Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,2,Mod(13,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.g (of order \(4\), 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: | \(0.558952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 27.1 | ||
Root | \(-0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 70.27 |
Dual form | 70.2.g.a.13.1 |
$q$-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 \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(57\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.30656 | − | 1.30656i | −0.754344 | − | 0.754344i | 0.220942 | − | 0.975287i | \(-0.429087\pi\) |
−0.975287 | + | 0.220942i | \(0.929087\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.158513 | − | 2.23044i | −0.0708890 | − | 0.997484i | ||||
\(6\) | 1.84776i | 0.754344i | ||||||||
\(7\) | −2.47247 | − | 0.941740i | −0.934507 | − | 0.355944i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0.414214i | 0.138071i | ||||||||
\(10\) | −1.46508 | + | 1.68925i | −0.463298 | + | 0.534187i | ||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 1.30656 | − | 1.30656i | 0.377172 | − | 0.377172i | ||||
\(13\) | 4.23671 | + | 4.23671i | 1.17505 | + | 1.17505i | 0.980989 | + | 0.194064i | \(0.0621670\pi\) |
0.194064 | + | 0.980989i | \(0.437833\pi\) | |||||||
\(14\) | 1.08239 | + | 2.41421i | 0.289281 | + | 0.645226i | ||||
\(15\) | −2.70711 | + | 3.12132i | −0.698972 | + | 0.805921i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.69552 | − | 3.69552i | 0.896295 | − | 0.896295i | −0.0988114 | − | 0.995106i | \(-0.531504\pi\) |
0.995106 | + | 0.0988114i | \(0.0315040\pi\) | |||||||
\(18\) | 0.292893 | − | 0.292893i | 0.0690356 | − | 0.0690356i | ||||
\(19\) | −1.39942 | −0.321048 | −0.160524 | − | 0.987032i | \(-0.551318\pi\) | ||||
−0.160524 | + | 0.987032i | \(0.551318\pi\) | |||||||
\(20\) | 2.23044 | − | 0.158513i | 0.498742 | − | 0.0354445i | ||||
\(21\) | 2.00000 | + | 4.46088i | 0.436436 | + | 0.973445i | ||||
\(22\) | −2.00000 | − | 2.00000i | −0.426401 | − | 0.426401i | ||||
\(23\) | 0.414214 | − | 0.414214i | 0.0863695 | − | 0.0863695i | −0.662602 | − | 0.748972i | \(-0.730548\pi\) |
0.748972 | + | 0.662602i | \(0.230548\pi\) | |||||||
\(24\) | −1.84776 | −0.377172 | ||||||||
\(25\) | −4.94975 | + | 0.707107i | −0.989949 | + | 0.141421i | ||||
\(26\) | − | 5.99162i | − | 1.17505i | ||||||
\(27\) | −3.37849 | + | 3.37849i | −0.650191 | + | 0.650191i | ||||
\(28\) | 0.941740 | − | 2.47247i | 0.177972 | − | 0.467254i | ||||
\(29\) | − | 0.828427i | − | 0.153835i | −0.997037 | − | 0.0769175i | \(-0.975492\pi\) | ||
0.997037 | − | 0.0769175i | \(-0.0245078\pi\) | |||||||
\(30\) | 4.12132 | − | 0.292893i | 0.752447 | − | 0.0534747i | ||||
\(31\) | − | 1.53073i | − | 0.274928i | −0.990507 | − | 0.137464i | \(-0.956105\pi\) | ||
0.990507 | − | 0.137464i | \(-0.0438951\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −3.69552 | − | 3.69552i | −0.643307 | − | 0.643307i | ||||
\(34\) | −5.22625 | −0.896295 | ||||||||
\(35\) | −1.70858 | + | 5.66399i | −0.288802 | + | 0.957389i | ||||
\(36\) | −0.414214 | −0.0690356 | ||||||||
\(37\) | 2.58579 | + | 2.58579i | 0.425101 | + | 0.425101i | 0.886956 | − | 0.461855i | \(-0.152816\pi\) |
−0.461855 | + | 0.886956i | \(0.652816\pi\) | |||||||
\(38\) | 0.989538 | + | 0.989538i | 0.160524 | + | 0.160524i | ||||
\(39\) | − | 11.0711i | − | 1.77279i | ||||||
\(40\) | −1.68925 | − | 1.46508i | −0.267093 | − | 0.231649i | ||||
\(41\) | − | 3.69552i | − | 0.577143i | −0.957458 | − | 0.288571i | \(-0.906820\pi\) | ||
0.957458 | − | 0.288571i | \(-0.0931803\pi\) | |||||||
\(42\) | 1.74011 | − | 4.56854i | 0.268505 | − | 0.704940i | ||||
\(43\) | 4.00000 | − | 4.00000i | 0.609994 | − | 0.609994i | −0.332950 | − | 0.942944i | \(-0.608044\pi\) |
0.942944 | + | 0.332950i | \(0.108044\pi\) | |||||||
\(44\) | 2.82843i | 0.426401i | ||||||||
\(45\) | 0.923880 | − | 0.0656581i | 0.137724 | − | 0.00978773i | ||||
\(46\) | −0.585786 | −0.0863695 | ||||||||
\(47\) | −1.08239 | + | 1.08239i | −0.157883 | + | 0.157883i | −0.781628 | − | 0.623745i | \(-0.785610\pi\) |
0.623745 | + | 0.781628i | \(0.285610\pi\) | |||||||
\(48\) | 1.30656 | + | 1.30656i | 0.188586 | + | 0.188586i | ||||
\(49\) | 5.22625 | + | 4.65685i | 0.746607 | + | 0.665265i | ||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | −9.65685 | −1.35223 | ||||||||
\(52\) | −4.23671 | + | 4.23671i | −0.587527 | + | 0.587527i | ||||
\(53\) | −8.24264 | + | 8.24264i | −1.13221 | + | 1.13221i | −0.142405 | + | 0.989808i | \(0.545484\pi\) |
−0.989808 | + | 0.142405i | \(0.954516\pi\) | |||||||
\(54\) | 4.77791 | 0.650191 | ||||||||
\(55\) | −0.448342 | − | 6.30864i | −0.0604544 | − | 0.850657i | ||||
\(56\) | −2.41421 | + | 1.08239i | −0.322613 | + | 0.144641i | ||||
\(57\) | 1.82843 | + | 1.82843i | 0.242181 | + | 0.242181i | ||||
\(58\) | −0.585786 | + | 0.585786i | −0.0769175 | + | 0.0769175i | ||||
\(59\) | 9.23880 | 1.20279 | 0.601394 | − | 0.798952i | \(-0.294612\pi\) | ||||
0.601394 | + | 0.798952i | \(0.294612\pi\) | |||||||
\(60\) | −3.12132 | − | 2.70711i | −0.402961 | − | 0.349486i | ||||
\(61\) | 6.43996i | 0.824552i | 0.911059 | + | 0.412276i | \(0.135266\pi\) | ||||
−0.911059 | + | 0.412276i | \(0.864734\pi\) | |||||||
\(62\) | −1.08239 | + | 1.08239i | −0.137464 | + | 0.137464i | ||||
\(63\) | 0.390081 | − | 1.02413i | 0.0491456 | − | 0.129029i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 8.77817 | − | 10.1213i | 1.08880 | − | 1.25540i | ||||
\(66\) | 5.22625i | 0.643307i | ||||||||
\(67\) | 10.4853 | + | 10.4853i | 1.28098 | + | 1.28098i | 0.940110 | + | 0.340871i | \(0.110722\pi\) |
0.340871 | + | 0.940110i | \(0.389278\pi\) | |||||||
\(68\) | 3.69552 | + | 3.69552i | 0.448147 | + | 0.448147i | ||||
\(69\) | −1.08239 | −0.130305 | ||||||||
\(70\) | 5.21319 | − | 2.79690i | 0.623096 | − | 0.334293i | ||||
\(71\) | −0.585786 | −0.0695201 | −0.0347600 | − | 0.999396i | \(-0.511067\pi\) | ||||
−0.0347600 | + | 0.999396i | \(0.511067\pi\) | |||||||
\(72\) | 0.292893 | + | 0.292893i | 0.0345178 | + | 0.0345178i | ||||
\(73\) | −4.14386 | − | 4.14386i | −0.485002 | − | 0.485002i | 0.421723 | − | 0.906725i | \(-0.361426\pi\) |
−0.906725 | + | 0.421723i | \(0.861426\pi\) | |||||||
\(74\) | − | 3.65685i | − | 0.425101i | ||||||
\(75\) | 7.39104 | + | 5.54328i | 0.853443 | + | 0.640083i | ||||
\(76\) | − | 1.39942i | − | 0.160524i | ||||||
\(77\) | −6.99321 | − | 2.66364i | −0.796950 | − | 0.303550i | ||||
\(78\) | −7.82843 | + | 7.82843i | −0.886395 | + | 0.886395i | ||||
\(79\) | 5.07107i | 0.570540i | 0.958447 | + | 0.285270i | \(0.0920832\pi\) | ||||
−0.958447 | + | 0.285270i | \(0.907917\pi\) | |||||||
\(80\) | 0.158513 | + | 2.23044i | 0.0177223 | + | 0.249371i | ||||
\(81\) | 10.0711 | 1.11901 | ||||||||
\(82\) | −2.61313 | + | 2.61313i | −0.288571 | + | 0.288571i | ||||
\(83\) | −5.31911 | − | 5.31911i | −0.583848 | − | 0.583848i | 0.352111 | − | 0.935958i | \(-0.385464\pi\) |
−0.935958 | + | 0.352111i | \(0.885464\pi\) | |||||||
\(84\) | −4.46088 | + | 2.00000i | −0.486722 | + | 0.218218i | ||||
\(85\) | −8.82843 | − | 7.65685i | −0.957577 | − | 0.830502i | ||||
\(86\) | −5.65685 | −0.609994 | ||||||||
\(87\) | −1.08239 | + | 1.08239i | −0.116045 | + | 0.116045i | ||||
\(88\) | 2.00000 | − | 2.00000i | 0.213201 | − | 0.213201i | ||||
\(89\) | −11.3492 | −1.20301 | −0.601506 | − | 0.798869i | \(-0.705432\pi\) | ||||
−0.601506 | + | 0.798869i | \(0.705432\pi\) | |||||||
\(90\) | −0.699709 | − | 0.606854i | −0.0737558 | − | 0.0639680i | ||||
\(91\) | −6.48528 | − | 14.4650i | −0.679842 | − | 1.51635i | ||||
\(92\) | 0.414214 | + | 0.414214i | 0.0431847 | + | 0.0431847i | ||||
\(93\) | −2.00000 | + | 2.00000i | −0.207390 | + | 0.207390i | ||||
\(94\) | 1.53073 | 0.157883 | ||||||||
\(95\) | 0.221825 | + | 3.12132i | 0.0227588 | + | 0.320241i | ||||
\(96\) | − | 1.84776i | − | 0.188586i | ||||||
\(97\) | 4.59220 | − | 4.59220i | 0.466267 | − | 0.466267i | −0.434436 | − | 0.900703i | \(-0.643052\pi\) |
0.900703 | + | 0.434436i | \(0.143052\pi\) | |||||||
\(98\) | −0.402625 | − | 6.98841i | −0.0406713 | − | 0.705936i | ||||
\(99\) | 1.17157i | 0.117748i | ||||||||
\(100\) | −0.707107 | − | 4.94975i | −0.0707107 | − | 0.494975i | ||||
\(101\) | 2.74444i | 0.273082i | 0.990634 | + | 0.136541i | \(0.0435986\pi\) | ||||
−0.990634 | + | 0.136541i | \(0.956401\pi\) | |||||||
\(102\) | 6.82843 | + | 6.82843i | 0.676115 | + | 0.676115i | ||||
\(103\) | 10.0042 | + | 10.0042i | 0.985739 | + | 0.985739i | 0.999900 | − | 0.0141603i | \(-0.00450753\pi\) |
−0.0141603 | + | 0.999900i | \(0.504508\pi\) | |||||||
\(104\) | 5.99162 | 0.587527 | ||||||||
\(105\) | 9.63272 | − | 5.16799i | 0.940057 | − | 0.504344i | ||||
\(106\) | 11.6569 | 1.13221 | ||||||||
\(107\) | −3.65685 | − | 3.65685i | −0.353521 | − | 0.353521i | 0.507897 | − | 0.861418i | \(-0.330423\pi\) |
−0.861418 | + | 0.507897i | \(0.830423\pi\) | |||||||
\(108\) | −3.37849 | − | 3.37849i | −0.325096 | − | 0.325096i | ||||
\(109\) | − | 12.1421i | − | 1.16301i | −0.813544 | − | 0.581503i | \(-0.802465\pi\) | ||
0.813544 | − | 0.581503i | \(-0.197535\pi\) | |||||||
\(110\) | −4.14386 | + | 4.77791i | −0.395102 | + | 0.455556i | ||||
\(111\) | − | 6.75699i | − | 0.641345i | ||||||
\(112\) | 2.47247 | + | 0.941740i | 0.233627 | + | 0.0889861i | ||||
\(113\) | 1.17157 | − | 1.17157i | 0.110212 | − | 0.110212i | −0.649850 | − | 0.760062i | \(-0.725168\pi\) |
0.760062 | + | 0.649850i | \(0.225168\pi\) | |||||||
\(114\) | − | 2.58579i | − | 0.242181i | ||||||
\(115\) | −0.989538 | − | 0.858221i | −0.0922749 | − | 0.0800296i | ||||
\(116\) | 0.828427 | 0.0769175 | ||||||||
\(117\) | −1.75490 | + | 1.75490i | −0.162241 | + | 0.162241i | ||||
\(118\) | −6.53281 | − | 6.53281i | −0.601394 | − | 0.601394i | ||||
