Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(391,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.391");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.6 | ||
Root | \(-0.449546 + 1.34086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.391 |
Dual form | 420.2.c.a.391.5 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.449546 | + | 1.34086i | −0.317877 | + | 0.948132i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.59582 | − | 1.20556i | −0.797908 | − | 0.602779i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0.449546 | − | 1.34086i | 0.183527 | − | 0.547404i | ||||
\(7\) | 1.40015 | + | 2.24490i | 0.529207 | + | 0.848493i | ||||
\(8\) | 2.33388 | − | 1.59781i | 0.825151 | − | 0.564912i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.34086 | − | 0.449546i | −0.424017 | − | 0.142159i | ||||
\(11\) | 3.99156i | 1.20350i | 0.798684 | + | 0.601751i | \(0.205530\pi\) | ||||
−0.798684 | + | 0.601751i | \(0.794470\pi\) | |||||||
\(12\) | 1.59582 | + | 1.20556i | 0.460672 | + | 0.348015i | ||||
\(13\) | − | 2.50547i | − | 0.694892i | −0.937700 | − | 0.347446i | \(-0.887049\pi\) | ||
0.937700 | − | 0.347446i | \(-0.112951\pi\) | |||||||
\(14\) | −3.63953 | + | 0.868219i | −0.972706 | + | 0.232041i | ||||
\(15\) | − | 1.00000i | − | 0.258199i | ||||||
\(16\) | 1.09326 | + | 3.84770i | 0.273315 | + | 0.961925i | ||||
\(17\) | − | 1.07705i | − | 0.261223i | −0.991434 | − | 0.130611i | \(-0.958306\pi\) | ||
0.991434 | − | 0.130611i | \(-0.0416940\pi\) | |||||||
\(18\) | −0.449546 | + | 1.34086i | −0.105959 | + | 0.316044i | ||||
\(19\) | −7.78975 | −1.78709 | −0.893546 | − | 0.448973i | \(-0.851790\pi\) | ||||
−0.893546 | + | 0.448973i | \(0.851790\pi\) | |||||||
\(20\) | 1.20556 | − | 1.59582i | 0.269571 | − | 0.356835i | ||||
\(21\) | −1.40015 | − | 2.24490i | −0.305538 | − | 0.489878i | ||||
\(22\) | −5.35213 | − | 1.79439i | −1.14108 | − | 0.382566i | ||||
\(23\) | 8.10651i | 1.69033i | 0.534509 | + | 0.845163i | \(0.320496\pi\) | ||||
−0.534509 | + | 0.845163i | \(0.679504\pi\) | |||||||
\(24\) | −2.33388 | + | 1.59781i | −0.476401 | + | 0.326152i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.35948 | + | 1.12632i | 0.658849 | + | 0.220890i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.471978 | − | 5.27041i | 0.0891955 | − | 0.996014i | ||||
\(29\) | −5.99783 | −1.11377 | −0.556885 | − | 0.830590i | \(-0.688003\pi\) | ||||
−0.556885 | + | 0.830590i | \(0.688003\pi\) | |||||||
\(30\) | 1.34086 | + | 0.449546i | 0.244807 | + | 0.0820756i | ||||
\(31\) | −6.32559 | −1.13611 | −0.568055 | − | 0.822991i | \(-0.692304\pi\) | ||||
−0.568055 | + | 0.822991i | \(0.692304\pi\) | |||||||
\(32\) | −5.65070 | − | 0.263812i | −0.998912 | − | 0.0466358i | ||||
\(33\) | − | 3.99156i | − | 0.694842i | ||||||
\(34\) | 1.44417 | + | 0.484184i | 0.247674 | + | 0.0830368i | ||||
\(35\) | −2.24490 | + | 1.40015i | −0.379458 | + | 0.236668i | ||||
\(36\) | −1.59582 | − | 1.20556i | −0.265969 | − | 0.200926i | ||||
\(37\) | 3.05357 | 0.502003 | 0.251002 | − | 0.967987i | \(-0.419240\pi\) | ||||
0.251002 | + | 0.967987i | \(0.419240\pi\) | |||||||
\(38\) | 3.50185 | − | 10.4450i | 0.568076 | − | 1.69440i | ||||
\(39\) | 2.50547i | 0.401196i | ||||||||
\(40\) | 1.59781 | + | 2.33388i | 0.252636 | + | 0.369019i | ||||
\(41\) | 9.32685i | 1.45661i | 0.685254 | + | 0.728305i | \(0.259691\pi\) | ||||
−0.685254 | + | 0.728305i | \(0.740309\pi\) | |||||||
\(42\) | 3.63953 | − | 0.868219i | 0.561592 | − | 0.133969i | ||||
\(43\) | − | 8.13000i | − | 1.23981i | −0.784676 | − | 0.619906i | \(-0.787171\pi\) | ||
0.784676 | − | 0.619906i | \(-0.212829\pi\) | |||||||
\(44\) | 4.81206 | − | 6.36980i | 0.725446 | − | 0.960284i | ||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | −10.8697 | − | 3.64425i | −1.60265 | − | 0.537316i | ||||
\(47\) | 9.01476 | 1.31494 | 0.657469 | − | 0.753482i | \(-0.271627\pi\) | ||||
0.657469 | + | 0.753482i | \(0.271627\pi\) | |||||||
\(48\) | −1.09326 | − | 3.84770i | −0.157798 | − | 0.555367i | ||||
\(49\) | −3.07916 | + | 6.28639i | −0.439880 | + | 0.898056i | ||||
\(50\) | 0.449546 | − | 1.34086i | 0.0635755 | − | 0.189626i | ||||
\(51\) | 1.07705i | 0.150817i | ||||||||
\(52\) | −3.02049 | + | 3.99827i | −0.418866 | + | 0.554460i | ||||
\(53\) | 2.86521 | 0.393566 | 0.196783 | − | 0.980447i | \(-0.436951\pi\) | ||||
0.196783 | + | 0.980447i | \(0.436951\pi\) | |||||||
\(54\) | 0.449546 | − | 1.34086i | 0.0611755 | − | 0.182468i | ||||
\(55\) | −3.99156 | −0.538222 | ||||||||
\(56\) | 6.85471 | + | 3.00215i | 0.916000 | + | 0.401179i | ||||
\(57\) | 7.78975 | 1.03178 | ||||||||
\(58\) | 2.69630 | − | 8.04226i | 0.354042 | − | 1.05600i | ||||
\(59\) | 9.68276 | 1.26059 | 0.630294 | − | 0.776356i | \(-0.282934\pi\) | ||||
0.630294 | + | 0.776356i | \(0.282934\pi\) | |||||||
\(60\) | −1.20556 | + | 1.59582i | −0.155637 | + | 0.206019i | ||||
\(61\) | 3.21235i | 0.411299i | 0.978626 | + | 0.205649i | \(0.0659307\pi\) | ||||
−0.978626 | + | 0.205649i | \(0.934069\pi\) | |||||||
\(62\) | 2.84365 | − | 8.48173i | 0.361143 | − | 1.07718i | ||||
\(63\) | 1.40015 | + | 2.24490i | 0.176402 | + | 0.282831i | ||||
\(64\) | 2.89399 | − | 7.45821i | 0.361748 | − | 0.932276i | ||||
\(65\) | 2.50547 | 0.310765 | ||||||||
\(66\) | 5.35213 | + | 1.79439i | 0.658802 | + | 0.220875i | ||||
\(67\) | 7.79060i | 0.951773i | 0.879507 | + | 0.475887i | \(0.157873\pi\) | ||||
−0.879507 | + | 0.475887i | \(0.842127\pi\) | |||||||
\(68\) | −1.29845 | + | 1.71877i | −0.157460 | + | 0.208432i | ||||
\(69\) | − | 8.10651i | − | 0.975910i | ||||||
\(70\) | −0.868219 | − | 3.63953i | −0.103772 | − | 0.435007i | ||||
\(71\) | − | 5.84987i | − | 0.694252i | −0.937819 | − | 0.347126i | \(-0.887158\pi\) | ||
0.937819 | − | 0.347126i | \(-0.112842\pi\) | |||||||
\(72\) | 2.33388 | − | 1.59781i | 0.275050 | − | 0.188304i | ||||
\(73\) | − | 5.73252i | − | 0.670941i | −0.942051 | − | 0.335470i | \(-0.891105\pi\) | ||
0.942051 | − | 0.335470i | \(-0.108895\pi\) | |||||||
\(74\) | −1.37272 | + | 4.09441i | −0.159575 | + | 0.475965i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 12.4310 | + | 9.39100i | 1.42593 | + | 1.07722i | ||||
\(77\) | −8.96067 | + | 5.58879i | −1.02116 | + | 0.636901i | ||||
\(78\) | −3.35948 | − | 1.12632i | −0.380387 | − | 0.127531i | ||||
\(79\) | 2.81801i | 0.317050i | 0.987355 | + | 0.158525i | \(0.0506739\pi\) | ||||
−0.987355 | + | 0.158525i | \(0.949326\pi\) | |||||||
\(80\) | −3.84770 | + | 1.09326i | −0.430186 | + | 0.122230i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.5060 | − | 4.19285i | −1.38106 | − | 0.463023i | ||||
\(83\) | −12.5103 | −1.37318 | −0.686590 | − | 0.727045i | \(-0.740893\pi\) | ||||
−0.686590 | + | 0.727045i | \(0.740893\pi\) | |||||||
\(84\) | −0.471978 | + | 5.27041i | −0.0514970 | + | 0.575049i | ||||
\(85\) | 1.07705 | 0.116822 | ||||||||
\(86\) | 10.9012 | + | 3.65481i | 1.17551 | + | 0.394108i | ||||
\(87\) | 5.99783 | 0.643035 | ||||||||
\(88\) | 6.37777 | + | 9.31583i | 0.679873 | + | 0.993071i | ||||
\(89\) | 3.51385i | 0.372467i | 0.982505 | + | 0.186234i | \(0.0596282\pi\) | ||||
−0.982505 | + | 0.186234i | \(0.940372\pi\) | |||||||
\(90\) | −1.34086 | − | 0.449546i | −0.141339 | − | 0.0473863i | ||||
\(91\) | 5.62453 | − | 3.50803i | 0.589611 | − | 0.367741i | ||||
\(92\) | 9.77288 | − | 12.9365i | 1.01889 | − | 1.34872i | ||||
\(93\) | 6.32559 | 0.655933 | ||||||||
\(94\) | −4.05255 | + | 12.0875i | −0.417989 | + | 1.24673i | ||||
\(95\) | − | 7.78975i | − | 0.799211i | ||||||
\(96\) | 5.65070 | + | 0.263812i | 0.576722 | + | 0.0269252i | ||||
\(97\) | 12.0136i | 1.21980i | 0.792479 | + | 0.609899i | \(0.208790\pi\) | ||||
−0.792479 | + | 0.609899i | \(0.791210\pi\) | |||||||
\(98\) | −7.04495 | − | 6.95475i | −0.711648 | − | 0.702536i | ||||
\(99\) | 3.99156i | 0.401167i | ||||||||
\(100\) | 1.59582 | + | 1.20556i | 0.159582 | + | 0.120556i | ||||
\(101\) | 0.260498i | 0.0259205i | 0.999916 | + | 0.0129602i | \(0.00412549\pi\) | ||||
−0.999916 | + | 0.0129602i | \(0.995875\pi\) | |||||||
\(102\) | −1.44417 | − | 0.484184i | −0.142994 | − | 0.0479413i | ||||
\(103\) | 1.76484 | 0.173895 | 0.0869475 | − | 0.996213i | \(-0.472289\pi\) | ||||
0.0869475 | + | 0.996213i | \(0.472289\pi\) | |||||||
\(104\) | −4.00327 | − | 5.84746i | −0.392553 | − | 0.573391i | ||||
\(105\) | 2.24490 | − | 1.40015i | 0.219080 | − | 0.136641i | ||||
\(106\) | −1.28804 | + | 3.84184i | −0.125106 | + | 0.373153i | ||||
\(107\) | 6.10229i | 0.589930i | 0.955508 | + | 0.294965i | \(0.0953081\pi\) | ||||
−0.955508 | + | 0.294965i | \(0.904692\pi\) | |||||||
\(108\) | 1.59582 | + | 1.20556i | 0.153557 | + | 0.116005i | ||||
\(109\) | 14.9561 | 1.43253 | 0.716265 | − | 0.697828i | \(-0.245850\pi\) | ||||
0.716265 | + | 0.697828i | \(0.245850\pi\) | |||||||
\(110\) | 1.79439 | − | 5.35213i | 0.171089 | − | 0.510306i | ||||
\(111\) | −3.05357 | −0.289832 | ||||||||
\(112\) | −7.10698 | + | 7.84161i | −0.671546 | + | 0.740963i | ||||
\(113\) | 11.8448 | 1.11427 | 0.557133 | − | 0.830423i | \(-0.311901\pi\) | ||||
0.557133 | + | 0.830423i | \(0.311901\pi\) | |||||||
\(114\) | −3.50185 | + | 10.4450i | −0.327979 | + | 0.978261i | ||||
\(115\) | −8.10651 | −0.755936 | ||||||||
\(116\) | 9.57144 | + | 7.23074i | 0.888686 | + | 0.671357i | ||||
