | 34.7709i | −0.540139 | − | 1.30401i | ||||
\(712\) | −6.58145 | − | 6.58145i | −0.246650 | − | 0.246650i | ||||
\(713\) | 18.0554 | 0.676181 | ||||||||
\(714\) | 2.81302 | + | 9.43000i | 0.105275 | + | 0.352909i | ||||
\(715\) | −8.90245 | −0.332933 | ||||||||
\(716\) | 17.7283 | + | 17.7283i | 0.662539 | + | 0.662539i | ||||
\(717\) | 5.48243 | + | 13.2358i | 0.204745 | + | 0.494298i | ||||
\(718\) | 14.8669i | 0.554829i | ||||||||
\(719\) | 26.5326 | − | 10.9902i | 0.989500 | − | 0.409864i | 0.171564 | − | 0.985173i | \(-0.445118\pi\) |
0.817936 | + | 0.575309i | \(0.195118\pi\) | |||||||
\(720\) | 9.63068 | − | 23.2505i | 0.358914 | − | 0.866495i | ||||
\(721\) | −0.911803 | − | 0.377681i | −0.0339573 | − | 0.0140656i | ||||
\(722\) | −27.7276 | + | 27.7276i | −1.03191 | + | 1.03191i | ||||
\(723\) | 1.65735 | − | 1.65735i | 0.0616373 | − | 0.0616373i | ||||
\(724\) | 9.31624 | + | 3.85891i | 0.346235 | + | 0.143415i | ||||
\(725\) | 5.34300 | − | 12.8991i | 0.198434 | − | 0.479062i | ||||
\(726\) | 5.09004 | − | 2.10836i | 0.188909 | − | 0.0782486i | ||||
\(727\) | − | 21.0642i | − | 0.781228i | −0.920554 | − | 0.390614i | \(-0.872263\pi\) | ||
0.920554 | − | 0.390614i | \(-0.127737\pi\) | |||||||
\(728\) | 0.445098 | + | 1.07456i | 0.0164964 | + | 0.0398259i | ||||
\(729\) | −29.7058 | − | 29.7058i | −1.10022 | − | 1.10022i | ||||
\(730\) | −26.2211 | −0.970486 | ||||||||
\(731\) | −4.21145 | − | 14.1179i | −0.155766 | − | 0.522171i | ||||
\(732\) | −43.4304 | −1.60523 | ||||||||
\(733\) | 30.3650 | + | 30.3650i | 1.12156 | + | 1.12156i | 0.991508 | + | 0.130048i | \(0.0415131\pi\) |
0.130048 | + | 0.991508i | \(0.458487\pi\) | |||||||
\(734\) | 4.12099 | + | 9.94896i | 0.152109 | + | 0.367223i | ||||
\(735\) | − | 32.5648i | − | 1.20117i | ||||||
\(736\) | −22.5553 | + | 9.34271i | −0.831400 | + | 0.344377i | ||||
\(737\) | −3.30415 | + | 7.97694i | −0.121710 | + | 0.293834i | ||||
\(738\) | −61.2424 | − | 25.3674i | −2.25436 | − | 0.933788i | ||||
\(739\) | −28.9638 | + | 28.9638i | −1.06545 | + | 1.06545i | −0.0677491 | + | 0.997702i | \(0.521582\pi\) |
−0.997702 | + | 0.0677491i | \(0.978418\pi\) | |||||||
\(740\) | −19.6645 | + | 19.6645i | −0.722880 | + | 0.722880i | ||||
\(741\) | −0.875146 | − | 0.362497i | −0.0321493 | − | 0.0133167i | ||||
\(742\) | −0.696623 | + | 1.68180i | −0.0255738 | + | 0.0617407i | ||||
\(743\) | −17.7140 | + | 7.33738i | −0.649864 | + | 0.269182i | −0.683166 | − | 0.730263i | \(-0.739398\pi\) |
0.0333025 | + | 0.999445i | \(0.489398\pi\) | |||||||
\(744\) | − | 8.65349i | − | 0.317252i | ||||||
\(745\) | 5.30817 | + | 12.8151i | 0.194476 | + | 0.469508i | ||||
\(746\) | 36.4449 | + | 36.4449i | 1.33434 | + | 1.33434i | ||||
\(747\) | 67.3595 | 2.46456 | ||||||||
\(748\) | 7.23569 | − | 5.88240i | 0.264563 | − | 0.215082i | ||||
