Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.5 | ||
Character | \(\chi\) | \(=\) | 930.491 |
Dual form | 930.2.o.d.161.14 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.118080 | + | 1.72802i | 0.0681736 | + | 0.997673i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | 1.72802 | − | 0.118080i | 0.705462 | − | 0.0482060i | ||||
\(7\) | 0.295093 | − | 0.511116i | 0.111535 | − | 0.193184i | −0.804855 | − | 0.593472i | \(-0.797757\pi\) |
0.916389 | + | 0.400288i | \(0.131090\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.97211 | + | 0.408090i | −0.990705 | + | 0.136030i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | −2.33844 | − | 4.05030i | −0.705067 | − | 1.22121i | −0.966668 | − | 0.256035i | \(-0.917584\pi\) |
0.261601 | − | 0.965176i | \(-0.415750\pi\) | |||||||
\(12\) | −0.118080 | − | 1.72802i | −0.0340868 | − | 0.498837i | ||||
\(13\) | 2.48977 | − | 1.43747i | 0.690538 | − | 0.398682i | −0.113275 | − | 0.993564i | \(-0.536134\pi\) |
0.803814 | + | 0.594881i | \(0.202801\pi\) | |||||||
\(14\) | −0.511116 | − | 0.295093i | −0.136601 | − | 0.0788669i | ||||
\(15\) | 0.966271 | + | 1.43747i | 0.249490 | + | 0.371153i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.50350 | − | 2.60413i | 0.364651 | − | 0.631595i | −0.624069 | − | 0.781369i | \(-0.714522\pi\) |
0.988720 | + | 0.149775i | \(0.0478549\pi\) | |||||||
\(18\) | 0.408090 | + | 2.97211i | 0.0961878 | + | 0.700534i | ||||
\(19\) | 1.44058 | − | 2.49515i | 0.330491 | − | 0.572427i | −0.652117 | − | 0.758118i | \(-0.726119\pi\) |
0.982608 | + | 0.185691i | \(0.0594524\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | 0.918064 | + | 0.449574i | 0.200338 | + | 0.0981051i | ||||
\(22\) | −4.05030 | + | 2.33844i | −0.863527 | + | 0.498557i | ||||
\(23\) | 0.585340 | 0.122052 | 0.0610259 | − | 0.998136i | \(-0.480563\pi\) | ||||
0.0610259 | + | 0.998136i | \(0.480563\pi\) | |||||||
\(24\) | −1.72802 | + | 0.118080i | −0.352731 | + | 0.0241030i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −1.43747 | − | 2.48977i | −0.281911 | − | 0.488284i | ||||
\(27\) | −1.05614 | − | 5.08769i | −0.203254 | − | 0.979126i | ||||
\(28\) | −0.295093 | + | 0.511116i | −0.0557673 | + | 0.0965918i | ||||
\(29\) | −5.47269 | −1.01625 | −0.508126 | − | 0.861283i | \(-0.669662\pi\) | ||||
−0.508126 | + | 0.861283i | \(0.669662\pi\) | |||||||
\(30\) | 1.43747 | − | 0.966271i | 0.262445 | − | 0.176416i | ||||
\(31\) | 4.99514 | − | 2.45939i | 0.897154 | − | 0.441719i | ||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 6.72288 | − | 4.51914i | 1.17030 | − | 0.786681i | ||||
\(34\) | −2.60413 | − | 1.50350i | −0.446605 | − | 0.257847i | ||||
\(35\) | − | 0.590186i | − | 0.0997596i | ||||||
\(36\) | 2.97211 | − | 0.408090i | 0.495352 | − | 0.0680150i | ||||
\(37\) | 4.88163 | + | 2.81841i | 0.802536 | + | 0.463344i | 0.844357 | − | 0.535781i | \(-0.179983\pi\) |
−0.0418213 | + | 0.999125i | \(0.513316\pi\) | |||||||
\(38\) | −2.49515 | − | 1.44058i | −0.404767 | − | 0.233692i | ||||
\(39\) | 2.77797 | + | 4.13264i | 0.444831 | + | 0.661752i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 4.52658 | − | 2.61342i | 0.706932 | − | 0.408148i | −0.102992 | − | 0.994682i | \(-0.532842\pi\) |
0.809924 | + | 0.586535i | \(0.199508\pi\) | |||||||
\(42\) | 0.449574 | − | 0.918064i | 0.0693708 | − | 0.141660i | ||||
\(43\) | 2.86939 | + | 1.65664i | 0.437578 | + | 0.252635i | 0.702570 | − | 0.711615i | \(-0.252036\pi\) |
−0.264992 | + | 0.964251i | \(0.585369\pi\) | |||||||
\(44\) | 2.33844 | + | 4.05030i | 0.352533 | + | 0.610606i | ||||
\(45\) | −2.36988 | + | 1.83947i | −0.353281 | + | 0.274213i | ||||
\(46\) | − | 0.585340i | − | 0.0863036i | ||||||
\(47\) | − | 5.89031i | − | 0.859191i | −0.903022 | − | 0.429595i | \(-0.858656\pi\) | ||
0.903022 | − | 0.429595i | \(-0.141344\pi\) | |||||||
\(48\) | 0.118080 | + | 1.72802i | 0.0170434 | + | 0.249418i | ||||
\(49\) | 3.32584 | + | 5.76052i | 0.475120 | + | 0.822932i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 4.67753 | + | 2.29058i | 0.654985 | + | 0.320745i | ||||
\(52\) | −2.48977 | + | 1.43747i | −0.345269 | + | 0.199341i | ||||
\(53\) | 0.900907 | + | 1.56042i | 0.123749 | + | 0.214340i | 0.921243 | − | 0.388987i | \(-0.127175\pi\) |
−0.797494 | + | 0.603327i | \(0.793842\pi\) | |||||||
\(54\) | −5.08769 | + | 1.05614i | −0.692347 | + | 0.143722i | ||||
\(55\) | −4.05030 | − | 2.33844i | −0.546142 | − | 0.315315i | ||||
\(56\) | 0.511116 | + | 0.295093i | 0.0683007 | + | 0.0394334i | ||||
\(57\) | 4.48178 | + | 2.19472i | 0.593626 | + | 0.290697i | ||||
\(58\) | 5.47269i | 0.718599i | ||||||||
\(59\) | 2.70209 | + | 1.56005i | 0.351783 | + | 0.203102i | 0.665470 | − | 0.746424i | \(-0.268231\pi\) |
−0.313687 | + | 0.949526i | \(0.601564\pi\) | |||||||
\(60\) | −0.966271 | − | 1.43747i | −0.124745 | − | 0.185577i | ||||
\(61\) | − | 3.09464i | − | 0.396228i | −0.980179 | − | 0.198114i | \(-0.936518\pi\) | ||
0.980179 | − | 0.198114i | \(-0.0634816\pi\) | |||||||
\(62\) | −2.45939 | − | 4.99514i | −0.312342 | − | 0.634383i | ||||
\(63\) | −0.668468 | + | 1.63952i | −0.0842191 | + | 0.206560i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.43747 | − | 2.48977i | 0.178296 | − | 0.308818i | ||||
\(66\) | −4.51914 | − | 6.72288i | −0.556267 | − | 0.827529i | ||||
\(67\) | −5.77223 | − | 9.99779i | −0.705190 | − | 1.22142i | −0.966623 | − | 0.256203i | \(-0.917528\pi\) |
0.261433 | − | 0.965222i | \(-0.415805\pi\) | |||||||
\(68\) | −1.50350 | + | 2.60413i | −0.182326 | + | 0.315797i | ||||
\(69\) | 0.0691170 | + | 1.01148i | 0.00832071 | + | 0.121768i | ||||
\(70\) | −0.590186 | −0.0705407 | ||||||||
\(71\) | −1.46261 | + | 0.844440i | −0.173580 | + | 0.100217i | −0.584273 | − | 0.811557i | \(-0.698620\pi\) |
0.410693 | + | 0.911774i | \(0.365287\pi\) | |||||||
\(72\) | −0.408090 | − | 2.97211i | −0.0480939 | − | 0.350267i | ||||
\(73\) | 2.55082 | − | 1.47272i | 0.298551 | − | 0.172369i | −0.343241 | − | 0.939248i | \(-0.611525\pi\) |
0.641792 | + | 0.766879i | \(0.278191\pi\) | |||||||
\(74\) | 2.81841 | − | 4.88163i | 0.327634 | − | 0.567479i | ||||
\(75\) | 1.55555 | + | 0.761750i | 0.179619 | + | 0.0879593i | ||||
\(76\) | −1.44058 | + | 2.49515i | −0.165245 | + | 0.286213i | ||||
\(77\) | −2.76023 | −0.314557 | ||||||||
\(78\) | 4.13264 | − | 2.77797i | 0.467929 | − | 0.314543i | ||||
\(79\) | 0.835902 | + | 0.482609i | 0.0940464 | + | 0.0542977i | 0.546286 | − | 0.837599i | \(-0.316041\pi\) |
−0.452239 | + | 0.891897i | \(0.649375\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | 8.66692 | − | 2.42578i | 0.962992 | − | 0.269531i | ||||
\(82\) | −2.61342 | − | 4.52658i | −0.288604 | − | 0.499877i | ||||
\(83\) | −5.93914 | − | 10.2869i | −0.651905 | − | 1.12913i | −0.982660 | − | 0.185416i | \(-0.940637\pi\) |
0.330755 | − | 0.943717i | \(-0.392697\pi\) | |||||||
\(84\) | −0.918064 | − | 0.449574i | −0.100169 | − | 0.0490525i | ||||
\(85\) | − | 3.00699i | − | 0.326154i | ||||||
\(86\) | 1.65664 | − | 2.86939i | 0.178640 | − | 0.309414i | ||||
\(87\) | −0.646216 | − | 9.45692i | −0.0692816 | − | 1.01389i | ||||
\(88\) | 4.05030 | − | 2.33844i | 0.431763 | − | 0.249279i | ||||
\(89\) | −0.409193 | −0.0433744 | −0.0216872 | − | 0.999765i | \(-0.506904\pi\) | ||||
−0.0216872 | + | 0.999765i | \(0.506904\pi\) | |||||||
\(90\) | 1.83947 | + | 2.36988i | 0.193898 | + | 0.249807i | ||||
\(91\) | − | 1.69675i | − | 0.177868i | ||||||
\(92\) | −0.585340 | −0.0610259 | ||||||||
\(93\) | 4.83970 | + | 8.34130i | 0.501853 | + | 0.864953i | ||||
\(94\) | −5.89031 | −0.607539 | ||||||||
\(95\) | − | 2.88115i | − | 0.295600i | ||||||
\(96\) | 1.72802 | − | 0.118080i | 0.176365 | − | 0.0120515i | ||||
\(97\) | −12.7800 | −1.29761 | −0.648805 | − | 0.760954i | \(-0.724731\pi\) | ||||
−0.648805 | + | 0.760954i | \(0.724731\pi\) | |||||||
\(98\) | 5.76052 | − | 3.32584i | 0.581901 | − | 0.335961i | ||||
\(99\) | 8.60300 | + | 11.0837i | 0.864634 | + | 1.11395i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 5.87075i | 0.584161i | 0.956394 | + | 0.292081i | \(0.0943476\pi\) | ||||
−0.956394 | + | 0.292081i | \(0.905652\pi\) | |||||||
\(102\) | 2.29058 | − | 4.67753i | 0.226801 | − | 0.463144i | ||||
\(103\) | −2.59197 | − | 4.48942i | −0.255394 | − | 0.442355i | 0.709608 | − | 0.704596i | \(-0.248872\pi\) |
−0.965002 | + | 0.262241i | \(0.915539\pi\) | |||||||
\(104\) | 1.43747 | + | 2.48977i | 0.140956 | + | 0.244142i | ||||
\(105\) | 1.01985 | − | 0.0696893i | 0.0995275 | − | 0.00680097i | ||||
\(106\) | 1.56042 | − | 0.900907i | 0.151561 | − | 0.0875038i | ||||
\(107\) | 8.33944 | + | 4.81478i | 0.806204 | + | 0.465462i | 0.845636 | − | 0.533760i | \(-0.179221\pi\) |
−0.0394317 | + | 0.999222i | \(0.512555\pi\) | |||||||
\(108\) | 1.05614 | + | 5.08769i | 0.101627 | + | 0.489563i | ||||
\(109\) | −12.5936 | −1.20625 | −0.603126 | − | 0.797646i | \(-0.706078\pi\) | ||||
−0.603126 | + | 0.797646i | \(0.706078\pi\) | |||||||
\(110\) | −2.33844 | + | 4.05030i | −0.222962 | + | 0.386181i | ||||
\(111\) | −4.29385 | + | 8.76837i | −0.407554 | + | 0.832257i | ||||
\(112\) | 0.295093 | − | 0.511116i | 0.0278837 | − | 0.0482959i | ||||
\(113\) | 5.55484 | − | 3.20709i | 0.522555 | − | 0.301697i | −0.215424 | − | 0.976521i | \(-0.569113\pi\) |
0.737979 | + | 0.674823i | \(0.235780\pi\) | |||||||
\(114\) | 2.19472 | − | 4.48178i | 0.205554 | − | 0.419757i | ||||
\(115\) | 0.506919 | − | 0.292670i | 0.0472704 | − | 0.0272916i | ||||
\(116\) | 5.47269 | 0.508126 | ||||||||
\(117\) | −6.81327 | + | 5.28838i | −0.629887 | + | 0.488911i | ||||
\(118\) | 1.56005 | − | 2.70209i | 0.143615 | − | 0.248748i | ||||
\(119\) | −0.887342 | − | 1.53692i | −0.0813425 | − | 0.140889i | ||||
\(120\) | −1.43747 | + | 0.966271i | −0.131222 | + | 0.0882081i | ||||
\(121\) | −5.43661 | + | 9.41649i | −0.494238 | + | 0.856045i | ||||
\(122\) | −3.09464 | −0.280175 | ||||||||
