Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([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("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 511.6 | ||
Character | \(\chi\) | \(=\) | 605.511 |
Dual form | 605.2.g.q.251.6 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.810808 | + | 2.49541i | 0.573328 | + | 1.76452i | 0.641804 | + | 0.766869i | \(0.278186\pi\) |
−0.0684758 | + | 0.997653i | \(0.521814\pi\) | |||||||
\(3\) | −1.08398 | − | 0.787560i | −0.625838 | − | 0.454698i | 0.229118 | − | 0.973399i | \(-0.426416\pi\) |
−0.854956 | + | 0.518701i | \(0.826416\pi\) | |||||||
\(4\) | −3.95163 | + | 2.87103i | −1.97582 | + | 1.43551i | ||||
\(5\) | 0.309017 | − | 0.951057i | 0.138197 | − | 0.425325i | ||||
\(6\) | 1.08638 | − | 3.34354i | 0.443514 | − | 1.36500i | ||||
\(7\) | 2.12272 | − | 1.54225i | 0.802314 | − | 0.582915i | −0.109278 | − | 0.994011i | \(-0.534854\pi\) |
0.911592 | + | 0.411096i | \(0.134854\pi\) | |||||||
\(8\) | −6.12296 | − | 4.44859i | −2.16479 | − | 1.57281i | ||||
\(9\) | −0.372282 | − | 1.14577i | −0.124094 | − | 0.381922i | ||||
\(10\) | 2.62383 | 0.829728 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.54461 | 1.88927 | ||||||||
\(13\) | −2.07910 | − | 6.39883i | −0.576640 | − | 1.77471i | −0.630526 | − | 0.776168i | \(-0.717161\pi\) |
0.0538866 | − | 0.998547i | \(-0.482839\pi\) | |||||||
\(14\) | 5.56966 | + | 4.04660i | 1.48856 | + | 1.08150i | ||||
\(15\) | −1.08398 | + | 0.787560i | −0.279883 | + | 0.203347i | ||||
\(16\) | 3.11774 | − | 9.59541i | 0.779435 | − | 2.39885i | ||||
\(17\) | 0.551150 | − | 1.69626i | 0.133673 | − | 0.411405i | −0.861708 | − | 0.507405i | \(-0.830605\pi\) |
0.995381 | + | 0.0960001i | \(0.0306049\pi\) | |||||||
\(18\) | 2.55731 | − | 1.85799i | 0.602763 | − | 0.437933i | ||||
\(19\) | 1.19772 | + | 0.870194i | 0.274776 | + | 0.199636i | 0.716636 | − | 0.697448i | \(-0.245681\pi\) |
−0.441860 | + | 0.897084i | \(0.645681\pi\) | |||||||
\(20\) | 1.50939 | + | 4.64542i | 0.337510 | + | 1.03875i | ||||
\(21\) | −3.51561 | −0.767169 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.20473 | 1.08526 | 0.542631 | − | 0.839971i | \(-0.317428\pi\) | ||||
0.542631 | + | 0.839971i | \(0.317428\pi\) | |||||||
\(24\) | 3.13365 | + | 9.64440i | 0.639654 | + | 1.96865i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | 14.2819 | − | 10.3764i | 2.80092 | − | 2.03499i | ||||
\(27\) | −1.74095 | + | 5.35808i | −0.335045 | + | 1.03116i | ||||
\(28\) | −3.96038 | + | 12.1888i | −0.748441 | + | 2.30347i | ||||
\(29\) | −0.952511 | + | 0.692040i | −0.176877 | + | 0.128509i | −0.672701 | − | 0.739914i | \(-0.734866\pi\) |
0.495824 | + | 0.868423i | \(0.334866\pi\) | |||||||
\(30\) | −2.84419 | − | 2.06642i | −0.519275 | − | 0.377276i | ||||
\(31\) | −1.41043 | − | 4.34085i | −0.253320 | − | 0.779639i | −0.994156 | − | 0.107953i | \(-0.965570\pi\) |
0.740836 | − | 0.671686i | \(-0.234430\pi\) | |||||||
\(32\) | 11.3356 | 2.00387 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.67975 | 0.802571 | ||||||||
\(35\) | −0.810808 | − | 2.49541i | −0.137052 | − | 0.421801i | ||||
\(36\) | 4.76065 | + | 3.45881i | 0.793441 | + | 0.576469i | ||||
\(37\) | 0.549932 | − | 0.399549i | 0.0904083 | − | 0.0656855i | −0.541663 | − | 0.840596i | \(-0.682205\pi\) |
0.632071 | + | 0.774910i | \(0.282205\pi\) | |||||||
\(38\) | −1.20037 | + | 3.69436i | −0.194726 | + | 0.599305i | ||||
\(39\) | −2.78574 | + | 8.57364i | −0.446076 | + | 1.37288i | ||||
\(40\) | −6.12296 | + | 4.44859i | −0.968125 | + | 0.703384i | ||||
\(41\) | −4.44898 | − | 3.23238i | −0.694815 | − | 0.504812i | 0.183425 | − | 0.983034i | \(-0.441282\pi\) |
−0.878239 | + | 0.478221i | \(0.841282\pi\) | |||||||
\(42\) | −2.85048 | − | 8.77289i | −0.439839 | − | 1.35369i | ||||
\(43\) | 3.80120 | 0.579677 | 0.289839 | − | 0.957076i | \(-0.406398\pi\) | ||||
0.289839 | + | 0.957076i | \(0.406398\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.20473 | −0.179591 | ||||||||
\(46\) | 4.22004 | + | 12.9879i | 0.622210 | + | 1.91497i | ||||
\(47\) | −5.38815 | − | 3.91472i | −0.785943 | − | 0.571021i | 0.120814 | − | 0.992675i | \(-0.461450\pi\) |
−0.906757 | + | 0.421654i | \(0.861450\pi\) | |||||||
\(48\) | −10.9365 | + | 7.94586i | −1.57855 | + | 1.14689i | ||||
\(49\) | −0.0356965 | + | 0.109863i | −0.00509950 | + | 0.0156946i | ||||
\(50\) | 0.810808 | − | 2.49541i | 0.114666 | − | 0.352904i | ||||
\(51\) | −1.93335 | + | 1.40466i | −0.270723 | + | 0.196692i | ||||
\(52\) | 26.5871 | + | 19.3166i | 3.68696 | + | 2.67873i | ||||
\(53\) | 4.41707 | + | 13.5943i | 0.606731 | + | 1.86733i | 0.484420 | + | 0.874836i | \(0.339031\pi\) |
0.122311 | + | 0.992492i | \(0.460969\pi\) | |||||||
\(54\) | −14.7822 | −2.01160 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.8582 | −2.65366 | ||||||||
\(57\) | −0.612978 | − | 1.88655i | −0.0811909 | − | 0.249880i | ||||
\(58\) | −2.49923 | − | 1.81579i | −0.328164 | − | 0.238425i | ||||
\(59\) | 3.14261 | − | 2.28324i | 0.409133 | − | 0.297253i | −0.364117 | − | 0.931353i | \(-0.618629\pi\) |
0.773251 | + | 0.634100i | \(0.218629\pi\) | |||||||
\(60\) | 2.02239 | − | 6.22429i | 0.261090 | − | 0.803553i | ||||
\(61\) | 0.992721 | − | 3.05528i | 0.127105 | − | 0.391189i | −0.867174 | − | 0.498006i | \(-0.834066\pi\) |
0.994279 | + | 0.106817i | \(0.0340659\pi\) | |||||||
\(62\) | 9.68861 | − | 7.03919i | 1.23045 | − | 0.893978i | ||||
\(63\) | −2.55731 | − | 1.85799i | −0.322191 | − | 0.234085i | ||||
\(64\) | 2.95551 | + | 9.09613i | 0.369439 | + | 1.13702i | ||||
\(65\) | −6.72812 | −0.834521 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.66012 | 0.569325 | 0.284662 | − | 0.958628i | \(-0.408119\pi\) | ||||
0.284662 | + | 0.958628i | \(0.408119\pi\) | |||||||
\(68\) | 2.69208 | + | 8.28538i | 0.326463 | + | 1.00475i | ||||
\(69\) | −5.64184 | − | 4.09904i | −0.679198 | − | 0.493466i | ||||
\(70\) | 5.56966 | − | 4.04660i | 0.665702 | − | 0.483661i | ||||
\(71\) | 1.20037 | − | 3.69436i | 0.142458 | − | 0.438440i | −0.854217 | − | 0.519916i | \(-0.825963\pi\) |
0.996675 | + | 0.0814756i | \(0.0259633\pi\) | |||||||
\(72\) | −2.81758 | + | 8.67161i | −0.332055 | + | 1.02196i | ||||
\(73\) | 2.88586 | − | 2.09670i | 0.337764 | − | 0.245400i | −0.405954 | − | 0.913894i | \(-0.633061\pi\) |
0.743718 | + | 0.668494i | \(0.233061\pi\) | |||||||
\(74\) | 1.44293 | + | 1.04835i | 0.167737 | + | 0.121868i | ||||
\(75\) | 0.414045 | + | 1.27430i | 0.0478098 | + | 0.147143i | ||||
\(76\) | −7.23130 | −0.829487 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −23.6535 | −2.67823 | ||||||||
\(79\) | −4.67753 | − | 14.3959i | −0.526263 | − | 1.61967i | −0.761805 | − | 0.647806i | \(-0.775687\pi\) |
0.235543 | − | 0.971864i | \(-0.424313\pi\) | |||||||
\(80\) | −8.16235 | − | 5.93029i | −0.912578 | − | 0.663027i | ||||
\(81\) | 3.18303 | − | 2.31260i | 0.353670 | − | 0.256956i | ||||
\(82\) | 4.45883 | − | 13.7229i | 0.492396 | − | 1.51544i | ||||
\(83\) | 2.26643 | − | 6.97535i | 0.248773 | − | 0.765644i | −0.746220 | − | 0.665699i | \(-0.768133\pi\) |
0.994993 | − | 0.0999446i | \(-0.0318666\pi\) | |||||||
\(84\) | 13.8924 | − | 10.0934i | 1.51578 | − | 1.10128i | ||||
\(85\) | −1.44293 | − | 1.04835i | −0.156508 | − | 0.113709i | ||||
\(86\) | 3.08204 | + | 9.48555i | 0.332345 | + | 1.02285i | ||||
\(87\) | 1.57753 | 0.169129 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.44872 | 0.365564 | 0.182782 | − | 0.983153i | \(-0.441490\pi\) | ||||
0.182782 | + | 0.983153i | \(0.441490\pi\) | |||||||
\(90\) | −0.976805 | − | 3.00630i | −0.102964 | − | 0.316891i | ||||
\(91\) | −14.2819 | − | 10.3764i | −1.49715 | − | 1.08775i | ||||
\(92\) | −20.5672 | + | 14.9429i | −2.14428 | + | 1.55791i | ||||
\(93\) | −1.88980 | + | 5.81620i | −0.195963 | + | 0.603112i | ||||
\(94\) | 5.40008 | − | 16.6197i | 0.556976 | − | 1.71420i | ||||
\(95\) | 1.19772 | − | 0.870194i | 0.122883 | − | 0.0892801i | ||||
\(96\) | −12.2876 | − | 8.92746i | −1.25410 | − | 0.911155i | ||||
\(97\) | 0.455807 | + | 1.40283i | 0.0462802 | + | 0.142436i | 0.971526 | − | 0.236931i | \(-0.0761417\pi\) |
−0.925246 | + | 0.379367i | \(0.876142\pi\) | |||||||
\(98\) | −0.303095 | −0.0306172 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.88448 | 0.488448 | ||||||||
\(101\) | −1.05455 | − | 3.24557i | −0.104932 | − | 0.322946i | 0.884783 | − | 0.466004i | \(-0.154307\pi\) |
−0.989714 | + | 0.143057i | \(0.954307\pi\) | |||||||
\(102\) | −5.07277 | − | 3.68559i | −0.502280 | − | 0.364927i | ||||
\(103\) | 4.02381 | − | 2.92347i | 0.396477 | − | 0.288058i | −0.371627 | − | 0.928382i | \(-0.621200\pi\) |
0.768105 | + | 0.640324i | \(0.221200\pi\) | |||||||
\(104\) | −15.7355 | + | 48.4288i | −1.54299 | + | 4.74884i | ||||
\(105\) | −1.08638 | + | 3.34354i | −0.106020 | + | 0.326296i | ||||
\(106\) | −30.3421 | + | 22.0448i | −2.94708 | + | 2.14118i | ||||
\(107\) | −5.71588 | − | 4.15283i | −0.552575 | − | 0.401469i | 0.276159 | − | 0.961112i | \(-0.410938\pi\) |
−0.828734 | + | 0.559643i | \(0.810938\pi\) | |||||||
\(108\) | −8.50362 | − | 26.1715i | −0.818262 | − | 2.51835i | ||||
\(109\) | −10.6439 | −1.01950 | −0.509750 | − | 0.860323i | \(-0.670262\pi\) | ||||
−0.509750 | + | 0.860323i | \(0.670262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.910786 | −0.0864480 | ||||||||
\(112\) | −8.18042 | − | 25.1767i | −0.772977 | − | 2.37898i | ||||
\(113\) | 11.1393 | + | 8.09320i | 1.04790 | + | 0.761344i | 0.971812 | − | 0.235757i | \(-0.0757570\pi\) |
0.0760879 | + | 0.997101i | \(0.475757\pi\) | |||||||
\(114\) | 4.21071 | − | 3.05926i | 0.394370 | − | 0.286526i | ||||
\(115\) | 1.60835 | − | 4.94999i | 0.149979 | − | 0.461589i | ||||
