Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,3,Mod(161,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.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: | \(4.41418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.161 |
Dual form | 162.3.b.a.161.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | − 5.19615i | − 1.03923i | −0.854400 | − | 0.519615i | \(-0.826075\pi\) | ||||
0.854400 | − | 0.519615i | \(-0.173925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.34847 | 0.906924 | 0.453462 | − | 0.891276i | \(-0.350189\pi\) | ||||
0.453462 | + | 0.891276i | \(0.350189\pi\) | |||||||
\(8\) | − 2.82843i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.34847 | 0.734847 | ||||||||
\(11\) | − 9.43879i | − 0.858072i | −0.903287 | − | 0.429036i | \(-0.858853\pi\) | ||||
0.903287 | − | 0.429036i | \(-0.141147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.6969 | 1.51515 | 0.757575 | − | 0.652749i | \(-0.226384\pi\) | ||||
0.757575 | + | 0.652749i | \(0.226384\pi\) | |||||||
\(14\) | 8.97809i | 0.641292i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 1.90702i | − 0.112178i | −0.998426 | − | 0.0560889i | \(-0.982137\pi\) | ||||
0.998426 | − | 0.0560889i | \(-0.0178630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.69694 | 0.247207 | 0.123604 | − | 0.992332i | \(-0.460555\pi\) | ||||
0.123604 | + | 0.992332i | \(0.460555\pi\) | |||||||
\(20\) | 10.3923i | 0.519615i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.3485 | 0.606749 | ||||||||
\(23\) | 9.43879i | 0.410382i | 0.978722 | + | 0.205191i | \(0.0657816\pi\) | ||||
−0.978722 | + | 0.205191i | \(0.934218\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.0800000 | ||||||||
\(26\) | 27.8557i | 1.07137i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12.6969 | −0.453462 | ||||||||
\(29\) | 3.28913i | 0.113418i | 0.998391 | + | 0.0567091i | \(0.0180608\pi\) | ||||
−0.998391 | + | 0.0567091i | \(0.981939\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −41.0454 | −1.32405 | −0.662023 | − | 0.749484i | \(-0.730302\pi\) | ||||
−0.662023 | + | 0.749484i | \(0.730302\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.69694 | 0.0793217 | ||||||||
\(35\) | − 32.9876i | − 0.942503i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.3031 | 0.467650 | 0.233825 | − | 0.972279i | \(-0.424876\pi\) | ||||
0.233825 | + | 0.972279i | \(0.424876\pi\) | |||||||
\(38\) | 6.64247i | 0.174802i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −14.6969 | −0.367423 | ||||||||
\(41\) | − 61.8289i | − 1.50802i | −0.656862 | − | 0.754011i | \(-0.728116\pi\) | ||||
0.656862 | − | 0.754011i | \(-0.271884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.954592 | 0.0221998 | 0.0110999 | − | 0.999938i | \(-0.496467\pi\) | ||||
0.0110999 | + | 0.999938i | \(0.496467\pi\) | |||||||
\(44\) | 18.8776i | 0.429036i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.3485 | −0.290184 | ||||||||
\(47\) | 14.1100i | 0.300213i | 0.988670 | + | 0.150107i | \(0.0479617\pi\) | ||||
−0.988670 | + | 0.150107i | \(0.952038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.69694 | −0.177489 | ||||||||
\(50\) | − 2.82843i | − 0.0565685i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −39.3939 | −0.757575 | ||||||||
\(53\) | − 9.53512i | − 0.179908i | −0.995946 | − | 0.0899539i | \(-0.971328\pi\) | ||||
0.995946 | − | 0.0899539i | \(-0.0286720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −49.0454 | −0.891735 | ||||||||
\(56\) | − 17.9562i | − 0.320646i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.65153 | −0.0801988 | ||||||||
\(59\) | 91.5274i | 1.55131i | 0.631156 | + | 0.775656i | \(0.282581\pi\) | ||||
−0.631156 | + | 0.775656i | \(0.717419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −75.0908 | −1.23100 | −0.615498 | − | 0.788138i | \(-0.711045\pi\) | ||||
−0.615498 | + | 0.788138i | \(0.711045\pi\) | |||||||
\(62\) | − 58.0470i | − 0.936241i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − 102.348i | − 1.57459i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30.9546 | 0.462009 | 0.231004 | − | 0.972953i | \(-0.425799\pi\) | ||||
0.231004 | + | 0.972953i | \(0.425799\pi\) | |||||||
\(68\) | 3.81405i | 0.0560889i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 46.6515 | 0.666450 | ||||||||
\(71\) | 85.9026i | 1.20990i | 0.796265 | + | 0.604948i | \(0.206806\pi\) | ||||
−0.796265 | + | 0.604948i | \(0.793194\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −96.0908 | −1.31631 | −0.658156 | − | 0.752881i | \(-0.728663\pi\) | ||||
−0.658156 | + | 0.752881i | \(0.728663\pi\) | |||||||
\(74\) | 24.4702i | 0.330679i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.39388 | −0.123604 | ||||||||
\(77\) | − 59.9219i | − 0.778206i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 29.7423 | 0.376485 | 0.188243 | − | 0.982123i | \(-0.439721\pi\) | ||||
0.188243 | + | 0.982123i | \(0.439721\pi\) | |||||||
\(80\) | − 20.7846i | − 0.259808i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 87.4393 | 1.06633 | ||||||||
\(83\) | 87.9060i | 1.05911i | 0.848276 | + | 0.529554i | \(0.177641\pi\) | ||||
−0.848276 | + | 0.529554i | \(0.822359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.90918 | −0.116579 | ||||||||
\(86\) | 1.35000i | 0.0156976i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −26.6969 | −0.303374 | ||||||||
\(89\) | − 41.3766i | − 0.464905i | −0.972608 | − | 0.232453i | \(-0.925325\pi\) | ||||
0.972608 | − | 0.232453i | \(-0.0746751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 125.045 | 1.37413 | ||||||||
\(92\) | − 18.8776i | − 0.205191i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −19.9546 | −0.212283 | ||||||||
\(95\) | − 24.4060i | − 0.256905i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 95.8786 | 0.988439 | 0.494219 | − | 0.869337i | \(-0.335454\pi\) | ||||
0.494219 | + | 0.869337i | \(0.335454\pi\) | |||||||
\(98\) | − 12.2993i | − 0.125503i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.0400000 | ||||||||
\(101\) | 157.931i | 1.56368i | 0.623482 | + | 0.781838i | \(0.285717\pi\) | ||||
−0.623482 | + | 0.781838i | \(0.714283\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 29.1362 | 0.282876 | 0.141438 | − | 0.989947i | \(-0.454827\pi\) | ||||
0.141438 | + | 0.989947i | \(0.454827\pi\) | |||||||
\(104\) | − 55.7114i | − 0.535686i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4847 | 0.127214 | ||||||||
\(107\) | 171.805i | 1.60566i | 0.596210 | + | 0.802829i | \(0.296673\pi\) | ||||
−0.596210 | + | 0.802829i | \(0.703327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 116.272 | 1.06672 | 0.533360 | − | 0.845888i | \(-0.320929\pi\) | ||||
0.533360 | + | 0.845888i | \(0.320929\pi\) | |||||||
\(110\) | − 69.3607i | − 0.630552i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 25.3939 | 0.226731 | ||||||||
