Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [430,2,Mod(257,430)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(430, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("430.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 430 = 2 \cdot 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 430.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: | \(3.43356728692\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.12 | ||
Character | \(\chi\) | \(=\) | 430.257 |
Dual form | 430.2.g.b.343.12 |
$q$-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 \(\left(\mathbb{Z}/430\mathbb{Z}\right)^\times\).
\(n\) | \(87\) | \(261\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.91446 | − | 1.91446i | −1.10532 | − | 1.10532i | −0.993758 | − | 0.111557i | \(-0.964416\pi\) |
−0.111557 | − | 0.993758i | \(-0.535584\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.21975 | − | 0.269648i | −0.992702 | − | 0.120590i | ||||
\(6\) | −2.70746 | −1.10532 | ||||||||
\(7\) | 1.02061 | − | 1.02061i | 0.385754 | − | 0.385754i | −0.487416 | − | 0.873170i | \(-0.662060\pi\) |
0.873170 | + | 0.487416i | \(0.162060\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 4.33033i | 1.44344i | ||||||||
\(10\) | −1.76027 | + | 1.37893i | −0.556646 | + | 0.436056i | ||||
\(11\) | −3.68947 | −1.11242 | −0.556208 | − | 0.831043i | \(-0.687744\pi\) | ||||
−0.556208 | + | 0.831043i | \(0.687744\pi\) | |||||||
\(12\) | −1.91446 | + | 1.91446i | −0.552658 | + | 0.552658i | ||||
\(13\) | −0.648955 | + | 0.648955i | −0.179988 | + | 0.179988i | −0.791350 | − | 0.611363i | \(-0.790622\pi\) |
0.611363 | + | 0.791350i | \(0.290622\pi\) | |||||||
\(14\) | − | 1.44336i | − | 0.385754i | ||||||
\(15\) | 3.73340 | + | 4.76586i | 0.963959 | + | 1.23054i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.53300 | + | 2.53300i | 0.614343 | + | 0.614343i | 0.944075 | − | 0.329731i | \(-0.106958\pi\) |
−0.329731 | + | 0.944075i | \(0.606958\pi\) | |||||||
\(18\) | 3.06201 | + | 3.06201i | 0.721722 | + | 0.721722i | ||||
\(19\) | 0.0313512 | 0.00719245 | 0.00359623 | − | 0.999994i | \(-0.498855\pi\) | ||||
0.00359623 | + | 0.999994i | \(0.498855\pi\) | |||||||
\(20\) | −0.269648 | + | 2.21975i | −0.0602951 | + | 0.496351i | ||||
\(21\) | −3.90784 | −0.852760 | ||||||||
\(22\) | −2.60885 | + | 2.60885i | −0.556208 | + | 0.556208i | ||||
\(23\) | 2.32349 | − | 2.32349i | 0.484481 | − | 0.484481i | −0.422078 | − | 0.906559i | \(-0.638699\pi\) |
0.906559 | + | 0.422078i | \(0.138699\pi\) | |||||||
\(24\) | 2.70746i | 0.552658i | ||||||||
\(25\) | 4.85458 | + | 1.19710i | 0.970916 | + | 0.239421i | ||||
\(26\) | 0.917760i | 0.179988i | ||||||||
\(27\) | 2.54687 | − | 2.54687i | 0.490146 | − | 0.490146i | ||||
\(28\) | −1.02061 | − | 1.02061i | −0.192877 | − | 0.192877i | ||||
\(29\) | −7.48270 | −1.38950 | −0.694751 | − | 0.719250i | \(-0.744486\pi\) | ||||
−0.694751 | + | 0.719250i | \(0.744486\pi\) | |||||||
\(30\) | 6.00988 | + | 0.730061i | 1.09725 | + | 0.133290i | ||||
\(31\) | −4.11398 | −0.738892 | −0.369446 | − | 0.929252i | \(-0.620453\pi\) | ||||
−0.369446 | + | 0.929252i | \(0.620453\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 7.06334 | + | 7.06334i | 1.22957 | + | 1.22957i | ||||
\(34\) | 3.58221 | 0.614343 | ||||||||
\(35\) | −2.54070 | + | 1.99029i | −0.429457 | + | 0.336421i | ||||
\(36\) | 4.33033 | 0.721722 | ||||||||
\(37\) | −2.60713 | + | 2.60713i | −0.428609 | + | 0.428609i | −0.888154 | − | 0.459545i | \(-0.848012\pi\) |
0.459545 | + | 0.888154i | \(0.348012\pi\) | |||||||
\(38\) | 0.0221686 | − | 0.0221686i | 0.00359623 | − | 0.00359623i | ||||
\(39\) | 2.48480 | 0.397886 | ||||||||
\(40\) | 1.37893 | + | 1.76027i | 0.218028 | + | 0.278323i | ||||
\(41\) | −10.1280 | −1.58173 | −0.790866 | − | 0.611990i | \(-0.790369\pi\) | ||||
−0.790866 | + | 0.611990i | \(0.790369\pi\) | |||||||
\(42\) | −2.76326 | + | 2.76326i | −0.426380 | + | 0.426380i | ||||
\(43\) | 4.41676 | − | 4.84688i | 0.673550 | − | 0.739142i | ||||
\(44\) | 3.68947i | 0.556208i | ||||||||
\(45\) | 1.16767 | − | 9.61226i | 0.174065 | − | 1.43291i | ||||
\(46\) | − | 3.28591i | − | 0.484481i | ||||||
\(47\) | −6.32263 | − | 6.32263i | −0.922250 | − | 0.922250i | 0.0749379 | − | 0.997188i | \(-0.476124\pi\) |
−0.997188 | + | 0.0749379i | \(0.976124\pi\) | |||||||
\(48\) | 1.91446 | + | 1.91446i | 0.276329 | + | 0.276329i | ||||
\(49\) | 4.91671i | 0.702388i | ||||||||
\(50\) | 4.27919 | − | 2.58623i | 0.605168 | − | 0.365748i | ||||
\(51\) | − | 9.69868i | − | 1.35809i | ||||||
\(52\) | 0.648955 | + | 0.648955i | 0.0899938 | + | 0.0899938i | ||||
\(53\) | 3.09229 | − | 3.09229i | 0.424759 | − | 0.424759i | −0.462080 | − | 0.886838i | \(-0.652897\pi\) |
0.886838 | + | 0.462080i | \(0.152897\pi\) | |||||||
\(54\) | − | 3.60182i | − | 0.490146i | ||||||
\(55\) | 8.18969 | + | 0.994857i | 1.10430 | + | 0.134147i | ||||
\(56\) | −1.44336 | −0.192877 | ||||||||
\(57\) | −0.0600207 | − | 0.0600207i | −0.00794993 | − | 0.00794993i | ||||
\(58\) | −5.29107 | + | 5.29107i | −0.694751 | + | 0.694751i | ||||
\(59\) | − | 14.1930i | − | 1.84777i | −0.382674 | − | 0.923884i | \(-0.624997\pi\) | ||
0.382674 | − | 0.923884i | \(-0.375003\pi\) | |||||||
\(60\) | 4.76586 | − | 3.73340i | 0.615270 | − | 0.481979i | ||||
\(61\) | − | 7.52367i | − | 0.963307i | −0.876362 | − | 0.481654i | \(-0.840036\pi\) | ||
0.876362 | − | 0.481654i | \(-0.159964\pi\) | |||||||
\(62\) | −2.90902 | + | 2.90902i | −0.369446 | + | 0.369446i | ||||
\(63\) | 4.41958 | + | 4.41958i | 0.556814 | + | 0.556814i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 1.61551 | − | 1.26553i | 0.200379 | − | 0.156969i | ||||
\(66\) | 9.98908 | 1.22957 | ||||||||
\(67\) | 1.07630 | + | 1.07630i | 0.131491 | + | 0.131491i | 0.769789 | − | 0.638298i | \(-0.220361\pi\) |
−0.638298 | + | 0.769789i | \(0.720361\pi\) | |||||||
\(68\) | 2.53300 | − | 2.53300i | 0.307172 | − | 0.307172i | ||||
\(69\) | −8.89647 | −1.07101 | ||||||||
\(70\) | −0.389199 | + | 3.20390i | −0.0465182 | + | 0.382939i | ||||
\(71\) | 4.73051i | 0.561408i | 0.959794 | + | 0.280704i | \(0.0905679\pi\) | ||||
−0.959794 | + | 0.280704i | \(0.909432\pi\) | |||||||
\(72\) | 3.06201 | − | 3.06201i | 0.360861 | − | 0.360861i | ||||
\(73\) | −4.95201 | − | 4.95201i | −0.579589 | − | 0.579589i | 0.355201 | − | 0.934790i | \(-0.384413\pi\) |
−0.934790 | + | 0.355201i | \(0.884413\pi\) | |||||||
\(74\) | 3.68703i | 0.428609i | ||||||||
\(75\) | −7.00210 | − | 11.5857i | −0.808533 | − | 1.33780i | ||||
\(76\) | − | 0.0313512i | − | 0.00359623i | ||||||
\(77\) | −3.76550 | + | 3.76550i | −0.429119 | + | 0.429119i | ||||
\(78\) | 1.75702 | − | 1.75702i | 0.198943 | − | 0.198943i | ||||
\(79\) | − | 2.04141i | − | 0.229677i | −0.993384 | − | 0.114838i | \(-0.963365\pi\) | ||
0.993384 | − | 0.114838i | \(-0.0366350\pi\) | |||||||
\(80\) | 2.21975 | + | 0.269648i | 0.248176 | + | 0.0301476i | ||||
\(81\) | 3.23922 | 0.359913 | ||||||||
\(82\) | −7.16159 | + | 7.16159i | −0.790866 | + | 0.790866i | ||||
\(83\) | −4.90419 | + | 4.90419i | −0.538305 | + | 0.538305i | −0.923031 | − | 0.384726i | \(-0.874296\pi\) |
0.384726 | + | 0.923031i | \(0.374296\pi\) | |||||||
\(84\) | 3.90784i | 0.426380i | ||||||||
\(85\) | −4.93961 | − | 6.30565i | −0.535776 | − | 0.683944i | ||||
\(86\) | −0.304139 | − | 6.55038i | −0.0327962 | − | 0.706346i | ||||
\(87\) | 14.3253 | + | 14.3253i | 1.53584 | + | 1.53584i | ||||
\(88\) | 2.60885 | + | 2.60885i | 0.278104 | + | 0.278104i | ||||
\(89\) | −9.71831 | −1.03014 | −0.515070 | − | 0.857148i | \(-0.672234\pi\) | ||||
−0.515070 | + | 0.857148i | \(0.672234\pi\) | |||||||
\(90\) | −5.97123 | − | 7.62256i | −0.629423 | − | 0.803488i | ||||
\(91\) | 1.32466i | 0.138862i | ||||||||
\(92\) | −2.32349 | − | 2.32349i | −0.242241 | − | 0.242241i | ||||
\(93\) | 7.87606 | + | 7.87606i | 0.816709 | + | 0.816709i | ||||
\(94\) | −8.94155 | −0.922250 | ||||||||
\(95\) | −0.0695918 | − | 0.00845379i | −0.00713997 | − | 0.000867340i | ||||
\(96\) | 2.70746 | 0.276329 | ||||||||
\(97\) | −10.1116 | − | 10.1116i | −1.02668 | − | 1.02668i | −0.999634 | − | 0.0270433i | \(-0.991391\pi\) |
−0.0270433 | − | 0.999634i | \(-0.508609\pi\) | |||||||
\(98\) | 3.47664 | + | 3.47664i | 0.351194 | + | 0.351194i | ||||
\(99\) | − | 15.9766i | − | 1.60571i | ||||||
\(100\) | 1.19710 | − | 4.85458i | 0.119710 | − | 0.485458i | ||||
\(101\) | 1.01624 | 0.101119 | 0.0505597 | − | 0.998721i | \(-0.483899\pi\) | ||||
0.0505597 | + | 0.998721i | \(0.483899\pi\) | |||||||
\(102\) | −6.85800 | − | 6.85800i | −0.679043 | − | 0.679043i | ||||
\(103\) | 12.2717 | − | 12.2717i | 1.20917 | − | 1.20917i | 0.237875 | − | 0.971296i | \(-0.423549\pi\) |
0.971296 | − | 0.237875i | \(-0.0764510\pi\) | |||||||
\(104\) | 0.917760 | 0.0899938 | ||||||||
\(105\) | 8.67442 | + | 1.05374i | 0.846537 | + | 0.102835i | ||||
\(106\) | − | 4.37316i | − | 0.424759i | ||||||
\(107\) | −6.96632 | − | 6.96632i | −0.673460 | − | 0.673460i | 0.285052 | − | 0.958512i | \(-0.407989\pi\) |
−0.958512 | + | 0.285052i | \(0.907989\pi\) | |||||||
\(108\) | −2.54687 | − | 2.54687i | −0.245073 | − | 0.245073i | ||||
\(109\) | 1.28166i | 0.122761i | 0.998114 | + | 0.0613803i | \(0.0195502\pi\) | ||||
−0.998114 | + | 0.0613803i | \(0.980450\pi\) | |||||||
\(110\) | 6.49446 | − | 5.08752i | 0.619222 | − | 0.485076i | ||||
\(111\) | 9.98249 | 0.947496 | ||||||||
\(112\) | −1.02061 | + | 1.02061i | −0.0964385 | + | 0.0964385i | ||||
