Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([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("230.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 93.9 | ||
Character | \(\chi\) | \(=\) | 230.93 |
Dual form | 230.3.f.b.47.9 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.83776 | + | 1.83776i | 0.612587 | + | 0.612587i | 0.943619 | − | 0.331032i | \(-0.107397\pi\) |
−0.331032 | + | 0.943619i | \(0.607397\pi\) | |||||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 4.99936 | − | 0.0803026i | 0.999871 | − | 0.0160605i | ||||
\(6\) | 3.67552 | 0.612587 | ||||||||
\(7\) | 5.10553 | − | 5.10553i | 0.729361 | − | 0.729361i | −0.241131 | − | 0.970493i | \(-0.577518\pi\) |
0.970493 | + | 0.241131i | \(0.0775184\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | − | 2.24526i | − | 0.249474i | ||||||
\(10\) | 4.91905 | − | 5.07966i | 0.491905 | − | 0.507966i | ||||
\(11\) | −18.3030 | −1.66391 | −0.831957 | − | 0.554841i | \(-0.812779\pi\) | ||||
−0.831957 | + | 0.554841i | \(0.812779\pi\) | |||||||
\(12\) | 3.67552 | − | 3.67552i | 0.306294 | − | 0.306294i | ||||
\(13\) | 14.0303 | + | 14.0303i | 1.07925 | + | 1.07925i | 0.996577 | + | 0.0826745i | \(0.0263462\pi\) |
0.0826745 | + | 0.996577i | \(0.473654\pi\) | |||||||
\(14\) | − | 10.2111i | − | 0.729361i | ||||||
\(15\) | 9.33520 | + | 9.04005i | 0.622347 | + | 0.602670i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 2.44563 | − | 2.44563i | 0.143861 | − | 0.143861i | −0.631508 | − | 0.775369i | \(-0.717564\pi\) |
0.775369 | + | 0.631508i | \(0.217564\pi\) | |||||||
\(18\) | −2.24526 | − | 2.24526i | −0.124737 | − | 0.124737i | ||||
\(19\) | 9.65125i | 0.507961i | 0.967209 | + | 0.253980i | \(0.0817398\pi\) | ||||
−0.967209 | + | 0.253980i | \(0.918260\pi\) | |||||||
\(20\) | −0.160605 | − | 9.99871i | −0.00803026 | − | 0.499936i | ||||
\(21\) | 18.7655 | 0.893595 | ||||||||
\(22\) | −18.3030 | + | 18.3030i | −0.831957 | + | 0.831957i | ||||
\(23\) | −3.39116 | − | 3.39116i | −0.147442 | − | 0.147442i | ||||
\(24\) | − | 7.35105i | − | 0.306294i | ||||||
\(25\) | 24.9871 | − | 0.802922i | 0.999484 | − | 0.0321169i | ||||
\(26\) | 28.0605 | 1.07925 | ||||||||
\(27\) | 20.6661 | − | 20.6661i | 0.765412 | − | 0.765412i | ||||
\(28\) | −10.2111 | − | 10.2111i | −0.364681 | − | 0.364681i | ||||
\(29\) | 2.47273i | 0.0852666i | 0.999091 | + | 0.0426333i | \(0.0135747\pi\) | ||||
−0.999091 | + | 0.0426333i | \(0.986425\pi\) | |||||||
\(30\) | 18.3752 | − | 0.295154i | 0.612508 | − | 0.00983847i | ||||
\(31\) | −6.19311 | −0.199778 | −0.0998888 | − | 0.994999i | \(-0.531849\pi\) | ||||
−0.0998888 | + | 0.994999i | \(0.531849\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | −33.6366 | − | 33.6366i | −1.01929 | − | 1.01929i | ||||
\(34\) | − | 4.89127i | − | 0.143861i | ||||||
\(35\) | 25.1144 | − | 25.9343i | 0.717553 | − | 0.740981i | ||||
\(36\) | −4.49053 | −0.124737 | ||||||||
\(37\) | −38.0892 | + | 38.0892i | −1.02944 | + | 1.02944i | −0.0298846 | + | 0.999553i | \(0.509514\pi\) |
−0.999553 | + | 0.0298846i | \(0.990486\pi\) | |||||||
\(38\) | 9.65125 | + | 9.65125i | 0.253980 | + | 0.253980i | ||||
\(39\) | 51.5686i | 1.32227i | ||||||||
\(40\) | −10.1593 | − | 9.83811i | −0.253983 | − | 0.245953i | ||||
\(41\) | −50.7049 | −1.23670 | −0.618352 | − | 0.785901i | \(-0.712199\pi\) | ||||
−0.618352 | + | 0.785901i | \(0.712199\pi\) | |||||||
\(42\) | 18.7655 | − | 18.7655i | 0.446797 | − | 0.446797i | ||||
\(43\) | −14.7480 | − | 14.7480i | −0.342977 | − | 0.342977i | 0.514508 | − | 0.857485i | \(-0.327974\pi\) |
−0.857485 | + | 0.514508i | \(0.827974\pi\) | |||||||
\(44\) | 36.6061i | 0.831957i | ||||||||
\(45\) | −0.180300 | − | 11.2249i | −0.00400668 | − | 0.249441i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | −23.7610 | + | 23.7610i | −0.505553 | + | 0.505553i | −0.913158 | − | 0.407605i | \(-0.866364\pi\) |
0.407605 | + | 0.913158i | \(0.366364\pi\) | |||||||
\(48\) | −7.35105 | − | 7.35105i | −0.153147 | − | 0.153147i | ||||
\(49\) | − | 3.13285i | − | 0.0639357i | ||||||
\(50\) | 24.1842 | − | 25.7900i | 0.483684 | − | 0.515801i | ||||
\(51\) | 8.98898 | 0.176255 | ||||||||
\(52\) | 28.0605 | − | 28.0605i | 0.539626 | − | 0.539626i | ||||
\(53\) | 51.8572 | + | 51.8572i | 0.978438 | + | 0.978438i | 0.999772 | − | 0.0213348i | \(-0.00679160\pi\) |
−0.0213348 | + | 0.999772i | \(0.506792\pi\) | |||||||
\(54\) | − | 41.3322i | − | 0.765412i | ||||||
\(55\) | −91.5034 | + | 1.46978i | −1.66370 | + | 0.0267233i | ||||
\(56\) | −20.4221 | −0.364681 | ||||||||
\(57\) | −17.7367 | + | 17.7367i | −0.311170 | + | 0.311170i | ||||
\(58\) | 2.47273 | + | 2.47273i | 0.0426333 | + | 0.0426333i | ||||
\(59\) | − | 16.9105i | − | 0.286619i | −0.989678 | − | 0.143309i | \(-0.954226\pi\) | ||
0.989678 | − | 0.143309i | \(-0.0457744\pi\) | |||||||
\(60\) | 18.0801 | − | 18.6704i | 0.301335 | − | 0.311173i | ||||
\(61\) | −25.6655 | −0.420746 | −0.210373 | − | 0.977621i | \(-0.567468\pi\) | ||||
−0.210373 | + | 0.977621i | \(0.567468\pi\) | |||||||
\(62\) | −6.19311 | + | 6.19311i | −0.0998888 | + | 0.0998888i | ||||
\(63\) | −11.4633 | − | 11.4633i | −0.181956 | − | 0.181956i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 71.2689 | + | 69.0156i | 1.09645 | + | 1.06178i | ||||
\(66\) | −67.2733 | −1.01929 | ||||||||
\(67\) | 44.7937 | − | 44.7937i | 0.668562 | − | 0.668562i | −0.288821 | − | 0.957383i | \(-0.593263\pi\) |
0.957383 | + | 0.288821i | \(0.0932632\pi\) | |||||||
\(68\) | −4.89127 | − | 4.89127i | −0.0719304 | − | 0.0719304i | ||||
\(69\) | − | 12.4643i | − | 0.180642i | ||||||
\(70\) | −0.819974 | − | 51.0487i | −0.0117139 | − | 0.729267i | ||||
\(71\) | −36.0845 | −0.508232 | −0.254116 | − | 0.967174i | \(-0.581785\pi\) | ||||
−0.254116 | + | 0.967174i | \(0.581785\pi\) | |||||||
\(72\) | −4.49053 | + | 4.49053i | −0.0623684 | + | 0.0623684i | ||||
\(73\) | −15.7669 | − | 15.7669i | −0.215985 | − | 0.215985i | 0.590819 | − | 0.806804i | \(-0.298805\pi\) |
−0.806804 | + | 0.590819i | \(0.798805\pi\) | |||||||
\(74\) | 76.1784i | 1.02944i | ||||||||
\(75\) | 47.3959 | + | 44.4448i | 0.631946 | + | 0.592597i | ||||
\(76\) | 19.3025 | 0.253980 | ||||||||
\(77\) | −93.4467 | + | 93.4467i | −1.21359 | + | 1.21359i | ||||
\(78\) | 51.5686 | + | 51.5686i | 0.661135 | + | 0.661135i | ||||
\(79\) | 15.5648i | 0.197023i | 0.995136 | + | 0.0985115i | \(0.0314081\pi\) | ||||
−0.995136 | + | 0.0985115i | \(0.968592\pi\) | |||||||
\(80\) | −19.9974 | + | 0.321210i | −0.249968 | + | 0.00401513i | ||||
\(81\) | 55.7514 | 0.688289 | ||||||||
\(82\) | −50.7049 | + | 50.7049i | −0.618352 | + | 0.618352i | ||||
\(83\) | −96.3047 | − | 96.3047i | −1.16030 | − | 1.16030i | −0.984410 | − | 0.175887i | \(-0.943721\pi\) |
−0.175887 | − | 0.984410i | \(-0.556279\pi\) | |||||||
\(84\) | − | 37.5310i | − | 0.446797i | ||||||
\(85\) | 12.0302 | − | 12.4230i | 0.141532 | − | 0.146153i | ||||
\(86\) | −29.4960 | −0.342977 | ||||||||
\(87\) | −4.54429 | + | 4.54429i | −0.0522332 | + | 0.0522332i | ||||
\(88\) | 36.6061 | + | 36.6061i | 0.415978 | + | 0.415978i | ||||
\(89\) | − | 26.4910i | − | 0.297651i | −0.988863 | − | 0.148826i | \(-0.952451\pi\) | ||
0.988863 | − | 0.148826i | \(-0.0475493\pi\) | |||||||
\(90\) | −11.4052 | − | 11.0446i | −0.126724 | − | 0.122717i | ||||
\(91\) | 143.264 | 1.57433 | ||||||||
\(92\) | −6.78233 | + | 6.78233i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | −11.3815 | − | 11.3815i | −0.122381 | − | 0.122381i | ||||
\(94\) | 47.5220i | 0.505553i | ||||||||
\(95\) | 0.775021 | + | 48.2500i | 0.00815811 | + | 0.507895i | ||||
\(96\) | −14.7021 | −0.153147 | ||||||||
\(97\) | −94.9705 | + | 94.9705i | −0.979078 | + | 0.979078i | −0.999786 | − | 0.0207078i | \(-0.993408\pi\) |
0.0207078 | + | 0.999786i | \(0.493408\pi\) | |||||||
\(98\) | −3.13285 | − | 3.13285i | −0.0319679 | − | 0.0319679i | ||||
\(99\) | 41.0951i | 0.415102i | ||||||||
\(100\) | −1.60584 | − | 49.9742i | −0.0160584 | − | 0.499742i | ||||
\(101\) | 128.681 | 1.27407 | 0.637033 | − | 0.770837i | \(-0.280162\pi\) | ||||
0.637033 | + | 0.770837i | \(0.280162\pi\) | |||||||
\(102\) | 8.98898 | − | 8.98898i | 0.0881273 | − | 0.0881273i | ||||
\(103\) | −15.4607 | − | 15.4607i | −0.150104 | − | 0.150104i | 0.628061 | − | 0.778164i | \(-0.283849\pi\) |
−0.778164 | + | 0.628061i | \(0.783849\pi\) | |||||||
\(104\) | − | 56.1211i | − | 0.539626i | ||||||
\(105\) | 93.8154 | − | 1.50692i | 0.893480 | − | 0.0143516i | ||||
\(106\) | 103.714 | 0.978438 | ||||||||
\(107\) | −132.427 | + | 132.427i | −1.23764 | + | 1.23764i | −0.276672 | + | 0.960965i | \(0.589231\pi\) |
−0.960965 | + | 0.276672i | \(0.910769\pi\) | |||||||
\(108\) | −41.3322 | − | 41.3322i | −0.382706 | − | 0.382706i | ||||
\(109\) | 131.307i | 1.20465i | 0.798249 | + | 0.602327i | \(0.205760\pi\) | ||||
−0.798249 | + | 0.602327i | \(0.794240\pi\) | |||||||
\(110\) | −90.0336 | + | 92.9732i | −0.818488 | + | 0.845211i | ||||
\(111\) | −139.998 | −1.26124 | ||||||||
\(112\) | −20.4221 | + | 20.4221i | −0.182340 | + | 0.182340i | ||||
\(113\) | −153.282 | − | 153.282i | −1.35648 | − | 1.35648i | −0.878221 | − | 0.478256i | \(-0.841269\pi\) |
−0.478256 | − | 0.878221i | \(-0.658731\pi\) | |||||||
\(114\) | 35.4734i | 0.311170i | ||||||||
\(115\) | −17.2260 | − | 16.6813i | −0.149791 | − | 0.145055i | ||||
