Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(16,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 256.2 | ||
Character | \(\chi\) | \(=\) | 315.256 |
Dual form | 315.2.k.c.16.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29282 | + | 2.23923i | −0.914164 | + | 1.58338i | −0.106043 | + | 0.994362i | \(0.533818\pi\) |
−0.808121 | + | 0.589017i | \(0.799515\pi\) | |||||||
\(3\) | 1.72292 | + | 0.177629i | 0.994727 | + | 0.102554i | ||||
\(4\) | −2.34278 | − | 4.05782i | −1.17139 | − | 2.02891i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.62518 | + | 3.62838i | −1.07173 | + | 1.48128i | ||||
\(7\) | −2.13970 | + | 1.55618i | −0.808730 | + | 0.588180i | ||||
\(8\) | 6.94392 | 2.45505 | ||||||||
\(9\) | 2.93690 | + | 0.612079i | 0.978965 | + | 0.204026i | ||||
\(10\) | −1.29282 | + | 2.23923i | −0.408826 | + | 0.708108i | ||||
\(11\) | 2.47043 | 0.744861 | 0.372431 | − | 0.928060i | \(-0.378524\pi\) | ||||
0.372431 | + | 0.928060i | \(0.378524\pi\) | |||||||
\(12\) | −3.31564 | − | 7.40743i | −0.957142 | − | 2.13834i | ||||
\(13\) | −3.19209 | + | 5.52887i | −0.885328 | + | 1.53343i | −0.0399902 | + | 0.999200i | \(0.512733\pi\) |
−0.845338 | + | 0.534233i | \(0.820601\pi\) | |||||||
\(14\) | −0.718397 | − | 6.80315i | −0.192000 | − | 1.81822i | ||||
\(15\) | 1.72292 | + | 0.177629i | 0.444856 | + | 0.0458635i | ||||
\(16\) | −4.29169 | + | 7.43343i | −1.07292 | + | 1.85836i | ||||
\(17\) | −2.57232 | + | 4.45539i | −0.623880 | + | 1.08059i | 0.364876 | + | 0.931056i | \(0.381111\pi\) |
−0.988756 | + | 0.149536i | \(0.952222\pi\) | |||||||
\(18\) | −5.16748 | + | 5.78509i | −1.21799 | + | 1.36356i | ||||
\(19\) | 0.825096 | + | 1.42911i | 0.189290 | + | 0.327860i | 0.945014 | − | 0.327031i | \(-0.106048\pi\) |
−0.755724 | + | 0.654891i | \(0.772715\pi\) | |||||||
\(20\) | −2.34278 | − | 4.05782i | −0.523862 | − | 0.907356i | ||||
\(21\) | −3.96295 | + | 2.30110i | −0.864786 | + | 0.502140i | ||||
\(22\) | −3.19382 | + | 5.53186i | −0.680925 | + | 1.17940i | ||||
\(23\) | 4.85733 | 1.01282 | 0.506411 | − | 0.862292i | \(-0.330972\pi\) | ||||
0.506411 | + | 0.862292i | \(0.330972\pi\) | |||||||
\(24\) | 11.9638 | + | 1.23344i | 2.44210 | + | 0.251774i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −8.25363 | − | 14.2957i | −1.61867 | − | 2.80362i | ||||
\(27\) | 4.95131 | + | 1.57624i | 0.952880 | + | 0.303347i | ||||
\(28\) | 11.3275 | + | 5.03672i | 2.14070 | + | 0.951851i | ||||
\(29\) | 0.321747 | + | 0.557282i | 0.0597469 | + | 0.103485i | 0.894352 | − | 0.447364i | \(-0.147637\pi\) |
−0.834605 | + | 0.550849i | \(0.814304\pi\) | |||||||
\(30\) | −2.62518 | + | 3.62838i | −0.479290 | + | 0.662448i | ||||
\(31\) | −0.273744 | − | 0.474138i | −0.0491659 | − | 0.0851578i | 0.840395 | − | 0.541974i | \(-0.182323\pi\) |
−0.889561 | + | 0.456816i | \(0.848990\pi\) | |||||||
\(32\) | −4.15288 | − | 7.19299i | −0.734132 | − | 1.27155i | ||||
\(33\) | 4.25634 | + | 0.438818i | 0.740934 | + | 0.0763884i | ||||
\(34\) | −6.65112 | − | 11.5201i | −1.14066 | − | 1.97568i | ||||
\(35\) | −2.13970 | + | 1.55618i | −0.361675 | + | 0.263042i | ||||
\(36\) | −4.39680 | − | 13.3514i | −0.732801 | − | 2.22523i | ||||
\(37\) | −3.30325 | − | 5.72139i | −0.543051 | − | 0.940591i | −0.998727 | − | 0.0504457i | \(-0.983936\pi\) |
0.455676 | − | 0.890146i | \(-0.349398\pi\) | |||||||
\(38\) | −4.26681 | −0.692169 | ||||||||
\(39\) | −6.48180 | + | 8.95879i | −1.03792 | + | 1.43455i | ||||
\(40\) | 6.94392 | 1.09793 | ||||||||
\(41\) | 4.42604 | − | 7.66613i | 0.691231 | − | 1.19725i | −0.280203 | − | 0.959941i | \(-0.590402\pi\) |
0.971435 | − | 0.237307i | \(-0.0762647\pi\) | |||||||
\(42\) | −0.0293057 | − | 11.8489i | −0.00452196 | − | 1.82832i | ||||
\(43\) | −3.75461 | − | 6.50318i | −0.572573 | − | 0.991726i | −0.996301 | − | 0.0859360i | \(-0.972612\pi\) |
0.423728 | − | 0.905790i | \(-0.360721\pi\) | |||||||
\(44\) | −5.78767 | − | 10.0245i | −0.872524 | − | 1.51126i | ||||
\(45\) | 2.93690 | + | 0.612079i | 0.437807 | + | 0.0912433i | ||||
\(46\) | −6.27966 | + | 10.8767i | −0.925886 | + | 1.60368i | ||||
\(47\) | 0.817715 | − | 1.41632i | 0.119276 | − | 0.206592i | −0.800205 | − | 0.599727i | \(-0.795276\pi\) |
0.919481 | + | 0.393134i | \(0.128609\pi\) | |||||||
\(48\) | −8.71462 | + | 12.0449i | −1.25785 | + | 1.73853i | ||||
\(49\) | 2.15662 | − | 6.65950i | 0.308089 | − | 0.951358i | ||||
\(50\) | −1.29282 | + | 2.23923i | −0.182833 | + | 0.316676i | ||||
\(51\) | −5.22331 | + | 7.21936i | −0.731409 | + | 1.01091i | ||||
\(52\) | 29.9135 | 4.14826 | ||||||||
\(53\) | 4.66364 | − | 8.07767i | 0.640601 | − | 1.10955i | −0.344698 | − | 0.938714i | \(-0.612019\pi\) |
0.985299 | − | 0.170840i | \(-0.0546480\pi\) | |||||||
\(54\) | −9.93074 | + | 9.04935i | −1.35140 | + | 1.23146i | ||||
\(55\) | 2.47043 | 0.333112 | ||||||||
\(56\) | −14.8579 | + | 10.8060i | −1.98547 | + | 1.44401i | ||||
\(57\) | 1.16772 | + | 2.60880i | 0.154669 | + | 0.345544i | ||||
\(58\) | −1.66385 | −0.218474 | ||||||||
\(59\) | 4.44642 | + | 7.70143i | 0.578875 | + | 1.00264i | 0.995609 | + | 0.0936122i | \(0.0298414\pi\) |
−0.416734 | + | 0.909029i | \(0.636825\pi\) | |||||||
\(60\) | −3.31564 | − | 7.40743i | −0.428047 | − | 0.956296i | ||||
\(61\) | 0.157313 | − | 0.272474i | 0.0201418 | − | 0.0348867i | −0.855779 | − | 0.517342i | \(-0.826922\pi\) |
0.875921 | + | 0.482455i | \(0.160255\pi\) | |||||||
\(62\) | 1.41561 | 0.179783 | ||||||||
\(63\) | −7.23658 | + | 3.26067i | −0.911723 | + | 0.410806i | ||||
\(64\) | 4.30897 | 0.538621 | ||||||||
\(65\) | −3.19209 | + | 5.52887i | −0.395931 | + | 0.685772i | ||||
\(66\) | −6.48531 | + | 8.96363i | −0.798287 | + | 1.10335i | ||||
\(67\) | 0.593254 | + | 1.02755i | 0.0724775 | + | 0.125535i | 0.899987 | − | 0.435918i | \(-0.143576\pi\) |
−0.827509 | + | 0.561452i | \(0.810243\pi\) | |||||||
\(68\) | 24.1056 | 2.92323 | ||||||||
\(69\) | 8.36878 | + | 0.862800i | 1.00748 | + | 0.103869i | ||||
\(70\) | −0.718397 | − | 6.80315i | −0.0858648 | − | 0.813132i | ||||
\(71\) | −1.21039 | −0.143647 | −0.0718235 | − | 0.997417i | \(-0.522882\pi\) | ||||
−0.0718235 | + | 0.997417i | \(0.522882\pi\) | |||||||
\(72\) | 20.3936 | + | 4.25023i | 2.40340 | + | 0.500894i | ||||
\(73\) | 6.30120 | − | 10.9140i | 0.737500 | − | 1.27739i | −0.216118 | − | 0.976367i | \(-0.569340\pi\) |
0.953618 | − | 0.301020i | \(-0.0973271\pi\) | |||||||
\(74\) | 17.0821 | 1.98575 | ||||||||
\(75\) | 1.72292 | + | 0.177629i | 0.198945 | + | 0.0205108i | ||||
\(76\) | 3.86604 | − | 6.69618i | 0.443465 | − | 0.768105i | ||||
\(77\) | −5.28597 | + | 3.84442i | −0.602392 | + | 0.438112i | ||||
\(78\) | −11.6810 | − | 26.0964i | −1.32261 | − | 2.95484i | ||||
\(79\) | −6.14958 | + | 10.6514i | −0.691882 | + | 1.19837i | 0.279339 | + | 0.960193i | \(0.409885\pi\) |
−0.971221 | + | 0.238182i | \(0.923449\pi\) | |||||||
\(80\) | −4.29169 | + | 7.43343i | −0.479826 | + | 0.831083i | ||||
\(81\) | 8.25072 | + | 3.59522i | 0.916747 | + | 0.399469i | ||||
\(82\) | 11.4442 | + | 19.8219i | 1.26380 | + | 2.18896i | ||||
\(83\) | 3.21667 | + | 5.57144i | 0.353076 | + | 0.611545i | 0.986787 | − | 0.162025i | \(-0.0518025\pi\) |
−0.633711 | + | 0.773570i | \(0.718469\pi\) | |||||||
\(84\) | 18.6218 | + | 10.6900i | 2.03180 | + | 1.16637i | ||||
\(85\) | −2.57232 | + | 4.45539i | −0.279008 | + | 0.483255i | ||||
\(86\) | 19.4162 | 2.09370 | ||||||||
\(87\) | 0.455355 | + | 1.01730i | 0.0488192 | + | 0.109066i | ||||
\(88\) | 17.1544 | 1.82867 | ||||||||
\(89\) | −1.44436 | − | 2.50171i | −0.153102 | − | 0.265181i | 0.779264 | − | 0.626696i | \(-0.215593\pi\) |
−0.932366 | + | 0.361515i | \(0.882260\pi\) | |||||||
\(90\) | −5.16748 | + | 5.78509i | −0.544700 | + | 0.609802i | ||||
\(91\) | −1.77379 | − | 16.7976i | −0.185943 | − | 1.76087i | ||||
\(92\) | −11.3797 | − | 19.7101i | −1.18641 | − | 2.05493i | ||||
\(93\) | −0.387418 | − | 0.865526i | −0.0401734 | − | 0.0897509i | ||||
\(94\) | 2.11432 | + | 3.66211i | 0.218076 | + | 0.377718i | ||||
\(95\) | 0.825096 | + | 1.42911i | 0.0846531 | + | 0.146623i | ||||
\(96\) | −5.87739 | − | 13.1306i | −0.599858 | − | 1.34014i | ||||
\(97\) | 5.53831 | + | 9.59263i | 0.562330 | + | 0.973984i | 0.997293 | + | 0.0735357i | \(0.0234283\pi\) |
−0.434963 | + | 0.900449i | \(0.643238\pi\) | |||||||
\(98\) | 12.1241 | + | 13.4387i | 1.22472 | + | 1.35752i | ||||
\(99\) | 7.25538 | + | 1.51210i | 0.729193 | + | 0.151971i | ||||
\(100\) | −2.34278 | − | 4.05782i | −0.234278 | − | 0.405782i | ||||
\(101\) | −15.3178 | −1.52418 | −0.762091 | − | 0.647470i | \(-0.775827\pi\) | ||||
−0.762091 | + | 0.647470i | \(0.775827\pi\) | |||||||
\(102\) | −9.41304 | − | 21.0296i | −0.932030 | − | 2.08224i | ||||
\(103\) | −8.87687 | −0.874664 | −0.437332 | − | 0.899300i | \(-0.644076\pi\) | ||||
−0.437332 | + | 0.899300i | \(0.644076\pi\) | |||||||
\(104\) | −22.1656 | + | 38.3920i | −2.17352 | + | 3.76465i | ||||
\(105\) | −3.96295 | + | 2.30110i | −0.386744 | + | 0.224564i | ||||
\(106\) | 12.0585 | + | 20.8860i | 1.17123 | + | 2.02863i | ||||
\(107\) | −0.437949 | − | 0.758550i | −0.0423381 | − | 0.0733317i | 0.844080 | − | 0.536218i | \(-0.180147\pi\) |
−0.886418 | + | 0.462886i | \(0.846814\pi\) | |||||||
\(108\) | −5.20375 | − | 23.7843i | −0.500731 | − | 2.28865i | ||||
\(109\) | 6.95218 | − | 12.0415i | 0.665898 | − | 1.15337i | −0.313143 | − | 0.949706i | \(-0.601382\pi\) |
0.979041 | − | 0.203663i | \(-0.0652848\pi\) | |||||||
\(110\) | −3.19382 | + | 5.53186i | −0.304519 | + | 0.527442i | ||||
\(111\) | −4.67494 | − | 10.4442i | −0.443726 | − | 0.991324i | ||||
\(112\) | −2.38481 | − | 22.5839i | −0.225343 | − | 2.13398i | ||||
\(113\) | 3.30719 | − | 5.72822i | 0.311114 | − | 0.538866i | −0.667489 | − | 0.744619i | \(-0.732631\pi\) |
0.978604 | + | 0.205753i | \(0.0659644\pi\) | |||||||
\(114\) | −7.35137 | − | 0.757908i | −0.688519 | − | 0.0709846i | ||||
\(115\) | 4.85733 | 0.452948 | ||||||||