\(113\) | 8.83308 | + | 8.83308i | 0.830946 | + | 0.830946i | 0.987646 | − | 0.156700i | \(-0.0500856\pi\) |
−0.156700 | + | 0.987646i | \(0.550086\pi\) | |||||||
\(114\) | −0.0848820 | −0.00794993 | ||||||||
\(115\) | −5.78409 | + | 4.53104i | −0.539369 | + | 0.422522i | ||||
\(116\) | 7.48270i | 0.694751i | ||||||||
\(117\) | −2.81019 | − | 2.81019i | −0.259802 | − | 0.259802i | ||||
\(118\) | −10.0359 | − | 10.0359i | −0.923884 | − | 0.923884i | ||||
\(119\) | 5.17041 | 0.473971 | ||||||||
\(120\) | 0.730061 | − | 6.00988i | 0.0666452 | − | 0.548625i | ||||
\(121\) | 2.61216 | 0.237469 | ||||||||
\(122\) | −5.32004 | − | 5.32004i | −0.481654 | − | 0.481654i | ||||
\(123\) | 19.3897 | + | 19.3897i | 1.74831 | + | 1.74831i | ||||
\(124\) | 4.11398i | 0.369446i | ||||||||
\(125\) | −10.4532 | − | 3.96630i | −0.934959 | − | 0.354756i | ||||
\(126\) | 6.25023 | 0.556814 | ||||||||
\(127\) | 14.2953 | + | 14.2953i | 1.26851 | + | 1.26851i | 0.946859 | + | 0.321647i | \(0.104237\pi\) |
0.321647 | + | 0.946859i | \(0.395763\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −17.7349 | + | 0.823444i | −1.56147 | + | 0.0725002i | ||||
\(130\) | 0.247472 | − | 2.03720i | 0.0217048 | − | 0.178674i | ||||
\(131\) | 16.6754i | 1.45694i | 0.685080 | + | 0.728468i | \(0.259767\pi\) | ||||
−0.685080 | + | 0.728468i | \(0.740233\pi\) | |||||||
\(132\) | 7.06334 | − | 7.06334i | 0.614785 | − | 0.614785i | ||||
\(133\) | 0.0319973 | − | 0.0319973i | 0.00277452 | − | 0.00277452i | ||||
\(134\) | 1.52212 | 0.131491 | ||||||||
\(135\) | −6.34018 | + | 4.96666i | −0.545676 | + | 0.427462i | ||||
\(136\) | − | 3.58221i | − | 0.307172i | ||||||
\(137\) | 8.14514 | − | 8.14514i | 0.695886 | − | 0.695886i | −0.267634 | − | 0.963521i | \(-0.586242\pi\) |
0.963521 | + | 0.267634i | \(0.0862420\pi\) | |||||||
\(138\) | −6.29075 | + | 6.29075i | −0.535504 | + | 0.535504i | ||||
\(139\) | 5.97569i | 0.506851i | 0.967355 | + | 0.253426i | \(0.0815573\pi\) | ||||
−0.967355 | + | 0.253426i | \(0.918443\pi\) | |||||||
\(140\) | 1.99029 | + | 2.54070i | 0.168210 | + | 0.214729i | ||||
\(141\) | 24.2089i | 2.03875i | ||||||||
\(142\) | 3.34497 | + | 3.34497i | 0.280704 | + | 0.280704i | ||||
\(143\) | 2.39430 | − | 2.39430i | 0.200221 | − | 0.200221i | ||||
\(144\) | − | 4.33033i | − | 0.360861i | ||||||
\(145\) | 16.6097 | + | 2.01770i | 1.37936 | + | 0.167560i | ||||
\(146\) | −7.00321 | −0.579589 | ||||||||
\(147\) | 9.41286 | − | 9.41286i | 0.776360 | − | 0.776360i | ||||
\(148\) | 2.60713 | + | 2.60713i | 0.214305 | + | 0.214305i | ||||
\(149\) | −3.51576 | −0.288023 | −0.144011 | − | 0.989576i | \(-0.546000\pi\) | ||||
−0.144011 | + | 0.989576i | \(0.546000\pi\) | |||||||
\(150\) | −13.1436 | − | 3.24111i | −1.07317 | − | 0.264635i | ||||
\(151\) | − | 10.6170i | − | 0.863999i | −0.901874 | − | 0.432000i | \(-0.857808\pi\) | ||
0.901874 | − | 0.432000i | \(-0.142192\pi\) | |||||||
\(152\) | −0.0221686 | − | 0.0221686i | −0.00179811 | − | 0.00179811i | ||||
\(153\) | −10.9687 | + | 10.9687i | −0.886770 | + | 0.886770i | ||||
\(154\) | 5.32522i | 0.429119i | ||||||||
\(155\) | 9.13201 | + | 1.10933i | 0.733500 | + | 0.0891033i | ||||
\(156\) | − | 2.48480i | − | 0.198943i | ||||||
\(157\) | −4.54306 | + | 4.54306i | −0.362576 | + | 0.362576i | −0.864760 | − | 0.502185i | \(-0.832530\pi\) |
0.502185 | + | 0.864760i | \(0.332530\pi\) | |||||||
\(158\) | −1.44350 | − | 1.44350i | −0.114838 | − | 0.114838i | ||||
\(159\) | −11.8401 | −0.938985 | ||||||||
\(160\) | 1.76027 | − | 1.37893i | 0.139162 | − | 0.109014i | ||||
\(161\) | − | 4.74275i | − | 0.373781i | ||||||
\(162\) | 2.29047 | − | 2.29047i | 0.179957 | − | 0.179957i | ||||
\(163\) | −5.62978 | − | 5.62978i | −0.440959 | − | 0.440959i | 0.451376 | − | 0.892334i | \(-0.350933\pi\) |
−0.892334 | + | 0.451376i | \(0.850933\pi\) | |||||||
\(164\) | 10.1280i | 0.790866i | ||||||||
\(165\) | −13.7742 | − | 17.5835i | −1.07232 | − | 1.36887i | ||||
\(166\) | 6.93557i | 0.538305i | ||||||||
\(167\) | −1.08392 | − | 1.08392i | −0.0838759 | − | 0.0838759i | 0.663924 | − | 0.747800i | \(-0.268890\pi\) |
−0.747800 | + | 0.663924i | \(0.768890\pi\) | |||||||
\(168\) | 2.76326 | + | 2.76326i | 0.213190 | + | 0.213190i | ||||
\(169\) | 12.1577i | 0.935209i | ||||||||
\(170\) | −7.95160 | − | 0.965935i | −0.609860 | − | 0.0740839i | ||||
\(171\) | 0.135761i | 0.0103819i | ||||||||
\(172\) | −4.84688 | − | 4.41676i | −0.369571 | − | 0.336775i | ||||
\(173\) | −11.2690 | + | 11.2690i | −0.856766 | + | 0.856766i | −0.990956 | − | 0.134190i | \(-0.957157\pi\) |
0.134190 | + | 0.990956i | \(0.457157\pi\) | |||||||
\(174\) | 20.2591 | 1.53584 | ||||||||
\(175\) | 6.17640 | − | 3.73285i | 0.466892 | − | 0.282177i | ||||
\(176\) | 3.68947 | 0.278104 | ||||||||
\(177\) | −27.1719 | + | 27.1719i | −2.04237 | + | 2.04237i | ||||
\(178\) | −6.87188 | + | 6.87188i | −0.515070 | + | 0.515070i | ||||
\(179\) | 20.4789 | 1.53067 | 0.765333 | − | 0.643634i | \(-0.222574\pi\) | ||||
0.765333 | + | 0.643634i | \(0.222574\pi\) | |||||||
\(180\) | −9.61226 | − | 1.16767i | −0.716455 | − | 0.0870327i | ||||
\(181\) | 5.42907 | 0.403540 | 0.201770 | − | 0.979433i | \(-0.435331\pi\) | ||||
0.201770 | + | 0.979433i | \(0.435331\pi\) | |||||||
\(182\) | 0.936675 | + | 0.936675i | 0.0694309 | + | 0.0694309i | ||||
\(183\) | −14.4038 | + | 14.4038i | −1.06476 | + | 1.06476i | ||||
\(184\) | −3.28591 | −0.242241 | ||||||||
\(185\) | 6.49018 | − | 5.08416i | 0.477167 | − | 0.373795i | ||||
\(186\) | 11.1384 | 0.816709 | ||||||||
\(187\) | −9.34543 | − | 9.34543i | −0.683405 | − | 0.683405i | ||||
\(188\) | −6.32263 | + | 6.32263i | −0.461125 | + | 0.461125i | ||||
\(189\) | − | 5.19872i | − | 0.378151i | ||||||
\(190\) | −0.0551866 | + | 0.0432311i | −0.00400365 | + | 0.00313631i | ||||
\(191\) | − | 11.5800i | − | 0.837897i | −0.908010 | − | 0.418948i | \(-0.862399\pi\) | ||
0.908010 | − | 0.418948i | \(-0.137601\pi\) | |||||||
\(192\) | 1.91446 | − | 1.91446i | 0.138164 | − | 0.138164i | ||||
\(193\) | 15.1912 | − | 15.1912i | 1.09349 | − | 1.09349i | 0.0983333 | − | 0.995154i | \(-0.468649\pi\) |
0.995154 | − | 0.0983333i | \(-0.0313511\pi\) | |||||||
\(194\) | −14.3000 | −1.02668 | ||||||||
\(195\) | −5.51563 | − | 0.670021i | −0.394982 | − | 0.0479812i | ||||
\(196\) | 4.91671 | 0.351194 | ||||||||
\(197\) | 0.310153 | + | 0.310153i | 0.0220975 | + | 0.0220975i | 0.718069 | − | 0.695972i | \(-0.245026\pi\) |
−0.695972 | + | 0.718069i | \(0.745026\pi\) | |||||||
\(198\) | −11.2972 | − | 11.2972i | −0.802855 | − | 0.802855i | ||||
\(199\) | 27.5168 | 1.95061 | 0.975307 | − | 0.220854i | \(-0.0708845\pi\) | ||||
0.975307 | + | 0.220854i | \(0.0708845\pi\) | |||||||
\(200\) | −2.58623 | − | 4.27919i | −0.182874 | − | 0.302584i | ||||
\(201\) | − | 4.12107i | − | 0.290678i | ||||||
\(202\) | 0.718588 | − | 0.718588i | 0.0505597 | − | 0.0505597i | ||||
\(203\) | −7.63691 | + | 7.63691i | −0.536006 | + | 0.536006i | ||||
\(204\) | −9.69868 | −0.679043 | ||||||||
\(205\) | 22.4817 | + | 2.73100i | 1.57019 | + | 0.190741i | ||||
\(206\) | − | 17.3549i | − | 1.20917i | ||||||
\(207\) | 10.0615 | + | 10.0615i | 0.699321 | + | 0.699321i | ||||
\(208\) | 0.648955 | − | 0.648955i | 0.0449969 | − | 0.0449969i | ||||
\(209\) | −0.115669 | −0.00800100 | ||||||||
\(210\) | 6.87885 | − | 5.38863i | 0.474686 | − | 0.371851i | ||||
\(211\) | − | 11.5577i | − | 0.795667i | −0.917458 | − | 0.397834i | \(-0.869762\pi\) | ||
0.917458 | − | 0.397834i | \(-0.130238\pi\) | |||||||
\(212\) | −3.09229 | − | 3.09229i | −0.212379 | − | 0.212379i | ||||
\(213\) | 9.05638 | − | 9.05638i | 0.620533 | − | 0.620533i | ||||
\(214\) | −9.85187 | −0.673460 | ||||||||
\(215\) | −11.1111 | + | 9.56789i | −0.757768 | + | 0.652524i | ||||
\(216\) | −3.60182 | −0.245073 | ||||||||
\(217\) | −4.19876 | + | 4.19876i | −0.285031 | + | 0.285031i | ||||
\(218\) | 0.906269 | + | 0.906269i | 0.0613803 | + | 0.0613803i | ||||
\(219\) | 18.9609i | 1.28126i | ||||||||
\(220\) | 0.994857 | − | 8.18969i | 0.0670733 | − | 0.552149i | ||||
\(221\) | −3.28761 | −0.221148 | ||||||||
\(222\) | 7.05869 | − | 7.05869i | 0.473748 | − | 0.473748i | ||||
\(223\) | −17.8690 | − | 17.8690i | −1.19660 | − | 1.19660i | −0.975178 | − | 0.221422i | \(-0.928930\pi\) |
−0.221422 | − | 0.975178i | \(-0.571070\pi\) | |||||||
\(224\) | 1.44336i | 0.0964385i | ||||||||
\(225\) | −5.18385 | + | 21.0219i | −0.345590 | + | 1.40146i | ||||
\(226\) | 12.4919 | 0.830946 | ||||||||
\(227\) | 10.8185 | − | 10.8185i | 0.718051 | − | 0.718051i | −0.250155 | − | 0.968206i | \(-0.580482\pi\) |
0.968206 | + | 0.250155i | \(0.0804816\pi\) | |||||||
\(228\) | −0.0600207 | + | 0.0600207i | −0.00397497 | + | 0.00397497i | ||||
\(229\) | − | 0.448544i | − | 0.0296406i | −0.999890 | − | 0.0148203i | \(-0.995282\pi\) | ||
0.999890 | − | 0.0148203i | \(-0.00471763\pi\) | |||||||
\(230\) | −0.886040 | + | 7.29390i | −0.0584237 | + | 0.480946i | ||||
\(231\) | 14.4178 | 0.948623 | ||||||||
\(232\) | 5.29107 | + | 5.29107i | 0.347376 | + | 0.347376i | ||||
\(233\) | 13.4741 | + | 13.4741i | 0.882716 | + | 0.882716i | 0.993810 | − | 0.111094i | \(-0.0354356\pi\) |
−0.111094 | + | 0.993810i | \(0.535436\pi\) | |||||||
\(234\) | −3.97421 | −0.259802 | ||||||||
\(235\) | 12.3298 | + | 15.7395i | 0.804306 | + | 1.02673i | ||||
\(236\) | −14.1930 | −0.923884 | ||||||||
\(237\) | −3.90821 | + | 3.90821i | −0.253865 | + | 0.253865i | ||||