\(749\) | 5.06501 | 0.185072 | ||||||||
\(750\) | 47.3921 | + | 47.3921i | 1.73052 | + | 1.73052i | ||||
\(751\) | −18.8445 | − | 45.4947i | −0.687647 | − | 1.66013i | −0.749469 | − | 0.662040i | \(-0.769691\pi\) |
0.0618218 | − | 0.998087i | \(-0.480309\pi\) | |||||||
\(752\) | 4.55523i | 0.166112i | ||||||||
\(753\) | 66.2603 | − | 27.4459i | 2.41466 | − | 1.00019i | ||||
\(754\) | 30.5972 | − | 73.8681i | 1.11428 | − | 2.69012i | ||||
\(755\) | −9.22905 | − | 3.82280i | −0.335879 | − | 0.139126i | ||||
\(756\) | 2.07538 | − | 2.07538i | 0.0754810 | − | 0.0754810i | ||||
\(757\) | −22.9498 | + | 22.9498i | −0.834124 | + | 0.834124i | −0.988078 | − | 0.153954i | \(-0.950799\pi\) |
0.153954 | + | 0.988078i | \(0.450799\pi\) | |||||||
\(758\) | −23.2578 | − | 9.63371i | −0.844762 | − | 0.349912i | ||||
\(759\) | 3.07211 | − | 7.41673i | 0.111511 | − | 0.269210i | ||||
\(760\) | −0.0638381 | + | 0.0264426i | −0.00231565 | + | 0.000959174i | ||||
\(761\) | − | 50.2368i | − | 1.82108i | −0.413418 | − | 0.910541i | \(-0.635665\pi\) | ||
0.413418 | − | 0.910541i | \(-0.364335\pi\) | |||||||
\(762\) | 32.1625 | + | 77.6471i | 1.16512 | + | 2.81286i | ||||
\(763\) | 1.60016 | + | 1.60016i | 0.0579296 | + | 0.0579296i | ||||
\(764\) | −53.1591 | −1.92323 | ||||||||
\(765\) | 19.2052 | + | 23.6235i | 0.694367 | + | 0.854110i | ||||
\(766\) | 18.9536 | 0.684820 | ||||||||
\(767\) | −29.5712 | − | 29.5712i | −1.06775 | − | 1.06775i | ||||
\(768\) | −11.2671 | − | 27.2012i | −0.406566 | − | 0.981538i | ||||
\(769\) | − | 9.58409i | − | 0.345611i | −0.984956 | − | 0.172806i | \(-0.944717\pi\) | ||
0.984956 | − | 0.172806i | \(-0.0552832\pi\) | |||||||
\(770\) | 1.47991 | − | 0.612999i | 0.0533323 | − | 0.0220910i | ||||
\(771\) | −15.5796 | + | 37.6125i | −0.561086 | + | 1.35458i | ||||
\(772\) | −27.9211 | − | 11.5653i | −1.00490 | − | 0.416244i | ||||
\(773\) | 8.63089 | − | 8.63089i | 0.310431 | − | 0.310431i | −0.534645 | − | 0.845077i | \(-0.679555\pi\) |
0.845077 | + | 0.534645i | \(0.179555\pi\) | |||||||
\(774\) | −21.5026 | + | 21.5026i | −0.772894 | + | 0.772894i | ||||
\(775\) | −9.93591 | − | 4.11559i | −0.356908 | − | 0.147836i | ||||
\(776\) | 2.06065 | − | 4.97486i | 0.0739731 | − | 0.178587i | ||||
\(777\) | 7.33253 | − | 3.03723i | 0.263053 | − | 0.108960i | ||||
\(778\) | 11.5846i | 0.415329i | ||||||||
\(779\) | −0.212866 | − | 0.513904i | −0.00762671 | − | 0.0184125i | ||||
\(780\) | 37.9962 | + | 37.9962i | 1.36048 | + | 1.36048i | ||||
\(781\) | −0.449424 | −0.0160817 | ||||||||
\(782\) | 2.62734 | − | 25.4682i | 0.0939535 | − | 0.910740i | ||||
\(783\) | −23.3437 | −0.834235 | ||||||||
\(784\) | −16.4174 | − | 16.4174i | −0.586334 | − | 0.586334i | ||||
\(785\) | −9.06523 | − | 21.8854i | −0.323552 | − | 0.781123i | ||||
