Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), degree \(2\), not 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.a.337.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | + | 5.19615i | 0.832050 | + | 1.44115i | 0.896410 | + | 0.443227i | \(0.146166\pi\) |
−0.0643593 | + | 0.997927i | \(0.520500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410i | 0.894427i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000 | 1.60591 | 0.802955 | − | 0.596040i | \(-0.203260\pi\) | ||||
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.50000 | − | 0.866025i | 0.327327 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | − | 3.46410i | 0.371391 | − | 0.643268i | −0.618389 | − | 0.785872i | \(-0.712214\pi\) |
0.989780 | + | 0.142605i | \(0.0455477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | − | 5.19615i | −0.538816 | − | 0.933257i | −0.998968 | − | 0.0454165i | \(-0.985539\pi\) |
0.460152 | − | 0.887840i | \(-0.347795\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | + | 0.866025i | −0.261116 | + | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 10.3923i | − | 1.66410i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | − | 5.19615i | 0.447214 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.50000 | + | 4.33013i | 1.05021 | + | 0.606339i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0000 | 1.64833 | 0.824163 | − | 0.566352i | \(-0.191646\pi\) | ||||
0.824163 | + | 0.566352i | \(0.191646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.5000 | − | 6.06218i | −1.39076 | − | 0.802955i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.50000 | − | 6.06218i | −0.455661 | − | 0.789228i | 0.543065 | − | 0.839691i | \(-0.317264\pi\) |
−0.998726 | + | 0.0504625i | \(0.983930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | − | 10.3923i | 0.768221 | − | 1.33060i | −0.170305 | − | 0.985391i | \(-0.554475\pi\) |
0.938527 | − | 0.345207i | \(-0.112191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | − | 10.3923i | 0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50000 | + | 11.2583i | 0.794101 | + | 1.37542i | 0.923408 | + | 0.383819i | \(0.125391\pi\) |
−0.129307 | + | 0.991605i | \(0.541275\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.92820i | − | 0.834058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | 0.117041 | 0.0585206 | − | 0.998286i | \(-0.481362\pi\) | ||||
0.0585206 | + | 0.998286i | \(0.481362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.50000 | + | 0.866025i | −0.173205 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.500000 | + | 0.866025i | 0.0569803 | + | 0.0986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00000 | + | 5.19615i | −0.337526 | + | 0.584613i | −0.983967 | − | 0.178352i | \(-0.942924\pi\) |
0.646440 | + | 0.762964i | \(0.276257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.00000 | − | 13.8564i | 0.878114 | − | 1.52094i | 0.0247060 | − | 0.999695i | \(-0.492135\pi\) |
0.853408 | − | 0.521243i | \(-0.174532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | + | 8.66025i | 0.542326 | + | 0.939336i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.00000 | + | 3.46410i | −0.643268 | + | 0.371391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.3923i | 1.07763i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.00000 | − | 12.1244i | −0.718185 | − | 1.24393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | − | 4.33013i | 0.253837 | − | 0.439658i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) |
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.00000 | − | 3.46410i | 0.199007 | − | 0.344691i | −0.749199 | − | 0.662344i | \(-0.769562\pi\) |
0.948207 | + | 0.317653i | \(0.102895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.00000 | − | 1.73205i | −0.292770 | − | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | −0.290021 | −0.145010 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | − | 1.73205i | −0.284747 | − | 0.164399i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.00000 | + | 8.66025i | 0.470360 | + | 0.814688i | 0.999425 | − | 0.0338931i | \(-0.0107906\pi\) |
−0.529065 | + | 0.848581i | \(0.677457\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | − | 6.92820i | 0.373002 | − | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.00000 | + | 15.5885i | −0.832050 | + | 1.44115i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.50000 | − | 4.33013i | 0.229175 | − | 0.396942i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.19615i | 0.468521i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.50000 | − | 0.866025i | 0.132068 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.00000 | − | 3.46410i | −0.174741 | − | 0.302660i | 0.765331 | − | 0.643637i | \(-0.222575\pi\) |
−0.940072 | + | 0.340977i | \(0.889242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.50000 | + | 6.06218i | −0.303488 | + | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.00000 | + | 5.19615i | −0.774597 | + | 0.447214i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.50000 | − | 16.4545i | 0.811640 | − | 1.40580i | −0.100076 | − | 0.994980i | \(-0.531909\pi\) |
0.911716 | − | 0.410822i | \(-0.134758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50000 | − | 4.33013i | −0.212047 | − | 0.367277i | 0.740308 | − | 0.672268i | \(-0.234680\pi\) |
−0.952355 | + | 0.304991i | \(0.901346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | 0.501745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73205i | 0.142857i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0000 | + | 20.7846i | 0.983078 | + | 1.70274i | 0.650183 | + | 0.759778i | \(0.274692\pi\) |
0.332896 | + | 0.942964i | \(0.391974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.50000 | − | 12.9904i | −0.606339 | − | 1.05021i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | + | 10.3923i | −0.481932 | + | 0.834730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | − | 1.73205i | −0.0798087 | − | 0.138233i | 0.823359 | − | 0.567521i | \(-0.192098\pi\) |