\(116\) | 1.50757 | − | 2.61118i | 0.139974 | − | 0.242442i | ||||
\(117\) | −12.7590 | + | 14.2839i | −1.17957 | + | 1.32055i | ||||
\(118\) | −22.9937 | −2.11675 | ||||||||
\(119\) | −1.42939 | − | 13.5362i | −0.131032 | − | 1.24086i | ||||
\(120\) | 11.9638 | + | 1.23344i | 1.09214 | + | 0.112597i | ||||
\(121\) | −4.89700 | −0.445182 | ||||||||
\(122\) | 0.406755 | + | 0.704521i | 0.0368259 | + | 0.0637843i | ||||
\(123\) | 8.98743 | − | 12.4219i | 0.810369 | − | 1.12005i | ||||
\(124\) | −1.28264 | + | 2.22161i | −0.115185 | + | 0.199506i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.05421 | − | 20.4199i | 0.183003 | − | 1.81915i | ||||
\(127\) | −13.0086 | −1.15432 | −0.577162 | − | 0.816630i | \(-0.695840\pi\) | ||||
−0.577162 | + | 0.816630i | \(0.695840\pi\) | |||||||
\(128\) | 2.73502 | − | 4.73719i | 0.241744 | − | 0.418712i | ||||
\(129\) | −5.31374 | − | 11.8714i | −0.467849 | − | 1.04522i | ||||
\(130\) | −8.25363 | − | 14.2957i | −0.723891 | − | 1.25382i | ||||
\(131\) | 2.25010 | 0.196592 | 0.0982960 | − | 0.995157i | \(-0.468661\pi\) | ||||
0.0982960 | + | 0.995157i | \(0.468661\pi\) | |||||||
\(132\) | −8.19104 | − | 18.2995i | −0.712938 | − | 1.59277i | ||||
\(133\) | −3.98941 | − | 1.77387i | −0.345925 | − | 0.153814i | ||||
\(134\) | −3.06789 | −0.265025 | ||||||||
\(135\) | 4.95131 | + | 1.57624i | 0.426141 | + | 0.135661i | ||||
\(136\) | −17.8620 | + | 30.9379i | −1.53165 | + | 2.65290i | ||||
\(137\) | 16.6485 | 1.42237 | 0.711187 | − | 0.703003i | \(-0.248158\pi\) | ||||
0.711187 | + | 0.703003i | \(0.248158\pi\) | |||||||
\(138\) | −12.7514 | + | 17.6242i | −1.08547 | + | 1.50027i | ||||
\(139\) | 8.78569 | − | 15.2173i | 0.745193 | − | 1.29071i | −0.204912 | − | 0.978780i | \(-0.565691\pi\) |
0.950105 | − | 0.311931i | \(-0.100976\pi\) | |||||||
\(140\) | 11.3275 | + | 5.03672i | 0.957351 | + | 0.425681i | ||||
\(141\) | 1.66044 | − | 2.29496i | 0.139834 | − | 0.193271i | ||||
\(142\) | 1.56482 | − | 2.71035i | 0.131317 | − | 0.227447i | ||||
\(143\) | −7.88583 | + | 13.6587i | −0.659446 | + | 1.14219i | ||||
\(144\) | −17.1541 | + | 19.2044i | −1.42951 | + | 1.60036i | ||||
\(145\) | 0.321747 | + | 0.557282i | 0.0267196 | + | 0.0462798i | ||||
\(146\) | 16.2927 | + | 28.2197i | 1.34839 | + | 2.33548i | ||||
\(147\) | 4.89860 | − | 11.0907i | 0.404030 | − | 0.914746i | ||||
\(148\) | −15.4776 | + | 26.8080i | −1.27225 | + | 2.20360i | ||||
\(149\) | 8.04259 | 0.658875 | 0.329437 | − | 0.944177i | \(-0.393141\pi\) | ||||
0.329437 | + | 0.944177i | \(0.393141\pi\) | |||||||
\(150\) | −2.62518 | + | 3.62838i | −0.214345 | + | 0.296256i | ||||
\(151\) | 12.0429 | 0.980037 | 0.490018 | − | 0.871712i | \(-0.336990\pi\) | ||||
0.490018 | + | 0.871712i | \(0.336990\pi\) | |||||||
\(152\) | 5.72940 | + | 9.92361i | 0.464716 | + | 0.804911i | ||||
\(153\) | −10.2817 | + | 11.5106i | −0.831226 | + | 0.930574i | ||||
\(154\) | −1.77475 | − | 16.8067i | −0.143013 | − | 1.35432i | ||||
\(155\) | −0.273744 | − | 0.474138i | −0.0219876 | − | 0.0380837i | ||||
\(156\) | 51.5386 | + | 5.31350i | 4.12639 | + | 0.425420i | ||||
\(157\) | −1.76403 | − | 3.05538i | −0.140785 | − | 0.243846i | 0.787008 | − | 0.616943i | \(-0.211629\pi\) |
−0.927792 | + | 0.373097i | \(0.878296\pi\) | |||||||
\(158\) | −15.9006 | − | 27.5407i | −1.26499 | − | 2.19102i | ||||
\(159\) | 9.46990 | − | 13.0888i | 0.751012 | − | 1.03801i | ||||
\(160\) | −4.15288 | − | 7.19299i | −0.328314 | − | 0.568656i | ||||
\(161\) | −10.3932 | + | 7.55887i | −0.819100 | + | 0.595722i | ||||
\(162\) | −18.7173 | + | 13.8273i | −1.47057 | + | 1.08638i | ||||
\(163\) | 1.15690 | + | 2.00380i | 0.0906150 | + | 0.156950i | 0.907770 | − | 0.419468i | \(-0.137783\pi\) |
−0.817155 | + | 0.576418i | \(0.804450\pi\) | |||||||
\(164\) | −41.4770 | −3.23881 | ||||||||
\(165\) | 4.25634 | + | 0.438818i | 0.331356 | + | 0.0341619i | ||||
\(166\) | −16.6344 | −1.29108 | ||||||||
\(167\) | 6.15059 | − | 10.6531i | 0.475947 | − | 0.824365i | −0.523673 | − | 0.851919i | \(-0.675439\pi\) |
0.999620 | + | 0.0275545i | \(0.00877197\pi\) | |||||||
\(168\) | −27.5184 | + | 15.9786i | −2.12309 | + | 1.23278i | ||||
\(169\) | −13.8789 | − | 24.0390i | −1.06761 | − | 1.84916i | ||||
\(170\) | −6.65112 | − | 11.5201i | −0.510117 | − | 0.883549i | ||||
\(171\) | 1.54849 | + | 4.70217i | 0.118416 | + | 0.359584i | ||||
\(172\) | −17.5925 | + | 30.4711i | −1.34141 | + | 2.32340i | ||||
\(173\) | 1.56719 | − | 2.71446i | 0.119151 | − | 0.206376i | −0.800280 | − | 0.599626i | \(-0.795316\pi\) |
0.919432 | + | 0.393250i | \(0.128649\pi\) | |||||||
\(174\) | −2.86667 | − | 0.295547i | −0.217322 | − | 0.0224054i | ||||
\(175\) | −2.13970 | + | 1.55618i | −0.161746 | + | 0.117636i | ||||
\(176\) | −10.6023 | + | 18.3637i | −0.799179 | + | 1.38422i | ||||
\(177\) | 6.29283 | + | 14.0587i | 0.472998 | + | 1.05672i | ||||
\(178\) | 7.46922 | 0.559842 | ||||||||
\(179\) | −7.24402 | + | 12.5470i | −0.541443 | + | 0.937808i | 0.457378 | + | 0.889272i | \(0.348789\pi\) |
−0.998821 | + | 0.0485352i | \(0.984545\pi\) | |||||||
\(180\) | −4.39680 | − | 13.3514i | −0.327718 | − | 0.995151i | ||||
\(181\) | 10.6671 | 0.792880 | 0.396440 | − | 0.918061i | \(-0.370245\pi\) | ||||
0.396440 | + | 0.918061i | \(0.370245\pi\) | |||||||
\(182\) | 39.9069 | + | 17.7444i | 2.95810 | + | 1.31530i | ||||
\(183\) | 0.319436 | − | 0.441507i | 0.0236134 | − | 0.0326371i | ||||
\(184\) | 33.7289 | 2.48653 | ||||||||
\(185\) | −3.30325 | − | 5.72139i | −0.242860 | − | 0.420645i | ||||
\(186\) | 2.43898 | + | 0.251453i | 0.178835 | + | 0.0184374i | ||||
\(187\) | −6.35473 | + | 11.0067i | −0.464704 | + | 0.804891i | ||||
\(188\) | −7.66292 | −0.558876 | ||||||||
\(189\) | −13.0472 | + | 4.33244i | −0.949046 | + | 0.315139i | ||||
\(190\) | −4.26681 | −0.309547 | ||||||||
\(191\) | −6.69720 | + | 11.5999i | −0.484592 | + | 0.839339i | −0.999843 | − | 0.0177007i | \(-0.994365\pi\) |
0.515251 | + | 0.857039i | \(0.327699\pi\) | |||||||
\(192\) | 7.42400 | + | 0.765396i | 0.535781 | + | 0.0552377i | ||||
\(193\) | −2.26582 | − | 3.92451i | −0.163097 | − | 0.282492i | 0.772881 | − | 0.634551i | \(-0.218815\pi\) |
−0.935978 | + | 0.352059i | \(0.885482\pi\) | |||||||
\(194\) | −28.6402 | −2.05625 | ||||||||
\(195\) | −6.48180 | + | 8.95879i | −0.464172 | + | 0.641552i | ||||
\(196\) | −32.0755 | + | 6.85060i | −2.29111 | + | 0.489328i | ||||
\(197\) | 1.62983 | 0.116121 | 0.0580603 | − | 0.998313i | \(-0.481508\pi\) | ||||
0.0580603 | + | 0.998313i | \(0.481508\pi\) | |||||||
\(198\) | −12.7659 | + | 14.2916i | −0.907230 | + | 1.01566i | ||||
\(199\) | −11.4805 | + | 19.8849i | −0.813833 | + | 1.40960i | 0.0963300 | + | 0.995349i | \(0.469290\pi\) |
−0.910163 | + | 0.414250i | \(0.864044\pi\) | |||||||
\(200\) | 6.94392 | 0.491009 | ||||||||
\(201\) | 0.839607 | + | 1.87576i | 0.0592213 | + | 0.132306i | ||||
\(202\) | 19.8032 | − | 34.3002i | 1.39335 | − | 2.41336i | ||||
\(203\) | −1.55567 | − | 0.691720i | −0.109187 | − | 0.0485493i | ||||
\(204\) | 41.5319 | + | 4.28184i | 2.90782 | + | 0.299789i | ||||
\(205\) | 4.42604 | − | 7.66613i | 0.309128 | − | 0.535425i | ||||
\(206\) | 11.4762 | − | 19.8774i | 0.799586 | − | 1.38492i | ||||
\(207\) | 14.2655 | + | 2.97307i | 0.991519 | + | 0.206643i | ||||
\(208\) | −27.3990 | − | 47.4564i | −1.89978 | − | 3.29051i | ||||
\(209\) | 2.03834 | + | 3.53051i | 0.140995 | + | 0.244210i | ||||
\(210\) | −0.0293057 | − | 11.8489i | −0.00202228 | − | 0.817650i | ||||
\(211\) | 4.10543 | − | 7.11081i | 0.282629 | − | 0.489528i | −0.689402 | − | 0.724379i | \(-0.742127\pi\) |
0.972032 | + | 0.234850i | \(0.0754600\pi\) | |||||||
\(212\) | −43.7036 | −3.00158 | ||||||||
\(213\) | −2.08540 | − | 0.215000i | −0.142890 | − | 0.0147316i | ||||
\(214\) | 2.26476 | 0.154816 | ||||||||
\(215\) | −3.75461 | − | 6.50318i | −0.256062 | − | 0.443513i | ||||
\(216\) | 34.3815 | + | 10.9453i | 2.33936 | + | 0.744731i | ||||
\(217\) | 1.32357 | + | 0.588519i | 0.0898500 | + | 0.0399513i | ||||
\(218\) | 17.9759 | + | 31.1351i | 1.21748 | + | 2.10874i | ||||
\(219\) | 12.7951 | − | 17.6847i | 0.864612 | − | 1.19502i | ||||
\(220\) | −5.78767 | − | 10.0245i | −0.390205 | − | 0.675854i | ||||
\(221\) | −16.4222 | − | 28.4441i | −1.10468 | − | 1.91336i | ||||
\(222\) | 29.4310 | + | 3.03426i | 1.97528 | + | 0.203646i | ||||
\(223\) | 1.75774 | + | 3.04449i | 0.117707 | + | 0.203874i | 0.918859 | − | 0.394587i | \(-0.129112\pi\) |
−0.801152 | + | 0.598461i | \(0.795779\pi\) | |||||||
\(224\) | 20.0795 | + | 8.92822i | 1.34162 | + | 0.596542i | ||||
\(225\) | 2.93690 | + | 0.612079i | 0.195793 | + | 0.0408053i | ||||
\(226\) | 8.55123 | + | 14.8112i | 0.568819 | + | 0.985224i | ||||
\(227\) | 13.8018 | 0.916058 | 0.458029 | − | 0.888937i | \(-0.348556\pi\) | ||||
0.458029 | + | 0.888937i | \(0.348556\pi\) | |||||||
\(228\) | 7.85031 | − | 10.8503i | 0.519899 | − | 0.718576i | ||||
\(229\) | 11.0517 | 0.730319 | 0.365159 | − | 0.930945i | \(-0.381015\pi\) | ||||
0.365159 | + | 0.930945i | \(0.381015\pi\) | |||||||
\(230\) | −6.27966 | + | 10.8767i | −0.414069 | + | 0.717188i | ||||
\(231\) | −9.79017 | + | 5.68469i | −0.644146 | + | 0.374025i | ||||
\(232\) | 2.23419 | + | 3.86972i | 0.146681 | + | 0.254060i | ||||
\(233\) | −10.9712 | − | 19.0026i | −0.718744 | − | 1.24490i | −0.961498 | − | 0.274814i | \(-0.911384\pi\) |
0.242753 | − | 0.970088i | \(-0.421949\pi\) | |||||||
\(234\) | −15.4899 | − | 47.0369i | −1.01261 | − | 3.07490i | ||||
\(235\) | 0.817715 | − | 1.41632i | 0.0533419 | − | 0.0923908i | ||||
\(236\) | 20.8340 | − | 36.0855i | 1.35618 | − | 2.34897i | ||||
\(237\) | −12.4872 | + | 17.2591i | −0.811132 | + | 1.12110i | ||||
\(238\) | 32.1587 | + | 14.2992i | 2.08454 | + | 0.926877i | ||||
\(239\) | 5.46109 | − | 9.45889i | 0.353249 | − | 0.611844i | −0.633568 | − | 0.773687i | \(-0.718410\pi\) |
0.986817 | + | 0.161843i | \(0.0517437\pi\) | |||||||
\(240\) | −8.71462 | + | 12.0449i | −0.562527 | + | 0.777493i | ||||