\(119\) | −12.6173 | + | 5.65685i | −1.15662 | + | 0.518563i | ||||
\(120\) | 0.292893 | + | 4.12132i | 0.0267374 | + | 0.376223i | ||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 4.55374 | − | 4.55374i | 0.412276 | − | 0.412276i | ||||
\(123\) | −4.82843 | + | 4.82843i | −0.435365 | + | 0.435365i | ||||
\(124\) | 1.53073 | 0.137464 | ||||||||
\(125\) | 2.36176 | + | 10.9280i | 0.211242 | + | 0.977434i | ||||
\(126\) | −1.00000 | + | 0.448342i | −0.0890871 | + | 0.0399414i | ||||
\(127\) | 3.58579 | + | 3.58579i | 0.318187 | + | 0.318187i | 0.848071 | − | 0.529883i | \(-0.177764\pi\) |
−0.529883 | + | 0.848071i | \(0.677764\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −10.4525 | −0.920292 | ||||||||
\(130\) | −13.3640 | + | 0.949747i | −1.17210 | + | 0.0832984i | ||||
\(131\) | 14.6508i | 1.28004i | 0.768357 | + | 0.640021i | \(0.221074\pi\) | ||||
−0.768357 | + | 0.640021i | \(0.778926\pi\) | |||||||
\(132\) | 3.69552 | − | 3.69552i | 0.321654 | − | 0.321654i | ||||
\(133\) | 3.46002 | + | 1.31789i | 0.300022 | + | 0.114275i | ||||
\(134\) | − | 14.8284i | − | 1.28098i | ||||||
\(135\) | 8.07107 | + | 7.00000i | 0.694647 | + | 0.602464i | ||||
\(136\) | − | 5.22625i | − | 0.448147i | ||||||
\(137\) | −8.17157 | − | 8.17157i | −0.698145 | − | 0.698145i | 0.265866 | − | 0.964010i | \(-0.414342\pi\) |
−0.964010 | + | 0.265866i | \(0.914342\pi\) | |||||||
\(138\) | 0.765367 | + | 0.765367i | 0.0651524 | + | 0.0651524i | ||||
\(139\) | 8.60474 | 0.729845 | 0.364922 | − | 0.931038i | \(-0.381095\pi\) | ||||
0.364922 | + | 0.931038i | \(0.381095\pi\) | |||||||
\(140\) | −5.66399 | − | 1.70858i | −0.478694 | − | 0.144401i | ||||
\(141\) | 2.82843 | 0.238197 | ||||||||
\(142\) | 0.414214 | + | 0.414214i | 0.0347600 | + | 0.0347600i | ||||
\(143\) | 11.9832 | + | 11.9832i | 1.00209 | + | 1.00209i | ||||
\(144\) | − | 0.414214i | − | 0.0345178i | ||||||
\(145\) | −1.84776 | + | 0.131316i | −0.153448 | + | 0.0109052i | ||||
\(146\) | 5.86030i | 0.485002i | ||||||||
\(147\) | −0.743954 | − | 12.9129i | −0.0613603 | − | 1.06504i | ||||
\(148\) | −2.58579 | + | 2.58579i | −0.212550 | + | 0.212550i | ||||
\(149\) | 17.3137i | 1.41839i | 0.705010 | + | 0.709197i | \(0.250942\pi\) | ||||
−0.705010 | + | 0.709197i | \(0.749058\pi\) | |||||||
\(150\) | −1.30656 | − | 9.14594i | −0.106680 | − | 0.746763i | ||||
\(151\) | −8.82843 | −0.718447 | −0.359224 | − | 0.933252i | \(-0.616958\pi\) | ||||
−0.359224 | + | 0.933252i | \(0.616958\pi\) | |||||||
\(152\) | −0.989538 | + | 0.989538i | −0.0802621 | + | 0.0802621i | ||||
\(153\) | 1.53073 | + | 1.53073i | 0.123752 | + | 0.123752i | ||||
\(154\) | 3.06147 | + | 6.82843i | 0.246700 | + | 0.550250i | ||||
\(155\) | −3.41421 | + | 0.242641i | −0.274236 | + | 0.0194894i | ||||
\(156\) | 11.0711 | 0.886395 | ||||||||
\(157\) | −10.2283 | + | 10.2283i | −0.816310 | + | 0.816310i | −0.985571 | − | 0.169261i | \(-0.945862\pi\) |
0.169261 | + | 0.985571i | \(0.445862\pi\) | |||||||
\(158\) | 3.58579 | − | 3.58579i | 0.285270 | − | 0.285270i | ||||
\(159\) | 21.5391 | 1.70816 | ||||||||
\(160\) | 1.46508 | − | 1.68925i | 0.115824 | − | 0.133547i | ||||
\(161\) | −1.41421 | + | 0.634051i | −0.111456 | + | 0.0499702i | ||||
\(162\) | −7.12132 | − | 7.12132i | −0.559504 | − | 0.559504i | ||||
\(163\) | 13.6569 | − | 13.6569i | 1.06969 | − | 1.06969i | 0.0723048 | − | 0.997383i | \(-0.476965\pi\) |
0.997383 | − | 0.0723048i | \(-0.0230354\pi\) | |||||||
\(164\) | 3.69552 | 0.288571 | ||||||||
\(165\) | −7.65685 | + | 8.82843i | −0.596085 | + | 0.687292i | ||||
\(166\) | 7.52235i | 0.583848i | ||||||||
\(167\) | 1.71644 | − | 1.71644i | 0.132822 | − | 0.132822i | −0.637570 | − | 0.770392i | \(-0.720060\pi\) |
0.770392 | + | 0.637570i | \(0.220060\pi\) | |||||||
\(168\) | 4.56854 | + | 1.74011i | 0.352470 | + | 0.134252i | ||||
\(169\) | 22.8995i | 1.76150i | ||||||||
\(170\) | 0.828427 | + | 11.6569i | 0.0635375 | + | 0.894040i | ||||
\(171\) | − | 0.579658i | − | 0.0443275i | ||||||
\(172\) | 4.00000 | + | 4.00000i | 0.304997 | + | 0.304997i | ||||
\(173\) | −13.2898 | − | 13.2898i | −1.01040 | − | 1.01040i | −0.999945 | − | 0.0104595i | \(-0.996671\pi\) |
−0.0104595 | − | 0.999945i | \(-0.503329\pi\) | |||||||
\(174\) | 1.53073 | 0.116045 | ||||||||
\(175\) | 12.9040 | + | 2.91307i | 0.975453 | + | 0.220208i | ||||
\(176\) | −2.82843 | −0.213201 | ||||||||
\(177\) | −12.0711 | − | 12.0711i | −0.907317 | − | 0.907317i | ||||
\(178\) | 8.02509 | + | 8.02509i | 0.601506 | + | 0.601506i | ||||
\(179\) | − | 13.6569i | − | 1.02076i | −0.859949 | − | 0.510381i | \(-0.829505\pi\) | ||
0.859949 | − | 0.510381i | \(-0.170495\pi\) | |||||||
\(180\) | 0.0656581 | + | 0.923880i | 0.00489387 | + | 0.0688619i | ||||
\(181\) | 8.79045i | 0.653389i | 0.945130 | + | 0.326695i | \(0.105935\pi\) | ||||
−0.945130 | + | 0.326695i | \(0.894065\pi\) | |||||||
\(182\) | −5.64255 | + | 14.8141i | −0.418253 | + | 1.09810i | ||||
\(183\) | 8.41421 | − | 8.41421i | 0.621997 | − | 0.621997i | ||||
\(184\) | − | 0.585786i | − | 0.0431847i | ||||||
\(185\) | 5.35757 | − | 6.17733i | 0.393896 | − | 0.454166i | ||||
\(186\) | 2.82843 | 0.207390 | ||||||||
\(187\) | 10.4525 | − | 10.4525i | 0.764363 | − | 0.764363i | ||||
\(188\) | −1.08239 | − | 1.08239i | −0.0789416 | − | 0.0789416i | ||||
\(189\) | 11.5349 | − | 5.17157i | 0.839040 | − | 0.376177i | ||||
\(190\) | 2.05025 | − | 2.36396i | 0.148741 | − | 0.171500i | ||||
\(191\) | 1.75736 | 0.127158 | 0.0635790 | − | 0.997977i | \(-0.479749\pi\) | ||||
0.0635790 | + | 0.997977i | \(0.479749\pi\) | |||||||
\(192\) | −1.30656 | + | 1.30656i | −0.0942931 | + | 0.0942931i | ||||
\(193\) | 8.24264 | − | 8.24264i | 0.593318 | − | 0.593318i | −0.345208 | − | 0.938526i | \(-0.612192\pi\) |
0.938526 | + | 0.345208i | \(0.112192\pi\) | |||||||
\(194\) | −6.49435 | −0.466267 | ||||||||
\(195\) | −24.6934 | + | 1.75490i | −1.76833 | + | 0.125671i | ||||
\(196\) | −4.65685 | + | 5.22625i | −0.332632 | + | 0.373304i | ||||
\(197\) | 0.585786 | + | 0.585786i | 0.0417356 | + | 0.0417356i | 0.727667 | − | 0.685931i | \(-0.240605\pi\) |
−0.685931 | + | 0.727667i | \(0.740605\pi\) | |||||||
\(198\) | 0.828427 | − | 0.828427i | 0.0588738 | − | 0.0588738i | ||||
\(199\) | −28.0334 | −1.98724 | −0.993618 | − | 0.112798i | \(-0.964019\pi\) | ||||
−0.993618 | + | 0.112798i | \(0.964019\pi\) | |||||||
\(200\) | −3.00000 | + | 4.00000i | −0.212132 | + | 0.282843i | ||||
\(201\) | − | 27.3994i | − | 1.93260i | ||||||
\(202\) | 1.94061 | − | 1.94061i | 0.136541 | − | 0.136541i | ||||
\(203\) | −0.780163 | + | 2.04826i | −0.0547567 | + | 0.143760i | ||||
\(204\) | − | 9.65685i | − | 0.676115i | ||||||
\(205\) | −8.24264 | + | 0.585786i | −0.575691 | + | 0.0409131i | ||||
\(206\) | − | 14.1480i | − | 0.985739i | ||||||
\(207\) | 0.171573 | + | 0.171573i | 0.0119251 | + | 0.0119251i | ||||
\(208\) | −4.23671 | − | 4.23671i | −0.293763 | − | 0.293763i | ||||
\(209\) | −3.95815 | −0.273791 | ||||||||
\(210\) | −10.4657 | − | 3.15704i | −0.722201 | − | 0.217857i | ||||
\(211\) | −10.3431 | −0.712052 | −0.356026 | − | 0.934476i | \(-0.615868\pi\) | ||||
−0.356026 | + | 0.934476i | \(0.615868\pi\) | |||||||
\(212\) | −8.24264 | − | 8.24264i | −0.566107 | − | 0.566107i | ||||
\(213\) | 0.765367 | + | 0.765367i | 0.0524421 | + | 0.0524421i | ||||
\(214\) | 5.17157i | 0.353521i | ||||||||
\(215\) | −9.55582 | − | 8.28772i | −0.651702 | − | 0.565218i | ||||
\(216\) | 4.77791i | 0.325096i | ||||||||
\(217\) | −1.44155 | + | 3.78470i | −0.0978590 | + | 0.256922i | ||||
\(218\) | −8.58579 | + | 8.58579i | −0.581503 | + | 0.581503i | ||||
\(219\) | 10.8284i | 0.731717i | ||||||||
\(220\) | 6.30864 | − | 0.448342i | 0.425329 | − | 0.0302272i | ||||
\(221\) | 31.3137 | 2.10639 | ||||||||
\(222\) | −4.77791 | + | 4.77791i | −0.320672 | + | 0.320672i | ||||
\(223\) | −6.75699 | − | 6.75699i | −0.452481 | − | 0.452481i | 0.443696 | − | 0.896177i | \(-0.353667\pi\) |
−0.896177 | + | 0.443696i | \(0.853667\pi\) | |||||||
\(224\) | −1.08239 | − | 2.41421i | −0.0723204 | − | 0.161306i | ||||
\(225\) | −0.292893 | − | 2.05025i | −0.0195262 | − | 0.136684i | ||||
\(226\) | −1.65685 | −0.110212 | ||||||||
\(227\) | 8.38057 | − | 8.38057i | 0.556238 | − | 0.556238i | −0.371996 | − | 0.928234i | \(-0.621327\pi\) |
0.928234 | + | 0.371996i | \(0.121327\pi\) | |||||||
\(228\) | −1.82843 | + | 1.82843i | −0.121091 | + | 0.121091i | ||||
\(229\) | −7.70806 | −0.509363 | −0.254682 | − | 0.967025i | \(-0.581971\pi\) | ||||
−0.254682 | + | 0.967025i | \(0.581971\pi\) | |||||||
\(230\) | 0.0928546 | + | 1.30656i | 0.00612265 | + | 0.0861522i | ||||
\(231\) | 5.65685 | + | 12.6173i | 0.372194 | + | 0.830157i | ||||
\(232\) | −0.585786 | − | 0.585786i | −0.0384588 | − | 0.0384588i | ||||
\(233\) | 3.00000 | − | 3.00000i | 0.196537 | − | 0.196537i | −0.601977 | − | 0.798513i | \(-0.705620\pi\) |
0.798513 | + | 0.601977i | \(0.205620\pi\) | |||||||
\(234\) | 2.48181 | 0.162241 | ||||||||
\(235\) | 2.58579 | + | 2.24264i | 0.168678 | + | 0.146294i | ||||
\(236\) | 9.23880i | 0.601394i | ||||||||
\(237\) | 6.62567 | − | 6.62567i | 0.430383 | − | 0.430383i | ||||
\(238\) | 12.9218 | + | 4.92177i | 0.837594 | + | 0.319031i | ||||
\(239\) | − | 6.48528i | − | 0.419498i | −0.977755 | − | 0.209749i | \(-0.932735\pi\) | ||
0.977755 | − | 0.209749i | \(-0.0672647\pi\) | |||||||
\(240\) | 2.70711 | − | 3.12132i | 0.174743 | − | 0.201480i | ||||
\(241\) | 6.75699i | 0.435256i | 0.976032 | + | 0.217628i | \(0.0698319\pi\) | ||||
−0.976032 | + | 0.217628i | \(0.930168\pi\) | |||||||
\(242\) | 2.12132 | + | 2.12132i | 0.136364 | + | 0.136364i | ||||
\(243\) | −3.02301 | − | 3.02301i | −0.193926 | − | 0.193926i | ||||
\(244\) | −6.43996 | −0.412276 | ||||||||