\(116\) | 1.77711 | − | 5.46937i | 0.165000 | − | 0.507818i | ||||
\(117\) | −6.55754 | + | 4.76434i | −0.606245 | + | 0.440463i | ||||
\(118\) | 8.24568 | + | 5.99084i | 0.759077 | + | 0.551501i | ||||
\(119\) | −1.44612 | − | 4.45071i | −0.132566 | − | 0.407996i | ||||
\(120\) | 10.1407 | 0.925717 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 8.42909 | 0.763134 | ||||||||
\(123\) | 2.27693 | + | 7.00768i | 0.205304 | + | 0.631862i | ||||
\(124\) | 18.0362 | + | 13.1041i | 1.61970 | + | 1.17678i | ||||
\(125\) | −0.809017 | + | 0.587785i | −0.0723607 | + | 0.0525731i | ||||
\(126\) | 2.56297 | − | 7.88801i | 0.228327 | − | 0.702720i | ||||
\(127\) | −3.80489 | + | 11.7102i | −0.337629 | + | 1.03912i | 0.627783 | + | 0.778388i | \(0.283963\pi\) |
−0.965412 | + | 0.260728i | \(0.916037\pi\) | |||||||
\(128\) | −1.96085 | + | 1.42464i | −0.173317 | + | 0.125922i | ||||
\(129\) | −4.12043 | − | 2.99367i | −0.362784 | − | 0.263578i | ||||
\(130\) | −5.45522 | − | 16.7894i | −0.478454 | − | 1.47253i | ||||
\(131\) | 19.5102 | 1.70461 | 0.852306 | − | 0.523043i | \(-0.175203\pi\) | ||||
0.852306 | + | 0.523043i | \(0.175203\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.88448 | 0.336827 | ||||||||
\(134\) | 3.77847 | + | 11.6289i | 0.326410 | + | 1.00459i | ||||
\(135\) | 4.55786 | + | 3.31148i | 0.392278 | + | 0.285007i | ||||
\(136\) | −10.9207 | + | 7.93432i | −0.936439 | + | 0.680362i | ||||
\(137\) | −2.64649 | + | 8.14507i | −0.226105 | + | 0.695881i | 0.772072 | + | 0.635535i | \(0.219220\pi\) |
−0.998178 | + | 0.0603458i | \(0.980780\pi\) | |||||||
\(138\) | 5.65433 | − | 17.4022i | 0.481329 | − | 1.48138i | ||||
\(139\) | −1.60480 | + | 1.16595i | −0.136117 | + | 0.0988949i | −0.653760 | − | 0.756702i | \(-0.726810\pi\) |
0.517643 | + | 0.855597i | \(0.326810\pi\) | |||||||
\(140\) | 10.3684 | + | 7.53309i | 0.876290 | + | 0.636662i | ||||
\(141\) | 2.75759 | + | 8.48699i | 0.232231 | + | 0.714733i | ||||
\(142\) | 10.1922 | 0.855313 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.1548 | −1.01290 | ||||||||
\(145\) | 0.363827 | + | 1.11974i | 0.0302142 | + | 0.0929896i | ||||
\(146\) | 7.57200 | + | 5.50138i | 0.626663 | + | 0.455297i | ||||
\(147\) | 0.125218 | − | 0.0909760i | 0.0103278 | − | 0.00750357i | ||||
\(148\) | −1.02601 | + | 3.15774i | −0.0843377 | + | 0.259565i | ||||
\(149\) | −5.67025 | + | 17.4512i | −0.464525 | + | 1.42966i | 0.395055 | + | 0.918658i | \(0.370726\pi\) |
−0.859579 | + | 0.511002i | \(0.829274\pi\) | |||||||
\(150\) | −2.84419 | + | 2.06642i | −0.232227 | + | 0.168723i | ||||
\(151\) | −13.9341 | − | 10.1237i | −1.13394 | − | 0.823854i | −0.147674 | − | 0.989036i | \(-0.547179\pi\) |
−0.986263 | + | 0.165182i | \(0.947179\pi\) | |||||||
\(152\) | −3.46245 | − | 10.6563i | −0.280842 | − | 0.864343i | ||||
\(153\) | −2.14871 | −0.173713 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.56424 | −0.366608 | ||||||||
\(156\) | −13.6069 | − | 41.8778i | −1.08943 | − | 3.35291i | ||||
\(157\) | 16.9064 | + | 12.2832i | 1.34928 | + | 0.980307i | 0.999047 | + | 0.0436428i | \(0.0138963\pi\) |
0.350229 | + | 0.936664i | \(0.386104\pi\) | |||||||
\(158\) | 32.1312 | − | 23.3447i | 2.55622 | − | 1.85720i | ||||
\(159\) | 5.91833 | − | 18.2148i | 0.469354 | − | 1.44452i | ||||
\(160\) | 3.50289 | − | 10.7808i | 0.276928 | − | 0.852296i | ||||
\(161\) | 11.0482 | − | 8.02699i | 0.870720 | − | 0.632615i | ||||
\(162\) | 8.35172 | + | 6.06788i | 0.656173 | + | 0.476738i | ||||
\(163\) | 2.92188 | + | 8.99261i | 0.228859 | + | 0.704356i | 0.997877 | + | 0.0651285i | \(0.0207457\pi\) |
−0.769018 | + | 0.639227i | \(0.779254\pi\) | |||||||
\(164\) | 26.8610 | 2.09749 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.2440 | 1.49362 | ||||||||
\(167\) | −2.91991 | − | 8.98655i | −0.225949 | − | 0.695400i | −0.998194 | − | 0.0600749i | \(-0.980866\pi\) |
0.772245 | − | 0.635325i | \(-0.219134\pi\) | |||||||
\(168\) | 21.5259 | + | 15.6395i | 1.66076 | + | 1.20661i | ||||
\(169\) | −26.1051 | + | 18.9664i | −2.00808 | + | 1.45896i | ||||
\(170\) | 1.44612 | − | 4.45071i | 0.110913 | − | 0.341354i | ||||
\(171\) | 0.551150 | − | 1.69626i | 0.0421475 | − | 0.129717i | ||||
\(172\) | −15.0209 | + | 10.9133i | −1.14534 | + | 0.832135i | ||||
\(173\) | 7.34819 | + | 5.33877i | 0.558672 | + | 0.405899i | 0.830973 | − | 0.556313i | \(-0.187784\pi\) |
−0.272300 | + | 0.962212i | \(0.587784\pi\) | |||||||
\(174\) | 1.27907 | + | 3.93658i | 0.0969662 | + | 0.298431i | ||||
\(175\) | −2.62383 | −0.198343 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.20473 | −0.391211 | ||||||||
\(178\) | 2.79625 | + | 8.60598i | 0.209588 | + | 0.645045i | ||||
\(179\) | 11.1393 | + | 8.09320i | 0.832593 | + | 0.604914i | 0.920292 | − | 0.391233i | \(-0.127951\pi\) |
−0.0876991 | + | 0.996147i | \(0.527951\pi\) | |||||||
\(180\) | 4.76065 | − | 3.45881i | 0.354838 | − | 0.257805i | ||||
\(181\) | −7.37258 | + | 22.6905i | −0.548000 | + | 1.68657i | 0.165749 | + | 0.986168i | \(0.446996\pi\) |
−0.713749 | + | 0.700402i | \(0.753004\pi\) | |||||||
\(182\) | 14.3136 | − | 44.0526i | 1.06099 | − | 3.26540i | ||||
\(183\) | −3.48231 | + | 2.53005i | −0.257420 | + | 0.187026i | ||||
\(184\) | −31.8684 | − | 23.1537i | −2.34937 | − | 1.70691i | ||||
\(185\) | −0.210055 | − | 0.646484i | −0.0154436 | − | 0.0475305i | ||||
\(186\) | −16.0461 | −1.17656 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 32.5313 | 2.37259 | ||||||||
\(189\) | 4.56795 | + | 14.0587i | 0.332269 | + | 1.02262i | ||||
\(190\) | 3.14261 | + | 2.28324i | 0.227989 | + | 0.165644i | ||||
\(191\) | −12.9952 | + | 9.44154i | −0.940297 | + | 0.683166i | −0.948492 | − | 0.316800i | \(-0.897391\pi\) |
0.00819487 | + | 0.999966i | \(0.497391\pi\) | |||||||
\(192\) | 3.96002 | − | 12.1877i | 0.285790 | − | 0.879571i | ||||
\(193\) | 6.63113 | − | 20.4085i | 0.477320 | − | 1.46904i | −0.365484 | − | 0.930818i | \(-0.619097\pi\) |
0.842804 | − | 0.538221i | \(-0.180903\pi\) | |||||||
\(194\) | −3.13107 | + | 2.27485i | −0.224798 | + | 0.163325i | ||||
\(195\) | 7.29317 | + | 5.29880i | 0.522275 | + | 0.379455i | ||||
\(196\) | −0.174359 | − | 0.536622i | −0.0124542 | − | 0.0383301i | ||||
\(197\) | 9.21494 | 0.656537 | 0.328269 | − | 0.944584i | \(-0.393535\pi\) | ||||
0.328269 | + | 0.944584i | \(0.393535\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.4880 | −1.16880 | −0.584401 | − | 0.811465i | \(-0.698670\pi\) | ||||
−0.584401 | + | 0.811465i | \(0.698670\pi\) | |||||||
\(200\) | 2.33876 | + | 7.19797i | 0.165375 | + | 0.508973i | ||||
\(201\) | −5.05150 | − | 3.67013i | −0.356305 | − | 0.258871i | ||||
\(202\) | 7.24399 | − | 5.26307i | 0.509686 | − | 0.370308i | ||||
\(203\) | −0.954620 | + | 2.93802i | −0.0670012 | + | 0.206208i | ||||
\(204\) | 3.60706 | − | 11.1014i | 0.252545 | − | 0.777252i | ||||
\(205\) | −4.44898 | + | 3.23238i | −0.310731 | + | 0.225759i | ||||
\(206\) | 10.5578 | + | 7.67068i | 0.735596 | + | 0.534441i | ||||
\(207\) | −1.93763 | − | 5.96340i | −0.134674 | − | 0.414485i | ||||
\(208\) | −67.8815 | −4.70673 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −9.22436 | −0.636541 | ||||||||
\(211\) | 4.58386 | + | 14.1077i | 0.315566 | + | 0.971213i | 0.975521 | + | 0.219907i | \(0.0705755\pi\) |
−0.659955 | + | 0.751306i | \(0.729424\pi\) | |||||||
\(212\) | −56.4844 | − | 41.0383i | −3.87936 | − | 2.81852i | ||||
\(213\) | −4.21071 | + | 3.05926i | −0.288513 | + | 0.209617i | ||||
\(214\) | 5.72854 | − | 17.6306i | 0.391595 | − | 1.20520i | ||||
\(215\) | 1.17463 | − | 3.61515i | 0.0801094 | − | 0.246551i | ||||
\(216\) | 34.4957 | − | 25.0626i | 2.34713 | − | 1.70529i | ||||
\(217\) | −9.68861 | − | 7.03919i | −0.657706 | − | 0.477851i | ||||
\(218\) | −8.63015 | − | 26.5609i | −0.584508 | − | 1.79893i | ||||
\(219\) | −4.77950 | −0.322968 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | −0.738473 | − | 2.27279i | −0.0495631 | − | 0.152539i | ||||
\(223\) | −18.9333 | − | 13.7558i | −1.26786 | − | 0.921157i | −0.268749 | − | 0.963210i | \(-0.586610\pi\) |
−0.999115 | + | 0.0420528i | \(0.986610\pi\) | |||||||
\(224\) | 24.0623 | − | 17.4823i | 1.60773 | − | 1.16809i | ||||
\(225\) | −0.372282 | + | 1.14577i | −0.0248188 | + | 0.0763844i | ||||
\(226\) | −11.1640 | + | 34.3592i | −0.742618 | + | 2.28554i | ||||
\(227\) | 2.12272 | − | 1.54225i | 0.140890 | − | 0.102363i | −0.515108 | − | 0.857125i | \(-0.672248\pi\) |
0.655998 | + | 0.754763i | \(0.272248\pi\) | |||||||
\(228\) | 7.83861 | + | 5.69508i | 0.519124 | + | 0.377166i | ||||
\(229\) | −6.80969 | − | 20.9581i | −0.449997 | − | 1.38495i | −0.876910 | − | 0.480655i | \(-0.840399\pi\) |
0.426913 | − | 0.904293i | \(-0.359601\pi\) | |||||||
\(230\) | 13.6563 | 0.900471 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.91079 | 0.585022 | ||||||||
\(233\) | 1.65161 | + | 5.08314i | 0.108201 | + | 0.333007i | 0.990468 | − | 0.137741i | \(-0.0439841\pi\) |
−0.882268 | + | 0.470748i | \(0.843984\pi\) | |||||||
\(234\) | −17.2059 | − | 12.5008i | −1.12478 | − | 0.817203i | ||||
\(235\) | −5.38815 | + | 3.91472i | −0.351484 | + | 0.255368i | ||||
\(236\) | −5.86319 | + | 18.0451i | −0.381661 | + | 1.17463i | ||||
\(237\) | −6.26731 | + | 19.2888i | −0.407105 | + | 1.25294i | ||||
\(238\) | 9.93382 | − | 7.21734i | 0.643914 | − | 0.467831i | ||||
\(239\) | 10.1790 | + | 7.39550i | 0.658427 | + | 0.478375i | 0.866131 | − | 0.499817i | \(-0.166599\pi\) |
−0.207705 | + | 0.978192i | \(0.566599\pi\) | |||||||
\(240\) | 4.17739 | + | 12.8567i | 0.269649 | + | 0.829895i | ||||
\(241\) | −4.28687 | −0.276141 | −0.138071 | − | 0.990422i | \(-0.544090\pi\) | ||||
