Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (of order \(3\), 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: | \(4.55147291521\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.121 |
Dual form | 570.2.i.b.391.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.50000 | − | 2.59808i | 0.416025 | − | 0.720577i | −0.579510 | − | 0.814965i | \(-0.696756\pi\) |
0.995535 | + | 0.0943882i | \(0.0300895\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.00000 | − | 3.46410i | −0.485071 | − | 0.840168i | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.00000 | + | 1.73205i | 0.917663 | + | 0.397360i | ||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0.500000 | + | 0.866025i | 0.109109 | + | 0.188982i | ||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.500000 | − | 0.866025i | 0.0944911 | − | 0.163663i | ||||
\(29\) | 5.00000 | − | 8.66025i | 0.928477 | − | 1.60817i | 0.142605 | − | 0.989780i | \(-0.454452\pi\) |
0.785872 | − | 0.618389i | \(-0.212214\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.00000 | 0.179605 | 0.0898027 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898027 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | −2.00000 | + | 3.46410i | −0.342997 | + | 0.594089i | ||||
\(35\) | −0.500000 | − | 0.866025i | −0.0845154 | − | 0.146385i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | −0.500000 | − | 4.33013i | −0.0811107 | − | 0.702439i | ||||
\(39\) | −3.00000 | −0.480384 | ||||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | −1.00000 | − | 1.73205i | −0.156174 | − | 0.270501i | 0.777312 | − | 0.629115i | \(-0.216583\pi\) |
−0.933486 | + | 0.358614i | \(0.883249\pi\) | |||||||
\(42\) | 0.500000 | − | 0.866025i | 0.0771517 | − | 0.133631i | ||||
\(43\) | 2.50000 | + | 4.33013i | 0.381246 | + | 0.660338i | 0.991241 | − | 0.132068i | \(-0.0421616\pi\) |
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −1.00000 | + | 1.73205i | −0.150756 | + | 0.261116i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | 1.50000 | + | 2.59808i | 0.208013 | + | 0.360288i | ||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 1.00000 | + | 1.73205i | 0.134840 | + | 0.233550i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −0.500000 | − | 4.33013i | −0.0662266 | − | 0.573539i | ||||
\(58\) | −10.0000 | −1.31306 | ||||||||
\(59\) | 1.00000 | + | 1.73205i | 0.130189 | + | 0.225494i | 0.923749 | − | 0.382998i | \(-0.125108\pi\) |
−0.793560 | + | 0.608492i | \(0.791775\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | −2.50000 | + | 4.33013i | −0.320092 | + | 0.554416i | −0.980507 | − | 0.196485i | \(-0.937047\pi\) |
0.660415 | + | 0.750901i | \(0.270381\pi\) | |||||||
\(62\) | −0.500000 | − | 0.866025i | −0.0635001 | − | 0.109985i | ||||
\(63\) | 0.500000 | − | 0.866025i | 0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | 0.372104 | ||||||||
\(66\) | −1.00000 | + | 1.73205i | −0.123091 | + | 0.213201i | ||||
\(67\) | 2.50000 | − | 4.33013i | 0.305424 | − | 0.529009i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
0.977356 | + | 0.211604i | \(0.0678686\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | −0.500000 | + | 0.866025i | −0.0597614 | + | 0.103510i | ||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | 2.50000 | + | 4.33013i | 0.290619 | + | 0.503367i | ||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −3.50000 | + | 2.59808i | −0.401478 | + | 0.298020i | ||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | 1.50000 | + | 2.59808i | 0.169842 | + | 0.294174i | ||||
\(79\) | 5.50000 | + | 9.52628i | 0.618798 | + | 1.07179i | 0.989705 | + | 0.143120i | \(0.0457135\pi\) |
−0.370907 | + | 0.928670i | \(0.620953\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.00000 | + | 1.73205i | −0.110432 | + | 0.191273i | ||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 2.00000 | − | 3.46410i | 0.216930 | − | 0.375735i | ||||
\(86\) | 2.50000 | − | 4.33013i | 0.269582 | − | 0.466930i | ||||
\(87\) | −10.0000 | −1.07211 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0.500000 | + | 0.866025i | 0.0527046 | + | 0.0912871i | ||||
\(91\) | −1.50000 | + | 2.59808i | −0.157243 | + | 0.272352i | ||||
\(92\) | 3.00000 | + | 5.19615i | 0.312772 | + | 0.541736i | ||||
