Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 553.16 | ||
Character | \(\chi\) | \(=\) | 690.553 |
Dual form | 690.3.k.b.277.16 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 3.93589 | + | 3.08362i | 0.787179 | + | 0.616725i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −1.42240 | + | 1.42240i | −0.203200 | + | 0.203200i | −0.801370 | − | 0.598170i | \(-0.795895\pi\) |
0.598170 | + | 0.801370i | \(0.295895\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | −7.01952 | + | 0.852269i | −0.701952 | + | 0.0852269i | ||||
\(11\) | 3.13344 | 0.284858 | 0.142429 | − | 0.989805i | \(-0.454509\pi\) | ||||
0.142429 | + | 0.989805i | \(0.454509\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.204124 | − | 0.204124i | ||||
\(13\) | −8.16946 | − | 8.16946i | −0.628420 | − | 0.628420i | 0.319250 | − | 0.947670i | \(-0.396569\pi\) |
−0.947670 | + | 0.319250i | \(0.896569\pi\) | |||||||
\(14\) | − | 2.84480i | − | 0.203200i | ||||||
\(15\) | 1.04381 | + | 8.59712i | 0.0695874 | + | 0.573141i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −8.80764 | + | 8.80764i | −0.518096 | + | 0.518096i | −0.916995 | − | 0.398899i | \(-0.869393\pi\) |
0.398899 | + | 0.916995i | \(0.369393\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | 33.0294i | 1.73839i | 0.494469 | + | 0.869196i | \(0.335363\pi\) | ||||
−0.494469 | + | 0.869196i | \(0.664637\pi\) | |||||||
\(20\) | 6.16725 | − | 7.87179i | 0.308362 | − | 0.393589i | ||||
\(21\) | −3.48416 | −0.165912 | ||||||||
\(22\) | −3.13344 | + | 3.13344i | −0.142429 | + | 0.142429i | ||||
\(23\) | 3.39116 | + | 3.39116i | 0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 5.98252 | + | 24.2736i | 0.239301 | + | 0.970946i | ||||
\(26\) | 16.3389 | 0.628420 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 2.84480 | + | 2.84480i | 0.101600 | + | 0.101600i | ||||
\(29\) | − | 8.67288i | − | 0.299065i | −0.988757 | − | 0.149532i | \(-0.952223\pi\) | ||
0.988757 | − | 0.149532i | \(-0.0477769\pi\) | |||||||
\(30\) | −9.64093 | − | 7.55331i | −0.321364 | − | 0.251777i | ||||
\(31\) | −47.5546 | −1.53402 | −0.767010 | − | 0.641636i | \(-0.778256\pi\) | ||||
−0.767010 | + | 0.641636i | \(0.778256\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | 3.83766 | + | 3.83766i | 0.116293 | + | 0.116293i | ||||
\(34\) | − | 17.6153i | − | 0.518096i | ||||||
\(35\) | −9.98457 | + | 1.21227i | −0.285273 | + | 0.0346362i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 18.6967 | − | 18.6967i | 0.505315 | − | 0.505315i | −0.407770 | − | 0.913085i | \(-0.633693\pi\) |
0.913085 | + | 0.407770i | \(0.133693\pi\) | |||||||
\(38\) | −33.0294 | − | 33.0294i | −0.869196 | − | 0.869196i | ||||
\(39\) | − | 20.0110i | − | 0.513103i | ||||||
\(40\) | 1.70454 | + | 14.0390i | 0.0426134 | + | 0.350976i | ||||
\(41\) | 21.0080 | 0.512390 | 0.256195 | − | 0.966625i | \(-0.417531\pi\) | ||||
0.256195 | + | 0.966625i | \(0.417531\pi\) | |||||||
\(42\) | 3.48416 | − | 3.48416i | 0.0829561 | − | 0.0829561i | ||||
\(43\) | 37.8115 | + | 37.8115i | 0.879337 | + | 0.879337i | 0.993466 | − | 0.114129i | \(-0.0364076\pi\) |
−0.114129 | + | 0.993466i | \(0.536408\pi\) | |||||||
\(44\) | − | 6.26687i | − | 0.142429i | ||||||
\(45\) | −9.25087 | + | 11.8077i | −0.205575 | + | 0.262393i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | −4.90320 | + | 4.90320i | −0.104323 | + | 0.104323i | −0.757342 | − | 0.653018i | \(-0.773502\pi\) |
0.653018 | + | 0.757342i | \(0.273502\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | 44.9536i | 0.917419i | ||||||||
\(50\) | −30.2562 | − | 18.2911i | −0.605123 | − | 0.365822i | ||||
\(51\) | −21.5742 | −0.423024 | ||||||||
\(52\) | −16.3389 | + | 16.3389i | −0.314210 | + | 0.314210i | ||||
\(53\) | 6.02763 | + | 6.02763i | 0.113729 | + | 0.113729i | 0.761681 | − | 0.647952i | \(-0.224374\pi\) |
−0.647952 | + | 0.761681i | \(0.724374\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 12.3329 | + | 9.66234i | 0.224234 | + | 0.175679i | ||||
\(56\) | −5.68960 | −0.101600 | ||||||||
\(57\) | −40.4526 | + | 40.4526i | −0.709695 | + | 0.709695i | ||||
\(58\) | 8.67288 | + | 8.67288i | 0.149532 | + | 0.149532i | ||||
\(59\) | 91.3726i | 1.54869i | 0.632765 | + | 0.774344i | \(0.281920\pi\) | ||||
−0.632765 | + | 0.774344i | \(0.718080\pi\) | |||||||
\(60\) | 17.1942 | − | 2.08762i | 0.286571 | − | 0.0347937i | ||||
\(61\) | −76.7830 | −1.25874 | −0.629369 | − | 0.777107i | \(-0.716687\pi\) | ||||
−0.629369 | + | 0.777107i | \(0.716687\pi\) | |||||||
\(62\) | 47.5546 | − | 47.5546i | 0.767010 | − | 0.767010i | ||||
\(63\) | −4.26720 | − | 4.26720i | −0.0677334 | − | 0.0677334i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −6.96258 | − | 57.3457i | −0.107117 | − | 0.882242i | ||||
\(66\) | −7.67532 | −0.116293 | ||||||||
\(67\) | 79.6346 | − | 79.6346i | 1.18858 | − | 1.18858i | 0.211114 | − | 0.977461i | \(-0.432291\pi\) |
0.977461 | − | 0.211114i | \(-0.0677093\pi\) | |||||||
\(68\) | 17.6153 | + | 17.6153i | 0.259048 | + | 0.259048i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | 8.77230 | − | 11.1968i | 0.125319 | − | 0.159955i | ||||
\(71\) | −123.580 | −1.74057 | −0.870283 | − | 0.492552i | \(-0.836064\pi\) | ||||
−0.870283 | + | 0.492552i | \(0.836064\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | 89.3944 | + | 89.3944i | 1.22458 | + | 1.22458i | 0.965986 | + | 0.258596i | \(0.0832598\pi\) |
0.258596 | + | 0.965986i | \(0.416740\pi\) | |||||||
\(74\) | 37.3933i | 0.505315i | ||||||||
\(75\) | −22.4020 | + | 37.0561i | −0.298693 | + | 0.494081i | ||||
\(76\) | 66.0589 | 0.869196 | ||||||||
\(77\) | −4.45700 | + | 4.45700i | −0.0578831 | + | 0.0578831i | ||||
\(78\) | 20.0110 | + | 20.0110i | 0.256552 | + | 0.256552i | ||||
\(79\) | − | 43.8149i | − | 0.554618i | −0.960781 | − | 0.277309i | \(-0.910557\pi\) | ||
0.960781 | − | 0.277309i | \(-0.0894427\pi\) | |||||||
\(80\) | −15.7436 | − | 12.3345i | −0.196795 | − | 0.154181i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −21.0080 | + | 21.0080i | −0.256195 | + | 0.256195i | ||||
\(83\) | −72.8343 | − | 72.8343i | −0.877522 | − | 0.877522i | 0.115756 | − | 0.993278i | \(-0.463071\pi\) |
−0.993278 | + | 0.115756i | \(0.963071\pi\) | |||||||
\(84\) | 6.96831i | 0.0829561i | ||||||||
\(85\) | −61.8254 | + | 7.50647i | −0.727357 | + | 0.0883115i | ||||
\(86\) | −75.6230 | −0.879337 | ||||||||
\(87\) | 10.6221 | − | 10.6221i | 0.122093 | − | 0.122093i | ||||
\(88\) | 6.26687 | + | 6.26687i | 0.0712145 | + | 0.0712145i | ||||
\(89\) | − | 85.1273i | − | 0.956487i | −0.878227 | − | 0.478243i | \(-0.841274\pi\) | ||
0.878227 | − | 0.478243i | \(-0.158726\pi\) | |||||||
\(90\) | −2.55681 | − | 21.0586i | −0.0284090 | − | 0.233984i | ||||
\(91\) | 23.2405 | 0.255390 | ||||||||
\(92\) | 6.78233 | − | 6.78233i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | −58.2422 | − | 58.2422i | −0.626261 | − | 0.626261i | ||||
\(94\) | − | 9.80641i | − | 0.104323i | ||||||
\(95\) | −101.850 | + | 130.000i | −1.07211 | + | 1.36842i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −104.892 | + | 104.892i | −1.08136 | + | 1.08136i | −0.0849800 | + | 0.996383i | \(0.527083\pi\) |
−0.996383 | + | 0.0849800i | \(0.972917\pi\) | |||||||
\(98\) | −44.9536 | − | 44.9536i | −0.458710 | − | 0.458710i | ||||
\(99\) | 9.40031i | 0.0949526i | ||||||||
\(100\) | 48.5473 | − | 11.9650i | 0.485473 | − | 0.119650i | ||||
\(101\) | −161.022 | −1.59428 | −0.797138 | − | 0.603798i | \(-0.793654\pi\) | ||||
−0.797138 | + | 0.603798i | \(0.793654\pi\) | |||||||
\(102\) | 21.5742 | − | 21.5742i | 0.211512 | − | 0.211512i | ||||
\(103\) | 51.2006 | + | 51.2006i | 0.497094 | + | 0.497094i | 0.910532 | − | 0.413438i | \(-0.135672\pi\) |
−0.413438 | + | 0.910532i | \(0.635672\pi\) | |||||||
\(104\) | − | 32.6779i | − | 0.314210i | ||||||
\(105\) | −13.7133 | − | 10.7438i | −0.130603 | − | 0.102322i | ||||
\(106\) | −12.0553 | −0.113729 | ||||||||
\(107\) | 88.6095 | − | 88.6095i | 0.828127 | − | 0.828127i | −0.159131 | − | 0.987257i | \(-0.550869\pi\) |
0.987257 | + | 0.159131i | \(0.0508692\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 45.9965i | 0.421986i | 0.977488 | + | 0.210993i | \(0.0676698\pi\) | ||||
−0.977488 | + | 0.210993i | \(0.932330\pi\) | |||||||
\(110\) | −21.9952 | + | 2.67053i | −0.199957 | + | 0.0242775i | ||||
\(111\) | 45.7973 | 0.412588 | ||||||||
\(112\) | 5.68960 | − | 5.68960i | 0.0508000 | − | 0.0508000i | ||||
\(113\) | −100.216 | − | 100.216i | −0.886871 | − | 0.886871i | 0.107350 | − | 0.994221i | \(-0.465763\pi\) |
−0.994221 | + | 0.107350i | \(0.965763\pi\) | |||||||
\(114\) | − | 80.9052i | − | 0.709695i | ||||||
\(115\) | 2.89018 | + | 23.8043i | 0.0251320 | + | 0.206994i | ||||
\(116\) | −17.3458 | −0.149532 | ||||||||
\(117\) | 24.5084 | − | 24.5084i | 0.209473 | − | 0.209473i | ||||
\(118\) | −91.3726 | − | 91.3726i | −0.774344 | − | 0.774344i | ||||
\(119\) | − | 25.0560i | − | 0.210554i | ||||||
\(120\) | −15.1066 | + | 19.2819i | −0.125888 | + | 0.160682i | ||||
\(121\) | −111.182 | −0.918856 | ||||||||
\(122\) | 76.7830 | − | 76.7830i | 0.629369 | − | 0.629369i | ||||
\(123\) | 25.7294 | + | 25.7294i | 0.209182 | + | 0.209182i | ||||
