Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(1781,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.1781");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1781.4 | ||
Root | \(1.08696 - 1.34852i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.1781 |
Dual form | 2268.2.t.b.2105.4 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0382122 | + | 0.0661855i | 0.0170890 | + | 0.0295991i | 0.874443 | − | 0.485127i | \(-0.161227\pi\) |
−0.857354 | + | 0.514727i | \(0.827893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.16592 | − | 1.51947i | 0.818642 | − | 0.574304i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.66300 | − | 2.69219i | −1.40595 | − | 0.811725i | −0.410954 | − | 0.911656i | \(-0.634804\pi\) |
−0.994994 | + | 0.0999316i | \(0.968138\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.31524i | 1.47418i | 0.675794 | + | 0.737091i | \(0.263801\pi\) | ||||
−0.675794 | + | 0.737091i | \(0.736199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.89092 | − | 3.27516i | 0.458615 | − | 0.794344i | −0.540273 | − | 0.841490i | \(-0.681679\pi\) |
0.998888 | + | 0.0471458i | \(0.0150125\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.33939 | + | 2.50535i | −0.995525 | + | 0.574767i | −0.906921 | − | 0.421300i | \(-0.861574\pi\) |
−0.0886040 | + | 0.996067i | \(0.528241\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.02463 | − | 1.16892i | 0.422164 | − | 0.243737i | −0.273839 | − | 0.961776i | \(-0.588293\pi\) |
0.696003 | + | 0.718039i | \(0.254960\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.49708 | − | 4.32507i | 0.499416 | − | 0.865014i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 10.2125i | − | 1.89642i | −0.317648 | − | 0.948209i | \(-0.602893\pi\) | ||
0.317648 | − | 0.948209i | \(-0.397107\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.97636 | − | 2.87310i | −0.893780 | − | 0.516024i | −0.0186031 | − | 0.999827i | \(-0.505922\pi\) |
−0.875177 | + | 0.483803i | \(0.839255\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.183331 | + | 0.0852905i | 0.0309887 | + | 0.0144167i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.354486 | + | 0.613988i | 0.0582771 | + | 0.100939i | 0.893692 | − | 0.448681i | \(-0.148106\pi\) |
−0.835415 | + | 0.549620i | \(0.814773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.59821 | 1.03047 | 0.515234 | − | 0.857050i | \(-0.327705\pi\) | ||||
0.515234 | + | 0.857050i | \(0.327705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.43304 | −0.218537 | −0.109268 | − | 0.994012i | \(-0.534851\pi\) | ||||
−0.109268 | + | 0.994012i | \(0.534851\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.46192 | + | 2.53213i | 0.213244 | + | 0.369349i | 0.952728 | − | 0.303825i | \(-0.0982639\pi\) |
−0.739484 | + | 0.673174i | \(0.764931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.38244 | − | 6.58209i | 0.340349 | − | 0.940299i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4835 | − | 6.05264i | −1.44002 | − | 0.831394i | −0.442167 | − | 0.896933i | \(-0.645790\pi\) |
−0.997850 | + | 0.0655390i | \(0.979123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.411498i | − | 0.0554863i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.289951 | − | 0.502210i | 0.0377484 | − | 0.0653822i | −0.846534 | − | 0.532335i | \(-0.821315\pi\) |
0.884282 | + | 0.466953i | \(0.154648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.40641 | − | 1.38934i | 0.308109 | − | 0.177887i | −0.337971 | − | 0.941156i | \(-0.609741\pi\) |
0.646080 | + | 0.763270i | \(0.276407\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.351792 | + | 0.203107i | −0.0436344 | + | 0.0251923i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.63593 | + | 4.56556i | −0.322030 | + | 0.557771i | −0.980907 | − | 0.194479i | \(-0.937698\pi\) |
0.658877 | + | 0.752251i | \(0.271032\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.32103i | − | 0.394134i | −0.980390 | − | 0.197067i | \(-0.936858\pi\) | ||
0.980390 | − | 0.197067i | \(-0.0631416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.17326 | − | 3.56413i | −0.722525 | − | 0.417150i | 0.0931564 | − | 0.995651i | \(-0.470304\pi\) |
−0.815681 | + | 0.578502i | \(0.803638\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.1904 | + | 1.25421i | −1.61714 | + | 0.142930i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.469123 | − | 0.812544i | −0.0527804 | − | 0.0914184i | 0.838428 | − | 0.545012i | \(-0.183475\pi\) |
−0.891208 | + | 0.453594i | \(0.850142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.9958 | −1.42648 | −0.713238 | − | 0.700922i | \(-0.752772\pi\) | ||||
−0.713238 | + | 0.700922i | \(0.752772\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.289025 | 0.0313491 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.51794 | + | 2.62915i | 0.160901 | + | 0.278689i | 0.935192 | − | 0.354141i | \(-0.115227\pi\) |
−0.774291 | + | 0.632830i | \(0.781893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.07632 | + | 11.5124i | 0.846629 | + | 1.20683i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.331636 | − | 0.191470i | −0.0340251 | − | 0.0196444i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.13816i | 0.724771i | 0.932028 | + | 0.362385i | \(0.118038\pi\) | ||||
−0.932028 | + | 0.362385i | \(0.881962\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.08628 | − | 7.07765i | 0.406600 | − | 0.704252i | −0.587906 | − | 0.808929i | \(-0.700048\pi\) |
0.994506 | + | 0.104677i | \(0.0333808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.46599 | − | 3.73314i | 0.637113 | − | 0.367837i | −0.146389 | − | 0.989227i | \(-0.546765\pi\) |
0.783502 | + | 0.621390i | \(0.213432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.99991 | + | 2.30935i | −0.386686 | + | 0.223253i | −0.680723 | − | 0.732541i | \(-0.738334\pi\) |