\(786\) | 103.402i | 3.68824i | ||||||||
\(787\) | −1.34290 | + | 0.556247i | −0.0478692 | + | 0.0198281i | −0.406490 | − | 0.913655i | \(-0.633247\pi\) |
0.358620 | + | 0.933483i | \(0.383247\pi\) | |||||||
\(788\) | −7.06044 | + | 17.0454i | −0.251518 | + | 0.607218i | ||||
\(789\) | −2.85616 | − | 1.18306i | −0.101682 | − | 0.0421181i | ||||
\(790\) | −23.8702 | + | 23.8702i | −0.849262 | + | 0.849262i | ||||
\(791\) | −0.835753 | + | 0.835753i | −0.0297160 | + | 0.0297160i | ||||
\(792\) | −2.05742 | − | 0.852212i | −0.0731073 | − | 0.0302820i | ||||
\(793\) | −13.6855 | + | 33.0397i | −0.485986 | + | 1.17327i | ||||
\(794\) | 6.69143 | − | 2.77168i | 0.237470 | − | 0.0983632i | ||||
\(795\) | 9.73032i | 0.345099i | ||||||||
\(796\) | −18.4619 | − | 44.5710i | −0.654366 | − | 1.57978i | ||||
\(797\) | 31.0017 | + | 31.0017i | 1.09813 | + | 1.09813i | 0.994629 | + | 0.103506i | \(0.0330061\pi\) |
0.103506 | + | 0.994629i | \(0.466994\pi\) | |||||||
\(798\) | 0.170442 | 0.00603357 | ||||||||
\(799\) | −4.84801 | − | 2.62020i | −0.171510 | − | 0.0926961i | ||||
\(800\) | 14.5418 | 0.514130 | ||||||||
\(801\) | 50.2261 | + | 50.2261i | 1.77465 | + | 1.77465i | ||||
\(802\) | 9.40094 | + | 22.6959i | 0.331959 | + | 0.801419i | ||||
\(803\) | − | 7.09126i | − | 0.250245i | ||||||
\(804\) | 48.1483 | − | 19.9437i | 1.69806 | − | 0.703360i | ||||
\(805\) | 0.893206 | − | 2.15639i | 0.0314814 | − | 0.0760028i | ||||
\(806\) | −56.8989 | − | 23.5683i | −2.00418 | − | 0.830157i | ||||
\(807\) | 59.6053 | − | 59.6053i | 2.09821 | − | 2.09821i | ||||
\(808\) | 6.39054 | − | 6.39054i | 0.224818 | − | 0.224818i | ||||
\(809\) | 22.4438 | + | 9.29651i | 0.789081 | + | 0.326848i | 0.740574 | − | 0.671975i | \(-0.234554\pi\) |
0.0485068 | + | 0.998823i | \(0.484554\pi\) | |||||||
\(810\) | −6.18745 | + | 14.9378i | −0.217405 | + | 0.524861i | ||||
\(811\) | 21.5830 | − | 8.93999i | 0.757883 | − | 0.313925i | 0.0299296 | − | 0.999552i | \(-0.490472\pi\) |
0.727953 | + | 0.685627i | \(0.240472\pi\) | |||||||
\(812\) | 7.63487i | 0.267932i | ||||||||
\(813\) | −20.9754 | − | 50.6391i | −0.735640 | − | 1.77599i | ||||
\(814\) | −10.0209 | − | 10.0209i | −0.351231 | − | 0.351231i | ||||
\(815\) | 39.8445 | 1.39569 | ||||||||
\(816\) | 37.3047 | + | 3.84842i | 1.30593 | + | 0.134722i | ||||
\(817\) | −0.255173 | −0.00892739 | ||||||||
\(818\) | −29.7102 | − | 29.7102i | −1.03879 | − | 1.03879i | ||||
\(819\) | −3.39674 | − | 8.20047i | −0.118692 | − | 0.286547i | ||||
\(820\) | 31.5541i | 1.10192i | ||||||||
\(821\) | −24.5267 | + | 10.1593i | −0.855986 | + | 0.354561i | −0.767136 | − | 0.641484i | \(-0.778319\pi\) |
−0.0888496 | + | 0.996045i | \(0.528319\pi\) | |||||||
\(822\) | 27.5773 | − | 66.5775i | 0.961868 | − | 2.32216i | ||||
