Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(289,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.j (of order \(3\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.447703281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.2 | ||
Root | \(-0.571299 - 1.29368i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.529 |
Dual form | 546.2.j.d.289.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.228205 | − | 0.395262i | −0.102056 | − | 0.176767i | 0.810475 | − | 0.585773i | \(-0.199209\pi\) |
−0.912532 | + | 0.409006i | \(0.865875\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −0.369922 | + | 2.61976i | −0.139817 | + | 0.990177i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.228205 | − | 0.395262i | −0.0721647 | − | 0.124993i | ||||
\(11\) | 1.91853 | + | 3.32300i | 0.578460 | + | 1.00192i | 0.995656 | + | 0.0931051i | \(0.0296793\pi\) |
−0.417197 | + | 0.908816i | \(0.636987\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −3.13422 | + | 1.78233i | −0.869275 | + | 0.494328i | ||||
\(14\) | −0.369922 | + | 2.61976i | −0.0988658 | + | 0.700161i | ||||
\(15\) | 0.228205 | − | 0.395262i | 0.0589222 | − | 0.102056i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.55187 | 0.376383 | 0.188192 | − | 0.982132i | \(-0.439737\pi\) | ||||
0.188192 | + | 0.982132i | \(0.439737\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.44122 | − | 2.49627i | 0.330639 | − | 0.572683i | −0.651998 | − | 0.758220i | \(-0.726069\pi\) |
0.982637 | + | 0.185537i | \(0.0594025\pi\) | |||||||
\(20\) | −0.228205 | − | 0.395262i | −0.0510281 | − | 0.0883833i | ||||
\(21\) | −2.45374 | + | 0.989520i | −0.535450 | + | 0.215931i | ||||
\(22\) | 1.91853 | + | 3.32300i | 0.409033 | + | 0.708465i | ||||
\(23\) | 3.24339 | 0.676294 | 0.338147 | − | 0.941093i | \(-0.390200\pi\) | ||||
0.338147 | + | 0.941093i | \(0.390200\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 2.39585 | − | 4.14973i | 0.479169 | − | 0.829945i | ||||
\(26\) | −3.13422 | + | 1.78233i | −0.614671 | + | 0.349543i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.369922 | + | 2.61976i | −0.0699087 | + | 0.495089i | ||||
\(29\) | −2.20552 | + | 3.82007i | −0.409554 | + | 0.709369i | −0.994840 | − | 0.101459i | \(-0.967649\pi\) |
0.585286 | + | 0.810827i | \(0.300982\pi\) | |||||||
\(30\) | 0.228205 | − | 0.395262i | 0.0416643 | − | 0.0721647i | ||||
\(31\) | 4.80098 | − | 8.31553i | 0.862281 | − | 1.49351i | −0.00744135 | − | 0.999972i | \(-0.502369\pi\) |
0.869722 | − | 0.493542i | \(-0.164298\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.91853 | + | 3.32300i | −0.333974 | + | 0.578460i | ||||
\(34\) | 1.55187 | 0.266143 | ||||||||
\(35\) | 1.11991 | − | 0.451626i | 0.189299 | − | 0.0763387i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 0.280491 | 0.0461124 | 0.0230562 | − | 0.999734i | \(-0.492660\pi\) | ||||
0.0230562 | + | 0.999734i | \(0.492660\pi\) | |||||||
\(38\) | 1.44122 | − | 2.49627i | 0.233797 | − | 0.404948i | ||||
\(39\) | −3.11065 | − | 1.82315i | −0.498102 | − | 0.291938i | ||||
\(40\) | −0.228205 | − | 0.395262i | −0.0360823 | − | 0.0624964i | ||||
\(41\) | −3.57277 | + | 6.18822i | −0.557973 | + | 0.966438i | 0.439692 | + | 0.898148i | \(0.355087\pi\) |
−0.997666 | + | 0.0682894i | \(0.978246\pi\) | |||||||
\(42\) | −2.45374 | + | 0.989520i | −0.378621 | + | 0.152686i | ||||
\(43\) | 1.21716 | + | 2.10818i | 0.185615 | + | 0.321494i | 0.943783 | − | 0.330564i | \(-0.107239\pi\) |
−0.758169 | + | 0.652058i | \(0.773906\pi\) | |||||||
\(44\) | 1.91853 | + | 3.32300i | 0.289230 | + | 0.500961i | ||||
\(45\) | 0.456409 | 0.0680375 | ||||||||
\(46\) | 3.24339 | 0.478212 | ||||||||
\(47\) | −3.93105 | − | 6.80879i | −0.573403 | − | 0.993163i | −0.996213 | − | 0.0869451i | \(-0.972290\pi\) |
0.422810 | − | 0.906218i | \(-0.361044\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −6.72632 | − | 1.93822i | −0.960902 | − | 0.276888i | ||||
\(50\) | 2.39585 | − | 4.14973i | 0.338824 | − | 0.586860i | ||||
\(51\) | 0.775934 | + | 1.34396i | 0.108653 | + | 0.188192i | ||||
\(52\) | −3.13422 | + | 1.78233i | −0.434638 | + | 0.247164i | ||||
\(53\) | 0.550397 | − | 0.953315i | 0.0756028 | − | 0.130948i | −0.825745 | − | 0.564043i | \(-0.809245\pi\) |
0.901348 | + | 0.433095i | \(0.142579\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.875637 | − | 1.51665i | 0.118071 | − | 0.204505i | ||||
\(56\) | −0.369922 | + | 2.61976i | −0.0494329 | + | 0.350081i | ||||
\(57\) | 2.88244 | 0.381789 | ||||||||
\(58\) | −2.20552 | + | 3.82007i | −0.289599 | + | 0.501599i | ||||
\(59\) | −9.36566 | −1.21930 | −0.609652 | − | 0.792669i | \(-0.708691\pi\) | ||||
−0.609652 | + | 0.792669i | \(0.708691\pi\) | |||||||
\(60\) | 0.228205 | − | 0.395262i | 0.0294611 | − | 0.0510281i | ||||
\(61\) | 5.55187 | − | 9.61612i | 0.710844 | − | 1.23122i | −0.253697 | − | 0.967284i | \(-0.581647\pi\) |
0.964541 | − | 0.263934i | \(-0.0850201\pi\) | |||||||
\(62\) | 4.80098 | − | 8.31553i | 0.609725 | − | 1.05607i | ||||
\(63\) | −2.08382 | − | 1.63024i | −0.262537 | − | 0.205391i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.41973 | + | 0.832102i | 0.176096 | + | 0.103210i | ||||
\(66\) | −1.91853 | + | 3.32300i | −0.236155 | + | 0.409033i | ||||
\(67\) | 0.894964 | + | 1.55012i | 0.109337 | + | 0.189378i | 0.915502 | − | 0.402314i | \(-0.131794\pi\) |
−0.806165 | + | 0.591691i | \(0.798461\pi\) | |||||||
\(68\) | 1.55187 | 0.188192 | ||||||||
\(69\) | 1.62170 | + | 2.80886i | 0.195229 | + | 0.338147i | ||||
\(70\) | 1.11991 | − | 0.451626i | 0.133855 | − | 0.0539796i | ||||
\(71\) | −5.06527 | − | 8.77331i | −0.601137 | − | 1.04120i | −0.992649 | − | 0.121027i | \(-0.961381\pi\) |
0.391512 | − | 0.920173i | \(-0.371952\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 1.40601 | − | 2.43529i | 0.164561 | − | 0.285029i | −0.771938 | − | 0.635698i | \(-0.780712\pi\) |
0.936499 | + | 0.350669i | \(0.114046\pi\) | |||||||
\(74\) | 0.280491 | 0.0326064 | ||||||||
\(75\) | 4.79169 | 0.553297 | ||||||||
\(76\) | 1.44122 | − | 2.49627i | 0.165319 | − | 0.286342i | ||||
\(77\) | −9.41517 | + | 3.79685i | −1.07296 | + | 0.432692i | ||||
\(78\) | −3.11065 | − | 1.82315i | −0.352211 | − | 0.206431i | ||||
\(79\) | 2.70966 | + | 4.69326i | 0.304860 | + | 0.528033i | 0.977230 | − | 0.212182i | \(-0.0680570\pi\) |
−0.672370 | + | 0.740215i | \(0.734724\pi\) | |||||||
\(80\) | −0.228205 | − | 0.395262i | −0.0255141 | − | 0.0441916i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.57277 | + | 6.18822i | −0.394547 | + | 0.683375i | ||||
\(83\) | 1.35738 | 0.148992 | 0.0744959 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744959 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(84\) | −2.45374 | + | 0.989520i | −0.267725 | + | 0.107965i | ||||
\(85\) | −0.354144 | − | 0.613395i | −0.0384123 | − | 0.0665320i | ||||
\(86\) | 1.21716 | + | 2.10818i | 0.131249 | + | 0.227330i | ||||
\(87\) | −4.41103 | −0.472912 | ||||||||
\(88\) | 1.91853 | + | 3.32300i | 0.204516 | + | 0.354233i | ||||
\(89\) | −0.179697 | −0.0190478 | −0.00952392 | − | 0.999955i | \(-0.503032\pi\) | ||||
−0.00952392 | + | 0.999955i | \(0.503032\pi\) | |||||||
\(90\) | 0.456409 | 0.0481098 | ||||||||
\(91\) | −3.50985 | − | 8.87023i | −0.367933 | − | 0.929852i | ||||
\(92\) | 3.24339 | 0.338147 | ||||||||
\(93\) | 9.60195 | 0.995676 | ||||||||
\(94\) | −3.93105 | − | 6.80879i | −0.405457 | − | 0.702273i | ||||
\(95\) | −1.31557 | −0.134975 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 4.73894 | + | 8.20808i | 0.481166 | + | 0.833405i | 0.999766 | − | 0.0216122i | \(-0.00687993\pi\) |
−0.518600 | + | 0.855017i | \(0.673547\pi\) | |||||||
\(98\) | −6.72632 | − | 1.93822i | −0.679460 | − | 0.195789i | ||||
\(99\) | −3.83707 | −0.385640 | ||||||||
\(100\) | 2.39585 | − | 4.14973i | 0.239585 | − | 0.414973i | ||||
\(101\) | −3.18107 | − | 5.50977i | −0.316528 | − | 0.548242i | 0.663233 | − | 0.748413i | \(-0.269184\pi\) |
−0.979761 | + | 0.200170i | \(0.935850\pi\) | |||||||
\(102\) | 0.775934 | + | 1.34396i | 0.0768290 | + | 0.133072i | ||||
\(103\) | −8.28934 | − | 14.3576i | −0.816773 | − | 1.41469i | −0.908048 | − | 0.418866i | \(-0.862428\pi\) |
0.0912754 | − | 0.995826i | \(-0.470906\pi\) | |||||||
\(104\) | −3.13422 | + | 1.78233i | −0.307335 | + | 0.174771i | ||||
\(105\) | 0.951075 | + | 0.744058i | 0.0928154 | + | 0.0726126i | ||||
\(106\) | 0.550397 | − | 0.953315i | 0.0534593 | − | 0.0925942i | ||||
\(107\) | 16.9205 | 1.63576 | 0.817882 | − | 0.575386i | \(-0.195148\pi\) | ||||
0.817882 | + | 0.575386i | \(0.195148\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 3.95108 | − | 6.84346i | 0.378444 | − | 0.655485i | −0.612392 | − | 0.790554i | \(-0.709792\pi\) |
0.990836 | + | 0.135070i | \(0.0431258\pi\) | |||||||
\(110\) | 0.875637 | − | 1.51665i | 0.0834887 | − | 0.144607i | ||||
\(111\) | 0.140245 | + | 0.242912i | 0.0133115 | + | 0.0230562i | ||||
\(112\) | −0.369922 | + | 2.61976i | −0.0349543 | + | 0.247544i | ||||
\(113\) | 3.40689 | + | 5.90091i | 0.320494 | + | 0.555111i | 0.980590 | − | 0.196070i | \(-0.0628179\pi\) |
−0.660096 | + | 0.751181i | \(0.729485\pi\) | |||||||
\(114\) | 2.88244 | 0.269965 | ||||||||
\(115\) | −0.740157 | − | 1.28199i | −0.0690200 | − | 0.119546i | ||||
\(116\) | −2.20552 | + | 3.82007i | −0.204777 | + | 0.354684i | ||||
\(117\) | 0.0235697 | − | 3.60547i | 0.00217902 | − | 0.333326i | ||||
\(118\) | −9.36566 | −0.862179 | ||||||||
\(119\) | −0.574070 | + | 4.06553i | −0.0526249 | + | 0.372686i | ||||
\(120\) | 0.228205 | − | 0.395262i | 0.0208321 | − | 0.0360823i | ||||
\(121\) | −1.86154 | + | 3.22428i | −0.169231 | + | 0.293117i | ||||
\(122\) | 5.55187 | − | 9.61612i | 0.502643 | − | 0.870602i | ||||