0.294037 | + | 0.955794i | \(0.405001\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.22792 | − | 9.05503i | 0.500744 | − | 0.867314i | −0.499256 | − | 0.866455i | \(-0.666393\pi\) |
1.00000 | 0.000859385i | \(-0.000273551\pi\) | ||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 19.2118i | − | 1.80730i | −0.428275 | − | 0.903648i | \(-0.640879\pi\) | ||
0.428275 | − | 0.903648i | \(-0.359121\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.154731 | + | 0.0893340i | 0.0144287 | + | 0.00833044i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.880922 | − | 9.96693i | −0.0807540 | − | 0.913667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.99573 | + | 15.5811i | 0.817793 | + | 1.41646i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.763798 | 0.0683162 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.26488 | 0.112240 | 0.0561198 | − | 0.998424i | \(-0.482127\pi\) | ||||
0.0561198 | + | 0.998424i | \(0.482127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.24394 | − | 12.5469i | −0.632906 | − | 1.09623i | −0.986955 | − | 0.160998i | \(-0.948529\pi\) |
0.354049 | − | 0.935227i | \(-0.384805\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.59200 | + | 12.0200i | −0.484888 | + | 1.04226i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3414 | + | 7.70264i | 1.13983 | + | 0.658081i | 0.946389 | − | 0.323030i | \(-0.104702\pi\) |
0.193442 | + | 0.981112i | \(0.438035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.432667i | 0.0366983i | 0.999832 | + | 0.0183492i | \(0.00584105\pi\) | ||||
−0.999832 | + | 0.0183492i | \(0.994159\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.3096 | − | 24.7850i | 1.19663 | − | 2.07262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.675921 | − | 0.390243i | 0.0561322 | − | 0.0324079i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.04535 | − | 2.33558i | 0.331408 | − | 0.191338i | −0.325058 | − | 0.945694i | \(-0.605384\pi\) |
0.656466 | + | 0.754356i | \(0.272051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.12276 | − | 7.14083i | 0.335506 | − | 0.581113i | −0.648076 | − | 0.761575i | \(-0.724426\pi\) |
0.983582 | + | 0.180463i | \(0.0577595\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.439151i | − | 0.0352734i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.2334 | − | 8.79500i | −1.21576 | − | 0.701917i | −0.251749 | − | 0.967793i | \(-0.581006\pi\) |
−0.964007 | + | 0.265875i | \(0.914339\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.60905 | − | 5.60814i | 0.205622 | − | 0.441984i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.27097 | − | 9.12959i | −0.412854 | − | 0.715085i | 0.582346 | − | 0.812941i | \(-0.302135\pi\) |
−0.995201 | + | 0.0978563i | \(0.968801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.18293 | −0.710596 | −0.355298 | − | 0.934753i | \(-0.615621\pi\) | ||||
−0.355298 | + | 0.934753i | \(0.615621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.2517 | −1.17321 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.22358 | + | 2.11931i | 0.0930274 | + | 0.161128i | 0.908784 | − | 0.417268i | \(-0.137012\pi\) |
−0.815756 | + | 0.578396i | \(0.803679\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.16332 | − | 13.1620i | −0.0879384 | − | 0.994953i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.05509 | − | 2.91856i | −0.377835 | − | 0.218143i | 0.299041 | − | 0.954240i | \(-0.403333\pi\) |
−0.676876 | + | 0.736097i | \(0.736667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.0704i | − | 1.19451i | −0.802053 | − | 0.597253i | \(-0.796259\pi\) | ||
0.802053 | − | 0.597253i | \(-0.203741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0270914 | + | 0.0469237i | −0.00199180 | + | 0.00344990i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.6347 | + | 10.1814i | −1.28958 | + | 0.744537i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.90415 | + | 3.98611i | −0.499567 | + | 0.288425i | −0.728535 | − | 0.685009i | \(-0.759798\pi\) |
0.228968 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.359027 | + | 0.621853i | −0.0258433 | + | 0.0447620i | −0.878658 | − | 0.477452i | \(-0.841560\pi\) |
0.852814 | + | 0.522214i | \(0.174894\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.5035i | 0.962083i | 0.876698 | + | 0.481042i | \(0.159741\pi\) | ||||
−0.876698 | + | 0.481042i | \(0.840259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2568 | + | 12.2726i | 1.50685 | + | 0.869983i | 0.999968 | + | 0.00796947i | \(0.00253679\pi\) |
0.506886 | + | 0.862013i | \(0.330797\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.5176 | − | 22.1195i | −1.08912 | − | 1.55249i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.252132 | + | 0.436706i | 0.0176097 | + | 0.0305009i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.9795 | 1.86621 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5675 | 1.62245 | 0.811227 | − | 0.584731i | \(-0.198800\pi\) | ||||
0.811227 | + | 0.584731i | \(0.198800\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0547597 | − | 0.0948465i | −0.00373458 | − | 0.00646848i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.1440 | + | 1.33849i | −1.02804 | + | 0.0908628i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.4083 | + | 10.0507i | 1.17101 | + | 0.676081i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.47655i | − | 0.500667i | −0.968160 | − | 0.250334i | \(-0.919460\pi\) | ||
0.968160 | − | 0.250334i | \(-0.0805403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.318701 | − | 0.552006i | 0.0211529 | − | 0.0366379i | −0.855255 | − | 0.518207i | \(-0.826600\pi\) |
0.876408 | + | 0.481569i | \(0.159933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.58351 | − | 0.914239i | 0.104641 | − | 0.0604146i | −0.446766 | − | 0.894651i | \(-0.647424\pi\) |