\(238\) | 3.65603 | − | 3.65603i | 0.236985 | − | 0.236985i | ||||
\(239\) | 4.55977i | 0.294947i | 0.989066 | + | 0.147474i | \(0.0471142\pi\) | ||||
−0.989066 | + | 0.147474i | \(0.952886\pi\) | |||||||
\(240\) | −3.73340 | − | 4.76586i | −0.240990 | − | 0.307635i | ||||
\(241\) | 6.10070i | 0.392981i | 0.980506 | + | 0.196490i | \(0.0629544\pi\) | ||||
−0.980506 | + | 0.196490i | \(0.937046\pi\) | |||||||
\(242\) | 1.84707 | − | 1.84707i | 0.118734 | − | 0.118734i | ||||
\(243\) | −13.8420 | − | 13.8420i | −0.887963 | − | 0.887963i | ||||
\(244\) | −7.52367 | −0.481654 | ||||||||
\(245\) | 1.32578 | − | 10.9139i | 0.0847011 | − | 0.697262i | ||||
\(246\) | 27.4212 | 1.74831 | ||||||||
\(247\) | −0.0203455 | + | 0.0203455i | −0.00129455 | + | 0.00129455i | ||||
\(248\) | 2.90902 | + | 2.90902i | 0.184723 | + | 0.184723i | ||||
\(249\) | 18.7778 | 1.18999 | ||||||||
\(250\) | −10.1961 | + | 4.58690i | −0.644858 | + | 0.290101i | ||||
\(251\) | −27.1856 | −1.71594 | −0.857970 | − | 0.513700i | \(-0.828275\pi\) | ||||
−0.857970 | + | 0.513700i | \(0.828275\pi\) | |||||||
\(252\) | 4.41958 | − | 4.41958i | 0.278407 | − | 0.278407i | ||||
\(253\) | −8.57244 | + | 8.57244i | −0.538944 | + | 0.538944i | ||||
\(254\) | 20.2167 | 1.26851 | ||||||||
\(255\) | −2.61523 | + | 21.5286i | −0.163772 | + | 1.34818i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.5176 | + | 10.5176i | −0.656068 | + | 0.656068i | −0.954447 | − | 0.298379i | \(-0.903554\pi\) |
0.298379 | + | 0.954447i | \(0.403554\pi\) | |||||||
\(258\) | −11.9582 | + | 13.1227i | −0.744485 | + | 0.816985i | ||||
\(259\) | 5.32172i | 0.330675i | ||||||||
\(260\) | −1.26553 | − | 1.61551i | −0.0784847 | − | 0.100189i | ||||
\(261\) | − | 32.4026i | − | 2.00567i | ||||||
\(262\) | 11.7913 | + | 11.7913i | 0.728468 | + | 0.728468i | ||||
\(263\) | −16.2714 | − | 16.2714i | −1.00334 | − | 1.00334i | −0.999994 | − | 0.00334334i | \(-0.998936\pi\) |
−0.00334334 | − | 0.999994i | \(-0.501064\pi\) | |||||||
\(264\) | − | 9.98908i | − | 0.614785i | ||||||
\(265\) | −7.69794 | + | 6.03028i | −0.472881 | + | 0.370437i | ||||
\(266\) | − | 0.0452510i | − | 0.00277452i | ||||||
\(267\) | 18.6053 | + | 18.6053i | 1.13863 | + | 1.13863i | ||||
\(268\) | 1.07630 | − | 1.07630i | 0.0657455 | − | 0.0657455i | ||||
\(269\) | − | 17.1705i | − | 1.04690i | −0.852055 | − | 0.523452i | \(-0.824644\pi\) | ||
0.852055 | − | 0.523452i | \(-0.175356\pi\) | |||||||
\(270\) | −0.971224 | + | 7.99514i | −0.0591068 | + | 0.486569i | ||||
\(271\) | −14.9966 | −0.910977 | −0.455488 | − | 0.890242i | \(-0.650535\pi\) | ||||
−0.455488 | + | 0.890242i | \(0.650535\pi\) | |||||||
\(272\) | −2.53300 | − | 2.53300i | −0.153586 | − | 0.153586i | ||||
\(273\) | 2.53601 | − | 2.53601i | 0.153486 | − | 0.153486i | ||||
\(274\) | − | 11.5190i | − | 0.695886i | ||||||
\(275\) | −17.9108 | − | 4.41667i | −1.08006 | − | 0.266335i | ||||
\(276\) | 8.89647i | 0.535504i | ||||||||
\(277\) | 13.1886 | − | 13.1886i | 0.792426 | − | 0.792426i | −0.189462 | − | 0.981888i | \(-0.560674\pi\) |
0.981888 | + | 0.189462i | \(0.0606743\pi\) | |||||||
\(278\) | 4.22545 | + | 4.22545i | 0.253426 | + | 0.253426i | ||||
\(279\) | − | 17.8149i | − | 1.06655i | ||||||
\(280\) | 3.20390 | + | 0.389199i | 0.191469 | + | 0.0232591i | ||||
\(281\) | −19.6850 | −1.17431 | −0.587154 | − | 0.809475i | \(-0.699752\pi\) | ||||
−0.587154 | + | 0.809475i | \(0.699752\pi\) | |||||||
\(282\) | 17.1183 | + | 17.1183i | 1.01938 | + | 1.01938i | ||||
\(283\) | −18.4977 | + | 18.4977i | −1.09958 | + | 1.09958i | −0.105116 | + | 0.994460i | \(0.533522\pi\) |
−0.994460 | + | 0.105116i | \(0.966478\pi\) | |||||||
\(284\) | 4.73051 | 0.280704 | ||||||||
\(285\) | 0.117046 | + | 0.149415i | 0.00693323 | + | 0.00885060i | ||||
\(286\) | − | 3.38604i | − | 0.200221i | ||||||
\(287\) | −10.3368 | + | 10.3368i | −0.610159 | + | 0.610159i | ||||
\(288\) | −3.06201 | − | 3.06201i | −0.180431 | − | 0.180431i | ||||
\(289\) | − | 4.16779i | − | 0.245164i | ||||||
\(290\) | 13.1716 | − | 10.3181i | 0.773461 | − | 0.605901i | ||||
\(291\) | 38.7166i | 2.26961i | ||||||||
\(292\) | −4.95201 | + | 4.95201i | −0.289795 | + | 0.289795i | ||||
\(293\) | 23.4809 | − | 23.4809i | 1.37177 | − | 1.37177i | 0.513952 | − | 0.857819i | \(-0.328181\pi\) |
0.857819 | − | 0.513952i | \(-0.171819\pi\) | |||||||
\(294\) | − | 13.3118i | − | 0.776360i | ||||||
\(295\) | −3.82711 | + | 31.5048i | −0.222823 | + | 1.83428i | ||||
\(296\) | 3.68703 | 0.214305 | ||||||||
\(297\) | −9.39660 | + | 9.39660i | −0.545246 | + | 0.545246i | ||||
\(298\) | −2.48602 | + | 2.48602i | −0.144011 | + | 0.144011i | ||||
\(299\) | 3.01568i | 0.174401i | ||||||||
\(300\) | −11.5857 | + | 7.00210i | −0.668902 | + | 0.404267i | ||||
\(301\) | −0.438982 | − | 9.45455i | −0.0253025 | − | 0.544951i | ||||
\(302\) | −7.50735 | − | 7.50735i | −0.432000 | − | 0.432000i | ||||
\(303\) | −1.94555 | − | 1.94555i | −0.111769 | − | 0.111769i | ||||
\(304\) | −0.0313512 | −0.00179811 | ||||||||
\(305\) | −2.02874 | + | 16.7007i | −0.116165 | + | 0.956277i | ||||
\(306\) | 15.5121i | 0.886770i | ||||||||
\(307\) | −9.55550 | − | 9.55550i | −0.545361 | − | 0.545361i | 0.379734 | − | 0.925096i | \(-0.376015\pi\) |
−0.925096 | + | 0.379734i | \(0.876015\pi\) | |||||||
\(308\) | 3.76550 | + | 3.76550i | 0.214559 | + | 0.214559i | ||||
\(309\) | −46.9876 | −2.67303 | ||||||||
\(310\) | 7.24172 | − | 5.67289i | 0.411302 | − | 0.322199i | ||||
\(311\) | 8.63845 | 0.489842 | 0.244921 | − | 0.969543i | \(-0.421238\pi\) | ||||
0.244921 | + | 0.969543i | \(0.421238\pi\) | |||||||
\(312\) | −1.75702 | − | 1.75702i | −0.0994715 | − | 0.0994715i | ||||
\(313\) | 12.9700 | + | 12.9700i | 0.733109 | + | 0.733109i | 0.971234 | − | 0.238126i | \(-0.0765330\pi\) |
−0.238126 | + | 0.971234i | \(0.576533\pi\) | |||||||
\(314\) | 6.42486i | 0.362576i | ||||||||
\(315\) | −8.61863 | − | 11.0021i | −0.485605 | − | 0.619897i | ||||
\(316\) | −2.04141 | −0.114838 | ||||||||
\(317\) | 4.42165 | + | 4.42165i | 0.248345 | + | 0.248345i | 0.820291 | − | 0.571946i | \(-0.193811\pi\) |
−0.571946 | + | 0.820291i | \(0.693811\pi\) | |||||||
\(318\) | −8.37225 | + | 8.37225i | −0.469492 | + | 0.469492i | ||||
\(319\) | 27.6072 | 1.54570 | ||||||||
\(320\) | 0.269648 | − | 2.21975i | 0.0150738 | − | 0.124088i | ||||
\(321\) | 26.6735i | 1.48877i | ||||||||
\(322\) | −3.35363 | − | 3.35363i | −0.186891 | − | 0.186891i | ||||
\(323\) | 0.0794126 | + | 0.0794126i | 0.00441864 | + | 0.00441864i | ||||
\(324\) | − | 3.23922i | − | 0.179957i | ||||||
\(325\) | −3.92727 | + | 2.37354i | −0.217846 | + | 0.131660i | ||||
\(326\) | −7.96171 | −0.440959 | ||||||||
\(327\) | 2.45368 | − | 2.45368i | 0.135689 | − | 0.135689i | ||||
\(328\) | 7.16159 | + | 7.16159i | 0.395433 | + | 0.395433i | ||||
\(329\) | −12.9059 | −0.711524 | ||||||||
\(330\) | −22.1732 | − | 2.69354i | −1.22060 | − | 0.148274i | ||||
\(331\) | 2.48208i | 0.136427i | 0.997671 | + | 0.0682137i | \(0.0217300\pi\) | ||||
−0.997671 | + | 0.0682137i | \(0.978270\pi\) | |||||||
\(332\) | 4.90419 | + | 4.90419i | 0.269152 | + | 0.269152i | ||||
\(333\) | −11.2897 | − | 11.2897i | −0.618673 | − | 0.618673i | ||||
\(334\) | −1.53289 | −0.0838759 | ||||||||
\(335\) | −2.09889 | − | 2.67934i | −0.114675 | − | 0.146388i | ||||
\(336\) | 3.90784 | 0.213190 | ||||||||
\(337\) | −3.35893 | − | 3.35893i | −0.182973 | − | 0.182973i | 0.609677 | − | 0.792650i | \(-0.291299\pi\) |
−0.792650 | + | 0.609677i | \(0.791299\pi\) | |||||||
\(338\) | 8.59680 | + | 8.59680i | 0.467604 | + | 0.467604i | ||||
\(339\) | − | 33.8212i | − | 1.83692i | ||||||
\(340\) | −6.30565 | + | 4.93961i | −0.341972 | + | 0.267888i | ||||
\(341\) | 15.1784 | 0.821956 | ||||||||
\(342\) | 0.0959976 | + | 0.0959976i | 0.00519095 | + | 0.00519095i | ||||
\(343\) | 12.1623 | + | 12.1623i | 0.656703 | + | 0.656703i | ||||
\(344\) | −6.55038 | + | 0.304139i | −0.353173 | + | 0.0163981i | ||||
\(345\) | 19.7479 | + | 2.39892i | 1.06319 | + | 0.129153i | ||||
\(346\) | 15.9368i | 0.856766i | ||||||||
\(347\) | −3.16238 | + | 3.16238i | −0.169766 | + | 0.169766i | −0.786876 | − | 0.617111i | \(-0.788303\pi\) |
0.617111 | + | 0.786876i | \(0.288303\pi\) | |||||||
\(348\) | 14.3253 | − | 14.3253i | 0.767919 | − | 0.767919i | ||||
\(349\) | 26.9669 | 1.44350 | 0.721751 | − | 0.692153i | \(-0.243337\pi\) | ||||
0.721751 | + | 0.692153i | \(0.243337\pi\) | |||||||
\(350\) | 1.72785 | − | 7.00690i | 0.0923574 | − | 0.374535i | ||||
\(351\) | 3.30561i | 0.176440i | ||||||||
\(352\) | 2.60885 | − | 2.60885i | 0.139052 | − | 0.139052i | ||||
\(353\) | 22.6884 | − | 22.6884i | 1.20758 | − | 1.20758i | 0.235773 | − | 0.971808i | \(-0.424238\pi\) |
0.971808 | − | 0.235773i | \(-0.0757623\pi\) | |||||||
\(354\) | 38.4269i | 2.04237i | ||||||||
\(355\) | 1.27557 | − | 10.5005i | 0.0677004 | − | 0.557311i | ||||
\(356\) | 9.71831i | 0.515070i | ||||||||
\(357\) | −9.89856 | − | 9.89856i | −0.523887 | − | 0.523887i | ||||
\(358\) | 14.4808 | − | 14.4808i | 0.765333 | − | 0.765333i | ||||
\(359\) | − | 11.4906i | − | 0.606452i | −0.952919 | − | 0.303226i | \(-0.901936\pi\) | ||
0.952919 | − | 0.303226i | \(-0.0980637\pi\) | |||||||
\(360\) | −7.62256 | + | 5.97123i | −0.401744 | + | 0.314711i | ||||
\(361\) | −18.9990 | −0.999948 | ||||||||
\(362\) | 3.83893 | − | 3.83893i | 0.201770 | − | 0.201770i | ||||