−0.903167 | + | 0.429289i | \(0.858764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.0000 | − | 10.3923i | −1.42749 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.00000 | + | 1.73205i | 0.233550 | + | 0.134840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.0000 | + | 17.3205i | 0.773823 | + | 1.34030i | 0.935454 | + | 0.353450i | \(0.114991\pi\) |
−0.161630 | + | 0.986851i | \(0.551675\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 19.9186i | −0.884615 | + | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5000 | + | 18.1865i | 0.802955 | + | 1.39076i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.00000 | + | 1.73205i | −0.0760286 | + | 0.131685i | −0.901533 | − | 0.432710i | \(-0.857557\pi\) |
0.825505 | + | 0.564396i | \(0.190891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | + | 0.866025i | 0.0377964 | + | 0.0654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.1244i | 0.911322i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.0000 | −1.79384 | −0.896922 | − | 0.442189i | \(-0.854202\pi\) | ||||
−0.896922 | + | 0.442189i | \(0.854202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.0000 | + | 10.3923i | −1.33060 | + | 0.768221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.50000 | + | 4.33013i | −0.182818 | + | 0.316650i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50000 | + | 2.59808i | 0.327327 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | − | 10.3923i | 0.434145 | − | 0.751961i | −0.563081 | − | 0.826402i | \(-0.690384\pi\) |
0.997225 | + | 0.0744412i | \(0.0237173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.50000 | − | 14.7224i | −0.611843 | − | 1.05974i | −0.990930 | − | 0.134382i | \(-0.957095\pi\) |
0.379086 | − | 0.925361i | \(-0.376238\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.0000 | + | 10.3923i | −1.28901 | + | 0.744208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 22.5167i | − | 1.58820i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | + | 3.46410i | 0.140372 | + | 0.243132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | + | 5.19615i | −0.209529 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.00000 | + | 10.3923i | −0.417029 | + | 0.722315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.50000 | − | 6.06218i | 0.242100 | − | 0.419330i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | − | 13.8564i | −0.550743 | − | 0.953914i | −0.998221 | − | 0.0596196i | \(-0.981011\pi\) |
0.447478 | − | 0.894295i | \(-0.352322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0000 | − | 6.92820i | −0.822226 | − | 0.474713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | 0.407307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.50000 | − | 0.866025i | −0.101361 | − | 0.0585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0000 | − | 25.9808i | −1.00901 | − | 1.74766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.00000 | + | 3.46410i | −0.133930 | + | 0.231973i | −0.925188 | − | 0.379509i | \(-0.876093\pi\) |
0.791258 | + | 0.611482i | \(0.209426\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | + | 22.5167i | 0.859064 | + | 1.48794i | 0.872823 | + | 0.488037i | \(0.162287\pi\) |
−0.0137585 | + | 0.999905i | \(0.504380\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.73205i | − | 0.113961i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.0000 | −1.89985 | −0.949927 | − | 0.312473i | \(-0.898843\pi\) | ||||
−0.949927 | + | 0.312473i | \(0.898843\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.00000 | − | 5.19615i | 0.584613 | − | 0.337526i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | + | 5.19615i | 0.194054 | + | 0.336111i | 0.946590 | − | 0.322440i | \(-0.104503\pi\) |
−0.752536 | + | 0.658551i | \(0.771170\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5000 | + | 19.9186i | −0.740780 | + | 1.28307i | 0.211360 | + | 0.977408i | \(0.432211\pi\) |
−0.952141 | + | 0.305661i | \(0.901123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | + | 1.73205i | −0.0638877 | + | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.0000 | + | 36.3731i | 1.33620 | + | 2.31436i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.0000 | + | 13.8564i | −1.52094 | + | 0.878114i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 17.3205i | − | 1.08465i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.50000 | + | 12.9904i | 0.467837 | + | 0.810318i | 0.999325 | − | 0.0367485i | \(-0.0117000\pi\) |
−0.531487 | + | 0.847066i | \(0.678367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | + | 1.73205i | −0.0621370 | + | 0.107624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0000 | 0.742781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.00000 | − | 15.5885i | 0.554964 | − | 0.961225i | −0.442943 | − | 0.896550i | \(-0.646065\pi\) |
0.997906 | − | 0.0646755i | \(-0.0206012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | − | 20.7846i | −0.737154 | − | 1.27679i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.00000 | + | 5.19615i | 0.550791 | + | 0.317999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.0000 | 1.21942 | 0.609711 | − | 0.792624i | \(-0.291286\pi\) | ||||
0.609711 | + | 0.792624i | \(0.291286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.00000 | 0.364474 | 0.182237 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182237 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.00000 | + | 5.19615i | 0.544705 | + | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.00000 | − | 15.5885i | 0.538816 | − | 0.933257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0000 | + | 19.0526i | −0.656205 | + | 1.13658i | 0.325385 | + | 0.945582i | \(0.394506\pi\) |