\(123\) | 5.05054 | + | 7.51342i | 0.455392 | + | 0.677463i | ||||
\(124\) | −4.99514 | + | 2.45939i | −0.448577 | + | 0.220859i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 1.63952 | + | 0.668468i | 0.146060 | + | 0.0595519i | ||||
\(127\) | −13.1713 | − | 7.60444i | −1.16876 | − | 0.674785i | −0.215374 | − | 0.976532i | \(-0.569097\pi\) |
−0.953388 | + | 0.301746i | \(0.902430\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −2.52389 | + | 5.15398i | −0.222216 | + | 0.453783i | ||||
\(130\) | −2.48977 | − | 1.43747i | −0.218367 | − | 0.126074i | ||||
\(131\) | 0.744839 | + | 0.430033i | 0.0650769 | + | 0.0375721i | 0.532185 | − | 0.846628i | \(-0.321371\pi\) |
−0.467109 | + | 0.884200i | \(0.654704\pi\) | |||||||
\(132\) | −6.72288 | + | 4.51914i | −0.585151 | + | 0.393340i | ||||
\(133\) | −0.850207 | − | 1.47260i | −0.0737223 | − | 0.127691i | ||||
\(134\) | −9.99779 | + | 5.77223i | −0.863678 | + | 0.498645i | ||||
\(135\) | −3.45849 | − | 3.87800i | −0.297659 | − | 0.333765i | ||||
\(136\) | 2.60413 | + | 1.50350i | 0.223302 | + | 0.128924i | ||||
\(137\) | 7.56206 | + | 13.0979i | 0.646071 | + | 1.11903i | 0.984053 | + | 0.177875i | \(0.0569222\pi\) |
−0.337982 | + | 0.941152i | \(0.609744\pi\) | |||||||
\(138\) | 1.01148 | − | 0.0691170i | 0.0861028 | − | 0.00588363i | ||||
\(139\) | 6.63378i | 0.562670i | 0.959610 | + | 0.281335i | \(0.0907772\pi\) | ||||
−0.959610 | + | 0.281335i | \(0.909223\pi\) | |||||||
\(140\) | 0.590186i | 0.0498798i | ||||||||
\(141\) | 10.1786 | − | 0.695530i | 0.857192 | − | 0.0585742i | ||||
\(142\) | 0.844440 | + | 1.46261i | 0.0708639 | + | 0.122740i | ||||
\(143\) | −11.6444 | − | 6.72288i | −0.973751 | − | 0.562195i | ||||
\(144\) | −2.97211 | + | 0.408090i | −0.247676 | + | 0.0340075i | ||||
\(145\) | −4.73949 | + | 2.73634i | −0.393593 | + | 0.227241i | ||||
\(146\) | −1.47272 | − | 2.55082i | −0.121883 | − | 0.211108i | ||||
\(147\) | −9.56159 | + | 6.42733i | −0.788627 | + | 0.530117i | ||||
\(148\) | −4.88163 | − | 2.81841i | −0.401268 | − | 0.231672i | ||||
\(149\) | 18.2286 | + | 10.5243i | 1.49334 | + | 0.862182i | 0.999971 | − | 0.00763584i | \(-0.00243059\pi\) |
0.493373 | + | 0.869818i | \(0.335764\pi\) | |||||||
\(150\) | 0.761750 | − | 1.55555i | 0.0621966 | − | 0.127010i | ||||
\(151\) | 16.8681i | 1.37271i | 0.727268 | + | 0.686353i | \(0.240790\pi\) | ||||
−0.727268 | + | 0.686353i | \(0.759210\pi\) | |||||||
\(152\) | 2.49515 | + | 1.44058i | 0.202383 | + | 0.116846i | ||||
\(153\) | −3.40584 | + | 8.35334i | −0.275346 | + | 0.675327i | ||||
\(154\) | 2.76023i | 0.222426i | ||||||||
\(155\) | 3.09622 | − | 4.62746i | 0.248695 | − | 0.371687i | ||||
\(156\) | −2.77797 | − | 4.13264i | −0.222416 | − | 0.330876i | ||||
\(157\) | 1.10936 | 0.0885362 | 0.0442681 | − | 0.999020i | \(-0.485904\pi\) | ||||
0.0442681 | + | 0.999020i | \(0.485904\pi\) | |||||||
\(158\) | 0.482609 | − | 0.835902i | 0.0383943 | − | 0.0665008i | ||||
\(159\) | −2.59005 | + | 1.74104i | −0.205405 | + | 0.138074i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | 0.172730 | − | 0.299176i | 0.0136130 | − | 0.0235784i | ||||
\(162\) | −2.42578 | − | 8.66692i | −0.190587 | − | 0.680938i | ||||
\(163\) | −9.25474 | −0.724887 | −0.362444 | − | 0.932006i | \(-0.618057\pi\) | ||||
−0.362444 | + | 0.932006i | \(0.618057\pi\) | |||||||
\(164\) | −4.52658 | + | 2.61342i | −0.353466 | + | 0.204074i | ||||
\(165\) | 3.56262 | − | 7.27513i | 0.277349 | − | 0.566368i | ||||
\(166\) | −10.2869 | + | 5.93914i | −0.798418 | + | 0.460967i | ||||
\(167\) | 4.64334 | − | 8.04251i | 0.359313 | − | 0.622348i | −0.628533 | − | 0.777783i | \(-0.716344\pi\) |
0.987846 | + | 0.155435i | \(0.0496778\pi\) | |||||||
\(168\) | −0.449574 | + | 0.918064i | −0.0346854 | + | 0.0708301i | ||||
\(169\) | −2.36736 | + | 4.10039i | −0.182105 | + | 0.315414i | ||||
\(170\) | −3.00699 | −0.230626 | ||||||||
\(171\) | −3.26331 | + | 8.00376i | −0.249551 | + | 0.612062i | ||||
\(172\) | −2.86939 | − | 1.65664i | −0.218789 | − | 0.126318i | ||||
\(173\) | −20.5960 | + | 11.8911i | −1.56588 | + | 0.904064i | −0.569244 | + | 0.822169i | \(0.692764\pi\) |
−0.996641 | + | 0.0818953i | \(0.973903\pi\) | |||||||
\(174\) | −9.45692 | + | 0.646216i | −0.716927 | + | 0.0489895i | ||||
\(175\) | −0.295093 | − | 0.511116i | −0.0223069 | − | 0.0386367i | ||||
\(176\) | −2.33844 | − | 4.05030i | −0.176267 | − | 0.305303i | ||||
\(177\) | −2.37674 | + | 4.85349i | −0.178647 | + | 0.364810i | ||||
\(178\) | 0.409193i | 0.0306703i | ||||||||
\(179\) | 8.98349 | − | 15.5599i | 0.671458 | − | 1.16300i | −0.306033 | − | 0.952021i | \(-0.599002\pi\) |
0.977491 | − | 0.210978i | \(-0.0676648\pi\) | |||||||
\(180\) | 2.36988 | − | 1.83947i | 0.176641 | − | 0.137106i | ||||
\(181\) | −0.555527 | + | 0.320734i | −0.0412920 | + | 0.0238399i | −0.520504 | − | 0.853859i | \(-0.674256\pi\) |
0.479212 | + | 0.877699i | \(0.340923\pi\) | |||||||
\(182\) | −1.69675 | −0.125771 | ||||||||
\(183\) | 5.34760 | − | 0.365416i | 0.395306 | − | 0.0270123i | ||||
\(184\) | 0.585340i | 0.0431518i | ||||||||
\(185\) | 5.63683 | 0.414428 | ||||||||
\(186\) | 8.34130 | − | 4.83970i | 0.611614 | − | 0.354864i | ||||
\(187\) | −14.0633 | −1.02841 | ||||||||
\(188\) | 5.89031i | 0.429595i | ||||||||
\(189\) | −2.91206 | − | 0.961533i | −0.211821 | − | 0.0699412i | ||||
\(190\) | −2.88115 | −0.209021 | ||||||||
\(191\) | −16.3559 | + | 9.44308i | −1.18347 | + | 0.683277i | −0.956815 | − | 0.290698i | \(-0.906113\pi\) |
−0.226656 | + | 0.973975i | \(0.572779\pi\) | |||||||
\(192\) | −0.118080 | − | 1.72802i | −0.00852171 | − | 0.124709i | ||||
\(193\) | −3.18956 | + | 5.52448i | −0.229590 | + | 0.397661i | −0.957687 | − | 0.287813i | \(-0.907072\pi\) |
0.728097 | + | 0.685474i | \(0.240405\pi\) | |||||||
\(194\) | 12.7800i | 0.917549i | ||||||||
\(195\) | 4.47211 | + | 2.18999i | 0.320255 | + | 0.156828i | ||||
\(196\) | −3.32584 | − | 5.76052i | −0.237560 | − | 0.411466i | ||||
\(197\) | 6.47331 | + | 11.2121i | 0.461204 | + | 0.798829i | 0.999021 | − | 0.0442328i | \(-0.0140843\pi\) |
−0.537817 | + | 0.843061i | \(0.680751\pi\) | |||||||
\(198\) | 11.0837 | − | 8.60300i | 0.787681 | − | 0.611389i | ||||
\(199\) | 12.4215 | − | 7.17157i | 0.880539 | − | 0.508379i | 0.00970264 | − | 0.999953i | \(-0.496912\pi\) |
0.870836 | + | 0.491574i | \(0.163578\pi\) | |||||||
\(200\) | 0.866025 | + | 0.500000i | 0.0612372 | + | 0.0353553i | ||||
\(201\) | 16.5948 | − | 11.1551i | 1.17051 | − | 0.786818i | ||||
\(202\) | 5.87075 | 0.413064 | ||||||||
\(203\) | −1.61495 | + | 2.79718i | −0.113347 | + | 0.196323i | ||||
\(204\) | −4.67753 | − | 2.29058i | −0.327492 | − | 0.160372i | ||||
\(205\) | 2.61342 | − | 4.52658i | 0.182529 | − | 0.316150i | ||||
\(206\) | −4.48942 | + | 2.59197i | −0.312793 | + | 0.180591i | ||||
\(207\) | −1.73970 | + | 0.238871i | −0.120917 | + | 0.0166027i | ||||
\(208\) | 2.48977 | − | 1.43747i | 0.172635 | − | 0.0996706i | ||||
\(209\) | −13.4748 | −0.932072 | ||||||||
\(210\) | −0.0696893 | − | 1.01985i | −0.00480902 | − | 0.0703766i | ||||
\(211\) | 0.525922 | − | 0.910924i | 0.0362060 | − | 0.0627106i | −0.847355 | − | 0.531027i | \(-0.821806\pi\) |
0.883561 | + | 0.468317i | \(0.155139\pi\) | |||||||
\(212\) | −0.900907 | − | 1.56042i | −0.0618746 | − | 0.107170i | ||||
\(213\) | −1.63192 | − | 2.42772i | −0.111817 | − | 0.166344i | ||||
\(214\) | 4.81478 | − | 8.33944i | 0.329132 | − | 0.570073i | ||||
\(215\) | 3.31328 | 0.225964 | ||||||||
\(216\) | 5.08769 | − | 1.05614i | 0.346173 | − | 0.0718610i | ||||
\(217\) | 0.216999 | − | 3.27884i | 0.0147308 | − | 0.222582i | ||||
\(218\) | 12.5936i | 0.852949i | ||||||||
\(219\) | 2.84609 | + | 4.23398i | 0.192321 | + | 0.286106i | ||||
\(220\) | 4.05030 | + | 2.33844i | 0.273071 | + | 0.157658i | ||||
\(221\) | − | 8.64492i | − | 0.581520i | ||||||
\(222\) | 8.76837 | + | 4.29385i | 0.588494 | + | 0.288185i | ||||
\(223\) | −6.76345 | − | 3.90488i | −0.452914 | − | 0.261490i | 0.256146 | − | 0.966638i | \(-0.417547\pi\) |
−0.709060 | + | 0.705148i | \(0.750881\pi\) | |||||||
\(224\) | −0.511116 | − | 0.295093i | −0.0341504 | − | 0.0197167i | ||||
\(225\) | −1.13264 | + | 2.77797i | −0.0755094 | + | 0.185198i | ||||
\(226\) | −3.20709 | − | 5.55484i | −0.213332 | − | 0.369502i | ||||
\(227\) | 18.1094 | − | 10.4554i | 1.20196 | − | 0.693952i | 0.240970 | − | 0.970533i | \(-0.422535\pi\) |
0.960991 | + | 0.276581i | \(0.0892013\pi\) | |||||||
\(228\) | −4.48178 | − | 2.19472i | −0.296813 | − | 0.145349i | ||||
\(229\) | 12.3777 | + | 7.14624i | 0.817938 | + | 0.472237i | 0.849705 | − | 0.527258i | \(-0.176780\pi\) |
−0.0317667 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(230\) | −0.292670 | − | 0.506919i | −0.0192981 | − | 0.0334253i | ||||
\(231\) | −0.325928 | − | 4.76973i | −0.0214445 | − | 0.313825i | ||||
\(232\) | − | 5.47269i | − | 0.359300i | ||||||
\(233\) | 16.5863i | 1.08661i | 0.839537 | + | 0.543303i | \(0.182827\pi\) | ||||
−0.839537 | + | 0.543303i | \(0.817173\pi\) | |||||||
\(234\) | 5.28838 | + | 6.81327i | 0.345712 | + | 0.445397i | ||||
\(235\) | −2.94516 | − | 5.10116i | −0.192121 | − | 0.332763i | ||||
\(236\) | −2.70209 | − | 1.56005i | −0.175891 | − | 0.101551i | ||||
\(237\) | −0.735254 | + | 1.50144i | −0.0477599 | + | 0.0975292i | ||||
\(238\) | −1.53692 | + | 0.887342i | −0.0996238 | + | 0.0575178i | ||||
\(239\) | −2.30620 | − | 3.99446i | −0.149176 | − | 0.258380i | 0.781747 | − | 0.623596i | \(-0.214329\pi\) |
−0.930923 | + | 0.365215i | \(0.880995\pi\) | |||||||
\(240\) | 0.966271 | + | 1.43747i | 0.0623725 | + | 0.0927883i | ||||
\(241\) | 18.4433 | + | 10.6482i | 1.18804 | + | 0.685913i | 0.957860 | − | 0.287236i | \(-0.0927365\pi\) |
0.230176 | + | 0.973149i | \(0.426070\pi\) | |||||||
\(242\) | 9.41649 | + | 5.43661i | 0.605315 | + | 0.349479i | ||||
\(243\) | 5.21519 | + | 14.6902i | 0.334555 | + | 0.942376i | ||||
\(244\) | 3.09464i | 0.198114i | ||||||||