\(363\) | −5.00087 | − | 5.00087i | −0.262478 | − | 0.262478i | ||||
\(364\) | 1.32466 | 0.0694309 | ||||||||
\(365\) | 9.65693 | + | 12.3275i | 0.505467 | + | 0.645253i | ||||
\(366\) | 20.3700i | 1.06476i | ||||||||
\(367\) | −7.66248 | − | 7.66248i | −0.399978 | − | 0.399978i | 0.478247 | − | 0.878225i | \(-0.341272\pi\) |
−0.878225 | + | 0.478247i | \(0.841272\pi\) | |||||||
\(368\) | −2.32349 | + | 2.32349i | −0.121120 | + | 0.121120i | ||||
\(369\) | − | 43.8577i | − | 2.28314i | ||||||
\(370\) | 0.994202 | − | 8.18429i | 0.0516861 | − | 0.425481i | ||||
\(371\) | − | 6.31204i | − | 0.327705i | ||||||
\(372\) | 7.87606 | − | 7.87606i | 0.408355 | − | 0.408355i | ||||
\(373\) | −7.61855 | − | 7.61855i | −0.394474 | − | 0.394474i | 0.481805 | − | 0.876279i | \(-0.339981\pi\) |
−0.876279 | + | 0.481805i | \(0.839981\pi\) | |||||||
\(374\) | −13.2164 | −0.683405 | ||||||||
\(375\) | 12.4189 | + | 27.6055i | 0.641307 | + | 1.42554i | ||||
\(376\) | 8.94155i | 0.461125i | ||||||||
\(377\) | 4.85593 | − | 4.85593i | 0.250093 | − | 0.250093i | ||||
\(378\) | −3.67605 | − | 3.67605i | −0.189076 | − | 0.189076i | ||||
\(379\) | 20.6244i | 1.05941i | 0.848183 | + | 0.529703i | \(0.177697\pi\) | ||||
−0.848183 | + | 0.529703i | \(0.822303\pi\) | |||||||
\(380\) | −0.00845379 | + | 0.0695918i | −0.000433670 | + | 0.00356998i | ||||
\(381\) | − | 54.7358i | − | 2.80420i | ||||||
\(382\) | −8.18827 | − | 8.18827i | −0.418948 | − | 0.418948i | ||||
\(383\) | −13.8575 | − | 13.8575i | −0.708085 | − | 0.708085i | 0.258047 | − | 0.966132i | \(-0.416921\pi\) |
−0.966132 | + | 0.258047i | \(0.916921\pi\) | |||||||
\(384\) | − | 2.70746i | − | 0.138164i | ||||||
\(385\) | 9.37383 | − | 7.34311i | 0.477735 | − | 0.374240i | ||||
\(386\) | − | 21.4836i | − | 1.09349i | ||||||
\(387\) | 20.9886 | + | 19.1260i | 1.06691 | + | 0.972231i | ||||
\(388\) | −10.1116 | + | 10.1116i | −0.513339 | + | 0.513339i | ||||
\(389\) | 26.3733 | 1.33718 | 0.668590 | − | 0.743631i | \(-0.266898\pi\) | ||||
0.668590 | + | 0.743631i | \(0.266898\pi\) | |||||||
\(390\) | −4.37392 | + | 3.42636i | −0.221482 | + | 0.173501i | ||||
\(391\) | 11.7708 | 0.595276 | ||||||||
\(392\) | 3.47664 | − | 3.47664i | 0.175597 | − | 0.175597i | ||||
\(393\) | 31.9244 | − | 31.9244i | 1.61037 | − | 1.61037i | ||||
\(394\) | 0.438622 | 0.0220975 | ||||||||
\(395\) | −0.550463 | + | 4.53143i | −0.0276968 | + | 0.228001i | ||||
\(396\) | −15.9766 | −0.802855 | ||||||||
\(397\) | 13.4243 | + | 13.4243i | 0.673746 | + | 0.673746i | 0.958578 | − | 0.284831i | \(-0.0919376\pi\) |
−0.284831 | + | 0.958578i | \(0.591938\pi\) | |||||||
\(398\) | 19.4573 | − | 19.4573i | 0.975307 | − | 0.975307i | ||||
\(399\) | −0.122515 | −0.00613344 | ||||||||
\(400\) | −4.85458 | − | 1.19710i | −0.242729 | − | 0.0598551i | ||||
\(401\) | −24.6103 | −1.22898 | −0.614490 | − | 0.788925i | \(-0.710638\pi\) | ||||
−0.614490 | + | 0.788925i | \(0.710638\pi\) | |||||||
\(402\) | −2.91404 | − | 2.91404i | −0.145339 | − | 0.145339i | ||||
\(403\) | 2.66979 | − | 2.66979i | 0.132991 | − | 0.132991i | ||||
\(404\) | − | 1.01624i | − | 0.0505597i | ||||||
\(405\) | −7.19025 | − | 0.873449i | −0.357287 | − | 0.0434020i | ||||
\(406\) | 10.8002i | 0.536006i | ||||||||
\(407\) | 9.61890 | − | 9.61890i | 0.476791 | − | 0.476791i | ||||
\(408\) | −6.85800 | + | 6.85800i | −0.339522 | + | 0.339522i | ||||
\(409\) | 14.8243 | 0.733013 | 0.366506 | − | 0.930416i | \(-0.380554\pi\) | ||||
0.366506 | + | 0.930416i | \(0.380554\pi\) | |||||||
\(410\) | 17.8281 | − | 13.9658i | 0.880465 | − | 0.689723i | ||||
\(411\) | −31.1871 | −1.53835 | ||||||||
\(412\) | −12.2717 | − | 12.2717i | −0.604586 | − | 0.604586i | ||||
\(413\) | −14.4855 | − | 14.4855i | −0.712784 | − | 0.712784i | ||||
\(414\) | 14.2291 | 0.699321 | ||||||||
\(415\) | 12.2085 | − | 9.56367i | 0.599291 | − | 0.469462i | ||||
\(416\) | − | 0.917760i | − | 0.0449969i | ||||||
\(417\) | 11.4402 | − | 11.4402i | 0.560231 | − | 0.560231i | ||||
\(418\) | −0.0817904 | + | 0.0817904i | −0.00400050 | + | 0.00400050i | ||||
\(419\) | −28.8761 | −1.41069 | −0.705344 | − | 0.708865i | \(-0.749208\pi\) | ||||
−0.705344 | + | 0.708865i | \(0.749208\pi\) | |||||||
\(420\) | 1.05374 | − | 8.67442i | 0.0514173 | − | 0.423268i | ||||
\(421\) | 1.17333i | 0.0571845i | 0.999591 | + | 0.0285922i | \(0.00910243\pi\) | ||||
−0.999591 | + | 0.0285922i | \(0.990898\pi\) | |||||||
\(422\) | −8.17255 | − | 8.17255i | −0.397834 | − | 0.397834i | ||||
\(423\) | 27.3791 | − | 27.3791i | 1.33122 | − | 1.33122i | ||||
\(424\) | −4.37316 | −0.212379 | ||||||||
\(425\) | 9.26440 | + | 15.3289i | 0.449389 | + | 0.743562i | ||||
\(426\) | − | 12.8077i | − | 0.620533i | ||||||
\(427\) | −7.67873 | − | 7.67873i | −0.371600 | − | 0.371600i | ||||
\(428\) | −6.96632 | + | 6.96632i | −0.336730 | + | 0.336730i | ||||
\(429\) | −9.16758 | −0.442615 | ||||||||
\(430\) | −1.09119 | + | 14.6222i | −0.0526216 | + | 0.705146i | ||||
\(431\) | −15.8267 | −0.762345 | −0.381173 | − | 0.924504i | \(-0.624480\pi\) | ||||
−0.381173 | + | 0.924504i | \(0.624480\pi\) | |||||||
\(432\) | −2.54687 | + | 2.54687i | −0.122536 | + | 0.122536i | ||||
\(433\) | −10.6823 | − | 10.6823i | −0.513358 | − | 0.513358i | 0.402195 | − | 0.915554i | \(-0.368247\pi\) |
−0.915554 | + | 0.402195i | \(0.868247\pi\) | |||||||
\(434\) | 5.93795i | 0.285031i | ||||||||
\(435\) | −27.9359 | − | 35.6615i | −1.33942 | − | 1.70984i | ||||
\(436\) | 1.28166 | 0.0613803 | ||||||||
\(437\) | 0.0728442 | − | 0.0728442i | 0.00348461 | − | 0.00348461i | ||||
\(438\) | 13.4074 | + | 13.4074i | 0.640629 | + | 0.640629i | ||||
\(439\) | 5.26194i | 0.251138i | 0.992085 | + | 0.125569i | \(0.0400757\pi\) | ||||
−0.992085 | + | 0.125569i | \(0.959924\pi\) | |||||||
\(440\) | −5.08752 | − | 6.49446i | −0.242538 | − | 0.309611i | ||||
\(441\) | −21.2910 | −1.01386 | ||||||||
\(442\) | −2.32469 | + | 2.32469i | −0.110574 | + | 0.110574i | ||||
\(443\) | 14.7566 | − | 14.7566i | 0.701106 | − | 0.701106i | −0.263542 | − | 0.964648i | \(-0.584891\pi\) |
0.964648 | + | 0.263542i | \(0.0848906\pi\) | |||||||
\(444\) | − | 9.98249i | − | 0.473748i | ||||||
\(445\) | 21.5722 | + | 2.62052i | 1.02262 | + | 0.124225i | ||||
\(446\) | −25.2707 | −1.19660 | ||||||||
\(447\) | 6.73080 | + | 6.73080i | 0.318356 | + | 0.318356i | ||||
\(448\) | 1.02061 | + | 1.02061i | 0.0482193 | + | 0.0482193i | ||||
\(449\) | −2.33693 | −0.110287 | −0.0551433 | − | 0.998478i | \(-0.517562\pi\) | ||||
−0.0551433 | + | 0.998478i | \(0.517562\pi\) | |||||||
\(450\) | 11.1992 | + | 18.5303i | 0.527936 | + | 0.873527i | ||||
\(451\) | 37.3670 | 1.75954 | ||||||||
\(452\) | 8.83308 | − | 8.83308i | 0.415473 | − | 0.415473i | ||||
\(453\) | −20.3259 | + | 20.3259i | −0.954992 | + | 0.954992i | ||||
\(454\) | − | 15.2997i | − | 0.718051i | ||||||
\(455\) | 0.357191 | − | 2.94041i | 0.0167454 | − | 0.137849i | ||||
\(456\) | 0.0848820i | 0.00397497i | ||||||||
\(457\) | 7.98362 | − | 7.98362i | 0.373458 | − | 0.373458i | −0.495277 | − | 0.868735i | \(-0.664933\pi\) |
0.868735 | + | 0.495277i | \(0.164933\pi\) | |||||||
\(458\) | −0.317169 | − | 0.317169i | −0.0148203 | − | 0.0148203i | ||||
\(459\) | 12.9025 | 0.602236 | ||||||||
\(460\) | 4.53104 | + | 5.78409i | 0.211261 | + | 0.269685i | ||||
\(461\) | 16.7949 | 0.782216 | 0.391108 | − | 0.920345i | \(-0.372092\pi\) | ||||
0.391108 | + | 0.920345i | \(0.372092\pi\) | |||||||
\(462\) | 10.1949 | − | 10.1949i | 0.474312 | − | 0.474312i | ||||
\(463\) | −9.85334 | − | 9.85334i | −0.457924 | − | 0.457924i | 0.440050 | − | 0.897973i | \(-0.354961\pi\) |
−0.897973 | + | 0.440050i | \(0.854961\pi\) | |||||||
\(464\) | 7.48270 | 0.347376 | ||||||||
\(465\) | −15.3591 | − | 19.6066i | −0.712262 | − | 0.909236i | ||||
\(466\) | 19.0552 | 0.882716 | ||||||||
\(467\) | 3.01945 | − | 3.01945i | 0.139723 | − | 0.139723i | −0.633785 | − | 0.773509i | \(-0.718500\pi\) |
0.773509 | + | 0.633785i | \(0.218500\pi\) | |||||||
\(468\) | −2.81019 | + | 2.81019i | −0.129901 | + | 0.129901i | ||||
\(469\) | 2.19696 | 0.101446 | ||||||||
\(470\) | 19.8480 | + | 2.41107i | 0.915520 | + | 0.111214i | ||||
\(471\) | 17.3950 | 0.801521 | ||||||||
\(472\) | −10.0359 | + | 10.0359i | −0.461942 | + | 0.461942i | ||||
\(473\) | −16.2955 | + | 17.8824i | −0.749267 | + | 0.822233i | ||||
\(474\) | 5.52704i | 0.253865i | ||||||||
\(475\) | 0.152197 | + | 0.0375306i | 0.00698327 | + | 0.00172202i | ||||
\(476\) | − | 5.17041i | − | 0.236985i | ||||||
\(477\) | 13.3906 | + | 13.3906i | 0.613116 | + | 0.613116i | ||||
\(478\) | 3.22425 | + | 3.22425i | 0.147474 | + | 0.147474i | ||||
\(479\) | − | 26.5511i | − | 1.21315i | −0.795026 | − | 0.606576i | \(-0.792543\pi\) | ||
0.795026 | − | 0.606576i | \(-0.207457\pi\) | |||||||
\(480\) | −6.00988 | − | 0.730061i | −0.274312 | − | 0.0333226i | ||||
\(481\) | − | 3.38381i | − | 0.154289i | ||||||
\(482\) | 4.31385 | + | 4.31385i | 0.196490 | + | 0.196490i | ||||
\(483\) | −9.07982 | + | 9.07982i | −0.413146 | + | 0.413146i | ||||
\(484\) | − | 2.61216i | − | 0.118734i | ||||||
\(485\) | 19.7187 | + | 25.1718i | 0.895378 | + | 1.14299i | ||||
\(486\) | −19.5755 | −0.887963 | ||||||||
\(487\) | −0.0809180 | − | 0.0809180i | −0.00366674 | − | 0.00366674i | 0.705271 | − | 0.708938i | \(-0.250825\pi\) |
−0.708938 | + | 0.705271i | \(0.750825\pi\) | |||||||
\(488\) | −5.32004 | + | 5.32004i | −0.240827 | + | 0.240827i | ||||
\(489\) | 21.5560i | 0.974796i | ||||||||