\(124\) | 95.1092i | 0.767010i | ||||||||
\(125\) | −51.3042 | + | 113.986i | −0.410434 | + | 0.911890i | ||||
\(126\) | 8.53440 | 0.0677334 | ||||||||
\(127\) | 17.0379 | − | 17.0379i | 0.134157 | − | 0.134157i | −0.636840 | − | 0.770996i | \(-0.719759\pi\) |
0.770996 | + | 0.636840i | \(0.219759\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 92.6189i | 0.717976i | ||||||||
\(130\) | 64.3083 | + | 50.3831i | 0.494679 | + | 0.387563i | ||||
\(131\) | 226.477 | 1.72884 | 0.864418 | − | 0.502774i | \(-0.167687\pi\) | ||||
0.864418 | + | 0.502774i | \(0.167687\pi\) | |||||||
\(132\) | 7.67532 | − | 7.67532i | 0.0581464 | − | 0.0581464i | ||||
\(133\) | −46.9811 | − | 46.9811i | −0.353241 | − | 0.353241i | ||||
\(134\) | 159.269i | 1.18858i | ||||||||
\(135\) | −25.7914 | + | 3.13144i | −0.191047 | + | 0.0231958i | ||||
\(136\) | −35.2306 | −0.259048 | ||||||||
\(137\) | −13.3335 | + | 13.3335i | −0.0973250 | + | 0.0973250i | −0.754093 | − | 0.656768i | \(-0.771923\pi\) |
0.656768 | + | 0.754093i | \(0.271923\pi\) | |||||||
\(138\) | −8.30662 | − | 8.30662i | −0.0601929 | − | 0.0601929i | ||||
\(139\) | 136.577i | 0.982566i | 0.871000 | + | 0.491283i | \(0.163472\pi\) | ||||
−0.871000 | + | 0.491283i | \(0.836528\pi\) | |||||||
\(140\) | 2.42453 | + | 19.9691i | 0.0173181 | + | 0.142637i | ||||
\(141\) | −12.0103 | −0.0851798 | ||||||||
\(142\) | 123.580 | − | 123.580i | 0.870283 | − | 0.870283i | ||||
\(143\) | −25.5985 | − | 25.5985i | −0.179011 | − | 0.179011i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 26.7439 | − | 34.1355i | 0.184441 | − | 0.235418i | ||||
\(146\) | −178.789 | −1.22458 | ||||||||
\(147\) | −55.0566 | + | 55.0566i | −0.374535 | + | 0.374535i | ||||
\(148\) | −37.3933 | − | 37.3933i | −0.252658 | − | 0.252658i | ||||
\(149\) | 21.6052i | 0.145001i | 0.997368 | + | 0.0725006i | \(0.0230979\pi\) | ||||
−0.997368 | + | 0.0725006i | \(0.976902\pi\) | |||||||
\(150\) | −14.6541 | − | 59.4580i | −0.0976941 | − | 0.396387i | ||||
\(151\) | 283.184 | 1.87539 | 0.937695 | − | 0.347459i | \(-0.112955\pi\) | ||||
0.937695 | + | 0.347459i | \(0.112955\pi\) | |||||||
\(152\) | −66.0589 | + | 66.0589i | −0.434598 | + | 0.434598i | ||||
\(153\) | −26.4229 | − | 26.4229i | −0.172699 | − | 0.172699i | ||||
\(154\) | − | 8.91400i | − | 0.0578831i | ||||||
\(155\) | −187.170 | − | 146.641i | −1.20755 | − | 0.946068i | ||||
\(156\) | −40.0220 | −0.256552 | ||||||||
\(157\) | 124.318 | − | 124.318i | 0.791832 | − | 0.791832i | −0.189960 | − | 0.981792i | \(-0.560836\pi\) |
0.981792 | + | 0.189960i | \(0.0608357\pi\) | |||||||
\(158\) | 43.8149 | + | 43.8149i | 0.277309 | + | 0.277309i | ||||
\(159\) | 14.7646i | 0.0928592i | ||||||||
\(160\) | 28.0781 | − | 3.40907i | 0.175488 | − | 0.0213067i | ||||
\(161\) | −9.64719 | −0.0599204 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 72.7999 | + | 72.7999i | 0.446625 | + | 0.446625i | 0.894231 | − | 0.447606i | \(-0.147723\pi\) |
−0.447606 | + | 0.894231i | \(0.647723\pi\) | |||||||
\(164\) | − | 42.0160i | − | 0.256195i | ||||||
\(165\) | 3.27072 | + | 26.9385i | 0.0198225 | + | 0.163264i | ||||
\(166\) | 145.669 | 0.877522 | ||||||||
\(167\) | 60.4809 | − | 60.4809i | 0.362161 | − | 0.362161i | −0.502447 | − | 0.864608i | \(-0.667567\pi\) |
0.864608 | + | 0.502447i | \(0.167567\pi\) | |||||||
\(168\) | −6.96831 | − | 6.96831i | −0.0414780 | − | 0.0414780i | ||||
\(169\) | − | 35.5197i | − | 0.210176i | ||||||
\(170\) | 54.3189 | − | 69.3319i | 0.319523 | − | 0.407834i | ||||
\(171\) | −99.0883 | −0.579464 | ||||||||
\(172\) | 75.6230 | − | 75.6230i | 0.439669 | − | 0.439669i | ||||
\(173\) | 96.5087 | + | 96.5087i | 0.557854 | + | 0.557854i | 0.928696 | − | 0.370842i | \(-0.120931\pi\) |
−0.370842 | + | 0.928696i | \(0.620931\pi\) | |||||||
\(174\) | 21.2441i | 0.122093i | ||||||||
\(175\) | −43.0364 | − | 26.0173i | −0.245922 | − | 0.148670i | ||||
\(176\) | −12.5337 | −0.0712145 | ||||||||
\(177\) | −111.908 | + | 111.908i | −0.632249 | + | 0.632249i | ||||
\(178\) | 85.1273 | + | 85.1273i | 0.478243 | + | 0.478243i | ||||
\(179\) | 115.452i | 0.644983i | 0.946572 | + | 0.322491i | \(0.104520\pi\) | ||||
−0.946572 | + | 0.322491i | \(0.895480\pi\) | |||||||
\(180\) | 23.6154 | + | 18.5017i | 0.131196 | + | 0.102787i | ||||
\(181\) | 182.511 | 1.00835 | 0.504174 | − | 0.863602i | \(-0.331797\pi\) | ||||
0.504174 | + | 0.863602i | \(0.331797\pi\) | |||||||
\(182\) | −23.2405 | + | 23.2405i | −0.127695 | + | 0.127695i | ||||
\(183\) | −94.0396 | − | 94.0396i | −0.513878 | − | 0.513878i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | 131.242 | − | 15.9346i | 0.709414 | − | 0.0861329i | ||||
\(186\) | 116.484 | 0.626261 | ||||||||
\(187\) | −27.5982 | + | 27.5982i | −0.147584 | + | 0.147584i | ||||
\(188\) | 9.80641 | + | 9.80641i | 0.0521617 | + | 0.0521617i | ||||
\(189\) | − | 10.4525i | − | 0.0553040i | ||||||
\(190\) | −28.1499 | − | 231.851i | −0.148158 | − | 1.22027i | ||||
\(191\) | −126.245 | −0.660969 | −0.330485 | − | 0.943811i | \(-0.607212\pi\) | ||||
−0.330485 | + | 0.943811i | \(0.607212\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −104.990 | − | 104.990i | −0.543989 | − | 0.543989i | 0.380707 | − | 0.924696i | \(-0.375681\pi\) |
−0.924696 | + | 0.380707i | \(0.875681\pi\) | |||||||
\(194\) | − | 209.784i | − | 1.08136i | ||||||
\(195\) | 61.7065 | − | 78.7612i | 0.316443 | − | 0.403904i | ||||
\(196\) | 89.9071 | 0.458710 | ||||||||
\(197\) | 189.425 | − | 189.425i | 0.961546 | − | 0.961546i | −0.0377412 | − | 0.999288i | \(-0.512016\pi\) |
0.999288 | + | 0.0377412i | \(0.0120163\pi\) | |||||||
\(198\) | −9.40031 | − | 9.40031i | −0.0474763 | − | 0.0474763i | ||||
\(199\) | 140.728i | 0.707178i | 0.935401 | + | 0.353589i | \(0.115039\pi\) | ||||
−0.935401 | + | 0.353589i | \(0.884961\pi\) | |||||||
\(200\) | −36.5822 | + | 60.5123i | −0.182911 | + | 0.302562i | ||||
\(201\) | 195.064 | 0.970468 | ||||||||
\(202\) | 161.022 | − | 161.022i | 0.797138 | − | 0.797138i | ||||
\(203\) | 12.3363 | + | 12.3363i | 0.0607700 | + | 0.0607700i | ||||
\(204\) | 43.1484i | 0.211512i | ||||||||
\(205\) | 82.6853 | + | 64.7808i | 0.403343 | + | 0.316004i | ||||
\(206\) | −102.401 | −0.497094 | ||||||||
\(207\) | −10.1735 | + | 10.1735i | −0.0491473 | + | 0.0491473i | ||||
\(208\) | 32.6779 | + | 32.6779i | 0.157105 | + | 0.157105i | ||||
\(209\) | 103.496i | 0.495194i | ||||||||
\(210\) | 24.4571 | − | 2.96944i | 0.116462 | − | 0.0141402i | ||||
\(211\) | 84.3383 | 0.399707 | 0.199854 | − | 0.979826i | \(-0.435953\pi\) | ||||
0.199854 | + | 0.979826i | \(0.435953\pi\) | |||||||
\(212\) | 12.0553 | − | 12.0553i | 0.0568644 | − | 0.0568644i | ||||
\(213\) | −151.354 | − | 151.354i | −0.710583 | − | 0.710583i | ||||
\(214\) | 177.219i | 0.828127i | ||||||||
\(215\) | 32.2256 | + | 265.419i | 0.149886 | + | 1.23450i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 67.6417 | − | 67.6417i | 0.311713 | − | 0.311713i | ||||
\(218\) | −45.9965 | − | 45.9965i | −0.210993 | − | 0.210993i | ||||
\(219\) | 218.971i | 0.999867i | ||||||||
\(220\) | 19.3247 | − | 24.6657i | 0.0878395 | − | 0.112117i | ||||
\(221\) | 143.907 | 0.651165 | ||||||||
\(222\) | −45.7973 | + | 45.7973i | −0.206294 | + | 0.206294i | ||||
\(223\) | 178.882 | + | 178.882i | 0.802163 | + | 0.802163i | 0.983433 | − | 0.181270i | \(-0.0580209\pi\) |
−0.181270 | + | 0.983433i | \(0.558021\pi\) | |||||||
\(224\) | 11.3792i | 0.0508000i | ||||||||
\(225\) | −72.8209 | + | 17.9475i | −0.323649 | + | 0.0797669i | ||||
\(226\) | 200.433 | 0.886871 | ||||||||
\(227\) | 159.186 | − | 159.186i | 0.701259 | − | 0.701259i | −0.263422 | − | 0.964681i | \(-0.584851\pi\) |
0.964681 | + | 0.263422i | \(0.0848510\pi\) | |||||||
\(228\) | 80.9052 | + | 80.9052i | 0.354848 | + | 0.354848i | ||||
\(229\) | 139.731i | 0.610178i | 0.952324 | + | 0.305089i | \(0.0986862\pi\) | ||||
−0.952324 | + | 0.305089i | \(0.901314\pi\) | |||||||
\(230\) | −26.6945 | − | 20.9142i | −0.116063 | − | 0.0909311i | ||||
\(231\) | −10.9174 | −0.0472614 | ||||||||
\(232\) | 17.3458 | − | 17.3458i | 0.0747662 | − | 0.0747662i | ||||
\(233\) | 63.6155 | + | 63.6155i | 0.273028 | + | 0.273028i | 0.830318 | − | 0.557290i | \(-0.188159\pi\) |
−0.557290 | + | 0.830318i | \(0.688159\pi\) | |||||||
\(234\) | 49.0168i | 0.209473i | ||||||||
\(235\) | −34.4181 | + | 4.17885i | −0.146460 | + | 0.0177823i | ||||
\(236\) | 182.745 | 0.774344 | ||||||||
\(237\) | 53.6620 | − | 53.6620i | 0.226422 | − | 0.226422i | ||||
\(238\) | 25.0560 | + | 25.0560i | 0.105277 | + | 0.105277i | ||||
\(239\) | − | 56.4515i | − | 0.236199i | −0.993002 | − | 0.118099i | \(-0.962320\pi\) | ||
0.993002 | − | 0.118099i | \(-0.0376801\pi\) | |||||||
\(240\) | −4.17525 | − | 34.3885i | −0.0173969 | − | 0.143285i | ||||
\(241\) | 88.4572 | 0.367042 | 0.183521 | − | 0.983016i | \(-0.441250\pi\) | ||||
0.183521 | + | 0.983016i | \(0.441250\pi\) | |||||||
\(242\) | 111.182 | − | 111.182i | 0.459428 | − | 0.459428i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 153.566i | 0.629369i | ||||||||
\(245\) | −138.620 | + | 176.932i | −0.565795 | + | 0.722173i | ||||
\(246\) | −51.4589 | −0.209182 | ||||||||