\(245\) | 5.76052 | + | 3.32584i | 0.368026 | + | 0.212480i | ||||
\(246\) | 7.51342 | − | 5.05054i | 0.479038 | − | 0.322011i | ||||
\(247\) | − | 8.28314i | − | 0.527043i | ||||||
\(248\) | 2.45939 | + | 4.99514i | 0.156171 | + | 0.317192i | ||||
\(249\) | 17.0747 | − | 11.4776i | 1.08206 | − | 0.727366i | ||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −13.6875 | + | 23.7075i | −0.863949 | + | 1.49640i | 0.00413772 | + | 0.999991i | \(0.498683\pi\) |
−0.868087 | + | 0.496412i | \(0.834650\pi\) | |||||||
\(252\) | 0.668468 | − | 1.63952i | 0.0421095 | − | 0.103280i | ||||
\(253\) | −1.36878 | − | 2.37080i | −0.0860546 | − | 0.149051i | ||||
\(254\) | −7.60444 | + | 13.1713i | −0.477145 | + | 0.826440i | ||||
\(255\) | 5.19614 | − | 0.355066i | 0.325395 | − | 0.0222351i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.08285 | − | 4.08929i | 0.441816 | − | 0.255083i | −0.262552 | − | 0.964918i | \(-0.584564\pi\) |
0.704368 | + | 0.709835i | \(0.251231\pi\) | |||||||
\(258\) | 5.15398 | + | 2.52389i | 0.320873 | + | 0.157131i | ||||
\(259\) | 2.88107 | − | 1.66339i | 0.179021 | − | 0.103358i | ||||
\(260\) | −1.43747 | + | 2.48977i | −0.0891481 | + | 0.154409i | ||||
\(261\) | 16.2655 | − | 2.23335i | 1.00681 | − | 0.138241i | ||||
\(262\) | 0.430033 | − | 0.744839i | 0.0265675 | − | 0.0460163i | ||||
\(263\) | 1.95456 | 0.120523 | 0.0602617 | − | 0.998183i | \(-0.480806\pi\) | ||||
0.0602617 | + | 0.998183i | \(0.480806\pi\) | |||||||
\(264\) | 4.51914 | + | 6.72288i | 0.278134 | + | 0.413765i | ||||
\(265\) | 1.56042 | + | 0.900907i | 0.0958557 | + | 0.0553423i | ||||
\(266\) | −1.47260 | + | 0.850207i | −0.0902910 | + | 0.0521295i | ||||
\(267\) | −0.0483176 | − | 0.707095i | −0.00295699 | − | 0.0432735i | ||||
\(268\) | 5.77223 | + | 9.99779i | 0.352595 | + | 0.610712i | ||||
\(269\) | 2.52744 | + | 4.37765i | 0.154101 | + | 0.266910i | 0.932731 | − | 0.360572i | \(-0.117419\pi\) |
−0.778631 | + | 0.627483i | \(0.784085\pi\) | |||||||
\(270\) | −3.87800 | + | 3.45849i | −0.236008 | + | 0.210477i | ||||
\(271\) | − | 9.67395i | − | 0.587651i | −0.955859 | − | 0.293825i | \(-0.905072\pi\) | ||
0.955859 | − | 0.293825i | \(-0.0949284\pi\) | |||||||
\(272\) | 1.50350 | − | 2.60413i | 0.0911628 | − | 0.157899i | ||||
\(273\) | 2.93202 | − | 0.200352i | 0.177454 | − | 0.0121259i | ||||
\(274\) | 13.0979 | − | 7.56206i | 0.791272 | − | 0.456841i | ||||
\(275\) | −4.67688 | −0.282027 | ||||||||
\(276\) | −0.0691170 | − | 1.01148i | −0.00416036 | − | 0.0608839i | ||||
\(277\) | − | 16.9377i | − | 1.01769i | −0.860859 | − | 0.508843i | \(-0.830073\pi\) | ||
0.860859 | − | 0.508843i | \(-0.169927\pi\) | |||||||
\(278\) | 6.63378 | 0.397868 | ||||||||
\(279\) | −13.8425 | + | 9.34804i | −0.828727 | + | 0.559653i | ||||
\(280\) | 0.590186 | 0.0352703 | ||||||||
\(281\) | 23.8706i | 1.42400i | 0.702180 | + | 0.711999i | \(0.252210\pi\) | ||||
−0.702180 | + | 0.711999i | \(0.747790\pi\) | |||||||
\(282\) | −0.695530 | − | 10.1786i | −0.0414182 | − | 0.606126i | ||||
\(283\) | −25.8177 | −1.53470 | −0.767352 | − | 0.641226i | \(-0.778426\pi\) | ||||
−0.767352 | + | 0.641226i | \(0.778426\pi\) | |||||||
\(284\) | 1.46261 | − | 0.844440i | 0.0867902 | − | 0.0501083i | ||||
\(285\) | 4.97869 | − | 0.340207i | 0.294912 | − | 0.0201521i | ||||
\(286\) | −6.72288 | + | 11.6444i | −0.397532 | + | 0.688546i | ||||
\(287\) | − | 3.08481i | − | 0.182090i | ||||||
\(288\) | 0.408090 | + | 2.97211i | 0.0240469 | + | 0.175134i | ||||
\(289\) | 3.97900 | + | 6.89183i | 0.234059 | + | 0.405402i | ||||
\(290\) | 2.73634 | + | 4.73949i | 0.160684 | + | 0.278312i | ||||
\(291\) | −1.50906 | − | 22.0841i | −0.0884629 | − | 1.29459i | ||||
\(292\) | −2.55082 | + | 1.47272i | −0.149276 | + | 0.0861844i | ||||
\(293\) | 14.1888 | + | 8.19189i | 0.828917 | + | 0.478575i | 0.853482 | − | 0.521123i | \(-0.174487\pi\) |
−0.0245650 | + | 0.999698i | \(0.507820\pi\) | |||||||
\(294\) | 6.42733 | + | 9.56159i | 0.374849 | + | 0.557643i | ||||
\(295\) | 3.12011 | 0.181660 | ||||||||
\(296\) | −2.81841 | + | 4.88163i | −0.163817 | + | 0.283739i | ||||
\(297\) | −18.1369 | + | 16.1749i | −1.05241 | + | 0.938565i | ||||
\(298\) | 10.5243 | − | 18.2286i | 0.609655 | − | 1.05595i | ||||
\(299\) | 1.45736 | − | 0.841408i | 0.0842814 | − | 0.0486599i | ||||
\(300\) | −1.55555 | − | 0.761750i | −0.0898097 | − | 0.0439797i | ||||
\(301\) | 1.69347 | − | 0.977726i | 0.0976101 | − | 0.0563552i | ||||
\(302\) | 16.8681 | 0.970650 | ||||||||
\(303\) | −10.1448 | + | 0.693219i | −0.582802 | + | 0.0398244i | ||||
\(304\) | 1.44058 | − | 2.49515i | 0.0826227 | − | 0.143107i | ||||
\(305\) | −1.54732 | − | 2.68004i | −0.0885993 | − | 0.153458i | ||||
\(306\) | 8.35334 | + | 3.40584i | 0.477528 | + | 0.194699i | ||||
\(307\) | −11.2930 | + | 19.5601i | −0.644527 | + | 1.11635i | 0.339884 | + | 0.940467i | \(0.389612\pi\) |
−0.984411 | + | 0.175886i | \(0.943721\pi\) | |||||||
\(308\) | 2.76023 | 0.157279 | ||||||||
\(309\) | 7.45175 | − | 5.00908i | 0.423915 | − | 0.284957i | ||||
\(310\) | −4.62746 | − | 3.09622i | −0.262822 | − | 0.175854i | ||||
\(311\) | − | 7.76670i | − | 0.440409i | −0.975454 | − | 0.220205i | \(-0.929327\pi\) | ||
0.975454 | − | 0.220205i | \(-0.0706725\pi\) | |||||||
\(312\) | −4.13264 | + | 2.77797i | −0.233965 | + | 0.157272i | ||||
\(313\) | −21.0679 | − | 12.1635i | −1.19083 | − | 0.687523i | −0.232332 | − | 0.972637i | \(-0.574635\pi\) |
−0.958494 | + | 0.285113i | \(0.907969\pi\) | |||||||
\(314\) | − | 1.10936i | − | 0.0626045i | ||||||
\(315\) | 0.240849 | + | 1.75410i | 0.0135703 | + | 0.0988323i | ||||
\(316\) | −0.835902 | − | 0.482609i | −0.0470232 | − | 0.0271489i | ||||
\(317\) | −10.8728 | − | 6.27740i | −0.610676 | − | 0.352574i | 0.162554 | − | 0.986700i | \(-0.448027\pi\) |
−0.773230 | + | 0.634126i | \(0.781360\pi\) | |||||||
\(318\) | 1.74104 | + | 2.59005i | 0.0976327 | + | 0.145243i | ||||
\(319\) | 12.7976 | + | 22.1660i | 0.716526 | + | 1.24106i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | −7.33532 | + | 14.9793i | −0.409417 | + | 0.836061i | ||||
\(322\) | −0.299176 | − | 0.172730i | −0.0166724 | − | 0.00962584i | ||||
\(323\) | −4.33180 | − | 7.50289i | −0.241028 | − | 0.417472i | ||||
\(324\) | −8.66692 | + | 2.42578i | −0.481496 | + | 0.134766i | ||||
\(325\) | − | 2.87494i | − | 0.159473i | ||||||
\(326\) | 9.25474i | 0.512573i | ||||||||
\(327\) | −1.48706 | − | 21.7621i | −0.0822346 | − | 1.20345i | ||||
\(328\) | 2.61342 | + | 4.52658i | 0.144302 | + | 0.249938i | ||||
\(329\) | −3.01063 | − | 1.73819i | −0.165982 | − | 0.0958295i | ||||
\(330\) | −7.27513 | − | 3.56262i | −0.400482 | − | 0.196116i | ||||
\(331\) | −21.1683 | + | 12.2215i | −1.16352 | + | 0.671757i | −0.952144 | − | 0.305649i | \(-0.901127\pi\) |
−0.211372 | + | 0.977406i | \(0.567793\pi\) | |||||||
\(332\) | 5.93914 | + | 10.2869i | 0.325953 | + | 0.564566i | ||||
\(333\) | −15.6589 | − | 6.38450i | −0.858105 | − | 0.349868i | ||||
\(334\) | −8.04251 | − | 4.64334i | −0.440066 | − | 0.254072i | ||||
\(335\) | −9.99779 | − | 5.77223i | −0.546238 | − | 0.315370i | ||||
\(336\) | 0.918064 | + | 0.449574i | 0.0500845 | + | 0.0245263i | ||||
\(337\) | − | 7.97132i | − | 0.434225i | −0.976147 | − | 0.217113i | \(-0.930336\pi\) | ||
0.976147 | − | 0.217113i | \(-0.0696639\pi\) | |||||||
\(338\) | 4.10039 | + | 2.36736i | 0.223032 | + | 0.128767i | ||||
\(339\) | 6.19783 | + | 9.22018i | 0.336620 | + | 0.500772i | ||||
\(340\) | 3.00699i | 0.163077i | ||||||||
\(341\) | −21.6421 | − | 14.4807i | −1.17198 | − | 0.784173i | ||||
\(342\) | 8.00376 | + | 3.26331i | 0.432794 | + | 0.176460i | ||||
\(343\) | 8.05703 | 0.435039 | ||||||||
\(344\) | −1.65664 | + | 2.86939i | −0.0893201 | + | 0.154707i | ||||
\(345\) | 0.565597 | + | 0.841408i | 0.0304507 | + | 0.0452999i | ||||
\(346\) | 11.8911 | + | 20.5960i | 0.639270 | + | 1.10725i | ||||
\(347\) | 15.3080 | − | 26.5142i | 0.821775 | − | 1.42336i | −0.0825838 | − | 0.996584i | \(-0.526317\pi\) |
0.904359 | − | 0.426772i | \(-0.140349\pi\) | |||||||
\(348\) | 0.646216 | + | 9.45692i | 0.0346408 | + | 0.506944i | ||||
\(349\) | 21.2775 | 1.13896 | 0.569479 | − | 0.822006i | \(-0.307145\pi\) | ||||
0.569479 | + | 0.822006i | \(0.307145\pi\) | |||||||
\(350\) | −0.511116 | + | 0.295093i | −0.0273203 | + | 0.0157734i | ||||
\(351\) | −9.94294 | − | 11.1490i | −0.530715 | − | 0.595090i | ||||
\(352\) | −4.05030 | + | 2.33844i | −0.215882 | + | 0.124639i | ||||
\(353\) | 11.3691 | − | 19.6918i | 0.605115 | − | 1.04809i | −0.386919 | − | 0.922114i | \(-0.626461\pi\) |
0.992033 | − | 0.125976i | \(-0.0402061\pi\) | |||||||
\(354\) | 4.85349 | + | 2.37674i | 0.257960 | + | 0.126323i | ||||
\(355\) | −0.844440 | + | 1.46261i | −0.0448182 | + | 0.0776275i | ||||
\(356\) | 0.409193 | 0.0216872 | ||||||||
\(357\) | 2.55105 | − | 1.71483i | 0.135016 | − | 0.0907582i | ||||
\(358\) | −15.5599 | − | 8.98349i | −0.822364 | − | 0.474792i | ||||
\(359\) | 1.29984 | − | 0.750465i | 0.0686031 | − | 0.0396080i | −0.465306 | − | 0.885150i | \(-0.654056\pi\) |
0.533909 | + | 0.845542i | \(0.320722\pi\) | |||||||
\(360\) | −1.83947 | − | 2.36988i | −0.0969488 | − | 0.124904i | ||||
\(361\) | 5.34948 | + | 9.26558i | 0.281552 | + | 0.487662i | ||||
\(362\) | 0.320734 | + | 0.555527i | 0.0168574 | + | 0.0291979i | ||||
\(363\) | −16.9139 | − | 8.28268i | −0.887747 | − | 0.434728i | ||||
\(364\) | 1.69675i | 0.0889338i | ||||||||
\(365\) | 1.47272 | − | 2.55082i | 0.0770857 | − | 0.133516i | ||||
\(366\) | −0.365416 | − | 5.34760i | −0.0191006 | − | 0.279524i | ||||
\(367\) | −2.43304 | + | 1.40472i | −0.127004 | + | 0.0733256i | −0.562156 | − | 0.827031i | \(-0.690028\pi\) |
0.435152 | + | 0.900357i | \(0.356695\pi\) | |||||||
\(368\) | 0.585340 | 0.0305129 | ||||||||
\(369\) | −12.3870 | + | 9.61463i | −0.644841 | + | 0.500518i | ||||
\(370\) | − | 5.63683i | − | 0.293045i | ||||||