\(113\) | 202.265i | 1.78995i | 0.446114 | + | 0.894976i | \(0.352808\pi\) | ||||
−0.446114 | + | 0.894976i | \(0.647192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 49.0454 | 0.426482 | ||||||||
\(116\) | − 6.57826i | − 0.0567091i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −129.439 | −1.09694 | ||||||||
\(119\) | − 12.1067i | − 0.101737i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.9092 | 0.263712 | ||||||||
\(122\) | − 106.194i | − 0.870446i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 82.0908 | 0.662023 | ||||||||
\(125\) | − 119.512i | − 0.956092i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0908 | 0.0794552 | 0.0397276 | − | 0.999211i | \(-0.487351\pi\) | ||||
0.0397276 | + | 0.999211i | \(0.487351\pi\) | |||||||
\(128\) | − 11.3137i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 144.742 | 1.11340 | ||||||||
\(131\) | 4.96021i | 0.0378642i | 0.999821 | + | 0.0189321i | \(0.00602663\pi\) | ||||
−0.999821 | + | 0.0189321i | \(0.993973\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 29.8184 | 0.224198 | ||||||||
\(134\) | 43.7764i | 0.326690i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.39388 | −0.0396609 | ||||||||
\(137\) | − 234.684i | − 1.71302i | −0.516129 | − | 0.856511i | \(-0.672627\pi\) | ||||
0.516129 | − | 0.856511i | \(-0.327373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 106.530 | 0.766404 | 0.383202 | − | 0.923665i | \(-0.374821\pi\) | ||||
0.383202 | + | 0.923665i | \(0.374821\pi\) | |||||||
\(140\) | 65.9752i | 0.471252i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −121.485 | −0.855526 | ||||||||
\(143\) | − 185.915i | − 1.30011i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.0908 | 0.117868 | ||||||||
\(146\) | − 135.893i | − 0.930774i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −34.6061 | −0.233825 | ||||||||
\(149\) | − 105.113i | − 0.705453i | −0.935726 | − | 0.352727i | \(-0.885255\pi\) | ||||
0.935726 | − | 0.352727i | \(-0.114745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −285.227 | −1.88892 | −0.944460 | − | 0.328625i | \(-0.893415\pi\) | ||||
−0.944460 | + | 0.328625i | \(0.893415\pi\) | |||||||
\(152\) | − 13.2849i | − 0.0874010i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 84.7423 | 0.550275 | ||||||||
\(155\) | 213.278i | 1.37599i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −197.182 | −1.25593 | −0.627967 | − | 0.778240i | \(-0.716113\pi\) | ||||
−0.627967 | + | 0.778240i | \(0.716113\pi\) | |||||||
\(158\) | 42.0620i | 0.266215i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 29.3939 | 0.183712 | ||||||||
\(161\) | 59.9219i | 0.372186i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −249.060 | −1.52798 | −0.763988 | − | 0.645230i | \(-0.776762\pi\) | ||||
−0.763988 | + | 0.645230i | \(0.776762\pi\) | |||||||
\(164\) | 123.658i | 0.754011i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −124.318 | −0.748903 | ||||||||
\(167\) | − 48.4365i | − 0.290039i | −0.989429 | − | 0.145019i | \(-0.953676\pi\) | ||||
0.989429 | − | 0.145019i | \(-0.0463244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 218.969 | 1.29568 | ||||||||
\(170\) | − 14.0137i | − 0.0824335i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.90918 | −0.0110999 | ||||||||
\(173\) | − 100.441i | − 0.580585i | −0.956938 | − | 0.290293i | \(-0.906247\pi\) | ||||
0.956938 | − | 0.290293i | \(-0.0937527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.6969 | −0.0725539 | ||||||||
\(176\) | − 37.7552i | − 0.214518i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 58.5153 | 0.328738 | ||||||||
\(179\) | 285.071i | 1.59257i | 0.604919 | + | 0.796287i | \(0.293206\pi\) | ||||
−0.604919 | + | 0.796287i | \(0.706794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 37.1214 | 0.205091 | 0.102545 | − | 0.994728i | \(-0.467301\pi\) | ||||
0.102545 | + | 0.994728i | \(0.467301\pi\) | |||||||
\(182\) | 176.841i | 0.971653i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 26.6969 | 0.145092 | ||||||||
\(185\) | − 89.9093i | − 0.485996i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.0000 | −0.0962567 | ||||||||
\(188\) | − 28.2201i | − 0.150107i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 34.5153 | 0.181660 | ||||||||
\(191\) | 17.9241i | 0.0938433i | 0.998899 | + | 0.0469217i | \(0.0149411\pi\) | ||||
−0.998899 | + | 0.0469217i | \(0.985059\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −95.4541 | −0.494581 | −0.247290 | − | 0.968941i | \(-0.579540\pi\) | ||||
−0.247290 | + | 0.968941i | \(0.579540\pi\) | |||||||
\(194\) | 135.593i | 0.698932i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.3939 | 0.0887443 | ||||||||
\(197\) | − 160.363i | − 0.814026i | −0.913422 | − | 0.407013i | \(-0.866570\pi\) | ||||
0.913422 | − | 0.407013i | \(-0.133430\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.51531 | 0.0327402 | 0.0163701 | − | 0.999866i | \(-0.494789\pi\) | ||||
0.0163701 | + | 0.999866i | \(0.494789\pi\) | |||||||
\(200\) | 5.65685i | 0.0282843i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −223.348 | −1.10569 | ||||||||
\(203\) | 20.8809i | 0.102862i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −321.272 | −1.56718 | ||||||||
\(206\) | 41.2048i | 0.200024i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 78.7878 | 0.378787 | ||||||||
\(209\) | − 44.3334i | − 0.212122i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −154.439 | −0.731940 | −0.365970 | − | 0.930627i | \(-0.619263\pi\) | ||||
−0.365970 | + | 0.930627i | \(0.619263\pi\) | |||||||
\(212\) | 19.0702i | 0.0899539i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −242.969 | −1.13537 | ||||||||
\(215\) | − 4.96021i | − 0.0230707i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −260.576 | −1.20081 | ||||||||
\(218\) | 164.434i | 0.754285i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 98.0908 | 0.445867 | ||||||||
\(221\) | − 37.5625i | − 0.169966i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 92.7730 | 0.416022 | 0.208011 | − | 0.978126i | \(-0.433301\pi\) | ||||
0.208011 | + | 0.978126i | \(0.433301\pi\) | |||||||
\(224\) | 35.9124i | 0.160323i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −286.045 | −1.26569 | ||||||||
\(227\) | − 169.802i | − 0.748026i | −0.927423 | − | 0.374013i | \(-0.877981\pi\) | ||||
0.927423 | − | 0.374013i | \(-0.122019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 407.545 | 1.77967 | 0.889836 | − | 0.456280i | \(-0.150819\pi\) | ||||
0.889836 | + | 0.456280i | \(0.150819\pi\) | |||||||
\(230\) | 69.3607i | 0.301568i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.30306 | 0.0400994 | ||||||||
\(233\) | − 15.2562i | − 0.0654772i | −0.999464 | − | 0.0327386i | \(-0.989577\pi\) | ||||