\(247\) | 269.833 | − | 269.833i | 1.09244 | − | 1.09244i | ||||
\(248\) | −95.1092 | − | 95.1092i | −0.383505 | − | 0.383505i | ||||
\(249\) | − | 178.407i | − | 0.716493i | ||||||
\(250\) | −62.6820 | − | 165.291i | −0.250728 | − | 0.661162i | ||||
\(251\) | 68.5838 | 0.273242 | 0.136621 | − | 0.990623i | \(-0.456376\pi\) | ||||
0.136621 | + | 0.990623i | \(0.456376\pi\) | |||||||
\(252\) | −8.53440 | + | 8.53440i | −0.0338667 | + | 0.0338667i | ||||
\(253\) | 10.6260 | + | 10.6260i | 0.0420000 | + | 0.0420000i | ||||
\(254\) | 34.0758i | 0.134157i | ||||||||
\(255\) | −84.9138 | − | 66.5268i | −0.332995 | − | 0.260889i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 133.320 | − | 133.320i | 0.518754 | − | 0.518754i | −0.398440 | − | 0.917194i | \(-0.630448\pi\) |
0.917194 | + | 0.398440i | \(0.130448\pi\) | |||||||
\(258\) | −92.6189 | − | 92.6189i | −0.358988 | − | 0.358988i | ||||
\(259\) | 53.1883i | 0.205360i | ||||||||
\(260\) | −114.691 | + | 13.9252i | −0.441121 | + | 0.0535583i | ||||
\(261\) | 26.0186 | 0.0996883 | ||||||||
\(262\) | −226.477 | + | 226.477i | −0.864418 | + | 0.864418i | ||||
\(263\) | 269.935 | + | 269.935i | 1.02637 | + | 1.02637i | 0.999643 | + | 0.0267265i | \(0.00850832\pi\) |
0.0267265 | + | 0.999643i | \(0.491492\pi\) | |||||||
\(264\) | 15.3506i | 0.0581464i | ||||||||
\(265\) | 5.13716 | + | 42.3110i | 0.0193855 | + | 0.159664i | ||||
\(266\) | 93.9621 | 0.353241 | ||||||||
\(267\) | 104.259 | − | 104.259i | 0.390484 | − | 0.390484i | ||||
\(268\) | −159.269 | − | 159.269i | −0.594288 | − | 0.594288i | ||||
\(269\) | − | 287.611i | − | 1.06919i | −0.845109 | − | 0.534593i | \(-0.820465\pi\) | ||
0.845109 | − | 0.534593i | \(-0.179535\pi\) | |||||||
\(270\) | 22.6599 | − | 28.9228i | 0.0839256 | − | 0.107121i | ||||
\(271\) | 146.523 | 0.540675 | 0.270338 | − | 0.962766i | \(-0.412865\pi\) | ||||
0.270338 | + | 0.962766i | \(0.412865\pi\) | |||||||
\(272\) | 35.2306 | − | 35.2306i | 0.129524 | − | 0.129524i | ||||
\(273\) | 28.4637 | + | 28.4637i | 0.104263 | + | 0.104263i | ||||
\(274\) | − | 26.6670i | − | 0.0973250i | ||||||
\(275\) | 18.7458 | + | 76.0599i | 0.0681667 | + | 0.276582i | ||||
\(276\) | 16.6132 | 0.0601929 | ||||||||
\(277\) | 75.7854 | − | 75.7854i | 0.273594 | − | 0.273594i | −0.556951 | − | 0.830545i | \(-0.688029\pi\) |
0.830545 | + | 0.556951i | \(0.188029\pi\) | |||||||
\(278\) | −136.577 | − | 136.577i | −0.491283 | − | 0.491283i | ||||
\(279\) | − | 142.664i | − | 0.511340i | ||||||
\(280\) | −22.3937 | − | 17.5446i | −0.0799774 | − | 0.0626593i | ||||
\(281\) | 461.843 | 1.64357 | 0.821785 | − | 0.569798i | \(-0.192979\pi\) | ||||
0.821785 | + | 0.569798i | \(0.192979\pi\) | |||||||
\(282\) | 12.0103 | − | 12.0103i | 0.0425899 | − | 0.0425899i | ||||
\(283\) | 17.7043 | + | 17.7043i | 0.0625594 | + | 0.0625594i | 0.737694 | − | 0.675135i | \(-0.235915\pi\) |
−0.675135 | + | 0.737694i | \(0.735915\pi\) | |||||||
\(284\) | 247.160i | 0.870283i | ||||||||
\(285\) | −283.958 | + | 34.4765i | −0.996344 | + | 0.120970i | ||||
\(286\) | 51.1970 | 0.179011 | ||||||||
\(287\) | −29.8818 | + | 29.8818i | −0.104118 | + | 0.104118i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 133.851i | 0.463152i | ||||||||
\(290\) | 7.39163 | + | 60.8795i | 0.0254884 | + | 0.209929i | ||||
\(291\) | −256.932 | −0.882929 | ||||||||
\(292\) | 178.789 | − | 178.789i | 0.612291 | − | 0.612291i | ||||
\(293\) | −135.640 | − | 135.640i | −0.462934 | − | 0.462934i | 0.436682 | − | 0.899616i | \(-0.356153\pi\) |
−0.899616 | + | 0.436682i | \(0.856153\pi\) | |||||||
\(294\) | − | 110.113i | − | 0.374535i | ||||||
\(295\) | −281.759 | + | 359.633i | −0.955114 | + | 1.21909i | ||||
\(296\) | 74.7866 | 0.252658 | ||||||||
\(297\) | −11.5130 | + | 11.5130i | −0.0387643 | + | 0.0387643i | ||||
\(298\) | −21.6052 | − | 21.6052i | −0.0725006 | − | 0.0725006i | ||||
\(299\) | − | 55.4080i | − | 0.185311i | ||||||
\(300\) | 74.1121 | + | 44.8039i | 0.247040 | + | 0.149346i | ||||
\(301\) | −107.566 | −0.357363 | ||||||||
\(302\) | −283.184 | + | 283.184i | −0.937695 | + | 0.937695i | ||||
\(303\) | −197.211 | − | 197.211i | −0.650860 | − | 0.650860i | ||||
\(304\) | − | 132.118i | − | 0.434598i | ||||||
\(305\) | −302.210 | − | 236.770i | −0.990852 | − | 0.776295i | ||||
\(306\) | 52.8458 | 0.172699 | ||||||||
\(307\) | −337.020 | + | 337.020i | −1.09779 | + | 1.09779i | −0.103116 | + | 0.994669i | \(0.532881\pi\) |
−0.994669 | + | 0.103116i | \(0.967119\pi\) | |||||||
\(308\) | 8.91400 | + | 8.91400i | 0.0289416 | + | 0.0289416i | ||||
\(309\) | 125.415i | 0.405875i | ||||||||
\(310\) | 333.810 | − | 40.5293i | 1.07681 | − | 0.130740i | ||||
\(311\) | 205.353 | 0.660298 | 0.330149 | − | 0.943929i | \(-0.392901\pi\) | ||||
0.330149 | + | 0.943929i | \(0.392901\pi\) | |||||||
\(312\) | 40.0220 | − | 40.0220i | 0.128276 | − | 0.128276i | ||||
\(313\) | −51.0361 | − | 51.0361i | −0.163055 | − | 0.163055i | 0.620864 | − | 0.783918i | \(-0.286782\pi\) |
−0.783918 | + | 0.620864i | \(0.786782\pi\) | |||||||
\(314\) | 248.635i | 0.791832i | ||||||||
\(315\) | −3.63680 | − | 29.9537i | −0.0115454 | − | 0.0950911i | ||||
\(316\) | −87.6297 | −0.277309 | ||||||||
\(317\) | 415.998 | − | 415.998i | 1.31230 | − | 1.31230i | 0.392580 | − | 0.919718i | \(-0.371583\pi\) |
0.919718 | − | 0.392580i | \(-0.128417\pi\) | |||||||
\(318\) | −14.7646 | − | 14.7646i | −0.0464296 | − | 0.0464296i | ||||
\(319\) | − | 27.1759i | − | 0.0851910i | ||||||
\(320\) | −24.6690 | + | 31.4871i | −0.0770906 | + | 0.0983973i | ||||
\(321\) | 217.048 | 0.676162 | ||||||||
\(322\) | 9.64719 | − | 9.64719i | 0.0299602 | − | 0.0299602i | ||||
\(323\) | −290.911 | − | 290.911i | −0.900654 | − | 0.900654i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 149.429 | − | 247.177i | 0.459781 | − | 0.760543i | ||||
\(326\) | −145.600 | −0.446625 | ||||||||
\(327\) | −56.3340 | + | 56.3340i | −0.172275 | + | 0.172275i | ||||
\(328\) | 42.0160 | + | 42.0160i | 0.128098 | + | 0.128098i | ||||
\(329\) | − | 13.9486i | − | 0.0423971i | ||||||
\(330\) | −30.2092 | − | 23.6678i | −0.0915432 | − | 0.0717206i | ||||
\(331\) | 624.517 | 1.88676 | 0.943379 | − | 0.331717i | \(-0.107628\pi\) | ||||
0.943379 | + | 0.331717i | \(0.107628\pi\) | |||||||
\(332\) | −145.669 | + | 145.669i | −0.438761 | + | 0.438761i | ||||
\(333\) | 56.0900 | + | 56.0900i | 0.168438 | + | 0.168438i | ||||
\(334\) | 120.962i | 0.362161i | ||||||||
\(335\) | 558.996 | − | 67.8701i | 1.66865 | − | 0.202597i | ||||
\(336\) | 13.9366 | 0.0414780 | ||||||||
\(337\) | −86.5233 | + | 86.5233i | −0.256746 | + | 0.256746i | −0.823729 | − | 0.566984i | \(-0.808110\pi\) |
0.566984 | + | 0.823729i | \(0.308110\pi\) | |||||||
\(338\) | 35.5197 | + | 35.5197i | 0.105088 | + | 0.105088i | ||||
\(339\) | − | 245.479i | − | 0.724127i | ||||||
\(340\) | 15.0129 | + | 123.651i | 0.0441557 | + | 0.363679i | ||||
\(341\) | −149.009 | −0.436978 | ||||||||
\(342\) | 99.0883 | − | 99.0883i | 0.289732 | − | 0.289732i | ||||
\(343\) | −133.640 | − | 133.640i | −0.389620 | − | 0.389620i | ||||
\(344\) | 151.246i | 0.439669i | ||||||||
\(345\) | −25.6145 | + | 32.6940i | −0.0742450 | + | 0.0947652i | ||||
\(346\) | −193.017 | −0.557854 | ||||||||
\(347\) | 382.830 | − | 382.830i | 1.10326 | − | 1.10326i | 0.109242 | − | 0.994015i | \(-0.465158\pi\) |
0.994015 | − | 0.109242i | \(-0.0348423\pi\) | |||||||
\(348\) | −21.2441 | − | 21.2441i | −0.0610464 | − | 0.0610464i | ||||
\(349\) | − | 392.877i | − | 1.12572i | −0.826552 | − | 0.562861i | \(-0.809701\pi\) | ||
0.826552 | − | 0.562861i | \(-0.190299\pi\) | |||||||
\(350\) | 69.0537 | − | 17.0191i | 0.197296 | − | 0.0486259i | ||||
\(351\) | 60.0331 | 0.171034 | ||||||||
\(352\) | 12.5337 | − | 12.5337i | 0.0356072 | − | 0.0356072i | ||||
\(353\) | −238.494 | − | 238.494i | −0.675620 | − | 0.675620i | 0.283386 | − | 0.959006i | \(-0.408542\pi\) |
−0.959006 | + | 0.283386i | \(0.908542\pi\) | |||||||
\(354\) | − | 223.816i | − | 0.632249i | ||||||
\(355\) | −486.398 | − | 381.075i | −1.37014 | − | 1.07345i | ||||
\(356\) | −170.255 | −0.478243 | ||||||||
\(357\) | 30.6872 | − | 30.6872i | 0.0859585 | − | 0.0859585i | ||||
\(358\) | −115.452 | − | 115.452i | −0.322491 | − | 0.322491i | ||||
\(359\) | 434.304i | 1.20976i | 0.796316 | + | 0.604881i | \(0.206779\pi\) | ||||
−0.796316 | + | 0.604881i | \(0.793221\pi\) | |||||||
\(360\) | −42.1171 | + | 5.11361i | −0.116992 | + | 0.0142045i | ||||
\(361\) | −729.943 | −2.02200 | ||||||||
\(362\) | −182.511 | + | 182.511i | −0.504174 | + | 0.504174i | ||||
\(363\) | −136.169 | − | 136.169i | −0.375121 | − | 0.375121i | ||||
\(364\) | − | 46.4810i | − | 0.127695i | ||||||
\(365\) | 76.1881 | + | 627.506i | 0.208734 | + | 1.71919i | ||||
\(366\) | 188.079 | 0.513878 | ||||||||
\(367\) | 139.615 | − | 139.615i | 0.380421 | − | 0.380421i | −0.490832 | − | 0.871254i | \(-0.663307\pi\) |
0.871254 | + | 0.490832i | \(0.163307\pi\) | |||||||
\(368\) | −13.5647 | − | 13.5647i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | 63.0240i | 0.170797i | ||||||||
\(370\) | −115.307 | + | 147.176i | −0.311640 | + | 0.397773i | ||||
\(371\) | −17.1474 | −0.0462194 | ||||||||