\(116\) | 4.94546 | 0.0426333 | ||||||||
\(117\) | 31.5016 | − | 31.5016i | 0.269245 | − | 0.269245i | ||||
\(118\) | −16.9105 | − | 16.9105i | −0.143309 | − | 0.143309i | ||||
\(119\) | − | 24.9725i | − | 0.209853i | ||||||
\(120\) | −0.590308 | − | 36.7505i | −0.00491923 | − | 0.306254i | ||||
\(121\) | 214.001 | 1.76861 | ||||||||
\(122\) | −25.6655 | + | 25.6655i | −0.210373 | + | 0.210373i | ||||
\(123\) | −93.1835 | − | 93.1835i | −0.757589 | − | 0.757589i | ||||
\(124\) | 12.3862i | 0.0998888i | ||||||||
\(125\) | 124.855 | − | 6.02062i | 0.998839 | − | 0.0481650i | ||||
\(126\) | −22.9265 | −0.181956 | ||||||||
\(127\) | −13.1904 | + | 13.1904i | −0.103861 | + | 0.103861i | −0.757128 | − | 0.653267i | \(-0.773398\pi\) |
0.653267 | + | 0.757128i | \(0.273398\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 54.2067i | − | 0.420207i | ||||||
\(130\) | 140.285 | − | 2.25333i | 1.07911 | − | 0.0173333i | ||||
\(131\) | 88.7690 | 0.677626 | 0.338813 | − | 0.940854i | \(-0.389975\pi\) | ||||
0.338813 | + | 0.940854i | \(0.389975\pi\) | |||||||
\(132\) | −67.2733 | + | 67.2733i | −0.509646 | + | 0.509646i | ||||
\(133\) | 49.2747 | + | 49.2747i | 0.370487 | + | 0.370487i | ||||
\(134\) | − | 89.5874i | − | 0.668562i | ||||||
\(135\) | 101.658 | − | 104.977i | 0.753020 | − | 0.777606i | ||||
\(136\) | −9.78253 | −0.0719304 | ||||||||
\(137\) | 180.247 | − | 180.247i | 1.31567 | − | 1.31567i | 0.398502 | − | 0.917167i | \(-0.369530\pi\) |
0.917167 | − | 0.398502i | \(-0.130470\pi\) | |||||||
\(138\) | −12.4643 | − | 12.4643i | −0.0903211 | − | 0.0903211i | ||||
\(139\) | − | 136.072i | − | 0.978932i | −0.872022 | − | 0.489466i | \(-0.837192\pi\) | ||
0.872022 | − | 0.489466i | \(-0.162808\pi\) | |||||||
\(140\) | −51.8687 | − | 50.2287i | −0.370491 | − | 0.358777i | ||||
\(141\) | −87.3341 | −0.619391 | ||||||||
\(142\) | −36.0845 | + | 36.0845i | −0.254116 | + | 0.254116i | ||||
\(143\) | −256.797 | − | 256.797i | −1.79578 | − | 1.79578i | ||||
\(144\) | 8.98105i | 0.0623684i | ||||||||
\(145\) | 0.198567 | + | 12.3621i | 0.00136943 | + | 0.0852556i | ||||
\(146\) | −31.5339 | −0.215985 | ||||||||
\(147\) | 5.75743 | − | 5.75743i | 0.0391662 | − | 0.0391662i | ||||
\(148\) | 76.1784 | + | 76.1784i | 0.514719 | + | 0.514719i | ||||
\(149\) | − | 271.727i | − | 1.82367i | −0.410557 | − | 0.911835i | \(-0.634666\pi\) | ||
0.410557 | − | 0.911835i | \(-0.365334\pi\) | |||||||
\(150\) | 91.8407 | − | 2.95116i | 0.612271 | − | 0.0196744i | ||||
\(151\) | 93.7692 | 0.620988 | 0.310494 | − | 0.950575i | \(-0.399505\pi\) | ||||
0.310494 | + | 0.950575i | \(0.399505\pi\) | |||||||
\(152\) | 19.3025 | − | 19.3025i | 0.126990 | − | 0.126990i | ||||
\(153\) | −5.49109 | − | 5.49109i | −0.0358895 | − | 0.0358895i | ||||
\(154\) | 186.893i | 1.21359i | ||||||||
\(155\) | −30.9615 | + | 0.497323i | −0.199752 | + | 0.00320853i | ||||
\(156\) | 103.137 | 0.661135 | ||||||||
\(157\) | 59.7004 | − | 59.7004i | 0.380257 | − | 0.380257i | −0.490937 | − | 0.871195i | \(-0.663346\pi\) |
0.871195 | + | 0.490937i | \(0.163346\pi\) | |||||||
\(158\) | 15.5648 | + | 15.5648i | 0.0985115 | + | 0.0985115i | ||||
\(159\) | 190.602i | 1.19876i | ||||||||
\(160\) | −19.6762 | + | 20.3186i | −0.122976 | + | 0.126991i | ||||
\(161\) | −34.6274 | −0.215077 | ||||||||
\(162\) | 55.7514 | − | 55.7514i | 0.344145 | − | 0.344145i | ||||
\(163\) | 36.7559 | + | 36.7559i | 0.225496 | + | 0.225496i | 0.810808 | − | 0.585312i | \(-0.199028\pi\) |
−0.585312 | + | 0.810808i | \(0.699028\pi\) | |||||||
\(164\) | 101.410i | 0.618352i | ||||||||
\(165\) | −170.863 | − | 165.460i | −1.03553 | − | 1.00279i | ||||
\(166\) | −192.609 | −1.16030 | ||||||||
\(167\) | 174.965 | − | 174.965i | 1.04769 | − | 1.04769i | 0.0488887 | − | 0.998804i | \(-0.484432\pi\) |
0.998804 | − | 0.0488887i | \(-0.0155680\pi\) | |||||||
\(168\) | −37.5310 | − | 37.5310i | −0.223399 | − | 0.223399i | ||||
\(169\) | 224.697i | 1.32957i | ||||||||
\(170\) | −0.392781 | − | 24.4532i | −0.00231048 | − | 0.143842i | ||||
\(171\) | 21.6696 | 0.126723 | ||||||||
\(172\) | −29.4960 | + | 29.4960i | −0.171489 | + | 0.171489i | ||||
\(173\) | 86.9948 | + | 86.9948i | 0.502860 | + | 0.502860i | 0.912326 | − | 0.409466i | \(-0.134285\pi\) |
−0.409466 | + | 0.912326i | \(0.634285\pi\) | |||||||
\(174\) | 9.08858i | 0.0522332i | ||||||||
\(175\) | 123.473 | − | 131.672i | 0.705560 | − | 0.752410i | ||||
\(176\) | 73.2122 | 0.415978 | ||||||||
\(177\) | 31.0775 | − | 31.0775i | 0.175579 | − | 0.175579i | ||||
\(178\) | −26.4910 | − | 26.4910i | −0.148826 | − | 0.148826i | ||||
\(179\) | 318.823i | 1.78113i | 0.454852 | + | 0.890567i | \(0.349692\pi\) | ||||
−0.454852 | + | 0.890567i | \(0.650308\pi\) | |||||||
\(180\) | −22.4497 | + | 0.360601i | −0.124721 | + | 0.00200334i | ||||
\(181\) | 345.259 | 1.90751 | 0.953754 | − | 0.300589i | \(-0.0971832\pi\) | ||||
0.953754 | + | 0.300589i | \(0.0971832\pi\) | |||||||
\(182\) | 143.264 | − | 143.264i | 0.787164 | − | 0.787164i | ||||
\(183\) | −47.1670 | − | 47.1670i | −0.257743 | − | 0.257743i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −187.363 | + | 193.480i | −1.01277 | + | 1.04584i | ||||
\(186\) | −22.7629 | −0.122381 | ||||||||
\(187\) | −44.7625 | + | 44.7625i | −0.239372 | + | 0.239372i | ||||
\(188\) | 47.5220 | + | 47.5220i | 0.252777 | + | 0.252777i | ||||
\(189\) | − | 211.023i | − | 1.11652i | ||||||
\(190\) | 49.0251 | + | 47.4750i | 0.258027 | + | 0.249869i | ||||
\(191\) | −81.7982 | −0.428263 | −0.214131 | − | 0.976805i | \(-0.568692\pi\) | ||||
−0.214131 | + | 0.976805i | \(0.568692\pi\) | |||||||
\(192\) | −14.7021 | + | 14.7021i | −0.0765734 | + | 0.0765734i | ||||
\(193\) | 167.652 | + | 167.652i | 0.868662 | + | 0.868662i | 0.992324 | − | 0.123662i | \(-0.0394639\pi\) |
−0.123662 | + | 0.992324i | \(0.539464\pi\) | |||||||
\(194\) | 189.941i | 0.979078i | ||||||||
\(195\) | 4.14109 | + | 257.810i | 0.0212364 | + | 1.32210i | ||||
\(196\) | −6.26570 | −0.0319679 | ||||||||
\(197\) | 8.30626 | − | 8.30626i | 0.0421637 | − | 0.0421637i | −0.685711 | − | 0.727874i | \(-0.740508\pi\) |
0.727874 | + | 0.685711i | \(0.240508\pi\) | |||||||
\(198\) | 41.0951 | + | 41.0951i | 0.207551 | + | 0.207551i | ||||
\(199\) | − | 165.150i | − | 0.829897i | −0.909845 | − | 0.414949i | \(-0.863800\pi\) | ||
0.909845 | − | 0.414949i | \(-0.136200\pi\) | |||||||
\(200\) | −51.5801 | − | 48.3684i | −0.257900 | − | 0.241842i | ||||
\(201\) | 164.640 | 0.819106 | ||||||||
\(202\) | 128.681 | − | 128.681i | 0.637033 | − | 0.637033i | ||||
\(203\) | 12.6246 | + | 12.6246i | 0.0621901 | + | 0.0621901i | ||||
\(204\) | − | 17.9780i | − | 0.0881273i | ||||||
\(205\) | −253.492 | + | 4.07173i | −1.23654 | + | 0.0198621i | ||||
\(206\) | −30.9214 | −0.150104 | ||||||||
\(207\) | −7.61406 | + | 7.61406i | −0.0367829 | + | 0.0367829i | ||||
\(208\) | −56.1211 | − | 56.1211i | −0.269813 | − | 0.269813i | ||||
\(209\) | − | 176.647i | − | 0.845202i | ||||||
\(210\) | 92.3084 | − | 95.3223i | 0.439564 | − | 0.453916i | ||||
\(211\) | 311.748 | 1.47748 | 0.738740 | − | 0.673990i | \(-0.235421\pi\) | ||||
0.738740 | + | 0.673990i | \(0.235421\pi\) | |||||||
\(212\) | 103.714 | − | 103.714i | 0.489219 | − | 0.489219i | ||||
\(213\) | −66.3147 | − | 66.3147i | −0.311337 | − | 0.311337i | ||||
\(214\) | 264.854i | 1.23764i | ||||||||
\(215\) | −74.9149 | − | 72.5463i | −0.348441 | − | 0.337425i | ||||
\(216\) | −82.6645 | −0.382706 | ||||||||
\(217\) | −31.6191 | + | 31.6191i | −0.145710 | + | 0.145710i | ||||
\(218\) | 131.307 | + | 131.307i | 0.602327 | + | 0.602327i | ||||
\(219\) | − | 57.9517i | − | 0.264620i | ||||||
\(220\) | 2.93956 | + | 183.007i | 0.0133617 | + | 0.831849i | ||||
\(221\) | 68.6257 | 0.310524 | ||||||||
\(222\) | −139.998 | + | 139.998i | −0.630621 | + | 0.630621i | ||||
\(223\) | −158.829 | − | 158.829i | −0.712240 | − | 0.712240i | 0.254764 | − | 0.967003i | \(-0.418002\pi\) |
−0.967003 | + | 0.254764i | \(0.918002\pi\) | |||||||
\(224\) | 40.8442i | 0.182340i | ||||||||
\(225\) | −1.80277 | − | 56.1026i | −0.00801232 | − | 0.249345i | ||||
\(226\) | −306.564 | −1.35648 | ||||||||
\(227\) | −222.888 | + | 222.888i | −0.981887 | + | 0.981887i | −0.999839 | − | 0.0179518i | \(-0.994285\pi\) |
0.0179518 | + | 0.999839i | \(0.494285\pi\) | |||||||
\(228\) | 35.4734 | + | 35.4734i | 0.155585 | + | 0.155585i | ||||
\(229\) | − | 28.9066i | − | 0.126230i | −0.998006 | − | 0.0631148i | \(-0.979897\pi\) | ||
0.998006 | − | 0.0631148i | \(-0.0201034\pi\) | |||||||
\(230\) | −33.9073 | + | 0.544639i | −0.147423 | + | 0.00236799i | ||||
\(231\) | −343.466 | −1.48686 | ||||||||
\(232\) | 4.94546 | − | 4.94546i | 0.0213166 | − | 0.0213166i | ||||
\(233\) | 259.464 | + | 259.464i | 1.11358 | + | 1.11358i | 0.992663 | + | 0.120918i | \(0.0385837\pi\) |
0.120918 | + | 0.992663i | \(0.461416\pi\) | |||||||
\(234\) | − | 63.0033i | − | 0.269245i | ||||||
\(235\) | −116.882 | + | 120.698i | −0.497369 | + | 0.513608i | ||||
\(236\) | −33.8210 | −0.143309 | ||||||||
\(237\) | −28.6044 | + | 28.6044i | −0.120694 | + | 0.120694i | ||||
\(238\) | −24.9725 | − | 24.9725i | −0.104926 | − | 0.104926i | ||||
\(239\) | − | 9.18860i | − | 0.0384460i | −0.999815 | − | 0.0192230i | \(-0.993881\pi\) | ||
