Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(293,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.x (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: | \(14.0856109166\) |
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: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1469.5 | ||
Root | \(1.08696 - 1.34852i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1469 |
Dual form | 1764.2.x.a.293.5 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.317569 | + | 1.70269i | 0.183349 | + | 0.983048i | ||||
\(4\) | 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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79830 | + | 1.08144i | −0.932767 | + | 0.360481i | ||||
\(10\) | 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 | ||||||||
\(13\) | 4.60313 | − | 2.65762i | 1.27668 | − | 0.737091i | 0.300442 | − | 0.953800i | \(-0.402866\pi\) |
0.976236 | + | 0.216709i | \(0.0695324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.100558 | + | 0.0860820i | −0.0259641 | + | 0.0222263i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.78183 | −0.917229 | −0.458615 | − | 0.888635i | \(-0.651654\pi\) | ||||
−0.458615 | + | 0.888635i | \(0.651654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.01070i | − | 1.14953i | −0.818317 | − | 0.574767i | \(-0.805093\pi\) | ||
0.818317 | − | 0.574767i | \(-0.194907\pi\) | |||||||
\(20\) | 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 | ||||||||
\(27\) | −2.73001 | − | 4.42120i | −0.525392 | − | 0.850861i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.84430 | + | 5.10626i | 1.64235 | + | 0.948209i | 0.979997 | + | 0.199013i | \(0.0637736\pi\) |
0.662349 | + | 0.749196i | \(0.269560\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.97636 | − | 2.87310i | 0.893780 | − | 0.516024i | 0.0186031 | − | 0.999827i | \(-0.494078\pi\) |
0.875177 | + | 0.483803i | \(0.160745\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.10313 | − | 8.79460i | 0.540185 | − | 1.53094i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.708972 | −0.116554 | −0.0582771 | − | 0.998300i | \(-0.518561\pi\) | ||||
−0.0582771 | + | 0.998300i | \(0.518561\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.98691 | + | 6.99372i | 0.958673 | + | 1.11989i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.29910 | − | 5.71422i | −0.515234 | − | 0.892411i | −0.999844 | − | 0.0176805i | \(-0.994372\pi\) |
0.484610 | − | 0.874730i | \(-0.338961\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.716520 | − | 1.24105i | 0.109268 | − | 0.189258i | −0.806206 | − | 0.591635i | \(-0.798483\pi\) |
0.915474 | + | 0.402377i | \(0.131816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.178505 | − | 0.143883i | −0.0266100 | − | 0.0214488i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.46192 | − | 2.53213i | 0.213244 | − | 0.369349i | −0.739484 | − | 0.673174i | \(-0.764931\pi\) |
0.952728 | + | 0.303825i | \(0.0982639\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.20099 | − | 6.43928i | −0.168173 | − | 0.901680i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1053i | 1.66279i | 0.555683 | + | 0.831394i | \(0.312457\pi\) | ||||
−0.555683 | + | 0.831394i | \(0.687543\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.411498i | − | 0.0554863i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.53166 | − | 1.59124i | 1.13005 | − | 0.210765i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.289951 | + | 0.502210i | 0.0377484 | + | 0.0653822i | 0.884282 | − | 0.466953i | \(-0.154648\pi\) |
−0.846534 | + | 0.532335i | \(0.821315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.40641 | − | 1.38934i | −0.308109 | − | 0.177887i | 0.337971 | − | 0.941156i | \(-0.390259\pi\) |
−0.646080 | + | 0.763270i | \(0.723593\pi\) | |||||||
\(62\) | 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 | 0.658877 | − | 0.752251i | \(-0.271032\pi\) |
−0.980907 | + | 0.194479i | \(0.937698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.63327 | + | 3.07610i | 0.317008 | + | 0.370319i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.32103i | − | 0.394134i | −0.980390 | − | 0.197067i | \(-0.936858\pi\) | ||
0.980390 | − | 0.197067i | \(-0.0631416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.12826i | 0.834300i | 0.908838 | + | 0.417150i | \(0.136971\pi\) | ||||
−0.908838 | + | 0.417150i | \(0.863029\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.15724 | + | 2.87824i | 0.941917 | + | 0.332351i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.469123 | + | 0.812544i | −0.0527804 | + | 0.0914184i | −0.891208 | − | 0.453594i | \(-0.850142\pi\) |
0.838428 | + | 0.545012i | \(0.183475\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.66096 | − | 6.05240i | 0.740107 | − | 0.672489i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.49790 | − | 11.2547i | 0.713238 | − | 1.23536i | −0.250398 | − | 0.968143i | \(-0.580561\pi\) |
0.963635 | − | 0.267221i | \(-0.0861053\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.144512 | − | 0.250303i | −0.0156746 | − | 0.0271491i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.88570 | + | 16.6807i | −0.631013 | + | 1.78836i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.03588 | −0.321802 | −0.160901 | − | 0.986971i | \(-0.551440\pi\) | ||||
−0.160901 | + | 0.986971i | \(0.551440\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.47234 | + | 7.56078i | 0.671150 | + | 0.784016i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.331636 | − | 0.191470i | 0.0340251 | − | 0.0196444i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.18183 | − | 3.56908i | −0.627670 | − | 0.362385i | 0.152179 | − | 0.988353i | \(-0.451371\pi\) |
−0.779849 | + | 0.625967i | \(0.784704\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.9599 | + | 2.49077i | 1.60403 | + | 0.250332i | ||||
