Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(4,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 4.7 | ||
Root | \(0.871638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.4 |
Dual form | 273.2.t.d.205.4 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.871638i | 0.616341i | 0.951331 | + | 0.308171i | \(0.0997168\pi\) | ||||
−0.951331 | + | 0.308171i | \(0.900283\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.24025 | 0.620123 | ||||||||
\(5\) | 1.34003 | − | 0.773665i | 0.599278 | − | 0.345993i | −0.169479 | − | 0.985534i | \(-0.554209\pi\) |
0.768758 | + | 0.639540i | \(0.220875\pi\) | |||||||
\(6\) | −0.754861 | + | 0.435819i | −0.308171 | + | 0.177922i | ||||
\(7\) | −2.02693 | + | 1.70046i | −0.766108 | + | 0.642712i | ||||
\(8\) | 2.82432i | 0.998549i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.674356 | + | 1.16802i | 0.213250 | + | 0.369360i | ||||
\(11\) | 3.13150 | − | 1.80798i | 0.944184 | − | 0.545125i | 0.0529148 | − | 0.998599i | \(-0.483149\pi\) |
0.891270 | + | 0.453474i | \(0.149816\pi\) | |||||||
\(12\) | 0.620123 | + | 1.07408i | 0.179014 | + | 0.310062i | ||||
\(13\) | −3.37483 | − | 1.26906i | −0.936010 | − | 0.351973i | ||||
\(14\) | −1.48218 | − | 1.76675i | −0.396130 | − | 0.472184i | ||||
\(15\) | 1.34003 | + | 0.773665i | 0.345993 | + | 0.199759i | ||||
\(16\) | 0.0187042 | 0.00467605 | ||||||||
\(17\) | 4.63205 | 1.12344 | 0.561718 | − | 0.827329i | \(-0.310141\pi\) | ||||
0.561718 | + | 0.827329i | \(0.310141\pi\) | |||||||
\(18\) | −0.754861 | − | 0.435819i | −0.177922 | − | 0.102724i | ||||
\(19\) | −0.508319 | − | 0.293478i | −0.116616 | − | 0.0673285i | 0.440557 | − | 0.897725i | \(-0.354781\pi\) |
−0.557174 | + | 0.830396i | \(0.688114\pi\) | |||||||
\(20\) | 1.66196 | − | 0.959535i | 0.371626 | − | 0.214559i | ||||
\(21\) | −2.48610 | − | 0.905145i | −0.542512 | − | 0.197519i | ||||
\(22\) | 1.57590 | + | 2.72954i | 0.335983 | + | 0.581940i | ||||
\(23\) | −2.28523 | −0.476503 | −0.238251 | − | 0.971204i | \(-0.576574\pi\) | ||||
−0.238251 | + | 0.971204i | \(0.576574\pi\) | |||||||
\(24\) | −2.44594 | + | 1.41216i | −0.499275 | + | 0.288256i | ||||
\(25\) | −1.30289 | + | 2.25666i | −0.260577 | + | 0.451333i | ||||
\(26\) | 1.10616 | − | 2.94163i | 0.216936 | − | 0.576902i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.51389 | + | 2.10899i | −0.475081 | + | 0.398561i | ||||
\(29\) | 1.07556 | − | 1.86293i | 0.199727 | − | 0.345937i | −0.748713 | − | 0.662894i | \(-0.769328\pi\) |
0.948440 | + | 0.316957i | \(0.102661\pi\) | |||||||
\(30\) | −0.674356 | + | 1.16802i | −0.123120 | + | 0.213250i | ||||
\(31\) | −8.99732 | − | 5.19461i | −1.61597 | − | 0.932979i | −0.987949 | − | 0.154781i | \(-0.950533\pi\) |
−0.628018 | − | 0.778199i | \(-0.716134\pi\) | |||||||
\(32\) | 5.66495i | 1.00143i | ||||||||
\(33\) | 3.13150 | + | 1.80798i | 0.545125 | + | 0.314728i | ||||
\(34\) | 4.03747i | 0.692420i | ||||||||
\(35\) | −1.40056 | + | 3.84682i | −0.236737 | + | 0.650232i | ||||
\(36\) | −0.620123 | + | 1.07408i | −0.103354 | + | 0.179014i | ||||
\(37\) | − | 5.80975i | − | 0.955116i | −0.878600 | − | 0.477558i | \(-0.841522\pi\) | ||
0.878600 | − | 0.477558i | \(-0.158478\pi\) | |||||||
\(38\) | 0.255807 | − | 0.443071i | 0.0414974 | − | 0.0718755i | ||||
\(39\) | −0.588380 | − | 3.55722i | −0.0942162 | − | 0.569611i | ||||
\(40\) | 2.18508 | + | 3.78467i | 0.345491 | + | 0.598409i | ||||
\(41\) | −1.60485 | − | 0.926561i | −0.250636 | − | 0.144704i | 0.369420 | − | 0.929263i | \(-0.379556\pi\) |
−0.620055 | + | 0.784558i | \(0.712890\pi\) | |||||||
\(42\) | 0.788959 | − | 2.16698i | 0.121739 | − | 0.334373i | ||||
\(43\) | 3.93747 | + | 6.81990i | 0.600459 | + | 1.04003i | 0.992752 | + | 0.120185i | \(0.0383487\pi\) |
−0.392293 | + | 0.919840i | \(0.628318\pi\) | |||||||
\(44\) | 3.88384 | − | 2.24233i | 0.585511 | − | 0.338045i | ||||
\(45\) | 1.54733i | 0.230662i | ||||||||
\(46\) | − | 1.99189i | − | 0.293688i | ||||||
\(47\) | 2.10152 | − | 1.21331i | 0.306538 | − | 0.176980i | −0.338838 | − | 0.940845i | \(-0.610034\pi\) |
0.645376 | + | 0.763865i | \(0.276701\pi\) | |||||||
\(48\) | 0.00935211 | + | 0.0161983i | 0.00134986 | + | 0.00233803i | ||||
\(49\) | 1.21689 | − | 6.89342i | 0.173842 | − | 0.984774i | ||||
\(50\) | −1.96699 | − | 1.13565i | −0.278175 | − | 0.160604i | ||||
\(51\) | 2.31602 | + | 4.01147i | 0.324308 | + | 0.561718i | ||||
\(52\) | −4.18562 | − | 1.57394i | −0.580442 | − | 0.218267i | ||||
\(53\) | 6.49352 | − | 11.2471i | 0.891954 | − | 1.54491i | 0.0544233 | − | 0.998518i | \(-0.482668\pi\) |
0.837530 | − | 0.546391i | \(-0.183999\pi\) | |||||||
\(54\) | − | 0.871638i | − | 0.118615i | ||||||
\(55\) | 2.79753 | − | 4.84547i | 0.377219 | − | 0.653363i | ||||
\(56\) | −4.80264 | − | 5.72471i | −0.641780 | − | 0.764996i | ||||
\(57\) | − | 0.586956i | − | 0.0777443i | ||||||
\(58\) | 1.62380 | + | 0.937502i | 0.213216 | + | 0.123100i | ||||
\(59\) | − | 5.41501i | − | 0.704975i | −0.935817 | − | 0.352487i | \(-0.885336\pi\) | ||
0.935817 | − | 0.352487i | \(-0.114664\pi\) | |||||||
\(60\) | 1.66196 | + | 0.959535i | 0.214559 | + | 0.123875i | ||||
\(61\) | 4.85421 | − | 8.40774i | 0.621518 | − | 1.07650i | −0.367685 | − | 0.929950i | \(-0.619850\pi\) |
0.989203 | − | 0.146550i | \(-0.0468170\pi\) | |||||||
\(62\) | 4.52782 | − | 7.84241i | 0.575034 | − | 0.995988i | ||||
\(63\) | −0.459174 | − | 2.60560i | −0.0578504 | − | 0.328275i | ||||
\(64\) | −4.90038 | −0.612547 | ||||||||
\(65\) | −5.50419 | + | 0.910418i | −0.682711 | + | 0.112923i | ||||
\(66\) | −1.57590 | + | 2.72954i | −0.193980 | + | 0.335983i | ||||
\(67\) | −1.66329 | + | 0.960298i | −0.203203 | + | 0.117319i | −0.598148 | − | 0.801385i | \(-0.704097\pi\) |
0.394946 | + | 0.918704i | \(0.370763\pi\) | |||||||
\(68\) | 5.74488 | 0.696669 | ||||||||
\(69\) | −1.14261 | − | 1.97906i | −0.137554 | − | 0.238251i | ||||
\(70\) | −3.35304 | − | 1.22078i | −0.400765 | − | 0.145911i | ||||
\(71\) | −9.14766 | + | 5.28141i | −1.08563 | + | 0.626788i | −0.932409 | − | 0.361405i | \(-0.882297\pi\) |
−0.153219 | + | 0.988192i | \(0.548964\pi\) | |||||||
\(72\) | −2.44594 | − | 1.41216i | −0.288256 | − | 0.166425i | ||||
\(73\) | −1.96780 | − | 1.13611i | −0.230313 | − | 0.132971i | 0.380403 | − | 0.924821i | \(-0.375785\pi\) |
−0.610717 | + | 0.791849i | \(0.709118\pi\) | |||||||
\(74\) | 5.06400 | 0.588678 | ||||||||
\(75\) | −2.60577 | −0.300889 | ||||||||
\(76\) | −0.630441 | − | 0.363985i | −0.0723165 | − | 0.0417520i | ||||
\(77\) | −3.27296 | + | 8.98963i | −0.372988 | + | 1.02446i | ||||
\(78\) | 3.10061 | − | 0.512855i | 0.351075 | − | 0.0580694i | ||||
\(79\) | 5.78378 | + | 10.0178i | 0.650726 | + | 1.12709i | 0.982947 | + | 0.183889i | \(0.0588686\pi\) |
−0.332221 | + | 0.943202i | \(0.607798\pi\) | |||||||
\(80\) | 0.0250642 | − | 0.0144708i | 0.00280226 | − | 0.00161788i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.807626 | − | 1.39885i | 0.0891874 | − | 0.154477i | ||||
\(83\) | 9.45200i | 1.03749i | 0.854928 | + | 0.518746i | \(0.173601\pi\) | ||||
−0.854928 | + | 0.518746i | \(0.826399\pi\) | |||||||
\(84\) | −3.08338 | − | 1.12260i | −0.336425 | − | 0.122486i | ||||
\(85\) | 6.20707 | − | 3.58365i | 0.673251 | − | 0.388702i | ||||
\(86\) | −5.94449 | + | 3.43205i | −0.641011 | + | 0.370088i | ||||
\(87\) | 2.15113 | 0.230625 | ||||||||
\(88\) | 5.10631 | + | 8.84438i | 0.544334 | + | 0.942814i | ||||
\(89\) | − | 12.6671i | − | 1.34272i | −0.741134 | − | 0.671358i | \(-0.765712\pi\) | ||
0.741134 | − | 0.671358i | \(-0.234288\pi\) | |||||||
\(90\) | −1.34871 | −0.142167 | ||||||||
\(91\) | 8.99853 | − | 3.16647i | 0.943302 | − | 0.331936i | ||||
\(92\) | −2.83424 | −0.295490 | ||||||||
\(93\) | − | 10.3892i | − | 1.07731i | ||||||
\(94\) | 1.05757 | + | 1.83177i | 0.109080 | + | 0.188932i | ||||
\(95\) | −0.908215 | −0.0931809 | ||||||||
\(96\) | −4.90599 | + | 2.83247i | −0.500716 | + | 0.289088i | ||||
\(97\) | −14.3826 | + | 8.30380i | −1.46033 | + | 0.843124i | −0.999026 | − | 0.0441172i | \(-0.985952\pi\) |
−0.461307 | + | 0.887241i | \(0.652619\pi\) | |||||||
\(98\) | 6.00857 | + | 1.06069i | 0.606957 | + | 0.107146i | ||||
\(99\) | 3.61595i | 0.363417i | ||||||||
\(100\) | −1.61590 | + | 2.79882i | −0.161590 | + | 0.279882i | ||||
\(101\) | −6.54956 | − | 11.3442i | −0.651705 | − | 1.12879i | −0.982709 | − | 0.185157i | \(-0.940721\pi\) |
0.331003 | − | 0.943630i | \(-0.392613\pi\) | |||||||
\(102\) | −3.49655 | + | 2.01873i | −0.346210 | + | 0.199885i | ||||
\(103\) | −0.0841095 | − | 0.145682i | −0.00828756 | − | 0.0143545i | 0.861852 | − | 0.507160i | \(-0.169305\pi\) |
−0.870139 | + | 0.492806i | \(0.835971\pi\) | |||||||
\(104\) | 3.58423 | − | 9.53162i | 0.351463 | − | 0.934652i | ||||
\(105\) | −4.03172 | + | 0.710493i | −0.393456 | + | 0.0693370i | ||||
\(106\) | 9.80341 | + | 5.66000i | 0.952191 | + | 0.549748i | ||||
\(107\) | −1.58262 | −0.152998 | −0.0764990 | − | 0.997070i | \(-0.524374\pi\) | ||||
−0.0764990 | + | 0.997070i | \(0.524374\pi\) | |||||||
\(108\) | −1.24025 | −0.119343 | ||||||||
\(109\) | 3.76860 | + | 2.17580i | 0.360966 | + | 0.208404i | 0.669504 | − | 0.742808i | \(-0.266506\pi\) |
−0.308538 | + | 0.951212i | \(0.599840\pi\) | |||||||
\(110\) | 4.22350 | + | 2.43844i | 0.402695 | + | 0.232496i | ||||
\(111\) | 5.03139 | − | 2.90487i | 0.477558 | − | 0.275718i | ||||
\(112\) | −0.0379121 | + | 0.0318057i | −0.00358236 | + | 0.00300536i | ||||
\(113\) | 6.62266 | + | 11.4708i | 0.623007 | + | 1.07908i | 0.988923 | + | 0.148432i | \(0.0474226\pi\) |
−0.365915 | + | 0.930648i | \(0.619244\pi\) | |||||||
\(114\) | 0.511614 | 0.0479170 | ||||||||
\(115\) | −3.06226 | + | 1.76800i | −0.285558 | + | 0.164867i | ||||
\(116\) | 1.33396 | − | 2.31049i | 0.123855 | − | 0.214524i | ||||
\(117\) | 2.78645 | − | 2.28816i | 0.257608 | − | 0.211541i | ||||