\(372\) | −116.484 | + | 116.484i | −0.313130 | + | 0.313130i | ||||
\(373\) | −78.8131 | − | 78.8131i | −0.211295 | − | 0.211295i | 0.593522 | − | 0.804817i | \(-0.297737\pi\) |
−0.804817 | + | 0.593522i | \(0.797737\pi\) | |||||||
\(374\) | − | 55.1964i | − | 0.147584i | ||||||
\(375\) | −202.439 | + | 76.7695i | −0.539837 | + | 0.204719i | ||||
\(376\) | −19.6128 | −0.0521617 | ||||||||
\(377\) | −70.8528 | + | 70.8528i | −0.187938 | + | 0.187938i | ||||
\(378\) | 10.4525 | + | 10.4525i | 0.0276520 | + | 0.0276520i | ||||
\(379\) | − | 59.0081i | − | 0.155694i | −0.996965 | − | 0.0778470i | \(-0.975195\pi\) | ||
0.996965 | − | 0.0778470i | \(-0.0248046\pi\) | |||||||
\(380\) | 260.001 | + | 203.701i | 0.684212 | + | 0.536055i | ||||
\(381\) | 41.7342 | 0.109539 | ||||||||
\(382\) | 126.245 | − | 126.245i | 0.330485 | − | 0.330485i | ||||
\(383\) | 101.487 | + | 101.487i | 0.264980 | + | 0.264980i | 0.827074 | − | 0.562094i | \(-0.190004\pi\) |
−0.562094 | + | 0.827074i | \(0.690004\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | −31.2860 | + | 3.79856i | −0.0812624 | + | 0.00986640i | ||||
\(386\) | 209.980 | 0.543989 | ||||||||
\(387\) | −113.435 | + | 113.435i | −0.293112 | + | 0.293112i | ||||
\(388\) | 209.784 | + | 209.784i | 0.540681 | + | 0.540681i | ||||
\(389\) | − | 276.824i | − | 0.711630i | −0.934556 | − | 0.355815i | \(-0.884203\pi\) | ||
0.934556 | − | 0.355815i | \(-0.115797\pi\) | |||||||
\(390\) | 17.0548 | + | 140.468i | 0.0437302 | + | 0.360174i | ||||
\(391\) | −59.7363 | −0.152778 | ||||||||
\(392\) | −89.9071 | + | 89.9071i | −0.229355 | + | 0.229355i | ||||
\(393\) | 277.377 | + | 277.377i | 0.705794 | + | 0.705794i | ||||
\(394\) | 378.849i | 0.961546i | ||||||||
\(395\) | 135.109 | − | 172.451i | 0.342047 | − | 0.436584i | ||||
\(396\) | 18.8006 | 0.0474763 | ||||||||
\(397\) | −304.445 | + | 304.445i | −0.766864 | + | 0.766864i | −0.977553 | − | 0.210689i | \(-0.932429\pi\) |
0.210689 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(398\) | −140.728 | − | 140.728i | −0.353589 | − | 0.353589i | ||||
\(399\) | − | 115.080i | − | 0.288420i | ||||||
\(400\) | −23.9301 | − | 97.0946i | −0.0598252 | − | 0.242736i | ||||
\(401\) | −506.097 | −1.26209 | −0.631044 | − | 0.775747i | \(-0.717373\pi\) | ||||
−0.631044 | + | 0.775747i | \(0.717373\pi\) | |||||||
\(402\) | −195.064 | + | 195.064i | −0.485234 | + | 0.485234i | ||||
\(403\) | 388.496 | + | 388.496i | 0.964009 | + | 0.964009i | ||||
\(404\) | 322.044i | 0.797138i | ||||||||
\(405\) | −35.4230 | − | 27.7526i | −0.0874643 | − | 0.0685250i | ||||
\(406\) | −24.6726 | −0.0607700 | ||||||||
\(407\) | 58.5848 | − | 58.5848i | 0.143943 | − | 0.143943i | ||||
\(408\) | −43.1484 | − | 43.1484i | −0.105756 | − | 0.105756i | ||||
\(409\) | − | 65.7017i | − | 0.160640i | −0.996769 | − | 0.0803200i | \(-0.974406\pi\) | ||
0.996769 | − | 0.0803200i | \(-0.0255942\pi\) | |||||||
\(410\) | −147.466 | + | 17.9045i | −0.359673 | + | 0.0436694i | ||||
\(411\) | −32.6603 | −0.0794655 | ||||||||
\(412\) | 102.401 | − | 102.401i | 0.248547 | − | 0.248547i | ||||
\(413\) | −129.968 | − | 129.968i | −0.314693 | − | 0.314693i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | −62.0744 | − | 511.262i | −0.149577 | − | 1.23196i | ||||
\(416\) | −65.3557 | −0.157105 | ||||||||
\(417\) | −167.272 | + | 167.272i | −0.401131 | + | 0.401131i | ||||
\(418\) | −103.496 | − | 103.496i | −0.247597 | − | 0.247597i | ||||
\(419\) | 496.707i | 1.18546i | 0.805402 | + | 0.592729i | \(0.201949\pi\) | ||||
−0.805402 | + | 0.592729i | \(0.798051\pi\) | |||||||
\(420\) | −21.4877 | + | 27.4265i | −0.0511611 | + | 0.0653013i | ||||
\(421\) | −452.792 | −1.07552 | −0.537758 | − | 0.843099i | \(-0.680728\pi\) | ||||
−0.537758 | + | 0.843099i | \(0.680728\pi\) | |||||||
\(422\) | −84.3383 | + | 84.3383i | −0.199854 | + | 0.199854i | ||||
\(423\) | −14.7096 | − | 14.7096i | −0.0347745 | − | 0.0347745i | ||||
\(424\) | 24.1105i | 0.0568644i | ||||||||
\(425\) | −266.485 | − | 161.102i | −0.627024 | − | 0.379063i | ||||
\(426\) | 302.708 | 0.710583 | ||||||||
\(427\) | 109.216 | − | 109.216i | 0.255776 | − | 0.255776i | ||||
\(428\) | −177.219 | − | 177.219i | −0.414063 | − | 0.414063i | ||||
\(429\) | − | 62.7033i | − | 0.146161i | ||||||
\(430\) | −297.644 | − | 233.193i | −0.692196 | − | 0.542309i | ||||
\(431\) | 375.766 | 0.871847 | 0.435924 | − | 0.899984i | \(-0.356422\pi\) | ||||
0.435924 | + | 0.899984i | \(0.356422\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 463.698 | + | 463.698i | 1.07090 | + | 1.07090i | 0.997287 | + | 0.0736079i | \(0.0234513\pi\) |
0.0736079 | + | 0.997287i | \(0.476549\pi\) | |||||||
\(434\) | 135.283i | 0.311713i | ||||||||
\(435\) | 74.5618 | − | 9.05286i | 0.171406 | − | 0.0208112i | ||||
\(436\) | 91.9930 | 0.210993 | ||||||||
\(437\) | −112.008 | + | 112.008i | −0.256312 | + | 0.256312i | ||||
\(438\) | −218.971 | − | 218.971i | −0.499933 | − | 0.499933i | ||||
\(439\) | 772.787i | 1.76033i | 0.474664 | + | 0.880167i | \(0.342570\pi\) | ||||
−0.474664 | + | 0.880167i | \(0.657430\pi\) | |||||||
\(440\) | 5.34106 | + | 43.9904i | 0.0121388 | + | 0.0999783i | ||||
\(441\) | −134.861 | −0.305806 | ||||||||
\(442\) | −143.907 | + | 143.907i | −0.325582 | + | 0.325582i | ||||
\(443\) | −314.253 | − | 314.253i | −0.709374 | − | 0.709374i | 0.257029 | − | 0.966404i | \(-0.417256\pi\) |
−0.966404 | + | 0.257029i | \(0.917256\pi\) | |||||||
\(444\) | − | 91.5946i | − | 0.206294i | ||||||
\(445\) | 262.501 | − | 335.052i | 0.589889 | − | 0.752926i | ||||
\(446\) | −357.765 | −0.802163 | ||||||||
\(447\) | −26.4608 | + | 26.4608i | −0.0591965 | + | 0.0591965i | ||||
\(448\) | −11.3792 | − | 11.3792i | −0.0254000 | − | 0.0254000i | ||||
\(449\) | 123.814i | 0.275756i | 0.990449 | + | 0.137878i | \(0.0440281\pi\) | ||||
−0.990449 | + | 0.137878i | \(0.955972\pi\) | |||||||
\(450\) | 54.8734 | − | 90.7685i | 0.121941 | − | 0.201708i | ||||
\(451\) | 65.8273 | 0.145958 | ||||||||
\(452\) | −200.433 | + | 200.433i | −0.443435 | + | 0.443435i | ||||
\(453\) | 346.828 | + | 346.828i | 0.765625 | + | 0.765625i | ||||
\(454\) | 318.372i | 0.701259i | ||||||||
\(455\) | 91.4721 | + | 71.6650i | 0.201038 | + | 0.157505i | ||||
\(456\) | −161.810 | −0.354848 | ||||||||
\(457\) | −83.6198 | + | 83.6198i | −0.182976 | + | 0.182976i | −0.792651 | − | 0.609676i | \(-0.791300\pi\) |
0.609676 | + | 0.792651i | \(0.291300\pi\) | |||||||
\(458\) | −139.731 | − | 139.731i | −0.305089 | − | 0.305089i | ||||
\(459\) | − | 64.7227i | − | 0.141008i | ||||||
\(460\) | 47.6087 | − | 5.78037i | 0.103497 | − | 0.0125660i | ||||
\(461\) | −350.628 | −0.760582 | −0.380291 | − | 0.924867i | \(-0.624176\pi\) | ||||
−0.380291 | + | 0.924867i | \(0.624176\pi\) | |||||||
\(462\) | 10.9174 | − | 10.9174i | 0.0236307 | − | 0.0236307i | ||||
\(463\) | −486.539 | − | 486.539i | −1.05084 | − | 1.05084i | −0.998636 | − | 0.0522029i | \(-0.983376\pi\) |
−0.0522029 | − | 0.998636i | \(-0.516624\pi\) | |||||||
\(464\) | 34.6915i | 0.0747662i | ||||||||
\(465\) | −49.6380 | − | 408.833i | −0.106748 | − | 0.879210i | ||||
\(466\) | −127.231 | −0.273028 | ||||||||
\(467\) | −392.159 | + | 392.159i | −0.839742 | + | 0.839742i | −0.988825 | − | 0.149083i | \(-0.952368\pi\) |
0.149083 | + | 0.988825i | \(0.452368\pi\) | |||||||
\(468\) | −49.0168 | − | 49.0168i | −0.104737 | − | 0.104737i | ||||
\(469\) | 226.545i | 0.483037i | ||||||||
\(470\) | 30.2393 | − | 38.5970i | 0.0643389 | − | 0.0821212i | ||||
\(471\) | 304.515 | 0.646528 | ||||||||
\(472\) | −182.745 | + | 182.745i | −0.387172 | + | 0.387172i | ||||
\(473\) | 118.480 | + | 118.480i | 0.250486 | + | 0.250486i | ||||
\(474\) | 107.324i | 0.226422i | ||||||||
\(475\) | −801.744 | + | 197.599i | −1.68788 | + | 0.415998i | ||||
\(476\) | −50.1120 | −0.105277 | ||||||||
\(477\) | −18.0829 | + | 18.0829i | −0.0379096 | + | 0.0379096i | ||||
\(478\) | 56.4515 | + | 56.4515i | 0.118099 | + | 0.118099i | ||||
\(479\) | 201.795i | 0.421283i | 0.977563 | + | 0.210642i | \(0.0675553\pi\) | ||||
−0.977563 | + | 0.210642i | \(0.932445\pi\) | |||||||
\(480\) | 38.5637 | + | 30.2132i | 0.0803411 | + | 0.0629442i | ||||
\(481\) | −305.483 | −0.635101 | ||||||||
\(482\) | −88.4572 | + | 88.4572i | −0.183521 | + | 0.183521i | ||||
\(483\) | −11.8153 | − | 11.8153i | −0.0244624 | − | 0.0244624i | ||||
\(484\) | 222.363i | 0.459428i | ||||||||
\(485\) | −736.293 | + | 89.3963i | −1.51813 | + | 0.184322i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −406.615 | + | 406.615i | −0.834939 | + | 0.834939i | −0.988188 | − | 0.153249i | \(-0.951026\pi\) |
0.153249 | + | 0.988188i | \(0.451026\pi\) | |||||||
\(488\) | −153.566 | − | 153.566i | −0.314684 | − | 0.314684i | ||||
\(489\) | 178.323i | 0.364668i | ||||||||
\(490\) | −38.3125 | − | 315.552i | −0.0781888 | − | 0.643984i | ||||
\(491\) | 128.249 | 0.261199 | 0.130599 | − | 0.991435i | \(-0.458310\pi\) | ||||
0.130599 | + | 0.991435i | \(0.458310\pi\) | |||||||
\(492\) | 51.4589 | − | 51.4589i | 0.104591 | − | 0.104591i | ||||
\(493\) | 76.3876 | + | 76.3876i | 0.154944 | + | 0.154944i | ||||
\(494\) | 539.666i | 1.09244i | ||||||||
\(495\) | −28.9870 | + | 36.9986i | −0.0585597 | + | 0.0747447i | ||||