\(490\) | −6.77981 | − | 8.65474i | −0.306280 | − | 0.390982i | ||||
\(491\) | − | 21.7824i | − | 0.983025i | −0.870870 | − | 0.491513i | \(-0.836444\pi\) | ||
0.870870 | − | 0.491513i | \(-0.163556\pi\) | |||||||
\(492\) | 19.3897 | − | 19.3897i | 0.874156 | − | 0.874156i | ||||
\(493\) | −18.9537 | − | 18.9537i | −0.853632 | − | 0.853632i | ||||
\(494\) | 0.0287729i | 0.00129455i | ||||||||
\(495\) | −4.30806 | + | 35.4641i | −0.193633 | + | 1.59399i | ||||
\(496\) | 4.11398 | 0.184723 | ||||||||
\(497\) | 4.82800 | + | 4.82800i | 0.216565 | + | 0.216565i | ||||
\(498\) | 13.2779 | − | 13.2779i | 0.594996 | − | 0.594996i | ||||
\(499\) | 6.35752 | 0.284602 | 0.142301 | − | 0.989823i | \(-0.454550\pi\) | ||||
0.142301 | + | 0.989823i | \(0.454550\pi\) | |||||||
\(500\) | −3.96630 | + | 10.4532i | −0.177378 | + | 0.467479i | ||||
\(501\) | 4.15023i | 0.185419i | ||||||||
\(502\) | −19.2231 | + | 19.2231i | −0.857970 | + | 0.857970i | ||||
\(503\) | −23.1386 | − | 23.1386i | −1.03170 | − | 1.03170i | −0.999481 | − | 0.0322186i | \(-0.989743\pi\) |
−0.0322186 | − | 0.999481i | \(-0.510257\pi\) | |||||||
\(504\) | − | 6.25023i | − | 0.278407i | ||||||
\(505\) | −2.25579 | − | 0.274026i | −0.100381 | − | 0.0121940i | ||||
\(506\) | 12.1233i | 0.538944i | ||||||||
\(507\) | 23.2755 | − | 23.2755i | 1.03370 | − | 1.03370i | ||||
\(508\) | 14.2953 | − | 14.2953i | 0.634253 | − | 0.634253i | ||||
\(509\) | 37.8927i | 1.67956i | 0.542923 | + | 0.839782i | \(0.317318\pi\) | ||||
−0.542923 | + | 0.839782i | \(0.682682\pi\) | |||||||
\(510\) | 13.3738 | + | 17.0723i | 0.592202 | + | 0.755974i | ||||
\(511\) | −10.1081 | −0.447158 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0.0798474 | − | 0.0798474i | 0.00352535 | − | 0.00352535i | ||||
\(514\) | 14.8741i | 0.656068i | ||||||||
\(515\) | −30.5493 | + | 23.9312i | −1.34616 | + | 1.05453i | ||||
\(516\) | 0.823444 | + | 17.7349i | 0.0362501 | + | 0.780735i | ||||
\(517\) | 23.3271 | + | 23.3271i | 1.02593 | + | 1.02593i | ||||
\(518\) | 3.76302 | + | 3.76302i | 0.165338 | + | 0.165338i | ||||
\(519\) | 43.1481 | 1.89399 | ||||||||
\(520\) | −2.03720 | − | 0.247472i | −0.0893371 | − | 0.0108524i | ||||
\(521\) | 44.0469i | 1.92973i | 0.262743 | + | 0.964866i | \(0.415373\pi\) | ||||
−0.262743 | + | 0.964866i | \(0.584627\pi\) | |||||||
\(522\) | −22.9121 | − | 22.9121i | −1.00283 | − | 1.00283i | ||||
\(523\) | 19.0964 | + | 19.0964i | 0.835026 | + | 0.835026i | 0.988199 | − | 0.153174i | \(-0.0489494\pi\) |
−0.153174 | + | 0.988199i | \(0.548949\pi\) | |||||||
\(524\) | 16.6754 | 0.728468 | ||||||||
\(525\) | −18.9709 | − | 4.67808i | −0.827958 | − | 0.204168i | ||||
\(526\) | −23.0112 | −1.00334 | ||||||||
\(527\) | −10.4207 | − | 10.4207i | −0.453934 | − | 0.453934i | ||||
\(528\) | −7.06334 | − | 7.06334i | −0.307393 | − | 0.307393i | ||||
\(529\) | 12.2028i | 0.530556i | ||||||||
\(530\) | −1.17921 | + | 9.70732i | −0.0512218 | + | 0.421659i | ||||
\(531\) | 61.4603 | 2.66715 | ||||||||
\(532\) | −0.0319973 | − | 0.0319973i | −0.00138726 | − | 0.00138726i | ||||
\(533\) | 6.57262 | − | 6.57262i | 0.284692 | − | 0.284692i | ||||
\(534\) | 26.3119 | 1.13863 | ||||||||
\(535\) | 13.5850 | + | 17.3420i | 0.587333 | + | 0.749758i | ||||
\(536\) | − | 1.52212i | − | 0.0657455i | ||||||
\(537\) | −39.2061 | − | 39.2061i | −1.69187 | − | 1.69187i | ||||
\(538\) | −12.1414 | − | 12.1414i | −0.523452 | − | 0.523452i | ||||
\(539\) | − | 18.1400i | − | 0.781347i | ||||||
\(540\) | 4.96666 | + | 6.34018i | 0.213731 | + | 0.272838i | ||||
\(541\) | −33.1678 | −1.42599 | −0.712997 | − | 0.701167i | \(-0.752663\pi\) | ||||
−0.712997 | + | 0.701167i | \(0.752663\pi\) | |||||||
\(542\) | −10.6042 | + | 10.6042i | −0.455488 | + | 0.455488i | ||||
\(543\) | −10.3938 | − | 10.3938i | −0.446039 | − | 0.446039i | ||||
\(544\) | −3.58221 | −0.153586 | ||||||||
\(545\) | 0.345596 | − | 2.84496i | 0.0148037 | − | 0.121865i | ||||
\(546\) | − | 3.58646i | − | 0.153486i | ||||||
\(547\) | −21.0500 | − | 21.0500i | −0.900033 | − | 0.900033i | 0.0954056 | − | 0.995438i | \(-0.469585\pi\) |
−0.995438 | + | 0.0954056i | \(0.969585\pi\) | |||||||
\(548\) | −8.14514 | − | 8.14514i | −0.347943 | − | 0.347943i | ||||
\(549\) | 32.5800 | 1.39048 | ||||||||
\(550\) | −15.7879 | + | 9.54179i | −0.673199 | + | 0.406864i | ||||
\(551\) | −0.234591 | −0.00999393 | ||||||||
\(552\) | 6.29075 | + | 6.29075i | 0.267752 | + | 0.267752i | ||||
\(553\) | −2.08348 | − | 2.08348i | −0.0885988 | − | 0.0885988i | ||||
\(554\) | − | 18.6515i | − | 0.792426i | ||||||
\(555\) | −22.1586 | − | 2.69176i | −0.940582 | − | 0.114259i | ||||
\(556\) | 5.97569 | 0.253426 | ||||||||
\(557\) | 7.14577 | + | 7.14577i | 0.302776 | + | 0.302776i | 0.842099 | − | 0.539323i | \(-0.181320\pi\) |
−0.539323 | + | 0.842099i | \(0.681320\pi\) | |||||||
\(558\) | −12.5970 | − | 12.5970i | −0.533275 | − | 0.533275i | ||||
\(559\) | 0.279127 | + | 6.01168i | 0.0118058 | + | 0.254267i | ||||
\(560\) | 2.54070 | − | 1.99029i | 0.107364 | − | 0.0841052i | ||||
\(561\) | 35.7829i | 1.51076i | ||||||||
\(562\) | −13.9194 | + | 13.9194i | −0.587154 | + | 0.587154i | ||||
\(563\) | 3.19095 | − | 3.19095i | 0.134482 | − | 0.134482i | −0.636661 | − | 0.771144i | \(-0.719685\pi\) |
0.771144 | + | 0.636661i | \(0.219685\pi\) | |||||||
\(564\) | 24.2089 | 1.01938 | ||||||||
\(565\) | −17.2254 | − | 21.9890i | −0.724678 | − | 0.925086i | ||||
\(566\) | 26.1598i | 1.09958i | ||||||||
\(567\) | 3.30597 | − | 3.30597i | 0.138838 | − | 0.138838i | ||||
\(568\) | 3.34497 | − | 3.34497i | 0.140352 | − | 0.140352i | ||||
\(569\) | 21.8508i | 0.916035i | 0.888943 | + | 0.458018i | \(0.151440\pi\) | ||||
−0.888943 | + | 0.458018i | \(0.848560\pi\) | |||||||
\(570\) | 0.188417 | + | 0.0228883i | 0.00789192 | + | 0.000958684i | ||||
\(571\) | 23.7035i | 0.991962i | 0.868333 | + | 0.495981i | \(0.165191\pi\) | ||||
−0.868333 | + | 0.495981i | \(0.834809\pi\) | |||||||
\(572\) | −2.39430 | − | 2.39430i | −0.100111 | − | 0.100111i | ||||
\(573\) | −22.1694 | + | 22.1694i | −0.926140 | + | 0.926140i | ||||
\(574\) | 14.6184i | 0.610159i | ||||||||
\(575\) | 14.0610 | − | 8.49811i | 0.586385 | − | 0.354396i | ||||
\(576\) | −4.33033 | −0.180431 | ||||||||
\(577\) | −2.26045 | + | 2.26045i | −0.0941037 | + | 0.0941037i | −0.752591 | − | 0.658488i | \(-0.771196\pi\) |
0.658488 | + | 0.752591i | \(0.271196\pi\) | |||||||
\(578\) | −2.94707 | − | 2.94707i | −0.122582 | − | 0.122582i | ||||
\(579\) | −58.1660 | −2.41730 | ||||||||
\(580\) | 2.01770 | − | 16.6097i | 0.0837802 | − | 0.689681i | ||||
\(581\) | 10.0105i | 0.415306i | ||||||||
\(582\) | 27.3767 | + | 27.3767i | 1.13480 | + | 1.13480i | ||||
\(583\) | −11.4089 | + | 11.4089i | −0.472508 | + | 0.472508i | ||||
\(584\) | 7.00321i | 0.289795i | ||||||||
\(585\) | 5.48015 | + | 6.99568i | 0.226577 | + | 0.289236i | ||||
\(586\) | − | 33.2071i | − | 1.37177i | ||||||
\(587\) | 26.6723 | − | 26.6723i | 1.10088 | − | 1.10088i | 0.106579 | − | 0.994304i | \(-0.466010\pi\) |
0.994304 | − | 0.106579i | \(-0.0339897\pi\) | |||||||
\(588\) | −9.41286 | − | 9.41286i | −0.388180 | − | 0.388180i | ||||
\(589\) | −0.128978 | −0.00531445 | ||||||||
\(590\) | 19.5711 | + | 24.9835i | 0.805730 | + | 1.02855i | ||||
\(591\) | − | 1.18755i | − | 0.0488493i | ||||||
\(592\) | 2.60713 | − | 2.60713i | 0.107152 | − | 0.107152i | ||||
\(593\) | 24.8475 | + | 24.8475i | 1.02037 | + | 1.02037i | 0.999788 | + | 0.0205776i | \(0.00655051\pi\) |
0.0205776 | + | 0.999788i | \(0.493449\pi\) | |||||||
\(594\) | 13.2888i | 0.545246i | ||||||||
\(595\) | −11.4770 | − | 1.39419i | −0.470512 | − | 0.0571563i | ||||
\(596\) | 3.51576i | 0.144011i | ||||||||
\(597\) | −52.6799 | − | 52.6799i | −2.15604 | − | 2.15604i | ||||
\(598\) | 2.13241 | + | 2.13241i | 0.0872006 | + | 0.0872006i | ||||
\(599\) | 31.9194i | 1.30419i | 0.758137 | + | 0.652095i | \(0.226110\pi\) | ||||
−0.758137 | + | 0.652095i | \(0.773890\pi\) | |||||||
\(600\) | −3.24111 | + | 13.1436i | −0.132318 | + | 0.536584i | ||||
\(601\) | − | 24.5020i | − | 0.999459i | −0.866182 | − | 0.499729i | \(-0.833433\pi\) | ||
0.866182 | − | 0.499729i | \(-0.166567\pi\) | |||||||
\(602\) | −6.99579 | − | 6.37497i | −0.285127 | − | 0.259824i | ||||
\(603\) | −4.66074 | + | 4.66074i | −0.189800 | + | 0.189800i | ||||
\(604\) | −10.6170 | −0.432000 | ||||||||
\(605\) | −5.79833 | − | 0.704363i | −0.235736 | − | 0.0286364i | ||||
\(606\) | −2.75142 | −0.111769 | ||||||||
\(607\) | −19.1505 | + | 19.1505i | −0.777296 | + | 0.777296i | −0.979370 | − | 0.202075i | \(-0.935232\pi\) |
0.202075 | + | 0.979370i | \(0.435232\pi\) | |||||||
\(608\) | −0.0221686 | + | 0.0221686i | −0.000899057 | + | 0.000899057i | ||||
\(609\) | 29.2412 | 1.18491 | ||||||||
\(610\) | 10.3746 | + | 13.2437i | 0.420056 | + | 0.536221i | ||||
\(611\) | 8.20620 | 0.331987 | ||||||||
\(612\) | 10.9687 | + | 10.9687i | 0.443385 | + | 0.443385i | ||||
\(613\) | −12.1307 | + | 12.1307i | −0.489956 | + | 0.489956i | −0.908292 | − | 0.418336i | \(-0.862613\pi\) |
0.418336 | + | 0.908292i | \(0.362613\pi\) | |||||||
\(614\) | −13.5135 | −0.545361 | ||||||||
\(615\) | −37.8119 | − | 48.2687i | −1.52472 | − | 1.94638i | ||||
\(616\) | 5.32522 | 0.214559 | ||||||||
\(617\) | 30.3013 | + | 30.3013i | 1.21988 | + | 1.21988i | 0.967672 | + | 0.252211i | \(0.0811578\pi\) |
0.252211 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(618\) | −33.2252 | + | 33.2252i | −1.33652 | + | 1.33652i | ||||