\(118\) | 4.71993 | 0.434505 | ||||||||
\(119\) | −9.38883 | + | 7.87659i | −0.860673 | + | 0.722046i | ||||
\(120\) | −2.18508 | + | 3.78467i | −0.199470 | + | 0.345491i | ||||
\(121\) | 1.03755 | − | 1.79709i | 0.0943226 | − | 0.163372i | ||||
\(122\) | 7.32851 | + | 4.23111i | 0.663492 | + | 0.383067i | ||||
\(123\) | − | 1.85312i | − | 0.167090i | ||||||
\(124\) | −11.1589 | − | 6.44259i | −1.00210 | − | 0.578562i | ||||
\(125\) | 11.7686i | 1.05262i | ||||||||
\(126\) | 2.27114 | − | 0.400233i | 0.202329 | − | 0.0356556i | ||||
\(127\) | 1.74707 | − | 3.02602i | 0.155028 | − | 0.268516i | −0.778041 | − | 0.628213i | \(-0.783787\pi\) |
0.933069 | + | 0.359697i | \(0.117120\pi\) | |||||||
\(128\) | 7.05854i | 0.623893i | ||||||||
\(129\) | −3.93747 | + | 6.81990i | −0.346675 | + | 0.600459i | ||||
\(130\) | −0.793555 | − | 4.79766i | −0.0695994 | − | 0.420783i | ||||
\(131\) | −3.04778 | − | 5.27892i | −0.266286 | − | 0.461221i | 0.701614 | − | 0.712558i | \(-0.252463\pi\) |
−0.967900 | + | 0.251336i | \(0.919130\pi\) | |||||||
\(132\) | 3.88384 | + | 2.24233i | 0.338045 | + | 0.195170i | ||||
\(133\) | 1.52937 | − | 0.269515i | 0.132614 | − | 0.0233699i | ||||
\(134\) | −0.837033 | − | 1.44978i | −0.0723086 | − | 0.125242i | ||||
\(135\) | −1.34003 | + | 0.773665i | −0.115331 | + | 0.0665865i | ||||
\(136\) | 13.0824i | 1.12181i | ||||||||
\(137\) | 2.47086i | 0.211099i | 0.994414 | + | 0.105550i | \(0.0336602\pi\) | ||||
−0.994414 | + | 0.105550i | \(0.966340\pi\) | |||||||
\(138\) | 1.72503 | − | 0.995945i | 0.146844 | − | 0.0847805i | ||||
\(139\) | 5.27760 | + | 9.14107i | 0.447640 | + | 0.775335i | 0.998232 | − | 0.0594393i | \(-0.0189313\pi\) |
−0.550592 | + | 0.834775i | \(0.685598\pi\) | |||||||
\(140\) | −1.73704 | + | 4.77101i | −0.146806 | + | 0.403224i | ||||
\(141\) | 2.10152 | + | 1.21331i | 0.176980 | + | 0.102179i | ||||
\(142\) | −4.60348 | − | 7.97346i | −0.386315 | − | 0.669118i | ||||
\(143\) | −12.8627 | + | 2.12755i | −1.07564 | + | 0.177915i | ||||
\(144\) | −0.00935211 | + | 0.0161983i | −0.000779342 | + | 0.00134986i | ||||
\(145\) | − | 3.32850i | − | 0.276417i | ||||||
\(146\) | 0.990275 | − | 1.71521i | 0.0819558 | − | 0.141952i | ||||
\(147\) | 6.57832 | − | 2.39285i | 0.542571 | − | 0.197359i | ||||
\(148\) | − | 7.20552i | − | 0.592290i | ||||||
\(149\) | 10.4409 | + | 6.02804i | 0.855350 | + | 0.493836i | 0.862452 | − | 0.506138i | \(-0.168927\pi\) |
−0.00710248 | + | 0.999975i | \(0.502261\pi\) | |||||||
\(150\) | − | 2.27129i | − | 0.185450i | ||||||
\(151\) | 5.84616 | + | 3.37528i | 0.475754 | + | 0.274677i | 0.718645 | − | 0.695377i | \(-0.244763\pi\) |
−0.242891 | + | 0.970053i | \(0.578096\pi\) | |||||||
\(152\) | 0.828877 | − | 1.43566i | 0.0672308 | − | 0.116447i | ||||
\(153\) | −2.31602 | + | 4.01147i | −0.187239 | + | 0.324308i | ||||
\(154\) | −7.83571 | − | 2.85284i | −0.631419 | − | 0.229888i | ||||
\(155\) | −16.0755 | −1.29122 | ||||||||
\(156\) | −0.729736 | − | 4.41183i | −0.0584257 | − | 0.353229i | ||||
\(157\) | −1.42832 | + | 2.47392i | −0.113992 | + | 0.197441i | −0.917376 | − | 0.398021i | \(-0.869697\pi\) |
0.803384 | + | 0.595461i | \(0.203031\pi\) | |||||||
\(158\) | −8.73190 | + | 5.04136i | −0.694673 | + | 0.401069i | ||||
\(159\) | 12.9870 | 1.02994 | ||||||||
\(160\) | 4.38277 | + | 7.59118i | 0.346489 | + | 0.600136i | ||||
\(161\) | 4.63199 | − | 3.88593i | 0.365052 | − | 0.306254i | ||||
\(162\) | 0.754861 | − | 0.435819i | 0.0593075 | − | 0.0342412i | ||||
\(163\) | −14.8902 | − | 8.59686i | −1.16629 | − | 0.673358i | −0.213487 | − | 0.976946i | \(-0.568482\pi\) |
−0.952804 | + | 0.303588i | \(0.901816\pi\) | |||||||
\(164\) | −1.99041 | − | 1.14916i | −0.155425 | − | 0.0897346i | ||||
\(165\) | 5.59507 | 0.435575 | ||||||||
\(166\) | −8.23873 | −0.639449 | ||||||||
\(167\) | 11.8526 | + | 6.84312i | 0.917185 | + | 0.529537i | 0.882736 | − | 0.469870i | \(-0.155699\pi\) |
0.0344489 | + | 0.999406i | \(0.489032\pi\) | |||||||
\(168\) | 2.55642 | − | 7.02156i | 0.197232 | − | 0.541725i | ||||
\(169\) | 9.77899 | + | 8.56571i | 0.752230 | + | 0.658901i | ||||
\(170\) | 3.12365 | + | 5.41032i | 0.239573 | + | 0.414952i | ||||
\(171\) | 0.508319 | − | 0.293478i | 0.0388721 | − | 0.0224428i | ||||
\(172\) | 4.88343 | + | 8.45836i | 0.372358 | + | 0.644944i | ||||
\(173\) | −9.15726 | + | 15.8608i | −0.696214 | + | 1.20588i | 0.273556 | + | 0.961856i | \(0.411800\pi\) |
−0.969770 | + | 0.244022i | \(0.921533\pi\) | |||||||
\(174\) | 1.87500i | 0.142144i | ||||||||
\(175\) | −1.19650 | − | 6.78960i | −0.0904470 | − | 0.513246i | ||||
\(176\) | 0.0585724 | − | 0.0338168i | 0.00441506 | − | 0.00254903i | ||||
\(177\) | 4.68954 | − | 2.70751i | 0.352487 | − | 0.203509i | ||||
\(178\) | 11.0412 | 0.827571 | ||||||||
\(179\) | 9.18131 | + | 15.9025i | 0.686243 | + | 1.18861i | 0.973044 | + | 0.230618i | \(0.0740748\pi\) |
−0.286801 | + | 0.957990i | \(0.592592\pi\) | |||||||
\(180\) | 1.91907i | 0.143039i | ||||||||
\(181\) | −18.0249 | −1.33978 | −0.669889 | − | 0.742462i | \(-0.733658\pi\) | ||||
−0.669889 | + | 0.742462i | \(0.733658\pi\) | |||||||
\(182\) | 2.76001 | + | 7.84346i | 0.204586 | + | 0.581396i | ||||
\(183\) | 9.70842 | 0.717667 | ||||||||
\(184\) | − | 6.45422i | − | 0.475811i | ||||||
\(185\) | −4.49480 | − | 7.78521i | −0.330464 | − | 0.572380i | ||||
\(186\) | 9.05564 | 0.663992 | ||||||||
\(187\) | 14.5053 | − | 8.37462i | 1.06073 | − | 0.612413i | ||||
\(188\) | 2.60640 | − | 1.50481i | 0.190092 | − | 0.109749i | ||||
\(189\) | 2.02693 | − | 1.70046i | 0.147437 | − | 0.123690i | ||||
\(190\) | − | 0.791635i | − | 0.0574313i | ||||||
\(191\) | −12.1990 | + | 21.1293i | −0.882691 | + | 1.52887i | −0.0343532 | + | 0.999410i | \(0.510937\pi\) |
−0.848338 | + | 0.529456i | \(0.822396\pi\) | |||||||
\(192\) | −2.45019 | − | 4.24385i | −0.176827 | − | 0.306274i | ||||
\(193\) | −10.4054 | + | 6.00758i | −0.748999 | + | 0.432435i | −0.825332 | − | 0.564647i | \(-0.809012\pi\) |
0.0763329 | + | 0.997082i | \(0.475679\pi\) | |||||||
\(194\) | −7.23792 | − | 12.5364i | −0.519652 | − | 0.900064i | ||||
\(195\) | −3.54054 | − | 4.31156i | −0.253543 | − | 0.308757i | ||||
\(196\) | 1.50925 | − | 8.54953i | 0.107803 | − | 0.610681i | ||||
\(197\) | −18.2189 | − | 10.5187i | −1.29804 | − | 0.749424i | −0.317975 | − | 0.948099i | \(-0.603003\pi\) |
−0.980065 | + | 0.198675i | \(0.936336\pi\) | |||||||
\(198\) | −3.15180 | −0.223989 | ||||||||
\(199\) | 1.08768 | 0.0771034 | 0.0385517 | − | 0.999257i | \(-0.487726\pi\) | ||||
0.0385517 | + | 0.999257i | \(0.487726\pi\) | |||||||
\(200\) | −6.37355 | − | 3.67977i | −0.450678 | − | 0.260199i | ||||
\(201\) | −1.66329 | − | 0.960298i | −0.117319 | − | 0.0677342i | ||||
\(202\) | 9.88801 | − | 5.70885i | 0.695718 | − | 0.401673i | ||||
\(203\) | 0.987740 | + | 5.60498i | 0.0693258 | + | 0.393392i | ||||
\(204\) | 2.87244 | + | 4.97521i | 0.201111 | + | 0.348334i | ||||
\(205\) | −2.86739 | −0.200267 | ||||||||
\(206\) | 0.126982 | − | 0.0733131i | 0.00884725 | − | 0.00510796i | ||||
\(207\) | 1.14261 | − | 1.97906i | 0.0794171 | − | 0.137554i | ||||
\(208\) | −0.0631236 | − | 0.0237367i | −0.00437683 | − | 0.00164585i | ||||
\(209\) | −2.12241 | −0.146810 | ||||||||
\(210\) | −0.619293 | − | 3.51421i | −0.0427353 | − | 0.242503i | ||||
\(211\) | 10.2015 | − | 17.6694i | 0.702297 | − | 1.21641i | −0.265361 | − | 0.964149i | \(-0.585491\pi\) |
0.967658 | − | 0.252266i | \(-0.0811757\pi\) | |||||||
\(212\) | 8.05357 | − | 13.9492i | 0.553121 | − | 0.958034i | ||||
\(213\) | −9.14766 | − | 5.28141i | −0.626788 | − | 0.361876i | ||||
\(214\) | − | 1.37948i | − | 0.0942990i | ||||||
\(215\) | 10.5526 | + | 6.09257i | 0.719684 | + | 0.415510i | ||||
\(216\) | − | 2.82432i | − | 0.192171i | ||||||
\(217\) | 27.0702 | − | 4.77045i | 1.83764 | − | 0.323839i | ||||
\(218\) | −1.89651 | + | 3.28485i | −0.128448 | + | 0.222478i | ||||
\(219\) | − | 2.27222i | − | 0.153542i | ||||||
\(220\) | 3.46963 | − | 6.00958i | 0.233922 | − | 0.405166i | ||||
\(221\) | −15.6324 | − | 5.87833i | −1.05155 | − | 0.395419i | ||||
\(222\) | 2.53200 | + | 4.38555i | 0.169937 | + | 0.294339i | ||||
\(223\) | −9.56277 | − | 5.52107i | −0.640371 | − | 0.369718i | 0.144387 | − | 0.989521i | \(-0.453879\pi\) |
−0.784757 | + | 0.619803i | \(0.787212\pi\) | |||||||
\(224\) | −9.63300 | − | 11.4825i | −0.643632 | − | 0.767204i | ||||
\(225\) | −1.30289 | − | 2.25666i | −0.0868590 | − | 0.150444i | ||||
\(226\) | −9.99837 | + | 5.77256i | −0.665082 | + | 0.383985i | ||||
\(227\) | 12.1047i | 0.803417i | 0.915767 | + | 0.401709i | \(0.131584\pi\) | ||||
−0.915767 | + | 0.401709i | \(0.868416\pi\) | |||||||
\(228\) | − | 0.727971i | − | 0.0482110i | ||||||
\(229\) | 12.4222 | − | 7.17199i | 0.820885 | − | 0.473938i | −0.0298364 | − | 0.999555i | \(-0.509499\pi\) |
0.850722 | + | 0.525617i | \(0.176165\pi\) | |||||||
\(230\) | −1.54106 | − | 2.66919i | −0.101614 | − | 0.176001i | ||||
\(231\) | −9.42173 | + | 1.66035i | −0.619904 | + | 0.109243i | ||||
\(232\) | 5.26152 | + | 3.03774i | 0.345435 | + | 0.199437i | ||||
\(233\) | 10.5498 | + | 18.2727i | 0.691137 | + | 1.19709i | 0.971465 | + | 0.237181i | \(0.0762234\pi\) |
−0.280328 | + | 0.959904i | \(0.590443\pi\) | |||||||
\(234\) | 1.99445 | + | 2.42878i | 0.130381 | + | 0.158774i | ||||
\(235\) | 1.87740 | − | 3.25175i | 0.122468 | − | 0.212120i | ||||
\(236\) | − | 6.71595i | − | 0.437171i | ||||||
\(237\) | −5.78378 | + | 10.0178i | −0.375697 | + | 0.650726i | ||||
\(238\) | −6.86554 | − | 8.18367i | −0.445027 | − | 0.530468i | ||||
\(239\) | − | 4.64324i | − | 0.300346i | −0.988660 | − | 0.150173i | \(-0.952017\pi\) | ||
0.988660 | − | 0.150173i | \(-0.0479831\pi\) | |||||||
\(240\) | 0.0250642 | + | 0.0144708i | 0.00161788 | + | 0.000934086i | ||||