\(123\) | −7.14554 | −0.644292 | ||||||||
\(124\) | 4.80098 | − | 8.31553i | 0.431140 | − | 0.746757i | ||||
\(125\) | −4.46902 | −0.399721 | ||||||||
\(126\) | −2.08382 | − | 1.63024i | −0.185641 | − | 0.145234i | ||||
\(127\) | 10.9334 | − | 18.9372i | 0.970183 | − | 1.68041i | 0.275190 | − | 0.961390i | \(-0.411259\pi\) |
0.694993 | − | 0.719016i | \(-0.255407\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.21716 | + | 2.10818i | −0.107165 | + | 0.185615i | ||||
\(130\) | 1.41973 | + | 0.832102i | 0.124518 | + | 0.0729802i | ||||
\(131\) | 4.72554 | + | 8.18487i | 0.412872 | + | 0.715116i | 0.995202 | − | 0.0978367i | \(-0.0311923\pi\) |
−0.582330 | + | 0.812952i | \(0.697859\pi\) | |||||||
\(132\) | −1.91853 | + | 3.32300i | −0.166987 | + | 0.289230i | ||||
\(133\) | 6.00649 | + | 4.69908i | 0.520829 | + | 0.407462i | ||||
\(134\) | 0.894964 | + | 1.55012i | 0.0773131 | + | 0.133910i | ||||
\(135\) | 0.228205 | + | 0.395262i | 0.0196407 | + | 0.0340187i | ||||
\(136\) | 1.55187 | 0.133072 | ||||||||
\(137\) | 2.44792 | 0.209140 | 0.104570 | − | 0.994518i | \(-0.466653\pi\) | ||||
0.104570 | + | 0.994518i | \(0.466653\pi\) | |||||||
\(138\) | 1.62170 | + | 2.80886i | 0.138048 | + | 0.239106i | ||||
\(139\) | −5.37228 | − | 9.30505i | −0.455670 | − | 0.789244i | 0.543056 | − | 0.839696i | \(-0.317267\pi\) |
−0.998726 | + | 0.0504521i | \(0.983934\pi\) | |||||||
\(140\) | 1.11991 | − | 0.451626i | 0.0946497 | − | 0.0381694i | ||||
\(141\) | 3.93105 | − | 6.80879i | 0.331054 | − | 0.573403i | ||||
\(142\) | −5.06527 | − | 8.77331i | −0.425068 | − | 0.736240i | ||||
\(143\) | −11.9358 | − | 6.99554i | −0.998119 | − | 0.584997i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 2.01324 | 0.167190 | ||||||||
\(146\) | 1.40601 | − | 2.43529i | 0.116362 | − | 0.201546i | ||||
\(147\) | −1.68461 | − | 6.79427i | −0.138945 | − | 0.560382i | ||||
\(148\) | 0.280491 | 0.0230562 | ||||||||
\(149\) | −4.65157 | + | 8.05676i | −0.381072 | + | 0.660035i | −0.991216 | − | 0.132255i | \(-0.957778\pi\) |
0.610144 | + | 0.792290i | \(0.291112\pi\) | |||||||
\(150\) | 4.79169 | 0.391240 | ||||||||
\(151\) | −10.3722 | + | 17.9651i | −0.844075 | + | 1.46198i | 0.0423464 | + | 0.999103i | \(0.486517\pi\) |
−0.886422 | + | 0.462878i | \(0.846817\pi\) | |||||||
\(152\) | 1.44122 | − | 2.49627i | 0.116898 | − | 0.202474i | ||||
\(153\) | −0.775934 | + | 1.34396i | −0.0627306 | + | 0.108653i | ||||
\(154\) | −9.41517 | + | 3.79685i | −0.758696 | + | 0.305959i | ||||
\(155\) | −4.38242 | −0.352004 | ||||||||
\(156\) | −3.11065 | − | 1.82315i | −0.249051 | − | 0.145969i | ||||
\(157\) | 3.22701 | − | 5.58934i | 0.257543 | − | 0.446078i | −0.708040 | − | 0.706172i | \(-0.750420\pi\) |
0.965583 | + | 0.260094i | \(0.0837536\pi\) | |||||||
\(158\) | 2.70966 | + | 4.69326i | 0.215569 | + | 0.373376i | ||||
\(159\) | 1.10079 | 0.0872986 | ||||||||
\(160\) | −0.228205 | − | 0.395262i | −0.0180412 | − | 0.0312482i | ||||
\(161\) | −1.19980 | + | 8.49692i | −0.0945576 | + | 0.669651i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −4.35887 | + | 7.54979i | −0.341413 | + | 0.591345i | −0.984695 | − | 0.174284i | \(-0.944239\pi\) |
0.643282 | + | 0.765629i | \(0.277572\pi\) | |||||||
\(164\) | −3.57277 | + | 6.18822i | −0.278987 | + | 0.483219i | ||||
\(165\) | 1.75127 | 0.136336 | ||||||||
\(166\) | 1.35738 | 0.105353 | ||||||||
\(167\) | −11.4560 | + | 19.8424i | −0.886491 | + | 1.53545i | −0.0424965 | + | 0.999097i | \(0.513531\pi\) |
−0.843995 | + | 0.536351i | \(0.819802\pi\) | |||||||
\(168\) | −2.45374 | + | 0.989520i | −0.189310 | + | 0.0763431i | ||||
\(169\) | 6.64663 | − | 11.1724i | 0.511280 | − | 0.859414i | ||||
\(170\) | −0.354144 | − | 0.613395i | −0.0271616 | − | 0.0470452i | ||||
\(171\) | 1.44122 | + | 2.49627i | 0.110213 | + | 0.190894i | ||||
\(172\) | 1.21716 | + | 2.10818i | 0.0928073 | + | 0.160747i | ||||
\(173\) | −3.79358 | + | 6.57067i | −0.288421 | + | 0.499559i | −0.973433 | − | 0.228972i | \(-0.926463\pi\) |
0.685012 | + | 0.728531i | \(0.259797\pi\) | |||||||
\(174\) | −4.41103 | −0.334400 | ||||||||
\(175\) | 9.98502 | + | 7.81162i | 0.754797 | + | 0.590503i | ||||
\(176\) | 1.91853 | + | 3.32300i | 0.144615 | + | 0.250480i | ||||
\(177\) | −4.68283 | − | 8.11090i | −0.351983 | − | 0.609652i | ||||
\(178\) | −0.179697 | −0.0134689 | ||||||||
\(179\) | −6.25205 | − | 10.8289i | −0.467300 | − | 0.809388i | 0.532002 | − | 0.846743i | \(-0.321440\pi\) |
−0.999302 | + | 0.0373555i | \(0.988107\pi\) | |||||||
\(180\) | 0.456409 | 0.0340187 | ||||||||
\(181\) | −2.26428 | −0.168303 | −0.0841513 | − | 0.996453i | \(-0.526818\pi\) | ||||
−0.0841513 | + | 0.996453i | \(0.526818\pi\) | |||||||
\(182\) | −3.50985 | − | 8.87023i | −0.260168 | − | 0.657505i | ||||
\(183\) | 11.1037 | 0.820812 | ||||||||
\(184\) | 3.24339 | 0.239106 | ||||||||
\(185\) | −0.0640093 | − | 0.110867i | −0.00470606 | − | 0.00815113i | ||||
\(186\) | 9.60195 | 0.704049 | ||||||||
\(187\) | 2.97731 | + | 5.15686i | 0.217723 | + | 0.377107i | ||||
\(188\) | −3.93105 | − | 6.80879i | −0.286702 | − | 0.496582i | ||||
\(189\) | 0.369922 | − | 2.61976i | 0.0269079 | − | 0.190560i | ||||
\(190\) | −1.31557 | −0.0954418 | ||||||||
\(191\) | 4.58649 | − | 7.94403i | 0.331867 | − | 0.574810i | −0.651011 | − | 0.759068i | \(-0.725655\pi\) |
0.982878 | + | 0.184258i | \(0.0589883\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 1.21993 | + | 2.11297i | 0.0878122 | + | 0.152095i | 0.906586 | − | 0.422021i | \(-0.138679\pi\) |
−0.818774 | + | 0.574116i | \(0.805346\pi\) | |||||||
\(194\) | 4.73894 | + | 8.20808i | 0.340236 | + | 0.589306i | ||||
\(195\) | −0.0107575 | + | 1.64557i | −0.000770357 | + | 0.117842i | ||||
\(196\) | −6.72632 | − | 1.93822i | −0.480451 | − | 0.138444i | ||||
\(197\) | −13.4334 | + | 23.2673i | −0.957091 | + | 1.65773i | −0.227581 | + | 0.973759i | \(0.573082\pi\) |
−0.729510 | + | 0.683971i | \(0.760252\pi\) | |||||||
\(198\) | −3.83707 | −0.272688 | ||||||||
\(199\) | −27.9019 | −1.97791 | −0.988957 | − | 0.148206i | \(-0.952650\pi\) | ||||
−0.988957 | + | 0.148206i | \(0.952650\pi\) | |||||||
\(200\) | 2.39585 | − | 4.14973i | 0.169412 | − | 0.293430i | ||||
\(201\) | −0.894964 | + | 1.55012i | −0.0631259 | + | 0.109337i | ||||
\(202\) | −3.18107 | − | 5.50977i | −0.223819 | − | 0.387666i | ||||
\(203\) | −9.19180 | − | 7.19106i | −0.645138 | − | 0.504713i | ||||
\(204\) | 0.775934 | + | 1.34396i | 0.0543263 | + | 0.0940959i | ||||
\(205\) | 3.26129 | 0.227779 | ||||||||
\(206\) | −8.28934 | − | 14.3576i | −0.577545 | − | 1.00034i | ||||
\(207\) | −1.62170 | + | 2.80886i | −0.112716 | + | 0.195229i | ||||
\(208\) | −3.13422 | + | 1.78233i | −0.217319 | + | 0.123582i | ||||
\(209\) | 11.0601 | 0.765045 | ||||||||
\(210\) | 0.951075 | + | 0.744058i | 0.0656304 | + | 0.0513449i | ||||
\(211\) | 10.9871 | − | 19.0301i | 0.756381 | − | 1.31009i | −0.188305 | − | 0.982111i | \(-0.560299\pi\) |
0.944685 | − | 0.327979i | \(-0.106367\pi\) | |||||||
\(212\) | 0.550397 | − | 0.953315i | 0.0378014 | − | 0.0654740i | ||||
\(213\) | 5.06527 | − | 8.77331i | 0.347067 | − | 0.601137i | ||||
\(214\) | 16.9205 | 1.15666 | ||||||||
\(215\) | 0.555521 | − | 0.962191i | 0.0378862 | − | 0.0656209i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 20.0087 | + | 15.6535i | 1.35828 | + | 1.06263i | ||||
\(218\) | 3.95108 | − | 6.84346i | 0.267601 | − | 0.463498i | ||||
\(219\) | 2.81202 | 0.190019 | ||||||||
\(220\) | 0.875637 | − | 1.51665i | 0.0590354 | − | 0.102252i | ||||
\(221\) | −4.86389 | + | 2.76593i | −0.327181 | + | 0.186057i | ||||
\(222\) | 0.140245 | + | 0.242912i | 0.00941265 | + | 0.0163032i | ||||
\(223\) | −6.87919 | + | 11.9151i | −0.460664 | + | 0.797894i | −0.998994 | − | 0.0448402i | \(-0.985722\pi\) |
0.538330 | + | 0.842734i | \(0.319055\pi\) | |||||||
\(224\) | −0.369922 | + | 2.61976i | −0.0247164 | + | 0.175040i | ||||
\(225\) | 2.39585 | + | 4.14973i | 0.159723 | + | 0.276648i | ||||
\(226\) | 3.40689 | + | 5.90091i | 0.226623 | + | 0.392523i | ||||
\(227\) | 18.8309 | 1.24985 | 0.624925 | − | 0.780685i | \(-0.285129\pi\) | ||||
0.624925 | + | 0.780685i | \(0.285129\pi\) | |||||||
\(228\) | 2.88244 | 0.190894 | ||||||||
\(229\) | 1.74812 | + | 3.02784i | 0.115519 | + | 0.200085i | 0.917987 | − | 0.396610i | \(-0.129814\pi\) |
−0.802468 | + | 0.596695i | \(0.796480\pi\) | |||||||
\(230\) | −0.740157 | − | 1.28199i | −0.0488045 | − | 0.0845319i | ||||
\(231\) | −7.99576 | − | 6.25535i | −0.526082 | − | 0.411572i | ||||
\(232\) | −2.20552 | + | 3.82007i | −0.144799 | + | 0.250800i | ||||
\(233\) | 9.74031 | + | 16.8707i | 0.638109 | + | 1.10524i | 0.985847 | + | 0.167645i | \(0.0536163\pi\) |
−0.347739 | + | 0.937592i | \(0.613050\pi\) | |||||||
\(234\) | 0.0235697 | − | 3.60547i | 0.00154080 | − | 0.235697i | ||||
\(235\) | −1.79417 | + | 3.10759i | −0.117039 | + | 0.202717i | ||||
\(236\) | −9.36566 | −0.609652 | ||||||||
\(237\) | −2.70966 | + | 4.69326i | −0.176011 | + | 0.304860i | ||||
\(238\) | −0.574070 | + | 4.06553i | −0.0372114 | + | 0.263529i | ||||
\(239\) | 12.5469 | 0.811592 | 0.405796 | − | 0.913964i | \(-0.366994\pi\) | ||||
0.405796 | + | 0.913964i | \(0.366994\pi\) | |||||||
\(240\) | 0.228205 | − | 0.395262i | 0.0147305 | − | 0.0255141i | ||||
\(241\) | −0.466451 | −0.0300467 | −0.0150234 | − | 0.999887i | \(-0.504782\pi\) | ||||
−0.0150234 | + | 0.999887i | \(0.504782\pi\) | |||||||
\(242\) | −1.86154 | + | 3.22428i | −0.119664 | + | 0.207265i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 5.55187 | − | 9.61612i | 0.355422 | − | 0.615609i | ||||
\(245\) | 0.768874 | + | 3.10097i | 0.0491215 | + | 0.198114i | ||||