\(93\) | −0.500000 | − | 0.866025i | −0.0518476 | − | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.500000 | + | 4.33013i | 0.0512989 | + | 0.444262i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.00000 | + | 1.73205i | 0.101535 | + | 0.175863i | 0.912317 | − | 0.409484i | \(-0.134291\pi\) |
−0.810782 | + | 0.585348i | \(0.800958\pi\) | |||||||
\(98\) | 3.00000 | + | 5.19615i | 0.303046 | + | 0.524891i | ||||
\(99\) | −1.00000 | + | 1.73205i | −0.100504 | + | 0.174078i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 19.0000 | 1.87213 | 0.936063 | − | 0.351833i | \(-0.114441\pi\) | ||||
0.936063 | + | 0.351833i | \(0.114441\pi\) | |||||||
\(104\) | 1.50000 | − | 2.59808i | 0.147087 | − | 0.254762i | ||||
\(105\) | −0.500000 | + | 0.866025i | −0.0487950 | + | 0.0845154i | ||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 9.00000 | + | 15.5885i | 0.862044 | + | 1.49310i | 0.869953 | + | 0.493135i | \(0.164149\pi\) |
−0.00790932 | + | 0.999969i | \(0.502518\pi\) | |||||||
\(110\) | 1.00000 | − | 1.73205i | 0.0953463 | − | 0.165145i | ||||
\(111\) | 2.50000 | + | 4.33013i | 0.237289 | + | 0.410997i | ||||
\(112\) | 0.500000 | + | 0.866025i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | −3.50000 | + | 2.59808i | −0.327805 | + | 0.243332i | ||||
\(115\) | 6.00000 | 0.559503 | ||||||||
\(116\) | 5.00000 | + | 8.66025i | 0.464238 | + | 0.804084i | ||||
\(117\) | 1.50000 | + | 2.59808i | 0.138675 | + | 0.240192i | ||||
\(118\) | 1.00000 | − | 1.73205i | 0.0920575 | − | 0.159448i | ||||
\(119\) | 2.00000 | + | 3.46410i | 0.183340 | + | 0.317554i | ||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 5.00000 | 0.452679 | ||||||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | −0.500000 | + | 0.866025i | −0.0449013 | + | 0.0777714i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −8.00000 | + | 13.8564i | −0.709885 | + | 1.22956i | 0.255014 | + | 0.966937i | \(0.417920\pi\) |
−0.964899 | + | 0.262620i | \(0.915413\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 2.50000 | − | 4.33013i | 0.220113 | − | 0.381246i | ||||
\(130\) | −1.50000 | − | 2.59808i | −0.131559 | − | 0.227866i | ||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 2.00000 | 0.174078 | ||||||||
\(133\) | −4.00000 | − | 1.73205i | −0.346844 | − | 0.150188i | ||||
\(134\) | −5.00000 | −0.431934 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | −2.00000 | − | 3.46410i | −0.171499 | − | 0.297044i | ||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | 3.00000 | + | 5.19615i | 0.255377 | + | 0.442326i | ||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.00000 | − | 5.19615i | 0.250873 | − | 0.434524i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | −5.50000 | + | 9.52628i | −0.455183 | + | 0.788400i | ||||
\(147\) | 3.00000 | + | 5.19615i | 0.247436 | + | 0.428571i | ||||
\(148\) | 2.50000 | − | 4.33013i | 0.205499 | − | 0.355934i | ||||
\(149\) | −9.00000 | − | 15.5885i | −0.737309 | − | 1.27706i | −0.953703 | − | 0.300750i | \(-0.902763\pi\) |
0.216394 | − | 0.976306i | \(-0.430570\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 4.00000 | + | 1.73205i | 0.324443 | + | 0.140488i | ||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 1.00000 | + | 1.73205i | 0.0805823 | + | 0.139573i | ||||
\(155\) | 0.500000 | + | 0.866025i | 0.0401610 | + | 0.0695608i | ||||
\(156\) | 1.50000 | − | 2.59808i | 0.120096 | − | 0.208013i | ||||
\(157\) | 6.50000 | + | 11.2583i | 0.518756 | + | 0.898513i | 0.999762 | + | 0.0217953i | \(0.00693820\pi\) |
−0.481006 | + | 0.876717i | \(0.659728\pi\) | |||||||
\(158\) | 5.50000 | − | 9.52628i | 0.437557 | − | 0.757870i | ||||
\(159\) | −12.0000 | −0.951662 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −3.00000 | + | 5.19615i | −0.236433 | + | 0.409514i | ||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −17.0000 | −1.33154 | −0.665771 | − | 0.746156i | \(-0.731897\pi\) | ||||
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 1.00000 | − | 1.73205i | 0.0778499 | − | 0.134840i | ||||
\(166\) | −1.00000 | − | 1.73205i | −0.0776151 | − | 0.134433i | ||||
\(167\) | −7.00000 | + | 12.1244i | −0.541676 | + | 0.938211i | 0.457132 | + | 0.889399i | \(0.348877\pi\) |
−0.998808 | + | 0.0488118i | \(0.984457\pi\) | |||||||
\(168\) | 0.500000 | + | 0.866025i | 0.0385758 | + | 0.0668153i | ||||