\(117\) | − | 2.50547i | − | 0.231631i | ||||||
\(118\) | −4.35285 | + | 12.9832i | −0.400712 | + | 1.19520i | ||||
\(119\) | 2.41787 | − | 1.50803i | 0.221646 | − | 0.138241i | ||||
\(120\) | −1.59781 | − | 2.33388i | −0.145860 | − | 0.213053i | ||||
\(121\) | −4.93258 | −0.448416 | ||||||||
\(122\) | −4.30731 | − | 1.44410i | −0.389966 | − | 0.130743i | ||||
\(123\) | − | 9.32685i | − | 0.840974i | ||||||
\(124\) | 10.0945 | + | 7.62587i | 0.906511 | + | 0.684823i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −3.63953 | + | 0.868219i | −0.324235 | + | 0.0773471i | ||||
\(127\) | − | 5.49406i | − | 0.487519i | −0.969836 | − | 0.243760i | \(-0.921619\pi\) | ||
0.969836 | − | 0.243760i | \(-0.0783808\pi\) | |||||||
\(128\) | 8.69944 | + | 7.23324i | 0.768929 | + | 0.639334i | ||||
\(129\) | 8.13000i | 0.715806i | ||||||||
\(130\) | −1.12632 | + | 3.35948i | −0.0987852 | + | 0.294646i | ||||
\(131\) | −9.93971 | −0.868436 | −0.434218 | − | 0.900808i | \(-0.642975\pi\) | ||||
−0.434218 | + | 0.900808i | \(0.642975\pi\) | |||||||
\(132\) | −4.81206 | + | 6.36980i | −0.418836 | + | 0.554420i | ||||
\(133\) | −10.9068 | − | 17.4872i | −0.945741 | − | 1.51633i | ||||
\(134\) | −10.4461 | − | 3.50224i | −0.902407 | − | 0.302547i | ||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | −1.72092 | − | 2.51370i | −0.147568 | − | 0.215548i | ||||
\(137\) | 16.4345 | 1.40409 | 0.702046 | − | 0.712132i | \(-0.252270\pi\) | ||||
0.702046 | + | 0.712132i | \(0.252270\pi\) | |||||||
\(138\) | 10.8697 | + | 3.64425i | 0.925291 | + | 0.310220i | ||||
\(139\) | 17.8065 | 1.51033 | 0.755164 | − | 0.655535i | \(-0.227557\pi\) | ||||
0.755164 | + | 0.655535i | \(0.227557\pi\) | |||||||
\(140\) | 5.27041 | + | 0.471978i | 0.445431 | + | 0.0398894i | ||||
\(141\) | −9.01476 | −0.759180 | ||||||||
\(142\) | 7.84386 | + | 2.62979i | 0.658242 | + | 0.220687i | ||||
\(143\) | 10.0007 | 0.836303 | ||||||||
\(144\) | 1.09326 | + | 3.84770i | 0.0911049 | + | 0.320642i | ||||
\(145\) | − | 5.99783i | − | 0.498093i | ||||||
\(146\) | 7.68651 | + | 2.57703i | 0.636140 | + | 0.213277i | ||||
\(147\) | 3.07916 | − | 6.28639i | 0.253965 | − | 0.518493i | ||||
\(148\) | −4.87293 | − | 3.68125i | −0.400553 | − | 0.302597i | ||||
\(149\) | −19.6876 | −1.61287 | −0.806434 | − | 0.591324i | \(-0.798605\pi\) | ||||
−0.806434 | + | 0.591324i | \(0.798605\pi\) | |||||||
\(150\) | −0.449546 | + | 1.34086i | −0.0367053 | + | 0.109481i | ||||
\(151\) | − | 13.2712i | − | 1.08000i | −0.841666 | − | 0.539998i | \(-0.818425\pi\) | ||
0.841666 | − | 0.539998i | \(-0.181575\pi\) | |||||||
\(152\) | −18.1803 | + | 12.4466i | −1.47462 | + | 1.00955i | ||||
\(153\) | − | 1.07705i | − | 0.0870743i | ||||||
\(154\) | −3.46555 | − | 14.5274i | −0.279262 | − | 1.17065i | ||||
\(155\) | − | 6.32559i | − | 0.508083i | ||||||
\(156\) | 3.02049 | − | 3.99827i | 0.241833 | − | 0.320118i | ||||
\(157\) | − | 19.3395i | − | 1.54346i | −0.635951 | − | 0.771730i | \(-0.719392\pi\) | ||
0.635951 | − | 0.771730i | \(-0.280608\pi\) | |||||||
\(158\) | −3.77855 | − | 1.26682i | −0.300606 | − | 0.100783i | ||||
\(159\) | −2.86521 | −0.227226 | ||||||||
\(160\) | 0.263812 | − | 5.65070i | 0.0208562 | − | 0.446727i | ||||
\(161\) | −18.1983 | + | 11.3503i | −1.43423 | + | 0.894531i | ||||
\(162\) | −0.449546 | + | 1.34086i | −0.0353197 | + | 0.105348i | ||||
\(163\) | 2.74676i | 0.215143i | 0.994197 | + | 0.107572i | \(0.0343075\pi\) | ||||
−0.994197 | + | 0.107572i | \(0.965693\pi\) | |||||||
\(164\) | 11.2441 | − | 14.8839i | 0.878014 | − | 1.16224i | ||||
\(165\) | 3.99156 | 0.310743 | ||||||||
\(166\) | 5.62394 | − | 16.7745i | 0.436502 | − | 1.30196i | ||||
\(167\) | 5.82171 | 0.450498 | 0.225249 | − | 0.974301i | \(-0.427680\pi\) | ||||
0.225249 | + | 0.974301i | \(0.427680\pi\) | |||||||
\(168\) | −6.85471 | − | 3.00215i | −0.528853 | − | 0.231621i | ||||
\(169\) | 6.72263 | 0.517125 | ||||||||
\(170\) | −0.484184 | + | 1.44417i | −0.0371352 | + | 0.110763i | ||||
\(171\) | −7.78975 | −0.595697 | ||||||||
\(172\) | −9.80118 | + | 12.9740i | −0.747333 | + | 0.989257i | ||||
\(173\) | 10.5651i | 0.803253i | 0.915804 | + | 0.401626i | \(0.131555\pi\) | ||||
−0.915804 | + | 0.401626i | \(0.868445\pi\) | |||||||
\(174\) | −2.69630 | + | 8.04226i | −0.204406 | + | 0.609682i | ||||
\(175\) | −1.40015 | − | 2.24490i | −0.105841 | − | 0.169699i | ||||
\(176\) | −15.3583 | + | 4.36381i | −1.15768 | + | 0.328935i | ||||
\(177\) | −9.68276 | −0.727801 | ||||||||
\(178\) | −4.71158 | − | 1.57964i | −0.353148 | − | 0.118399i | ||||
\(179\) | − | 4.59887i | − | 0.343736i | −0.985120 | − | 0.171868i | \(-0.945020\pi\) | ||
0.985120 | − | 0.171868i | \(-0.0549802\pi\) | |||||||
\(180\) | 1.20556 | − | 1.59582i | 0.0898570 | − | 0.118945i | ||||
\(181\) | 9.42719i | 0.700717i | 0.936616 | + | 0.350359i | \(0.113940\pi\) | ||||
−0.936616 | + | 0.350359i | \(0.886060\pi\) | |||||||
\(182\) | 2.17529 | + | 9.11873i | 0.161244 | + | 0.675925i | ||||
\(183\) | − | 3.21235i | − | 0.237464i | ||||||
\(184\) | 12.9527 | + | 18.9196i | 0.954885 | + | 1.39477i | ||||
\(185\) | 3.05357i | 0.224503i | ||||||||
\(186\) | −2.84365 | + | 8.48173i | −0.208506 | + | 0.621911i | ||||
\(187\) | 4.29911 | 0.314382 | ||||||||
\(188\) | −14.3859 | − | 10.8678i | −1.04920 | − | 0.792617i | ||||
\(189\) | −1.40015 | − | 2.24490i | −0.101846 | − | 0.163293i | ||||
\(190\) | 10.4450 | + | 3.50185i | 0.757758 | + | 0.254051i | ||||
\(191\) | 5.02689i | 0.363733i | 0.983323 | + | 0.181866i | \(0.0582139\pi\) | ||||
−0.983323 | + | 0.181866i | \(0.941786\pi\) | |||||||
\(192\) | −2.89399 | + | 7.45821i | −0.208855 | + | 0.538250i | ||||
\(193\) | 15.8775 | 1.14288 | 0.571442 | − | 0.820642i | \(-0.306384\pi\) | ||||
0.571442 | + | 0.820642i | \(0.306384\pi\) | |||||||
\(194\) | −16.1086 | − | 5.40068i | −1.15653 | − | 0.387746i | ||||
\(195\) | −2.50547 | −0.179420 | ||||||||
\(196\) | 12.4924 | − | 6.31982i | 0.892314 | − | 0.451416i | ||||
\(197\) | −10.1289 | −0.721651 | −0.360826 | − | 0.932633i | \(-0.617505\pi\) | ||||
−0.360826 | + | 0.932633i | \(0.617505\pi\) | |||||||
\(198\) | −5.35213 | − | 1.79439i | −0.380359 | − | 0.127522i | ||||
\(199\) | 1.13945 | 0.0807737 | 0.0403869 | − | 0.999184i | \(-0.487141\pi\) | ||||
0.0403869 | + | 0.999184i | \(0.487141\pi\) | |||||||
\(200\) | −2.33388 | + | 1.59781i | −0.165030 | + | 0.112982i | ||||
\(201\) | − | 7.79060i | − | 0.549507i | ||||||
\(202\) | −0.349291 | − | 0.117106i | −0.0245760 | − | 0.00823953i | ||||
\(203\) | −8.39786 | − | 13.4645i | −0.589414 | − | 0.945025i | ||||
\(204\) | 1.29845 | − | 1.71877i | 0.0909094 | − | 0.120338i | ||||
\(205\) | −9.32685 | −0.651415 | ||||||||
\(206\) | −0.793378 | + | 2.36641i | −0.0552773 | + | 0.164875i | ||||
\(207\) | 8.10651i | 0.563442i | ||||||||
\(208\) | 9.64029 | − | 2.73912i | 0.668434 | − | 0.189924i | ||||
\(209\) | − | 31.0933i | − | 2.15077i | ||||||
\(210\) | 0.868219 | + | 3.63953i | 0.0599128 | + | 0.251152i | ||||
\(211\) | − | 16.8644i | − | 1.16099i | −0.814263 | − | 0.580497i | \(-0.802858\pi\) | ||
0.814263 | − | 0.580497i | \(-0.197142\pi\) | |||||||
\(212\) | −4.57234 | − | 3.45417i | −0.314030 | − | 0.237233i | ||||
\(213\) | 5.84987i | 0.400827i | ||||||||
\(214\) | −8.18232 | − | 2.74326i | −0.559332 | − | 0.187525i | ||||
\(215\) | 8.13000 | 0.554461 | ||||||||
\(216\) | −2.33388 | + | 1.59781i | −0.158800 | + | 0.108717i | ||||
\(217\) | −8.85677 | − | 14.2003i | −0.601237 | − | 0.963981i | ||||
\(218\) | −6.72344 | + | 20.0540i | −0.455369 | + | 1.35823i | ||||
\(219\) | 5.73252i | 0.387368i | ||||||||
\(220\) | 6.36980 | + | 4.81206i | 0.429452 | + | 0.324429i | ||||
\(221\) | −2.69851 | −0.181522 | ||||||||
\(222\) | 1.37272 | − | 4.09441i | 0.0921309 | − | 0.274799i | ||||
\(223\) | 1.84769 | 0.123730 | 0.0618652 | − | 0.998085i | \(-0.480295\pi\) | ||||
0.0618652 | + | 0.998085i | \(0.480295\pi\) | |||||||
\(224\) | −7.31959 | − | 13.0546i | −0.489061 | − | 0.872250i | ||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −5.32479 | + | 15.8822i | −0.354200 | + | 1.05647i | ||||
\(227\) | 26.0109 | 1.72640 | 0.863201 | − | 0.504861i | \(-0.168456\pi\) | ||||
0.863201 | + | 0.504861i | \(0.168456\pi\) | |||||||
\(228\) | −12.4310 | − | 9.39100i | −0.823264 | − | 0.621934i | ||||
\(229\) | − | 14.8172i | − | 0.979146i | −0.871962 | − | 0.489573i | \(-0.837153\pi\) | ||
0.871962 | − | 0.489573i | \(-0.162847\pi\) | |||||||
\(230\) | 3.64425 | − | 10.8697i | 0.240295 | − | 0.716727i | ||||
\(231\) | 8.96067 | − | 5.58879i | 0.589569 | − | 0.367715i | ||||
\(232\) | −13.9982 | + | 9.58342i | −0.919028 | + | 0.629182i | ||||
\(233\) | −3.41871 | −0.223967 | −0.111983 | − | 0.993710i | \(-0.535720\pi\) | ||||
−0.111983 | + | 0.993710i | \(0.535720\pi\) | |||||||
\(234\) | 3.35948 | + | 1.12632i | 0.219616 | + | 0.0736301i | ||||
\(235\) | 9.01476i | 0.588058i | ||||||||
\(236\) | −15.4519 | − | 11.6731i | −1.00583 | − | 0.759856i | ||||
\(237\) | − | 2.81801i | − | 0.183049i | ||||||
\(238\) | 0.935114 | + | 3.91996i | 0.0606144 | + | 0.254093i | ||||
\(239\) | 2.84316i | 0.183909i | 0.995763 | + | 0.0919544i | \(0.0293114\pi\) | ||||
−0.995763 | + | 0.0919544i | \(0.970689\pi\) | |||||||
\(240\) | 3.84770 | − | 1.09326i | 0.248368 | − | 0.0705695i | ||||