\(100\) | 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 | ||||||||
\(107\) | − | 4.61870i | − | 0.446507i | −0.974760 | − | 0.223253i | \(-0.928332\pi\) | ||
0.974760 | − | 0.223253i | \(-0.0716677\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4558 | −1.00149 | −0.500744 | − | 0.865595i | \(-0.666940\pi\) | ||||
−0.500744 | + | 0.865595i | \(0.666940\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.225148 | − | 1.20716i | −0.0213701 | − | 0.114578i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.6379 | + | 9.60591i | −1.56516 | + | 0.903648i | −0.568445 | + | 0.822721i | \(0.692455\pi\) |
−0.996720 | + | 0.0809270i | \(0.974212\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.154731 | + | 0.0893340i | 0.0144287 | + | 0.00833044i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.0069 | + | 12.4148i | −0.925136 | + | 1.14775i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.99573 | + | 15.5811i | 0.817793 | + | 1.41646i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.68184 | − | 7.43201i | 0.782815 | − | 0.670122i | ||||
\(124\) | 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 | ||||||||
\(129\) | 2.34067 | + | 0.825892i | 0.206084 | + | 0.0727157i | ||||
\(130\) | 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 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.188300 | − | 0.349631i | 0.0162062 | − | 0.0300915i | ||||
\(136\) | 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 | ||||||||
\(139\) | 0.374701 | − | 0.216333i | 0.0317817 | − | 0.0183492i | −0.484025 | − | 0.875054i | \(-0.660826\pi\) |
0.515807 | + | 0.856705i | \(0.327492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.77569 | + | 1.68508i | 0.402185 | + | 0.141909i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −28.6192 | −2.39326 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.780486i | 0.0648159i | ||||||||
\(146\) | 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 | ||||||||
\(153\) | 10.5827 | − | 4.08984i | 0.855561 | − | 0.330644i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.380316 | + | 0.219575i | 0.0305477 | + | 0.0176367i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2334 | − | 8.79500i | 1.21576 | − | 0.701917i | 0.251749 | − | 0.967793i | \(-0.418994\pi\) |
0.964007 | + | 0.265875i | \(0.0856609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.6115 | + | 3.84426i | −1.63460 | + | 0.304870i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5419 | 0.825709 | 0.412854 | − | 0.910797i | \(-0.364532\pi\) | ||||
0.412854 | + | 0.910797i | \(0.364532\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.700653 | − | 0.130679i | 0.0545457 | − | 0.0101733i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.59146 | + | 7.95265i | 0.355298 | + | 0.615395i | 0.987169 | − | 0.159679i | \(-0.0510460\pi\) |
−0.631871 | + | 0.775074i | \(0.717713\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.62587 | − | 13.2084i | 0.586605 | − | 1.01603i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.41879 | + | 14.0214i | 0.414385 | + | 1.07225i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.22358 | − | 2.11931i | 0.0930274 | − | 0.161128i | −0.815756 | − | 0.578396i | \(-0.803679\pi\) |
0.908784 | + | 0.417268i | \(0.137012\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.763028 | + | 0.653183i | −0.0573527 | + | 0.0490963i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.83712i | 0.436287i | 0.975917 | + | 0.218143i | \(0.0700001\pi\) | ||||
−0.975917 | + | 0.218143i | \(0.930000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.0704i | − | 1.19451i | −0.802053 | − | 0.597253i | \(-0.796259\pi\) | ||
0.802053 | − | 0.597253i | \(-0.203741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.60141 | − | 4.53857i | 0.118380 | − | 0.335501i | ||||
\(184\) | 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 | \(-0.240202\pi\) |
−0.228968 | + | 0.973434i | \(0.573535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.359027 | − | 0.621853i | −0.0258433 | − | 0.0447620i | 0.852814 | − | 0.522214i | \(-0.174894\pi\) |
−0.878658 | + | 0.477452i | \(0.841560\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.234110 | + | 0.663492i | −0.0167650 | + | 0.0475137i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.5035i | 0.962083i | 0.876698 | + | 0.481042i | \(0.159741\pi\) | ||||
−0.876698 | + | 0.481042i | \(0.840259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 24.5452i | − | 1.73997i | −0.493082 | − | 0.869983i | \(-0.664130\pi\) | ||
0.493082 | − | 0.869983i | \(-0.335870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.93663 | − | 5.93804i | 0.489272 | − | 0.418837i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.252132 | − | 0.436706i | 0.0176097 | − | 0.0305009i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.40139 | + | 5.46051i | −0.305918 | + | 0.379531i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.4897 | + | 23.3649i | −0.933105 | + | 1.61618i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7838 | − | 20.4101i | −0.811227 | − | 1.40509i | −0.912005 | − | 0.410178i | \(-0.865467\pi\) |
0.100778 | − | 0.994909i | \(-0.467867\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.65468 | − | 1.05466i | 0.387453 | − | 0.0722639i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.109519 | 0.00746916 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.1372 | + | 2.26372i | −0.820157 | + | 0.152968i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.4083 | + | 10.0507i | −1.17101 | + | 0.676081i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.47489 | + | 3.73828i | 0.433590 | + | 0.250334i | 0.700875 | − | 0.713284i | \(-0.252793\pi\) |
−0.267285 | + | 0.963618i | \(0.586126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.31026 | + | 14.8033i | −0.154017 | + | 0.986886i | ||||