\(169\) | 2.00000 | + | 3.46410i | 0.153846 | + | 0.266469i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | −3.50000 | + | 2.59808i | −0.267652 | + | 0.198680i | ||||
\(172\) | −5.00000 | −0.381246 | ||||||||
\(173\) | 13.0000 | + | 22.5167i | 0.988372 | + | 1.71191i | 0.625871 | + | 0.779926i | \(0.284744\pi\) |
0.362500 | + | 0.931984i | \(0.381923\pi\) | |||||||
\(174\) | 5.00000 | + | 8.66025i | 0.379049 | + | 0.656532i | ||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | −1.00000 | − | 1.73205i | −0.0753778 | − | 0.130558i | ||||
\(177\) | 1.00000 | − | 1.73205i | 0.0751646 | − | 0.130189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0000 | −0.747435 | −0.373718 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373718 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | 3.00000 | − | 5.19615i | 0.222988 | − | 0.386227i | −0.732726 | − | 0.680524i | \(-0.761752\pi\) |
0.955714 | + | 0.294297i | \(0.0950855\pi\) | |||||||
\(182\) | 3.00000 | 0.222375 | ||||||||
\(183\) | 5.00000 | 0.369611 | ||||||||
\(184\) | 3.00000 | − | 5.19615i | 0.221163 | − | 0.383065i | ||||
\(185\) | −2.50000 | − | 4.33013i | −0.183804 | − | 0.318357i | ||||
\(186\) | −0.500000 | + | 0.866025i | −0.0366618 | + | 0.0635001i | ||||
\(187\) | −4.00000 | − | 6.92820i | −0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 3.50000 | − | 2.59808i | 0.253917 | − | 0.188484i | ||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −12.5000 | − | 21.6506i | −0.899770 | − | 1.55845i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
−0.0719816 | − | 0.997406i | \(-0.522932\pi\) | |||||||
\(194\) | 1.00000 | − | 1.73205i | 0.0717958 | − | 0.124354i | ||||
\(195\) | −1.50000 | − | 2.59808i | −0.107417 | − | 0.186052i | ||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 2.00000 | 0.142134 | ||||||||
\(199\) | −2.50000 | + | 4.33013i | −0.177220 | + | 0.306955i | −0.940927 | − | 0.338608i | \(-0.890044\pi\) |
0.763707 | + | 0.645563i | \(0.223377\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −5.00000 | −0.352673 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | −5.00000 | + | 8.66025i | −0.350931 | + | 0.607831i | ||||
\(204\) | −2.00000 | − | 3.46410i | −0.140028 | − | 0.242536i | ||||
\(205\) | 1.00000 | − | 1.73205i | 0.0698430 | − | 0.120972i | ||||
\(206\) | −9.50000 | − | 16.4545i | −0.661896 | − | 1.14644i | ||||
\(207\) | 3.00000 | + | 5.19615i | 0.208514 | + | 0.361158i | ||||
\(208\) | −3.00000 | −0.208013 | ||||||||
\(209\) | 8.00000 | + | 3.46410i | 0.553372 | + | 0.239617i | ||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | 2.50000 | + | 4.33013i | 0.172107 | + | 0.298098i | 0.939156 | − | 0.343490i | \(-0.111609\pi\) |
−0.767049 | + | 0.641588i | \(0.778276\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00000 | + | 3.46410i | 0.136717 | + | 0.236801i | ||||
\(215\) | −2.50000 | + | 4.33013i | −0.170499 | + | 0.295312i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.00000 | −0.0678844 | ||||||||
\(218\) | 9.00000 | − | 15.5885i | 0.609557 | − | 1.05578i | ||||
\(219\) | −5.50000 | + | 9.52628i | −0.371656 | + | 0.643726i | ||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 2.50000 | − | 4.33013i | 0.167789 | − | 0.290619i | ||||
\(223\) | 0.500000 | + | 0.866025i | 0.0334825 | + | 0.0579934i | 0.882281 | − | 0.470723i | \(-0.156007\pi\) |
−0.848799 | + | 0.528716i | \(0.822674\pi\) | |||||||
\(224\) | 0.500000 | − | 0.866025i | 0.0334077 | − | 0.0578638i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | −7.00000 | − | 12.1244i | −0.465633 | − | 0.806500i | ||||
\(227\) | −18.0000 | −1.19470 | −0.597351 | − | 0.801980i | \(-0.703780\pi\) | ||||
−0.597351 | + | 0.801980i | \(0.703780\pi\) | |||||||
\(228\) | 4.00000 | + | 1.73205i | 0.264906 | + | 0.114708i | ||||
\(229\) | −5.00000 | −0.330409 | −0.165205 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165205 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(230\) | −3.00000 | − | 5.19615i | −0.197814 | − | 0.342624i | ||||
\(231\) | 1.00000 | + | 1.73205i | 0.0657952 | + | 0.113961i | ||||
\(232\) | 5.00000 | − | 8.66025i | 0.328266 | − | 0.568574i | ||||
\(233\) | 2.00000 | + | 3.46410i | 0.131024 | + | 0.226941i | 0.924072 | − | 0.382219i | \(-0.124840\pi\) |
−0.793047 | + | 0.609160i | \(0.791507\pi\) | |||||||