\(241\) | 20.0977i | 1.29461i | 0.762233 | + | 0.647303i | \(0.224103\pi\) | ||||
−0.762233 | + | 0.647303i | \(0.775897\pi\) | |||||||
\(242\) | 2.21742 | − | 6.61390i | 0.142541 | − | 0.425158i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.87267 | − | 5.12632i | 0.247922 | − | 0.328179i | ||||
\(245\) | −6.28639 | − | 3.07916i | −0.401623 | − | 0.196720i | ||||
\(246\) | 12.5060 | + | 4.19285i | 0.797354 | + | 0.267326i | ||||
\(247\) | 19.5170i | 1.24183i | ||||||||
\(248\) | −14.7632 | + | 10.1071i | −0.937462 | + | 0.641802i | ||||
\(249\) | 12.5103 | 0.792805 | ||||||||
\(250\) | 1.34086 | + | 0.449546i | 0.0848035 | + | 0.0284318i | ||||
\(251\) | −15.7417 | −0.993607 | −0.496803 | − | 0.867863i | \(-0.665493\pi\) | ||||
−0.496803 | + | 0.867863i | \(0.665493\pi\) | |||||||
\(252\) | 0.471978 | − | 5.27041i | 0.0297318 | − | 0.332005i | ||||
\(253\) | −32.3577 | −2.03431 | ||||||||
\(254\) | 7.36677 | + | 2.46983i | 0.462232 | + | 0.154971i | ||||
\(255\) | −1.07705 | −0.0674474 | ||||||||
\(256\) | −13.6096 | + | 8.41306i | −0.850598 | + | 0.525816i | ||||
\(257\) | 7.43670i | 0.463889i | 0.972729 | + | 0.231944i | \(0.0745087\pi\) | ||||
−0.972729 | + | 0.231944i | \(0.925491\pi\) | |||||||
\(258\) | −10.9012 | − | 3.65481i | −0.678679 | − | 0.227539i | ||||
\(259\) | 4.27545 | + | 6.85496i | 0.265664 | + | 0.425946i | ||||
\(260\) | −3.99827 | − | 3.02049i | −0.247962 | − | 0.187323i | ||||
\(261\) | −5.99783 | −0.371256 | ||||||||
\(262\) | 4.46836 | − | 13.3278i | 0.276056 | − | 0.823392i | ||||
\(263\) | 8.49327i | 0.523718i | 0.965106 | + | 0.261859i | \(0.0843355\pi\) | ||||
−0.965106 | + | 0.261859i | \(0.915665\pi\) | |||||||
\(264\) | −6.37777 | − | 9.31583i | −0.392525 | − | 0.573350i | ||||
\(265\) | 2.86521i | 0.176008i | ||||||||
\(266\) | 28.3510 | − | 6.76321i | 1.73831 | − | 0.414679i | ||||
\(267\) | − | 3.51385i | − | 0.215044i | ||||||
\(268\) | 9.39202 | − | 12.4324i | 0.573709 | − | 0.759428i | ||||
\(269\) | 5.94512i | 0.362480i | 0.983439 | + | 0.181240i | \(0.0580111\pi\) | ||||
−0.983439 | + | 0.181240i | \(0.941989\pi\) | |||||||
\(270\) | 1.34086 | + | 0.449546i | 0.0816022 | + | 0.0273585i | ||||
\(271\) | −11.2023 | −0.680490 | −0.340245 | − | 0.940337i | \(-0.610510\pi\) | ||||
−0.340245 | + | 0.940337i | \(0.610510\pi\) | |||||||
\(272\) | 4.14416 | − | 1.17749i | 0.251277 | − | 0.0713960i | ||||
\(273\) | −5.62453 | + | 3.50803i | −0.340412 | + | 0.212316i | ||||
\(274\) | −7.38806 | + | 22.0363i | −0.446329 | + | 1.33126i | ||||
\(275\) | − | 3.99156i | − | 0.240700i | ||||||
\(276\) | −9.77288 | + | 12.9365i | −0.588258 | + | 0.778686i | ||||
\(277\) | 2.17155 | 0.130476 | 0.0652378 | − | 0.997870i | \(-0.479219\pi\) | ||||
0.0652378 | + | 0.997870i | \(0.479219\pi\) | |||||||
\(278\) | −8.00485 | + | 23.8761i | −0.480099 | + | 1.43199i | ||||
\(279\) | −6.32559 | −0.378703 | ||||||||
\(280\) | −3.00215 | + | 6.85471i | −0.179413 | + | 0.409647i | ||||
\(281\) | 1.72189 | 0.102720 | 0.0513598 | − | 0.998680i | \(-0.483644\pi\) | ||||
0.0513598 | + | 0.998680i | \(0.483644\pi\) | |||||||
\(282\) | 4.05255 | − | 12.0875i | 0.241326 | − | 0.719803i | ||||
\(283\) | 6.51271 | 0.387140 | 0.193570 | − | 0.981086i | \(-0.437993\pi\) | ||||
0.193570 | + | 0.981086i | \(0.437993\pi\) | |||||||
\(284\) | −7.05236 | + | 9.33532i | −0.418481 | + | 0.553949i | ||||
\(285\) | 7.78975i | 0.461425i | ||||||||
\(286\) | −4.49579 | + | 13.4096i | −0.265842 | + | 0.792926i | ||||
\(287\) | −20.9379 | + | 13.0590i | −1.23592 | + | 0.770847i | ||||
\(288\) | −5.65070 | − | 0.263812i | −0.332971 | − | 0.0155453i | ||||
\(289\) | 15.8400 | 0.931763 | ||||||||
\(290\) | 8.04226 | + | 2.69630i | 0.472258 | + | 0.158332i | ||||
\(291\) | − | 12.0136i | − | 0.704250i | ||||||
\(292\) | −6.91089 | + | 9.14805i | −0.404429 | + | 0.535349i | ||||
\(293\) | 9.20381i | 0.537692i | 0.963183 | + | 0.268846i | \(0.0866423\pi\) | ||||
−0.963183 | + | 0.268846i | \(0.913358\pi\) | |||||||
\(294\) | 7.04495 | + | 6.95475i | 0.410870 | + | 0.405610i | ||||
\(295\) | 9.68276i | 0.563752i | ||||||||
\(296\) | 7.12666 | − | 4.87903i | 0.414229 | − | 0.283588i | ||||
\(297\) | − | 3.99156i | − | 0.231614i | ||||||
\(298\) | 8.85047 | − | 26.3983i | 0.512694 | − | 1.52921i | ||||
\(299\) | 20.3106 | 1.17459 | ||||||||
\(300\) | −1.59582 | − | 1.20556i | −0.0921345 | − | 0.0696029i | ||||
\(301\) | 18.2510 | − | 11.3832i | 1.05197 | − | 0.656117i | ||||
\(302\) | 17.7949 | + | 5.96603i | 1.02398 | + | 0.343306i | ||||
\(303\) | − | 0.260498i | − | 0.0149652i | ||||||
\(304\) | −8.51621 | − | 29.9726i | −0.488438 | − | 1.71905i | ||||
\(305\) | −3.21235 | −0.183938 | ||||||||
\(306\) | 1.44417 | + | 0.484184i | 0.0825579 | + | 0.0276789i | ||||
\(307\) | 32.5750 | 1.85916 | 0.929578 | − | 0.368626i | \(-0.120172\pi\) | ||||
0.929578 | + | 0.368626i | \(0.120172\pi\) | |||||||
\(308\) | 21.0372 | + | 1.88393i | 1.19870 | + | 0.107347i | ||||
\(309\) | −1.76484 | −0.100398 | ||||||||
\(310\) | 8.48173 | + | 2.84365i | 0.481730 | + | 0.161508i | ||||
\(311\) | −27.3621 | −1.55156 | −0.775781 | − | 0.631002i | \(-0.782644\pi\) | ||||
−0.775781 | + | 0.631002i | \(0.782644\pi\) | |||||||
\(312\) | 4.00327 | + | 5.84746i | 0.226641 | + | 0.331047i | ||||
\(313\) | 19.7088i | 1.11401i | 0.830510 | + | 0.557004i | \(0.188049\pi\) | ||||
−0.830510 | + | 0.557004i | \(0.811951\pi\) | |||||||
\(314\) | 25.9316 | + | 8.69400i | 1.46340 | + | 0.490631i | ||||
\(315\) | −2.24490 | + | 1.40015i | −0.126486 | + | 0.0788895i | ||||
\(316\) | 3.39727 | − | 4.49702i | 0.191111 | − | 0.252977i | ||||
\(317\) | −0.854973 | −0.0480201 | −0.0240100 | − | 0.999712i | \(-0.507643\pi\) | ||||
−0.0240100 | + | 0.999712i | \(0.507643\pi\) | |||||||
\(318\) | 1.28804 | − | 3.84184i | 0.0722298 | − | 0.215440i | ||||
\(319\) | − | 23.9407i | − | 1.34042i | ||||||
\(320\) | 7.45821 | + | 2.89399i | 0.416926 | + | 0.161779i | ||||
\(321\) | − | 6.10229i | − | 0.340596i | ||||||
\(322\) | −7.03823 | − | 29.5039i | −0.392225 | − | 1.64419i | ||||
\(323\) | 8.38994i | 0.466829i | ||||||||
\(324\) | −1.59582 | − | 1.20556i | −0.0886565 | − | 0.0669755i | ||||
\(325\) | 2.50547i | 0.138978i | ||||||||
\(326\) | −3.68303 | − | 1.23480i | −0.203984 | − | 0.0683891i | ||||
\(327\) | −14.9561 | −0.827072 | ||||||||
\(328\) | 14.9026 | + | 21.7677i | 0.822856 | + | 1.20192i | ||||
\(329\) | 12.6220 | + | 20.2372i | 0.695874 | + | 1.11572i | ||||
\(330\) | −1.79439 | + | 5.35213i | −0.0987781 | + | 0.294625i | ||||
\(331\) | 4.23740i | 0.232909i | 0.993196 | + | 0.116454i | \(0.0371529\pi\) | ||||
−0.993196 | + | 0.116454i | \(0.962847\pi\) | |||||||
\(332\) | 19.9641 | + | 15.0818i | 1.09567 | + | 0.827724i | ||||
\(333\) | 3.05357 | 0.167334 | ||||||||
\(334\) | −2.61713 | + | 7.80611i | −0.143203 | + | 0.427131i | ||||
\(335\) | −7.79060 | −0.425646 | ||||||||
\(336\) | 7.10698 | − | 7.84161i | 0.387717 | − | 0.427795i | ||||
\(337\) | 20.5956 | 1.12191 | 0.560956 | − | 0.827846i | \(-0.310434\pi\) | ||||
0.560956 | + | 0.827846i | \(0.310434\pi\) | |||||||
\(338\) | −3.02213 | + | 9.01411i | −0.164382 | + | 0.490303i | ||||
\(339\) | −11.8448 | −0.643322 | ||||||||
\(340\) | −1.71877 | − | 1.29845i | −0.0932135 | − | 0.0704181i | ||||
\(341\) | − | 25.2490i | − | 1.36731i | ||||||
\(342\) | 3.50185 | − | 10.4450i | 0.189359 | − | 0.564799i | ||||
\(343\) | −18.4236 | + | 1.88948i | −0.994782 | + | 0.102022i | ||||
\(344\) | −12.9902 | − | 18.9744i | −0.700385 | − | 1.02303i | ||||
\(345\) | 8.10651 | 0.436440 | ||||||||
\(346\) | −14.1664 | − | 4.74952i | −0.761590 | − | 0.255336i | ||||
\(347\) | − | 13.8257i | − | 0.742200i | −0.928593 | − | 0.371100i | \(-0.878981\pi\) | ||
0.928593 | − | 0.371100i | \(-0.121019\pi\) | |||||||
\(348\) | −9.57144 | − | 7.23074i | −0.513083 | − | 0.387608i | ||||
\(349\) | 8.06666i | 0.431798i | 0.976416 | + | 0.215899i | \(0.0692683\pi\) | ||||
−0.976416 | + | 0.215899i | \(0.930732\pi\) | |||||||
\(350\) | 3.63953 | − | 0.868219i | 0.194541 | − | 0.0464082i | ||||
\(351\) | 2.50547i | 0.133732i | ||||||||
\(352\) | 1.05302 | − | 22.5551i | 0.0561262 | − | 1.20219i | ||||
\(353\) | 7.67694i | 0.408602i | 0.978908 | + | 0.204301i | \(0.0654922\pi\) | ||||
−0.978908 | + | 0.204301i | \(0.934508\pi\) | |||||||
\(354\) | 4.35285 | − | 12.9832i | 0.231351 | − | 0.690051i | ||||
\(355\) | 5.84987 | 0.310479 | ||||||||
\(356\) | 4.23615 | − | 5.60746i | 0.224516 | − | 0.297195i | ||||
\(357\) | −2.41787 | + | 1.50803i | −0.127967 | + | 0.0798134i | ||||
\(358\) | 6.16645 | + | 2.06741i | 0.325907 | + | 0.109266i | ||||
\(359\) | − | 21.6267i | − | 1.14141i | −0.821154 | − | 0.570706i | \(-0.806670\pi\) | ||
0.821154 | − | 0.570706i | \(-0.193330\pi\) | |||||||
\(360\) | 1.59781 | + | 2.33388i | 0.0842121 | + | 0.123006i | ||||
\(361\) | 41.6802 | 2.19369 | ||||||||
\(362\) | −12.6405 | − | 4.23796i | −0.664372 | − | 0.222742i | ||||
\(363\) | 4.93258 | 0.258893 | ||||||||
\(364\) | −13.2048 | − | 1.18253i | −0.692122 | − | 0.0619812i | ||||
\(365\) | 5.73252 | 0.300054 | ||||||||
\(366\) | 4.30731 | + | 1.44410i | 0.225147 | + | 0.0754843i | ||||
\(367\) | −6.62228 | −0.345680 | −0.172840 | − | 0.984950i | \(-0.555294\pi\) | ||||
−0.172840 | + | 0.984950i | \(0.555294\pi\) | |||||||