0.999815 | − | 0.0192230i | \(-0.00611925\pi\) | |||||||
\(240\) | −37.3408 | − | 36.1602i | −0.155587 | − | 0.150667i | ||||
\(241\) | −67.4055 | −0.279691 | −0.139845 | − | 0.990173i | \(-0.544661\pi\) | ||||
−0.139845 | + | 0.990173i | \(0.544661\pi\) | |||||||
\(242\) | 214.001 | − | 214.001i | 0.884303 | − | 0.884303i | ||||
\(243\) | −83.5372 | − | 83.5372i | −0.343774 | − | 0.343774i | ||||
\(244\) | 51.3310i | 0.210373i | ||||||||
\(245\) | −0.251576 | − | 15.6622i | −0.00102684 | − | 0.0639275i | ||||
\(246\) | −186.367 | −0.757589 | ||||||||
\(247\) | −135.410 | + | 135.410i | −0.548217 | + | 0.548217i | ||||
\(248\) | 12.3862 | + | 12.3862i | 0.0499444 | + | 0.0499444i | ||||
\(249\) | − | 353.970i | − | 1.42157i | ||||||
\(250\) | 118.834 | − | 130.876i | 0.475337 | − | 0.523502i | ||||
\(251\) | −77.9583 | −0.310591 | −0.155295 | − | 0.987868i | \(-0.549633\pi\) | ||||
−0.155295 | + | 0.987868i | \(0.549633\pi\) | |||||||
\(252\) | −22.9265 | + | 22.9265i | −0.0909782 | + | 0.0909782i | ||||
\(253\) | 62.0686 | + | 62.0686i | 0.245331 | + | 0.245331i | ||||
\(254\) | 26.3807i | 0.103861i | ||||||||
\(255\) | 44.9391 | − | 0.721838i | 0.176232 | − | 0.00283074i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 277.635 | − | 277.635i | 1.08029 | − | 1.08029i | 0.0838088 | − | 0.996482i | \(-0.473291\pi\) |
0.996482 | − | 0.0838088i | \(-0.0267085\pi\) | |||||||
\(258\) | −54.2067 | − | 54.2067i | −0.210103 | − | 0.210103i | ||||
\(259\) | 388.931i | 1.50166i | ||||||||
\(260\) | 138.031 | − | 142.538i | 0.530889 | − | 0.548223i | ||||
\(261\) | 5.55193 | 0.0212718 | ||||||||
\(262\) | 88.7690 | − | 88.7690i | 0.338813 | − | 0.338813i | ||||
\(263\) | −363.481 | − | 363.481i | −1.38206 | − | 1.38206i | −0.840960 | − | 0.541097i | \(-0.818009\pi\) |
−0.541097 | − | 0.840960i | \(-0.681991\pi\) | |||||||
\(264\) | 134.547i | 0.509646i | ||||||||
\(265\) | 263.417 | + | 255.088i | 0.994026 | + | 0.962597i | ||||
\(266\) | 98.5495 | 0.370487 | ||||||||
\(267\) | 48.6841 | − | 48.6841i | 0.182337 | − | 0.182337i | ||||
\(268\) | −89.5874 | − | 89.5874i | −0.334281 | − | 0.334281i | ||||
\(269\) | 95.2110i | 0.353944i | 0.984216 | + | 0.176972i | \(0.0566303\pi\) | ||||
−0.984216 | + | 0.176972i | \(0.943370\pi\) | |||||||
\(270\) | −3.31909 | − | 206.634i | −0.0122929 | − | 0.765313i | ||||
\(271\) | 313.682 | 1.15750 | 0.578749 | − | 0.815506i | \(-0.303541\pi\) | ||||
0.578749 | + | 0.815506i | \(0.303541\pi\) | |||||||
\(272\) | −9.78253 | + | 9.78253i | −0.0359652 | + | 0.0359652i | ||||
\(273\) | 263.285 | + | 263.285i | 0.964413 | + | 0.964413i | ||||
\(274\) | − | 360.493i | − | 1.31567i | ||||||
\(275\) | −457.340 | + | 14.6959i | −1.66305 | + | 0.0534397i | ||||
\(276\) | −24.9286 | −0.0903211 | ||||||||
\(277\) | 191.916 | − | 191.916i | 0.692836 | − | 0.692836i | −0.270019 | − | 0.962855i | \(-0.587030\pi\) |
0.962855 | + | 0.270019i | \(0.0870299\pi\) | |||||||
\(278\) | −136.072 | − | 136.072i | −0.489466 | − | 0.489466i | ||||
\(279\) | 13.9052i | 0.0498393i | ||||||||
\(280\) | −102.097 | + | 1.63995i | −0.364634 | + | 0.00585696i | ||||
\(281\) | −196.577 | −0.699561 | −0.349781 | − | 0.936832i | \(-0.613744\pi\) | ||||
−0.349781 | + | 0.936832i | \(0.613744\pi\) | |||||||
\(282\) | −87.3341 | + | 87.3341i | −0.309696 | + | 0.309696i | ||||
\(283\) | 29.9409 | + | 29.9409i | 0.105798 | + | 0.105798i | 0.758024 | − | 0.652226i | \(-0.226165\pi\) |
−0.652226 | + | 0.758024i | \(0.726165\pi\) | |||||||
\(284\) | 72.1690i | 0.254116i | ||||||||
\(285\) | −87.2478 | + | 90.0964i | −0.306133 | + | 0.316128i | ||||
\(286\) | −513.593 | −1.79578 | ||||||||
\(287\) | −258.875 | + | 258.875i | −0.902004 | + | 0.902004i | ||||
\(288\) | 8.98105 | + | 8.98105i | 0.0311842 | + | 0.0311842i | ||||
\(289\) | 277.038i | 0.958608i | ||||||||
\(290\) | 12.5606 | + | 12.1635i | 0.0433125 | + | 0.0419431i | ||||
\(291\) | −349.066 | −1.19954 | ||||||||
\(292\) | −31.5339 | + | 31.5339i | −0.107993 | + | 0.107993i | ||||
\(293\) | 160.923 | + | 160.923i | 0.549227 | + | 0.549227i | 0.926217 | − | 0.376990i | \(-0.123041\pi\) |
−0.376990 | + | 0.926217i | \(0.623041\pi\) | |||||||
\(294\) | − | 11.5149i | − | 0.0391662i | ||||||
\(295\) | −1.35796 | − | 84.5416i | −0.00460324 | − | 0.286582i | ||||
\(296\) | 152.357 | 0.514719 | ||||||||
\(297\) | −378.253 | + | 378.253i | −1.27358 | + | 1.27358i | ||||
\(298\) | −271.727 | − | 271.727i | −0.911835 | − | 0.911835i | ||||
\(299\) | − | 95.1579i | − | 0.318254i | ||||||
\(300\) | 88.8895 | − | 94.7918i | 0.296298 | − | 0.315973i | ||||
\(301\) | −150.593 | −0.500309 | ||||||||
\(302\) | 93.7692 | − | 93.7692i | 0.310494 | − | 0.310494i | ||||
\(303\) | 236.484 | + | 236.484i | 0.780476 | + | 0.780476i | ||||
\(304\) | − | 38.6050i | − | 0.126990i | ||||||
\(305\) | −128.311 | + | 2.06100i | −0.420691 | + | 0.00675739i | ||||
\(306\) | −10.9822 | −0.0358895 | ||||||||
\(307\) | −173.652 | + | 173.652i | −0.565643 | + | 0.565643i | −0.930905 | − | 0.365262i | \(-0.880979\pi\) |
0.365262 | + | 0.930905i | \(0.380979\pi\) | |||||||
\(308\) | 186.893 | + | 186.893i | 0.606797 | + | 0.606797i | ||||
\(309\) | − | 56.8262i | − | 0.183903i | ||||||
\(310\) | −30.4642 | + | 31.4589i | −0.0982717 | + | 0.101480i | ||||
\(311\) | −549.290 | −1.76621 | −0.883103 | − | 0.469179i | \(-0.844550\pi\) | ||||
−0.883103 | + | 0.469179i | \(0.844550\pi\) | |||||||
\(312\) | 103.137 | − | 103.137i | 0.330568 | − | 0.330568i | ||||
\(313\) | 199.770 | + | 199.770i | 0.638244 | + | 0.638244i | 0.950122 | − | 0.311878i | \(-0.100958\pi\) |
−0.311878 | + | 0.950122i | \(0.600958\pi\) | |||||||
\(314\) | − | 119.401i | − | 0.380257i | ||||||
\(315\) | −58.2294 | − | 56.3883i | −0.184855 | − | 0.179011i | ||||
\(316\) | 31.1296 | 0.0985115 | ||||||||
\(317\) | −5.02560 | + | 5.02560i | −0.0158536 | + | 0.0158536i | −0.714989 | − | 0.699136i | \(-0.753568\pi\) |
0.699136 | + | 0.714989i | \(0.253568\pi\) | |||||||
\(318\) | 190.602 | + | 190.602i | 0.599378 | + | 0.599378i | ||||
\(319\) | − | 45.2585i | − | 0.141876i | ||||||
\(320\) | 0.642421 | + | 39.9948i | 0.00200756 | + | 0.124984i | ||||
\(321\) | −486.739 | −1.51632 | ||||||||
\(322\) | −34.6274 | + | 34.6274i | −0.107538 | + | 0.107538i | ||||
\(323\) | 23.6034 | + | 23.6034i | 0.0730756 | + | 0.0730756i | ||||
\(324\) | − | 111.503i | − | 0.344145i | ||||||
\(325\) | 361.841 | + | 339.310i | 1.11336 | + | 1.04403i | ||||
\(326\) | 73.5118 | 0.225496 | ||||||||
\(327\) | −241.312 | + | 241.312i | −0.737956 | + | 0.737956i | ||||
\(328\) | 101.410 | + | 101.410i | 0.309176 | + | 0.309176i | ||||
\(329\) | 242.625i | 0.737462i | ||||||||
\(330\) | −336.323 | + | 5.40222i | −1.01916 | + | 0.0163704i | ||||
\(331\) | −89.5027 | −0.270401 | −0.135200 | − | 0.990818i | \(-0.543168\pi\) | ||||
−0.135200 | + | 0.990818i | \(0.543168\pi\) | |||||||
\(332\) | −192.609 | + | 192.609i | −0.580149 | + | 0.580149i | ||||
\(333\) | 85.5203 | + | 85.5203i | 0.256818 | + | 0.256818i | ||||
\(334\) | − | 349.929i | − | 1.04769i | ||||||
\(335\) | 220.342 | − | 227.537i | 0.657739 | − | 0.679214i | ||||
\(336\) | −75.0620 | −0.223399 | ||||||||
\(337\) | −119.687 | + | 119.687i | −0.355156 | + | 0.355156i | −0.862024 | − | 0.506868i | \(-0.830803\pi\) |
0.506868 | + | 0.862024i | \(0.330803\pi\) | |||||||
\(338\) | 224.697 | + | 224.697i | 0.664783 | + | 0.664783i | ||||
\(339\) | − | 563.391i | − | 1.66192i | ||||||
\(340\) | −24.8460 | − | 24.0604i | −0.0730763 | − | 0.0707659i | ||||
\(341\) | 113.353 | 0.332413 | ||||||||
\(342\) | 21.6696 | − | 21.6696i | 0.0633614 | − | 0.0633614i | ||||
\(343\) | 234.176 | + | 234.176i | 0.682729 | + | 0.682729i | ||||
\(344\) | 58.9921i | 0.171489i | ||||||||
\(345\) | −1.00092 | − | 62.3135i | −0.00290121 | − | 0.180619i | ||||
\(346\) | 173.990 | 0.502860 | ||||||||
\(347\) | 234.971 | − | 234.971i | 0.677148 | − | 0.677148i | −0.282206 | − | 0.959354i | \(-0.591066\pi\) |
0.959354 | + | 0.282206i | \(0.0910660\pi\) | |||||||
\(348\) | 9.08858 | + | 9.08858i | 0.0261166 | + | 0.0261166i | ||||
\(349\) | 67.9780i | 0.194779i | 0.995246 | + | 0.0973896i | \(0.0310493\pi\) | ||||
−0.995246 | + | 0.0973896i | \(0.968951\pi\) | |||||||
\(350\) | −8.19869 | − | 255.145i | −0.0234248 | − | 0.728985i | ||||
\(351\) | 579.902 | 1.65214 | ||||||||
\(352\) | 73.2122 | − | 73.2122i | 0.207989 | − | 0.207989i | ||||
\(353\) | −295.700 | − | 295.700i | −0.837676 | − | 0.837676i | 0.150876 | − | 0.988553i | \(-0.451790\pi\) |
−0.988553 | + | 0.150876i | \(0.951790\pi\) | |||||||
\(354\) | − | 62.1549i | − | 0.175579i | ||||||
\(355\) | −180.399 | + | 2.89768i | −0.508167 | + | 0.00816248i | ||||
\(356\) | −52.9819 | −0.148826 | ||||||||
\(357\) | 45.8935 | − | 45.8935i | 0.128553 | − | 0.128553i | ||||
\(358\) | 318.823 | + | 318.823i | 0.890567 | + | 0.890567i | ||||
\(359\) | − | 214.204i | − | 0.596670i | −0.954461 | − | 0.298335i | \(-0.903569\pi\) | ||
0.954461 | − | 0.298335i | \(-0.0964312\pi\) | |||||||
\(360\) | −22.0891 | + | 22.8103i | −0.0613587 | + | 0.0633620i | ||||
\(361\) | 267.853 | 0.741976 | ||||||||
\(362\) | 345.259 | − | 345.259i | 0.953754 | − | 0.953754i | ||||
\(363\) | 393.284 | + | 393.284i | 1.08343 | + | 1.08343i | ||||
\(364\) | − | 286.528i | − | 0.787164i | ||||||