\(234\) | 1.50000 | − | 2.59808i | 0.0980581 | − | 0.169842i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | −0.130189 | ||||||||
\(237\) | 5.50000 | − | 9.52628i | 0.357263 | − | 0.618798i | ||||
\(238\) | 2.00000 | − | 3.46410i | 0.129641 | − | 0.224544i | ||||
\(239\) | −18.0000 | −1.16432 | −0.582162 | − | 0.813073i | \(-0.697793\pi\) | ||||
−0.582162 | + | 0.813073i | \(0.697793\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −2.50000 | + | 4.33013i | −0.161039 | + | 0.278928i | −0.935242 | − | 0.354010i | \(-0.884818\pi\) |
0.774202 | + | 0.632938i | \(0.218151\pi\) | |||||||
\(242\) | 3.50000 | + | 6.06218i | 0.224989 | + | 0.389692i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −2.50000 | − | 4.33013i | −0.160046 | − | 0.277208i | ||||
\(245\) | −3.00000 | − | 5.19615i | −0.191663 | − | 0.331970i | ||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 10.5000 | − | 7.79423i | 0.668099 | − | 0.495935i | ||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −1.00000 | − | 1.73205i | −0.0633724 | − | 0.109764i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 1.00000 | − | 1.73205i | 0.0631194 | − | 0.109326i | −0.832739 | − | 0.553666i | \(-0.813228\pi\) |
0.895858 | + | 0.444340i | \(0.146562\pi\) | |||||||
\(252\) | 0.500000 | + | 0.866025i | 0.0314970 | + | 0.0545545i | ||||
\(253\) | 6.00000 | − | 10.3923i | 0.377217 | − | 0.653359i | ||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.00000 | − | 5.19615i | 0.187135 | − | 0.324127i | −0.757159 | − | 0.653231i | \(-0.773413\pi\) |
0.944294 | + | 0.329104i | \(0.106747\pi\) | |||||||
\(258\) | −5.00000 | −0.311286 | ||||||||
\(259\) | 5.00000 | 0.310685 | ||||||||
\(260\) | −1.50000 | + | 2.59808i | −0.0930261 | + | 0.161126i | ||||
\(261\) | 5.00000 | + | 8.66025i | 0.309492 | + | 0.536056i | ||||
\(262\) | 3.00000 | − | 5.19615i | 0.185341 | − | 0.321019i | ||||
\(263\) | 5.00000 | + | 8.66025i | 0.308313 | + | 0.534014i | 0.977993 | − | 0.208635i | \(-0.0669022\pi\) |
−0.669680 | + | 0.742650i | \(0.733569\pi\) | |||||||
\(264\) | −1.00000 | − | 1.73205i | −0.0615457 | − | 0.106600i | ||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | 0.500000 | + | 4.33013i | 0.0306570 | + | 0.265497i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.50000 | + | 4.33013i | 0.152712 | + | 0.264505i | ||||
\(269\) | −5.00000 | − | 8.66025i | −0.304855 | − | 0.528025i | 0.672374 | − | 0.740212i | \(-0.265275\pi\) |
−0.977229 | + | 0.212187i | \(0.931941\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | 4.00000 | + | 6.92820i | 0.242983 | + | 0.420858i | 0.961563 | − | 0.274586i | \(-0.0885408\pi\) |
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(272\) | −2.00000 | + | 3.46410i | −0.121268 | + | 0.210042i | ||||
\(273\) | 3.00000 | 0.181568 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 3.00000 | − | 5.19615i | 0.180579 | − | 0.312772i | ||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | −9.00000 | −0.539784 | ||||||||
\(279\) | −0.500000 | + | 0.866025i | −0.0299342 | + | 0.0518476i | ||||
\(280\) | −0.500000 | − | 0.866025i | −0.0298807 | − | 0.0517549i | ||||
\(281\) | 15.0000 | − | 25.9808i | 0.894825 | − | 1.54988i | 0.0608039 | − | 0.998150i | \(-0.480634\pi\) |
0.834021 | − | 0.551733i | \(-0.186033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | − | 6.92820i | −0.237775 | − | 0.411839i | 0.722300 | − | 0.691580i | \(-0.243085\pi\) |
−0.960076 | + | 0.279741i | \(0.909752\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.50000 | − | 2.59808i | 0.207322 | − | 0.153897i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 1.00000 | + | 1.73205i | 0.0590281 | + | 0.102240i | ||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | −5.00000 | − | 8.66025i | −0.293610 | − | 0.508548i | ||||
\(291\) | 1.00000 | − | 1.73205i | 0.0586210 | − | 0.101535i | ||||
\(292\) | 11.0000 | 0.643726 | ||||||||
\(293\) | −26.0000 | −1.51894 | −0.759468 | − | 0.650545i | \(-0.774541\pi\) | ||||
−0.759468 | + | 0.650545i | \(0.774541\pi\) | |||||||
\(294\) | 3.00000 | − | 5.19615i | 0.174964 | − | 0.303046i | ||||
\(295\) | −1.00000 | + | 1.73205i | −0.0582223 | + | 0.100844i | ||||
\(296\) | −5.00000 | −0.290619 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | −9.00000 | + | 15.5885i | −0.521356 | + | 0.903015i | ||||
\(299\) | −9.00000 | − | 15.5885i | −0.520483 | − | 0.901504i | ||||