0.551407 | + | 0.834236i | \(0.314091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.4232 | + | 10.0593i | −1.14143 | + | 0.659007i | −0.946785 | − | 0.321866i | \(-0.895690\pi\) |
−0.194649 | + | 0.980873i | \(0.562357\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.111727 | + | 0.193516i | −0.00728825 | + | 0.0126236i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.78808i | − | 0.180346i | −0.995926 | − | 0.0901730i | \(-0.971258\pi\) | ||
0.995926 | − | 0.0901730i | \(-0.0287420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0304 | + | 11.5645i | 1.29027 | + | 0.744938i | 0.978702 | − | 0.205286i | \(-0.0658126\pi\) |
0.311568 | + | 0.950224i | \(0.399146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.526678 | − | 0.0938333i | 0.0336482 | − | 0.00599479i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3165 | − | 23.0649i | −0.847310 | − | 1.46758i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.6541 | −1.17743 | −0.588717 | − | 0.808339i | \(-0.700367\pi\) | ||||
−0.588717 | + | 0.808339i | \(0.700367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.5878 | −0.791388 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.43687 | + | 9.41694i | 0.339143 | + | 0.587413i | 0.984272 | − | 0.176661i | \(-0.0565297\pi\) |
−0.645129 | + | 0.764074i | \(0.723196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.70072 | + | 0.791220i | 0.105678 | + | 0.0491640i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.4519 | − | 9.49852i | −1.01447 | − | 0.585704i | −0.101972 | − | 0.994787i | \(-0.532515\pi\) |
−0.912497 | + | 0.409083i | \(0.865849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.925140i | − | 0.0568309i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.29788 | − | 7.44415i | 0.262046 | − | 0.453878i | −0.704739 | − | 0.709467i | \(-0.748936\pi\) |
0.966786 | + | 0.255589i | \(0.0822693\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.58706 | − | 0.916292i | 0.0964073 | − | 0.0556608i | −0.451021 | − | 0.892513i | \(-0.648940\pi\) |
0.547429 | + | 0.836852i | \(0.315607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.2878 | + | 13.4452i | −1.40431 | + | 0.810776i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.90931 | + | 13.6993i | −0.475224 | + | 0.823113i | −0.999597 | − | 0.0283760i | \(-0.990966\pi\) |
0.524373 | + | 0.851489i | \(0.324300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.4998i | 0.686023i | 0.939331 | + | 0.343012i | \(0.111447\pi\) | ||||
−0.939331 | + | 0.343012i | \(0.888553\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.59806 | + | 4.96409i | 0.511101 | + | 0.295085i | 0.733286 | − | 0.679920i | \(-0.237986\pi\) |
−0.222185 | + | 0.975005i | \(0.571319\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.2912 | − | 10.0258i | 0.843584 | − | 0.591802i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.34887 | + | 2.33631i | 0.0793454 | + | 0.137430i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2720 | 1.00904 | 0.504520 | − | 0.863400i | \(-0.331670\pi\) | ||||
0.504520 | + | 0.863400i | \(0.331670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0443187 | 0.00258034 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.21308 | + | 10.7614i | 0.359312 | + | 0.622346i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.10385 | + | 2.17746i | −0.178903 | + | 0.125507i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.183908 | + | 0.106180i | 0.0105306 | + | 0.00607982i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6425i | 1.23520i | 0.786490 | + | 0.617602i | \(0.211896\pi\) | ||||
−0.786490 | + | 0.617602i | \(0.788104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.1016 | + | 17.4964i | −0.572808 | + | 0.992133i | 0.423468 | + | 0.905911i | \(0.360813\pi\) |
−0.996276 | + | 0.0862215i | \(0.972521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.9146 | − | 10.9203i | 1.06911 | − | 0.617254i | 0.141175 | − | 0.989985i | \(-0.454912\pi\) |
0.927939 | + | 0.372731i | \(0.121579\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.5288 | + | 12.4297i | −1.20918 | + | 0.698120i | −0.962580 | − | 0.270997i | \(-0.912647\pi\) |
−0.246599 | + | 0.969117i | \(0.579313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.4940 | + | 47.6210i | −1.53937 | + | 2.66626i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.9496i | 1.05439i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.9888 | + | 13.2726i | 1.27519 | + | 0.736230i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.01390 | + | 3.26305i | 0.386689 | + | 0.179898i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.07219 | − | 13.9814i | −0.443688 | − | 0.768490i | 0.554272 | − | 0.832336i | \(-0.312997\pi\) |
−0.997960 | + | 0.0638459i | \(0.979663\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.402898 | −0.0220127 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.6304 | 0.851444 | 0.425722 | − | 0.904854i | \(-0.360020\pi\) | ||||
0.425722 | + | 0.904854i | \(0.360020\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.4698 | + | 26.7946i | 0.837739 | + | 1.45101i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.84108 | − | 17.8764i | −0.261394 | − | 0.965232i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.0445 | + | 16.1915i | 1.50551 | + | 0.869206i | 0.999980 | + | 0.00639573i | \(0.00203584\pi\) |
0.505529 | + | 0.862810i | \(0.331297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 30.0708i | − | 1.60965i | −0.593510 | − | 0.804827i | \(-0.702258\pi\) | ||
0.593510 | − | 0.804827i | \(-0.297742\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.50607 | − | 14.7329i | 0.452733 | − | 0.784156i | −0.545822 | − | 0.837901i | \(-0.683783\pi\) |