\(246\) | −7.14554 | −0.455583 | ||||||||
\(247\) | −0.0679384 | + | 10.3926i | −0.00432282 | + | 0.661264i | ||||
\(248\) | 4.80098 | − | 8.31553i | 0.304862 | − | 0.528037i | ||||
\(249\) | 0.678689 | + | 1.17552i | 0.0430102 | + | 0.0744959i | ||||
\(250\) | −4.46902 | −0.282646 | ||||||||
\(251\) | 12.7935 | + | 22.1590i | 0.807517 | + | 1.39866i | 0.914579 | + | 0.404408i | \(0.132522\pi\) |
−0.107062 | + | 0.994252i | \(0.534144\pi\) | |||||||
\(252\) | −2.08382 | − | 1.63024i | −0.131268 | − | 0.102696i | ||||
\(253\) | 6.22256 | + | 10.7778i | 0.391209 | + | 0.677594i | ||||
\(254\) | 10.9334 | − | 18.9372i | 0.686023 | − | 1.18823i | ||||
\(255\) | 0.354144 | − | 0.613395i | 0.0221773 | − | 0.0384123i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.77611 | −0.235547 | −0.117774 | − | 0.993040i | \(-0.537576\pi\) | ||||
−0.117774 | + | 0.993040i | \(0.537576\pi\) | |||||||
\(258\) | −1.21716 | + | 2.10818i | −0.0757768 | + | 0.131249i | ||||
\(259\) | −0.103760 | + | 0.734819i | −0.00644731 | + | 0.0456594i | ||||
\(260\) | 1.41973 | + | 0.832102i | 0.0880478 | + | 0.0516048i | ||||
\(261\) | −2.20552 | − | 3.82007i | −0.136518 | − | 0.236456i | ||||
\(262\) | 4.72554 | + | 8.18487i | 0.291945 | + | 0.505663i | ||||
\(263\) | −9.84358 | − | 17.0496i | −0.606981 | − | 1.05132i | −0.991735 | − | 0.128303i | \(-0.959047\pi\) |
0.384754 | − | 0.923019i | \(-0.374286\pi\) | |||||||
\(264\) | −1.91853 | + | 3.32300i | −0.118078 | + | 0.204516i | ||||
\(265\) | −0.502413 | −0.0308630 | ||||||||
\(266\) | 6.00649 | + | 4.69908i | 0.368282 | + | 0.288119i | ||||
\(267\) | −0.0898485 | − | 0.155622i | −0.00549864 | − | 0.00952392i | ||||
\(268\) | 0.894964 | + | 1.55012i | 0.0546686 | + | 0.0946888i | ||||
\(269\) | −8.78165 | −0.535427 | −0.267713 | − | 0.963499i | \(-0.586268\pi\) | ||||
−0.267713 | + | 0.963499i | \(0.586268\pi\) | |||||||
\(270\) | 0.228205 | + | 0.395262i | 0.0138881 | + | 0.0240549i | ||||
\(271\) | 28.8027 | 1.74964 | 0.874820 | − | 0.484448i | \(-0.160980\pi\) | ||||
0.874820 | + | 0.484448i | \(0.160980\pi\) | |||||||
\(272\) | 1.55187 | 0.0940959 | ||||||||
\(273\) | 5.92692 | − | 7.47474i | 0.358713 | − | 0.452392i | ||||
\(274\) | 2.44792 | 0.147884 | ||||||||
\(275\) | 18.3860 | 1.10872 | ||||||||
\(276\) | 1.62170 | + | 2.80886i | 0.0976146 | + | 0.169074i | ||||
\(277\) | 6.94992 | 0.417580 | 0.208790 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208790 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(278\) | −5.37228 | − | 9.30505i | −0.322208 | − | 0.558080i | ||||
\(279\) | 4.80098 | + | 8.31553i | 0.287427 | + | 0.497838i | ||||
\(280\) | 1.11991 | − | 0.451626i | 0.0669275 | − | 0.0269898i | ||||
\(281\) | −12.5116 | −0.746381 | −0.373190 | − | 0.927755i | \(-0.621736\pi\) | ||||
−0.373190 | + | 0.927755i | \(0.621736\pi\) | |||||||
\(282\) | 3.93105 | − | 6.80879i | 0.234091 | − | 0.405457i | ||||
\(283\) | −5.60195 | − | 9.70287i | −0.333001 | − | 0.576775i | 0.650097 | − | 0.759851i | \(-0.274728\pi\) |
−0.983099 | + | 0.183075i | \(0.941395\pi\) | |||||||
\(284\) | −5.06527 | − | 8.77331i | −0.300569 | − | 0.520600i | ||||
\(285\) | −0.657787 | − | 1.13932i | −0.0389639 | − | 0.0674875i | ||||
\(286\) | −11.9358 | − | 6.99554i | −0.705776 | − | 0.413655i | ||||
\(287\) | −14.8900 | − | 11.6490i | −0.878931 | − | 0.687617i | ||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −14.5917 | −0.858335 | ||||||||
\(290\) | 2.01324 | 0.118221 | ||||||||
\(291\) | −4.73894 | + | 8.20808i | −0.277802 | + | 0.481166i | ||||
\(292\) | 1.40601 | − | 2.43529i | 0.0822807 | − | 0.142514i | ||||
\(293\) | 14.2699 | + | 24.7162i | 0.833657 | + | 1.44394i | 0.895119 | + | 0.445827i | \(0.147090\pi\) |
−0.0614625 | + | 0.998109i | \(0.519576\pi\) | |||||||
\(294\) | −1.68461 | − | 6.79427i | −0.0982487 | − | 0.396250i | ||||
\(295\) | 2.13729 | + | 3.70189i | 0.124438 | + | 0.215532i | ||||
\(296\) | 0.280491 | 0.0163032 | ||||||||
\(297\) | −1.91853 | − | 3.32300i | −0.111325 | − | 0.192820i | ||||
\(298\) | −4.65157 | + | 8.05676i | −0.269458 | + | 0.466715i | ||||
\(299\) | −10.1655 | + | 5.78078i | −0.587886 | + | 0.334311i | ||||
\(300\) | 4.79169 | 0.276648 | ||||||||
\(301\) | −5.97317 | + | 2.40880i | −0.344288 | + | 0.138841i | ||||
\(302\) | −10.3722 | + | 17.9651i | −0.596851 | + | 1.03378i | ||||
\(303\) | 3.18107 | − | 5.50977i | 0.182747 | − | 0.316528i | ||||
\(304\) | 1.44122 | − | 2.49627i | 0.0826597 | − | 0.143171i | ||||
\(305\) | −5.06785 | −0.290184 | ||||||||
\(306\) | −0.775934 | + | 1.34396i | −0.0443572 | + | 0.0768290i | ||||
\(307\) | −23.1907 | −1.32356 | −0.661781 | − | 0.749698i | \(-0.730199\pi\) | ||||
−0.661781 | + | 0.749698i | \(0.730199\pi\) | |||||||
\(308\) | −9.41517 | + | 3.79685i | −0.536479 | + | 0.216346i | ||||
\(309\) | 8.28934 | − | 14.3576i | 0.471564 | − | 0.816773i | ||||
\(310\) | −4.38242 | −0.248905 | ||||||||
\(311\) | 11.6740 | − | 20.2200i | 0.661973 | − | 1.14657i | −0.318123 | − | 0.948049i | \(-0.603052\pi\) |
0.980096 | − | 0.198522i | \(-0.0636142\pi\) | |||||||
\(312\) | −3.11065 | − | 1.82315i | −0.176106 | − | 0.103215i | ||||
\(313\) | 7.26499 | + | 12.5833i | 0.410641 | + | 0.711252i | 0.994960 | − | 0.100273i | \(-0.0319715\pi\) |
−0.584319 | + | 0.811524i | \(0.698638\pi\) | |||||||
\(314\) | 3.22701 | − | 5.58934i | 0.182111 | − | 0.315425i | ||||
\(315\) | −0.168836 | + | 1.19568i | −0.00951282 | + | 0.0673692i | ||||
\(316\) | 2.70966 | + | 4.69326i | 0.152430 | + | 0.264017i | ||||
\(317\) | 1.64596 | + | 2.85089i | 0.0924463 | + | 0.160122i | 0.908540 | − | 0.417798i | \(-0.137198\pi\) |
−0.816094 | + | 0.577920i | \(0.803865\pi\) | |||||||
\(318\) | 1.10079 | 0.0617294 | ||||||||
\(319\) | −16.9254 | −0.947642 | ||||||||
\(320\) | −0.228205 | − | 0.395262i | −0.0127570 | − | 0.0220958i | ||||
\(321\) | 8.46023 | + | 14.6536i | 0.472204 | + | 0.817882i | ||||
\(322\) | −1.19980 | + | 8.49692i | −0.0668624 | + | 0.473515i | ||||
\(323\) | 2.23659 | − | 3.87388i | 0.124447 | − | 0.215549i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −0.112939 | + | 17.2763i | −0.00626472 | + | 0.958318i | ||||
\(326\) | −4.35887 | + | 7.54979i | −0.241416 | + | 0.418144i | ||||
\(327\) | 7.90215 | 0.436990 | ||||||||
\(328\) | −3.57277 | + | 6.18822i | −0.197273 | + | 0.341687i | ||||
\(329\) | 19.2916 | − | 7.77971i | 1.06358 | − | 0.428909i | ||||
\(330\) | 1.75127 | 0.0964044 | ||||||||
\(331\) | −8.05285 | + | 13.9480i | −0.442625 | + | 0.766649i | −0.997883 | − | 0.0650290i | \(-0.979286\pi\) |
0.555258 | + | 0.831678i | \(0.312619\pi\) | |||||||
\(332\) | 1.35738 | 0.0744959 | ||||||||
\(333\) | −0.140245 | + | 0.242912i | −0.00768540 | + | 0.0133115i | ||||
\(334\) | −11.4560 | + | 19.8424i | −0.626844 | + | 1.08573i | ||||
\(335\) | 0.408470 | − | 0.707490i | 0.0223171 | − | 0.0386543i | ||||
\(336\) | −2.45374 | + | 0.989520i | −0.133863 | + | 0.0539827i | ||||
\(337\) | −14.9134 | −0.812383 | −0.406192 | − | 0.913788i | \(-0.633143\pi\) | ||||
−0.406192 | + | 0.913788i | \(0.633143\pi\) | |||||||
\(338\) | 6.64663 | − | 11.1724i | 0.361529 | − | 0.607698i | ||||
\(339\) | −3.40689 | + | 5.90091i | −0.185037 | + | 0.320494i | ||||
\(340\) | −0.354144 | − | 0.613395i | −0.0192061 | − | 0.0332660i | ||||
\(341\) | 36.8433 | 1.99518 | ||||||||
\(342\) | 1.44122 | + | 2.49627i | 0.0779323 | + | 0.134983i | ||||
\(343\) | 7.56588 | − | 16.9044i | 0.408519 | − | 0.912750i | ||||
\(344\) | 1.21716 | + | 2.10818i | 0.0656246 | + | 0.113665i | ||||
\(345\) | 0.740157 | − | 1.28199i | 0.0398487 | − | 0.0690200i | ||||
\(346\) | −3.79358 | + | 6.57067i | −0.203944 | + | 0.353242i | ||||
\(347\) | 28.8011 | 1.54612 | 0.773062 | − | 0.634330i | \(-0.218724\pi\) | ||||
0.773062 | + | 0.634330i | \(0.218724\pi\) | |||||||
\(348\) | −4.41103 | −0.236456 | ||||||||
\(349\) | 2.50740 | − | 4.34294i | 0.134218 | − | 0.232472i | −0.791081 | − | 0.611712i | \(-0.790481\pi\) |
0.925298 | + | 0.379240i | \(0.123814\pi\) | |||||||
\(350\) | 9.98502 | + | 7.81162i | 0.533722 | + | 0.417549i | ||||
\(351\) | 3.13422 | − | 1.78233i | 0.167292 | − | 0.0951335i | ||||
\(352\) | 1.91853 | + | 3.32300i | 0.102258 | + | 0.177116i | ||||
\(353\) | 5.78333 | + | 10.0170i | 0.307816 | + | 0.533152i | 0.977884 | − | 0.209147i | \(-0.0670687\pi\) |
−0.670069 | + | 0.742299i | \(0.733735\pi\) | |||||||
\(354\) | −4.68283 | − | 8.11090i | −0.248890 | − | 0.431089i | ||||
\(355\) | −2.31184 | + | 4.00422i | −0.122700 | + | 0.212522i | ||||
\(356\) | −0.179697 | −0.00952392 | ||||||||
\(357\) | −3.80789 | + | 1.53560i | −0.201535 | + | 0.0812728i | ||||
\(358\) | −6.25205 | − | 10.8289i | −0.330431 | − | 0.572324i | ||||
\(359\) | −14.9173 | − | 25.8375i | −0.787306 | − | 1.36365i | −0.927612 | − | 0.373546i | \(-0.878142\pi\) |
0.140306 | − | 0.990108i | \(-0.455191\pi\) | |||||||
\(360\) | 0.456409 | 0.0240549 | ||||||||
\(361\) | 5.34576 | + | 9.25913i | 0.281356 | + | 0.487323i | ||||
\(362\) | −2.26428 | −0.119008 | ||||||||
\(363\) | −3.72308 | −0.195411 | ||||||||
\(364\) | −3.50985 | − | 8.87023i | −0.183966 | − | 0.464926i | ||||
\(365\) | −1.28343 | −0.0671780 | ||||||||
\(366\) | 11.1037 | 0.580402 | ||||||||
\(367\) | −3.63895 | − | 6.30284i | −0.189951 | − | 0.329006i | 0.755282 | − | 0.655400i | \(-0.227500\pi\) |
−0.945234 | + | 0.326394i | \(0.894166\pi\) | |||||||
\(368\) | 3.24339 | 0.169074 | ||||||||
\(369\) | −3.57277 | − | 6.18822i | −0.185991 | − | 0.322146i | ||||
\(370\) | −0.0640093 | − | 0.110867i | −0.00332768 | − | 0.00576372i | ||||
\(371\) | 2.29386 | + | 1.79456i | 0.119091 | + | 0.0931690i | ||||
\(372\) | 9.60195 | 0.497838 | ||||||||
\(373\) | −15.5458 | + | 26.9261i | −0.804932 | + | 1.39418i | 0.111405 | + | 0.993775i | \(0.464465\pi\) |