\(365\) | −80.0906 | − | 77.5584i | −0.219426 | − | 0.212489i | ||||
\(366\) | −94.3341 | −0.257743 | ||||||||
\(367\) | 234.582 | − | 234.582i | 0.639189 | − | 0.639189i | −0.311166 | − | 0.950355i | \(-0.600720\pi\) |
0.950355 | + | 0.311166i | \(0.100720\pi\) | |||||||
\(368\) | 13.5647 | + | 13.5647i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 113.846i | 0.308525i | ||||||||
\(370\) | 6.11732 | + | 380.843i | 0.0165333 | + | 1.02931i | ||||
\(371\) | 529.517 | 1.42727 | ||||||||
\(372\) | −22.7629 | + | 22.7629i | −0.0611906 | + | 0.0611906i | ||||
\(373\) | −396.584 | − | 396.584i | −1.06323 | − | 1.06323i | −0.997861 | − | 0.0653653i | \(-0.979179\pi\) |
−0.0653653 | − | 0.997861i | \(-0.520821\pi\) | |||||||
\(374\) | 89.5251i | 0.239372i | ||||||||
\(375\) | 240.518 | + | 218.389i | 0.641382 | + | 0.582371i | ||||
\(376\) | 95.0440 | 0.252777 | ||||||||
\(377\) | −34.6931 | + | 34.6931i | −0.0920240 | + | 0.0920240i | ||||
\(378\) | −211.023 | − | 211.023i | −0.558262 | − | 0.558262i | ||||
\(379\) | − | 395.959i | − | 1.04475i | −0.852717 | − | 0.522374i | \(-0.825047\pi\) | ||
0.852717 | − | 0.522374i | \(-0.174953\pi\) | |||||||
\(380\) | 96.5001 | − | 1.55004i | 0.253948 | − | 0.00407906i | ||||
\(381\) | −48.4815 | −0.127248 | ||||||||
\(382\) | −81.7982 | + | 81.7982i | −0.214131 | + | 0.214131i | ||||
\(383\) | 351.592 | + | 351.592i | 0.917996 | + | 0.917996i | 0.996884 | − | 0.0788876i | \(-0.0251368\pi\) |
−0.0788876 | + | 0.996884i | \(0.525137\pi\) | |||||||
\(384\) | 29.4042i | 0.0765734i | ||||||||
\(385\) | −459.669 | + | 474.677i | −1.19395 | + | 1.23293i | ||||
\(386\) | 335.304 | 0.868662 | ||||||||
\(387\) | −33.1132 | + | 33.1132i | −0.0855638 | + | 0.0855638i | ||||
\(388\) | 189.941 | + | 189.941i | 0.489539 | + | 0.489539i | ||||
\(389\) | − | 559.908i | − | 1.43935i | −0.694310 | − | 0.719676i | \(-0.744290\pi\) | ||
0.694310 | − | 0.719676i | \(-0.255710\pi\) | |||||||
\(390\) | 261.951 | + | 253.668i | 0.671668 | + | 0.650432i | ||||
\(391\) | −16.5871 | −0.0424222 | ||||||||
\(392\) | −6.26570 | + | 6.26570i | −0.0159839 | + | 0.0159839i | ||||
\(393\) | 163.136 | + | 163.136i | 0.415105 | + | 0.415105i | ||||
\(394\) | − | 16.6125i | − | 0.0421637i | ||||||
\(395\) | 1.24990 | + | 77.8140i | 0.00316429 | + | 0.196998i | ||||
\(396\) | 82.1903 | 0.207551 | ||||||||
\(397\) | −142.412 | + | 142.412i | −0.358720 | + | 0.358720i | −0.863341 | − | 0.504621i | \(-0.831632\pi\) |
0.504621 | + | 0.863341i | \(0.331632\pi\) | |||||||
\(398\) | −165.150 | − | 165.150i | −0.414949 | − | 0.414949i | ||||
\(399\) | 181.111i | 0.453911i | ||||||||
\(400\) | −99.9484 | + | 3.21169i | −0.249871 | + | 0.00802922i | ||||
\(401\) | −677.211 | −1.68881 | −0.844403 | − | 0.535708i | \(-0.820045\pi\) | ||||
−0.844403 | + | 0.535708i | \(0.820045\pi\) | |||||||
\(402\) | 164.640 | − | 164.640i | 0.409553 | − | 0.409553i | ||||
\(403\) | −86.8909 | − | 86.8909i | −0.215610 | − | 0.215610i | ||||
\(404\) | − | 257.361i | − | 0.637033i | ||||||
\(405\) | 278.721 | − | 4.47698i | 0.688200 | − | 0.0110543i | ||||
\(406\) | 25.2492 | 0.0621901 | ||||||||
\(407\) | 697.148 | − | 697.148i | 1.71290 | − | 1.71290i | ||||
\(408\) | −17.9780 | − | 17.9780i | −0.0440636 | − | 0.0440636i | ||||
\(409\) | − | 349.594i | − | 0.854753i | −0.904074 | − | 0.427376i | \(-0.859438\pi\) | ||
0.904074 | − | 0.427376i | \(-0.140562\pi\) | |||||||
\(410\) | −249.420 | + | 257.563i | −0.608341 | + | 0.628203i | ||||
\(411\) | 662.501 | 1.61192 | ||||||||
\(412\) | −30.9214 | + | 30.9214i | −0.0750519 | + | 0.0750519i | ||||
\(413\) | −86.3370 | − | 86.3370i | −0.209048 | − | 0.209048i | ||||
\(414\) | 15.2281i | 0.0367829i | ||||||||
\(415\) | −489.195 | − | 473.728i | −1.17878 | − | 1.14151i | ||||
\(416\) | −112.242 | −0.269813 | ||||||||
\(417\) | 250.067 | − | 250.067i | 0.599681 | − | 0.599681i | ||||
\(418\) | −176.647 | − | 176.647i | −0.422601 | − | 0.422601i | ||||
\(419\) | 127.172i | 0.303513i | 0.988418 | + | 0.151756i | \(0.0484929\pi\) | ||||
−0.988418 | + | 0.151756i | \(0.951507\pi\) | |||||||
\(420\) | −3.01384 | − | 187.631i | −0.00717580 | − | 0.446740i | ||||
\(421\) | 123.176 | 0.292580 | 0.146290 | − | 0.989242i | \(-0.453267\pi\) | ||||
0.146290 | + | 0.989242i | \(0.453267\pi\) | |||||||
\(422\) | 311.748 | − | 311.748i | 0.738740 | − | 0.738740i | ||||
\(423\) | 53.3497 | + | 53.3497i | 0.126122 | + | 0.126122i | ||||
\(424\) | − | 207.429i | − | 0.489219i | ||||||
\(425\) | 59.1456 | − | 63.0729i | 0.139166 | − | 0.148407i | ||||
\(426\) | −132.629 | −0.311337 | ||||||||
\(427\) | −131.036 | + | 131.036i | −0.306876 | + | 0.306876i | ||||
\(428\) | 264.854 | + | 264.854i | 0.618818 | + | 0.618818i | ||||
\(429\) | − | 943.862i | − | 2.20014i | ||||||
\(430\) | −147.461 | + | 2.36861i | −0.342933 | + | 0.00550839i | ||||
\(431\) | 158.451 | 0.367636 | 0.183818 | − | 0.982960i | \(-0.441154\pi\) | ||||
0.183818 | + | 0.982960i | \(0.441154\pi\) | |||||||
\(432\) | −82.6645 | + | 82.6645i | −0.191353 | + | 0.191353i | ||||
\(433\) | −384.013 | − | 384.013i | −0.886867 | − | 0.886867i | 0.107354 | − | 0.994221i | \(-0.465762\pi\) |
−0.994221 | + | 0.107354i | \(0.965762\pi\) | |||||||
\(434\) | 63.2382i | 0.145710i | ||||||||
\(435\) | −22.3536 | + | 23.0834i | −0.0513876 | + | 0.0530654i | ||||
\(436\) | 262.615 | 0.602327 | ||||||||
\(437\) | 32.7290 | − | 32.7290i | 0.0748947 | − | 0.0748947i | ||||
\(438\) | −57.9517 | − | 57.9517i | −0.132310 | − | 0.132310i | ||||
\(439\) | 744.209i | 1.69524i | 0.530607 | + | 0.847618i | \(0.321964\pi\) | ||||
−0.530607 | + | 0.847618i | \(0.678036\pi\) | |||||||
\(440\) | 185.946 | + | 180.067i | 0.422605 | + | 0.409244i | ||||
\(441\) | −7.03407 | −0.0159503 | ||||||||
\(442\) | 68.6257 | − | 68.6257i | 0.155262 | − | 0.155262i | ||||
\(443\) | −56.2374 | − | 56.2374i | −0.126947 | − | 0.126947i | 0.640779 | − | 0.767726i | \(-0.278612\pi\) |
−0.767726 | + | 0.640779i | \(0.778612\pi\) | |||||||
\(444\) | 279.996i | 0.630621i | ||||||||
\(445\) | −2.12729 | − | 132.438i | −0.00478043 | − | 0.297613i | ||||
\(446\) | −317.659 | −0.712240 | ||||||||
\(447\) | 499.369 | − | 499.369i | 1.11716 | − | 1.11716i | ||||
\(448\) | 40.8442 | + | 40.8442i | 0.0911702 | + | 0.0911702i | ||||
\(449\) | 338.053i | 0.752903i | 0.926436 | + | 0.376452i | \(0.122856\pi\) | ||||
−0.926436 | + | 0.376452i | \(0.877144\pi\) | |||||||
\(450\) | −57.9054 | − | 54.2998i | −0.128679 | − | 0.120666i | ||||
\(451\) | 928.053 | 2.05777 | ||||||||
\(452\) | −306.564 | + | 306.564i | −0.678238 | + | 0.678238i | ||||
\(453\) | 172.326 | + | 172.326i | 0.380410 | + | 0.380410i | ||||
\(454\) | 445.777i | 0.981887i | ||||||||
\(455\) | 716.227 | − | 11.5045i | 1.57412 | − | 0.0252845i | ||||
\(456\) | 70.9468 | 0.155585 | ||||||||
\(457\) | −170.026 | + | 170.026i | −0.372048 | + | 0.372048i | −0.868223 | − | 0.496175i | \(-0.834737\pi\) |
0.496175 | + | 0.868223i | \(0.334737\pi\) | |||||||
\(458\) | −28.9066 | − | 28.9066i | −0.0631148 | − | 0.0631148i | ||||
\(459\) | − | 101.083i | − | 0.220225i | ||||||
\(460\) | −33.3626 | + | 34.4519i | −0.0725275 | + | 0.0748955i | ||||
\(461\) | −645.832 | −1.40094 | −0.700469 | − | 0.713683i | \(-0.747026\pi\) | ||||
−0.700469 | + | 0.713683i | \(0.747026\pi\) | |||||||
\(462\) | −343.466 | + | 343.466i | −0.743432 | + | 0.743432i | ||||
\(463\) | −94.2218 | − | 94.2218i | −0.203503 | − | 0.203503i | 0.597996 | − | 0.801499i | \(-0.295964\pi\) |
−0.801499 | + | 0.597996i | \(0.795964\pi\) | |||||||
\(464\) | − | 9.89092i | − | 0.0213166i | ||||||
\(465\) | −57.8139 | − | 55.9860i | −0.124331 | − | 0.120400i | ||||
\(466\) | 518.928 | 1.11358 | ||||||||
\(467\) | 361.092 | − | 361.092i | 0.773216 | − | 0.773216i | −0.205451 | − | 0.978667i | \(-0.565866\pi\) |
0.978667 | + | 0.205451i | \(0.0658661\pi\) | |||||||
\(468\) | −63.0033 | − | 63.0033i | −0.134622 | − | 0.134622i | ||||
\(469\) | − | 457.391i | − | 0.975247i | ||||||
\(470\) | 3.81614 | + | 237.579i | 0.00811945 | + | 0.505488i | ||||
\(471\) | 219.430 | 0.465882 | ||||||||
\(472\) | −33.8210 | + | 33.8210i | −0.0716546 | + | 0.0716546i | ||||
\(473\) | 269.934 | + | 269.934i | 0.570684 | + | 0.570684i | ||||
\(474\) | 57.2089i | 0.120694i | ||||||||
\(475\) | 7.74921 | + | 241.157i | 0.0163141 | + | 0.507699i | ||||
\(476\) | −49.9450 | −0.104926 | ||||||||
\(477\) | 116.433 | − | 116.433i | 0.244094 | − | 0.244094i | ||||
\(478\) | −9.18860 | − | 9.18860i | −0.0192230 | − | 0.0192230i | ||||
\(479\) | 617.686i | 1.28953i | 0.764380 | + | 0.644766i | \(0.223045\pi\) | ||||
−0.764380 | + | 0.644766i | \(0.776955\pi\) | |||||||
\(480\) | −73.5010 | + | 1.18062i | −0.153127 | + | 0.00245962i | ||||
\(481\) | −1068.80 | −2.22204 | ||||||||
\(482\) | −67.4055 | + | 67.4055i | −0.139845 | + | 0.139845i | ||||
\(483\) | −63.6369 | − | 63.6369i | −0.131753 | − | 0.131753i | ||||
\(484\) | − | 428.003i | − | 0.884303i | ||||||
\(485\) | −467.165 | + | 482.418i | −0.963227 | + | 0.994676i | ||||
\(486\) | −167.074 | −0.343774 | ||||||||
\(487\) | −393.032 | + | 393.032i | −0.807047 | + | 0.807047i | −0.984186 | − | 0.177139i | \(-0.943316\pi\) |
0.177139 | + | 0.984186i | \(0.443316\pi\) | |||||||
\(488\) | 51.3310 | + | 51.3310i | 0.105186 | + | 0.105186i | ||||
\(489\) | 135.097i | 0.276273i | ||||||||