\(300\) | −0.500000 | + | 0.866025i | −0.0288675 | + | 0.0500000i | ||||
\(301\) | −2.50000 | − | 4.33013i | −0.144098 | − | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | −0.500000 | − | 4.33013i | −0.0286770 | − | 0.248350i | ||||
\(305\) | −5.00000 | −0.286299 | ||||||||
\(306\) | −2.00000 | − | 3.46410i | −0.114332 | − | 0.198030i | ||||
\(307\) | −2.00000 | − | 3.46410i | −0.114146 | − | 0.197707i | 0.803292 | − | 0.595585i | \(-0.203080\pi\) |
−0.917438 | + | 0.397879i | \(0.869747\pi\) | |||||||
\(308\) | 1.00000 | − | 1.73205i | 0.0569803 | − | 0.0986928i | ||||
\(309\) | −9.50000 | − | 16.4545i | −0.540436 | − | 0.936063i | ||||
\(310\) | 0.500000 | − | 0.866025i | 0.0283981 | − | 0.0491869i | ||||
\(311\) | −10.0000 | −0.567048 | −0.283524 | − | 0.958965i | \(-0.591504\pi\) | ||||
−0.283524 | + | 0.958965i | \(0.591504\pi\) | |||||||
\(312\) | −3.00000 | −0.169842 | ||||||||
\(313\) | −9.00000 | + | 15.5885i | −0.508710 | + | 0.881112i | 0.491239 | + | 0.871025i | \(0.336544\pi\) |
−0.999949 | + | 0.0100869i | \(0.996789\pi\) | |||||||
\(314\) | 6.50000 | − | 11.2583i | 0.366816 | − | 0.635344i | ||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | −11.0000 | −0.618798 | ||||||||
\(317\) | −15.0000 | + | 25.9808i | −0.842484 | + | 1.45922i | 0.0453045 | + | 0.998973i | \(0.485574\pi\) |
−0.887788 | + | 0.460252i | \(0.847759\pi\) | |||||||
\(318\) | 6.00000 | + | 10.3923i | 0.336463 | + | 0.582772i | ||||
\(319\) | 10.0000 | − | 17.3205i | 0.559893 | − | 0.969762i | ||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 2.00000 | + | 3.46410i | 0.111629 | + | 0.193347i | ||||
\(322\) | 6.00000 | 0.334367 | ||||||||
\(323\) | −2.00000 | − | 17.3205i | −0.111283 | − | 0.963739i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.50000 | + | 2.59808i | 0.0832050 | + | 0.144115i | ||||
\(326\) | 8.50000 | + | 14.7224i | 0.470771 | + | 0.815400i | ||||
\(327\) | 9.00000 | − | 15.5885i | 0.497701 | − | 0.862044i | ||||
\(328\) | −1.00000 | − | 1.73205i | −0.0552158 | − | 0.0956365i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.00000 | −0.110096 | ||||||||
\(331\) | 5.00000 | 0.274825 | 0.137412 | − | 0.990514i | \(-0.456121\pi\) | ||||
0.137412 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(332\) | −1.00000 | + | 1.73205i | −0.0548821 | + | 0.0950586i | ||||
\(333\) | 2.50000 | − | 4.33013i | 0.136999 | − | 0.237289i | ||||
\(334\) | 14.0000 | 0.766046 | ||||||||
\(335\) | 5.00000 | 0.273179 | ||||||||
\(336\) | 0.500000 | − | 0.866025i | 0.0272772 | − | 0.0472456i | ||||
\(337\) | −11.5000 | − | 19.9186i | −0.626445 | − | 1.08503i | −0.988260 | − | 0.152784i | \(-0.951176\pi\) |
0.361815 | − | 0.932250i | \(-0.382157\pi\) | |||||||
\(338\) | 2.00000 | − | 3.46410i | 0.108786 | − | 0.188422i | ||||
\(339\) | −7.00000 | − | 12.1244i | −0.380188 | − | 0.658505i | ||||
\(340\) | 2.00000 | + | 3.46410i | 0.108465 | + | 0.187867i | ||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | 4.00000 | + | 1.73205i | 0.216295 | + | 0.0936586i | ||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 2.50000 | + | 4.33013i | 0.134791 | + | 0.233465i | ||||
\(345\) | −3.00000 | − | 5.19615i | −0.161515 | − | 0.279751i | ||||
\(346\) | 13.0000 | − | 22.5167i | 0.698884 | − | 1.21050i | ||||
\(347\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(348\) | 5.00000 | − | 8.66025i | 0.268028 | − | 0.464238i | ||||
\(349\) | 17.0000 | 0.909989 | 0.454995 | − | 0.890494i | \(-0.349641\pi\) | ||||
0.454995 | + | 0.890494i | \(0.349641\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 1.50000 | − | 2.59808i | 0.0800641 | − | 0.138675i | ||||
\(352\) | −1.00000 | + | 1.73205i | −0.0533002 | + | 0.0923186i | ||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | −2.00000 | −0.106299 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.00000 | − | 3.46410i | 0.105851 | − | 0.183340i | ||||
\(358\) | 5.00000 | + | 8.66025i | 0.264258 | + | 0.457709i | ||||
\(359\) | 1.00000 | + | 1.73205i | 0.0527780 | + | 0.0914141i | 0.891207 | − | 0.453596i | \(-0.149859\pi\) |
−0.838429 | + | 0.545010i | \(0.816526\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | −6.00000 | −0.315353 | ||||||||
\(363\) | 3.50000 | + | 6.06218i | 0.183702 | + | 0.318182i | ||||
\(364\) | −1.50000 | − | 2.59808i | −0.0786214 | − | 0.136176i | ||||