−0.916337 | + | 0.400408i | \(0.868868\pi\) | |||||||
\(374\) | 2.97731 | + | 5.15686i | 0.153953 | + | 0.266655i | ||||
\(375\) | −2.23451 | − | 3.87028i | −0.115390 | − | 0.199861i | ||||
\(376\) | −3.93105 | − | 6.80879i | −0.202729 | − | 0.351136i | ||||
\(377\) | 0.103967 | − | 15.9039i | 0.00535457 | − | 0.819091i | ||||
\(378\) | 0.369922 | − | 2.61976i | 0.0190267 | − | 0.134746i | ||||
\(379\) | −9.33146 | + | 16.1626i | −0.479325 | + | 0.830215i | −0.999719 | − | 0.0237115i | \(-0.992452\pi\) |
0.520394 | + | 0.853926i | \(0.325785\pi\) | |||||||
\(380\) | −1.31557 | −0.0674875 | ||||||||
\(381\) | 21.8668 | 1.12027 | ||||||||
\(382\) | 4.58649 | − | 7.94403i | 0.234665 | − | 0.406452i | ||||
\(383\) | −4.48135 | + | 7.76192i | −0.228986 | + | 0.396616i | −0.957508 | − | 0.288407i | \(-0.906874\pi\) |
0.728522 | + | 0.685023i | \(0.240208\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 3.64934 | + | 2.85500i | 0.185988 | + | 0.145504i | ||||
\(386\) | 1.21993 | + | 2.11297i | 0.0620926 | + | 0.107548i | ||||
\(387\) | −2.43431 | −0.123743 | ||||||||
\(388\) | 4.73894 | + | 8.20808i | 0.240583 | + | 0.416702i | ||||
\(389\) | −14.5103 | + | 25.1326i | −0.735702 | + | 1.27427i | 0.218712 | + | 0.975789i | \(0.429814\pi\) |
−0.954415 | + | 0.298484i | \(0.903519\pi\) | |||||||
\(390\) | −0.0107575 | + | 1.64557i | −0.000544725 | + | 0.0833268i | ||||
\(391\) | 5.03332 | 0.254546 | ||||||||
\(392\) | −6.72632 | − | 1.93822i | −0.339730 | − | 0.0978947i | ||||
\(393\) | −4.72554 | + | 8.18487i | −0.238372 | + | 0.412872i | ||||
\(394\) | −13.4334 | + | 23.2673i | −0.676765 | + | 1.17219i | ||||
\(395\) | 1.23671 | − | 2.14205i | 0.0622257 | − | 0.107778i | ||||
\(396\) | −3.83707 | −0.192820 | ||||||||
\(397\) | 2.17445 | − | 3.76625i | 0.109132 | − | 0.189023i | −0.806287 | − | 0.591525i | \(-0.798526\pi\) |
0.915419 | + | 0.402502i | \(0.131859\pi\) | |||||||
\(398\) | −27.9019 | −1.39860 | ||||||||
\(399\) | −1.06628 | + | 7.55132i | −0.0533807 | + | 0.378039i | ||||
\(400\) | 2.39585 | − | 4.14973i | 0.119792 | − | 0.207486i | ||||
\(401\) | 9.55124 | 0.476966 | 0.238483 | − | 0.971147i | \(-0.423350\pi\) | ||||
0.238483 | + | 0.971147i | \(0.423350\pi\) | |||||||
\(402\) | −0.894964 | + | 1.55012i | −0.0446367 | + | 0.0773131i | ||||
\(403\) | −0.226316 | + | 34.6196i | −0.0112736 | + | 1.72452i | ||||
\(404\) | −3.18107 | − | 5.50977i | −0.158264 | − | 0.274121i | ||||
\(405\) | −0.228205 | + | 0.395262i | −0.0113396 | + | 0.0196407i | ||||
\(406\) | −9.19180 | − | 7.19106i | −0.456181 | − | 0.356886i | ||||
\(407\) | 0.538131 | + | 0.932070i | 0.0266741 | + | 0.0462010i | ||||
\(408\) | 0.775934 | + | 1.34396i | 0.0384145 | + | 0.0665358i | ||||
\(409\) | 1.27024 | 0.0628094 | 0.0314047 | − | 0.999507i | \(-0.490002\pi\) | ||||
0.0314047 | + | 0.999507i | \(0.490002\pi\) | |||||||
\(410\) | 3.26129 | 0.161064 | ||||||||
\(411\) | 1.22396 | + | 2.11996i | 0.0603736 | + | 0.104570i | ||||
\(412\) | −8.28934 | − | 14.3576i | −0.408386 | − | 0.707346i | ||||
\(413\) | 3.46456 | − | 24.5358i | 0.170480 | − | 1.20733i | ||||
\(414\) | −1.62170 | + | 2.80886i | −0.0797020 | + | 0.138048i | ||||
\(415\) | −0.309760 | − | 0.536520i | −0.0152055 | − | 0.0263368i | ||||
\(416\) | −3.13422 | + | 1.78233i | −0.153668 | + | 0.0873857i | ||||
\(417\) | 5.37228 | − | 9.30505i | 0.263081 | − | 0.455670i | ||||
\(418\) | 11.0601 | 0.540968 | ||||||||
\(419\) | 5.25472 | − | 9.10144i | 0.256710 | − | 0.444634i | −0.708649 | − | 0.705561i | \(-0.750695\pi\) |
0.965359 | + | 0.260927i | \(0.0840282\pi\) | |||||||
\(420\) | 0.951075 | + | 0.744058i | 0.0464077 | + | 0.0363063i | ||||
\(421\) | −1.14121 | −0.0556192 | −0.0278096 | − | 0.999613i | \(-0.508853\pi\) | ||||
−0.0278096 | + | 0.999613i | \(0.508853\pi\) | |||||||
\(422\) | 10.9871 | − | 19.0301i | 0.534842 | − | 0.926373i | ||||
\(423\) | 7.86211 | 0.382269 | ||||||||
\(424\) | 0.550397 | − | 0.953315i | 0.0267296 | − | 0.0462971i | ||||
\(425\) | 3.71804 | − | 6.43983i | 0.180351 | − | 0.312378i | ||||
\(426\) | 5.06527 | − | 8.77331i | 0.245413 | − | 0.425068i | ||||
\(427\) | 23.1382 | + | 18.1018i | 1.11974 | + | 0.876007i | ||||
\(428\) | 16.9205 | 0.817882 | ||||||||
\(429\) | 0.0904387 | − | 13.8344i | 0.00436642 | − | 0.667933i | ||||
\(430\) | 0.555521 | − | 0.962191i | 0.0267896 | − | 0.0464010i | ||||
\(431\) | −15.6637 | − | 27.1303i | −0.754493 | − | 1.30682i | −0.945626 | − | 0.325257i | \(-0.894549\pi\) |
0.191132 | − | 0.981564i | \(-0.438784\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −7.06113 | − | 12.2302i | −0.339336 | − | 0.587748i | 0.644972 | − | 0.764206i | \(-0.276869\pi\) |
−0.984308 | + | 0.176459i | \(0.943536\pi\) | |||||||
\(434\) | 20.0087 | + | 15.6535i | 0.960450 | + | 0.751393i | ||||
\(435\) | 1.00662 | + | 1.74351i | 0.0482637 | + | 0.0835951i | ||||
\(436\) | 3.95108 | − | 6.84346i | 0.189222 | − | 0.327742i | ||||
\(437\) | 4.67445 | − | 8.09638i | 0.223609 | − | 0.387302i | ||||
\(438\) | 2.81202 | 0.134364 | ||||||||
\(439\) | −6.46132 | −0.308382 | −0.154191 | − | 0.988041i | \(-0.549277\pi\) | ||||
−0.154191 | + | 0.988041i | \(0.549277\pi\) | |||||||
\(440\) | 0.875637 | − | 1.51665i | 0.0417443 | − | 0.0723033i | ||||
\(441\) | 5.04170 | − | 4.85605i | 0.240081 | − | 0.231241i | ||||
\(442\) | −4.86389 | + | 2.76593i | −0.231352 | + | 0.131562i | ||||
\(443\) | −5.70730 | − | 9.88534i | −0.271162 | − | 0.469667i | 0.697998 | − | 0.716100i | \(-0.254075\pi\) |
−0.969160 | + | 0.246434i | \(0.920741\pi\) | |||||||
\(444\) | 0.140245 | + | 0.242912i | 0.00665575 | + | 0.0115281i | ||||
\(445\) | 0.0410077 | + | 0.0710274i | 0.00194395 | + | 0.00336702i | ||||
\(446\) | −6.87919 | + | 11.9151i | −0.325739 | + | 0.564196i | ||||
\(447\) | −9.30314 | −0.440024 | ||||||||
\(448\) | −0.369922 | + | 2.61976i | −0.0174772 | + | 0.123772i | ||||
\(449\) | −19.8942 | − | 34.4578i | −0.938867 | − | 1.62617i | −0.767589 | − | 0.640942i | \(-0.778544\pi\) |
−0.171278 | − | 0.985223i | \(-0.554790\pi\) | |||||||
\(450\) | 2.39585 | + | 4.14973i | 0.112941 | + | 0.195620i | ||||
\(451\) | −27.4179 | −1.29106 | ||||||||
\(452\) | 3.40689 | + | 5.90091i | 0.160247 | + | 0.277556i | ||||
\(453\) | −20.7443 | −0.974654 | ||||||||
\(454\) | 18.8309 | 0.883778 | ||||||||
\(455\) | −2.70510 | + | 3.41154i | −0.126817 | + | 0.159935i | ||||
\(456\) | 2.88244 | 0.134983 | ||||||||
\(457\) | −5.25285 | −0.245718 | −0.122859 | − | 0.992424i | \(-0.539206\pi\) | ||||
−0.122859 | + | 0.992424i | \(0.539206\pi\) | |||||||
\(458\) | 1.74812 | + | 3.02784i | 0.0816844 | + | 0.141481i | ||||
\(459\) | −1.55187 | −0.0724350 | ||||||||
\(460\) | −0.740157 | − | 1.28199i | −0.0345100 | − | 0.0597731i | ||||
\(461\) | 9.59122 | + | 16.6125i | 0.446707 | + | 0.773720i | 0.998169 | − | 0.0604800i | \(-0.0192631\pi\) |
−0.551462 | + | 0.834200i | \(0.685930\pi\) | |||||||
\(462\) | −7.99576 | − | 6.25535i | −0.371996 | − | 0.291025i | ||||
\(463\) | −17.5580 | −0.815988 | −0.407994 | − | 0.912985i | \(-0.633772\pi\) | ||||
−0.407994 | + | 0.912985i | \(0.633772\pi\) | |||||||
\(464\) | −2.20552 | + | 3.82007i | −0.102389 | + | 0.177342i | ||||
\(465\) | −2.19121 | − | 3.79529i | −0.101615 | − | 0.176002i | ||||
\(466\) | 9.74031 | + | 16.8707i | 0.451211 | + | 0.781520i | ||||
\(467\) | −1.54111 | − | 2.66928i | −0.0713141 | − | 0.123520i | 0.828163 | − | 0.560487i | \(-0.189386\pi\) |
−0.899477 | + | 0.436967i | \(0.856053\pi\) | |||||||
\(468\) | 0.0235697 | − | 3.60547i | 0.00108951 | − | 0.166663i | ||||
\(469\) | −4.39202 | + | 1.77117i | −0.202805 | + | 0.0817849i | ||||
\(470\) | −1.79417 | + | 3.10759i | −0.0827589 | + | 0.143343i | ||||
\(471\) | 6.45402 | 0.297385 | ||||||||
\(472\) | −9.36566 | −0.431089 | ||||||||
\(473\) | −4.67031 | + | 8.08921i | −0.214741 | + | 0.371942i | ||||
\(474\) | −2.70966 | + | 4.69326i | −0.124459 | + | 0.215569i | ||||
\(475\) | −6.90589 | − | 11.9613i | −0.316864 | − | 0.548824i | ||||
\(476\) | −0.574070 | + | 4.06553i | −0.0263125 | + | 0.186343i | ||||
\(477\) | 0.550397 | + | 0.953315i | 0.0252009 | + | 0.0436493i | ||||
\(478\) | 12.5469 | 0.573882 | ||||||||
\(479\) | −9.18104 | − | 15.9020i | −0.419493 | − | 0.726582i | 0.576396 | − | 0.817171i | \(-0.304459\pi\) |
−0.995888 | + | 0.0905882i | \(0.971125\pi\) | |||||||
\(480\) | 0.228205 | − | 0.395262i | 0.0104161 | − | 0.0180412i | ||||
\(481\) | −0.879119 | + | 0.499926i | −0.0400844 | + | 0.0227946i | ||||
\(482\) | −0.466451 | −0.0212463 | ||||||||
\(483\) | −7.95845 | + | 3.20940i | −0.362122 | + | 0.146033i | ||||
\(484\) | −1.86154 | + | 3.22428i | −0.0846155 | + | 0.146558i | ||||
\(485\) | 2.16290 | − | 3.74625i | 0.0982121 | − | 0.170108i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 18.0106 | 0.816138 | 0.408069 | − | 0.912951i | \(-0.366202\pi\) | ||||
0.408069 | + | 0.912951i | \(0.366202\pi\) | |||||||
\(488\) | 5.55187 | − | 9.61612i | 0.251321 | − | 0.435301i | ||||
\(489\) | −8.71775 | −0.394230 | ||||||||
\(490\) | 0.768874 | + | 3.10097i | 0.0347342 | + | 0.140087i | ||||
\(491\) | −7.98794 | + | 13.8355i | −0.360491 | + | 0.624388i | −0.988042 | − | 0.154187i | \(-0.950724\pi\) |
0.627551 | + | 0.778576i | \(0.284057\pi\) | |||||||
\(492\) | −7.14554 | −0.322146 | ||||||||
\(493\) | −3.42267 | + | 5.92824i | −0.154149 | + | 0.266995i | ||||
\(494\) | −0.0679384 | + | 10.3926i | −0.00305669 | + | 0.467584i | ||||
\(495\) | 0.875637 | + | 1.51665i | 0.0393569 | + | 0.0681682i | ||||
\(496\) | 4.80098 | − | 8.31553i | 0.215570 | − | 0.373379i | ||||
\(497\) | 24.8577 | − | 10.0244i | 1.11502 | − | 0.449655i | ||||
\(498\) | 0.678689 | + | 1.17552i | 0.0304128 | + | 0.0526765i | ||||