−0.981590 | + | 0.190999i | \(0.938827\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.2487i | 1.43637i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.00000 | 0.177084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.50000 | + | 4.33013i | −0.439658 | + | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.00000 | + | 12.1244i | −0.407556 | + | 0.705907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.50000 | − | 2.59808i | −0.261116 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.500000 | − | 0.866025i | −0.0288195 | − | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.00000 | + | 3.46410i | −0.344691 | + | 0.199007i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.0000 | −1.37424 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.00000 | −0.399511 | −0.199756 | − | 0.979846i | \(-0.564015\pi\) | ||||
−0.199756 | + | 0.979846i | \(0.564015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 24.2487i | − | 1.37946i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.00000 | + | 1.73205i | 0.0567048 | + | 0.0982156i | 0.892984 | − | 0.450088i | \(-0.148607\pi\) |
−0.836280 | + | 0.548303i | \(0.815274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | − | 14.7224i | 0.480448 | − | 0.832161i | −0.519300 | − | 0.854592i | \(-0.673807\pi\) |
0.999748 | + | 0.0224310i | \(0.00714060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.00000 | + | 5.19615i | 0.169031 | + | 0.292770i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | − | 5.19615i | 0.168497 | − | 0.291845i | −0.769395 | − | 0.638774i | \(-0.779442\pi\) |
0.937892 | + | 0.346929i | \(0.112775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | − | 3.46410i | −0.111979 | − | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50000 | + | 2.59808i | 0.251166 | + | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.0000 | −1.94745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.00000 | + | 1.73205i | 0.165900 | + | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | − | 6.92820i | 0.219860 | − | 0.380808i | −0.734905 | − | 0.678170i | \(-0.762773\pi\) |
0.954765 | + | 0.297361i | \(0.0961066\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00000 | + | 5.19615i | 0.164399 | + | 0.284747i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.0000 | − | 22.5167i | 0.710266 | − | 1.23022i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | + | 7.79423i | 0.245131 | + | 0.424579i | 0.962168 | − | 0.272456i | \(-0.0878358\pi\) |
−0.717038 | + | 0.697034i | \(0.754502\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 17.3205i | − | 0.940721i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.0000 | + | 6.92820i | −0.646058 | + | 0.373002i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.50000 | − | 2.59808i | −0.0805242 | − | 0.139472i | 0.822951 | − | 0.568112i | \(-0.192326\pi\) |
−0.903475 | + | 0.428640i | \(0.858993\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00000 | − | 12.1244i | 0.374701 | − | 0.649002i | −0.615581 | − | 0.788074i | \(-0.711079\pi\) |
0.990282 | + | 0.139072i | \(0.0444119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.0000 | − | 15.5885i | 1.44115 | − | 0.832050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.50000 | − | 12.9904i | 0.399185 | − | 0.691408i | −0.594441 | − | 0.804139i | \(-0.702627\pi\) |
0.993626 | + | 0.112731i | \(0.0359599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | − | 13.8564i | −0.424596 | − | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.50000 | + | 4.33013i | −0.396942 | + | 0.229175i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.00000 | −0.105556 | −0.0527780 | − | 0.998606i | \(-0.516808\pi\) | ||||
−0.0527780 | + | 0.998606i | \(0.516808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 17.3205i | − | 0.909091i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.00000 | − | 1.73205i | −0.0523424 | − | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0000 | + | 19.0526i | −0.574195 | + | 0.994535i | 0.421933 | + | 0.906627i | \(0.361352\pi\) |
−0.996129 | + | 0.0879086i | \(0.971982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.50000 | − | 7.79423i | 0.234261 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | − | 19.0526i | −0.569558 | − | 0.986504i | −0.996610 | − | 0.0822766i | \(-0.973781\pi\) |
0.427051 | − | 0.904227i | \(-0.359552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.0000 | + | 10.3923i | 0.929516 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0000 | 0.873231 | 0.436616 | − | 0.899648i | \(-0.356177\pi\) | ||||
0.436616 | + | 0.899648i | \(0.356177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | − | 10.3923i | −0.922168 | − | 0.532414i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.00000 | + | 3.46410i | 0.102195 | + | 0.177007i | 0.912589 | − | 0.408879i | \(-0.134080\pi\) |
−0.810394 | + | 0.585886i | \(0.800747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | − | 1.73205i | 0.0509647 | − | 0.0882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | −0.152499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.00000 | + | 6.92820i | −0.202808 | + | 0.351274i | −0.949432 | − | 0.313972i | \(-0.898340\pi\) |
0.746624 | + | 0.665246i | \(0.231673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0000 | − | 17.3205i | −0.505722 | − | 0.875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.92820i | 0.349482i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0000 | 0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000 | 0.903394 | 0.451697 | − | 0.892171i | \(-0.350819\pi\) | ||||
0.451697 | + | 0.892171i | \(0.350819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.5000 | − | 6.06218i | 0.525657 | − | 0.303488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.50000 | − | 7.79423i | −0.224719 | − | 0.389225i | 0.731516 | − | 0.681824i | \(-0.238813\pi\) |