\(371\) | 1.06341 | 0.0552092 | ||||||||
\(372\) | −4.83970 | − | 8.34130i | −0.250927 | − | 0.432476i | ||||
\(373\) | 21.9797 | 1.13807 | 0.569033 | − | 0.822315i | \(-0.307318\pi\) | ||||
0.569033 | + | 0.822315i | \(0.307318\pi\) | |||||||
\(374\) | 14.0633i | 0.727198i | ||||||||
\(375\) | 1.72802 | − | 0.118080i | 0.0892346 | − | 0.00609764i | ||||
\(376\) | 5.89031 | 0.303770 | ||||||||
\(377\) | −13.6257 | + | 7.86682i | −0.701761 | + | 0.405162i | ||||
\(378\) | −0.961533 | + | 2.91206i | −0.0494559 | + | 0.149780i | ||||
\(379\) | −10.2057 | + | 17.6768i | −0.524232 | + | 0.907997i | 0.475370 | + | 0.879786i | \(0.342314\pi\) |
−0.999602 | + | 0.0282108i | \(0.991019\pi\) | |||||||
\(380\) | 2.88115i | 0.147800i | ||||||||
\(381\) | 11.5854 | − | 23.6582i | 0.593536 | − | 1.21205i | ||||
\(382\) | 9.44308 | + | 16.3559i | 0.483150 | + | 0.836840i | ||||
\(383\) | 16.0251 | + | 27.7563i | 0.818845 | + | 1.41828i | 0.906534 | + | 0.422133i | \(0.138718\pi\) |
−0.0876892 | + | 0.996148i | \(0.527948\pi\) | |||||||
\(384\) | −1.72802 | + | 0.118080i | −0.0881827 | + | 0.00602576i | ||||
\(385\) | −2.39043 | + | 1.38011i | −0.121828 | + | 0.0703371i | ||||
\(386\) | 5.52448 | + | 3.18956i | 0.281189 | + | 0.162344i | ||||
\(387\) | −9.20421 | − | 3.75276i | −0.467876 | − | 0.190763i | ||||
\(388\) | 12.7800 | 0.648805 | ||||||||
\(389\) | 18.6651 | − | 32.3290i | 0.946360 | − | 1.63914i | 0.193356 | − | 0.981129i | \(-0.438063\pi\) |
0.753005 | − | 0.658015i | \(-0.228604\pi\) | |||||||
\(390\) | 2.18999 | − | 4.47211i | 0.110894 | − | 0.226454i | ||||
\(391\) | 0.880056 | − | 1.52430i | 0.0445063 | − | 0.0770872i | ||||
\(392\) | −5.76052 | + | 3.32584i | −0.290950 | + | 0.167980i | ||||
\(393\) | −0.655155 | + | 1.33788i | −0.0330482 | + | 0.0674869i | ||||
\(394\) | 11.2121 | − | 6.47331i | 0.564857 | − | 0.326120i | ||||
\(395\) | 0.965217 | 0.0485653 | ||||||||
\(396\) | −8.60300 | − | 11.0837i | −0.432317 | − | 0.556975i | ||||
\(397\) | 18.0304 | − | 31.2296i | 0.904921 | − | 1.56737i | 0.0838969 | − | 0.996474i | \(-0.473263\pi\) |
0.821024 | − | 0.570894i | \(-0.193403\pi\) | |||||||
\(398\) | −7.17157 | − | 12.4215i | −0.359478 | − | 0.622635i | ||||
\(399\) | 2.44429 | − | 1.64306i | 0.122368 | − | 0.0822559i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −36.7308 | −1.83425 | −0.917125 | − | 0.398599i | \(-0.869496\pi\) | ||||
−0.917125 | + | 0.398599i | \(0.869496\pi\) | |||||||
\(402\) | −11.1551 | − | 16.5948i | −0.556364 | − | 0.827674i | ||||
\(403\) | 8.90146 | − | 13.3037i | 0.443413 | − | 0.662703i | ||||
\(404\) | − | 5.87075i | − | 0.292081i | ||||||
\(405\) | 6.29289 | − | 6.43425i | 0.312696 | − | 0.319720i | ||||
\(406\) | 2.79718 | + | 1.61495i | 0.138822 | + | 0.0801487i | ||||
\(407\) | − | 26.3628i | − | 1.30675i | ||||||
\(408\) | −2.29058 | + | 4.67753i | −0.113400 | + | 0.231572i | ||||
\(409\) | 29.9703 | + | 17.3034i | 1.48194 | + | 0.855597i | 0.999790 | − | 0.0204926i | \(-0.00652345\pi\) |
0.482148 | + | 0.876090i | \(0.339857\pi\) | |||||||
\(410\) | −4.52658 | − | 2.61342i | −0.223552 | − | 0.129068i | ||||
\(411\) | −21.7405 | + | 14.6140i | −1.07238 | + | 0.720856i | ||||
\(412\) | 2.59197 | + | 4.48942i | 0.127697 | + | 0.221178i | ||||
\(413\) | 1.59474 | − | 0.920722i | 0.0784719 | − | 0.0453058i | ||||
\(414\) | 0.238871 | + | 1.73970i | 0.0117399 | + | 0.0855014i | ||||
\(415\) | −10.2869 | − | 5.93914i | −0.504964 | − | 0.291541i | ||||
\(416\) | −1.43747 | − | 2.48977i | −0.0704778 | − | 0.122071i | ||||
\(417\) | −11.4633 | + | 0.783318i | −0.561361 | + | 0.0383593i | ||||
\(418\) | 13.4748i | 0.659074i | ||||||||
\(419\) | − | 2.99848i | − | 0.146485i | −0.997314 | − | 0.0732426i | \(-0.976665\pi\) | ||
0.997314 | − | 0.0732426i | \(-0.0233347\pi\) | |||||||
\(420\) | −1.01985 | + | 0.0696893i | −0.0497637 | + | 0.00340049i | ||||
\(421\) | −9.94262 | − | 17.2211i | −0.484574 | − | 0.839306i | 0.515269 | − | 0.857028i | \(-0.327692\pi\) |
−0.999843 | + | 0.0177220i | \(0.994359\pi\) | |||||||
\(422\) | −0.910924 | − | 0.525922i | −0.0443431 | − | 0.0256015i | ||||
\(423\) | 2.40378 | + | 17.5067i | 0.116876 | + | 0.851204i | ||||
\(424\) | −1.56042 | + | 0.900907i | −0.0757806 | + | 0.0437519i | ||||
\(425\) | −1.50350 | − | 2.60413i | −0.0729303 | − | 0.126319i | ||||
\(426\) | −2.42772 | + | 1.63192i | −0.117623 | + | 0.0790666i | ||||
\(427\) | −1.58172 | − | 0.913206i | −0.0765447 | − | 0.0441931i | ||||
\(428\) | −8.33944 | − | 4.81478i | −0.403102 | − | 0.232731i | ||||
\(429\) | 10.2423 | − | 20.9156i | 0.494503 | − | 1.00981i | ||||
\(430\) | − | 3.31328i | − | 0.159781i | ||||||
\(431\) | 5.57553 | + | 3.21903i | 0.268564 | + | 0.155055i | 0.628235 | − | 0.778024i | \(-0.283778\pi\) |
−0.359671 | + | 0.933079i | \(0.617111\pi\) | |||||||
\(432\) | −1.05614 | − | 5.08769i | −0.0508134 | − | 0.244782i | ||||
\(433\) | − | 29.7643i | − | 1.43038i | −0.698929 | − | 0.715191i | \(-0.746339\pi\) | ||
0.698929 | − | 0.715191i | \(-0.253661\pi\) | |||||||
\(434\) | −3.27884 | − | 0.216999i | −0.157389 | − | 0.0104163i | ||||
\(435\) | −5.28810 | − | 7.86682i | −0.253545 | − | 0.377185i | ||||
\(436\) | 12.5936 | 0.603126 | ||||||||
\(437\) | 0.843226 | − | 1.46051i | 0.0403370 | − | 0.0698657i | ||||
\(438\) | 4.23398 | − | 2.84609i | 0.202307 | − | 0.135992i | ||||
\(439\) | 19.7500 | + | 34.2079i | 0.942614 | + | 1.63266i | 0.760459 | + | 0.649386i | \(0.224974\pi\) |
0.182155 | + | 0.983270i | \(0.441693\pi\) | |||||||
\(440\) | 2.33844 | − | 4.05030i | 0.111481 | − | 0.193090i | ||||
\(441\) | −12.2356 | − | 15.7637i | −0.582647 | − | 0.750652i | ||||
\(442\) | −8.64492 | −0.411197 | ||||||||
\(443\) | −10.5606 | + | 6.09717i | −0.501750 | + | 0.289685i | −0.729436 | − | 0.684049i | \(-0.760217\pi\) |
0.227686 | + | 0.973735i | \(0.426884\pi\) | |||||||
\(444\) | 4.29385 | − | 8.76837i | 0.203777 | − | 0.416128i | ||||
\(445\) | −0.354372 | + | 0.204597i | −0.0167988 | + | 0.00969881i | ||||
\(446\) | −3.90488 | + | 6.76345i | −0.184902 | + | 0.320259i | ||||
\(447\) | −16.0337 | + | 32.7421i | −0.758370 | + | 1.54865i | ||||
\(448\) | −0.295093 | + | 0.511116i | −0.0139418 | + | 0.0241480i | ||||
\(449\) | 1.10717 | 0.0522506 | 0.0261253 | − | 0.999659i | \(-0.491683\pi\) | ||||
0.0261253 | + | 0.999659i | \(0.491683\pi\) | |||||||
\(450\) | 2.77797 | + | 1.13264i | 0.130955 | + | 0.0533932i | ||||
\(451\) | −21.1703 | − | 12.2227i | −0.996869 | − | 0.575542i | ||||
\(452\) | −5.55484 | + | 3.20709i | −0.261278 | + | 0.150849i | ||||
\(453\) | −29.1484 | + | 1.99179i | −1.36951 | + | 0.0935824i | ||||
\(454\) | −10.4554 | − | 18.1094i | −0.490698 | − | 0.849914i | ||||
\(455\) | −0.848374 | − | 1.46943i | −0.0397724 | − | 0.0688878i | ||||
\(456\) | −2.19472 | + | 4.48178i | −0.102777 | + | 0.209878i | ||||
\(457\) | − | 8.27976i | − | 0.387311i | −0.981070 | − | 0.193655i | \(-0.937966\pi\) | ||
0.981070 | − | 0.193655i | \(-0.0620344\pi\) | |||||||
\(458\) | 7.14624 | − | 12.3777i | 0.333922 | − | 0.578370i | ||||
\(459\) | −14.8369 | − | 4.89900i | −0.692527 | − | 0.228666i | ||||
\(460\) | −0.506919 | + | 0.292670i | −0.0236352 | + | 0.0136458i | ||||
\(461\) | −19.4170 | −0.904338 | −0.452169 | − | 0.891932i | \(-0.649350\pi\) | ||||
−0.452169 | + | 0.891932i | \(0.649350\pi\) | |||||||
\(462\) | −4.76973 | + | 0.325928i | −0.221908 | + | 0.0151636i | ||||
\(463\) | 34.1138i | 1.58540i | 0.609610 | + | 0.792702i | \(0.291326\pi\) | ||||
−0.609610 | + | 0.792702i | \(0.708674\pi\) | |||||||
\(464\) | −5.47269 | −0.254063 | ||||||||
\(465\) | 8.36195 | + | 4.80393i | 0.387776 | + | 0.222777i | ||||
\(466\) | 16.5863 | 0.768347 | ||||||||
\(467\) | − | 25.2788i | − | 1.16976i | −0.811118 | − | 0.584882i | \(-0.801141\pi\) | ||
0.811118 | − | 0.584882i | \(-0.198859\pi\) | |||||||
\(468\) | 6.81327 | − | 5.28838i | 0.314943 | − | 0.244455i | ||||
\(469\) | −6.81337 | −0.314612 | ||||||||
\(470\) | −5.10116 | + | 2.94516i | −0.235299 | + | 0.135850i | ||||
\(471\) | 0.130993 | + | 1.91699i | 0.00603583 | + | 0.0883302i | ||||
\(472\) | −1.56005 | + | 2.70209i | −0.0718073 | + | 0.124374i | ||||
\(473\) | − | 15.4958i | − | 0.712499i | ||||||
\(474\) | 1.50144 | + | 0.735254i | 0.0689636 | + | 0.0337713i | ||||
\(475\) | −1.44058 | − | 2.49515i | −0.0660981 | − | 0.114485i | ||||
\(476\) | 0.887342 | + | 1.53692i | 0.0406712 | + | 0.0704446i | ||||
\(477\) | −3.31439 | − | 4.27009i | −0.151755 | − | 0.195514i | ||||
\(478\) | −3.99446 | + | 2.30620i | −0.182702 | + | 0.105483i | ||||
\(479\) | 16.1197 | + | 9.30670i | 0.736527 | + | 0.425234i | 0.820805 | − | 0.571208i | \(-0.193525\pi\) |
−0.0842784 | + | 0.996442i | \(0.526859\pi\) | |||||||
\(480\) | 1.43747 | − | 0.966271i | 0.0656112 | − | 0.0441040i | ||||
\(481\) | 16.2055 | 0.738909 | ||||||||
\(482\) | 10.6482 | − | 18.4433i | 0.485013 | − | 0.840068i | ||||
\(483\) | 0.537379 | + | 0.263154i | 0.0244516 | + | 0.0119739i | ||||
\(484\) | 5.43661 | − | 9.41649i | 0.247119 | − | 0.428022i | ||||
\(485\) | −11.0678 | + | 6.38999i | −0.502562 | + | 0.290155i | ||||
\(486\) | 14.6902 | − | 5.21519i | 0.666361 | − | 0.236566i | ||||
\(487\) | 6.09365 | − | 3.51817i | 0.276130 | − | 0.159424i | −0.355540 | − | 0.934661i | \(-0.615703\pi\) |
0.631670 | + | 0.775237i | \(0.282370\pi\) | |||||||
\(488\) | 3.09464 | 0.140088 | ||||||||
\(489\) | −1.09280 | − | 15.9924i | −0.0494182 | − | 0.723201i | ||||
\(490\) | 3.32584 | − | 5.76052i | 0.150246 | − | 0.260234i | ||||
\(491\) | −13.2084 | − | 22.8777i | −0.596088 | − | 1.03245i | −0.993392 | − | 0.114768i | \(-0.963388\pi\) |
0.397304 | − | 0.917687i | \(-0.369946\pi\) | |||||||
\(492\) | −5.05054 | − | 7.51342i | −0.227696 | − | 0.338731i | ||||
\(493\) | −8.22816 | + | 14.2516i | −0.370578 | + | 0.641860i | ||||
\(494\) | −8.28314 | −0.372676 | ||||||||
\(495\) | 12.9922 | + | 5.29723i | 0.583958 | + | 0.238093i | ||||