0.998555 | + | 0.0537453i | \(0.0171159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.219804 | − | 0.126904i | 0.0116660 | − | 0.00673537i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.2692 | + | 14.5892i | −1.33366 | + | 0.769987i | −0.985858 | − | 0.167583i | \(-0.946404\pi\) |
−0.347798 | + | 0.937570i | \(0.613070\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.05356 | − | 5.28892i | 0.160714 | − | 0.278364i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.544774i | − | 0.0285148i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6981 | + | 9.06329i | 0.819433 | + | 0.473100i | 0.850221 | − | 0.526426i | \(-0.176468\pi\) |
−0.0307880 | + | 0.999526i | \(0.509802\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.9032 | + | 2.81975i | −1.65633 | + | 0.146394i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1823 | + | 17.6362i | 0.527219 | + | 0.913170i | 0.999497 | + | 0.0317200i | \(0.0100985\pi\) |
−0.472278 | + | 0.881450i | \(0.656568\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 54.2820 | 2.79566 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9961 | −1.12986 | −0.564931 | − | 0.825138i | \(-0.691097\pi\) | ||||
−0.564931 | + | 0.825138i | \(0.691097\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.3127 | + | 28.2544i | 0.833538 | + | 1.44373i | 0.895215 | + | 0.445634i | \(0.147022\pi\) |
−0.0616774 | + | 0.998096i | \(0.519645\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.625257 | − | 0.891272i | −0.0318660 | − | 0.0454234i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.6400 | + | 7.87504i | 0.691574 | + | 0.399280i | 0.804201 | − | 0.594357i | \(-0.202593\pi\) |
−0.112628 | + | 0.993637i | \(0.535927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.84131i | − | 0.447124i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0358524 | − | 0.0620983i | 0.00180393 | − | 0.00312450i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.95864 | + | 1.70817i | −0.148490 | + | 0.0857308i | −0.572404 | − | 0.819972i | \(-0.693989\pi\) |
0.423914 | + | 0.905702i | \(0.360656\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.851348 | − | 0.491526i | 0.0425143 | − | 0.0245456i | −0.478592 | − | 0.878037i | \(-0.658853\pi\) |
0.521106 | + | 0.853492i | \(0.325519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.2712 | − | 26.4505i | 0.760713 | − | 1.31759i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.81737i | − | 0.189220i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0195 | − | 14.4450i | −1.23714 | − | 0.714260i | −0.268627 | − | 0.963244i | \(-0.586570\pi\) |
−0.968508 | + | 0.248984i | \(0.919903\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.135080 | − | 1.52832i | −0.00664684 | − | 0.0752037i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.496599 | − | 0.860135i | −0.0243771 | − | 0.0422223i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.5785 | 0.614501 | 0.307251 | − | 0.951629i | \(-0.400591\pi\) | ||||
0.307251 | + | 0.951629i | \(0.400591\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0463 | 1.26942 | 0.634710 | − | 0.772750i | \(-0.281120\pi\) | ||||
0.634710 | + | 0.772750i | \(0.281120\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.44354 | − | 16.3567i | −0.458079 | − | 0.793416i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.10104 | − | 6.66566i | 0.150070 | − | 0.322574i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.28454 | − | 3.62838i | −0.302716 | − | 0.174773i | 0.340947 | − | 0.940083i | \(-0.389252\pi\) |
−0.643662 | + | 0.765310i | \(0.722586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.29113i | 0.398446i | 0.979954 | + | 0.199223i | \(0.0638419\pi\) | ||||
−0.979954 | + | 0.199223i | \(0.936158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.85710 | + | 10.1448i | −0.280183 | + | 0.485292i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.83357 | − | 1.63596i | 0.135239 | − | 0.0780802i | −0.430854 | − | 0.902422i | \(-0.641788\pi\) |
0.566093 | + | 0.824341i | \(0.308454\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.46737 | − | 1.42454i | 0.117228 | − | 0.0676817i | −0.440239 | − | 0.897880i | \(-0.645106\pi\) |
0.557468 | + | 0.830199i | \(0.311773\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.116008 | + | 0.200931i | −0.00549929 | + | 0.00952505i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.9802i | − | 0.942925i | −0.881886 | − | 0.471463i | \(-0.843726\pi\) | ||
0.881886 | − | 0.471463i | \(-0.156274\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.7675 | − | 17.7636i | −1.44878 | − | 0.836455i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.453339 | + | 0.974450i | −0.0212529 | + | 0.0456829i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.15008 | − | 15.8484i | −0.428023 | − | 0.741357i | 0.568675 | − | 0.822563i | \(-0.307456\pi\) |
−0.996697 | + | 0.0812053i | \(0.974123\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.05908 | 0.421923 | 0.210962 | − | 0.977494i | \(-0.432340\pi\) | ||||
0.210962 | + | 0.977494i | \(0.432340\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.6454 | −1.00595 | −0.502974 | − | 0.864302i | \(-0.667761\pi\) | ||||
−0.502974 | + | 0.864302i | \(0.667761\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.7761 | + | 23.8610i | 0.637484 | + | 1.10415i | 0.985983 | + | 0.166845i | \(0.0533580\pi\) |
−0.348500 | + | 0.937309i | \(0.613309\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.22800 | + | 13.8938i | 0.0567038 | + | 0.641558i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.68227 | + | 3.85801i | 0.307251 | + | 0.177392i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.0242i | 1.14819i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.47325 | − | 4.28380i | 0.113006 | − | 0.195732i | −0.803975 | − | 0.594663i | \(-0.797285\pi\) |