\(245\) | 9.55842 | − | 12.3950i | 0.610665 | − | 0.791889i | ||||
\(246\) | 6.82843 | 0.435365 | ||||||||
\(247\) | −5.92893 | − | 5.92893i | −0.377249 | − | 0.377249i | ||||
\(248\) | −1.08239 | − | 1.08239i | −0.0687320 | − | 0.0687320i | ||||
\(249\) | 13.8995i | 0.880845i | ||||||||
\(250\) | 6.05728 | − | 9.39731i | 0.383096 | − | 0.594338i | ||||
\(251\) | 14.0936i | 0.889582i | 0.895634 | + | 0.444791i | \(0.146722\pi\) | ||||
−0.895634 | + | 0.444791i | \(0.853278\pi\) | |||||||
\(252\) | 1.02413 | + | 0.390081i | 0.0645143 | + | 0.0245728i | ||||
\(253\) | 1.17157 | − | 1.17157i | 0.0736562 | − | 0.0736562i | ||||
\(254\) | − | 5.07107i | − | 0.318187i | ||||||
\(255\) | 1.53073 | + | 21.5391i | 0.0958583 | + | 1.34883i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.83938 | − | 7.83938i | 0.489007 | − | 0.489007i | −0.418986 | − | 0.907993i | \(-0.637614\pi\) |
0.907993 | + | 0.418986i | \(0.137614\pi\) | |||||||
\(258\) | 7.39104 | + | 7.39104i | 0.460146 | + | 0.460146i | ||||
\(259\) | −3.95815 | − | 8.82843i | −0.245948 | − | 0.548572i | ||||
\(260\) | 10.1213 | + | 8.77817i | 0.627698 | + | 0.544399i | ||||
\(261\) | 0.343146 | 0.0212402 | ||||||||
\(262\) | 10.3596 | − | 10.3596i | 0.640021 | − | 0.640021i | ||||
\(263\) | −19.4142 | + | 19.4142i | −1.19713 | + | 1.19713i | −0.222110 | + | 0.975022i | \(0.571294\pi\) |
−0.975022 | + | 0.222110i | \(0.928706\pi\) | |||||||
\(264\) | −5.22625 | −0.321654 | ||||||||
\(265\) | 19.6913 | + | 17.0782i | 1.20963 | + | 1.04910i | ||||
\(266\) | −1.51472 | − | 3.37849i | −0.0928734 | − | 0.207149i | ||||
\(267\) | 14.8284 | + | 14.8284i | 0.907485 | + | 0.907485i | ||||
\(268\) | −10.4853 | + | 10.4853i | −0.640490 | + | 0.640490i | ||||
\(269\) | 26.8966 | 1.63992 | 0.819958 | − | 0.572424i | \(-0.193997\pi\) | ||||
0.819958 | + | 0.572424i | \(0.193997\pi\) | |||||||
\(270\) | −0.757359 | − | 10.6569i | −0.0460914 | − | 0.648555i | ||||
\(271\) | − | 18.7402i | − | 1.13839i | −0.822203 | − | 0.569194i | \(-0.807255\pi\) | ||
0.822203 | − | 0.569194i | \(-0.192745\pi\) | |||||||
\(272\) | −3.69552 | + | 3.69552i | −0.224074 | + | 0.224074i | ||||
\(273\) | −10.4261 | + | 27.3729i | −0.631014 | + | 1.65668i | ||||
\(274\) | 11.5563i | 0.698145i | ||||||||
\(275\) | −14.0000 | + | 2.00000i | −0.844232 | + | 0.120605i | ||||
\(276\) | − | 1.08239i | − | 0.0651524i | ||||||
\(277\) | −1.75736 | − | 1.75736i | −0.105589 | − | 0.105589i | 0.652338 | − | 0.757928i | \(-0.273788\pi\) |
−0.757928 | + | 0.652338i | \(0.773788\pi\) | |||||||
\(278\) | −6.08447 | − | 6.08447i | −0.364922 | − | 0.364922i | ||||
\(279\) | 0.634051 | 0.0379596 | ||||||||
\(280\) | 2.79690 | + | 5.21319i | 0.167147 | + | 0.311548i | ||||
\(281\) | −5.65685 | −0.337460 | −0.168730 | − | 0.985662i | \(-0.553967\pi\) | ||||
−0.168730 | + | 0.985662i | \(0.553967\pi\) | |||||||
\(282\) | −2.00000 | − | 2.00000i | −0.119098 | − | 0.119098i | ||||
\(283\) | −3.15432 | − | 3.15432i | −0.187505 | − | 0.187505i | 0.607112 | − | 0.794617i | \(-0.292328\pi\) |
−0.794617 | + | 0.607112i | \(0.792328\pi\) | |||||||
\(284\) | − | 0.585786i | − | 0.0347600i | ||||||
\(285\) | 3.78837 | − | 4.36803i | 0.224404 | − | 0.258740i | ||||
\(286\) | − | 16.9469i | − | 1.00209i | ||||||
\(287\) | −3.48022 | + | 9.13707i | −0.205431 | + | 0.539344i | ||||
\(288\) | −0.292893 | + | 0.292893i | −0.0172589 | + | 0.0172589i | ||||
\(289\) | − | 10.3137i | − | 0.606689i | ||||||
\(290\) | 1.39942 | + | 1.21371i | 0.0821766 | + | 0.0712714i | ||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 4.14386 | − | 4.14386i | 0.242501 | − | 0.242501i | ||||
\(293\) | 2.38896 | + | 2.38896i | 0.139564 | + | 0.139564i | 0.773437 | − | 0.633873i | \(-0.218536\pi\) |
−0.633873 | + | 0.773437i | \(0.718536\pi\) | |||||||
\(294\) | −8.60474 | + | 9.65685i | −0.501839 | + | 0.563199i | ||||
\(295\) | −1.46447 | − | 20.6066i | −0.0852645 | − | 1.19976i | ||||
\(296\) | 3.65685 | 0.212550 | ||||||||
\(297\) | −9.55582 | + | 9.55582i | −0.554485 | + | 0.554485i | ||||
\(298\) | 12.2426 | − | 12.2426i | 0.709197 | − | 0.709197i | ||||
\(299\) | 3.50981 | 0.202977 | ||||||||
\(300\) | −5.54328 | + | 7.39104i | −0.320041 | + | 0.426722i | ||||
\(301\) | −13.6569 | + | 6.12293i | −0.787168 | + | 0.352920i | ||||
\(302\) | 6.24264 | + | 6.24264i | 0.359224 | + | 0.359224i | ||||
\(303\) | 3.58579 | − | 3.58579i | 0.205998 | − | 0.205998i | ||||
\(304\) | 1.39942 | 0.0802621 | ||||||||
\(305\) | 14.3640 | − | 1.02082i | 0.822478 | − | 0.0584517i | ||||
\(306\) | − | 2.16478i | − | 0.123752i | ||||||
\(307\) | −23.1626 | + | 23.1626i | −1.32196 | + | 1.32196i | −0.409776 | + | 0.912186i | \(0.634393\pi\) |
−0.912186 | + | 0.409776i | \(0.865607\pi\) | |||||||
\(308\) | 2.66364 | − | 6.99321i | 0.151775 | − | 0.398475i | ||||
\(309\) | − | 26.1421i | − | 1.48717i | ||||||
\(310\) | 2.58579 | + | 2.24264i | 0.146863 | + | 0.127373i | ||||
\(311\) | − | 3.43289i | − | 0.194661i | −0.995252 | − | 0.0973305i | \(-0.968970\pi\) | ||
0.995252 | − | 0.0973305i | \(-0.0310304\pi\) | |||||||
\(312\) | −7.82843 | − | 7.82843i | −0.443197 | − | 0.443197i | ||||
\(313\) | 6.75699 | + | 6.75699i | 0.381927 | + | 0.381927i | 0.871796 | − | 0.489869i | \(-0.162955\pi\) |
−0.489869 | + | 0.871796i | \(0.662955\pi\) | |||||||
\(314\) | 14.4650 | 0.816310 | ||||||||
\(315\) | −2.34610 | − | 0.707716i | −0.132188 | − | 0.0398753i | ||||
\(316\) | −5.07107 | −0.285270 | ||||||||
\(317\) | 21.8995 | + | 21.8995i | 1.23000 | + | 1.23000i | 0.963963 | + | 0.266035i | \(0.0857136\pi\) |
0.266035 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(318\) | −15.2304 | − | 15.2304i | −0.854079 | − | 0.854079i | ||||
\(319\) | − | 2.34315i | − | 0.131191i | ||||||
\(320\) | −2.23044 | + | 0.158513i | −0.124686 | + | 0.00886113i | ||||
\(321\) | 9.55582i | 0.533354i | ||||||||
\(322\) | 1.44834 | + | 0.551658i | 0.0807129 | + | 0.0307427i | ||||
\(323\) | −5.17157 | + | 5.17157i | −0.287754 | + | 0.287754i | ||||
\(324\) | 10.0711i | 0.559504i | ||||||||
\(325\) | −23.9665 | − | 17.9749i | −1.32942 | − | 0.997066i | ||||
\(326\) | −19.3137 | −1.06969 | ||||||||
\(327\) | −15.8645 | + | 15.8645i | −0.877307 | + | 0.877307i | ||||
\(328\) | −2.61313 | − | 2.61313i | −0.144286 | − | 0.144286i | ||||
\(329\) | 3.69552 | − | 1.65685i | 0.203741 | − | 0.0913453i | ||||
\(330\) | 11.6569 | − | 0.828427i | 0.641689 | − | 0.0456034i | ||||
\(331\) | 23.3137 | 1.28144 | 0.640719 | − | 0.767776i | \(-0.278637\pi\) | ||||
0.640719 | + | 0.767776i | \(0.278637\pi\) | |||||||
\(332\) | 5.31911 | − | 5.31911i | 0.291924 | − | 0.291924i | ||||
\(333\) | −1.07107 | + | 1.07107i | −0.0586942 | + | 0.0586942i | ||||
\(334\) | −2.42742 | −0.132822 | ||||||||
\(335\) | 21.7248 | − | 25.0489i | 1.18695 | − | 1.36857i | ||||
\(336\) | −2.00000 | − | 4.46088i | −0.109109 | − | 0.243361i | ||||
\(337\) | 3.75736 | + | 3.75736i | 0.204676 | + | 0.204676i | 0.802000 | − | 0.597324i | \(-0.203769\pi\) |
−0.597324 | + | 0.802000i | \(0.703769\pi\) | |||||||
\(338\) | 16.1924 | − | 16.1924i | 0.880750 | − | 0.880750i | ||||
\(339\) | −3.06147 | −0.166276 | ||||||||
\(340\) | 7.65685 | − | 8.82843i | 0.415251 | − | 0.478789i | ||||
\(341\) | − | 4.32957i | − | 0.234459i | ||||||
\(342\) | −0.409880 | + | 0.409880i | −0.0221638 | + | 0.0221638i | ||||
\(343\) | −8.53622 | − | 16.4357i | −0.460913 | − | 0.887445i | ||||
\(344\) | − | 5.65685i | − | 0.304997i | ||||||
\(345\) | 0.171573 | + | 2.41421i | 0.00923717 | + | 0.129977i | ||||
\(346\) | 18.7946i | 1.01040i | ||||||||
\(347\) | −5.31371 | − | 5.31371i | −0.285255 | − | 0.285255i | 0.549946 | − | 0.835200i | \(-0.314648\pi\) |
−0.835200 | + | 0.549946i | \(0.814648\pi\) | |||||||
\(348\) | −1.08239 | − | 1.08239i | −0.0580223 | − | 0.0580223i | ||||
\(349\) | −2.66752 | −0.142789 | −0.0713945 | − | 0.997448i | \(-0.522745\pi\) | ||||
−0.0713945 | + | 0.997448i | \(0.522745\pi\) | |||||||
\(350\) | −7.06467 | − | 11.1844i | −0.377623 | − | 0.597830i | ||||
\(351\) | −28.6274 | −1.52802 | ||||||||
\(352\) | 2.00000 | + | 2.00000i | 0.106600 | + | 0.106600i | ||||
\(353\) | −8.47343 | − | 8.47343i | −0.450995 | − | 0.450995i | 0.444690 | − | 0.895685i | \(-0.353314\pi\) |
−0.895685 | + | 0.444690i | \(0.853314\pi\) | |||||||
\(354\) | 17.0711i | 0.907317i | ||||||||
\(355\) | 0.0928546 | + | 1.30656i | 0.00492821 | + | 0.0693452i | ||||
\(356\) | − | 11.3492i | − | 0.601506i | ||||||
\(357\) | 23.8763 | + | 9.09425i | 1.26367 | + | 0.481318i | ||||
\(358\) | −9.65685 | + | 9.65685i | −0.510381 | + | 0.510381i | ||||
\(359\) | − | 16.9706i | − | 0.895672i | −0.894116 | − | 0.447836i | \(-0.852195\pi\) | ||
0.894116 | − | 0.447836i | \(-0.147805\pi\) | |||||||
\(360\) | 0.606854 | − | 0.699709i | 0.0319840 | − | 0.0368779i | ||||
\(361\) | −17.0416 | −0.896928 | ||||||||
\(362\) | 6.21579 | − | 6.21579i | 0.326695 | − | 0.326695i | ||||
\(363\) | 3.91969 | + | 3.91969i | 0.205730 | + | 0.205730i | ||||
\(364\) | 14.4650 | − | 6.48528i | 0.758174 | − | 0.339921i | ||||
\(365\) | −8.58579 | + | 9.89949i | −0.449401 | + | 0.518163i | ||||
\(366\) | −11.8995 | −0.621997 | ||||||||
\(367\) | −3.06147 | + | 3.06147i | −0.159807 | + | 0.159807i | −0.782481 | − | 0.622674i | \(-0.786046\pi\) |
0.622674 | + | 0.782481i | \(0.286046\pi\) | |||||||
\(368\) | −0.414214 | + | 0.414214i | −0.0215924 | + | 0.0215924i | ||||
\(369\) | 1.53073 | 0.0796868 | ||||||||
\(370\) | −8.15640 | + | 0.579658i | −0.424031 | + | 0.0301350i | ||||
\(371\) | 28.1421 | − | 12.6173i | 1.46107 | − | 0.655057i | ||||
\(372\) | −2.00000 | − | 2.00000i | −0.103695 | − | 0.103695i | ||||
\(373\) | −15.0711 | + | 15.0711i | −0.780350 | + | 0.780350i | −0.979890 | − | 0.199539i | \(-0.936055\pi\) |