\(823\) | 34.8437 | + | 14.4327i | 1.21457 | + | 0.503093i | 0.895681 | − | 0.444698i | \(-0.146689\pi\) |
0.318893 | + | 0.947791i | \(0.396689\pi\) | |||||||
\(824\) | 0.870218 | − | 0.870218i | 0.0303155 | − | 0.0303155i | ||||
\(825\) | −3.38117 | + | 3.38117i | −0.117717 | + | 0.117717i | ||||
\(826\) | 6.95201 | + | 2.87962i | 0.241891 | + | 0.100195i | ||||
\(827\) | 2.96855 | − | 7.16671i | 0.103227 | − | 0.249211i | −0.863825 | − | 0.503792i | \(-0.831938\pi\) |
0.967051 | + | 0.254581i | \(0.0819377\pi\) | |||||||
\(828\) | −25.9110 | + | 10.7327i | −0.900471 | + | 0.372987i | ||||
\(829\) | 28.8180i | 1.00089i | 0.865768 | + | 0.500446i | \(0.166830\pi\) | ||||
−0.865768 | + | 0.500446i | \(0.833170\pi\) | |||||||
\(830\) | −23.1211 | − | 55.8193i | −0.802545 | − | 1.93751i | ||||
\(831\) | 32.9181 | + | 32.9181i | 1.14192 | + | 1.14192i | ||||
\(832\) | 49.3963 | 1.71251 | ||||||||
\(833\) | 26.9159 | − | 8.02915i | 0.932581 | − | 0.278194i | ||||
\(834\) | 107.108 | 3.70886 | ||||||||
\(835\) | 17.9660 | + | 17.9660i | 0.621739 | + | 0.621739i | ||||
\(836\) | −0.0618083 | − | 0.149218i | −0.00213769 | − | 0.00516083i | ||||
\(837\) | 17.9811i | 0.621517i | ||||||||
\(838\) | −64.5841 | + | 26.7516i | −2.23102 | + | 0.924118i | ||||
\(839\) | 5.35489 | − | 12.9279i | 0.184871 | − | 0.446319i | −0.804087 | − | 0.594512i | \(-0.797345\pi\) |
0.988959 | + | 0.148192i | \(0.0473455\pi\) | |||||||
\(840\) | −1.03350 | − | 0.428090i | −0.0356592 | − | 0.0147705i | ||||
\(841\) | 22.4320 | − | 22.4320i | 0.773517 | − | 0.773517i | ||||
\(842\) | −19.2685 | + | 19.2685i | −0.664035 | + | 0.664035i | ||||
\(843\) | 12.7805 | + | 5.29387i | 0.440185 | + | 0.182331i | ||||
\(844\) | −1.45382 | + | 3.50983i | −0.0500425 | + | 0.120813i | ||||
\(845\) | 19.3660 | − | 8.02166i | 0.666211 | − | 0.275953i | ||||
\(846\) | 11.3746i | 0.391067i | ||||||||
\(847\) | 0.165780 | + | 0.400229i | 0.00569628 | + | 0.0137520i | ||||
\(848\) | 4.90549 | + | 4.90549i | 0.168455 | + | 0.168455i | ||||
\(849\) | −60.1544 | −2.06449 | ||||||||
\(850\) | −7.25110 | + | 13.4163i | −0.248711 | + | 0.460174i | ||||
\(851\) | −20.6496 | −0.707860 | ||||||||
\(852\) | 1.91817 | + | 1.91817i | 0.0657154 | + | 0.0657154i | ||||
\(853\) | −16.6133 | − | 40.1080i | −0.568828 | − | 1.37327i | −0.902544 | − | 0.430598i | \(-0.858303\pi\) |
0.333716 | − | 0.942674i | \(-0.391697\pi\) | |||||||
\(854\) | − | 6.43475i | − | 0.220193i | ||||||
\(855\) | 0.487178 | − | 0.201796i | 0.0166611 | − | 0.00690126i | ||||
\(856\) | −2.41700 | + | 5.83516i | −0.0826115 | + | 0.199442i | ||||
\(857\) | 2.09096 | + | 0.866103i | 0.0714257 | + | 0.0295855i | 0.418110 | − | 0.908396i | \(-0.362693\pi\) |
−0.346685 | + | 0.937982i | \(0.612693\pi\) | |||||||
\(858\) | −19.3626 | + | 19.3626i | −0.661027 | + | 0.661027i | ||||