0.916981 | + | 0.398931i | \(0.130619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.26349 | + | 1.88418i | −0.148802 | + | 0.0859110i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.472443 | + | 0.272765i | −0.0214525 | + | 0.0123856i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.78573 | + | 8.28913i | −0.216862 | + | 0.375616i | −0.953847 | − | 0.300293i | \(-0.902916\pi\) |
0.736985 | + | 0.675909i | \(0.236249\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 38.1062i | − | 1.71971i | −0.510538 | − | 0.859855i | \(-0.670554\pi\) | ||
0.510538 | − | 0.859855i | \(-0.329446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.4477 | − | 19.3110i | −1.50641 | − | 0.869725i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.04620 | − | 7.19310i | −0.226353 | − | 0.322655i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4192 | + | 21.5107i | 0.555960 | + | 0.962951i | 0.997828 | + | 0.0658709i | \(0.0209825\pi\) |
−0.441868 | + | 0.897080i | \(0.645684\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.2820 | −1.21645 | −0.608223 | − | 0.793766i | \(-0.708117\pi\) | ||||
−0.608223 | + | 0.793766i | \(0.708117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.624584 | 0.0277936 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.8860 | + | 36.1757i | 0.925758 | + | 1.60346i | 0.790338 | + | 0.612671i | \(0.209905\pi\) |
0.135420 | + | 0.990788i | \(0.456762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.7864 | + | 1.66042i | −0.831060 | + | 0.0734528i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.494160 | + | 0.285303i | 0.0217753 | + | 0.0125720i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15.7431i | − | 0.692380i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.02629 | − | 3.50963i | 0.0887732 | − | 0.153760i | −0.818220 | − | 0.574906i | \(-0.805039\pi\) |
0.906993 | + | 0.421146i | \(0.138372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2429 | − | 15.1514i | 1.14752 | − | 0.662523i | 0.199241 | − | 0.979951i | \(-0.436152\pi\) |
0.948282 | + | 0.317428i | \(0.102819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.8198 | + | 10.8656i | −0.819801 | + | 0.473312i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.76726 | + | 15.1853i | −0.381185 | + | 0.660232i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.0710i | 1.51910i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.305691 | − | 0.176491i | −0.0132162 | − | 0.00763037i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.8296 | + | 24.2783i | −1.24178 | + | 1.04574i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.82681 | + | 15.2885i | 0.379494 | + | 0.657303i | 0.990989 | − | 0.133946i | \(-0.0427647\pi\) |
−0.611495 | + | 0.791249i | \(0.709431\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.799082 | 0.0342289 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.36639 | 0.186693 | 0.0933466 | − | 0.995634i | \(-0.470244\pi\) | ||||
0.0933466 | + | 0.995634i | \(0.470244\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.5859 | + | 44.3161i | 1.09000 | + | 1.88793i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.25072 | − | 1.04709i | −0.0957102 | − | 0.0445269i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.7527 | + | 8.51750i | 0.625094 | + | 0.360898i | 0.778849 | − | 0.627211i | \(-0.215804\pi\) |
−0.153756 | + | 0.988109i | \(0.549137\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.61695i | − | 0.322163i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.45992 | − | 11.1889i | 0.272253 | − | 0.471556i | −0.697185 | − | 0.716891i | \(-0.745564\pi\) |
0.969438 | + | 0.245335i | \(0.0788978\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.27155 | − | 0.734127i | 0.0534943 | − | 0.0308850i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.8280 | + | 10.8704i | −0.789313 | + | 0.455710i | −0.839720 | − | 0.543019i | \(-0.817281\pi\) |
0.0504079 | + | 0.998729i | \(0.483948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.8254 | − | 29.1425i | 0.704122 | − | 1.21958i | −0.262885 | − | 0.964827i | \(-0.584674\pi\) |
0.967007 | − | 0.254748i | \(-0.0819925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 11.6755i | − | 0.486904i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5598 | + | 7.25141i | 0.522871 | + | 0.301880i | 0.738109 | − | 0.674682i | \(-0.235719\pi\) |
−0.215237 | + | 0.976562i | \(0.569052\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.1479 | + | 19.7467i | −1.16777 | + | 0.819231i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.5897 | + | 56.4469i | 1.34973 | + | 2.33779i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.6834 | 1.30771 | 0.653857 | − | 0.756618i | \(-0.273150\pi\) | ||||
0.653857 | + | 0.756618i | \(0.273150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.7925 | 1.18637 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.54101 | + | 6.13320i | 0.145412 | + | 0.251860i | 0.929526 | − | 0.368755i | \(-0.120216\pi\) |
−0.784115 | + | 0.620616i | \(0.786883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.626005 | − | 0.439163i | 0.0256637 | − | 0.0180039i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.20178 | − | 3.00325i | −0.212539 | − | 0.122709i | 0.389952 | − | 0.920835i | \(-0.372492\pi\) |
−0.602491 | + | 0.798126i | \(0.705825\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 0.612087i | − | 0.0249675i | −0.999922 | − | 0.0124838i | \(-0.996026\pi\) | ||
0.999922 | − | 0.0124838i | \(-0.00397381\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.687494 | + | 1.19077i | −0.0279506 | + | 0.0484119i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.77500 | + | 1.02480i | −0.0720450 | + | 0.0415952i | −0.535590 | − | 0.844478i | \(-0.679911\pi\) |