\(496\) | 190.218 | 0.383505 | ||||||||
\(497\) | 175.780 | − | 175.780i | 0.353683 | − | 0.353683i | ||||
\(498\) | 178.407 | + | 178.407i | 0.358247 | + | 0.358247i | ||||
\(499\) | 395.030i | 0.791644i | 0.918327 | + | 0.395822i | \(0.129540\pi\) | ||||
−0.918327 | + | 0.395822i | \(0.870460\pi\) | |||||||
\(500\) | 227.973 | + | 102.608i | 0.455945 | + | 0.205217i | ||||
\(501\) | 148.147 | 0.295703 | ||||||||
\(502\) | −68.5838 | + | 68.5838i | −0.136621 | + | 0.136621i | ||||
\(503\) | 194.782 | + | 194.782i | 0.387241 | + | 0.387241i | 0.873702 | − | 0.486461i | \(-0.161713\pi\) |
−0.486461 | + | 0.873702i | \(0.661713\pi\) | |||||||
\(504\) | − | 17.0688i | − | 0.0338667i | ||||||
\(505\) | −633.765 | − | 496.531i | −1.25498 | − | 0.983229i | ||||
\(506\) | −21.2520 | −0.0420000 | ||||||||
\(507\) | 43.5026 | − | 43.5026i | 0.0858039 | − | 0.0858039i | ||||
\(508\) | −34.0758 | − | 34.0758i | −0.0670784 | − | 0.0670784i | ||||
\(509\) | − | 366.809i | − | 0.720646i | −0.932828 | − | 0.360323i | \(-0.882666\pi\) | ||
0.932828 | − | 0.360323i | \(-0.117334\pi\) | |||||||
\(510\) | 151.441 | − | 18.3870i | 0.296942 | − | 0.0360530i | ||||
\(511\) | −254.309 | −0.497670 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −121.358 | − | 121.358i | −0.236565 | − | 0.236565i | ||||
\(514\) | 266.639i | 0.518754i | ||||||||
\(515\) | 43.6367 | + | 359.404i | 0.0847315 | + | 0.697872i | ||||
\(516\) | 185.238 | 0.358988 | ||||||||
\(517\) | −15.3639 | + | 15.3639i | −0.0297174 | + | 0.0297174i | ||||
\(518\) | −53.1883 | − | 53.1883i | −0.102680 | − | 0.102680i | ||||
\(519\) | 236.397i | 0.455485i | ||||||||
\(520\) | 100.766 | − | 128.617i | 0.193781 | − | 0.247340i | ||||
\(521\) | 301.749 | 0.579173 | 0.289587 | − | 0.957152i | \(-0.406482\pi\) | ||||
0.289587 | + | 0.957152i | \(0.406482\pi\) | |||||||
\(522\) | −26.0186 | + | 26.0186i | −0.0498442 | + | 0.0498442i | ||||
\(523\) | −323.972 | − | 323.972i | −0.619449 | − | 0.619449i | 0.325941 | − | 0.945390i | \(-0.394319\pi\) |
−0.945390 | + | 0.325941i | \(0.894319\pi\) | |||||||
\(524\) | − | 452.955i | − | 0.864418i | ||||||
\(525\) | −20.8440 | − | 84.5731i | −0.0397029 | − | 0.161092i | ||||
\(526\) | −539.870 | −1.02637 | ||||||||
\(527\) | 418.844 | − | 418.844i | 0.794770 | − | 0.794770i | ||||
\(528\) | −15.3506 | − | 15.3506i | −0.0290732 | − | 0.0290732i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | −47.4482 | − | 37.1739i | −0.0895249 | − | 0.0701394i | ||||
\(531\) | −274.118 | −0.516229 | ||||||||
\(532\) | −93.9621 | + | 93.9621i | −0.176621 | + | 0.176621i | ||||
\(533\) | −171.624 | − | 171.624i | −0.321996 | − | 0.321996i | ||||
\(534\) | 208.519i | 0.390484i | ||||||||
\(535\) | 621.996 | − | 75.5191i | 1.16261 | − | 0.141157i | ||||
\(536\) | 318.538 | 0.594288 | ||||||||
\(537\) | −141.399 | + | 141.399i | −0.263313 | + | 0.263313i | ||||
\(538\) | 287.611 | + | 287.611i | 0.534593 | + | 0.534593i | ||||
\(539\) | 140.859i | 0.261334i | ||||||||
\(540\) | 6.26287 | + | 51.5827i | 0.0115979 | + | 0.0955235i | ||||
\(541\) | −38.7881 | −0.0716970 | −0.0358485 | − | 0.999357i | \(-0.511413\pi\) | ||||
−0.0358485 | + | 0.999357i | \(0.511413\pi\) | |||||||
\(542\) | −146.523 | + | 146.523i | −0.270338 | + | 0.270338i | ||||
\(543\) | 223.529 | + | 223.529i | 0.411656 | + | 0.411656i | ||||
\(544\) | 70.4611i | 0.129524i | ||||||||
\(545\) | −141.836 | + | 181.037i | −0.260250 | + | 0.332179i | ||||
\(546\) | −56.9274 | −0.104263 | ||||||||
\(547\) | 539.005 | − | 539.005i | 0.985383 | − | 0.985383i | −0.0145113 | − | 0.999895i | \(-0.504619\pi\) |
0.999895 | + | 0.0145113i | \(0.00461926\pi\) | |||||||
\(548\) | 26.6670 | + | 26.6670i | 0.0486625 | + | 0.0486625i | ||||
\(549\) | − | 230.349i | − | 0.419579i | ||||||
\(550\) | −94.8058 | − | 57.3141i | −0.172374 | − | 0.104207i | ||||
\(551\) | 286.460 | 0.519892 | ||||||||
\(552\) | −16.6132 | + | 16.6132i | −0.0300965 | + | 0.0300965i | ||||
\(553\) | 62.3223 | + | 62.3223i | 0.112699 | + | 0.112699i | ||||
\(554\) | 151.571i | 0.273594i | ||||||||
\(555\) | 180.253 | + | 141.222i | 0.324781 | + | 0.254453i | ||||
\(556\) | 273.153 | 0.491283 | ||||||||
\(557\) | −239.468 | + | 239.468i | −0.429925 | + | 0.429925i | −0.888603 | − | 0.458678i | \(-0.848323\pi\) |
0.458678 | + | 0.888603i | \(0.348323\pi\) | |||||||
\(558\) | 142.664 | + | 142.664i | 0.255670 | + | 0.255670i | ||||
\(559\) | − | 617.800i | − | 1.10519i | ||||||
\(560\) | 39.9383 | − | 4.84907i | 0.0713183 | − | 0.00865905i | ||||
\(561\) | −67.6015 | −0.120502 | ||||||||
\(562\) | −461.843 | + | 461.843i | −0.821785 | + | 0.821785i | ||||
\(563\) | 316.131 | + | 316.131i | 0.561512 | + | 0.561512i | 0.929737 | − | 0.368225i | \(-0.120034\pi\) |
−0.368225 | + | 0.929737i | \(0.620034\pi\) | |||||||
\(564\) | 24.0207i | 0.0425899i | ||||||||
\(565\) | −85.4113 | − | 703.471i | −0.151170 | − | 1.24508i | ||||
\(566\) | −35.4086 | −0.0625594 | ||||||||
\(567\) | 12.8016 | − | 12.8016i | 0.0225778 | − | 0.0225778i | ||||
\(568\) | −247.160 | − | 247.160i | −0.435141 | − | 0.435141i | ||||
\(569\) | − | 235.711i | − | 0.414256i | −0.978314 | − | 0.207128i | \(-0.933588\pi\) | ||
0.978314 | − | 0.207128i | \(-0.0664116\pi\) | |||||||
\(570\) | 249.481 | − | 318.434i | 0.437687 | − | 0.558657i | ||||
\(571\) | 930.317 | 1.62928 | 0.814638 | − | 0.579969i | \(-0.196935\pi\) | ||||
0.814638 | + | 0.579969i | \(0.196935\pi\) | |||||||
\(572\) | −51.1970 | + | 51.1970i | −0.0895053 | + | 0.0895053i | ||||
\(573\) | −154.618 | − | 154.618i | −0.269840 | − | 0.269840i | ||||
\(574\) | − | 59.7636i | − | 0.104118i | ||||||
\(575\) | −62.0282 | + | 102.604i | −0.107875 | + | 0.178441i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −480.176 | + | 480.176i | −0.832193 | + | 0.832193i | −0.987816 | − | 0.155623i | \(-0.950261\pi\) |
0.155623 | + | 0.987816i | \(0.450261\pi\) | |||||||
\(578\) | −133.851 | − | 133.851i | −0.231576 | − | 0.231576i | ||||
\(579\) | − | 257.172i | − | 0.444165i | ||||||
\(580\) | −68.2711 | − | 53.4878i | −0.117709 | − | 0.0922204i | ||||
\(581\) | 207.199 | 0.356625 | ||||||||
\(582\) | 256.932 | − | 256.932i | 0.441464 | − | 0.441464i | ||||
\(583\) | 18.8872 | + | 18.8872i | 0.0323966 | + | 0.0323966i | ||||
\(584\) | 357.578i | 0.612291i | ||||||||
\(585\) | 172.037 | − | 20.8877i | 0.294081 | − | 0.0357055i | ||||
\(586\) | 271.279 | 0.462934 | ||||||||
\(587\) | 175.266 | − | 175.266i | 0.298579 | − | 0.298579i | −0.541878 | − | 0.840457i | \(-0.682287\pi\) |
0.840457 | + | 0.541878i | \(0.182287\pi\) | |||||||
\(588\) | 110.113 | + | 110.113i | 0.187267 | + | 0.187267i | ||||
\(589\) | − | 1570.70i | − | 2.66673i | ||||||
\(590\) | −77.8740 | − | 641.391i | −0.131990 | − | 1.08710i | ||||
\(591\) | 463.994 | 0.785099 | ||||||||
\(592\) | −74.7866 | + | 74.7866i | −0.126329 | + | 0.126329i | ||||
\(593\) | 204.328 | + | 204.328i | 0.344567 | + | 0.344567i | 0.858081 | − | 0.513514i | \(-0.171657\pi\) |
−0.513514 | + | 0.858081i | \(0.671657\pi\) | |||||||
\(594\) | − | 23.0260i | − | 0.0387643i | ||||||
\(595\) | 77.2632 | − | 98.6177i | 0.129854 | − | 0.165744i | ||||
\(596\) | 43.2103 | 0.0725006 | ||||||||
\(597\) | −172.356 | + | 172.356i | −0.288704 | + | 0.288704i | ||||
\(598\) | 55.4080 | + | 55.4080i | 0.0926555 | + | 0.0926555i | ||||
\(599\) | − | 353.006i | − | 0.589326i | −0.955601 | − | 0.294663i | \(-0.904793\pi\) | ||
0.955601 | − | 0.294663i | \(-0.0952074\pi\) | |||||||
\(600\) | −118.916 | + | 29.3082i | −0.198193 | + | 0.0488470i | ||||
\(601\) | −377.286 | −0.627763 | −0.313882 | − | 0.949462i | \(-0.601630\pi\) | ||||
−0.313882 | + | 0.949462i | \(0.601630\pi\) | |||||||
\(602\) | 107.566 | − | 107.566i | 0.178681 | − | 0.178681i | ||||
\(603\) | 238.904 | + | 238.904i | 0.396192 | + | 0.396192i | ||||
\(604\) | − | 566.368i | − | 0.937695i | ||||||
\(605\) | −437.599 | − | 342.842i | −0.723304 | − | 0.566681i | ||||
\(606\) | 394.421 | 0.650860 | ||||||||
\(607\) | 582.145 | − | 582.145i | 0.959053 | − | 0.959053i | −0.0401409 | − | 0.999194i | \(-0.512781\pi\) |
0.999194 | + | 0.0401409i | \(0.0127807\pi\) | |||||||
\(608\) | 132.118 | + | 132.118i | 0.217299 | + | 0.217299i | ||||
\(609\) | 30.2177i | 0.0496185i | ||||||||
\(610\) | 538.980 | − | 65.4397i | 0.883573 | − | 0.107278i | ||||
\(611\) | 80.1131 | 0.131118 | ||||||||
\(612\) | −52.8458 | + | 52.8458i | −0.0863494 | + | 0.0863494i | ||||
\(613\) | −88.4721 | − | 88.4721i | −0.144326 | − | 0.144326i | 0.631252 | − | 0.775578i | \(-0.282542\pi\) |
−0.775578 | + | 0.631252i | \(0.782542\pi\) | |||||||
\(614\) | − | 674.040i | − | 1.09779i | ||||||
\(615\) | 21.9284 | + | 180.608i | 0.0356559 | + | 0.293672i | ||||
\(616\) | −17.8280 | −0.0289416 | ||||||||
\(617\) | 604.135 | − | 604.135i | 0.979149 | − | 0.979149i | −0.0206376 | − | 0.999787i | \(-0.506570\pi\) |
0.999787 | + | 0.0206376i | \(0.00656963\pi\) | |||||||
\(618\) | −125.415 | − | 125.415i | −0.202938 | − | 0.202938i | ||||
\(619\) | − | 822.499i | − | 1.32875i | −0.747397 | − | 0.664377i | \(-0.768697\pi\) | ||
0.747397 | − | 0.664377i | \(-0.231303\pi\) | |||||||
\(620\) | −293.281 | + | 374.340i | −0.473034 | + | 0.603774i | ||||
