Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [87,3,Mod(59,87)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(87, base_ring=CyclotomicField(2))
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("87.59");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 87 = 3 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 87.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.37057829993\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 54 x^{16} + 1187 x^{14} + 13673 x^{12} + 88449 x^{10} + 318861 x^{8} + 593533 x^{6} + \cdots + 15341 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 59.11 | ||
Root | \(0.591999i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 87.59 |
Dual form | 87.3.b.a.59.8 |
$q$-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 \(\left(\mathbb{Z}/87\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(59\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.591999i | 0.295999i | 0.988987 | + | 0.148000i | \(0.0472835\pi\) | ||||
−0.988987 | + | 0.148000i | \(0.952717\pi\) | |||||||
\(3\) | 1.87458 | − | 2.34221i | 0.624860 | − | 0.780737i | ||||
\(4\) | 3.64954 | 0.912384 | ||||||||
\(5\) | − | 5.79366i | − | 1.15873i | −0.815068 | − | 0.579366i | \(-0.803300\pi\) | ||
0.815068 | − | 0.579366i | \(-0.196700\pi\) | |||||||
\(6\) | 1.38659 | + | 1.10975i | 0.231098 | + | 0.184958i | ||||
\(7\) | −9.59672 | −1.37096 | −0.685480 | − | 0.728091i | \(-0.740408\pi\) | ||||
−0.685480 | + | 0.728091i | \(0.740408\pi\) | |||||||
\(8\) | 4.52852i | 0.566065i | ||||||||
\(9\) | −1.97189 | − | 8.78132i | −0.219099 | − | 0.975703i | ||||
\(10\) | 3.42984 | 0.342984 | ||||||||
\(11\) | 11.6953i | 1.06320i | 0.846994 | + | 0.531602i | \(0.178410\pi\) | ||||
−0.846994 | + | 0.531602i | \(0.821590\pi\) | |||||||
\(12\) | 6.84135 | − | 8.54798i | 0.570113 | − | 0.712332i | ||||
\(13\) | 21.0935 | 1.62257 | 0.811287 | − | 0.584648i | \(-0.198767\pi\) | ||||
0.811287 | + | 0.584648i | \(0.198767\pi\) | |||||||
\(14\) | − | 5.68125i | − | 0.405803i | ||||||
\(15\) | −13.5700 | − | 10.8607i | −0.904664 | − | 0.724046i | ||||
\(16\) | 11.9173 | 0.744830 | ||||||||
\(17\) | 25.9337i | 1.52551i | 0.646688 | + | 0.762755i | \(0.276154\pi\) | ||||
−0.646688 | + | 0.762755i | \(0.723846\pi\) | |||||||
\(18\) | 5.19853 | − | 1.16736i | 0.288807 | − | 0.0648532i | ||||
\(19\) | −9.59174 | −0.504829 | −0.252414 | − | 0.967619i | \(-0.581225\pi\) | ||||
−0.252414 | + | 0.967619i | \(0.581225\pi\) | |||||||
\(20\) | − | 21.1442i | − | 1.05721i | ||||||
\(21\) | −17.9898 | + | 22.4775i | −0.856659 | + | 1.07036i | ||||
\(22\) | −6.92358 | −0.314708 | ||||||||
\(23\) | 5.25325i | 0.228402i | 0.993458 | + | 0.114201i | \(0.0364308\pi\) | ||||
−0.993458 | + | 0.114201i | \(0.963569\pi\) | |||||||
\(24\) | 10.6067 | + | 8.48907i | 0.441947 | + | 0.353711i | ||||
\(25\) | −8.56649 | −0.342660 | ||||||||
\(26\) | 12.4873i | 0.480281i | ||||||||
\(27\) | −24.2642 | − | 11.8427i | −0.898673 | − | 0.438619i | ||||
\(28\) | −35.0236 | −1.25084 | ||||||||
\(29\) | − | 5.38516i | − | 0.185695i | ||||||
\(30\) | 6.42951 | − | 8.03340i | 0.214317 | − | 0.267780i | ||||
\(31\) | 8.67080 | 0.279703 | 0.139852 | − | 0.990172i | \(-0.455337\pi\) | ||||
0.139852 | + | 0.990172i | \(0.455337\pi\) | |||||||
\(32\) | 25.1691i | 0.786534i | ||||||||
\(33\) | 27.3927 | + | 21.9237i | 0.830083 | + | 0.664355i | ||||
\(34\) | −15.3527 | −0.451550 | ||||||||
\(35\) | 55.6001i | 1.58858i | ||||||||
\(36\) | −7.19649 | − | 32.0478i | −0.199903 | − | 0.890216i | ||||
\(37\) | −55.8395 | −1.50918 | −0.754588 | − | 0.656199i | \(-0.772163\pi\) | ||||
−0.754588 | + | 0.656199i | \(0.772163\pi\) | |||||||
\(38\) | − | 5.67830i | − | 0.149429i | ||||||
\(39\) | 39.5414 | − | 49.4053i | 1.01388 | − | 1.26680i | ||||
\(40\) | 26.2367 | 0.655917 | ||||||||
\(41\) | − | 62.0334i | − | 1.51301i | −0.653988 | − | 0.756505i | \(-0.726905\pi\) | ||
0.653988 | − | 0.756505i | \(-0.273095\pi\) | |||||||
\(42\) | −13.3067 | − | 10.6500i | −0.316826 | − | 0.253570i | ||||
\(43\) | −23.0437 | −0.535901 | −0.267950 | − | 0.963433i | \(-0.586346\pi\) | ||||
−0.267950 | + | 0.963433i | \(0.586346\pi\) | |||||||
\(44\) | 42.6823i | 0.970052i | ||||||||
\(45\) | −50.8760 | + | 11.4245i | −1.13058 | + | 0.253877i | ||||
\(46\) | −3.10992 | −0.0676069 | ||||||||
\(47\) | 34.6532i | 0.737302i | 0.929568 | + | 0.368651i | \(0.120180\pi\) | ||||
−0.929568 | + | 0.368651i | \(0.879820\pi\) | |||||||
\(48\) | 22.3399 | − | 27.9128i | 0.465414 | − | 0.581516i | ||||
\(49\) | 43.0970 | 0.879531 | ||||||||
\(50\) | − | 5.07135i | − | 0.101427i | ||||||
\(51\) | 60.7421 | + | 48.6147i | 1.19102 | + | 0.953230i | ||||
\(52\) | 76.9814 | 1.48041 | ||||||||
\(53\) | − | 22.0743i | − | 0.416496i | −0.978076 | − | 0.208248i | \(-0.933224\pi\) | ||
0.978076 | − | 0.208248i | \(-0.0667761\pi\) | |||||||
\(54\) | 7.01088 | − | 14.3644i | 0.129831 | − | 0.266007i | ||||
\(55\) | 67.7583 | 1.23197 | ||||||||
\(56\) | − | 43.4589i | − | 0.776052i | ||||||
\(57\) | −17.9805 | + | 22.4659i | −0.315447 | + | 0.394138i | ||||
\(58\) | 3.18801 | 0.0549657 | ||||||||
\(59\) | 7.52808i | 0.127595i | 0.997963 | + | 0.0637973i | \(0.0203211\pi\) | ||||
−0.997963 | + | 0.0637973i | \(0.979679\pi\) | |||||||
\(60\) | −49.5241 | − | 39.6365i | −0.825402 | − | 0.660608i | ||||
\(61\) | 6.95229 | 0.113972 | 0.0569860 | − | 0.998375i | \(-0.481851\pi\) | ||||
0.0569860 | + | 0.998375i | \(0.481851\pi\) | |||||||
\(62\) | 5.13311i | 0.0827920i | ||||||||
\(63\) | 18.9237 | + | 84.2719i | 0.300376 | + | 1.33765i | ||||
\(64\) | 32.7690 | 0.512016 | ||||||||
\(65\) | − | 122.208i | − | 1.88013i | ||||||
\(66\) | −12.9788 | + | 16.2165i | −0.196649 | + | 0.245704i | ||||
\(67\) | −99.9467 | −1.49174 | −0.745871 | − | 0.666090i | \(-0.767967\pi\) | ||||
−0.745871 | + | 0.666090i | \(0.767967\pi\) | |||||||
\(68\) | 94.6459i | 1.39185i | ||||||||
\(69\) | 12.3042 | + | 9.84765i | 0.178322 | + | 0.142720i | ||||
\(70\) | −32.9152 | −0.470217 | ||||||||
\(71\) | − | 137.582i | − | 1.93778i | −0.247499 | − | 0.968888i | \(-0.579609\pi\) | ||
0.247499 | − | 0.968888i | \(-0.420391\pi\) | |||||||
\(72\) | 39.7664 | − | 8.92975i | 0.552311 | − | 0.124024i | ||||
\(73\) | 39.2838 | 0.538134 | 0.269067 | − | 0.963121i | \(-0.413285\pi\) | ||||
0.269067 | + | 0.963121i | \(0.413285\pi\) | |||||||
\(74\) | − | 33.0569i | − | 0.446715i | ||||||
\(75\) | −16.0586 | + | 20.0645i | −0.214114 | + | 0.267527i | ||||
\(76\) | −35.0054 | −0.460598 | ||||||||
\(77\) | − | 112.236i | − | 1.45761i | ||||||
\(78\) | 29.2479 | + | 23.4085i | 0.374973 | + | 0.300109i | ||||
\(79\) | 8.63722 | 0.109332 | 0.0546659 | − | 0.998505i | \(-0.482591\pi\) | ||||
0.0546659 | + | 0.998505i | \(0.482591\pi\) | |||||||
\(80\) | − | 69.0446i | − | 0.863058i | ||||||
\(81\) | −73.2233 | + | 34.6316i | −0.903991 | + | 0.427551i | ||||
\(82\) | 36.7237 | 0.447850 | ||||||||
\(83\) | 54.4522i | 0.656051i | 0.944669 | + | 0.328025i | \(0.106383\pi\) | ||||
−0.944669 | + | 0.328025i | \(0.893617\pi\) | |||||||
\(84\) | −65.6546 | + | 82.0326i | −0.781602 | + | 0.976578i | ||||
\(85\) | 150.251 | 1.76766 | ||||||||
\(86\) | − | 13.6419i | − | 0.158626i | ||||||
\(87\) | −12.6132 | − | 10.0949i | −0.144979 | − | 0.116034i | ||||
\(88\) | −52.9622 | −0.601843 | ||||||||
\(89\) | 83.2696i | 0.935614i | 0.883831 | + | 0.467807i | \(0.154956\pi\) | ||||
−0.883831 | + | 0.467807i | \(0.845044\pi\) | |||||||
\(90\) | −6.76327 | − | 30.1185i | −0.0751475 | − | 0.334650i | ||||
\(91\) | −202.428 | −2.22448 | ||||||||
\(92\) | 19.1719i | 0.208391i | ||||||||
\(93\) | 16.2541 | − | 20.3088i | 0.174776 | − | 0.218375i | ||||
\(94\) | −20.5146 | −0.218241 | ||||||||
\(95\) | 55.5713i | 0.584961i | ||||||||
\(96\) | 58.9513 | + | 47.1815i | 0.614076 | + | 0.491474i | ||||
\(97\) | −41.9422 | −0.432394 | −0.216197 | − | 0.976350i | \(-0.569365\pi\) | ||||
−0.216197 | + | 0.976350i | \(0.569365\pi\) | |||||||
\(98\) | 25.5134i | 0.260341i | ||||||||
\(99\) | 102.700 | − | 23.0618i | 1.03737 | − | 0.232947i | ||||
\(100\) | −31.2637 | −0.312637 | ||||||||
\(101\) | 63.9348i | 0.633018i | 0.948589 | + | 0.316509i | \(0.102511\pi\) | ||||
−0.948589 | + | 0.316509i | \(0.897489\pi\) | |||||||
\(102\) | −28.7799 | + | 35.9592i | −0.282156 | + | 0.352541i | ||||
\(103\) | 28.1857 | 0.273648 | 0.136824 | − | 0.990595i | \(-0.456311\pi\) | ||||
0.136824 | + | 0.990595i | \(0.456311\pi\) | |||||||
\(104\) | 95.5221i | 0.918482i | ||||||||
\(105\) | 130.227 | + | 104.227i | 1.24026 | + | 0.992638i | ||||