\(241\) | 8.03989i | 0.517895i | 0.965891 | + | 0.258948i | \(0.0833757\pi\) | ||||
−0.965891 | + | 0.258948i | \(0.916624\pi\) | |||||||
\(242\) | 1.56641 | + | 0.904367i | 0.100693 | + | 0.0581349i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 6.02042 | − | 10.4277i | 0.385418 | − | 0.667563i | ||||
\(245\) | −3.70252 | − | 10.1788i | −0.236546 | − | 0.650301i | ||||
\(246\) | 1.61525 | 0.102985 | ||||||||
\(247\) | 1.34305 | + | 1.63553i | 0.0854563 | + | 0.104066i | ||||
\(248\) | 14.6713 | − | 25.4114i | 0.931625 | − | 1.61362i | ||||
\(249\) | −8.18567 | + | 4.72600i | −0.518746 | + | 0.299498i | ||||
\(250\) | −10.2580 | −0.648773 | ||||||||
\(251\) | 6.22683 | + | 10.7852i | 0.393034 | + | 0.680755i | 0.992848 | − | 0.119384i | \(-0.0380921\pi\) |
−0.599814 | + | 0.800140i | \(0.704759\pi\) | |||||||
\(252\) | −0.569488 | − | 3.23159i | −0.0358744 | − | 0.203571i | ||||
\(253\) | −7.15620 | + | 4.13163i | −0.449906 | + | 0.259753i | ||||
\(254\) | 2.63760 | + | 1.52282i | 0.165498 | + | 0.0955501i | ||||
\(255\) | 6.20707 | + | 3.58365i | 0.388702 | + | 0.224417i | ||||
\(256\) | −15.9533 | −0.997078 | ||||||||
\(257\) | 7.17256 | 0.447412 | 0.223706 | − | 0.974657i | \(-0.428185\pi\) | ||||
0.223706 | + | 0.974657i | \(0.428185\pi\) | |||||||
\(258\) | −5.94449 | − | 3.43205i | −0.370088 | − | 0.213670i | ||||
\(259\) | 9.87922 | + | 11.7759i | 0.613865 | + | 0.731722i | ||||
\(260\) | −6.82655 | + | 1.12914i | −0.423365 | + | 0.0700265i | ||||
\(261\) | 1.07556 | + | 1.86293i | 0.0665757 | + | 0.115312i | ||||
\(262\) | 4.60131 | − | 2.65657i | 0.284270 | − | 0.164123i | ||||
\(263\) | −8.67804 | − | 15.0308i | −0.535111 | − | 0.926839i | −0.999158 | − | 0.0410286i | \(-0.986937\pi\) |
0.464047 | − | 0.885810i | \(-0.346397\pi\) | |||||||
\(264\) | −5.10631 | + | 8.84438i | −0.314271 | + | 0.544334i | ||||
\(265\) | − | 20.0952i | − | 1.23444i | ||||||
\(266\) | 0.234920 | + | 1.33306i | 0.0144038 | + | 0.0817353i | ||||
\(267\) | 10.9701 | − | 6.33357i | 0.671358 | − | 0.387608i | ||||
\(268\) | −2.06288 | + | 1.19101i | −0.126011 | + | 0.0727523i | ||||
\(269\) | 11.2092 | 0.683435 | 0.341717 | − | 0.939803i | \(-0.388991\pi\) | ||||
0.341717 | + | 0.939803i | \(0.388991\pi\) | |||||||
\(270\) | −0.674356 | − | 1.16802i | −0.0410400 | − | 0.0710834i | ||||
\(271\) | 25.6318i | 1.55702i | 0.627632 | + | 0.778510i | \(0.284024\pi\) | ||||
−0.627632 | + | 0.778510i | \(0.715976\pi\) | |||||||
\(272\) | 0.0866388 | 0.00525325 | ||||||||
\(273\) | 7.24150 | + | 6.20972i | 0.438276 | + | 0.375829i | ||||
\(274\) | −2.15369 | −0.130109 | ||||||||
\(275\) | 9.42234i | 0.568188i | ||||||||
\(276\) | −1.41712 | − | 2.45453i | −0.0853007 | − | 0.147745i | ||||
\(277\) | −12.4061 | −0.745413 | −0.372706 | − | 0.927949i | \(-0.621570\pi\) | ||||
−0.372706 | + | 0.927949i | \(0.621570\pi\) | |||||||
\(278\) | −7.96771 | + | 4.60016i | −0.477871 | + | 0.275899i | ||||
\(279\) | 8.99732 | − | 5.19461i | 0.538656 | − | 0.310993i | ||||
\(280\) | −10.8647 | − | 3.95563i | −0.649288 | − | 0.236394i | ||||
\(281\) | − | 30.8640i | − | 1.84119i | −0.390513 | − | 0.920597i | \(-0.627702\pi\) | ||
0.390513 | − | 0.920597i | \(-0.372298\pi\) | |||||||
\(282\) | −1.05757 | + | 1.83177i | −0.0629774 | + | 0.109080i | ||||
\(283\) | −5.36758 | − | 9.29692i | −0.319069 | − | 0.552644i | 0.661225 | − | 0.750188i | \(-0.270037\pi\) |
−0.980294 | + | 0.197543i | \(0.936704\pi\) | |||||||
\(284\) | −11.3454 | + | 6.55025i | −0.673223 | + | 0.388686i | ||||
\(285\) | −0.454108 | − | 0.786537i | −0.0268990 | − | 0.0465905i | ||||
\(286\) | −1.85446 | − | 11.2116i | −0.109656 | − | 0.662959i | ||||
\(287\) | 4.82850 | − | 0.850905i | 0.285017 | − | 0.0502273i | ||||
\(288\) | −4.90599 | − | 2.83247i | −0.289088 | − | 0.166905i | ||||
\(289\) | 4.45585 | 0.262109 | ||||||||
\(290\) | 2.90125 | 0.170367 | ||||||||
\(291\) | −14.3826 | − | 8.30380i | −0.843124 | − | 0.486778i | ||||
\(292\) | −2.44055 | − | 1.40905i | −0.142823 | − | 0.0824586i | ||||
\(293\) | −0.0137087 | + | 0.00791474i | −0.000800872 | + | 0.000462384i | −0.500400 | − | 0.865794i | \(-0.666814\pi\) |
0.499600 | + | 0.866257i | \(0.333481\pi\) | |||||||
\(294\) | 2.08570 | + | 5.73392i | 0.121640 | + | 0.334409i | ||||
\(295\) | −4.18941 | − | 7.25626i | −0.243917 | − | 0.422476i | ||||
\(296\) | 16.4086 | 0.953730 | ||||||||
\(297\) | −3.13150 | + | 1.80798i | −0.181708 | + | 0.104909i | ||||
\(298\) | −5.25427 | + | 9.10067i | −0.304372 | + | 0.527188i | ||||
\(299\) | 7.71225 | + | 2.90008i | 0.446011 | + | 0.167716i | ||||
\(300\) | −3.23180 | −0.186588 | ||||||||
\(301\) | −19.5779 | − | 7.12796i | −1.12845 | − | 0.410849i | ||||
\(302\) | −2.94203 | + | 5.09574i | −0.169295 | + | 0.293227i | ||||
\(303\) | 6.54956 | − | 11.3442i | 0.376262 | − | 0.651705i | ||||
\(304\) | −0.00950771 | − | 0.00548928i | −0.000545305 | − | 0.000314832i | ||||
\(305\) | − | 15.0221i | − | 0.860164i | ||||||
\(306\) | −3.49655 | − | 2.01873i | −0.199885 | − | 0.115403i | ||||
\(307\) | 22.7982i | 1.30116i | 0.759437 | + | 0.650581i | \(0.225474\pi\) | ||||
−0.759437 | + | 0.650581i | \(0.774526\pi\) | |||||||
\(308\) | −4.05928 | + | 11.1494i | −0.231299 | + | 0.635293i | ||||
\(309\) | 0.0841095 | − | 0.145682i | 0.00478482 | − | 0.00828756i | ||||
\(310\) | − | 14.0121i | − | 0.795831i | ||||||
\(311\) | 1.79592 | − | 3.11062i | 0.101837 | − | 0.176387i | −0.810604 | − | 0.585594i | \(-0.800861\pi\) |
0.912442 | + | 0.409207i | \(0.134195\pi\) | |||||||
\(312\) | 10.0467 | − | 1.66178i | 0.568784 | − | 0.0940795i | ||||
\(313\) | 4.08399 | + | 7.07368i | 0.230841 | + | 0.399828i | 0.958056 | − | 0.286582i | \(-0.0925190\pi\) |
−0.727215 | + | 0.686410i | \(0.759186\pi\) | |||||||
\(314\) | −2.15637 | − | 1.24498i | −0.121691 | − | 0.0702582i | ||||
\(315\) | −2.63117 | − | 3.13633i | −0.148249 | − | 0.176712i | ||||
\(316\) | 7.17331 | + | 12.4245i | 0.403530 | + | 0.698935i | ||||
\(317\) | 19.6172 | − | 11.3260i | 1.10181 | − | 0.636131i | 0.165116 | − | 0.986274i | \(-0.447200\pi\) |
0.936696 | + | 0.350143i | \(0.113867\pi\) | |||||||
\(318\) | 11.3200i | 0.634794i | ||||||||
\(319\) | − | 7.77836i | − | 0.435505i | ||||||
\(320\) | −6.56664 | + | 3.79125i | −0.367086 | + | 0.211937i | ||||
\(321\) | −0.791312 | − | 1.37059i | −0.0441667 | − | 0.0764990i | ||||
\(322\) | 3.38712 | + | 4.03742i | 0.188757 | + | 0.224997i | ||||
\(323\) | −2.35456 | − | 1.35940i | −0.131011 | − | 0.0756393i | ||||
\(324\) | −0.620123 | − | 1.07408i | −0.0344513 | − | 0.0596714i | ||||
\(325\) | 7.26086 | − | 5.96243i | 0.402760 | − | 0.330736i | ||||
\(326\) | 7.49336 | − | 12.9789i | 0.415019 | − | 0.718833i | ||||
\(327\) | 4.35160i | 0.240644i | ||||||||
\(328\) | 2.61691 | − | 4.53262i | 0.144495 | − | 0.250272i | ||||
\(329\) | −2.19645 | + | 6.03285i | −0.121094 | + | 0.332602i | ||||
\(330\) | 4.87688i | 0.268463i | ||||||||
\(331\) | −15.5467 | − | 8.97589i | −0.854524 | − | 0.493360i | 0.00765059 | − | 0.999971i | \(-0.497565\pi\) |
−0.862175 | + | 0.506611i | \(0.830898\pi\) | |||||||
\(332\) | 11.7228i | 0.643373i | ||||||||
\(333\) | 5.03139 | + | 2.90487i | 0.275718 | + | 0.159186i | ||||
\(334\) | −5.96473 | + | 10.3312i | −0.326376 | + | 0.565299i | ||||
\(335\) | −1.48590 | + | 2.57365i | −0.0811833 | + | 0.140614i | ||||
\(336\) | −0.0465006 | − | 0.0169300i | −0.00253682 | − | 0.000923609i | ||||
\(337\) | −5.23244 | −0.285029 | −0.142515 | − | 0.989793i | \(-0.545519\pi\) | ||||
−0.142515 | + | 0.989793i | \(0.545519\pi\) | |||||||
\(338\) | −7.46620 | + | 8.52374i | −0.406108 | + | 0.463630i | ||||
\(339\) | −6.62266 | + | 11.4708i | −0.359693 | + | 0.623007i | ||||
\(340\) | 7.69829 | − | 4.44461i | 0.417498 | − | 0.241043i | ||||
\(341\) | −37.5669 | −2.03436 | ||||||||
\(342\) | 0.255807 | + | 0.443071i | 0.0138325 | + | 0.0239585i | ||||
\(343\) | 9.25540 | + | 16.0417i | 0.499744 | + | 0.866173i | ||||
\(344\) | −19.2616 | + | 11.1207i | −1.03852 | + | 0.599588i | ||||
\(345\) | −3.06226 | − | 1.76800i | −0.164867 | − | 0.0951859i | ||||
\(346\) | −13.8249 | − | 7.98182i | −0.743232 | − | 0.429105i | ||||
\(347\) | 16.3188 | 0.876039 | 0.438019 | − | 0.898966i | \(-0.355680\pi\) | ||||
0.438019 | + | 0.898966i | \(0.355680\pi\) | |||||||
\(348\) | 2.66793 | 0.143016 | ||||||||
\(349\) | 23.6336 | + | 13.6449i | 1.26508 | + | 0.730394i | 0.974053 | − | 0.226321i | \(-0.0726698\pi\) |
0.291027 | + | 0.956715i | \(0.406003\pi\) | |||||||
\(350\) | 5.91808 | − | 1.04292i | 0.316335 | − | 0.0557462i | ||||
\(351\) | 3.37483 | + | 1.26906i | 0.180135 | + | 0.0677373i | ||||
\(352\) | 10.2421 | + | 17.7398i | 0.545905 | + | 0.945536i | ||||
\(353\) | 24.6048 | − | 14.2056i | 1.30958 | − | 0.756087i | 0.327555 | − | 0.944832i | \(-0.393775\pi\) |
0.982026 | + | 0.188745i | \(0.0604419\pi\) | |||||||
\(354\) | 2.35997 | + | 4.08758i | 0.125431 | + | 0.217253i | ||||
\(355\) | −8.17208 | + | 14.1545i | −0.433729 | + | 0.751240i | ||||
\(356\) | − | 15.7104i | − | 0.832649i | ||||||
\(357\) | −11.5157 | − | 4.19267i | −0.609478 | − | 0.221900i | ||||
\(358\) | −13.8612 | + | 8.00278i | −0.732588 | + | 0.422960i | ||||
\(359\) | 4.79342 | − | 2.76748i | 0.252987 | − | 0.146062i | −0.368144 | − | 0.929769i | \(-0.620007\pi\) |
0.621131 | + | 0.783707i | \(0.286673\pi\) | |||||||
\(360\) | −4.37016 | −0.230328 | ||||||||
\(361\) | −9.32774 | − | 16.1561i | −0.490934 | − | 0.850322i | ||||
\(362\) | − | 15.7112i | − | 0.825760i | ||||||
\(363\) | 2.07510 | 0.108914 | ||||||||
\(364\) | 11.1604 | − | 3.92720i | 0.584963 | − | 0.205841i | ||||
\(365\) | −3.51587 | −0.184029 | ||||||||
\(366\) | 8.46223i | 0.442328i | ||||||||
\(367\) | 13.2877 | + | 23.0149i | 0.693611 | + | 1.20137i | 0.970647 | + | 0.240510i | \(0.0773146\pi\) |
−0.277036 | + | 0.960860i | \(0.589352\pi\) | |||||||
\(368\) | −0.0427434 | −0.00222815 | ||||||||