\(499\) | −4.06656 | − | 7.04348i | −0.182044 | − | 0.315309i | 0.760532 | − | 0.649300i | \(-0.224938\pi\) |
−0.942576 | + | 0.333990i | \(0.891605\pi\) | |||||||
\(500\) | −4.46902 | −0.199861 | ||||||||
\(501\) | −22.9120 | −1.02363 | ||||||||
\(502\) | 12.7935 | + | 22.1590i | 0.571001 | + | 0.989002i | ||||
\(503\) | −18.8326 | − | 32.6190i | −0.839705 | − | 1.45441i | −0.890142 | − | 0.455684i | \(-0.849395\pi\) |
0.0504368 | − | 0.998727i | \(-0.483939\pi\) | |||||||
\(504\) | −2.08382 | − | 1.63024i | −0.0928207 | − | 0.0726168i | ||||
\(505\) | −1.45187 | + | 2.51471i | −0.0646073 | + | 0.111903i | ||||
\(506\) | 6.22256 | + | 10.7778i | 0.276626 | + | 0.479131i | ||||
\(507\) | 12.9989 | + | 0.169960i | 0.577301 | + | 0.00754820i | ||||
\(508\) | 10.9334 | − | 18.9372i | 0.485092 | − | 0.840203i | ||||
\(509\) | −27.7558 | −1.23025 | −0.615127 | − | 0.788428i | \(-0.710895\pi\) | ||||
−0.615127 | + | 0.788428i | \(0.710895\pi\) | |||||||
\(510\) | 0.354144 | − | 0.613395i | 0.0156817 | − | 0.0271616i | ||||
\(511\) | 5.85975 | + | 4.58428i | 0.259220 | + | 0.202797i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.44122 | + | 2.49627i | −0.0636315 | + | 0.110213i | ||||
\(514\) | −3.77611 | −0.166557 | ||||||||
\(515\) | −3.78333 | + | 6.55292i | −0.166713 | + | 0.288756i | ||||
\(516\) | −1.21716 | + | 2.10818i | −0.0535823 | + | 0.0928073i | ||||
\(517\) | 15.0837 | − | 26.1258i | 0.663381 | − | 1.14901i | ||||
\(518\) | −0.103760 | + | 0.734819i | −0.00455894 | + | 0.0322861i | ||||
\(519\) | −7.58716 | −0.333039 | ||||||||
\(520\) | 1.41973 | + | 0.832102i | 0.0622592 | + | 0.0364901i | ||||
\(521\) | −7.66182 | + | 13.2707i | −0.335671 | + | 0.581398i | −0.983613 | − | 0.180291i | \(-0.942296\pi\) |
0.647943 | + | 0.761689i | \(0.275630\pi\) | |||||||
\(522\) | −2.20552 | − | 3.82007i | −0.0965328 | − | 0.167200i | ||||
\(523\) | 25.0767 | 1.09653 | 0.548263 | − | 0.836306i | \(-0.315289\pi\) | ||||
0.548263 | + | 0.836306i | \(0.315289\pi\) | |||||||
\(524\) | 4.72554 | + | 8.18487i | 0.206436 | + | 0.357558i | ||||
\(525\) | −1.77255 | + | 12.5531i | −0.0773605 | + | 0.547862i | ||||
\(526\) | −9.84358 | − | 17.0496i | −0.429201 | − | 0.743397i | ||||
\(527\) | 7.45048 | − | 12.9046i | 0.324548 | − | 0.562134i | ||||
\(528\) | −1.91853 | + | 3.32300i | −0.0834934 | + | 0.144615i | ||||
\(529\) | −12.4804 | −0.542626 | ||||||||
\(530\) | −0.502413 | −0.0218234 | ||||||||
\(531\) | 4.68283 | − | 8.11090i | 0.203217 | − | 0.351983i | ||||
\(532\) | 6.00649 | + | 4.69908i | 0.260414 | + | 0.203731i | ||||
\(533\) | 0.168419 | − | 25.7631i | 0.00729502 | − | 1.11592i | ||||
\(534\) | −0.0898485 | − | 0.155622i | −0.00388812 | − | 0.00673443i | ||||
\(535\) | −3.86133 | − | 6.68802i | −0.166940 | − | 0.289148i | ||||
\(536\) | 0.894964 | + | 1.55012i | 0.0386565 | + | 0.0669551i | ||||
\(537\) | 6.25205 | − | 10.8289i | 0.269796 | − | 0.467300i | ||||
\(538\) | −8.78165 | −0.378604 | ||||||||
\(539\) | −6.46398 | − | 26.0701i | −0.278423 | − | 1.12292i | ||||
\(540\) | 0.228205 | + | 0.395262i | 0.00982037 | + | 0.0170094i | ||||
\(541\) | −14.2260 | − | 24.6402i | −0.611624 | − | 1.05936i | −0.990967 | − | 0.134107i | \(-0.957183\pi\) |
0.379343 | − | 0.925256i | \(-0.376150\pi\) | |||||||
\(542\) | 28.8027 | 1.23718 | ||||||||
\(543\) | −1.13214 | − | 1.96092i | −0.0485848 | − | 0.0841513i | ||||
\(544\) | 1.55187 | 0.0665358 | ||||||||
\(545\) | −3.60662 | −0.154490 | ||||||||
\(546\) | 5.92692 | − | 7.47474i | 0.253649 | − | 0.319889i | ||||
\(547\) | 4.99706 | 0.213659 | 0.106829 | − | 0.994277i | \(-0.465930\pi\) | ||||
0.106829 | + | 0.994277i | \(0.465930\pi\) | |||||||
\(548\) | 2.44792 | 0.104570 | ||||||||
\(549\) | 5.55187 | + | 9.61612i | 0.236948 | + | 0.410406i | ||||
\(550\) | 18.3860 | 0.783983 | ||||||||
\(551\) | 6.35728 | + | 11.0111i | 0.270829 | + | 0.469090i | ||||
\(552\) | 1.62170 | + | 2.80886i | 0.0690240 | + | 0.119553i | ||||
\(553\) | −13.2976 | + | 5.36252i | −0.565471 | + | 0.228037i | ||||
\(554\) | 6.94992 | 0.295274 | ||||||||
\(555\) | 0.0640093 | − | 0.110867i | 0.00271704 | − | 0.00470606i | ||||
\(556\) | −5.37228 | − | 9.30505i | −0.227835 | − | 0.394622i | ||||
\(557\) | −15.8565 | − | 27.4643i | −0.671861 | − | 1.16370i | −0.977376 | − | 0.211511i | \(-0.932162\pi\) |
0.305514 | − | 0.952187i | \(-0.401172\pi\) | |||||||
\(558\) | 4.80098 | + | 8.31553i | 0.203242 | + | 0.352025i | ||||
\(559\) | −7.57228 | − | 4.43811i | −0.320274 | − | 0.187712i | ||||
\(560\) | 1.11991 | − | 0.451626i | 0.0473249 | − | 0.0190847i | ||||
\(561\) | −2.97731 | + | 5.15686i | −0.125702 | + | 0.217723i | ||||
\(562\) | −12.5116 | −0.527771 | ||||||||
\(563\) | 23.8948 | 1.00705 | 0.503523 | − | 0.863982i | \(-0.332037\pi\) | ||||
0.503523 | + | 0.863982i | \(0.332037\pi\) | |||||||
\(564\) | 3.93105 | − | 6.80879i | 0.165527 | − | 0.286702i | ||||
\(565\) | 1.55494 | − | 2.69323i | 0.0654167 | − | 0.113305i | ||||
\(566\) | −5.60195 | − | 9.70287i | −0.235468 | − | 0.407842i | ||||
\(567\) | 2.45374 | − | 0.989520i | 0.103047 | − | 0.0415559i | ||||
\(568\) | −5.06527 | − | 8.77331i | −0.212534 | − | 0.368120i | ||||
\(569\) | −38.4641 | −1.61250 | −0.806249 | − | 0.591577i | \(-0.798506\pi\) | ||||
−0.806249 | + | 0.591577i | \(0.798506\pi\) | |||||||
\(570\) | −0.657787 | − | 1.13932i | −0.0275517 | − | 0.0477209i | ||||
\(571\) | 15.8854 | − | 27.5143i | 0.664782 | − | 1.15144i | −0.314563 | − | 0.949237i | \(-0.601858\pi\) |
0.979344 | − | 0.202199i | \(-0.0648088\pi\) | |||||||
\(572\) | −11.9358 | − | 6.99554i | −0.499059 | − | 0.292498i | ||||
\(573\) | 9.17297 | 0.383207 | ||||||||
\(574\) | −14.8900 | − | 11.6490i | −0.621498 | − | 0.486219i | ||||
\(575\) | 7.77067 | − | 13.4592i | 0.324059 | − | 0.561287i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 10.1750 | − | 17.6236i | 0.423591 | − | 0.733682i | −0.572696 | − | 0.819768i | \(-0.694103\pi\) |
0.996288 | + | 0.0860858i | \(0.0274359\pi\) | |||||||
\(578\) | −14.5917 | −0.606935 | ||||||||
\(579\) | −1.21993 | + | 2.11297i | −0.0506984 | + | 0.0878122i | ||||
\(580\) | 2.01324 | 0.0835951 | ||||||||
\(581\) | −0.502124 | + | 3.55601i | −0.0208316 | + | 0.147528i | ||||
\(582\) | −4.73894 | + | 8.20808i | −0.196435 | + | 0.340236i | ||||
\(583\) | 4.22382 | 0.174933 | ||||||||
\(584\) | 1.40601 | − | 2.43529i | 0.0581812 | − | 0.100773i | ||||
\(585\) | −1.43049 | + | 0.813470i | −0.0591433 | + | 0.0336328i | ||||
\(586\) | 14.2699 | + | 24.7162i | 0.589484 | + | 1.02102i | ||||
\(587\) | −11.7425 | + | 20.3386i | −0.484664 | + | 0.839462i | −0.999845 | − | 0.0176191i | \(-0.994391\pi\) |
0.515181 | + | 0.857081i | \(0.327725\pi\) | |||||||
\(588\) | −1.68461 | − | 6.79427i | −0.0694723 | − | 0.280191i | ||||
\(589\) | −13.8385 | − | 23.9691i | −0.570207 | − | 0.987628i | ||||
\(590\) | 2.13729 | + | 3.70189i | 0.0879907 | + | 0.152404i | ||||
\(591\) | −26.8668 | −1.10515 | ||||||||
\(592\) | 0.280491 | 0.0115281 | ||||||||
\(593\) | −0.268350 | − | 0.464796i | −0.0110198 | − | 0.0190869i | 0.860463 | − | 0.509513i | \(-0.170174\pi\) |
−0.871483 | + | 0.490426i | \(0.836841\pi\) | |||||||
\(594\) | −1.91853 | − | 3.32300i | −0.0787184 | − | 0.136344i | ||||
\(595\) | 1.73795 | − | 0.700864i | 0.0712492 | − | 0.0287326i | ||||
\(596\) | −4.65157 | + | 8.05676i | −0.190536 | + | 0.330018i | ||||
\(597\) | −13.9509 | − | 24.1638i | −0.570974 | − | 0.988957i | ||||
\(598\) | −10.1655 | + | 5.78078i | −0.415698 | + | 0.236394i | ||||
\(599\) | 9.68962 | − | 16.7829i | 0.395907 | − | 0.685731i | −0.597309 | − | 0.802011i | \(-0.703764\pi\) |
0.993217 | + | 0.116280i | \(0.0370969\pi\) | |||||||
\(600\) | 4.79169 | 0.195620 | ||||||||
\(601\) | 7.74999 | − | 13.4234i | 0.316129 | − | 0.547551i | −0.663548 | − | 0.748134i | \(-0.730950\pi\) |
0.979677 | + | 0.200583i | \(0.0642835\pi\) | |||||||
\(602\) | −5.97317 | + | 2.40880i | −0.243448 | + | 0.0981753i | ||||
\(603\) | −1.78993 | −0.0728915 | ||||||||
\(604\) | −10.3722 | + | 17.9651i | −0.422038 | + | 0.730991i | ||||
\(605\) | 1.69925 | 0.0690843 | ||||||||
\(606\) | 3.18107 | − | 5.50977i | 0.129222 | − | 0.223819i | ||||
\(607\) | −7.87631 | + | 13.6422i | −0.319690 | + | 0.553719i | −0.980423 | − | 0.196902i | \(-0.936912\pi\) |
0.660734 | + | 0.750620i | \(0.270245\pi\) | |||||||
\(608\) | 1.44122 | − | 2.49627i | 0.0584492 | − | 0.101237i | ||||
\(609\) | 1.63174 | − | 11.5559i | 0.0661214 | − | 0.468267i | ||||
\(610\) | −5.06785 | −0.205191 | ||||||||
\(611\) | 24.4562 | + | 14.3338i | 0.989394 | + | 0.579883i | ||||
\(612\) | −0.775934 | + | 1.34396i | −0.0313653 | + | 0.0543263i | ||||
\(613\) | −15.5441 | − | 26.9231i | −0.627818 | − | 1.08741i | −0.987989 | − | 0.154527i | \(-0.950615\pi\) |
0.360170 | − | 0.932887i | \(-0.382719\pi\) | |||||||
\(614\) | −23.1907 | −0.935899 | ||||||||
\(615\) | 1.63065 | + | 2.82436i | 0.0657540 | + | 0.113889i | ||||
\(616\) | −9.41517 | + | 3.79685i | −0.379348 | + | 0.152980i | ||||
\(617\) | 9.39918 | + | 16.2799i | 0.378397 | + | 0.655403i | 0.990829 | − | 0.135120i | \(-0.0431421\pi\) |
−0.612432 | + | 0.790523i | \(0.709809\pi\) | |||||||
\(618\) | 8.28934 | − | 14.3576i | 0.333446 | − | 0.577545i | ||||
\(619\) | −10.6461 | + | 18.4396i | −0.427904 | + | 0.741152i | −0.996687 | − | 0.0813361i | \(-0.974081\pi\) |
0.568783 | + | 0.822488i | \(0.307415\pi\) | |||||||
\(620\) | −4.38242 | −0.176002 | ||||||||
\(621\) | −3.24339 | −0.130153 | ||||||||
\(622\) | 11.6740 | − | 20.2200i | 0.468086 | − | 0.810749i | ||||
\(623\) | 0.0664738 | − | 0.470763i | 0.00266322 | − | 0.0188607i | ||||
\(624\) | −3.11065 | − | 1.82315i | −0.124526 | − | 0.0729844i | ||||