\(619\) | 28.6337i | 1.15089i | 0.817842 | + | 0.575443i | \(0.195170\pi\) | ||||
−0.817842 | + | 0.575443i | \(0.804830\pi\) | |||||||
\(620\) | 1.10933 | − | 9.13201i | 0.0445516 | − | 0.366750i | ||||
\(621\) | − | 11.8353i | − | 0.474933i | ||||||
\(622\) | 6.10831 | − | 6.10831i | 0.244921 | − | 0.244921i | ||||
\(623\) | −9.91860 | + | 9.91860i | −0.397380 | + | 0.397380i | ||||
\(624\) | −2.48480 | −0.0994715 | ||||||||
\(625\) | 22.1339 | + | 11.6229i | 0.885356 | + | 0.464914i | ||||
\(626\) | 18.3424 | 0.733109 | ||||||||
\(627\) | 0.221444 | + | 0.221444i | 0.00884363 | + | 0.00884363i | ||||
\(628\) | 4.54306 | + | 4.54306i | 0.181288 | + | 0.181288i | ||||
\(629\) | −13.2077 | −0.526626 | ||||||||
\(630\) | −13.8739 | − | 1.68536i | −0.552751 | − | 0.0671464i | ||||
\(631\) | − | 4.03917i | − | 0.160797i | −0.996763 | − | 0.0803983i | \(-0.974381\pi\) | ||
0.996763 | − | 0.0803983i | \(-0.0256192\pi\) | |||||||
\(632\) | −1.44350 | + | 1.44350i | −0.0574192 | + | 0.0574192i | ||||
\(633\) | −22.1268 | + | 22.1268i | −0.879463 | + | 0.879463i | ||||
\(634\) | 6.25316 | 0.248345 | ||||||||
\(635\) | −27.8774 | − | 35.5868i | −1.10628 | − | 1.41222i | ||||
\(636\) | 11.8401i | 0.469492i | ||||||||
\(637\) | −3.19072 | − | 3.19072i | −0.126421 | − | 0.126421i | ||||
\(638\) | 19.5212 | − | 19.5212i | 0.772852 | − | 0.772852i | ||||
\(639\) | −20.4847 | −0.810361 | ||||||||
\(640\) | −1.37893 | − | 1.76027i | −0.0545070 | − | 0.0695808i | ||||
\(641\) | − | 8.70502i | − | 0.343828i | −0.985112 | − | 0.171914i | \(-0.945005\pi\) | ||
0.985112 | − | 0.171914i | \(-0.0549951\pi\) | |||||||
\(642\) | 18.8610 | + | 18.8610i | 0.744386 | + | 0.744386i | ||||
\(643\) | −14.1834 | + | 14.1834i | −0.559340 | + | 0.559340i | −0.929119 | − | 0.369780i | \(-0.879433\pi\) |
0.369780 | + | 0.929119i | \(0.379433\pi\) | |||||||
\(644\) | −4.74275 | −0.186891 | ||||||||
\(645\) | 39.5891 | + | 2.95434i | 1.55882 | + | 0.116327i | ||||
\(646\) | 0.112306 | 0.00441864 | ||||||||
\(647\) | −9.23223 | + | 9.23223i | −0.362956 | + | 0.362956i | −0.864900 | − | 0.501944i | \(-0.832618\pi\) |
0.501944 | + | 0.864900i | \(0.332618\pi\) | |||||||
\(648\) | −2.29047 | − | 2.29047i | −0.0899783 | − | 0.0899783i | ||||
\(649\) | 52.3645i | 2.05549i | ||||||||
\(650\) | −1.09865 | + | 4.45534i | −0.0430927 | + | 0.174753i | ||||
\(651\) | 16.0768 | 0.630098 | ||||||||
\(652\) | −5.62978 | + | 5.62978i | −0.220479 | + | 0.220479i | ||||
\(653\) | 5.36237 | + | 5.36237i | 0.209846 | + | 0.209846i | 0.804202 | − | 0.594356i | \(-0.202593\pi\) |
−0.594356 | + | 0.804202i | \(0.702593\pi\) | |||||||
\(654\) | − | 3.47003i | − | 0.135689i | ||||||
\(655\) | 4.49649 | − | 37.0152i | 0.175692 | − | 1.44630i | ||||
\(656\) | 10.1280 | 0.395433 | ||||||||
\(657\) | 21.4439 | − | 21.4439i | 0.836605 | − | 0.836605i | ||||
\(658\) | −9.12583 | + | 9.12583i | −0.355762 | + | 0.355762i | ||||
\(659\) | 8.85409i | 0.344906i | 0.985018 | + | 0.172453i | \(0.0551693\pi\) | ||||
−0.985018 | + | 0.172453i | \(0.944831\pi\) | |||||||
\(660\) | −17.5835 | + | 13.7742i | −0.684436 | + | 0.536162i | ||||
\(661\) | 22.3457 | 0.869148 | 0.434574 | − | 0.900636i | \(-0.356899\pi\) | ||||
0.434574 | + | 0.900636i | \(0.356899\pi\) | |||||||
\(662\) | 1.75509 | + | 1.75509i | 0.0682137 | + | 0.0682137i | ||||
\(663\) | 6.29400 | + | 6.29400i | 0.244439 | + | 0.244439i | ||||
\(664\) | 6.93557 | 0.269152 | ||||||||
\(665\) | −0.0796540 | + | 0.0623980i | −0.00308885 | + | 0.00241969i | ||||
\(666\) | −15.9661 | −0.618673 | ||||||||
\(667\) | −17.3860 | + | 17.3860i | −0.673188 | + | 0.673188i | ||||
\(668\) | −1.08392 | + | 1.08392i | −0.0419379 | + | 0.0419379i | ||||
\(669\) | 68.4192i | 2.64524i | ||||||||
\(670\) | −3.37872 | − | 0.410436i | −0.130531 | − | 0.0158565i | ||||
\(671\) | 27.7583i | 1.07160i | ||||||||
\(672\) | 2.76326 | − | 2.76326i | 0.106595 | − | 0.106595i | ||||
\(673\) | −20.2442 | − | 20.2442i | −0.780358 | − | 0.780358i | 0.199533 | − | 0.979891i | \(-0.436057\pi\) |
−0.979891 | + | 0.199533i | \(0.936057\pi\) | |||||||
\(674\) | −4.75024 | −0.182973 | ||||||||
\(675\) | 15.4129 | − | 9.31513i | 0.593241 | − | 0.358539i | ||||
\(676\) | 12.1577 | 0.467604 | ||||||||
\(677\) | 25.3721 | − | 25.3721i | 0.975129 | − | 0.975129i | −0.0245695 | − | 0.999698i | \(-0.507822\pi\) |
0.999698 | + | 0.0245695i | \(0.00782151\pi\) | |||||||
\(678\) | −23.9152 | − | 23.9152i | −0.918458 | − | 0.918458i | ||||
\(679\) | −20.6400 | −0.792090 | ||||||||
\(680\) | −0.965935 | + | 7.95160i | −0.0370419 | + | 0.304930i | ||||
\(681\) | −41.4233 | −1.58735 | ||||||||
\(682\) | 10.7327 | − | 10.7327i | 0.410978 | − | 0.410978i | ||||
\(683\) | −8.18342 | + | 8.18342i | −0.313130 | + | 0.313130i | −0.846121 | − | 0.532991i | \(-0.821068\pi\) |
0.532991 | + | 0.846121i | \(0.321068\pi\) | |||||||
\(684\) | 0.135761 | 0.00519095 | ||||||||
\(685\) | −20.2765 | + | 15.8838i | −0.774725 | + | 0.606891i | ||||
\(686\) | 17.2001 | 0.656703 | ||||||||
\(687\) | −0.858721 | + | 0.858721i | −0.0327622 | + | 0.0327622i | ||||
\(688\) | −4.41676 | + | 4.84688i | −0.168387 | + | 0.184785i | ||||
\(689\) | 4.01351i | 0.152903i | ||||||||
\(690\) | 15.6602 | − | 12.2676i | 0.596173 | − | 0.467020i | ||||
\(691\) | 43.2645i | 1.64586i | 0.568143 | + | 0.822930i | \(0.307662\pi\) | ||||
−0.568143 | + | 0.822930i | \(0.692338\pi\) | |||||||
\(692\) | 11.2690 | + | 11.2690i | 0.428383 | + | 0.428383i | ||||
\(693\) | −16.3059 | − | 16.3059i | −0.619409 | − | 0.619409i | ||||
\(694\) | 4.47229i | 0.169766i | ||||||||
\(695\) | 1.61133 | − | 13.2645i | 0.0611214 | − | 0.503153i | ||||
\(696\) | − | 20.2591i | − | 0.767919i | ||||||
\(697\) | −25.6543 | − | 25.6543i | −0.971726 | − | 0.971726i | ||||
\(698\) | 19.0684 | − | 19.0684i | 0.721751 | − | 0.721751i | ||||
\(699\) | − | 51.5912i | − | 1.95136i | ||||||
\(700\) | −3.73285 | − | 6.17640i | −0.141089 | − | 0.233446i | ||||
\(701\) | 7.64559 | 0.288770 | 0.144385 | − | 0.989522i | \(-0.453880\pi\) | ||||
0.144385 | + | 0.989522i | \(0.453880\pi\) | |||||||
\(702\) | 2.33742 | + | 2.33742i | 0.0882201 | + | 0.0882201i | ||||
\(703\) | −0.0817365 | + | 0.0817365i | −0.00308275 | + | 0.00308275i | ||||
\(704\) | − | 3.68947i | − | 0.139052i | ||||||
\(705\) | 6.52788 | − | 53.7376i | 0.245854 | − | 2.02388i | ||||
\(706\) | − | 32.0862i | − | 1.20758i | ||||||
\(707\) | 1.03718 | − | 1.03718i | 0.0390072 | − | 0.0390072i | ||||
\(708\) | 27.1719 | + | 27.1719i | 1.02118 | + | 1.02118i | ||||
\(709\) | − | 40.1277i | − | 1.50703i | −0.657433 | − | 0.753513i | \(-0.728358\pi\) | ||
0.657433 | − | 0.753513i | \(-0.271642\pi\) | |||||||
\(710\) | −6.52304 | − | 8.32697i | −0.244805 | − | 0.312506i | ||||
\(711\) | 8.83999 | 0.331526 | ||||||||
\(712\) | 6.87188 | + | 6.87188i | 0.257535 | + | 0.257535i | ||||
\(713\) | −9.55879 | + | 9.55879i | −0.357979 | + | 0.357979i | ||||
\(714\) | −13.9987 | −0.523887 | ||||||||
\(715\) | −5.96035 | + | 4.66912i | −0.222905 | + | 0.174615i | ||||
\(716\) | − | 20.4789i | − | 0.765333i | ||||||
\(717\) | 8.72952 | − | 8.72952i | 0.326010 | − | 0.326010i | ||||
\(718\) | −8.12510 | − | 8.12510i | −0.303226 | − | 0.303226i | ||||
\(719\) | − | 28.6609i | − | 1.06887i | −0.845209 | − | 0.534436i | \(-0.820524\pi\) | ||
0.845209 | − | 0.534436i | \(-0.179476\pi\) | |||||||
\(720\) | −1.16767 | + | 9.61226i | −0.0435163 | + | 0.358228i | ||||
\(721\) | − | 25.0493i | − | 0.932885i | ||||||
\(722\) | −13.4343 | + | 13.4343i | −0.499974 | + | 0.499974i | ||||
\(723\) | 11.6796 | − | 11.6796i | 0.434368 | − | 0.434368i | ||||
\(724\) | − | 5.42907i | − | 0.201770i | ||||||
\(725\) | −36.3254 | − | 8.95756i | −1.34909 | − | 0.332675i | ||||
\(726\) | −7.07230 | −0.262478 | ||||||||
\(727\) | −16.4761 | + | 16.4761i | −0.611066 | + | 0.611066i | −0.943224 | − | 0.332158i | \(-0.892223\pi\) |
0.332158 | + | 0.943224i | \(0.392223\pi\) | |||||||
\(728\) | 0.936675 | − | 0.936675i | 0.0347155 | − | 0.0347155i | ||||
\(729\) | 43.2822i | 1.60305i | ||||||||
\(730\) | 15.5454 | + | 1.88840i | 0.575360 | + | 0.0698929i | ||||
\(731\) | 23.4648 | − | 1.08949i | 0.867878 | − | 0.0402962i | ||||
\(732\) | 14.4038 | + | 14.4038i | 0.532379 | + | 0.532379i | ||||
\(733\) | −9.63596 | − | 9.63596i | −0.355912 | − | 0.355912i | 0.506391 | − | 0.862304i | \(-0.330979\pi\) |
−0.862304 | + | 0.506391i | \(0.830979\pi\) | |||||||
\(734\) | −10.8364 | −0.399978 | ||||||||
\(735\) | −23.4324 | + | 18.3560i | −0.864316 | + | 0.677073i | ||||
\(736\) | 3.28591i | 0.121120i | ||||||||
\(737\) | −3.97097 | − | 3.97097i | −0.146273 | − | 0.146273i | ||||
\(738\) | −31.0121 | − | 31.0121i | −1.14157 | − | 1.14157i | ||||
\(739\) | −44.4359 | −1.63460 | −0.817300 | − | 0.576212i | \(-0.804530\pi\) | ||||
−0.817300 | + | 0.576212i | \(0.804530\pi\) | |||||||
\(740\) | −5.08416 | − | 6.49018i | −0.186898 | − | 0.238584i | ||||
\(741\) | 0.0779014 | 0.00286178 | ||||||||
\(742\) | −4.46329 | − | 4.46329i | −0.163852 | − | 0.163852i | ||||
\(743\) | −0.0453056 | − | 0.0453056i | −0.00166210 | − | 0.00166210i | 0.706275 | − | 0.707937i | \(-0.250374\pi\) |
−0.707937 | + | 0.706275i | \(0.750374\pi\) | |||||||
\(744\) | − | 11.1384i | − | 0.408355i | ||||||
\(745\) | 7.80411 | + | 0.948019i | 0.285921 | + | 0.0347327i | ||||
\(746\) | −10.7743 | −0.394474 | ||||||||