\(369\) | 1.60485 | − | 0.926561i | 0.0835452 | − | 0.0482348i | ||||
\(370\) | 6.78589 | − | 3.91784i | 0.352782 | − | 0.203679i | ||||
\(371\) | 5.96331 | + | 33.8391i | 0.309599 | + | 1.75684i | ||||
\(372\) | − | 12.8852i | − | 0.668066i | ||||||
\(373\) | 8.05846 | − | 13.9577i | 0.417251 | − | 0.722701i | −0.578410 | − | 0.815746i | \(-0.696327\pi\) |
0.995662 | + | 0.0930452i | \(0.0296601\pi\) | |||||||
\(374\) | 7.29964 | + | 12.6434i | 0.377456 | + | 0.653772i | ||||
\(375\) | −10.1919 | + | 5.88432i | −0.526309 | + | 0.303865i | ||||
\(376\) | 3.42679 | + | 5.93537i | 0.176723 | + | 0.306094i | ||||
\(377\) | −5.99401 | + | 4.92212i | −0.308707 | + | 0.253502i | ||||
\(378\) | 1.48218 | + | 1.76675i | 0.0762353 | + | 0.0908718i | ||||
\(379\) | 7.43319 | + | 4.29156i | 0.381817 | + | 0.220442i | 0.678609 | − | 0.734500i | \(-0.262583\pi\) |
−0.296791 | + | 0.954942i | \(0.595917\pi\) | |||||||
\(380\) | −1.12641 | −0.0577836 | ||||||||
\(381\) | 3.49415 | 0.179011 | ||||||||
\(382\) | −18.4171 | − | 10.6331i | −0.942303 | − | 0.544039i | ||||
\(383\) | 0.782628 | + | 0.451851i | 0.0399904 | + | 0.0230885i | 0.519862 | − | 0.854250i | \(-0.325983\pi\) |
−0.479871 | + | 0.877339i | \(0.659317\pi\) | |||||||
\(384\) | −6.11288 | + | 3.52927i | −0.311946 | + | 0.180102i | ||||
\(385\) | 2.56911 | + | 14.5785i | 0.130934 | + | 0.742990i | ||||
\(386\) | −5.23644 | − | 9.06977i | −0.266528 | − | 0.461639i | ||||
\(387\) | −7.87494 | −0.400306 | ||||||||
\(388\) | −17.8380 | + | 10.2988i | −0.905586 | + | 0.522841i | ||||
\(389\) | 12.3500 | − | 21.3909i | 0.626171 | − | 1.08456i | −0.362142 | − | 0.932123i | \(-0.617955\pi\) |
0.988313 | − | 0.152437i | \(-0.0487122\pi\) | |||||||
\(390\) | 3.75812 | − | 3.08607i | 0.190300 | − | 0.156269i | ||||
\(391\) | −10.5853 | −0.535320 | ||||||||
\(392\) | 19.4692 | + | 3.43690i | 0.983345 | + | 0.173590i | ||||
\(393\) | 3.04778 | − | 5.27892i | 0.153740 | − | 0.266286i | ||||
\(394\) | 9.16847 | − | 15.8803i | 0.461901 | − | 0.800036i | ||||
\(395\) | 15.5008 | + | 8.94941i | 0.779932 | + | 0.450294i | ||||
\(396\) | 4.48467i | 0.225363i | ||||||||
\(397\) | 13.7267 | + | 7.92513i | 0.688925 | + | 0.397751i | 0.803209 | − | 0.595697i | \(-0.203124\pi\) |
−0.114284 | + | 0.993448i | \(0.536458\pi\) | |||||||
\(398\) | 0.948061i | 0.0475220i | ||||||||
\(399\) | 0.998094 | + | 1.18972i | 0.0499672 | + | 0.0595605i | ||||
\(400\) | −0.0243695 | + | 0.0422091i | −0.00121847 | + | 0.00211046i | ||||
\(401\) | − | 38.0735i | − | 1.90130i | −0.310267 | − | 0.950650i | \(-0.600418\pi\) | ||
0.310267 | − | 0.950650i | \(-0.399582\pi\) | |||||||
\(402\) | 0.837033 | − | 1.44978i | 0.0417474 | − | 0.0723086i | ||||
\(403\) | 23.7722 | + | 28.9491i | 1.18418 | + | 1.44205i | ||||
\(404\) | −8.12307 | − | 14.0696i | −0.404138 | − | 0.699987i | ||||
\(405\) | −1.34003 | − | 0.773665i | −0.0665865 | − | 0.0384437i | ||||
\(406\) | −4.88551 | + | 0.860952i | −0.242464 | + | 0.0427284i | ||||
\(407\) | −10.5039 | − | 18.1932i | −0.520658 | − | 0.901806i | ||||
\(408\) | −11.3297 | + | 6.54120i | −0.560903 | + | 0.323838i | ||||
\(409\) | 5.91319i | 0.292389i | 0.989256 | + | 0.146194i | \(0.0467025\pi\) | ||||
−0.989256 | + | 0.146194i | \(0.953298\pi\) | |||||||
\(410\) | − | 2.49933i | − | 0.123433i | ||||||
\(411\) | −2.13982 | + | 1.23543i | −0.105550 | + | 0.0609392i | ||||
\(412\) | −0.104317 | − | 0.180682i | −0.00513931 | − | 0.00890154i | ||||
\(413\) | 9.20800 | + | 10.9759i | 0.453096 | + | 0.540087i | ||||
\(414\) | 1.72503 | + | 0.995945i | 0.0847805 | + | 0.0489480i | ||||
\(415\) | 7.31268 | + | 12.6659i | 0.358965 | + | 0.621746i | ||||
\(416\) | 7.18915 | − | 19.1183i | 0.352477 | − | 0.937350i | ||||
\(417\) | −5.27760 | + | 9.14107i | −0.258445 | + | 0.447640i | ||||
\(418\) | − | 1.84997i | − | 0.0904850i | ||||||
\(419\) | −6.63834 | + | 11.4979i | −0.324304 | + | 0.561711i | −0.981371 | − | 0.192121i | \(-0.938463\pi\) |
0.657067 | + | 0.753832i | \(0.271797\pi\) | |||||||
\(420\) | −5.00033 | + | 0.881186i | −0.243991 | + | 0.0429975i | ||||
\(421\) | 23.3548i | 1.13824i | 0.822254 | + | 0.569121i | \(0.192716\pi\) | ||||
−0.822254 | + | 0.569121i | \(0.807284\pi\) | |||||||
\(422\) | 15.4014 | + | 8.89198i | 0.749727 | + | 0.432855i | ||||
\(423\) | 2.42663i | 0.117987i | ||||||||
\(424\) | 31.7655 | + | 18.3398i | 1.54267 | + | 0.890659i | ||||
\(425\) | −6.03503 | + | 10.4530i | −0.292742 | + | 0.507044i | ||||
\(426\) | 4.60348 | − | 7.97346i | 0.223039 | − | 0.386315i | ||||
\(427\) | 4.45785 | + | 25.2963i | 0.215730 | + | 1.22417i | ||||
\(428\) | −1.96284 | −0.0948776 | ||||||||
\(429\) | −8.27388 | − | 10.0757i | −0.399467 | − | 0.486458i | ||||
\(430\) | −5.31051 | + | 9.19808i | −0.256096 | + | 0.443571i | ||||
\(431\) | −6.25962 | + | 3.61400i | −0.301515 | + | 0.174080i | −0.643123 | − | 0.765762i | \(-0.722362\pi\) |
0.341608 | + | 0.939843i | \(0.389028\pi\) | |||||||
\(432\) | −0.0187042 | −0.000899907 | ||||||||
\(433\) | −11.8710 | − | 20.5611i | −0.570482 | − | 0.988103i | −0.996516 | − | 0.0833965i | \(-0.973423\pi\) |
0.426035 | − | 0.904707i | \(-0.359910\pi\) | |||||||
\(434\) | 4.15811 | + | 23.5954i | 0.199596 | + | 1.13261i | ||||
\(435\) | 2.88257 | − | 1.66425i | 0.138208 | − | 0.0797947i | ||||
\(436\) | 4.67399 | + | 2.69853i | 0.223843 | + | 0.129236i | ||||
\(437\) | 1.16162 | + | 0.670664i | 0.0555680 | + | 0.0320822i | ||||
\(438\) | 1.98055 | 0.0946344 | ||||||||
\(439\) | −28.4573 | −1.35819 | −0.679097 | − | 0.734048i | \(-0.737629\pi\) | ||||
−0.679097 | + | 0.734048i | \(0.737629\pi\) | |||||||
\(440\) | 13.6852 | + | 7.90114i | 0.652415 | + | 0.376672i | ||||
\(441\) | 5.36143 | + | 4.50057i | 0.255306 | + | 0.214313i | ||||
\(442\) | 5.12378 | − | 13.6258i | 0.243713 | − | 0.648112i | ||||
\(443\) | −10.4345 | − | 18.0731i | −0.495760 | − | 0.858681i | 0.504228 | − | 0.863570i | \(-0.331777\pi\) |
−0.999988 | + | 0.00488943i | \(0.998444\pi\) | |||||||
\(444\) | 6.24016 | − | 3.60276i | 0.296145 | − | 0.170979i | ||||
\(445\) | −9.80013 | − | 16.9743i | −0.464571 | − | 0.804660i | ||||
\(446\) | 4.81238 | − | 8.33528i | 0.227873 | − | 0.394687i | ||||
\(447\) | 12.0561i | 0.570233i | ||||||||
\(448\) | 9.93273 | − | 8.33288i | 0.469277 | − | 0.393692i | ||||
\(449\) | 5.13399 | − | 2.96411i | 0.242288 | − | 0.139885i | −0.373940 | − | 0.927453i | \(-0.621993\pi\) |
0.616228 | + | 0.787568i | \(0.288660\pi\) | |||||||
\(450\) | 1.96699 | − | 1.13565i | 0.0927250 | − | 0.0535348i | ||||
\(451\) | −6.70080 | −0.315528 | ||||||||
\(452\) | 8.21373 | + | 14.2266i | 0.386341 | + | 0.669163i | ||||
\(453\) | 6.75057i | 0.317169i | ||||||||
\(454\) | −10.5509 | −0.495179 | ||||||||
\(455\) | 9.60848 | − | 11.2050i | 0.450453 | − | 0.525298i | ||||
\(456\) | 1.65775 | 0.0776315 | ||||||||
\(457\) | 23.2685i | 1.08845i | 0.838938 | + | 0.544227i | \(0.183177\pi\) | ||||
−0.838938 | + | 0.544227i | \(0.816823\pi\) | |||||||
\(458\) | 6.25138 | + | 10.8277i | 0.292108 | + | 0.505946i | ||||
\(459\) | −4.63205 | −0.216205 | ||||||||
\(460\) | −3.79796 | + | 2.19275i | −0.177081 | + | 0.102238i | ||||
\(461\) | −6.80211 | + | 3.92720i | −0.316806 | + | 0.182908i | −0.649968 | − | 0.759962i | \(-0.725218\pi\) |
0.333162 | + | 0.942870i | \(0.391884\pi\) | |||||||
\(462\) | −1.44722 | − | 8.21234i | −0.0673310 | − | 0.382073i | ||||
\(463\) | − | 22.0674i | − | 1.02556i | −0.858520 | − | 0.512780i | \(-0.828616\pi\) | ||
0.858520 | − | 0.512780i | \(-0.171384\pi\) | |||||||
\(464\) | 0.0201176 | − | 0.0348446i | 0.000933935 | − | 0.00161762i | ||||
\(465\) | −8.03777 | − | 13.9218i | −0.372743 | − | 0.645609i | ||||
\(466\) | −15.9272 | + | 9.19557i | −0.737813 | + | 0.425977i | ||||
\(467\) | −5.20349 | − | 9.01270i | −0.240789 | − | 0.417058i | 0.720150 | − | 0.693818i | \(-0.244073\pi\) |
−0.960939 | + | 0.276760i | \(0.910739\pi\) | |||||||
\(468\) | 3.45589 | − | 2.83788i | 0.159748 | − | 0.131181i | ||||
\(469\) | 1.73842 | − | 4.77480i | 0.0802727 | − | 0.220480i | ||||
\(470\) | 2.83435 | + | 1.63641i | 0.130739 | + | 0.0754820i | ||||
\(471\) | −2.85664 | −0.131627 | ||||||||
\(472\) | 15.2938 | 0.703952 | ||||||||
\(473\) | 24.6604 | + | 14.2377i | 1.13389 | + | 0.654650i | ||||
\(474\) | −8.73190 | − | 5.04136i | −0.401069 | − | 0.231558i | ||||
\(475\) | 1.32456 | − | 0.764737i | 0.0607751 | − | 0.0350885i | ||||
\(476\) | −11.6445 | + | 9.76892i | −0.533723 | + | 0.447758i | ||||
\(477\) | 6.49352 | + | 11.2471i | 0.297318 | + | 0.514970i | ||||
\(478\) | 4.04723 | 0.185116 | ||||||||
\(479\) | 25.3070 | − | 14.6110i | 1.15631 | − | 0.667595i | 0.205892 | − | 0.978575i | \(-0.433990\pi\) |
0.950417 | + | 0.310980i | \(0.100657\pi\) | |||||||
\(480\) | −4.38277 | + | 7.59118i | −0.200045 | + | 0.346489i | ||||
\(481\) | −7.37290 | + | 19.6069i | −0.336175 | + | 0.893998i | ||||
\(482\) | −7.00788 | −0.319200 | ||||||||
\(483\) | 5.68131 | + | 2.06846i | 0.258509 | + | 0.0941182i | ||||
\(484\) | 1.28682 | − | 2.22883i | 0.0584916 | − | 0.101311i | ||||
\(485\) | −12.8487 | + | 22.2546i | −0.583430 | + | 1.01053i | ||||
\(486\) | 0.754861 | + | 0.435819i | 0.0342412 | + | 0.0197692i | ||||
\(487\) | − | 41.0749i | − | 1.86128i | −0.365933 | − | 0.930641i | \(-0.619250\pi\) | ||
0.365933 | − | 0.930641i | \(-0.380750\pi\) | |||||||
\(488\) | 23.7462 | + | 13.7099i | 1.07494 | + | 0.620616i | ||||
\(489\) | − | 17.1937i | − | 0.777527i | ||||||
\(490\) | 8.87226 | − | 3.22726i | 0.400808 | − | 0.145793i | ||||
\(491\) | −6.32263 | + | 10.9511i | −0.285336 | + | 0.494217i | −0.972691 | − | 0.232105i | \(-0.925439\pi\) |
0.687355 | + | 0.726322i | \(0.258772\pi\) | |||||||
\(492\) | − | 2.29833i | − | 0.103617i | ||||||
\(493\) | 4.98206 | − | 8.62918i | 0.224381 | − | 0.388639i | ||||
\(494\) | −1.42559 | + | 1.17066i | −0.0641402 | + | 0.0526703i | ||||