\(496\) | 4.99514 | − | 2.45939i | 0.224288 | − | 0.110430i | ||||
\(497\) | 0.996753i | 0.0447105i | ||||||||
\(498\) | −11.4776 | − | 17.0747i | −0.514325 | − | 0.765134i | ||||
\(499\) | 10.7088 | + | 6.18273i | 0.479392 | + | 0.276777i | 0.720163 | − | 0.693805i | \(-0.244067\pi\) |
−0.240771 | + | 0.970582i | \(0.577400\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 14.4459 | + | 7.07413i | 0.645396 | + | 0.316049i | ||||
\(502\) | 23.7075 | + | 13.6875i | 1.05812 | + | 0.610904i | ||||
\(503\) | −14.3552 | − | 8.28798i | −0.640067 | − | 0.369543i | 0.144574 | − | 0.989494i | \(-0.453819\pi\) |
−0.784640 | + | 0.619951i | \(0.787152\pi\) | |||||||
\(504\) | −1.63952 | − | 0.668468i | −0.0730300 | − | 0.0297759i | ||||
\(505\) | 2.93537 | + | 5.08422i | 0.130622 | + | 0.226245i | ||||
\(506\) | −2.37080 | + | 1.36878i | −0.105395 | + | 0.0608498i | ||||
\(507\) | −7.36509 | − | 3.60667i | −0.327095 | − | 0.160178i | ||||
\(508\) | 13.1713 | + | 7.60444i | 0.584381 | + | 0.337393i | ||||
\(509\) | −19.8929 | − | 34.4556i | −0.881739 | − | 1.52722i | −0.849406 | − | 0.527740i | \(-0.823039\pi\) |
−0.0323336 | − | 0.999477i | \(-0.510294\pi\) | |||||||
\(510\) | −0.355066 | − | 5.19614i | −0.0157226 | − | 0.230089i | ||||
\(511\) | − | 1.73836i | − | 0.0769003i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −14.2160 | − | 4.69398i | −0.627651 | − | 0.207244i | ||||
\(514\) | −4.08929 | − | 7.08285i | −0.180371 | − | 0.312411i | ||||
\(515\) | −4.48942 | − | 2.59197i | −0.197827 | − | 0.114216i | ||||
\(516\) | 2.52389 | − | 5.15398i | 0.111108 | − | 0.226891i | ||||
\(517\) | −23.8575 | + | 13.7742i | −1.04925 | + | 0.605787i | ||||
\(518\) | −1.66339 | − | 2.88107i | −0.0730850 | − | 0.126587i | ||||
\(519\) | −22.9801 | − | 34.1862i | −1.00871 | − | 1.50061i | ||||
\(520\) | 2.48977 | + | 1.43747i | 0.109184 | + | 0.0630372i | ||||
\(521\) | 26.6298 | + | 15.3747i | 1.16667 | + | 0.673578i | 0.952894 | − | 0.303304i | \(-0.0980897\pi\) |
0.213778 | + | 0.976882i | \(0.431423\pi\) | |||||||
\(522\) | −2.23335 | − | 16.2655i | −0.0977511 | − | 0.711919i | ||||
\(523\) | − | 13.9900i | − | 0.611740i | −0.952073 | − | 0.305870i | \(-0.901053\pi\) | ||
0.952073 | − | 0.305870i | \(-0.0989473\pi\) | |||||||
\(524\) | −0.744839 | − | 0.430033i | −0.0325384 | − | 0.0187861i | ||||
\(525\) | 0.848374 | − | 0.570279i | 0.0370261 | − | 0.0248890i | ||||
\(526\) | − | 1.95456i | − | 0.0852229i | ||||||
\(527\) | 1.10561 | − | 16.7057i | 0.0481610 | − | 0.727711i | ||||
\(528\) | 6.72288 | − | 4.51914i | 0.292576 | − | 0.196670i | ||||
\(529\) | −22.6574 | −0.985103 | ||||||||
\(530\) | 0.900907 | − | 1.56042i | 0.0391329 | − | 0.0677802i | ||||
\(531\) | −8.66758 | − | 3.53396i | −0.376141 | − | 0.153361i | ||||
\(532\) | 0.850207 | + | 1.47260i | 0.0368612 | + | 0.0638454i | ||||
\(533\) | 7.51342 | − | 13.0136i | 0.325443 | − | 0.563683i | ||||
\(534\) | −0.707095 | + | 0.0483176i | −0.0305990 | + | 0.00209091i | ||||
\(535\) | 9.62956 | 0.416322 | ||||||||
\(536\) | 9.99779 | − | 5.77223i | 0.431839 | − | 0.249322i | ||||
\(537\) | 27.9485 | + | 13.6863i | 1.20607 | + | 0.590610i | ||||
\(538\) | 4.37765 | − | 2.52744i | 0.188734 | − | 0.108966i | ||||
\(539\) | 15.5546 | − | 26.9413i | 0.669983 | − | 1.16044i | ||||
\(540\) | 3.45849 | + | 3.87800i | 0.148830 | + | 0.166883i | ||||
\(541\) | 1.99719 | − | 3.45923i | 0.0858657 | − | 0.148724i | −0.819894 | − | 0.572515i | \(-0.805968\pi\) |
0.905760 | + | 0.423791i | \(0.139301\pi\) | |||||||
\(542\) | −9.67395 | −0.415532 | ||||||||
\(543\) | −0.619831 | − | 0.922090i | −0.0265995 | − | 0.0395707i | ||||
\(544\) | −2.60413 | − | 1.50350i | −0.111651 | − | 0.0644618i | ||||
\(545\) | −10.9064 | + | 6.29682i | −0.467179 | + | 0.269726i | ||||
\(546\) | −0.200352 | − | 2.93202i | −0.00857429 | − | 0.125479i | ||||
\(547\) | 11.5236 | + | 19.9595i | 0.492714 | + | 0.853407i | 0.999965 | − | 0.00839225i | \(-0.00267137\pi\) |
−0.507250 | + | 0.861799i | \(0.669338\pi\) | |||||||
\(548\) | −7.56206 | − | 13.0979i | −0.323035 | − | 0.559514i | ||||
\(549\) | 1.26289 | + | 9.19762i | 0.0538989 | + | 0.392545i | ||||
\(550\) | 4.67688i | 0.199423i | ||||||||
\(551\) | −7.88382 | + | 13.6552i | −0.335862 | + | 0.581730i | ||||
\(552\) | −1.01148 | + | 0.0691170i | −0.0430514 | + | 0.00294182i | ||||
\(553\) | 0.493338 | − | 0.284829i | 0.0209789 | − | 0.0121121i | ||||
\(554\) | −16.9377 | −0.719613 | ||||||||
\(555\) | 0.665598 | + | 9.74056i | 0.0282530 | + | 0.413464i | ||||
\(556\) | − | 6.63378i | − | 0.281335i | ||||||
\(557\) | 11.0586 | 0.468570 | 0.234285 | − | 0.972168i | \(-0.424725\pi\) | ||||
0.234285 | + | 0.972168i | \(0.424725\pi\) | |||||||
\(558\) | 9.34804 | + | 13.8425i | 0.395734 | + | 0.585999i | ||||
\(559\) | 9.52549 | 0.402885 | ||||||||
\(560\) | − | 0.590186i | − | 0.0249399i | ||||||
\(561\) | −1.66060 | − | 24.3018i | −0.0701107 | − | 1.02602i | ||||
\(562\) | 23.8706 | 1.00692 | ||||||||
\(563\) | −34.4726 | + | 19.9027i | −1.45285 | + | 0.838801i | −0.998642 | − | 0.0520969i | \(-0.983410\pi\) |
−0.454204 | + | 0.890898i | \(0.650076\pi\) | |||||||
\(564\) | −10.1786 | + | 0.695530i | −0.428596 | + | 0.0292871i | ||||
\(565\) | 3.20709 | − | 5.55484i | 0.134923 | − | 0.233694i | ||||
\(566\) | 25.8177i | 1.08520i | ||||||||
\(567\) | 1.31769 | − | 5.14563i | 0.0553379 | − | 0.216096i | ||||
\(568\) | −0.844440 | − | 1.46261i | −0.0354319 | − | 0.0613699i | ||||
\(569\) | 23.4121 | + | 40.5509i | 0.981485 | + | 1.69998i | 0.656622 | + | 0.754220i | \(0.271985\pi\) |
0.324863 | + | 0.945761i | \(0.394682\pi\) | |||||||
\(570\) | −0.340207 | − | 4.97869i | −0.0142497 | − | 0.208534i | ||||
\(571\) | −33.4816 | + | 19.3306i | −1.40116 | + | 0.808962i | −0.994512 | − | 0.104622i | \(-0.966637\pi\) |
−0.406651 | + | 0.913584i | \(0.633303\pi\) | |||||||
\(572\) | 11.6444 | + | 6.72288i | 0.486875 | + | 0.281098i | ||||
\(573\) | −18.2491 | − | 27.1483i | −0.762369 | − | 1.13414i | ||||
\(574\) | −3.08481 | −0.128757 | ||||||||
\(575\) | 0.292670 | − | 0.506919i | 0.0122052 | − | 0.0211400i | ||||
\(576\) | 2.97211 | − | 0.408090i | 0.123838 | − | 0.0170038i | ||||
\(577\) | 11.0818 | − | 19.1942i | 0.461340 | − | 0.799064i | −0.537688 | − | 0.843144i | \(-0.680702\pi\) |
0.999028 | + | 0.0440797i | \(0.0140356\pi\) | |||||||
\(578\) | 6.89183 | − | 3.97900i | 0.286662 | − | 0.165505i | ||||
\(579\) | −9.92304 | − | 4.85930i | −0.412388 | − | 0.201945i | ||||
\(580\) | 4.73949 | − | 2.73634i | 0.196796 | − | 0.113620i | ||||
\(581\) | −7.01039 | −0.290840 | ||||||||
\(582\) | −22.0841 | + | 1.50906i | −0.915415 | + | 0.0625527i | ||||
\(583\) | 4.21344 | − | 7.29789i | 0.174503 | − | 0.302248i | ||||
\(584\) | 1.47272 | + | 2.55082i | 0.0609416 | + | 0.105554i | ||||
\(585\) | −3.25627 | + | 7.98650i | −0.134630 | + | 0.330201i | ||||
\(586\) | 8.19189 | − | 14.1888i | 0.338404 | − | 0.586133i | ||||
\(587\) | 21.7332 | 0.897027 | 0.448513 | − | 0.893776i | \(-0.351954\pi\) | ||||
0.448513 | + | 0.893776i | \(0.351954\pi\) | |||||||
\(588\) | 9.56159 | − | 6.42733i | 0.394313 | − | 0.265058i | ||||
\(589\) | 1.05934 | − | 16.0066i | 0.0436492 | − | 0.659539i | ||||
\(590\) | − | 3.12011i | − | 0.128453i | ||||||
\(591\) | −18.6104 | + | 12.5099i | −0.765528 | + | 0.514590i | ||||
\(592\) | 4.88163 | + | 2.81841i | 0.200634 | + | 0.115836i | ||||
\(593\) | 13.3440i | 0.547971i | 0.961734 | + | 0.273986i | \(0.0883421\pi\) | ||||
−0.961734 | + | 0.273986i | \(0.911658\pi\) | |||||||
\(594\) | 16.1749 | + | 18.1369i | 0.663665 | + | 0.744168i | ||||
\(595\) | −1.53692 | − | 0.887342i | −0.0630076 | − | 0.0363775i | ||||
\(596\) | −18.2286 | − | 10.5243i | −0.746672 | − | 0.431091i | ||||
\(597\) | 13.8594 | + | 20.6178i | 0.567226 | + | 0.843832i | ||||
\(598\) | −0.841408 | − | 1.45736i | −0.0344077 | − | 0.0595960i | ||||
\(599\) | 24.6222 | − | 14.2156i | 1.00603 | − | 0.580834i | 0.0960062 | − | 0.995381i | \(-0.469393\pi\) |
0.910028 | + | 0.414547i | \(0.136060\pi\) | |||||||
\(600\) | −0.761750 | + | 1.55555i | −0.0310983 | + | 0.0635051i | ||||
\(601\) | −18.4011 | − | 10.6239i | −0.750596 | − | 0.433357i | 0.0753129 | − | 0.997160i | \(-0.476004\pi\) |
−0.825909 | + | 0.563803i | \(0.809338\pi\) | |||||||
\(602\) | −0.977726 | − | 1.69347i | −0.0398491 | − | 0.0690207i | ||||
\(603\) | 21.2357 | + | 27.3590i | 0.864785 | + | 1.11414i | ||||
\(604\) | − | 16.8681i | − | 0.686353i | ||||||
\(605\) | 10.8732i | 0.442060i | ||||||||
\(606\) | 0.693219 | + | 10.1448i | 0.0281601 | + | 0.412103i | ||||
\(607\) | 20.5818 | + | 35.6487i | 0.835389 | + | 1.44694i | 0.893714 | + | 0.448638i | \(0.148091\pi\) |
−0.0583248 | + | 0.998298i | \(0.518576\pi\) | |||||||
\(608\) | −2.49515 | − | 1.44058i | −0.101192 | − | 0.0584231i | ||||
\(609\) | −5.02427 | − | 2.46038i | −0.203594 | − | 0.0996995i | ||||
\(610\) | −2.68004 | + | 1.54732i | −0.108511 | + | 0.0626491i | ||||
\(611\) | −8.46715 | − | 14.6655i | −0.342544 | − | 0.593304i | ||||
\(612\) | 3.40584 | − | 8.35334i | 0.137673 | − | 0.337664i | ||||
\(613\) | 20.0322 | + | 11.5656i | 0.809091 | + | 0.467129i | 0.846640 | − | 0.532166i | \(-0.178622\pi\) |
−0.0375491 | + | 0.999295i | \(0.511955\pi\) | |||||||
\(614\) | 19.5601 | + | 11.2930i | 0.789381 | + | 0.455749i | ||||
\(615\) | 8.13061 | + | 3.98154i | 0.327858 | + | 0.160551i | ||||
\(616\) | − | 2.76023i | − | 0.111213i | ||||||
\(617\) | 18.4259 | + | 10.6382i | 0.741800 | + | 0.428278i | 0.822723 | − | 0.568442i | \(-0.192454\pi\) |
−0.0809236 | + | 0.996720i | \(0.525787\pi\) | |||||||
\(618\) | −5.00908 | − | 7.45175i | −0.201495 | − | 0.299753i | ||||
\(619\) | − | 10.3600i | − | 0.416402i | −0.978086 | − | 0.208201i | \(-0.933239\pi\) | ||
0.978086 | − | 0.208201i | \(-0.0667609\pi\) | |||||||
\(620\) | −3.09622 | + | 4.62746i | −0.124347 | + | 0.185843i | ||||
\(621\) | −0.618199 | − | 2.97803i | −0.0248075 | − | 0.119504i | ||||