\(621\) | −24.9199 | −0.0401286 | ||||||||
\(622\) | −205.353 | + | 205.353i | −0.330149 | + | 0.330149i | ||||
\(623\) | 121.085 | + | 121.085i | 0.194358 | + | 0.194358i | ||||
\(624\) | 80.0441i | 0.128276i | ||||||||
\(625\) | −553.419 | + | 290.435i | −0.885470 | + | 0.464696i | ||||
\(626\) | 102.072 | 0.163055 | ||||||||
\(627\) | −126.756 | + | 126.756i | −0.202162 | + | 0.202162i | ||||
\(628\) | −248.635 | − | 248.635i | −0.395916 | − | 0.395916i | ||||
\(629\) | 329.347i | 0.523604i | ||||||||
\(630\) | 33.5905 | + | 26.3169i | 0.0533183 | + | 0.0417728i | ||||
\(631\) | −190.298 | −0.301582 | −0.150791 | − | 0.988566i | \(-0.548182\pi\) | ||||
−0.150791 | + | 0.988566i | \(0.548182\pi\) | |||||||
\(632\) | 87.6297 | − | 87.6297i | 0.138655 | − | 0.138655i | ||||
\(633\) | 103.293 | + | 103.293i | 0.163180 | + | 0.163180i | ||||
\(634\) | 831.997i | 1.31230i | ||||||||
\(635\) | 119.598 | − | 14.5209i | 0.188343 | − | 0.0228675i | ||||
\(636\) | 29.5292 | 0.0464296 | ||||||||
\(637\) | 367.246 | − | 367.246i | 0.576525 | − | 0.576525i | ||||
\(638\) | 27.1759 | + | 27.1759i | 0.0425955 | + | 0.0425955i | ||||
\(639\) | − | 370.740i | − | 0.580189i | ||||||
\(640\) | −6.81815 | − | 56.1561i | −0.0106534 | − | 0.0877440i | ||||
\(641\) | 490.787 | 0.765658 | 0.382829 | − | 0.923819i | \(-0.374950\pi\) | ||||
0.382829 | + | 0.923819i | \(0.374950\pi\) | |||||||
\(642\) | −217.048 | + | 217.048i | −0.338081 | + | 0.338081i | ||||
\(643\) | 159.376 | + | 159.376i | 0.247863 | + | 0.247863i | 0.820093 | − | 0.572230i | \(-0.193921\pi\) |
−0.572230 | + | 0.820093i | \(0.693921\pi\) | |||||||
\(644\) | 19.2944i | 0.0299602i | ||||||||
\(645\) | −285.602 | + | 364.538i | −0.442794 | + | 0.565175i | ||||
\(646\) | 581.823 | 0.900654 | ||||||||
\(647\) | 518.536 | − | 518.536i | 0.801446 | − | 0.801446i | −0.181875 | − | 0.983322i | \(-0.558217\pi\) |
0.983322 | + | 0.181875i | \(0.0582167\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 286.310i | 0.441156i | ||||||||
\(650\) | 97.7479 | + | 396.605i | 0.150381 | + | 0.610162i | ||||
\(651\) | 165.688 | 0.254512 | ||||||||
\(652\) | 145.600 | − | 145.600i | 0.223313 | − | 0.223313i | ||||
\(653\) | 33.5738 | + | 33.5738i | 0.0514148 | + | 0.0514148i | 0.732347 | − | 0.680932i | \(-0.238425\pi\) |
−0.680932 | + | 0.732347i | \(0.738425\pi\) | |||||||
\(654\) | − | 112.668i | − | 0.172275i | ||||||
\(655\) | 891.391 | + | 698.372i | 1.36090 | + | 1.06622i | ||||
\(656\) | −84.0320 | −0.128098 | ||||||||
\(657\) | −268.183 | + | 268.183i | −0.408194 | + | 0.408194i | ||||
\(658\) | 13.9486 | + | 13.9486i | 0.0211985 | + | 0.0211985i | ||||
\(659\) | 69.0686i | 0.104808i | 0.998626 | + | 0.0524041i | \(0.0166884\pi\) | ||||
−0.998626 | + | 0.0524041i | \(0.983312\pi\) | |||||||
\(660\) | 53.8771 | − | 6.54144i | 0.0816319 | − | 0.00991127i | ||||
\(661\) | −1025.91 | −1.55205 | −0.776026 | − | 0.630701i | \(-0.782768\pi\) | ||||
−0.776026 | + | 0.630701i | \(0.782768\pi\) | |||||||
\(662\) | −624.517 | + | 624.517i | −0.943379 | + | 0.943379i | ||||
\(663\) | 176.250 | + | 176.250i | 0.265837 | + | 0.265837i | ||||
\(664\) | − | 291.337i | − | 0.438761i | ||||||
\(665\) | −40.0405 | − | 329.785i | −0.0602113 | − | 0.495917i | ||||
\(666\) | −112.180 | −0.168438 | ||||||||
\(667\) | 29.4112 | − | 29.4112i | 0.0440947 | − | 0.0440947i | ||||
\(668\) | −120.962 | − | 120.962i | −0.181081 | − | 0.181081i | ||||
\(669\) | 438.170i | 0.654963i | ||||||||
\(670\) | −491.126 | + | 626.866i | −0.733024 | + | 0.935622i | ||||
\(671\) | −240.595 | −0.358561 | ||||||||
\(672\) | −13.9366 | + | 13.9366i | −0.0207390 | + | 0.0207390i | ||||
\(673\) | 36.3139 | + | 36.3139i | 0.0539583 | + | 0.0539583i | 0.733571 | − | 0.679613i | \(-0.237852\pi\) |
−0.679613 | + | 0.733571i | \(0.737852\pi\) | |||||||
\(674\) | − | 173.047i | − | 0.256746i | ||||||
\(675\) | −111.168 | − | 67.2059i | −0.164694 | − | 0.0995643i | ||||
\(676\) | −71.0394 | −0.105088 | ||||||||
\(677\) | 564.145 | − | 564.145i | 0.833302 | − | 0.833302i | −0.154665 | − | 0.987967i | \(-0.549430\pi\) |
0.987967 | + | 0.154665i | \(0.0494299\pi\) | |||||||
\(678\) | 245.479 | + | 245.479i | 0.362063 | + | 0.362063i | ||||
\(679\) | − | 298.397i | − | 0.439466i | ||||||
\(680\) | −138.664 | − | 108.638i | −0.203917 | − | 0.159761i | ||||
\(681\) | 389.924 | 0.572576 | ||||||||
\(682\) | 149.009 | − | 149.009i | 0.218489 | − | 0.218489i | ||||
\(683\) | 120.894 | + | 120.894i | 0.177005 | + | 0.177005i | 0.790049 | − | 0.613044i | \(-0.210055\pi\) |
−0.613044 | + | 0.790049i | \(0.710055\pi\) | |||||||
\(684\) | 198.177i | 0.289732i | ||||||||
\(685\) | −93.5949 | + | 11.3637i | −0.136635 | + | 0.0165894i | ||||
\(686\) | 267.279 | 0.389620 | ||||||||
\(687\) | −171.135 | + | 171.135i | −0.249104 | + | 0.249104i | ||||
\(688\) | −151.246 | − | 151.246i | −0.219834 | − | 0.219834i | ||||
\(689\) | − | 98.4850i | − | 0.142939i | ||||||
\(690\) | −7.07948 | − | 58.3085i | −0.0102601 | − | 0.0845051i | ||||
\(691\) | −979.008 | −1.41680 | −0.708400 | − | 0.705812i | \(-0.750582\pi\) | ||||
−0.708400 | + | 0.705812i | \(0.750582\pi\) | |||||||
\(692\) | 193.017 | − | 193.017i | 0.278927 | − | 0.278927i | ||||
\(693\) | −13.3710 | − | 13.3710i | −0.0192944 | − | 0.0192944i | ||||
\(694\) | 765.660i | 1.10326i | ||||||||
\(695\) | −421.151 | + | 537.551i | −0.605973 | + | 0.773455i | ||||
\(696\) | 42.4883 | 0.0610464 | ||||||||
\(697\) | −185.031 | + | 185.031i | −0.265468 | + | 0.265468i | ||||
\(698\) | 392.877 | + | 392.877i | 0.562861 | + | 0.562861i | ||||
\(699\) | 155.825i | 0.222926i | ||||||||
\(700\) | −52.0346 | + | 86.0727i | −0.0743351 | + | 0.122961i | ||||
\(701\) | −941.739 | −1.34342 | −0.671711 | − | 0.740813i | \(-0.734440\pi\) | ||||
−0.671711 | + | 0.740813i | \(0.734440\pi\) | |||||||
\(702\) | −60.0331 | + | 60.0331i | −0.0855172 | + | 0.0855172i | ||||
\(703\) | 617.540 | + | 617.540i | 0.878435 | + | 0.878435i | ||||
\(704\) | 25.0675i | 0.0356072i | ||||||||
\(705\) | −47.2714 | − | 37.0354i | −0.0670517 | − | 0.0525325i | ||||
\(706\) | 476.988 | 0.675620 | ||||||||
\(707\) | 229.037 | − | 229.037i | 0.323957 | − | 0.323957i | ||||
\(708\) | 223.816 | + | 223.816i | 0.316124 | + | 0.316124i | ||||
\(709\) | 754.542i | 1.06423i | 0.846671 | + | 0.532117i | \(0.178603\pi\) | ||||
−0.846671 | + | 0.532117i | \(0.821397\pi\) | |||||||
\(710\) | 867.473 | − | 105.323i | 1.22179 | − | 0.148343i | ||||
\(711\) | 131.445 | 0.184873 | ||||||||
\(712\) | 170.255 | − | 170.255i | 0.239122 | − | 0.239122i | ||||
\(713\) | −161.265 | − | 161.265i | −0.226179 | − | 0.226179i | ||||
\(714\) | 61.3744i | 0.0859585i | ||||||||
\(715\) | −21.8168 | − | 179.689i | −0.0305130 | − | 0.251314i | ||||
\(716\) | 230.904 | 0.322491 | ||||||||
\(717\) | 69.1386 | − | 69.1386i | 0.0964277 | − | 0.0964277i | ||||
\(718\) | −434.304 | − | 434.304i | −0.604881 | − | 0.604881i | ||||
\(719\) | 266.966i | 0.371302i | 0.982616 | + | 0.185651i | \(0.0594394\pi\) | ||||
−0.982616 | + | 0.185651i | \(0.940561\pi\) | |||||||
\(720\) | 37.0035 | − | 47.2307i | 0.0513937 | − | 0.0655982i | ||||
\(721\) | −145.656 | −0.202019 | ||||||||
\(722\) | 729.943 | − | 729.943i | 1.01100 | − | 1.01100i | ||||
\(723\) | 108.337 | + | 108.337i | 0.149844 | + | 0.149844i | ||||
\(724\) | − | 365.022i | − | 0.504174i | ||||||
\(725\) | 210.522 | − | 51.8857i | 0.290376 | − | 0.0715664i | ||||
\(726\) | 272.338 | 0.375121 | ||||||||
\(727\) | −767.189 | + | 767.189i | −1.05528 | + | 1.05528i | −0.0569010 | + | 0.998380i | \(0.518122\pi\) |
−0.998380 | + | 0.0569010i | \(0.981878\pi\) | |||||||
\(728\) | 46.4810 | + | 46.4810i | 0.0638475 | + | 0.0638475i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −703.694 | − | 551.318i | −0.963964 | − | 0.755230i | ||||
\(731\) | −666.060 | −0.911163 | ||||||||
\(732\) | −188.079 | + | 188.079i | −0.256939 | + | 0.256939i | ||||
\(733\) | 633.411 | + | 633.411i | 0.864135 | + | 0.864135i | 0.991815 | − | 0.127680i | \(-0.0407531\pi\) |
−0.127680 | + | 0.991815i | \(0.540753\pi\) | |||||||
\(734\) | 279.229i | 0.380421i | ||||||||
\(735\) | −386.471 | + | 46.9230i | −0.525811 | + | 0.0638409i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 249.530 | − | 249.530i | 0.338575 | − | 0.338575i | ||||
\(738\) | −63.0240 | − | 63.0240i | −0.0853984 | − | 0.0853984i | ||||
\(739\) | − | 228.825i | − | 0.309641i | −0.987943 | − | 0.154820i | \(-0.950520\pi\) | ||
0.987943 | − | 0.154820i | \(-0.0494799\pi\) | |||||||
\(740\) | −31.8692 | − | 262.483i | −0.0430664 | − | 0.354707i | ||||
\(741\) | 660.953 | 0.891974 | ||||||||
\(742\) | 17.1474 | − | 17.1474i | 0.0231097 | − | 0.0231097i | ||||
\(743\) | −391.292 | − | 391.292i | −0.526638 | − | 0.526638i | 0.392931 | − | 0.919568i | \(-0.371461\pi\) |
−0.919568 | + | 0.392931i | \(0.871461\pi\) | |||||||
\(744\) | − | 232.969i | − | 0.313130i | ||||||
\(745\) | −66.6222 | + | 85.0356i | −0.0894258 | + | 0.114142i | ||||
\(746\) | 157.626 | 0.211295 | ||||||||
\(747\) | 218.503 | − | 218.503i | 0.292507 | − | 0.292507i | ||||
\(748\) | 55.1964 | + | 55.1964i | 0.0737919 | + | 0.0737919i | ||||