0.999464 | − | 0.0327386i | \(-0.0104229\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 73.3179 | 0.311991 | ||||||||
\(236\) | − 183.055i | − 0.775656i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.1214 | 0.0719388 | ||||||||
\(239\) | 56.5364i | 0.236554i | 0.992981 | + | 0.118277i | \(0.0377371\pi\) | ||||
−0.992981 | + | 0.118277i | \(0.962263\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 84.2122 | 0.349428 | 0.174714 | − | 0.984619i | \(-0.444100\pi\) | ||||
0.174714 | + | 0.984619i | \(0.444100\pi\) | |||||||
\(242\) | 45.1264i | 0.186473i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 150.182 | 0.615498 | ||||||||
\(245\) | 45.1906i | 0.184452i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 92.5153 | 0.374556 | ||||||||
\(248\) | 116.094i | 0.468121i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 169.015 | 0.676059 | ||||||||
\(251\) | − 218.903i | − 0.872123i | −0.899917 | − | 0.436062i | \(-0.856373\pi\) | ||||
0.899917 | − | 0.436062i | \(-0.143627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 89.0908 | 0.352138 | ||||||||
\(254\) | 14.2706i | 0.0561833i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 12.8242i | − 0.0498998i | −0.999689 | − | 0.0249499i | \(-0.992057\pi\) | ||||
0.999689 | − | 0.0249499i | \(-0.00794262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 109.848 | 0.424123 | ||||||||
\(260\) | 204.697i | 0.787295i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.01479 | −0.0267740 | ||||||||
\(263\) | − 336.464i | − 1.27933i | −0.768653 | − | 0.639666i | \(-0.779073\pi\) | ||||
0.768653 | − | 0.639666i | \(-0.220927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −49.5459 | −0.186966 | ||||||||
\(266\) | 42.1695i | 0.158532i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −61.9092 | −0.231004 | ||||||||
\(269\) | − 60.4468i | − 0.224709i | −0.993668 | − | 0.112355i | \(-0.964161\pi\) | ||||
0.993668 | − | 0.112355i | \(-0.0358393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 274.636 | 1.01342 | 0.506708 | − | 0.862118i | \(-0.330862\pi\) | ||||
0.506708 | + | 0.862118i | \(0.330862\pi\) | |||||||
\(272\) | − 7.62809i | − 0.0280445i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 331.893 | 1.21129 | ||||||||
\(275\) | 18.8776i | 0.0686458i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −49.0000 | −0.176895 | −0.0884477 | − | 0.996081i | \(-0.528191\pi\) | ||||
−0.0884477 | + | 0.996081i | \(0.528191\pi\) | |||||||
\(278\) | 150.656i | 0.541929i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −93.3031 | −0.333225 | ||||||||
\(281\) | 343.086i | 1.22095i | 0.792037 | + | 0.610473i | \(0.209021\pi\) | ||||
−0.792037 | + | 0.610473i | \(0.790979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −343.409 | −1.21346 | −0.606729 | − | 0.794909i | \(-0.707519\pi\) | ||||
−0.606729 | + | 0.794909i | \(0.707519\pi\) | |||||||
\(284\) | − 171.805i | − 0.604948i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 262.924 | 0.919315 | ||||||||
\(287\) | − 392.519i | − 1.36766i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 285.363 | 0.987416 | ||||||||
\(290\) | 24.1701i | 0.0833450i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 192.182 | 0.658156 | ||||||||
\(293\) | − 286.453i | − 0.977655i | −0.872380 | − | 0.488828i | \(-0.837425\pi\) | ||||
0.872380 | − | 0.488828i | \(-0.162575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 475.590 | 1.61217 | ||||||||
\(296\) | − 48.9404i | − 0.165339i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 148.652 | 0.498831 | ||||||||
\(299\) | 185.915i | 0.621790i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.06020 | 0.0201336 | ||||||||
\(302\) | − 403.372i | − 1.33567i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.7878 | 0.0618018 | ||||||||
\(305\) | 390.183i | 1.27929i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 154.091 | 0.501924 | 0.250962 | − | 0.967997i | \(-0.419253\pi\) | ||||
0.250962 | + | 0.967997i | \(0.419253\pi\) | |||||||
\(308\) | 119.844i | 0.389103i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −301.621 | −0.972971 | ||||||||
\(311\) | − 71.9853i | − 0.231464i | −0.993280 | − | 0.115732i | \(-0.963079\pi\) | ||||
0.993280 | − | 0.115732i | \(-0.0369214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −367.606 | −1.17446 | −0.587230 | − | 0.809420i | \(-0.699782\pi\) | ||||
−0.587230 | + | 0.809420i | \(0.699782\pi\) | |||||||
\(314\) | − 278.857i | − 0.888079i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −59.4847 | −0.188243 | ||||||||
\(317\) | 107.597i | 0.339424i | 0.985494 | + | 0.169712i | \(0.0542838\pi\) | ||||
−0.985494 | + | 0.169712i | \(0.945716\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.0454 | 0.0973210 | ||||||||
\(320\) | 41.5692i | 0.129904i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −84.7423 | −0.263175 | ||||||||
\(323\) | − 8.95717i | − 0.0277312i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −39.3939 | −0.121212 | ||||||||
\(326\) | − 352.224i | − 1.08044i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −174.879 | −0.533166 | ||||||||
\(329\) | 89.5771i | 0.272271i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1975 | 0.0519561 | 0.0259780 | − | 0.999663i | \(-0.491730\pi\) | ||||
0.0259780 | + | 0.999663i | \(0.491730\pi\) | |||||||
\(332\) | − 175.812i | − 0.529554i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 68.4995 | 0.205088 | ||||||||
\(335\) | − 160.845i | − 0.480134i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 364.394 | 1.08129 | 0.540644 | − | 0.841252i | \(-0.318181\pi\) | ||||
0.540644 | + | 0.841252i | \(0.318181\pi\) | |||||||
\(338\) | 309.669i | 0.916182i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.8184 | 0.0582893 | ||||||||
\(341\) | 387.419i | 1.13613i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −366.287 | −1.06789 | ||||||||
\(344\) | − 2.69999i | − 0.00784882i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 142.045 | 0.410536 | ||||||||
\(347\) | 583.394i | 1.68125i | 0.541616 | + | 0.840626i | \(0.317813\pi\) | ||||
−0.541616 | + | 0.840626i | \(0.682187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 312.757 | 0.896152 | 0.448076 | − | 0.893995i | \(-0.352109\pi\) | ||||
0.448076 | + | 0.893995i | \(0.352109\pi\) | |||||||
\(350\) | − 17.9562i | − 0.0513034i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 53.3939 | 0.151687 | ||||||||
\(353\) | 37.6156i | 0.106560i | 0.998580 | + | 0.0532798i | \(0.0169675\pi\) | ||||
−0.998580 | + | 0.0532798i | \(0.983032\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 446.363 | 1.25736 | ||||||||
\(356\) | 82.7531i | 0.232453i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −403.151 | −1.12612 | ||||||||
\(359\) | 294.028i | 0.819019i | 0.912306 | + | 0.409510i | \(0.134300\pi\) | ||||