\(368\) | −31.1914 | + | 8.86251i | −1.62597 | + | 0.461990i | ||||
\(369\) | 9.32685i | 0.485536i | ||||||||
\(370\) | −4.09441 | − | 1.37272i | −0.212858 | − | 0.0713643i | ||||
\(371\) | 4.01172 | + | 6.43210i | 0.208278 | + | 0.333938i | ||||
\(372\) | −10.0945 | − | 7.62587i | −0.523374 | − | 0.395383i | ||||
\(373\) | −31.1585 | −1.61332 | −0.806662 | − | 0.591013i | \(-0.798728\pi\) | ||||
−0.806662 | + | 0.591013i | \(0.798728\pi\) | |||||||
\(374\) | −1.93265 | + | 5.76451i | −0.0999349 | + | 0.298076i | ||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 21.0394 | − | 14.4039i | 1.08502 | − | 0.742825i | ||||
\(377\) | 15.0274i | 0.773949i | ||||||||
\(378\) | 3.63953 | − | 0.868219i | 0.187197 | − | 0.0446563i | ||||
\(379\) | 31.1885i | 1.60204i | 0.598635 | + | 0.801022i | \(0.295710\pi\) | ||||
−0.598635 | + | 0.801022i | \(0.704290\pi\) | |||||||
\(380\) | −9.39100 | + | 12.4310i | −0.481748 | + | 0.637697i | ||||
\(381\) | 5.49406i | 0.281469i | ||||||||
\(382\) | −6.74036 | − | 2.25982i | −0.344867 | − | 0.115622i | ||||
\(383\) | 27.9907 | 1.43026 | 0.715128 | − | 0.698993i | \(-0.246368\pi\) | ||||
0.715128 | + | 0.698993i | \(0.246368\pi\) | |||||||
\(384\) | −8.69944 | − | 7.23324i | −0.443941 | − | 0.369120i | ||||
\(385\) | −5.58879 | − | 8.96067i | −0.284831 | − | 0.456678i | ||||
\(386\) | −7.13766 | + | 21.2895i | −0.363297 | + | 1.08361i | ||||
\(387\) | − | 8.13000i | − | 0.413271i | ||||||
\(388\) | 14.4831 | − | 19.1715i | 0.735269 | − | 0.973286i | ||||
\(389\) | 15.7502 | 0.798568 | 0.399284 | − | 0.916827i | \(-0.369259\pi\) | ||||
0.399284 | + | 0.916827i | \(0.369259\pi\) | |||||||
\(390\) | 1.12632 | − | 3.35948i | 0.0570336 | − | 0.170114i | ||||
\(391\) | 8.73111 | 0.441551 | ||||||||
\(392\) | 2.85809 | + | 19.5916i | 0.144355 | + | 0.989526i | ||||
\(393\) | 9.93971 | 0.501392 | ||||||||
\(394\) | 4.55339 | − | 13.5814i | 0.229397 | − | 0.684221i | ||||
\(395\) | −2.81801 | −0.141789 | ||||||||
\(396\) | 4.81206 | − | 6.36980i | 0.241815 | − | 0.320095i | ||||
\(397\) | 11.3689i | 0.570589i | 0.958440 | + | 0.285294i | \(0.0920914\pi\) | ||||
−0.958440 | + | 0.285294i | \(0.907909\pi\) | |||||||
\(398\) | −0.512237 | + | 1.52785i | −0.0256761 | + | 0.0765841i | ||||
\(399\) | 10.9068 | + | 17.4872i | 0.546024 | + | 0.875456i | ||||
\(400\) | −1.09326 | − | 3.84770i | −0.0546629 | − | 0.192385i | ||||
\(401\) | 12.7623 | 0.637319 | 0.318659 | − | 0.947869i | \(-0.396767\pi\) | ||||
0.318659 | + | 0.947869i | \(0.396767\pi\) | |||||||
\(402\) | 10.4461 | + | 3.50224i | 0.521005 | + | 0.174676i | ||||
\(403\) | 15.8486i | 0.789473i | ||||||||
\(404\) | 0.314045 | − | 0.415706i | 0.0156243 | − | 0.0206822i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 21.8293 | − | 5.20743i | 1.08337 | − | 0.258440i | ||||
\(407\) | 12.1885i | 0.604162i | ||||||||
\(408\) | 1.72092 | + | 2.51370i | 0.0851984 | + | 0.124447i | ||||
\(409\) | 1.91649i | 0.0947643i | 0.998877 | + | 0.0473822i | \(0.0150879\pi\) | ||||
−0.998877 | + | 0.0473822i | \(0.984912\pi\) | |||||||
\(410\) | 4.19285 | − | 12.5060i | 0.207070 | − | 0.617628i | ||||
\(411\) | −16.4345 | −0.810653 | ||||||||
\(412\) | −2.81636 | − | 2.12762i | −0.138752 | − | 0.104820i | ||||
\(413\) | 13.5573 | + | 21.7368i | 0.667112 | + | 1.06960i | ||||
\(414\) | −10.8697 | − | 3.64425i | −0.534217 | − | 0.179105i | ||||
\(415\) | − | 12.5103i | − | 0.614104i | ||||||
\(416\) | −0.660972 | + | 14.1576i | −0.0324068 | + | 0.694136i | ||||
\(417\) | −17.8065 | −0.871989 | ||||||||
\(418\) | 41.6918 | + | 13.9779i | 2.03921 | + | 0.683680i | ||||
\(419\) | −13.7105 | −0.669800 | −0.334900 | − | 0.942254i | \(-0.608703\pi\) | ||||
−0.334900 | + | 0.942254i | \(0.608703\pi\) | |||||||
\(420\) | −5.27041 | − | 0.471978i | −0.257170 | − | 0.0230302i | ||||
\(421\) | 7.87629 | 0.383867 | 0.191933 | − | 0.981408i | \(-0.438524\pi\) | ||||
0.191933 | + | 0.981408i | \(0.438524\pi\) | |||||||
\(422\) | 22.6128 | + | 7.58133i | 1.10077 | + | 0.369053i | ||||
\(423\) | 9.01476 | 0.438313 | ||||||||
\(424\) | 6.68704 | − | 4.57806i | 0.324752 | − | 0.222330i | ||||
\(425\) | 1.07705i | 0.0522446i | ||||||||
\(426\) | −7.84386 | − | 2.62979i | −0.380036 | − | 0.127414i | ||||
\(427\) | −7.21140 | + | 4.49777i | −0.348984 | + | 0.217662i | ||||
\(428\) | 7.35666 | − | 9.73813i | 0.355598 | − | 0.470710i | ||||
\(429\) | −10.0007 | −0.482840 | ||||||||
\(430\) | −3.65481 | + | 10.9012i | −0.176251 | + | 0.525702i | ||||
\(431\) | − | 22.3788i | − | 1.07795i | −0.842322 | − | 0.538974i | \(-0.818812\pi\) | ||
0.842322 | − | 0.538974i | \(-0.181188\pi\) | |||||||
\(432\) | −1.09326 | − | 3.84770i | −0.0525994 | − | 0.185122i | ||||
\(433\) | − | 33.9772i | − | 1.63284i | −0.577460 | − | 0.816419i | \(-0.695956\pi\) | ||
0.577460 | − | 0.816419i | \(-0.304044\pi\) | |||||||
\(434\) | 23.0222 | − | 5.49199i | 1.10510 | − | 0.263624i | ||||
\(435\) | 5.99783i | 0.287574i | ||||||||
\(436\) | −23.8671 | − | 18.0304i | −1.14303 | − | 0.863499i | ||||
\(437\) | − | 63.1477i | − | 3.02076i | ||||||
\(438\) | −7.68651 | − | 2.57703i | −0.367276 | − | 0.123135i | ||||
\(439\) | −2.97475 | −0.141977 | −0.0709886 | − | 0.997477i | \(-0.522615\pi\) | ||||
−0.0709886 | + | 0.997477i | \(0.522615\pi\) | |||||||
\(440\) | −9.31583 | + | 6.37777i | −0.444115 | + | 0.304048i | ||||
\(441\) | −3.07916 | + | 6.28639i | −0.146627 | + | 0.299352i | ||||
\(442\) | 1.21311 | − | 3.61833i | 0.0577016 | − | 0.172106i | ||||
\(443\) | 20.4095i | 0.969684i | 0.874602 | + | 0.484842i | \(0.161123\pi\) | ||||
−0.874602 | + | 0.484842i | \(0.838877\pi\) | |||||||
\(444\) | 4.87293 | + | 3.68125i | 0.231259 | + | 0.174705i | ||||
\(445\) | −3.51385 | −0.166572 | ||||||||
\(446\) | −0.830622 | + | 2.47750i | −0.0393311 | + | 0.117313i | ||||
\(447\) | 19.6876 | 0.931190 | ||||||||
\(448\) | 20.7949 | − | 3.94589i | 0.982469 | − | 0.186426i | ||||
\(449\) | −11.0234 | −0.520226 | −0.260113 | − | 0.965578i | \(-0.583760\pi\) | ||||
−0.260113 | + | 0.965578i | \(0.583760\pi\) | |||||||
\(450\) | 0.449546 | − | 1.34086i | 0.0211918 | − | 0.0632088i | ||||
\(451\) | −37.2287 | −1.75303 | ||||||||
\(452\) | −18.9021 | − | 14.2796i | −0.889082 | − | 0.671656i | ||||
\(453\) | 13.2712i | 0.623536i | ||||||||
\(454\) | −11.6931 | + | 34.8769i | −0.548784 | + | 1.63686i | ||||
\(455\) | 3.50803 | + | 5.62453i | 0.164459 | + | 0.263682i | ||||
\(456\) | 18.1803 | − | 12.4466i | 0.851372 | − | 0.582864i | ||||
\(457\) | 0.409340 | 0.0191481 | 0.00957406 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957406 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(458\) | 19.8678 | + | 6.66101i | 0.928360 | + | 0.311248i | ||||
\(459\) | 1.07705i | 0.0502724i | ||||||||
\(460\) | 12.9365 | + | 9.77288i | 0.603168 | + | 0.455663i | ||||
\(461\) | − | 23.9577i | − | 1.11582i | −0.829901 | − | 0.557910i | \(-0.811603\pi\) | ||
0.829901 | − | 0.557910i | \(-0.188397\pi\) | |||||||
\(462\) | 3.46555 | + | 14.5274i | 0.161232 | + | 0.675877i | ||||
\(463\) | 10.1008i | 0.469424i | 0.972065 | + | 0.234712i | \(0.0754147\pi\) | ||||
−0.972065 | + | 0.234712i | \(0.924585\pi\) | |||||||
\(464\) | −6.55718 | − | 23.0779i | −0.304409 | − | 1.07136i | ||||
\(465\) | 6.32559i | 0.293342i | ||||||||
\(466\) | 1.53687 | − | 4.58401i | 0.0711940 | − | 0.212350i | ||||
\(467\) | −38.6883 | −1.79028 | −0.895140 | − | 0.445785i | \(-0.852924\pi\) | ||||
−0.895140 | + | 0.445785i | \(0.852924\pi\) | |||||||
\(468\) | −3.02049 | + | 3.99827i | −0.139622 | + | 0.184820i | ||||
\(469\) | −17.4891 | + | 10.9080i | −0.807573 | + | 0.503685i | ||||
\(470\) | −12.0875 | − | 4.05255i | −0.557557 | − | 0.186930i | ||||
\(471\) | 19.3395i | 0.891117i | ||||||||
\(472\) | 22.5984 | − | 15.4712i | 1.04018 | − | 0.712122i | ||||
\(473\) | 32.4514 | 1.49212 | ||||||||
\(474\) | 3.77855 | + | 1.26682i | 0.173555 | + | 0.0581872i | ||||
\(475\) | 7.78975 | 0.357418 | ||||||||
\(476\) | −5.67649 | − | 0.508344i | −0.260182 | − | 0.0232999i | ||||
\(477\) | 2.86521 | 0.131189 | ||||||||
\(478\) | −3.81228 | − | 1.27813i | −0.174370 | − | 0.0584604i | ||||
\(479\) | 7.91710 | 0.361742 | 0.180871 | − | 0.983507i | \(-0.442108\pi\) | ||||
0.180871 | + | 0.983507i | \(0.442108\pi\) | |||||||
\(480\) | −0.263812 | + | 5.65070i | −0.0120413 | + | 0.257918i | ||||
\(481\) | − | 7.65062i | − | 0.348838i | ||||||
\(482\) | −26.9482 | − | 9.03484i | −1.22746 | − | 0.411526i | ||||
\(483\) | 18.1983 | − | 11.3503i | 0.828052 | − | 0.516458i | ||||
\(484\) | 7.87149 | + | 5.94651i | 0.357795 | + | 0.270296i | ||||
\(485\) | −12.0136 | −0.545510 | ||||||||
\(486\) | 0.449546 | − | 1.34086i | 0.0203918 | − | 0.0608227i | ||||
\(487\) | − | 28.5984i | − | 1.29592i | −0.761676 | − | 0.647958i | \(-0.775623\pi\) | ||
0.761676 | − | 0.647958i | \(-0.224377\pi\) | |||||||
\(488\) | 5.13273 | + | 7.49723i | 0.232348 | + | 0.339384i | ||||
\(489\) | − | 2.74676i | − | 0.124213i | ||||||
\(490\) | 6.95475 | − | 7.04495i | 0.314184 | − | 0.318259i | ||||
\(491\) | 23.6318i | 1.06649i | 0.845961 | + | 0.533244i | \(0.179027\pi\) | ||||
−0.845961 | + | 0.533244i | \(0.820973\pi\) | |||||||
\(492\) | −11.2441 | + | 14.8839i | −0.506921 | + | 0.671020i | ||||
\(493\) | 6.45996i | 0.290942i | ||||||||