\(749\) | 252.076i | 0.336551i | ||||||||
\(750\) | 125.669 | − | 279.208i | 0.167559 | − | 0.372278i | ||||
\(751\) | 430.557 | 0.573312 | 0.286656 | − | 0.958034i | \(-0.407456\pi\) | ||||
0.286656 | + | 0.958034i | \(0.407456\pi\) | |||||||
\(752\) | 19.6128 | − | 19.6128i | 0.0260809 | − | 0.0260809i | ||||
\(753\) | 83.9976 | + | 83.9976i | 0.111551 | + | 0.111551i | ||||
\(754\) | − | 141.706i | − | 0.187938i | ||||||
\(755\) | 1114.58 | + | 873.233i | 1.47627 | + | 1.15660i | ||||
\(756\) | −20.9049 | −0.0276520 | ||||||||
\(757\) | −788.836 | + | 788.836i | −1.04206 | + | 1.04206i | −0.0429790 | + | 0.999076i | \(0.513685\pi\) |
−0.999076 | + | 0.0429790i | \(0.986315\pi\) | |||||||
\(758\) | 59.0081 | + | 59.0081i | 0.0778470 | + | 0.0778470i | ||||
\(759\) | 26.0283i | 0.0342929i | ||||||||
\(760\) | −463.701 | + | 56.2999i | −0.610133 | + | 0.0740788i | ||||
\(761\) | 1041.88 | 1.36909 | 0.684546 | − | 0.728969i | \(-0.260000\pi\) | ||||
0.684546 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(762\) | −41.7342 | + | 41.7342i | −0.0547693 | + | 0.0547693i | ||||
\(763\) | −65.4255 | − | 65.4255i | −0.0857477 | − | 0.0857477i | ||||
\(764\) | 252.490i | 0.330485i | ||||||||
\(765\) | −22.5194 | − | 185.476i | −0.0294372 | − | 0.242452i | ||||
\(766\) | −202.975 | −0.264980 | ||||||||
\(767\) | 746.465 | − | 746.465i | 0.973227 | − | 0.973227i | ||||
\(768\) | 19.5959 | + | 19.5959i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 920.965i | − | 1.19761i | −0.800893 | − | 0.598807i | \(-0.795642\pi\) | ||
0.800893 | − | 0.598807i | \(-0.204358\pi\) | |||||||
\(770\) | 27.4874 | − | 35.0846i | 0.0356980 | − | 0.0455644i | ||||
\(771\) | 326.565 | 0.423561 | ||||||||
\(772\) | −209.980 | + | 209.980i | −0.271994 | + | 0.271994i | ||||
\(773\) | 95.8217 | + | 95.8217i | 0.123961 | + | 0.123961i | 0.766366 | − | 0.642405i | \(-0.222063\pi\) |
−0.642405 | + | 0.766366i | \(0.722063\pi\) | |||||||
\(774\) | − | 226.869i | − | 0.293112i | ||||||
\(775\) | −284.496 | − | 1154.32i | −0.367092 | − | 1.48945i | ||||
\(776\) | −419.569 | −0.540681 | ||||||||
\(777\) | −65.1421 | + | 65.1421i | −0.0838379 | + | 0.0838379i | ||||
\(778\) | 276.824 | + | 276.824i | 0.355815 | + | 0.355815i | ||||
\(779\) | 693.882i | 0.890735i | ||||||||
\(780\) | −157.522 | − | 123.413i | −0.201952 | − | 0.158222i | ||||
\(781\) | −387.231 | −0.495814 | ||||||||
\(782\) | 59.7363 | − | 59.7363i | 0.0763891 | − | 0.0763891i | ||||
\(783\) | 31.8662 | + | 31.8662i | 0.0406976 | + | 0.0406976i | ||||
\(784\) | − | 179.814i | − | 0.229355i | ||||||
\(785\) | 872.650 | − | 105.952i | 1.11166 | − | 0.134971i | ||||
\(786\) | −554.754 | −0.705794 | ||||||||
\(787\) | 552.775 | − | 552.775i | 0.702382 | − | 0.702382i | −0.262539 | − | 0.964921i | \(-0.584560\pi\) |
0.964921 | + | 0.262539i | \(0.0845598\pi\) | |||||||
\(788\) | −378.849 | − | 378.849i | −0.480773 | − | 0.480773i | ||||
\(789\) | 661.203i | 0.838027i | ||||||||
\(790\) | 37.3420 | + | 307.559i | 0.0472684 | + | 0.389315i | ||||
\(791\) | 285.096 | 0.360424 | ||||||||
\(792\) | −18.8006 | + | 18.8006i | −0.0237382 | + | 0.0237382i | ||||
\(793\) | 627.276 | + | 627.276i | 0.791016 | + | 0.791016i | ||||
\(794\) | − | 608.890i | − | 0.766864i | ||||||
\(795\) | −45.5285 | + | 58.1119i | −0.0572686 | + | 0.0730968i | ||||
\(796\) | 281.457 | 0.353589 | ||||||||
\(797\) | −844.895 | + | 844.895i | −1.06009 | + | 1.06009i | −0.0620189 | + | 0.998075i | \(0.519754\pi\) |
−0.998075 | + | 0.0620189i | \(0.980246\pi\) | |||||||
\(798\) | 115.080 | + | 115.080i | 0.144210 | + | 0.144210i | ||||
\(799\) | − | 86.3713i | − | 0.108099i | ||||||
\(800\) | 121.025 | + | 73.1645i | 0.151281 | + | 0.0914556i | ||||
\(801\) | 255.382 | 0.318829 | ||||||||
\(802\) | 506.097 | − | 506.097i | 0.631044 | − | 0.631044i | ||||
\(803\) | 280.112 | + | 280.112i | 0.348832 | + | 0.348832i | ||||
\(804\) | − | 390.128i | − | 0.485234i | ||||||
\(805\) | −37.9703 | − | 29.7483i | −0.0471681 | − | 0.0369544i | ||||
\(806\) | −776.991 | −0.964009 | ||||||||
\(807\) | 352.250 | − | 352.250i | 0.436494 | − | 0.436494i | ||||
\(808\) | −322.044 | − | 322.044i | −0.398569 | − | 0.398569i | ||||
\(809\) | − | 1058.13i | − | 1.30795i | −0.756518 | − | 0.653973i | \(-0.773101\pi\) | ||
0.756518 | − | 0.653973i | \(-0.226899\pi\) | |||||||
\(810\) | 63.1757 | − | 7.67042i | 0.0779946 | − | 0.00946965i | ||||
\(811\) | −1149.17 | −1.41697 | −0.708487 | − | 0.705723i | \(-0.750622\pi\) | ||||
−0.708487 | + | 0.705723i | \(0.750622\pi\) | |||||||
\(812\) | 24.6726 | − | 24.6726i | 0.0303850 | − | 0.0303850i | ||||
\(813\) | 179.453 | + | 179.453i | 0.220730 | + | 0.220730i | ||||
\(814\) | 117.170i | 0.143943i | ||||||||
\(815\) | 62.0451 | + | 511.020i | 0.0761290 | + | 0.627019i | ||||
\(816\) | 86.2969 | 0.105756 | ||||||||
\(817\) | −1248.89 | + | 1248.89i | −1.52863 | + | 1.52863i | ||||
\(818\) | 65.7017 | + | 65.7017i | 0.0803200 | + | 0.0803200i | ||||
\(819\) | 69.7215i | 0.0851300i | ||||||||
\(820\) | 129.562 | − | 165.371i | 0.158002 | − | 0.201671i | ||||
\(821\) | −741.536 | −0.903211 | −0.451606 | − | 0.892218i | \(-0.649149\pi\) | ||||
−0.451606 | + | 0.892218i | \(0.649149\pi\) | |||||||
\(822\) | 32.6603 | − | 32.6603i | 0.0397327 | − | 0.0397327i | ||||
\(823\) | 937.263 | + | 937.263i | 1.13884 | + | 1.13884i | 0.988659 | + | 0.150178i | \(0.0479846\pi\) |
0.150178 | + | 0.988659i | \(0.452015\pi\) | |||||||
\(824\) | 204.803i | 0.248547i | ||||||||
\(825\) | −70.1951 | + | 116.113i | −0.0850850 | + | 0.140743i | ||||
\(826\) | 259.937 | 0.314693 | ||||||||
\(827\) | −205.141 | + | 205.141i | −0.248055 | + | 0.248055i | −0.820172 | − | 0.572117i | \(-0.806122\pi\) |
0.572117 | + | 0.820172i | \(0.306122\pi\) | |||||||
\(828\) | 20.3470 | + | 20.3470i | 0.0245737 | + | 0.0245737i | ||||
\(829\) | − | 83.5409i | − | 0.100773i | −0.998730 | − | 0.0503866i | \(-0.983955\pi\) | ||
0.998730 | − | 0.0503866i | \(-0.0160453\pi\) | |||||||
\(830\) | 573.336 | + | 449.187i | 0.690766 | + | 0.541190i | ||||
\(831\) | 185.636 | 0.223388 | ||||||||
\(832\) | 65.3557 | − | 65.3557i | 0.0785525 | − | 0.0785525i | ||||
\(833\) | −395.935 | − | 395.935i | −0.475312 | − | 0.475312i | ||||
\(834\) | − | 334.543i | − | 0.401131i | ||||||
\(835\) | 424.547 | − | 51.5460i | 0.508439 | − | 0.0617317i | ||||
\(836\) | 206.991 | 0.247597 | ||||||||
\(837\) | 174.727 | − | 174.727i | 0.208754 | − | 0.208754i | ||||
\(838\) | −496.707 | − | 496.707i | −0.592729 | − | 0.592729i | ||||
\(839\) | − | 1253.41i | − | 1.49393i | −0.664865 | − | 0.746964i | \(-0.731511\pi\) | ||
0.664865 | − | 0.746964i | \(-0.268489\pi\) | |||||||
\(840\) | −5.93887 | − | 48.9142i | −0.00707009 | − | 0.0582312i | ||||
\(841\) | 765.781 | 0.910560 | ||||||||
\(842\) | 452.792 | − | 452.792i | 0.537758 | − | 0.537758i | ||||
\(843\) | 565.640 | + | 565.640i | 0.670984 | + | 0.670984i | ||||
\(844\) | − | 168.677i | − | 0.199854i | ||||||
\(845\) | 109.529 | − | 139.802i | 0.129621 | − | 0.165446i | ||||
\(846\) | 29.4192 | 0.0347745 | ||||||||
\(847\) | 158.145 | − | 158.145i | 0.186712 | − | 0.186712i | ||||
\(848\) | −24.1105 | − | 24.1105i | −0.0284322 | − | 0.0284322i | ||||
\(849\) | 43.3665i | 0.0510795i | ||||||||
\(850\) | 427.587 | − | 105.384i | 0.503043 | − | 0.123981i | ||||
\(851\) | 126.807 | 0.149009 | ||||||||
\(852\) | −302.708 | + | 302.708i | −0.355291 | + | 0.355291i | ||||
\(853\) | −337.158 | − | 337.158i | −0.395262 | − | 0.395262i | 0.481296 | − | 0.876558i | \(-0.340166\pi\) |
−0.876558 | + | 0.481296i | \(0.840166\pi\) | |||||||
\(854\) | 218.432i | 0.255776i | ||||||||
\(855\) | −390.001 | − | 305.551i | −0.456141 | − | 0.357370i | ||||
\(856\) | 354.438 | 0.414063 | ||||||||
\(857\) | 208.941 | − | 208.941i | 0.243806 | − | 0.243806i | −0.574617 | − | 0.818423i | \(-0.694849\pi\) |
0.818423 | + | 0.574617i | \(0.194849\pi\) | |||||||
\(858\) | 62.7033 | + | 62.7033i | 0.0730807 | + | 0.0730807i | ||||
\(859\) | 562.758i | 0.655132i | 0.944828 | + | 0.327566i | \(0.106228\pi\) | ||||
−0.944828 | + | 0.327566i | \(0.893772\pi\) | |||||||
\(860\) | 530.837 | − | 64.4511i | 0.617252 | − | 0.0749432i | ||||
\(861\) | −73.1951 | −0.0850118 | ||||||||
\(862\) | −375.766 | + | 375.766i | −0.435924 | + | 0.435924i | ||||
\(863\) | 489.121 | + | 489.121i | 0.566768 | + | 0.566768i | 0.931222 | − | 0.364453i | \(-0.118744\pi\) |
−0.364453 | + | 0.931222i | \(0.618744\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 82.2513 | + | 677.444i | 0.0950882 | + | 0.783173i | ||||
\(866\) | −927.395 | −1.07090 | ||||||||
\(867\) | −163.933 | + | 163.933i | −0.189081 | + | 0.189081i | ||||
\(868\) | −135.283 | − | 135.283i | −0.155856 | − | 0.155856i | ||||
\(869\) | − | 137.291i | − | 0.157987i | ||||||
\(870\) | −65.5090 | + | 83.6147i | −0.0752976 | + | 0.0961088i | ||||
\(871\) | −1301.14 | −1.49385 | ||||||||
\(872\) | −91.9930 | + | 91.9930i | −0.105497 | + | 0.105497i | ||||
\(873\) | −314.677 | − | 314.677i | −0.360454 | − | 0.360454i | ||||
\(874\) | − | 224.016i | − | 0.256312i | ||||||
\(875\) | −89.1590 | − | 235.109i | −0.101896 | − | 0.268696i | ||||
\(876\) | 437.942 | 0.499933 | ||||||||