\(226\) | 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 | ||||||||
\(233\) | − | 20.1186i | − | 1.31801i | −0.752136 | − | 0.659007i | \(-0.770977\pi\) | ||
0.752136 | − | 0.659007i | \(-0.229023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.223454 | 0.0145765 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.53249 | − | 0.540731i | −0.0995458 | − | 0.0351242i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.41455 | + | 1.39404i | −0.156184 | + | 0.0901730i | −0.576055 | − | 0.817411i | \(-0.695409\pi\) |
0.419871 | + | 0.907584i | \(0.362075\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 12.4207 | + | 9.41949i | 0.796787 | + | 0.604261i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3165 | − | 23.0649i | −0.847310 | − | 1.46758i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.2268 | + | 7.48976i | 1.34519 | + | 0.474645i | ||||
\(250\) | 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 | ||||||||
\(255\) | 0.380295 | − | 0.325548i | 0.0238150 | − | 0.0203866i | ||||
\(256\) | 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 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.2711 | − | 4.72424i | −1.87374 | − | 0.292423i | ||||
\(262\) | 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 | ||||||||
\(265\) | −0.801194 | + | 0.462570i | −0.0492170 | + | 0.0284154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.964101 | − | 5.16915i | −0.0590020 | − | 0.316347i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.59576 | −0.524093 | −0.262046 | − | 0.965055i | \(-0.584397\pi\) | ||||
−0.262046 | + | 0.965055i | \(0.584397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.83258i | 0.111322i | 0.998450 | + | 0.0556608i | \(0.0177265\pi\) | ||||
−0.998450 | + | 0.0556608i | \(0.982273\pi\) | |||||||
\(272\) | 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 | ||||||||
\(279\) | −10.8182 | + | 13.4214i | −0.647671 | + | 0.803521i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.95916 | − | 5.74992i | −0.594114 | − | 0.343012i | 0.172609 | − | 0.984990i | \(-0.444780\pi\) |
−0.766722 | + | 0.641979i | \(0.778114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.59806 | + | 4.96409i | −0.511101 | + | 0.295085i | −0.733286 | − | 0.679920i | \(-0.762014\pi\) |
0.222185 | + | 0.975005i | \(0.428681\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.431331 | + | 0.503868i | 0.0255499 | + | 0.0298466i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.69774 | −0.158691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.11388 | − | 11.6592i | 0.241160 | − | 0.683473i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.63598 | − | 14.9580i | −0.504520 | − | 0.873854i | −0.999986 | − | 0.00522664i | \(-0.998336\pi\) |
0.495467 | − | 0.868627i | \(-0.334997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0221594 | + | 0.0383812i | −0.00129017 | + | 0.00223464i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.827372 | + | 27.9658i | 0.0480090 | + | 1.62274i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.21308 | − | 10.7614i | 0.359312 | − | 0.622346i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.3487 | + | 4.71003i | 0.766863 | + | 0.270584i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.212359i | − | 0.0121596i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6425i | 1.23520i | 0.786490 | + | 0.617602i | \(0.211896\pi\) | ||||
−0.786490 | + | 0.617602i | \(0.788104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.40978 | + | 9.82404i | 0.478416 | + | 0.558870i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.1016 | − | 17.4964i | −0.572808 | − | 0.992133i | −0.996276 | − | 0.0862215i | \(-0.972521\pi\) |
0.423468 | − | 0.905911i | \(-0.360813\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.9146 | − | 10.9203i | −1.06911 | − | 0.617254i | −0.141175 | − | 0.989985i | \(-0.545088\pi\) |
−0.927939 | + | 0.372731i | \(0.878421\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.5288 | + | 12.4297i | 1.20918 | + | 0.698120i | 0.962580 | − | 0.270997i | \(-0.0873535\pi\) |
0.246599 | + | 0.969117i | \(0.420687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.4940 | − | 47.6210i | −1.53937 | − | 2.66626i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.86421 | − | 1.46676i | 0.438938 | − | 0.0818664i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.9496i | 1.05439i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 26.5451i | − | 1.47246i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.32045 | − | 17.8030i | −0.183621 | − | 0.984511i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.07219 | + | 13.9814i | −0.443688 | + | 0.768490i | −0.997960 | − | 0.0638459i | \(-0.979663\pi\) |
0.554272 | + | 0.832336i | \(0.312997\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.98392 | − | 0.766713i | 0.108718 | − | 0.0420156i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.201449 | − | 0.348920i | 0.0110063 | − | 0.0190635i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.81522 | − | 13.5364i | −0.425722 | − | 0.737372i | 0.570765 | − | 0.821113i | \(-0.306647\pi\) |
−0.996488 | + | 0.0837408i | \(0.973313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.6396 | − | 25.2787i | −1.17530 | − | 1.37295i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.9397 | −1.67548 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.102970 | + | 0.291829i | −0.00554373 | + | 0.0157115i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.0445 | + | 16.1915i | −1.50551 | + | 0.869206i | −0.505529 | + | 0.862810i | \(0.668703\pi\) |
−0.999980 | + | 0.00639573i | \(0.997964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0421 | + | 15.0354i | 1.39400 | + | 0.804827i | 0.993755 | − | 0.111581i | \(-0.0355915\pi\) |