\(241\) | 11.6949 | 0.753333 | 0.376666 | − | 0.926349i | \(-0.377070\pi\) | ||||
0.376666 | + | 0.926349i | \(0.377070\pi\) | |||||||
\(242\) | 6.33095 | − | 10.9655i | 0.406969 | − | 0.704891i | ||||
\(243\) | 13.5767 | + | 7.65984i | 0.870946 | + | 0.491379i | ||||
\(244\) | −1.47420 | −0.0943759 | ||||||||
\(245\) | 2.15662 | − | 6.65950i | 0.137781 | − | 0.425460i | ||||
\(246\) | 16.1964 | + | 36.1843i | 1.03265 | + | 2.30703i | ||||
\(247\) | −10.5351 | −0.670335 | ||||||||
\(248\) | −1.90086 | − | 3.29238i | −0.120704 | − | 0.209066i | ||||
\(249\) | 4.55242 | + | 10.1705i | 0.288498 | + | 0.644530i | ||||
\(250\) | −1.29282 | + | 2.23923i | −0.0817653 | + | 0.141622i | ||||
\(251\) | −1.99070 | −0.125652 | −0.0628261 | − | 0.998024i | \(-0.520011\pi\) | ||||
−0.0628261 | + | 0.998024i | \(0.520011\pi\) | |||||||
\(252\) | 30.1849 | + | 21.7257i | 1.90147 | + | 1.36859i | ||||
\(253\) | 11.9997 | 0.754412 | ||||||||
\(254\) | 16.8178 | − | 29.1292i | 1.05524 | − | 1.82773i | ||||
\(255\) | −5.22331 | + | 7.21936i | −0.327096 | + | 0.452094i | ||||
\(256\) | 11.3808 | + | 19.7121i | 0.711297 | + | 1.23200i | ||||
\(257\) | −1.68925 | −0.105372 | −0.0526862 | − | 0.998611i | \(-0.516778\pi\) | ||||
−0.0526862 | + | 0.998611i | \(0.516778\pi\) | |||||||
\(258\) | 33.4525 | + | 3.44887i | 2.08266 | + | 0.214717i | ||||
\(259\) | 15.9715 | + | 7.10162i | 0.992418 | + | 0.441273i | ||||
\(260\) | 29.9135 | 1.85516 | ||||||||
\(261\) | 0.603837 | + | 1.83361i | 0.0373766 | + | 0.113498i | ||||
\(262\) | −2.90898 | + | 5.03850i | −0.179717 | + | 0.311279i | ||||
\(263\) | −22.8153 | −1.40685 | −0.703426 | − | 0.710769i | \(-0.748347\pi\) | ||||
−0.703426 | + | 0.710769i | \(0.748347\pi\) | |||||||
\(264\) | 29.5557 | + | 3.04712i | 1.81903 | + | 0.187537i | ||||
\(265\) | 4.66364 | − | 8.07767i | 0.286485 | − | 0.496207i | ||||
\(266\) | 9.12970 | − | 6.63992i | 0.559778 | − | 0.407120i | ||||
\(267\) | −2.04414 | − | 4.56680i | −0.125100 | − | 0.279484i | ||||
\(268\) | 2.77973 | − | 4.81463i | 0.169799 | − | 0.294101i | ||||
\(269\) | 2.76740 | − | 4.79328i | 0.168732 | − | 0.292252i | −0.769243 | − | 0.638957i | \(-0.779366\pi\) |
0.937974 | + | 0.346705i | \(0.112700\pi\) | |||||||
\(270\) | −9.93074 | + | 9.04935i | −0.604365 | + | 0.550726i | ||||
\(271\) | −4.37567 | − | 7.57888i | −0.265803 | − | 0.460384i | 0.701971 | − | 0.712206i | \(-0.252304\pi\) |
−0.967774 | + | 0.251821i | \(0.918970\pi\) | |||||||
\(272\) | −22.0792 | − | 38.2424i | −1.33875 | − | 2.31878i | ||||
\(273\) | −0.0723583 | − | 29.2559i | −0.00437932 | − | 1.77065i | ||||
\(274\) | −21.5235 | + | 37.2798i | −1.30028 | + | 2.25216i | ||||
\(275\) | 2.47043 | 0.148972 | ||||||||
\(276\) | −16.1051 | − | 35.9803i | −0.969416 | − | 2.16576i | ||||
\(277\) | −27.9996 | −1.68233 | −0.841167 | − | 0.540775i | \(-0.818131\pi\) | ||||
−0.841167 | + | 0.540775i | \(0.818131\pi\) | |||||||
\(278\) | 22.7167 | + | 39.3465i | 1.36246 | + | 2.35984i | ||||
\(279\) | −0.513747 | − | 1.56005i | −0.0307572 | − | 0.0933976i | ||||
\(280\) | −14.8579 | + | 10.8060i | −0.887929 | + | 0.645780i | ||||
\(281\) | −6.08424 | − | 10.5382i | −0.362955 | − | 0.628657i | 0.625490 | − | 0.780232i | \(-0.284899\pi\) |
−0.988446 | + | 0.151575i | \(0.951566\pi\) | |||||||
\(282\) | 2.99231 | + | 6.68509i | 0.178189 | + | 0.398091i | ||||
\(283\) | −0.526203 | − | 0.911410i | −0.0312795 | − | 0.0541777i | 0.849962 | − | 0.526844i | \(-0.176625\pi\) |
−0.881241 | + | 0.472666i | \(0.843292\pi\) | |||||||
\(284\) | 2.83568 | + | 4.91155i | 0.168267 | + | 0.291447i | ||||
\(285\) | 1.16772 | + | 2.60880i | 0.0691700 | + | 0.154532i | ||||
\(286\) | −20.3900 | − | 35.3165i | −1.20568 | − | 2.08831i | ||||
\(287\) | 2.45947 | + | 23.2909i | 0.145178 | + | 1.37482i | ||||
\(288\) | −7.79389 | − | 23.6670i | −0.459259 | − | 1.39459i | ||||
\(289\) | −4.73369 | − | 8.19899i | −0.278452 | − | 0.482294i | ||||
\(290\) | −1.66385 | −0.0977045 | ||||||||
\(291\) | 7.83813 | + | 17.5111i | 0.459479 | + | 1.02652i | ||||
\(292\) | −59.0494 | −3.45560 | ||||||||
\(293\) | −9.43289 | + | 16.3382i | −0.551075 | + | 0.954490i | 0.447122 | + | 0.894473i | \(0.352449\pi\) |
−0.998197 | + | 0.0600173i | \(0.980884\pi\) | |||||||
\(294\) | 18.5017 | + | 25.3074i | 1.07904 | + | 1.47596i | ||||
\(295\) | 4.44642 | + | 7.70143i | 0.258881 | + | 0.448395i | ||||
\(296\) | −22.9375 | − | 39.7289i | −1.33321 | − | 2.30919i | ||||
\(297\) | 12.2318 | + | 3.89398i | 0.709763 | + | 0.225952i | ||||
\(298\) | −10.3976 | + | 18.0093i | −0.602319 | + | 1.04325i | ||||
\(299\) | −15.5050 | + | 26.8555i | −0.896680 | + | 1.55310i | ||||
\(300\) | −3.31564 | − | 7.40743i | −0.191428 | − | 0.427668i | ||||
\(301\) | 18.1538 | + | 8.07200i | 1.04637 | + | 0.465262i | ||||
\(302\) | −15.5693 | + | 26.9669i | −0.895914 | + | 1.55177i | ||||
\(303\) | −26.3914 | − | 2.72088i | −1.51614 | − | 0.156311i | ||||
\(304\) | −14.1642 | −0.812375 | ||||||||
\(305\) | 0.157313 | − | 0.272474i | 0.00900771 | − | 0.0156018i | ||||
\(306\) | −12.4824 | − | 37.9043i | −0.713574 | − | 2.16684i | ||||
\(307\) | −31.4153 | −1.79296 | −0.896482 | − | 0.443080i | \(-0.853886\pi\) | ||||
−0.896482 | + | 0.443080i | \(0.853886\pi\) | |||||||
\(308\) | 27.9838 | + | 12.4428i | 1.59453 | + | 0.708997i | ||||
\(309\) | −15.2941 | − | 1.57678i | −0.870052 | − | 0.0897002i | ||||
\(310\) | 1.41561 | 0.0804012 | ||||||||
\(311\) | 9.15720 | + | 15.8607i | 0.519257 | + | 0.899380i | 0.999750 | + | 0.0223811i | \(0.00712473\pi\) |
−0.480492 | + | 0.876999i | \(0.659542\pi\) | |||||||
\(312\) | −45.0091 | + | 62.2091i | −2.54814 | + | 3.52189i | ||||
\(313\) | −3.20703 | + | 5.55473i | −0.181272 | + | 0.313972i | −0.942314 | − | 0.334731i | \(-0.891355\pi\) |
0.761042 | + | 0.648703i | \(0.224688\pi\) | |||||||
\(314\) | 9.12229 | 0.514801 | ||||||||
\(315\) | −7.23658 | + | 3.26067i | −0.407735 | + | 0.183718i | ||||
\(316\) | 57.6285 | 3.24186 | ||||||||
\(317\) | −4.74118 | + | 8.21197i | −0.266291 | + | 0.461230i | −0.967901 | − | 0.251331i | \(-0.919132\pi\) |
0.701610 | + | 0.712561i | \(0.252465\pi\) | |||||||
\(318\) | 17.0659 | + | 38.1268i | 0.957009 | + | 2.13804i | ||||
\(319\) | 0.794852 | + | 1.37672i | 0.0445032 | + | 0.0770818i | ||||
\(320\) | 4.30897 | 0.240879 | ||||||||
\(321\) | −0.619810 | − | 1.38471i | −0.0345944 | − | 0.0772870i | ||||
\(322\) | −3.48949 | − | 33.0451i | −0.194462 | − | 1.84153i | ||||
\(323\) | −8.48966 | −0.472377 | ||||||||
\(324\) | −4.74087 | − | 41.9027i | −0.263382 | − | 2.32793i | ||||
\(325\) | −3.19209 | + | 5.52887i | −0.177066 | + | 0.306687i | ||||
\(326\) | −5.98264 | −0.331348 | ||||||||
\(327\) | 14.1170 | − | 19.5117i | 0.780670 | − | 1.07900i | ||||
\(328\) | 30.7341 | − | 53.2329i | 1.69700 | − | 2.93930i | ||||
\(329\) | 0.454389 | + | 4.30302i | 0.0250513 | + | 0.237233i | ||||
\(330\) | −6.48531 | + | 8.96363i | −0.357005 | + | 0.493432i | ||||
\(331\) | −6.50291 | + | 11.2634i | −0.357432 | + | 0.619091i | −0.987531 | − | 0.157424i | \(-0.949681\pi\) |
0.630099 | + | 0.776515i | \(0.283014\pi\) | |||||||
\(332\) | 15.0719 | − | 26.1053i | 0.827179 | − | 1.43272i | ||||
\(333\) | −6.19935 | − | 18.8250i | −0.339722 | − | 1.03160i | ||||
\(334\) | 15.9033 | + | 27.5453i | 0.870188 | + | 1.50721i | ||||
\(335\) | 0.593254 | + | 1.02755i | 0.0324129 | + | 0.0561409i | ||||
\(336\) | −0.0972839 | − | 39.3339i | −0.00530727 | − | 2.14584i | ||||
\(337\) | −0.631277 | + | 1.09340i | −0.0343879 | + | 0.0595615i | −0.882707 | − | 0.469924i | \(-0.844281\pi\) |
0.848319 | + | 0.529485i | \(0.177615\pi\) | |||||||
\(338\) | 71.7720 | 3.90388 | ||||||||
\(339\) | 6.71552 | − | 9.28181i | 0.364737 | − | 0.504119i | ||||
\(340\) | 24.1056 | 1.30731 | ||||||||
\(341\) | −0.676264 | − | 1.17132i | −0.0366217 | − | 0.0634307i | ||||
\(342\) | −12.5312 | − | 2.61163i | −0.677609 | − | 0.141221i | ||||
\(343\) | 5.74886 | + | 17.6054i | 0.310409 | + | 0.950603i | ||||
\(344\) | −26.0717 | − | 45.1575i | −1.40569 | − | 2.43473i | ||||
\(345\) | 8.36878 | + | 0.862800i | 0.450560 | + | 0.0464516i | ||||
\(346\) | 4.05220 | + | 7.01862i | 0.217848 | + | 0.377324i | ||||
\(347\) | 11.7238 | + | 20.3063i | 0.629368 | + | 1.09010i | 0.987679 | + | 0.156496i | \(0.0500197\pi\) |
−0.358310 | + | 0.933603i | \(0.616647\pi\) | |||||||
\(348\) | 3.06123 | − | 4.23107i | 0.164099 | − | 0.226809i | ||||
\(349\) | 1.25503 | + | 2.17378i | 0.0671804 | + | 0.116360i | 0.897659 | − | 0.440690i | \(-0.145266\pi\) |
−0.830479 | + | 0.557050i | \(0.811933\pi\) | |||||||
\(350\) | −0.718397 | − | 6.80315i | −0.0383999 | − | 0.363644i | ||||
\(351\) | −24.5199 | + | 22.3436i | −1.30877 | + | 1.19262i | ||||
\(352\) | −10.2594 | − | 17.7698i | −0.546826 | − | 0.947131i | ||||
\(353\) | 0.724165 | 0.0385434 | 0.0192717 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192717 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(354\) | −39.6164 | − | 4.08435i | −2.10559 | − | 0.217081i | ||||
\(355\) | −1.21039 | −0.0642409 | ||||||||
\(356\) | −6.76766 | + | 11.7219i | −0.358685 | + | 0.621261i | ||||
\(357\) | −0.0583093 | − | 23.5757i | −0.00308606 | − | 1.24776i | ||||
\(358\) | −18.7305 | − | 32.4421i | −0.989936 | − | 1.71462i | ||||
\(359\) | 11.5624 | + | 20.0267i | 0.610241 | + | 1.05697i | 0.991199 | + | 0.132377i | \(0.0422609\pi\) |
−0.380958 | + | 0.924592i | \(0.624406\pi\) | |||||||
\(360\) | 20.3936 | + | 4.25023i | 1.07484 | + | 0.224007i | ||||
\(361\) | 8.13843 | − | 14.0962i | 0.428339 | − | 0.741904i | ||||
\(362\) | −13.7907 | + | 23.8862i | −0.724823 | + | 1.25543i | ||||
\(363\) | −8.43713 | − | 0.869847i | −0.442834 | − | 0.0456551i | ||||
\(364\) | −64.0059 | + | 46.5508i | −3.35482 | + | 2.43992i | ||||
\(365\) | 6.30120 | − | 10.9140i | 0.329820 | − | 0.571265i | ||||
\(366\) | 0.575663 | + | 1.28608i | 0.0300904 | + | 0.0672246i | ||||
\(367\) | −0.530037 | −0.0276677 | −0.0138339 | − | 0.999904i | \(-0.504404\pi\) | ||||