0.463545 | + | 0.886073i | \(0.346577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.4588 | + | 7.77047i | −0.544487 | + | 0.314360i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.93166 | + | 8.54189i | −0.199188 | + | 0.345003i | −0.948265 | − | 0.317479i | \(-0.897164\pi\) |
0.749077 | + | 0.662482i | \(0.230497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.8055i | 1.07915i | 0.841937 | + | 0.539575i | \(0.181415\pi\) | ||||
−0.841937 | + | 0.539575i | \(0.818585\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0603011 | − | 0.0348148i | −0.00242370 | − | 0.00139933i | 0.498788 | − | 0.866724i | \(-0.333779\pi\) |
−0.501211 | + | 0.865325i | \(0.667112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.28264 | + | 3.38807i | 0.291773 | + | 0.135740i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4562 | − | 21.5748i | −0.498248 | − | 0.862992i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.68121 | 0.106907 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8214 | 0.470603 | 0.235301 | − | 0.971922i | \(-0.424392\pi\) | ||||
0.235301 | + | 0.971922i | \(0.424392\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0483338 | + | 0.0837165i | 0.00191807 | + | 0.00332219i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.9854 | + | 12.6632i | 1.38617 | + | 0.501736i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.7673 | + | 10.2580i | 0.701766 | + | 0.405165i | 0.808005 | − | 0.589176i | \(-0.200547\pi\) |
−0.106239 | + | 0.994341i | \(0.533881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0226i | 0.710743i | 0.934725 | + | 0.355372i | \(0.115646\pi\) | ||||
−0.934725 | + | 0.355372i | \(0.884354\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.11827 | − | 15.7933i | 0.358476 | − | 0.620899i | −0.629230 | − | 0.777219i | \(-0.716630\pi\) |
0.987706 | + | 0.156320i | \(0.0499631\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.70409 | + | 1.56121i | −0.106145 | + | 0.0612827i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.79559 | − | 4.50079i | 0.305065 | − | 0.176129i | −0.339651 | − | 0.940552i | \(-0.610309\pi\) |
0.644716 | + | 0.764422i | \(0.276976\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.553614 | − | 0.958888i | 0.0216315 | − | 0.0374669i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 35.1959i | − | 1.37104i | −0.728055 | − | 0.685519i | \(-0.759575\pi\) | ||
0.728055 | − | 0.685519i | \(-0.240425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.8797 | + | 6.28141i | 0.423172 | + | 0.244318i | 0.696433 | − | 0.717621i | \(-0.254769\pi\) |
−0.273262 | + | 0.961940i | \(0.588102\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.00923 | + | 0.0892002i | −0.0391363 | + | 0.00345904i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.9376 | − | 20.6765i | −0.462226 | − | 0.800599i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.9614 | −0.577580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.7826 | −1.84188 | −0.920942 | − | 0.389699i | \(-0.872579\pi\) | ||||
−0.920942 | + | 0.389699i | \(0.872579\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.5235 | + | 32.0837i | 0.711918 | + | 1.23308i | 0.964136 | + | 0.265407i | \(0.0855064\pi\) |
−0.252219 | + | 0.967670i | \(0.581160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.8462 | + | 15.4607i | 0.416239 | + | 0.593328i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.6844 | + | 12.5195i | 0.829732 | + | 0.479046i | 0.853761 | − | 0.520665i | \(-0.174316\pi\) |
−0.0240289 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.17734i | 0.0449839i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.1712 | − | 55.7222i | 1.22563 | − | 2.12285i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.2655 | + | 23.2473i | −1.53177 | + | 0.884370i | −0.532493 | + | 0.846434i | \(0.678745\pi\) |
−0.999280 | + | 0.0379352i | \(0.987922\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0286363 | + | 0.0165332i | −0.00108624 | + | 0.000627139i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.4767 | − | 21.6102i | 0.472587 | − | 0.818545i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0041i | 1.35986i | 0.733279 | + | 0.679928i | \(0.237989\pi\) | ||||
−0.733279 | + | 0.679928i | \(0.762011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.07651 | − | 1.77622i | −0.116033 | − | 0.0669915i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.90368 | − | 21.5386i | −0.0715952 | − | 0.810043i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.9158 | − | 27.5670i | −0.597731 | − | 1.03530i | −0.993155 | − | 0.116802i | \(-0.962736\pi\) |
0.395424 | − | 0.918499i | \(-0.370598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.4337 | −0.503096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.18721 | 0.0817969 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.0271 | + | 34.6879i | 0.746883 | + | 1.29364i | 0.949310 | + | 0.314342i | \(0.101784\pi\) |
−0.202427 | + | 0.979297i | \(0.564883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.33245 | − | 17.9106i | 0.310317 | − | 0.667024i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −44.1699 | − | 25.5015i | −1.64043 | − | 0.947101i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.91723i | − | 0.145282i | −0.997358 | − | 0.0726411i | \(-0.976857\pi\) | ||
0.997358 | − | 0.0726411i | \(-0.0231428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.70976 | + | 4.69344i | −0.100224 | + | 0.173593i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.4239 | + | 11.7918i | −0.754376 | + | 0.435539i | −0.827273 | − | 0.561800i | \(-0.810109\pi\) |
0.0728971 | + | 0.997339i | \(0.476776\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.5827 | − | 14.1928i | 0.905514 | − | 0.522798i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.8641 | − | 29.2094i | 0.620355 | − | 1.07449i | −0.369065 | − | 0.929404i | \(-0.620322\pi\) |