0.199539 | + | 0.979890i | \(0.436055\pi\) | |||||||
\(374\) | −14.7821 | −0.764363 | ||||||||
\(375\) | 11.1924 | − | 17.3640i | 0.577972 | − | 0.896671i | ||||
\(376\) | 1.53073i | 0.0789416i | ||||||||
\(377\) | 3.50981 | − | 3.50981i | 0.180764 | − | 0.180764i | ||||
\(378\) | −11.8133 | − | 4.49955i | −0.607608 | − | 0.231432i | ||||
\(379\) | 6.14214i | 0.315500i | 0.987479 | + | 0.157750i | \(0.0504241\pi\) | ||||
−0.987479 | + | 0.157750i | \(0.949576\pi\) | |||||||
\(380\) | −3.12132 | + | 0.221825i | −0.160120 | + | 0.0113794i | ||||
\(381\) | − | 9.37011i | − | 0.480045i | ||||||
\(382\) | −1.24264 | − | 1.24264i | −0.0635790 | − | 0.0635790i | ||||
\(383\) | 10.6382 | + | 10.6382i | 0.543587 | + | 0.543587i | 0.924579 | − | 0.380991i | \(-0.124417\pi\) |
−0.380991 | + | 0.924579i | \(0.624417\pi\) | |||||||
\(384\) | 1.84776 | 0.0942931 | ||||||||
\(385\) | −4.83259 | + | 16.0202i | −0.246292 | + | 0.816464i | ||||
\(386\) | −11.6569 | −0.593318 | ||||||||
\(387\) | 1.65685 | + | 1.65685i | 0.0842226 | + | 0.0842226i | ||||
\(388\) | 4.59220 | + | 4.59220i | 0.233134 | + | 0.233134i | ||||
\(389\) | 0.142136i | 0.00720656i | 0.999994 | + | 0.00360328i | \(0.00114696\pi\) | ||||
−0.999994 | + | 0.00360328i | \(0.998853\pi\) | |||||||
\(390\) | 18.7018 | + | 16.2200i | 0.947001 | + | 0.821329i | ||||
\(391\) | − | 3.06147i | − | 0.154825i | ||||||
\(392\) | 6.98841 | − | 0.402625i | 0.352968 | − | 0.0203356i | ||||
\(393\) | 19.1421 | − | 19.1421i | 0.965593 | − | 0.965593i | ||||
\(394\) | − | 0.828427i | − | 0.0417356i | ||||||
\(395\) | 11.3107 | − | 0.803828i | 0.569104 | − | 0.0404450i | ||||
\(396\) | −1.17157 | −0.0588738 | ||||||||
\(397\) | −1.12085 | + | 1.12085i | −0.0562540 | + | 0.0562540i | −0.734674 | − | 0.678420i | \(-0.762665\pi\) |
0.678420 | + | 0.734674i | \(0.262665\pi\) | |||||||
\(398\) | 19.8226 | + | 19.8226i | 0.993618 | + | 0.993618i | ||||
\(399\) | −2.79884 | − | 6.24264i | −0.140117 | − | 0.312523i | ||||
\(400\) | 4.94975 | − | 0.707107i | 0.247487 | − | 0.0353553i | ||||
\(401\) | −19.7574 | −0.986635 | −0.493318 | − | 0.869849i | \(-0.664216\pi\) | ||||
−0.493318 | + | 0.869849i | \(0.664216\pi\) | |||||||
\(402\) | −19.3743 | + | 19.3743i | −0.966301 | + | 0.966301i | ||||
\(403\) | 6.48528 | − | 6.48528i | 0.323055 | − | 0.323055i | ||||
\(404\) | −2.74444 | −0.136541 | ||||||||
\(405\) | −1.59639 | − | 22.4629i | −0.0793253 | − | 1.11619i | ||||
\(406\) | 2.00000 | − | 0.896683i | 0.0992583 | − | 0.0445016i | ||||
\(407\) | 7.31371 | + | 7.31371i | 0.362527 | + | 0.362527i | ||||
\(408\) | −6.82843 | + | 6.82843i | −0.338058 | + | 0.338058i | ||||
\(409\) | 24.9719 | 1.23478 | 0.617392 | − | 0.786656i | \(-0.288189\pi\) | ||||
0.617392 | + | 0.786656i | \(0.288189\pi\) | |||||||
\(410\) | 6.24264 | + | 5.41421i | 0.308302 | + | 0.267389i | ||||
\(411\) | 21.3533i | 1.05328i | ||||||||
\(412\) | −10.0042 | + | 10.0042i | −0.492870 | + | 0.492870i | ||||
\(413\) | −22.8427 | − | 8.70054i | −1.12401 | − | 0.428126i | ||||
\(414\) | − | 0.242641i | − | 0.0119251i | ||||||
\(415\) | −11.0208 | + | 12.7071i | −0.540991 | + | 0.623767i | ||||
\(416\) | 5.99162i | 0.293763i | ||||||||
\(417\) | −11.2426 | − | 11.2426i | −0.550554 | − | 0.550554i | ||||
\(418\) | 2.79884 | + | 2.79884i | 0.136895 | + | 0.136895i | ||||
\(419\) | −11.5893 | −0.566174 | −0.283087 | − | 0.959094i | \(-0.591358\pi\) | ||||
−0.283087 | + | 0.959094i | \(0.591358\pi\) | |||||||
\(420\) | 5.16799 | + | 9.63272i | 0.252172 | + | 0.470029i | ||||
\(421\) | 17.7990 | 0.867470 | 0.433735 | − | 0.901041i | \(-0.357195\pi\) | ||||
0.433735 | + | 0.901041i | \(0.357195\pi\) | |||||||
\(422\) | 7.31371 | + | 7.31371i | 0.356026 | + | 0.356026i | ||||
\(423\) | −0.448342 | − | 0.448342i | −0.0217991 | − | 0.0217991i | ||||
\(424\) | 11.6569i | 0.566107i | ||||||||
\(425\) | −15.6788 | + | 20.9050i | −0.760531 | + | 1.01404i | ||||
\(426\) | − | 1.08239i | − | 0.0524421i | ||||||
\(427\) | 6.06477 | − | 15.9226i | 0.293495 | − | 0.770550i | ||||
\(428\) | 3.65685 | − | 3.65685i | 0.176761 | − | 0.176761i | ||||
\(429\) | − | 31.3137i | − | 1.51184i | ||||||
\(430\) | 0.896683 | + | 12.6173i | 0.0432419 | + | 0.608460i | ||||
\(431\) | 5.65685 | 0.272481 | 0.136241 | − | 0.990676i | \(-0.456498\pi\) | ||||
0.136241 | + | 0.990676i | \(0.456498\pi\) | |||||||
\(432\) | 3.37849 | − | 3.37849i | 0.162548 | − | 0.162548i | ||||
\(433\) | 10.4525 | + | 10.4525i | 0.502315 | + | 0.502315i | 0.912157 | − | 0.409841i | \(-0.134416\pi\) |
−0.409841 | + | 0.912157i | \(0.634416\pi\) | |||||||
\(434\) | 3.69552 | − | 1.65685i | 0.177391 | − | 0.0795315i | ||||
\(435\) | 2.58579 | + | 2.24264i | 0.123979 | + | 0.107526i | ||||
\(436\) | 12.1421 | 0.581503 | ||||||||
\(437\) | −0.579658 | + | 0.579658i | −0.0277288 | + | 0.0277288i | ||||
\(438\) | 7.65685 | − | 7.65685i | 0.365859 | − | 0.365859i | ||||
\(439\) | 13.8854 | 0.662713 | 0.331357 | − | 0.943506i | \(-0.392494\pi\) | ||||
0.331357 | + | 0.943506i | \(0.392494\pi\) | |||||||
\(440\) | −4.77791 | − | 4.14386i | −0.227778 | − | 0.197551i | ||||
\(441\) | −1.92893 | + | 2.16478i | −0.0918539 | + | 0.103085i | ||||
\(442\) | −22.1421 | − | 22.1421i | −1.05319 | − | 1.05319i | ||||
\(443\) | −4.14214 | + | 4.14214i | −0.196799 | + | 0.196799i | −0.798626 | − | 0.601827i | \(-0.794440\pi\) |
0.601827 | + | 0.798626i | \(0.294440\pi\) | |||||||
\(444\) | 6.75699 | 0.320672 | ||||||||
\(445\) | 1.79899 | + | 25.3137i | 0.0852803 | + | 1.19998i | ||||
\(446\) | 9.55582i | 0.452481i | ||||||||
\(447\) | 22.6215 | − | 22.6215i | 1.06996 | − | 1.06996i | ||||
\(448\) | −0.941740 | + | 2.47247i | −0.0444930 | + | 0.116813i | ||||
\(449\) | 25.6569i | 1.21082i | 0.795913 | + | 0.605411i | \(0.206991\pi\) | ||||
−0.795913 | + | 0.605411i | \(0.793009\pi\) | |||||||
\(450\) | −1.24264 | + | 1.65685i | −0.0585786 | + | 0.0781049i | ||||
\(451\) | − | 10.4525i | − | 0.492189i | ||||||
\(452\) | 1.17157 | + | 1.17157i | 0.0551062 | + | 0.0551062i | ||||
\(453\) | 11.5349 | + | 11.5349i | 0.541957 | + | 0.541957i | ||||
\(454\) | −11.8519 | −0.556238 | ||||||||
\(455\) | −31.2355 | + | 16.7579i | −1.46434 | + | 0.785624i | ||||
\(456\) | 2.58579 | 0.121091 | ||||||||
\(457\) | −1.65685 | − | 1.65685i | −0.0775044 | − | 0.0775044i | 0.667292 | − | 0.744796i | \(-0.267453\pi\) |
−0.744796 | + | 0.667292i | \(0.767453\pi\) | |||||||
\(458\) | 5.45042 | + | 5.45042i | 0.254682 | + | 0.254682i | ||||
\(459\) | 24.9706i | 1.16553i | ||||||||
\(460\) | 0.858221 | − | 0.989538i | 0.0400148 | − | 0.0461374i | ||||
\(461\) | − | 34.0250i | − | 1.58470i | −0.610064 | − | 0.792352i | \(-0.708856\pi\) | ||
0.610064 | − | 0.792352i | \(-0.291144\pi\) | |||||||
\(462\) | 4.92177 | − | 12.9218i | 0.228981 | − | 0.601175i | ||||
\(463\) | −12.9706 | + | 12.9706i | −0.602793 | + | 0.602793i | −0.941053 | − | 0.338260i | \(-0.890162\pi\) |
0.338260 | + | 0.941053i | \(0.390162\pi\) | |||||||
\(464\) | 0.828427i | 0.0384588i | ||||||||
\(465\) | 4.77791 | + | 4.14386i | 0.221570 | + | 0.192167i | ||||
\(466\) | −4.24264 | −0.196537 | ||||||||
\(467\) | −17.4337 | + | 17.4337i | −0.806734 | + | 0.806734i | −0.984138 | − | 0.177404i | \(-0.943230\pi\) |
0.177404 | + | 0.984138i | \(0.443230\pi\) | |||||||
\(468\) | −1.75490 | − | 1.75490i | −0.0811205 | − | 0.0811205i | ||||
\(469\) | −16.0502 | − | 35.7990i | −0.741128 | − | 1.65304i | ||||
\(470\) | −0.242641 | − | 3.41421i | −0.0111922 | − | 0.157486i | ||||
\(471\) | 26.7279 | 1.23156 | ||||||||
\(472\) | 6.53281 | − | 6.53281i | 0.300697 | − | 0.300697i | ||||
\(473\) | 11.3137 | − | 11.3137i | 0.520205 | − | 0.520205i | ||||
\(474\) | −9.37011 | −0.430383 | ||||||||
\(475\) | 6.92676 | − | 0.989538i | 0.317822 | − | 0.0454031i | ||||
\(476\) | −5.65685 | − | 12.6173i | −0.259281 | − | 0.578312i | ||||
\(477\) | −3.41421 | − | 3.41421i | −0.156326 | − | 0.156326i | ||||
\(478\) | −4.58579 | + | 4.58579i | −0.209749 | + | 0.209749i | ||||
\(479\) | 11.0866 | 0.506558 | 0.253279 | − | 0.967393i | \(-0.418491\pi\) | ||||
0.253279 | + | 0.967393i | \(0.418491\pi\) | |||||||
\(480\) | −4.12132 | + | 0.292893i | −0.188112 | + | 0.0133687i | ||||
\(481\) | 21.9105i | 0.999032i | ||||||||
\(482\) | 4.77791 | − | 4.77791i | 0.217628 | − | 0.217628i | ||||
\(483\) | 2.67619 | + | 1.01933i | 0.121771 | + | 0.0463812i | ||||
\(484\) | − | 3.00000i | − | 0.136364i | ||||||
\(485\) | −10.9706 | − | 9.51472i | −0.498148 | − | 0.432041i | ||||
\(486\) | 4.27518i | 0.193926i | ||||||||
\(487\) | 1.10051 | + | 1.10051i | 0.0498686 | + | 0.0498686i | 0.731601 | − | 0.681733i | \(-0.238773\pi\) |
−0.681733 | + | 0.731601i | \(0.738773\pi\) | |||||||
\(488\) | 4.55374 | + | 4.55374i | 0.206138 | + | 0.206138i | ||||
\(489\) | −35.6871 | −1.61383 | ||||||||
\(490\) | −15.5234 | + | 2.00578i | −0.701277 | + | 0.0906121i | ||||
\(491\) | 25.1716 | 1.13598 | 0.567989 | − | 0.823036i | \(-0.307722\pi\) | ||||
0.567989 | + | 0.823036i | \(0.307722\pi\) | |||||||
\(492\) | −4.82843 | − | 4.82843i | −0.217682 | − | 0.217682i | ||||
\(493\) | −3.06147 | − | 3.06147i | −0.137882 | − | 0.137882i | ||||
\(494\) | 8.38478i | 0.377249i | ||||||||
\(495\) | 2.61313 | − | 0.185709i | 0.117451 | − | 0.00834701i | ||||
\(496\) | 1.53073i | 0.0687320i | ||||||||
\(497\) | 1.44834 | + | 0.551658i | 0.0649670 | + | 0.0247453i | ||||
\(498\) | 9.82843 | − | 9.82843i | 0.440422 | − | 0.440422i | ||||
\(499\) | 7.51472i | 0.336405i | 0.985752 | + | 0.168203i | \(0.0537963\pi\) | ||||
−0.985752 | + | 0.168203i | \(0.946204\pi\) | |||||||
\(500\) | −10.9280 | + | 2.36176i | −0.488717 | + | 0.105621i | ||||
\(501\) | −4.48528 | −0.200388 | ||||||||
\(502\) | 9.96570 | − | 9.96570i | 0.444791 | − | 0.444791i | ||||