\(490\) | −15.9138 | − | 15.4107i | −0.0324772 | − | 0.0314503i | ||||
\(491\) | −896.627 | −1.82612 | −0.913062 | − | 0.407821i | \(-0.866289\pi\) | ||||
−0.913062 | + | 0.407821i | \(0.866289\pi\) | |||||||
\(492\) | −186.367 | + | 186.367i | −0.378795 | + | 0.378795i | ||||
\(493\) | 6.04739 | + | 6.04739i | 0.0122665 | + | 0.0122665i | ||||
\(494\) | 270.819i | 0.548217i | ||||||||
\(495\) | 3.30005 | + | 205.449i | 0.00666676 | + | 0.415049i | ||||
\(496\) | 24.7724 | 0.0499444 | ||||||||
\(497\) | −184.230 | + | 184.230i | −0.370685 | + | 0.370685i | ||||
\(498\) | −353.970 | − | 353.970i | −0.710783 | − | 0.710783i | ||||
\(499\) | − | 699.998i | − | 1.40280i | −0.712767 | − | 0.701401i | \(-0.752558\pi\) | ||
0.712767 | − | 0.701401i | \(-0.247442\pi\) | |||||||
\(500\) | −12.0412 | − | 249.710i | −0.0240825 | − | 0.499420i | ||||
\(501\) | 643.087 | 1.28361 | ||||||||
\(502\) | −77.9583 | + | 77.9583i | −0.155295 | + | 0.155295i | ||||
\(503\) | −471.150 | − | 471.150i | −0.936679 | − | 0.936679i | 0.0614321 | − | 0.998111i | \(-0.480433\pi\) |
−0.998111 | + | 0.0614321i | \(0.980433\pi\) | |||||||
\(504\) | 45.8530i | 0.0909782i | ||||||||
\(505\) | 643.320 | − | 10.3334i | 1.27390 | − | 0.0204621i | ||||
\(506\) | 124.137 | 0.245331 | ||||||||
\(507\) | −412.939 | + | 412.939i | −0.814475 | + | 0.814475i | ||||
\(508\) | 26.3807 | + | 26.3807i | 0.0519305 | + | 0.0519305i | ||||
\(509\) | − | 574.088i | − | 1.12787i | −0.825818 | − | 0.563937i | \(-0.809286\pi\) | ||
0.825818 | − | 0.563937i | \(-0.190714\pi\) | |||||||
\(510\) | 44.2173 | − | 45.6609i | 0.0867005 | − | 0.0895313i | ||||
\(511\) | −160.997 | −0.315063 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 199.454 | + | 199.454i | 0.388799 | + | 0.388799i | ||||
\(514\) | − | 555.269i | − | 1.08029i | ||||||
\(515\) | −78.5351 | − | 76.0520i | −0.152495 | − | 0.147674i | ||||
\(516\) | −108.413 | −0.210103 | ||||||||
\(517\) | 434.899 | − | 434.899i | 0.841197 | − | 0.841197i | ||||
\(518\) | 388.931 | + | 388.931i | 0.750832 | + | 0.750832i | ||||
\(519\) | 319.751i | 0.616091i | ||||||||
\(520\) | −4.50667 | − | 280.569i | −0.00866667 | − | 0.539556i | ||||
\(521\) | −468.012 | −0.898296 | −0.449148 | − | 0.893457i | \(-0.648272\pi\) | ||||
−0.449148 | + | 0.893457i | \(0.648272\pi\) | |||||||
\(522\) | 5.55193 | − | 5.55193i | 0.0106359 | − | 0.0106359i | ||||
\(523\) | 705.372 | + | 705.372i | 1.34870 | + | 1.34870i | 0.887072 | + | 0.461632i | \(0.152736\pi\) |
0.461632 | + | 0.887072i | \(0.347264\pi\) | |||||||
\(524\) | − | 177.538i | − | 0.338813i | ||||||
\(525\) | 468.895 | − | 15.0672i | 0.893134 | − | 0.0286995i | ||||
\(526\) | −726.962 | −1.38206 | ||||||||
\(527\) | −15.1461 | + | 15.1461i | −0.0287402 | + | 0.0287402i | ||||
\(528\) | 134.547 | + | 134.547i | 0.254823 | + | 0.254823i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | 518.505 | − | 8.32853i | 0.978311 | − | 0.0157142i | ||||
\(531\) | −37.9685 | −0.0715038 | ||||||||
\(532\) | 98.5495 | − | 98.5495i | 0.185243 | − | 0.185243i | ||||
\(533\) | −711.403 | − | 711.403i | −1.33471 | − | 1.33471i | ||||
\(534\) | − | 97.3681i | − | 0.182337i | ||||||
\(535\) | −651.416 | + | 672.684i | −1.21760 | + | 1.25735i | ||||
\(536\) | −179.175 | −0.334281 | ||||||||
\(537\) | −585.921 | + | 585.921i | −1.09110 | + | 1.09110i | ||||
\(538\) | 95.2110 | + | 95.2110i | 0.176972 | + | 0.176972i | ||||
\(539\) | 57.3407i | 0.106383i | ||||||||
\(540\) | −209.954 | − | 203.315i | −0.388803 | − | 0.376510i | ||||
\(541\) | 277.505 | 0.512947 | 0.256474 | − | 0.966551i | \(-0.417439\pi\) | ||||
0.256474 | + | 0.966551i | \(0.417439\pi\) | |||||||
\(542\) | 313.682 | − | 313.682i | 0.578749 | − | 0.578749i | ||||
\(543\) | 634.504 | + | 634.504i | 1.16851 | + | 1.16851i | ||||
\(544\) | 19.5651i | 0.0359652i | ||||||||
\(545\) | 10.5443 | + | 656.452i | 0.0193474 | + | 1.20450i | ||||
\(546\) | 526.570 | 0.964413 | ||||||||
\(547\) | 264.729 | − | 264.729i | 0.483965 | − | 0.483965i | −0.422430 | − | 0.906395i | \(-0.638823\pi\) |
0.906395 | + | 0.422430i | \(0.138823\pi\) | |||||||
\(548\) | −360.493 | − | 360.493i | −0.657835 | − | 0.657835i | ||||
\(549\) | 57.6258i | 0.104965i | ||||||||
\(550\) | −442.644 | + | 472.036i | −0.804808 | + | 0.858247i | ||||
\(551\) | −23.8649 | −0.0433121 | ||||||||
\(552\) | −24.9286 | + | 24.9286i | −0.0451605 | + | 0.0451605i | ||||
\(553\) | 79.4666 | + | 79.4666i | 0.143701 | + | 0.143701i | ||||
\(554\) | − | 383.831i | − | 0.692836i | ||||||
\(555\) | −699.899 | + | 11.2422i | −1.26108 | + | 0.0202562i | ||||
\(556\) | −272.143 | −0.489466 | ||||||||
\(557\) | −336.498 | + | 336.498i | −0.604125 | + | 0.604125i | −0.941405 | − | 0.337279i | \(-0.890493\pi\) |
0.337279 | + | 0.941405i | \(0.390493\pi\) | |||||||
\(558\) | 13.9052 | + | 13.9052i | 0.0249196 | + | 0.0249196i | ||||
\(559\) | − | 413.837i | − | 0.740317i | ||||||
\(560\) | −100.457 | + | 103.737i | −0.179388 | + | 0.185245i | ||||
\(561\) | −164.526 | −0.293272 | ||||||||
\(562\) | −196.577 | + | 196.577i | −0.349781 | + | 0.349781i | ||||
\(563\) | −40.9563 | − | 40.9563i | −0.0727465 | − | 0.0727465i | 0.669797 | − | 0.742544i | \(-0.266381\pi\) |
−0.742544 | + | 0.669797i | \(0.766381\pi\) | |||||||
\(564\) | 174.668i | 0.309696i | ||||||||
\(565\) | −778.619 | − | 754.001i | −1.37809 | − | 1.33452i | ||||
\(566\) | 59.8819 | 0.105798 | ||||||||
\(567\) | 284.641 | − | 284.641i | 0.502012 | − | 0.502012i | ||||
\(568\) | 72.1690 | + | 72.1690i | 0.127058 | + | 0.127058i | ||||
\(569\) | − | 33.7512i | − | 0.0593168i | −0.999560 | − | 0.0296584i | \(-0.990558\pi\) | ||
0.999560 | − | 0.0296584i | \(-0.00944194\pi\) | |||||||
\(570\) | 2.84861 | + | 177.344i | 0.00499756 | + | 0.311130i | ||||
\(571\) | 669.004 | 1.17164 | 0.585818 | − | 0.810443i | \(-0.300773\pi\) | ||||
0.585818 | + | 0.810443i | \(0.300773\pi\) | |||||||
\(572\) | −513.593 | + | 513.593i | −0.897890 | + | 0.897890i | ||||
\(573\) | −150.326 | − | 150.326i | −0.262348 | − | 0.262348i | ||||
\(574\) | 517.750i | 0.902004i | ||||||||
\(575\) | −87.4582 | − | 82.0125i | −0.152101 | − | 0.142631i | ||||
\(576\) | 17.9621 | 0.0311842 | ||||||||
\(577\) | −19.7627 | + | 19.7627i | −0.0342508 | + | 0.0342508i | −0.724025 | − | 0.689774i | \(-0.757710\pi\) |
0.689774 | + | 0.724025i | \(0.257710\pi\) | |||||||
\(578\) | 277.038 | + | 277.038i | 0.479304 | + | 0.479304i | ||||
\(579\) | 616.208i | 1.06426i | ||||||||
\(580\) | 24.7241 | − | 0.397133i | 0.0426278 | − | 0.000684713i | ||||
\(581\) | −983.372 | −1.69255 | ||||||||
\(582\) | −349.066 | + | 349.066i | −0.599771 | + | 0.599771i | ||||
\(583\) | −949.144 | − | 949.144i | −1.62804 | − | 1.62804i | ||||
\(584\) | 63.0677i | 0.107993i | ||||||||
\(585\) | 154.958 | − | 160.017i | 0.264886 | − | 0.273534i | ||||
\(586\) | 321.847 | 0.549227 | ||||||||
\(587\) | 747.545 | − | 747.545i | 1.27350 | − | 1.27350i | 0.329262 | − | 0.944239i | \(-0.393200\pi\) |
0.944239 | − | 0.329262i | \(-0.106800\pi\) | |||||||
\(588\) | −11.5149 | − | 11.5149i | −0.0195831 | − | 0.0195831i | ||||
\(589\) | − | 59.7712i | − | 0.101479i | ||||||
\(590\) | −85.8995 | − | 83.1836i | −0.145592 | − | 0.140989i | ||||
\(591\) | 30.5298 | 0.0516579 | ||||||||
\(592\) | 152.357 | − | 152.357i | 0.257359 | − | 0.257359i | ||||
\(593\) | 336.503 | + | 336.503i | 0.567459 | + | 0.567459i | 0.931416 | − | 0.363957i | \(-0.118574\pi\) |
−0.363957 | + | 0.931416i | \(0.618574\pi\) | |||||||
\(594\) | 756.506i | 1.27358i | ||||||||
\(595\) | −2.00536 | − | 124.846i | −0.00337035 | − | 0.209826i | ||||
\(596\) | −543.454 | −0.911835 | ||||||||
\(597\) | 303.505 | − | 303.505i | 0.508384 | − | 0.508384i | ||||
\(598\) | −95.1579 | − | 95.1579i | −0.159127 | − | 0.159127i | ||||
\(599\) | 888.211i | 1.48282i | 0.671050 | + | 0.741412i | \(0.265843\pi\) | ||||
−0.671050 | + | 0.741412i | \(0.734157\pi\) | |||||||
\(600\) | −5.90232 | − | 183.681i | −0.00983720 | − | 0.306136i | ||||
\(601\) | −337.568 | −0.561676 | −0.280838 | − | 0.959755i | \(-0.590612\pi\) | ||||
−0.280838 | + | 0.959755i | \(0.590612\pi\) | |||||||
\(602\) | −150.593 | + | 150.593i | −0.250154 | + | 0.250154i | ||||
\(603\) | −100.574 | − | 100.574i | −0.166789 | − | 0.166789i | ||||
\(604\) | − | 187.538i | − | 0.310494i | ||||||
\(605\) | 1069.87 | − | 17.1849i | 1.76838 | − | 0.0284047i | ||||
\(606\) | 472.969 | 0.780476 | ||||||||
\(607\) | −214.915 | + | 214.915i | −0.354061 | + | 0.354061i | −0.861618 | − | 0.507557i | \(-0.830549\pi\) |
0.507557 | + | 0.861618i | \(0.330549\pi\) | |||||||
\(608\) | −38.6050 | − | 38.6050i | −0.0634951 | − | 0.0634951i | ||||
\(609\) | 46.4020i | 0.0761938i | ||||||||
\(610\) | −126.250 | + | 130.372i | −0.206967 | + | 0.213724i | ||||
\(611\) | −666.746 | −1.09124 | ||||||||
\(612\) | −10.9822 | + | 10.9822i | −0.0179447 | + | 0.0179447i | ||||
\(613\) | −224.804 | − | 224.804i | −0.366728 | − | 0.366728i | 0.499554 | − | 0.866283i | \(-0.333497\pi\) |
−0.866283 | + | 0.499554i | \(0.833497\pi\) | |||||||
\(614\) | 347.305i | 0.565643i | ||||||||
\(615\) | −473.340 | − | 458.374i | −0.769659 | − | 0.745324i | ||||
\(616\) | 373.787 | 0.606797 | ||||||||
\(617\) | −45.7498 | + | 45.7498i | −0.0741487 | + | 0.0741487i | −0.743209 | − | 0.669060i | \(-0.766697\pi\) |