\(495\) | 2.79753 | + | 4.84547i | 0.125740 | + | 0.217788i | ||||
\(496\) | −0.168288 | − | 0.0971611i | −0.00755635 | − | 0.00436266i | ||||
\(497\) | 9.56087 | − | 26.2603i | 0.428864 | − | 1.17793i | ||||
\(498\) | −4.11936 | − | 7.13495i | −0.184593 | − | 0.319725i | ||||
\(499\) | 12.8737 | − | 7.43261i | 0.576304 | − | 0.332729i | −0.183359 | − | 0.983046i | \(-0.558697\pi\) |
0.759663 | + | 0.650317i | \(0.225364\pi\) | |||||||
\(500\) | 14.5960i | 0.652753i | ||||||||
\(501\) | 13.6862i | 0.611456i | ||||||||
\(502\) | −9.40079 | + | 5.42755i | −0.419578 | + | 0.242243i | ||||
\(503\) | −13.9385 | − | 24.1422i | −0.621488 | − | 1.07645i | −0.989209 | − | 0.146513i | \(-0.953195\pi\) |
0.367721 | − | 0.929936i | \(-0.380138\pi\) | |||||||
\(504\) | 7.35906 | − | 1.29685i | 0.327799 | − | 0.0577665i | ||||
\(505\) | −17.5532 | − | 10.1343i | −0.781106 | − | 0.450972i | ||||
\(506\) | −3.60129 | − | 6.23762i | −0.160097 | − | 0.277296i | ||||
\(507\) | −2.52863 | + | 12.7517i | −0.112300 | + | 0.566323i | ||||
\(508\) | 2.16680 | − | 3.75301i | 0.0961363 | − | 0.166513i | ||||
\(509\) | 31.6545i | 1.40306i | 0.712640 | + | 0.701530i | \(0.247499\pi\) | ||||
−0.712640 | + | 0.701530i | \(0.752501\pi\) | |||||||
\(510\) | −3.12365 | + | 5.41032i | −0.138317 | + | 0.239573i | ||||
\(511\) | 5.92049 | − | 1.04334i | 0.261907 | − | 0.0461547i | ||||
\(512\) | 0.211612i | 0.00935202i | ||||||||
\(513\) | 0.508319 | + | 0.293478i | 0.0224428 | + | 0.0129574i | ||||
\(514\) | 6.25187i | 0.275758i | ||||||||
\(515\) | −0.225418 | − | 0.130145i | −0.00993310 | − | 0.00573488i | ||||
\(516\) | −4.88343 | + | 8.45836i | −0.214981 | + | 0.372358i | ||||
\(517\) | 4.38728 | − | 7.59900i | 0.192952 | − | 0.334203i | ||||
\(518\) | −10.2644 | + | 8.61111i | −0.450991 | + | 0.378350i | ||||
\(519\) | −18.3145 | −0.803918 | ||||||||
\(520\) | −2.57132 | − | 15.5456i | −0.112760 | − | 0.681720i | ||||
\(521\) | 16.3636 | − | 28.3425i | 0.716901 | − | 1.24171i | −0.245321 | − | 0.969442i | \(-0.578893\pi\) |
0.962222 | − | 0.272267i | \(-0.0877733\pi\) | |||||||
\(522\) | −1.62380 | + | 0.937502i | −0.0710718 | + | 0.0410333i | ||||
\(523\) | −3.04966 | −0.133352 | −0.0666761 | − | 0.997775i | \(-0.521239\pi\) | ||||
−0.0666761 | + | 0.997775i | \(0.521239\pi\) | |||||||
\(524\) | −3.78000 | − | 6.54716i | −0.165130 | − | 0.286014i | ||||
\(525\) | 5.28172 | − | 4.43100i | 0.230513 | − | 0.193385i | ||||
\(526\) | 13.1014 | − | 7.56411i | 0.571249 | − | 0.329811i | ||||
\(527\) | −41.6760 | − | 24.0617i | −1.81544 | − | 1.04814i | ||||
\(528\) | 0.0585724 | + | 0.0338168i | 0.00254903 | + | 0.00147169i | ||||
\(529\) | −17.7777 | −0.772945 | ||||||||
\(530\) | 17.5158 | 0.760837 | ||||||||
\(531\) | 4.68954 | + | 2.70751i | 0.203509 | + | 0.117496i | ||||
\(532\) | 1.89680 | − | 0.334265i | 0.0822368 | − | 0.0144922i | ||||
\(533\) | 4.24024 | + | 5.16364i | 0.183665 | + | 0.223662i | ||||
\(534\) | 5.52059 | + | 9.56194i | 0.238899 | + | 0.413785i | ||||
\(535\) | −2.12076 | + | 1.22442i | −0.0916884 | + | 0.0529363i | ||||
\(536\) | −2.71219 | − | 4.69766i | −0.117149 | − | 0.202908i | ||||
\(537\) | −9.18131 | + | 15.9025i | −0.396203 | + | 0.686243i | ||||
\(538\) | 9.77034i | 0.421229i | ||||||||
\(539\) | −8.65242 | − | 23.7869i | −0.372686 | − | 1.02457i | ||||
\(540\) | −1.66196 | + | 0.959535i | −0.0715195 | + | 0.0412918i | ||||
\(541\) | −31.3496 | + | 18.0997i | −1.34782 | + | 0.778166i | −0.987941 | − | 0.154831i | \(-0.950517\pi\) |
−0.359883 | + | 0.932998i | \(0.617183\pi\) | |||||||
\(542\) | −22.3416 | −0.959656 | ||||||||
\(543\) | −9.01243 | − | 15.6100i | −0.386760 | − | 0.669889i | ||||
\(544\) | 26.2403i | 1.12504i | ||||||||
\(545\) | 6.73336 | 0.288425 | ||||||||
\(546\) | −5.41263 | + | 6.31197i | −0.231639 | + | 0.270127i | ||||
\(547\) | −14.4610 | −0.618310 | −0.309155 | − | 0.951012i | \(-0.600046\pi\) | ||||
−0.309155 | + | 0.951012i | \(0.600046\pi\) | |||||||
\(548\) | 3.06447i | 0.130908i | ||||||||
\(549\) | 4.85421 | + | 8.40774i | 0.207173 | + | 0.358833i | ||||
\(550\) | −8.21287 | −0.350198 | ||||||||
\(551\) | −1.09346 | + | 0.631309i | −0.0465829 | + | 0.0268947i | ||||
\(552\) | 5.58952 | − | 3.22711i | 0.237906 | − | 0.137355i | ||||
\(553\) | −28.7582 | − | 10.4703i | −1.22292 | − | 0.445243i | ||||
\(554\) | − | 10.8137i | − | 0.459429i | ||||||
\(555\) | 4.49480 | − | 7.78521i | 0.190793 | − | 0.330464i | ||||
\(556\) | 6.54552 | + | 11.3372i | 0.277592 | + | 0.480803i | ||||
\(557\) | −20.3907 | + | 11.7726i | −0.863983 | + | 0.498821i | −0.865344 | − | 0.501178i | \(-0.832900\pi\) |
0.00136123 | + | 0.999999i | \(0.499567\pi\) | |||||||
\(558\) | 4.52782 | + | 7.84241i | 0.191678 | + | 0.331996i | ||||
\(559\) | −4.63346 | − | 28.0129i | −0.195974 | − | 1.18482i | ||||
\(560\) | −0.0261963 | + | 0.0719518i | −0.00110700 | + | 0.00304052i | ||||
\(561\) | 14.5053 | + | 8.37462i | 0.612413 | + | 0.353577i | ||||
\(562\) | 26.9023 | 1.13480 | ||||||||
\(563\) | −30.6510 | −1.29179 | −0.645894 | − | 0.763427i | \(-0.723515\pi\) | ||||
−0.645894 | + | 0.763427i | \(0.723515\pi\) | |||||||
\(564\) | 2.60640 | + | 1.50481i | 0.109749 | + | 0.0633638i | ||||
\(565\) | 17.7491 | + | 10.2474i | 0.746709 | + | 0.431113i | ||||
\(566\) | 8.10355 | − | 4.67859i | 0.340618 | − | 0.196656i | ||||
\(567\) | 2.48610 | + | 0.905145i | 0.104407 | + | 0.0380125i | ||||
\(568\) | −14.9164 | − | 25.8360i | −0.625878 | − | 1.08405i | ||||
\(569\) | 18.2733 | 0.766057 | 0.383028 | − | 0.923737i | \(-0.374881\pi\) | ||||
0.383028 | + | 0.923737i | \(0.374881\pi\) | |||||||
\(570\) | 0.685576 | − | 0.395818i | 0.0287156 | − | 0.0165790i | ||||
\(571\) | 9.31271 | − | 16.1301i | 0.389725 | − | 0.675023i | −0.602688 | − | 0.797977i | \(-0.705904\pi\) |
0.992412 | + | 0.122954i | \(0.0392369\pi\) | |||||||
\(572\) | −15.9530 | + | 2.63869i | −0.667026 | + | 0.110329i | ||||
\(573\) | −24.3981 | −1.01924 | ||||||||
\(574\) | 0.741681 | + | 4.20870i | 0.0309572 | + | 0.175668i | ||||
\(575\) | 2.97739 | − | 5.15699i | 0.124166 | − | 0.215061i | ||||
\(576\) | 2.45019 | − | 4.24385i | 0.102091 | − | 0.176827i | ||||
\(577\) | −17.9758 | − | 10.3783i | −0.748341 | − | 0.432055i | 0.0767533 | − | 0.997050i | \(-0.475545\pi\) |
−0.825094 | + | 0.564995i | \(0.808878\pi\) | |||||||
\(578\) | 3.88389i | 0.161549i | ||||||||
\(579\) | −10.4054 | − | 6.00758i | −0.432435 | − | 0.249666i | ||||
\(580\) | − | 4.12816i | − | 0.171413i | ||||||
\(581\) | −16.0727 | − | 19.1586i | −0.666809 | − | 0.794831i | ||||
\(582\) | 7.23792 | − | 12.5364i | 0.300021 | − | 0.519652i | ||||
\(583\) | − | 46.9605i | − | 1.94490i | ||||||
\(584\) | 3.20874 | − | 5.55769i | 0.132778 | − | 0.229979i | ||||
\(585\) | 1.96365 | − | 5.22198i | 0.0811869 | − | 0.215902i | ||||
\(586\) | −0.00689879 | − | 0.0119491i | −0.000284986 | − | 0.000493611i | ||||
\(587\) | 12.5550 | + | 7.24864i | 0.518201 | + | 0.299183i | 0.736198 | − | 0.676766i | \(-0.236619\pi\) |
−0.217998 | + | 0.975949i | \(0.569952\pi\) | |||||||
\(588\) | 8.15874 | − | 2.96772i | 0.336461 | − | 0.122387i | ||||
\(589\) | 3.04901 | + | 5.28104i | 0.125632 | + | 0.217601i | ||||
\(590\) | 6.32484 | − | 3.65165i | 0.260389 | − | 0.150336i | ||||
\(591\) | − | 21.0373i | − | 0.865360i | ||||||
\(592\) | − | 0.108667i | − | 0.00446618i | ||||||
\(593\) | 4.53361 | − | 2.61748i | 0.186173 | − | 0.107487i | −0.404017 | − | 0.914752i | \(-0.632386\pi\) |
0.590190 | + | 0.807265i | \(0.299053\pi\) | |||||||
\(594\) | −1.57590 | − | 2.72954i | −0.0646600 | − | 0.111994i | ||||
\(595\) | −6.48745 | + | 17.8187i | −0.265959 | + | 0.730494i | ||||
\(596\) | 12.9493 | + | 7.47626i | 0.530422 | + | 0.306239i | ||||
\(597\) | 0.543838 | + | 0.941956i | 0.0222578 | + | 0.0385517i | ||||
\(598\) | −2.52782 | + | 6.72230i | −0.103370 | + | 0.274895i | ||||
\(599\) | −7.47791 | + | 12.9521i | −0.305539 | + | 0.529209i | −0.977381 | − | 0.211485i | \(-0.932170\pi\) |
0.671842 | + | 0.740694i | \(0.265503\pi\) | |||||||
\(600\) | − | 7.35954i | − | 0.300452i | ||||||
\(601\) | −23.0757 | + | 39.9683i | −0.941278 | + | 1.63034i | −0.178240 | + | 0.983987i | \(0.557040\pi\) |
−0.763038 | + | 0.646354i | \(0.776293\pi\) | |||||||
\(602\) | 6.21301 | − | 17.0649i | 0.253223 | − | 0.695512i | ||||
\(603\) | − | 1.92060i | − | 0.0782127i | ||||||
\(604\) | 7.25068 | + | 4.18618i | 0.295026 | + | 0.170333i | ||||
\(605\) | − | 3.21086i | − | 0.130540i | ||||||
\(606\) | 9.88801 | + | 5.70885i | 0.401673 | + | 0.231906i | ||||
\(607\) | 21.8090 | − | 37.7743i | 0.885201 | − | 1.53321i | 0.0397170 | − | 0.999211i | \(-0.487354\pi\) |
0.845484 | − | 0.534001i | \(-0.179312\pi\) | |||||||
\(608\) | 1.66254 | − | 2.87960i | 0.0674249 | − | 0.116783i | ||||
\(609\) | −4.36018 | + | 3.65790i | −0.176684 | + | 0.148225i | ||||
\(610\) | 13.0939 | 0.530155 | ||||||||
\(611\) | −8.63205 | + | 1.42778i | −0.349215 | + | 0.0577618i | ||||
\(612\) | −2.87244 | + | 4.97521i | −0.116111 | + | 0.201111i | ||||
\(613\) | 15.6112 | − | 9.01312i | 0.630530 | − | 0.364036i | −0.150428 | − | 0.988621i | \(-0.548065\pi\) |
0.780957 | + | 0.624585i | \(0.214732\pi\) | |||||||
\(614\) | −19.8718 | −0.801960 | ||||||||
\(615\) | −1.43370 | − | 2.48323i | −0.0578122 | − | 0.100134i | ||||
\(616\) | −25.3896 | − | 9.24389i | −1.02298 | − | 0.372447i | ||||
\(617\) | 32.3120 | − | 18.6554i | 1.30083 | − | 0.751036i | 0.320286 | − | 0.947321i | \(-0.396221\pi\) |
0.980547 | + | 0.196285i | \(0.0628876\pi\) | |||||||
\(618\) | 0.126982 | + | 0.0733131i | 0.00510796 | + | 0.00294908i | ||||
\(619\) | −0.272738 | − | 0.157465i | −0.0109623 | − | 0.00632906i | 0.494509 | − | 0.869173i | \(-0.335348\pi\) |
−0.505471 | + | 0.862844i | \(0.668681\pi\) | |||||||
\(620\) | −19.9376 | −0.800715 | ||||||||
\(621\) | 2.28523 | 0.0917030 | ||||||||