\(747\) | −21.2368 | − | 21.2368i | −0.777013 | − | 0.777013i | ||||
\(748\) | −9.34543 | + | 9.34543i | −0.341703 | + | 0.341703i | ||||
\(749\) | −14.2198 | −0.519580 | ||||||||
\(750\) | 28.3015 | + | 10.7386i | 1.03342 | + | 0.392118i | ||||
\(751\) | − | 3.91932i | − | 0.143018i | −0.997440 | − | 0.0715091i | \(-0.977219\pi\) | ||
0.997440 | − | 0.0715091i | \(-0.0227815\pi\) | |||||||
\(752\) | 6.32263 | + | 6.32263i | 0.230563 | + | 0.230563i | ||||
\(753\) | 52.0458 | + | 52.0458i | 1.89665 | + | 1.89665i | ||||
\(754\) | − | 6.86732i | − | 0.250093i | ||||||
\(755\) | −2.86285 | + | 23.5671i | −0.104190 | + | 0.857694i | ||||
\(756\) | −5.19872 | −0.189076 | ||||||||
\(757\) | 10.6675 | − | 10.6675i | 0.387717 | − | 0.387717i | −0.486156 | − | 0.873872i | \(-0.661601\pi\) |
0.873872 | + | 0.486156i | \(0.161601\pi\) | |||||||
\(758\) | 14.5837 | + | 14.5837i | 0.529703 | + | 0.529703i | ||||
\(759\) | 32.8232 | 1.19141 | ||||||||
\(760\) | 0.0432311 | + | 0.0551866i | 0.00156816 | + | 0.00200183i | ||||
\(761\) | 51.5873i | 1.87004i | 0.354597 | + | 0.935019i | \(0.384618\pi\) | ||||
−0.354597 | + | 0.935019i | \(0.615382\pi\) | |||||||
\(762\) | −38.7041 | − | 38.7041i | −1.40210 | − | 1.40210i | ||||
\(763\) | 1.30807 | + | 1.30807i | 0.0473554 | + | 0.0473554i | ||||
\(764\) | −11.5800 | −0.418948 | ||||||||
\(765\) | 27.3056 | − | 21.3902i | 0.987235 | − | 0.773363i | ||||
\(766\) | −19.5975 | −0.708085 | ||||||||
\(767\) | 9.21059 | + | 9.21059i | 0.332575 | + | 0.332575i | ||||
\(768\) | −1.91446 | − | 1.91446i | −0.0690822 | − | 0.0690822i | ||||
\(769\) | − | 27.6619i | − | 0.997512i | −0.866742 | − | 0.498756i | \(-0.833790\pi\) | ||
0.866742 | − | 0.498756i | \(-0.166210\pi\) | |||||||
\(770\) | 1.43594 | − | 11.8207i | 0.0517476 | − | 0.425987i | ||||
\(771\) | 40.2710 | 1.45032 | ||||||||
\(772\) | −15.1912 | − | 15.1912i | −0.546743 | − | 0.546743i | ||||
\(773\) | 18.4198 | + | 18.4198i | 0.662514 | + | 0.662514i | 0.955972 | − | 0.293458i | \(-0.0948061\pi\) |
−0.293458 | + | 0.955972i | \(0.594806\pi\) | |||||||
\(774\) | 28.3653 | − | 1.31702i | 1.01957 | − | 0.0473394i | ||||
\(775\) | −19.9716 | − | 4.92486i | −0.717402 | − | 0.176906i | ||||
\(776\) | 14.3000i | 0.513339i | ||||||||
\(777\) | 10.1882 | − | 10.1882i | 0.365501 | − | 0.365501i | ||||
\(778\) | 18.6487 | − | 18.6487i | 0.668590 | − | 0.668590i | ||||
\(779\) | −0.317525 | −0.0113765 | ||||||||
\(780\) | −0.670021 | + | 5.51563i | −0.0239906 | + | 0.197491i | ||||
\(781\) | − | 17.4530i | − | 0.624519i | ||||||
\(782\) | 8.32322 | − | 8.32322i | 0.297638 | − | 0.297638i | ||||
\(783\) | −19.0575 | + | 19.0575i | −0.681059 | + | 0.681059i | ||||
\(784\) | − | 4.91671i | − | 0.175597i | ||||||
\(785\) | 11.3095 | − | 8.85943i | 0.403653 | − | 0.316207i | ||||
\(786\) | − | 45.1479i | − | 1.61037i | ||||||
\(787\) | 19.9428 | + | 19.9428i | 0.710885 | + | 0.710885i | 0.966720 | − | 0.255835i | \(-0.0823505\pi\) |
−0.255835 | + | 0.966720i | \(0.582350\pi\) | |||||||
\(788\) | 0.310153 | − | 0.310153i | 0.0110487 | − | 0.0110487i | ||||
\(789\) | 62.3020i | 2.21801i | ||||||||
\(790\) | 2.81497 | + | 3.59344i | 0.100152 | + | 0.127849i | ||||
\(791\) | 18.0302 | 0.641082 | ||||||||
\(792\) | −11.2972 | + | 11.2972i | −0.401428 | + | 0.401428i | ||||
\(793\) | 4.88252 | + | 4.88252i | 0.173383 | + | 0.173383i | ||||
\(794\) | 18.9848 | 0.673746 | ||||||||
\(795\) | 26.2822 | + | 3.19267i | 0.932132 | + | 0.113232i | ||||
\(796\) | − | 27.5168i | − | 0.975307i | ||||||
\(797\) | −6.01324 | − | 6.01324i | −0.213000 | − | 0.213000i | 0.592541 | − | 0.805541i | \(-0.298125\pi\) |
−0.805541 | + | 0.592541i | \(0.798125\pi\) | |||||||
\(798\) | −0.0866314 | + | 0.0866314i | −0.00306672 | + | 0.00306672i | ||||
\(799\) | − | 32.0305i | − | 1.13316i | ||||||
\(800\) | −4.27919 | + | 2.58623i | −0.151292 | + | 0.0914369i | ||||
\(801\) | − | 42.0835i | − | 1.48695i | ||||||
\(802\) | −17.4021 | + | 17.4021i | −0.614490 | + | 0.614490i | ||||
\(803\) | 18.2703 | + | 18.2703i | 0.644744 | + | 0.644744i | ||||
\(804\) | −4.12107 | −0.145339 | ||||||||
\(805\) | −1.27887 | + | 10.5277i | −0.0450744 | + | 0.371053i | ||||
\(806\) | − | 3.77565i | − | 0.132991i | ||||||
\(807\) | −32.8723 | + | 32.8723i | −1.15716 | + | 1.15716i | ||||
\(808\) | −0.718588 | − | 0.718588i | −0.0252798 | − | 0.0252798i | ||||
\(809\) | 2.69059i | 0.0945959i | 0.998881 | + | 0.0472980i | \(0.0150610\pi\) | ||||
−0.998881 | + | 0.0472980i | \(0.984939\pi\) | |||||||
\(810\) | −5.70190 | + | 4.46665i | −0.200344 | + | 0.156942i | ||||
\(811\) | 1.60017i | 0.0561897i | 0.999605 | + | 0.0280948i | \(0.00894404\pi\) | ||||
−0.999605 | + | 0.0280948i | \(0.991056\pi\) | |||||||
\(812\) | 7.63691 | + | 7.63691i | 0.268003 | + | 0.268003i | ||||
\(813\) | 28.7104 | + | 28.7104i | 1.00692 | + | 1.00692i | ||||
\(814\) | − | 13.6032i | − | 0.476791i | ||||||
\(815\) | 10.9786 | + | 14.0148i | 0.384565 | + | 0.490916i | ||||
\(816\) | 9.69868i | 0.339522i | ||||||||
\(817\) | 0.138471 | − | 0.151955i | 0.00484448 | − | 0.00531625i | ||||
\(818\) | 10.4823 | − | 10.4823i | 0.366506 | − | 0.366506i | ||||
\(819\) | −5.73621 | −0.200439 | ||||||||
\(820\) | 2.73100 | − | 22.4817i | 0.0953707 | − | 0.785094i | ||||
\(821\) | −30.4124 | −1.06140 | −0.530700 | − | 0.847560i | \(-0.678071\pi\) | ||||
−0.530700 | + | 0.847560i | \(0.678071\pi\) | |||||||
\(822\) | −22.0526 | + | 22.0526i | −0.769174 | + | 0.769174i | ||||
\(823\) | 25.4456 | − | 25.4456i | 0.886978 | − | 0.886978i | −0.107253 | − | 0.994232i | \(-0.534206\pi\) |
0.994232 | + | 0.107253i | \(0.0342056\pi\) | |||||||
\(824\) | −17.3549 | −0.604586 | ||||||||
\(825\) | 25.8340 | + | 42.7451i | 0.899425 | + | 1.48819i | ||||
\(826\) | −20.4856 | −0.712784 | ||||||||
\(827\) | 34.4225 | + | 34.4225i | 1.19699 | + | 1.19699i | 0.975064 | + | 0.221924i | \(0.0712338\pi\) |
0.221924 | + | 0.975064i | \(0.428766\pi\) | |||||||
\(828\) | 10.0615 | − | 10.0615i | 0.349661 | − | 0.349661i | ||||
\(829\) | −48.6795 | −1.69071 | −0.845354 | − | 0.534207i | \(-0.820610\pi\) | ||||
−0.845354 | + | 0.534207i | \(0.820610\pi\) | |||||||
\(830\) | 1.87016 | − | 15.3952i | 0.0649143 | − | 0.534376i | ||||
\(831\) | −50.4982 | −1.75176 | ||||||||
\(832\) | −0.648955 | − | 0.648955i | −0.0224984 | − | 0.0224984i | ||||
\(833\) | −12.4541 | + | 12.4541i | −0.431507 | + | 0.431507i | ||||
\(834\) | − | 16.1789i | − | 0.560231i | ||||||
\(835\) | 2.11374 | + | 2.69830i | 0.0731492 | + | 0.0933784i | ||||
\(836\) | 0.115669i | 0.00400050i | ||||||||
\(837\) | −10.4778 | + | 10.4778i | −0.362165 | + | 0.362165i | ||||
\(838\) | −20.4185 | + | 20.4185i | −0.705344 | + | 0.705344i | ||||
\(839\) | −5.13321 | −0.177218 | −0.0886090 | − | 0.996066i | \(-0.528242\pi\) | ||||
−0.0886090 | + | 0.996066i | \(0.528242\pi\) | |||||||
\(840\) | −5.38863 | − | 6.87885i | −0.185926 | − | 0.237343i | ||||
\(841\) | 26.9908 | 0.930717 | ||||||||
\(842\) | 0.829667 | + | 0.829667i | 0.0285922 | + | 0.0285922i | ||||
\(843\) | 37.6862 | + | 37.6862i | 1.29798 | + | 1.29798i | ||||
\(844\) | −11.5577 | −0.397834 | ||||||||
\(845\) | 3.27830 | − | 26.9871i | 0.112777 | − | 0.928384i | ||||
\(846\) | − | 38.7199i | − | 1.33122i | ||||||
\(847\) | 2.66599 | − | 2.66599i | 0.0916045 | − | 0.0916045i | ||||
\(848\) | −3.09229 | + | 3.09229i | −0.106190 | + | 0.106190i | ||||
\(849\) | 70.8264 | 2.43076 | ||||||||
\(850\) | 17.3901 | + | 4.28827i | 0.596476 | + | 0.147086i | ||||
\(851\) | 12.1153i | 0.415306i | ||||||||
\(852\) | −9.05638 | − | 9.05638i | −0.310266 | − | 0.310266i | ||||
\(853\) | 15.1328 | − | 15.1328i | 0.518137 | − | 0.518137i | −0.398870 | − | 0.917007i | \(-0.630598\pi\) |
0.917007 | + | 0.398870i | \(0.130598\pi\) | |||||||
\(854\) | −10.8594 | −0.371600 | ||||||||
\(855\) | 0.0366077 | − | 0.301356i | 0.00125196 | − | 0.0103061i | ||||
\(856\) | 9.85187i | 0.336730i | ||||||||
\(857\) | −25.5613 | − | 25.5613i | −0.873156 | − | 0.873156i | 0.119659 | − | 0.992815i | \(-0.461820\pi\) |
−0.992815 | + | 0.119659i | \(0.961820\pi\) | |||||||
\(858\) | −6.48246 | + | 6.48246i | −0.221307 | + | 0.221307i | ||||
\(859\) | 43.5692 | 1.48656 | 0.743281 | − | 0.668979i | \(-0.233269\pi\) | ||||
0.743281 | + | 0.668979i | \(0.233269\pi\) | |||||||
\(860\) | 9.56789 | + | 11.1111i | 0.326262 | + | 0.378884i | ||||
\(861\) | 39.5786 | 1.34884 | ||||||||
\(862\) | −11.1912 | + | 11.1912i | −0.381173 | + | 0.381173i | ||||
\(863\) | 18.0267 | + | 18.0267i | 0.613637 | + | 0.613637i | 0.943892 | − | 0.330255i | \(-0.107135\pi\) |
−0.330255 | + | 0.943892i | \(0.607135\pi\) | |||||||
\(864\) | 3.60182i | 0.122536i | ||||||||
\(865\) | 28.0530 | − | 21.9757i | 0.953831 | − | 0.747196i | ||||
\(866\) | −15.1070 | −0.513358 | ||||||||
\(867\) | −7.97908 | + | 7.97908i | −0.270984 | + | 0.270984i | ||||
\(868\) | 4.19876 | + | 4.19876i | 0.142515 | + | 0.142515i | ||||
\(869\) | 7.53172i | 0.255496i | ||||||||
\(870\) | −44.9701 | − | 5.46283i | −1.52463 | − | 0.185207i | ||||
\(871\) | −1.39694 | −0.0473335 | ||||||||
\(872\) | 0.906269 | − | 0.906269i | 0.0306901 | − | 0.0306901i | ||||
\(873\) | 43.7866 | − | 43.7866i | 1.48195 | − | 1.48195i | ||||
\(874\) | − | 0.103017i | − | 0.00348461i | ||||||
\(875\) | −14.7166 | + | 6.62055i | −0.497513 | + | 0.223815i | ||||
\(876\) | 18.9609 | 0.640629 | ||||||||
\(877\) | −10.0042 | − | 10.0042i | −0.337818 | − | 0.337818i | 0.517727 | − | 0.855546i | \(-0.326778\pi\) |