−0.0138339 | + | 0.999904i | \(0.504404\pi\) | |||||||
\(368\) | −20.8462 | + | 36.1066i | −1.08668 | + | 1.88219i | ||||
\(369\) | 17.6911 | − | 19.8055i | 0.920962 | − | 1.03103i | ||||
\(370\) | 17.0821 | 0.888054 | ||||||||
\(371\) | 2.59150 | + | 24.5412i | 0.134544 | + | 1.27412i | ||||
\(372\) | −2.60451 | + | 3.59981i | −0.135038 | + | 0.186642i | ||||
\(373\) | 16.4305 | 0.850737 | 0.425369 | − | 0.905020i | \(-0.360144\pi\) | ||||
0.425369 | + | 0.905020i | \(0.360144\pi\) | |||||||
\(374\) | −16.4311 | − | 28.4595i | −0.849631 | − | 1.47160i | ||||
\(375\) | 1.72292 | + | 0.177629i | 0.0889711 | + | 0.00917270i | ||||
\(376\) | 5.67815 | − | 9.83484i | 0.292828 | − | 0.507193i | ||||
\(377\) | −4.10819 | −0.211582 | ||||||||
\(378\) | 7.16638 | − | 34.8169i | 0.368599 | − | 1.79079i | ||||
\(379\) | 3.76572 | 0.193432 | 0.0967160 | − | 0.995312i | \(-0.469166\pi\) | ||||
0.0967160 | + | 0.995312i | \(0.469166\pi\) | |||||||
\(380\) | 3.86604 | − | 6.69618i | 0.198324 | − | 0.343507i | ||||
\(381\) | −22.4127 | − | 2.31069i | −1.14824 | − | 0.118380i | ||||
\(382\) | −17.3166 | − | 29.9932i | −0.885994 | − | 1.53459i | ||||
\(383\) | −7.91395 | −0.404384 | −0.202192 | − | 0.979346i | \(-0.564807\pi\) | ||||
−0.202192 | + | 0.979346i | \(0.564807\pi\) | |||||||
\(384\) | 5.55367 | − | 7.67598i | 0.283410 | − | 0.391713i | ||||
\(385\) | −5.28597 | + | 3.84442i | −0.269398 | + | 0.195930i | ||||
\(386\) | 11.7172 | 0.596390 | ||||||||
\(387\) | −7.04645 | − | 21.3973i | −0.358191 | − | 1.08769i | ||||
\(388\) | 25.9501 | − | 44.9469i | 1.31742 | − | 2.28183i | ||||
\(389\) | 30.9240 | 1.56791 | 0.783953 | − | 0.620820i | \(-0.213200\pi\) | ||||
0.783953 | + | 0.620820i | \(0.213200\pi\) | |||||||
\(390\) | −11.6810 | − | 26.0964i | −0.591490 | − | 1.32144i | ||||
\(391\) | −12.4946 | + | 21.6413i | −0.631880 | + | 1.09445i | ||||
\(392\) | 14.9754 | − | 46.2430i | 0.756372 | − | 2.33563i | ||||
\(393\) | 3.87674 | + | 0.399682i | 0.195555 | + | 0.0201613i | ||||
\(394\) | −2.10708 | + | 3.64957i | −0.106153 | + | 0.183863i | ||||
\(395\) | −6.14958 | + | 10.6514i | −0.309419 | + | 0.535929i | ||||
\(396\) | −10.8620 | − | 32.9835i | −0.545835 | − | 1.65748i | ||||
\(397\) | 12.1376 | + | 21.0230i | 0.609171 | + | 1.05512i | 0.991377 | + | 0.131038i | \(0.0418311\pi\) |
−0.382206 | + | 0.924077i | \(0.624836\pi\) | |||||||
\(398\) | −29.6846 | − | 51.4152i | −1.48795 | − | 2.57721i | ||||
\(399\) | −6.55833 | − | 3.76486i | −0.328327 | − | 0.188479i | ||||
\(400\) | −4.29169 | + | 7.43343i | −0.214585 | + | 0.371671i | ||||
\(401\) | −35.4068 | −1.76813 | −0.884065 | − | 0.467365i | \(-0.845203\pi\) | ||||
−0.884065 | + | 0.467365i | \(0.845203\pi\) | |||||||
\(402\) | −5.28573 | − | 0.544945i | −0.263628 | − | 0.0271794i | ||||
\(403\) | 3.49527 | 0.174112 | ||||||||
\(404\) | 35.8863 | + | 62.1570i | 1.78541 | + | 3.09242i | ||||
\(405\) | 8.25072 | + | 3.59522i | 0.409982 | + | 0.178648i | ||||
\(406\) | 3.56013 | − | 2.58924i | 0.176686 | − | 0.128502i | ||||
\(407\) | −8.16043 | − | 14.1343i | −0.404497 | − | 0.700610i | ||||
\(408\) | −36.2702 | + | 50.1307i | −1.79564 | + | 2.48184i | ||||
\(409\) | 10.8919 | + | 18.8653i | 0.538568 | + | 0.932827i | 0.998981 | + | 0.0451225i | \(0.0143678\pi\) |
−0.460413 | + | 0.887705i | \(0.652299\pi\) | |||||||
\(410\) | 11.4442 | + | 19.8219i | 0.565187 | + | 0.978933i | ||||
\(411\) | 28.6840 | + | 2.95724i | 1.41488 | + | 0.145870i | ||||
\(412\) | 20.7966 | + | 36.0207i | 1.02457 | + | 1.77461i | ||||
\(413\) | −21.4988 | − | 9.55931i | −1.05789 | − | 0.470383i | ||||
\(414\) | −25.1001 | + | 28.1001i | −1.23360 | + | 1.38104i | ||||
\(415\) | 3.21667 | + | 5.57144i | 0.157900 | + | 0.273491i | ||||
\(416\) | 53.0255 | 2.59979 | ||||||||
\(417\) | 17.8401 | − | 24.6575i | 0.873631 | − | 1.20748i | ||||
\(418\) | −10.5408 | −0.515570 | ||||||||
\(419\) | −1.62516 | + | 2.81486i | −0.0793943 | + | 0.137515i | −0.902989 | − | 0.429664i | \(-0.858632\pi\) |
0.823594 | + | 0.567179i | \(0.191965\pi\) | |||||||
\(420\) | 18.6218 | + | 10.6900i | 0.908648 | + | 0.521616i | ||||
\(421\) | −11.3571 | − | 19.6710i | −0.553510 | − | 0.958707i | −0.998018 | − | 0.0629324i | \(-0.979955\pi\) |
0.444508 | − | 0.895775i | \(-0.353379\pi\) | |||||||
\(422\) | 10.6152 | + | 18.3860i | 0.516739 | + | 0.895018i | ||||
\(423\) | 3.26845 | − | 3.65909i | 0.158917 | − | 0.177911i | ||||
\(424\) | 32.3840 | − | 56.0907i | 1.57270 | − | 2.72400i | ||||
\(425\) | −2.57232 | + | 4.45539i | −0.124776 | + | 0.216118i | ||||
\(426\) | 3.17749 | − | 4.39175i | 0.153950 | − | 0.212781i | ||||
\(427\) | 0.0874157 | + | 0.827819i | 0.00423034 | + | 0.0400610i | ||||
\(428\) | −2.05204 | + | 3.55423i | −0.0991890 | + | 0.171800i | ||||
\(429\) | −16.0128 | + | 22.1320i | −0.773106 | + | 1.06854i | ||||
\(430\) | 19.4162 | 0.936332 | ||||||||
\(431\) | 6.07416 | − | 10.5208i | 0.292582 | − | 0.506767i | −0.681837 | − | 0.731504i | \(-0.738819\pi\) |
0.974420 | + | 0.224737i | \(0.0721522\pi\) | |||||||
\(432\) | −32.9664 | + | 30.0405i | −1.58609 | + | 1.44532i | ||||
\(433\) | −11.8389 | −0.568941 | −0.284471 | − | 0.958685i | \(-0.591818\pi\) | ||||
−0.284471 | + | 0.958685i | \(0.591818\pi\) | |||||||
\(434\) | −3.02898 | + | 2.20294i | −0.145396 | + | 0.105745i | ||||
\(435\) | 0.455355 | + | 1.01730i | 0.0218326 | + | 0.0487760i | ||||
\(436\) | −65.1498 | −3.12011 | ||||||||
\(437\) | 4.00776 | + | 6.94165i | 0.191717 | + | 0.332064i | ||||
\(438\) | 23.0583 | + | 51.5144i | 1.10177 | + | 2.46145i | ||||
\(439\) | −14.9274 | + | 25.8550i | −0.712445 | + | 1.23399i | 0.251492 | + | 0.967859i | \(0.419079\pi\) |
−0.963937 | + | 0.266131i | \(0.914255\pi\) | |||||||
\(440\) | 17.1544 | 0.817805 | ||||||||
\(441\) | 10.4099 | − | 18.2382i | 0.495710 | − | 0.868488i | ||||
\(442\) | 84.9240 | 4.03942 | ||||||||
\(443\) | −0.566390 | + | 0.981015i | −0.0269100 | + | 0.0466095i | −0.879167 | − | 0.476514i | \(-0.841900\pi\) |
0.852257 | + | 0.523124i | \(0.175233\pi\) | |||||||
\(444\) | −31.4285 | + | 43.4387i | −1.49153 | + | 2.06151i | ||||
\(445\) | −1.44436 | − | 2.50171i | −0.0684694 | − | 0.118592i | ||||
\(446\) | −9.08977 | −0.430413 | ||||||||
\(447\) | 13.8567 | + | 1.42859i | 0.655401 | + | 0.0675702i | ||||
\(448\) | −9.21990 | + | 6.70552i | −0.435599 | + | 0.316806i | ||||
\(449\) | −23.0291 | −1.08681 | −0.543406 | − | 0.839470i | \(-0.682866\pi\) | ||||
−0.543406 | + | 0.839470i | \(0.682866\pi\) | |||||||
\(450\) | −5.16748 | + | 5.78509i | −0.243597 | + | 0.272712i | ||||
\(451\) | 10.9342 | − | 18.9386i | 0.514871 | − | 0.891783i | ||||
\(452\) | −30.9921 | −1.45775 | ||||||||
\(453\) | 20.7489 | + | 2.13916i | 0.974870 | + | 0.100507i | ||||
\(454\) | −17.8433 | + | 30.9055i | −0.837427 | + | 1.45047i | ||||
\(455\) | −1.77379 | − | 16.7976i | −0.0831564 | − | 0.787483i | ||||
\(456\) | 8.10857 | + | 18.1153i | 0.379719 | + | 0.848326i | ||||
\(457\) | 11.8422 | − | 20.5113i | 0.553955 | − | 0.959478i | −0.444029 | − | 0.896012i | \(-0.646451\pi\) |
0.997984 | − | 0.0634658i | \(-0.0202154\pi\) | |||||||
\(458\) | −14.2879 | + | 24.7474i | −0.667631 | + | 1.15637i | ||||
\(459\) | −19.7591 | + | 18.0054i | −0.922277 | + | 0.840422i | ||||
\(460\) | −11.3797 | − | 19.7101i | −0.530579 | − | 0.918990i | ||||
\(461\) | −12.4889 | − | 21.6313i | −0.581664 | − | 1.00747i | −0.995282 | − | 0.0970216i | \(-0.969068\pi\) |
0.413618 | − | 0.910451i | \(-0.364265\pi\) | |||||||
\(462\) | −0.0723974 | − | 29.2718i | −0.00336823 | − | 1.36185i | ||||
\(463\) | 3.19536 | − | 5.53453i | 0.148501 | − | 0.257212i | −0.782173 | − | 0.623062i | \(-0.785888\pi\) |
0.930674 | + | 0.365850i | \(0.119222\pi\) | |||||||
\(464\) | −5.52336 | −0.256415 | ||||||||
\(465\) | −0.387418 | − | 0.865526i | −0.0179661 | − | 0.0401378i | ||||
\(466\) | 56.7350 | 2.62820 | ||||||||
\(467\) | −18.1461 | − | 31.4300i | −0.839702 | − | 1.45441i | −0.890144 | − | 0.455679i | \(-0.849396\pi\) |
0.0504425 | − | 0.998727i | \(-0.483937\pi\) | |||||||
\(468\) | 87.8529 | + | 18.3094i | 4.06100 | + | 0.846354i | ||||
\(469\) | −2.86843 | − | 1.27543i | −0.132452 | − | 0.0588939i | ||||
\(470\) | 2.11432 | + | 3.66211i | 0.0975264 | + | 0.168921i | ||||
\(471\) | −2.49655 | − | 5.57751i | −0.115035 | − | 0.256998i | ||||
\(472\) | 30.8756 | + | 53.4781i | 1.42116 | + | 2.46153i | ||||
\(473\) | −9.27549 | − | 16.0656i | −0.426488 | − | 0.738698i | ||||
\(474\) | −22.5035 | − | 50.2748i | −1.03362 | − | 2.30920i | ||||
\(475\) | 0.825096 | + | 1.42911i | 0.0378580 | + | 0.0655720i | ||||
\(476\) | −51.5786 | + | 37.5126i | −2.36410 | + | 1.71939i | ||||
\(477\) | 18.6408 | − | 20.8688i | 0.853504 | − | 0.955515i | ||||
\(478\) | 14.1204 | + | 24.4573i | 0.645854 | + | 1.11865i | ||||
\(479\) | 20.6282 | 0.942526 | 0.471263 | − | 0.881993i | \(-0.343798\pi\) | ||||
0.471263 | + | 0.881993i | \(0.343798\pi\) | |||||||
\(480\) | −5.87739 | − | 13.1306i | −0.268265 | − | 0.599328i | ||||
\(481\) | 42.1771 | 1.92311 | ||||||||
\(482\) | −15.1194 | + | 26.1876i | −0.688670 | + | 1.19281i | ||||
\(483\) | −19.2493 | + | 11.1772i | −0.875875 | + | 0.508579i | ||||
\(484\) | 11.4726 | + | 19.8711i | 0.521482 | + | 0.903233i | ||||
\(485\) | 5.53831 | + | 9.59263i | 0.251482 | + | 0.435579i | ||||
\(486\) | −34.7045 | + | 20.4986i | −1.57423 | + | 0.929836i | ||||
\(487\) | −4.41678 | + | 7.65008i | −0.200143 | + | 0.346658i | −0.948574 | − | 0.316554i | \(-0.897474\pi\) |
0.748431 | + | 0.663212i | \(0.230807\pi\) | |||||||
\(488\) | 1.09237 | − | 1.89204i | 0.0494491 | − | 0.0856484i | ||||
\(489\) | 1.63730 | + | 3.65788i | 0.0740415 | + | 0.165415i | ||||
\(490\) | 12.1241 | + | 13.4387i | 0.547709 | + | 0.607100i | ||||
\(491\) | 8.71841 | − | 15.1007i | 0.393456 | − | 0.681486i | −0.599447 | − | 0.800415i | \(-0.704613\pi\) |
0.992903 | + | 0.118929i | \(0.0379459\pi\) | |||||||
\(492\) | −71.4615 | − | 7.36750i | −3.22173 | − | 0.332152i | ||||