−0.956235 | + | 0.292599i | \(0.905480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000 | − | 31.1769i | 0.896644 | − | 1.55303i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.00000 | − | 1.73205i | 0.0495682 | − | 0.0858546i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.50000 | − | 9.52628i | −0.271957 | − | 0.471044i | 0.697406 | − | 0.716677i | \(-0.254338\pi\) |
−0.969363 | + | 0.245633i | \(0.921004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.5000 | + | 16.4545i | −1.40580 | + | 0.811640i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.00000 | 0.344447 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.0000 | −1.57082 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.66025i | 0.424094i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | − | 10.3923i | −0.293119 | − | 0.507697i | 0.681426 | − | 0.731887i | \(-0.261360\pi\) |
−0.974546 | + | 0.224189i | \(0.928027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | − | 10.3923i | 0.292422 | − | 0.506490i | −0.681960 | − | 0.731390i | \(-0.738872\pi\) |
0.974382 | + | 0.224900i | \(0.0722054\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.50000 | + | 4.33013i | −0.121268 | + | 0.210042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | + | 10.3923i | 0.290360 | + | 0.502919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.00000 | − | 5.19615i | −0.434524 | − | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.0000 | + | 6.92820i | 0.575356 | + | 0.332182i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.0000 | + | 24.2487i | 0.669711 | + | 1.15997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | + | 20.7846i | −0.572729 | + | 0.991995i | 0.423556 | + | 0.905870i | \(0.360782\pi\) |
−0.996284 | + | 0.0861252i | \(0.972552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50000 | − | 2.59808i | 0.0714286 | − | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.50000 | − | 6.06218i | 0.166290 | − | 0.288023i | −0.770823 | − | 0.637050i | \(-0.780155\pi\) |
0.937113 | + | 0.349027i | \(0.113488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | + | 10.3923i | 0.284427 | + | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 41.5692i | − | 1.96616i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0000 | 0.802280 | 0.401140 | − | 0.916017i | \(-0.368614\pi\) | ||||
0.401140 | + | 0.916017i | \(0.368614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.00000 | −0.141264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.0000 | + | 8.66025i | −0.704761 | + | 0.406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | + | 10.3923i | 0.281284 | + | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.500000 | + | 0.866025i | −0.0233890 | + | 0.0405110i | −0.877483 | − | 0.479608i | \(-0.840779\pi\) |
0.854094 | + | 0.520119i | \(0.174112\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.9808i | 1.21268i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.00000 | + | 12.1244i | −0.326023 | + | 0.564688i | −0.981719 | − | 0.190337i | \(-0.939042\pi\) |
0.655696 | + | 0.755025i | \(0.272375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | − | 6.92820i | −0.185896 | − | 0.321981i | 0.757982 | − | 0.652275i | \(-0.226185\pi\) |
−0.943878 | + | 0.330294i | \(0.892852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.0000 | − | 10.3923i | 0.834730 | − | 0.481932i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.0000 | 0.601568 | 0.300784 | − | 0.953692i | \(-0.402752\pi\) | ||||
0.300784 | + | 0.953692i | \(0.402752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.0000 | −0.600284 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.46410i | 0.159617i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.500000 | + | 0.866025i | 0.0229900 | + | 0.0398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.50000 | − | 6.06218i | 0.160591 | − | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.0000 | + | 31.1769i | 0.824163 | + | 1.42749i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0000 | + | 17.3205i | −0.456912 | + | 0.791394i | −0.998796 | − | 0.0490589i | \(-0.984378\pi\) |
0.541884 | + | 0.840453i | \(0.317711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | + | 10.3923i | 0.273576 | + | 0.473848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.00000 | + | 3.46410i | 0.273009 | + | 0.157622i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0000 | −0.454077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0000 | 0.453143 | 0.226572 | − | 0.973995i | \(-0.427248\pi\) | ||||
0.226572 | + | 0.973995i | \(0.427248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.00000 | − | 3.46410i | −0.271329 | − | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.5000 | + | 28.5788i | 0.744635 | + | 1.28974i | 0.950365 | + | 0.311136i | \(0.100710\pi\) |
−0.205731 | + | 0.978609i | \(0.565957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | + | 17.3205i | −0.450377 | + | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.00000 | − | 5.19615i | −0.134840 | − | 0.233550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.00000 | + | 6.92820i | −0.179425 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5000 | − | 25.1147i | −0.649109 | − | 1.12429i | −0.983336 | − | 0.181797i | \(-0.941809\pi\) |
0.334227 | − | 0.942493i | \(-0.391525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 34.6410i | − | 1.54765i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.5000 | − | 19.9186i | 1.53220 | − | 0.884615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.500000 | + | 0.866025i | −0.0221187 | + | 0.0383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 36.3731i | − | 1.60591i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.0000 | − | 24.2487i | 0.616914 | − | 1.06853i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.00000 | − | 1.73205i | 0.131685 | − | 0.0760286i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | −0.394297 | −0.197149 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197149 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.0000 | 1.22435 | 0.612177 | − | 0.790721i | \(-0.290294\pi\) | ||||