−0.855546 | + | 0.517727i | \(0.826778\pi\) | |||||||
\(878\) | 3.72075 | + | 3.72075i | 0.125569 | + | 0.125569i | ||||
\(879\) | −89.9067 | −3.03248 | ||||||||
\(880\) | −8.18969 | − | 0.994857i | −0.276074 | − | 0.0335366i | ||||
\(881\) | 35.4715 | 1.19506 | 0.597532 | − | 0.801845i | \(-0.296148\pi\) | ||||
0.597532 | + | 0.801845i | \(0.296148\pi\) | |||||||
\(882\) | −15.0550 | + | 15.0550i | −0.506929 | + | 0.506929i | ||||
\(883\) | −30.5919 | + | 30.5919i | −1.02950 | + | 1.02950i | −0.0299490 | + | 0.999551i | \(0.509534\pi\) |
−0.999551 | + | 0.0299490i | \(0.990466\pi\) | |||||||
\(884\) | 3.28761i | 0.110574i | ||||||||
\(885\) | 67.6417 | − | 52.9880i | 2.27375 | − | 1.78117i | ||||
\(886\) | − | 20.8690i | − | 0.701106i | ||||||
\(887\) | 3.08773 | − | 3.08773i | 0.103676 | − | 0.103676i | −0.653366 | − | 0.757042i | \(-0.726644\pi\) |
0.757042 | + | 0.653366i | \(0.226644\pi\) | |||||||
\(888\) | −7.05869 | − | 7.05869i | −0.236874 | − | 0.236874i | ||||
\(889\) | 29.1799 | 0.978663 | ||||||||
\(890\) | 17.1069 | − | 13.4009i | 0.573423 | − | 0.449198i | ||||
\(891\) | −11.9510 | −0.400373 | ||||||||
\(892\) | −17.8690 | + | 17.8690i | −0.598300 | + | 0.598300i | ||||
\(893\) | −0.198222 | − | 0.198222i | −0.00663324 | − | 0.00663324i | ||||
\(894\) | 9.51878 | 0.318356 | ||||||||
\(895\) | −45.4581 | − | 5.52210i | −1.51950 | − | 0.184584i | ||||
\(896\) | 1.44336 | 0.0482193 | ||||||||
\(897\) | 5.77340 | − | 5.77340i | 0.192768 | − | 0.192768i | ||||
\(898\) | −1.65246 | + | 1.65246i | −0.0551433 | + | 0.0551433i | ||||
\(899\) | 30.7837 | 1.02669 | ||||||||
\(900\) | 21.0219 | + | 5.18385i | 0.700732 | + | 0.172795i | ||||
\(901\) | 15.6656 | 0.521896 | ||||||||
\(902\) | 26.4224 | − | 26.4224i | 0.879771 | − | 0.879771i | ||||
\(903\) | −17.2600 | + | 18.9408i | −0.574376 | + | 0.630310i | ||||
\(904\) | − | 12.4919i | − | 0.415473i | ||||||
\(905\) | −12.0512 | − | 1.46394i | −0.400595 | − | 0.0486630i | ||||
\(906\) | 28.7451i | 0.954992i | ||||||||
\(907\) | 12.6922 | + | 12.6922i | 0.421436 | + | 0.421436i | 0.885698 | − | 0.464262i | \(-0.153680\pi\) |
−0.464262 | + | 0.885698i | \(0.653680\pi\) | |||||||
\(908\) | −10.8185 | − | 10.8185i | −0.359025 | − | 0.359025i | ||||
\(909\) | 4.40064i | 0.145960i | ||||||||
\(910\) | −1.82661 | − | 2.33176i | −0.0605516 | − | 0.0772970i | ||||
\(911\) | 17.3644i | 0.575308i | 0.957734 | + | 0.287654i | \(0.0928752\pi\) | ||||
−0.957734 | + | 0.287654i | \(0.907125\pi\) | |||||||
\(912\) | 0.0600207 | + | 0.0600207i | 0.00198748 | + | 0.00198748i | ||||
\(913\) | 18.0938 | − | 18.0938i | 0.598819 | − | 0.598819i | ||||
\(914\) | − | 11.2905i | − | 0.373458i | ||||||
\(915\) | 35.8567 | − | 28.0888i | 1.18539 | − | 0.928589i | ||||
\(916\) | −0.448544 | −0.0148203 | ||||||||
\(917\) | 17.0191 | + | 17.0191i | 0.562019 | + | 0.562019i | ||||
\(918\) | 9.12342 | − | 9.12342i | 0.301118 | − | 0.301118i | ||||
\(919\) | − | 48.4350i | − | 1.59772i | −0.601515 | − | 0.798862i | \(-0.705436\pi\) | ||
0.601515 | − | 0.798862i | \(-0.294564\pi\) | |||||||
\(920\) | 7.29390 | + | 0.886040i | 0.240473 | + | 0.0292119i | ||||
\(921\) | 36.5873i | 1.20559i | ||||||||
\(922\) | 11.8758 | − | 11.8758i | 0.391108 | − | 0.391108i | ||||
\(923\) | −3.06988 | − | 3.06988i | −0.101046 | − | 0.101046i | ||||
\(924\) | − | 14.4178i | − | 0.474312i | ||||||
\(925\) | −15.7775 | + | 9.53551i | −0.518761 | + | 0.313526i | ||||
\(926\) | −13.9347 | −0.457924 | ||||||||
\(927\) | 53.1407 | + | 53.1407i | 1.74537 | + | 1.74537i | ||||
\(928\) | 5.29107 | − | 5.29107i | 0.173688 | − | 0.173688i | ||||
\(929\) | 5.86211 | 0.192330 | 0.0961649 | − | 0.995365i | \(-0.469342\pi\) | ||||
0.0961649 | + | 0.995365i | \(0.469342\pi\) | |||||||
\(930\) | −24.7245 | − | 3.00346i | −0.810749 | − | 0.0984872i | ||||
\(931\) | 0.154145i | 0.00505189i | ||||||||
\(932\) | 13.4741 | − | 13.4741i | 0.441358 | − | 0.441358i | ||||
\(933\) | −16.5380 | − | 16.5380i | −0.541429 | − | 0.541429i | ||||
\(934\) | − | 4.27014i | − | 0.139723i | ||||||
\(935\) | 18.2245 | + | 23.2645i | 0.596006 | + | 0.760830i | ||||
\(936\) | 3.97421i | 0.129901i | ||||||||
\(937\) | −31.9484 | + | 31.9484i | −1.04371 | + | 1.04371i | −0.0447071 | + | 0.999000i | \(0.514235\pi\) |
−0.999000 | + | 0.0447071i | \(0.985765\pi\) | |||||||
\(938\) | 1.55349 | − | 1.55349i | 0.0507232 | − | 0.0507232i | ||||
\(939\) | − | 49.6612i | − | 1.62063i | ||||||
\(940\) | 15.7395 | − | 12.3298i | 0.513367 | − | 0.402153i | ||||
\(941\) | 37.5860 | 1.22527 | 0.612634 | − | 0.790367i | \(-0.290110\pi\) | ||||
0.612634 | + | 0.790367i | \(0.290110\pi\) | |||||||
\(942\) | 12.3001 | − | 12.3001i | 0.400760 | − | 0.400760i | ||||
\(943\) | −23.5324 | + | 23.5324i | −0.766319 | + | 0.766319i | ||||
\(944\) | 14.1930i | 0.461942i | ||||||||
\(945\) | −1.40183 | + | 11.5399i | −0.0456014 | + | 0.375392i | ||||
\(946\) | 1.12211 | + | 24.1674i | 0.0364830 | + | 0.785750i | ||||
\(947\) | 12.3138 | + | 12.3138i | 0.400145 | + | 0.400145i | 0.878284 | − | 0.478139i | \(-0.158688\pi\) |
−0.478139 | + | 0.878284i | \(0.658688\pi\) | |||||||
\(948\) | 3.90821 | + | 3.90821i | 0.126933 | + | 0.126933i | ||||
\(949\) | 6.42726 | 0.208638 | ||||||||
\(950\) | 0.134158 | − | 0.0810813i | 0.00435265 | − | 0.00263062i | ||||
\(951\) | − | 16.9302i | − | 0.548998i | ||||||
\(952\) | −3.65603 | − | 3.65603i | −0.118493 | − | 0.118493i | ||||
\(953\) | −30.8857 | − | 30.8857i | −1.00048 | − | 1.00048i | −1.00000 | 0.000484952i | \(-0.999846\pi\) | |
−0.000484952 | − | 1.00000i | \(-0.500154\pi\) | |||||||
\(954\) | 18.9372 | 0.613116 | ||||||||
\(955\) | −3.12252 | + | 25.7046i | −0.101042 | + | 0.831782i | ||||
\(956\) | 4.55977 | 0.147474 | ||||||||
\(957\) | −52.8529 | − | 52.8529i | −1.70849 | − | 1.70849i | ||||
\(958\) | −18.7745 | − | 18.7745i | −0.606576 | − | 0.606576i | ||||
\(959\) | − | 16.6260i | − | 0.536882i | ||||||
\(960\) | −4.76586 | + | 3.73340i | −0.153817 | + | 0.120495i | ||||
\(961\) | −14.0752 | −0.454038 | ||||||||
\(962\) | −2.39272 | − | 2.39272i | −0.0771443 | − | 0.0771443i | ||||
\(963\) | 30.1665 | − | 30.1665i | 0.972102 | − | 0.972102i | ||||
\(964\) | 6.10070 | 0.196490 | ||||||||
\(965\) | −37.8170 | + | 29.6244i | −1.21737 | + | 0.953643i | ||||
\(966\) | 12.8408i | 0.413146i | ||||||||
\(967\) | −16.6658 | − | 16.6658i | −0.535935 | − | 0.535935i | 0.386398 | − | 0.922332i | \(-0.373719\pi\) |
−0.922332 | + | 0.386398i | \(0.873719\pi\) | |||||||
\(968\) | −1.84707 | − | 1.84707i | −0.0593672 | − | 0.0593672i | ||||
\(969\) | − | 0.304065i | − | 0.00976798i | ||||||
\(970\) | 31.7423 | + | 3.85596i | 1.01919 | + | 0.123807i | ||||
\(971\) | −2.89870 | −0.0930237 | −0.0465119 | − | 0.998918i | \(-0.514811\pi\) | ||||
−0.0465119 | + | 0.998918i | \(0.514811\pi\) | |||||||
\(972\) | −13.8420 | + | 13.8420i | −0.443982 | + | 0.443982i | ||||
\(973\) | 6.09884 | + | 6.09884i | 0.195520 | + | 0.195520i | ||||
\(974\) | −0.114435 | −0.00366674 | ||||||||
\(975\) | 12.0627 | + | 2.97456i | 0.386314 | + | 0.0952621i | ||||
\(976\) | 7.52367i | 0.240827i | ||||||||
\(977\) | 10.5011 | + | 10.5011i | 0.335959 | + | 0.335959i | 0.854844 | − | 0.518885i | \(-0.173653\pi\) |
−0.518885 | + | 0.854844i | \(0.673653\pi\) | |||||||
\(978\) | 15.2424 | + | 15.2424i | 0.487398 | + | 0.487398i | ||||
\(979\) | 35.8554 | 1.14594 | ||||||||
\(980\) | −10.9139 | − | 1.32578i | −0.348631 | − | 0.0423506i | ||||
\(981\) | −5.55000 | −0.177198 | ||||||||
\(982\) | −15.4025 | − | 15.4025i | −0.491513 | − | 0.491513i | ||||
\(983\) | −13.4594 | − | 13.4594i | −0.429287 | − | 0.429287i | 0.459099 | − | 0.888385i | \(-0.348172\pi\) |
−0.888385 | + | 0.459099i | \(0.848172\pi\) | |||||||
\(984\) | − | 27.4212i | − | 0.874156i | ||||||
\(985\) | −0.604829 | − | 0.772094i | −0.0192715 | − | 0.0246009i | ||||
\(986\) | −26.8046 | −0.853632 | ||||||||
\(987\) | 24.7078 | + | 24.7078i | 0.786458 | + | 0.786458i | ||||
\(988\) | 0.0203455 | + | 0.0203455i | 0.000647276 | + | 0.000647276i | ||||
\(989\) | −0.999374 | − | 21.5240i | −0.0317782 | − | 0.684422i | ||||
\(990\) | 22.0306 | + | 28.1232i | 0.700180 | + | 0.893813i | ||||
\(991\) | − | 52.5804i | − | 1.67027i | −0.550045 | − | 0.835135i | \(-0.685389\pi\) | ||
0.550045 | − | 0.835135i | \(-0.314611\pi\) | |||||||
\(992\) | 2.90902 | − | 2.90902i | 0.0923616 | − | 0.0923616i | ||||
\(993\) | 4.75184 | − | 4.75184i | 0.150795 | − | 0.150795i | ||||
\(994\) | 6.82782 | 0.216565 | ||||||||
\(995\) | −61.0804 | − | 7.41985i | −1.93638 | − | 0.235225i | ||||
\(996\) | − | 18.7778i | − | 0.594996i | ||||||
\(997\) | 21.9441 | − | 21.9441i | 0.694976 | − | 0.694976i | −0.268346 | − | 0.963323i | \(-0.586477\pi\) |
0.963323 | + | 0.268346i | \(0.0864771\pi\) | |||||||
\(998\) | 4.49545 | − | 4.49545i | 0.142301 | − | 0.142301i | ||||
\(999\) | 13.2800i | 0.420162i |
(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 | 430.2.g.b.257.12 | yes | 40 | |
5.3 | odd | 4 | inner | 430.2.g.b.343.9 | yes | 40 | |
43.42 | odd | 2 | inner | 430.2.g.b.257.9 | ✓ | 40 | |
215.128 | even | 4 | inner | 430.2.g.b.343.12 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
430.2.g.b.257.9 | ✓ | 40 | 43.42 | odd | 2 | inner | |
430.2.g.b.257.12 | yes | 40 | 1.1 | even | 1 | trivial | |
430.2.g.b.343.9 | yes | 40 | 5.3 | odd | 4 | inner | |
430.2.g.b.343.12 | yes | 40 | 215.128 | even | 4 | inner |