\(503\) | −18.1062 | − | 18.1062i | −0.807314 | − | 0.807314i | 0.176912 | − | 0.984227i | \(-0.443389\pi\) |
−0.984227 | + | 0.176912i | \(0.943389\pi\) | |||||||
\(504\) | −0.448342 | − | 1.00000i | −0.0199707 | − | 0.0445435i | ||||
\(505\) | 6.12132 | − | 0.435029i | 0.272395 | − | 0.0193585i | ||||
\(506\) | −1.65685 | −0.0736562 | ||||||||
\(507\) | 29.9196 | − | 29.9196i | 1.32878 | − | 1.32878i | ||||
\(508\) | −3.58579 | + | 3.58579i | −0.159094 | + | 0.159094i | ||||
\(509\) | −14.4650 | −0.641152 | −0.320576 | − | 0.947223i | \(-0.603876\pi\) | ||||
−0.320576 | + | 0.947223i | \(0.603876\pi\) | |||||||
\(510\) | 14.1480 | − | 16.3128i | 0.626485 | − | 0.722343i | ||||
\(511\) | 6.34315 | + | 14.1480i | 0.280604 | + | 0.625872i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 4.72792 | − | 4.72792i | 0.208743 | − | 0.208743i | ||||
\(514\) | −11.0866 | −0.489007 | ||||||||
\(515\) | 20.7279 | − | 23.8995i | 0.913381 | − | 1.05314i | ||||
\(516\) | − | 10.4525i | − | 0.460146i | ||||||
\(517\) | −3.06147 | + | 3.06147i | −0.134643 | + | 0.134643i | ||||
\(518\) | −3.44381 | + | 9.04148i | −0.151312 | + | 0.397260i | ||||
\(519\) | 34.7279i | 1.52439i | ||||||||
\(520\) | −0.949747 | − | 13.3640i | −0.0416492 | − | 0.586048i | ||||
\(521\) | 36.6925i | 1.60753i | 0.594947 | + | 0.803765i | \(0.297173\pi\) | ||||
−0.594947 | + | 0.803765i | \(0.702827\pi\) | |||||||
\(522\) | −0.242641 | − | 0.242641i | −0.0106201 | − | 0.0106201i | ||||
\(523\) | −1.75490 | − | 1.75490i | −0.0767366 | − | 0.0767366i | 0.667697 | − | 0.744433i | \(-0.267280\pi\) |
−0.744433 | + | 0.667697i | \(0.767280\pi\) | |||||||
\(524\) | −14.6508 | −0.640021 | ||||||||
\(525\) | −13.0538 | − | 20.6660i | −0.569715 | − | 0.901940i | ||||
\(526\) | 27.4558 | 1.19713 | ||||||||
\(527\) | −5.65685 | − | 5.65685i | −0.246416 | − | 0.246416i | ||||
\(528\) | 3.69552 | + | 3.69552i | 0.160827 | + | 0.160827i | ||||
\(529\) | 22.6569i | 0.985081i | ||||||||
\(530\) | −1.84776 | − | 25.9999i | −0.0802615 | − | 1.12937i | ||||
\(531\) | 3.82683i | 0.166070i | ||||||||
\(532\) | −1.31789 | + | 3.46002i | −0.0571377 | + | 0.150011i | ||||
\(533\) | 15.6569 | − | 15.6569i | 0.678174 | − | 0.678174i | ||||
\(534\) | − | 20.9706i | − | 0.907485i | ||||||
\(535\) | −7.57675 | + | 8.73606i | −0.327571 | + | 0.377693i | ||||
\(536\) | 14.8284 | 0.640490 | ||||||||
\(537\) | −17.8435 | + | 17.8435i | −0.770006 | + | 0.770006i | ||||
\(538\) | −19.0188 | − | 19.0188i | −0.819958 | − | 0.819958i | ||||
\(539\) | 14.7821 | + | 13.1716i | 0.636709 | + | 0.567340i | ||||
\(540\) | −7.00000 | + | 8.07107i | −0.301232 | + | 0.347323i | ||||
\(541\) | 10.9706 | 0.471661 | 0.235831 | − | 0.971794i | \(-0.424219\pi\) | ||||
0.235831 | + | 0.971794i | \(0.424219\pi\) | |||||||
\(542\) | −13.2513 | + | 13.2513i | −0.569194 | + | 0.569194i | ||||
\(543\) | 11.4853 | − | 11.4853i | 0.492881 | − | 0.492881i | ||||
\(544\) | 5.22625 | 0.224074 | ||||||||
\(545\) | −27.0823 | + | 1.92468i | −1.16008 | + | 0.0824443i | ||||
\(546\) | 26.7279 | − | 11.9832i | 1.14385 | − | 0.512835i | ||||
\(547\) | −30.6274 | − | 30.6274i | −1.30953 | − | 1.30953i | −0.921751 | − | 0.387783i | \(-0.873241\pi\) |
−0.387783 | − | 0.921751i | \(-0.626759\pi\) | |||||||
\(548\) | 8.17157 | − | 8.17157i | 0.349072 | − | 0.349072i | ||||
\(549\) | −2.66752 | −0.113847 | ||||||||
\(550\) | 11.3137 | + | 8.48528i | 0.482418 | + | 0.361814i | ||||
\(551\) | 1.15932i | 0.0493885i | ||||||||
\(552\) | −0.765367 | + | 0.765367i | −0.0325762 | + | 0.0325762i | ||||
\(553\) | 4.77563 | − | 12.5381i | 0.203080 | − | 0.533173i | ||||
\(554\) | 2.48528i | 0.105589i | ||||||||
\(555\) | −15.0711 | + | 1.07107i | −0.639731 | + | 0.0454643i | ||||
\(556\) | 8.60474i | 0.364922i | ||||||||
\(557\) | −26.7279 | − | 26.7279i | −1.13250 | − | 1.13250i | −0.989761 | − | 0.142738i | \(-0.954409\pi\) |
−0.142738 | − | 0.989761i | \(-0.545591\pi\) | |||||||
\(558\) | −0.448342 | − | 0.448342i | −0.0189798 | − | 0.0189798i | ||||
\(559\) | 33.8937 | 1.43355 | ||||||||
\(560\) | 1.70858 | − | 5.66399i | 0.0722006 | − | 0.239347i | ||||
\(561\) | −27.3137 | −1.15319 | ||||||||
\(562\) | 4.00000 | + | 4.00000i | 0.168730 | + | 0.168730i | ||||
\(563\) | −3.54827 | − | 3.54827i | −0.149542 | − | 0.149542i | 0.628372 | − | 0.777913i | \(-0.283722\pi\) |
−0.777913 | + | 0.628372i | \(0.783722\pi\) | |||||||
\(564\) | 2.82843i | 0.119098i | ||||||||
\(565\) | −2.79884 | − | 2.42742i | −0.117748 | − | 0.102122i | ||||
\(566\) | 4.46088i | 0.187505i | ||||||||
\(567\) | −24.9004 | − | 9.48433i | −1.04572 | − | 0.398304i | ||||
\(568\) | −0.414214 | + | 0.414214i | −0.0173800 | + | 0.0173800i | ||||
\(569\) | 1.41421i | 0.0592869i | 0.999561 | + | 0.0296435i | \(0.00943719\pi\) | ||||
−0.999561 | + | 0.0296435i | \(0.990563\pi\) | |||||||
\(570\) | −5.76745 | + | 0.409880i | −0.241572 | + | 0.0171680i | ||||
\(571\) | −25.4558 | −1.06529 | −0.532647 | − | 0.846338i | \(-0.678803\pi\) | ||||
−0.532647 | + | 0.846338i | \(0.678803\pi\) | |||||||
\(572\) | −11.9832 | + | 11.9832i | −0.501044 | + | 0.501044i | ||||
\(573\) | −2.29610 | − | 2.29610i | −0.0959210 | − | 0.0959210i | ||||
\(574\) | 8.92177 | − | 4.00000i | 0.372387 | − | 0.166957i | ||||
\(575\) | −1.75736 | + | 2.34315i | −0.0732869 | + | 0.0977159i | ||||
\(576\) | 0.414214 | 0.0172589 | ||||||||
\(577\) | 26.3170 | − | 26.3170i | 1.09559 | − | 1.09559i | 0.100670 | − | 0.994920i | \(-0.467901\pi\) |
0.994920 | − | 0.100670i | \(-0.0320986\pi\) | |||||||
\(578\) | −7.29289 | + | 7.29289i | −0.303344 | + | 0.303344i | ||||
\(579\) | −21.5391 | −0.895133 | ||||||||
\(580\) | −0.131316 | − | 1.84776i | −0.00545261 | − | 0.0767240i | ||||
\(581\) | 8.14214 | + | 18.1606i | 0.337793 | + | 0.753427i | ||||
\(582\) | 8.48528 | + | 8.48528i | 0.351726 | + | 0.351726i | ||||
\(583\) | −23.3137 | + | 23.3137i | −0.965555 | + | 0.965555i | ||||
\(584\) | −5.86030 | −0.242501 | ||||||||
\(585\) | 4.19239 | + | 3.63604i | 0.173334 | + | 0.150332i | ||||
\(586\) | − | 3.37849i | − | 0.139564i | ||||||
\(587\) | −16.0886 | + | 16.0886i | −0.664049 | + | 0.664049i | −0.956332 | − | 0.292283i | \(-0.905585\pi\) |
0.292283 | + | 0.956332i | \(0.405585\pi\) | |||||||
\(588\) | 12.9129 | − | 0.743954i | 0.532519 | − | 0.0306801i | ||||
\(589\) | 2.14214i | 0.0882652i | ||||||||
\(590\) | −13.5355 | + | 15.6066i | −0.557249 | + | 0.642514i | ||||
\(591\) | − | 1.53073i | − | 0.0629660i | ||||||
\(592\) | −2.58579 | − | 2.58579i | −0.106275 | − | 0.106275i | ||||
\(593\) | 22.8841 | + | 22.8841i | 0.939737 | + | 0.939737i | 0.998285 | − | 0.0585480i | \(-0.0186471\pi\) |
−0.0585480 | + | 0.998285i | \(0.518647\pi\) | |||||||
\(594\) | 13.5140 | 0.554485 | ||||||||
\(595\) | 14.6173 | + | 27.2455i | 0.599250 | + | 1.11695i | ||||
\(596\) | −17.3137 | −0.709197 | ||||||||
\(597\) | 36.6274 | + | 36.6274i | 1.49906 | + | 1.49906i | ||||
\(598\) | −2.48181 | − | 2.48181i | −0.101489 | − | 0.101489i | ||||
\(599\) | 18.5269i | 0.756989i | 0.925604 | + | 0.378495i | \(0.123558\pi\) | ||||
−0.925604 | + | 0.378495i | \(0.876442\pi\) | |||||||
\(600\) | 9.14594 | − | 1.30656i | 0.373381 | − | 0.0533402i | ||||
\(601\) | − | 16.5754i | − | 0.676126i | −0.941123 | − | 0.338063i | \(-0.890228\pi\) | ||
0.941123 | − | 0.338063i | \(-0.109772\pi\) | |||||||
\(602\) | 13.9864 | + | 5.32729i | 0.570044 | + | 0.217124i | ||||
\(603\) | −4.34315 | + | 4.34315i | −0.176867 | + | 0.176867i | ||||
\(604\) | − | 8.82843i | − | 0.359224i | ||||||
\(605\) | 0.475538 | + | 6.69133i | 0.0193334 | + | 0.272041i | ||||
\(606\) | −5.07107 | −0.205998 | ||||||||
\(607\) | 21.5391 | − | 21.5391i | 0.874243 | − | 0.874243i | −0.118688 | − | 0.992932i | \(-0.537869\pi\) |
0.992932 | + | 0.118688i | \(0.0378689\pi\) | |||||||
\(608\) | −0.989538 | − | 0.989538i | −0.0401311 | − | 0.0401311i | ||||
\(609\) | 3.69552 | − | 1.65685i | 0.149750 | − | 0.0671391i | ||||
\(610\) | −10.8787 | − | 9.43503i | −0.440465 | − | 0.382013i | ||||
\(611\) | −9.17157 | −0.371042 | ||||||||
\(612\) | −1.53073 | + | 1.53073i | −0.0618762 | + | 0.0618762i | ||||
\(613\) | 19.8995 | − | 19.8995i | 0.803733 | − | 0.803733i | −0.179944 | − | 0.983677i | \(-0.557592\pi\) |
0.983677 | + | 0.179944i | \(0.0575916\pi\) | |||||||
\(614\) | 32.7569 | 1.32196 | ||||||||
\(615\) | 11.5349 | + | 10.0042i | 0.465132 | + | 0.403407i | ||||
\(616\) | −6.82843 | + | 3.06147i | −0.275125 | + | 0.123350i | ||||
\(617\) | −28.4853 | − | 28.4853i | −1.14677 | − | 1.14677i | −0.987183 | − | 0.159591i | \(-0.948982\pi\) |
−0.159591 | − | 0.987183i | \(-0.551018\pi\) | |||||||
\(618\) | −18.4853 | + | 18.4853i | −0.743587 | + | 0.743587i | ||||
\(619\) | 0.688444 | 0.0276709 | 0.0138354 | − | 0.999904i | \(-0.495596\pi\) | ||||
0.0138354 | + | 0.999904i | \(0.495596\pi\) | |||||||
\(620\) | −0.242641 | − | 3.41421i | −0.00974468 | − | 0.137118i | ||||
\(621\) | 2.79884i | 0.112313i | ||||||||
\(622\) | −2.42742 | + | 2.42742i | −0.0973305 | + | 0.0973305i | ||||
\(623\) | 28.0606 | + | 10.6880i | 1.12422 | + | 0.428205i | ||||
\(624\) | 11.0711i | 0.443197i | ||||||||
\(625\) | 24.0000 | − | 7.00000i | 0.960000 | − | 0.280000i | ||||
\(626\) | − | 9.55582i | − | 0.381927i | ||||||
\(627\) | 5.17157 | + | 5.17157i | 0.206533 | + | 0.206533i | ||||
\(628\) | −10.2283 | − | 10.2283i | −0.408155 | − | 0.408155i | ||||
\(629\) | 19.1116 | 0.762031 | ||||||||
\(630\) | 1.15851 | + | 2.15937i | 0.0461562 | + | 0.0860315i | ||||
\(631\) | 41.3553 | 1.64633 | 0.823165 | − | 0.567802i | \(-0.192206\pi\) | ||||
0.823165 | + | 0.567802i | \(0.192206\pi\) | |||||||
\(632\) | 3.58579 | + | 3.58579i | 0.142635 | + | 0.142635i | ||||
\(633\) | 13.5140 | + | 13.5140i | 0.537132 | + | 0.537132i | ||||
\(634\) | − | 30.9706i | − | 1.23000i | ||||||