0.612177 | + | 0.790721i | \(0.290294\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.73205i | − | 0.0755929i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.0000 | + | 25.9808i | 0.653410 | + | 1.13174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.5000 | − | 18.1865i | 0.455661 | − | 0.789228i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.00000 | − | 15.5885i | 0.389833 | − | 0.675211i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | + | 5.19615i | 0.129701 | + | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.0000 | + | 20.7846i | 1.55351 | + | 0.896922i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.0000 | −1.03184 | −0.515920 | − | 0.856637i | \(-0.672550\pi\) | ||||
−0.515920 | + | 0.856637i | \(0.672550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | + | 3.46410i | 0.0856706 | + | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5000 | + | 18.1865i | −0.448948 | + | 0.777600i | −0.998318 | − | 0.0579790i | \(-0.981534\pi\) |
0.549370 | + | 0.835579i | \(0.314868\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.0000 | 1.53644 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0000 | − | 24.2487i | 0.596420 | − | 1.03303i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.00000 | − | 5.19615i | −0.127573 | − | 0.220963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.92820i | 0.294086i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.0000 | −1.18640 | −0.593199 | − | 0.805056i | \(-0.702135\pi\) | ||||
−0.593199 | + | 0.805056i | \(0.702135\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.50000 | − | 4.33013i | 0.316650 | − | 0.182818i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.5000 | + | 26.8468i | 0.653247 | + | 1.13146i | 0.982330 | + | 0.187156i | \(0.0599271\pi\) |
−0.329083 | + | 0.944301i | \(0.606740\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | − | 17.3205i | 0.420703 | − | 0.728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.50000 | − | 7.79423i | −0.188982 | − | 0.327327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.50000 | − | 12.9904i | 0.314416 | − | 0.544585i | −0.664897 | − | 0.746935i | \(-0.731525\pi\) |
0.979313 | + | 0.202350i | \(0.0648579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.5000 | − | 28.5788i | −0.690504 | − | 1.19599i | −0.971673 | − | 0.236329i | \(-0.924056\pi\) |
0.281170 | − | 0.959658i | \(-0.409278\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.0000 | + | 10.3923i | −0.751961 | + | 0.434145i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.0000 | −1.45707 | −0.728535 | − | 0.685009i | \(-0.759798\pi\) | ||||
−0.728535 | + | 0.685009i | \(0.759798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.4449i | 1.22369i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | + | 13.8564i | 0.331896 | + | 0.574861i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | − | 10.3923i | 0.248495 | − | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.0000 | 1.48842 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.5000 | + | 40.7032i | −0.969949 | + | 1.68000i | −0.274263 | + | 0.961655i | \(0.588434\pi\) |
−0.695686 | + | 0.718346i | \(0.744900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.0000 | − | 36.3731i | −0.865290 | − | 1.49873i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.0000 | − | 8.66025i | −0.617018 | − | 0.356235i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.0000 | −0.409960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.0000 | + | 12.1244i | 0.859473 | + | 0.496217i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | + | 20.7846i | 0.490307 | + | 0.849236i | 0.999938 | − | 0.0111569i | \(-0.00355143\pi\) |
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.50000 | − | 16.4545i | 0.387513 | − | 0.671192i | −0.604601 | − | 0.796528i | \(-0.706668\pi\) |
0.992114 | + | 0.125336i | \(0.0400009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.5000 | + | 33.7750i | −0.794101 | + | 1.37542i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0000 | − | 17.3205i | 0.406558 | − | 0.704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.0000 | − | 20.7846i | −0.487065 | − | 0.843621i | 0.512824 | − | 0.858494i | \(-0.328599\pi\) |
−0.999889 | + | 0.0148722i | \(0.995266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 6.92820i | − | 0.280745i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.0000 | 1.69636 | 0.848182 | − | 0.529705i | \(-0.177697\pi\) | ||||
0.848182 | + | 0.529705i | \(0.177697\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.00000 | − | 5.19615i | 0.362915 | − | 0.209529i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.50000 | + | 14.7224i | 0.342197 | + | 0.592703i | 0.984840 | − | 0.173463i | \(-0.0554956\pi\) |
−0.642643 | + | 0.766165i | \(0.722162\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5000 | − | 32.0429i | 0.743578 | − | 1.28791i | −0.207279 | − | 0.978282i | \(-0.566461\pi\) |
0.950856 | − | 0.309633i | \(-0.100206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0000 | − | 10.3923i | 0.722315 | − | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.00000 | − | 5.19615i | 0.120192 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.5000 | + | 6.06218i | −0.419330 | + | 0.242100i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.7128i | 1.10149i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0000 | − | 20.7846i | −0.476205 | − | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | − | 5.19615i | 0.118864 | − | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | + | 20.7846i | 0.474713 | + | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.500000 | + | 0.866025i | −0.0197488 | + | 0.0342059i | −0.875731 | − | 0.482800i | \(-0.839620\pi\) |