\(365\) | 5.50000 | − | 9.52628i | 0.287883 | − | 0.498628i | ||||
\(366\) | −2.50000 | − | 4.33013i | −0.130677 | − | 0.226339i | ||||
\(367\) | 3.50000 | − | 6.06218i | 0.182699 | − | 0.316443i | −0.760100 | − | 0.649806i | \(-0.774850\pi\) |
0.942799 | + | 0.333363i | \(0.108183\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | −2.50000 | + | 4.33013i | −0.129969 | + | 0.225113i | ||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | 1.00000 | 0.0518476 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | −4.00000 | + | 6.92820i | −0.206835 | + | 0.358249i | ||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0000 | − | 25.9808i | −0.772539 | − | 1.33808i | ||||
\(378\) | 0.500000 | + | 0.866025i | 0.0257172 | + | 0.0445435i | ||||
\(379\) | −11.0000 | −0.565032 | −0.282516 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282516 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(380\) | −4.00000 | − | 1.73205i | −0.205196 | − | 0.0888523i | ||||
\(381\) | 16.0000 | 0.819705 | ||||||||
\(382\) | −8.00000 | − | 13.8564i | −0.409316 | − | 0.708955i | ||||
\(383\) | 18.0000 | + | 31.1769i | 0.919757 | + | 1.59307i | 0.799783 | + | 0.600289i | \(0.204948\pi\) |
0.119974 | + | 0.992777i | \(0.461719\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −1.00000 | − | 1.73205i | −0.0509647 | − | 0.0882735i | ||||
\(386\) | −12.5000 | + | 21.6506i | −0.636233 | + | 1.10199i | ||||
\(387\) | −5.00000 | −0.254164 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | 5.00000 | − | 8.66025i | 0.253510 | − | 0.439092i | −0.710980 | − | 0.703213i | \(-0.751748\pi\) |
0.964490 | + | 0.264120i | \(0.0850816\pi\) | |||||||
\(390\) | −1.50000 | + | 2.59808i | −0.0759555 | + | 0.131559i | ||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | −6.00000 | −0.303046 | ||||||||
\(393\) | 3.00000 | − | 5.19615i | 0.151330 | − | 0.262111i | ||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | −5.50000 | + | 9.52628i | −0.276735 | + | 0.479319i | ||||
\(396\) | −1.00000 | − | 1.73205i | −0.0502519 | − | 0.0870388i | ||||
\(397\) | 0.500000 | + | 0.866025i | 0.0250943 | + | 0.0434646i | 0.878300 | − | 0.478110i | \(-0.158678\pi\) |
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 5.00000 | 0.250627 | ||||||||
\(399\) | 0.500000 | + | 4.33013i | 0.0250313 | + | 0.216777i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 19.0000 | + | 32.9090i | 0.948815 | + | 1.64340i | 0.747927 | + | 0.663781i | \(0.231049\pi\) |
0.200888 | + | 0.979614i | \(0.435617\pi\) | |||||||
\(402\) | 2.50000 | + | 4.33013i | 0.124689 | + | 0.215967i | ||||
\(403\) | 1.50000 | − | 2.59808i | 0.0747203 | − | 0.129419i | ||||
\(404\) | −3.00000 | − | 5.19615i | −0.149256 | − | 0.258518i | ||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 10.0000 | 0.496292 | ||||||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | −2.00000 | + | 3.46410i | −0.0990148 | + | 0.171499i | ||||
\(409\) | 15.0000 | − | 25.9808i | 0.741702 | − | 1.28467i | −0.210017 | − | 0.977698i | \(-0.567352\pi\) |
0.951720 | − | 0.306968i | \(-0.0993146\pi\) | |||||||
\(410\) | −2.00000 | −0.0987730 | ||||||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | −9.50000 | + | 16.4545i | −0.468031 | + | 0.810654i | ||||
\(413\) | −1.00000 | − | 1.73205i | −0.0492068 | − | 0.0852286i | ||||
\(414\) | 3.00000 | − | 5.19615i | 0.147442 | − | 0.255377i | ||||
\(415\) | 1.00000 | + | 1.73205i | 0.0490881 | + | 0.0850230i | ||||
\(416\) | 1.50000 | + | 2.59808i | 0.0735436 | + | 0.127381i | ||||
\(417\) | −9.00000 | −0.440732 | ||||||||
\(418\) | −1.00000 | − | 8.66025i | −0.0489116 | − | 0.423587i | ||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | −0.500000 | − | 0.866025i | −0.0243975 | − | 0.0422577i | ||||
\(421\) | 7.00000 | + | 12.1244i | 0.341159 | + | 0.590905i | 0.984648 | − | 0.174550i | \(-0.0558472\pi\) |
−0.643489 | + | 0.765455i | \(0.722514\pi\) | |||||||
\(422\) | 2.50000 | − | 4.33013i | 0.121698 | − | 0.210787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | − | 10.3923i | 0.291386 | − | 0.504695i | ||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.50000 | − | 4.33013i | 0.120983 | − | 0.209550i | ||||
\(428\) | 2.00000 | − | 3.46410i | 0.0966736 | − | 0.167444i | ||||
\(429\) | −6.00000 | −0.289683 | ||||||||