\(859\) | 14.7177 | − | 14.7177i | 0.502161 | − | 0.502161i | −0.409948 | − | 0.912109i | \(-0.634453\pi\) |
0.912109 | + | 0.409948i | \(0.134453\pi\) | |||||||
\(860\) | 13.3734 | + | 5.53943i | 0.456028 | + | 0.188893i | ||||
\(861\) | 3.44617 | − | 8.31980i | 0.117445 | − | 0.283538i | ||||
\(862\) | −18.1577 | + | 7.52118i | −0.618455 | + | 0.256172i | ||||
\(863\) | − | 31.9101i | − | 1.08623i | −0.839658 | − | 0.543116i | \(-0.817244\pi\) | ||
0.839658 | − | 0.543116i | \(-0.182756\pi\) | |||||||
\(864\) | −9.30425 | − | 22.4624i | −0.316537 | − | 0.764188i | ||||
\(865\) | −16.6000 | − | 16.6000i | −0.564418 | − | 0.564418i | ||||
\(866\) | 36.0396 | 1.22468 | ||||||||
\(867\) | −25.5537 | + | 37.4887i | −0.867849 | + | 1.27318i | ||||
\(868\) | 5.88097 | 0.199613 | ||||||||
\(869\) | −6.45547 | − | 6.45547i | −0.218987 | − | 0.218987i | ||||
\(870\) | 29.4280 | + | 71.0455i | 0.997703 | + | 2.40867i | ||||
\(871\) | − | 42.9134i | − | 1.45407i | ||||||
\(872\) | −2.60705 | + | 1.07988i | −0.0882860 | + | 0.0365693i | ||||
\(873\) | −15.7258 | + | 37.9654i | −0.532237 | + | 1.28493i | ||||
\(874\) | −0.409699 | − | 0.169703i | −0.0138583 | − | 0.00574028i | ||||
\(875\) | −3.72644 | + | 3.72644i | −0.125977 | + | 0.125977i | ||||
\(876\) | −30.2659 | + | 30.2659i | −1.02259 | + | 1.02259i | ||||
\(877\) | 44.6270 | + | 18.4851i | 1.50695 | + | 0.624198i | 0.974925 | − | 0.222533i | \(-0.0714324\pi\) |
0.532022 | + | 0.846731i | \(0.321432\pi\) | |||||||
\(878\) | 10.1179 | − | 24.4268i | 0.341463 | − | 0.824364i | ||||
\(879\) | −12.3302 | + | 5.10733i | −0.415887 | + | 0.172266i | ||||
\(880\) | − | 6.10463i | − | 0.205787i | ||||||
\(881\) | 15.7848 | + | 38.1078i | 0.531803 | + | 1.28389i | 0.930328 | + | 0.366729i | \(0.119522\pi\) |
−0.398525 | + | 0.917157i | \(0.630478\pi\) | |||||||
\(882\) | −40.9948 | − | 40.9948i | −1.38037 | − | 1.38037i | ||||
\(883\) | −57.0972 | −1.92147 | −0.960737 | − | 0.277462i | \(-0.910507\pi\) | ||||
−0.960737 | + | 0.277462i | \(0.910507\pi\) | |||||||
\(884\) | −22.0368 | + | 40.7735i | −0.741179 | + | 1.37136i | ||||
\(885\) | 40.2220 | 1.35205 | ||||||||
\(886\) | 10.4232 | + | 10.4232i | 0.350173 | + | 0.350173i | ||||
\(887\) | −5.80868 | − | 14.0234i | −0.195036 | − | 0.470859i | 0.795861 | − | 0.605479i | \(-0.207019\pi\) |
−0.990897 | + | 0.134620i | \(0.957019\pi\) | |||||||
\(888\) | 9.89681i | 0.332115i | ||||||||
\(889\) | −6.10539 | + | 2.52893i | −0.204768 | + | 0.0848177i | ||||
\(890\) | 24.3811 | − | 58.8612i | 0.817256 | − | 1.97303i | ||||
\(891\) | −4.03980 | − | 1.67334i | −0.135338 | − | 0.0560590i | ||||
\(892\) | −31.0298 | + | 31.0298i | −1.03896 | + | 1.03896i | ||||
\(893\) | −0.0674917 | + | 0.0674917i | −0.00225853 | + | 0.00225853i | ||||