0.855982 | + | 0.517005i | \(0.172953\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.50000 | − | 6.06218i | −0.138027 | − | 0.239069i | 0.788723 | − | 0.614749i | \(-0.210743\pi\) |
−0.926750 | + | 0.375680i | \(0.877409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.00000 | − | 1.73205i | −0.118125 | − | 0.0681994i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.00000 | −0.274774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.00000 | − | 5.19615i | −0.352738 | − | 0.203653i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | + | 6.92820i | −0.156293 | + | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.50000 | + | 2.59808i | 0.0585206 | + | 0.101361i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.00000 | − | 13.8564i | 0.311636 | − | 0.539769i | −0.667081 | − | 0.744985i | \(-0.732456\pi\) |
0.978717 | + | 0.205216i | \(0.0657898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | − | 24.2487i | −0.544537 | − | 0.943166i | −0.998636 | − | 0.0522143i | \(-0.983372\pi\) |
0.454099 | − | 0.890951i | \(-0.349961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 51.9615i | 2.01802i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.0000 | 0.542897 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | 0.619522 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.00000 | − | 3.46410i | 0.231973 | − | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | − | 10.3923i | −0.231627 | − | 0.401190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | + | 12.1244i | −0.269830 | + | 0.467360i | −0.968818 | − | 0.247774i | \(-0.920301\pi\) |
0.698988 | + | 0.715134i | \(0.253634\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.50000 | − | 2.59808i | −0.173205 | − | 0.100000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.0000 | + | 25.9808i | −0.576497 | + | 0.998522i | 0.419380 | + | 0.907811i | \(0.362247\pi\) |
−0.995877 | + | 0.0907112i | \(0.971086\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.50000 | + | 4.33013i | 0.0959412 | + | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | + | 2.59808i | −0.172440 | + | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.0000 | −1.49229 | −0.746147 | − | 0.665782i | \(-0.768098\pi\) | ||||
−0.746147 | + | 0.665782i | \(0.768098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.0000 | −1.45191 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 45.0333i | − | 1.71813i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.0000 | + | 62.3538i | 1.37149 | + | 2.37549i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0000 | − | 27.7128i | 0.608669 | − | 1.05425i | −0.382791 | − | 0.923835i | \(-0.625037\pi\) |
0.991460 | − | 0.130410i | \(-0.0416295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.50000 | + | 2.59808i | −0.0569803 | + | 0.0986928i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.00000 | + | 8.66025i | −0.189661 | + | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.50000 | + | 12.9904i | 0.284083 | + | 0.492046i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 43.5000 | + | 25.1147i | 1.64532 | + | 0.949927i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.00000 | 0.302156 | 0.151078 | − | 0.988522i | \(-0.451726\pi\) | ||||
0.151078 | + | 0.988522i | \(0.451726\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0000 | 0.528020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.00000 | + | 3.46410i | 0.0752177 | + | 0.130281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.0000 | −0.675053 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.0000 | − | 20.7846i | 0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | − | 10.3923i | −0.224387 | − | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 10.3923i | − | 0.388108i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.00000 | −0.223762 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.5000 | − | 19.9186i | 1.28307 | − | 0.740780i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | − | 3.46410i | −0.0742781 | − | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.00000 | + | 12.1244i | −0.259616 | + | 0.449667i | −0.966139 | − | 0.258022i | \(-0.916929\pi\) |
0.706523 | + | 0.707690i | \(0.250263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50000 | − | 4.33013i | 0.0924658 | − | 0.160156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.00000 | + | 15.5885i | 0.332423 | + | 0.575773i | 0.982986 | − | 0.183679i | \(-0.0588007\pi\) |
−0.650564 | + | 0.759452i | \(0.725467\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.00000 | − | 1.73205i | 0.110657 | − | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.0000 | 0.478861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.0000 | 1.21392 | 0.606962 | − | 0.794731i | \(-0.292388\pi\) | ||||
0.606962 | + | 0.794731i | \(0.292388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 72.7461i | − | 2.67240i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.0000 | − | 41.5692i | 0.879292 | − | 1.52298i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 48.0000 | 1.75623 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.50000 | − | 2.59808i | 0.0548088 | − | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.00000 | − | 15.5885i | −0.328415 | − | 0.568831i | 0.653783 | − | 0.756682i | \(-0.273181\pi\) |
−0.982197 | + | 0.187851i | \(0.939848\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.50000 | + | 2.59808i | 0.163989 | + | 0.0946792i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.0000 | −0.727875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.0000 | −1.74459 | −0.872295 | − | 0.488980i | \(-0.837369\pi\) | ||||
−0.872295 | + | 0.488980i | \(0.837369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.00000 | − | 3.46410i | −0.217786 | − | 0.125739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.00000 | − | 8.66025i | −0.181250 | − | 0.313934i | 0.761057 | − | 0.648686i | \(-0.224681\pi\) |