\(430\) | 5.00000 | 0.241121 | ||||||||
\(431\) | 10.0000 | − | 17.3205i | 0.481683 | − | 0.834300i | −0.518096 | − | 0.855323i | \(-0.673359\pi\) |
0.999779 | + | 0.0210230i | \(0.00669232\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −14.5000 | + | 25.1147i | −0.696826 | + | 1.20694i | 0.272736 | + | 0.962089i | \(0.412071\pi\) |
−0.969561 | + | 0.244848i | \(0.921262\pi\) | |||||||
\(434\) | 0.500000 | + | 0.866025i | 0.0240008 | + | 0.0415705i | ||||
\(435\) | −5.00000 | − | 8.66025i | −0.239732 | − | 0.415227i | ||||
\(436\) | −18.0000 | −0.862044 | ||||||||
\(437\) | 21.0000 | − | 15.5885i | 1.00457 | − | 0.745697i | ||||
\(438\) | 11.0000 | 0.525600 | ||||||||
\(439\) | 20.5000 | + | 35.5070i | 0.978412 | + | 1.69466i | 0.668184 | + | 0.743996i | \(0.267072\pi\) |
0.310228 | + | 0.950662i | \(0.399595\pi\) | |||||||
\(440\) | 1.00000 | + | 1.73205i | 0.0476731 | + | 0.0825723i | ||||
\(441\) | 3.00000 | − | 5.19615i | 0.142857 | − | 0.247436i | ||||
\(442\) | 6.00000 | + | 10.3923i | 0.285391 | + | 0.494312i | ||||
\(443\) | −6.00000 | + | 10.3923i | −0.285069 | + | 0.493753i | −0.972626 | − | 0.232377i | \(-0.925350\pi\) |
0.687557 | + | 0.726130i | \(0.258683\pi\) | |||||||
\(444\) | −5.00000 | −0.237289 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.500000 | − | 0.866025i | 0.0236757 | − | 0.0410075i | ||||
\(447\) | −9.00000 | + | 15.5885i | −0.425685 | + | 0.737309i | ||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 28.0000 | 1.32140 | 0.660701 | − | 0.750649i | \(-0.270259\pi\) | ||||
0.660701 | + | 0.750649i | \(0.270259\pi\) | |||||||
\(450\) | −0.500000 | + | 0.866025i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | −2.00000 | − | 3.46410i | −0.0941763 | − | 0.163118i | ||||
\(452\) | −7.00000 | + | 12.1244i | −0.329252 | + | 0.570282i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.00000 | + | 15.5885i | 0.422391 | + | 0.731603i | ||||
\(455\) | −3.00000 | −0.140642 | ||||||||
\(456\) | −0.500000 | − | 4.33013i | −0.0234146 | − | 0.202777i | ||||
\(457\) | 23.0000 | 1.07589 | 0.537947 | − | 0.842978i | \(-0.319200\pi\) | ||||
0.537947 | + | 0.842978i | \(0.319200\pi\) | |||||||
\(458\) | 2.50000 | + | 4.33013i | 0.116817 | + | 0.202334i | ||||
\(459\) | −2.00000 | − | 3.46410i | −0.0933520 | − | 0.161690i | ||||
\(460\) | −3.00000 | + | 5.19615i | −0.139876 | + | 0.242272i | ||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 1.00000 | − | 1.73205i | 0.0465242 | − | 0.0805823i | ||||
\(463\) | 1.00000 | 0.0464739 | 0.0232370 | − | 0.999730i | \(-0.492603\pi\) | ||||
0.0232370 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(464\) | −10.0000 | −0.464238 | ||||||||
\(465\) | 0.500000 | − | 0.866025i | 0.0231869 | − | 0.0401610i | ||||
\(466\) | 2.00000 | − | 3.46410i | 0.0926482 | − | 0.160471i | ||||
\(467\) | 30.0000 | 1.38823 | 0.694117 | − | 0.719862i | \(-0.255795\pi\) | ||||
0.694117 | + | 0.719862i | \(0.255795\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | −2.50000 | + | 4.33013i | −0.115439 | + | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.50000 | − | 11.2583i | 0.299504 | − | 0.518756i | ||||
\(472\) | 1.00000 | + | 1.73205i | 0.0460287 | + | 0.0797241i | ||||
\(473\) | 5.00000 | + | 8.66025i | 0.229900 | + | 0.398199i | ||||
\(474\) | −11.0000 | −0.505247 | ||||||||
\(475\) | −3.50000 | + | 2.59808i | −0.160591 | + | 0.119208i | ||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | 6.00000 | + | 10.3923i | 0.274721 | + | 0.475831i | ||||
\(478\) | 9.00000 | + | 15.5885i | 0.411650 | + | 0.712999i | ||||
\(479\) | −21.0000 | + | 36.3731i | −0.959514 | + | 1.66193i | −0.235833 | + | 0.971794i | \(0.575782\pi\) |
−0.723681 | + | 0.690134i | \(0.757551\pi\) | |||||||
\(480\) | 0.500000 | + | 0.866025i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | −7.50000 | + | 12.9904i | −0.341971 | + | 0.592310i | ||||
\(482\) | 5.00000 | 0.227744 | ||||||||
\(483\) | 6.00000 | 0.273009 | ||||||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | −1.00000 | + | 1.73205i | −0.0454077 | + | 0.0786484i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | −2.50000 | + | 4.33013i | −0.113170 | + | 0.196016i | ||||
\(489\) | 8.50000 | + | 14.7224i | 0.384383 | + | 0.665771i | ||||
\(490\) | −3.00000 | + | 5.19615i | −0.135526 | + | 0.234738i | ||||