\(494\) | −26.1695 | − | 8.77378i | −1.17742 | − | 0.394751i | ||||
\(495\) | −3.99156 | −0.179407 | ||||||||
\(496\) | −6.91550 | − | 24.3390i | −0.310515 | − | 1.09285i | ||||
\(497\) | 13.1324 | − | 8.19069i | 0.589068 | − | 0.367403i | ||||
\(498\) | −5.62394 | + | 16.7745i | −0.252015 | + | 0.751684i | ||||
\(499\) | 0.663011i | 0.0296805i | 0.999890 | + | 0.0148402i | \(0.00472397\pi\) | ||||
−0.999890 | + | 0.0148402i | \(0.995276\pi\) | |||||||
\(500\) | −1.20556 | + | 1.59582i | −0.0539142 | + | 0.0713671i | ||||
\(501\) | −5.82171 | −0.260095 | ||||||||
\(502\) | 7.07662 | − | 21.1074i | 0.315845 | − | 0.942070i | ||||
\(503\) | −19.7450 | −0.880385 | −0.440192 | − | 0.897904i | \(-0.645090\pi\) | ||||
−0.440192 | + | 0.897904i | \(0.645090\pi\) | |||||||
\(504\) | 6.85471 | + | 3.00215i | 0.305333 | + | 0.133726i | ||||
\(505\) | −0.260498 | −0.0115920 | ||||||||
\(506\) | 14.5463 | − | 43.3871i | 0.646661 | − | 1.92879i | ||||
\(507\) | −6.72263 | −0.298562 | ||||||||
\(508\) | −6.62341 | + | 8.76751i | −0.293866 | + | 0.388995i | ||||
\(509\) | − | 24.6928i | − | 1.09449i | −0.836972 | − | 0.547245i | \(-0.815676\pi\) | ||
0.836972 | − | 0.547245i | \(-0.184324\pi\) | |||||||
\(510\) | 0.484184 | − | 1.44417i | 0.0214400 | − | 0.0639491i | ||||
\(511\) | 12.8689 | − | 8.02639i | 0.569288 | − | 0.355066i | ||||
\(512\) | −5.16261 | − | 22.0306i | −0.228157 | − | 0.973624i | ||||
\(513\) | 7.78975 | 0.343926 | ||||||||
\(514\) | −9.97158 | − | 3.34314i | −0.439828 | − | 0.147460i | ||||
\(515\) | 1.76484i | 0.0777682i | ||||||||
\(516\) | 9.80118 | − | 12.9740i | 0.431473 | − | 0.571148i | ||||
\(517\) | 35.9830i | 1.58253i | ||||||||
\(518\) | −11.1136 | + | 2.65116i | −0.488302 | + | 0.116485i | ||||
\(519\) | − | 10.5651i | − | 0.463758i | ||||||
\(520\) | 5.84746 | − | 4.00327i | 0.256428 | − | 0.175555i | ||||
\(521\) | 13.0343i | 0.571042i | 0.958372 | + | 0.285521i | \(0.0921666\pi\) | ||||
−0.958372 | + | 0.285521i | \(0.907833\pi\) | |||||||
\(522\) | 2.69630 | − | 8.04226i | 0.118014 | − | 0.352000i | ||||
\(523\) | 21.5279 | 0.941348 | 0.470674 | − | 0.882307i | \(-0.344011\pi\) | ||||
0.470674 | + | 0.882307i | \(0.344011\pi\) | |||||||
\(524\) | 15.8619 | + | 11.9829i | 0.692932 | + | 0.523475i | ||||
\(525\) | 1.40015 | + | 2.24490i | 0.0611075 | + | 0.0979755i | ||||
\(526\) | −11.3883 | − | 3.81812i | −0.496553 | − | 0.166478i | ||||
\(527\) | 6.81297i | 0.296778i | ||||||||
\(528\) | 15.3583 | − | 4.36381i | 0.668386 | − | 0.189910i | ||||
\(529\) | −42.7156 | −1.85720 | ||||||||
\(530\) | −3.84184 | − | 1.28804i | −0.166879 | − | 0.0559490i | ||||
\(531\) | 9.68276 | 0.420196 | ||||||||
\(532\) | −3.67659 | + | 41.0552i | −0.159400 | + | 1.77997i | ||||
\(533\) | 23.3681 | 1.01219 | ||||||||
\(534\) | 4.71158 | + | 1.57964i | 0.203890 | + | 0.0683576i | ||||
\(535\) | −6.10229 | −0.263825 | ||||||||
\(536\) | 12.4479 | + | 18.1823i | 0.537668 | + | 0.785357i | ||||
\(537\) | 4.59887i | 0.198456i | ||||||||
\(538\) | −7.97158 | − | 2.67261i | −0.343679 | − | 0.115224i | ||||
\(539\) | −25.0925 | − | 12.2907i | −1.08081 | − | 0.529397i | ||||
\(540\) | −1.20556 | + | 1.59582i | −0.0518790 | + | 0.0686730i | ||||
\(541\) | −17.3274 | −0.744965 | −0.372482 | − | 0.928039i | \(-0.621493\pi\) | ||||
−0.372482 | + | 0.928039i | \(0.621493\pi\) | |||||||
\(542\) | 5.03595 | − | 15.0207i | 0.216312 | − | 0.645195i | ||||
\(543\) | − | 9.42719i | − | 0.404559i | ||||||
\(544\) | −0.284138 | + | 6.08608i | −0.0121823 | + | 0.260939i | ||||
\(545\) | 14.9561i | 0.640647i | ||||||||
\(546\) | −2.17529 | − | 9.11873i | −0.0930940 | − | 0.390246i | ||||
\(547\) | − | 5.19581i | − | 0.222157i | −0.993812 | − | 0.111079i | \(-0.964569\pi\) | ||
0.993812 | − | 0.111079i | \(-0.0354305\pi\) | |||||||
\(548\) | −26.2264 | − | 19.8127i | −1.12034 | − | 0.846357i | ||||
\(549\) | 3.21235i | 0.137100i | ||||||||
\(550\) | 5.35213 | + | 1.79439i | 0.228216 | + | 0.0765132i | ||||
\(551\) | 46.7216 | 1.99041 | ||||||||
\(552\) | −12.9527 | − | 18.9196i | −0.551303 | − | 0.805273i | ||||
\(553\) | −6.32615 | + | 3.94563i | −0.269015 | + | 0.167785i | ||||
\(554\) | −0.976211 | + | 2.91174i | −0.0414752 | + | 0.123708i | ||||
\(555\) | − | 3.05357i | − | 0.129617i | ||||||
\(556\) | −28.4159 | − | 21.4668i | −1.20510 | − | 0.910395i | ||||
\(557\) | 10.4597 | 0.443190 | 0.221595 | − | 0.975139i | \(-0.428874\pi\) | ||||
0.221595 | + | 0.975139i | \(0.428874\pi\) | |||||||
\(558\) | 2.84365 | − | 8.48173i | 0.120381 | − | 0.359060i | ||||
\(559\) | −20.3694 | −0.861536 | ||||||||
\(560\) | −7.84161 | − | 7.10698i | −0.331369 | − | 0.300325i | ||||
\(561\) | −4.29911 | −0.181509 | ||||||||
\(562\) | −0.774071 | + | 2.30882i | −0.0326522 | + | 0.0973917i | ||||
\(563\) | 1.94438 | 0.0819459 | 0.0409730 | − | 0.999160i | \(-0.486954\pi\) | ||||
0.0409730 | + | 0.999160i | \(0.486954\pi\) | |||||||
\(564\) | 14.3859 | + | 10.8678i | 0.605756 | + | 0.457618i | ||||
\(565\) | 11.8448i | 0.498315i | ||||||||
\(566\) | −2.92777 | + | 8.73264i | −0.123063 | + | 0.367060i | ||||
\(567\) | 1.40015 | + | 2.24490i | 0.0588008 | + | 0.0942770i | ||||
\(568\) | −9.34700 | − | 13.6529i | −0.392191 | − | 0.572863i | ||||
\(569\) | −5.72219 | −0.239887 | −0.119943 | − | 0.992781i | \(-0.538271\pi\) | ||||
−0.119943 | + | 0.992781i | \(0.538271\pi\) | |||||||
\(570\) | −10.4450 | − | 3.50185i | −0.437492 | − | 0.146676i | ||||
\(571\) | 42.2732i | 1.76908i | 0.466466 | + | 0.884539i | \(0.345527\pi\) | ||||
−0.466466 | + | 0.884539i | \(0.654473\pi\) | |||||||
\(572\) | −15.9593 | − | 12.0565i | −0.667293 | − | 0.504106i | ||||
\(573\) | − | 5.02689i | − | 0.210001i | ||||||
\(574\) | −8.09774 | − | 33.9454i | −0.337993 | − | 1.41685i | ||||
\(575\) | − | 8.10651i | − | 0.338065i | ||||||
\(576\) | 2.89399 | − | 7.45821i | 0.120583 | − | 0.310759i | ||||
\(577\) | − | 0.216956i | − | 0.00903200i | −0.999990 | − | 0.00451600i | \(-0.998563\pi\) | ||
0.999990 | − | 0.00451600i | \(-0.00143749\pi\) | |||||||
\(578\) | −7.12080 | + | 21.2392i | −0.296186 | + | 0.883434i | ||||
\(579\) | −15.8775 | −0.659845 | ||||||||
\(580\) | −7.23074 | + | 9.57144i | −0.300240 | + | 0.397432i | ||||
\(581\) | −17.5162 | − | 28.0843i | −0.726696 | − | 1.16513i | ||||
\(582\) | 16.1086 | + | 5.40068i | 0.667722 | + | 0.223865i | ||||
\(583\) | 11.4366i | 0.473658i | ||||||||
\(584\) | −9.15950 | − | 13.3790i | −0.379023 | − | 0.553627i | ||||
\(585\) | 2.50547 | 0.103588 | ||||||||
\(586\) | −12.3410 | − | 4.13754i | −0.509803 | − | 0.170920i | ||||
\(587\) | −6.61005 | −0.272826 | −0.136413 | − | 0.990652i | \(-0.543557\pi\) | ||||
−0.136413 | + | 0.990652i | \(0.543557\pi\) | |||||||
\(588\) | −12.4924 | + | 6.31982i | −0.515178 | + | 0.260625i | ||||
\(589\) | 49.2747 | 2.03033 | ||||||||
\(590\) | −12.9832 | − | 4.35285i | −0.534511 | − | 0.179204i | ||||
\(591\) | 10.1289 | 0.416646 | ||||||||
\(592\) | 3.33834 | + | 11.7492i | 0.137205 | + | 0.482889i | ||||
\(593\) | − | 19.2223i | − | 0.789365i | −0.918818 | − | 0.394682i | \(-0.870855\pi\) | ||
0.918818 | − | 0.394682i | \(-0.129145\pi\) | |||||||
\(594\) | 5.35213 | + | 1.79439i | 0.219601 | + | 0.0736248i | ||||
\(595\) | 1.50803 | + | 2.41787i | 0.0618232 | + | 0.0991230i | ||||
\(596\) | 31.4177 | + | 23.7345i | 1.28692 | + | 0.972203i | ||||
\(597\) | −1.13945 | −0.0466347 | ||||||||
\(598\) | −9.13056 | + | 27.2337i | −0.373376 | + | 1.11367i | ||||
\(599\) | 29.5976i | 1.20933i | 0.796481 | + | 0.604663i | \(0.206692\pi\) | ||||
−0.796481 | + | 0.604663i | \(0.793308\pi\) | |||||||
\(600\) | 2.33388 | − | 1.59781i | 0.0952802 | − | 0.0652304i | ||||
\(601\) | 42.7644i | 1.74440i | 0.489154 | + | 0.872198i | \(0.337306\pi\) | ||||
−0.489154 | + | 0.872198i | \(0.662694\pi\) | |||||||
\(602\) | 7.05861 | + | 29.5894i | 0.287688 | + | 1.20597i | ||||
\(603\) | 7.79060i | 0.317258i | ||||||||
\(604\) | −15.9992 | + | 21.1784i | −0.650999 | + | 0.861738i | ||||
\(605\) | − | 4.93258i | − | 0.200538i | ||||||
\(606\) | 0.349291 | + | 0.117106i | 0.0141890 | + | 0.00475709i | ||||
\(607\) | −43.6339 | −1.77104 | −0.885522 | − | 0.464598i | \(-0.846199\pi\) | ||||
−0.885522 | + | 0.464598i | \(0.846199\pi\) | |||||||
\(608\) | 44.0175 | + | 2.05503i | 1.78515 | + | 0.0833424i | ||||
\(609\) | 8.39786 | + | 13.4645i | 0.340299 | + | 0.545611i | ||||
\(610\) | 1.44410 | − | 4.30731i | 0.0584699 | − | 0.174398i | ||||
\(611\) | − | 22.5862i | − | 0.913740i | ||||||
\(612\) | −1.29845 | + | 1.71877i | −0.0524866 | + | 0.0694773i | ||||
\(613\) | −41.2984 | −1.66803 | −0.834013 | − | 0.551744i | \(-0.813963\pi\) | ||||
−0.834013 | + | 0.551744i | \(0.813963\pi\) | |||||||
\(614\) | −14.6440 | + | 43.6786i | −0.590983 | + | 1.76272i | ||||
\(615\) | 9.32685 | 0.376095 | ||||||||
\(616\) | −11.9833 | + | 27.3610i | −0.482820 | + | 1.10241i | ||||
\(617\) | −2.12487 | −0.0855439 | −0.0427719 | − | 0.999085i | \(-0.513619\pi\) | ||||
−0.0427719 | + | 0.999085i | \(0.513619\pi\) | |||||||
\(618\) | 0.793378 | − | 2.36641i | 0.0319144 | − | 0.0951909i | ||||
\(619\) | 21.1221 | 0.848970 | 0.424485 | − | 0.905435i | \(-0.360455\pi\) | ||||
0.424485 | + | 0.905435i | \(0.360455\pi\) | |||||||
\(620\) | −7.62587 | + | 10.0945i | −0.306262 | + | 0.405404i | ||||
\(621\) | − | 8.10651i | − | 0.325303i | ||||||