\(625\) | −10.9594 | − | 18.9822i | −0.438375 | − | 0.759288i | ||||
\(626\) | 7.26499 | + | 12.5833i | 0.290367 | + | 0.502931i | ||||
\(627\) | 5.53006 | + | 9.57835i | 0.220849 | + | 0.382522i | ||||
\(628\) | 3.22701 | − | 5.58934i | 0.128772 | − | 0.223039i | ||||
\(629\) | 0.435285 | 0.0173559 | ||||||||
\(630\) | −0.168836 | + | 1.19568i | −0.00672658 | + | 0.0476372i | ||||
\(631\) | −4.63522 | − | 8.02844i | −0.184525 | − | 0.319607i | 0.758891 | − | 0.651218i | \(-0.225741\pi\) |
−0.943416 | + | 0.331610i | \(0.892408\pi\) | |||||||
\(632\) | 2.70966 | + | 4.69326i | 0.107784 | + | 0.186688i | ||||
\(633\) | 21.9741 | 0.873393 | ||||||||
\(634\) | 1.64596 | + | 2.85089i | 0.0653694 | + | 0.113223i | ||||
\(635\) | −9.98022 | −0.396053 | ||||||||
\(636\) | 1.10079 | 0.0436493 | ||||||||
\(637\) | 24.5363 | − | 5.91369i | 0.972162 | − | 0.234309i | ||||
\(638\) | −16.9254 | −0.670084 | ||||||||
\(639\) | 10.1305 | 0.400758 | ||||||||
\(640\) | −0.228205 | − | 0.395262i | −0.00902058 | − | 0.0156241i | ||||
\(641\) | 43.7593 | 1.72839 | 0.864194 | − | 0.503158i | \(-0.167829\pi\) | ||||
0.864194 | + | 0.503158i | \(0.167829\pi\) | |||||||
\(642\) | 8.46023 | + | 14.6536i | 0.333899 | + | 0.578330i | ||||
\(643\) | 10.6905 | + | 18.5165i | 0.421593 | + | 0.730220i | 0.996095 | − | 0.0882825i | \(-0.0281378\pi\) |
−0.574503 | + | 0.818503i | \(0.694805\pi\) | |||||||
\(644\) | −1.19980 | + | 8.49692i | −0.0472788 | + | 0.334826i | ||||
\(645\) | 1.11104 | 0.0437473 | ||||||||
\(646\) | 2.23659 | − | 3.87388i | 0.0879973 | − | 0.152416i | ||||
\(647\) | 4.06922 | + | 7.04810i | 0.159978 | + | 0.277089i | 0.934860 | − | 0.355016i | \(-0.115524\pi\) |
−0.774883 | + | 0.632105i | \(0.782191\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −17.9683 | − | 31.1221i | −0.705318 | − | 1.22165i | ||||
\(650\) | −0.112939 | + | 17.2763i | −0.00442983 | + | 0.677633i | ||||
\(651\) | −3.55197 | + | 25.1548i | −0.139213 | + | 0.985896i | ||||
\(652\) | −4.35887 | + | 7.54979i | −0.170707 | + | 0.295673i | ||||
\(653\) | −19.8789 | −0.777920 | −0.388960 | − | 0.921255i | \(-0.627166\pi\) | ||||
−0.388960 | + | 0.921255i | \(0.627166\pi\) | |||||||
\(654\) | 7.90215 | 0.308999 | ||||||||
\(655\) | 2.15678 | − | 3.73565i | 0.0842723 | − | 0.145964i | ||||
\(656\) | −3.57277 | + | 6.18822i | −0.139493 | + | 0.241609i | ||||
\(657\) | 1.40601 | + | 2.43529i | 0.0548538 | + | 0.0950095i | ||||
\(658\) | 19.2916 | − | 7.77971i | 0.752064 | − | 0.303285i | ||||
\(659\) | −4.78352 | − | 8.28530i | −0.186339 | − | 0.322749i | 0.757688 | − | 0.652617i | \(-0.226329\pi\) |
−0.944027 | + | 0.329868i | \(0.892996\pi\) | |||||||
\(660\) | 1.75127 | 0.0681682 | ||||||||
\(661\) | 5.70934 | + | 9.88887i | 0.222068 | + | 0.384632i | 0.955436 | − | 0.295199i | \(-0.0953861\pi\) |
−0.733368 | + | 0.679832i | \(0.762053\pi\) | |||||||
\(662\) | −8.05285 | + | 13.9480i | −0.312983 | + | 0.542103i | ||||
\(663\) | −4.82732 | − | 2.82929i | −0.187477 | − | 0.109880i | ||||
\(664\) | 1.35738 | 0.0526765 | ||||||||
\(665\) | 0.486660 | − | 3.44649i | 0.0188718 | − | 0.133649i | ||||
\(666\) | −0.140245 | + | 0.242912i | −0.00543440 | + | 0.00941265i | ||||
\(667\) | −7.15336 | + | 12.3900i | −0.276979 | + | 0.479742i | ||||
\(668\) | −11.4560 | + | 19.8424i | −0.443246 | + | 0.767724i | ||||
\(669\) | −13.7584 | −0.531929 | ||||||||
\(670\) | 0.408470 | − | 0.707490i | 0.0157806 | − | 0.0273327i | ||||
\(671\) | 42.6058 | 1.64478 | ||||||||
\(672\) | −2.45374 | + | 0.989520i | −0.0946552 | + | 0.0381716i | ||||
\(673\) | −7.10491 | + | 12.3061i | −0.273874 | + | 0.474364i | −0.969850 | − | 0.243701i | \(-0.921639\pi\) |
0.695976 | + | 0.718065i | \(0.254972\pi\) | |||||||
\(674\) | −14.9134 | −0.574442 | ||||||||
\(675\) | −2.39585 | + | 4.14973i | −0.0922161 | + | 0.159723i | ||||
\(676\) | 6.64663 | − | 11.1724i | 0.255640 | − | 0.429707i | ||||
\(677\) | 7.31125 | + | 12.6635i | 0.280994 | + | 0.486696i | 0.971630 | − | 0.236507i | \(-0.0760025\pi\) |
−0.690636 | + | 0.723203i | \(0.742669\pi\) | |||||||
\(678\) | −3.40689 | + | 5.90091i | −0.130841 | + | 0.226623i | ||||
\(679\) | −23.2563 | + | 9.37855i | −0.892494 | + | 0.359916i | ||||
\(680\) | −0.354144 | − | 0.613395i | −0.0135808 | − | 0.0235226i | ||||
\(681\) | 9.41545 | + | 16.3080i | 0.360801 | + | 0.624925i | ||||
\(682\) | 36.8433 | 1.41080 | ||||||||
\(683\) | −35.1710 | −1.34578 | −0.672890 | − | 0.739743i | \(-0.734947\pi\) | ||||
−0.672890 | + | 0.739743i | \(0.734947\pi\) | |||||||
\(684\) | 1.44122 | + | 2.49627i | 0.0551065 | + | 0.0954472i | ||||
\(685\) | −0.558628 | − | 0.967572i | −0.0213441 | − | 0.0369690i | ||||
\(686\) | 7.56588 | − | 16.9044i | 0.288866 | − | 0.645412i | ||||
\(687\) | −1.74812 | + | 3.02784i | −0.0666950 | + | 0.115519i | ||||
\(688\) | 1.21716 | + | 2.10818i | 0.0464036 | + | 0.0803734i | ||||
\(689\) | −0.0259454 | + | 3.96888i | −0.000988442 | + | 0.151202i | ||||
\(690\) | 0.740157 | − | 1.28199i | 0.0281773 | − | 0.0488045i | ||||
\(691\) | 13.8115 | 0.525413 | 0.262707 | − | 0.964876i | \(-0.415385\pi\) | ||||
0.262707 | + | 0.964876i | \(0.415385\pi\) | |||||||
\(692\) | −3.79358 | + | 6.57067i | −0.144210 | + | 0.249779i | ||||
\(693\) | 1.41942 | − | 10.0522i | 0.0539191 | − | 0.381852i | ||||
\(694\) | 28.8011 | 1.09327 | ||||||||
\(695\) | −2.45196 | + | 4.24691i | −0.0930080 | + | 0.161095i | ||||
\(696\) | −4.41103 | −0.167200 | ||||||||
\(697\) | −5.54447 | + | 9.60331i | −0.210012 | + | 0.363751i | ||||
\(698\) | 2.50740 | − | 4.34294i | 0.0949064 | − | 0.164383i | ||||
\(699\) | −9.74031 | + | 16.8707i | −0.368412 | + | 0.638109i | ||||
\(700\) | 9.98502 | + | 7.81162i | 0.377398 | + | 0.295252i | ||||
\(701\) | −17.6965 | −0.668387 | −0.334193 | − | 0.942504i | \(-0.608464\pi\) | ||||
−0.334193 | + | 0.942504i | \(0.608464\pi\) | |||||||
\(702\) | 3.13422 | − | 1.78233i | 0.118293 | − | 0.0672695i | ||||
\(703\) | 0.404249 | − | 0.700180i | 0.0152465 | − | 0.0264078i | ||||
\(704\) | 1.91853 | + | 3.32300i | 0.0723074 | + | 0.125240i | ||||
\(705\) | −3.58834 | −0.135145 | ||||||||
\(706\) | 5.78333 | + | 10.0170i | 0.217659 | + | 0.376996i | ||||
\(707\) | 15.6110 | − | 6.29545i | 0.587113 | − | 0.236765i | ||||
\(708\) | −4.68283 | − | 8.11090i | −0.175991 | − | 0.304826i | ||||
\(709\) | −17.4342 | + | 30.1969i | −0.654755 | + | 1.13407i | 0.327201 | + | 0.944955i | \(0.393895\pi\) |
−0.981955 | + | 0.189113i | \(0.939439\pi\) | |||||||
\(710\) | −2.31184 | + | 4.00422i | −0.0867617 | + | 0.150276i | ||||
\(711\) | −5.41931 | −0.203240 | ||||||||
\(712\) | −0.179697 | −0.00673443 | ||||||||
\(713\) | 15.5715 | − | 26.9705i | 0.583155 | − | 1.01005i | ||||
\(714\) | −3.80789 | + | 1.53560i | −0.142507 | + | 0.0574686i | ||||
\(715\) | −0.0412771 | + | 6.31417i | −0.00154367 | + | 0.236137i | ||||
\(716\) | −6.25205 | − | 10.8289i | −0.233650 | − | 0.404694i | ||||
\(717\) | 6.27346 | + | 10.8659i | 0.234286 | + | 0.405796i | ||||
\(718\) | −14.9173 | − | 25.8375i | −0.556709 | − | 0.964249i | ||||
\(719\) | −1.55552 | + | 2.69424i | −0.0580112 | + | 0.100478i | −0.893573 | − | 0.448919i | \(-0.851809\pi\) |
0.835561 | + | 0.549397i | \(0.185143\pi\) | |||||||
\(720\) | 0.456409 | 0.0170094 | ||||||||
\(721\) | 40.6798 | − | 16.4049i | 1.51499 | − | 0.610951i | ||||
\(722\) | 5.34576 | + | 9.25913i | 0.198949 | + | 0.344589i | ||||
\(723\) | −0.233225 | − | 0.403958i | −0.00867375 | − | 0.0150234i | ||||
\(724\) | −2.26428 | −0.0841513 | ||||||||
\(725\) | 10.5682 | + | 18.3046i | 0.392491 | + | 0.679815i | ||||
\(726\) | −3.72308 | −0.138176 | ||||||||
\(727\) | 22.0591 | 0.818128 | 0.409064 | − | 0.912506i | \(-0.365855\pi\) | ||||
0.409064 | + | 0.912506i | \(0.365855\pi\) | |||||||
\(728\) | −3.50985 | − | 8.87023i | −0.130084 | − | 0.328752i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.28343 | −0.0475020 | ||||||||
\(731\) | 1.88887 | + | 3.27161i | 0.0698622 | + | 0.121005i | ||||
\(732\) | 11.1037 | 0.410406 | ||||||||
\(733\) | −24.6272 | − | 42.6555i | −0.909626 | − | 1.57552i | −0.814585 | − | 0.580045i | \(-0.803035\pi\) |
−0.0950410 | − | 0.995473i | \(-0.530298\pi\) | |||||||
\(734\) | −3.63895 | − | 6.30284i | −0.134316 | − | 0.232642i | ||||
\(735\) | −2.30108 | + | 2.21635i | −0.0848766 | + | 0.0817512i | ||||
\(736\) | 3.24339 | 0.119553 | ||||||||
\(737\) | −3.43403 | + | 5.94792i | −0.126494 | + | 0.219095i | ||||
\(738\) | −3.57277 | − | 6.18822i | −0.131516 | − | 0.227792i | ||||
\(739\) | 17.0688 | + | 29.5640i | 0.627886 | + | 1.08753i | 0.987975 | + | 0.154613i | \(0.0494130\pi\) |
−0.360089 | + | 0.932918i | \(0.617254\pi\) | |||||||
\(740\) | −0.0640093 | − | 0.110867i | −0.00235303 | − | 0.00407556i | ||||
\(741\) | −9.03420 | + | 5.13745i | −0.331880 | + | 0.188729i | ||||
\(742\) | 2.29386 | + | 1.79456i | 0.0842101 | + | 0.0658804i | ||||
\(743\) | −20.1806 | + | 34.9539i | −0.740356 | + | 1.28233i | 0.211977 | + | 0.977275i | \(0.432010\pi\) |
−0.952333 | + | 0.305060i | \(0.901324\pi\) | |||||||
\(744\) | 9.60195 | 0.352025 | ||||||||
\(745\) | 4.24604 | 0.155563 | ||||||||
\(746\) | −15.5458 | + | 26.9261i | −0.569173 | + | 0.985836i | ||||
\(747\) | −0.678689 | + | 1.17552i | −0.0248320 | + | 0.0430102i | ||||
\(748\) | 2.97731 | + | 5.15686i | 0.108861 | + | 0.188553i | ||||
\(749\) | −6.25925 | + | 44.3276i | −0.228708 | + | 1.61970i | ||||
\(750\) | −2.23451 | − | 3.87028i | −0.0815928 | − | 0.141323i | ||||
\(751\) | −33.8569 | −1.23546 | −0.617729 | − | 0.786391i | \(-0.711947\pi\) | ||||
−0.617729 | + | 0.786391i | \(0.711947\pi\) | |||||||
\(752\) | −3.93105 | − | 6.80879i | −0.143351 | − | 0.248291i | ||||