−0.138071 | + | 0.990422i | \(0.544090\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.6298 | 0.746052 | ||||||||
\(244\) | 4.84893 | + | 14.9235i | 0.310421 | + | 0.955378i | ||||
\(245\) | 0.0934546 | + | 0.0678988i | 0.00597060 | + | 0.00433789i | ||||
\(246\) | −15.6409 | + | 11.3638i | −0.997227 | + | 0.724528i | ||||
\(247\) | 3.07804 | − | 9.47323i | 0.195851 | − | 0.602767i | ||||
\(248\) | −10.6747 | + | 32.8532i | −0.677842 | + | 2.08618i | ||||
\(249\) | −7.95027 | + | 5.77621i | −0.503828 | + | 0.366052i | ||||
\(250\) | −2.12272 | − | 1.54225i | −0.134253 | − | 0.0975404i | ||||
\(251\) | 3.10961 | + | 9.57040i | 0.196277 | + | 0.604078i | 0.999959 | + | 0.00901968i | \(0.00287109\pi\) |
−0.803682 | + | 0.595058i | \(0.797129\pi\) | |||||||
\(252\) | 15.4399 | 0.972621 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −32.3069 | −2.02712 | ||||||||
\(255\) | 0.738473 | + | 2.27279i | 0.0462450 | + | 0.142327i | ||||
\(256\) | 10.3303 | + | 7.50541i | 0.645644 | + | 0.469088i | ||||
\(257\) | 2.56092 | − | 1.86062i | 0.159746 | − | 0.116062i | −0.505041 | − | 0.863095i | \(-0.668523\pi\) |
0.664786 | + | 0.747033i | \(0.268523\pi\) | |||||||
\(258\) | 4.12956 | − | 12.7095i | 0.257095 | − | 0.791257i | ||||
\(259\) | 0.551150 | − | 1.69626i | 0.0342468 | − | 0.105401i | ||||
\(260\) | 26.5871 | − | 19.3166i | 1.64886 | − | 1.19797i | ||||
\(261\) | 1.14752 | + | 0.833721i | 0.0710296 | + | 0.0516060i | ||||
\(262\) | 15.8190 | + | 48.6859i | 0.977302 | + | 3.00783i | ||||
\(263\) | 22.3681 | 1.37928 | 0.689638 | − | 0.724155i | \(-0.257770\pi\) | ||||
0.689638 | + | 0.724155i | \(0.257770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.2939 | 0.878070 | ||||||||
\(266\) | 3.14957 | + | 9.69338i | 0.193113 | + | 0.594339i | ||||
\(267\) | −3.73836 | − | 2.71607i | −0.228784 | − | 0.166221i | ||||
\(268\) | −18.4151 | + | 13.3793i | −1.12488 | + | 0.817273i | ||||
\(269\) | 4.93614 | − | 15.1919i | 0.300962 | − | 0.926266i | −0.680191 | − | 0.733035i | \(-0.738103\pi\) |
0.981153 | − | 0.193231i | \(-0.0618967\pi\) | |||||||
\(270\) | −4.56795 | + | 14.0587i | −0.277996 | + | 0.855585i | ||||
\(271\) | 12.6530 | − | 9.19294i | 0.768615 | − | 0.558431i | −0.132926 | − | 0.991126i | \(-0.542437\pi\) |
0.901541 | + | 0.432695i | \(0.142437\pi\) | |||||||
\(272\) | −14.5580 | − | 10.5770i | −0.882710 | − | 0.641326i | ||||
\(273\) | 7.30932 | + | 22.4958i | 0.442380 | + | 1.36151i | ||||
\(274\) | −22.4711 | −1.35753 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 34.0629 | 2.05035 | ||||||||
\(277\) | 7.38043 | + | 22.7146i | 0.443447 | + | 1.36479i | 0.884178 | + | 0.467150i | \(0.154719\pi\) |
−0.440731 | + | 0.897639i | \(0.645281\pi\) | |||||||
\(278\) | −4.21071 | − | 3.05926i | −0.252542 | − | 0.183482i | ||||
\(279\) | −4.44852 | + | 3.23204i | −0.266326 | + | 0.193497i | ||||
\(280\) | −6.13652 | + | 18.8863i | −0.366727 | + | 1.12867i | ||||
\(281\) | 3.78356 | − | 11.6446i | 0.225708 | − | 0.694659i | −0.772511 | − | 0.635002i | \(-0.780999\pi\) |
0.998219 | − | 0.0596571i | \(-0.0190007\pi\) | |||||||
\(282\) | −18.9426 | + | 13.7626i | −1.12802 | + | 0.819553i | ||||
\(283\) | 16.8709 | + | 12.2575i | 1.00287 | + | 0.728630i | 0.962702 | − | 0.270563i | \(-0.0872098\pi\) |
0.0401707 | + | 0.999193i | \(0.487210\pi\) | |||||||
\(284\) | 5.86319 | + | 18.0451i | 0.347917 | + | 1.07078i | ||||
\(285\) | −1.98364 | −0.117501 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.4291 | −0.851722 | ||||||||
\(288\) | −4.22004 | − | 12.9879i | −0.248668 | − | 0.765322i | ||||
\(289\) | 11.1797 | + | 8.12256i | 0.657632 | + | 0.477797i | ||||
\(290\) | −2.49923 | + | 1.81579i | −0.146760 | + | 0.106627i | ||||
\(291\) | 0.610726 | − | 1.87962i | 0.0358014 | − | 0.110185i | ||||
\(292\) | −5.38416 | + | 16.5708i | −0.315084 | + | 0.969730i | ||||
\(293\) | −11.5936 | + | 8.42327i | −0.677307 | + | 0.492093i | −0.872463 | − | 0.488680i | \(-0.837479\pi\) |
0.195156 | + | 0.980772i | \(0.437479\pi\) | |||||||
\(294\) | 0.328550 | + | 0.238706i | 0.0191614 | + | 0.0139216i | ||||
\(295\) | −1.20037 | − | 3.69436i | −0.0698883 | − | 0.215094i | ||||
\(296\) | −5.14464 | −0.299026 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −48.1455 | −2.78899 | ||||||||
\(299\) | −10.8212 | − | 33.3042i | −0.625805 | − | 1.92603i | ||||
\(300\) | −5.29470 | − | 3.84682i | −0.305690 | − | 0.222096i | ||||
\(301\) | 8.06889 | − | 5.86239i | 0.465083 | − | 0.337903i | ||||
\(302\) | 13.9649 | − | 42.9796i | 0.803590 | − | 2.47320i | ||||
\(303\) | −1.41297 | + | 4.34866i | −0.0811728 | + | 0.249824i | ||||
\(304\) | 12.0841 | − | 8.77958i | 0.693068 | − | 0.503543i | ||||
\(305\) | −2.59898 | − | 1.88827i | −0.148817 | − | 0.108122i | ||||
\(306\) | −1.74219 | − | 5.36190i | −0.0995943 | − | 0.306520i | ||||
\(307\) | 10.2952 | 0.587580 | 0.293790 | − | 0.955870i | \(-0.405083\pi\) | ||||
0.293790 | + | 0.955870i | \(0.405083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.66414 | −0.379110 | ||||||||
\(310\) | −3.70072 | − | 11.3896i | −0.210187 | − | 0.646888i | ||||
\(311\) | 15.4944 | + | 11.2573i | 0.878606 | + | 0.638345i | 0.932882 | − | 0.360181i | \(-0.117285\pi\) |
−0.0542760 | + | 0.998526i | \(0.517285\pi\) | |||||||
\(312\) | 55.1976 | − | 40.1034i | 3.12495 | − | 2.27041i | ||||
\(313\) | −4.62713 | + | 14.2408i | −0.261541 | + | 0.804939i | 0.730930 | + | 0.682453i | \(0.239087\pi\) |
−0.992470 | + | 0.122486i | \(0.960913\pi\) | |||||||
\(314\) | −16.9438 | + | 52.1477i | −0.956195 | + | 2.94286i | ||||
\(315\) | −2.55731 | + | 1.85799i | −0.144088 | + | 0.104686i | ||||
\(316\) | 59.8150 | + | 43.4581i | 3.36486 | + | 2.44471i | ||||
\(317\) | 3.76334 | + | 11.5824i | 0.211370 | + | 0.650531i | 0.999391 | + | 0.0348827i | \(0.0111057\pi\) |
−0.788021 | + | 0.615648i | \(0.788894\pi\) | |||||||
\(318\) | 50.2519 | 2.81799 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 9.56424 | 0.534657 | ||||||||
\(321\) | 2.92532 | + | 9.00320i | 0.163275 | + | 0.502510i | ||||
\(322\) | 28.9886 | + | 21.0614i | 1.61547 | + | 1.17371i | ||||
\(323\) | 2.13620 | − | 1.55204i | 0.118862 | − | 0.0863580i | ||||
\(324\) | −5.93859 | + | 18.2771i | −0.329922 | + | 1.01539i | ||||
\(325\) | −2.07910 | + | 6.39883i | −0.115328 | + | 0.354943i | ||||
\(326\) | −20.0712 | + | 14.5826i | −1.11164 | + | 0.807654i | ||||
\(327\) | 11.5378 | + | 8.38270i | 0.638042 | + | 0.463565i | ||||
\(328\) | 12.8614 | + | 39.5834i | 0.710154 | + | 2.18563i | ||||
\(329\) | −17.4750 | −0.963430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.8319 | −0.870199 | −0.435099 | − | 0.900382i | \(-0.643287\pi\) | ||||
−0.435099 | + | 0.900382i | \(0.643287\pi\) | |||||||
\(332\) | 11.0703 | + | 34.0710i | 0.607563 | + | 1.86989i | ||||
\(333\) | −0.662520 | − | 0.481349i | −0.0363059 | − | 0.0263778i | ||||
\(334\) | 20.0576 | − | 14.5727i | 1.09751 | − | 0.797385i | ||||
\(335\) | 1.44006 | − | 4.43204i | 0.0786787 | − | 0.242148i | ||||
\(336\) | −10.9607 | + | 33.7337i | −0.597958 | + | 1.84033i | ||||
\(337\) | −5.44317 | + | 3.95469i | −0.296508 | + | 0.215426i | −0.726086 | − | 0.687604i | \(-0.758662\pi\) |
0.429578 | + | 0.903030i | \(0.358662\pi\) | |||||||
\(338\) | −68.4953 | − | 49.7647i | −3.72565 | − | 2.70684i | ||||
\(339\) | −5.70097 | − | 17.5458i | −0.309634 | − | 0.952956i | ||||
\(340\) | 8.71176 | 0.472462 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.67975 | 0.253052 | ||||||||
\(343\) | 5.76932 | + | 17.7561i | 0.311514 | + | 0.958741i | ||||
\(344\) | −23.2746 | − | 16.9100i | −1.25488 | − | 0.911725i | ||||
\(345\) | −5.64184 | + | 4.09904i | −0.303746 | + | 0.220685i | ||||
\(346\) | −7.36446 | + | 22.6655i | −0.395916 | + | 1.21850i | ||||
\(347\) | 10.3532 | − | 31.8638i | 0.555788 | − | 1.71054i | −0.138066 | − | 0.990423i | \(-0.544088\pi\) |
0.693853 | − | 0.720116i | \(-0.255912\pi\) | |||||||
\(348\) | −6.23381 | + | 4.52913i | −0.334167 | + | 0.242787i | ||||
\(349\) | −18.4247 | − | 13.3863i | −0.986252 | − | 0.716554i | −0.0271551 | − | 0.999631i | \(-0.508645\pi\) |
−0.959097 | + | 0.283077i | \(0.908645\pi\) | |||||||
\(350\) | −2.12742 | − | 6.54753i | −0.113716 | − | 0.349980i | ||||
\(351\) | 37.9050 | 2.02322 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.4617 | −0.822942 | −0.411471 | − | 0.911423i | \(-0.634985\pi\) | ||||
−0.411471 | + | 0.911423i | \(0.634985\pi\) | |||||||
\(354\) | −4.22004 | − | 12.9879i | −0.224292 | − | 0.690301i | ||||
\(355\) | −3.14261 | − | 2.28324i | −0.166793 | − | 0.121182i | ||||
\(356\) | −13.6281 | + | 9.90137i | −0.722286 | + | 0.524772i | ||||
\(357\) | −1.93763 | + | 5.96340i | −0.102550 | + | 0.315617i | ||||
\(358\) | −11.1640 | + | 34.3592i | −0.590035 | + | 1.81594i | ||||
\(359\) | −7.75526 | + | 5.63453i | −0.409307 | + | 0.297379i | −0.773321 | − | 0.634014i | \(-0.781406\pi\) |
0.364014 | + | 0.931393i | \(0.381406\pi\) | |||||||
\(360\) | 7.37651 | + | 5.35935i | 0.388776 | + | 0.282463i | ||||
\(361\) | −5.19403 | − | 15.9856i | −0.273370 | − | 0.841346i | ||||
\(362\) | −62.5998 | −3.29017 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 86.2280 | 4.51957 | ||||||||
\(365\) | −1.10230 | − | 3.39253i | −0.0576970 | − | 0.177573i | ||||
\(366\) | −9.13699 | − | 6.63841i | −0.477598 | − | 0.346995i | ||||
\(367\) | 8.76857 | − | 6.37074i | 0.457716 | − | 0.332550i | −0.334919 | − | 0.942247i | \(-0.608709\pi\) |
0.792635 | + | 0.609697i | \(0.208709\pi\) | |||||||
\(368\) | 16.2270 | − | 49.9415i | 0.845890 | − | 2.60338i | ||||
\(369\) | −2.04727 | + | 6.30085i | −0.106577 | + | 0.328009i | ||||
\(370\) | 1.44293 | − | 1.04835i | 0.0750143 | − | 0.0545011i | ||||