\(894\) | 39.4175 | + | 16.3273i | 1.31832 | + | 0.546066i | ||||
\(895\) | −7.59854 | + | 18.3445i | −0.253991 | + | 0.613189i | ||||
\(896\) | −1.71481 | + | 0.710297i | −0.0572877 | + | 0.0237293i | ||||
\(897\) | 39.8997i | 1.33221i | ||||||||
\(898\) | 2.15074 | + | 5.19234i | 0.0717711 | + | 0.173271i | ||||
\(899\) | −33.0742 | − | 33.0742i | −1.10309 | − | 1.10309i | ||||
\(900\) | 16.7053 | 0.556843 | ||||||||
\(901\) | −8.04244 | + | 2.39910i | −0.267933 | + | 0.0799256i | ||||
\(902\) | −16.0797 | −0.535397 | ||||||||
\(903\) | −2.92113 | − | 2.92113i | −0.0972092 | − | 0.0972092i | ||||
\(904\) | −0.564014 | − | 1.36165i | −0.0187588 | − | 0.0452878i | ||||
\(905\) | 7.98606i | 0.265466i | ||||||||
\(906\) | −28.3874 | + | 11.7584i | −0.943107 | + | 0.390648i | ||||
\(907\) | 1.39625 | − | 3.37083i | 0.0463616 | − | 0.111927i | −0.899002 | − | 0.437944i | \(-0.855707\pi\) |
0.945364 | + | 0.326017i | \(0.105707\pi\) | |||||||
\(908\) | 11.2221 | + | 4.64835i | 0.372419 | + | 0.154261i | ||||
\(909\) | −48.7691 | + | 48.7691i | −1.61757 | + | 1.61757i | ||||
\(910\) | −5.62960 | + | 5.62960i | −0.186620 | + | 0.186620i | ||||
\(911\) | −49.8359 | − | 20.6427i | −1.65114 | − | 0.683923i | −0.653787 | − | 0.756679i | \(-0.726821\pi\) |
−0.997350 | + | 0.0727558i | \(0.976821\pi\) | |||||||
\(912\) | 0.248573 | − | 0.600109i | 0.00823109 | − | 0.0198716i | ||||
\(913\) | 15.0958 | − | 6.25290i | 0.499599 | − | 0.206941i | ||||
\(914\) | − | 30.0558i | − | 0.994159i | ||||||
\(915\) | −13.1626 | − | 31.7772i | −0.435141 | − | 1.05052i | ||||
\(916\) | −19.4210 | − | 19.4210i | −0.641686 | − | 0.641686i | ||||
\(917\) | −8.13051 | −0.268493 | ||||||||
\(918\) | 25.3633 | + | 2.61652i | 0.837114 | + | 0.0863582i | ||||
\(919\) | 27.6984 | 0.913688 | 0.456844 | − | 0.889547i | \(-0.348980\pi\) | ||||
0.456844 | + | 0.889547i | \(0.348980\pi\) | |||||||
\(920\) | 2.05804 | + | 2.05804i | 0.0678516 | + | 0.0678516i | ||||
\(921\) | −3.73523 | − | 9.01764i | −0.123080 | − | 0.297141i | ||||
\(922\) | 53.8614i | 1.77383i | ||||||||
\(923\) | 2.06369 | − | 0.854808i | 0.0679272 | − | 0.0281363i | ||||
\(924\) | 1.00064 | − | 2.41576i | 0.0329187 | − | 0.0794727i | ||||
\(925\) | 11.3635 | + | 4.70692i | 0.373630 | + | 0.154762i | ||||
\(926\) | 4.15546 | − | 4.15546i | 0.136557 | − | 0.136557i | ||||
\(927\) | −6.64103 | + | 6.64103i | −0.218120 | + | 0.218120i | ||||
\(928\) | 58.4313 | + | 24.2030i | 1.91810 | + | 0.794504i | ||||
\(929\) | −19.5644 | + | 47.2327i | −0.641887 | + | 1.54965i | 0.182243 | + | 0.983253i | \(0.441664\pi\) |
−0.824131 | + | 0.566400i | \(0.808336\pi\) | |||||||
\(930\) | 54.7247 | − | 22.6677i | 1.79449 | − | 0.743304i | ||||
\(931\) | − | 0.486489i | − | 0.0159440i | ||||||
\(932\) | −8.78638 | − | 21.2122i | −0.287808 | − | 0.694829i | ||||