\(493\) | −3.31055 | −0.149100 | ||||||||
\(494\) | 13.6201 | − | 23.5907i | 0.612796 | − | 1.06139i | ||||
\(495\) | 7.25538 | + | 1.51210i | 0.326105 | + | 0.0679636i | ||||
\(496\) | 4.69930 | 0.211005 | ||||||||
\(497\) | 2.58987 | − | 1.88358i | 0.116172 | − | 0.0844903i | ||||
\(498\) | −28.6596 | − | 2.95474i | −1.28427 | − | 0.132405i | ||||
\(499\) | 30.8164 | 1.37953 | 0.689767 | − | 0.724032i | \(-0.257713\pi\) | ||||
0.689767 | + | 0.724032i | \(0.257713\pi\) | |||||||
\(500\) | −2.34278 | − | 4.05782i | −0.104772 | − | 0.181471i | ||||
\(501\) | 12.4893 | − | 17.2620i | 0.557980 | − | 0.771208i | ||||
\(502\) | 2.57363 | − | 4.45765i | 0.114867 | − | 0.198955i | ||||
\(503\) | 23.0337 | 1.02702 | 0.513512 | − | 0.858083i | \(-0.328344\pi\) | ||||
0.513512 | + | 0.858083i | \(0.328344\pi\) | |||||||
\(504\) | −50.2502 | + | 22.6418i | −2.23832 | + | 1.00855i | ||||
\(505\) | −15.3178 | −0.681635 | ||||||||
\(506\) | −15.5134 | + | 26.8701i | −0.689657 | + | 1.19452i | ||||
\(507\) | −19.6423 | − | 43.8826i | −0.872343 | − | 1.94889i | ||||
\(508\) | 30.4762 | + | 52.7864i | 1.35216 | + | 2.34202i | ||||
\(509\) | −23.9878 | −1.06324 | −0.531620 | − | 0.846983i | \(-0.678416\pi\) | ||||
−0.531620 | + | 0.846983i | \(0.678416\pi\) | |||||||
\(510\) | −9.41304 | − | 21.0296i | −0.416816 | − | 0.931205i | ||||
\(511\) | 3.50146 | + | 33.1585i | 0.154895 | + | 1.46684i | ||||
\(512\) | −47.9131 | −2.11748 | ||||||||
\(513\) | 1.83269 | + | 8.37651i | 0.0809153 | + | 0.369832i | ||||
\(514\) | 2.18390 | − | 3.78262i | 0.0963276 | − | 0.166844i | ||||
\(515\) | −8.87687 | −0.391161 | ||||||||
\(516\) | −35.7229 | + | 49.3742i | −1.57261 | + | 2.17358i | ||||
\(517\) | 2.02010 | − | 3.49892i | 0.0888441 | − | 0.153882i | ||||
\(518\) | −36.5505 | + | 26.5827i | −1.60594 | + | 1.16798i | ||||
\(519\) | 3.18231 | − | 4.39841i | 0.139688 | − | 0.193069i | ||||
\(520\) | −22.1656 | + | 38.3920i | −0.972028 | + | 1.68360i | ||||
\(521\) | 2.82741 | − | 4.89722i | 0.123871 | − | 0.214551i | −0.797420 | − | 0.603425i | \(-0.793802\pi\) |
0.921291 | + | 0.388874i | \(0.127136\pi\) | |||||||
\(522\) | −4.88655 | − | 1.01841i | −0.213878 | − | 0.0445744i | ||||
\(523\) | −2.01049 | − | 3.48227i | −0.0879126 | − | 0.152269i | 0.818716 | − | 0.574199i | \(-0.194686\pi\) |
−0.906629 | + | 0.421930i | \(0.861353\pi\) | |||||||
\(524\) | −5.27149 | − | 9.13049i | −0.230286 | − | 0.398867i | ||||
\(525\) | −3.96295 | + | 2.30110i | −0.172957 | + | 0.100428i | ||||
\(526\) | 29.4961 | − | 51.0888i | 1.28609 | − | 2.22758i | ||||
\(527\) | 2.81663 | 0.122694 | ||||||||
\(528\) | −21.5288 | + | 29.7559i | −0.936922 | + | 1.29496i | ||||
\(529\) | 0.593633 | 0.0258101 | ||||||||
\(530\) | 12.0585 | + | 20.8860i | 0.523789 | + | 0.907229i | ||||
\(531\) | 8.34480 | + | 25.3399i | 0.362133 | + | 1.09966i | ||||
\(532\) | 2.14829 | + | 20.3441i | 0.0931400 | + | 0.882027i | ||||
\(533\) | 28.2567 | + | 48.9420i | 1.22393 | + | 2.11991i | ||||
\(534\) | 12.8689 | + | 1.32675i | 0.556890 | + | 0.0574140i | ||||
\(535\) | −0.437949 | − | 0.758550i | −0.0189342 | − | 0.0327950i | ||||
\(536\) | 4.11951 | + | 7.13520i | 0.177936 | + | 0.308194i | ||||
\(537\) | −14.7096 | + | 20.3307i | −0.634764 | + | 0.877336i | ||||
\(538\) | 7.15553 | + | 12.3937i | 0.308497 | + | 0.534332i | ||||
\(539\) | 5.32777 | − | 16.4518i | 0.229483 | − | 0.708629i | ||||
\(540\) | −5.20375 | − | 23.7843i | −0.223934 | − | 1.02351i | ||||
\(541\) | −20.6577 | − | 35.7801i | −0.888142 | − | 1.53831i | −0.842069 | − | 0.539369i | \(-0.818663\pi\) |
−0.0460730 | − | 0.998938i | \(-0.514671\pi\) | |||||||
\(542\) | 22.6279 | 0.971950 | ||||||||
\(543\) | 18.3786 | + | 1.89478i | 0.788700 | + | 0.0813130i | ||||
\(544\) | 42.7302 | 1.83204 | ||||||||
\(545\) | 6.95218 | − | 12.0415i | 0.297799 | − | 0.515803i | ||||
\(546\) | 65.6045 | + | 37.6607i | 2.80761 | + | 1.61173i | ||||
\(547\) | −9.86882 | − | 17.0933i | −0.421960 | − | 0.730857i | 0.574171 | − | 0.818736i | \(-0.305325\pi\) |
−0.996131 | + | 0.0878787i | \(0.971991\pi\) | |||||||
\(548\) | −39.0037 | − | 67.5564i | −1.66616 | − | 2.88587i | ||||
\(549\) | 0.628787 | − | 0.703939i | 0.0268360 | − | 0.0300434i | ||||
\(550\) | −3.19382 | + | 5.53186i | −0.136185 | + | 0.235879i | ||||
\(551\) | −0.530945 | + | 0.919623i | −0.0226190 | + | 0.0391773i | ||||
\(552\) | 58.1121 | + | 5.99121i | 2.47342 | + | 0.255003i | ||||
\(553\) | −3.41720 | − | 32.3606i | −0.145314 | − | 1.37611i | ||||
\(554\) | 36.1986 | − | 62.6977i | 1.53793 | − | 2.66377i | ||||
\(555\) | −4.67494 | − | 10.4442i | −0.198440 | − | 0.443334i | ||||
\(556\) | −82.3318 | −3.49165 | ||||||||
\(557\) | −3.38731 | + | 5.86700i | −0.143525 | + | 0.248593i | −0.928822 | − | 0.370527i | \(-0.879177\pi\) |
0.785297 | + | 0.619120i | \(0.212510\pi\) | |||||||
\(558\) | 4.15750 | + | 0.866465i | 0.176001 | + | 0.0366804i | ||||
\(559\) | 47.9403 | 2.02766 | ||||||||
\(560\) | −2.38481 | − | 22.5839i | −0.100777 | − | 0.954345i | ||||
\(561\) | −12.9038 | + | 17.8349i | −0.544798 | + | 0.752990i | ||||
\(562\) | 31.4634 | 1.32720 | ||||||||
\(563\) | 14.1126 | + | 24.4437i | 0.594773 | + | 1.03018i | 0.993579 | + | 0.113142i | \(0.0360915\pi\) |
−0.398806 | + | 0.917035i | \(0.630575\pi\) | |||||||
\(564\) | −13.2026 | − | 1.36115i | −0.555929 | − | 0.0573149i | ||||
\(565\) | 3.30719 | − | 5.72822i | 0.139135 | − | 0.240988i | ||||
\(566\) | 2.72115 | 0.114378 | ||||||||
\(567\) | −23.2489 | + | 5.14689i | −0.976360 | + | 0.216149i | ||||
\(568\) | −8.40485 | −0.352660 | ||||||||
\(569\) | −19.8886 | + | 34.4480i | −0.833773 | + | 1.44414i | 0.0612526 | + | 0.998122i | \(0.480490\pi\) |
−0.895026 | + | 0.446015i | \(0.852843\pi\) | |||||||
\(570\) | −7.35137 | − | 0.757908i | −0.307915 | − | 0.0317453i | ||||
\(571\) | −16.4549 | − | 28.5007i | −0.688615 | − | 1.19272i | −0.972286 | − | 0.233794i | \(-0.924886\pi\) |
0.283671 | − | 0.958922i | \(-0.408448\pi\) | |||||||
\(572\) | 73.8991 | 3.08988 | ||||||||
\(573\) | −13.5992 | + | 18.7961i | −0.568115 | + | 0.785216i | ||||
\(574\) | −55.3335 | − | 24.6037i | −2.30957 | − | 1.02694i | ||||
\(575\) | 4.85733 | 0.202565 | ||||||||
\(576\) | 12.6550 | + | 2.63743i | 0.527292 | + | 0.109893i | ||||
\(577\) | −9.93085 | + | 17.2007i | −0.413427 | + | 0.716076i | −0.995262 | − | 0.0972307i | \(-0.969002\pi\) |
0.581835 | + | 0.813307i | \(0.302335\pi\) | |||||||
\(578\) | 24.4793 | 1.01820 | ||||||||
\(579\) | −3.20671 | − | 7.16409i | −0.133266 | − | 0.297729i | ||||
\(580\) | 1.50757 | − | 2.61118i | 0.0625983 | − | 0.108423i | ||||
\(581\) | −15.5529 | − | 6.91549i | −0.645242 | − | 0.286903i | ||||
\(582\) | −49.3447 | − | 5.08732i | −2.04541 | − | 0.210876i | ||||
\(583\) | 11.5212 | − | 19.9553i | 0.477159 | − | 0.826463i | ||||
\(584\) | 43.7550 | − | 75.7859i | 1.81060 | − | 3.13604i | ||||
\(585\) | −12.7590 | + | 14.2839i | −0.527518 | + | 0.590567i | ||||
\(586\) | −24.3901 | − | 42.2449i | −1.00755 | − | 1.74512i | ||||
\(587\) | −12.3770 | − | 21.4375i | −0.510852 | − | 0.884822i | −0.999921 | − | 0.0125770i | \(-0.995997\pi\) |
0.489068 | − | 0.872245i | \(-0.337337\pi\) | |||||||
\(588\) | −56.4804 | + | 6.10549i | −2.32921 | + | 0.251786i | ||||
\(589\) | 0.451730 | − | 0.782420i | 0.0186132 | − | 0.0322390i | ||||
\(590\) | −22.9937 | −0.946638 | ||||||||
\(591\) | 2.80806 | + | 0.289504i | 0.115508 | + | 0.0119086i | ||||
\(592\) | 56.7061 | 2.33061 | ||||||||
\(593\) | −2.69526 | − | 4.66833i | −0.110681 | − | 0.191706i | 0.805364 | − | 0.592781i | \(-0.201970\pi\) |
−0.916045 | + | 0.401075i | \(0.868637\pi\) | |||||||
\(594\) | −24.5331 | + | 22.3557i | −1.00661 | + | 0.917267i | ||||
\(595\) | −1.42939 | − | 13.5362i | −0.0585993 | − | 0.554930i | ||||
\(596\) | −18.8420 | − | 32.6354i | −0.771800 | − | 1.33680i | ||||
\(597\) | −23.3121 | + | 32.2207i | −0.954102 | + | 1.31871i | ||||
\(598\) | −40.0906 | − | 69.4389i | −1.63943 | − | 2.83957i | ||||
\(599\) | 2.54350 | + | 4.40548i | 0.103925 | + | 0.180003i | 0.913298 | − | 0.407291i | \(-0.133527\pi\) |
−0.809374 | + | 0.587294i | \(0.800193\pi\) | |||||||
\(600\) | 11.9638 | + | 1.23344i | 0.488420 | + | 0.0503549i | ||||
\(601\) | 9.14504 | + | 15.8397i | 0.373034 | + | 0.646114i | 0.990031 | − | 0.140852i | \(-0.0449842\pi\) |
−0.616997 | + | 0.786966i | \(0.711651\pi\) | |||||||
\(602\) | −41.5448 | + | 30.2151i | −1.69324 | + | 1.23147i | ||||
\(603\) | 1.11339 | + | 3.38092i | 0.0453406 | + | 0.137682i | ||||
\(604\) | −28.2139 | − | 48.8679i | −1.14801 | − | 1.98841i | ||||
\(605\) | −4.89700 | −0.199091 | ||||||||
\(606\) | 40.2121 | − | 55.5789i | 1.63350 | − | 2.25774i | ||||
\(607\) | 28.0586 | 1.13886 | 0.569431 | − | 0.822039i | \(-0.307164\pi\) | ||||
0.569431 | + | 0.822039i | \(0.307164\pi\) | |||||||
\(608\) | 6.85305 | − | 11.8698i | 0.277928 | − | 0.481385i | ||||
\(609\) | −2.55743 | − | 1.46811i | −0.103632 | − | 0.0594908i | ||||
\(610\) | 0.406755 | + | 0.704521i | 0.0164690 | + | 0.0285252i | ||||
\(611\) | 5.22045 | + | 9.04208i | 0.211197 | + | 0.365804i | ||||
\(612\) | 70.7956 | + | 14.7545i | 2.86174 | + | 0.596416i | ||||
\(613\) | −6.77692 | + | 11.7380i | −0.273717 | + | 0.474092i | −0.969811 | − | 0.243859i | \(-0.921587\pi\) |
0.696094 | + | 0.717951i | \(0.254920\pi\) | |||||||
\(614\) | 40.6144 | − | 70.3462i | 1.63906 | − | 2.83894i | ||||
\(615\) | 8.98743 | − | 12.4219i | 0.362408 | − | 0.500900i | ||||
\(616\) | −36.7053 | + | 26.6953i | −1.47890 | + | 1.07559i | ||||
\(617\) | 20.9055 | − | 36.2094i | 0.841624 | − | 1.45774i | −0.0468963 | − | 0.998900i | \(-0.514933\pi\) |
0.888521 | − | 0.458836i | \(-0.151734\pi\) | |||||||
\(618\) | 23.3034 | − | 32.2086i | 0.937399 | − | 1.29562i | ||||
\(619\) | −17.1479 | −0.689230 | −0.344615 | − | 0.938744i | \(-0.611991\pi\) | ||||
−0.344615 | + | 0.938744i | \(0.611991\pi\) | |||||||
\(620\) | −1.28264 | + | 2.22161i | −0.0515122 | + | 0.0892218i | ||||