\(622\) | 12.3005 | − | 36.6888i | 0.493206 | − | 1.47109i | ||||
\(623\) | −7.88825 | + | 4.91992i | −0.316036 | + | 0.197112i | ||||
\(624\) | −9.64029 | + | 2.73912i | −0.385920 | + | 0.109653i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −26.4268 | − | 8.86002i | −1.05623 | − | 0.354118i | ||||
\(627\) | 31.0933i | 1.24175i | ||||||||
\(628\) | −23.3149 | + | 30.8623i | −0.930365 | + | 1.23154i | ||||
\(629\) | − | 3.28884i | − | 0.131135i | ||||||
\(630\) | −0.868219 | − | 3.63953i | −0.0345907 | − | 0.145002i | ||||
\(631\) | − | 3.20820i | − | 0.127716i | −0.997959 | − | 0.0638582i | \(-0.979659\pi\) | ||
0.997959 | − | 0.0638582i | \(-0.0203406\pi\) | |||||||
\(632\) | 4.50265 | + | 6.57689i | 0.179106 | + | 0.261615i | ||||
\(633\) | 16.8644i | 0.670300i | ||||||||
\(634\) | 0.384350 | − | 1.14640i | 0.0152645 | − | 0.0455294i | ||||
\(635\) | 5.49406 | 0.218025 | ||||||||
\(636\) | 4.57234 | + | 3.45417i | 0.181305 | + | 0.136967i | ||||
\(637\) | 15.7504 | + | 7.71474i | 0.624052 | + | 0.305669i | ||||
\(638\) | 32.1012 | + | 10.7625i | 1.27090 | + | 0.426090i | ||||
\(639\) | − | 5.84987i | − | 0.231417i | ||||||
\(640\) | −7.23324 | + | 8.69944i | −0.285919 | + | 0.343875i | ||||
\(641\) | −14.2121 | −0.561345 | −0.280673 | − | 0.959804i | \(-0.590558\pi\) | ||||
−0.280673 | + | 0.959804i | \(0.590558\pi\) | |||||||
\(642\) | 8.18232 | + | 2.74326i | 0.322930 | + | 0.108268i | ||||
\(643\) | −7.89830 | −0.311479 | −0.155739 | − | 0.987798i | \(-0.549776\pi\) | ||||
−0.155739 | + | 0.987798i | \(0.549776\pi\) | |||||||
\(644\) | 42.7247 | + | 3.82610i | 1.68359 | + | 0.150769i | ||||
\(645\) | −8.13000 | −0.320118 | ||||||||
\(646\) | −11.2497 | − | 3.77167i | −0.442615 | − | 0.148394i | ||||
\(647\) | 0.910960 | 0.0358135 | 0.0179068 | − | 0.999840i | \(-0.494300\pi\) | ||||
0.0179068 | + | 0.999840i | \(0.494300\pi\) | |||||||
\(648\) | 2.33388 | − | 1.59781i | 0.0916834 | − | 0.0627680i | ||||
\(649\) | 38.6494i | 1.51712i | ||||||||
\(650\) | −3.35948 | − | 1.12632i | −0.131770 | − | 0.0441781i | ||||
\(651\) | 8.85677 | + | 14.2003i | 0.347124 | + | 0.556554i | ||||
\(652\) | 3.31138 | − | 4.38333i | 0.129684 | − | 0.171664i | ||||
\(653\) | 1.82376 | 0.0713691 | 0.0356846 | − | 0.999363i | \(-0.488639\pi\) | ||||
0.0356846 | + | 0.999363i | \(0.488639\pi\) | |||||||
\(654\) | 6.72344 | − | 20.0540i | 0.262907 | − | 0.784173i | ||||
\(655\) | − | 9.93971i | − | 0.388377i | ||||||
\(656\) | −35.8869 | + | 10.1967i | −1.40115 | + | 0.398113i | ||||
\(657\) | − | 5.73252i | − | 0.223647i | ||||||
\(658\) | −32.8095 | + | 7.82678i | −1.27905 | + | 0.305120i | ||||
\(659\) | − | 6.38815i | − | 0.248847i | −0.992229 | − | 0.124423i | \(-0.960292\pi\) | ||
0.992229 | − | 0.124423i | \(-0.0397081\pi\) | |||||||
\(660\) | −6.36980 | − | 4.81206i | −0.247944 | − | 0.187309i | ||||
\(661\) | − | 16.7429i | − | 0.651222i | −0.945504 | − | 0.325611i | \(-0.894430\pi\) | ||
0.945504 | − | 0.325611i | \(-0.105570\pi\) | |||||||
\(662\) | −5.68177 | − | 1.90491i | −0.220828 | − | 0.0740364i | ||||
\(663\) | 2.69851 | 0.104802 | ||||||||
\(664\) | −29.1974 | + | 19.9891i | −1.13308 | + | 0.775726i | ||||
\(665\) | 17.4872 | − | 10.9068i | 0.678125 | − | 0.422948i | ||||
\(666\) | −1.37272 | + | 4.09441i | −0.0531918 | + | 0.158655i | ||||
\(667\) | − | 48.6215i | − | 1.88263i | ||||||
\(668\) | −9.29038 | − | 7.01841i | −0.359456 | − | 0.271551i | ||||
\(669\) | −1.84769 | −0.0714358 | ||||||||
\(670\) | 3.50224 | − | 10.4461i | 0.135303 | − | 0.403569i | ||||
\(671\) | −12.8223 | −0.494999 | ||||||||
\(672\) | 7.31959 | + | 13.0546i | 0.282359 | + | 0.503594i | ||||
\(673\) | −35.5295 | −1.36956 | −0.684782 | − | 0.728748i | \(-0.740102\pi\) | ||||
−0.684782 | + | 0.728748i | \(0.740102\pi\) | |||||||
\(674\) | −9.25866 | + | 27.6158i | −0.356630 | + | 1.06372i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −10.7281 | − | 8.10452i | −0.412619 | − | 0.311712i | ||||
\(677\) | − | 12.3173i | − | 0.473391i | −0.971584 | − | 0.236696i | \(-0.923936\pi\) | ||
0.971584 | − | 0.236696i | \(-0.0760644\pi\) | |||||||
\(678\) | 5.32479 | − | 15.8822i | 0.204497 | − | 0.609954i | ||||
\(679\) | −26.9694 | + | 16.8209i | −1.03499 | + | 0.645525i | ||||
\(680\) | 2.51370 | − | 1.72092i | 0.0963961 | − | 0.0659944i | ||||
\(681\) | −26.0109 | −0.996738 | ||||||||
\(682\) | 33.8554 | + | 11.3506i | 1.29639 | + | 0.434637i | ||||
\(683\) | 5.01785i | 0.192003i | 0.995381 | + | 0.0960014i | \(0.0306053\pi\) | ||||
−0.995381 | + | 0.0960014i | \(0.969395\pi\) | |||||||
\(684\) | 12.4310 | + | 9.39100i | 0.475311 | + | 0.359074i | ||||
\(685\) | 16.4345i | 0.627929i | ||||||||
\(686\) | 5.74875 | − | 25.5529i | 0.219488 | − | 0.975615i | ||||
\(687\) | 14.8172i | 0.565310i | ||||||||
\(688\) | 31.2818 | − | 8.88819i | 1.19261 | − | 0.338859i | ||||
\(689\) | − | 7.17868i | − | 0.273486i | ||||||
\(690\) | −3.64425 | + | 10.8697i | −0.138734 | + | 0.413803i | ||||
\(691\) | 31.8714 | 1.21245 | 0.606224 | − | 0.795294i | \(-0.292684\pi\) | ||||
0.606224 | + | 0.795294i | \(0.292684\pi\) | |||||||
\(692\) | 12.7369 | − | 16.8600i | 0.484184 | − | 0.640922i | ||||
\(693\) | −8.96067 | + | 5.58879i | −0.340388 | + | 0.212300i | ||||
\(694\) | 18.5383 | + | 6.21527i | 0.703703 | + | 0.235928i | ||||
\(695\) | 17.8065i | 0.675440i | ||||||||
\(696\) | 13.9982 | − | 9.58342i | 0.530601 | − | 0.363258i | ||||
\(697\) | 10.0455 | 0.380500 | ||||||||
\(698\) | −10.8163 | − | 3.62634i | −0.409402 | − | 0.137259i | ||||
\(699\) | 3.41871 | 0.129307 | ||||||||
\(700\) | −0.471978 | + | 5.27041i | −0.0178391 | + | 0.199203i | ||||
\(701\) | 20.4325 | 0.771725 | 0.385862 | − | 0.922556i | \(-0.373904\pi\) | ||||
0.385862 | + | 0.922556i | \(0.373904\pi\) | |||||||
\(702\) | −3.35948 | − | 1.12632i | −0.126796 | − | 0.0425104i | ||||
\(703\) | −23.7865 | −0.897126 | ||||||||
\(704\) | 29.7699 | + | 11.5515i | 1.12200 | + | 0.435365i | ||||
\(705\) | − | 9.01476i | − | 0.339516i | ||||||
\(706\) | −10.2937 | − | 3.45114i | −0.387409 | − | 0.129885i | ||||
\(707\) | −0.584791 | + | 0.364735i | −0.0219933 | + | 0.0137173i | ||||
\(708\) | 15.4519 | + | 11.6731i | 0.580718 | + | 0.438703i | ||||
\(709\) | −42.4953 | −1.59594 | −0.797972 | − | 0.602695i | \(-0.794094\pi\) | ||||
−0.797972 | + | 0.602695i | \(0.794094\pi\) | |||||||
\(710\) | −2.62979 | + | 7.84386i | −0.0986942 | + | 0.294375i | ||||
\(711\) | 2.81801i | 0.105683i | ||||||||
\(712\) | 5.61448 | + | 8.20090i | 0.210411 | + | 0.307342i | ||||
\(713\) | − | 51.2785i | − | 1.92039i | ||||||
\(714\) | −0.935114 | − | 3.91996i | −0.0349958 | − | 0.146701i | ||||
\(715\) | 10.0007i | 0.374006i | ||||||||
\(716\) | −5.54421 | + | 7.33895i | −0.207197 | + | 0.274270i | ||||
\(717\) | − | 2.84316i | − | 0.106180i | ||||||
\(718\) | 28.9984 | + | 9.72219i | 1.08221 | + | 0.362829i | ||||
\(719\) | −3.58392 | −0.133658 | −0.0668289 | − | 0.997764i | \(-0.521288\pi\) | ||||
−0.0668289 | + | 0.997764i | \(0.521288\pi\) | |||||||
\(720\) | −3.84770 | + | 1.09326i | −0.143395 | + | 0.0407433i | ||||
\(721\) | 2.47104 | + | 3.96190i | 0.0920264 | + | 0.147549i | ||||
\(722\) | −18.7372 | + | 55.8873i | −0.697326 | + | 2.07991i | ||||
\(723\) | − | 20.0977i | − | 0.747441i | ||||||
\(724\) | 11.3650 | − | 15.0441i | 0.422378 | − | 0.559108i | ||||
\(725\) | 5.99783 | 0.222754 | ||||||||
\(726\) | −2.21742 | + | 6.61390i | −0.0822963 | + | 0.245465i | ||||
\(727\) | 21.1835 | 0.785652 | 0.392826 | − | 0.919613i | \(-0.371497\pi\) | ||||
0.392826 | + | 0.919613i | \(0.371497\pi\) | |||||||
\(728\) | 7.52179 | − | 17.1743i | 0.278776 | − | 0.636521i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.57703 | + | 7.68651i | −0.0953803 | + | 0.284491i | ||||
\(731\) | −8.75641 | −0.323867 | ||||||||
\(732\) | −3.87267 | + | 5.12632i | −0.143138 | + | 0.189474i | ||||
\(733\) | − | 27.6118i | − | 1.01986i | −0.860215 | − | 0.509932i | \(-0.829670\pi\) | ||
0.860215 | − | 0.509932i | \(-0.170330\pi\) | |||||||
\(734\) | 2.97702 | − | 8.87956i | 0.109884 | − | 0.327751i | ||||
\(735\) | 6.28639 | + | 3.07916i | 0.231877 | + | 0.113577i | ||||
\(736\) | 2.13859 | − | 45.8075i | 0.0788296 | − | 1.68849i | ||||
\(737\) | −31.0967 | −1.14546 | ||||||||
\(738\) | −12.5060 | − | 4.19285i | −0.460353 | − | 0.154341i | ||||
\(739\) | − | 18.3419i | − | 0.674716i | −0.941376 | − | 0.337358i | \(-0.890467\pi\) | ||
0.941376 | − | 0.337358i | \(-0.109533\pi\) | |||||||
\(740\) | 3.68125 | − | 4.87293i | 0.135326 | − | 0.179133i | ||||
\(741\) | − | 19.5170i | − | 0.716974i | ||||||
\(742\) | −10.4280 | + | 2.48762i | −0.382824 | + | 0.0913236i | ||||
\(743\) | − | 47.9531i | − | 1.75923i | −0.475688 | − | 0.879614i | \(-0.657801\pi\) | ||
0.475688 | − | 0.879614i | \(-0.342199\pi\) | |||||||
\(744\) | 14.7632 | − | 10.1071i | 0.541244 | − | 0.370545i | ||||
\(745\) | − | 19.6876i | − | 0.721296i | ||||||
\(746\) | 14.0072 | − | 41.7792i | 0.512839 | − | 1.52964i | ||||
\(747\) | −12.5103 | −0.457726 | ||||||||
\(748\) | −6.86059 | − | 5.18283i | −0.250848 | − | 0.189503i | ||||
\(749\) | −13.6990 | + | 8.54411i | −0.500552 | + | 0.312195i | ||||
\(750\) | −1.34086 | − | 0.449546i | −0.0489613 | − | 0.0164151i | ||||
\(751\) | − | 51.3906i | − | 1.87527i | −0.347624 | − | 0.937634i | \(-0.613011\pi\) | ||