0.669060 | + | 0.743209i | \(0.266697\pi\) | |||||||
\(618\) | −56.8262 | − | 56.8262i | −0.0919517 | − | 0.0919517i | ||||
\(619\) | − | 984.136i | − | 1.58988i | −0.606688 | − | 0.794940i | \(-0.707502\pi\) | ||
0.606688 | − | 0.794940i | \(-0.292498\pi\) | |||||||
\(620\) | 0.994645 | + | 61.9231i | 0.00160427 | + | 0.0998759i | ||||
\(621\) | −140.164 | −0.225708 | ||||||||
\(622\) | −549.290 | + | 549.290i | −0.883103 | + | 0.883103i | ||||
\(623\) | −135.250 | − | 135.250i | −0.217095 | − | 0.217095i | ||||
\(624\) | − | 206.274i | − | 0.330568i | ||||||
\(625\) | 623.711 | − | 40.1254i | 0.997937 | − | 0.0642006i | ||||
\(626\) | 399.541 | 0.638244 | ||||||||
\(627\) | 324.636 | − | 324.636i | 0.517760 | − | 0.517760i | ||||
\(628\) | −119.401 | − | 119.401i | −0.190129 | − | 0.190129i | ||||
\(629\) | 186.304i | 0.296191i | ||||||||
\(630\) | −114.618 | + | 1.84106i | −0.181933 | + | 0.00292231i | ||||
\(631\) | 496.798 | 0.787318 | 0.393659 | − | 0.919257i | \(-0.371209\pi\) | ||||
0.393659 | + | 0.919257i | \(0.371209\pi\) | |||||||
\(632\) | 31.1296 | − | 31.1296i | 0.0492558 | − | 0.0492558i | ||||
\(633\) | 572.919 | + | 572.919i | 0.905086 | + | 0.905086i | ||||
\(634\) | 10.0512i | 0.0158536i | ||||||||
\(635\) | −64.8841 | + | 67.0025i | −0.102180 | + | 0.105516i | ||||
\(636\) | 381.205 | 0.599378 | ||||||||
\(637\) | 43.9547 | − | 43.9547i | 0.0690027 | − | 0.0690027i | ||||
\(638\) | −45.2585 | − | 45.2585i | −0.0709381 | − | 0.0709381i | ||||
\(639\) | 81.0192i | 0.126791i | ||||||||
\(640\) | 40.6373 | + | 39.3524i | 0.0634957 | + | 0.0614882i | ||||
\(641\) | 549.603 | 0.857415 | 0.428708 | − | 0.903443i | \(-0.358969\pi\) | ||||
0.428708 | + | 0.903443i | \(0.358969\pi\) | |||||||
\(642\) | −486.739 | + | 486.739i | −0.758160 | + | 0.758160i | ||||
\(643\) | −175.464 | − | 175.464i | −0.272883 | − | 0.272883i | 0.557377 | − | 0.830260i | \(-0.311808\pi\) |
−0.830260 | + | 0.557377i | \(0.811808\pi\) | |||||||
\(644\) | 69.2548i | 0.107538i | ||||||||
\(645\) | −4.35294 | − | 270.998i | −0.00674874 | − | 0.420153i | ||||
\(646\) | 47.2068 | 0.0730756 | ||||||||
\(647\) | 453.474 | − | 453.474i | 0.700886 | − | 0.700886i | −0.263714 | − | 0.964601i | \(-0.584948\pi\) |
0.964601 | + | 0.263714i | \(0.0849476\pi\) | |||||||
\(648\) | −111.503 | − | 111.503i | −0.172072 | − | 0.172072i | ||||
\(649\) | 309.514i | 0.476908i | ||||||||
\(650\) | 701.151 | − | 22.5304i | 1.07869 | − | 0.0346622i | ||||
\(651\) | −116.217 | −0.178520 | ||||||||
\(652\) | 73.5118 | − | 73.5118i | 0.112748 | − | 0.112748i | ||||
\(653\) | −108.171 | − | 108.171i | −0.165652 | − | 0.165652i | 0.619413 | − | 0.785065i | \(-0.287371\pi\) |
−0.785065 | + | 0.619413i | \(0.787371\pi\) | |||||||
\(654\) | 482.623i | 0.737956i | ||||||||
\(655\) | 443.788 | − | 7.12838i | 0.677539 | − | 0.0108830i | ||||
\(656\) | 202.819 | 0.309176 | ||||||||
\(657\) | −35.4009 | + | 35.4009i | −0.0538827 | + | 0.0538827i | ||||
\(658\) | 242.625 | + | 242.625i | 0.368731 | + | 0.368731i | ||||
\(659\) | 746.059i | 1.13211i | 0.824368 | + | 0.566054i | \(0.191531\pi\) | ||||
−0.824368 | + | 0.566054i | \(0.808469\pi\) | |||||||
\(660\) | −330.921 | + | 341.725i | −0.501395 | + | 0.517765i | ||||
\(661\) | −129.940 | −0.196580 | −0.0982902 | − | 0.995158i | \(-0.531337\pi\) | ||||
−0.0982902 | + | 0.995158i | \(0.531337\pi\) | |||||||
\(662\) | −89.5027 | + | 89.5027i | −0.135200 | + | 0.135200i | ||||
\(663\) | 126.118 | + | 126.118i | 0.190223 | + | 0.190223i | ||||
\(664\) | 385.219i | 0.580149i | ||||||||
\(665\) | 250.299 | + | 242.385i | 0.376389 | + | 0.364489i | ||||
\(666\) | 171.041 | 0.256818 | ||||||||
\(667\) | 8.38544 | − | 8.38544i | 0.0125719 | − | 0.0125719i | ||||
\(668\) | −349.929 | − | 349.929i | −0.523846 | − | 0.523846i | ||||
\(669\) | − | 583.781i | − | 0.872618i | ||||||
\(670\) | −7.19410 | − | 447.879i | −0.0107375 | − | 0.668476i | ||||
\(671\) | 469.756 | 0.700084 | ||||||||
\(672\) | −75.0620 | + | 75.0620i | −0.111699 | + | 0.111699i | ||||
\(673\) | −343.345 | − | 343.345i | −0.510171 | − | 0.510171i | 0.404408 | − | 0.914579i | \(-0.367478\pi\) |
−0.914579 | + | 0.404408i | \(0.867478\pi\) | |||||||
\(674\) | 239.375i | 0.355156i | ||||||||
\(675\) | 499.793 | − | 532.980i | 0.740434 | − | 0.789599i | ||||
\(676\) | 449.393 | 0.664783 | ||||||||
\(677\) | −334.906 | + | 334.906i | −0.494691 | + | 0.494691i | −0.909781 | − | 0.415089i | \(-0.863750\pi\) |
0.415089 | + | 0.909781i | \(0.363750\pi\) | |||||||
\(678\) | −563.391 | − | 563.391i | −0.830960 | − | 0.830960i | ||||
\(679\) | 969.750i | 1.42820i | ||||||||
\(680\) | −48.9063 | + | 0.785563i | −0.0719211 | + | 0.00115524i | ||||
\(681\) | −819.231 | −1.20298 | ||||||||
\(682\) | 113.353 | − | 113.353i | 0.166206 | − | 0.166206i | ||||
\(683\) | 242.992 | + | 242.992i | 0.355772 | + | 0.355772i | 0.862252 | − | 0.506480i | \(-0.169054\pi\) |
−0.506480 | + | 0.862252i | \(0.669054\pi\) | |||||||
\(684\) | − | 43.3392i | − | 0.0633614i | ||||||
\(685\) | 886.643 | − | 915.592i | 1.29437 | − | 1.33663i | ||||
\(686\) | 468.352 | 0.682729 | ||||||||
\(687\) | 53.1234 | − | 53.1234i | 0.0773267 | − | 0.0773267i | ||||
\(688\) | 58.9921 | + | 58.9921i | 0.0857443 | + | 0.0857443i | ||||
\(689\) | 1455.14i | 2.11196i | ||||||||
\(690\) | −63.3144 | − | 61.3126i | −0.0917600 | − | 0.0888588i | ||||
\(691\) | −369.702 | −0.535025 | −0.267512 | − | 0.963554i | \(-0.586202\pi\) | ||||
−0.267512 | + | 0.963554i | \(0.586202\pi\) | |||||||
\(692\) | 173.990 | − | 173.990i | 0.251430 | − | 0.251430i | ||||
\(693\) | 209.812 | + | 209.812i | 0.302760 | + | 0.302760i | ||||
\(694\) | − | 469.941i | − | 0.677148i | ||||||
\(695\) | −10.9269 | − | 680.270i | −0.0157222 | − | 0.978806i | ||||
\(696\) | 18.1772 | 0.0261166 | ||||||||
\(697\) | −124.005 | + | 124.005i | −0.177913 | + | 0.177913i | ||||
\(698\) | 67.9780 | + | 67.9780i | 0.0973896 | + | 0.0973896i | ||||
\(699\) | 953.667i | 1.36433i | ||||||||
\(700\) | −263.343 | − | 246.946i | −0.376205 | − | 0.352780i | ||||
\(701\) | −72.5797 | −0.103537 | −0.0517687 | − | 0.998659i | \(-0.516486\pi\) | ||||
−0.0517687 | + | 0.998659i | \(0.516486\pi\) | |||||||
\(702\) | 579.902 | − | 579.902i | 0.826071 | − | 0.826071i | ||||
\(703\) | −367.609 | − | 367.609i | −0.522914 | − | 0.522914i | ||||
\(704\) | − | 146.424i | − | 0.207989i | ||||||
\(705\) | −436.614 | + | 7.01316i | −0.619311 | + | 0.00994774i | ||||
\(706\) | −591.399 | −0.837676 | ||||||||
\(707\) | 656.982 | − | 656.982i | 0.929254 | − | 0.929254i | ||||
\(708\) | −62.1549 | − | 62.1549i | −0.0877894 | − | 0.0877894i | ||||
\(709\) | 171.177i | 0.241435i | 0.992687 | + | 0.120718i | \(0.0385195\pi\) | ||||
−0.992687 | + | 0.120718i | \(0.961480\pi\) | |||||||
\(710\) | −177.502 | + | 183.297i | −0.250002 | + | 0.258165i | ||||
\(711\) | 34.9471 | 0.0491520 | ||||||||
\(712\) | −52.9819 | + | 52.9819i | −0.0744128 | + | 0.0744128i | ||||
\(713\) | 21.0018 | + | 21.0018i | 0.0294556 | + | 0.0294556i | ||||
\(714\) | − | 91.7870i | − | 0.128553i | ||||||
\(715\) | −1304.44 | − | 1263.20i | −1.82439 | − | 1.76671i | ||||
\(716\) | 637.646 | 0.890567 | ||||||||
\(717\) | 16.8865 | − | 16.8865i | 0.0235515 | − | 0.0235515i | ||||
\(718\) | −214.204 | − | 214.204i | −0.298335 | − | 0.298335i | ||||
\(719\) | 880.854i | 1.22511i | 0.790428 | + | 0.612555i | \(0.209858\pi\) | ||||
−0.790428 | + | 0.612555i | \(0.790142\pi\) | |||||||
\(720\) | 0.721202 | + | 44.8995i | 0.00100167 | + | 0.0623604i | ||||
\(721\) | −157.870 | −0.218960 | ||||||||
\(722\) | 267.853 | − | 267.853i | 0.370988 | − | 0.370988i | ||||
\(723\) | −123.875 | − | 123.875i | −0.171335 | − | 0.171335i | ||||
\(724\) | − | 690.518i | − | 0.953754i | ||||||
\(725\) | 1.98541 | + | 61.7864i | 0.00273850 | + | 0.0852226i | ||||
\(726\) | 786.567 | 1.08343 | ||||||||
\(727\) | −448.270 | + | 448.270i | −0.616603 | + | 0.616603i | −0.944658 | − | 0.328056i | \(-0.893607\pi\) |
0.328056 | + | 0.944658i | \(0.393607\pi\) | |||||||
\(728\) | −286.528 | − | 286.528i | −0.393582 | − | 0.393582i | ||||
\(729\) | − | 808.806i | − | 1.10947i | ||||||
\(730\) | −157.649 | + | 2.53225i | −0.215958 | + | 0.00346884i | ||||
\(731\) | −72.1365 | −0.0986819 | ||||||||
\(732\) | −94.3341 | + | 94.3341i | −0.128872 | + | 0.128872i | ||||
\(733\) | −270.164 | − | 270.164i | −0.368573 | − | 0.368573i | 0.498383 | − | 0.866957i | \(-0.333927\pi\) |
−0.866957 | + | 0.498383i | \(0.833927\pi\) | |||||||
\(734\) | − | 469.165i | − | 0.639189i | ||||||
\(735\) | 28.3211 | − | 29.2458i | 0.0385321 | − | 0.0397902i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −819.861 | + | 819.861i | −1.11243 | + | 1.11243i | ||||
\(738\) | 113.846 | + | 113.846i | 0.154263 | + | 0.154263i | ||||
\(739\) | 1322.07i | 1.78900i | 0.447067 | + | 0.894501i | \(0.352469\pi\) | ||||
−0.447067 | + | 0.894501i | \(0.647531\pi\) | |||||||
\(740\) | 386.960 | + | 374.726i | 0.522919 | + | 0.506386i | ||||
\(741\) | −497.701 | −0.671662 | ||||||||
\(742\) | 529.517 | − | 529.517i | 0.713634 | − | 0.713634i | ||||
\(743\) | 83.1674 | + | 83.1674i | 0.111935 | + | 0.111935i | 0.760856 | − | 0.648921i | \(-0.224779\pi\) |
−0.648921 | + | 0.760856i | \(0.724779\pi\) | |||||||
\(744\) | 45.5258i | 0.0611906i | ||||||||