\(371\) | 30.3421 | + | 22.0448i | 1.57528 | + | 1.14451i | ||||
\(372\) | −9.23069 | − | 28.4091i | −0.478589 | − | 1.47295i | ||||
\(373\) | −10.0212 | −0.518878 | −0.259439 | − | 0.965759i | \(-0.583538\pi\) | ||||
−0.259439 | + | 0.965759i | \(0.583538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.33988 | 0.0691909 | ||||||||
\(376\) | 15.5764 | + | 47.9394i | 0.803294 | + | 2.47228i | ||||
\(377\) | 6.40861 | + | 4.65613i | 0.330060 | + | 0.239803i | ||||
\(378\) | −31.3785 | + | 22.7978i | −1.61394 | + | 1.17259i | ||||
\(379\) | 1.29533 | − | 3.98661i | 0.0665366 | − | 0.204778i | −0.912261 | − | 0.409610i | \(-0.865665\pi\) |
0.978797 | + | 0.204832i | \(0.0656647\pi\) | |||||||
\(380\) | −2.23459 | + | 6.87737i | −0.114632 | + | 0.352802i | ||||
\(381\) | 13.3470 | − | 9.69713i | 0.683785 | − | 0.496799i | ||||
\(382\) | −34.0971 | − | 24.7730i | −1.74456 | − | 1.26750i | ||||
\(383\) | 5.94672 | + | 18.3021i | 0.303863 | + | 0.935195i | 0.980099 | + | 0.198510i | \(0.0636101\pi\) |
−0.676236 | + | 0.736685i | \(0.736390\pi\) | |||||||
\(384\) | 3.24753 | 0.165725 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 56.3042 | 2.86581 | ||||||||
\(387\) | −1.41512 | − | 4.35528i | −0.0719345 | − | 0.221392i | ||||
\(388\) | −5.82875 | − | 4.23483i | −0.295910 | − | 0.214991i | ||||
\(389\) | 22.9942 | − | 16.7063i | 1.16585 | − | 0.847042i | 0.175347 | − | 0.984507i | \(-0.443895\pi\) |
0.990507 | + | 0.137465i | \(0.0438954\pi\) | |||||||
\(390\) | −7.30932 | + | 22.4958i | −0.370122 | + | 1.13912i | ||||
\(391\) | 2.86859 | − | 8.82860i | 0.145071 | − | 0.446481i | ||||
\(392\) | 0.707302 | − | 0.513885i | 0.0357241 | − | 0.0259551i | ||||
\(393\) | −21.1487 | − | 15.3654i | −1.06681 | − | 0.775084i | ||||
\(394\) | 7.47154 | + | 22.9951i | 0.376411 | + | 1.15847i | ||||
\(395\) | −15.1368 | −0.761615 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.1784 | −1.11310 | −0.556552 | − | 0.830813i | \(-0.687876\pi\) | ||||
−0.556552 | + | 0.830813i | \(0.687876\pi\) | |||||||
\(398\) | −13.3686 | − | 41.1443i | −0.670107 | − | 2.06238i | ||||
\(399\) | −4.21071 | − | 3.05926i | −0.210799 | − | 0.153155i | ||||
\(400\) | −8.16235 | + | 5.93029i | −0.408117 | + | 0.296515i | ||||
\(401\) | 6.82182 | − | 20.9954i | 0.340665 | − | 1.04846i | −0.623198 | − | 0.782064i | \(-0.714167\pi\) |
0.963864 | − | 0.266396i | \(-0.0858330\pi\) | |||||||
\(402\) | 5.06268 | − | 15.5813i | 0.252503 | − | 0.777126i | ||||
\(403\) | −24.8439 | + | 18.0502i | −1.23756 | + | 0.899142i | ||||
\(404\) | 13.4853 | + | 9.79765i | 0.670919 | + | 0.487451i | ||||
\(405\) | −1.21581 | − | 3.74187i | −0.0604140 | − | 0.185935i | ||||
\(406\) | −8.10557 | −0.402273 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 18.0866 | 0.895418 | ||||||||
\(409\) | 7.62386 | + | 23.4638i | 0.376975 | + | 1.16021i | 0.942136 | + | 0.335230i | \(0.108814\pi\) |
−0.565161 | + | 0.824981i | \(0.691186\pi\) | |||||||
\(410\) | −11.6734 | − | 8.48121i | −0.576507 | − | 0.418857i | ||||
\(411\) | 9.28349 | − | 6.74485i | 0.457921 | − | 0.332699i | ||||
\(412\) | −7.50724 | + | 23.1049i | −0.369855 | + | 1.13830i | ||||
\(413\) | 3.14957 | − | 9.69338i | 0.154980 | − | 0.476980i | ||||
\(414\) | 13.3101 | − | 9.67035i | 0.654156 | − | 0.475272i | ||||
\(415\) | −5.93358 | − | 4.31100i | −0.291268 | − | 0.211619i | ||||
\(416\) | −23.5679 | − | 72.5345i | −1.15551 | − | 3.55629i | ||||
\(417\) | 2.65783 | 0.130155 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.6535 | 0.862428 | 0.431214 | − | 0.902250i | \(-0.358085\pi\) | ||||
0.431214 | + | 0.902250i | \(0.358085\pi\) | |||||||
\(420\) | −5.30642 | − | 16.3315i | −0.258927 | − | 0.796895i | ||||
\(421\) | −1.23373 | − | 0.896358i | −0.0601284 | − | 0.0436858i | 0.557315 | − | 0.830301i | \(-0.311832\pi\) |
−0.617443 | + | 0.786615i | \(0.711832\pi\) | |||||||
\(422\) | −31.4878 | + | 22.8772i | −1.53280 | + | 1.11365i | ||||
\(423\) | −2.47944 | + | 7.63094i | −0.120555 | + | 0.371029i | ||||
\(424\) | 33.4301 | − | 102.887i | 1.62351 | − | 4.99665i | ||||
\(425\) | −1.44293 | + | 1.04835i | −0.0699923 | + | 0.0508524i | ||||
\(426\) | −11.0482 | − | 8.02699i | −0.535287 | − | 0.388909i | ||||
\(427\) | −2.60473 | − | 8.01654i | −0.126052 | − | 0.387948i | ||||
\(428\) | 34.5099 | 1.66810 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.97370 | 0.480974 | ||||||||
\(431\) | −5.17583 | − | 15.9296i | −0.249311 | − | 0.767300i | −0.994897 | − | 0.100891i | \(-0.967831\pi\) |
0.745587 | − | 0.666409i | \(-0.232169\pi\) | |||||||
\(432\) | 45.9852 | + | 33.4102i | 2.21246 | + | 1.60745i | ||||
\(433\) | −6.04742 | + | 4.39371i | −0.290621 | + | 0.211148i | −0.723537 | − | 0.690286i | \(-0.757485\pi\) |
0.432916 | + | 0.901434i | \(0.357485\pi\) | |||||||
\(434\) | 9.71006 | − | 29.8845i | 0.466098 | − | 1.43450i | ||||
\(435\) | 0.487483 | − | 1.50032i | 0.0233730 | − | 0.0719348i | ||||
\(436\) | 42.0607 | − | 30.5589i | 2.01434 | − | 1.46351i | ||||
\(437\) | 6.23381 | + | 4.52913i | 0.298204 | + | 0.216658i | ||||
\(438\) | −3.87525 | − | 11.9268i | −0.185167 | − | 0.569885i | ||||
\(439\) | 17.4585 | 0.833250 | 0.416625 | − | 0.909078i | \(-0.363213\pi\) | ||||
0.416625 | + | 0.909078i | \(0.363213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.139166 | 0.00662695 | ||||||||
\(442\) | −9.72970 | − | 29.9449i | −0.462794 | − | 1.42433i | ||||
\(443\) | 11.8794 | + | 8.63091i | 0.564408 | + | 0.410067i | 0.833070 | − | 0.553168i | \(-0.186581\pi\) |
−0.268661 | + | 0.963235i | \(0.586581\pi\) | |||||||
\(444\) | 3.59909 | − | 2.61489i | 0.170805 | − | 0.124097i | ||||
\(445\) | 1.06571 | − | 3.27993i | 0.0505197 | − | 0.155484i | ||||
\(446\) | 18.9752 | − | 58.3996i | 0.898500 | − | 2.76530i | ||||
\(447\) | 19.8903 | − | 14.4512i | 0.940781 | − | 0.683517i | ||||
\(448\) | 20.3022 | + | 14.7504i | 0.959190 | + | 0.696892i | ||||
\(449\) | −0.403974 | − | 1.24330i | −0.0190647 | − | 0.0586752i | 0.941072 | − | 0.338208i | \(-0.109821\pi\) |
−0.960136 | + | 0.279532i | \(0.909821\pi\) | |||||||
\(450\) | −3.16101 | −0.149011 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −67.2543 | −3.16338 | ||||||||
\(453\) | 7.13128 | + | 21.9478i | 0.335057 | + | 1.03120i | ||||
\(454\) | 5.56966 | + | 4.04660i | 0.261397 | + | 0.189916i | ||||
\(455\) | −14.2819 | + | 10.3764i | −0.669548 | + | 0.486455i | ||||
\(456\) | −4.63926 | + | 14.2782i | −0.217253 | + | 0.668637i | ||||
\(457\) | 3.14957 | − | 9.69338i | 0.147331 | − | 0.453437i | −0.849973 | − | 0.526827i | \(-0.823382\pi\) |
0.997303 | + | 0.0733895i | \(0.0233816\pi\) | |||||||
\(458\) | 46.7776 | − | 33.9859i | 2.18577 | − | 1.58806i | ||||
\(459\) | 8.12920 | + | 5.90621i | 0.379439 | + | 0.275678i | ||||
\(460\) | 7.85596 | + | 24.1782i | 0.366286 | + | 1.12731i | ||||
\(461\) | −4.12180 | −0.191971 | −0.0959857 | − | 0.995383i | \(-0.530600\pi\) | ||||
−0.0959857 | + | 0.995383i | \(0.530600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.7623 | 1.52259 | 0.761296 | − | 0.648404i | \(-0.224563\pi\) | ||||
0.761296 | + | 0.648404i | \(0.224563\pi\) | |||||||
\(464\) | 3.67073 | + | 11.2973i | 0.170409 | + | 0.524465i | ||||
\(465\) | 4.94756 | + | 3.59461i | 0.229437 | + | 0.166696i | ||||
\(466\) | −11.3454 | + | 8.24289i | −0.525564 | + | 0.381845i | ||||
\(467\) | 11.7162 | − | 36.0588i | 0.542161 | − | 1.66860i | −0.185485 | − | 0.982647i | \(-0.559386\pi\) |
0.727646 | − | 0.685953i | \(-0.240614\pi\) | |||||||
\(468\) | 12.2345 | − | 37.6538i | 0.565538 | − | 1.74055i | ||||
\(469\) | 9.89215 | − | 7.18707i | 0.456777 | − | 0.331868i | ||||
\(470\) | −14.1376 | − | 10.2716i | −0.652119 | − | 0.473792i | ||||
\(471\) | −8.65248 | − | 26.6296i | −0.398685 | − | 1.22703i | ||||
\(472\) | −29.3993 | −1.35321 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −53.2150 | −2.44425 | ||||||||
\(475\) | −0.457488 | − | 1.40800i | −0.0209910 | − | 0.0646037i | ||||
\(476\) | 18.4927 | + | 13.4357i | 0.847610 | + | 0.615824i | ||||
\(477\) | 13.9315 | − | 10.1219i | 0.637882 | − | 0.463448i | ||||
\(478\) | −10.2016 | + | 31.3972i | −0.466609 | + | 1.43607i | ||||
\(479\) | −1.99626 | + | 6.14386i | −0.0912116 | + | 0.280720i | −0.986248 | − | 0.165273i | \(-0.947149\pi\) |
0.895036 | + | 0.445993i | \(0.147149\pi\) | |||||||
\(480\) | −12.2876 | + | 8.92746i | −0.560849 | + | 0.407481i | ||||
\(481\) | −3.70001 | − | 2.68822i | −0.168706 | − | 0.122572i | ||||
\(482\) | −3.47583 | − | 10.6975i | −0.158320 | − | 0.487257i | ||||
\(483\) | −18.2978 | −0.832579 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.47502 | 0.0669774 | ||||||||
\(486\) | 9.42954 | + | 29.0211i | 0.427732 | + | 1.31643i | ||||
\(487\) | −35.1612 | − | 25.5461i | −1.59331 | − | 1.15761i | −0.899019 | − | 0.437909i | \(-0.855719\pi\) |
−0.694288 | − | 0.719697i | \(-0.744281\pi\) | |||||||
\(488\) | −19.6701 | + | 14.2912i | −0.890423 | + | 0.646930i | ||||
\(489\) | 3.91496 | − | 12.0490i | 0.177040 | − | 0.544874i | ||||
\(490\) | −0.0936615 | + | 0.288261i | −0.00423120 | + | 0.0130223i | ||||
\(491\) | 4.41213 | − | 3.20560i | 0.199117 | − | 0.144667i | −0.483759 | − | 0.875201i | \(-0.660729\pi\) |
0.682876 | + | 0.730534i | \(0.260729\pi\) | |||||||
\(492\) | −29.1169 | − | 21.1546i | −1.31269 | − | 0.953725i | ||||
\(493\) | 0.648906 | + | 1.99713i | 0.0292253 | + | 0.0899461i | ||||
\(494\) | 26.1353 | 1.17588 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −46.0496 | −2.06769 | ||||||||
\(497\) | −3.14957 | − | 9.69338i | −0.141278 | − | 0.434808i | ||||
\(498\) | −20.8602 | − | 15.1558i | −0.934766 | − | 0.679147i | ||||