−0.912306 | + | 0.409510i | \(0.865700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −338.939 | −0.938889 | ||||||||
\(362\) | 52.4976i | 0.145021i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −250.091 | −0.687063 | ||||||||
\(365\) | 499.303i | 1.36795i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.2270 | −0.0905369 | −0.0452684 | − | 0.998975i | \(-0.514414\pi\) | ||||
−0.0452684 | + | 0.998975i | \(0.514414\pi\) | |||||||
\(368\) | 37.7552i | 0.102596i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 127.151 | 0.343651 | ||||||||
\(371\) | − 60.5334i | − 0.163163i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −225.030 | −0.603296 | −0.301648 | − | 0.953419i | \(-0.597537\pi\) | ||||
−0.301648 | + | 0.953419i | \(0.597537\pi\) | |||||||
\(374\) | − 25.4558i | − 0.0680638i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 39.9092 | 0.106141 | ||||||||
\(377\) | 64.7858i | 0.171846i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −166.334 | −0.438875 | −0.219438 | − | 0.975627i | \(-0.570422\pi\) | ||||
−0.219438 | + | 0.975627i | \(0.570422\pi\) | |||||||
\(380\) | 48.8120i | 0.128453i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.3485 | −0.0663572 | ||||||||
\(383\) | − 736.987i | − 1.92425i | −0.272613 | − | 0.962124i | \(-0.587888\pi\) | ||||
0.272613 | − | 0.962124i | \(-0.412112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −311.363 | −0.808736 | ||||||||
\(386\) | − 134.992i | − 0.349721i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −191.757 | −0.494219 | ||||||||
\(389\) | 169.373i | 0.435407i | 0.976015 | + | 0.217704i | \(0.0698566\pi\) | ||||
−0.976015 | + | 0.217704i | \(0.930143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.0460358 | ||||||||
\(392\) | 24.5987i | 0.0627517i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 226.788 | 0.575603 | ||||||||
\(395\) | − 154.546i | − 0.391255i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −256.272 | −0.645523 | −0.322761 | − | 0.946480i | \(-0.604611\pi\) | ||||
−0.322761 | + | 0.946480i | \(0.604611\pi\) | |||||||
\(398\) | 9.21404i | 0.0231508i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | −0.0200000 | ||||||||
\(401\) | 261.382i | 0.651826i | 0.945400 | + | 0.325913i | \(0.105672\pi\) | ||||
−0.945400 | + | 0.325913i | \(0.894328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −808.469 | −2.00613 | ||||||||
\(404\) | − 315.862i | − 0.781838i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −29.5301 | −0.0727342 | ||||||||
\(407\) | − 163.320i | − 0.401278i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −443.788 | −1.08506 | −0.542528 | − | 0.840038i | \(-0.682533\pi\) | ||||
−0.542528 | + | 0.840038i | \(0.682533\pi\) | |||||||
\(410\) | − 454.348i | − 1.10817i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −58.2724 | −0.141438 | ||||||||
\(413\) | 581.059i | 1.40692i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 456.773 | 1.10066 | ||||||||
\(416\) | 111.423i | 0.267843i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 62.6969 | 0.149993 | ||||||||
\(419\) | 10.7679i | 0.0256990i | 0.999917 | + | 0.0128495i | \(0.00409023\pi\) | ||||
−0.999917 | + | 0.0128495i | \(0.995910\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 254.303 | 0.604045 | 0.302023 | − | 0.953301i | \(-0.402338\pi\) | ||||
0.302023 | + | 0.953301i | \(0.402338\pi\) | |||||||
\(422\) | − 218.410i | − 0.517560i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.9694 | −0.0636070 | ||||||||
\(425\) | 3.81405i | 0.00897423i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −476.712 | −1.11642 | ||||||||
\(428\) | − 343.611i | − 0.802829i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.01479 | 0.0163135 | ||||||||
\(431\) | − 698.663i | − 1.62103i | −0.585719 | − | 0.810514i | \(-0.699188\pi\) | ||||
0.585719 | − | 0.810514i | \(-0.300812\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 211.728 | 0.488978 | 0.244489 | − | 0.969652i | \(-0.421380\pi\) | ||||
0.244489 | + | 0.969652i | \(0.421380\pi\) | |||||||
\(434\) | − 368.509i | − 0.849100i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −232.545 | −0.533360 | ||||||||
\(437\) | 44.3334i | 0.101449i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 279.863 | 0.637501 | 0.318750 | − | 0.947839i | \(-0.396737\pi\) | ||||
0.318750 | + | 0.947839i | \(0.396737\pi\) | |||||||
\(440\) | 138.721i | 0.315276i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 53.1214 | 0.120184 | ||||||||
\(443\) | 551.254i | 1.24437i | 0.782872 | + | 0.622183i | \(0.213754\pi\) | ||||
−0.782872 | + | 0.622183i | \(0.786246\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −214.999 | −0.483144 | ||||||||
\(446\) | 131.201i | 0.294172i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −50.7878 | −0.113366 | ||||||||
\(449\) | − 542.865i | − 1.20905i | −0.796585 | − | 0.604527i | \(-0.793362\pi\) | ||||
0.796585 | − | 0.604527i | \(-0.206638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −583.590 | −1.29399 | ||||||||
\(452\) | − 404.529i | − 0.894976i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 240.136 | 0.528934 | ||||||||
\(455\) | − 649.755i | − 1.42803i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 92.3643 | 0.202110 | 0.101055 | − | 0.994881i | \(-0.467778\pi\) | ||||
0.101055 | + | 0.994881i | \(0.467778\pi\) | |||||||
\(458\) | 576.356i | 1.25842i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −98.0908 | −0.213241 | ||||||||
\(461\) | 229.820i | 0.498525i | 0.968436 | + | 0.249263i | \(0.0801882\pi\) | ||||
−0.968436 | + | 0.249263i | \(0.919812\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −510.803 | −1.10325 | −0.551623 | − | 0.834094i | \(-0.685991\pi\) | ||||
−0.551623 | + | 0.834094i | \(0.685991\pi\) | |||||||
\(464\) | 13.1565i | 0.0283546i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.5755 | 0.0462994 | ||||||||
\(467\) | 833.657i | 1.78513i | 0.450915 | + | 0.892567i | \(0.351098\pi\) | ||||
−0.450915 | + | 0.892567i | \(0.648902\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 196.514 | 0.419007 | ||||||||
\(470\) | 103.687i | 0.220611i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 258.879 | 0.548472 | ||||||||
\(473\) | − 9.01020i | − 0.0190490i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.39388 | −0.0197766 | ||||||||
\(476\) | 24.2134i | 0.0508684i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −79.9546 | −0.167269 | ||||||||
\(479\) | − 657.190i | − 1.37201i | −0.727599 | − | 0.686003i | \(-0.759364\pi\) | ||||
0.727599 | − | 0.686003i | \(-0.240636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 340.817 | 0.708560 | ||||||||
\(482\) | 119.094i | 0.247083i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −63.8184 | −0.131856 | ||||||||