−0.942306 | + | 0.334752i | \(0.891348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00000 | − | 1.73205i | 0.0362024 | − | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.0000 | + | 25.9808i | −0.542326 | + | 0.939336i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.0000 | − | 36.3731i | 0.758266 | − | 1.31336i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.0000 | − | 19.0526i | −0.396670 | − | 0.687053i | 0.596643 | − | 0.802507i | \(-0.296501\pi\) |
−0.993313 | + | 0.115454i | \(0.963168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 25.9808i | − | 0.935674i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −52.0000 | −1.87031 | −0.935155 | − | 0.354239i | \(-0.884740\pi\) | ||||
−0.935155 | + | 0.354239i | \(0.884740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.00000 | − | 1.73205i | 0.107624 | − | 0.0621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.5000 | − | 18.1865i | −0.376202 | − | 0.651600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | − | 6.92820i | 0.143131 | − | 0.247911i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.0000 | − | 10.3923i | −0.643268 | − | 0.371391i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | + | 3.46410i | −0.0713831 | + | 0.123639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.00000 | − | 10.3923i | −0.213877 | − | 0.370446i | 0.739048 | − | 0.673653i | \(-0.235276\pi\) |
−0.952925 | + | 0.303207i | \(0.901942\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.0000 | + | 15.5885i | −0.961225 | + | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.0000 | −0.355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 72.0000 | 2.55679 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 41.5692i | 1.47431i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.00000 | + | 10.3923i | 0.212531 | + | 0.368114i | 0.952506 | − | 0.304520i | \(-0.0984960\pi\) |
−0.739975 | + | 0.672634i | \(0.765163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00000 | − | 15.5885i | −0.317999 | − | 0.550791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.500000 | − | 0.866025i | 0.0176446 | − | 0.0305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | + | 6.92820i | 0.140981 | + | 0.244187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.0000 | − | 17.3205i | −1.05605 | − | 0.609711i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.0000 | −1.51180 | −0.755900 | − | 0.654687i | \(-0.772800\pi\) | ||||
−0.755900 | + | 0.654687i | \(0.772800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.0000 | −1.08856 | −0.544279 | − | 0.838905i | \(-0.683197\pi\) | ||||
−0.544279 | + | 0.838905i | \(0.683197\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.00000 | − | 5.19615i | −0.315644 | − | 0.182237i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | − | 6.92820i | −0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.50000 | + | 6.06218i | −0.122449 | + | 0.212089i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.00000 | − | 15.5885i | −0.314485 | − | 0.544705i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0000 | + | 39.8372i | −0.802706 | + | 1.39033i | 0.115124 | + | 0.993351i | \(0.463274\pi\) |
−0.917829 | + | 0.396976i | \(0.870060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0000 | + | 29.4449i | 0.592583 | + | 1.02638i | 0.993883 | + | 0.110437i | \(0.0352250\pi\) |
−0.401300 | + | 0.915947i | \(0.631442\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.73205i | 0.0603023i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.00000 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.00000 | − | 1.73205i | 0.104069 | − | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.50000 | + | 4.33013i | 0.0866199 | + | 0.150030i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.0000 | − | 34.6410i | 0.692129 | − | 1.19880i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.0000 | + | 15.5885i | −0.933257 | + | 0.538816i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.0000 | + | 17.3205i | −0.345238 | + | 0.597970i | −0.985397 | − | 0.170272i | \(-0.945535\pi\) |
0.640159 | + | 0.768243i | \(0.278869\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.0000 | − | 19.0526i | 1.13658 | − | 0.656205i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46.0000 | 1.58245 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0000 | −0.343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 6.92820i | − | 0.237775i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | + | 6.92820i | 0.137118 | + | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | + | 38.1051i | −0.753266 | + | 1.30469i | 0.192966 | + | 0.981205i | \(0.438189\pi\) |
−0.946232 | + | 0.323489i | \(0.895144\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.0000 | − | 36.3731i | 0.718185 | − | 1.24393i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.0000 | + | 25.9808i | −0.512390 | + | 0.887486i | 0.487507 | + | 0.873119i | \(0.337907\pi\) |
−0.999897 | + | 0.0143666i | \(0.995427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.5000 | + | 25.1147i | 0.494734 | + | 0.856904i | 0.999982 | − | 0.00607046i | \(-0.00193230\pi\) |
−0.505248 | + | 0.862974i | \(0.668599\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.50000 | − | 2.59808i | −0.153360 | − | 0.0885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.0000 | −1.29354 | −0.646768 | − | 0.762687i | \(-0.723880\pi\) | ||||
−0.646768 | + | 0.762687i | \(0.723880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.00000 | 0.136004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0000 | − | 6.92820i | −0.407541 | − | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000 | + | 5.19615i | 0.101768 | + | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.0000 | + | 67.5500i | −1.32146 | + | 2.28884i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.0000 | 0.507673 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.00000 | − | 10.3923i | 0.202837 | − | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.00000 | − | 13.8564i | −0.270141 | − | 0.467898i | 0.698757 | − | 0.715359i | \(-0.253737\pi\) |