\(106\) | 13.0679 | 0.123282 | ||||||||
\(107\) | 20.5837i | 0.192371i | 0.995363 | + | 0.0961854i | \(0.0306642\pi\) | ||||
−0.995363 | + | 0.0961854i | \(0.969336\pi\) | |||||||
\(108\) | −88.5530 | − | 43.2204i | −0.819935 | − | 0.400189i | ||||
\(109\) | 53.4297 | 0.490181 | 0.245091 | − | 0.969500i | \(-0.421182\pi\) | ||||
0.245091 | + | 0.969500i | \(0.421182\pi\) | |||||||
\(110\) | 40.1128i | 0.364662i | ||||||||
\(111\) | −104.676 | + | 130.788i | −0.943025 | + | 1.17827i | ||||
\(112\) | −114.367 | −1.02113 | ||||||||
\(113\) | − | 31.6405i | − | 0.280005i | −0.990151 | − | 0.140002i | \(-0.955289\pi\) | ||
0.990151 | − | 0.140002i | \(-0.0447110\pi\) | |||||||
\(114\) | −13.2998 | − | 10.6444i | −0.116665 | − | 0.0933722i | ||||
\(115\) | 30.4356 | 0.264657 | ||||||||
\(116\) | − | 19.6534i | − | 0.169426i | ||||||
\(117\) | −41.5940 | − | 185.229i | −0.355505 | − | 1.58315i | ||||
\(118\) | −4.45662 | −0.0377679 | ||||||||
\(119\) | − | 248.878i | − | 2.09141i | ||||||
\(120\) | 49.1828 | − | 61.4518i | 0.409857 | − | 0.512099i | ||||
\(121\) | −15.7790 | −0.130405 | ||||||||
\(122\) | 4.11575i | 0.0337356i | ||||||||
\(123\) | −145.295 | − | 116.287i | −1.18126 | − | 0.945420i | ||||
\(124\) | 31.6444 | 0.255197 | ||||||||
\(125\) | − | 95.2102i | − | 0.761681i | ||||||
\(126\) | −49.8889 | + | 11.2028i | −0.395943 | + | 0.0889111i | ||||
\(127\) | 139.865 | 1.10130 | 0.550648 | − | 0.834737i | \(-0.314381\pi\) | ||||
0.550648 | + | 0.834737i | \(0.314381\pi\) | |||||||
\(128\) | 120.076i | 0.938090i | ||||||||
\(129\) | −43.1974 | + | 53.9733i | −0.334863 | + | 0.418397i | ||||
\(130\) | 72.3472 | 0.556517 | ||||||||
\(131\) | 16.6624i | 0.127194i | 0.997976 | + | 0.0635969i | \(0.0202572\pi\) | ||||
−0.997976 | + | 0.0635969i | \(0.979743\pi\) | |||||||
\(132\) | 99.9708 | + | 80.0114i | 0.757355 | + | 0.606147i | ||||
\(133\) | 92.0493 | 0.692100 | ||||||||
\(134\) | − | 59.1684i | − | 0.441555i | ||||||
\(135\) | −68.6127 | + | 140.578i | −0.508242 | + | 1.04132i | ||||
\(136\) | −117.441 | −0.863537 | ||||||||
\(137\) | − | 91.6710i | − | 0.669132i | −0.942372 | − | 0.334566i | \(-0.891410\pi\) | ||
0.942372 | − | 0.334566i | \(-0.108590\pi\) | |||||||
\(138\) | −5.82980 | + | 7.28408i | −0.0422449 | + | 0.0527832i | ||||
\(139\) | −96.5441 | −0.694562 | −0.347281 | − | 0.937761i | \(-0.612895\pi\) | ||||
−0.347281 | + | 0.937761i | \(0.612895\pi\) | |||||||
\(140\) | 202.915i | 1.44939i | ||||||||
\(141\) | 81.1650 | + | 64.9602i | 0.575638 | + | 0.460711i | ||||
\(142\) | 81.4485 | 0.573581 | ||||||||
\(143\) | 246.693i | 1.72513i | ||||||||
\(144\) | −23.4996 | − | 104.649i | −0.163191 | − | 0.726732i | ||||
\(145\) | −31.1998 | −0.215171 | ||||||||
\(146\) | 23.2560i | 0.159287i | ||||||||
\(147\) | 80.7889 | − | 100.942i | 0.549584 | − | 0.686682i | ||||
\(148\) | −203.788 | −1.37695 | ||||||||
\(149\) | − | 194.129i | − | 1.30288i | −0.758701 | − | 0.651440i | \(-0.774165\pi\) | ||
0.758701 | − | 0.651440i | \(-0.225835\pi\) | |||||||
\(150\) | −11.8782 | − | 9.50666i | −0.0791878 | − | 0.0633777i | ||||
\(151\) | 52.4709 | 0.347489 | 0.173745 | − | 0.984791i | \(-0.444413\pi\) | ||||
0.173745 | + | 0.984791i | \(0.444413\pi\) | |||||||
\(152\) | − | 43.4364i | − | 0.285766i | ||||||
\(153\) | 227.732 | − | 51.1384i | 1.48844 | − | 0.334238i | ||||
\(154\) | 66.4436 | 0.431452 | ||||||||
\(155\) | − | 50.2357i | − | 0.324101i | ||||||
\(156\) | 144.308 | − | 180.307i | 0.925051 | − | 1.15581i | ||||
\(157\) | 145.640 | 0.927645 | 0.463822 | − | 0.885928i | \(-0.346478\pi\) | ||||
0.463822 | + | 0.885928i | \(0.346478\pi\) | |||||||
\(158\) | 5.11322i | 0.0323622i | ||||||||
\(159\) | −51.7026 | − | 41.3800i | −0.325173 | − | 0.260252i | ||||
\(160\) | 145.821 | 0.911382 | ||||||||
\(161\) | − | 50.4140i | − | 0.313130i | ||||||
\(162\) | −20.5019 | − | 43.3481i | −0.126555 | − | 0.267581i | ||||
\(163\) | −170.407 | −1.04544 | −0.522719 | − | 0.852505i | \(-0.675082\pi\) | ||||
−0.522719 | + | 0.852505i | \(0.675082\pi\) | |||||||
\(164\) | − | 226.393i | − | 1.38045i | ||||||
\(165\) | 127.018 | − | 158.704i | 0.769809 | − | 0.961844i | ||||
\(166\) | −32.2356 | −0.194191 | ||||||||
\(167\) | 329.268i | 1.97167i | 0.167731 | + | 0.985833i | \(0.446356\pi\) | ||||
−0.167731 | + | 0.985833i | \(0.553644\pi\) | |||||||
\(168\) | −101.790 | − | 81.4673i | −0.605892 | − | 0.484924i | ||||
\(169\) | 275.934 | 1.63275 | ||||||||
\(170\) | 88.9483i | 0.523225i | ||||||||
\(171\) | 18.9139 | + | 84.2282i | 0.110607 | + | 0.492563i | ||||
\(172\) | −84.0990 | −0.488948 | ||||||||
\(173\) | − | 223.353i | − | 1.29106i | −0.763735 | − | 0.645530i | \(-0.776637\pi\) | ||
0.763735 | − | 0.645530i | \(-0.223363\pi\) | |||||||
\(174\) | 5.97619 | − | 7.46699i | 0.0343459 | − | 0.0429137i | ||||
\(175\) | 82.2102 | 0.469773 | ||||||||
\(176\) | 139.376i | 0.791906i | ||||||||
\(177\) | 17.6324 | + | 14.1120i | 0.0996178 | + | 0.0797288i | ||||
\(178\) | −49.2955 | −0.276941 | ||||||||
\(179\) | − | 22.3994i | − | 0.125136i | −0.998041 | − | 0.0625681i | \(-0.980071\pi\) | ||
0.998041 | − | 0.0625681i | \(-0.0199291\pi\) | |||||||
\(180\) | −185.674 | + | 41.6940i | −1.03152 | + | 0.231634i | ||||
\(181\) | 143.446 | 0.792521 | 0.396260 | − | 0.918138i | \(-0.370308\pi\) | ||||
0.396260 | + | 0.918138i | \(0.370308\pi\) | |||||||
\(182\) | − | 119.837i | − | 0.658446i | ||||||
\(183\) | 13.0326 | − | 16.2837i | 0.0712165 | − | 0.0889820i | ||||
\(184\) | −23.7894 | −0.129290 | ||||||||
\(185\) | 323.515i | 1.74873i | ||||||||
\(186\) | 12.0228 | + | 9.62242i | 0.0646388 | + | 0.0517335i | ||||
\(187\) | −303.301 | −1.62193 | ||||||||
\(188\) | 126.468i | 0.672702i | ||||||||
\(189\) | 232.856 | + | 113.651i | 1.23204 | + | 0.601329i | ||||
\(190\) | −32.8981 | −0.173148 | ||||||||
\(191\) | − | 36.2678i | − | 0.189884i | −0.995483 | − | 0.0949418i | \(-0.969734\pi\) | ||
0.995483 | − | 0.0949418i | \(-0.0302665\pi\) | |||||||
\(192\) | 61.4282 | − | 76.7519i | 0.319938 | − | 0.399750i | ||||
\(193\) | −259.170 | −1.34285 | −0.671424 | − | 0.741073i | \(-0.734317\pi\) | ||||
−0.671424 | + | 0.741073i | \(0.734317\pi\) | |||||||
\(194\) | − | 24.8297i | − | 0.127988i | ||||||
\(195\) | −286.238 | − | 229.090i | −1.46789 | − | 1.17482i | ||||
\(196\) | 157.284 | 0.802470 | ||||||||
\(197\) | 119.924i | 0.608753i | 0.952552 | + | 0.304377i | \(0.0984481\pi\) | ||||
−0.952552 | + | 0.304377i | \(0.901552\pi\) | |||||||
\(198\) | 13.6525 | + | 60.7982i | 0.0689523 | + | 0.307061i | ||||
\(199\) | 127.606 | 0.641236 | 0.320618 | − | 0.947209i | \(-0.396109\pi\) | ||||
0.320618 | + | 0.947209i | \(0.396109\pi\) | |||||||
\(200\) | − | 38.7935i | − | 0.193967i | ||||||
\(201\) | −187.358 | + | 234.096i | −0.932131 | + | 1.16466i | ||||
\(202\) | −37.8493 | −0.187373 | ||||||||
\(203\) | 51.6799i | 0.254581i | ||||||||
\(204\) | 221.680 | + | 177.421i | 1.08667 | + | 0.869712i | ||||
\(205\) | −359.400 | −1.75317 | ||||||||
\(206\) | 16.6859i | 0.0809996i | ||||||||
\(207\) | 46.1305 | − | 10.3588i | 0.222853 | − | 0.0500427i | ||||
\(208\) | 251.377 | 1.20854 | ||||||||
\(209\) | − | 112.178i | − | 0.536736i | ||||||
\(210\) | −61.7022 | + | 77.0943i | −0.293820 | + | 0.367116i | ||||
\(211\) | −158.883 | −0.752999 | −0.376500 | − | 0.926417i | \(-0.622872\pi\) | ||||
−0.376500 | + | 0.926417i | \(0.622872\pi\) | |||||||
\(212\) | − | 80.5609i | − | 0.380004i | ||||||
\(213\) | −322.246 | − | 257.909i | −1.51289 | − | 1.21084i | ||||
\(214\) | −12.1855 | −0.0569417 | ||||||||
\(215\) | 133.508i | 0.620966i | ||||||||
\(216\) | 53.6300 | − | 109.881i | 0.248287 | − | 0.508707i | ||||
\(217\) | −83.2113 | −0.383462 | ||||||||
\(218\) | 31.6303i | 0.145093i | ||||||||
\(219\) | 73.6407 | − | 92.0109i | 0.336259 | − | 0.420141i | ||||
\(220\) | 247.287 | 1.12403 | ||||||||
\(221\) | 547.031i | 2.47525i | ||||||||
\(222\) | −77.4263 | − | 61.9679i | −0.348767 | − | 0.279135i | ||||
\(223\) | −400.363 | −1.79535 | −0.897675 | − | 0.440659i | \(-0.854745\pi\) | ||||
−0.897675 | + | 0.440659i | \(0.854745\pi\) | |||||||
\(224\) | − | 241.541i | − | 1.07831i | ||||||
\(225\) | 16.8922 | + | 75.2251i | 0.0750764 | + | 0.334334i | ||||
\(226\) | 18.7312 | 0.0828812 | ||||||||
\(227\) | − | 100.145i | − | 0.441167i | −0.975368 | − | 0.220583i | \(-0.929204\pi\) | ||
0.975368 | − | 0.220583i | \(-0.0707961\pi\) | |||||||
\(228\) | −65.6205 | + | 81.9900i | −0.287809 | + | 0.359605i | ||||
\(229\) | 196.830 | 0.859521 | 0.429761 | − | 0.902943i | \(-0.358598\pi\) | ||||