\(485\) | − 498.200i | − 1.02722i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −351.666 | −0.722107 | −0.361054 | − | 0.932545i | \(-0.617583\pi\) | ||||
−0.361054 | + | 0.932545i | \(0.617583\pi\) | |||||||
\(488\) | 212.389i | 0.435223i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −63.9092 | −0.130427 | ||||||||
\(491\) | 245.418i | 0.499834i | 0.968267 | + | 0.249917i | \(0.0804033\pi\) | ||||
−0.968267 | + | 0.249917i | \(0.919597\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.27245 | 0.0127230 | ||||||||
\(494\) | 130.836i | 0.264851i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −164.182 | −0.331011 | ||||||||
\(497\) | 545.350i | 1.09728i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 630.226 | 1.26298 | 0.631489 | − | 0.775385i | \(-0.282444\pi\) | ||||
0.631489 | + | 0.775385i | \(0.282444\pi\) | |||||||
\(500\) | 239.023i | 0.478046i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 309.576 | 0.616684 | ||||||||
\(503\) | − 286.891i | − 0.570360i | −0.958474 | − | 0.285180i | \(-0.907947\pi\) | ||||
0.958474 | − | 0.285180i | \(-0.0920534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 820.635 | 1.62502 | ||||||||
\(506\) | 125.993i | 0.248999i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20.1816 | −0.0397276 | ||||||||
\(509\) | 872.323i | 1.71380i | 0.515485 | + | 0.856898i | \(0.327612\pi\) | ||||
−0.515485 | + | 0.856898i | \(0.672388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −610.030 | −1.19380 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.1362 | 0.0352845 | ||||||||
\(515\) | − 151.396i | − 0.293973i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 133.182 | 0.257605 | ||||||||
\(518\) | 155.348i | 0.299901i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −289.485 | −0.556701 | ||||||||
\(521\) | − 206.132i | − 0.395646i | −0.980238 | − | 0.197823i | \(-0.936613\pi\) | ||||
0.980238 | − | 0.197823i | \(-0.0633872\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 884.817 | 1.69181 | 0.845906 | − | 0.533333i | \(-0.179061\pi\) | ||||
0.845906 | + | 0.533333i | \(0.179061\pi\) | |||||||
\(524\) | − 9.92041i | − 0.0189321i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 475.832 | 0.904624 | ||||||||
\(527\) | 78.2746i | 0.148529i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 439.909 | 0.831586 | ||||||||
\(530\) | − 70.0685i | − 0.132205i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −59.6367 | −0.112099 | ||||||||
\(533\) | − 1217.84i | − 2.28488i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 892.727 | 1.66865 | ||||||||
\(536\) | − 87.5528i | − 0.163345i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 85.4847 | 0.158893 | ||||||||
\(539\) | 82.0886i | 0.152298i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −509.151 | −0.941129 | −0.470565 | − | 0.882365i | \(-0.655950\pi\) | ||||
−0.470565 | + | 0.882365i | \(0.655950\pi\) | |||||||
\(542\) | 388.394i | 0.716593i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.7878 | 0.0198304 | ||||||||
\(545\) | − 604.169i | − 1.10857i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 548.044 | 1.00191 | 0.500955 | − | 0.865474i | \(-0.332982\pi\) | ||||
0.500955 | + | 0.865474i | \(0.332982\pi\) | |||||||
\(548\) | 469.368i | 0.856511i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26.6969 | −0.0485399 | ||||||||
\(551\) | 15.4488i | 0.0280378i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 188.818 | 0.341444 | ||||||||
\(554\) | − 69.2965i | − 0.125084i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −213.060 | −0.383202 | ||||||||
\(557\) | 406.542i | 0.729879i | 0.931031 | + | 0.364939i | \(0.118910\pi\) | ||||
−0.931031 | + | 0.364939i | \(0.881090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.8025 | 0.0336360 | ||||||||
\(560\) | − 131.950i | − 0.235626i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −485.196 | −0.863339 | ||||||||
\(563\) | − 606.471i | − 1.07721i | −0.842557 | − | 0.538607i | \(-0.818951\pi\) | ||||
0.842557 | − | 0.538607i | \(-0.181049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1051.00 | 1.86017 | ||||||||
\(566\) | − 485.653i | − 0.858045i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 242.969 | 0.427763 | ||||||||
\(569\) | 259.755i | 0.456511i | 0.973601 | + | 0.228255i | \(0.0733021\pi\) | ||||
−0.973601 | + | 0.228255i | \(0.926698\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −87.8332 | −0.153823 | −0.0769117 | − | 0.997038i | \(-0.524506\pi\) | ||||
−0.0769117 | + | 0.997038i | \(0.524506\pi\) | |||||||
\(572\) | 371.831i | 0.650054i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 555.106 | 0.967083 | ||||||||
\(575\) | − 18.8776i | − 0.0328306i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −132.091 | −0.228927 | −0.114463 | − | 0.993427i | \(-0.536515\pi\) | ||||
−0.114463 | + | 0.993427i | \(0.536515\pi\) | |||||||
\(578\) | 403.565i | 0.698209i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −34.1816 | −0.0589338 | ||||||||
\(581\) | 558.069i | 0.960531i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −90.0000 | −0.154374 | ||||||||
\(584\) | 271.786i | 0.465387i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 405.106 | 0.691306 | ||||||||
\(587\) | 567.666i | 0.967064i | 0.875327 | + | 0.483532i | \(0.160646\pi\) | ||||
−0.875327 | + | 0.483532i | \(0.839354\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −192.788 | −0.327314 | ||||||||
\(590\) | 672.586i | 1.13998i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 69.2122 | 0.116913 | ||||||||
\(593\) | 77.0321i | 0.129902i | 0.997888 | + | 0.0649512i | \(0.0206892\pi\) | ||||
−0.997888 | + | 0.0649512i | \(0.979311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −62.9082 | −0.105728 | ||||||||
\(596\) | 210.225i | 0.352727i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −262.924 | −0.439672 | ||||||||
\(599\) | − 883.250i | − 1.47454i | −0.675598 | − | 0.737270i | \(-0.736115\pi\) | ||||
0.675598 | − | 0.737270i | \(-0.263885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −795.091 | −1.32295 | −0.661473 | − | 0.749969i | \(-0.730068\pi\) | ||||
−0.661473 | + | 0.749969i | \(0.730068\pi\) | |||||||
\(602\) | 8.57042i | 0.0142366i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 570.454 | 0.944460 | ||||||||
\(605\) | − 165.805i | − 0.274058i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −296.743 | −0.488869 | −0.244434 | − | 0.969666i | \(-0.578602\pi\) | ||||
−0.244434 | + | 0.969666i | \(0.578602\pi\) | |||||||
\(608\) | 26.5699i | 0.0437005i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −551.803 | −0.904594 | ||||||||
\(611\) | 277.924i | 0.454868i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −517.181 | −0.843688 | −0.421844 | − | 0.906668i | \(-0.638617\pi\) | ||||
−0.421844 | + | 0.906668i | \(0.638617\pi\) | |||||||