0.400246 | + | 0.916408i | \(0.368925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.3165 | − | 13.0960i | −1.29792 | − | 0.699014i | ||||
\(352\) | 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 | ||||||||
\(359\) | − | 29.1783i | − | 1.53997i | −0.638060 | − | 0.769987i | \(-0.720263\pi\) | ||
0.638060 | − | 0.769987i | \(-0.279737\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.10712 | −0.321427 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.6729 | + | 20.2650i | −1.24251 | + | 1.06364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.471788 | + | 0.272387i | −0.0246945 | + | 0.0142574i | ||||
\(366\) | 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 | ||||||||
\(369\) | 15.4115 | + | 12.4223i | 0.802290 | + | 0.646679i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | ||||||||
\(375\) | 0.242559 | + | 1.30051i | 0.0125257 | + | 0.0671581i | ||||
\(376\) | 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 | ||||||||
\(381\) | 0.401686 | + | 2.15369i | 0.0205790 | + | 0.110337i | ||||
\(382\) | 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 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.662914 | + | 4.24770i | −0.0336978 | + | 0.215923i | ||||
\(388\) | 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 | ||||||||
\(391\) | −7.65680 | + | 4.42066i | −0.387221 | + | 0.223562i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.0630 | − | 16.3187i | 0.961600 | − | 0.823168i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.0717049 | −0.00360786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.41635i | − | 0.171462i | −0.996318 | − | 0.0857308i | \(-0.972678\pi\) | ||
0.996318 | − | 0.0857308i | \(-0.0273225\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 0.655112 | + | 0.209583i | 0.0325528 | + | 0.0104143i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.30594 | + | 1.90868i | 0.163869 | + | 0.0946099i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.0195 | − | 14.4450i | 1.23714 | − | 0.714260i | 0.268627 | − | 0.963244i | \(-0.413430\pi\) |
0.968508 | + | 0.248984i | \(0.0800966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.87840 | + | 25.1623i | −0.437939 | + | 1.24117i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.993198 | 0.0487542 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.487342 | + | 0.569298i | 0.0238652 | + | 0.0278786i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.28926 | − | 10.8933i | −0.307251 | − | 0.532174i | 0.670509 | − | 0.741901i | \(-0.266076\pi\) |
−0.977760 | + | 0.209727i | \(0.932742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0232 | + | 22.5568i | −0.634710 | + | 1.09935i | 0.351866 | + | 0.936050i | \(0.385547\pi\) |
−0.986576 | + | 0.163300i | \(0.947786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.35255 | + | 8.66664i | −0.0657633 | + | 0.421386i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.44354 | + | 16.3567i | −0.458079 | + | 0.793416i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.08858 | − | 48.7296i | −0.438801 | − | 2.35269i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.25676i | 0.349546i | 0.984609 | + | 0.174773i | \(0.0559192\pi\) | ||||
−0.984609 | + | 0.174773i | \(0.944081\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.29113i | 0.398446i | 0.979954 | + | 0.199223i | \(0.0638419\pi\) | ||||
−0.979954 | + | 0.199223i | \(0.936158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.32893 | + | 0.247858i | −0.0637171 | + | 0.0118839i | ||||
\(436\) | 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 | \(-0.358212\pi\) |
−0.566093 | + | 0.824341i | \(0.691546\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.46737 | − | 1.42454i | −0.117228 | − | 0.0676817i | 0.440239 | − | 0.897880i | \(-0.354894\pi\) |
−0.557468 | + | 0.830199i | \(0.688227\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.116008 | − | 0.200931i | −0.00549929 | − | 0.00952505i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.26145 | + | 6.14626i | 0.248858 | + | 0.290708i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.9802i | − | 0.942925i | −0.881886 | − | 0.471463i | \(-0.843726\pi\) | ||
0.881886 | − | 0.471463i | \(-0.156274\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.5272i | 1.67291i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.4679 | + | 4.75207i | 0.632776 | + | 0.223272i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.15008 | + | 15.8484i | −0.428023 | + | 0.741357i | −0.996697 | − | 0.0812053i | \(-0.974123\pi\) |
0.568675 | + | 0.822563i | \(0.307456\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.3245 | + | 16.7202i | 0.481904 | + | 0.780434i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.52954 | + | 7.84539i | −0.210962 | + | 0.365396i | −0.952016 | − | 0.306049i | \(-0.900993\pi\) |
0.741054 | + | 0.671445i | \(0.234326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.8227 | + | 18.7455i | 0.502974 | + | 0.871176i | 0.999994 | + | 0.00343694i | \(0.00109401\pi\) |
−0.497021 | + | 0.867739i | \(0.665573\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.253092 | + | 0.717289i | −0.0117369 | + | 0.0332635i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.5523 | −1.27497 | −0.637484 | − | 0.770464i | \(-0.720025\pi\) | ||||
−0.637484 | + | 0.770464i | \(0.720025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.8128 | + | 23.1447i | 0.912926 | + | 1.06645i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.68227 | + | 3.85801i | −0.307251 | + | 0.177392i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.6716 | − | 12.5121i | −0.994362 | − | 0.574095i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.0912 | − | 33.8742i | −0.599403 | − | 1.55099i | ||||
\(478\) | 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 | ||||||||