0.429761 | + | 0.902943i | \(0.358598\pi\) | |||||||
\(230\) | 18.0178i | 0.0783383i | ||||||||
\(231\) | −262.880 | − | 210.396i | −1.13801 | − | 0.910804i | ||||
\(232\) | 24.3868 | 0.105116 | ||||||||
\(233\) | 364.954i | 1.56633i | 0.621816 | + | 0.783164i | \(0.286395\pi\) | ||||
−0.621816 | + | 0.783164i | \(0.713605\pi\) | |||||||
\(234\) | 109.655 | − | 24.6236i | 0.468612 | − | 0.105229i | ||||
\(235\) | 200.769 | 0.854335 | ||||||||
\(236\) | 27.4740i | 0.116415i | ||||||||
\(237\) | 16.1912 | − | 20.2302i | 0.0683171 | − | 0.0853594i | ||||
\(238\) | 147.336 | 0.619057 | ||||||||
\(239\) | 129.400i | 0.541422i | 0.962661 | + | 0.270711i | \(0.0872588\pi\) | ||||
−0.962661 | + | 0.270711i | \(0.912741\pi\) | |||||||
\(240\) | −161.717 | − | 129.430i | −0.673821 | − | 0.539291i | ||||
\(241\) | −78.9952 | −0.327781 | −0.163890 | − | 0.986479i | \(-0.552404\pi\) | ||||
−0.163890 | + | 0.986479i | \(0.552404\pi\) | |||||||
\(242\) | − | 9.34114i | − | 0.0385997i | ||||||
\(243\) | −56.1484 | + | 236.424i | −0.231063 | + | 0.972939i | ||||
\(244\) | 25.3726 | 0.103986 | ||||||||
\(245\) | − | 249.690i | − | 1.01914i | ||||||
\(246\) | 68.8415 | − | 86.0146i | 0.279844 | − | 0.349653i | ||||
\(247\) | −202.323 | −0.819122 | ||||||||
\(248\) | 39.2659i | 0.158330i | ||||||||
\(249\) | 127.538 | + | 102.075i | 0.512203 | + | 0.409940i | ||||
\(250\) | 56.3643 | 0.225457 | ||||||||
\(251\) | 102.882i | 0.409890i | 0.978773 | + | 0.204945i | \(0.0657015\pi\) | ||||
−0.978773 | + | 0.204945i | \(0.934298\pi\) | |||||||
\(252\) | 69.0627 | + | 307.553i | 0.274058 | + | 1.22045i | ||||
\(253\) | −61.4381 | −0.242838 | ||||||||
\(254\) | 82.7997i | 0.325983i | ||||||||
\(255\) | 281.657 | − | 351.919i | 1.10454 | − | 1.38007i | ||||
\(256\) | 59.9915 | 0.234342 | ||||||||
\(257\) | − | 157.221i | − | 0.611756i | −0.952071 | − | 0.305878i | \(-0.901050\pi\) | ||
0.952071 | − | 0.305878i | \(-0.0989500\pi\) | |||||||
\(258\) | −31.9521 | − | 25.5728i | −0.123845 | − | 0.0991193i | ||||
\(259\) | 535.876 | 2.06902 | ||||||||
\(260\) | − | 446.004i | − | 1.71540i | ||||||
\(261\) | −47.2889 | + | 10.6190i | −0.181183 | + | 0.0406857i | ||||
\(262\) | −9.86411 | −0.0376493 | ||||||||
\(263\) | − | 407.396i | − | 1.54903i | −0.632553 | − | 0.774517i | \(-0.717993\pi\) | ||
0.632553 | − | 0.774517i | \(-0.282007\pi\) | |||||||
\(264\) | −99.2819 | + | 124.048i | −0.376068 | + | 0.469881i | ||||
\(265\) | −127.891 | −0.482607 | ||||||||
\(266\) | 54.4931i | 0.204861i | ||||||||
\(267\) | 195.035 | + | 156.096i | 0.730468 | + | 0.584628i | ||||
\(268\) | −364.759 | −1.36104 | ||||||||
\(269\) | − | 119.369i | − | 0.443752i | −0.975075 | − | 0.221876i | \(-0.928782\pi\) | ||
0.975075 | − | 0.221876i | \(-0.0712180\pi\) | |||||||
\(270\) | −83.2222 | − | 40.6186i | −0.308230 | − | 0.150439i | ||||
\(271\) | 310.345 | 1.14518 | 0.572591 | − | 0.819841i | \(-0.305938\pi\) | ||||
0.572591 | + | 0.819841i | \(0.305938\pi\) | |||||||
\(272\) | 309.058i | 1.13624i | ||||||||
\(273\) | −379.468 | + | 474.129i | −1.38999 | + | 1.73674i | ||||
\(274\) | 54.2691 | 0.198063 | ||||||||
\(275\) | − | 100.187i | − | 0.364317i | ||||||
\(276\) | 44.9047 | + | 35.9394i | 0.162698 | + | 0.130215i | ||||
\(277\) | −34.2997 | −0.123826 | −0.0619128 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619128 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(278\) | − | 57.1540i | − | 0.205590i | ||||||
\(279\) | −17.0979 | − | 76.1411i | −0.0612827 | − | 0.272907i | ||||
\(280\) | −251.786 | −0.899236 | ||||||||
\(281\) | − | 418.400i | − | 1.48897i | −0.667641 | − | 0.744483i | \(-0.732696\pi\) | ||
0.667641 | − | 0.744483i | \(-0.267304\pi\) | |||||||
\(282\) | −38.4564 | + | 48.0496i | −0.136370 | + | 0.170389i | ||||
\(283\) | 106.001 | 0.374562 | 0.187281 | − | 0.982306i | \(-0.440032\pi\) | ||||
0.187281 | + | 0.982306i | \(0.440032\pi\) | |||||||
\(284\) | − | 502.111i | − | 1.76800i | ||||||
\(285\) | 130.160 | + | 104.173i | 0.456700 | + | 0.365519i | ||||
\(286\) | −146.042 | −0.510637 | ||||||||
\(287\) | 595.317i | 2.07428i | ||||||||
\(288\) | 221.018 | − | 49.6307i | 0.767423 | − | 0.172329i | ||||
\(289\) | −383.555 | −1.32718 | ||||||||
\(290\) | − | 18.4703i | − | 0.0636905i | ||||||
\(291\) | −78.6241 | + | 98.2374i | −0.270186 | + | 0.337586i | ||||
\(292\) | 143.368 | 0.490985 | ||||||||
\(293\) | − | 44.3924i | − | 0.151510i | −0.997126 | − | 0.0757550i | \(-0.975863\pi\) | ||
0.997126 | − | 0.0757550i | \(-0.0241367\pi\) | |||||||
\(294\) | 59.7577 | + | 47.8269i | 0.203258 | + | 0.162677i | ||||
\(295\) | 43.6152 | 0.147848 | ||||||||
\(296\) | − | 252.870i | − | 0.854292i | ||||||
\(297\) | 138.504 | − | 283.776i | 0.466342 | − | 0.955474i | ||||
\(298\) | 114.924 | 0.385651 | ||||||||
\(299\) | 110.809i | 0.370600i | ||||||||
\(300\) | −58.6064 | + | 73.2262i | −0.195355 | + | 0.244087i | ||||
\(301\) | 221.144 | 0.734699 | ||||||||
\(302\) | 31.0627i | 0.102857i | ||||||||
\(303\) | 149.749 | + | 119.851i | 0.494220 | + | 0.395548i | ||||
\(304\) | −114.307 | −0.376011 | ||||||||
\(305\) | − | 40.2792i | − | 0.132063i | ||||||
\(306\) | 30.2739 | + | 134.817i | 0.0989342 | + | 0.440578i | ||||
\(307\) | −16.6849 | −0.0543481 | −0.0271740 | − | 0.999631i | \(-0.508651\pi\) | ||||
−0.0271740 | + | 0.999631i | \(0.508651\pi\) | |||||||
\(308\) | − | 409.610i | − | 1.32990i | ||||||
\(309\) | 52.8364 | − | 66.0169i | 0.170992 | − | 0.213647i | ||||
\(310\) | 29.7395 | 0.0959338 | ||||||||
\(311\) | − | 270.662i | − | 0.870297i | −0.900359 | − | 0.435148i | \(-0.856696\pi\) | ||
0.900359 | − | 0.435148i | \(-0.143304\pi\) | |||||||
\(312\) | 223.733 | + | 179.064i | 0.717093 | + | 0.573923i | ||||
\(313\) | −106.195 | −0.339281 | −0.169640 | − | 0.985506i | \(-0.554261\pi\) | ||||
−0.169640 | + | 0.985506i | \(0.554261\pi\) | |||||||
\(314\) | 86.2189i | 0.274582i | ||||||||
\(315\) | 488.243 | − | 109.637i | 1.54998 | − | 0.348055i | ||||
\(316\) | 31.5218 | 0.0997527 | ||||||||
\(317\) | − | 125.017i | − | 0.394374i | −0.980366 | − | 0.197187i | \(-0.936819\pi\) | ||
0.980366 | − | 0.197187i | \(-0.0631806\pi\) | |||||||
\(318\) | 24.4969 | − | 30.6079i | 0.0770343 | − | 0.0962511i | ||||
\(319\) | 62.9809 | 0.197432 | ||||||||
\(320\) | − | 189.853i | − | 0.593289i | ||||||
\(321\) | 48.2113 | + | 38.5858i | 0.150191 | + | 0.120205i | ||||
\(322\) | 29.8450 | 0.0926864 | ||||||||
\(323\) | − | 248.749i | − | 0.770121i | ||||||
\(324\) | −267.231 | + | 126.389i | −0.824787 | + | 0.390091i | ||||
\(325\) | −180.697 | −0.555991 | ||||||||
\(326\) | − | 100.880i | − | 0.309449i | ||||||
\(327\) | 100.158 | − | 125.144i | 0.306295 | − | 0.382702i | ||||
\(328\) | 280.919 | 0.856461 | ||||||||
\(329\) | − | 332.557i | − | 1.01081i | ||||||
\(330\) | 93.9527 | + | 75.1948i | 0.284705 | + | 0.227863i | ||||
\(331\) | 461.247 | 1.39350 | 0.696748 | − | 0.717316i | \(-0.254630\pi\) | ||||
0.696748 | + | 0.717316i | \(0.254630\pi\) | |||||||
\(332\) | 198.725i | 0.598570i | ||||||||
\(333\) | 110.110 | + | 490.345i | 0.330659 | + | 1.47251i | ||||
\(334\) | −194.926 | −0.583612 | ||||||||
\(335\) | 579.057i | 1.72853i | ||||||||
\(336\) | −214.390 | + | 267.871i | −0.638065 | + | 0.797235i | ||||
\(337\) | 560.751 | 1.66395 | 0.831975 | − | 0.554813i | \(-0.187210\pi\) | ||||
0.831975 | + | 0.554813i | \(0.187210\pi\) | |||||||
\(338\) | 163.353i | 0.483293i | ||||||||
\(339\) | −74.1088 | − | 59.3128i | −0.218610 | − | 0.174964i | ||||
\(340\) | 548.346 | 1.61278 | ||||||||
\(341\) | 101.407i | 0.297382i | ||||||||
\(342\) | −49.8630 | + | 11.1970i | −0.145798 | + | 0.0327397i | ||||
\(343\) | 56.6492 | 0.165158 | ||||||||
\(344\) | − | 104.354i | − | 0.303355i | ||||||
\(345\) | 57.0539 | − | 71.2864i | 0.165374 | − | 0.206627i | ||||
\(346\) | 132.225 | 0.382153 | ||||||||
\(347\) | 256.975i | 0.740562i | 0.928920 | + | 0.370281i | \(0.120739\pi\) | ||||
−0.928920 | + | 0.370281i | \(0.879261\pi\) | |||||||
\(348\) | −46.0323 | − | 36.8418i | −0.132277 | − | 0.105867i | ||||
\(349\) | −405.643 | −1.16230 | −0.581150 | − | 0.813796i | \(-0.697397\pi\) | ||||
−0.581150 | + | 0.813796i | \(0.697397\pi\) | |||||||
\(350\) | 48.6683i | 0.139052i | ||||||||
\(351\) | −511.816 | − | 249.804i | −1.45816 | − | 0.711692i | ||||
\(352\) | −294.359 | −0.836247 | ||||||||
\(353\) | − | 276.988i | − | 0.784668i | −0.919823 | − | 0.392334i | \(-0.871668\pi\) | ||
0.919823 | − | 0.392334i | \(-0.128332\pi\) | |||||||
\(354\) | −8.35429 | + | 10.4383i | −0.0235997 | + | 0.0294868i | ||||
\(355\) | −797.104 | −2.24536 | ||||||||