\(622\) | 2.71133 | + | 1.56539i | 0.108715 | + | 0.0627664i | ||||
\(623\) | 21.5399 | + | 25.6754i | 0.862979 | + | 1.02866i | ||||
\(624\) | −0.0110052 | − | 0.0665350i | −0.000440560 | − | 0.00266353i | ||||
\(625\) | 2.59055 | + | 4.48697i | 0.103622 | + | 0.179479i | ||||
\(626\) | −6.16569 | + | 3.55976i | −0.246431 | + | 0.142277i | ||||
\(627\) | −1.06120 | − | 1.83806i | −0.0423804 | − | 0.0734049i | ||||
\(628\) | −1.77147 | + | 3.06827i | −0.0706893 | + | 0.122437i | ||||
\(629\) | − | 26.9110i | − | 1.07301i | ||||||
\(630\) | 2.73375 | − | 2.29343i | 0.108915 | − | 0.0913723i | ||||
\(631\) | 22.1441 | − | 12.7849i | 0.881542 | − | 0.508958i | 0.0103751 | − | 0.999946i | \(-0.496697\pi\) |
0.871166 | + | 0.490988i | \(0.163364\pi\) | |||||||
\(632\) | −28.2935 | + | 16.3353i | −1.12546 | + | 0.649782i | ||||
\(633\) | 20.4029 | 0.810943 | ||||||||
\(634\) | 9.87217 | + | 17.0991i | 0.392074 | + | 0.679092i | ||||
\(635\) | − | 5.40660i | − | 0.214554i | ||||||
\(636\) | 16.1071 | 0.638689 | ||||||||
\(637\) | −12.8550 | + | 21.7198i | −0.509332 | + | 0.860570i | ||||
\(638\) | 6.77992 | 0.268420 | ||||||||
\(639\) | − | 10.5628i | − | 0.417858i | ||||||
\(640\) | 5.46094 | + | 9.45863i | 0.215863 | + | 0.373885i | ||||
\(641\) | 15.3433 | 0.606026 | 0.303013 | − | 0.952986i | \(-0.402007\pi\) | ||||
0.303013 | + | 0.952986i | \(0.402007\pi\) | |||||||
\(642\) | 1.19466 | − | 0.689738i | 0.0471495 | − | 0.0272218i | ||||
\(643\) | −13.2667 | + | 7.65954i | −0.523188 | + | 0.302063i | −0.738238 | − | 0.674540i | \(-0.764342\pi\) |
0.215050 | + | 0.976603i | \(0.431009\pi\) | |||||||
\(644\) | 5.74481 | − | 4.81951i | 0.226377 | − | 0.189915i | ||||
\(645\) | 12.1851i | 0.479789i | ||||||||
\(646\) | 1.18491 | − | 2.05232i | 0.0466196 | − | 0.0807476i | ||||
\(647\) | −9.23247 | − | 15.9911i | −0.362966 | − | 0.628675i | 0.625482 | − | 0.780239i | \(-0.284903\pi\) |
−0.988448 | + | 0.151563i | \(0.951569\pi\) | |||||||
\(648\) | 2.44594 | − | 1.41216i | 0.0960854 | − | 0.0554749i | ||||
\(649\) | −9.79021 | − | 16.9571i | −0.384299 | − | 0.665626i | ||||
\(650\) | 5.19708 | + | 6.32884i | 0.203846 | + | 0.248238i | ||||
\(651\) | 17.6664 | + | 21.0582i | 0.692401 | + | 0.825337i | ||||
\(652\) | −18.4675 | − | 10.6622i | −0.723244 | − | 0.417565i | ||||
\(653\) | 32.2841 | 1.26337 | 0.631687 | − | 0.775223i | \(-0.282363\pi\) | ||||
0.631687 | + | 0.775223i | \(0.282363\pi\) | |||||||
\(654\) | −3.79302 | −0.148319 | ||||||||
\(655\) | −8.16822 | − | 4.71593i | −0.319159 | − | 0.184266i | ||||
\(656\) | −0.0300175 | − | 0.0173306i | −0.00117199 | − | 0.000676646i | ||||
\(657\) | 1.96780 | − | 1.13611i | 0.0767710 | − | 0.0443238i | ||||
\(658\) | −5.25846 | − | 1.91451i | −0.204996 | − | 0.0746353i | ||||
\(659\) | −1.93680 | − | 3.35464i | −0.0754471 | − | 0.130678i | 0.825834 | − | 0.563914i | \(-0.190705\pi\) |
−0.901281 | + | 0.433236i | \(0.857372\pi\) | |||||||
\(660\) | 6.93926 | 0.270110 | ||||||||
\(661\) | 21.7811 | − | 12.5753i | 0.847185 | − | 0.489123i | −0.0125149 | − | 0.999922i | \(-0.503984\pi\) |
0.859700 | + | 0.510799i | \(0.170650\pi\) | |||||||
\(662\) | 7.82373 | − | 13.5511i | 0.304078 | − | 0.526679i | ||||
\(663\) | −2.72540 | − | 16.4772i | −0.105846 | − | 0.639922i | ||||
\(664\) | −26.6955 | −1.03599 | ||||||||
\(665\) | 1.84089 | − | 1.54438i | 0.0713866 | − | 0.0598885i | ||||
\(666\) | −2.53200 | + | 4.38555i | −0.0981130 | + | 0.169937i | ||||
\(667\) | −2.45790 | + | 4.25722i | −0.0951704 | + | 0.164840i | ||||
\(668\) | 14.7002 | + | 8.48716i | 0.568768 | + | 0.328378i | ||||
\(669\) | − | 11.0421i | − | 0.426914i | ||||||
\(670\) | −2.24329 | − | 1.29517i | −0.0866660 | − | 0.0500366i | ||||
\(671\) | − | 35.1052i | − | 1.35522i | ||||||
\(672\) | 5.12760 | − | 14.0837i | 0.197801 | − | 0.543289i | ||||
\(673\) | 5.11747 | − | 8.86372i | 0.197264 | − | 0.341671i | −0.750376 | − | 0.661011i | \(-0.770128\pi\) |
0.947640 | + | 0.319339i | \(0.103461\pi\) | |||||||
\(674\) | − | 4.56080i | − | 0.175675i | ||||||
\(675\) | 1.30289 | − | 2.25666i | 0.0501481 | − | 0.0868590i | ||||
\(676\) | 12.1284 | + | 10.6236i | 0.466475 | + | 0.408600i | ||||
\(677\) | −14.7224 | − | 25.4999i | −0.565827 | − | 0.980041i | −0.996972 | − | 0.0777582i | \(-0.975224\pi\) |
0.431146 | − | 0.902282i | \(-0.358110\pi\) | |||||||
\(678\) | −9.99837 | − | 5.77256i | −0.383985 | − | 0.221694i | ||||
\(679\) | 15.0323 | − | 41.2882i | 0.576886 | − | 1.58450i | ||||
\(680\) | 10.1214 | + | 17.5308i | 0.388138 | + | 0.672274i | ||||
\(681\) | −10.4830 | + | 6.05235i | −0.401709 | + | 0.231927i | ||||
\(682\) | − | 32.7447i | − | 1.25386i | ||||||
\(683\) | 18.8866i | 0.722675i | 0.932435 | + | 0.361338i | \(0.117680\pi\) | ||||
−0.932435 | + | 0.361338i | \(0.882320\pi\) | |||||||
\(684\) | 0.630441 | − | 0.363985i | 0.0241055 | − | 0.0139173i | ||||
\(685\) | 1.91161 | + | 3.31101i | 0.0730390 | + | 0.126507i | ||||
\(686\) | −13.9826 | + | 8.06736i | −0.533858 | + | 0.308013i | ||||
\(687\) | 12.4222 | + | 7.17199i | 0.473938 | + | 0.273628i | ||||
\(688\) | 0.0736473 | + | 0.127561i | 0.00280778 | + | 0.00486321i | ||||
\(689\) | −36.1878 | + | 29.7164i | −1.37864 | + | 1.13211i | ||||
\(690\) | 1.54106 | − | 2.66919i | 0.0586670 | − | 0.101614i | ||||
\(691\) | − | 4.84472i | − | 0.184302i | −0.995745 | − | 0.0921508i | \(-0.970626\pi\) | ||
0.995745 | − | 0.0921508i | \(-0.0293742\pi\) | |||||||
\(692\) | −11.3573 | + | 19.6714i | −0.431738 | + | 0.747793i | ||||
\(693\) | −6.14877 | − | 7.32928i | −0.233572 | − | 0.278416i | ||||
\(694\) | 14.2241i | 0.539939i | ||||||||
\(695\) | 14.1442 | + | 8.16618i | 0.536522 | + | 0.309761i | ||||
\(696\) | 6.07548i | 0.230290i | ||||||||
\(697\) | −7.43374 | − | 4.29187i | −0.281573 | − | 0.162566i | ||||
\(698\) | −11.8934 | + | 20.6000i | −0.450172 | + | 0.779721i | ||||
\(699\) | −10.5498 | + | 18.2727i | −0.399028 | + | 0.691137i | ||||
\(700\) | −1.48396 | − | 8.42078i | −0.0560883 | − | 0.318276i | ||||
\(701\) | 3.10557 | 0.117296 | 0.0586479 | − | 0.998279i | \(-0.481321\pi\) | ||||
0.0586479 | + | 0.998279i | \(0.481321\pi\) | |||||||
\(702\) | −1.10616 | + | 2.94163i | −0.0417493 | + | 0.111025i | ||||
\(703\) | −1.70503 | + | 2.95320i | −0.0643066 | + | 0.111382i | ||||
\(704\) | −15.3456 | + | 8.85976i | −0.578358 | + | 0.333915i | ||||
\(705\) | 3.75479 | 0.141414 | ||||||||
\(706\) | 12.3821 | + | 21.4465i | 0.466008 | + | 0.807149i | ||||
\(707\) | 32.5658 | + | 11.8566i | 1.22476 | + | 0.445913i | ||||
\(708\) | 5.81618 | − | 3.35798i | 0.218586 | − | 0.126200i | ||||
\(709\) | 14.3519 | + | 8.28608i | 0.538997 | + | 0.311190i | 0.744672 | − | 0.667430i | \(-0.232606\pi\) |
−0.205675 | + | 0.978620i | \(0.565939\pi\) | |||||||
\(710\) | −12.3376 | − | 7.12310i | −0.463021 | − | 0.267325i | ||||
\(711\) | −11.5676 | −0.433817 | ||||||||
\(712\) | 35.7761 | 1.34077 | ||||||||
\(713\) | 20.5609 | + | 11.8709i | 0.770012 | + | 0.444567i | ||||
\(714\) | 3.65449 | − | 10.0376i | 0.136766 | − | 0.375647i | ||||
\(715\) | −15.5904 | + | 12.8024i | −0.583047 | + | 0.478783i | ||||
\(716\) | 11.3871 | + | 19.7230i | 0.425555 | + | 0.737084i | ||||
\(717\) | 4.02116 | − | 2.32162i | 0.150173 | − | 0.0867025i | ||||
\(718\) | 2.41224 | + | 4.17813i | 0.0900241 | + | 0.155926i | ||||
\(719\) | −8.40488 | + | 14.5577i | −0.313449 | + | 0.542910i | −0.979107 | − | 0.203348i | \(-0.934818\pi\) |
0.665658 | + | 0.746257i | \(0.268151\pi\) | |||||||
\(720\) | 0.0289416i | 0.00107859i | ||||||||
\(721\) | 0.418210 | + | 0.152263i | 0.0155750 | + | 0.00567055i | ||||
\(722\) | 14.0823 | − | 8.13042i | 0.524089 | − | 0.302583i | ||||
\(723\) | −6.96275 | + | 4.01995i | −0.258948 | + | 0.149503i | ||||
\(724\) | −22.3553 | −0.830827 | ||||||||
\(725\) | 2.80267 | + | 4.85437i | 0.104089 | + | 0.180287i | ||||
\(726\) | 1.80873i | 0.0671284i | ||||||||
\(727\) | 36.2622 | 1.34489 | 0.672444 | − | 0.740148i | \(-0.265244\pi\) | ||||
0.672444 | + | 0.740148i | \(0.265244\pi\) | |||||||
\(728\) | 8.94312 | + | 25.4148i | 0.331454 | + | 0.941933i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 3.06456i | − | 0.113425i | ||||||
\(731\) | 18.2385 | + | 31.5901i | 0.674577 | + | 1.16840i | ||||
\(732\) | 12.0408 | 0.445042 | ||||||||
\(733\) | −1.19882 | + | 0.692138i | −0.0442794 | + | 0.0255647i | −0.521976 | − | 0.852960i | \(-0.674805\pi\) |
0.477697 | + | 0.878525i | \(0.341472\pi\) | |||||||
\(734\) | −20.0607 | + | 11.5820i | −0.740454 | + | 0.427501i | ||||
\(735\) | 6.96386 | − | 8.29589i | 0.256866 | − | 0.305999i | ||||
\(736\) | − | 12.9457i | − | 0.477184i | ||||||
\(737\) | −3.47239 | + | 6.01436i | −0.127907 | + | 0.221542i | ||||
\(738\) | 0.807626 | + | 1.39885i | 0.0297291 | + | 0.0514924i | ||||
\(739\) | 36.5792 | − | 21.1190i | 1.34559 | − | 0.776876i | 0.357967 | − | 0.933734i | \(-0.383470\pi\) |
0.987621 | + | 0.156859i | \(0.0501367\pi\) | |||||||
\(740\) | −5.57465 | − | 9.65558i | −0.204928 | − | 0.354946i | ||||
\(741\) | −0.744881 | + | 1.98088i | −0.0273639 | + | 0.0727694i | ||||
\(742\) | −29.4954 | + | 5.19785i | −1.08281 | + | 0.190819i | ||||
\(743\) | −10.7785 | − | 6.22298i | −0.395425 | − | 0.228299i | 0.289083 | − | 0.957304i | \(-0.406650\pi\) |
−0.684508 | + | 0.729005i | \(0.739983\pi\) | |||||||
\(744\) | 29.3425 | 1.07575 | ||||||||
\(745\) | 18.6547 | 0.683457 | ||||||||
\(746\) | 12.1660 | + | 7.02407i | 0.445430 | + | 0.257169i | ||||
\(747\) | −8.18567 | − | 4.72600i | −0.299498 | − | 0.172915i | ||||
\(748\) | 17.9901 | − | 10.3866i | 0.657784 | − | 0.379772i | ||||
\(749\) | 3.20787 | − | 2.69118i | 0.117213 | − | 0.0983337i | ||||
\(750\) | −5.12900 | − | 8.88368i | −0.187284 | − | 0.324386i | ||||
\(751\) | −30.0111 | −1.09512 | −0.547560 | − | 0.836766i | \(-0.684443\pi\) | ||||
−0.547560 | + | 0.836766i | \(0.684443\pi\) | |||||||