\(485\) | − | 0.545530i | − | 0.0247713i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.57146 | 0.433724 | 0.216862 | − | 0.976202i | \(-0.430418\pi\) | ||||
0.216862 | + | 0.976202i | \(0.430418\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.34780 | + | 17.9496i | 0.151393 | + | 0.811711i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.0010 | + | 19.0531i | −1.48931 | + | 0.859855i | −0.999925 | − | 0.0122119i | \(-0.996113\pi\) |
−0.489387 | + | 0.872067i | \(0.662779\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.4477 | − | 19.3110i | −1.50641 | − | 0.869725i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.445011 | + | 1.15149i | 0.0200018 | + | 0.0517558i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 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 | ||||||||
\(501\) | −12.0828 | + | 10.3434i | −0.539819 | + | 0.462107i | ||||
\(502\) | 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 | ||||||||
\(507\) | 24.9115 | + | 8.78990i | 1.10636 | + | 0.390373i | ||||
\(508\) | 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 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.1533 | + | 13.6793i | −0.978093 | + | 0.603955i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.494160 | + | 0.285303i | 0.0217753 | + | 0.0125720i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.6339 | + | 7.87154i | −0.599619 | + | 0.346190i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.99710 | + | 1.41036i | 0.175453 | + | 0.0619078i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.05257 | −0.177546 | −0.0887732 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887732 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.3027i | 1.32505i | 0.749042 | + | 0.662523i | \(0.230514\pi\) | ||||
−0.749042 | + | 0.662523i | \(0.769486\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | −1.35448 | − | 1.09177i | −0.0587795 | − | 0.0473788i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.3724 | − | 17.5355i | −1.31558 | − | 0.759548i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.305691 | − | 0.176491i | 0.0132162 | − | 0.00763037i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.93880 | + | 1.85369i | −0.428891 | + | 0.0799926i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.6536 | −0.758988 | −0.379494 | − | 0.925194i | \(-0.623902\pi\) | ||||
−0.379494 | + | 0.925194i | \(0.623902\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.3630 | − | 5.10348i | 1.17426 | − | 0.219011i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.399541 | − | 0.692026i | −0.0171145 | − | 0.0296431i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.18319 | + | 3.78140i | −0.0933466 | + | 0.161681i | −0.908917 | − | 0.416976i | \(-0.863090\pi\) |
0.815571 | + | 0.578657i | \(0.196423\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.23634 | + | 1.28540i | 0.351518 | + | 0.0548594i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.5859 | − | 44.3161i | 1.09000 | − | 1.88793i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0712930 | − | 0.0610297i | 0.00302622 | − | 0.00259057i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17.0350i | − | 0.721796i | −0.932605 | − | 0.360898i | \(-0.882470\pi\) | ||
0.932605 | − | 0.360898i | \(-0.117530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.61695i | − | 0.322163i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.7355 | + | 33.2597i | −0.495474 | + | 1.40423i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.45992 | + | 11.1889i | 0.272253 | + | 0.471556i | 0.969438 | − | 0.245335i | \(-0.0788978\pi\) |
−0.697185 | + | 0.716891i | \(0.745564\pi\) | |||||||
\(564\) | 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 | \(-0.182719\pi\) |
−0.0504079 | + | 0.998729i | \(0.516052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.8254 | + | 29.1425i | 0.704122 | + | 1.21958i | 0.967007 | + | 0.254748i | \(0.0819925\pi\) |
−0.262885 | + | 0.964827i | \(0.584674\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.59457 | + | 13.0215i | −0.191941 | + | 0.543980i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 11.6755i | − | 0.486904i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.5028i | − | 0.603760i | −0.953346 | − | 0.301880i | \(-0.902386\pi\) | ||
0.953346 | − | 0.301880i | \(-0.0976142\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.944806 | − | 0.808793i | 0.0392648 | − | 0.0336123i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.5897 | − | 56.4469i | 1.34973 | − | 2.33779i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.20407 | − | 0.187912i | −0.0497821 | − | 0.00776919i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.8417 | + | 27.4386i | −0.653857 | + | 1.13251i | 0.328322 | + | 0.944566i | \(0.393517\pi\) |
−0.982179 | + | 0.187948i | \(0.939816\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.3963 | − | 24.9350i | −0.593187 | − | 1.02743i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.9922 | + | 4.28829i | −0.945774 | + | 0.176397i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.08201 | −0.290823 | −0.145412 | − | 0.989371i | \(-0.546451\pi\) | ||||
−0.145412 | + | 0.989371i | \(0.546451\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41.7929 | − | 7.79481i | 1.71047 | − | 0.319020i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.20178 | − | 3.00325i | 0.212539 | − | 0.122709i | −0.389952 | − | 0.920835i | \(-0.627508\pi\) |
0.602491 | + | 0.798126i | \(0.294175\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.530083 | + | 0.306043i | 0.0216225 | + | 0.0124838i | 0.510772 | − | 0.859716i | \(-0.329360\pi\) |
−0.489150 | + | 0.872200i | \(0.662693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.3135 | + | 9.92519i | 0.501444 | + | 0.404185i | ||||