\(356\) | 303.896i | 0.853639i | ||||||||
\(357\) | −582.925 | − | 466.542i | −1.63284 | − | 1.30684i | ||||
\(358\) | 13.2604 | 0.0370403 | ||||||||
\(359\) | 252.513i | 0.703380i | 0.936117 | + | 0.351690i | \(0.114393\pi\) | ||||
−0.936117 | + | 0.351690i | \(0.885607\pi\) | |||||||
\(360\) | −51.7359 | − | 230.393i | −0.143711 | − | 0.639980i | ||||
\(361\) | −268.998 | −0.745148 | ||||||||
\(362\) | 84.9200i | 0.234586i | ||||||||
\(363\) | −29.5790 | + | 36.9577i | −0.0814848 | + | 0.101812i | ||||
\(364\) | −738.769 | −2.02959 | ||||||||
\(365\) | − | 227.597i | − | 0.623554i | ||||||
\(366\) | 9.63994 | + | 7.71530i | 0.0263386 | + | 0.0210801i | ||||
\(367\) | 377.542 | 1.02872 | 0.514362 | − | 0.857573i | \(-0.328029\pi\) | ||||
0.514362 | + | 0.857573i | \(0.328029\pi\) | |||||||
\(368\) | 62.6044i | 0.170121i | ||||||||
\(369\) | −544.735 | + | 122.323i | −1.47625 | + | 0.331499i | ||||
\(370\) | −191.521 | −0.517623 | ||||||||
\(371\) | 211.841i | 0.570999i | ||||||||
\(372\) | 59.3200 | − | 74.1179i | 0.159462 | − | 0.199242i | ||||
\(373\) | 113.060 | 0.303111 | 0.151555 | − | 0.988449i | \(-0.451572\pi\) | ||||
0.151555 | + | 0.988449i | \(0.451572\pi\) | |||||||
\(374\) | − | 179.554i | − | 0.480090i | ||||||
\(375\) | −223.002 | − | 178.479i | −0.594672 | − | 0.475944i | ||||
\(376\) | −156.928 | −0.417360 | ||||||||
\(377\) | − | 113.592i | − | 0.301305i | ||||||
\(378\) | −67.2814 | + | 137.851i | −0.177993 | + | 0.364685i | ||||
\(379\) | 405.803 | 1.07072 | 0.535360 | − | 0.844624i | \(-0.320176\pi\) | ||||
0.535360 | + | 0.844624i | \(0.320176\pi\) | |||||||
\(380\) | 202.809i | 0.533709i | ||||||||
\(381\) | 262.188 | − | 327.592i | 0.688156 | − | 0.859822i | ||||
\(382\) | 21.4705 | 0.0562054 | ||||||||
\(383\) | 454.658i | 1.18710i | 0.804798 | + | 0.593548i | \(0.202273\pi\) | ||||
−0.804798 | + | 0.593548i | \(0.797727\pi\) | |||||||
\(384\) | 281.242 | + | 225.091i | 0.732401 | + | 0.586175i | ||||
\(385\) | −650.258 | −1.68898 | ||||||||
\(386\) | − | 153.428i | − | 0.397482i | ||||||
\(387\) | 45.4398 | + | 202.355i | 0.117415 | + | 0.522880i | ||||
\(388\) | −153.070 | −0.394509 | ||||||||
\(389\) | 562.968i | 1.44722i | 0.690209 | + | 0.723610i | \(0.257518\pi\) | ||||
−0.690209 | + | 0.723610i | \(0.742482\pi\) | |||||||
\(390\) | 135.621 | − | 169.452i | 0.347745 | − | 0.434493i | ||||
\(391\) | −136.236 | −0.348430 | ||||||||
\(392\) | 195.166i | 0.497872i | ||||||||
\(393\) | 39.0268 | + | 31.2350i | 0.0993048 | + | 0.0794783i | ||||
\(394\) | −70.9951 | −0.180191 | ||||||||
\(395\) | − | 50.0411i | − | 0.126686i | ||||||
\(396\) | 374.807 | − | 84.1648i | 0.946482 | − | 0.212537i | ||||
\(397\) | 484.369 | 1.22007 | 0.610037 | − | 0.792373i | \(-0.291155\pi\) | ||||
0.610037 | + | 0.792373i | \(0.291155\pi\) | |||||||
\(398\) | 75.5425i | 0.189805i | ||||||||
\(399\) | 172.554 | − | 215.599i | 0.432466 | − | 0.540348i | ||||
\(400\) | −102.089 | −0.255223 | ||||||||
\(401\) | 274.521i | 0.684591i | 0.939592 | + | 0.342295i | \(0.111204\pi\) | ||||
−0.939592 | + | 0.342295i | \(0.888796\pi\) | |||||||
\(402\) | −138.585 | − | 110.916i | −0.344738 | − | 0.275910i | ||||
\(403\) | 182.897 | 0.453840 | ||||||||
\(404\) | 233.333i | 0.577556i | ||||||||
\(405\) | 200.644 | + | 424.231i | 0.495417 | + | 1.04748i | ||||
\(406\) | −30.5945 | −0.0753558 | ||||||||
\(407\) | − | 653.058i | − | 1.60456i | ||||||
\(408\) | −220.153 | + | 275.071i | −0.539590 | + | 0.674195i | ||||
\(409\) | −137.445 | −0.336051 | −0.168026 | − | 0.985783i | \(-0.553739\pi\) | ||||
−0.168026 | + | 0.985783i | \(0.553739\pi\) | |||||||
\(410\) | − | 212.765i | − | 0.518938i | ||||||
\(411\) | −214.713 | − | 171.845i | −0.522415 | − | 0.418114i | ||||
\(412\) | 102.865 | 0.249672 | ||||||||
\(413\) | − | 72.2449i | − | 0.174927i | ||||||
\(414\) | 6.13242 | + | 27.3092i | 0.0148126 | + | 0.0659643i | ||||
\(415\) | 315.478 | 0.760187 | ||||||||
\(416\) | 530.903i | 1.27621i | ||||||||
\(417\) | −180.980 | + | 226.126i | −0.434004 | + | 0.542270i | ||||
\(418\) | 66.4092 | 0.158874 | ||||||||
\(419\) | − | 624.266i | − | 1.48990i | −0.667122 | − | 0.744948i | \(-0.732474\pi\) | ||
0.667122 | − | 0.744948i | \(-0.267526\pi\) | |||||||
\(420\) | 475.269 | + | 380.380i | 1.13159 | + | 0.905667i | ||||
\(421\) | 385.339 | 0.915295 | 0.457648 | − | 0.889134i | \(-0.348692\pi\) | ||||
0.457648 | + | 0.889134i | \(0.348692\pi\) | |||||||
\(422\) | − | 94.0584i | − | 0.222887i | ||||||
\(423\) | 304.301 | − | 68.3323i | 0.719387 | − | 0.161542i | ||||
\(424\) | 99.9637 | 0.235763 | ||||||||
\(425\) | − | 222.160i | − | 0.522730i | ||||||
\(426\) | 152.682 | − | 190.769i | 0.358408 | − | 0.447815i | ||||
\(427\) | −66.7191 | −0.156251 | ||||||||
\(428\) | 75.1209i | 0.175516i | ||||||||
\(429\) | 577.808 | + | 462.447i | 1.34687 | + | 1.07796i | ||||
\(430\) | −79.0363 | −0.183805 | ||||||||
\(431\) | − | 336.616i | − | 0.781010i | −0.920601 | − | 0.390505i | \(-0.872300\pi\) | ||
0.920601 | − | 0.390505i | \(-0.127700\pi\) | |||||||
\(432\) | −289.163 | − | 141.133i | −0.669358 | − | 0.326697i | ||||
\(433\) | −819.659 | −1.89298 | −0.946488 | − | 0.322738i | \(-0.895397\pi\) | ||||
−0.946488 | + | 0.322738i | \(0.895397\pi\) | |||||||
\(434\) | − | 49.2610i | − | 0.113505i | ||||||
\(435\) | −58.4866 | + | 73.0765i | −0.134452 | + | 0.167992i | ||||
\(436\) | 194.994 | 0.447234 | ||||||||
\(437\) | − | 50.3878i | − | 0.115304i | ||||||
\(438\) | 54.4704 | + | 43.5952i | 0.124362 | + | 0.0995324i | ||||
\(439\) | −173.257 | −0.394662 | −0.197331 | − | 0.980337i | \(-0.563227\pi\) | ||||
−0.197331 | + | 0.980337i | \(0.563227\pi\) | |||||||
\(440\) | 306.845i | 0.697374i | ||||||||
\(441\) | −84.9827 | − | 378.449i | −0.192704 | − | 0.858161i | ||||
\(442\) | −323.842 | −0.732673 | ||||||||
\(443\) | − | 172.338i | − | 0.389025i | −0.980900 | − | 0.194513i | \(-0.937687\pi\) | ||
0.980900 | − | 0.194513i | \(-0.0623125\pi\) | |||||||
\(444\) | −382.018 | + | 477.315i | −0.860401 | + | 1.07503i | ||||
\(445\) | 482.436 | 1.08413 | ||||||||
\(446\) | − | 237.014i | − | 0.531422i | ||||||
\(447\) | −454.691 | − | 363.911i | −1.01721 | − | 0.814118i | ||||
\(448\) | −314.475 | −0.701953 | ||||||||
\(449\) | − | 70.7383i | − | 0.157546i | −0.996893 | − | 0.0787731i | \(-0.974900\pi\) | ||
0.996893 | − | 0.0787731i | \(-0.0251003\pi\) | |||||||
\(450\) | −44.5332 | + | 10.0002i | −0.0989626 | + | 0.0222226i | ||||
\(451\) | 725.496 | 1.60864 | ||||||||
\(452\) | − | 115.473i | − | 0.255472i | ||||||
\(453\) | 98.3610 | − | 122.898i | 0.217132 | − | 0.271298i | ||||
\(454\) | 59.2856 | 0.130585 | ||||||||
\(455\) | 1172.80i | 2.57758i | ||||||||
\(456\) | −101.737 | − | 81.4250i | −0.223108 | − | 0.178564i | ||||
\(457\) | −46.7867 | −0.102378 | −0.0511890 | − | 0.998689i | \(-0.516301\pi\) | ||||
−0.0511890 | + | 0.998689i | \(0.516301\pi\) | |||||||
\(458\) | 116.523i | 0.254418i | ||||||||
\(459\) | 307.125 | − | 629.259i | 0.669118 | − | 1.37093i | ||||
\(460\) | 111.076 | 0.241469 | ||||||||
\(461\) | 582.934i | 1.26450i | 0.774765 | + | 0.632250i | \(0.217868\pi\) | ||||
−0.774765 | + | 0.632250i | \(0.782132\pi\) | |||||||
\(462\) | 124.554 | − | 155.625i | 0.269597 | − | 0.336850i | ||||
\(463\) | 879.627 | 1.89984 | 0.949921 | − | 0.312489i | \(-0.101163\pi\) | ||||
0.949921 | + | 0.312489i | \(0.101163\pi\) | |||||||
\(464\) | − | 64.1765i | − | 0.138311i | ||||||
\(465\) | −117.662 | − | 94.1709i | −0.253038 | − | 0.202518i | ||||
\(466\) | −216.053 | −0.463632 | ||||||||
\(467\) | − | 12.3860i | − | 0.0265225i | −0.999912 | − | 0.0132612i | \(-0.995779\pi\) | ||
0.999912 | − | 0.0132612i | \(-0.00422131\pi\) | |||||||
\(468\) | −151.799 | − | 675.999i | −0.324357 | − | 1.44444i | ||||
\(469\) | 959.161 | 2.04512 | ||||||||
\(470\) | 118.855i | 0.252883i | ||||||||
\(471\) | 273.014 | − | 341.120i | 0.579649 | − | 0.724246i | ||||
\(472\) | −34.0911 | −0.0722268 | ||||||||
\(473\) | − | 269.502i | − | 0.569773i | ||||||
\(474\) | 11.9762 | + | 9.58515i | 0.0252663 | + | 0.0202218i | ||||
\(475\) | 82.1676 | 0.172984 | ||||||||
\(476\) | − | 908.290i | − | 1.90817i | ||||||
\(477\) | −193.841 | + | 43.5281i | −0.406376 | + | 0.0912538i | ||||
\(478\) | −76.6046 | −0.160261 | ||||||||
\(479\) | 98.8167i | 0.206298i | 0.994666 | + | 0.103149i | \(0.0328918\pi\) | ||||
−0.994666 | + | 0.103149i | \(0.967108\pi\) | |||||||
\(480\) | 273.353 | − | 341.544i | 0.569486 | − | 0.711549i | ||||
\(481\) | −1177.85 | −2.44875 | ||||||||
\(482\) | − | 46.7650i | − | 0.0970229i | ||||||