\(621\) | 24.0501 | + | 7.65631i | 0.965099 | + | 0.307237i | ||||
\(622\) | −47.3546 | −1.89875 | ||||||||
\(623\) | 6.98361 | + | 3.10522i | 0.279792 | + | 0.124408i | ||||
\(624\) | −38.7766 | − | 86.6304i | −1.55231 | − | 3.46799i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.29223 | − | 14.3626i | −0.331424 | − | 0.574044i | ||||
\(627\) | 2.88477 | + | 6.44484i | 0.115207 | + | 0.257382i | ||||
\(628\) | −8.26545 | + | 14.3162i | −0.329827 | + | 0.571278i | ||||
\(629\) | 33.9881 | 1.35519 | ||||||||
\(630\) | 2.05421 | − | 20.4199i | 0.0818416 | − | 0.813547i | ||||
\(631\) | −2.79587 | −0.111302 | −0.0556508 | − | 0.998450i | \(-0.517723\pi\) | ||||
−0.0556508 | + | 0.998450i | \(0.517723\pi\) | |||||||
\(632\) | −42.7022 | + | 73.9623i | −1.69860 | + | 2.94206i | ||||
\(633\) | 8.33640 | − | 11.5221i | 0.331342 | − | 0.457963i | ||||
\(634\) | −12.2590 | − | 21.2333i | −0.486868 | − | 0.843280i | ||||
\(635\) | −13.0086 | −0.516229 | ||||||||
\(636\) | −75.2978 | − | 7.76301i | −2.98575 | − | 0.307823i | ||||
\(637\) | 29.9354 | + | 33.1814i | 1.18608 | + | 1.31470i | ||||
\(638\) | −4.11041 | −0.162733 | ||||||||
\(639\) | −3.55479 | − | 0.740855i | −0.140625 | − | 0.0293078i | ||||
\(640\) | 2.73502 | − | 4.73719i | 0.108111 | − | 0.187254i | ||||
\(641\) | 13.7919 | 0.544746 | 0.272373 | − | 0.962192i | \(-0.412191\pi\) | ||||
0.272373 | + | 0.962192i | \(0.412191\pi\) | |||||||
\(642\) | 3.90200 | + | 0.402286i | 0.154000 | + | 0.0158770i | ||||
\(643\) | −6.91039 | + | 11.9691i | −0.272519 | + | 0.472017i | −0.969506 | − | 0.245067i | \(-0.921190\pi\) |
0.696987 | + | 0.717084i | \(0.254523\pi\) | |||||||
\(644\) | 55.0215 | + | 24.4650i | 2.16815 | + | 0.964056i | ||||
\(645\) | −5.31374 | − | 11.8714i | −0.209228 | − | 0.467435i | ||||
\(646\) | 10.9756 | − | 19.0103i | 0.431830 | − | 0.747952i | ||||
\(647\) | 14.5042 | − | 25.1221i | 0.570220 | − | 0.987650i | −0.426323 | − | 0.904571i | \(-0.640191\pi\) |
0.996543 | − | 0.0830790i | \(-0.0264754\pi\) | |||||||
\(648\) | 57.2923 | + | 24.9649i | 2.25065 | + | 0.980716i | ||||
\(649\) | 10.9846 | + | 19.0258i | 0.431181 | + | 0.746828i | ||||
\(650\) | −8.25363 | − | 14.2957i | −0.323734 | − | 0.560723i | ||||
\(651\) | 2.17587 | + | 1.24907i | 0.0852791 | + | 0.0489551i | ||||
\(652\) | 5.42071 | − | 9.38894i | 0.212291 | − | 0.367699i | ||||
\(653\) | −34.9087 | −1.36608 | −0.683042 | − | 0.730379i | \(-0.739343\pi\) | ||||
−0.683042 | + | 0.730379i | \(0.739343\pi\) | |||||||
\(654\) | 25.4405 | + | 56.8363i | 0.994802 | + | 2.22248i | ||||
\(655\) | 2.25010 | 0.0879186 | ||||||||
\(656\) | 37.9904 | + | 65.8013i | 1.48328 | + | 2.56911i | ||||
\(657\) | 25.1862 | − | 28.1965i | 0.982607 | − | 1.10005i | ||||
\(658\) | −10.2229 | − | 4.54556i | −0.398531 | − | 0.177204i | ||||
\(659\) | 16.9405 | + | 29.3418i | 0.659908 | + | 1.14299i | 0.980639 | + | 0.195824i | \(0.0627382\pi\) |
−0.320731 | + | 0.947170i | \(0.603928\pi\) | |||||||
\(660\) | −8.19104 | − | 18.2995i | −0.318836 | − | 0.712308i | ||||
\(661\) | 10.6327 | + | 18.4164i | 0.413566 | + | 0.716317i | 0.995277 | − | 0.0970789i | \(-0.0309499\pi\) |
−0.581711 | + | 0.813395i | \(0.697617\pi\) | |||||||
\(662\) | −16.8142 | − | 29.1231i | −0.653504 | − | 1.13190i | ||||
\(663\) | −23.2416 | − | 51.9239i | −0.902630 | − | 2.01656i | ||||
\(664\) | 22.3363 | + | 38.6876i | 0.866817 | + | 1.50137i | ||||
\(665\) | −3.98941 | − | 1.77387i | −0.154702 | − | 0.0687875i | ||||
\(666\) | 50.1682 | + | 10.4556i | 1.94398 | + | 0.405145i | ||||
\(667\) | 1.56283 | + | 2.70690i | 0.0605131 | + | 0.104812i | ||||
\(668\) | −57.6380 | −2.23008 | ||||||||
\(669\) | 2.48765 | + | 5.55763i | 0.0961781 | + | 0.214870i | ||||
\(670\) | −3.06789 | −0.118523 | ||||||||
\(671\) | 0.388630 | − | 0.673126i | 0.0150029 | − | 0.0259858i | ||||
\(672\) | 33.0094 | + | 18.9493i | 1.27337 | + | 0.730985i | ||||
\(673\) | −6.96999 | − | 12.0724i | −0.268673 | − | 0.465356i | 0.699846 | − | 0.714294i | \(-0.253252\pi\) |
−0.968520 | + | 0.248938i | \(0.919919\pi\) | |||||||
\(674\) | −1.63226 | − | 2.82716i | −0.0628723 | − | 0.108898i | ||||
\(675\) | 4.95131 | + | 1.57624i | 0.190576 | + | 0.0606695i | ||||
\(676\) | −65.0306 | + | 112.636i | −2.50118 | + | 4.33217i | ||||
\(677\) | −0.108664 | + | 0.188212i | −0.00417630 | + | 0.00723356i | −0.868106 | − | 0.496379i | \(-0.834663\pi\) |
0.863930 | + | 0.503612i | \(0.167996\pi\) | |||||||
\(678\) | 12.1022 | + | 27.0374i | 0.464782 | + | 1.03836i | ||||
\(679\) | −26.7782 | − | 11.9067i | −1.02765 | − | 0.456939i | ||||
\(680\) | −17.8620 | + | 30.9379i | −0.684976 | + | 1.18641i | ||||
\(681\) | 23.7794 | + | 2.45160i | 0.911228 | + | 0.0939453i | ||||
\(682\) | 3.49716 | 0.133913 | ||||||||
\(683\) | −1.92685 | + | 3.33741i | −0.0737290 | + | 0.127702i | −0.900533 | − | 0.434788i | \(-0.856823\pi\) |
0.826804 | + | 0.562490i | \(0.190157\pi\) | |||||||
\(684\) | 15.4528 | − | 17.2997i | 0.590851 | − | 0.661469i | ||||
\(685\) | 16.6485 | 0.636105 | ||||||||
\(686\) | −46.8549 | − | 9.88764i | −1.78893 | − | 0.377512i | ||||
\(687\) | 19.0412 | + | 1.96310i | 0.726468 | + | 0.0748970i | ||||
\(688\) | 64.4546 | 2.45731 | ||||||||
\(689\) | 29.7736 | + | 51.5694i | 1.13428 | + | 1.96464i | ||||
\(690\) | −12.7514 | + | 17.6242i | −0.485436 | + | 0.670942i | ||||
\(691\) | −15.7278 | + | 27.2414i | −0.598314 | + | 1.03631i | 0.394756 | + | 0.918786i | \(0.370829\pi\) |
−0.993070 | + | 0.117524i | \(0.962504\pi\) | |||||||
\(692\) | −14.6864 | −0.558292 | ||||||||
\(693\) | −17.8774 | + | 8.05524i | −0.679107 | + | 0.305993i | ||||
\(694\) | −60.6274 | −2.30138 | ||||||||
\(695\) | 8.78569 | − | 15.2173i | 0.333260 | − | 0.577224i | ||||
\(696\) | 3.16195 | + | 7.06407i | 0.119853 | + | 0.267763i | ||||
\(697\) | 22.7704 | + | 39.4395i | 0.862491 | + | 1.49388i | ||||
\(698\) | −6.49015 | −0.245656 | ||||||||
\(699\) | −15.5270 | − | 34.6887i | −0.587285 | − | 1.31205i | ||||
\(700\) | 11.3275 | + | 5.03672i | 0.428141 | + | 0.190370i | ||||
\(701\) | −1.08645 | −0.0410348 | −0.0205174 | − | 0.999789i | \(-0.506531\pi\) | ||||
−0.0205174 | + | 0.999789i | \(0.506531\pi\) | |||||||
\(702\) | −18.3328 | − | 83.7921i | −0.691928 | − | 3.16253i | ||||
\(703\) | 5.45100 | − | 9.44140i | 0.205588 | − | 0.356089i | ||||
\(704\) | 10.6450 | 0.401198 | ||||||||
\(705\) | 1.66044 | − | 2.29496i | 0.0625357 | − | 0.0864333i | ||||
\(706\) | −0.936217 | + | 1.62158i | −0.0352350 | + | 0.0610288i | ||||
\(707\) | 32.7755 | − | 23.8373i | 1.23265 | − | 0.896493i | ||||
\(708\) | 42.3051 | − | 58.4717i | 1.58992 | − | 2.19750i | ||||
\(709\) | −14.3400 | + | 24.8376i | −0.538549 | + | 0.932795i | 0.460433 | + | 0.887694i | \(0.347694\pi\) |
−0.998982 | + | 0.0451005i | \(0.985639\pi\) | |||||||
\(710\) | 1.56482 | − | 2.71035i | 0.0587267 | − | 0.101718i | ||||
\(711\) | −24.5802 | + | 27.5180i | −0.921828 | + | 1.03200i | ||||
\(712\) | −10.0295 | − | 17.3717i | −0.375873 | − | 0.651031i | ||||
\(713\) | −1.32966 | − | 2.30305i | −0.0497963 | − | 0.0862497i | ||||
\(714\) | 52.8668 | + | 30.3486i | 1.97849 | + | 1.13577i | ||||
\(715\) | −7.88583 | + | 13.6587i | −0.294913 | + | 0.510805i | ||||
\(716\) | 67.8846 | 2.53697 | ||||||||
\(717\) | 11.0892 | − | 15.3268i | 0.414133 | − | 0.572391i | ||||
\(718\) | −59.7927 | −2.23144 | ||||||||
\(719\) | −11.6921 | − | 20.2512i | −0.436040 | − | 0.755244i | 0.561340 | − | 0.827585i | \(-0.310286\pi\) |
−0.997380 | + | 0.0723419i | \(0.976953\pi\) | |||||||
\(720\) | −17.1541 | + | 19.2044i | −0.639295 | + | 0.715704i | ||||
\(721\) | 18.9938 | − | 13.8140i | 0.707367 | − | 0.514460i | ||||
\(722\) | 21.0431 | + | 36.4477i | 0.783143 | + | 1.35644i | ||||
\(723\) | 20.1493 | + | 2.07734i | 0.749361 | + | 0.0772572i | ||||
\(724\) | −24.9907 | − | 43.2852i | −0.928773 | − | 1.60868i | ||||
\(725\) | 0.321747 | + | 0.557282i | 0.0119494 | + | 0.0206969i | ||||
\(726\) | 12.8555 | − | 17.7682i | 0.477113 | − | 0.659438i | ||||
\(727\) | −13.5709 | − | 23.5056i | −0.503318 | − | 0.871773i | −0.999993 | − | 0.00383592i | \(-0.998779\pi\) |
0.496674 | − | 0.867937i | \(-0.334554\pi\) | |||||||
\(728\) | −12.3170 | − | 116.641i | −0.456499 | − | 4.32300i | ||||
\(729\) | 22.0309 | + | 15.6089i | 0.815961 | + | 0.578107i | ||||
\(730\) | 16.2927 | + | 28.2197i | 0.603019 | + | 1.04446i | ||||
\(731\) | 38.6323 | 1.42887 | ||||||||
\(732\) | −2.53992 | − | 0.261860i | −0.0938783 | − | 0.00967862i | ||||
\(733\) | −36.2657 | −1.33951 | −0.669753 | − | 0.742584i | \(-0.733600\pi\) | ||||
−0.669753 | + | 0.742584i | \(0.733600\pi\) | |||||||
\(734\) | 0.685244 | − | 1.18688i | 0.0252928 | − | 0.0438084i | ||||
\(735\) | 4.89860 | − | 11.0907i | 0.180688 | − | 0.409087i | ||||
\(736\) | −20.1719 | − | 34.9387i | −0.743545 | − | 1.28786i | ||||
\(737\) | 1.46559 | + | 2.53848i | 0.0539857 | + | 0.0935060i | ||||
\(738\) | 21.4778 | + | 65.2196i | 0.790608 | + | 2.40076i | ||||
\(739\) | −24.8169 | + | 42.9841i | −0.912903 | + | 1.58119i | −0.102961 | + | 0.994685i | \(0.532832\pi\) |
−0.809942 | + | 0.586510i | \(0.800502\pi\) | |||||||
\(740\) | −15.4776 | + | 26.8080i | −0.568967 | + | 0.985480i | ||||
\(741\) | −18.1512 | − | 1.87134i | −0.666801 | − | 0.0687455i | ||||
\(742\) | −58.3039 | − | 25.9245i | −2.14041 | − | 0.951718i | ||||
\(743\) | 16.3452 | − | 28.3107i | 0.599647 | − | 1.03862i | −0.393226 | − | 0.919442i | \(-0.628641\pi\) |
0.992873 | − | 0.119177i | \(-0.0380257\pi\) | |||||||
\(744\) | −2.69020 | − | 6.01014i | −0.0986275 | − | 0.220343i | ||||
\(745\) | 8.04259 | 0.294658 | ||||||||
\(746\) | −21.2417 | + | 36.7917i | −0.777713 | + | 1.34704i | ||||
\(747\) | 6.03687 | + | 18.3316i | 0.220878 | + | 0.670718i | ||||
\(748\) | 59.5510 | 2.17740 | ||||||||
\(749\) | 2.11752 | + | 0.941541i | 0.0773724 | + | 0.0344032i | ||||
\(750\) | −2.62518 | + | 3.62838i | −0.0958580 | + | 0.132490i | ||||
\(751\) | 25.7330 | 0.939011 | 0.469505 | − | 0.882930i | \(-0.344432\pi\) | ||||