\(753\) | −12.7935 | + | 22.1590i | −0.466220 | + | 0.807517i | ||||
\(754\) | 0.103967 | − | 15.9039i | 0.00378625 | − | 0.579185i | ||||
\(755\) | 9.46791 | 0.344573 | ||||||||
\(756\) | 0.369922 | − | 2.61976i | 0.0134539 | − | 0.0952799i | ||||
\(757\) | −10.3752 | + | 17.9704i | −0.377094 | + | 0.653146i | −0.990638 | − | 0.136515i | \(-0.956410\pi\) |
0.613544 | + | 0.789660i | \(0.289743\pi\) | |||||||
\(758\) | −9.33146 | + | 16.1626i | −0.338934 | + | 0.587050i | ||||
\(759\) | −6.22256 | + | 10.7778i | −0.225865 | + | 0.391209i | ||||
\(760\) | −1.31557 | −0.0477209 | ||||||||
\(761\) | −0.578590 | + | 1.00215i | −0.0209739 | + | 0.0363278i | −0.876322 | − | 0.481726i | \(-0.840010\pi\) |
0.855348 | + | 0.518054i | \(0.173343\pi\) | |||||||
\(762\) | 21.8668 | 0.792151 | ||||||||
\(763\) | 16.4667 | + | 12.8824i | 0.596133 | + | 0.466375i | ||||
\(764\) | 4.58649 | − | 7.94403i | 0.165933 | − | 0.287405i | ||||
\(765\) | 0.708287 | 0.0256082 | ||||||||
\(766\) | −4.48135 | + | 7.76192i | −0.161918 | + | 0.280450i | ||||
\(767\) | 29.3540 | − | 16.6926i | 1.05991 | − | 0.602737i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 16.9810 | − | 29.4120i | 0.612352 | − | 1.06063i | −0.378491 | − | 0.925605i | \(-0.623557\pi\) |
0.990843 | − | 0.135020i | \(-0.0431099\pi\) | |||||||
\(770\) | 3.64934 | + | 2.85500i | 0.131513 | + | 0.102887i | ||||
\(771\) | −1.88805 | − | 3.27020i | −0.0679966 | − | 0.117774i | ||||
\(772\) | 1.21993 | + | 2.11297i | 0.0439061 | + | 0.0760476i | ||||
\(773\) | −25.5169 | −0.917778 | −0.458889 | − | 0.888494i | \(-0.651753\pi\) | ||||
−0.458889 | + | 0.888494i | \(0.651753\pi\) | |||||||
\(774\) | −2.43431 | −0.0874995 | ||||||||
\(775\) | −23.0048 | − | 39.8455i | −0.826357 | − | 1.43129i | ||||
\(776\) | 4.73894 | + | 8.20808i | 0.170118 | + | 0.294653i | ||||
\(777\) | −0.688252 | + | 0.277551i | −0.0246909 | + | 0.00995709i | ||||
\(778\) | −14.5103 | + | 25.1326i | −0.520220 | + | 0.901048i | ||||
\(779\) | 10.2983 | + | 17.8372i | 0.368975 | + | 0.639084i | ||||
\(780\) | −0.0107575 | + | 1.64557i | −0.000385179 | + | 0.0589209i | ||||
\(781\) | 19.4358 | − | 33.6638i | 0.695467 | − | 1.20458i | ||||
\(782\) | 5.03332 | 0.179991 | ||||||||
\(783\) | 2.20552 | − | 3.82007i | 0.0788187 | − | 0.136518i | ||||
\(784\) | −6.72632 | − | 1.93822i | −0.240226 | − | 0.0692220i | ||||
\(785\) | −2.94567 | −0.105136 | ||||||||
\(786\) | −4.72554 | + | 8.18487i | −0.168554 | + | 0.291945i | ||||
\(787\) | 50.0135 | 1.78279 | 0.891395 | − | 0.453227i | \(-0.149727\pi\) | ||||
0.891395 | + | 0.453227i | \(0.149727\pi\) | |||||||
\(788\) | −13.4334 | + | 23.2673i | −0.478545 | + | 0.828865i | ||||
\(789\) | 9.84358 | − | 17.0496i | 0.350441 | − | 0.606981i | ||||
\(790\) | 1.23671 | − | 2.14205i | 0.0440002 | − | 0.0762107i | ||||
\(791\) | −16.7193 | + | 6.74238i | −0.594469 | + | 0.239731i | ||||
\(792\) | −3.83707 | −0.136344 | ||||||||
\(793\) | −0.261712 | + | 40.0342i | −0.00929368 | + | 1.42166i | ||||
\(794\) | 2.17445 | − | 3.76625i | 0.0771682 | − | 0.133659i | ||||
\(795\) | −0.251206 | − | 0.435102i | −0.00890937 | − | 0.0154315i | ||||
\(796\) | −27.9019 | −0.988957 | ||||||||
\(797\) | 3.59277 | + | 6.22286i | 0.127262 | + | 0.220425i | 0.922615 | − | 0.385722i | \(-0.126048\pi\) |
−0.795353 | + | 0.606147i | \(0.792714\pi\) | |||||||
\(798\) | −1.06628 | + | 7.55132i | −0.0377459 | + | 0.267314i | ||||
\(799\) | −6.10048 | − | 10.5663i | −0.215819 | − | 0.373810i | ||||
\(800\) | 2.39585 | − | 4.14973i | 0.0847059 | − | 0.146715i | ||||
\(801\) | 0.0898485 | − | 0.155622i | 0.00317464 | − | 0.00549864i | ||||
\(802\) | 9.55124 | 0.337266 | ||||||||
\(803\) | 10.7899 | 0.380768 | ||||||||
\(804\) | −0.894964 | + | 1.55012i | −0.0315629 | + | 0.0546686i | ||||
\(805\) | 3.63231 | − | 1.46480i | 0.128022 | − | 0.0516274i | ||||
\(806\) | −0.226316 | + | 34.6196i | −0.00797163 | + | 1.21942i | ||||
\(807\) | −4.39082 | − | 7.60513i | −0.154564 | − | 0.267713i | ||||
\(808\) | −3.18107 | − | 5.50977i | −0.111909 | − | 0.193833i | ||||
\(809\) | −9.92635 | − | 17.1929i | −0.348992 | − | 0.604471i | 0.637079 | − | 0.770799i | \(-0.280143\pi\) |
−0.986071 | + | 0.166327i | \(0.946809\pi\) | |||||||
\(810\) | −0.228205 | + | 0.395262i | −0.00801829 | + | 0.0138881i | ||||
\(811\) | −49.7806 | −1.74803 | −0.874016 | − | 0.485897i | \(-0.838493\pi\) | ||||
−0.874016 | + | 0.485897i | \(0.838493\pi\) | |||||||
\(812\) | −9.19180 | − | 7.19106i | −0.322569 | − | 0.252357i | ||||
\(813\) | 14.4014 | + | 24.9439i | 0.505077 | + | 0.874820i | ||||
\(814\) | 0.538131 | + | 0.932070i | 0.0188615 | + | 0.0326690i | ||||
\(815\) | 3.97886 | 0.139373 | ||||||||
\(816\) | 0.775934 | + | 1.34396i | 0.0271631 | + | 0.0470479i | ||||
\(817\) | 7.01676 | 0.245485 | ||||||||
\(818\) | 1.27024 | 0.0444130 | ||||||||
\(819\) | 9.43677 | + | 1.39549i | 0.329747 | + | 0.0487624i | ||||
\(820\) | 3.26129 | 0.113889 | ||||||||
\(821\) | −13.1416 | −0.458644 | −0.229322 | − | 0.973351i | \(-0.573651\pi\) | ||||
−0.229322 | + | 0.973351i | \(0.573651\pi\) | |||||||
\(822\) | 1.22396 | + | 2.11996i | 0.0426906 | + | 0.0739422i | ||||
\(823\) | 33.0483 | 1.15199 | 0.575995 | − | 0.817453i | \(-0.304615\pi\) | ||||
0.575995 | + | 0.817453i | \(0.304615\pi\) | |||||||
\(824\) | −8.28934 | − | 14.3576i | −0.288773 | − | 0.500169i | ||||
\(825\) | 9.19302 | + | 15.9228i | 0.320060 | + | 0.554360i | ||||
\(826\) | 3.46456 | − | 24.5358i | 0.120548 | − | 0.853710i | ||||
\(827\) | 14.9763 | 0.520779 | 0.260389 | − | 0.965504i | \(-0.416149\pi\) | ||||
0.260389 | + | 0.965504i | \(0.416149\pi\) | |||||||
\(828\) | −1.62170 | + | 2.80886i | −0.0563578 | + | 0.0976146i | ||||
\(829\) | 27.8983 | + | 48.3212i | 0.968947 | + | 1.67827i | 0.698613 | + | 0.715500i | \(0.253801\pi\) |
0.270334 | + | 0.962767i | \(0.412866\pi\) | |||||||
\(830\) | −0.309760 | − | 0.536520i | −0.0107519 | − | 0.0186229i | ||||
\(831\) | 3.47496 | + | 6.01880i | 0.120545 | + | 0.208790i | ||||
\(832\) | −3.13422 | + | 1.78233i | −0.108659 | + | 0.0617910i | ||||
\(833\) | −10.4384 | − | 3.00786i | −0.361668 | − | 0.104216i | ||||
\(834\) | 5.37228 | − | 9.30505i | 0.186027 | − | 0.322208i | ||||
\(835\) | 10.4572 | 0.361888 | ||||||||
\(836\) | 11.0601 | 0.382522 | ||||||||
\(837\) | −4.80098 | + | 8.31553i | −0.165946 | + | 0.287427i | ||||
\(838\) | 5.25472 | − | 9.10144i | 0.181521 | − | 0.314404i | ||||
\(839\) | 26.0623 | + | 45.1412i | 0.899770 | + | 1.55845i | 0.827788 | + | 0.561041i | \(0.189599\pi\) |
0.0719812 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(840\) | 0.951075 | + | 0.744058i | 0.0328152 | + | 0.0256724i | ||||
\(841\) | 4.77139 | + | 8.26429i | 0.164531 | + | 0.284976i | ||||
\(842\) | −1.14121 | −0.0393287 | ||||||||
\(843\) | −6.25581 | − | 10.8354i | −0.215462 | − | 0.373190i | ||||
\(844\) | 10.9871 | − | 19.0301i | 0.378190 | − | 0.655045i | ||||
\(845\) | −5.93281 | − | 0.0775714i | −0.204095 | − | 0.00266854i | ||||
\(846\) | 7.86211 | 0.270305 | ||||||||
\(847\) | −7.75823 | − | 6.06953i | −0.266576 | − | 0.208551i | ||||
\(848\) | 0.550397 | − | 0.953315i | 0.0189007 | − | 0.0327370i | ||||
\(849\) | 5.60195 | − | 9.70287i | 0.192258 | − | 0.333001i | ||||
\(850\) | 3.71804 | − | 6.43983i | 0.127528 | − | 0.220884i | ||||
\(851\) | 0.909741 | 0.0311855 | ||||||||
\(852\) | 5.06527 | − | 8.77331i | 0.173533 | − | 0.300569i | ||||
\(853\) | 23.6670 | 0.810344 | 0.405172 | − | 0.914241i | \(-0.367212\pi\) | ||||
0.405172 | + | 0.914241i | \(0.367212\pi\) | |||||||
\(854\) | 23.1382 | + | 18.1018i | 0.791773 | + | 0.619431i | ||||
\(855\) | 0.657787 | − | 1.13932i | 0.0224958 | − | 0.0389639i | ||||
\(856\) | 16.9205 | 0.578330 | ||||||||
\(857\) | −24.0347 | + | 41.6292i | −0.821008 | + | 1.42203i | 0.0839243 | + | 0.996472i | \(0.473255\pi\) |
−0.904932 | + | 0.425556i | \(0.860079\pi\) | |||||||
\(858\) | 0.0904387 | − | 13.8344i | 0.00308753 | − | 0.472300i | ||||
\(859\) | 7.34891 | + | 12.7287i | 0.250742 | + | 0.434297i | 0.963730 | − | 0.266878i | \(-0.0859922\pi\) |
−0.712989 | + | 0.701176i | \(0.752659\pi\) | |||||||
\(860\) | 0.555521 | − | 0.962191i | 0.0189431 | − | 0.0328104i | ||||
\(861\) | 2.64329 | − | 18.7196i | 0.0900832 | − | 0.637963i | ||||
\(862\) | −15.6637 | − | 27.1303i | −0.533507 | − | 0.924062i | ||||
\(863\) | −13.6332 | − | 23.6134i | −0.464080 | − | 0.803810i | 0.535080 | − | 0.844802i | \(-0.320282\pi\) |
−0.999159 | + | 0.0409917i | \(0.986948\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 3.46285 | 0.117740 | ||||||||
\(866\) | −7.06113 | − | 12.2302i | −0.239947 | − | 0.415600i | ||||
\(867\) | −7.29585 | − | 12.6368i | −0.247780 | − | 0.429168i | ||||
\(868\) | 20.0087 | + | 15.6535i | 0.679141 | + | 0.531315i | ||||
\(869\) | −10.3971 | + | 18.0084i | −0.352698 | + | 0.610892i | ||||
\(870\) | 1.00662 | + | 1.74351i | 0.0341276 | + | 0.0591107i | ||||
\(871\) | −5.56783 | − | 3.26330i | −0.188659 | − | 0.110573i | ||||
\(872\) | 3.95108 | − | 6.84346i | 0.133800 | − | 0.231749i | ||||
\(873\) | −9.47788 | −0.320778 | ||||||||
\(874\) | 4.67445 | − | 8.09638i | 0.158116 | − | 0.273864i | ||||
\(875\) | 1.65319 | − | 11.7078i | 0.0558880 | − | 0.395795i | ||||
\(876\) | 2.81202 | 0.0950095 | ||||||||
\(877\) | 13.6066 | − | 23.5673i | 0.459461 | − | 0.795811i | −0.539471 | − | 0.842004i | \(-0.681376\pi\) |
0.998933 | + | 0.0461935i | \(0.0147091\pi\) | |||||||
\(878\) | −6.46132 | −0.218059 | ||||||||
\(879\) | −14.2699 | + | 24.7162i | −0.481312 | + | 0.833657i | ||||
\(880\) | 0.875637 | − | 1.51665i | 0.0295177 | − | 0.0511262i | ||||
\(881\) | 5.52376 | − | 9.56743i | 0.186100 | − | 0.322335i | −0.757847 | − | 0.652433i | \(-0.773748\pi\) |