\(745\) | −21.8204 | − | 1358.46i | −0.0292891 | − | 1.82343i | ||||
\(746\) | −793.167 | −1.06323 | ||||||||
\(747\) | −216.229 | + | 216.229i | −0.289464 | + | 0.289464i | ||||
\(748\) | 89.5251 | + | 89.5251i | 0.119686 | + | 0.119686i | ||||
\(749\) | 1352.22i | 1.80537i | ||||||||
\(750\) | 458.907 | − | 22.1289i | 0.611876 | − | 0.0295053i | ||||
\(751\) | −60.0818 | −0.0800025 | −0.0400012 | − | 0.999200i | \(-0.512736\pi\) | ||||
−0.0400012 | + | 0.999200i | \(0.512736\pi\) | |||||||
\(752\) | 95.0440 | − | 95.0440i | 0.126388 | − | 0.126388i | ||||
\(753\) | −143.269 | − | 143.269i | −0.190264 | − | 0.190264i | ||||
\(754\) | 69.3861i | 0.0920240i | ||||||||
\(755\) | 468.786 | − | 7.52991i | 0.620908 | − | 0.00997339i | ||||
\(756\) | −422.046 | −0.558262 | ||||||||
\(757\) | 628.103 | − | 628.103i | 0.829727 | − | 0.829727i | −0.157752 | − | 0.987479i | \(-0.550425\pi\) |
0.987479 | + | 0.157752i | \(0.0504246\pi\) | |||||||
\(758\) | −395.959 | − | 395.959i | −0.522374 | − | 0.522374i | ||||
\(759\) | 228.135i | 0.300573i | ||||||||
\(760\) | 94.9500 | − | 98.0501i | 0.124934 | − | 0.129013i | ||||
\(761\) | 1236.91 | 1.62537 | 0.812684 | − | 0.582704i | \(-0.198005\pi\) | ||||
0.812684 | + | 0.582704i | \(0.198005\pi\) | |||||||
\(762\) | −48.4815 | + | 48.4815i | −0.0636240 | + | 0.0636240i | ||||
\(763\) | 670.393 | + | 670.393i | 0.878628 | + | 0.878628i | ||||
\(764\) | 163.596i | 0.214131i | ||||||||
\(765\) | −27.8928 | − | 27.0110i | −0.0364612 | − | 0.0353084i | ||||
\(766\) | 703.185 | 0.917996 | ||||||||
\(767\) | 237.259 | − | 237.259i | 0.309333 | − | 0.309333i | ||||
\(768\) | 29.4042 | + | 29.4042i | 0.0382867 | + | 0.0382867i | ||||
\(769\) | − | 335.147i | − | 0.435822i | −0.975969 | − | 0.217911i | \(-0.930076\pi\) | ||
0.975969 | − | 0.217911i | \(-0.0699242\pi\) | |||||||
\(770\) | 15.0080 | + | 934.347i | 0.0194909 | + | 1.21344i | ||||
\(771\) | 1020.45 | 1.32354 | ||||||||
\(772\) | 335.304 | − | 335.304i | 0.434331 | − | 0.434331i | ||||
\(773\) | 280.124 | + | 280.124i | 0.362386 | + | 0.362386i | 0.864691 | − | 0.502305i | \(-0.167514\pi\) |
−0.502305 | + | 0.864691i | \(0.667514\pi\) | |||||||
\(774\) | 66.2264i | 0.0855638i | ||||||||
\(775\) | −154.748 | + | 4.97258i | −0.199675 | + | 0.00641624i | ||||
\(776\) | 379.882 | 0.489539 | ||||||||
\(777\) | −714.763 | + | 714.763i | −0.919901 | + | 0.919901i | ||||
\(778\) | −559.908 | − | 559.908i | −0.719676 | − | 0.719676i | ||||
\(779\) | − | 489.365i | − | 0.628197i | ||||||
\(780\) | 515.619 | − | 8.28218i | 0.661050 | − | 0.0106182i | ||||
\(781\) | 660.456 | 0.845655 | ||||||||
\(782\) | −16.5871 | + | 16.5871i | −0.0212111 | + | 0.0212111i | ||||
\(783\) | 51.1017 | + | 51.1017i | 0.0652640 | + | 0.0652640i | ||||
\(784\) | 12.5314i | 0.0159839i | ||||||||
\(785\) | 293.669 | − | 303.258i | 0.374101 | − | 0.386316i | ||||
\(786\) | 326.273 | 0.415105 | ||||||||
\(787\) | −567.531 | + | 567.531i | −0.721132 | + | 0.721132i | −0.968836 | − | 0.247704i | \(-0.920324\pi\) |
0.247704 | + | 0.968836i | \(0.420324\pi\) | |||||||
\(788\) | −16.6125 | − | 16.6125i | −0.0210819 | − | 0.0210819i | ||||
\(789\) | − | 1335.98i | − | 1.69326i | ||||||
\(790\) | 79.0639 | + | 76.5642i | 0.100081 | + | 0.0969167i | ||||
\(791\) | −1565.17 | −1.97872 | ||||||||
\(792\) | 82.1903 | − | 82.1903i | 0.103776 | − | 0.103776i | ||||
\(793\) | −360.094 | − | 360.094i | −0.454090 | − | 0.454090i | ||||
\(794\) | 284.824i | 0.358720i | ||||||||
\(795\) | 15.3059 | + | 952.889i | 0.0192527 | + | 1.19860i | ||||
\(796\) | −330.299 | −0.414949 | ||||||||
\(797\) | 158.078 | − | 158.078i | 0.198341 | − | 0.198341i | −0.600947 | − | 0.799289i | \(-0.705210\pi\) |
0.799289 | + | 0.600947i | \(0.205210\pi\) | |||||||
\(798\) | 181.111 | + | 181.111i | 0.226956 | + | 0.226956i | ||||
\(799\) | 116.221i | 0.145459i | ||||||||
\(800\) | −96.7367 | + | 103.160i | −0.120921 | + | 0.128950i | ||||
\(801\) | −59.4791 | −0.0742561 | ||||||||
\(802\) | −677.211 | + | 677.211i | −0.844403 | + | 0.844403i | ||||
\(803\) | 288.583 | + | 288.583i | 0.359381 | + | 0.359381i | ||||
\(804\) | − | 329.280i | − | 0.409553i | ||||||
\(805\) | −173.115 | + | 2.78067i | −0.215049 | + | 0.00345425i | ||||
\(806\) | −173.782 | −0.215610 | ||||||||
\(807\) | −174.975 | + | 174.975i | −0.216822 | + | 0.216822i | ||||
\(808\) | −257.361 | − | 257.361i | −0.318516 | − | 0.318516i | ||||
\(809\) | 647.019i | 0.799776i | 0.916564 | + | 0.399888i | \(0.130951\pi\) | ||||
−0.916564 | + | 0.399888i | \(0.869049\pi\) | |||||||
\(810\) | 274.244 | − | 283.198i | 0.338573 | − | 0.349627i | ||||
\(811\) | −168.302 | −0.207525 | −0.103762 | − | 0.994602i | \(-0.533088\pi\) | ||||
−0.103762 | + | 0.994602i | \(0.533088\pi\) | |||||||
\(812\) | 25.2492 | − | 25.2492i | 0.0310951 | − | 0.0310951i | ||||
\(813\) | 576.473 | + | 576.473i | 0.709068 | + | 0.709068i | ||||
\(814\) | − | 1394.30i | − | 1.71290i | ||||||
\(815\) | 186.707 | + | 180.804i | 0.229089 | + | 0.221846i | ||||
\(816\) | −35.9559 | −0.0440636 | ||||||||
\(817\) | 142.337 | − | 142.337i | 0.174219 | − | 0.174219i | ||||
\(818\) | −349.594 | − | 349.594i | −0.427376 | − | 0.427376i | ||||
\(819\) | − | 321.665i | − | 0.392753i | ||||||
\(820\) | 8.14346 | + | 506.983i | 0.00993105 | + | 0.618272i | ||||
\(821\) | 1095.40 | 1.33423 | 0.667114 | − | 0.744956i | \(-0.267530\pi\) | ||||
0.667114 | + | 0.744956i | \(0.267530\pi\) | |||||||
\(822\) | 662.501 | − | 662.501i | 0.805962 | − | 0.805962i | ||||
\(823\) | −465.668 | − | 465.668i | −0.565818 | − | 0.565818i | 0.365136 | − | 0.930954i | \(-0.381022\pi\) |
−0.930954 | + | 0.365136i | \(0.881022\pi\) | |||||||
\(824\) | 61.8428i | 0.0750519i | ||||||||
\(825\) | −867.490 | − | 813.474i | −1.05150 | − | 0.986030i | ||||
\(826\) | −172.674 | −0.209048 | ||||||||
\(827\) | −592.352 | + | 592.352i | −0.716266 | + | 0.716266i | −0.967838 | − | 0.251573i | \(-0.919052\pi\) |
0.251573 | + | 0.967838i | \(0.419052\pi\) | |||||||
\(828\) | 15.2281 | + | 15.2281i | 0.0183914 | + | 0.0183914i | ||||
\(829\) | − | 1358.47i | − | 1.63869i | −0.573304 | − | 0.819343i | \(-0.694338\pi\) | ||
0.573304 | − | 0.819343i | \(-0.305662\pi\) | |||||||
\(830\) | −962.922 | + | 15.4670i | −1.16015 | + | 0.0186350i | ||||
\(831\) | 705.391 | 0.848846 | ||||||||
\(832\) | −112.242 | + | 112.242i | −0.134906 | + | 0.134906i | ||||
\(833\) | −7.66180 | − | 7.66180i | −0.00919784 | − | 0.00919784i | ||||
\(834\) | − | 500.134i | − | 0.599681i | ||||||
\(835\) | 860.661 | − | 888.761i | 1.03073 | − | 1.06438i | ||||
\(836\) | −353.295 | −0.422601 | ||||||||
\(837\) | −127.987 | + | 127.987i | −0.152912 | + | 0.152912i | ||||
\(838\) | 127.172 | + | 127.172i | 0.151756 | + | 0.151756i | ||||
\(839\) | 573.703i | 0.683794i | 0.939737 | + | 0.341897i | \(0.111069\pi\) | ||||
−0.939737 | + | 0.341897i | \(0.888931\pi\) | |||||||
\(840\) | −190.645 | − | 184.617i | −0.226958 | − | 0.219782i | ||||
\(841\) | 834.886 | 0.992730 | ||||||||
\(842\) | 123.176 | − | 123.176i | 0.146290 | − | 0.146290i | ||||
\(843\) | −361.261 | − | 361.261i | −0.428542 | − | 0.428542i | ||||
\(844\) | − | 623.497i | − | 0.738740i | ||||||
\(845\) | 18.0437 | + | 1123.34i | 0.0213535 | + | 1.32939i | ||||
\(846\) | 106.699 | 0.126122 | ||||||||
\(847\) | 1092.59 | − | 1092.59i | 1.28995 | − | 1.28995i | ||||
\(848\) | −207.429 | − | 207.429i | −0.244609 | − | 0.244609i | ||||
\(849\) | 110.049i | 0.129621i | ||||||||
\(850\) | −3.92731 | − | 122.219i | −0.00462036 | − | 0.143787i | ||||
\(851\) | 258.334 | 0.303565 | ||||||||
\(852\) | −132.629 | + | 132.629i | −0.155668 | + | 0.155668i | ||||
\(853\) | −382.807 | − | 382.807i | −0.448777 | − | 0.448777i | 0.446171 | − | 0.894948i | \(-0.352787\pi\) |
−0.894948 | + | 0.446171i | \(0.852787\pi\) | |||||||
\(854\) | 262.072i | 0.306876i | ||||||||
\(855\) | 108.334 | − | 1.74012i | 0.126706 | − | 0.00203523i | ||||
\(856\) | 529.708 | 0.618818 | ||||||||
\(857\) | −371.449 | + | 371.449i | −0.433430 | + | 0.433430i | −0.889793 | − | 0.456364i | \(-0.849152\pi\) |
0.456364 | + | 0.889793i | \(0.349152\pi\) | |||||||
\(858\) | −943.862 | − | 943.862i | −1.10007 | − | 1.10007i | ||||
\(859\) | − | 200.800i | − | 0.233760i | −0.993146 | − | 0.116880i | \(-0.962711\pi\) | ||
0.993146 | − | 0.116880i | \(-0.0372893\pi\) | |||||||
\(860\) | −145.093 | + | 149.830i | −0.168712 | + | 0.174221i | ||||
\(861\) | −951.502 | −1.10511 | ||||||||
\(862\) | 158.451 | − | 158.451i | 0.183818 | − | 0.183818i | ||||
\(863\) | 606.257 | + | 606.257i | 0.702499 | + | 0.702499i | 0.964946 | − | 0.262447i | \(-0.0845295\pi\) |
−0.262447 | + | 0.964946i | \(0.584530\pi\) | |||||||
\(864\) | 165.329i | 0.191353i | ||||||||
\(865\) | 441.904 | + | 427.932i | 0.510871 | + | 0.494719i | ||||
\(866\) | −768.026 | −0.886867 | ||||||||
\(867\) | −509.129 | + | 509.129i | −0.587231 | + | 0.587231i | ||||
\(868\) | 63.2382 | + | 63.2382i | 0.0728550 | + | 0.0728550i | ||||
\(869\) | − | 284.884i | − | 0.327829i | ||||||
\(870\) | 0.729836 | + | 45.4370i | 0.000838892 | + | 0.0522265i | ||||
\(871\) | 1256.93 | 1.44309 | ||||||||
\(872\) | 262.615 | − | 262.615i | 0.301164 | − | 0.301164i | ||||
\(873\) | 213.234 | + | 213.234i | 0.244254 | + | 0.244254i | ||||
\(874\) | − | 65.4580i | − | 0.0748947i | ||||||