0.347624 | − | 0.937634i | \(-0.386989\pi\) | |||||||
\(752\) | 9.85546 | + | 34.6861i | 0.359392 | + | 1.26487i | ||||
\(753\) | 15.7417 | 0.573659 | ||||||||
\(754\) | −20.1496 | − | 6.75550i | −0.733806 | − | 0.246021i | ||||
\(755\) | 13.2712 | 0.482989 | ||||||||
\(756\) | −0.471978 | + | 5.27041i | −0.0171657 | + | 0.191683i | ||||
\(757\) | −7.69109 | −0.279537 | −0.139769 | − | 0.990184i | \(-0.544636\pi\) | ||||
−0.139769 | + | 0.990184i | \(0.544636\pi\) | |||||||
\(758\) | −41.8194 | − | 14.0207i | −1.51895 | − | 0.509253i | ||||
\(759\) | 32.3577 | 1.17451 | ||||||||
\(760\) | −12.4466 | − | 18.1803i | −0.451484 | − | 0.659470i | ||||
\(761\) | − | 48.0926i | − | 1.74336i | −0.490080 | − | 0.871678i | \(-0.663032\pi\) | ||
0.490080 | − | 0.871678i | \(-0.336968\pi\) | |||||||
\(762\) | −7.36677 | − | 2.46983i | −0.266870 | − | 0.0894727i | ||||
\(763\) | 20.9407 | + | 33.5749i | 0.758105 | + | 1.21549i | ||||
\(764\) | 6.06021 | − | 8.02199i | 0.219251 | − | 0.290225i | ||||
\(765\) | 1.07705 | 0.0389408 | ||||||||
\(766\) | −12.5831 | + | 37.5316i | −0.454646 | + | 1.35607i | ||||
\(767\) | − | 24.2599i | − | 0.875973i | ||||||
\(768\) | 13.6096 | − | 8.41306i | 0.491093 | − | 0.303580i | ||||
\(769\) | − | 46.2666i | − | 1.66842i | −0.551449 | − | 0.834209i | \(-0.685925\pi\) | ||
0.551449 | − | 0.834209i | \(-0.314075\pi\) | |||||||
\(770\) | 14.5274 | − | 3.46555i | 0.523532 | − | 0.124890i | ||||
\(771\) | − | 7.43670i | − | 0.267826i | ||||||
\(772\) | −25.3375 | − | 19.1412i | −0.911917 | − | 0.688907i | ||||
\(773\) | 37.7785i | 1.35880i | 0.733768 | + | 0.679400i | \(0.237760\pi\) | ||||
−0.733768 | + | 0.679400i | \(0.762240\pi\) | |||||||
\(774\) | 10.9012 | + | 3.65481i | 0.391835 | + | 0.131369i | ||||
\(775\) | 6.32559 | 0.227222 | ||||||||
\(776\) | 19.1955 | + | 28.0383i | 0.689079 | + | 1.00652i | ||||
\(777\) | −4.27545 | − | 6.85496i | −0.153381 | − | 0.245920i | ||||
\(778\) | −7.08046 | + | 21.1189i | −0.253847 | + | 0.757148i | ||||
\(779\) | − | 72.6538i | − | 2.60309i | ||||||
\(780\) | 3.99827 | + | 3.02049i | 0.143161 | + | 0.108151i | ||||
\(781\) | 23.3501 | 0.835533 | ||||||||
\(782\) | −3.92504 | + | 11.7072i | −0.140359 | + | 0.418649i | ||||
\(783\) | 5.99783 | 0.214345 | ||||||||
\(784\) | −27.5545 | − | 4.97504i | −0.984088 | − | 0.177680i | ||||
\(785\) | 19.3395 | 0.690256 | ||||||||
\(786\) | −4.46836 | + | 13.3278i | −0.159381 | + | 0.475386i | ||||
\(787\) | 11.0579 | 0.394172 | 0.197086 | − | 0.980386i | \(-0.436852\pi\) | ||||
0.197086 | + | 0.980386i | \(0.436852\pi\) | |||||||
\(788\) | 16.1638 | + | 12.2109i | 0.575811 | + | 0.434996i | ||||
\(789\) | − | 8.49327i | − | 0.302368i | ||||||
\(790\) | 1.26682 | − | 3.77855i | 0.0450716 | − | 0.134435i | ||||
\(791\) | 16.5845 | + | 26.5904i | 0.589677 | + | 0.945447i | ||||
\(792\) | 6.37777 | + | 9.31583i | 0.226624 | + | 0.331024i | ||||
\(793\) | 8.04843 | 0.285808 | ||||||||
\(794\) | −15.2441 | − | 5.11085i | −0.540993 | − | 0.181377i | ||||
\(795\) | − | 2.86521i | − | 0.101618i | ||||||
\(796\) | −1.81836 | − | 1.37368i | −0.0644500 | − | 0.0486887i | ||||
\(797\) | 35.7434i | 1.26610i | 0.774113 | + | 0.633048i | \(0.218196\pi\) | ||||
−0.774113 | + | 0.633048i | \(0.781804\pi\) | |||||||
\(798\) | −28.3510 | + | 6.76321i | −1.00362 | + | 0.239415i | ||||
\(799\) | − | 9.70934i | − | 0.343492i | ||||||
\(800\) | 5.65070 | + | 0.263812i | 0.199782 | + | 0.00932715i | ||||
\(801\) | 3.51385i | 0.124156i | ||||||||
\(802\) | −5.73725 | + | 17.1125i | −0.202589 | + | 0.604262i | ||||
\(803\) | 22.8817 | 0.807478 | ||||||||
\(804\) | −9.39202 | + | 12.4324i | −0.331231 | + | 0.438456i | ||||
\(805\) | −11.3503 | − | 18.1983i | −0.400047 | − | 0.641407i | ||||
\(806\) | −21.2507 | − | 7.12466i | −0.748524 | − | 0.250956i | ||||
\(807\) | − | 5.94512i | − | 0.209278i | ||||||
\(808\) | 0.416226 | + | 0.607970i | 0.0146428 | + | 0.0213883i | ||||
\(809\) | −7.42802 | −0.261155 | −0.130578 | − | 0.991438i | \(-0.541683\pi\) | ||||
−0.130578 | + | 0.991438i | \(0.541683\pi\) | |||||||
\(810\) | −1.34086 | − | 0.449546i | −0.0471131 | − | 0.0157954i | ||||
\(811\) | 49.8603 | 1.75083 | 0.875416 | − | 0.483370i | \(-0.160587\pi\) | ||||
0.875416 | + | 0.483370i | \(0.160587\pi\) | |||||||
\(812\) | −2.83085 | + | 31.6110i | −0.0993432 | + | 1.10933i | ||||
\(813\) | 11.2023 | 0.392881 | ||||||||
\(814\) | −16.3431 | − | 5.47930i | −0.572825 | − | 0.192049i | ||||
\(815\) | −2.74676 | −0.0962149 | ||||||||
\(816\) | −4.14416 | + | 1.17749i | −0.145075 | + | 0.0412205i | ||||
\(817\) | 63.3306i | 2.21566i | ||||||||
\(818\) | −2.56975 | − | 0.861551i | −0.0898491 | − | 0.0301234i | ||||
\(819\) | 5.62453 | − | 3.50803i | 0.196537 | − | 0.122580i | ||||
\(820\) | 14.8839 | + | 11.2441i | 0.519770 | + | 0.392660i | ||||
\(821\) | 32.6401 | 1.13915 | 0.569574 | − | 0.821940i | \(-0.307108\pi\) | ||||
0.569574 | + | 0.821940i | \(0.307108\pi\) | |||||||
\(822\) | 7.38806 | − | 22.0363i | 0.257688 | − | 0.768606i | ||||
\(823\) | − | 35.2404i | − | 1.22840i | −0.789150 | − | 0.614201i | \(-0.789478\pi\) | ||
0.789150 | − | 0.614201i | \(-0.210522\pi\) | |||||||
\(824\) | 4.11893 | − | 2.81989i | 0.143490 | − | 0.0982354i | ||||
\(825\) | 3.99156i | 0.138968i | ||||||||
\(826\) | −35.2407 | + | 8.40676i | −1.22618 | + | 0.292508i | ||||
\(827\) | − | 16.9100i | − | 0.588019i | −0.955802 | − | 0.294010i | \(-0.905010\pi\) | ||
0.955802 | − | 0.294010i | \(-0.0949898\pi\) | |||||||
\(828\) | 9.77288 | − | 12.9365i | 0.339631 | − | 0.449575i | ||||
\(829\) | 6.01900i | 0.209049i | 0.994522 | + | 0.104524i | \(0.0333320\pi\) | ||||
−0.994522 | + | 0.104524i | \(0.966668\pi\) | |||||||
\(830\) | 16.7745 | + | 5.62394i | 0.582252 | + | 0.195210i | ||||
\(831\) | −2.17155 | −0.0753301 | ||||||||
\(832\) | −18.6863 | − | 7.25079i | −0.647831 | − | 0.251376i | ||||
\(833\) | 6.77076 | + | 3.31641i | 0.234593 | + | 0.114907i | ||||
\(834\) | 8.00485 | − | 23.8761i | 0.277185 | − | 0.826760i | ||||
\(835\) | 5.82171i | 0.201469i | ||||||||
\(836\) | −37.4848 | + | 49.6192i | −1.29644 | + | 1.71611i | ||||
\(837\) | 6.32559 | 0.218644 | ||||||||
\(838\) | 6.16349 | − | 18.3838i | 0.212914 | − | 0.635059i | ||||
\(839\) | −28.4981 | −0.983864 | −0.491932 | − | 0.870634i | \(-0.663709\pi\) | ||||
−0.491932 | + | 0.870634i | \(0.663709\pi\) | |||||||
\(840\) | 3.00215 | − | 6.85471i | 0.103584 | − | 0.236510i | ||||
\(841\) | 6.97399 | 0.240482 | ||||||||
\(842\) | −3.54076 | + | 10.5610i | −0.122023 | + | 0.363956i | ||||
\(843\) | −1.72189 | −0.0593052 | ||||||||
\(844\) | −20.3310 | + | 26.9125i | −0.699822 | + | 0.926366i | ||||
\(845\) | 6.72263i | 0.231265i | ||||||||
\(846\) | −4.05255 | + | 12.0875i | −0.139330 | + | 0.415578i | ||||
\(847\) | −6.90635 | − | 11.0732i | −0.237305 | − | 0.380478i | ||||
\(848\) | 3.13241 | + | 11.0244i | 0.107567 | + | 0.378581i | ||||
\(849\) | −6.51271 | −0.223516 | ||||||||
\(850\) | −1.44417 | − | 0.484184i | −0.0495347 | − | 0.0166074i | ||||
\(851\) | 24.7538i | 0.848549i | ||||||||
\(852\) | 7.05236 | − | 9.33532i | 0.241610 | − | 0.319823i | ||||
\(853\) | 19.8203i | 0.678635i | 0.940672 | + | 0.339317i | \(0.110196\pi\) | ||||
−0.940672 | + | 0.339317i | \(0.889804\pi\) | |||||||
\(854\) | −2.78902 | − | 11.6914i | −0.0954383 | − | 0.400073i | ||||
\(855\) | − | 7.78975i | − | 0.266404i | ||||||
\(856\) | 9.75031 | + | 14.2420i | 0.333259 | + | 0.486782i | ||||
\(857\) | 28.1486i | 0.961539i | 0.876847 | + | 0.480769i | \(0.159643\pi\) | ||||
−0.876847 | + | 0.480769i | \(0.840357\pi\) | |||||||
\(858\) | 4.49579 | − | 13.4096i | 0.153484 | − | 0.457796i | ||||
\(859\) | −47.6978 | −1.62743 | −0.813715 | − | 0.581265i | \(-0.802558\pi\) | ||||
−0.813715 | + | 0.581265i | \(0.802558\pi\) | |||||||
\(860\) | −12.9740 | − | 9.80118i | −0.442409 | − | 0.334218i | ||||
\(861\) | 20.9379 | − | 13.0590i | 0.713560 | − | 0.445049i | ||||
\(862\) | 30.0068 | + | 10.0603i | 1.02204 | + | 0.342655i | ||||
\(863\) | − | 4.53008i | − | 0.154206i | −0.997023 | − | 0.0771028i | \(-0.975433\pi\) | ||
0.997023 | − | 0.0771028i | \(-0.0245670\pi\) | |||||||
\(864\) | 5.65070 | + | 0.263812i | 0.192241 | + | 0.00897506i | ||||
\(865\) | −10.5651 | −0.359226 | ||||||||
\(866\) | 45.5586 | + | 15.2743i | 1.54815 | + | 0.519042i | ||||
\(867\) | −15.8400 | −0.537953 | ||||||||
\(868\) | −2.98554 | + | 33.3385i | −0.101336 | + | 1.13158i | ||||
\(869\) | −11.2483 | −0.381571 | ||||||||
\(870\) | −8.04226 | − | 2.69630i | −0.272658 | − | 0.0914133i | ||||
\(871\) | 19.5191 | 0.661379 | ||||||||
\(872\) | 34.9056 | − | 23.8970i | 1.18205 | − | 0.809254i | ||||
\(873\) | 12.0136i | 0.406599i | ||||||||
\(874\) | 84.6723 | + | 28.3878i | 2.86408 | + | 0.960232i | ||||
\(875\) | 2.24490 | − | 1.40015i | 0.0758915 | − | 0.0473337i | ||||
\(876\) | 6.91089 | − | 9.14805i | 0.233497 | − | 0.309084i | ||||
\(877\) | 45.2414 | 1.52769 | 0.763847 | − | 0.645397i | \(-0.223308\pi\) | ||||
0.763847 | + | 0.645397i | \(0.223308\pi\) | |||||||
\(878\) | 1.33729 | − | 3.98873i | 0.0451313 | − | 0.134613i | ||||
\(879\) | − | 9.20381i | − | 0.310437i | ||||||
\(880\) | −4.36381 | − | 15.3583i | −0.147104 | − | 0.517729i | ||||
\(881\) | 6.77716i | 0.228328i | 0.993462 | + | 0.114164i | \(0.0364190\pi\) | ||||