\(614\) | 217.917i | 0.354914i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −169.485 | −0.275137 | ||||||||
\(617\) | − 265.476i | − 0.430268i | −0.976584 | − | 0.215134i | \(-0.930981\pi\) | ||||
0.976584 | − | 0.215134i | \(-0.0690189\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −197.045 | −0.318329 | −0.159164 | − | 0.987252i | \(-0.550880\pi\) | ||||
−0.159164 | + | 0.987252i | \(0.550880\pi\) | |||||||
\(620\) | − 426.556i | − 0.687994i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 101.803 | 0.163670 | ||||||||
\(623\) | − 262.678i | − 0.421634i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −671.000 | −1.07360 | ||||||||
\(626\) | − 519.874i | − 0.830469i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 394.363 | 0.627967 | ||||||||
\(629\) | − 32.9973i | − 0.0524600i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −160.879 | −0.254958 | −0.127479 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127479 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(632\) | − 84.1241i | − 0.133108i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −152.166 | −0.240009 | ||||||||
\(635\) | − 52.4334i | − 0.0825723i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −171.303 | −0.268922 | ||||||||
\(638\) | 43.9048i | 0.0688164i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −58.7878 | −0.0918559 | ||||||||
\(641\) | 309.337i | 0.482585i | 0.970452 | + | 0.241293i | \(0.0775714\pi\) | ||||
−0.970452 | + | 0.241293i | \(0.922429\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 394.591 | 0.613672 | 0.306836 | − | 0.951762i | \(-0.400730\pi\) | ||||
0.306836 | + | 0.951762i | \(0.400730\pi\) | |||||||
\(644\) | − 119.844i | − 0.186093i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.6674 | 0.0196089 | ||||||||
\(647\) | − 418.736i | − 0.647196i | −0.946195 | − | 0.323598i | \(-0.895108\pi\) | ||||
0.946195 | − | 0.323598i | \(-0.104892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 863.908 | 1.33114 | ||||||||
\(650\) | − 55.7114i | − 0.0857098i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 498.120 | 0.763988 | ||||||||
\(653\) | − 530.725i | − 0.812749i | −0.913707 | − | 0.406375i | \(-0.866793\pi\) | ||||
0.913707 | − | 0.406375i | \(-0.133207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.7740 | 0.0393496 | ||||||||
\(656\) | − 247.316i | − 0.377006i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −126.681 | −0.192524 | ||||||||
\(659\) | − 358.193i | − 0.543539i | −0.962362 | − | 0.271770i | \(-0.912391\pi\) | ||||
0.962362 | − | 0.271770i | \(-0.0876089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −222.271 | −0.336265 | −0.168133 | − | 0.985764i | \(-0.553774\pi\) | ||||
−0.168133 | + | 0.985764i | \(0.553774\pi\) | |||||||
\(662\) | 24.3209i | 0.0367385i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 248.636 | 0.374451 | ||||||||
\(665\) | − 154.941i | − 0.232994i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.0454 | −0.0465448 | ||||||||
\(668\) | 96.8729i | 0.145019i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 227.469 | 0.339506 | ||||||||
\(671\) | 708.767i | 1.05628i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −289.211 | −0.429734 | −0.214867 | − | 0.976643i | \(-0.568932\pi\) | ||||
−0.214867 | + | 0.976643i | \(0.568932\pi\) | |||||||
\(674\) | 515.331i | 0.764586i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −437.939 | −0.647838 | ||||||||
\(677\) | − 464.451i | − 0.686043i | −0.939328 | − | 0.343022i | \(-0.888550\pi\) | ||||
0.939328 | − | 0.343022i | \(-0.111450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 608.682 | 0.896439 | ||||||||
\(680\) | 28.0274i | 0.0412168i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −547.893 | −0.803363 | ||||||||
\(683\) | − 1126.36i | − 1.64913i | −0.565767 | − | 0.824565i | \(-0.691420\pi\) | ||||
0.565767 | − | 0.824565i | \(-0.308580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1219.45 | −1.78022 | ||||||||
\(686\) | − 518.008i | − 0.755114i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.81837 | 0.00554996 | ||||||||
\(689\) | − 187.813i | − 0.272587i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1037.68 | 1.50171 | 0.750855 | − | 0.660467i | \(-0.229642\pi\) | ||||
0.750855 | + | 0.660467i | \(0.229642\pi\) | |||||||
\(692\) | 200.883i | 0.290293i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −825.044 | −1.18882 | ||||||||
\(695\) | − 553.547i | − 0.796470i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −117.909 | −0.169167 | ||||||||
\(698\) | 442.305i | 0.633675i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25.3939 | 0.0362770 | ||||||||
\(701\) | 778.180i | 1.11010i | 0.831817 | + | 0.555050i | \(0.187301\pi\) | ||||
−0.831817 | + | 0.555050i | \(0.812699\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.2714 | 0.115607 | ||||||||
\(704\) | 75.5103i | 0.107259i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −53.1964 | −0.0753490 | ||||||||
\(707\) | 1002.62i | 1.41814i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1172.03 | −1.65307 | −0.826536 | − | 0.562883i | \(-0.809692\pi\) | ||||
−0.826536 | + | 0.562883i | \(0.809692\pi\) | |||||||
\(710\) | 631.253i | 0.889089i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −117.031 | −0.164369 | ||||||||
\(713\) | − 387.419i | − 0.543365i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −966.044 | −1.35111 | ||||||||
\(716\) | − 570.142i | − 0.796287i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −415.818 | −0.579134 | ||||||||
\(719\) | − 515.416i | − 0.716851i | −0.933558 | − | 0.358426i | \(-0.883314\pi\) | ||||
0.933558 | − | 0.358426i | \(-0.116686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 184.970 | 0.256547 | ||||||||
\(722\) | − 479.332i | − 0.663894i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −74.2429 | −0.102545 | ||||||||
\(725\) | − 6.57826i | − 0.00907346i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −841.409 | −1.15737 | −0.578685 | − | 0.815551i | \(-0.696434\pi\) | ||||
−0.578685 | + | 0.815551i | \(0.696434\pi\) | |||||||
\(728\) | − 353.682i | − 0.485827i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −706.120 | −0.967288 | ||||||||
\(731\) | − 1.82043i | − 0.00249033i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 606.362 | 0.827234 | 0.413617 | − | 0.910451i | \(-0.364265\pi\) | ||||
0.413617 | + | 0.910451i | \(0.364265\pi\) | |||||||
\(734\) | − 46.9901i | − 0.0640192i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −53.3939 | −0.0725460 | ||||||||
\(737\) | − 292.174i | − 0.396437i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −389.362 | −0.526877 | −0.263439 | − | 0.964676i | \(-0.584857\pi\) | ||||
−0.263439 | + | 0.964676i | \(0.584857\pi\) | |||||||