\(635\) | 7.42950 | − | 8.56628i | 0.294831 | − | 0.339943i | ||||
\(636\) | 21.5391i | 0.854079i | ||||||||
\(637\) | 2.41237 | + | 41.8719i | 0.0955818 | + | 1.65902i | ||||
\(638\) | −1.65685 | + | 1.65685i | −0.0655955 | + | 0.0655955i | ||||
\(639\) | − | 0.242641i | − | 0.00959872i | ||||||
\(640\) | 1.68925 | + | 1.46508i | 0.0667733 | + | 0.0579122i | ||||
\(641\) | −37.2132 | −1.46983 | −0.734917 | − | 0.678158i | \(-0.762779\pi\) | ||||
−0.734917 | + | 0.678158i | \(0.762779\pi\) | |||||||
\(642\) | 6.75699 | − | 6.75699i | 0.266677 | − | 0.266677i | ||||
\(643\) | 20.9435 | + | 20.9435i | 0.825930 | + | 0.825930i | 0.986951 | − | 0.161021i | \(-0.0514787\pi\) |
−0.161021 | + | 0.986951i | \(0.551479\pi\) | |||||||
\(644\) | −0.634051 | − | 1.41421i | −0.0249851 | − | 0.0557278i | ||||
\(645\) | 1.65685 | + | 23.3137i | 0.0652386 | + | 0.917976i | ||||
\(646\) | 7.31371 | 0.287754 | ||||||||
\(647\) | −23.8896 | + | 23.8896i | −0.939195 | + | 0.939195i | −0.998254 | − | 0.0590593i | \(-0.981190\pi\) |
0.0590593 | + | 0.998254i | \(0.481190\pi\) | |||||||
\(648\) | 7.12132 | − | 7.12132i | 0.279752 | − | 0.279752i | ||||
\(649\) | 26.1313 | 1.02574 | ||||||||
\(650\) | 4.23671 | + | 29.6570i | 0.166178 | + | 1.16324i | ||||
\(651\) | 6.82843 | − | 3.06147i | 0.267627 | − | 0.119988i | ||||
\(652\) | 13.6569 | + | 13.6569i | 0.534844 | + | 0.534844i | ||||
\(653\) | 8.72792 | − | 8.72792i | 0.341550 | − | 0.341550i | −0.515400 | − | 0.856950i | \(-0.672357\pi\) |
0.856950 | + | 0.515400i | \(0.172357\pi\) | |||||||
\(654\) | 22.4357 | 0.877307 | ||||||||
\(655\) | 32.6777 | − | 2.32233i | 1.27682 | − | 0.0907410i | ||||
\(656\) | 3.69552i | 0.144286i | ||||||||
\(657\) | 1.71644 | − | 1.71644i | 0.0669648 | − | 0.0669648i | ||||
\(658\) | −3.78470 | − | 1.44155i | −0.147543 | − | 0.0561976i | ||||
\(659\) | − | 29.6569i | − | 1.15527i | −0.816296 | − | 0.577634i | \(-0.803976\pi\) | ||
0.816296 | − | 0.577634i | \(-0.196024\pi\) | |||||||
\(660\) | −8.82843 | − | 7.65685i | −0.343646 | − | 0.298043i | ||||
\(661\) | − | 47.5390i | − | 1.84905i | −0.381118 | − | 0.924526i | \(-0.624461\pi\) | ||
0.381118 | − | 0.924526i | \(-0.375539\pi\) | |||||||
\(662\) | −16.4853 | − | 16.4853i | −0.640719 | − | 0.640719i | ||||
\(663\) | −40.9133 | − | 40.9133i | −1.58894 | − | 1.58894i | ||||
\(664\) | −7.52235 | −0.291924 | ||||||||
\(665\) | 2.39101 | − | 7.92628i | 0.0927196 | − | 0.307368i | ||||
\(666\) | 1.51472 | 0.0586942 | ||||||||
\(667\) | −0.343146 | − | 0.343146i | −0.0132867 | − | 0.0132867i | ||||
\(668\) | 1.71644 | + | 1.71644i | 0.0664112 | + | 0.0664112i | ||||
\(669\) | 17.6569i | 0.682653i | ||||||||
\(670\) | −33.0740 | + | 2.35049i | −1.27776 | + | 0.0908075i | ||||
\(671\) | 18.2150i | 0.703181i | ||||||||
\(672\) | −1.74011 | + | 4.56854i | −0.0671261 | + | 0.176235i | ||||
\(673\) | −22.7990 | + | 22.7990i | −0.878836 | + | 0.878836i | −0.993414 | − | 0.114578i | \(-0.963448\pi\) |
0.114578 | + | 0.993414i | \(0.463448\pi\) | |||||||
\(674\) | − | 5.31371i | − | 0.204676i | ||||||
\(675\) | 14.3337 | − | 19.1116i | 0.551706 | − | 0.735607i | ||||
\(676\) | −22.8995 | −0.880750 | ||||||||
\(677\) | 22.4742 | − | 22.4742i | 0.863754 | − | 0.863754i | −0.128018 | − | 0.991772i | \(-0.540862\pi\) |
0.991772 | + | 0.128018i | \(0.0408615\pi\) | |||||||
\(678\) | 2.16478 | + | 2.16478i | 0.0831380 | + | 0.0831380i | ||||
\(679\) | −15.6788 | + | 7.02944i | −0.601695 | + | 0.269765i | ||||
\(680\) | −11.6569 | + | 0.828427i | −0.447020 | + | 0.0317687i | ||||
\(681\) | −21.8995 | −0.839190 | ||||||||
\(682\) | −3.06147 | + | 3.06147i | −0.117230 | + | 0.117230i | ||||
\(683\) | −25.3137 | + | 25.3137i | −0.968602 | + | 0.968602i | −0.999522 | − | 0.0309197i | \(-0.990156\pi\) |
0.0309197 | + | 0.999522i | \(0.490156\pi\) | |||||||
\(684\) | 0.579658 | 0.0221638 | ||||||||
\(685\) | −16.9309 | + | 19.5215i | −0.646897 | + | 0.745879i | ||||
\(686\) | −5.58579 | + | 17.6578i | −0.213266 | + | 0.674179i | ||||
\(687\) | 10.0711 | + | 10.0711i | 0.384235 | + | 0.384235i | ||||
\(688\) | −4.00000 | + | 4.00000i | −0.152499 | + | 0.152499i | ||||
\(689\) | −69.8434 | −2.66082 | ||||||||
\(690\) | 1.58579 | − | 1.82843i | 0.0603699 | − | 0.0696070i | ||||
\(691\) | − | 25.1033i | − | 0.954973i | −0.878639 | − | 0.477487i | \(-0.841548\pi\) | ||
0.878639 | − | 0.477487i | \(-0.158452\pi\) | |||||||
\(692\) | 13.2898 | − | 13.2898i | 0.505202 | − | 0.505202i | ||||
\(693\) | 1.10332 | − | 2.89668i | 0.0419115 | − | 0.110036i | ||||
\(694\) | 7.51472i | 0.285255i | ||||||||
\(695\) | −1.36396 | − | 19.1924i | −0.0517380 | − | 0.728009i | ||||
\(696\) | 1.53073i | 0.0580223i | ||||||||
\(697\) | −13.6569 | − | 13.6569i | −0.517290 | − | 0.517290i | ||||
\(698\) | 1.88622 | + | 1.88622i | 0.0713945 | + | 0.0713945i | ||||
\(699\) | −7.83938 | −0.296512 | ||||||||
\(700\) | −2.91307 | + | 12.9040i | −0.110104 | + | 0.487727i | ||||
\(701\) | −13.1127 | −0.495260 | −0.247630 | − | 0.968855i | \(-0.579652\pi\) | ||||
−0.247630 | + | 0.968855i | \(0.579652\pi\) | |||||||
\(702\) | 20.2426 | + | 20.2426i | 0.764009 | + | 0.764009i | ||||
\(703\) | −3.61859 | − | 3.61859i | −0.136478 | − | 0.136478i | ||||
\(704\) | − | 2.82843i | − | 0.106600i | ||||||
\(705\) | −0.448342 | − | 6.30864i | −0.0168855 | − | 0.237597i | ||||
\(706\) | 11.9832i | 0.450995i | ||||||||
\(707\) | 2.58455 | − | 6.78556i | 0.0972020 | − | 0.255197i | ||||
\(708\) | 12.0711 | − | 12.0711i | 0.453659 | − | 0.453659i | ||||
\(709\) | − | 41.3137i | − | 1.55157i | −0.630998 | − | 0.775784i | \(-0.717354\pi\) | ||
0.630998 | − | 0.775784i | \(-0.282646\pi\) | |||||||
\(710\) | 0.858221 | − | 0.989538i | 0.0322085 | − | 0.0371367i | ||||
\(711\) | −2.10051 | −0.0787751 | ||||||||
\(712\) | −8.02509 | + | 8.02509i | −0.300753 | + | 0.300753i | ||||
\(713\) | −0.634051 | − | 0.634051i | −0.0237454 | − | 0.0237454i | ||||
\(714\) | −10.4525 | − | 23.3137i | −0.391175 | − | 0.872494i | ||||
\(715\) | 24.8284 | − | 28.6274i | 0.928531 | − | 1.07060i | ||||
\(716\) | 13.6569 | 0.510381 | ||||||||
\(717\) | −8.47343 | + | 8.47343i | −0.316446 | + | 0.316446i | ||||
\(718\) | −12.0000 | + | 12.0000i | −0.447836 | + | 0.447836i | ||||
\(719\) | −43.7122 | −1.63019 | −0.815094 | − | 0.579328i | \(-0.803315\pi\) | ||||
−0.815094 | + | 0.579328i | \(0.803315\pi\) | |||||||
\(720\) | −0.923880 | + | 0.0656581i | −0.0344310 | + | 0.00244693i | ||||
\(721\) | −15.3137 | − | 34.1563i | −0.570312 | − | 1.27205i | ||||
\(722\) | 12.0503 | + | 12.0503i | 0.448464 | + | 0.448464i | ||||
\(723\) | 8.82843 | − | 8.82843i | 0.328333 | − | 0.328333i | ||||
\(724\) | −8.79045 | −0.326695 | ||||||||
\(725\) | 0.585786 | + | 4.10051i | 0.0217556 | + | 0.152289i | ||||
\(726\) | − | 5.54328i | − | 0.205730i | ||||||
\(727\) | 22.8841 | − | 22.8841i | 0.848724 | − | 0.848724i | −0.141250 | − | 0.989974i | \(-0.545112\pi\) |
0.989974 | + | 0.141250i | \(0.0451122\pi\) | |||||||
\(728\) | −14.8141 | − | 5.64255i | −0.549048 | − | 0.209127i | ||||
\(729\) | − | 22.3137i | − | 0.826434i | ||||||
\(730\) | 13.0711 | − | 0.928932i | 0.483782 | − | 0.0343813i | ||||
\(731\) | − | 29.5641i | − | 1.09347i | ||||||
\(732\) | 8.41421 | + | 8.41421i | 0.310998 | + | 0.310998i | ||||
\(733\) | −21.9489 | − | 21.9489i | −0.810703 | − | 0.810703i | 0.174037 | − | 0.984739i | \(-0.444319\pi\) |
−0.984739 | + | 0.174037i | \(0.944319\pi\) | |||||||
\(734\) | 4.32957 | 0.159807 | ||||||||
\(735\) | −28.6836 | + | 3.70620i | −1.05801 | + | 0.136705i | ||||
\(736\) | 0.585786 | 0.0215924 | ||||||||
\(737\) | 29.6569 | + | 29.6569i | 1.09242 | + | 1.09242i | ||||
\(738\) | −1.08239 | − | 1.08239i | −0.0398434 | − | 0.0398434i | ||||
\(739\) | − | 9.65685i | − | 0.355233i | −0.984100 | − | 0.177617i | \(-0.943161\pi\) | ||
0.984100 | − | 0.177617i | \(-0.0568387\pi\) | |||||||
\(740\) | 6.17733 | + | 5.35757i | 0.227083 | + | 0.196948i | ||||
\(741\) | 15.4930i | 0.569151i | ||||||||
\(742\) | −28.8213 | − | 10.9777i | −1.05806 | − | 0.403005i | ||||
\(743\) | 27.0416 | − | 27.0416i | 0.992061 | − | 0.992061i | −0.00790753 | − | 0.999969i | \(-0.502517\pi\) |
0.999969 | + | 0.00790753i | \(0.00251707\pi\) | |||||||
\(744\) | 2.82843i | 0.103695i | ||||||||
\(745\) | 38.6172 | − | 2.74444i | 1.41483 | − | 0.100549i | ||||
\(746\) | 21.3137 | 0.780350 | ||||||||
\(747\) | 2.20325 | − | 2.20325i | 0.0806126 | − | 0.0806126i | ||||
\(748\) | 10.4525 | + | 10.4525i | 0.382181 | + | 0.382181i | ||||
\(749\) | 5.59767 | + | 12.4853i | 0.204534 | + | 0.456202i | ||||
\(750\) | −20.1924 | + | 4.36396i | −0.737322 | + | 0.159349i | ||||
\(751\) | −2.48528 | −0.0906892 | −0.0453446 | − | 0.998971i | \(-0.514439\pi\) | ||||
−0.0453446 | + | 0.998971i | \(0.514439\pi\) | |||||||
\(752\) | 1.08239 | − | 1.08239i | 0.0394708 | − | 0.0394708i | ||||
\(753\) | 18.4142 | − | 18.4142i | 0.671051 | − | 0.671051i | ||||
\(754\) | −4.96362 | −0.180764 | ||||||||
\(755\) | 1.39942 | + | 19.6913i | 0.0509300 | + | 0.716640i | ||||
\(756\) | 5.17157 | + | 11.5349i | 0.188088 | + | 0.419520i | ||||
\(757\) | 7.89949 | + | 7.89949i | 0.287112 | + | 0.287112i | 0.835937 | − | 0.548825i | \(-0.184925\pi\) |
−0.548825 | + | 0.835937i | \(0.684925\pi\) | |||||||
\(758\) | 4.34315 | − | 4.34315i | 0.157750 | − | 0.157750i | ||||
\(759\) | −3.06147 | −0.111124 | ||||||||
\(760\) | 2.36396 | + | 2.05025i | 0.0857499 | + | 0.0743705i | ||||
\(761\) | − | 26.3939i | − | 0.956778i | −0.878148 | − | 0.478389i | \(-0.841221\pi\) | ||
0.878148 | − | 0.478389i | \(-0.158779\pi\) | |||||||
\(762\) | −6.62567 | + | 6.62567i | −0.240023 | + | 0.240023i | ||||
\(763\) | −11.4347 | + | 30.0211i | −0.413965 | + | 1.08684i | ||||
\(764\) | 1.75736i | 0.0635790i | ||||||||