\(752\) | 0.0393073 | − | 0.0226941i | 0.00143339 | − | 0.000827568i | ||||
\(753\) | −6.22683 | + | 10.7852i | −0.226918 | + | 0.393034i | ||||
\(754\) | −4.29031 | − | 5.22461i | −0.156244 | − | 0.190269i | ||||
\(755\) | 10.4454 | 0.380145 | ||||||||
\(756\) | 2.51389 | − | 2.10899i | 0.0914294 | − | 0.0767031i | ||||
\(757\) | −19.8603 | + | 34.3991i | −0.721835 | + | 1.25026i | 0.238428 | + | 0.971160i | \(0.423368\pi\) |
−0.960263 | + | 0.279095i | \(0.909965\pi\) | |||||||
\(758\) | −3.74068 | + | 6.47906i | −0.135868 | + | 0.235330i | ||||
\(759\) | −7.15620 | − | 4.13163i | −0.259753 | − | 0.149969i | ||||
\(760\) | − | 2.56509i | − | 0.0930457i | ||||||
\(761\) | 6.49915 | + | 3.75229i | 0.235594 | + | 0.136020i | 0.613150 | − | 0.789966i | \(-0.289902\pi\) |
−0.377556 | + | 0.925987i | \(0.623235\pi\) | |||||||
\(762\) | 3.04563i | 0.110332i | ||||||||
\(763\) | −11.3385 | + | 1.99814i | −0.410483 | + | 0.0723375i | ||||
\(764\) | −15.1298 | + | 26.2056i | −0.547377 | + | 0.948085i | ||||
\(765\) | 7.16730i | 0.259134i | ||||||||
\(766\) | −0.393850 | + | 0.682169i | −0.0142304 | + | 0.0246478i | ||||
\(767\) | −6.87196 | + | 18.2748i | −0.248132 | + | 0.659863i | ||||
\(768\) | −7.97663 | − | 13.8159i | −0.287832 | − | 0.498539i | ||||
\(769\) | 13.1246 | + | 7.57747i | 0.473284 | + | 0.273251i | 0.717613 | − | 0.696442i | \(-0.245234\pi\) |
−0.244329 | + | 0.969692i | \(0.578568\pi\) | |||||||
\(770\) | −12.7072 | + | 2.23933i | −0.457936 | + | 0.0806999i | ||||
\(771\) | 3.58628 | + | 6.21162i | 0.129157 | + | 0.223706i | ||||
\(772\) | −12.9053 | + | 7.45088i | −0.464472 | + | 0.268163i | ||||
\(773\) | − | 10.4241i | − | 0.374929i | −0.982271 | − | 0.187464i | \(-0.939973\pi\) | ||
0.982271 | − | 0.187464i | \(-0.0600269\pi\) | |||||||
\(774\) | − | 6.86410i | − | 0.246725i | ||||||
\(775\) | 23.4450 | − | 13.5360i | 0.842168 | − | 0.486226i | ||||
\(776\) | −23.4526 | − | 40.6211i | −0.841900 | − | 1.45821i | ||||
\(777\) | −5.25866 | + | 14.4436i | −0.188653 | + | 0.518162i | ||||
\(778\) | 18.6451 | + | 10.7648i | 0.668459 | + | 0.385935i | ||||
\(779\) | 0.543851 | + | 0.941977i | 0.0194855 | + | 0.0337498i | ||||
\(780\) | −4.39114 | − | 5.34740i | −0.157228 | − | 0.191468i | ||||
\(781\) | −19.0973 | + | 33.0775i | −0.683355 | + | 1.18361i | ||||
\(782\) | − | 9.22653i | − | 0.329940i | ||||||
\(783\) | −1.07556 | + | 1.86293i | −0.0384375 | + | 0.0665757i | ||||
\(784\) | 0.0227610 | − | 0.128936i | 0.000812894 | − | 0.00460485i | ||||
\(785\) | 4.42016i | 0.157762i | ||||||||
\(786\) | 4.60131 | + | 2.65657i | 0.164123 | + | 0.0947566i | ||||
\(787\) | 13.9207i | 0.496220i | 0.968732 | + | 0.248110i | \(0.0798095\pi\) | ||||
−0.968732 | + | 0.248110i | \(0.920190\pi\) | |||||||
\(788\) | −22.5959 | − | 13.0457i | −0.804945 | − | 0.464735i | ||||
\(789\) | 8.67804 | − | 15.0308i | 0.308946 | − | 0.535111i | ||||
\(790\) | −7.80065 | + | 13.5111i | −0.277535 | + | 0.480704i | ||||
\(791\) | −32.9292 | − | 11.9889i | −1.17083 | − | 0.426277i | ||||
\(792\) | −10.2126 | −0.362889 | ||||||||
\(793\) | −27.0520 | + | 22.2144i | −0.960646 | + | 0.788858i | ||||
\(794\) | −6.90785 | + | 11.9647i | −0.245150 | + | 0.424613i | ||||
\(795\) | 17.4030 | − | 10.0476i | 0.617220 | − | 0.356352i | ||||
\(796\) | 1.34899 | 0.0478136 | ||||||||
\(797\) | 21.6516 | + | 37.5016i | 0.766938 | + | 1.32838i | 0.939216 | + | 0.343327i | \(0.111554\pi\) |
−0.172278 | + | 0.985048i | \(0.555113\pi\) | |||||||
\(798\) | −1.03701 | + | 0.869977i | −0.0367096 | + | 0.0307969i | ||||
\(799\) | 9.73434 | − | 5.62012i | 0.344376 | − | 0.198826i | ||||
\(800\) | −12.7839 | − | 7.38078i | −0.451979 | − | 0.260950i | ||||
\(801\) | 10.9701 | + | 6.33357i | 0.387608 | + | 0.223786i | ||||
\(802\) | 33.1863 | 1.17185 | ||||||||
\(803\) | −8.21622 | −0.289944 | ||||||||
\(804\) | −2.06288 | − | 1.19101i | −0.0727523 | − | 0.0420036i | ||||
\(805\) | 3.20059 | − | 8.79086i | 0.112806 | − | 0.309837i | ||||
\(806\) | −25.2331 | + | 20.7208i | −0.888798 | + | 0.729858i | ||||
\(807\) | 5.60458 | + | 9.70742i | 0.197291 | + | 0.341717i | ||||
\(808\) | 32.0396 | − | 18.4981i | 1.12715 | − | 0.650760i | ||||
\(809\) | −3.46635 | − | 6.00389i | −0.121870 | − | 0.211086i | 0.798635 | − | 0.601816i | \(-0.205556\pi\) |
−0.920505 | + | 0.390730i | \(0.872223\pi\) | |||||||
\(810\) | 0.674356 | − | 1.16802i | 0.0236945 | − | 0.0410400i | ||||
\(811\) | 9.46114i | 0.332226i | 0.986107 | + | 0.166113i | \(0.0531216\pi\) | ||||
−0.986107 | + | 0.166113i | \(0.946878\pi\) | |||||||
\(812\) | 1.22504 | + | 6.95155i | 0.0429905 | + | 0.243952i | ||||
\(813\) | −22.1978 | + | 12.8159i | −0.778510 | + | 0.449473i | ||||
\(814\) | 15.8579 | − | 9.15558i | 0.555820 | − | 0.320903i | ||||
\(815\) | −26.6044 | −0.931910 | ||||||||
\(816\) | 0.0433194 | + | 0.0750314i | 0.00151648 | + | 0.00262662i | ||||
\(817\) | − | 4.62225i | − | 0.161712i | ||||||
\(818\) | −5.15417 | −0.180211 | ||||||||
\(819\) | −1.75702 | + | 9.37619i | −0.0613954 | + | 0.327630i | ||||
\(820\) | −3.55627 | −0.124190 | ||||||||
\(821\) | 21.0073i | 0.733158i | 0.930387 | + | 0.366579i | \(0.119471\pi\) | ||||
−0.930387 | + | 0.366579i | \(0.880529\pi\) | |||||||
\(822\) | −1.07685 | − | 1.86515i | −0.0375593 | − | 0.0650547i | ||||
\(823\) | −32.7312 | −1.14094 | −0.570469 | − | 0.821319i | \(-0.693239\pi\) | ||||
−0.570469 | + | 0.821319i | \(0.693239\pi\) | |||||||
\(824\) | 0.411453 | − | 0.237552i | 0.0143336 | − | 0.00827553i | ||||
\(825\) | −8.15998 | + | 4.71117i | −0.284094 | + | 0.164022i | ||||
\(826\) | −9.56698 | + | 8.02604i | −0.332878 | + | 0.279262i | ||||
\(827\) | − | 5.50483i | − | 0.191422i | −0.995409 | − | 0.0957109i | \(-0.969488\pi\) | ||
0.995409 | − | 0.0957109i | \(-0.0305124\pi\) | |||||||
\(828\) | 1.41712 | − | 2.45453i | 0.0492484 | − | 0.0853007i | ||||
\(829\) | −10.1624 | − | 17.6019i | −0.352956 | − | 0.611338i | 0.633810 | − | 0.773489i | \(-0.281490\pi\) |
−0.986766 | + | 0.162151i | \(0.948157\pi\) | |||||||
\(830\) | −11.0401 | + | 6.37401i | −0.383208 | + | 0.221245i | ||||
\(831\) | −6.20307 | − | 10.7440i | −0.215182 | − | 0.372706i | ||||
\(832\) | 16.5380 | + | 6.21886i | 0.573351 | + | 0.215600i | ||||
\(833\) | 5.63671 | − | 31.9306i | 0.195300 | − | 1.10633i | ||||
\(834\) | −7.96771 | − | 4.60016i | −0.275899 | − | 0.159290i | ||||
\(835\) | 21.1771 | 0.732865 | ||||||||
\(836\) | −2.63231 | −0.0910402 | ||||||||
\(837\) | 8.99732 | + | 5.19461i | 0.310993 | + | 0.179552i | ||||
\(838\) | −10.0220 | − | 5.78623i | −0.346206 | − | 0.199882i | ||||
\(839\) | −48.2439 | + | 27.8536i | −1.66556 | + | 0.961614i | −0.695580 | + | 0.718448i | \(0.744853\pi\) |
−0.969985 | + | 0.243166i | \(0.921814\pi\) | |||||||
\(840\) | −2.00666 | − | 11.3869i | −0.0692364 | − | 0.392885i | ||||
\(841\) | 12.1863 | + | 21.1073i | 0.420218 | + | 0.727839i | ||||
\(842\) | −20.3569 | −0.701546 | ||||||||
\(843\) | 26.7290 | − | 15.4320i | 0.920597 | − | 0.531507i | ||||
\(844\) | 12.6523 | − | 21.9145i | 0.435511 | − | 0.754327i | ||||
\(845\) | 19.7311 | + | 3.91263i | 0.678770 | + | 0.134598i | ||||
\(846\) | −2.11514 | −0.0727201 | ||||||||
\(847\) | 0.952830 | + | 5.40688i | 0.0327396 | + | 0.185783i | ||||
\(848\) | 0.121456 | − | 0.210368i | 0.00417082 | − | 0.00722408i | ||||
\(849\) | 5.36758 | − | 9.29692i | 0.184215 | − | 0.319069i | ||||
\(850\) | −9.11121 | − | 5.26036i | −0.312512 | − | 0.180429i | ||||
\(851\) | 13.2766i | 0.455115i | ||||||||
\(852\) | −11.3454 | − | 6.55025i | −0.388686 | − | 0.224408i | ||||
\(853\) | − | 32.5630i | − | 1.11493i | −0.830199 | − | 0.557467i | \(-0.811773\pi\) | ||
0.830199 | − | 0.557467i | \(-0.188227\pi\) | |||||||
\(854\) | −22.0492 | + | 3.88563i | −0.754508 | + | 0.132964i | ||||
\(855\) | 0.454108 | − | 0.786537i | 0.0155302 | − | 0.0268990i | ||||
\(856\) | − | 4.46984i | − | 0.152776i | ||||||
\(857\) | −3.97771 | + | 6.88960i | −0.135876 | + | 0.235344i | −0.925932 | − | 0.377691i | \(-0.876718\pi\) |
0.790056 | + | 0.613035i | \(0.210052\pi\) | |||||||
\(858\) | 8.78234 | − | 7.21183i | 0.299824 | − | 0.246208i | ||||
\(859\) | 15.3344 | + | 26.5599i | 0.523201 | + | 0.906211i | 0.999635 | + | 0.0270012i | \(0.00859580\pi\) |
−0.476434 | + | 0.879210i | \(0.658071\pi\) | |||||||
\(860\) | 13.0879 | + | 7.55628i | 0.446293 | + | 0.257667i | ||||
\(861\) | 3.15115 | + | 3.75615i | 0.107391 | + | 0.128009i | ||||
\(862\) | −3.15010 | − | 5.45613i | −0.107293 | − | 0.185836i | ||||
\(863\) | −20.2659 | + | 11.7005i | −0.689860 | + | 0.398291i | −0.803560 | − | 0.595224i | \(-0.797063\pi\) |
0.113699 | + | 0.993515i | \(0.463730\pi\) | |||||||
\(864\) | − | 5.66495i | − | 0.192726i | ||||||
\(865\) | 28.3386i | 0.963542i | ||||||||
\(866\) | 17.9218 | − | 10.3472i | 0.609009 | − | 0.351612i | ||||
\(867\) | 2.22793 | + | 3.85888i | 0.0756643 | + | 0.131054i | ||||
\(868\) | 33.5737 | − | 5.91654i | 1.13956 | − | 0.200820i | ||||
\(869\) | 36.2239 | + | 20.9139i | 1.22881 | + | 0.709454i | ||||
\(870\) | 1.45062 | + | 2.51256i | 0.0491808 | + | 0.0851836i | ||||
\(871\) | 6.83198 | − | 1.13004i | 0.231493 | − | 0.0382900i | ||||
\(872\) | −6.14516 | + | 10.6437i | −0.208101 | + | 0.360442i | ||||
\(873\) | − | 16.6076i | − | 0.562082i | ||||||
\(874\) | −0.584577 | + | 1.01252i | −0.0197736 | + | 0.0342489i | ||||
\(875\) | −20.0121 | − | 23.8542i | −0.676531 | − | 0.806419i | ||||
\(876\) | − | 2.81811i | − | 0.0952150i | ||||||
\(877\) | 10.7865 | + | 6.22761i | 0.364236 | + | 0.210291i | 0.670937 | − | 0.741514i | \(-0.265892\pi\) |
−0.306702 | + | 0.951806i | \(0.599225\pi\) | |||||||
\(878\) | − | 24.8045i | − | 0.837111i | ||||||
\(879\) | −0.0137087 | − | 0.00791474i | −0.000462384 | − | 0.000266957i | ||||
\(880\) | 0.0523257 | − | 0.0906307i | 0.00176390 | − | 0.00305516i | ||||