\(604\) | 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 | ||||||||
\(611\) | − | 15.5409i | − | 0.628719i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.86332 | 0.398376 | 0.199188 | − | 0.979961i | \(-0.436170\pi\) | ||||
0.199188 | + | 0.979961i | \(0.436170\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.823644 | + | 0.290619i | 0.0332125 | + | 0.0117189i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2143 | − | 13.4028i | 0.934571 | − | 0.539575i | 0.0463170 | − | 0.998927i | \(-0.485252\pi\) |
0.888254 | + | 0.459352i | \(0.151918\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | −10.6953 | − | 5.76012i | −0.429187 | − | 0.231146i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4562 | − | 21.5748i | −0.498248 | − | 0.862992i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −44.0671 | − | 15.5489i | −1.75987 | − | 0.620961i | ||||
\(628\) | 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 | ||||||||
\(633\) | 31.0098 | − | 26.5457i | 1.23253 | − | 1.05510i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0483338 | + | 0.0837165i | 0.00191807 | + | 0.00332219i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.59151 | + | 9.29324i | 0.142078 | + | 0.367635i | ||||
\(640\) | 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 | ||||||||
\(643\) | 15.6081 | − | 9.01132i | 0.615522 | − | 0.355372i | −0.159602 | − | 0.987182i | \(-0.551021\pi\) |
0.775123 | + | 0.631810i | \(0.217688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0347800 | + | 0.186477i | 0.00136946 | + | 0.00734254i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.2365 | −0.716952 | −0.358476 | − | 0.933539i | \(-0.616704\pi\) | ||||
−0.358476 | + | 0.933539i | \(0.616704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.12241i | − | 0.122565i | ||||||
\(650\) | 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 | ||||||||
\(657\) | −7.70881 | − | 19.9470i | −0.300749 | − | 0.778207i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.4806 | + | 17.5980i | 1.18735 | + | 0.685519i | 0.957704 | − | 0.287754i | \(-0.0929086\pi\) |
0.229650 | + | 0.973273i | \(0.426242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8797 | + | 6.28141i | −0.423172 | + | 0.244318i | −0.696433 | − | 0.717621i | \(-0.745231\pi\) |
0.273262 | + | 0.961940i | \(0.411898\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.6415 | − | 26.4491i | −0.879322 | − | 1.02720i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.8752 | 0.924452 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.30890 | + | 12.2119i | −0.166592 | + | 0.472139i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.48072 | + | 12.9570i | 0.288790 | + | 0.500199i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.8913 | − | 41.3810i | 0.920942 | − | 1.59512i | 0.122982 | − | 0.992409i | \(-0.460754\pi\) |
0.797960 | − | 0.602710i | \(-0.205913\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9391 | + | 0.767411i | −0.998395 | + | 0.0295377i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.5235 | − | 32.0837i | 0.711918 | − | 1.23308i | −0.252219 | − | 0.967670i | \(-0.581160\pi\) |
0.964136 | − | 0.265407i | \(-0.0855064\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.04110 | + | 0.367348i | 0.0398952 | + | 0.0140768i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 25.0390i | − | 0.958092i | −0.877790 | − | 0.479046i | \(-0.840983\pi\) | ||
0.877790 | − | 0.479046i | \(-0.159017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.17734i | 0.0449839i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.05954 | + | 2.40589i | 0.0785763 | + | 0.0917904i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.1712 | + | 55.7222i | 1.22563 | + | 2.12285i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.2655 | + | 23.2473i | 1.53177 | + | 0.884370i | 0.999280 | + | 0.0379352i | \(0.0120781\pi\) |
0.532493 | + | 0.846434i | \(0.321255\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 34.2558 | − | 6.38905i | 1.29567 | − | 0.241656i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0041i | 1.35986i | 0.733279 | + | 0.679928i | \(0.237989\pi\) | ||||
−0.733279 | + | 0.679928i | \(0.762011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.55244i | 0.133983i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.0709620 | + | 0.380472i | 0.00267258 | + | 0.0143294i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.9158 | + | 27.5670i | −0.597731 | + | 1.03530i | 0.395424 | + | 0.918499i | \(0.370598\pi\) |
−0.993155 | + | 0.116802i | \(0.962736\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.434025 | − | 2.78107i | 0.0162772 | − | 0.104298i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.71685 | − | 11.6339i | 0.251548 | − | 0.435694i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.09360 | − | 1.89418i | −0.0408985 | − | 0.0708382i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.14041 | − | 3.66852i | −0.117281 | − | 0.137004i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.0541 | −1.49377 | −0.746883 | − | 0.664955i | \(-0.768450\pi\) | ||||
−0.746883 | + | 0.664955i | \(0.768450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.3298 | + | 37.7780i | −0.495740 | + | 1.40498i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44.1699 | − | 25.5015i | 1.64043 | − | 0.947101i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.39242 | + | 1.95862i | 0.125818 | + | 0.0726411i | 0.561588 | − | 0.827417i | \(-0.310191\pi\) |
−0.435770 | + | 0.900058i | \(0.643524\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.0940 | + | 24.1399i | −0.447927 | + | 0.894070i | ||||
\(730\) | 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 | ||||||||
\(737\) | 28.3856i | 1.04560i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.7282 | −1.24071 | −0.620355 | − | 0.784321i | \(-0.713011\pi\) | ||||