\(483\) | −118.080 | − | 94.5051i | −0.244472 | − | 0.195663i | ||||
\(484\) | −57.5860 | −0.118979 | ||||||||
\(485\) | 242.999i | 0.501029i | ||||||||
\(486\) | −139.963 | − | 33.2398i | −0.287989 | − | 0.0683946i | ||||
\(487\) | −372.714 | −0.765326 | −0.382663 | − | 0.923888i | \(-0.624993\pi\) | ||||
−0.382663 | + | 0.923888i | \(0.624993\pi\) | |||||||
\(488\) | 31.4836i | 0.0645155i | ||||||||
\(489\) | −319.441 | + | 399.128i | −0.653253 | + | 0.816212i | ||||
\(490\) | 147.816 | 0.301665 | ||||||||
\(491\) | 168.548i | 0.343274i | 0.985160 | + | 0.171637i | \(0.0549057\pi\) | ||||
−0.985160 | + | 0.171637i | \(0.945094\pi\) | |||||||
\(492\) | −530.260 | − | 424.392i | −1.07776 | − | 0.862586i | ||||
\(493\) | 139.657 | 0.283280 | ||||||||
\(494\) | − | 119.775i | − | 0.242460i | ||||||
\(495\) | −133.612 | − | 595.008i | −0.269923 | − | 1.20204i | ||||
\(496\) | 103.332 | 0.208331 | ||||||||
\(497\) | 1320.34i | 2.65661i | ||||||||
\(498\) | −60.4283 | + | 75.5026i | −0.121342 | + | 0.151612i | ||||
\(499\) | −64.2216 | −0.128701 | −0.0643503 | − | 0.997927i | \(-0.520498\pi\) | ||||
−0.0643503 | + | 0.997927i | \(0.520498\pi\) | |||||||
\(500\) | − | 347.473i | − | 0.694946i | ||||||
\(501\) | 771.215 | + | 617.240i | 1.53935 | + | 1.23202i | ||||
\(502\) | −60.9062 | −0.121327 | ||||||||
\(503\) | − | 540.746i | − | 1.07504i | −0.843251 | − | 0.537521i | \(-0.819361\pi\) | ||
0.843251 | − | 0.537521i | \(-0.180639\pi\) | |||||||
\(504\) | −381.627 | + | 85.6963i | −0.757196 | + | 0.170032i | ||||
\(505\) | 370.417 | 0.733498 | ||||||||
\(506\) | − | 36.3713i | − | 0.0718800i | ||||||
\(507\) | 517.262 | − | 646.296i | 1.02024 | − | 1.27475i | ||||
\(508\) | 510.441 | 1.00481 | ||||||||
\(509\) | − | 331.526i | − | 0.651328i | −0.945486 | − | 0.325664i | \(-0.894412\pi\) | ||
0.945486 | − | 0.325664i | \(-0.105588\pi\) | |||||||
\(510\) | 208.336 | + | 166.741i | 0.408501 | + | 0.326943i | ||||
\(511\) | −376.996 | −0.737761 | ||||||||
\(512\) | 515.817i | 1.00746i | ||||||||
\(513\) | 232.736 | + | 113.592i | 0.453676 | + | 0.221427i | ||||
\(514\) | 93.0749 | 0.181080 | ||||||||
\(515\) | − | 163.299i | − | 0.317085i | ||||||
\(516\) | −157.650 | + | 196.977i | −0.305524 | + | 0.381739i | ||||
\(517\) | −405.278 | −0.783903 | ||||||||
\(518\) | 317.238i | 0.612429i | ||||||||
\(519\) | −523.140 | − | 418.694i | −1.00798 | − | 0.806732i | ||||
\(520\) | 553.423 | 1.06427 | ||||||||
\(521\) | 560.227i | 1.07529i | 0.843171 | + | 0.537646i | \(0.180686\pi\) | ||||
−0.843171 | + | 0.537646i | \(0.819314\pi\) | |||||||
\(522\) | −6.28641 | − | 27.9950i | −0.0120429 | − | 0.0536302i | ||||
\(523\) | 569.804 | 1.08949 | 0.544746 | − | 0.838601i | \(-0.316626\pi\) | ||||
0.544746 | + | 0.838601i | \(0.316626\pi\) | |||||||
\(524\) | 60.8100i | 0.116050i | ||||||||
\(525\) | 154.110 | − | 192.554i | 0.293542 | − | 0.366769i | ||||
\(526\) | 241.178 | 0.458513 | ||||||||
\(527\) | 224.866i | 0.426690i | ||||||||
\(528\) | 326.447 | + | 261.271i | 0.618270 | + | 0.494831i | ||||
\(529\) | 501.403 | 0.947832 | ||||||||
\(530\) | − | 75.7112i | − | 0.142851i | ||||||
\(531\) | 66.1065 | − | 14.8446i | 0.124494 | − | 0.0279559i | ||||
\(532\) | 335.937 | 0.631461 | ||||||||
\(533\) | − | 1308.50i | − | 2.45497i | ||||||
\(534\) | −92.4085 | + | 115.460i | −0.173050 | + | 0.216218i | ||||
\(535\) | 119.255 | 0.222906 | ||||||||
\(536\) | − | 452.611i | − | 0.844423i | ||||||
\(537\) | −52.4641 | − | 41.9895i | −0.0976984 | − | 0.0781927i | ||||
\(538\) | 70.6665 | 0.131350 | ||||||||
\(539\) | 504.031i | 0.935122i | ||||||||
\(540\) | −250.405 | + | 513.046i | −0.463712 | + | 0.950085i | ||||
\(541\) | −775.645 | −1.43373 | −0.716863 | − | 0.697214i | \(-0.754423\pi\) | ||||
−0.716863 | + | 0.697214i | \(0.754423\pi\) | |||||||
\(542\) | 183.724i | 0.338973i | ||||||||
\(543\) | 268.902 | − | 335.981i | 0.495215 | − | 0.618750i | ||||
\(544\) | −652.726 | −1.19986 | ||||||||
\(545\) | − | 309.554i | − | 0.567989i | ||||||
\(546\) | −280.684 | − | 224.645i | −0.514073 | − | 0.411437i | ||||
\(547\) | −810.832 | −1.48232 | −0.741162 | − | 0.671326i | \(-0.765725\pi\) | ||||
−0.741162 | + | 0.671326i | \(0.765725\pi\) | |||||||
\(548\) | − | 334.557i | − | 0.610505i | ||||||
\(549\) | −13.7092 | − | 61.0503i | −0.0249711 | − | 0.111203i | ||||
\(550\) | 59.3108 | 0.107838 | ||||||||
\(551\) | 51.6531i | 0.0937443i | ||||||||
\(552\) | −44.5952 | + | 55.7199i | −0.0807885 | + | 0.100942i | ||||
\(553\) | −82.8889 | −0.149890 | ||||||||
\(554\) | − | 20.3054i | − | 0.0366523i | ||||||
\(555\) | 757.741 | + | 606.456i | 1.36530 | + | 1.09271i | ||||
\(556\) | −352.341 | −0.633707 | ||||||||
\(557\) | 18.0342i | 0.0323775i | 0.999869 | + | 0.0161887i | \(0.00515326\pi\) | ||||
−0.999869 | + | 0.0161887i | \(0.994847\pi\) | |||||||
\(558\) | 45.0755 | − | 10.1219i | 0.0807804 | − | 0.0181397i | ||||
\(559\) | −486.072 | −0.869539 | ||||||||
\(560\) | 662.602i | 1.18322i | ||||||||
\(561\) | −568.562 | + | 710.394i | −1.01348 | + | 1.26630i | ||||
\(562\) | 247.692 | 0.440733 | ||||||||
\(563\) | − | 39.9304i | − | 0.0709243i | −0.999371 | − | 0.0354622i | \(-0.988710\pi\) | ||
0.999371 | − | 0.0354622i | \(-0.0112903\pi\) | |||||||
\(564\) | 296.215 | + | 237.075i | 0.525203 | + | 0.420345i | ||||
\(565\) | −183.315 | −0.324450 | ||||||||
\(566\) | 62.7525i | 0.110870i | ||||||||
\(567\) | 702.703 | − | 332.350i | 1.23934 | − | 0.586155i | ||||
\(568\) | 623.043 | 1.09691 | ||||||||
\(569\) | 761.946i | 1.33910i | 0.742768 | + | 0.669549i | \(0.233512\pi\) | ||||
−0.742768 | + | 0.669549i | \(0.766488\pi\) | |||||||
\(570\) | −61.6702 | + | 77.0543i | −0.108193 | + | 0.135183i | ||||
\(571\) | −1064.02 | −1.86344 | −0.931718 | − | 0.363182i | \(-0.881690\pi\) | ||||
−0.931718 | + | 0.363182i | \(0.881690\pi\) | |||||||
\(572\) | 900.317i | 1.57398i | ||||||||
\(573\) | −84.9467 | − | 67.9869i | −0.148249 | − | 0.118651i | ||||
\(574\) | −352.427 | −0.613984 | ||||||||
\(575\) | − | 45.0019i | − | 0.0782642i | ||||||
\(576\) | −64.6170 | − | 287.755i | −0.112182 | − | 0.499575i | ||||
\(577\) | 973.716 | 1.68755 | 0.843774 | − | 0.536698i | \(-0.180329\pi\) | ||||
0.843774 | + | 0.536698i | \(0.180329\pi\) | |||||||
\(578\) | − | 227.064i | − | 0.392844i | ||||||
\(579\) | −485.835 | + | 607.030i | −0.839093 | + | 1.04841i | ||||
\(580\) | −113.865 | −0.196319 | ||||||||
\(581\) | − | 522.563i | − | 0.899419i | ||||||
\(582\) | −58.1565 | − | 46.5454i | −0.0999252 | − | 0.0799748i | ||||
\(583\) | 258.164 | 0.442820 | ||||||||
\(584\) | 177.897i | 0.304619i | ||||||||
\(585\) | −1073.15 | + | 240.982i | −1.83445 | + | 0.411935i | ||||
\(586\) | 26.2803 | 0.0448469 | ||||||||
\(587\) | − | 58.2841i | − | 0.0992915i | −0.998767 | − | 0.0496458i | \(-0.984191\pi\) | ||
0.998767 | − | 0.0496458i | \(-0.0158092\pi\) | |||||||
\(588\) | 294.842 | − | 368.393i | 0.501432 | − | 0.626518i | ||||
\(589\) | −83.1681 | −0.141202 | ||||||||
\(590\) | 25.8201i | 0.0437629i | ||||||||
\(591\) | 280.888 | + | 224.808i | 0.475276 | + | 0.380386i | ||||
\(592\) | −665.455 | −1.12408 | ||||||||
\(593\) | 1049.87i | 1.77043i | 0.465180 | + | 0.885216i | \(0.345990\pi\) | ||||
−0.465180 | + | 0.885216i | \(0.654010\pi\) | |||||||
\(594\) | 167.995 | + | 81.9940i | 0.282820 | + | 0.138037i | ||||
\(595\) | −1441.91 | −2.42339 | ||||||||
\(596\) | − | 708.481i | − | 1.18873i | ||||||
\(597\) | 239.208 | − | 298.880i | 0.400683 | − | 0.500636i | ||||
\(598\) | −65.5990 | −0.109697 | ||||||||
\(599\) | − | 737.946i | − | 1.23196i | −0.787761 | − | 0.615982i | \(-0.788760\pi\) | ||
0.787761 | − | 0.615982i | \(-0.211240\pi\) | |||||||
\(600\) | −90.8625 | − | 72.7216i | −0.151438 | − | 0.121203i | ||||
\(601\) | 1149.40 | 1.91247 | 0.956237 | − | 0.292595i | \(-0.0945186\pi\) | ||||
0.956237 | + | 0.292595i | \(0.0945186\pi\) | |||||||
\(602\) | 130.917i | 0.217470i | ||||||||
\(603\) | 197.084 | + | 877.665i | 0.326839 | + | 1.45550i | ||||
\(604\) | 191.495 | 0.317044 | ||||||||
\(605\) | 91.4180i | 0.151104i | ||||||||
\(606\) | −70.9517 | + | 88.6511i | −0.117082 | + | 0.146289i | ||||
\(607\) | −852.763 | −1.40488 | −0.702441 | − | 0.711742i | \(-0.747907\pi\) | ||||
−0.702441 | + | 0.711742i | \(0.747907\pi\) | |||||||
\(608\) | − | 241.415i | − | 0.397065i | ||||||
\(609\) | 121.045 | + | 96.8782i | 0.198761 | + | 0.159077i | ||||
\(610\) | 23.8452 | 0.0390905 | ||||||||
\(611\) | 730.956i | 1.19633i | ||||||||
\(612\) | 831.116 | − | 186.631i | 1.35803 | − | 0.304953i | ||||