0.469505 | + | 0.882930i | \(0.344432\pi\) | |||||||
\(752\) | 7.01876 | + | 12.1569i | 0.255948 | + | 0.443315i | ||||
\(753\) | −3.42982 | − | 0.353606i | −0.124990 | − | 0.0128861i | ||||
\(754\) | 5.31116 | − | 9.19920i | 0.193421 | − | 0.335015i | ||||
\(755\) | 12.0429 | 0.438286 | ||||||||
\(756\) | 48.1471 | + | 42.7933i | 1.75109 | + | 1.55638i | ||||
\(757\) | −43.8620 | −1.59419 | −0.797096 | − | 0.603852i | \(-0.793632\pi\) | ||||
−0.797096 | + | 0.603852i | \(0.793632\pi\) | |||||||
\(758\) | −4.86841 | + | 8.43233i | −0.176829 | + | 0.306276i | ||||
\(759\) | 20.6744 | + | 2.13148i | 0.750435 | + | 0.0773679i | ||||
\(760\) | 5.72940 | + | 9.92361i | 0.207827 | + | 0.359967i | ||||
\(761\) | −2.38547 | −0.0864730 | −0.0432365 | − | 0.999065i | \(-0.513767\pi\) | ||||
−0.0432365 | + | 0.999065i | \(0.513767\pi\) | |||||||
\(762\) | 34.1498 | − | 47.2000i | 1.23712 | − | 1.70987i | ||||
\(763\) | 3.86319 | + | 36.5841i | 0.139857 | + | 1.32443i | ||||
\(764\) | 62.7603 | 2.27059 | ||||||||
\(765\) | −10.2817 | + | 11.5106i | −0.371736 | + | 0.416165i | ||||
\(766\) | 10.2313 | − | 17.7212i | 0.369673 | − | 0.640293i | ||||
\(767\) | −56.7736 | −2.04998 | ||||||||
\(768\) | 16.1067 | + | 35.9838i | 0.581200 | + | 1.29845i | ||||
\(769\) | −3.73404 | + | 6.46755i | −0.134653 | + | 0.233226i | −0.925465 | − | 0.378833i | \(-0.876325\pi\) |
0.790812 | + | 0.612059i | \(0.209659\pi\) | |||||||
\(770\) | −1.77475 | − | 16.8067i | −0.0639574 | − | 0.605671i | ||||
\(771\) | −2.91044 | − | 0.300058i | −0.104817 | − | 0.0108063i | ||||
\(772\) | −10.6166 | + | 18.3885i | −0.382101 | + | 0.661818i | ||||
\(773\) | 3.01784 | − | 5.22705i | 0.108544 | − | 0.188004i | −0.806637 | − | 0.591048i | \(-0.798714\pi\) |
0.915181 | + | 0.403044i | \(0.132048\pi\) | |||||||
\(774\) | 57.0234 | + | 11.8842i | 2.04966 | + | 0.427170i | ||||
\(775\) | −0.273744 | − | 0.474138i | −0.00983317 | − | 0.0170316i | ||||
\(776\) | 38.4576 | + | 66.6105i | 1.38055 | + | 2.39118i | ||||
\(777\) | 26.2561 | + | 15.0725i | 0.941932 | + | 0.540723i | ||||
\(778\) | −39.9792 | + | 69.2460i | −1.43332 | + | 2.48259i | ||||
\(779\) | 14.6076 | 0.523373 | ||||||||
\(780\) | 51.5386 | + | 5.31350i | 1.84538 | + | 0.190254i | ||||
\(781\) | −2.99018 | −0.106997 | ||||||||
\(782\) | −32.3066 | − | 55.9568i | −1.15528 | − | 2.00101i | ||||
\(783\) | 0.714660 | + | 3.26643i | 0.0255399 | + | 0.116733i | ||||
\(784\) | 40.2474 | + | 44.6116i | 1.43741 | + | 1.59327i | ||||
\(785\) | −1.76403 | − | 3.05538i | −0.0629608 | − | 0.109051i | ||||
\(786\) | −5.90691 | + | 8.16421i | −0.210693 | + | 0.291208i | ||||
\(787\) | −0.777771 | − | 1.34714i | −0.0277245 | − | 0.0480203i | 0.851830 | − | 0.523818i | \(-0.175493\pi\) |
−0.879555 | + | 0.475798i | \(0.842159\pi\) | |||||||
\(788\) | −3.81834 | − | 6.61355i | −0.136023 | − | 0.235598i | ||||
\(789\) | −39.3089 | − | 4.05265i | −1.39943 | − | 0.144278i | ||||
\(790\) | −15.9006 | − | 27.5407i | −0.565719 | − | 0.979854i | ||||
\(791\) | 1.83774 | + | 17.4033i | 0.0653426 | + | 0.618788i | ||||
\(792\) | 50.3808 | + | 10.4999i | 1.79020 | + | 0.373096i | ||||
\(793\) | 1.00431 | + | 1.73952i | 0.0356643 | + | 0.0617723i | ||||
\(794\) | −62.7673 | −2.22753 | ||||||||
\(795\) | 9.46990 | − | 13.0888i | 0.335863 | − | 0.464211i | ||||
\(796\) | 107.585 | 3.81327 | ||||||||
\(797\) | −25.6596 | + | 44.4438i | −0.908911 | + | 1.57428i | −0.0933310 | + | 0.995635i | \(0.529751\pi\) |
−0.815580 | + | 0.578645i | \(0.803582\pi\) | |||||||
\(798\) | 16.9092 | − | 9.81835i | 0.598578 | − | 0.347566i | ||||
\(799\) | 4.20686 | + | 7.28649i | 0.148828 | + | 0.257777i | ||||
\(800\) | −4.15288 | − | 7.19299i | −0.146826 | − | 0.254311i | ||||
\(801\) | −2.71070 | − | 8.23133i | −0.0957779 | − | 0.290840i | ||||
\(802\) | 45.7747 | − | 79.2840i | 1.61636 | − | 2.79962i | ||||
\(803\) | 15.5666 | − | 26.9622i | 0.549335 | − | 0.951476i | ||||
\(804\) | 5.64447 | − | 7.80146i | 0.199065 | − | 0.275136i | ||||
\(805\) | −10.3932 | + | 7.55887i | −0.366313 | + | 0.266415i | ||||
\(806\) | −4.51876 | + | 7.82672i | −0.159167 | + | 0.275684i | ||||
\(807\) | 5.61943 | − | 7.76687i | 0.197813 | − | 0.273407i | ||||
\(808\) | −106.366 | −3.74193 | ||||||||
\(809\) | 3.47119 | − | 6.01228i | 0.122041 | − | 0.211381i | −0.798532 | − | 0.601953i | \(-0.794389\pi\) |
0.920572 | + | 0.390572i | \(0.127723\pi\) | |||||||
\(810\) | −18.7173 | + | 13.8273i | −0.657658 | + | 0.485842i | ||||
\(811\) | −24.8086 | −0.871147 | −0.435573 | − | 0.900153i | \(-0.643454\pi\) | ||||
−0.435573 | + | 0.900153i | \(0.643454\pi\) | |||||||
\(812\) | 0.837726 | + | 7.93318i | 0.0293984 | + | 0.278400i | ||||
\(813\) | −6.19270 | − | 13.8350i | −0.217187 | − | 0.485216i | ||||
\(814\) | 42.2000 | 1.47911 | ||||||||
\(815\) | 1.15690 | + | 2.00380i | 0.0405243 | + | 0.0701901i | ||||
\(816\) | −31.2478 | − | 69.8104i | −1.09389 | − | 2.44385i | ||||
\(817\) | 6.19583 | − | 10.7315i | 0.216765 | − | 0.375448i | ||||
\(818\) | −56.3250 | −1.96936 | ||||||||
\(819\) | 5.07202 | − | 50.4185i | 0.177231 | − | 1.76176i | ||||
\(820\) | −41.4770 | −1.44844 | ||||||||
\(821\) | 20.1841 | − | 34.9598i | 0.704429 | − | 1.22011i | −0.262469 | − | 0.964941i | \(-0.584537\pi\) |
0.966897 | − | 0.255166i | \(-0.0821301\pi\) | |||||||
\(822\) | −43.7052 | + | 60.4069i | −1.52440 | + | 2.10693i | ||||
\(823\) | 0.713665 | + | 1.23610i | 0.0248768 | + | 0.0430879i | 0.878196 | − | 0.478301i | \(-0.158747\pi\) |
−0.853319 | + | 0.521389i | \(0.825414\pi\) | |||||||
\(824\) | −61.6402 | −2.14734 | ||||||||
\(825\) | 4.25634 | + | 0.438818i | 0.148187 | + | 0.0152777i | ||||
\(826\) | 49.1997 | − | 35.7824i | 1.71188 | − | 1.24503i | ||||
\(827\) | 55.1650 | 1.91827 | 0.959137 | − | 0.282941i | \(-0.0913101\pi\) | ||||
0.959137 | + | 0.282941i | \(0.0913101\pi\) | |||||||
\(828\) | −21.3567 | − | 64.8519i | −0.742197 | − | 2.25376i | ||||
\(829\) | 25.1626 | − | 43.5829i | 0.873933 | − | 1.51370i | 0.0160370 | − | 0.999871i | \(-0.494895\pi\) |
0.857896 | − | 0.513824i | \(-0.171772\pi\) | |||||||
\(830\) | −16.6344 | −0.577387 | ||||||||
\(831\) | −48.2411 | − | 4.97353i | −1.67346 | − | 0.172530i | ||||
\(832\) | −13.7546 | + | 23.8237i | −0.476856 | + | 0.825939i | ||||
\(833\) | 24.1232 | + | 26.7390i | 0.835819 | + | 0.926451i | ||||
\(834\) | 32.1499 | + | 71.8259i | 1.11326 | + | 2.48713i | ||||
\(835\) | 6.15059 | − | 10.6531i | 0.212850 | − | 0.368667i | ||||
\(836\) | 9.55077 | − | 16.5424i | 0.330320 | − | 0.572131i | ||||
\(837\) | −0.608036 | − | 2.77909i | −0.0210168 | − | 0.0960595i | ||||
\(838\) | −4.20209 | − | 7.27823i | −0.145159 | − | 0.251422i | ||||
\(839\) | −6.27310 | − | 10.8653i | −0.216572 | − | 0.375113i | 0.737186 | − | 0.675690i | \(-0.236154\pi\) |
−0.953758 | + | 0.300577i | \(0.902821\pi\) | |||||||
\(840\) | −27.5184 | + | 15.9786i | −0.949474 | + | 0.551315i | ||||
\(841\) | 14.2930 | − | 24.7561i | 0.492861 | − | 0.853660i | ||||
\(842\) | 58.7307 | 2.02400 | ||||||||
\(843\) | −8.61076 | − | 19.2372i | −0.296570 | − | 0.662565i | ||||
\(844\) | −38.4725 | −1.32428 | ||||||||
\(845\) | −13.8789 | − | 24.0390i | −0.477450 | − | 0.826967i | ||||
\(846\) | 3.96804 | + | 12.0494i | 0.136424 | + | 0.414266i | ||||
\(847\) | 10.4781 | − | 7.62060i | 0.360032 | − | 0.261847i | ||||
\(848\) | 40.0298 | + | 69.3337i | 1.37463 | + | 2.38093i | ||||
\(849\) | −0.744712 | − | 1.66375i | −0.0255585 | − | 0.0570999i | ||||
\(850\) | −6.65112 | − | 11.5201i | −0.228131 | − | 0.395135i | ||||
\(851\) | −16.0450 | − | 27.7907i | −0.550014 | − | 0.952652i | ||||
\(852\) | 4.01322 | + | 8.96589i | 0.137491 | + | 0.307166i | ||||
\(853\) | −6.22697 | − | 10.7854i | −0.213207 | − | 0.369286i | 0.739509 | − | 0.673147i | \(-0.235058\pi\) |
−0.952717 | + | 0.303860i | \(0.901724\pi\) | |||||||
\(854\) | −1.96669 | − | 0.874479i | −0.0672989 | − | 0.0299240i | ||||
\(855\) | 1.54849 | + | 4.70217i | 0.0529574 | + | 0.160811i | ||||
\(856\) | −3.04108 | − | 5.26731i | −0.103942 | − | 0.180033i | ||||
\(857\) | −1.91756 | −0.0655027 | −0.0327514 | − | 0.999464i | \(-0.510427\pi\) | ||||
−0.0327514 | + | 0.999464i | \(0.510427\pi\) | |||||||
\(858\) | −28.8570 | − | 64.4692i | −0.985163 | − | 2.20094i | ||||
\(859\) | −35.0395 | −1.19553 | −0.597766 | − | 0.801671i | \(-0.703945\pi\) | ||||
−0.597766 | + | 0.801671i | \(0.703945\pi\) | |||||||
\(860\) | −17.5925 | + | 30.4711i | −0.599899 | + | 1.03905i | ||||
\(861\) | 0.100329 | + | 40.5652i | 0.00341921 | + | 1.38246i | ||||
\(862\) | 15.7056 | + | 27.2030i | 0.534936 | + | 0.926536i | ||||
\(863\) | 22.3784 | + | 38.7606i | 0.761771 | + | 1.31943i | 0.941937 | + | 0.335789i | \(0.109003\pi\) |
−0.180166 | + | 0.983636i | \(0.557664\pi\) | |||||||
\(864\) | −9.22431 | − | 42.1607i | −0.313817 | − | 1.43434i | ||||
\(865\) | 1.56719 | − | 2.71446i | 0.0532861 | − | 0.0922943i | ||||
\(866\) | 15.3056 | − | 26.5101i | 0.520106 | − | 0.900849i | ||||
\(867\) | −6.69939 | − | 14.9670i | −0.227523 | − | 0.508307i | ||||
\(868\) | −0.712741 | − | 6.74959i | −0.0241920 | − | 0.229096i | ||||
\(869\) | −15.1921 | + | 26.3134i | −0.515356 | + | 0.892622i | ||||
\(870\) | −2.86667 | − | 0.295547i | −0.0971894 | − | 0.0100200i | ||||
\(871\) | −7.57489 | −0.256665 | ||||||||
\(872\) | 48.2754 | − | 83.6154i | 1.63481 | − | 2.83157i | ||||
\(873\) | 10.3940 | + | 31.5624i | 0.351783 | + | 1.06823i | ||||
\(874\) | −20.7253 | −0.701044 | ||||||||
\(875\) | −2.13970 | + | 1.55618i | −0.0723350 | + | 0.0526084i | ||||
\(876\) | −101.737 | − | 10.4889i | −3.43738 | − | 0.354385i | ||||
\(877\) | −25.4155 | −0.858220 | −0.429110 | − | 0.903252i | \(-0.641173\pi\) | ||||
−0.429110 | + | 0.903252i | \(0.641173\pi\) | |||||||
\(878\) | −38.5969 | − | 66.8518i | −1.30258 | − | 2.25614i | ||||
\(879\) | −19.1542 | + | 26.4739i | −0.646056 | + | 0.892943i | ||||
\(880\) | −10.6023 | + | 18.3637i | −0.357404 | + | 0.619041i | ||||