−0.620355 | + | 0.784321i | \(0.713011\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.0434 | − | 29.9986i | 1.28735 | − | 1.10203i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.4003 | − | 16.9743i | 1.07859 | − | 0.622725i | 0.148076 | − | 0.988976i | \(-0.452692\pi\) |
0.930516 | + | 0.366251i | \(0.119359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.309164 | + | 0.178496i | 0.0113269 | + | 0.00653958i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.01177 | + | 38.5211i | −0.219959 | + | 1.40941i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | ||||||||
\(753\) | −5.92395 | − | 31.7621i | −0.215881 | − | 1.15747i | ||||
\(754\) | 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 | ||||||||
\(759\) | −3.99749 | − | 21.4331i | −0.145100 | − | 0.777972i | ||||
\(760\) | 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 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.675077 | + | 0.544140i | 0.0244074 | + | 0.0196734i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.66937 | + | 1.54116i | 0.0963852 | + | 0.0556480i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0816 | − | 13.9035i | 0.868404 | − | 0.501373i | 0.00158643 | − | 0.999999i | \(-0.499495\pi\) |
0.866818 | + | 0.498625i | \(0.166162\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.3075 | + | 12.2478i | −0.515273 | + | 0.441095i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.8448 | −0.461994 | −0.230997 | − | 0.972954i | \(-0.574199\pi\) | ||||
−0.230997 | + | 0.972954i | \(0.574199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 28.6975i | − | 1.03084i | ||||||
\(776\) | 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 | ||||||||
\(783\) | −1.56927 | − | 53.0426i | −0.0560812 | − | 1.89559i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.16420 | + | 0.672153i | 0.0415522 | + | 0.0239902i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.55243 | − | 3.78305i | 0.233569 | − | 0.134851i | −0.378648 | − | 0.925541i | \(-0.623611\pi\) |
0.612217 | + | 0.790689i | \(0.290278\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.9484 | − | 31.0289i | 0.389774 | − | 1.10466i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7693 | −0.524474 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.04205 | − | 1.21729i | −0.0369576 | − | 0.0431727i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.03362 | + | 6.98643i | 0.142878 | + | 0.247472i | 0.928579 | − | 0.371134i | \(-0.121031\pi\) |
−0.785701 | + | 0.618606i | \(0.787698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.52875 | + | 9.57608i | −0.195593 | + | 0.338777i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.49529 | − | 3.28313i | 0.300166 | − | 0.116004i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.1906 | − | 33.2391i | 0.677222 | − | 1.17298i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.72975 | − | 14.6359i | −0.0960917 | − | 0.515208i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 0.0980908i | − | 0.00344869i | −0.999999 | − | 0.00172435i | \(-0.999451\pi\) | ||
0.999999 | − | 0.00172435i | \(-0.000548876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.3085i | − | 1.06428i | −0.846658 | − | 0.532138i | \(-0.821389\pi\) | ||
0.846658 | − | 0.532138i | \(-0.178611\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.12032 | + | 0.581972i | −0.109434 | + | 0.0204107i | ||||
\(814\) | 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 | \(-0.204451\pi\) |
−0.118424 | + | 0.992963i | \(0.537784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.2655 | + | 21.2445i | 0.427549 | + | 0.740536i | 0.996655 | − | 0.0817282i | \(-0.0260439\pi\) |
−0.569106 | + | 0.822264i | \(0.692711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.2885 | − | 35.3821i | −1.05451 | − | 1.23185i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 40.3057i | − | 1.40157i | −0.713375 | − | 0.700783i | \(-0.752834\pi\) | ||
0.713375 | − | 0.700783i | \(-0.247166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 54.0493i | 1.87721i | 0.344993 | + | 0.938605i | \(0.387881\pi\) | ||||
−0.344993 | + | 0.938605i | \(0.612119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.8374 | − | 9.11661i | −0.896291 | − | 0.316252i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.350900 | + | 0.607777i | −0.0121434 | + | 0.0210330i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.2881 | − | 14.1579i | −0.908649 | − | 0.489368i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.8650 | − | 20.5507i | 0.409624 | − | 0.709489i | −0.585224 | − | 0.810872i | \(-0.698993\pi\) |
0.994847 | + | 0.101383i | \(0.0323267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.6478 | + | 65.2079i | 1.29820 | + | 2.24855i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.62761 | − | 18.7833i | 0.228267 | − | 0.646933i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.16561 | 0.0400980 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.1828 | − | 13.0634i | −0.383792 | − | 0.448334i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.43540 | + | 0.828731i | −0.0492050 | + | 0.0284085i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.0748 | − | 27.7560i | −1.64605 | − | 0.950347i | −0.978621 | − | 0.205674i | \(-0.934061\pi\) |
−0.667429 | − | 0.744673i | \(-0.732605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.720953 | + | 0.894436i | −0.0246561 | + | 0.0305891i | ||||
\(856\) | 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 | ||||||||
\(863\) | − | 26.3020i | − | 0.895330i | −0.894201 | − | 0.447665i | \(-0.852256\pi\) | ||