\(740\) | 179.819i | 0.242998i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 85.6072 | 0.115374 | ||||||||
\(743\) | 1044.75i | 1.40612i | 0.711129 | + | 0.703061i | \(0.248184\pi\) | ||||
−0.711129 | + | 0.703061i | \(0.751816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −546.181 | −0.733128 | ||||||||
\(746\) | − 318.240i | − 0.426595i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 36.0000 | 0.0481283 | ||||||||
\(749\) | 1090.70i | 1.45621i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1291.83 | −1.72015 | −0.860074 | − | 0.510169i | \(-0.829583\pi\) | ||||
−0.860074 | + | 0.510169i | \(0.829583\pi\) | |||||||
\(752\) | 56.4401i | 0.0750533i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −91.6209 | −0.121513 | ||||||||
\(755\) | 1482.08i | 1.96302i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1042.36 | 1.37697 | 0.688483 | − | 0.725252i | \(-0.258277\pi\) | ||||
0.688483 | + | 0.725252i | \(0.258277\pi\) | |||||||
\(758\) | − 235.231i | − 0.310332i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −69.0306 | −0.0908298 | ||||||||
\(761\) | − 325.171i | − 0.427295i | −0.976911 | − | 0.213647i | \(-0.931466\pi\) | ||||
0.976911 | − | 0.213647i | \(-0.0685344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 738.152 | 0.967434 | ||||||||
\(764\) | − 35.8481i | − 0.0469217i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1042.26 | 1.36065 | ||||||||
\(767\) | 1802.81i | 2.35047i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 342.696 | 0.445638 | 0.222819 | − | 0.974860i | \(-0.428474\pi\) | ||||
0.222819 | + | 0.974860i | \(0.428474\pi\) | |||||||
\(770\) | − 440.334i | − 0.571863i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 190.908 | 0.247290 | ||||||||
\(773\) | − 532.579i | − 0.688977i | −0.938791 | − | 0.344488i | \(-0.888052\pi\) | ||||
0.938791 | − | 0.344488i | \(-0.111948\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 82.0908 | 0.105924 | ||||||||
\(776\) | − 271.186i | − 0.349466i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −239.530 | −0.307879 | ||||||||
\(779\) | − 290.407i | − 0.372794i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 810.817 | 1.03818 | ||||||||
\(782\) | 25.4558i | 0.0325522i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −34.7878 | −0.0443721 | ||||||||
\(785\) | 1024.59i | 1.30520i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −103.954 | −0.132088 | −0.0660442 | − | 0.997817i | \(-0.521038\pi\) | ||||
−0.0660442 | + | 0.997817i | \(0.521038\pi\) | |||||||
\(788\) | 320.726i | 0.407013i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 218.561 | 0.276659 | ||||||||
\(791\) | 1284.07i | 1.62335i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1479.06 | −1.86514 | ||||||||
\(794\) | − 362.424i | − 0.456453i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.0306 | −0.0163701 | ||||||||
\(797\) | − 1104.28i | − 1.38554i | −0.721158 | − | 0.692770i | \(-0.756390\pi\) | ||||
0.721158 | − | 0.692770i | \(-0.243610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.9082 | 0.0336773 | ||||||||
\(800\) | − 11.3137i | − 0.0141421i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −369.650 | −0.460911 | ||||||||
\(803\) | 906.981i | 1.12949i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 311.363 | 0.386787 | ||||||||
\(806\) | − 1143.35i | − 1.41855i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 446.697 | 0.552843 | ||||||||
\(809\) | − 256.465i | − 0.317015i | −0.987358 | − | 0.158508i | \(-0.949332\pi\) | ||||
0.987358 | − | 0.158508i | \(-0.0506683\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 735.362 | 0.906735 | 0.453368 | − | 0.891324i | \(-0.350222\pi\) | ||||
0.453368 | + | 0.891324i | \(0.350222\pi\) | |||||||
\(812\) | − 41.7619i | − 0.0514309i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 230.969 | 0.283746 | ||||||||
\(815\) | 1294.15i | 1.58792i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.48366 | 0.00548796 | ||||||||
\(818\) | − 627.611i | − 0.767250i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 642.545 | 0.783591 | ||||||||
\(821\) | − 1245.29i | − 1.51680i | −0.651792 | − | 0.758398i | \(-0.725982\pi\) | ||||
0.651792 | − | 0.758398i | \(-0.274018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1542.26 | −1.87395 | −0.936973 | − | 0.349402i | \(-0.886385\pi\) | ||||
−0.936973 | + | 0.349402i | \(0.886385\pi\) | |||||||
\(824\) | − 82.4097i | − 0.100012i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −821.741 | −0.994844 | ||||||||
\(827\) | 955.707i | 1.15563i | 0.816167 | + | 0.577815i | \(0.196095\pi\) | ||||
−0.816167 | + | 0.577815i | \(0.803905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1082.88 | 1.30625 | 0.653123 | − | 0.757252i | \(-0.273458\pi\) | ||||
0.653123 | + | 0.757252i | \(0.273458\pi\) | |||||||
\(830\) | 645.975i | 0.778283i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −157.576 | −0.189394 | ||||||||
\(833\) | 16.5853i | 0.0199103i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −251.683 | −0.301417 | ||||||||
\(836\) | 88.6669i | 0.106061i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.2281 | −0.0181719 | ||||||||
\(839\) | − 1043.59i | − 1.24385i | −0.783075 | − | 0.621927i | \(-0.786350\pi\) | ||||
0.783075 | − | 0.621927i | \(-0.213650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 830.182 | 0.987136 | ||||||||
\(842\) | 359.639i | 0.427125i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 308.879 | 0.365970 | ||||||||
\(845\) | − 1137.80i | − 1.34651i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 202.574 | 0.239167 | ||||||||
\(848\) | − 38.1405i | − 0.0449770i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.39388 | −0.00634574 | ||||||||
\(851\) | 163.320i | 0.191915i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 473.817 | 0.555472 | 0.277736 | − | 0.960657i | \(-0.410416\pi\) | ||||
0.277736 | + | 0.960657i | \(0.410416\pi\) | |||||||
\(854\) | − 674.172i | − 0.789429i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 485.939 | 0.567685 | ||||||||
\(857\) | − 916.762i | − 1.06973i | −0.844936 | − | 0.534867i | \(-0.820362\pi\) | ||||
0.844936 | − | 0.534867i | \(-0.179638\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 957.802 | 1.11502 | 0.557510 | − | 0.830170i | \(-0.311757\pi\) | ||||
0.557510 | + | 0.830170i | \(0.311757\pi\) | |||||||
\(860\) | 9.92041i | 0.0115354i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 988.059 | 1.14624 | ||||||||
\(863\) | − 524.200i | − 0.607416i | −0.952765 | − | 0.303708i | \(-0.901775\pi\) | ||||
0.952765 | − | 0.303708i | \(-0.0982247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −521.908 | −0.603362 | ||||||||
\(866\) | 299.428i | 0.345760i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 521.151 | 0.600404 | ||||||||