\(499\) | −10.1030 | + | 7.34025i | −0.452272 | + | 0.328595i | −0.790492 | − | 0.612472i | \(-0.790175\pi\) |
0.338220 | + | 0.941067i | \(0.390175\pi\) | |||||||
\(500\) | 1.50939 | − | 4.64542i | 0.0675019 | − | 0.207750i | ||||
\(501\) | −3.91232 | + | 12.0409i | −0.174789 | + | 0.537946i | ||||
\(502\) | −21.3608 | + | 15.5195i | −0.953378 | + | 0.692670i | ||||
\(503\) | 16.8709 | + | 12.2575i | 0.752238 | + | 0.546533i | 0.896520 | − | 0.443004i | \(-0.146087\pi\) |
−0.144282 | + | 0.989537i | \(0.546087\pi\) | |||||||
\(504\) | 7.39284 | + | 22.7528i | 0.329303 | + | 1.01349i | ||||
\(505\) | −3.41259 | −0.151858 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 43.2347 | 1.92012 | ||||||||
\(508\) | −18.5849 | − | 57.1985i | −0.824572 | − | 2.53777i | ||||
\(509\) | 21.5014 | + | 15.6217i | 0.953033 | + | 0.692419i | 0.951522 | − | 0.307580i | \(-0.0995191\pi\) |
0.00151069 | + | 0.999999i | \(0.499519\pi\) | |||||||
\(510\) | −5.07277 | + | 3.68559i | −0.224626 | + | 0.163201i | ||||
\(511\) | 2.89225 | − | 8.90142i | 0.127945 | − | 0.393776i | ||||
\(512\) | −11.8511 | + | 36.4741i | −0.523751 | + | 1.61194i | ||||
\(513\) | −6.74774 | + | 4.90252i | −0.297920 | + | 0.216452i | ||||
\(514\) | 6.71941 | + | 4.88194i | 0.296381 | + | 0.215333i | ||||
\(515\) | −1.53696 | − | 4.73027i | −0.0677264 | − | 0.208440i | ||||
\(516\) | 24.8773 | 1.09516 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.67975 | 0.205617 | ||||||||
\(519\) | −3.76071 | − | 11.5743i | −0.165077 | − | 0.508054i | ||||
\(520\) | 41.1960 | + | 29.9307i | 1.80657 | + | 1.31255i | ||||
\(521\) | 18.6392 | − | 13.5421i | 0.816596 | − | 0.593292i | −0.0991393 | − | 0.995074i | \(-0.531609\pi\) |
0.915735 | + | 0.401782i | \(0.131609\pi\) | |||||||
\(522\) | −1.15006 | + | 3.53952i | −0.0503367 | + | 0.154920i | ||||
\(523\) | −0.365665 | + | 1.12540i | −0.0159894 | + | 0.0492104i | −0.958733 | − | 0.284308i | \(-0.908236\pi\) |
0.942743 | + | 0.333519i | \(0.108236\pi\) | |||||||
\(524\) | −77.0970 | + | 56.0143i | −3.36800 | + | 2.44699i | ||||
\(525\) | 2.84419 | + | 2.06642i | 0.124131 | + | 0.0901861i | ||||
\(526\) | 18.1362 | + | 55.8176i | 0.790777 | + | 2.43376i | ||||
\(527\) | −8.14058 | −0.354609 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.08921 | 0.177792 | ||||||||
\(530\) | 11.5896 | + | 35.6693i | 0.503422 | + | 1.54937i | ||||
\(531\) | −3.78600 | − | 2.75069i | −0.164298 | − | 0.119370i | ||||
\(532\) | −15.3500 | + | 11.1525i | −0.665509 | + | 0.483520i | ||||
\(533\) | −11.4335 | + | 35.1887i | −0.495240 | + | 1.52419i | ||||
\(534\) | 3.74663 | − | 11.5309i | 0.162133 | − | 0.498993i | ||||
\(535\) | −5.71588 | + | 4.15283i | −0.247119 | + | 0.179543i | ||||
\(536\) | −28.5337 | − | 20.7310i | −1.23247 | − | 0.895442i | ||||
\(537\) | −5.70097 | − | 17.5458i | −0.246015 | − | 0.757156i | ||||
\(538\) | 41.9123 | 1.80697 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −27.5183 | −1.18420 | ||||||||
\(541\) | −9.76663 | − | 30.0586i | −0.419900 | − | 1.29232i | −0.907794 | − | 0.419417i | \(-0.862235\pi\) |
0.487894 | − | 0.872903i | \(-0.337765\pi\) | |||||||
\(542\) | 33.1993 | + | 24.1207i | 1.42603 | + | 1.03607i | ||||
\(543\) | 25.8619 | − | 18.7897i | 1.10984 | − | 0.806345i | ||||
\(544\) | 6.24761 | − | 19.2282i | 0.267864 | − | 0.824401i | ||||
\(545\) | −3.28914 | + | 10.1229i | −0.140891 | + | 0.433619i | ||||
\(546\) | −50.2097 | + | 36.4795i | −2.14878 | + | 1.56118i | ||||
\(547\) | 4.02856 | + | 2.92692i | 0.172249 | + | 0.125146i | 0.670570 | − | 0.741847i | \(-0.266050\pi\) |
−0.498321 | + | 0.866993i | \(0.666050\pi\) | |||||||
\(548\) | −12.9268 | − | 39.7845i | −0.552204 | − | 1.69951i | ||||
\(549\) | −3.87021 | −0.165177 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.74305 | −0.0742564 | ||||||||
\(552\) | 16.3098 | + | 50.1965i | 0.694192 | + | 2.13650i | ||||
\(553\) | −32.1312 | − | 23.3447i | −1.36636 | − | 0.992717i | ||||
\(554\) | −50.6982 | + | 36.8344i | −2.15396 | + | 1.56494i | ||||
\(555\) | −0.281448 | + | 0.866209i | −0.0119468 | + | 0.0367685i | ||||
\(556\) | 2.99408 | − | 9.21483i | 0.126977 | − | 0.390796i | ||||
\(557\) | 20.3297 | − | 14.7704i | 0.861399 | − | 0.625843i | −0.0668666 | − | 0.997762i | \(-0.521300\pi\) |
0.928265 | + | 0.371919i | \(0.121300\pi\) | |||||||
\(558\) | −11.6722 | − | 8.48032i | −0.494122 | − | 0.359001i | ||||
\(559\) | −7.90309 | − | 24.3232i | −0.334265 | − | 1.02876i | ||||
\(560\) | −26.4724 | −1.11866 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 32.1258 | 1.35515 | ||||||||
\(563\) | −3.50289 | − | 10.7808i | −0.147629 | − | 0.454356i | 0.849711 | − | 0.527250i | \(-0.176777\pi\) |
−0.997340 | + | 0.0728935i | \(0.976777\pi\) | |||||||
\(564\) | −35.2633 | − | 25.6203i | −1.48485 | − | 1.07881i | ||||
\(565\) | 11.1393 | − | 8.09320i | 0.468635 | − | 0.340483i | ||||
\(566\) | −16.9083 | + | 52.0384i | −0.710708 | + | 2.18734i | ||||
\(567\) | 3.19007 | − | 9.81803i | 0.133970 | − | 0.412319i | ||||
\(568\) | −23.7845 | + | 17.2805i | −0.997977 | + | 0.725073i | ||||
\(569\) | 9.67527 | + | 7.02949i | 0.405608 | + | 0.294692i | 0.771821 | − | 0.635839i | \(-0.219346\pi\) |
−0.366213 | + | 0.930531i | \(0.619346\pi\) | |||||||
\(570\) | −1.60835 | − | 4.94999i | −0.0673664 | − | 0.207332i | ||||
\(571\) | −29.8054 | −1.24732 | −0.623659 | − | 0.781697i | \(-0.714355\pi\) | ||||
−0.623659 | + | 0.781697i | \(0.714355\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.5223 | 0.899108 | ||||||||
\(574\) | −11.6992 | − | 36.0065i | −0.488316 | − | 1.50288i | ||||
\(575\) | −4.21071 | − | 3.05926i | −0.175599 | − | 0.127580i | ||||
\(576\) | 9.32176 | − | 6.77265i | 0.388406 | − | 0.282194i | ||||
\(577\) | −5.71240 | + | 17.5810i | −0.237810 | + | 0.731905i | 0.758926 | + | 0.651177i | \(0.225724\pi\) |
−0.996736 | + | 0.0807279i | \(0.974276\pi\) | |||||||
\(578\) | −11.2045 | + | 34.4839i | −0.466045 | + | 1.43434i | ||||
\(579\) | −23.2610 | + | 16.9001i | −0.966693 | + | 0.702344i | ||||
\(580\) | −4.65252 | − | 3.38026i | −0.193186 | − | 0.140357i | ||||
\(581\) | −5.94672 | − | 18.3021i | −0.246712 | − | 0.759300i | ||||
\(582\) | 5.18561 | 0.214950 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −26.9973 | −1.11716 | ||||||||
\(585\) | 2.50476 | + | 7.70886i | 0.103559 | + | 0.318722i | ||||
\(586\) | −30.4197 | − | 22.1012i | −1.25663 | − | 0.912993i | ||||
\(587\) | 2.17122 | − | 1.57748i | 0.0896157 | − | 0.0651097i | −0.542075 | − | 0.840330i | \(-0.682361\pi\) |
0.631691 | + | 0.775220i | \(0.282361\pi\) | |||||||
\(588\) | −0.233620 | + | 0.719007i | −0.00963431 | + | 0.0296514i | ||||
\(589\) | 2.08809 | − | 6.42647i | 0.0860381 | − | 0.264798i | ||||
\(590\) | 8.24568 | − | 5.99084i | 0.339469 | − | 0.246639i | ||||
\(591\) | −9.98884 | − | 7.25731i | −0.410886 | − | 0.298526i | ||||
\(592\) | −2.11929 | − | 6.52252i | −0.0871025 | − | 0.268074i | ||||
\(593\) | −28.7251 | −1.17960 | −0.589800 | − | 0.807550i | \(-0.700793\pi\) | ||||
−0.589800 | + | 0.807550i | \(0.700793\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.67975 | −0.191851 | ||||||||
\(596\) | −27.6962 | − | 85.2402i | −1.13448 | − | 3.49158i | ||||
\(597\) | 17.8727 | + | 12.9853i | 0.731481 | + | 0.531452i | ||||
\(598\) | 74.3337 | − | 54.0066i | 3.03973 | − | 2.20849i | ||||
\(599\) | −10.5624 | + | 32.5078i | −0.431569 | + | 1.32823i | 0.464994 | + | 0.885314i | \(0.346057\pi\) |
−0.896562 | + | 0.442918i | \(0.853943\pi\) | |||||||
\(600\) | 3.13365 | − | 9.64440i | 0.127931 | − | 0.393731i | ||||
\(601\) | 26.2585 | − | 19.0779i | 1.07111 | − | 0.778205i | 0.0949959 | − | 0.995478i | \(-0.469716\pi\) |
0.976111 | + | 0.217273i | \(0.0697162\pi\) | |||||||
\(602\) | 21.1714 | + | 15.3819i | 0.862882 | + | 0.626920i | ||||
\(603\) | −1.73488 | − | 5.33941i | −0.0706498 | − | 0.217438i | ||||
\(604\) | 84.1276 | 3.42310 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.9973 | −0.487359 | ||||||||
\(607\) | 1.65161 | + | 5.08314i | 0.0670368 | + | 0.206318i | 0.978964 | − | 0.204035i | \(-0.0654055\pi\) |
−0.911927 | + | 0.410353i | \(0.865406\pi\) | |||||||
\(608\) | 13.5769 | + | 9.86417i | 0.550615 | + | 0.400045i | ||||
\(609\) | 3.34866 | − | 2.43294i | 0.135694 | − | 0.0985877i | ||||
\(610\) | 2.60473 | − | 8.01654i | 0.105463 | − | 0.324580i | ||||
\(611\) | −13.8471 | + | 42.6170i | −0.560193 | + | 1.72410i | ||||
\(612\) | 8.49089 | − | 6.16899i | 0.343224 | − | 0.249367i | ||||
\(613\) | 24.4368 | + | 17.7544i | 0.986994 | + | 0.717093i | 0.959261 | − | 0.282522i | \(-0.0911711\pi\) |
0.0277333 | + | 0.999615i | \(0.491171\pi\) | |||||||
\(614\) | 8.34746 | + | 25.6909i | 0.336876 | + | 1.03680i | ||||
\(615\) | 7.36831 | 0.297119 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.973697 | 0.0391996 | 0.0195998 | − | 0.999808i | \(-0.493761\pi\) | ||||
0.0195998 | + | 0.999808i | \(0.493761\pi\) | |||||||
\(618\) | −5.40334 | − | 16.6298i | −0.217354 | − | 0.668947i | ||||
\(619\) | −1.47368 | − | 1.07069i | −0.0592323 | − | 0.0430348i | 0.557775 | − | 0.829992i | \(-0.311655\pi\) |
−0.617007 | + | 0.786957i | \(0.711655\pi\) | |||||||
\(620\) | 18.0362 | − | 13.1041i | 0.724350 | − | 0.526271i | ||||
\(621\) | −9.06116 | + | 27.8874i | −0.363612 | + | 1.11908i | ||||
\(622\) | −15.5287 | + | 47.7924i | −0.622644 | + | 1.91630i | ||||
\(623\) | 7.32068 | − | 5.31879i | 0.293297 | − | 0.213093i | ||||
\(624\) | 73.5824 | + | 53.4607i | 2.94565 | + | 2.14014i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | −39.2884 | −1.57028 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −102.073 | −4.07316 | ||||||||