0.894201 | − | 0.447665i | \(-0.147744\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.187024 | 0.00635899 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.856720 | − | 4.59342i | −0.0290957 | − | 0.156001i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.37504 | − | 2.52593i | 0.148413 | − | 0.0856863i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.2670 | − | 14.0106i | −0.822256 | − | 0.474730i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.1584 | + | 3.30206i | 0.716103 | + | 0.111758i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 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 | ||||||||
\(879\) | 22.7262 | − | 19.4546i | 0.766537 | − | 0.656187i | ||||
\(880\) | 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 | ||||||||
\(885\) | −0.0723883 | − | 0.0255418i | −0.00243331 | − | 0.000858580i | ||||
\(886\) | 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 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −47.3543 | + | 10.2898i | −1.58643 | + | 0.344722i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.6877 | − | 7.32526i | −0.424579 | − | 0.245131i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.386333 | + | 0.223049i | −0.0129137 | + | 0.00745572i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.2964 | + | 7.16147i | 0.677676 | + | 0.239114i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.6832 | 1.95719 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 45.7801i | − | 1.52516i | ||||||
\(902\) | 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 | ||||||||
\(909\) | −3.78057 | + | 24.2245i | −0.125394 | + | 0.803475i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.8739 | + | 16.6703i | 0.956634 | + | 0.552313i | 0.895136 | − | 0.445794i | \(-0.147079\pi\) |
0.0614988 | + | 0.998107i | \(0.480412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.5995 | + | 34.9871i | −2.00555 | + | 1.15791i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.361581 | − | 0.0674387i | 0.0119535 | − | 0.00222945i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.46967 | 0.114454 | 0.0572270 | − | 0.998361i | \(-0.481774\pi\) | ||||
0.0572270 | + | 0.998361i | \(0.481774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.8505 | + | 6.87300i | −1.21427 | + | 0.226473i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.82603 | − | 15.2871i | −0.290512 | − | 0.503182i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.77036 | + | 3.06635i | −0.0582090 | + | 0.100821i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.0566 | + | 17.4390i | −0.461679 | + | 0.572774i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.57680 | + | 13.1234i | −0.248587 | + | 0.430565i | −0.963134 | − | 0.269022i | \(-0.913299\pi\) |
0.714547 | + | 0.699587i | \(0.246633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.5831 | − | 22.7562i | 0.870290 | − | 0.745004i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.55622i | 0.0508937i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6651i | 1.09979i | 0.835233 | + | 0.549896i | \(0.185333\pi\) | ||||
−0.835233 | + | 0.549896i | \(0.814667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.5872 | − | 35.6736i | 0.410769 | − | 1.16416i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8980 | + | 32.7323i | 0.616058 | + | 1.06704i | 0.990198 | + | 0.139671i | \(0.0446045\pi\) |
−0.374140 | + | 0.927372i | \(0.622062\pi\) | |||||||
\(942\) | 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 | \(-0.390215\pi\) |
−0.645974 | + | 0.763360i | \(0.723548\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.9442 | + | 32.8123i | 0.614955 | + | 1.06513i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.3270 | + | 40.6042i | −0.464584 | + | 1.31668i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.0914i | − | 0.359284i | −0.983732 | − | 0.179642i | \(-0.942506\pi\) | ||
0.983732 | − | 0.179642i | \(-0.0574939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.609273i | 0.0197156i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 72.3525 | − | 61.9367i | 2.33882 | − | 2.00213i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00942 | − | 1.74838i | 0.0325621 | − | 0.0563992i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.99486 | + | 12.9245i | 0.160957 | + | 0.416487i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0274384 | − | 0.0475248i | 0.000883275 | − | 0.00152988i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.1446 | + | 34.8915i | 0.647807 | + | 1.12203i | 0.983646 | + | 0.180115i | \(0.0576470\pi\) |
−0.335839 | + | 0.941920i | \(0.609020\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.2653 | + | 6.01782i | −1.03651 | + | 0.193320i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.6916 | 1.53050 | 0.765248 | − | 0.643736i | \(-0.222616\pi\) | ||||
0.765248 | + | 0.643736i | \(0.222616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 45.1981 | − | 8.42992i | 1.44750 | − | 0.269973i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.4540 | − | 8.34504i | 0.462426 | − | 0.266982i | −0.250638 | − | 0.968081i | \(-0.580640\pi\) |
0.713064 | + | 0.701099i | \(0.247307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1563 | + | 8.17314i | 0.452437 | + | 0.261215i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.2586 | − | 11.3074i | 0.934155 | − | 0.361017i | ||||
\(982\) | 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 | ||||||||
\(989\) | − | 3.35022i | − | 0.106531i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.19550 | 0.260339 | 0.130169 | − | 0.991492i | \(-0.458448\pi\) | ||||
0.130169 | + | 0.991492i | \(0.458448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.3695 | − | 9.30435i | −0.836812 | − | 0.295265i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.62454 | − | 0.937928i | 0.0515014 | − | 0.0297343i | ||||
\(996\) | 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 | ||||||||
\(999\) | 1.93550 | + | 3.13451i | 0.0612366 | + | 0.0991714i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))