\(765\) | 3.17157 | − | 3.65685i | 0.114668 | − | 0.132214i | ||||
\(766\) | − | 15.0447i | − | 0.543587i | ||||||
\(767\) | 39.1421 | + | 39.1421i | 1.41334 | + | 1.41334i | ||||
\(768\) | −1.30656 | − | 1.30656i | −0.0471465 | − | 0.0471465i | ||||
\(769\) | 17.5809 | 0.633984 | 0.316992 | − | 0.948428i | \(-0.397327\pi\) | ||||
0.316992 | + | 0.948428i | \(0.397327\pi\) | |||||||
\(770\) | 14.7451 | − | 7.91082i | 0.531378 | − | 0.285086i | ||||
\(771\) | −20.4853 | −0.737759 | ||||||||
\(772\) | 8.24264 | + | 8.24264i | 0.296659 | + | 0.296659i | ||||
\(773\) | 14.6892 | + | 14.6892i | 0.528334 | + | 0.528334i | 0.920076 | − | 0.391741i | \(-0.128127\pi\) |
−0.391741 | + | 0.920076i | \(0.628127\pi\) | |||||||
\(774\) | − | 2.34315i | − | 0.0842226i | ||||||
\(775\) | 1.08239 | + | 7.57675i | 0.0388807 | + | 0.272165i | ||||
\(776\) | − | 6.49435i | − | 0.233134i | ||||||
\(777\) | −6.36332 | + | 16.7065i | −0.228283 | + | 0.599341i | ||||
\(778\) | 0.100505 | − | 0.100505i | 0.00360328 | − | 0.00360328i | ||||
\(779\) | 5.17157i | 0.185291i | ||||||||
\(780\) | −1.75490 | − | 24.6934i | −0.0628357 | − | 0.884165i | ||||
\(781\) | −1.65685 | −0.0592869 | ||||||||
\(782\) | −2.16478 | + | 2.16478i | −0.0774125 | + | 0.0774125i | ||||
\(783\) | 2.79884 | + | 2.79884i | 0.100022 | + | 0.100022i | ||||
\(784\) | −5.22625 | − | 4.65685i | −0.186652 | − | 0.166316i | ||||
\(785\) | 24.4350 | + | 21.1924i | 0.872124 | + | 0.756389i | ||||
\(786\) | −27.0711 | −0.965593 | ||||||||
\(787\) | −24.3764 | + | 24.3764i | −0.868923 | + | 0.868923i | −0.992353 | − | 0.123430i | \(-0.960611\pi\) |
0.123430 | + | 0.992353i | \(0.460611\pi\) | |||||||
\(788\) | −0.585786 | + | 0.585786i | −0.0208678 | + | 0.0208678i | ||||
\(789\) | 50.7318 | 1.80610 | ||||||||
\(790\) | −8.56628 | − | 7.42950i | −0.304775 | − | 0.264330i | ||||
\(791\) | −4.00000 | + | 1.79337i | −0.142224 | + | 0.0637648i | ||||
\(792\) | 0.828427 | + | 0.828427i | 0.0294369 | + | 0.0294369i | ||||
\(793\) | −27.2843 | + | 27.2843i | −0.968893 | + | 0.968893i | ||||
\(794\) | 1.58513 | 0.0562540 | ||||||||
\(795\) | −3.41421 | − | 48.0416i | −0.121090 | − | 1.70386i | ||||
\(796\) | − | 28.0334i | − | 0.993618i | ||||||
\(797\) | −16.6683 | + | 16.6683i | −0.590421 | + | 0.590421i | −0.937745 | − | 0.347324i | \(-0.887090\pi\) |
0.347324 | + | 0.937745i | \(0.387090\pi\) | |||||||
\(798\) | −2.43514 | + | 6.39329i | −0.0862030 | + | 0.226320i | ||||
\(799\) | 8.00000i | 0.283020i | ||||||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | − | 4.70099i | − | 0.166101i | ||||||
\(802\) | 13.9706 | + | 13.9706i | 0.493318 | + | 0.493318i | ||||
\(803\) | −11.7206 | − | 11.7206i | −0.413611 | − | 0.413611i | ||||
\(804\) | 27.3994 | 0.966301 | ||||||||
\(805\) | 1.63838 | + | 3.05382i | 0.0577455 | + | 0.107633i | ||||
\(806\) | −9.17157 | −0.323055 | ||||||||
\(807\) | −35.1421 | − | 35.1421i | −1.23706 | − | 1.23706i | ||||
\(808\) | 1.94061 | + | 1.94061i | 0.0682705 | + | 0.0682705i | ||||
\(809\) | 33.8995i | 1.19184i | 0.803043 | + | 0.595921i | \(0.203213\pi\) | ||||
−0.803043 | + | 0.595921i | \(0.796787\pi\) | |||||||
\(810\) | −14.7549 | + | 17.0125i | −0.518433 | + | 0.597759i | ||||
\(811\) | 50.6005i | 1.77682i | 0.459048 | + | 0.888411i | \(0.348191\pi\) | ||||
−0.459048 | + | 0.888411i | \(0.651809\pi\) | |||||||
\(812\) | −2.04826 | − | 0.780163i | −0.0718800 | − | 0.0273784i | ||||
\(813\) | −24.4853 | + | 24.4853i | −0.858736 | + | 0.858736i | ||||
\(814\) | − | 10.3431i | − | 0.362527i | ||||||
\(815\) | −32.6256 | − | 28.2960i | −1.14283 | − | 0.991167i | ||||
\(816\) | 9.65685 | 0.338058 | ||||||||
\(817\) | −5.59767 | + | 5.59767i | −0.195838 | + | 0.195838i | ||||
\(818\) | −17.6578 | − | 17.6578i | −0.617392 | − | 0.617392i | ||||
\(819\) | 5.99162 | − | 2.68629i | 0.209364 | − | 0.0938666i | ||||
\(820\) | −0.585786 | − | 8.24264i | −0.0204565 | − | 0.287845i | ||||
\(821\) | −34.4853 | −1.20354 | −0.601772 | − | 0.798668i | \(-0.705539\pi\) | ||||
−0.601772 | + | 0.798668i | \(0.705539\pi\) | |||||||
\(822\) | 15.0991 | − | 15.0991i | 0.526642 | − | 0.526642i | ||||
\(823\) | −2.34315 | + | 2.34315i | −0.0816769 | + | 0.0816769i | −0.746765 | − | 0.665088i | \(-0.768394\pi\) |
0.665088 | + | 0.746765i | \(0.268394\pi\) | |||||||
\(824\) | 14.1480 | 0.492870 | ||||||||
\(825\) | 20.9050 | + | 15.6788i | 0.727819 | + | 0.545864i | ||||
\(826\) | 10.0000 | + | 22.3044i | 0.347945 | + | 0.776070i | ||||
\(827\) | −7.51472 | − | 7.51472i | −0.261312 | − | 0.261312i | 0.564275 | − | 0.825587i | \(-0.309156\pi\) |
−0.825587 | + | 0.564275i | \(0.809156\pi\) | |||||||
\(828\) | −0.171573 | + | 0.171573i | −0.00596257 | + | 0.00596257i | ||||
\(829\) | 40.8589 | 1.41909 | 0.709545 | − | 0.704660i | \(-0.248901\pi\) | ||||
0.709545 | + | 0.704660i | \(0.248901\pi\) | |||||||
\(830\) | 16.7782 | − | 1.19239i | 0.582379 | − | 0.0413884i | ||||
\(831\) | 4.59220i | 0.159302i | ||||||||
\(832\) | 4.23671 | − | 4.23671i | 0.146882 | − | 0.146882i | ||||
\(833\) | 36.5232 | − | 2.10422i | 1.26545 | − | 0.0729069i | ||||
\(834\) | 15.8995i | 0.550554i | ||||||||
\(835\) | −4.10051 | − | 3.55635i | −0.141904 | − | 0.123073i | ||||
\(836\) | − | 3.95815i | − | 0.136895i | ||||||
\(837\) | 5.17157 | + | 5.17157i | 0.178756 | + | 0.178756i | ||||
\(838\) | 8.19486 | + | 8.19486i | 0.283087 | + | 0.283087i | ||||
\(839\) | 20.6424 | 0.712654 | 0.356327 | − | 0.934361i | \(-0.384029\pi\) | ||||
0.356327 | + | 0.934361i | \(0.384029\pi\) | |||||||
\(840\) | 3.15704 | − | 10.4657i | 0.108928 | − | 0.361100i | ||||
\(841\) | 28.3137 | 0.976335 | ||||||||
\(842\) | −12.5858 | − | 12.5858i | −0.433735 | − | 0.433735i | ||||
\(843\) | 7.39104 | + | 7.39104i | 0.254561 | + | 0.254561i | ||||
\(844\) | − | 10.3431i | − | 0.356026i | ||||||
\(845\) | 51.0760 | − | 3.62986i | 1.75707 | − | 0.124871i | ||||
\(846\) | 0.634051i | 0.0217991i | ||||||||
\(847\) | 7.41742 | + | 2.82522i | 0.254866 | + | 0.0970757i | ||||
\(848\) | 8.24264 | − | 8.24264i | 0.283053 | − | 0.283053i | ||||
\(849\) | 8.24264i | 0.282887i | ||||||||
\(850\) | 25.8686 | − | 3.69552i | 0.887287 | − | 0.126755i | ||||
\(851\) | 2.14214 | 0.0734315 | ||||||||
\(852\) | −0.765367 | + | 0.765367i | −0.0262210 | + | 0.0262210i | ||||
\(853\) | −26.7268 | − | 26.7268i | −0.915110 | − | 0.915110i | 0.0815587 | − | 0.996669i | \(-0.474010\pi\) |
−0.996669 | + | 0.0815587i | \(0.974010\pi\) | |||||||
\(854\) | −15.5474 | + | 6.97056i | −0.532022 | + | 0.238528i | ||||
\(855\) | −1.29289 | + | 0.0918831i | −0.0442160 | + | 0.00314234i | ||||
\(856\) | −5.17157 | −0.176761 | ||||||||
\(857\) | −11.4580 | + | 11.4580i | −0.391397 | + | 0.391397i | −0.875185 | − | 0.483788i | \(-0.839261\pi\) |
0.483788 | + | 0.875185i | \(0.339261\pi\) | |||||||
\(858\) | −22.1421 | + | 22.1421i | −0.755920 | + | 0.755920i | ||||
\(859\) | −40.6732 | −1.38775 | −0.693876 | − | 0.720094i | \(-0.744099\pi\) | ||||
−0.693876 | + | 0.720094i | \(0.744099\pi\) | |||||||
\(860\) | 8.28772 | − | 9.55582i | 0.282609 | − | 0.325851i | ||||
\(861\) | 16.4853 | − | 7.39104i | 0.561817 | − | 0.251886i | ||||
\(862\) | −4.00000 | − | 4.00000i | −0.136241 | − | 0.136241i | ||||
\(863\) | −2.44365 | + | 2.44365i | −0.0831828 | + | 0.0831828i | −0.747474 | − | 0.664291i | \(-0.768734\pi\) |
0.664291 | + | 0.747474i | \(0.268734\pi\) | |||||||
\(864\) | −4.77791 | −0.162548 | ||||||||
\(865\) | −27.5355 | + | 31.7487i | −0.936236 | + | 1.07949i | ||||
\(866\) | − | 14.7821i | − | 0.502315i | ||||||
\(867\) | −13.4755 | + | 13.4755i | −0.457652 | + | 0.457652i | ||||
\(868\) | −3.78470 | − | 1.44155i | −0.128461 | − | 0.0489295i | ||||
\(869\) | 14.3431i | 0.486558i | ||||||||
\(870\) | −0.242641 | − | 3.41421i | −0.00822629 | − | 0.115753i | ||||
\(871\) | 88.8463i | 3.01044i | ||||||||
\(872\) | −8.58579 | − | 8.58579i | −0.290751 | − | 0.290751i | ||||
\(873\) | 1.90215 | + | 1.90215i | 0.0643781 | + | 0.0643781i | ||||
\(874\) | 0.819760 | 0.0277288 | ||||||||
\(875\) | 4.45199 | − | 29.2435i | 0.150505 | − | 0.988609i | ||||
\(876\) | −10.8284 | −0.365859 | ||||||||
\(877\) | −21.5563 | − | 21.5563i | −0.727906 | − | 0.727906i | 0.242296 | − | 0.970202i | \(-0.422099\pi\) |
−0.970202 | + | 0.242296i | \(0.922099\pi\) | |||||||
\(878\) | −9.81845 | − | 9.81845i | −0.331357 | − | 0.331357i | ||||
\(879\) | − | 6.24264i | − | 0.210559i | ||||||
\(880\) | 0.448342 | + | 6.30864i | 0.0151136 | + | 0.212664i | ||||
\(881\) | − | 13.5140i | − | 0.455297i | −0.973743 | − | 0.227649i | \(-0.926896\pi\) | ||
0.973743 | − | 0.227649i | \(-0.0731038\pi\) | |||||||
\(882\) | 2.89469 | − | 0.166773i | 0.0974694 | − | 0.00561553i | ||||
\(883\) | −28.8284 | + | 28.8284i | −0.970154 | + | 0.970154i | −0.999567 | − | 0.0294135i | \(-0.990636\pi\) |
0.0294135 | + | 0.999567i | \(0.490636\pi\) | |||||||
\(884\) | 31.3137i | 1.05319i | ||||||||
\(885\) | −25.0104 | + | 28.8372i | −0.840716 | + | 0.969353i | ||||
\(886\) | 5.85786 | 0.196799 | ||||||||
\(887\) | 32.5487 | − | 32.5487i | 1.09288 | − | 1.09288i | 0.0976580 | − | 0.995220i | \(-0.468865\pi\) |
0.995220 | − | 0.0976580i | \(-0.0311351\pi\) | |||||||
\(888\) | −4.77791 | − | 4.77791i | −0.160336 | − | 0.160336i | ||||
\(889\) | −5.48888 | − | 12.2426i | −0.184091 | − | 0.410605i | ||||
\(890\) | 16.6274 | − | 19.1716i | 0.557352 | − | 0.642633i | ||||
\(891\) | 28.4853 | 0.954293 | ||||||||
\(892\) | 6.75699 | − | 6.75699i | 0.226241 | − | 0.226241i | ||||
\(893\) | 1.51472 | − | 1.51472i | 0.0506881 | − | 0.0506881i | ||||
\(894\) | −31.9916 | −1.06996 | ||||||||
\(895\) | −30.4608 | + | 2.16478i | −1.01819 | + | 0.0723608i | ||||
\(896\) | 2.41421 | − | 1.08239i | 0.0806532 | − | 0.0361602i | ||||