\(613\) | −823.924 | −1.34408 | −0.672042 | − | 0.740513i | \(-0.734583\pi\) | ||||
−0.672042 | + | 0.740513i | \(0.734583\pi\) | |||||||
\(614\) | − | 9.87742i | − | 0.0160870i | ||||||
\(615\) | −673.725 | + | 841.791i | −1.09549 | + | 1.36877i | ||||
\(616\) | 508.263 | 0.825102 | ||||||||
\(617\) | 47.3880i | 0.0768038i | 0.999262 | + | 0.0384019i | \(0.0122267\pi\) | ||||
−0.999262 | + | 0.0384019i | \(0.987773\pi\) | |||||||
\(618\) | 39.0819 | + | 31.2791i | 0.0632394 | + | 0.0506134i | ||||
\(619\) | −505.631 | −0.816852 | −0.408426 | − | 0.912792i | \(-0.633922\pi\) | ||||
−0.408426 | + | 0.912792i | \(0.633922\pi\) | |||||||
\(620\) | − | 183.337i | − | 0.295705i | ||||||
\(621\) | 62.2128 | − | 127.466i | 0.100182 | − | 0.205259i | ||||
\(622\) | 160.232 | 0.257607 | ||||||||
\(623\) | − | 799.115i | − | 1.28269i | ||||||
\(624\) | 471.226 | − | 588.777i | 0.755170 | − | 0.943552i | ||||
\(625\) | −765.777 | −1.22524 | ||||||||
\(626\) | − | 62.8673i | − | 0.100427i | ||||||
\(627\) | −262.744 | − | 210.286i | −0.419050 | − | 0.335385i | ||||
\(628\) | 531.520 | 0.846369 | ||||||||
\(629\) | − | 1448.12i | − | 2.30226i | ||||||
\(630\) | 64.9052 | + | 289.039i | 0.103024 | + | 0.458792i | ||||
\(631\) | −254.186 | −0.402830 | −0.201415 | − | 0.979506i | \(-0.564554\pi\) | ||||
−0.201415 | + | 0.979506i | \(0.564554\pi\) | |||||||
\(632\) | 39.1138i | 0.0618889i | ||||||||
\(633\) | −297.839 | + | 372.137i | −0.470519 | + | 0.587894i | ||||
\(634\) | 74.0096 | 0.116734 | ||||||||
\(635\) | − | 810.328i | − | 1.27611i | ||||||
\(636\) | −188.690 | − | 151.018i | −0.296683 | − | 0.237449i | ||||
\(637\) | 909.066 | 1.42710 | ||||||||
\(638\) | 37.2846i | 0.0584398i | ||||||||
\(639\) | −1208.15 | + | 271.297i | −1.89069 | + | 0.424565i | ||||
\(640\) | 695.677 | 1.08700 | ||||||||
\(641\) | 429.687i | 0.670339i | 0.942158 | + | 0.335169i | \(0.108794\pi\) | ||||
−0.942158 | + | 0.335169i | \(0.891206\pi\) | |||||||
\(642\) | −22.8427 | + | 28.5410i | −0.0355806 | + | 0.0444564i | ||||
\(643\) | 972.930 | 1.51311 | 0.756556 | − | 0.653929i | \(-0.226881\pi\) | ||||
0.756556 | + | 0.653929i | \(0.226881\pi\) | |||||||
\(644\) | − | 183.988i | − | 0.285695i | ||||||
\(645\) | 312.703 | + | 250.271i | 0.484810 | + | 0.388017i | ||||
\(646\) | 147.259 | 0.227955 | ||||||||
\(647\) | 477.680i | 0.738300i | 0.929370 | + | 0.369150i | \(0.120351\pi\) | ||||
−0.929370 | + | 0.369150i | \(0.879649\pi\) | |||||||
\(648\) | −156.830 | − | 331.593i | −0.242022 | − | 0.511717i | ||||
\(649\) | −88.0429 | −0.135659 | ||||||||
\(650\) | − | 106.972i | − | 0.164573i | ||||||
\(651\) | −155.986 | + | 194.898i | −0.239610 | + | 0.299383i | ||||
\(652\) | −621.905 | −0.953842 | ||||||||
\(653\) | − | 1265.67i | − | 1.93823i | −0.246604 | − | 0.969116i | \(-0.579315\pi\) | ||
0.246604 | − | 0.969116i | \(-0.420685\pi\) | |||||||
\(654\) | 74.0849 | + | 59.2936i | 0.113280 | + | 0.0906631i | ||||
\(655\) | 96.5362 | 0.147383 | ||||||||
\(656\) | − | 739.269i | − | 1.12693i | ||||||
\(657\) | −77.4634 | − | 344.964i | −0.117905 | − | 0.525059i | ||||
\(658\) | 196.873 | 0.299199 | ||||||||
\(659\) | − | 390.420i | − | 0.592443i | −0.955119 | − | 0.296221i | \(-0.904273\pi\) | ||
0.955119 | − | 0.296221i | \(-0.0957266\pi\) | |||||||
\(660\) | 463.559 | − | 579.197i | 0.702362 | − | 0.877571i | ||||
\(661\) | −523.839 | −0.792495 | −0.396248 | − | 0.918144i | \(-0.629688\pi\) | ||||
−0.396248 | + | 0.918144i | \(0.629688\pi\) | |||||||
\(662\) | 273.058i | 0.412474i | ||||||||
\(663\) | 1281.26 | + | 1025.45i | 1.93252 | + | 1.54669i | ||||
\(664\) | −246.588 | −0.371367 | ||||||||
\(665\) | − | 533.302i | − | 0.801958i | ||||||
\(666\) | −290.284 | + | 65.1847i | −0.435861 | + | 0.0978749i | ||||
\(667\) | 28.2896 | 0.0424132 | ||||||||
\(668\) | 1201.68i | 1.79892i | ||||||||
\(669\) | −750.513 | + | 937.734i | −1.12184 | + | 1.40169i | ||||
\(670\) | −342.801 | −0.511644 | ||||||||
\(671\) | 81.3088i | 0.121176i | ||||||||
\(672\) | −565.739 | − | 452.787i | −0.841873 | − | 0.673791i | ||||
\(673\) | 313.476 | 0.465789 | 0.232894 | − | 0.972502i | \(-0.425180\pi\) | ||||
0.232894 | + | 0.972502i | \(0.425180\pi\) | |||||||
\(674\) | 331.964i | 0.492528i | ||||||||
\(675\) | 207.859 | + | 101.451i | 0.307939 | + | 0.150297i | ||||
\(676\) | 1007.03 | 1.48969 | ||||||||
\(677\) | 417.075i | 0.616064i | 0.951376 | + | 0.308032i | \(0.0996704\pi\) | ||||
−0.951376 | + | 0.308032i | \(0.900330\pi\) | |||||||
\(678\) | 35.1131 | − | 43.8723i | 0.0517892 | − | 0.0647084i | ||||
\(679\) | 402.508 | 0.592795 | ||||||||
\(680\) | 680.413i | 1.00061i | ||||||||
\(681\) | −234.560 | − | 187.730i | −0.344435 | − | 0.275668i | ||||
\(682\) | −60.0330 | −0.0880249 | ||||||||
\(683\) | 189.165i | 0.276962i | 0.990365 | + | 0.138481i | \(0.0442220\pi\) | ||||
−0.990365 | + | 0.138481i | \(0.955778\pi\) | |||||||
\(684\) | 69.0269 | + | 307.394i | 0.100917 | + | 0.449406i | ||||
\(685\) | −531.111 | −0.775344 | ||||||||
\(686\) | 33.5362i | 0.0488866i | ||||||||
\(687\) | 368.975 | − | 461.018i | 0.537081 | − | 0.671060i | ||||
\(688\) | −274.619 | −0.399155 | ||||||||
\(689\) | − | 465.623i | − | 0.675795i | ||||||
\(690\) | 42.2015 | + | 33.7759i | 0.0611616 | + | 0.0489505i | ||||
\(691\) | 140.199 | 0.202893 | 0.101446 | − | 0.994841i | \(-0.467653\pi\) | ||||
0.101446 | + | 0.994841i | \(0.467653\pi\) | |||||||
\(692\) | − | 815.136i | − | 1.17794i | ||||||
\(693\) | −985.581 | + | 221.317i | −1.42220 | + | 0.319361i | ||||
\(694\) | −152.129 | −0.219206 | ||||||||
\(695\) | 559.343i | 0.804811i | ||||||||
\(696\) | 45.7151 | − | 57.1190i | 0.0656826 | − | 0.0820676i | ||||
\(697\) | 1608.75 | 2.30811 | ||||||||
\(698\) | − | 240.140i | − | 0.344040i | ||||||
\(699\) | 854.799 | + | 684.136i | 1.22289 | + | 0.978736i | ||||
\(700\) | 300.029 | 0.428613 | ||||||||
\(701\) | − | 927.437i | − | 1.32302i | −0.749936 | − | 0.661510i | \(-0.769916\pi\) | ||
0.749936 | − | 0.661510i | \(-0.230084\pi\) | |||||||
\(702\) | 147.884 | − | 302.994i | 0.210661 | − | 0.431616i | ||||
\(703\) | 535.598 | 0.761875 | ||||||||
\(704\) | 383.242i | 0.544378i | ||||||||
\(705\) | 376.357 | − | 470.242i | 0.533840 | − | 0.667010i | ||||
\(706\) | 163.976 | 0.232261 | ||||||||
\(707\) | − | 613.565i | − | 0.867842i | ||||||
\(708\) | 64.3499 | + | 51.5023i | 0.0908897 | + | 0.0727433i | ||||
\(709\) | 763.851 | 1.07736 | 0.538682 | − | 0.842509i | \(-0.318923\pi\) | ||||
0.538682 | + | 0.842509i | \(0.318923\pi\) | |||||||
\(710\) | − | 471.885i | − | 0.664626i | ||||||
\(711\) | −17.0317 | − | 75.8462i | −0.0239545 | − | 0.106675i | ||||
\(712\) | −377.088 | −0.529618 | ||||||||
\(713\) | 45.5499i | 0.0638849i | ||||||||
\(714\) | 276.192 | − | 345.091i | 0.386824 | − | 0.483320i | ||||
\(715\) | 1429.26 | 1.99896 | ||||||||
\(716\) | − | 81.7474i | − | 0.114172i | ||||||
\(717\) | 303.082 | + | 242.571i | 0.422708 | + | 0.338313i | ||||
\(718\) | −149.488 | −0.208200 | ||||||||
\(719\) | 957.517i | 1.33173i | 0.746070 | + | 0.665867i | \(0.231938\pi\) | ||||
−0.746070 | + | 0.665867i | \(0.768062\pi\) | |||||||
\(720\) | −606.303 | + | 136.149i | −0.842088 | + | 0.189095i | ||||
\(721\) | −270.491 | −0.375160 | ||||||||
\(722\) | − | 159.247i | − | 0.220563i | ||||||
\(723\) | −148.083 | + | 185.023i | −0.204817 | + | 0.255910i | ||||
\(724\) | 523.513 | 0.723084 | ||||||||
\(725\) | 46.1320i | 0.0636303i | ||||||||
\(726\) | −21.8789 | − | 17.5107i | −0.0301362 | − | 0.0241194i | ||||
\(727\) | 192.761 | 0.265145 | 0.132573 | − | 0.991173i | \(-0.457676\pi\) | ||||
0.132573 | + | 0.991173i | \(0.457676\pi\) | |||||||
\(728\) | − | 916.699i | − | 1.25920i | ||||||
\(729\) | 448.500 | + | 574.708i | 0.615226 | + | 0.788350i | ||||
\(730\) | 134.737 | 0.184571 | ||||||||
\(731\) | − | 597.608i | − | 0.817522i | ||||||
\(732\) | 47.5631 | − | 59.4280i | 0.0649768 | − | 0.0811858i | ||||
\(733\) | 211.579 | 0.288648 | 0.144324 | − | 0.989530i | \(-0.453899\pi\) | ||||
0.144324 | + | 0.989530i | \(0.453899\pi\) | |||||||
\(734\) | 223.504i | 0.304502i | ||||||||
\(735\) | −584.825 | − | 468.063i | −0.795681 | − | 0.636821i | ||||
\(736\) | −132.220 | −0.179646 | ||||||||
\(737\) | − | 1168.90i | − | 1.58603i | ||||||
\(738\) | −72.4151 | − | 322.483i | −0.0981235 | − | 0.436968i | ||||
\(739\) | −929.012 | −1.25712 | −0.628560 | − | 0.777761i | \(-0.716356\pi\) | ||||
−0.628560 | + | 0.777761i | \(0.716356\pi\) | |||||||
\(740\) | 1180.68i | 1.59551i | ||||||||
\(741\) | −379.271 | + | 473.883i | −0.511837 | + | 0.639518i | ||||