\(881\) | 0.980893 | − | 1.69896i | 0.0330471 | − | 0.0572393i | −0.849029 | − | 0.528347i | \(-0.822812\pi\) |
0.882076 | + | 0.471107i | \(0.156146\pi\) | |||||||
\(882\) | −3.92287 | + | 4.67322i | −0.132090 | + | 0.157356i | ||||
\(883\) | −32.7262 | −1.10132 | −0.550662 | − | 0.834728i | \(-0.685625\pi\) | ||||
−0.550662 | + | 0.834728i | \(0.685625\pi\) | |||||||
\(884\) | −19.3880 | − | 7.29058i | −0.652089 | − | 0.245209i | ||||
\(885\) | 4.18941 | − | 7.25626i | 0.140825 | − | 0.243917i | ||||
\(886\) | 15.7532 | − | 9.09514i | 0.529241 | − | 0.305557i | ||||
\(887\) | 28.7197 | 0.964313 | 0.482157 | − | 0.876085i | \(-0.339854\pi\) | ||||
0.482157 | + | 0.876085i | \(0.339854\pi\) | |||||||
\(888\) | 8.20430 | + | 14.2103i | 0.275318 | + | 0.476865i | ||||
\(889\) | 1.60442 | + | 9.10436i | 0.0538106 | + | 0.305350i | ||||
\(890\) | 14.7955 | − | 8.54217i | 0.495945 | − | 0.286334i | ||||
\(891\) | −3.13150 | − | 1.80798i | −0.104909 | − | 0.0605694i | ||||
\(892\) | −11.8602 | − | 6.84749i | −0.397109 | − | 0.229271i | ||||
\(893\) | −1.42432 | −0.0476632 | ||||||||
\(894\) | −10.5085 | −0.351458 | ||||||||
\(895\) | 24.6064 | + | 14.2065i | 0.822501 | + | 0.474871i | ||||
\(896\) | −12.0027 | − | 14.3072i | −0.400984 | − | 0.477969i | ||||
\(897\) | 1.34458 | + | 8.12905i | 0.0448943 | + | 0.271421i | ||||
\(898\) | 2.58363 | + | 4.47498i | 0.0862170 | + | 0.149332i | ||||
\(899\) | −19.3544 | + | 11.1743i | −0.645505 | + | 0.372682i | ||||
\(900\) | −1.61590 | − | 2.79882i | −0.0538633 | − | 0.0932940i | ||||
\(901\) | 30.0783 | − | 52.0971i | 1.00205 | − | 1.73561i | ||||
\(902\) | − | 5.84067i | − | 0.194473i | ||||||
\(903\) | −3.61597 | − | 20.5190i | −0.120332 | − | 0.682828i | ||||
\(904\) | −32.3972 | + | 18.7045i | −1.07751 | + | 0.622103i | ||||
\(905\) | −24.1538 | + | 13.9452i | −0.802899 | + | 0.463554i | ||||
\(906\) | −5.88405 | −0.195485 | ||||||||
\(907\) | −13.8335 | − | 23.9603i | −0.459333 | − | 0.795588i | 0.539593 | − | 0.841926i | \(-0.318578\pi\) |
−0.998926 | + | 0.0463383i | \(0.985245\pi\) | |||||||
\(908\) | 15.0128i | 0.498218i | ||||||||
\(909\) | 13.0991 | 0.434470 | ||||||||
\(910\) | 9.76670 | + | 8.37512i | 0.323763 | + | 0.277633i | ||||
\(911\) | −34.4320 | −1.14078 | −0.570392 | − | 0.821373i | \(-0.693209\pi\) | ||||
−0.570392 | + | 0.821373i | \(0.693209\pi\) | |||||||
\(912\) | − | 0.0109786i | − | 0.000363536i | ||||||
\(913\) | 17.0890 | + | 29.5990i | 0.565563 | + | 0.979584i | ||||
\(914\) | −20.2817 | −0.670859 | ||||||||
\(915\) | 13.0095 | − | 7.51106i | 0.430082 | − | 0.248308i | ||||
\(916\) | 15.4066 | − | 8.89503i | 0.509050 | − | 0.293900i | ||||
\(917\) | 15.1542 | + | 5.51737i | 0.500436 | + | 0.182200i | ||||
\(918\) | − | 4.03747i | − | 0.133256i | ||||||
\(919\) | −15.7158 | + | 27.2206i | −0.518417 | + | 0.897924i | 0.481354 | + | 0.876526i | \(0.340145\pi\) |
−0.999771 | + | 0.0213979i | \(0.993188\pi\) | |||||||
\(920\) | −4.99340 | − | 8.64882i | −0.164628 | − | 0.285143i | ||||
\(921\) | −19.7438 | + | 11.3991i | −0.650581 | + | 0.375613i | ||||
\(922\) | −3.42310 | − | 5.92898i | −0.112734 | − | 0.195261i | ||||
\(923\) | 37.5742 | − | 6.21495i | 1.23677 | − | 0.204568i | ||||
\(924\) | −11.6853 | + | 2.05924i | −0.384417 | + | 0.0677441i | ||||
\(925\) | 13.1106 | + | 7.56943i | 0.431075 | + | 0.248881i | ||||
\(926\) | 19.2348 | 0.632095 | ||||||||
\(927\) | 0.168219 | 0.00552504 | ||||||||
\(928\) | 10.5534 | + | 6.09301i | 0.346432 | + | 0.200013i | ||||
\(929\) | 40.3910 | + | 23.3198i | 1.32519 | + | 0.765097i | 0.984551 | − | 0.175099i | \(-0.0560244\pi\) |
0.340636 | + | 0.940195i | \(0.389358\pi\) | |||||||
\(930\) | 12.1348 | − | 7.00603i | 0.397916 | − | 0.229737i | ||||
\(931\) | −2.64164 | + | 3.14692i | −0.0865762 | + | 0.103136i | ||||
\(932\) | 13.0843 | + | 22.6627i | 0.428590 | + | 0.742340i | ||||
\(933\) | 3.59183 | 0.117591 | ||||||||
\(934\) | 7.85582 | − | 4.53556i | 0.257050 | − | 0.148408i | ||||
\(935\) | 12.9583 | − | 22.4444i | 0.423782 | − | 0.734012i | ||||
\(936\) | 6.46251 | + | 7.86984i | 0.211234 | + | 0.257234i | ||||
\(937\) | 3.16478 | 0.103389 | 0.0516945 | − | 0.998663i | \(-0.483538\pi\) | ||||
0.0516945 | + | 0.998663i | \(0.483538\pi\) | |||||||
\(938\) | 4.16190 | + | 1.51527i | 0.135891 | + | 0.0494754i | ||||
\(939\) | −4.08399 | + | 7.07368i | −0.133276 | + | 0.230841i | ||||
\(940\) | 2.32843 | − | 4.03297i | 0.0759451 | − | 0.131541i | ||||
\(941\) | −15.6164 | − | 9.01615i | −0.509081 | − | 0.293918i | 0.223375 | − | 0.974733i | \(-0.428293\pi\) |
−0.732456 | + | 0.680814i | \(0.761626\pi\) | |||||||
\(942\) | − | 2.48996i | − | 0.0811272i | ||||||
\(943\) | 3.66745 | + | 2.11740i | 0.119428 | + | 0.0689521i | ||||
\(944\) | − | 0.101284i | − | 0.00329650i | ||||||
\(945\) | 1.40056 | − | 3.84682i | 0.0455601 | − | 0.125137i | ||||
\(946\) | −12.4101 | + | 21.4950i | −0.403488 | + | 0.698862i | ||||
\(947\) | − | 44.6351i | − | 1.45045i | −0.688513 | − | 0.725224i | \(-0.741736\pi\) | ||
0.688513 | − | 0.725224i | \(-0.258264\pi\) | |||||||
\(948\) | −7.17331 | + | 12.4245i | −0.232978 | + | 0.403530i | ||||
\(949\) | 5.19920 | + | 6.33142i | 0.168773 | + | 0.205527i | ||||
\(950\) | 0.666574 | + | 1.15454i | 0.0216265 | + | 0.0374582i | ||||
\(951\) | 19.6172 | + | 11.3260i | 0.636131 | + | 0.367271i | ||||
\(952\) | −22.2460 | − | 26.5171i | −0.720999 | − | 0.859424i | ||||
\(953\) | 19.2233 | + | 33.2957i | 0.622702 | + | 1.07855i | 0.988980 | + | 0.148047i | \(0.0472986\pi\) |
−0.366278 | + | 0.930505i | \(0.619368\pi\) | |||||||
\(954\) | −9.80341 | + | 5.66000i | −0.317397 | + | 0.183249i | ||||
\(955\) | 37.7518i | 1.22162i | ||||||||
\(956\) | − | 5.75876i | − | 0.186252i | ||||||
\(957\) | 6.73626 | − | 3.88918i | 0.217752 | − | 0.125719i | ||||
\(958\) | 12.7355 | + | 22.0586i | 0.411466 | + | 0.712681i | ||||
\(959\) | −4.20158 | − | 5.00825i | −0.135676 | − | 0.161725i | ||||
\(960\) | −6.56664 | − | 3.79125i | −0.211937 | − | 0.122362i | ||||
\(961\) | 38.4679 | + | 66.6284i | 1.24090 | + | 2.14930i | ||||
\(962\) | −17.0901 | − | 6.42650i | −0.551008 | − | 0.207199i | ||||
\(963\) | 0.791312 | − | 1.37059i | 0.0254997 | − | 0.0441667i | ||||
\(964\) | 9.97145i | 0.321159i | ||||||||
\(965\) | −9.29571 | + | 16.1006i | −0.299239 | + | 0.518298i | ||||
\(966\) | −1.80295 | + | 4.95205i | −0.0580089 | + | 0.159330i | ||||
\(967\) | 34.6858i | 1.11542i | 0.830036 | + | 0.557710i | \(0.188320\pi\) | ||||
−0.830036 | + | 0.557710i | \(0.811680\pi\) | |||||||
\(968\) | 5.07556 | + | 2.93037i | 0.163135 | + | 0.0941858i | ||||
\(969\) | − | 2.71881i | − | 0.0873407i | ||||||
\(970\) | −19.3980 | − | 11.1994i | −0.622832 | − | 0.359592i | ||||
\(971\) | 1.89234 | − | 3.27762i | 0.0607280 | − | 0.105184i | −0.834063 | − | 0.551669i | \(-0.813991\pi\) |
0.894791 | + | 0.446485i | \(0.147324\pi\) | |||||||
\(972\) | 0.620123 | − | 1.07408i | 0.0198905 | − | 0.0344513i | ||||
\(973\) | −26.2413 | − | 9.55398i | −0.841258 | − | 0.306287i | ||||
\(974\) | 35.8025 | 1.14719 | ||||||||
\(975\) | 8.79404 | + | 3.30687i | 0.281635 | + | 0.105905i | ||||
\(976\) | 0.0907942 | − | 0.157260i | 0.00290625 | − | 0.00503377i | ||||
\(977\) | −0.219135 | + | 0.126518i | −0.00701076 | + | 0.00404767i | −0.503501 | − | 0.863994i | \(-0.667955\pi\) |
0.496491 | + | 0.868042i | \(0.334622\pi\) | |||||||
\(978\) | 14.9867 | 0.479222 | ||||||||
\(979\) | −22.9019 | − | 39.6672i | −0.731948 | − | 1.26777i | ||||
\(980\) | −4.59204 | − | 12.6243i | −0.146687 | − | 0.403267i | ||||
\(981\) | −3.76860 | + | 2.17580i | −0.120322 | + | 0.0694680i | ||||
\(982\) | −9.54541 | − | 5.51104i | −0.304606 | − | 0.175864i | ||||
\(983\) | −6.88388 | − | 3.97441i | −0.219562 | − | 0.126764i | 0.386186 | − | 0.922421i | \(-0.373792\pi\) |
−0.605747 | + | 0.795657i | \(0.707126\pi\) | |||||||
\(984\) | 5.23382 | 0.166848 | ||||||||
\(985\) | −32.5517 | −1.03718 | ||||||||
\(986\) | 7.52152 | + | 4.34255i | 0.239534 | + | 0.138295i | ||||
\(987\) | −6.32282 | + | 1.11424i | −0.201258 | + | 0.0354668i | ||||
\(988\) | 1.66571 | + | 2.02846i | 0.0529934 | + | 0.0645338i | ||||
\(989\) | −8.99801 | − | 15.5850i | −0.286120 | − | 0.495575i | ||||
\(990\) | −4.22350 | + | 2.43844i | −0.134232 | + | 0.0774986i | ||||
\(991\) | −14.2131 | − | 24.6177i | −0.451493 | − | 0.782008i | 0.546986 | − | 0.837142i | \(-0.315775\pi\) |
−0.998479 | + | 0.0551333i | \(0.982442\pi\) | |||||||
\(992\) | 29.4272 | − | 50.9694i | 0.934314 | − | 1.61828i | ||||
\(993\) | − | 17.9518i | − | 0.569683i | ||||||
\(994\) | 22.8894 | + | 8.33363i | 0.726009 | + | 0.264327i | ||||
\(995\) | 1.45752 | − | 0.841497i | 0.0462064 | − | 0.0266773i | ||||
\(996\) | −10.1523 | + | 5.86141i | −0.321686 | + | 0.185726i | ||||
\(997\) | −44.8636 | −1.42084 | −0.710422 | − | 0.703776i | \(-0.751496\pi\) | ||||
−0.710422 | + | 0.703776i | \(0.751496\pi\) | |||||||
\(998\) | 6.47855 | + | 11.2212i | 0.205075 | + | 0.355200i | ||||
\(999\) | 5.80975i | 0.183812i |
(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 | 273.2.t.d.4.7 | ✓ | 20 | |
3.2 | odd | 2 | 819.2.bm.g.550.4 | 20 | |||
7.2 | even | 3 | 273.2.bl.d.121.7 | yes | 20 | ||
13.10 | even | 6 | 273.2.bl.d.88.7 | yes | 20 | ||
21.2 | odd | 6 | 819.2.do.g.667.4 | 20 | |||
39.23 | odd | 6 | 819.2.do.g.361.4 | 20 | |||
91.23 | even | 6 | inner | 273.2.t.d.205.4 | yes | 20 | |
273.23 | odd | 6 | 819.2.bm.g.478.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.d.4.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
273.2.t.d.205.4 | yes | 20 | 91.23 | even | 6 | inner | |
273.2.bl.d.88.7 | yes | 20 | 13.10 | even | 6 | ||
273.2.bl.d.121.7 | yes | 20 | 7.2 | even | 3 | ||
819.2.bm.g.478.7 | 20 | 273.23 | odd | 6 | |||
819.2.bm.g.550.4 | 20 | 3.2 | odd | 2 | |||
819.2.do.g.361.4 | 20 | 39.23 | odd | 6 | |||
819.2.do.g.667.4 | 20 | 21.2 | odd | 6 |