−0.968898 | + | 0.247462i | \(0.920404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.0000 | −1.78359 | −0.891796 | − | 0.452438i | \(-0.850554\pi\) | ||||
−0.891796 | + | 0.452438i | \(0.850554\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.0000 | − | 12.1244i | 0.705907 | − | 0.407556i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.00000 | − | 5.19615i | −0.100730 | − | 0.174470i | 0.811256 | − | 0.584692i | \(-0.198785\pi\) |
−0.911986 | + | 0.410222i | \(0.865451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.00000 | + | 10.3923i | −0.201234 | + | 0.348547i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.50000 | + | 7.79423i | 0.150756 | + | 0.261116i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | + | 41.5692i | 0.802232 | + | 1.38951i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.0000 | − | 20.7846i | 1.20201 | − | 0.693978i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −60.0000 | −1.99889 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.73205i | 0.0576390i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5000 | + | 23.3827i | −0.448260 | + | 0.776409i | −0.998273 | − | 0.0587469i | \(-0.981290\pi\) |
0.550013 | + | 0.835156i | \(0.314623\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | − | 13.8564i | −0.264761 | − | 0.458580i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.0000 | + | 20.7846i | 1.19012 | + | 0.687118i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.00000 | 0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.5000 | + | 6.06218i | 0.345987 | + | 0.199756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | + | 41.5692i | 0.789970 | + | 1.36827i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | − | 1.73205i | 0.0328798 | − | 0.0569495i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.0000 | + | 36.3731i | −0.689730 | + | 1.19465i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | − | 15.5885i | 0.295280 | − | 0.511441i | −0.679770 | − | 0.733426i | \(-0.737920\pi\) |
0.975050 | + | 0.221985i | \(0.0712536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.50000 | − | 6.06218i | −0.114708 | − | 0.198680i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 3.46410i | − | 0.113410i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.0000 | 0.327035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.5000 | + | 14.7224i | −0.832161 | + | 0.480448i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0000 | − | 17.3205i | −0.325991 | − | 0.564632i | 0.655722 | − | 0.755003i | \(-0.272364\pi\) |
−0.981712 | + | 0.190370i | \(0.939031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | − | 10.3923i | 0.195387 | − | 0.338420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 10.3923i | − | 0.338062i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.5000 | + | 32.0429i | −0.601169 | + | 1.04126i | 0.391475 | + | 0.920189i | \(0.371965\pi\) |
−0.992644 | + | 0.121067i | \(0.961368\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.00000 | + | 5.19615i | 0.0973841 | + | 0.168674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.00000 | + | 5.19615i | −0.291845 | + | 0.168497i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0000 | −1.13376 | −0.566881 | − | 0.823800i | \(-0.691850\pi\) | ||||
−0.566881 | + | 0.823800i | \(0.691850\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0000 | −0.776622 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.92820i | 0.223957i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.50000 | + | 16.4545i | 0.306771 | + | 0.531343i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.50000 | − | 7.79423i | −0.145010 | − | 0.251166i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.0000 | + | 29.4449i | −0.547249 | + | 0.947864i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.00000 | + | 12.1244i | 0.225105 | + | 0.389893i | 0.956351 | − | 0.292221i | \(-0.0943942\pi\) |
−0.731246 | + | 0.682114i | \(0.761061\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 52.5000 | + | 30.3109i | 1.68654 | + | 0.973726i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.00000 | 0.160293 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.00000 | − | 5.19615i | −0.288231 | − | 0.166410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.50000 | + | 12.9904i | 0.239946 | + | 0.415599i | 0.960699 | − | 0.277594i | \(-0.0895368\pi\) |
−0.720752 | + | 0.693193i | \(0.756204\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00000 | + | 5.19615i | −0.0958804 | + | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00000 | − | 5.19615i | −0.0957826 | − | 0.165900i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.0000 | + | 51.9615i | −0.956851 | + | 1.65732i | −0.226778 | + | 0.973946i | \(0.572819\pi\) |
−0.730073 | + | 0.683369i | \(0.760514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | − | 17.3205i | −0.318626 | − | 0.551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0000 | 0.889449 | 0.444725 | − | 0.895667i | \(-0.353302\pi\) | ||||
0.444725 | + | 0.895667i | \(0.353302\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.0000 | + | 6.92820i | −0.380808 | + | 0.219860i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0000 | + | 24.2487i | 0.443830 | + | 0.768736i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.00000 | + | 1.73205i | −0.0316703 | + | 0.0548546i | −0.881426 | − | 0.472322i | \(-0.843416\pi\) |
0.849756 | + | 0.527176i | \(0.176749\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 10.3923i | − | 0.328798i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))