0.989420 | − | 0.145083i | \(-0.0463448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.9485i | 1.24545i | 0.782441 | + | 0.622725i | \(0.213975\pi\) | ||||
−0.782441 | + | 0.622725i | \(0.786025\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.309164 | + | 0.178496i | 0.0113269 | + | 0.00653958i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.15452 | + | 11.0796i | −0.188342 | + | 0.404840i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.69831 | − | 2.94157i | −0.0619724 | − | 0.107339i | 0.833375 | − | 0.552709i | \(-0.186406\pi\) |
−0.895347 | + | 0.445369i | \(0.853072\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.630160 | 0.0229339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.1344 | 1.05891 | 0.529454 | − | 0.848339i | \(-0.322397\pi\) | ||||
0.529454 | + | 0.848339i | \(0.322397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.36288 | + | 14.4849i | 0.303154 | + | 0.525079i | 0.976849 | − | 0.213931i | \(-0.0686269\pi\) |
−0.673694 | + | 0.739010i | \(0.735294\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.43553 | − | 27.5561i | −0.0881723 | − | 0.997599i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.66937 | + | 1.54116i | 0.0963852 | + | 0.0556480i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.8070i | 1.00275i | 0.865231 | + | 0.501373i | \(0.167172\pi\) | ||||
−0.865231 | + | 0.501373i | \(0.832828\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.42238 | − | 11.1239i | 0.230997 | − | 0.400098i | −0.727105 | − | 0.686526i | \(-0.759135\pi\) |
0.958102 | + | 0.286428i | \(0.0924679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.8527 | + | 14.3487i | −0.892736 | + | 0.515421i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.6322 | + | 16.5308i | −1.02586 | + | 0.592278i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.94083 | + | 15.4860i | −0.319928 | + | 0.554132i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.34431i | − | 0.0479804i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.55243 | − | 3.78305i | −0.233569 | − | 0.134851i | 0.378648 | − | 0.925541i | \(-0.376389\pi\) |
−0.612217 | + | 0.790689i | \(0.709722\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.1917 | − | 41.6113i | −1.03794 | − | 1.47953i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.38467 | + | 12.7906i | 0.262237 | + | 0.454208i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.06724 | −0.285756 | −0.142878 | − | 0.989740i | \(-0.545636\pi\) | ||||
−0.142878 | + | 0.989740i | \(0.545636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0575 | 0.391186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.1906 | + | 33.2391i | 0.677222 | + | 1.17298i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.470876 | − | 0.0416181i | 0.0165962 | − | 0.00146684i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.0849492 | + | 0.0490454i | 0.00298665 | + | 0.00172435i | 0.501493 | − | 0.865162i | \(-0.332784\pi\) |
−0.498506 | + | 0.866886i | \(0.666118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.3085i | − | 1.06428i | −0.846658 | − | 0.532138i | \(-0.821389\pi\) | ||
0.846658 | − | 0.532138i | \(-0.178611\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.402831 | − | 0.697724i | 0.0141106 | − | 0.0244402i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.21853 | − | 3.59027i | 0.217559 | − | 0.125608i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.5499 | + | 11.2871i | −0.682295 | + | 0.393923i | −0.800719 | − | 0.599040i | \(-0.795549\pi\) |
0.118424 | + | 0.992963i | \(0.462216\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.2655 | − | 21.2445i | 0.427549 | − | 0.740536i | −0.569106 | − | 0.822264i | \(-0.692711\pi\) |
0.996655 | + | 0.0817282i | \(0.0260439\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 40.3057i | − | 1.40157i | −0.713375 | − | 0.700783i | \(-0.752834\pi\) | ||
0.713375 | − | 0.700783i | \(-0.247166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.8081 | − | 27.0247i | −1.62571 | − | 0.938605i | −0.985353 | − | 0.170529i | \(-0.945452\pi\) |
−0.640359 | − | 0.768076i | \(-0.721214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.0524 | − | 20.2491i | −0.590832 | − | 0.701589i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.350900 | − | 0.607777i | −0.0121434 | − | 0.0210330i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.7299 | −0.819247 | −0.409624 | − | 0.912255i | \(-0.634340\pi\) | ||||
−0.409624 | + | 0.912255i | \(0.634340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −75.2956 | −2.59640 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.582803 | − | 1.00944i | −0.0200490 | − | 0.0347259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.1589 | + | 20.0787i | 1.48296 | + | 0.689911i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.43540 | + | 0.828731i | 0.0492050 | + | 0.0284085i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.5120i | 1.90069i | 0.311191 | + | 0.950347i | \(0.399272\pi\) | ||||
−0.311191 | + | 0.950347i | \(0.600728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.3048 | − | 26.5088i | 0.522803 | − | 0.905522i | −0.476845 | − | 0.878988i | \(-0.658220\pi\) |
0.999648 | − | 0.0265343i | \(-0.00844714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.4944 | − | 21.0700i | 1.24517 | − | 0.718900i | 0.275030 | − | 0.961436i | \(-0.411312\pi\) |
0.970143 | + | 0.242535i | \(0.0779790\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.7782 | + | 13.1510i | −0.775379 | + | 0.447665i | −0.834790 | − | 0.550568i | \(-0.814411\pi\) |