\(897\) | −4.58579 | − | 4.58579i | −0.153115 | − | 0.153115i | ||||
\(898\) | 18.1421 | − | 18.1421i | 0.605411 | − | 0.605411i | ||||
\(899\) | −1.26810 | −0.0422935 | ||||||||
\(900\) | 2.05025 | − | 0.292893i | 0.0683418 | − | 0.00976311i | ||||
\(901\) | 60.9217i | 2.02959i | ||||||||
\(902\) | −7.39104 | + | 7.39104i | −0.246095 | + | 0.246095i | ||||
\(903\) | 25.8435 | + | 9.84354i | 0.860019 | + | 0.327572i | ||||
\(904\) | − | 1.65685i | − | 0.0551062i | ||||||
\(905\) | 19.6066 | − | 1.39340i | 0.651745 | − | 0.0463181i | ||||
\(906\) | − | 16.3128i | − | 0.541957i | ||||||
\(907\) | 11.1716 | + | 11.1716i | 0.370946 | + | 0.370946i | 0.867822 | − | 0.496876i | \(-0.165520\pi\) |
−0.496876 | + | 0.867822i | \(0.665520\pi\) | |||||||
\(908\) | 8.38057 | + | 8.38057i | 0.278119 | + | 0.278119i | ||||
\(909\) | −1.13679 | −0.0377048 | ||||||||
\(910\) | 33.9365 | + | 10.2371i | 1.12498 | + | 0.339358i | ||||
\(911\) | −28.1421 | −0.932391 | −0.466195 | − | 0.884682i | \(-0.654376\pi\) | ||||
−0.466195 | + | 0.884682i | \(0.654376\pi\) | |||||||
\(912\) | −1.82843 | − | 1.82843i | −0.0605453 | − | 0.0605453i | ||||
\(913\) | −15.0447 | − | 15.0447i | −0.497907 | − | 0.497907i | ||||
\(914\) | 2.34315i | 0.0775044i | ||||||||
\(915\) | −20.1012 | − | 17.4337i | −0.664524 | − | 0.576339i | ||||
\(916\) | − | 7.70806i | − | 0.254682i | ||||||
\(917\) | 13.7972 | − | 36.2236i | 0.455624 | − | 1.19621i | ||||
\(918\) | 17.6569 | − | 17.6569i | 0.582763 | − | 0.582763i | ||||
\(919\) | 8.38478i | 0.276588i | 0.990391 | + | 0.138294i | \(0.0441619\pi\) | ||||
−0.990391 | + | 0.138294i | \(0.955838\pi\) | |||||||
\(920\) | −1.30656 | + | 0.0928546i | −0.0430761 | + | 0.00306132i | ||||
\(921\) | 60.5269 | 1.99443 | ||||||||
\(922\) | −24.0593 | + | 24.0593i | −0.792352 | + | 0.792352i | ||||
\(923\) | −2.48181 | − | 2.48181i | −0.0816898 | − | 0.0816898i | ||||
\(924\) | −12.6173 | + | 5.65685i | −0.415078 | + | 0.186097i | ||||
\(925\) | −14.6274 | − | 10.9706i | −0.480947 | − | 0.360710i | ||||
\(926\) | 18.3431 | 0.602793 | ||||||||
\(927\) | −4.14386 | + | 4.14386i | −0.136102 | + | 0.136102i | ||||
\(928\) | 0.585786 | − | 0.585786i | 0.0192294 | − | 0.0192294i | ||||
\(929\) | 33.2597 | 1.09121 | 0.545607 | − | 0.838041i | \(-0.316299\pi\) | ||||
0.545607 | + | 0.838041i | \(0.316299\pi\) | |||||||
\(930\) | −0.448342 | − | 6.30864i | −0.0147017 | − | 0.206869i | ||||
\(931\) | −7.31371 | − | 6.51688i | −0.239697 | − | 0.213582i | ||||
\(932\) | 3.00000 | + | 3.00000i | 0.0982683 | + | 0.0982683i | ||||
\(933\) | −4.48528 | + | 4.48528i | −0.146842 | + | 0.146842i | ||||
\(934\) | 24.6549 | 0.806734 | ||||||||
\(935\) | −24.9706 | − | 21.6569i | −0.816625 | − | 0.708255i | ||||
\(936\) | 2.48181i | 0.0811205i | ||||||||
\(937\) | 17.7666 | − | 17.7666i | 0.580410 | − | 0.580410i | −0.354606 | − | 0.935016i | \(-0.615385\pi\) |
0.935016 | + | 0.354606i | \(0.115385\pi\) | |||||||
\(938\) | −13.9645 | + | 36.6629i | −0.455958 | + | 1.19709i | ||||
\(939\) | − | 17.6569i | − | 0.576210i | ||||||
\(940\) | −2.24264 | + | 2.58579i | −0.0731469 | + | 0.0843391i | ||||
\(941\) | 23.3099i | 0.759881i | 0.925011 | + | 0.379940i | \(0.124056\pi\) | ||||
−0.925011 | + | 0.379940i | \(0.875944\pi\) | |||||||
\(942\) | −18.8995 | − | 18.8995i | −0.615779 | − | 0.615779i | ||||
\(943\) | −1.53073 | − | 1.53073i | −0.0498475 | − | 0.0498475i | ||||
\(944\) | −9.23880 | −0.300697 | ||||||||
\(945\) | −13.3633 | − | 24.9082i | −0.434709 | − | 0.810263i | ||||
\(946\) | −16.0000 | −0.520205 | ||||||||
\(947\) | 22.9706 | + | 22.9706i | 0.746443 | + | 0.746443i | 0.973809 | − | 0.227366i | \(-0.0730115\pi\) |
−0.227366 | + | 0.973809i | \(0.573011\pi\) | |||||||
\(948\) | 6.62567 | + | 6.62567i | 0.215192 | + | 0.215192i | ||||
\(949\) | − | 35.1127i | − | 1.13981i | ||||||
\(950\) | −5.59767 | − | 4.19825i | −0.181612 | − | 0.136209i | ||||
\(951\) | − | 57.2261i | − | 1.85568i | ||||||
\(952\) | −4.92177 | + | 12.9218i | −0.159515 | + | 0.418797i | ||||
\(953\) | 23.1421 | − | 23.1421i | 0.749647 | − | 0.749647i | −0.224766 | − | 0.974413i | \(-0.572162\pi\) |
0.974413 | + | 0.224766i | \(0.0721616\pi\) | |||||||
\(954\) | 4.82843i | 0.156326i | ||||||||
\(955\) | −0.278564 | − | 3.91969i | −0.00901411 | − | 0.126838i | ||||
\(956\) | 6.48528 | 0.209749 | ||||||||
\(957\) | −3.06147 | + | 3.06147i | −0.0989632 | + | 0.0989632i | ||||
\(958\) | −7.83938 | − | 7.83938i | −0.253279 | − | 0.253279i | ||||
\(959\) | 12.5085 | + | 27.8995i | 0.403921 | + | 0.900922i | ||||
\(960\) | 3.12132 | + | 2.70711i | 0.100740 | + | 0.0873715i | ||||
\(961\) | 28.6569 | 0.924415 | ||||||||
\(962\) | 15.4930 | − | 15.4930i | 0.499516 | − | 0.499516i | ||||
\(963\) | 1.51472 | − | 1.51472i | 0.0488111 | − | 0.0488111i | ||||
\(964\) | −6.75699 | −0.217628 | ||||||||
\(965\) | −19.6913 | − | 17.0782i | −0.633885 | − | 0.549766i | ||||
\(966\) | −1.17157 | − | 2.61313i | −0.0376947 | − | 0.0840759i | ||||
\(967\) | −2.21320 | − | 2.21320i | −0.0711718 | − | 0.0711718i | 0.670625 | − | 0.741797i | \(-0.266026\pi\) |
−0.741797 | + | 0.670625i | \(0.766026\pi\) | |||||||
\(968\) | −2.12132 | + | 2.12132i | −0.0681818 | + | 0.0681818i | ||||
\(969\) | 13.5140 | 0.434131 | ||||||||
\(970\) | 1.02944 | + | 14.4853i | 0.0330532 | + | 0.465094i | ||||
\(971\) | − | 18.5320i | − | 0.594720i | −0.954765 | − | 0.297360i | \(-0.903894\pi\) | ||
0.954765 | − | 0.297360i | \(-0.0961061\pi\) | |||||||
\(972\) | 3.02301 | − | 3.02301i | 0.0969630 | − | 0.0969630i | ||||
\(973\) | −21.2750 | − | 8.10343i | −0.682045 | − | 0.259784i | ||||
\(974\) | − | 1.55635i | − | 0.0498686i | ||||||
\(975\) | 7.82843 | + | 54.7990i | 0.250710 | + | 1.75497i | ||||
\(976\) | − | 6.43996i | − | 0.206138i | ||||||
\(977\) | −25.8284 | − | 25.8284i | −0.826325 | − | 0.826325i | 0.160682 | − | 0.987006i | \(-0.448631\pi\) |
−0.987006 | + | 0.160682i | \(0.948631\pi\) | |||||||
\(978\) | 25.2346 | + | 25.2346i | 0.806913 | + | 0.806913i | ||||
\(979\) | −32.1003 | −1.02593 | ||||||||
\(980\) | 12.3950 | + | 9.55842i | 0.395945 | + | 0.305332i | ||||
\(981\) | 5.02944 | 0.160578 | ||||||||
\(982\) | −17.7990 | − | 17.7990i | −0.567989 | − | 0.567989i | ||||
\(983\) | −28.7444 | − | 28.7444i | −0.916804 | − | 0.916804i | 0.0799920 | − | 0.996796i | \(-0.474511\pi\) |
−0.996796 | + | 0.0799920i | \(0.974511\pi\) | |||||||
\(984\) | 6.82843i | 0.217682i | ||||||||
\(985\) | 1.21371 | − | 1.39942i | 0.0386720 | − | 0.0445892i | ||||
\(986\) | 4.32957i | 0.137882i | ||||||||
\(987\) | −6.99321 | − | 2.66364i | −0.222596 | − | 0.0847847i | ||||
\(988\) | 5.92893 | − | 5.92893i | 0.188624 | − | 0.188624i | ||||
\(989\) | − | 3.31371i | − | 0.105370i | ||||||
\(990\) | −1.97908 | − | 1.71644i | −0.0628991 | − | 0.0545521i | ||||
\(991\) | −32.5858 | −1.03512 | −0.517561 | − | 0.855646i | \(-0.673160\pi\) | ||||
−0.517561 | + | 0.855646i | \(0.673160\pi\) | |||||||
\(992\) | 1.08239 | − | 1.08239i | 0.0343660 | − | 0.0343660i | ||||
\(993\) | −30.4608 | − | 30.4608i | −0.966645 | − | 0.966645i | ||||
\(994\) | −0.634051 | − | 1.41421i | −0.0201109 | − | 0.0448561i | ||||
\(995\) | 4.44365 | + | 62.5269i | 0.140873 | + | 1.98224i | ||||
\(996\) | −13.8995 | −0.440422 | ||||||||
\(997\) | 0.464273 | − | 0.464273i | 0.0147037 | − | 0.0147037i | −0.699717 | − | 0.714420i | \(-0.746690\pi\) |
0.714420 | + | 0.699717i | \(0.246690\pi\) | |||||||
\(998\) | 5.31371 | − | 5.31371i | 0.168203 | − | 0.168203i | ||||
\(999\) | −17.4721 | −0.552793 |
(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 | 70.2.g.a.27.1 | yes | 8 | |
3.2 | odd | 2 | 630.2.p.a.307.4 | 8 | |||
4.3 | odd | 2 | 560.2.bj.c.97.4 | 8 | |||
5.2 | odd | 4 | 350.2.g.a.293.3 | 8 | |||
5.3 | odd | 4 | inner | 70.2.g.a.13.2 | yes | 8 | |
5.4 | even | 2 | 350.2.g.a.307.4 | 8 | |||
7.2 | even | 3 | 490.2.l.a.227.2 | 16 | |||
7.3 | odd | 6 | 490.2.l.a.117.4 | 16 | |||
7.4 | even | 3 | 490.2.l.a.117.3 | 16 | |||
7.5 | odd | 6 | 490.2.l.a.227.1 | 16 | |||
7.6 | odd | 2 | inner | 70.2.g.a.27.2 | yes | 8 | |
15.8 | even | 4 | 630.2.p.a.433.3 | 8 | |||
20.3 | even | 4 | 560.2.bj.c.433.1 | 8 | |||
21.20 | even | 2 | 630.2.p.a.307.3 | 8 | |||
28.27 | even | 2 | 560.2.bj.c.97.1 | 8 | |||
35.3 | even | 12 | 490.2.l.a.313.2 | 16 | |||
35.13 | even | 4 | inner | 70.2.g.a.13.1 | ✓ | 8 | |
35.18 | odd | 12 | 490.2.l.a.313.1 | 16 | |||
35.23 | odd | 12 | 490.2.l.a.423.4 | 16 | |||
35.27 | even | 4 | 350.2.g.a.293.4 | 8 | |||
35.33 | even | 12 | 490.2.l.a.423.3 | 16 | |||
35.34 | odd | 2 | 350.2.g.a.307.3 | 8 | |||
105.83 | odd | 4 | 630.2.p.a.433.4 | 8 | |||
140.83 | odd | 4 | 560.2.bj.c.433.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.g.a.13.1 | ✓ | 8 | 35.13 | even | 4 | inner | |
70.2.g.a.13.2 | yes | 8 | 5.3 | odd | 4 | inner | |
70.2.g.a.27.1 | yes | 8 | 1.1 | even | 1 | trivial | |
70.2.g.a.27.2 | yes | 8 | 7.6 | odd | 2 | inner | |
350.2.g.a.293.3 | 8 | 5.2 | odd | 4 | |||
350.2.g.a.293.4 | 8 | 35.27 | even | 4 | |||
350.2.g.a.307.3 | 8 | 35.34 | odd | 2 | |||
350.2.g.a.307.4 | 8 | 5.4 | even | 2 | |||
490.2.l.a.117.3 | 16 | 7.4 | even | 3 | |||
490.2.l.a.117.4 | 16 | 7.3 | odd | 6 | |||
490.2.l.a.227.1 | 16 | 7.5 | odd | 6 | |||
490.2.l.a.227.2 | 16 | 7.2 | even | 3 | |||
490.2.l.a.313.1 | 16 | 35.18 | odd | 12 | |||
490.2.l.a.313.2 | 16 | 35.3 | even | 12 | |||
490.2.l.a.423.3 | 16 | 35.33 | even | 12 | |||
490.2.l.a.423.4 | 16 | 35.23 | odd | 12 | |||
560.2.bj.c.97.1 | 8 | 28.27 | even | 2 | |||
560.2.bj.c.97.4 | 8 | 4.3 | odd | 2 | |||
560.2.bj.c.433.1 | 8 | 20.3 | even | 4 | |||
560.2.bj.c.433.4 | 8 | 140.83 | odd | 4 | |||
630.2.p.a.307.3 | 8 | 21.20 | even | 2 | |||
630.2.p.a.307.4 | 8 | 3.2 | odd | 2 | |||
630.2.p.a.433.3 | 8 | 15.8 | even | 4 | |||
630.2.p.a.433.4 | 8 | 105.83 | odd | 4 |