\(933\) | −36.4744 | − | 36.4744i | −1.19412 | − | 1.19412i | ||||
\(934\) | −38.6992 | −1.26628 | ||||||||
\(935\) | 6.49699 | + | 3.51143i | 0.212474 | + | 0.114836i | ||||
\(936\) | 11.0683 | 0.361778 | ||||||||
\(937\) | −23.8738 | − | 23.8738i | −0.779921 | − | 0.779921i | 0.199896 | − | 0.979817i | \(-0.435940\pi\) |
−0.979817 | + | 0.199896i | \(0.935940\pi\) | |||||||
\(938\) | 2.95491 | + | 7.13377i | 0.0964811 | + | 0.232926i | ||||
\(939\) | 78.7896i | 2.57120i | ||||||||
\(940\) | 5.00231 | − | 2.07202i | 0.163157 | − | 0.0675820i | ||||
\(941\) | −3.47504 | + | 8.38949i | −0.113283 | + | 0.273489i | −0.970345 | − | 0.241724i | \(-0.922287\pi\) |
0.857062 | + | 0.515213i | \(0.172287\pi\) | |||||||
\(942\) | −67.3167 | − | 27.8835i | −2.19330 | − | 0.908493i | ||||
\(943\) | −16.5675 | + | 16.5675i | −0.539511 | + | 0.539511i | ||||
\(944\) | 20.2777 | − | 20.2777i | 0.659984 | − | 0.659984i | ||||
\(945\) | 2.14751 | + | 0.889529i | 0.0698586 | + | 0.0289364i | ||||
\(946\) | −2.82285 | + | 6.81496i | −0.0917788 | + | 0.221574i | ||||
\(947\) | −54.7988 | + | 22.6984i | −1.78072 | + | 0.737599i | −0.788217 | + | 0.615398i | \(0.788995\pi\) |
−0.992505 | + | 0.122202i | \(0.961005\pi\) | |||||||
\(948\) | 55.1047i | 1.78972i | ||||||||
\(949\) | 13.4876 | + | 32.5620i | 0.437827 | + | 1.05701i | ||||
\(950\) | 0.186775 | + | 0.186775i | 0.00605979 | + | 0.00605979i | ||||
\(951\) | −21.8205 | −0.707577 | ||||||||
\(952\) | 0.0990119 | − | 0.959774i | 0.00320900 | − | 0.0311065i | ||||
\(953\) | −34.3735 | −1.11347 | −0.556734 | − | 0.830691i | \(-0.687946\pi\) | ||||
−0.556734 | + | 0.830691i | \(0.687946\pi\) | |||||||
\(954\) | 12.2492 | + | 12.2492i | 0.396582 | + | 0.396582i | ||||
\(955\) | −16.1111 | − | 38.8955i | −0.521342 | − | 1.25863i | ||||
\(956\) | − | 12.1408i | − | 0.392662i | ||||||
\(957\) | −19.2136 | + | 7.95855i | −0.621089 | + | 0.257263i | ||||
\(958\) | 6.41734 | − | 15.4928i | 0.207335 | − | 0.500551i | ||||
\(959\) | 5.23498 | + | 2.16840i | 0.169046 | + | 0.0700213i | ||||
\(960\) | −33.5938 | + | 33.5938i | −1.08424 | + | 1.08424i | ||||
\(961\) | −3.55598 | + | 3.55598i | −0.114709 | + | 0.114709i | ||||
\(962\) | 65.0741 | + | 26.9546i | 2.09807 | + | 0.869050i | ||||
\(963\) | 18.4453 | − | 44.5308i | 0.594390 | − | 1.43498i | ||||
\(964\) | −1.83509 | + | 0.760120i | −0.0591044 | + | 0.0244818i | ||||
\(965\) | − | 23.9345i | − | 0.770479i | ||||||
\(966\) | −2.74739 | − | 6.63278i | −0.0883958 | − | 0.213406i | ||||
\(967\) | −4.98941 | − | 4.98941i | −0.160449 | − | 0.160449i | 0.622317 | − | 0.782765i | \(-0.286192\pi\) |
−0.782765 | + | 0.622317i | \(0.786192\pi\) | |||||||
\(968\) | −0.540195 | −0.0173625 | ||||||||
\(969\) | 0.495698 | + | 0.609737i | 0.0159241 | + | 0.0195876i | ||||