\(875\) | 606.712 | − | 668.189i | 0.693385 | − | 0.763644i | ||||
\(876\) | −115.903 | −0.132310 | ||||||||
\(877\) | −1052.02 | + | 1052.02i | −1.19957 | + | 1.19957i | −0.225277 | + | 0.974295i | \(0.572329\pi\) |
−0.974295 | + | 0.225277i | \(0.927671\pi\) | |||||||
\(878\) | 744.209 | + | 744.209i | 0.847618 | + | 0.847618i | ||||
\(879\) | 591.478i | 0.672899i | ||||||||
\(880\) | 366.014 | − | 5.87913i | 0.415925 | − | 0.00668083i | ||||
\(881\) | 556.146 | 0.631267 | 0.315633 | − | 0.948881i | \(-0.397783\pi\) | ||||
0.315633 | + | 0.948881i | \(0.397783\pi\) | |||||||
\(882\) | −7.03407 | + | 7.03407i | −0.00797514 | + | 0.00797514i | ||||
\(883\) | −216.393 | − | 216.393i | −0.245066 | − | 0.245066i | 0.573876 | − | 0.818942i | \(-0.305439\pi\) |
−0.818942 | + | 0.573876i | \(0.805439\pi\) | |||||||
\(884\) | − | 137.251i | − | 0.155262i | ||||||
\(885\) | 152.872 | − | 157.863i | 0.172736 | − | 0.178376i | ||||
\(886\) | −112.475 | −0.126947 | ||||||||
\(887\) | 403.720 | − | 403.720i | 0.455153 | − | 0.455153i | −0.441908 | − | 0.897060i | \(-0.645698\pi\) |
0.897060 | + | 0.441908i | \(0.145698\pi\) | |||||||
\(888\) | 279.996 | + | 279.996i | 0.315310 | + | 0.315310i | ||||
\(889\) | 134.688i | 0.151505i | ||||||||
\(890\) | −134.565 | − | 130.310i | −0.151197 | − | 0.146416i | ||||
\(891\) | −1020.42 | −1.14525 | ||||||||
\(892\) | −317.659 | + | 317.659i | −0.356120 | + | 0.356120i | ||||
\(893\) | −229.323 | − | 229.323i | −0.256801 | − | 0.256801i | ||||
\(894\) | − | 998.738i | − | 1.11716i | ||||||
\(895\) | 25.6023 | + | 1593.91i | 0.0286059 | + | 1.78090i | ||||
\(896\) | 81.6885 | 0.0911702 | ||||||||
\(897\) | 174.878 | − | 174.878i | 0.194958 | − | 0.194958i | ||||
\(898\) | 338.053 | + | 338.053i | 0.376452 | + | 0.376452i | ||||
\(899\) | − | 15.3139i | − | 0.0170344i | ||||||
\(900\) | −112.205 | + | 3.60554i | −0.124672 | + | 0.00400616i | ||||
\(901\) | 253.647 | 0.281518 | ||||||||
\(902\) | 928.053 | − | 928.053i | 1.02888 | − | 1.02888i | ||||
\(903\) | −276.754 | − | 276.754i | −0.306483 | − | 0.306483i | ||||
\(904\) | 613.127i | 0.678238i | ||||||||
\(905\) | 1726.07 | − | 27.7252i | 1.90726 | − | 0.0306356i | ||||
\(906\) | 344.651 | 0.380410 | ||||||||
\(907\) | 171.091 | − | 171.091i | 0.188633 | − | 0.188633i | −0.606472 | − | 0.795105i | \(-0.707416\pi\) |
0.795105 | + | 0.606472i | \(0.207416\pi\) | |||||||
\(908\) | 445.777 | + | 445.777i | 0.490944 | + | 0.490944i | ||||
\(909\) | − | 288.922i | − | 0.317846i | ||||||
\(910\) | 704.722 | − | 727.731i | 0.774420 | − | 0.799705i | ||||
\(911\) | 534.110 | 0.586290 | 0.293145 | − | 0.956068i | \(-0.405298\pi\) | ||||
0.293145 | + | 0.956068i | \(0.405298\pi\) | |||||||
\(912\) | 70.9468 | − | 70.9468i | 0.0777926 | − | 0.0777926i | ||||
\(913\) | 1762.67 | + | 1762.67i | 1.93063 | + | 1.93063i | ||||
\(914\) | 340.052i | 0.372048i | ||||||||
\(915\) | −239.592 | − | 232.017i | −0.261850 | − | 0.253571i | ||||
\(916\) | −57.8132 | −0.0631148 | ||||||||
\(917\) | 453.213 | − | 453.213i | 0.494234 | − | 0.494234i | ||||
\(918\) | −101.083 | − | 101.083i | −0.110113 | − | 0.110113i | ||||
\(919\) | − | 185.175i | − | 0.201497i | −0.994912 | − | 0.100748i | \(-0.967876\pi\) | ||
0.994912 | − | 0.100748i | \(-0.0321237\pi\) | |||||||
\(920\) | 1.08928 | + | 67.8146i | 0.00118400 | + | 0.0737115i | ||||
\(921\) | −638.264 | −0.693012 | ||||||||
\(922\) | −645.832 | + | 645.832i | −0.700469 | + | 0.700469i | ||||
\(923\) | −506.275 | − | 506.275i | −0.548510 | − | 0.548510i | ||||
\(924\) | 686.931i | 0.743432i | ||||||||
\(925\) | −921.156 | + | 982.322i | −0.995845 | + | 1.06197i | ||||
\(926\) | −188.444 | −0.203503 | ||||||||
\(927\) | −34.7133 | + | 34.7133i | −0.0374470 | + | 0.0374470i | ||||
\(928\) | −9.89092 | − | 9.89092i | −0.0106583 | − | 0.0106583i | ||||
\(929\) | − | 101.644i | − | 0.109412i | −0.998502 | − | 0.0547061i | \(-0.982578\pi\) | ||
0.998502 | − | 0.0547061i | \(-0.0174222\pi\) | |||||||
\(930\) | −113.800 | + | 1.82792i | −0.122365 | + | 0.00196551i | ||||
\(931\) | 30.2359 | 0.0324768 | ||||||||
\(932\) | 518.928 | − | 518.928i | 0.556790 | − | 0.556790i | ||||
\(933\) | −1009.46 | − | 1009.46i | −1.08196 | − | 1.08196i | ||||
\(934\) | − | 722.184i | − | 0.773216i | ||||||
\(935\) | −220.189 | + | 227.378i | −0.235496 | + | 0.243185i | ||||
\(936\) | −126.007 | −0.134622 | ||||||||
\(937\) | 21.4820 | − | 21.4820i | 0.0229263 | − | 0.0229263i | −0.695551 | − | 0.718477i | \(-0.744840\pi\) |
0.718477 | + | 0.695551i | \(0.244840\pi\) | |||||||
\(938\) | −457.391 | − | 457.391i | −0.487624 | − | 0.487624i | ||||
\(939\) | 734.261i | 0.781961i | ||||||||
\(940\) | 241.396 | + | 233.763i | 0.256804 | + | 0.248684i | ||||
\(941\) | −235.909 | −0.250700 | −0.125350 | − | 0.992113i | \(-0.540005\pi\) | ||||
−0.125350 | + | 0.992113i | \(0.540005\pi\) | |||||||
\(942\) | 219.430 | − | 219.430i | 0.232941 | − | 0.232941i | ||||
\(943\) | 171.949 | + | 171.949i | 0.182342 | + | 0.182342i | ||||
\(944\) | 67.6420i | 0.0716546i | ||||||||
\(945\) | −16.9457 | − | 1054.98i | −0.0179319 | − | 1.11638i | ||||
\(946\) | 539.867 | 0.570684 | ||||||||
\(947\) | 177.068 | − | 177.068i | 0.186978 | − | 0.186978i | −0.607410 | − | 0.794388i | \(-0.707792\pi\) |
0.794388 | + | 0.607410i | \(0.207792\pi\) | |||||||
\(948\) | 57.2089 | + | 57.2089i | 0.0603469 | + | 0.0603469i | ||||
\(949\) | − | 442.429i | − | 0.466205i | ||||||
\(950\) | 248.906 | + | 233.408i | 0.262006 | + | 0.245692i | ||||
\(951\) | −18.4717 | −0.0194235 | ||||||||
\(952\) | −49.9450 | + | 49.9450i | −0.0524632 | + | 0.0524632i | ||||
\(953\) | −1163.43 | − | 1163.43i | −1.22081 | − | 1.22081i | −0.967345 | − | 0.253464i | \(-0.918430\pi\) |
−0.253464 | − | 0.967345i | \(-0.581570\pi\) | |||||||
\(954\) | − | 232.866i | − | 0.244094i | ||||||
\(955\) | −408.938 | + | 6.56861i | −0.428208 | + | 0.00687812i | ||||
\(956\) | −18.3772 | −0.0192230 | ||||||||
\(957\) | 83.1743 | − | 83.1743i | 0.0869115 | − | 0.0869115i | ||||
\(958\) | 617.686 | + | 617.686i | 0.644766 | + | 0.644766i | ||||
\(959\) | − | 1840.51i | − | 1.91920i | ||||||
\(960\) | −72.3204 | + | 74.6816i | −0.0753337 | + | 0.0777933i | ||||
\(961\) | −922.645 | −0.960089 | ||||||||
\(962\) | −1068.80 | + | 1068.80i | −1.11102 | + | 1.11102i | ||||
\(963\) | 297.334 | + | 297.334i | 0.308758 | + | 0.308758i | ||||
\(964\) | 134.811i | 0.139845i | ||||||||
\(965\) | 851.614 | + | 824.688i | 0.882501 | + | 0.854599i | ||||
\(966\) | −127.274 | −0.131753 | ||||||||
\(967\) | −748.555 | + | 748.555i | −0.774101 | + | 0.774101i | −0.978821 | − | 0.204720i | \(-0.934372\pi\) |
0.204720 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(968\) | −428.003 | − | 428.003i | −0.442152 | − | 0.442152i | ||||
\(969\) | 86.7549i | 0.0895304i | ||||||||
\(970\) | 15.2528 | + | 949.583i | 0.0157245 | + | 0.978951i | ||||
\(971\) | −90.4980 | −0.0932008 | −0.0466004 | − | 0.998914i | \(-0.514839\pi\) | ||||
−0.0466004 | + | 0.998914i | \(0.514839\pi\) | |||||||
\(972\) | −167.074 | + | 167.074i | −0.171887 | + | 0.171887i | ||||
\(973\) | −694.717 | − | 694.717i | −0.713995 | − | 0.713995i | ||||
\(974\) | 786.064i | 0.807047i | ||||||||
\(975\) | 41.4056 | + | 1288.55i | 0.0424672 | + | 1.32159i | ||||
\(976\) | 102.662 | 0.105186 | ||||||||
\(977\) | −1094.75 | + | 1094.75i | −1.12052 | + | 1.12052i | −0.128859 | + | 0.991663i | \(0.541132\pi\) |
−0.991663 | + | 0.128859i | \(0.958868\pi\) | |||||||
\(978\) | 135.097 | + | 135.097i | 0.138136 | + | 0.138136i | ||||
\(979\) | 484.865i | 0.495266i | ||||||||
\(980\) | −31.3245 | + | 0.503152i | −0.0319637 | + | 0.000513420i | ||||
\(981\) | 294.819 | 0.300529 | ||||||||
\(982\) | −896.627 | + | 896.627i | −0.913062 | + | 0.913062i | ||||
\(983\) | −392.242 | − | 392.242i | −0.399026 | − | 0.399026i | 0.478864 | − | 0.877889i | \(-0.341049\pi\) |
−0.877889 | + | 0.478864i | \(0.841049\pi\) | |||||||
\(984\) | 372.734i | 0.378795i | ||||||||
\(985\) | 40.8589 | − | 42.1929i | 0.0414811 | − | 0.0428355i | ||||
\(986\) | 12.0948 | 0.0122665 | ||||||||
\(987\) | −445.887 | + | 445.887i | −0.451760 | + | 0.451760i | ||||
\(988\) | 270.819 | + | 270.819i | 0.274109 | + | 0.274109i | ||||
\(989\) | 100.026i | 0.101138i | ||||||||
\(990\) | 208.749 | + | 202.149i | 0.210858 | + | 0.204191i | ||||
\(991\) | −70.8250 | −0.0714682 | −0.0357341 | − | 0.999361i | \(-0.511377\pi\) | ||||
−0.0357341 | + | 0.999361i | \(0.511377\pi\) | |||||||
\(992\) | 24.7724 | − | 24.7724i | 0.0249722 | − | 0.0249722i | ||||
\(993\) | −164.485 | − | 164.485i | −0.165644 | − | 0.165644i | ||||
\(994\) | 368.461i | 0.370685i | ||||||||
\(995\) | −13.2619 | − | 825.641i | −0.0133286 | − | 0.829790i | ||||
\(996\) | −707.940 | −0.710783 | ||||||||
\(997\) | −1054.46 | + | 1054.46i | −1.05763 | + | 1.05763i | −0.0594004 | + | 0.998234i | \(0.518919\pi\) |
−0.998234 | + | 0.0594004i | \(0.981081\pi\) | |||||||
\(998\) | −699.998 | − | 699.998i | −0.701401 | − | 0.701401i | ||||
\(999\) | 1574.31i | 1.57589i |
(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 | 230.3.f.b.93.9 | yes | 24 | |
5.2 | odd | 4 | inner | 230.3.f.b.47.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.b.47.9 | ✓ | 24 | 5.2 | odd | 4 | inner | |
230.3.f.b.93.9 | yes | 24 | 1.1 | even | 1 | trivial |