\(629\) | −0.374646 | − | 1.15304i | −0.0149381 | − | 0.0459748i | ||||
\(630\) | −6.70994 | − | 4.87506i | −0.267330 | − | 0.194227i | ||||
\(631\) | 26.1772 | − | 19.0189i | 1.04210 | − | 0.757130i | 0.0714054 | − | 0.997447i | \(-0.477252\pi\) |
0.970694 | + | 0.240318i | \(0.0772516\pi\) | |||||||
\(632\) | −35.4014 | + | 108.954i | −1.40819 | + | 4.33396i | ||||
\(633\) | 6.14181 | − | 18.9026i | 0.244115 | − | 0.751309i | ||||
\(634\) | −25.8514 | + | 18.7822i | −1.02669 | + | 0.745935i | ||||
\(635\) | 9.96133 | + | 7.23733i | 0.395303 | + | 0.287205i | ||||
\(636\) | 28.9080 | + | 88.9697i | 1.14628 | + | 3.52788i | ||||
\(637\) | 0.777208 | 0.0307941 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.67975 | −0.185128 | ||||||||
\(640\) | 0.748980 | + | 2.30512i | 0.0296060 | + | 0.0911180i | ||||
\(641\) | 11.1393 | + | 8.09320i | 0.439977 | + | 0.319662i | 0.785626 | − | 0.618702i | \(-0.212341\pi\) |
−0.345649 | + | 0.938364i | \(0.612341\pi\) | |||||||
\(642\) | −20.0948 | + | 14.5997i | −0.793079 | + | 0.576206i | ||||
\(643\) | 9.93832 | − | 30.5870i | 0.391929 | − | 1.20623i | −0.539399 | − | 0.842051i | \(-0.681348\pi\) |
0.931328 | − | 0.364183i | \(-0.118652\pi\) | |||||||
\(644\) | −20.6127 | + | 63.4394i | −0.812254 | + | 2.49986i | ||||
\(645\) | −4.12043 | + | 2.99367i | −0.162242 | + | 0.117876i | ||||
\(646\) | 5.60503 | + | 4.07230i | 0.220527 | + | 0.160222i | ||||
\(647\) | 6.02006 | + | 18.5278i | 0.236673 | + | 0.728404i | 0.996895 | + | 0.0787410i | \(0.0250900\pi\) |
−0.760222 | + | 0.649663i | \(0.774910\pi\) | |||||||
\(648\) | −29.7774 | −1.16977 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −17.6535 | −0.692425 | ||||||||
\(651\) | 4.95851 | + | 15.2607i | 0.194339 | + | 0.598115i | ||||
\(652\) | −37.3642 | − | 27.1467i | −1.46330 | − | 1.06315i | ||||
\(653\) | −0.630757 | + | 0.458272i | −0.0246834 | + | 0.0179336i | −0.600059 | − | 0.799956i | \(-0.704856\pi\) |
0.575375 | + | 0.817890i | \(0.304856\pi\) | |||||||
\(654\) | −11.5633 | + | 35.5883i | −0.452163 | + | 1.39161i | ||||
\(655\) | 6.02898 | − | 18.5553i | 0.235572 | − | 0.725015i | ||||
\(656\) | −44.8868 | + | 32.6121i | −1.75253 | + | 1.27329i | ||||
\(657\) | −3.47668 | − | 2.52596i | −0.135638 | − | 0.0985469i | ||||
\(658\) | −14.1689 | − | 43.6074i | −0.552361 | − | 1.69999i | ||||
\(659\) | −28.1929 | −1.09824 | −0.549119 | − | 0.835744i | \(-0.685037\pi\) | ||||
−0.549119 | + | 0.835744i | \(0.685037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.70340 | 0.0662547 | 0.0331274 | − | 0.999451i | \(-0.489453\pi\) | ||||
0.0331274 | + | 0.999451i | \(0.489453\pi\) | |||||||
\(662\) | −12.8366 | − | 39.5070i | −0.498909 | − | 1.53548i | ||||
\(663\) | 13.0078 | + | 9.45072i | 0.505181 | + | 0.367035i | ||||
\(664\) | −44.9077 | + | 32.6274i | −1.74276 | + | 1.26619i | ||||
\(665\) | 1.20037 | − | 3.69436i | 0.0465484 | − | 0.143261i | ||||
\(666\) | 0.663987 | − | 2.04354i | 0.0257290 | − | 0.0791856i | ||||
\(667\) | −4.95756 | + | 3.60188i | −0.191958 | + | 0.139465i | ||||
\(668\) | 37.3390 | + | 27.1284i | 1.44469 | + | 1.04963i | ||||
\(669\) | 9.68980 | + | 29.8221i | 0.374629 | + | 1.15299i | ||||
\(670\) | 12.2274 | 0.472385 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −39.8515 | −1.53731 | ||||||||
\(673\) | 3.40056 | + | 10.4658i | 0.131082 | + | 0.403429i | 0.994960 | − | 0.100272i | \(-0.0319713\pi\) |
−0.863878 | + | 0.503701i | \(0.831971\pi\) | |||||||
\(674\) | −14.2819 | − | 10.3764i | −0.550120 | − | 0.399685i | ||||
\(675\) | 4.55786 | − | 3.31148i | 0.175432 | − | 0.127459i | ||||
\(676\) | 48.7044 | − | 149.897i | 1.87325 | − | 5.76526i | ||||
\(677\) | −6.61012 | + | 20.3439i | −0.254048 | + | 0.781878i | 0.739968 | + | 0.672642i | \(0.234840\pi\) |
−0.994016 | + | 0.109236i | \(0.965160\pi\) | |||||||
\(678\) | 39.1615 | − | 28.4525i | 1.50399 | − | 1.09271i | ||||
\(679\) | 3.13107 | + | 2.27485i | 0.120159 | + | 0.0873009i | ||||
\(680\) | 4.17132 | + | 12.8380i | 0.159963 | + | 0.492315i | ||||
\(681\) | −3.51561 | −0.134718 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.0959 | 1.30464 | 0.652321 | − | 0.757942i | \(-0.273795\pi\) | ||||
0.652321 | + | 0.757942i | \(0.273795\pi\) | |||||||
\(684\) | 2.69208 | + | 8.28538i | 0.102934 | + | 0.316799i | ||||
\(685\) | 6.92861 | + | 5.03393i | 0.264729 | + | 0.192337i | ||||
\(686\) | −39.6310 | + | 28.7936i | −1.51312 | + | 1.09935i | ||||
\(687\) | −9.12414 | + | 28.0812i | −0.348108 | + | 1.07137i | ||||
\(688\) | 11.8511 | − | 36.4741i | 0.451821 | − | 1.39056i | ||||
\(689\) | 77.8043 | − | 56.5281i | 2.96411 | − | 2.15355i | ||||
\(690\) | −14.8032 | − | 10.7552i | −0.563549 | − | 0.409443i | ||||
\(691\) | 14.3136 | + | 44.0528i | 0.544516 | + | 1.67585i | 0.722138 | + | 0.691749i | \(0.243160\pi\) |
−0.177622 | + | 0.984099i | \(0.556840\pi\) | |||||||
\(692\) | −44.3651 | −1.68651 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 87.9077 | 3.33693 | ||||||||
\(695\) | 0.612978 | + | 1.88655i | 0.0232516 | + | 0.0715610i | ||||
\(696\) | −9.65914 | − | 7.01778i | −0.366129 | − | 0.266008i | ||||
\(697\) | −7.93502 | + | 5.76513i | −0.300560 | + | 0.218370i | ||||
\(698\) | 18.4655 | − | 56.8310i | 0.698930 | − | 2.15108i | ||||
\(699\) | 2.21296 | − | 6.81078i | 0.0837017 | − | 0.257607i | ||||
\(700\) | 10.3684 | − | 7.53309i | 0.391889 | − | 0.284724i | ||||
\(701\) | −35.0828 | − | 25.4891i | −1.32506 | − | 0.962711i | −0.999854 | − | 0.0170666i | \(-0.994567\pi\) |
−0.325203 | − | 0.945644i | \(-0.605433\pi\) | |||||||
\(702\) | 30.7337 | + | 94.5886i | 1.15997 | + | 3.57002i | ||||
\(703\) | 1.00635 | 0.0379552 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.92375 | 0.336088 | ||||||||
\(706\) | −12.5365 | − | 38.5832i | −0.471816 | − | 1.45210i | ||||
\(707\) | −7.24399 | − | 5.26307i | −0.272438 | − | 0.197938i | ||||
\(708\) | 20.5672 | − | 14.9429i | 0.772962 | − | 0.561589i | ||||
\(709\) | 5.92646 | − | 18.2398i | 0.222573 | − | 0.685009i | −0.775956 | − | 0.630787i | \(-0.782732\pi\) |
0.998529 | − | 0.0542219i | \(-0.0172678\pi\) | |||||||
\(710\) | 3.14957 | − | 9.69338i | 0.118201 | − | 0.363786i | ||||
\(711\) | −14.7530 | + | 10.7187i | −0.553282 | + | 0.401983i | ||||
\(712\) | −21.1164 | − | 15.3419i | −0.791370 | − | 0.574964i | ||||
\(713\) | −7.34089 | − | 22.5929i | −0.274919 | − | 0.846112i | ||||
\(714\) | −16.4522 | −0.615708 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −67.2543 | −2.51341 | ||||||||
\(717\) | −5.20950 | − | 16.0332i | −0.194552 | − | 0.598771i | ||||
\(718\) | −20.3485 | − | 14.7840i | −0.759399 | − | 0.551736i | ||||
\(719\) | 26.1263 | − | 18.9819i | 0.974348 | − | 0.707906i | 0.0179100 | − | 0.999840i | \(-0.494299\pi\) |
0.956438 | + | 0.291934i | \(0.0942988\pi\) | |||||||
\(720\) | −3.75603 | + | 11.5599i | −0.139979 | + | 0.430811i | ||||
\(721\) | 4.03271 | − | 12.4114i | 0.150186 | − | 0.462225i | ||||
\(722\) | 35.6792 | − | 25.9225i | 1.32784 | − | 0.964734i | ||||
\(723\) | 4.64689 | + | 3.37616i | 0.172820 | + | 0.125561i | ||||
\(724\) | −36.0113 | − | 110.831i | −1.33835 | − | 4.11901i | ||||
\(725\) | 1.17737 | 0.0437264 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.8622 | −1.51550 | −0.757748 | − | 0.652548i | \(-0.773700\pi\) | ||||
−0.757748 | + | 0.652548i | \(0.773700\pi\) | |||||||
\(728\) | 41.2872 | + | 127.069i | 1.53021 | + | 4.70949i | ||||
\(729\) | −22.1556 | − | 16.0970i | −0.820577 | − | 0.596184i | ||||
\(730\) | 7.57200 | − | 5.50138i | 0.280252 | − | 0.203615i | ||||
\(731\) | 2.09503 | − | 6.44784i | 0.0774875 | − | 0.238482i | ||||
\(732\) | 6.49697 | − | 19.9956i | 0.240135 | − | 0.739059i | ||||
\(733\) | 8.02880 | − | 5.83326i | 0.296550 | − | 0.215457i | −0.429554 | − | 0.903041i | \(-0.641329\pi\) |
0.726104 | + | 0.687585i | \(0.241329\pi\) | |||||||
\(734\) | 23.0072 | + | 16.7157i | 0.849213 | + | 0.616989i | ||||
\(735\) | −0.0478289 | − | 0.147202i | −0.00176420 | − | 0.00542964i | ||||
\(736\) | 58.9987 | 2.17472 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −17.3832 | −0.639883 | ||||||||
\(739\) | 10.3127 | + | 31.7392i | 0.379358 | + | 1.16754i | 0.940491 | + | 0.339818i | \(0.110366\pi\) |
−0.561133 | + | 0.827726i | \(0.689634\pi\) | |||||||
\(740\) | 2.68614 | + | 1.95159i | 0.0987443 | + | 0.0717419i | ||||
\(741\) | −10.7973 | + | 7.84468i | −0.396648 | + | 0.288181i | ||||
\(742\) | −30.4093 | + | 93.5901i | −1.11636 | + | 3.43580i | ||||
\(743\) | 1.17647 | − | 3.62081i | 0.0431606 | − | 0.132835i | −0.927154 | − | 0.374680i | \(-0.877753\pi\) |
0.970315 | + | 0.241845i | \(0.0777526\pi\) | |||||||
\(744\) | 37.4451 | − | 27.2054i | 1.37280 | − | 0.997399i | ||||
\(745\) | 14.8449 | + | 10.7855i | 0.543875 | + | 0.395148i | ||||
\(746\) | −8.12528 | − | 25.0070i | −0.297487 | − | 0.915572i | ||||
\(747\) | −8.83587 | −0.323287 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.5379 | −0.677361 | ||||||||
\(750\) | 1.08638 | + | 3.34354i | 0.0396691 | + | 0.122089i | ||||
\(751\) | −18.2105 | − | 13.2307i | −0.664509 | − | 0.482794i | 0.203674 | − | 0.979039i | \(-0.434712\pi\) |
−0.868183 | + | 0.496245i | \(0.834712\pi\) | |||||||
\(752\) | −54.3622 | + | 39.4965i | −1.98239 | + | 1.44029i | ||||
\(753\) | 4.16650 | − | 12.8232i | 0.151836 | − | 0.467302i | ||||
\(754\) | −6.42280 | + | 19.7673i | −0.233904 | + | 0.719884i | ||||
\(755\) | −13.9341 | + | 10.1237i | −0.507112 | + | 0.368439i | ||||
\(756\) | −58.4137 | − | 42.4401i | −2.12449 | − | 1.54353i | ||||
\(757\) | −10.4116 | − | 32.0437i | −0.378417 | − | 1.16465i | −0.941144 | − | 0.338005i | \(-0.890248\pi\) |
0.562728 | − | 0.826642i | \(-0.309752\pi\) | |||||||