\(622\) | −7.76670 | −0.311416 | ||||||||
\(623\) | −0.120750 | + | 0.209145i | −0.00483775 | + | 0.00837922i | ||||
\(624\) | 2.77797 | + | 4.13264i | 0.111208 | + | 0.165438i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −12.1635 | + | 21.0679i | −0.486152 | + | 0.842041i | ||||
\(627\) | −1.59111 | − | 23.2847i | −0.0635427 | − | 0.929903i | ||||
\(628\) | −1.10936 | −0.0442681 | ||||||||
\(629\) | 14.6790 | − | 8.47494i | 0.585291 | − | 0.337918i | ||||
\(630\) | 1.75410 | − | 0.240849i | 0.0698850 | − | 0.00959565i | ||||
\(631\) | 33.6528 | − | 19.4294i | 1.33970 | − | 0.773474i | 0.352934 | − | 0.935648i | \(-0.385184\pi\) |
0.986762 | + | 0.162174i | \(0.0518506\pi\) | |||||||
\(632\) | −0.482609 | + | 0.835902i | −0.0191971 | + | 0.0332504i | ||||
\(633\) | 1.63620 | + | 0.801242i | 0.0650330 | + | 0.0318465i | ||||
\(634\) | −6.27740 | + | 10.8728i | −0.249307 | + | 0.431813i | ||||
\(635\) | −15.2089 | −0.603546 | ||||||||
\(636\) | 2.59005 | − | 1.74104i | 0.102702 | − | 0.0690368i | ||||
\(637\) | 16.5612 | + | 9.56159i | 0.656177 | + | 0.378844i | ||||
\(638\) | 22.1660 | − | 12.7976i | 0.877561 | − | 0.506660i | ||||
\(639\) | 4.00245 | − | 3.10665i | 0.158334 | − | 0.122897i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 4.55356 | + | 7.88700i | 0.179855 | + | 0.311518i | 0.941831 | − | 0.336088i | \(-0.109104\pi\) |
−0.761976 | + | 0.647606i | \(0.775771\pi\) | |||||||
\(642\) | 14.9793 | + | 7.33532i | 0.591184 | + | 0.289502i | ||||
\(643\) | − | 11.1693i | − | 0.440473i | −0.975446 | − | 0.220237i | \(-0.929317\pi\) | ||
0.975446 | − | 0.220237i | \(-0.0706830\pi\) | |||||||
\(644\) | −0.172730 | + | 0.299176i | −0.00680650 | + | 0.0117892i | ||||
\(645\) | 0.391233 | + | 5.72542i | 0.0154048 | + | 0.225438i | ||||
\(646\) | −7.50289 | + | 4.33180i | −0.295197 | + | 0.170432i | ||||
\(647\) | 18.5912 | 0.730894 | 0.365447 | − | 0.930832i | \(-0.380916\pi\) | ||||
0.365447 | + | 0.930832i | \(0.380916\pi\) | |||||||
\(648\) | 2.42578 | + | 8.66692i | 0.0952937 | + | 0.340469i | ||||
\(649\) | − | 14.5924i | − | 0.572801i | ||||||
\(650\) | −2.87494 | −0.112764 | ||||||||
\(651\) | 5.69153 | − | 0.0121882i | 0.223069 | − | 0.000477692i | ||||
\(652\) | 9.25474 | 0.362444 | ||||||||
\(653\) | 42.6892i | 1.67056i | 0.549826 | + | 0.835279i | \(0.314694\pi\) | ||||
−0.549826 | + | 0.835279i | \(0.685306\pi\) | |||||||
\(654\) | −21.7621 | + | 1.48706i | −0.850964 | + | 0.0581486i | ||||
\(655\) | 0.860066 | 0.0336055 | ||||||||
\(656\) | 4.52658 | − | 2.61342i | 0.176733 | − | 0.102037i | ||||
\(657\) | −6.98034 | + | 5.41806i | −0.272329 | + | 0.211379i | ||||
\(658\) | −1.73819 | + | 3.01063i | −0.0677617 | + | 0.117367i | ||||
\(659\) | − | 12.6930i | − | 0.494449i | −0.968958 | − | 0.247225i | \(-0.920481\pi\) | ||
0.968958 | − | 0.247225i | \(-0.0795185\pi\) | |||||||
\(660\) | −3.56262 | + | 7.27513i | −0.138675 | + | 0.283184i | ||||
\(661\) | 18.7942 | + | 32.5526i | 0.731011 | + | 1.26615i | 0.956451 | + | 0.291892i | \(0.0942847\pi\) |
−0.225440 | + | 0.974257i | \(0.572382\pi\) | |||||||
\(662\) | 12.2215 | + | 21.1683i | 0.475004 | + | 0.822731i | ||||
\(663\) | 14.9386 | − | 1.02079i | 0.580167 | − | 0.0396444i | ||||
\(664\) | 10.2869 | − | 5.93914i | 0.399209 | − | 0.230483i | ||||
\(665\) | −1.47260 | − | 0.850207i | −0.0571050 | − | 0.0329696i | ||||
\(666\) | −6.38450 | + | 15.6589i | −0.247394 | + | 0.606772i | ||||
\(667\) | −3.20338 | −0.124035 | ||||||||
\(668\) | −4.64334 | + | 8.04251i | −0.179656 | + | 0.311174i | ||||
\(669\) | 5.94909 | − | 12.1485i | 0.230005 | − | 0.469687i | ||||
\(670\) | −5.77223 | + | 9.99779i | −0.223001 | + | 0.386248i | ||||
\(671\) | −12.5342 | + | 7.23663i | −0.483878 | + | 0.279367i | ||||
\(672\) | 0.449574 | − | 0.918064i | 0.0173427 | − | 0.0354151i | ||||
\(673\) | 7.30862 | − | 4.21963i | 0.281726 | − | 0.162655i | −0.352478 | − | 0.935820i | \(-0.614661\pi\) |
0.634205 | + | 0.773165i | \(0.281328\pi\) | |||||||
\(674\) | −7.97132 | −0.307044 | ||||||||
\(675\) | −4.93414 | − | 1.62920i | −0.189915 | − | 0.0627081i | ||||
\(676\) | 2.36736 | − | 4.10039i | 0.0910523 | − | 0.157707i | ||||
\(677\) | −1.34626 | − | 2.33179i | −0.0517410 | − | 0.0896180i | 0.838995 | − | 0.544139i | \(-0.183144\pi\) |
−0.890736 | + | 0.454521i | \(0.849810\pi\) | |||||||
\(678\) | 9.22018 | − | 6.19783i | 0.354099 | − | 0.238026i | ||||
\(679\) | −3.77128 | + | 6.53205i | −0.144729 | + | 0.250677i | ||||
\(680\) | 3.00699 | 0.115313 | ||||||||
\(681\) | 20.2056 | + | 30.0588i | 0.774280 | + | 1.15185i | ||||
\(682\) | −14.4807 | + | 21.6421i | −0.554494 | + | 0.828718i | ||||
\(683\) | − | 14.9285i | − | 0.571223i | −0.958345 | − | 0.285612i | \(-0.907803\pi\) | ||
0.958345 | − | 0.285612i | \(-0.0921967\pi\) | |||||||
\(684\) | 3.26331 | − | 8.00376i | 0.124776 | − | 0.306031i | ||||
\(685\) | 13.0979 | + | 7.56206i | 0.500444 | + | 0.288932i | ||||
\(686\) | − | 8.05703i | − | 0.307619i | ||||||
\(687\) | −10.8873 | + | 22.2327i | −0.415376 | + | 0.848229i | ||||
\(688\) | 2.86939 | + | 1.65664i | 0.109394 | + | 0.0631589i | ||||
\(689\) | 4.48611 | + | 2.59005i | 0.170907 | + | 0.0986732i | ||||
\(690\) | 0.841408 | − | 0.565597i | 0.0320319 | − | 0.0215319i | ||||
\(691\) | −1.72141 | − | 2.98157i | −0.0654856 | − | 0.113424i | 0.831424 | − | 0.555639i | \(-0.187526\pi\) |
−0.896909 | + | 0.442215i | \(0.854193\pi\) | |||||||
\(692\) | 20.5960 | − | 11.8911i | 0.782942 | − | 0.452032i | ||||
\(693\) | 8.20372 | − | 1.12642i | 0.311633 | − | 0.0427892i | ||||
\(694\) | −26.5142 | − | 15.3080i | −1.00647 | − | 0.581083i | ||||
\(695\) | 3.31689 | + | 5.74502i | 0.125817 | + | 0.217921i | ||||
\(696\) | 9.45692 | − | 0.646216i | 0.358464 | − | 0.0244948i | ||||
\(697\) | − | 15.7171i | − | 0.595326i | ||||||
\(698\) | − | 21.2775i | − | 0.805364i | ||||||
\(699\) | −28.6615 | + | 1.95852i | −1.08408 | + | 0.0740779i | ||||
\(700\) | 0.295093 | + | 0.511116i | 0.0111535 | + | 0.0193184i | ||||
\(701\) | −12.4708 | − | 7.20002i | −0.471015 | − | 0.271941i | 0.245649 | − | 0.969359i | \(-0.420999\pi\) |
−0.716665 | + | 0.697418i | \(0.754332\pi\) | |||||||
\(702\) | −11.1490 | + | 9.94294i | −0.420793 | + | 0.375272i | ||||
\(703\) | 14.0647 | − | 8.12027i | 0.530461 | − | 0.306262i | ||||
\(704\) | 2.33844 | + | 4.05030i | 0.0881333 | + | 0.152651i | ||||
\(705\) | 8.46715 | − | 5.69164i | 0.318891 | − | 0.214360i | ||||
\(706\) | −19.6918 | − | 11.3691i | −0.741111 | − | 0.427881i | ||||
\(707\) | 3.00063 | + | 1.73242i | 0.112850 | + | 0.0651542i | ||||
\(708\) | 2.37674 | − | 4.85349i | 0.0893235 | − | 0.182405i | ||||
\(709\) | − | 29.8336i | − | 1.12043i | −0.828349 | − | 0.560213i | \(-0.810719\pi\) | ||
0.828349 | − | 0.560213i | \(-0.189281\pi\) | |||||||
\(710\) | 1.46261 | + | 0.844440i | 0.0548909 | + | 0.0316913i | ||||
\(711\) | −2.68135 | − | 1.09324i | −0.100558 | − | 0.0409999i | ||||
\(712\) | − | 0.409193i | − | 0.0153352i | ||||||
\(713\) | 2.92385 | − | 1.43958i | 0.109499 | − | 0.0539126i | ||||
\(714\) | −1.71483 | − | 2.55105i | −0.0641757 | − | 0.0954708i | ||||
\(715\) | −13.4458 | −0.502843 | ||||||||
\(716\) | −8.98349 | + | 15.5599i | −0.335729 | + | 0.581499i | ||||
\(717\) | 6.63020 | − | 4.45684i | 0.247609 | − | 0.166444i | ||||
\(718\) | −0.750465 | − | 1.29984i | −0.0280071 | − | 0.0485097i | ||||
\(719\) | −6.94656 | + | 12.0318i | −0.259063 | + | 0.448710i | −0.965991 | − | 0.258575i | \(-0.916747\pi\) |
0.706928 | + | 0.707285i | \(0.250080\pi\) | |||||||
\(720\) | −2.36988 | + | 1.83947i | −0.0883203 | + | 0.0685531i | ||||
\(721\) | −3.05948 | −0.113941 | ||||||||
\(722\) | 9.26558 | − | 5.34948i | 0.344829 | − | 0.199087i | ||||
\(723\) | −16.2226 | + | 33.1277i | −0.603324 | + | 1.23203i | ||||
\(724\) | 0.555527 | − | 0.320734i | 0.0206460 | − | 0.0119200i | ||||
\(725\) | −2.73634 | + | 4.73949i | −0.101625 | + | 0.176020i | ||||
\(726\) | −8.28268 | + | 16.9139i | −0.307399 | + | 0.627732i | ||||
\(727\) | 0.865765 | − | 1.49955i | 0.0321095 | − | 0.0556152i | −0.849524 | − | 0.527550i | \(-0.823111\pi\) |
0.881634 | + | 0.471935i | \(0.156444\pi\) | |||||||
\(728\) | 1.69675 | 0.0628857 | ||||||||
\(729\) | −24.7692 | + | 10.7466i | −0.917376 | + | 0.398022i | ||||
\(730\) | −2.55082 | − | 1.47272i | −0.0944103 | − | 0.0545078i | ||||
\(731\) | 8.62822 | − | 4.98151i | 0.319126 | − | 0.184248i | ||||
\(732\) | −5.34760 | + | 0.365416i | −0.197653 | + | 0.0135062i | ||||
\(733\) | 16.9702 | + | 29.3932i | 0.626808 | + | 1.08566i | 0.988188 | + | 0.153245i | \(0.0489724\pi\) |
−0.361380 | + | 0.932419i | \(0.617694\pi\) | |||||||
\(734\) | 1.40472 | + | 2.43304i | 0.0518490 | + | 0.0898051i | ||||
\(735\) | −5.06692 | + | 10.3470i | −0.186896 | + | 0.381656i | ||||
\(736\) | − | 0.585340i | − | 0.0215759i | ||||||
\(737\) | −26.9960 | + | 46.7585i | −0.994412 | + | 1.72237i | ||||
\(738\) | 9.61463 | + | 12.3870i | 0.353919 | + | 0.455971i | ||||
\(739\) | −25.3227 | + | 14.6201i | −0.931511 | + | 0.537808i | −0.887289 | − | 0.461213i | \(-0.847414\pi\) |
−0.0442221 | + | 0.999022i | \(0.514081\pi\) | |||||||
\(740\) | −5.63683 | −0.207214 | ||||||||
\(741\) | 14.3134 | − | 0.978075i | 0.525817 | − | 0.0359305i | ||||
\(742\) | − | 1.06341i | − | 0.0390388i | ||||||
\(743\) | 50.4374 | 1.85037 | 0.925184 | − | 0.379519i | \(-0.123910\pi\) | ||||
0.925184 | + | 0.379519i | \(0.123910\pi\) | |||||||
\(744\) | −8.34130 | + | 4.83970i | −0.305807 | + | 0.177432i | ||||
\(745\) | 21.0486 | 0.771159 | ||||||||
\(746\) | − | 21.9797i | − | 0.804734i | ||||||
\(747\) | 21.8498 | + | 28.1501i | 0.799442 | + | 1.02996i | ||||
\(748\) | 14.0633 | 0.514207 | ||||||||
\(749\) | 4.92182 | − | 2.84161i | 0.179839 | − | 0.103830i | ||||
\(750\) | −0.118080 | − | 1.72802i | −0.00431168 | − | 0.0630984i | ||||
\(751\) | 20.3241 | − | 35.2024i | 0.741637 | − | 1.28455i | −0.210112 | − | 0.977677i | \(-0.567383\pi\) |