\(869\) | − 280.732i | − 0.323052i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 609.711 | 0.700012 | ||||||||
\(872\) | − 328.868i | − 0.377142i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −62.6969 | −0.0717356 | ||||||||
\(875\) | − 758.715i | − 0.867103i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1007.76 | 1.14909 | 0.574547 | − | 0.818471i | \(-0.305178\pi\) | ||||
0.574547 | + | 0.818471i | \(0.305178\pi\) | |||||||
\(878\) | 395.786i | 0.450781i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −196.182 | −0.222934 | ||||||||
\(881\) | 1536.71i | 1.74428i | 0.489254 | + | 0.872141i | \(0.337269\pi\) | ||||
−0.489254 | + | 0.872141i | \(0.662731\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −294.213 | −0.333197 | −0.166599 | − | 0.986025i | \(-0.553278\pi\) | ||||
−0.166599 | + | 0.986025i | \(0.553278\pi\) | |||||||
\(884\) | 75.1250i | 0.0849831i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −779.591 | −0.879900 | ||||||||
\(887\) | − 574.803i | − 0.648031i | −0.946052 | − | 0.324015i | \(-0.894967\pi\) | ||||
0.946052 | − | 0.324015i | \(-0.105033\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 64.0612 | 0.0720599 | ||||||||
\(890\) | − 304.054i | − 0.341634i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −185.546 | −0.208011 | ||||||||
\(893\) | 66.2739i | 0.0742149i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1481.27 | 1.65505 | ||||||||
\(896\) | − 71.8247i | − 0.0801615i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 767.728 | 0.854930 | ||||||||
\(899\) | − 135.004i | − 0.150171i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1837 | −0.0201817 | ||||||||
\(902\) | − 825.321i | − 0.914990i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 572.091 | 0.632844 | ||||||||
\(905\) | − 192.889i | − 0.213137i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −510.074 | −0.562375 | −0.281187 | − | 0.959653i | \(-0.590728\pi\) | ||||
−0.281187 | + | 0.959653i | \(0.590728\pi\) | |||||||
\(908\) | 339.604i | 0.374013i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 918.892 | 1.00977 | ||||||||
\(911\) | 927.371i | 1.01797i | 0.860775 | + | 0.508985i | \(0.169979\pi\) | ||||
−0.860775 | + | 0.508985i | \(0.830021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 829.727 | 0.908791 | ||||||||
\(914\) | 130.623i | 0.142913i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −815.090 | −0.889836 | ||||||||
\(917\) | 31.4897i | 0.0343399i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1240.63 | −1.34998 | −0.674991 | − | 0.737826i | \(-0.735853\pi\) | ||||
−0.674991 | + | 0.737826i | \(0.735853\pi\) | |||||||
\(920\) | − 138.721i | − 0.150784i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −325.015 | −0.352511 | ||||||||
\(923\) | 1692.02i | 1.83317i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.6061 | −0.0374120 | ||||||||
\(926\) | − 722.384i | − 0.780112i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18.6061 | −0.0200497 | ||||||||
\(929\) | − 338.992i | − 0.364900i | −0.983215 | − | 0.182450i | \(-0.941597\pi\) | ||||
0.983215 | − | 0.182450i | \(-0.0584028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.8490 | −0.0438765 | ||||||||
\(932\) | 30.5124i | 0.0327386i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1178.97 | −1.26228 | ||||||||
\(935\) | 93.5307i | 0.100033i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1322.21 | 1.41111 | 0.705556 | − | 0.708655i | \(-0.250698\pi\) | ||||
0.705556 | + | 0.708655i | \(0.250698\pi\) | |||||||
\(938\) | 277.913i | 0.296283i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −146.636 | −0.155995 | ||||||||
\(941\) | − 359.093i | − 0.381608i | −0.981628 | − | 0.190804i | \(-0.938891\pi\) | ||||
0.981628 | − | 0.190804i | \(-0.0611095\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 583.590 | 0.618866 | ||||||||
\(944\) | 366.110i | 0.387828i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.7423 | 0.0134697 | ||||||||
\(947\) | 775.792i | 0.819210i | 0.912263 | + | 0.409605i | \(0.134333\pi\) | ||||
−0.912263 | + | 0.409605i | \(0.865667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1892.69 | −1.99441 | ||||||||
\(950\) | − 13.2849i | − 0.0139842i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −34.2429 | −0.0359694 | ||||||||
\(953\) | − 465.082i | − 0.488019i | −0.969773 | − | 0.244010i | \(-0.921537\pi\) | ||||
0.969773 | − | 0.244010i | \(-0.0784628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 93.1362 | 0.0975248 | ||||||||
\(956\) | − 113.073i | − 0.118277i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 929.408 | 0.970154 | ||||||||
\(959\) | − 1489.88i | − 1.55358i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 723.725 | 0.753096 | ||||||||
\(962\) | 481.989i | 0.501028i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −168.424 | −0.174714 | ||||||||
\(965\) | 495.994i | 0.513983i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1224.23 | 1.26600 | 0.633002 | − | 0.774150i | \(-0.281822\pi\) | ||||
0.633002 | + | 0.774150i | \(0.281822\pi\) | |||||||
\(968\) | − 90.2528i | − 0.0932364i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 704.561 | 0.726351 | ||||||||
\(971\) | − 658.702i | − 0.678375i | −0.940719 | − | 0.339188i | \(-0.889848\pi\) | ||||
0.940719 | − | 0.339188i | \(-0.110152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 676.303 | 0.695070 | ||||||||
\(974\) | − 497.331i | − 0.510607i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −300.363 | −0.307749 | ||||||||
\(977\) | 1518.34i | 1.55408i | 0.629449 | + | 0.777042i | \(0.283281\pi\) | ||||
−0.629449 | + | 0.777042i | \(0.716719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −390.545 | −0.398922 | ||||||||
\(980\) | − 90.3812i | − 0.0922258i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −347.074 | −0.353436 | ||||||||
\(983\) | − 827.840i | − 0.842157i | −0.907024 | − | 0.421078i | \(-0.861652\pi\) | ||||
0.907024 | − | 0.421078i | \(-0.138348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −833.271 | −0.845961 | ||||||||
\(986\) | 8.87058i | 0.00899653i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −185.031 | −0.187278 | ||||||||
\(989\) | 9.01020i | 0.00911041i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 429.546 | 0.433447 | 0.216723 | − | 0.976233i | \(-0.430463\pi\) | ||||
0.216723 | + | 0.976233i | \(0.430463\pi\) | |||||||
\(992\) | − 232.188i | − 0.234060i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −771.242 | −0.775897 | ||||||||
\(995\) | − 33.8545i | − 0.0340247i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −694.998 | −0.697089 | −0.348545 | − | 0.937292i | \(-0.613324\pi\) | ||||
−0.348545 | + | 0.937292i | \(0.613324\pi\) | |||||||
\(998\) | 891.274i | 0.893060i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))