\(881\) | −7.62133 | −0.256769 | −0.128385 | − | 0.991724i | \(-0.540979\pi\) | ||||
−0.128385 | + | 0.991724i | \(0.540979\pi\) | |||||||
\(882\) | 27.3816 | + | 46.8891i | 0.921985 | + | 1.57884i | ||||
\(883\) | −37.5533 | −1.26377 | −0.631884 | − | 0.775063i | \(-0.717718\pi\) | ||||
−0.631884 | + | 0.775063i | \(0.717718\pi\) | |||||||
\(884\) | −76.9473 | + | 133.277i | −2.58802 | + | 4.48258i | ||||
\(885\) | 6.29283 | + | 14.0587i | 0.211531 | + | 0.472580i | ||||
\(886\) | −1.46448 | − | 2.53656i | −0.0492003 | − | 0.0852173i | ||||
\(887\) | 33.8614 | 1.13695 | 0.568477 | − | 0.822699i | \(-0.307533\pi\) | ||||
0.568477 | + | 0.822699i | \(0.307533\pi\) | |||||||
\(888\) | −32.4624 | − | 72.5240i | −1.08937 | − | 2.43375i | ||||
\(889\) | 27.8344 | − | 20.2436i | 0.933536 | − | 0.678950i | ||||
\(890\) | 7.46922 | 0.250369 | ||||||||
\(891\) | 20.3828 | + | 8.88173i | 0.682849 | + | 0.297549i | ||||
\(892\) | 8.23599 | − | 14.2651i | 0.275761 | − | 0.477632i | ||||
\(893\) | 2.69878 | 0.0903111 | ||||||||
\(894\) | −21.1133 | + | 29.1816i | −0.706133 | + | 0.975977i | ||||
\(895\) | −7.24402 | + | 12.5470i | −0.242141 | + | 0.419400i | ||||
\(896\) | 1.51980 | + | 14.3923i | 0.0507729 | + | 0.480814i | ||||
\(897\) | −31.4842 | + | 43.5158i | −1.05123 | + | 1.45295i | ||||
\(898\) | 29.7726 | − | 51.5677i | 0.993525 | − | 1.72084i | ||||
\(899\) | 0.176153 | − | 0.305105i | 0.00587502 | − | 0.0101758i | ||||
\(900\) | −4.39680 | − | 13.3514i | −0.146560 | − | 0.445045i | ||||
\(901\) | 23.9928 | + | 41.5567i | 0.799316 | + | 1.38446i | ||||
\(902\) | 28.2720 | + | 48.9685i | 0.941354 | + | 1.63047i | ||||
\(903\) | 29.8438 | + | 17.1320i | 0.993139 | + | 0.570119i | ||||
\(904\) | 22.9649 | − | 39.7763i | 0.763800 | − | 1.32294i | ||||
\(905\) | 10.6671 | 0.354587 | ||||||||
\(906\) | −31.6148 | + | 43.6962i | −1.05033 | + | 1.45171i | ||||
\(907\) | −43.3282 | −1.43869 | −0.719345 | − | 0.694653i | \(-0.755558\pi\) | ||||
−0.719345 | + | 0.694653i | \(0.755558\pi\) | |||||||
\(908\) | −32.3346 | − | 56.0052i | −1.07306 | − | 1.85860i | ||||
\(909\) | −44.9869 | − | 9.37572i | −1.49212 | − | 0.310973i | ||||
\(910\) | 39.9069 | + | 17.7444i | 1.32290 | + | 0.588220i | ||||
\(911\) | 6.17647 | + | 10.6980i | 0.204636 | + | 0.354439i | 0.950017 | − | 0.312199i | \(-0.101066\pi\) |
−0.745381 | + | 0.666639i | \(0.767732\pi\) | |||||||
\(912\) | −24.4038 | − | 2.51597i | −0.808091 | − | 0.0833122i | ||||
\(913\) | 7.94655 | + | 13.7638i | 0.262992 | + | 0.455516i | ||||
\(914\) | 30.6197 | + | 53.0350i | 1.01281 | + | 1.75424i | ||||
\(915\) | 0.319436 | − | 0.441507i | 0.0105602 | − | 0.0145958i | ||||
\(916\) | −25.8918 | − | 44.8459i | −0.855489 | − | 1.48175i | ||||
\(917\) | −4.81453 | + | 3.50155i | −0.158990 | + | 0.115631i | ||||
\(918\) | −14.7734 | − | 67.5232i | −0.487593 | − | 2.22860i | ||||
\(919\) | −24.8285 | − | 43.0042i | −0.819017 | − | 1.41858i | −0.906407 | − | 0.422405i | \(-0.861186\pi\) |
0.0873901 | − | 0.996174i | \(-0.472147\pi\) | |||||||
\(920\) | 33.7289 | 1.11201 | ||||||||
\(921\) | −54.1259 | − | 5.58025i | −1.78351 | − | 0.183875i | ||||
\(922\) | 64.5836 | 2.12695 | ||||||||
\(923\) | 3.86368 | − | 6.69209i | 0.127175 | − | 0.220273i | ||||
\(924\) | 46.0036 | + | 26.4087i | 1.51341 | + | 0.868783i | ||||
\(925\) | −3.30325 | − | 5.72139i | −0.108610 | − | 0.188118i | ||||
\(926\) | 8.26208 | + | 14.3103i | 0.271509 | + | 0.470267i | ||||
\(927\) | −26.0704 | − | 5.43334i | −0.856265 | − | 0.178454i | ||||
\(928\) | 2.67235 | − | 4.62865i | 0.0877243 | − | 0.151943i | ||||
\(929\) | 16.7303 | − | 28.9778i | 0.548905 | − | 0.950731i | −0.449445 | − | 0.893308i | \(-0.648378\pi\) |
0.998350 | − | 0.0574232i | \(-0.0182884\pi\) | |||||||
\(930\) | 2.43898 | + | 0.251453i | 0.0799773 | + | 0.00824546i | ||||
\(931\) | 11.2966 | − | 2.41269i | 0.370230 | − | 0.0790726i | ||||
\(932\) | −51.4061 | + | 89.0379i | −1.68386 | + | 2.91653i | ||||
\(933\) | 12.9598 | + | 28.9533i | 0.424285 | + | 0.947890i | ||||
\(934\) | 93.8388 | 3.07050 | ||||||||
\(935\) | −6.35473 | + | 11.0067i | −0.207822 | + | 0.359958i | ||||
\(936\) | −88.5971 | + | 99.1862i | −2.89589 | + | 3.24200i | ||||
\(937\) | −17.1934 | −0.561685 | −0.280842 | − | 0.959754i | \(-0.590614\pi\) | ||||
−0.280842 | + | 0.959754i | \(0.590614\pi\) | |||||||
\(938\) | 6.56436 | − | 4.77418i | 0.214334 | − | 0.155883i | ||||
\(939\) | −6.51212 | + | 9.00069i | −0.212515 | + | 0.293726i | ||||
\(940\) | −7.66292 | −0.249937 | ||||||||
\(941\) | 1.34774 | + | 2.33435i | 0.0439349 | + | 0.0760976i | 0.887157 | − | 0.461468i | \(-0.152677\pi\) |
−0.843222 | + | 0.537566i | \(0.819344\pi\) | |||||||
\(942\) | 15.7170 | + | 1.62038i | 0.512086 | + | 0.0527948i | ||||
\(943\) | 21.4987 | − | 37.2369i | 0.700095 | − | 1.21260i | ||||
\(944\) | −76.3307 | −2.48435 | ||||||||
\(945\) | −13.0472 | + | 4.33244i | −0.424426 | + | 0.140934i | ||||
\(946\) | 47.9663 | 1.55952 | ||||||||
\(947\) | 15.6590 | − | 27.1222i | 0.508849 | − | 0.881352i | −0.491099 | − | 0.871104i | \(-0.663405\pi\) |
0.999947 | − | 0.0102481i | \(-0.00326213\pi\) | |||||||
\(948\) | 99.2892 | + | 10.2365i | 3.22476 | + | 0.332465i | ||||
\(949\) | 40.2281 | + | 69.6770i | 1.30586 | + | 2.26181i | ||||
\(950\) | −4.26681 | −0.138434 | ||||||||
\(951\) | −9.62735 | + | 13.3064i | −0.312188 | + | 0.431489i | ||||
\(952\) | −9.92557 | − | 93.9942i | −0.321690 | − | 3.04637i | ||||
\(953\) | 35.9575 | 1.16478 | 0.582389 | − | 0.812910i | \(-0.302118\pi\) | ||||
0.582389 | + | 0.812910i | \(0.302118\pi\) | |||||||
\(954\) | 22.6308 | + | 68.7208i | 0.732699 | + | 2.22492i | ||||
\(955\) | −6.69720 | + | 11.5999i | −0.216716 | + | 0.375364i | ||||
\(956\) | −51.1766 | −1.65517 | ||||||||
\(957\) | 1.12492 | + | 2.51317i | 0.0363635 | + | 0.0812393i | ||||
\(958\) | −26.6686 | + | 46.1914i | −0.861624 | + | 1.49238i | ||||
\(959\) | −35.6227 | + | 25.9080i | −1.15032 | + | 0.836612i | ||||
\(960\) | 7.42400 | + | 0.765396i | 0.239609 | + | 0.0247031i | ||||
\(961\) | 15.3501 | − | 26.5872i | 0.495165 | − | 0.857652i | ||||
\(962\) | −54.5276 | + | 94.4445i | −1.75804 | + | 3.04501i | ||||
\(963\) | −0.821918 | − | 2.49584i | −0.0264859 | − | 0.0804273i | ||||
\(964\) | −27.3985 | − | 47.4557i | −0.882447 | − | 1.52844i | ||||
\(965\) | −2.26582 | − | 3.92451i | −0.0729392 | − | 0.126334i | ||||
\(966\) | −0.142347 | − | 57.5539i | −0.00457995 | − | 1.85177i | ||||
\(967\) | 4.02540 | − | 6.97220i | 0.129448 | − | 0.224211i | −0.794015 | − | 0.607898i | \(-0.792013\pi\) |
0.923463 | + | 0.383688i | \(0.125346\pi\) | |||||||
\(968\) | −34.0044 | −1.09294 | ||||||||
\(969\) | −14.6270 | − | 1.50801i | −0.469887 | − | 0.0484441i | ||||
\(970\) | −28.6402 | −0.919582 | ||||||||
\(971\) | 11.8256 | + | 20.4825i | 0.379501 | + | 0.657316i | 0.990990 | − | 0.133938i | \(-0.0427622\pi\) |
−0.611488 | + | 0.791253i | \(0.709429\pi\) | |||||||
\(972\) | −0.725011 | − | 73.0371i | −0.0232547 | − | 2.34267i | ||||
\(973\) | 4.88204 | + | 46.2325i | 0.156511 | + | 1.48214i | ||||
\(974\) | −11.4202 | − | 19.7804i | −0.365928 | − | 0.633805i | ||||
\(975\) | −6.48180 | + | 8.95879i | −0.207584 | + | 0.286911i | ||||
\(976\) | 1.35028 | + | 2.33875i | 0.0432213 | + | 0.0748615i | ||||
\(977\) | 5.63008 | + | 9.75159i | 0.180122 | + | 0.311981i | 0.941922 | − | 0.335832i | \(-0.109017\pi\) |
−0.761800 | + | 0.647813i | \(0.775684\pi\) | |||||||
\(978\) | −10.3076 | − | 1.06269i | −0.329601 | − | 0.0339810i | ||||
\(979\) | −3.56819 | − | 6.18029i | −0.114040 | − | 0.197523i | ||||
\(980\) | −32.0755 | + | 6.85060i | −1.02462 | + | 0.218834i | ||||
\(981\) | 27.7882 | − | 31.1094i | 0.887209 | − | 0.993248i | ||||
\(982\) | 22.5427 | + | 39.0451i | 0.719367 | + | 1.24598i | ||||
\(983\) | −2.37956 | −0.0758962 | −0.0379481 | − | 0.999280i | \(-0.512082\pi\) | ||||
−0.0379481 | + | 0.999280i | \(0.512082\pi\) | |||||||
\(984\) | 62.4080 | − | 86.2568i | 1.98949 | − | 2.74977i | ||||
\(985\) | 1.62983 | 0.0519307 | ||||||||
\(986\) | 4.27995 | − | 7.41310i | 0.136302 | − | 0.236081i | ||||
\(987\) | 0.0185359 | + | 7.49446i | 0.000590005 | + | 0.238551i | ||||
\(988\) | 24.6815 | + | 42.7497i | 0.785224 | + | 1.36005i | ||||
\(989\) | −18.2374 | − | 31.5881i | −0.579915 | − | 1.00444i | ||||
\(990\) | −12.7659 | + | 14.2916i | −0.405726 | + | 0.454218i | ||||
\(991\) | −17.5174 | + | 30.3409i | −0.556457 | + | 0.963812i | 0.441331 | + | 0.897344i | \(0.354506\pi\) |
−0.997789 | + | 0.0664679i | \(0.978827\pi\) | |||||||
\(992\) | −2.27365 | + | 3.93808i | −0.0721884 | + | 0.125034i | ||||
\(993\) | −13.2047 | + | 18.2508i | −0.419038 | + | 0.579171i | ||||
\(994\) | 0.869541 | + | 8.23447i | 0.0275802 | + | 0.261182i | ||||
\(995\) | −11.4805 | + | 19.8849i | −0.363957 | + | 0.630392i | ||||
\(996\) | 30.6048 | − | 42.3002i | 0.969749 | − | 1.34033i | ||||
\(997\) | −31.3795 | −0.993797 | −0.496899 | − | 0.867809i | \(-0.665528\pi\) | ||||
−0.496899 | + | 0.867809i | \(0.665528\pi\) | |||||||
\(998\) | −39.8402 | + | 69.0053i | −1.26112 | + | 2.18432i | ||||
\(999\) | −7.33712 | − | 33.5351i | −0.232136 | − | 1.06100i |
(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 | 315.2.k.c.256.2 | yes | 36 | |
3.2 | odd | 2 | 945.2.k.c.361.17 | 36 | |||
7.2 | even | 3 | 315.2.l.c.121.17 | yes | 36 | ||
9.2 | odd | 6 | 945.2.l.c.46.2 | 36 | |||
9.7 | even | 3 | 315.2.l.c.151.17 | yes | 36 | ||
21.2 | odd | 6 | 945.2.l.c.226.2 | 36 | |||
63.2 | odd | 6 | 945.2.k.c.856.17 | 36 | |||
63.16 | even | 3 | inner | 315.2.k.c.16.2 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.k.c.16.2 | ✓ | 36 | 63.16 | even | 3 | inner | |
315.2.k.c.256.2 | yes | 36 | 1.1 | even | 1 | trivial | |
315.2.l.c.121.17 | yes | 36 | 7.2 | even | 3 | ||
315.2.l.c.151.17 | yes | 36 | 9.7 | even | 3 | ||
945.2.k.c.361.17 | 36 | 3.2 | odd | 2 | |||
945.2.k.c.856.17 | 36 | 63.2 | odd | 6 | |||
945.2.l.c.46.2 | 36 | 9.2 | odd | 6 | |||
945.2.l.c.226.2 | 36 | 21.2 | odd | 6 |