\(970\) | 36.8589 | 1.18347 | ||||||||
\(971\) | 12.9818 | + | 12.9818i | 0.416606 | + | 0.416606i | 0.884032 | − | 0.467426i | \(-0.154819\pi\) |
−0.467426 | + | 0.884032i | \(0.654819\pi\) | |||||||
\(972\) | 17.8784 | + | 43.1623i | 0.573451 | + | 1.38443i | ||||
\(973\) | 8.42192i | 0.269995i | ||||||||
\(974\) | 1.35977 | − | 0.563233i | 0.0435697 | − | 0.0180472i | ||||
\(975\) | 9.09482 | − | 21.9568i | 0.291267 | − | 0.703182i | ||||
\(976\) | −22.6562 | − | 9.38449i | −0.725206 | − | 0.300390i | ||||
\(977\) | 2.44744 | − | 2.44744i | 0.0783006 | − | 0.0783006i | −0.666872 | − | 0.745172i | \(-0.732367\pi\) |
0.745172 | + | 0.666872i | \(0.232367\pi\) | |||||||
\(978\) | 86.6606 | − | 86.6606i | 2.77110 | − | 2.77110i | ||||
\(979\) | 15.9185 | + | 6.59365i | 0.508757 | + | 0.210734i | ||||
\(980\) | −10.5609 | + | 25.4964i | −0.337357 | + | 0.814452i | ||||
\(981\) | 19.8956 | − | 8.24104i | 0.635218 | − | 0.263116i | ||||
\(982\) | 34.8242i | 1.11129i | ||||||||
\(983\) | 8.02576 | + | 19.3759i | 0.255982 | + | 0.617995i | 0.998665 | − | 0.0516476i | \(-0.0164473\pi\) |
−0.742683 | + | 0.669643i | \(0.766447\pi\) | |||||||
\(984\) | 7.94035 | + | 7.94035i | 0.253129 | + | 0.253129i | ||||
\(985\) | −14.6117 | −0.465566 | ||||||||
\(986\) | −51.4658 | + | 41.8402i | −1.63901 | + | 1.33246i | ||||
\(987\) | −1.54524 | −0.0491856 | ||||||||
\(988\) | 0.567629 | + | 0.567629i | 0.0180587 | + | 0.0180587i | ||||
\(989\) | 4.11320 | + | 9.93014i | 0.130792 | + | 0.315760i | ||||
\(990\) | − | 15.2435i | − | 0.484470i | ||||||
\(991\) | −19.1003 | + | 7.91161i | −0.606742 | + | 0.251321i | −0.664835 | − | 0.746991i | \(-0.731498\pi\) |
0.0580930 | + | 0.998311i | \(0.481498\pi\) | |||||||
\(992\) | 18.6430 | − | 45.0083i | 0.591917 | − | 1.42901i | ||||
\(993\) | −30.1795 | − | 12.5008i | −0.957718 | − | 0.396700i | ||||
\(994\) | −0.284200 | + | 0.284200i | −0.00901429 | + | 0.00901429i | ||||
\(995\) | 27.0165 | − | 27.0165i | 0.856482 | − | 0.856482i | ||||
\(996\) | −91.1176 | − | 37.7421i | −2.88717 | − | 1.19591i | ||||
\(997\) | 0.785914 | − | 1.89736i | 0.0248901 | − | 0.0600901i | −0.910946 | − | 0.412526i | \(-0.864647\pi\) |
0.935836 | + | 0.352436i | \(0.114647\pi\) | |||||||
\(998\) | 8.19602 | − | 3.39490i | 0.259441 | − | 0.107464i | ||||
\(999\) | − | 20.5646i | − | 0.650635i |
(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 | 187.2.h.a.100.2 | ✓ | 56 | |
17.5 | odd | 16 | 3179.2.a.bi.1.24 | 28 | |||
17.8 | even | 8 | inner | 187.2.h.a.144.2 | yes | 56 | |
17.12 | odd | 16 | 3179.2.a.bh.1.24 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.h.a.100.2 | ✓ | 56 | 1.1 | even | 1 | trivial | |
187.2.h.a.144.2 | yes | 56 | 17.8 | even | 8 | inner | |
3179.2.a.bh.1.24 | 28 | 17.12 | odd | 16 | |||
3179.2.a.bi.1.24 | 28 | 17.5 | odd | 16 |