0.943947 | + | 0.330098i | \(0.107082\pi\) | |||||||
\(882\) | 5.04170 | − | 4.85605i | 0.169763 | − | 0.163512i | ||||
\(883\) | 42.1202 | 1.41746 | 0.708729 | − | 0.705481i | \(-0.249269\pi\) | ||||
0.708729 | + | 0.705481i | \(0.249269\pi\) | |||||||
\(884\) | −4.86389 | + | 2.76593i | −0.163590 | + | 0.0930285i | ||||
\(885\) | −2.13729 | + | 3.70189i | −0.0718441 | + | 0.124438i | ||||
\(886\) | −5.70730 | − | 9.88534i | −0.191741 | − | 0.332104i | ||||
\(887\) | 45.4690 | 1.52670 | 0.763349 | − | 0.645986i | \(-0.223554\pi\) | ||||
0.763349 | + | 0.645986i | \(0.223554\pi\) | |||||||
\(888\) | 0.140245 | + | 0.242912i | 0.00470632 | + | 0.00815159i | ||||
\(889\) | 45.5665 | + | 35.6482i | 1.52825 | + | 1.19560i | ||||
\(890\) | 0.0410077 | + | 0.0710274i | 0.00137458 | + | 0.00238084i | ||||
\(891\) | 1.91853 | − | 3.32300i | 0.0642733 | − | 0.111325i | ||||
\(892\) | −6.87919 | + | 11.9151i | −0.230332 | + | 0.398947i | ||||
\(893\) | −22.6621 | −0.758357 | ||||||||
\(894\) | −9.30314 | −0.311144 | ||||||||
\(895\) | −2.85349 | + | 4.94240i | −0.0953818 | + | 0.165206i | ||||
\(896\) | −0.369922 | + | 2.61976i | −0.0123582 | + | 0.0875201i | ||||
\(897\) | −10.0891 | − | 5.91319i | −0.336864 | − | 0.197436i | ||||
\(898\) | −19.8942 | − | 34.4578i | −0.663879 | − | 1.14987i | ||||
\(899\) | 21.1773 | + | 36.6801i | 0.706301 | + | 1.22335i | ||||
\(900\) | 2.39585 | + | 4.14973i | 0.0798615 | + | 0.138324i | ||||
\(901\) | 0.854144 | − | 1.47942i | 0.0284557 | − | 0.0492866i | ||||
\(902\) | −27.4179 | −0.912917 | ||||||||
\(903\) | −5.07267 | − | 3.96852i | −0.168808 | − | 0.132064i | ||||
\(904\) | 3.40689 | + | 5.90091i | 0.113312 | + | 0.196261i | ||||
\(905\) | 0.516719 | + | 0.894984i | 0.0171763 | + | 0.0297503i | ||||
\(906\) | −20.7443 | −0.689185 | ||||||||
\(907\) | 20.8135 | + | 36.0500i | 0.691101 | + | 1.19702i | 0.971478 | + | 0.237132i | \(0.0762073\pi\) |
−0.280377 | + | 0.959890i | \(0.590459\pi\) | |||||||
\(908\) | 18.8309 | 0.624925 | ||||||||
\(909\) | 6.36213 | 0.211019 | ||||||||
\(910\) | −2.70510 | + | 3.41154i | −0.0896732 | + | 0.113091i | ||||
\(911\) | 50.3137 | 1.66697 | 0.833484 | − | 0.552544i | \(-0.186343\pi\) | ||||
0.833484 | + | 0.552544i | \(0.186343\pi\) | |||||||
\(912\) | 2.88244 | 0.0954472 | ||||||||
\(913\) | 2.60418 | + | 4.51057i | 0.0861857 | + | 0.149278i | ||||
\(914\) | −5.25285 | −0.173749 | ||||||||
\(915\) | −2.53392 | − | 4.38889i | −0.0837690 | − | 0.145092i | ||||
\(916\) | 1.74812 | + | 3.02784i | 0.0577596 | + | 0.100043i | ||||
\(917\) | −23.1905 | + | 9.35202i | −0.765818 | + | 0.308831i | ||||
\(918\) | −1.55187 | −0.0512193 | ||||||||
\(919\) | −13.8093 | + | 23.9184i | −0.455526 | + | 0.788994i | −0.998718 | − | 0.0506142i | \(-0.983882\pi\) |
0.543192 | + | 0.839608i | \(0.317215\pi\) | |||||||
\(920\) | −0.740157 | − | 1.28199i | −0.0244023 | − | 0.0422660i | ||||
\(921\) | −11.5953 | − | 20.0837i | −0.382079 | − | 0.661781i | ||||
\(922\) | 9.59122 | + | 16.6125i | 0.315870 | + | 0.547103i | ||||
\(923\) | 31.5125 | + | 18.4695i | 1.03725 | + | 0.607931i | ||||
\(924\) | −7.99576 | − | 6.25535i | −0.263041 | − | 0.205786i | ||||
\(925\) | 0.672012 | − | 1.16396i | 0.0220956 | − | 0.0382707i | ||||
\(926\) | −17.5580 | −0.576990 | ||||||||
\(927\) | 16.5787 | 0.544515 | ||||||||
\(928\) | −2.20552 | + | 3.82007i | −0.0723996 | + | 0.125400i | ||||
\(929\) | −6.14703 | + | 10.6470i | −0.201677 | + | 0.349316i | −0.949069 | − | 0.315068i | \(-0.897973\pi\) |
0.747392 | + | 0.664384i | \(0.231306\pi\) | |||||||
\(930\) | −2.19121 | − | 3.79529i | −0.0718526 | − | 0.124452i | ||||
\(931\) | −14.5324 | + | 13.9973i | −0.476281 | + | 0.458743i | ||||
\(932\) | 9.74031 | + | 16.8707i | 0.319054 | + | 0.552618i | ||||
\(933\) | 23.3481 | 0.764381 | ||||||||
\(934\) | −1.54111 | − | 2.66928i | −0.0504267 | − | 0.0873416i | ||||
\(935\) | 1.35887 | − | 2.35364i | 0.0444399 | − | 0.0769722i | ||||
\(936\) | 0.0235697 | − | 3.60547i | 0.000770401 | − | 0.117849i | ||||
\(937\) | 10.2719 | 0.335569 | 0.167785 | − | 0.985824i | \(-0.446339\pi\) | ||||
0.167785 | + | 0.985824i | \(0.446339\pi\) | |||||||
\(938\) | −4.39202 | + | 1.77117i | −0.143405 | + | 0.0578307i | ||||
\(939\) | −7.26499 | + | 12.5833i | −0.237084 | + | 0.410641i | ||||
\(940\) | −1.79417 | + | 3.10759i | −0.0585194 | + | 0.101359i | ||||
\(941\) | −22.3097 | + | 38.6416i | −0.727276 | + | 1.25968i | 0.230754 | + | 0.973012i | \(0.425881\pi\) |
−0.958030 | + | 0.286667i | \(0.907453\pi\) | |||||||
\(942\) | 6.45402 | 0.210283 | ||||||||
\(943\) | −11.5879 | + | 20.0708i | −0.377354 | + | 0.653596i | ||||
\(944\) | −9.36566 | −0.304826 | ||||||||
\(945\) | −1.11991 | + | 0.451626i | −0.0364307 | + | 0.0146914i | ||||
\(946\) | −4.67031 | + | 8.08921i | −0.151845 | + | 0.263003i | ||||
\(947\) | −27.4108 | −0.890732 | −0.445366 | − | 0.895349i | \(-0.646926\pi\) | ||||
−0.445366 | + | 0.895349i | \(0.646926\pi\) | |||||||
\(948\) | −2.70966 | + | 4.69326i | −0.0880055 | + | 0.152430i | ||||
\(949\) | −0.0662787 | + | 10.1387i | −0.00215150 | + | 0.329116i | ||||
\(950\) | −6.90589 | − | 11.9613i | −0.224057 | − | 0.388077i | ||||
\(951\) | −1.64596 | + | 2.85089i | −0.0533739 | + | 0.0924463i | ||||
\(952\) | −0.574070 | + | 4.06553i | −0.0186057 | + | 0.131765i | ||||
\(953\) | −21.0794 | − | 36.5107i | −0.682830 | − | 1.18270i | −0.974114 | − | 0.226059i | \(-0.927416\pi\) |
0.291284 | − | 0.956637i | \(-0.405918\pi\) | |||||||
\(954\) | 0.550397 | + | 0.953315i | 0.0178198 | + | 0.0308647i | ||||
\(955\) | −4.18663 | −0.135476 | ||||||||
\(956\) | 12.5469 | 0.405796 | ||||||||
\(957\) | −8.46271 | − | 14.6579i | −0.273561 | − | 0.473821i | ||||
\(958\) | −9.18104 | − | 15.9020i | −0.296626 | − | 0.513771i | ||||
\(959\) | −0.905541 | + | 6.41298i | −0.0292414 | + | 0.207086i | ||||
\(960\) | 0.228205 | − | 0.395262i | 0.00736527 | − | 0.0127570i | ||||
\(961\) | −30.5987 | − | 52.9986i | −0.987056 | − | 1.70963i | ||||
\(962\) | −0.879119 | + | 0.499926i | −0.0283439 | + | 0.0161182i | ||||
\(963\) | −8.46023 | + | 14.6536i | −0.272627 | + | 0.472204i | ||||
\(964\) | −0.466451 | −0.0150234 | ||||||||
\(965\) | 0.556786 | − | 0.964381i | 0.0179236 | − | 0.0310445i | ||||
\(966\) | −7.95845 | + | 3.20940i | −0.256059 | + | 0.103261i | ||||
\(967\) | 49.9926 | 1.60765 | 0.803827 | − | 0.594863i | \(-0.202794\pi\) | ||||
0.803827 | + | 0.594863i | \(0.202794\pi\) | |||||||
\(968\) | −1.86154 | + | 3.22428i | −0.0598322 | + | 0.103632i | ||||
\(969\) | 4.47317 | 0.143699 | ||||||||
\(970\) | 2.16290 | − | 3.74625i | 0.0694464 | − | 0.120285i | ||||
\(971\) | 5.53767 | − | 9.59152i | 0.177712 | − | 0.307806i | −0.763384 | − | 0.645945i | \(-0.776464\pi\) |
0.941097 | + | 0.338138i | \(0.109797\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 26.3644 | − | 10.6319i | 0.845203 | − | 0.340845i | ||||
\(974\) | 18.0106 | 0.577097 | ||||||||
\(975\) | −15.0182 | + | 8.54035i | −0.480967 | + | 0.273510i | ||||
\(976\) | 5.55187 | − | 9.61612i | 0.177711 | − | 0.307804i | ||||
\(977\) | −26.1222 | − | 45.2449i | −0.835722 | − | 1.44751i | −0.893441 | − | 0.449180i | \(-0.851716\pi\) |
0.0577193 | − | 0.998333i | \(-0.481617\pi\) | |||||||
\(978\) | −8.71775 | −0.278763 | ||||||||
\(979\) | −0.344755 | − | 0.597132i | −0.0110184 | − | 0.0190844i | ||||
\(980\) | 0.768874 | + | 3.10097i | 0.0245608 | + | 0.0990568i | ||||
\(981\) | 3.95108 | + | 6.84346i | 0.126148 | + | 0.218495i | ||||
\(982\) | −7.98794 | + | 13.8355i | −0.254906 | + | 0.441509i | ||||
\(983\) | 18.4322 | − | 31.9255i | 0.587896 | − | 1.01827i | −0.406611 | − | 0.913601i | \(-0.633290\pi\) |
0.994508 | − | 0.104665i | \(-0.0333770\pi\) | |||||||
\(984\) | −7.14554 | −0.227792 | ||||||||
\(985\) | 12.2623 | 0.390708 | ||||||||
\(986\) | −3.42267 | + | 5.92824i | −0.109000 | + | 0.188794i | ||||
\(987\) | 16.3832 | + | 12.8171i | 0.521484 | + | 0.407974i | ||||
\(988\) | −0.0679384 | + | 10.3926i | −0.00216141 | + | 0.330632i | ||||
\(989\) | 3.94771 | + | 6.83764i | 0.125530 | + | 0.217424i | ||||
\(990\) | 0.875637 | + | 1.51665i | 0.0278296 | + | 0.0482022i | ||||
\(991\) | −26.1658 | − | 45.3204i | −0.831182 | − | 1.43965i | −0.897101 | − | 0.441825i | \(-0.854331\pi\) |
0.0659186 | − | 0.997825i | \(-0.479002\pi\) | |||||||
\(992\) | 4.80098 | − | 8.31553i | 0.152431 | − | 0.264018i | ||||
\(993\) | −16.1057 | −0.511099 | ||||||||
\(994\) | 24.8577 | − | 10.0244i | 0.788440 | − | 0.317954i | ||||
\(995\) | 6.36734 | + | 11.0286i | 0.201858 | + | 0.349629i | ||||
\(996\) | 0.678689 | + | 1.17552i | 0.0215051 | + | 0.0372479i | ||||
\(997\) | −20.0859 | −0.636126 | −0.318063 | − | 0.948070i | \(-0.603032\pi\) | ||||
−0.318063 | + | 0.948070i | \(0.603032\pi\) | |||||||
\(998\) | −4.06656 | − | 7.04348i | −0.128725 | − | 0.222957i | ||||
\(999\) | −0.280491 | −0.00887433 |
(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 | 546.2.j.d.529.2 | yes | 8 | |
3.2 | odd | 2 | 1638.2.m.g.1621.3 | 8 | |||
7.2 | even | 3 | 546.2.k.b.373.2 | yes | 8 | ||
13.3 | even | 3 | 546.2.k.b.445.2 | yes | 8 | ||
21.2 | odd | 6 | 1638.2.p.i.919.3 | 8 | |||
39.29 | odd | 6 | 1638.2.p.i.991.3 | 8 | |||
91.16 | even | 3 | inner | 546.2.j.d.289.2 | ✓ | 8 | |
273.107 | odd | 6 | 1638.2.m.g.289.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.d.289.2 | ✓ | 8 | 91.16 | even | 3 | inner | |
546.2.j.d.529.2 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.k.b.373.2 | yes | 8 | 7.2 | even | 3 | ||
546.2.k.b.445.2 | yes | 8 | 13.3 | even | 3 | ||
1638.2.m.g.289.3 | 8 | 273.107 | odd | 6 | |||
1638.2.m.g.1621.3 | 8 | 3.2 | odd | 2 | |||
1638.2.p.i.919.3 | 8 | 21.2 | odd | 6 | |||
1638.2.p.i.991.3 | 8 | 39.29 | odd | 6 |