\(758\) | 10.9985 | 0.399483 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.2047 | −0.406438 | ||||||||
\(761\) | 5.80084 | + | 17.8531i | 0.210280 | + | 0.647176i | 0.999455 | + | 0.0330075i | \(0.0105085\pi\) |
−0.789175 | + | 0.614169i | \(0.789491\pi\) | |||||||
\(762\) | 35.0201 | + | 25.4436i | 1.26865 | + | 0.921725i | ||||
\(763\) | −22.5940 | + | 16.4155i | −0.817959 | + | 0.594282i | ||||
\(764\) | 24.2452 | − | 74.6190i | 0.877160 | − | 2.69962i | ||||
\(765\) | −0.663987 | + | 2.04354i | −0.0240065 | + | 0.0738844i | ||||
\(766\) | −40.8497 | + | 29.6790i | −1.47596 | + | 1.07235i | ||||
\(767\) | −21.1439 | − | 15.3619i | −0.763462 | − | 0.554687i | ||||
\(768\) | −5.28692 | − | 16.2715i | −0.190775 | − | 0.587146i | ||||
\(769\) | −21.5618 | −0.777539 | −0.388770 | − | 0.921335i | \(-0.627100\pi\) | ||||
−0.388770 | + | 0.921335i | \(0.627100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.24134 | −0.152748 | ||||||||
\(772\) | 32.3897 | + | 99.6852i | 1.16573 | + | 3.58775i | ||||
\(773\) | 18.9174 | + | 13.7443i | 0.680411 | + | 0.494347i | 0.873494 | − | 0.486835i | \(-0.161849\pi\) |
−0.193083 | + | 0.981182i | \(0.561849\pi\) | |||||||
\(774\) | 9.72083 | − | 7.06260i | 0.349408 | − | 0.253860i | ||||
\(775\) | −1.41043 | + | 4.34085i | −0.0506640 | + | 0.155928i | ||||
\(776\) | 3.44973 | − | 10.6172i | 0.123838 | − | 0.381135i | ||||
\(777\) | −1.93335 | + | 1.40466i | −0.0693584 | + | 0.0503919i | ||||
\(778\) | 60.3329 | + | 43.8344i | 2.16304 | + | 1.57154i | ||||
\(779\) | −2.51584 | − | 7.74296i | −0.0901394 | − | 0.277420i | ||||
\(780\) | −44.0329 | −1.57663 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 24.3569 | 0.870999 | ||||||||
\(783\) | −2.04973 | − | 6.30843i | −0.0732515 | − | 0.225445i | ||||
\(784\) | 0.942884 | + | 0.685045i | 0.0336744 | + | 0.0244659i | ||||
\(785\) | 16.9064 | − | 12.2832i | 0.603415 | − | 0.438407i | ||||
\(786\) | 21.1955 | − | 65.2331i | 0.756019 | − | 2.32679i | ||||
\(787\) | 7.75476 | − | 23.8667i | 0.276427 | − | 0.850756i | −0.712411 | − | 0.701763i | \(-0.752397\pi\) |
0.988838 | − | 0.148993i | \(-0.0476033\pi\) | |||||||
\(788\) | −36.4140 | + | 26.4563i | −1.29720 | + | 0.942468i | ||||
\(789\) | −24.2466 | − | 17.6162i | −0.863203 | − | 0.627154i | ||||
\(790\) | −12.2730 | − | 37.7725i | −0.436655 | − | 1.34389i | ||||
\(791\) | 36.1274 | 1.28454 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.6142 | −0.767542 | ||||||||
\(794\) | −17.9824 | − | 55.3443i | −0.638173 | − | 1.96410i | ||||
\(795\) | −15.4944 | − | 11.2573i | −0.549530 | − | 0.399257i | ||||
\(796\) | 65.1544 | − | 47.3375i | 2.30934 | − | 1.67783i | ||||
\(797\) | −3.73177 | + | 11.4852i | −0.132186 | + | 0.406827i | −0.995142 | − | 0.0984529i | \(-0.968611\pi\) |
0.862956 | + | 0.505280i | \(0.168611\pi\) | |||||||
\(798\) | 4.22004 | − | 12.9879i | 0.149388 | − | 0.459768i | ||||
\(799\) | −9.61008 | + | 6.98214i | −0.339980 | + | 0.247010i | ||||
\(800\) | −9.17069 | − | 6.66289i | −0.324233 | − | 0.235569i | ||||
\(801\) | −1.28390 | − | 3.95143i | −0.0453643 | − | 0.139617i | ||||
\(802\) | 57.9233 | 2.04534 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 30.4987 | 1.07561 | ||||||||
\(805\) | −4.22004 | − | 12.9879i | −0.148737 | − | 0.457765i | ||||
\(806\) | −65.1862 | − | 47.3605i | −2.29609 | − | 1.66820i | ||||
\(807\) | −17.3152 | + | 12.5802i | −0.609525 | + | 0.442846i | ||||
\(808\) | −7.98125 | + | 24.5638i | −0.280779 | + | 0.864150i | ||||
\(809\) | 2.81574 | − | 8.66595i | 0.0989961 | − | 0.304679i | −0.889278 | − | 0.457366i | \(-0.848793\pi\) |
0.988275 | + | 0.152688i | \(0.0487928\pi\) | |||||||
\(810\) | 8.35172 | − | 6.06788i | 0.293449 | − | 0.213204i | ||||
\(811\) | −2.41895 | − | 1.75747i | −0.0849409 | − | 0.0617132i | 0.544504 | − | 0.838758i | \(-0.316718\pi\) |
−0.629445 | + | 0.777045i | \(0.716718\pi\) | |||||||
\(812\) | −4.66282 | − | 14.3507i | −0.163633 | − | 0.503611i | ||||
\(813\) | −20.9556 | −0.734946 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.45539 | 0.331208 | ||||||||
\(816\) | 7.45061 | + | 22.9306i | 0.260824 | + | 0.802732i | ||||
\(817\) | 4.55277 | + | 3.30778i | 0.159281 | + | 0.115725i | ||||
\(818\) | −52.3704 | + | 38.0493i | −1.83109 | + | 1.33036i | ||||
\(819\) | −6.57206 | + | 20.2267i | −0.229646 | + | 0.706779i | ||||
\(820\) | 8.30050 | − | 25.5463i | 0.289866 | − | 0.892116i | ||||
\(821\) | −28.5337 | + | 20.7310i | −0.995835 | + | 0.723516i | −0.961191 | − | 0.275884i | \(-0.911030\pi\) |
−0.0346436 | + | 0.999400i | \(0.511030\pi\) | |||||||
\(822\) | 24.3583 | + | 17.6973i | 0.849593 | + | 0.617266i | ||||
\(823\) | 4.80755 | + | 14.7961i | 0.167581 | + | 0.515760i | 0.999217 | − | 0.0395600i | \(-0.0125956\pi\) |
−0.831636 | + | 0.555320i | \(0.812596\pi\) | |||||||
\(824\) | −37.6429 | −1.31135 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.7427 | 0.930496 | ||||||||
\(827\) | −3.25374 | − | 10.0140i | −0.113144 | − | 0.348220i | 0.878412 | − | 0.477905i | \(-0.158604\pi\) |
−0.991555 | + | 0.129684i | \(0.958604\pi\) | |||||||
\(828\) | 24.7779 | + | 18.0022i | 0.861091 | + | 0.625619i | ||||
\(829\) | −20.7310 | + | 15.0619i | −0.720016 | + | 0.523122i | −0.886389 | − | 0.462941i | \(-0.846794\pi\) |
0.166373 | + | 0.986063i | \(0.446794\pi\) | |||||||
\(830\) | 5.94672 | − | 18.3021i | 0.206414 | − | 0.635276i | ||||
\(831\) | 9.88886 | − | 30.4348i | 0.343041 | − | 1.05577i | ||||
\(832\) | 52.0597 | − | 37.8236i | 1.80485 | − | 1.31130i | ||||
\(833\) | 0.166682 | + | 0.121101i | 0.00577518 | + | 0.00419592i | ||||
\(834\) | 2.15499 | + | 6.63238i | 0.0746212 | + | 0.229661i | ||||
\(835\) | −9.44902 | −0.326997 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.7141 | 0.888809 | ||||||||
\(838\) | 14.3136 | + | 44.0526i | 0.494454 | + | 1.52177i | ||||
\(839\) | −21.1362 | − | 15.3564i | −0.729704 | − | 0.530161i | 0.159766 | − | 0.987155i | \(-0.448926\pi\) |
−0.889470 | + | 0.456994i | \(0.848926\pi\) | |||||||
\(840\) | 21.5259 | − | 15.6395i | 0.742715 | − | 0.539614i | ||||
\(841\) | −8.53313 | + | 26.2623i | −0.294246 | + | 0.905596i | ||||
\(842\) | 1.23646 | − | 3.80544i | 0.0426113 | − | 0.131144i | ||||
\(843\) | −13.2721 | + | 9.64278i | −0.457117 | + | 0.332115i | ||||
\(844\) | −58.6173 | − | 42.5879i | −2.01769 | − | 1.46594i | ||||
\(845\) | 9.97125 | + | 30.6884i | 0.343021 | + | 1.05571i | ||||
\(846\) | −21.0527 | −0.723806 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 144.215 | 4.95235 | ||||||||
\(849\) | −8.63433 | − | 26.5737i | −0.296330 | − | 0.912009i | ||||
\(850\) | −3.78600 | − | 2.75069i | −0.129859 | − | 0.0943479i | ||||
\(851\) | 2.86225 | − | 2.07955i | 0.0981166 | − | 0.0712859i | ||||
\(852\) | 7.85596 | − | 24.1782i | 0.269141 | − | 0.828330i | ||||
\(853\) | 0.851310 | − | 2.62006i | 0.0291483 | − | 0.0897092i | −0.935424 | − | 0.353528i | \(-0.884982\pi\) |
0.964572 | + | 0.263819i | \(0.0849820\pi\) | |||||||
\(854\) | 17.8926 | − | 12.9998i | 0.612273 | − | 0.444842i | ||||
\(855\) | −1.44293 | − | 1.04835i | −0.0493471 | − | 0.0358528i | ||||
\(856\) | 16.5239 | + | 50.8552i | 0.564774 | + | 1.73820i | ||||
\(857\) | 20.3164 | 0.693997 | 0.346998 | − | 0.937866i | \(-0.387201\pi\) | ||||
0.346998 | + | 0.937866i | \(0.387201\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6249 | 0.771951 | 0.385975 | − | 0.922509i | \(-0.373865\pi\) | ||||
0.385975 | + | 0.922509i | \(0.373865\pi\) | |||||||
\(860\) | 5.73748 | + | 17.6582i | 0.195647 | + | 0.602138i | ||||
\(861\) | 15.6409 | + | 11.3638i | 0.533040 | + | 0.387276i | ||||
\(862\) | 35.5542 | − | 25.8316i | 1.21098 | − | 0.879829i | ||||
\(863\) | 13.3214 | − | 40.9989i | 0.453465 | − | 1.39562i | −0.419464 | − | 0.907772i | \(-0.637782\pi\) |
0.872928 | − | 0.487848i | \(-0.162218\pi\) | |||||||
\(864\) | −19.7347 | + | 60.7370i | −0.671387 | + | 2.06632i | ||||
\(865\) | 7.34819 | − | 5.33877i | 0.249846 | − | 0.181524i | ||||
\(866\) | −15.8674 | − | 11.5283i | −0.539196 | − | 0.391749i | ||||
\(867\) | −5.72165 | − | 17.6094i | −0.194317 | − | 0.598048i | ||||
\(868\) | 58.4955 | 1.98547 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.13917 | 0.140331 | ||||||||
\(871\) | −9.68888 | − | 29.8193i | −0.328295 | − | 1.01039i | ||||
\(872\) | 65.1721 | + | 47.3503i | 2.20701 | + | 1.60348i | ||||
\(873\) | 1.43763 | − | 1.04450i | 0.0486563 | − | 0.0353509i | ||||
\(874\) | −6.24761 | + | 19.2282i | −0.211329 | + | 0.650402i | ||||
\(875\) | −0.810808 | + | 2.49541i | −0.0274103 | + | 0.0843603i | ||||
\(876\) | 18.8868 | − | 13.7221i | 0.638126 | − | 0.463626i | ||||
\(877\) | 13.4987 | + | 9.80735i | 0.455817 | + | 0.331171i | 0.791888 | − | 0.610666i | \(-0.209098\pi\) |
−0.336071 | + | 0.941837i | \(0.609098\pi\) | |||||||
\(878\) | 14.1555 | + | 43.5662i | 0.477726 | + | 1.47029i | ||||
\(879\) | 19.2011 | 0.647638 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.5116 | −1.46594 | −0.732972 | − | 0.680259i | \(-0.761867\pi\) | ||||
−0.732972 | + | 0.680259i | \(0.761867\pi\) | |||||||
\(882\) | 0.112837 | + | 0.347276i | 0.00379941 | + | 0.0116934i | ||||
\(883\) | 21.8431 | + | 15.8700i | 0.735080 | + | 0.534067i | 0.891167 | − | 0.453676i | \(-0.149888\pi\) |
−0.156086 | + | 0.987743i | \(0.549888\pi\) | |||||||
\(884\) | 47.4196 | − | 34.4523i | 1.59489 | − | 1.15876i | ||||
\(885\) | −1.60835 | + | 4.94999i | −0.0540641 | + | 0.166392i | ||||
\(886\) | −11.9057 | + | 36.6420i | −0.399981 | + | 1.23101i | ||||
\(887\) | 18.5591 | − | 13.4840i | 0.623153 | − | 0.452747i | −0.230869 | − | 0.972985i | \(-0.574157\pi\) |
0.854021 | + | 0.520238i | \(0.174157\pi\) | |||||||