\(877\) | 208.653 | − | 208.653i | 0.237916 | − | 0.237916i | −0.578071 | − | 0.815987i | \(-0.696194\pi\) |
0.815987 | + | 0.578071i | \(0.196194\pi\) | |||||||
\(878\) | −772.787 | − | 772.787i | −0.880167 | − | 0.880167i | ||||
\(879\) | − | 332.248i | − | 0.377984i | ||||||
\(880\) | −49.3315 | − | 38.6494i | −0.0560585 | − | 0.0439197i | ||||
\(881\) | −1167.86 | −1.32561 | −0.662804 | − | 0.748793i | \(-0.730634\pi\) | ||||
−0.662804 | + | 0.748793i | \(0.730634\pi\) | |||||||
\(882\) | 134.861 | − | 134.861i | 0.152903 | − | 0.152903i | ||||
\(883\) | 903.097 | + | 903.097i | 1.02276 | + | 1.02276i | 0.999735 | + | 0.0230253i | \(0.00732981\pi\) |
0.0230253 | + | 0.999735i | \(0.492670\pi\) | |||||||
\(884\) | − | 287.815i | − | 0.325582i | ||||||
\(885\) | −785.541 | + | 95.3757i | −0.887617 | + | 0.107769i | ||||
\(886\) | 628.506 | 0.709374 | ||||||||
\(887\) | 505.164 | − | 505.164i | 0.569520 | − | 0.569520i | −0.362474 | − | 0.931994i | \(-0.618068\pi\) |
0.931994 | + | 0.362474i | \(0.118068\pi\) | |||||||
\(888\) | 91.5946 | + | 91.5946i | 0.103147 | + | 0.103147i | ||||
\(889\) | 48.4695i | 0.0545214i | ||||||||
\(890\) | 72.5514 | + | 597.553i | 0.0815184 | + | 0.671408i | ||||
\(891\) | −28.2009 | −0.0316509 | ||||||||
\(892\) | 357.765 | − | 357.765i | 0.401082 | − | 0.401082i | ||||
\(893\) | −161.950 | − | 161.950i | −0.181355 | − | 0.181355i | ||||
\(894\) | − | 52.9216i | − | 0.0591965i | ||||||
\(895\) | −356.010 | + | 454.406i | −0.397777 | + | 0.507717i | ||||
\(896\) | 22.7584 | 0.0254000 | ||||||||
\(897\) | 67.8607 | − | 67.8607i | 0.0756529 | − | 0.0756529i | ||||
\(898\) | −123.814 | − | 123.814i | −0.137878 | − | 0.137878i | ||||
\(899\) | 412.435i | 0.458771i | ||||||||
\(900\) | 35.8951 | + | 145.642i | 0.0398834 | + | 0.161824i | ||||
\(901\) | −106.178 | −0.117845 | ||||||||
\(902\) | −65.8273 | + | 65.8273i | −0.0729792 | + | 0.0729792i | ||||
\(903\) | −131.741 | − | 131.741i | −0.145893 | − | 0.145893i | ||||
\(904\) | − | 400.866i | − | 0.443435i | ||||||
\(905\) | 718.344 | + | 562.795i | 0.793750 | + | 0.621873i | ||||
\(906\) | −693.656 | −0.765625 | ||||||||
\(907\) | 84.5950 | − | 84.5950i | 0.0932690 | − | 0.0932690i | −0.658933 | − | 0.752202i | \(-0.728992\pi\) |
0.752202 | + | 0.658933i | \(0.228992\pi\) | |||||||
\(908\) | −318.372 | − | 318.372i | −0.350630 | − | 0.350630i | ||||
\(909\) | − | 483.065i | − | 0.531425i | ||||||
\(910\) | −163.137 | + | 19.8071i | −0.179272 | + | 0.0217661i | ||||
\(911\) | 669.856 | 0.735297 | 0.367649 | − | 0.929965i | \(-0.380163\pi\) | ||||
0.367649 | + | 0.929965i | \(0.380163\pi\) | |||||||
\(912\) | 161.810 | − | 161.810i | 0.177424 | − | 0.177424i | ||||
\(913\) | −228.222 | − | 228.222i | −0.249969 | − | 0.249969i | ||||
\(914\) | − | 167.240i | − | 0.182976i | ||||||
\(915\) | −80.1470 | − | 660.113i | −0.0875923 | − | 0.721435i | ||||
\(916\) | 279.462 | 0.305089 | ||||||||
\(917\) | −322.142 | + | 322.142i | −0.351299 | + | 0.351299i | ||||
\(918\) | 64.7227 | + | 64.7227i | 0.0705040 | + | 0.0705040i | ||||
\(919\) | − | 1375.28i | − | 1.49650i | −0.663419 | − | 0.748248i | \(-0.730895\pi\) | ||
0.663419 | − | 0.748248i | \(-0.269105\pi\) | |||||||
\(920\) | −41.8283 | + | 53.3891i | −0.0454656 | + | 0.0580316i | ||||
\(921\) | −825.528 | −0.896338 | ||||||||
\(922\) | 350.628 | − | 350.628i | 0.380291 | − | 0.380291i | ||||
\(923\) | 1009.58 | + | 1009.58i | 1.09381 | + | 1.09381i | ||||
\(924\) | 21.8348i | 0.0236307i | ||||||||
\(925\) | 565.689 | + | 341.983i | 0.611556 | + | 0.369711i | ||||
\(926\) | 973.077 | 1.05084 | ||||||||
\(927\) | −153.602 | + | 153.602i | −0.165698 | + | 0.165698i | ||||
\(928\) | −34.6915 | − | 34.6915i | −0.0373831 | − | 0.0373831i | ||||
\(929\) | − | 713.121i | − | 0.767622i | −0.923412 | − | 0.383811i | \(-0.874611\pi\) | ||
0.923412 | − | 0.383811i | \(-0.125389\pi\) | |||||||
\(930\) | 458.471 | + | 359.194i | 0.492979 | + | 0.386231i | ||||
\(931\) | −1484.79 | −1.59483 | ||||||||
\(932\) | 127.231 | − | 127.231i | 0.136514 | − | 0.136514i | ||||
\(933\) | 251.505 | + | 251.505i | 0.269566 | + | 0.269566i | ||||
\(934\) | − | 784.319i | − | 0.839742i | ||||||
\(935\) | −193.726 | + | 23.5211i | −0.207194 | + | 0.0251562i | ||||
\(936\) | 98.0336 | 0.104737 | ||||||||
\(937\) | 38.9789 | − | 38.9789i | 0.0415997 | − | 0.0415997i | −0.686001 | − | 0.727601i | \(-0.740635\pi\) |
0.727601 | + | 0.686001i | \(0.240635\pi\) | |||||||
\(938\) | −226.545 | − | 226.545i | −0.241519 | − | 0.241519i | ||||
\(939\) | − | 125.012i | − | 0.133134i | ||||||
\(940\) | 8.35769 | + | 68.8362i | 0.00889116 | + | 0.0732301i | ||||
\(941\) | −220.600 | −0.234432 | −0.117216 | − | 0.993106i | \(-0.537397\pi\) | ||||
−0.117216 | + | 0.993106i | \(0.537397\pi\) | |||||||
\(942\) | −304.515 | + | 304.515i | −0.323264 | + | 0.323264i | ||||
\(943\) | 71.2416 | + | 71.2416i | 0.0755478 | + | 0.0755478i | ||||
\(944\) | − | 365.490i | − | 0.387172i | ||||||
\(945\) | 32.2315 | − | 41.1398i | 0.0341074 | − | 0.0435342i | ||||
\(946\) | −236.960 | −0.250486 | ||||||||
\(947\) | 266.506 | − | 266.506i | 0.281422 | − | 0.281422i | −0.552254 | − | 0.833676i | \(-0.686232\pi\) |
0.833676 | + | 0.552254i | \(0.186232\pi\) | |||||||
\(948\) | −107.324 | − | 107.324i | −0.113211 | − | 0.113211i | ||||
\(949\) | − | 1460.61i | − | 1.53910i | ||||||
\(950\) | 604.145 | − | 999.344i | 0.635942 | − | 1.05194i | ||||
\(951\) | 1018.98 | 1.07149 | ||||||||
\(952\) | 50.1120 | − | 50.1120i | 0.0526386 | − | 0.0526386i | ||||
\(953\) | 258.995 | + | 258.995i | 0.271768 | + | 0.271768i | 0.829812 | − | 0.558043i | \(-0.188448\pi\) |
−0.558043 | + | 0.829812i | \(0.688448\pi\) | |||||||
\(954\) | − | 36.1658i | − | 0.0379096i | ||||||
\(955\) | −496.887 | − | 389.293i | −0.520301 | − | 0.407636i | ||||
\(956\) | −112.903 | −0.118099 | ||||||||
\(957\) | 33.2836 | − | 33.2836i | 0.0347791 | − | 0.0347791i | ||||
\(958\) | −201.795 | − | 201.795i | −0.210642 | − | 0.210642i | ||||
\(959\) | − | 37.9312i | − | 0.0395529i | ||||||
\(960\) | −68.7770 | + | 8.35049i | −0.0716427 | + | 0.00869843i | ||||
\(961\) | 1300.44 | 1.35322 | ||||||||
\(962\) | 305.483 | − | 305.483i | 0.317550 | − | 0.317550i | ||||
\(963\) | 265.829 | + | 265.829i | 0.276042 | + | 0.276042i | ||||
\(964\) | − | 176.914i | − | 0.183521i | ||||||
\(965\) | −89.4796 | − | 736.978i | −0.0927249 | − | 0.763708i | ||||
\(966\) | 23.6307 | 0.0244624 | ||||||||
\(967\) | −648.945 | + | 648.945i | −0.671091 | + | 0.671091i | −0.957967 | − | 0.286877i | \(-0.907383\pi\) |
0.286877 | + | 0.957967i | \(0.407383\pi\) | |||||||
\(968\) | −222.363 | − | 222.363i | −0.229714 | − | 0.229714i | ||||
\(969\) | − | 712.584i | − | 0.735381i | ||||||
\(970\) | 646.896 | − | 825.689i | 0.666903 | − | 0.851226i | ||||
\(971\) | −1081.55 | −1.11385 | −0.556924 | − | 0.830563i | \(-0.688019\pi\) | ||||
−0.556924 | + | 0.830563i | \(0.688019\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −194.267 | − | 194.267i | −0.199658 | − | 0.199658i | ||||
\(974\) | − | 813.231i | − | 0.834939i | ||||||
\(975\) | 485.740 | − | 119.716i | 0.498195 | − | 0.122786i | ||||
\(976\) | 307.132 | 0.314684 | ||||||||
\(977\) | −987.221 | + | 987.221i | −1.01046 | + | 1.01046i | −0.0105173 | + | 0.999945i | \(0.503348\pi\) |
−0.999945 | + | 0.0105173i | \(0.996652\pi\) | |||||||
\(978\) | −178.323 | − | 178.323i | −0.182334 | − | 0.182334i | ||||
\(979\) | − | 266.741i | − | 0.272463i | ||||||
\(980\) | 353.865 | + | 277.240i | 0.361087 | + | 0.282898i | ||||
\(981\) | −137.990 | −0.140662 | ||||||||
\(982\) | −128.249 | + | 128.249i | −0.130599 | + | 0.130599i | ||||
\(983\) | −1025.65 | − | 1025.65i | −1.04338 | − | 1.04338i | −0.999015 | − | 0.0443674i | \(-0.985873\pi\) |
−0.0443674 | − | 0.999015i | \(-0.514127\pi\) | |||||||
\(984\) | 102.918i | 0.104591i | ||||||||
\(985\) | 1329.67 | − | 161.441i | 1.34992 | − | 0.163899i | ||||
\(986\) | −152.775 | −0.154944 | ||||||||
\(987\) | 17.0835 | − | 17.0835i | 0.0173085 | − | 0.0173085i | ||||
\(988\) | −539.666 | − | 539.666i | −0.546220 | − | 0.546220i | ||||
\(989\) | 256.450i | 0.259302i | ||||||||
\(990\) | −8.01159 | − | 65.9857i | −0.00809252 | − | 0.0666522i | ||||
\(991\) | −596.884 | −0.602304 | −0.301152 | − | 0.953576i | \(-0.597371\pi\) | ||||
−0.301152 | + | 0.953576i | \(0.597371\pi\) | |||||||
\(992\) | −190.218 | + | 190.218i | −0.191752 | + | 0.191752i | ||||
\(993\) | 764.874 | + | 764.874i | 0.770266 | + | 0.770266i | ||||
\(994\) | 351.561i | 0.353683i | ||||||||
\(995\) | −433.954 | + | 553.892i | −0.436134 | + | 0.556676i | ||||
\(996\) | −356.814 | −0.358247 | ||||||||
\(997\) | 22.8112 | − | 22.8112i | 0.0228799 | − | 0.0228799i | −0.695574 | − | 0.718454i | \(-0.744850\pi\) |
0.718454 | + | 0.695574i | \(0.244850\pi\) | |||||||
\(998\) | −395.030 | − | 395.030i | −0.395822 | − | 0.395822i | ||||
\(999\) | 137.392i | 0.137529i |
(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 | 690.3.k.b.553.16 | yes | 48 | |
5.2 | odd | 4 | inner | 690.3.k.b.277.16 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.16 | ✓ | 48 | 5.2 | odd | 4 | inner | |
690.3.k.b.553.16 | yes | 48 | 1.1 | even | 1 | trivial |