\(742\) | −125.409 | −0.169015 | ||||||||
\(743\) | − | 714.016i | − | 0.960990i | −0.876997 | − | 0.480495i | \(-0.840457\pi\) | ||
0.876997 | − | 0.480495i | \(-0.159543\pi\) | |||||||
\(744\) | 91.9689 | + | 73.6071i | 0.123614 | + | 0.0989342i | ||||
\(745\) | −1124.72 | −1.50969 | ||||||||
\(746\) | 66.9316i | 0.0897206i | ||||||||
\(747\) | 478.162 | − | 107.374i | 0.640110 | − | 0.143740i | ||||
\(748\) | −1106.91 | −1.47982 | ||||||||
\(749\) | − | 197.536i | − | 0.263733i | ||||||
\(750\) | 105.659 | − | 132.017i | 0.140879 | − | 0.176023i | ||||
\(751\) | 309.044 | 0.411510 | 0.205755 | − | 0.978603i | \(-0.434035\pi\) | ||||
0.205755 | + | 0.978603i | \(0.434035\pi\) | |||||||
\(752\) | 412.971i | 0.549164i | ||||||||
\(753\) | 240.972 | + | 192.861i | 0.320016 | + | 0.256124i | ||||
\(754\) | 67.2462 | 0.0891860 | ||||||||
\(755\) | − | 303.999i | − | 0.402647i | ||||||
\(756\) | 849.818 | + | 414.774i | 1.12410 | + | 0.548643i | ||||
\(757\) | −349.474 | −0.461656 | −0.230828 | − | 0.972995i | \(-0.574143\pi\) | ||||
−0.230828 | + | 0.972995i | \(0.574143\pi\) | |||||||
\(758\) | 240.235i | 0.316933i | ||||||||
\(759\) | −115.171 | + | 143.901i | −0.151740 | + | 0.189593i | ||||
\(760\) | −251.656 | −0.331126 | ||||||||
\(761\) | 1364.48i | 1.79301i | 0.443035 | + | 0.896504i | \(0.353902\pi\) | ||||
−0.443035 | + | 0.896504i | \(0.646098\pi\) | |||||||
\(762\) | 193.934 | + | 155.215i | 0.254507 | + | 0.203694i | ||||
\(763\) | −512.750 | −0.672019 | ||||||||
\(764\) | − | 132.361i | − | 0.173247i | ||||||
\(765\) | −296.278 | − | 1319.40i | −0.387292 | − | 1.72471i | ||||
\(766\) | −269.157 | −0.351380 | ||||||||
\(767\) | 158.793i | 0.207032i | ||||||||
\(768\) | 112.459 | − | 140.513i | 0.146431 | − | 0.182959i | ||||
\(769\) | −565.496 | −0.735365 | −0.367683 | − | 0.929951i | \(-0.619849\pi\) | ||||
−0.367683 | + | 0.929951i | \(0.619849\pi\) | |||||||
\(770\) | − | 384.952i | − | 0.499937i | ||||||
\(771\) | −368.245 | − | 294.724i | −0.477621 | − | 0.382262i | ||||
\(772\) | −945.850 | −1.22519 | ||||||||
\(773\) | 911.843i | 1.17962i | 0.807544 | + | 0.589808i | \(0.200797\pi\) | ||||
−0.807544 | + | 0.589808i | \(0.799203\pi\) | |||||||
\(774\) | −119.794 | + | 26.9003i | −0.154772 | + | 0.0347549i | ||||
\(775\) | −74.2784 | −0.0958430 | ||||||||
\(776\) | − | 189.936i | − | 0.244763i | ||||||
\(777\) | 1004.54 | − | 1255.13i | 1.29285 | − | 1.61536i | ||||
\(778\) | −333.277 | −0.428376 | ||||||||
\(779\) | 595.008i | 0.763810i | ||||||||
\(780\) | −1044.63 | − | 836.071i | −1.33928 | − | 1.07189i | ||||
\(781\) | 1609.06 | 2.06025 | ||||||||
\(782\) | − | 80.6516i | − | 0.103135i | ||||||
\(783\) | −63.7750 | + | 130.667i | −0.0814495 | + | 0.166879i | ||||
\(784\) | 513.599 | 0.655101 | ||||||||
\(785\) | − | 843.790i | − | 1.07489i | ||||||
\(786\) | −18.4911 | + | 23.1038i | −0.0235255 | + | 0.0293942i | ||||
\(787\) | −57.4282 | −0.0729710 | −0.0364855 | − | 0.999334i | \(-0.511616\pi\) | ||||
−0.0364855 | + | 0.999334i | \(0.511616\pi\) | |||||||
\(788\) | 437.669i | 0.555417i | ||||||||
\(789\) | −954.207 | − | 763.697i | −1.20939 | − | 0.967930i | ||||
\(790\) | 29.6243 | 0.0374991 | ||||||||
\(791\) | 303.645i | 0.383875i | ||||||||
\(792\) | 104.436 | + | 465.078i | 0.131863 | + | 0.587220i | ||||
\(793\) | 146.648 | 0.184928 | ||||||||
\(794\) | 286.746i | 0.361141i | ||||||||
\(795\) | −239.742 | + | 299.547i | −0.301562 | + | 0.376789i | ||||
\(796\) | 465.702 | 0.585053 | ||||||||
\(797\) | 574.353i | 0.720644i | 0.932828 | + | 0.360322i | \(0.117333\pi\) | ||||
−0.932828 | + | 0.360322i | \(0.882667\pi\) | |||||||
\(798\) | 127.634 | + | 102.152i | 0.159943 | + | 0.128010i | ||||
\(799\) | −898.684 | −1.12476 | ||||||||
\(800\) | − | 215.611i | − | 0.269513i | ||||||
\(801\) | 731.218 | − | 164.199i | 0.912881 | − | 0.204992i | ||||
\(802\) | −162.516 | −0.202638 | ||||||||
\(803\) | 459.434i | 0.572147i | ||||||||
\(804\) | −683.771 | + | 854.343i | −0.850461 | + | 1.06262i | ||||
\(805\) | −292.081 | −0.362834 | ||||||||
\(806\) | 108.275i | 0.134336i | ||||||||
\(807\) | −279.588 | − | 223.767i | −0.346453 | − | 0.277283i | ||||
\(808\) | −289.530 | −0.358329 | ||||||||
\(809\) | 516.585i | 0.638548i | 0.947663 | + | 0.319274i | \(0.103439\pi\) | ||||
−0.947663 | + | 0.319274i | \(0.896561\pi\) | |||||||
\(810\) | −251.144 | + | 118.781i | −0.310054 | + | 0.146643i | ||||
\(811\) | 1219.71 | 1.50396 | 0.751981 | − | 0.659185i | \(-0.229098\pi\) | ||||
0.751981 | + | 0.659185i | \(0.229098\pi\) | |||||||
\(812\) | 188.608i | 0.232276i | ||||||||
\(813\) | 581.766 | − | 726.892i | 0.715579 | − | 0.894086i | ||||
\(814\) | 386.609 | 0.474950 | ||||||||
\(815\) | 987.277i | 1.21138i | ||||||||
\(816\) | 723.880 | + | 579.355i | 0.887107 | + | 0.709994i | ||||
\(817\) | 221.030 | 0.270538 | ||||||||
\(818\) | − | 81.3673i | − | 0.0994710i | ||||||
\(819\) | 399.166 | + | 1777.59i | 0.487383 | + | 2.17044i | ||||
\(820\) | −1311.64 | −1.59957 | ||||||||
\(821\) | 760.688i | 0.926539i | 0.886218 | + | 0.463269i | \(0.153324\pi\) | ||||
−0.886218 | + | 0.463269i | \(0.846676\pi\) | |||||||
\(822\) | 101.732 | − | 127.110i | 0.123761 | − | 0.154635i | ||||
\(823\) | −809.343 | −0.983406 | −0.491703 | − | 0.870763i | \(-0.663625\pi\) | ||||
−0.491703 | + | 0.870763i | \(0.663625\pi\) | |||||||
\(824\) | 127.640i | 0.154902i | ||||||||
\(825\) | −234.660 | − | 187.809i | −0.284436 | − | 0.227647i | ||||
\(826\) | 42.7689 | 0.0517783 | ||||||||
\(827\) | − | 240.652i | − | 0.290995i | −0.989359 | − | 0.145497i | \(-0.953522\pi\) | ||
0.989359 | − | 0.145497i | \(-0.0464782\pi\) | |||||||
\(828\) | 168.355 | − | 37.8050i | 0.203327 | − | 0.0456582i | ||||
\(829\) | −1477.23 | −1.78194 | −0.890970 | − | 0.454062i | \(-0.849974\pi\) | ||||
−0.890970 | + | 0.454062i | \(0.849974\pi\) | |||||||
\(830\) | 186.762i | 0.225015i | ||||||||
\(831\) | −64.2975 | + | 80.3370i | −0.0773737 | + | 0.0966751i | ||||
\(832\) | 691.212 | 0.830784 | ||||||||
\(833\) | 1117.66i | 1.34173i | ||||||||
\(834\) | −133.867 | − | 107.140i | −0.160512 | − | 0.128465i | ||||
\(835\) | 1907.67 | 2.28463 | ||||||||
\(836\) | − | 409.397i | − | 0.489710i | ||||||
\(837\) | −210.390 | − | 102.686i | −0.251362 | − | 0.122683i | ||||
\(838\) | 369.565 | 0.441008 | ||||||||
\(839\) | − | 790.443i | − | 0.942125i | −0.882100 | − | 0.471062i | \(-0.843871\pi\) | ||
0.882100 | − | 0.471062i | \(-0.156129\pi\) | |||||||
\(840\) | −471.994 | + | 589.736i | −0.561897 | + | 0.702067i | ||||
\(841\) | −29.0000 | −0.0344828 | ||||||||
\(842\) | 228.120i | 0.270927i | ||||||||
\(843\) | −979.980 | − | 784.324i | −1.16249 | − | 0.930396i | ||||
\(844\) | −579.849 | −0.687025 | ||||||||
\(845\) | − | 1598.67i | − | 1.89192i | ||||||
\(846\) | 40.4527 | + | 180.146i | 0.0478164 | + | 0.212938i | ||||
\(847\) | 151.426 | 0.178780 | ||||||||
\(848\) | − | 263.065i | − | 0.310218i | ||||||
\(849\) | 198.708 | − | 248.277i | 0.234049 | − | 0.292434i | ||||
\(850\) | 131.519 | 0.154728 | ||||||||
\(851\) | − | 293.339i | − | 0.344699i | ||||||
\(852\) | −1176.05 | − | 941.248i | −1.38034 | − | 1.10475i | ||||
\(853\) | 143.410 | 0.168124 | 0.0840619 | − | 0.996461i | \(-0.473211\pi\) | ||||
0.0840619 | + | 0.996461i | \(0.473211\pi\) | |||||||
\(854\) | − | 39.4977i | − | 0.0462502i | ||||||
\(855\) | 487.989 | − | 109.581i | 0.570748 | − | 0.128164i | ||||
\(856\) | −93.2136 | −0.108894 | ||||||||
\(857\) | 1071.85i | 1.25070i | 0.780346 | + | 0.625348i | \(0.215043\pi\) | ||||
−0.780346 | + | 0.625348i | \(0.784957\pi\) | |||||||
\(858\) | −273.768 | + | 342.062i | −0.319077 | + | 0.398673i | ||||
\(859\) | 686.666 | 0.799379 | 0.399689 | − | 0.916651i | \(-0.369118\pi\) | ||||
0.399689 | + | 0.916651i | \(0.369118\pi\) | |||||||
\(860\) | 487.241i | 0.566559i | ||||||||
\(861\) | 1394.36 | + | 1115.97i | 1.61946 | + | 1.29613i | ||||
\(862\) | 199.276 | 0.231179 | ||||||||
\(863\) | − | 1573.31i | − | 1.82307i | −0.411224 | − | 0.911535i | \(-0.634898\pi\) | ||
0.411224 | − | 0.911535i | \(-0.365102\pi\) | |||||||
\(864\) | 298.070 | − | 610.707i | 0.344989 | − | 0.706837i | ||||
\(865\) | −1294.03 | −1.49599 | ||||||||
\(866\) | − | 485.237i | − | 0.560320i | ||||||
\(867\) | −719.004 | + | 898.365i | −0.829301 | + | 1.03618i | ||||
\(868\) | −303.683 | −0.349865 | ||||||||
\(869\) | 101.014i | 0.116242i | ||||||||
\(870\) | −43.2612 | − | 34.6240i | −0.0497255 | − | 0.0397977i | ||||
\(871\) | −2108.22 | −2.42046 | ||||||||
\(872\) | 241.958i | 0.277474i | ||||||||