0.0594112 | + | 0.998234i | \(0.481078\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0935118 | + | 0.161967i | −0.00317950 | + | 0.00550705i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.05186i | 0.171373i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.2670 | − | 14.0106i | −0.822256 | − | 0.474730i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.65433 | − | 1.16057i | 0.0559265 | − | 0.0392343i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.8533 | − | 30.9228i | −0.602863 | − | 1.04419i | −0.992385 | − | 0.123172i | \(-0.960693\pi\) |
0.389522 | − | 0.921017i | \(-0.372640\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.4482 | 0.419392 | 0.209696 | − | 0.977767i | \(-0.432753\pi\) | ||||
0.209696 | + | 0.977767i | \(0.432753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.35637 | 0.0792982 | 0.0396491 | − | 0.999214i | \(-0.487376\pi\) | ||||
0.0396491 | + | 0.999214i | \(0.487376\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.7299 | − | 28.9770i | −0.561734 | − | 0.972952i | −0.997345 | − | 0.0728170i | \(-0.976801\pi\) |
0.435611 | − | 0.900135i | \(-0.356532\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.73962 | − | 1.92194i | 0.0918841 | − | 0.0644597i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.6877 | − | 7.32526i | −0.424579 | − | 0.245131i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 0.446099i | − | 0.0149114i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.3416 | + | 50.8212i | −0.978597 | + | 1.69498i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.6468 | + | 22.8901i | −1.32083 | + | 0.762579i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.06363 | − | 0.614087i | 0.0353563 | − | 0.0204130i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.467962 | − | 0.810535i | 0.0155384 | − | 0.0269134i | −0.858152 | − | 0.513396i | \(-0.828387\pi\) |
0.873690 | + | 0.486483i | \(0.161720\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33.3407i | − | 1.10463i | −0.833637 | − | 0.552313i | \(-0.813745\pi\) | ||
0.833637 | − | 0.552313i | \(-0.186255\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 60.5995 | + | 34.9871i | 2.00555 | + | 1.15791i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.7544 | − | 16.1686i | −1.14769 | − | 0.533935i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.73484 | − | 3.00483i | −0.0572270 | − | 0.0991200i | 0.835993 | − | 0.548741i | \(-0.184893\pi\) |
−0.893220 | + | 0.449621i | \(0.851559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.6521 | 0.581025 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.54072 | 0.116418 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.57680 | − | 13.1234i | −0.248587 | − | 0.430565i | 0.714547 | − | 0.699587i | \(-0.246633\pi\) |
−0.963134 | + | 0.269022i | \(0.913299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.15209 | + | 34.5312i | 0.201627 | + | 1.13171i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.34772 | − | 0.778108i | −0.0440752 | − | 0.0254468i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6651i | 1.09979i | 0.835233 | + | 0.549896i | \(0.185333\pi\) | ||||
−0.835233 | + | 0.549896i | \(0.814667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8980 | − | 32.7323i | 0.616058 | − | 1.06704i | −0.374140 | − | 0.927372i | \(-0.622062\pi\) |
0.990198 | − | 0.139671i | \(-0.0446045\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3589 | − | 7.71277i | 0.435026 | − | 0.251162i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.47426 | − | 5.46997i | 0.307872 | − | 0.177750i | −0.338102 | − | 0.941110i | \(-0.609785\pi\) |
0.645974 | + | 0.763360i | \(0.276452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.9442 | − | 32.8123i | 0.614955 | − | 1.06513i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.0914i | − | 0.359284i | −0.983732 | − | 0.179642i | \(-0.942506\pi\) | ||
0.983732 | − | 0.179642i | \(-0.0574939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.527646 | − | 0.304637i | −0.0170742 | − | 0.00985781i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.6003 | − | 3.58843i | 1.31105 | − | 0.115877i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00942 | + | 1.74838i | 0.0325621 | + | 0.0563992i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.0548769 | −0.00176655 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.2892 | −1.29561 | −0.647807 | − | 0.761805i | \(-0.724314\pi\) | ||||
−0.647807 | + | 0.761805i | \(0.724314\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.8458 | − | 41.3021i | −0.765248 | − | 1.32545i | −0.940115 | − | 0.340856i | \(-0.889283\pi\) |
0.174867 | − | 0.984592i | \(-0.444050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.657423 | + | 0.937123i | 0.0210760 | + | 0.0300428i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.4540 | − | 8.34504i | −0.462426 | − | 0.266982i | 0.250638 | − | 0.968081i | \(-0.419360\pi\) |
−0.713064 | + | 0.701099i | \(0.752693\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16.3463i | − | 0.522430i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9255 | − | 29.3157i | 0.539838 | − | 0.935027i | −0.459074 | − | 0.888398i | \(-0.651819\pi\) |
0.998912 | − | 0.0466291i | \(-0.0148479\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.893735 | + | 0.515998i | −0.0284768 | + | 0.0164411i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.90137 | + | 1.67511i | −0.0922583 | + | 0.0532653i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.09775 | + | 7.09751i | −0.130169 | + | 0.225460i | −0.923742 | − | 0.383016i | \(-0.874885\pi\) |
0.793572 | + | 0.608476i | \(0.208219\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.87586i | 0.0594686i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.7391 | + | 10.8190i | 0.593472 | + | 0.342641i | 0.766469 | − | 0.642281i | \(-0.222012\pi\) |
−0.172997 | + | 0.984922i | \(0.555345\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))