0.951749 | − | 0.306876i | \(-0.0992837\pi\) | |||||||
\(752\) | − | 5.89031i | − | 0.214798i | ||||||
\(753\) | −42.5833 | − | 20.8530i | −1.55182 | − | 0.759924i | ||||
\(754\) | 7.86682 | + | 13.6257i | 0.286493 | + | 0.496220i | ||||
\(755\) | 8.43405 | + | 14.6082i | 0.306946 | + | 0.531647i | ||||
\(756\) | 2.91206 | + | 0.961533i | 0.105910 | + | 0.0349706i | ||||
\(757\) | −9.92590 | + | 5.73072i | −0.360763 | + | 0.208287i | −0.669415 | − | 0.742888i | \(-0.733455\pi\) |
0.308652 | + | 0.951175i | \(0.400122\pi\) | |||||||
\(758\) | 17.6768 | + | 10.2057i | 0.642051 | + | 0.370688i | ||||
\(759\) | 3.93517 | − | 2.64523i | 0.142838 | − | 0.0960158i | ||||
\(760\) | 2.88115 | 0.104510 | ||||||||
\(761\) | 12.8069 | − | 22.1823i | 0.464251 | − | 0.804106i | −0.534917 | − | 0.844905i | \(-0.679657\pi\) |
0.999167 | + | 0.0407988i | \(0.0129903\pi\) | |||||||
\(762\) | −23.6582 | − | 11.5854i | −0.857046 | − | 0.419694i | ||||
\(763\) | −3.71629 | + | 6.43681i | −0.134539 | + | 0.233028i | ||||
\(764\) | 16.3559 | − | 9.44308i | 0.591735 | − | 0.341639i | ||||
\(765\) | 1.22712 | + | 8.93712i | 0.0443668 | + | 0.323122i | ||||
\(766\) | 27.7563 | − | 16.0251i | 1.00288 | − | 0.579011i | ||||
\(767\) | 8.97013 | 0.323893 | ||||||||
\(768\) | 0.118080 | + | 1.72802i | 0.00426085 | + | 0.0623546i | ||||
\(769\) | −23.5436 | + | 40.7787i | −0.849004 | + | 1.47052i | 0.0330933 | + | 0.999452i | \(0.489464\pi\) |
−0.882098 | + | 0.471067i | \(0.843869\pi\) | |||||||
\(770\) | 1.38011 | + | 2.39043i | 0.0497359 | + | 0.0861451i | ||||
\(771\) | 7.90272 | + | 11.7565i | 0.284609 | + | 0.423398i | ||||
\(772\) | 3.18956 | − | 5.52448i | 0.114795 | − | 0.198830i | ||||
\(773\) | −0.831188 | −0.0298958 | −0.0149479 | − | 0.999888i | \(-0.504758\pi\) | ||||
−0.0149479 | + | 0.999888i | \(0.504758\pi\) | |||||||
\(774\) | −3.75276 | + | 9.20421i | −0.134890 | + | 0.330838i | ||||
\(775\) | 0.367679 | − | 5.55561i | 0.0132074 | − | 0.199563i | ||||
\(776\) | − | 12.7800i | − | 0.458775i | ||||||
\(777\) | 3.21457 | + | 4.78214i | 0.115322 | + | 0.171558i | ||||
\(778\) | −32.3290 | − | 18.6651i | −1.15905 | − | 0.669178i | ||||
\(779\) | − | 15.0593i | − | 0.539556i | ||||||
\(780\) | −4.47211 | − | 2.18999i | −0.160127 | − | 0.0784141i | ||||
\(781\) | 6.84047 | + | 3.94935i | 0.244771 | + | 0.141319i | ||||
\(782\) | −1.52430 | − | 0.880056i | −0.0545089 | − | 0.0314707i | ||||
\(783\) | 5.77990 | + | 27.8433i | 0.206557 | + | 0.995039i | ||||
\(784\) | 3.32584 | + | 5.76052i | 0.118780 | + | 0.205733i | ||||
\(785\) | 0.960730 | − | 0.554678i | 0.0342899 | − | 0.0197973i | ||||
\(786\) | 1.33788 | + | 0.655155i | 0.0477204 | + | 0.0233686i | ||||
\(787\) | 25.4996 | + | 14.7222i | 0.908961 | + | 0.524789i | 0.880097 | − | 0.474794i | \(-0.157478\pi\) |
0.0288644 | + | 0.999583i | \(0.490811\pi\) | |||||||
\(788\) | −6.47331 | − | 11.2121i | −0.230602 | − | 0.399414i | ||||
\(789\) | 0.230795 | + | 3.37752i | 0.00821651 | + | 0.120243i | ||||
\(790\) | − | 0.965217i | − | 0.0343409i | ||||||
\(791\) | − | 3.78555i | − | 0.134599i | ||||||
\(792\) | −11.0837 | + | 8.60300i | −0.393841 | + | 0.305694i | ||||
\(793\) | −4.44845 | − | 7.70494i | −0.157969 | − | 0.273611i | ||||
\(794\) | −31.2296 | − | 18.0304i | −1.10830 | − | 0.639876i | ||||
\(795\) | −1.37253 | + | 2.80281i | −0.0486787 | + | 0.0994055i | ||||
\(796\) | −12.4215 | + | 7.17157i | −0.440269 | + | 0.254190i | ||||
\(797\) | 13.6953 | + | 23.7209i | 0.485111 | + | 0.840237i | 0.999854 | − | 0.0171076i | \(-0.00544579\pi\) |
−0.514742 | + | 0.857345i | \(0.672112\pi\) | |||||||
\(798\) | −1.64306 | − | 2.44429i | −0.0581637 | − | 0.0865271i | ||||
\(799\) | −15.3391 | − | 8.85606i | −0.542660 | − | 0.313305i | ||||
\(800\) | −0.866025 | − | 0.500000i | −0.0306186 | − | 0.0176777i | ||||
\(801\) | 1.21617 | − | 0.166988i | 0.0429712 | − | 0.00590022i | ||||
\(802\) | 36.7308i | 1.29701i | ||||||||
\(803\) | −11.9299 | − | 6.88773i | −0.420997 | − | 0.243063i | ||||
\(804\) | −16.5948 | + | 11.1551i | −0.585254 | + | 0.393409i | ||||
\(805\) | − | 0.345459i | − | 0.0121758i | ||||||
\(806\) | −13.3037 | − | 8.90146i | −0.468602 | − | 0.313541i | ||||
\(807\) | −7.26624 | + | 4.88438i | −0.255784 | + | 0.171938i | ||||
\(808\) | −5.87075 | −0.206532 | ||||||||
\(809\) | −3.74578 | + | 6.48788i | −0.131695 | + | 0.228102i | −0.924330 | − | 0.381594i | \(-0.875375\pi\) |
0.792635 | + | 0.609696i | \(0.208709\pi\) | |||||||
\(810\) | −6.43425 | − | 6.29289i | −0.226077 | − | 0.221109i | ||||
\(811\) | 0.458412 | + | 0.793993i | 0.0160970 | + | 0.0278809i | 0.873962 | − | 0.485995i | \(-0.161543\pi\) |
−0.857865 | + | 0.513876i | \(0.828209\pi\) | |||||||
\(812\) | 1.61495 | − | 2.79718i | 0.0566737 | − | 0.0981617i | ||||
\(813\) | 16.7168 | − | 1.14230i | 0.586283 | − | 0.0400623i | ||||
\(814\) | −26.3628 | −0.924015 | ||||||||
\(815\) | −8.01484 | + | 4.62737i | −0.280748 | + | 0.162090i | ||||
\(816\) | 4.67753 | + | 2.29058i | 0.163746 | + | 0.0801862i | ||||
\(817\) | 8.26714 | − | 4.77303i | 0.289231 | − | 0.166987i | ||||
\(818\) | 17.3034 | − | 29.9703i | 0.604999 | − | 1.04789i | ||||
\(819\) | 0.692426 | + | 5.04293i | 0.0241953 | + | 0.176214i | ||||
\(820\) | −2.61342 | + | 4.52658i | −0.0912646 | + | 0.158075i | ||||
\(821\) | −1.80737 | −0.0630775 | −0.0315388 | − | 0.999503i | \(-0.510041\pi\) | ||||
−0.0315388 | + | 0.999503i | \(0.510041\pi\) | |||||||
\(822\) | 14.6140 | + | 21.7405i | 0.509722 | + | 0.758286i | ||||
\(823\) | 20.8385 | + | 12.0311i | 0.726386 | + | 0.419379i | 0.817098 | − | 0.576498i | \(-0.195581\pi\) |
−0.0907129 | + | 0.995877i | \(0.528915\pi\) | |||||||
\(824\) | 4.48942 | − | 2.59197i | 0.156396 | − | 0.0902954i | ||||
\(825\) | −0.552247 | − | 8.08175i | −0.0192268 | − | 0.281370i | ||||
\(826\) | −0.920722 | − | 1.59474i | −0.0320360 | − | 0.0554880i | ||||
\(827\) | −26.1422 | − | 45.2796i | −0.909052 | − | 1.57452i | −0.815384 | − | 0.578921i | \(-0.803474\pi\) |
−0.0936684 | − | 0.995603i | \(-0.529859\pi\) | |||||||
\(828\) | 1.73970 | − | 0.238871i | 0.0604586 | − | 0.00830136i | ||||
\(829\) | − | 32.6536i | − | 1.13411i | −0.823681 | − | 0.567054i | \(-0.808083\pi\) | ||
0.823681 | − | 0.567054i | \(-0.191917\pi\) | |||||||
\(830\) | −5.93914 | + | 10.2869i | −0.206151 | + | 0.357063i | ||||
\(831\) | 29.2687 | − | 2.00000i | 1.01532 | − | 0.0693794i | ||||
\(832\) | −2.48977 | + | 1.43747i | −0.0863173 | + | 0.0498353i | ||||
\(833\) | 20.0015 | 0.693013 | ||||||||
\(834\) | 0.783318 | + | 11.4633i | 0.0271241 | + | 0.396942i | ||||
\(835\) | − | 9.28669i | − | 0.321379i | ||||||
\(836\) | 13.4748 | 0.466036 | ||||||||
\(837\) | −17.7881 | − | 22.8163i | −0.614848 | − | 0.788646i | ||||
\(838\) | −2.99848 | −0.103581 | ||||||||
\(839\) | 28.5391i | 0.985281i | 0.870233 | + | 0.492640i | \(0.163968\pi\) | ||||
−0.870233 | + | 0.492640i | \(0.836032\pi\) | |||||||
\(840\) | 0.0696893 | + | 1.01985i | 0.00240451 | + | 0.0351883i | ||||
\(841\) | 0.950308 | 0.0327692 | ||||||||
\(842\) | −17.2211 | + | 9.94262i | −0.593479 | + | 0.342645i | ||||
\(843\) | −41.2488 | + | 2.81864i | −1.42069 | + | 0.0970792i | ||||
\(844\) | −0.525922 | + | 0.910924i | −0.0181030 | + | 0.0313553i | ||||
\(845\) | 4.73472i | 0.162879i | ||||||||
\(846\) | 17.5067 | − | 2.40378i | 0.601892 | − | 0.0826436i | ||||
\(847\) | 3.20861 | + | 5.55748i | 0.110249 | + | 0.190957i | ||||
\(848\) | 0.900907 | + | 1.56042i | 0.0309373 | + | 0.0535849i | ||||
\(849\) | −3.04856 | − | 44.6136i | −0.104626 | − | 1.53113i | ||||
\(850\) | −2.60413 | + | 1.50350i | −0.0893210 | + | 0.0515695i | ||||
\(851\) | 2.85741 | + | 1.64973i | 0.0979509 | + | 0.0565520i | ||||
\(852\) | 1.63192 | + | 2.42772i | 0.0559085 | + | 0.0831722i | ||||
\(853\) | 17.2191 | 0.589572 | 0.294786 | − | 0.955563i | \(-0.404752\pi\) | ||||
0.294786 | + | 0.955563i | \(0.404752\pi\) | |||||||
\(854\) | −0.913206 | + | 1.58172i | −0.0312493 | + | 0.0541253i | ||||
\(855\) | 1.17577 | + | 8.56311i | 0.0402105 | + | 0.292852i | ||||
\(856\) | −4.81478 | + | 8.33944i | −0.164566 | + | 0.285036i | ||||
\(857\) | −43.7696 | + | 25.2704i | −1.49514 | + | 0.863221i | −0.999984 | − | 0.00558224i | \(-0.998223\pi\) |
−0.495158 | + | 0.868803i | \(0.664890\pi\) | |||||||
\(858\) | −20.9156 | − | 10.2423i | −0.714045 | − | 0.349667i | ||||
\(859\) | 1.79144 | − | 1.03429i | 0.0611230 | − | 0.0352894i | −0.469127 | − | 0.883131i | \(-0.655431\pi\) |
0.530250 | + | 0.847841i | \(0.322098\pi\) | |||||||
\(860\) | −3.31328 | −0.112982 | ||||||||
\(861\) | 5.33061 | − | 0.364254i | 0.181667 | − | 0.0124138i | ||||
\(862\) | 3.21903 | − | 5.57553i | 0.109641 | − | 0.189903i | ||||
\(863\) | 3.41935 | + | 5.92248i | 0.116396 | + | 0.201604i | 0.918337 | − | 0.395800i | \(-0.129533\pi\) |
−0.801941 | + | 0.597403i | \(0.796199\pi\) | |||||||
\(864\) | −5.08769 | + | 1.05614i | −0.173087 | + | 0.0359305i | ||||
\(865\) | −11.8911 | + | 20.5960i | −0.404310 | + | 0.700285i | ||||
\(866\) | −29.7643 | −1.01143 | ||||||||
\(867\) | −11.4394 | + | 7.68959i | −0.388502 | + | 0.261152i | ||||
\(868\) | −0.216999 | + | 3.27884i | −0.00736541 | + | 0.111291i | ||||
\(869\) | − | 4.51421i | − | 0.153134i | ||||||
\(870\) | −7.86682 | + | 5.28810i | −0.266710 | + | 0.179283i | ||||
\(871\) | −28.7431 | − | 16.5948i | −0.973921 | − | 0.562294i | ||||
\(872\) | − | 12.5936i | − | 0.426474i | ||||||
\(873\) | 37.9836 | − | 5.21539i | 1.28555 | − | 0.176514i | ||||
\(874\) | −1.46051 | − | 0.843226i | −0.0494025 | − | 0.0285225i | ||||
\(875\) | −0.511116 | − | 0.295093i | −0.0172789 | − | 0.00997596i | ||||
\(876\) | −2.84609 | − | 4.23398i | −0.0961605 | − | 0.143053i | ||||
\(877\) | 21.8766 | + | 37.8914i | 0.738721 | + | 1.27950i | 0.953071 | + | 0.302746i | \(0.0979034\pi\) |
−0.214350 | + | 0.976757i | \(0.568763\pi\) | |||||||