\(888\) | 5.57671 | + | 4.05172i | 0.187142 | + | 0.135967i | ||||
\(889\) | 9.98338 | + | 30.7257i | 0.334832 | + | 1.03051i | ||||
\(890\) | 9.04886 | 0.303318 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 114.311 | 3.82740 | ||||||||
\(893\) | −3.04693 | − | 9.37748i | −0.101962 | − | 0.313805i | ||||
\(894\) | 52.1889 | + | 37.9174i | 1.74546 | + | 1.26815i | ||||
\(895\) | 11.1393 | − | 8.09320i | 0.372347 | − | 0.270526i | ||||
\(896\) | −1.96520 | + | 6.04825i | −0.0656526 | + | 0.202058i | ||||
\(897\) | −14.4990 | + | 44.6235i | −0.484109 | + | 1.48993i | ||||
\(898\) | 2.77501 | − | 2.01616i | 0.0926033 | − | 0.0672802i | ||||
\(899\) | 4.34749 | + | 3.15863i | 0.144997 | + | 0.105346i | ||||
\(900\) | −1.81841 | − | 5.59648i | −0.0606135 | − | 0.186549i | ||||
\(901\) | 25.4941 | 0.849331 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.3635 | −0.444710 | ||||||||
\(904\) | −32.2023 | − | 99.1086i | −1.07103 | − | 3.29630i | ||||
\(905\) | 19.3017 | + | 14.0235i | 0.641609 | + | 0.466156i | ||||
\(906\) | −48.9867 | + | 35.5909i | −1.62747 | + | 1.18243i | ||||
\(907\) | 12.8964 | − | 39.6911i | 0.428219 | − | 1.31792i | −0.471659 | − | 0.881781i | \(-0.656345\pi\) |
0.899878 | − | 0.436141i | \(-0.143655\pi\) | |||||||
\(908\) | −3.96038 | + | 12.1888i | −0.131430 | + | 0.404499i | ||||
\(909\) | −3.32607 | + | 2.41653i | −0.110319 | + | 0.0801514i | ||||
\(910\) | −37.4734 | − | 27.2260i | −1.24223 | − | 0.902533i | ||||
\(911\) | −11.9673 | − | 36.8316i | −0.396495 | − | 1.22029i | −0.927791 | − | 0.373100i | \(-0.878295\pi\) |
0.531296 | − | 0.847186i | \(-0.321705\pi\) | |||||||
\(912\) | −20.0134 | −0.662708 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.7427 | 0.884569 | ||||||||
\(915\) | 1.33012 | + | 4.09370i | 0.0439726 | + | 0.135334i | ||||
\(916\) | 87.0805 | + | 63.2677i | 2.87722 | + | 2.09042i | ||||
\(917\) | 41.4147 | − | 30.0895i | 1.36763 | − | 0.993644i | ||||
\(918\) | −8.14720 | + | 25.0745i | −0.268898 | + | 0.827582i | ||||
\(919\) | −0.881305 | + | 2.71238i | −0.0290716 | + | 0.0894730i | −0.964540 | − | 0.263938i | \(-0.914978\pi\) |
0.935468 | + | 0.353411i | \(0.114978\pi\) | |||||||
\(920\) | −31.8684 | + | 23.1537i | −1.05067 | + | 0.763355i | ||||
\(921\) | −11.1599 | − | 8.10812i | −0.367730 | − | 0.267172i | ||||
\(922\) | −3.34199 | − | 10.2856i | −0.110063 | − | 0.338738i | ||||
\(923\) | −26.1353 | −0.860253 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.679754 | −0.0223502 | ||||||||
\(926\) | 26.5639 | + | 81.7554i | 0.872945 | + | 2.68665i | ||||
\(927\) | −4.84760 | − | 3.52199i | −0.159216 | − | 0.115677i | ||||
\(928\) | −10.7973 | + | 7.84468i | −0.354438 | + | 0.257514i | ||||
\(929\) | −4.08779 | + | 12.5809i | −0.134116 | + | 0.412767i | −0.995451 | − | 0.0952697i | \(-0.969629\pi\) |
0.861335 | + | 0.508037i | \(0.169629\pi\) | |||||||
\(930\) | −4.95851 | + | 15.2607i | −0.162596 | + | 0.500419i | ||||
\(931\) | −0.138356 | + | 0.100522i | −0.00453444 | + | 0.00329446i | ||||
\(932\) | −21.1204 | − | 15.3449i | −0.691821 | − | 0.502637i | ||||
\(933\) | −7.92984 | − | 24.4055i | −0.259611 | − | 0.799001i | ||||
\(934\) | 99.4810 | 3.25512 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 61.3462 | 2.00516 | ||||||||
\(937\) | 0.519316 | + | 1.59829i | 0.0169653 | + | 0.0522139i | 0.959181 | − | 0.282794i | \(-0.0912611\pi\) |
−0.942215 | + | 0.335008i | \(0.891261\pi\) | |||||||
\(938\) | 25.9553 | + | 18.8576i | 0.847471 | + | 0.615724i | ||||
\(939\) | 16.2312 | − | 11.7927i | 0.529686 | − | 0.384840i | ||||
\(940\) | 10.0527 | − | 30.9391i | 0.327883 | − | 1.00912i | ||||
\(941\) | −4.53795 | + | 13.9664i | −0.147933 | + | 0.455291i | −0.997377 | − | 0.0723886i | \(-0.976938\pi\) |
0.849443 | + | 0.527680i | \(0.176938\pi\) | |||||||
\(942\) | 59.4362 | − | 43.1830i | 1.93654 | − | 1.40698i | ||||
\(943\) | −23.1558 | − | 16.8236i | −0.754055 | − | 0.547853i | ||||
\(944\) | −12.1108 | − | 37.2732i | −0.394173 | − | 1.21314i | ||||
\(945\) | 14.7822 | 0.480865 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.6535 | 0.573660 | 0.286830 | − | 0.957981i | \(-0.407399\pi\) | ||||
0.286830 | + | 0.957981i | \(0.407399\pi\) | |||||||
\(948\) | −30.6126 | − | 94.2158i | −0.994250 | − | 3.05999i | ||||
\(949\) | −19.4164 | − | 14.1068i | −0.630283 | − | 0.457928i | ||||
\(950\) | 3.14261 | − | 2.28324i | 0.101960 | − | 0.0740782i | ||||
\(951\) | 5.04241 | − | 15.5190i | 0.163511 | − | 0.503237i | ||||
\(952\) | −10.9448 | + | 33.6847i | −0.354724 | + | 1.09173i | ||||
\(953\) | −17.6106 | + | 12.7948i | −0.570462 | + | 0.414465i | −0.835273 | − | 0.549835i | \(-0.814690\pi\) |
0.264811 | + | 0.964300i | \(0.414690\pi\) | |||||||
\(954\) | 36.5540 | + | 26.5580i | 1.18348 | + | 0.859849i | ||||
\(955\) | 4.96371 | + | 15.2767i | 0.160622 | + | 0.494344i | ||||
\(956\) | −61.4564 | −1.98764 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.9500 | −0.547631 | ||||||||
\(959\) | 6.94395 | + | 21.3713i | 0.224232 | + | 0.690115i | ||||
\(960\) | −10.3675 | − | 7.53241i | −0.334609 | − | 0.243107i | ||||
\(961\) | 8.22587 | − | 5.97645i | 0.265351 | − | 0.192789i | ||||
\(962\) | 3.70820 | − | 11.4127i | 0.119557 | − | 0.367960i | ||||
\(963\) | −2.63025 | + | 8.09509i | −0.0847588 | + | 0.260861i | ||||
\(964\) | 16.9401 | − | 12.3077i | 0.545604 | − | 0.396405i | ||||
\(965\) | −17.3605 | − | 12.6132i | −0.558855 | − | 0.406032i | ||||
\(966\) | −14.8360 | − | 45.6605i | −0.477340 | − | 1.46910i | ||||
\(967\) | −14.0684 | −0.452409 | −0.226204 | − | 0.974080i | \(-0.572632\pi\) | ||||
−0.226204 | + | 0.974080i | \(0.572632\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.53793 | −0.113655 | ||||||||
\(970\) | 1.19596 | + | 3.68079i | 0.0384000 | + | 0.118183i | ||||
\(971\) | 11.9187 | + | 8.65946i | 0.382490 | + | 0.277895i | 0.762371 | − | 0.647140i | \(-0.224035\pi\) |
−0.379881 | + | 0.925035i | \(0.624035\pi\) | |||||||
\(972\) | −45.9567 | + | 33.3895i | −1.47406 | + | 1.07097i | ||||
\(973\) | −1.60835 | + | 4.94999i | −0.0515613 | + | 0.158689i | ||||
\(974\) | 35.2391 | − | 108.455i | 1.12913 | − | 3.47511i | ||||
\(975\) | 7.29317 | − | 5.29880i | 0.233568 | − | 0.169697i | ||||
\(976\) | −26.2216 | − | 19.0511i | −0.839335 | − | 0.609812i | ||||
\(977\) | 4.06105 | + | 12.4986i | 0.129924 | + | 0.399866i | 0.994766 | − | 0.102179i | \(-0.0325813\pi\) |
−0.864842 | + | 0.502045i | \(0.832581\pi\) | |||||||
\(978\) | 33.2415 | 1.06294 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.564237 | −0.0180239 | ||||||||
\(981\) | 3.96253 | + | 12.1954i | 0.126514 | + | 0.389370i | ||||
\(982\) | 11.5767 | + | 8.41095i | 0.369426 | + | 0.268404i | ||||
\(983\) | −14.8987 | + | 10.8245i | −0.475193 | + | 0.345248i | −0.799462 | − | 0.600717i | \(-0.794882\pi\) |
0.324269 | + | 0.945965i | \(0.394882\pi\) | |||||||
\(984\) | 17.2327 | − | 53.0369i | 0.549360 | − | 1.69076i | ||||
\(985\) | 2.84757 | − | 8.76393i | 0.0907312 | − | 0.279242i | ||||
\(986\) | −4.45752 | + | 3.23857i | −0.141956 | + | 0.103137i | ||||
\(987\) | 18.9426 | + | 13.7626i | 0.602951 | + | 0.438069i | ||||
\(988\) | 15.0346 | + | 46.2718i | 0.478315 | + | 1.47210i | ||||
\(989\) | 19.7842 | 0.629101 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.3591 | 1.40911 | 0.704557 | − | 0.709647i | \(-0.251146\pi\) | ||||
0.704557 | + | 0.709647i | \(0.251146\pi\) | |||||||
\(992\) | −15.9880 | − | 49.2061i | −0.507620 | − | 1.56229i | ||||
\(993\) | 17.1615 | + | 12.4686i | 0.544603 | + | 0.395678i | ||||
\(994\) | 21.6353 | − | 15.7189i | 0.686229 | − | 0.498575i | ||||
\(995\) | −5.09507 | + | 15.6810i | −0.161524 | + | 0.497121i | ||||
\(996\) | 14.8329 | − | 45.6509i | 0.469998 | − | 1.44650i | ||||
\(997\) | −40.8497 | + | 29.6790i | −1.29372 | + | 0.939944i | −0.999873 | − | 0.0159081i | \(-0.994936\pi\) |
−0.293848 | + | 0.955852i | \(0.594936\pi\) | |||||||
\(998\) | −26.5085 | − | 19.2596i | −0.839113 | − | 0.609651i | ||||
\(999\) | 1.18341 | + | 3.64218i | 0.0374416 | + | 0.115233i |
(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 | 605.2.g.q.511.6 | 24 | ||
11.2 | odd | 10 | inner | 605.2.g.q.251.1 | 24 | ||
11.3 | even | 5 | 605.2.a.m.1.6 | yes | 6 | ||
11.4 | even | 5 | inner | 605.2.g.q.366.1 | 24 | ||
11.5 | even | 5 | inner | 605.2.g.q.81.1 | 24 | ||
11.6 | odd | 10 | inner | 605.2.g.q.81.6 | 24 | ||
11.7 | odd | 10 | inner | 605.2.g.q.366.6 | 24 | ||
11.8 | odd | 10 | 605.2.a.m.1.1 | ✓ | 6 | ||
11.9 | even | 5 | inner | 605.2.g.q.251.6 | 24 | ||
11.10 | odd | 2 | inner | 605.2.g.q.511.1 | 24 | ||
33.8 | even | 10 | 5445.2.a.bx.1.6 | 6 | |||
33.14 | odd | 10 | 5445.2.a.bx.1.1 | 6 | |||
44.3 | odd | 10 | 9680.2.a.cw.1.4 | 6 | |||
44.19 | even | 10 | 9680.2.a.cw.1.3 | 6 | |||
55.14 | even | 10 | 3025.2.a.bg.1.1 | 6 | |||
55.19 | odd | 10 | 3025.2.a.bg.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.m.1.1 | ✓ | 6 | 11.8 | odd | 10 | ||
605.2.a.m.1.6 | yes | 6 | 11.3 | even | 5 | ||
605.2.g.q.81.1 | 24 | 11.5 | even | 5 | inner | ||
605.2.g.q.81.6 | 24 | 11.6 | odd | 10 | inner | ||
605.2.g.q.251.1 | 24 | 11.2 | odd | 10 | inner | ||
605.2.g.q.251.6 | 24 | 11.9 | even | 5 | inner | ||
605.2.g.q.366.1 | 24 | 11.4 | even | 5 | inner | ||
605.2.g.q.366.6 | 24 | 11.7 | odd | 10 | inner | ||
605.2.g.q.511.1 | 24 | 11.10 | odd | 2 | inner | ||
605.2.g.q.511.6 | 24 | 1.1 | even | 1 | trivial | ||
3025.2.a.bg.1.1 | 6 | 55.14 | even | 10 | |||
3025.2.a.bg.1.6 | 6 | 55.19 | odd | 10 | |||
5445.2.a.bx.1.1 | 6 | 33.14 | odd | 10 | |||
5445.2.a.bx.1.6 | 6 | 33.8 | even | 10 | |||
9680.2.a.cw.1.3 | 6 | 44.19 | even | 10 | |||
9680.2.a.cw.1.4 | 6 | 44.3 | odd | 10 |