−0.993462 | + | 0.114164i | \(0.963581\pi\) | |||||||
\(882\) | −7.04495 | − | 6.95475i | −0.237216 | − | 0.234179i | ||||
\(883\) | − | 16.8172i | − | 0.565943i | −0.959128 | − | 0.282971i | \(-0.908680\pi\) | ||
0.959128 | − | 0.282971i | \(-0.0913202\pi\) | |||||||
\(884\) | 4.30633 | + | 3.25321i | 0.144838 | + | 0.109417i | ||||
\(885\) | − | 9.68276i | − | 0.325483i | ||||||
\(886\) | −27.3663 | − | 9.17501i | −0.919388 | − | 0.308240i | ||||
\(887\) | 43.9171 | 1.47459 | 0.737296 | − | 0.675570i | \(-0.236102\pi\) | ||||
0.737296 | + | 0.675570i | \(0.236102\pi\) | |||||||
\(888\) | −7.12666 | + | 4.87903i | −0.239155 | + | 0.163730i | ||||
\(889\) | 12.3336 | − | 7.69251i | 0.413656 | − | 0.257998i | ||||
\(890\) | 1.57964 | − | 4.71158i | 0.0529496 | − | 0.157933i | ||||
\(891\) | 3.99156i | 0.133722i | ||||||||
\(892\) | −2.94857 | − | 2.22750i | −0.0987255 | − | 0.0745822i | ||||
\(893\) | −70.2227 | −2.34991 | ||||||||
\(894\) | −8.85047 | + | 26.3983i | −0.296004 | + | 0.882891i | ||||
\(895\) | 4.59887 | 0.153723 | ||||||||
\(896\) | −4.05740 | + | 29.6570i | −0.135548 | + | 0.990771i | ||||
\(897\) | −20.3106 | −0.678152 | ||||||||
\(898\) | 4.95552 | − | 14.7808i | 0.165368 | − | 0.493242i | ||||
\(899\) | 37.9398 | 1.26536 | ||||||||
\(900\) | 1.59582 | + | 1.20556i | 0.0531939 | + | 0.0401853i | ||||
\(901\) | − | 3.08597i | − | 0.102808i | ||||||
\(902\) | 16.7360 | − | 49.9185i | 0.557249 | − | 1.66211i | ||||
\(903\) | −18.2510 | + | 11.3832i | −0.607357 | + | 0.378810i | ||||
\(904\) | 27.6444 | − | 18.9258i | 0.919438 | − | 0.629463i | ||||
\(905\) | −9.42719 | −0.313370 | ||||||||
\(906\) | −17.7949 | − | 5.96603i | −0.591194 | − | 0.198208i | ||||
\(907\) | 1.93060i | 0.0641044i | 0.999486 | + | 0.0320522i | \(0.0102043\pi\) | ||||
−0.999486 | + | 0.0320522i | \(0.989796\pi\) | |||||||
\(908\) | −41.5085 | − | 31.3576i | −1.37751 | − | 1.04064i | ||||
\(909\) | 0.260498i | 0.00864016i | ||||||||
\(910\) | −9.11873 | + | 2.17529i | −0.302283 | + | 0.0721103i | ||||
\(911\) | − | 2.73855i | − | 0.0907323i | −0.998970 | − | 0.0453661i | \(-0.985555\pi\) | ||
0.998970 | − | 0.0453661i | \(-0.0144454\pi\) | |||||||
\(912\) | 8.51621 | + | 29.9726i | 0.282000 | + | 0.992492i | ||||
\(913\) | − | 49.9355i | − | 1.65262i | ||||||
\(914\) | −0.184017 | + | 0.548868i | −0.00608675 | + | 0.0181549i | ||||
\(915\) | 3.21235 | 0.106197 | ||||||||
\(916\) | −17.8630 | + | 23.6455i | −0.590209 | + | 0.781269i | ||||
\(917\) | −13.9171 | − | 22.3137i | −0.459582 | − | 0.736862i | ||||
\(918\) | −1.44417 | − | 0.484184i | −0.0476648 | − | 0.0159804i | ||||
\(919\) | 23.3016i | 0.768648i | 0.923198 | + | 0.384324i | \(0.125565\pi\) | ||||
−0.923198 | + | 0.384324i | \(0.874435\pi\) | |||||||
\(920\) | −18.9196 | + | 12.9527i | −0.623762 | + | 0.427038i | ||||
\(921\) | −32.5750 | −1.07338 | ||||||||
\(922\) | 32.1239 | + | 10.7701i | 1.05795 | + | 0.354694i | ||||
\(923\) | −14.6567 | −0.482430 | ||||||||
\(924\) | −21.0372 | − | 1.88393i | −0.692072 | − | 0.0619768i | ||||
\(925\) | −3.05357 | −0.100401 | ||||||||
\(926\) | −13.5438 | − | 4.54077i | −0.445076 | − | 0.149219i | ||||
\(927\) | 1.76484 | 0.0579650 | ||||||||
\(928\) | 33.8919 | + | 1.58230i | 1.11256 | + | 0.0519415i | ||||
\(929\) | − | 27.8007i | − | 0.912110i | −0.889952 | − | 0.456055i | \(-0.849262\pi\) | ||
0.889952 | − | 0.456055i | \(-0.150738\pi\) | |||||||
\(930\) | −8.48173 | − | 2.84365i | −0.278127 | − | 0.0932468i | ||||
\(931\) | 23.9859 | − | 48.9694i | 0.786106 | − | 1.60491i | ||||
\(932\) | 5.45563 | + | 4.12145i | 0.178705 | + | 0.135003i | ||||
\(933\) | 27.3621 | 0.895795 | ||||||||
\(934\) | 17.3922 | − | 51.8756i | 0.569089 | − | 1.69742i | ||||
\(935\) | 4.29911i | 0.140596i | ||||||||
\(936\) | −4.00327 | − | 5.84746i | −0.130851 | − | 0.191130i | ||||
\(937\) | 8.85962i | 0.289431i | 0.989473 | + | 0.144716i | \(0.0462267\pi\) | ||||
−0.989473 | + | 0.144716i | \(0.953773\pi\) | |||||||
\(938\) | −6.76394 | − | 28.3541i | −0.220851 | − | 0.925796i | ||||
\(939\) | − | 19.7088i | − | 0.643173i | ||||||
\(940\) | 10.8678 | − | 14.3859i | 0.354469 | − | 0.469216i | ||||
\(941\) | 53.7586i | 1.75248i | 0.481873 | + | 0.876241i | \(0.339957\pi\) | ||||
−0.481873 | + | 0.876241i | \(0.660043\pi\) | |||||||
\(942\) | −25.9316 | − | 8.69400i | −0.844896 | − | 0.283266i | ||||
\(943\) | −75.6082 | −2.46214 | ||||||||
\(944\) | 10.5858 | + | 37.2564i | 0.344537 | + | 1.21259i | ||||
\(945\) | 2.24490 | − | 1.40015i | 0.0730266 | − | 0.0455469i | ||||
\(946\) | −14.5884 | + | 43.5128i | −0.474310 | + | 1.41472i | ||||
\(947\) | − | 16.1410i | − | 0.524513i | −0.964998 | − | 0.262257i | \(-0.915533\pi\) | ||
0.964998 | − | 0.262257i | \(-0.0844667\pi\) | |||||||
\(948\) | −3.39727 | + | 4.49702i | −0.110338 | + | 0.146056i | ||||
\(949\) | −14.3626 | −0.466231 | ||||||||
\(950\) | −3.50185 | + | 10.4450i | −0.113615 | + | 0.338880i | ||||
\(951\) | 0.854973 | 0.0277244 | ||||||||
\(952\) | 3.23346 | − | 7.38286i | 0.104797 | − | 0.239280i | ||||
\(953\) | 31.2699 | 1.01293 | 0.506466 | − | 0.862260i | \(-0.330952\pi\) | ||||
0.506466 | + | 0.862260i | \(0.330952\pi\) | |||||||
\(954\) | −1.28804 | + | 3.84184i | −0.0417019 | + | 0.124384i | ||||
\(955\) | −5.02689 | −0.162666 | ||||||||
\(956\) | 3.42760 | − | 4.53716i | 0.110856 | − | 0.146742i | ||||
\(957\) | 23.9407i | 0.773894i | ||||||||
\(958\) | −3.55911 | + | 10.6157i | −0.114989 | + | 0.342979i | ||||
\(959\) | 23.0107 | + | 36.8938i | 0.743055 | + | 1.19136i | ||||
\(960\) | −7.45821 | − | 2.89399i | −0.240713 | − | 0.0934030i | ||||
\(961\) | 9.01306 | 0.290744 | ||||||||
\(962\) | 10.2584 | + | 3.43931i | 0.330744 | + | 0.110888i | ||||
\(963\) | 6.10229i | 0.196643i | ||||||||
\(964\) | 24.2289 | − | 32.0722i | 0.780361 | − | 1.03298i | ||||
\(965\) | 15.8775i | 0.511114i | ||||||||
\(966\) | 7.03823 | + | 29.5039i | 0.226451 | + | 0.949273i | ||||
\(967\) | − | 29.6531i | − | 0.953581i | −0.879017 | − | 0.476791i | \(-0.841800\pi\) | ||
0.879017 | − | 0.476791i | \(-0.158200\pi\) | |||||||
\(968\) | −11.5120 | + | 7.88134i | −0.370011 | + | 0.253316i | ||||
\(969\) | − | 8.38994i | − | 0.269524i | ||||||
\(970\) | 5.40068 | − | 16.1086i | 0.173405 | − | 0.517215i | ||||
\(971\) | 50.3454 | 1.61566 | 0.807831 | − | 0.589414i | \(-0.200641\pi\) | ||||
0.807831 | + | 0.589414i | \(0.200641\pi\) | |||||||
\(972\) | 1.59582 | + | 1.20556i | 0.0511858 | + | 0.0386683i | ||||
\(973\) | 24.9318 | + | 39.9739i | 0.799276 | + | 1.28150i | ||||
\(974\) | 38.3464 | + | 12.8563i | 1.22870 | + | 0.411942i | ||||
\(975\) | − | 2.50547i | − | 0.0802392i | ||||||
\(976\) | −12.3601 | + | 3.51193i | −0.395639 | + | 0.112414i | ||||
\(977\) | −40.8268 | −1.30617 | −0.653083 | − | 0.757286i | \(-0.726525\pi\) | ||||
−0.653083 | + | 0.757286i | \(0.726525\pi\) | |||||||
\(978\) | 3.68303 | + | 1.23480i | 0.117770 | + | 0.0394845i | ||||
\(979\) | −14.0258 | −0.448265 | ||||||||
\(980\) | 6.31982 | + | 12.4924i | 0.201879 | + | 0.399055i | ||||
\(981\) | 14.9561 | 0.477510 | ||||||||
\(982\) | −31.6870 | − | 10.6236i | −1.01117 | − | 0.339012i | ||||
\(983\) | 18.2294 | 0.581427 | 0.290713 | − | 0.956810i | \(-0.406107\pi\) | ||||
0.290713 | + | 0.956810i | \(0.406107\pi\) | |||||||
\(984\) | −14.9026 | − | 21.7677i | −0.475076 | − | 0.693930i | ||||
\(985\) | − | 10.1289i | − | 0.322732i | ||||||
\(986\) | −8.66191 | − | 2.90405i | −0.275851 | − | 0.0924838i | ||||
\(987\) | −12.6220 | − | 20.2372i | −0.401763 | − | 0.644159i | ||||
\(988\) | 23.5288 | − | 31.1455i | 0.748552 | − | 0.990870i | ||||
\(989\) | 65.9059 | 2.09569 | ||||||||
\(990\) | 1.79439 | − | 5.35213i | 0.0570296 | − | 0.170102i | ||||
\(991\) | 58.5653i | 1.86039i | 0.367070 | + | 0.930193i | \(0.380361\pi\) | ||||
−0.367070 | + | 0.930193i | \(0.619639\pi\) | |||||||
\(992\) | 35.7440 | + | 1.66876i | 1.13487 | + | 0.0529833i | ||||
\(993\) | − | 4.23740i | − | 0.134470i | ||||||
\(994\) | 5.07897 | + | 21.2908i | 0.161095 | + | 0.675303i | ||||
\(995\) | 1.13945i | 0.0361231i | ||||||||
\(996\) | −19.9641 | − | 15.0818i | −0.632586 | − | 0.477887i | ||||
\(997\) | − | 61.3384i | − | 1.94261i | −0.237846 | − | 0.971303i | \(-0.576441\pi\) | ||
0.237846 | − | 0.971303i | \(-0.423559\pi\) | |||||||
\(998\) | −0.889006 | − | 0.298054i | −0.0281410 | − | 0.00943475i | ||||
\(999\) | −3.05357 | −0.0966106 |
(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 | 420.2.c.a.391.6 | yes | 16 | |
3.2 | odd | 2 | 1260.2.c.d.811.11 | 16 | |||
4.3 | odd | 2 | 420.2.c.b.391.5 | yes | 16 | ||
7.6 | odd | 2 | 420.2.c.b.391.6 | yes | 16 | ||
12.11 | even | 2 | 1260.2.c.e.811.12 | 16 | |||
21.20 | even | 2 | 1260.2.c.e.811.11 | 16 | |||
28.27 | even | 2 | inner | 420.2.c.a.391.5 | ✓ | 16 | |
84.83 | odd | 2 | 1260.2.c.d.811.12 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.c.a.391.5 | ✓ | 16 | 28.27 | even | 2 | inner | |
420.2.c.a.391.6 | yes | 16 | 1.1 | even | 1 | trivial | |
420.2.c.b.391.5 | yes | 16 | 4.3 | odd | 2 | ||
420.2.c.b.391.6 | yes | 16 | 7.6 | odd | 2 | ||
1260.2.c.d.811.11 | 16 | 3.2 | odd | 2 | |||
1260.2.c.d.811.12 | 16 | 84.83 | odd | 2 | |||
1260.2.c.e.811.11 | 16 | 21.20 | even | 2 | |||
1260.2.c.e.811.12 | 16 | 12.11 | even | 2 |