\(873\) | 82.7055 | + | 368.308i | 0.0947371 | + | 0.421888i | ||||
\(874\) | 29.8295 | 0.0341299 | ||||||||
\(875\) | 913.705i | 1.04423i | ||||||||
\(876\) | 268.754 | − | 335.797i | 0.306797 | − | 0.383330i | ||||
\(877\) | 299.913 | 0.341976 | 0.170988 | − | 0.985273i | \(-0.445304\pi\) | ||||
0.170988 | + | 0.985273i | \(0.445304\pi\) | |||||||
\(878\) | − | 102.568i | − | 0.116820i | ||||||
\(879\) | −103.976 | − | 83.2172i | −0.118289 | − | 0.0946726i | ||||
\(880\) | 807.494 | 0.917607 | ||||||||
\(881\) | 271.490i | 0.308161i | 0.988058 | + | 0.154081i | \(0.0492416\pi\) | ||||
−0.988058 | + | 0.154081i | \(0.950758\pi\) | |||||||
\(882\) | 224.041 | − | 50.3096i | 0.254015 | − | 0.0570404i | ||||
\(883\) | 1279.48 | 1.44901 | 0.724507 | − | 0.689267i | \(-0.242067\pi\) | ||||
0.724507 | + | 0.689267i | \(0.242067\pi\) | |||||||
\(884\) | 1996.41i | 2.25838i | ||||||||
\(885\) | 81.7601 | − | 102.156i | 0.0923843 | − | 0.115430i | ||||
\(886\) | 102.024 | 0.115151 | ||||||||
\(887\) | − | 920.613i | − | 1.03790i | −0.854806 | − | 0.518948i | \(-0.826324\pi\) | ||
0.854806 | − | 0.518948i | \(-0.173676\pi\) | |||||||
\(888\) | −592.275 | − | 474.026i | −0.666977 | − | 0.533813i | ||||
\(889\) | −1342.24 | −1.50983 | ||||||||
\(890\) | 285.601i | 0.320901i | ||||||||
\(891\) | −405.026 | − | 856.365i | −0.454574 | − | 0.961128i | ||||
\(892\) | −1461.14 | −1.63805 | ||||||||
\(893\) | − | 332.384i | − | 0.372211i | ||||||
\(894\) | 215.435 | − | 269.176i | 0.240978 | − | 0.301092i | ||||
\(895\) | −129.774 | −0.144999 | ||||||||
\(896\) | − | 1152.33i | − | 1.28608i | ||||||
\(897\) | 259.539 | + | 207.721i | 0.289341 | + | 0.231573i | ||||
\(898\) | 41.8770 | 0.0466336 | ||||||||
\(899\) | − | 46.6937i | − | 0.0519396i | ||||||
\(900\) | 61.6487 | + | 274.537i | 0.0684985 | + | 0.305041i | ||||
\(901\) | 572.467 | 0.635368 | ||||||||
\(902\) | 429.493i | 0.476156i | ||||||||
\(903\) | 414.553 | − | 517.966i | 0.459084 | − | 0.573606i | ||||
\(904\) | 143.285 | 0.158501 | ||||||||
\(905\) | − | 831.079i | − | 0.918319i | ||||||
\(906\) | 72.7554 | + | 58.2296i | 0.0803040 | + | 0.0642711i | ||||
\(907\) | 481.775 | 0.531174 | 0.265587 | − | 0.964087i | \(-0.414434\pi\) | ||||
0.265587 | + | 0.964087i | \(0.414434\pi\) | |||||||
\(908\) | − | 365.482i | − | 0.402514i | ||||||
\(909\) | 561.432 | − | 126.073i | 0.617637 | − | 0.138694i | ||||
\(910\) | −694.296 | −0.762963 | ||||||||
\(911\) | 1331.08i | 1.46112i | 0.682848 | + | 0.730560i | \(0.260741\pi\) | ||||
−0.682848 | + | 0.730560i | \(0.739259\pi\) | |||||||
\(912\) | −214.278 | + | 267.732i | −0.234954 | + | 0.293566i | ||||
\(913\) | −636.832 | −0.697516 | ||||||||
\(914\) | − | 27.6977i | − | 0.0303038i | ||||||
\(915\) | −94.3423 | − | 75.5066i | −0.103106 | − | 0.0825209i | ||||
\(916\) | 718.340 | 0.784214 | ||||||||
\(917\) | − | 159.904i | − | 0.174378i | ||||||
\(918\) | 372.520 | + | 181.818i | 0.405796 | + | 0.198058i | ||||
\(919\) | 599.380 | 0.652209 | 0.326105 | − | 0.945334i | \(-0.394264\pi\) | ||||
0.326105 | + | 0.945334i | \(0.394264\pi\) | |||||||
\(920\) | 137.828i | 0.149813i | ||||||||
\(921\) | −31.2771 | + | 39.0794i | −0.0339600 | + | 0.0424315i | ||||
\(922\) | −345.096 | −0.374291 | ||||||||
\(923\) | − | 2902.08i | − | 3.14419i | ||||||
\(924\) | −959.392 | − | 767.847i | −1.03830 | − | 0.831003i | ||||
\(925\) | 478.349 | 0.517134 | ||||||||
\(926\) | 520.738i | 0.562352i | ||||||||
\(927\) | −55.5792 | − | 247.508i | −0.0599560 | − | 0.266999i | ||||
\(928\) | 135.540 | 0.146056 | ||||||||
\(929\) | 470.013i | 0.505934i | 0.967475 | + | 0.252967i | \(0.0814064\pi\) | ||||
−0.967475 | + | 0.252967i | \(0.918594\pi\) | |||||||
\(930\) | 55.7490 | − | 69.6561i | 0.0599452 | − | 0.0748990i | ||||
\(931\) | −413.376 | −0.444012 | ||||||||
\(932\) | 1331.91i | 1.42909i | ||||||||
\(933\) | −633.948 | − | 507.379i | −0.679473 | − | 0.543814i | ||||
\(934\) | 7.33250 | 0.00785064 | ||||||||
\(935\) | 1757.22i | 1.87938i | ||||||||
\(936\) | 838.811 | − | 188.359i | 0.896165 | − | 0.201239i | ||||
\(937\) | 1645.52 | 1.75615 | 0.878077 | − | 0.478520i | \(-0.158826\pi\) | ||||
0.878077 | + | 0.478520i | \(0.158826\pi\) | |||||||
\(938\) | 567.822i | 0.605354i | ||||||||
\(939\) | −199.071 | + | 248.731i | −0.212003 | + | 0.264889i | ||||
\(940\) | 732.713 | 0.779482 | ||||||||
\(941\) | − | 1059.13i | − | 1.12554i | −0.826614 | − | 0.562769i | \(-0.809736\pi\) | ||
0.826614 | − | 0.562769i | \(-0.190264\pi\) | |||||||
\(942\) | 201.943 | + | 161.624i | 0.214376 | + | 0.171576i | ||||
\(943\) | 325.877 | 0.345575 | ||||||||
\(944\) | 89.7142i | 0.0950363i | ||||||||
\(945\) | 658.457 | − | 1349.09i | 0.696780 | − | 1.42761i | ||||
\(946\) | 159.545 | 0.168652 | ||||||||
\(947\) | 965.803i | 1.01985i | 0.860217 | + | 0.509927i | \(0.170328\pi\) | ||||
−0.860217 | + | 0.509927i | \(0.829672\pi\) | |||||||
\(948\) | 59.0902 | − | 73.8308i | 0.0623315 | − | 0.0778806i | ||||
\(949\) | 828.632 | 0.873163 | ||||||||
\(950\) | 48.6431i | 0.0512033i | ||||||||
\(951\) | −292.815 | − | 234.354i | −0.307902 | − | 0.246429i | ||||
\(952\) | 1127.05 | 1.18387 | ||||||||
\(953\) | 1825.37i | 1.91539i | 0.287778 | + | 0.957697i | \(0.407084\pi\) | ||||
−0.287778 | + | 0.957697i | \(0.592916\pi\) | |||||||
\(954\) | −25.7686 | − | 114.754i | −0.0270111 | − | 0.120287i | ||||
\(955\) | −210.123 | −0.220024 | ||||||||
\(956\) | 472.250i | 0.493985i | ||||||||
\(957\) | 118.063 | − | 147.514i | 0.123368 | − | 0.154143i | ||||
\(958\) | −58.4994 | −0.0610641 | ||||||||
\(959\) | 879.741i | 0.917353i | ||||||||
\(960\) | −444.674 | − | 355.894i | −0.463203 | − | 0.370723i | ||||
\(961\) | −885.817 | −0.921766 | ||||||||
\(962\) | − | 697.286i | − | 0.724829i | ||||||
\(963\) | 180.752 | − | 40.5888i | 0.187697 | − | 0.0421483i | ||||
\(964\) | −288.296 | −0.299062 | ||||||||
\(965\) | 1501.54i | 1.55600i | ||||||||
\(966\) | 55.9469 | − | 69.9033i | 0.0579161 | − | 0.0723637i | ||||
\(967\) | 338.117 | 0.349655 | 0.174828 | − | 0.984599i | \(-0.444063\pi\) | ||||
0.174828 | + | 0.984599i | \(0.444063\pi\) | |||||||
\(968\) | − | 71.4554i | − | 0.0738175i | ||||||
\(969\) | −582.622 | − | 466.300i | −0.601261 | − | 0.481218i | ||||
\(970\) | −143.855 | −0.148304 | ||||||||
\(971\) | 535.373i | 0.551363i | 0.961249 | + | 0.275681i | \(0.0889035\pi\) | ||||
−0.961249 | + | 0.275681i | \(0.911097\pi\) | |||||||
\(972\) | −204.916 | + | 862.839i | −0.210819 | + | 0.887694i | ||||
\(973\) | 926.506 | 0.952216 | ||||||||
\(974\) | − | 220.646i | − | 0.226536i | ||||||
\(975\) | −338.731 | + | 423.230i | −0.347417 | + | 0.434082i | ||||
\(976\) | 82.8523 | 0.0848896 | ||||||||
\(977\) | − | 1076.35i | − | 1.10169i | −0.834608 | − | 0.550844i | \(-0.814306\pi\) | ||
0.834608 | − | 0.550844i | \(-0.185694\pi\) | |||||||
\(978\) | −236.283 | − | 189.109i | −0.241598 | − | 0.193363i | ||||
\(979\) | −973.859 | −0.994749 | ||||||||
\(980\) | − | 911.251i | − | 0.929848i | ||||||
\(981\) | −105.358 | − | 469.184i | −0.107398 | − | 0.478271i | ||||
\(982\) | −99.7800 | −0.101609 | ||||||||
\(983\) | − | 1369.52i | − | 1.39320i | −0.717459 | − | 0.696601i | \(-0.754695\pi\) | ||
0.717459 | − | 0.696601i | \(-0.245305\pi\) | |||||||
\(984\) | 526.606 | − | 657.972i | 0.535169 | − | 0.668671i | ||||
\(985\) | 694.801 | 0.705382 | ||||||||
\(986\) | 82.6768i | 0.0838507i | ||||||||
\(987\) | −778.918 | − | 623.405i | −0.789177 | − | 0.631616i | ||||
\(988\) | −738.386 | −0.747354 | ||||||||
\(989\) | − | 121.055i | − | 0.122401i | ||||||
\(990\) | 352.244 | − | 79.0982i | 0.355802 | − | 0.0798972i | ||||
\(991\) | −1341.80 | −1.35399 | −0.676994 | − | 0.735989i | \(-0.736718\pi\) | ||||
−0.676994 | + | 0.735989i | \(0.736718\pi\) | |||||||
\(992\) | 218.236i | 0.219996i | ||||||||
\(993\) | 864.645 | − | 1080.34i | 0.870741 | − | 1.08795i | ||||
\(994\) | −781.638 | −0.786356 | ||||||||
\(995\) | − | 739.305i | − | 0.743020i | ||||||
\(996\) | 465.456 | + | 372.527i | 0.467326 | + | 0.374023i | ||||
\(997\) | 316.615 | 0.317567 | 0.158784 | − | 0.987313i | \(-0.449243\pi\) | ||||
0.158784 | + | 0.987313i | \(0.449243\pi\) | |||||||
\(998\) | − | 38.0191i | − | 0.0380953i | ||||||
\(999\) | 1354.90 | + | 661.292i | 1.35626 | + | 0.661954i |
(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 | 87.3.b.a.59.11 | yes | 18 | |
3.2 | odd | 2 | inner | 87.3.b.a.59.8 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.3.b.a.59.8 | ✓ | 18 | 3.2 | odd | 2 | inner | |
87.3.b.a.59.11 | yes | 18 | 1.1 | even | 1 | trivial |