\(878\) | 34.2079 | − | 19.7500i | 1.15446 | − | 0.666529i | ||||
\(879\) | −12.4803 | + | 25.4858i | −0.420952 | + | 0.859614i | ||||
\(880\) | −4.05030 | − | 2.33844i | −0.136536 | − | 0.0788288i | ||||
\(881\) | 11.3488 | + | 19.6568i | 0.382352 | + | 0.662253i | 0.991398 | − | 0.130882i | \(-0.0417808\pi\) |
−0.609046 | + | 0.793135i | \(0.708447\pi\) | |||||||
\(882\) | −15.7637 | + | 12.2356i | −0.530791 | + | 0.411994i | ||||
\(883\) | − | 31.4192i | − | 1.05734i | −0.848828 | − | 0.528670i | \(-0.822691\pi\) | ||
0.848828 | − | 0.528670i | \(-0.177309\pi\) | |||||||
\(884\) | 8.64492i | 0.290760i | ||||||||
\(885\) | 0.368423 | + | 5.39162i | 0.0123844 | + | 0.181237i | ||||
\(886\) | 6.09717 | + | 10.5606i | 0.204839 | + | 0.354791i | ||||
\(887\) | 0.322462 | + | 0.186174i | 0.0108272 | + | 0.00625110i | 0.505404 | − | 0.862883i | \(-0.331344\pi\) |
−0.494577 | + | 0.869134i | \(0.664677\pi\) | |||||||
\(888\) | −8.76837 | − | 4.29385i | −0.294247 | − | 0.144092i | ||||
\(889\) | −7.77350 | + | 4.48803i | −0.260715 | + | 0.150524i | ||||
\(890\) | 0.204597 | + | 0.354372i | 0.00685810 | + | 0.0118786i | ||||
\(891\) | −30.0922 | − | 29.4311i | −1.00813 | − | 0.985979i | ||||
\(892\) | 6.76345 | + | 3.90488i | 0.226457 | + | 0.130745i | ||||
\(893\) | −14.6972 | − | 8.48544i | −0.491824 | − | 0.283954i | ||||
\(894\) | 32.7421 | + | 16.0337i | 1.09506 | + | 0.536248i | ||||
\(895\) | − | 17.9670i | − | 0.600570i | ||||||
\(896\) | 0.511116 | + | 0.295093i | 0.0170752 | + | 0.00985836i | ||||
\(897\) | 1.62606 | + | 2.41900i | 0.0542925 | + | 0.0807680i | ||||
\(898\) | − | 1.10717i | − | 0.0369468i | ||||||
\(899\) | −27.3368 | + | 13.4595i | −0.911735 | + | 0.448898i | ||||
\(900\) | 1.13264 | − | 2.77797i | 0.0377547 | − | 0.0925990i | ||||
\(901\) | 5.41804 | 0.180501 | ||||||||
\(902\) | −12.2227 | + | 21.1703i | −0.406970 | + | 0.704893i | ||||
\(903\) | 1.88950 | + | 2.81090i | 0.0628785 | + | 0.0935410i | ||||
\(904\) | 3.20709 | + | 5.55484i | 0.106666 | + | 0.184751i | ||||
\(905\) | −0.320734 | + | 0.555527i | −0.0106615 | + | 0.0184663i | ||||
\(906\) | 1.99179 | + | 29.1484i | 0.0661727 | + | 0.968392i | ||||
\(907\) | 8.92989 | 0.296512 | 0.148256 | − | 0.988949i | \(-0.452634\pi\) | ||||
0.148256 | + | 0.988949i | \(0.452634\pi\) | |||||||
\(908\) | −18.1094 | + | 10.4554i | −0.600980 | + | 0.346976i | ||||
\(909\) | −2.39580 | − | 17.4485i | −0.0794635 | − | 0.578731i | ||||
\(910\) | −1.46943 | + | 0.848374i | −0.0487110 | + | 0.0281233i | ||||
\(911\) | −0.293706 | + | 0.508715i | −0.00973093 | + | 0.0168545i | −0.870850 | − | 0.491549i | \(-0.836431\pi\) |
0.861119 | + | 0.508404i | \(0.169764\pi\) | |||||||
\(912\) | 4.48178 | + | 2.19472i | 0.148406 | + | 0.0726743i | ||||
\(913\) | −27.7767 | + | 48.1106i | −0.919273 | + | 1.59223i | ||||
\(914\) | −8.27976 | −0.273870 | ||||||||
\(915\) | 4.44845 | − | 2.99026i | 0.147061 | − | 0.0988550i | ||||
\(916\) | −12.3777 | − | 7.14624i | −0.408969 | − | 0.236118i | ||||
\(917\) | 0.439593 | − | 0.253799i | 0.0145166 | − | 0.00838119i | ||||
\(918\) | −4.89900 | + | 14.8369i | −0.161691 | + | 0.489691i | ||||
\(919\) | −7.00363 | − | 12.1306i | −0.231028 | − | 0.400153i | 0.727083 | − | 0.686550i | \(-0.240876\pi\) |
−0.958111 | + | 0.286397i | \(0.907542\pi\) | |||||||
\(920\) | 0.292670 | + | 0.506919i | 0.00964904 | + | 0.0167126i | ||||
\(921\) | −35.1337 | − | 17.2049i | −1.15770 | − | 0.566921i | ||||
\(922\) | 19.4170i | 0.639463i | ||||||||
\(923\) | −2.42772 | + | 4.20493i | −0.0799092 | + | 0.138407i | ||||
\(924\) | 0.325928 | + | 4.76973i | 0.0107223 | + | 0.156913i | ||||
\(925\) | 4.88163 | − | 2.81841i | 0.160507 | − | 0.0926689i | ||||
\(926\) | 34.1138 | 1.12105 | ||||||||
\(927\) | 9.53571 | + | 12.2853i | 0.313194 | + | 0.403502i | ||||
\(928\) | 5.47269i | 0.179650i | ||||||||
\(929\) | 1.83007 | 0.0600427 | 0.0300214 | − | 0.999549i | \(-0.490442\pi\) | ||||
0.0300214 | + | 0.999549i | \(0.490442\pi\) | |||||||
\(930\) | 4.80393 | − | 8.36195i | 0.157527 | − | 0.274199i | ||||
\(931\) | 19.1645 | 0.628091 | ||||||||
\(932\) | − | 16.5863i | − | 0.543303i | ||||||
\(933\) | 13.4210 | − | 0.917094i | 0.439385 | − | 0.0300243i | ||||
\(934\) | −25.2788 | −0.827148 | ||||||||
\(935\) | −12.1792 | + | 7.03167i | −0.398303 | + | 0.229960i | ||||
\(936\) | −5.28838 | − | 6.81327i | −0.172856 | − | 0.222699i | ||||
\(937\) | 6.77296 | − | 11.7311i | 0.221263 | − | 0.383239i | −0.733929 | − | 0.679226i | \(-0.762315\pi\) |
0.955192 | + | 0.295988i | \(0.0956487\pi\) | |||||||
\(938\) | 6.81337i | 0.222464i | ||||||||
\(939\) | 18.5311 | − | 37.8420i | 0.604741 | − | 1.23493i | ||||
\(940\) | 2.94516 | + | 5.10116i | 0.0960604 | + | 0.166382i | ||||
\(941\) | −8.67450 | − | 15.0247i | −0.282781 | − | 0.489790i | 0.689288 | − | 0.724487i | \(-0.257923\pi\) |
−0.972069 | + | 0.234697i | \(0.924590\pi\) | |||||||
\(942\) | 1.91699 | − | 0.130993i | 0.0624589 | − | 0.00426798i | ||||
\(943\) | 2.64958 | − | 1.52974i | 0.0862823 | − | 0.0498151i | ||||
\(944\) | 2.70209 | + | 1.56005i | 0.0879457 | + | 0.0507755i | ||||
\(945\) | −3.00268 | + | 0.623317i | −0.0976772 | + | 0.0202765i | ||||
\(946\) | −15.4958 | −0.503813 | ||||||||
\(947\) | −7.70416 | + | 13.3440i | −0.250352 | + | 0.433622i | −0.963623 | − | 0.267267i | \(-0.913880\pi\) |
0.713271 | + | 0.700888i | \(0.247213\pi\) | |||||||
\(948\) | 0.735254 | − | 1.50144i | 0.0238799 | − | 0.0487646i | ||||
\(949\) | 4.23398 | − | 7.33347i | 0.137441 | − | 0.238054i | ||||
\(950\) | −2.49515 | + | 1.44058i | −0.0809534 | + | 0.0467384i | ||||
\(951\) | 9.56362 | − | 19.5296i | 0.310122 | − | 0.633292i | ||||
\(952\) | 1.53692 | − | 0.887342i | 0.0498119 | − | 0.0287589i | ||||
\(953\) | 11.3217 | 0.366744 | 0.183372 | − | 0.983044i | \(-0.441299\pi\) | ||||
0.183372 | + | 0.983044i | \(0.441299\pi\) | |||||||
\(954\) | −4.27009 | + | 3.31439i | −0.138249 | + | 0.107307i | ||||
\(955\) | −9.44308 | + | 16.3559i | −0.305571 | + | 0.529264i | ||||
\(956\) | 2.30620 | + | 3.99446i | 0.0745880 | + | 0.129190i | ||||
\(957\) | −36.7922 | + | 24.7318i | −1.18932 | + | 0.799466i | ||||
\(958\) | 9.30670 | − | 16.1197i | 0.300686 | − | 0.520803i | ||||
\(959\) | 8.92604 | 0.288237 | ||||||||
\(960\) | −0.966271 | − | 1.43747i | −0.0311863 | − | 0.0463941i | ||||
\(961\) | 18.9028 | − | 24.5700i | 0.609769 | − | 0.792579i | ||||
\(962\) | − | 16.2055i | − | 0.522488i | ||||||
\(963\) | −26.7506 | − | 10.9068i | −0.862027 | − | 0.351468i | ||||
\(964\) | −18.4433 | − | 10.6482i | −0.594018 | − | 0.342956i | ||||
\(965\) | 6.37912i | 0.205351i | ||||||||
\(966\) | 0.263154 | − | 0.537379i | 0.00846683 | − | 0.0172899i | ||||
\(967\) | −22.2534 | − | 12.8480i | −0.715620 | − | 0.413163i | 0.0975186 | − | 0.995234i | \(-0.468909\pi\) |
−0.813138 | + | 0.582070i | \(0.802243\pi\) | |||||||
\(968\) | −9.41649 | − | 5.43661i | −0.302658 | − | 0.174739i | ||||
\(969\) | 12.4537 | − | 8.37138i | 0.400069 | − | 0.268928i | ||||
\(970\) | 6.38999 | + | 11.0678i | 0.205170 | + | 0.355365i | ||||
\(971\) | −13.0504 | + | 7.53462i | −0.418806 | + | 0.241798i | −0.694566 | − | 0.719429i | \(-0.744404\pi\) |
0.275761 | + | 0.961226i | \(0.411070\pi\) | |||||||
\(972\) | −5.21519 | − | 14.6902i | −0.167277 | − | 0.471188i | ||||
\(973\) | 3.39063 | + | 1.95758i | 0.108699 | + | 0.0627572i | ||||
\(974\) | −3.51817 | − | 6.09365i | −0.112730 | − | 0.195253i | ||||
\(975\) | 4.96796 | − | 0.339474i | 0.159102 | − | 0.0108719i | ||||
\(976\) | − | 3.09464i | − | 0.0990570i | ||||||
\(977\) | 45.0714i | 1.44196i | 0.692956 | + | 0.720980i | \(0.256308\pi\) | ||||
−0.692956 | + | 0.720980i | \(0.743692\pi\) | |||||||
\(978\) | −15.9924 | + | 1.09280i | −0.511380 | + | 0.0349439i | ||||
\(979\) | 0.956875 | + | 1.65736i | 0.0305818 | + | 0.0529693i | ||||
\(980\) | −5.76052 | − | 3.32584i | −0.184013 | − | 0.106240i | ||||
\(981\) | 37.4297 | − | 5.13934i | 1.19504 | − | 0.164086i | ||||
\(982\) | −22.8777 | + | 13.2084i | −0.730056 | + | 0.421498i | ||||
\(983\) | −19.1329 | − | 33.1392i | −0.610245 | − | 1.05697i | −0.991199 | − | 0.132381i | \(-0.957738\pi\) |
0.380954 | − | 0.924594i | \(-0.375596\pi\) | |||||||
\(984\) | −7.51342 | + | 5.05054i | −0.239519 | + | 0.161005i | ||||
\(985\) | 11.2121 | + | 6.47331i | 0.357247 | + | 0.206257i | ||||
\(986\) | 14.2516 | + | 8.22816i | 0.453863 | + | 0.262038i | ||||
\(987\) | 2.64813 | − | 5.40768i | 0.0842910 | − | 0.172128i | ||||
\(988\) | 8.28314i | 0.263522i | ||||||||
\(989\) | 1.67957 | + | 0.969698i | 0.0534071 | + | 0.0308346i | ||||
\(990\) | 5.29723 | − | 12.9922i | 0.168357 | − | 0.412921i | ||||
\(991\) | 25.5729i | 0.812351i | 0.913795 | + | 0.406176i | \(0.133138\pi\) | ||||
−0.913795 | + | 0.406176i | \(0.866862\pi\) | |||||||
\(992\) | −2.45939 | − | 4.99514i | −0.0780856 | − | 0.158596i | ||||
\(993\) | −23.6186 | − | 35.1362i | −0.749515 | − | 1.11501i | ||||
\(994\) | 0.996753 | 0.0316151 | ||||||||
\(995\) | 7.17157 | − | 12.4215i | 0.227354 | − | 0.393789i | ||||
\(996\) | −17.0747 | + | 11.4776i | −0.541032 | + | 0.363683i | ||||
\(997\) | −16.6915 | − | 28.9106i | −0.528626 | − | 0.915607i | −0.999443 | − | 0.0333761i | \(-0.989374\pi\) |
0.470817 | − | 0.882231i | \(-0.343959\pi\) | |||||||
\(998\) | 6.18273 | − | 10.7088i | 0.195711 | − | 0.338981i | ||||
\(999\) | 9.18354 | − | 27.8129i | 0.290554 | − | 0.879960i |
(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 | 930.2.o.d.491.5 | yes | 36 | |
3.2 | odd | 2 | inner | 930.2.o.d.491.17 | yes | 36 | |
31.6 | odd | 6 | inner | 930.2.o.d.161.8 | ✓ | 36 | |
93.68 | even | 6 | inner | 930.2.o.d.161.14 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.d.161.8 | ✓ | 36 | 31.6 | odd | 6 | inner | |
930.2.o.d.161.14 | yes | 36 | 93.68 | even | 6 | inner | |
930.2.o.d.491.5 | yes | 36 | 1.1 | even | 1 | trivial | |
930.2.o.d.491.17 | yes | 36 | 3.2 | odd | 2 | inner |