\(491\) | −14.0000 | − | 24.2487i | −0.631811 | − | 1.09433i | −0.987181 | − | 0.159603i | \(-0.948978\pi\) |
0.355370 | − | 0.934726i | \(-0.384355\pi\) | |||||||
\(492\) | −1.00000 | − | 1.73205i | −0.0450835 | − | 0.0780869i | ||||
\(493\) | −40.0000 | −1.80151 | ||||||||
\(494\) | −12.0000 | − | 5.19615i | −0.539906 | − | 0.233786i | ||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | −0.500000 | − | 0.866025i | −0.0224507 | − | 0.0388857i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.00000 | + | 1.73205i | −0.0448111 | + | 0.0776151i | ||||
\(499\) | 12.5000 | + | 21.6506i | 0.559577 | + | 0.969216i | 0.997532 | + | 0.0702185i | \(0.0223697\pi\) |
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 14.0000 | 0.625474 | ||||||||
\(502\) | −2.00000 | −0.0892644 | ||||||||
\(503\) | −22.0000 | + | 38.1051i | −0.980932 | + | 1.69902i | −0.322151 | + | 0.946688i | \(0.604406\pi\) |
−0.658781 | + | 0.752335i | \(0.728928\pi\) | |||||||
\(504\) | 0.500000 | − | 0.866025i | 0.0222718 | − | 0.0385758i | ||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 2.00000 | − | 3.46410i | 0.0888231 | − | 0.153846i | ||||
\(508\) | −8.00000 | − | 13.8564i | −0.354943 | − | 0.614779i | ||||
\(509\) | 4.00000 | − | 6.92820i | 0.177297 | − | 0.307087i | −0.763657 | − | 0.645622i | \(-0.776598\pi\) |
0.940954 | + | 0.338535i | \(0.109931\pi\) | |||||||
\(510\) | 2.00000 | + | 3.46410i | 0.0885615 | + | 0.153393i | ||||
\(511\) | 5.50000 | + | 9.52628i | 0.243306 | + | 0.421418i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.00000 | + | 1.73205i | 0.176604 | + | 0.0764719i | ||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | 9.50000 | + | 16.4545i | 0.418620 | + | 0.725071i | ||||
\(516\) | 2.50000 | + | 4.33013i | 0.110056 | + | 0.190623i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.50000 | − | 4.33013i | −0.109844 | − | 0.190255i | ||||
\(519\) | 13.0000 | − | 22.5167i | 0.570637 | − | 0.988372i | ||||
\(520\) | 3.00000 | 0.131559 | ||||||||
\(521\) | 8.00000 | 0.350486 | 0.175243 | − | 0.984525i | \(-0.443929\pi\) | ||||
0.175243 | + | 0.984525i | \(0.443929\pi\) | |||||||
\(522\) | 5.00000 | − | 8.66025i | 0.218844 | − | 0.379049i | ||||
\(523\) | 5.50000 | − | 9.52628i | 0.240498 | − | 0.416555i | −0.720358 | − | 0.693602i | \(-0.756023\pi\) |
0.960856 | + | 0.277047i | \(0.0893559\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 5.00000 | − | 8.66025i | 0.218010 | − | 0.377605i | ||||
\(527\) | −2.00000 | − | 3.46410i | −0.0871214 | − | 0.150899i | ||||
\(528\) | −1.00000 | + | 1.73205i | −0.0435194 | + | 0.0753778i | ||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | −6.00000 | − | 10.3923i | −0.260623 | − | 0.451413i | ||||
\(531\) | −2.00000 | −0.0867926 | ||||||||
\(532\) | 3.50000 | − | 2.59808i | 0.151744 | − | 0.112641i | ||||
\(533\) | −6.00000 | −0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.00000 | − | 3.46410i | −0.0864675 | − | 0.149766i | ||||
\(536\) | 2.50000 | − | 4.33013i | 0.107984 | − | 0.187033i | ||||
\(537\) | 5.00000 | + | 8.66025i | 0.215766 | + | 0.373718i | ||||
\(538\) | −5.00000 | + | 8.66025i | −0.215565 | + | 0.373370i | ||||
\(539\) | −12.0000 | −0.516877 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 4.50000 | − | 7.79423i | 0.193470 | − | 0.335100i | −0.752928 | − | 0.658103i | \(-0.771359\pi\) |
0.946398 | + | 0.323003i | \(0.104692\pi\) | |||||||
\(542\) | 4.00000 | − | 6.92820i | 0.171815 | − | 0.297592i | ||||
\(543\) | −6.00000 | −0.257485 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | −9.00000 | + | 15.5885i | −0.385518 | + | 0.667736i | ||||
\(546\) | −1.50000 | − | 2.59808i | −0.0641941 | − | 0.111187i | ||||
\(547\) | 4.50000 | − | 7.79423i | 0.192406 | − | 0.333257i | −0.753641 | − | 0.657286i | \(-0.771704\pi\) |
0.946047 | + | 0.324029i | \(0.105038\pi\) | |||||||
\(548\) | 1.00000 | + | 1.73205i | 0.0427179 | + | 0.0739895i | ||||
\(549\) | −2.50000 | − | 4.33013i | −0.106697 | − | 0.184805i | ||||
\(550\) | 2.00000 | 0.0852803 | ||||||||
\(551\) | 35.0000 | − | 25.9808i | 1.49105 | − | 1.10682i | ||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | −5.50000 | − | 9.52628i | −0.233884 | − | 0.405099i | ||||
\(554\) | 5.00000 | + | 8.66025i | 0.212430 | + | 0.367939i | ||||
\(555\) | −2.50000 | + | 4.33013i | −0.106119 | + | 0.183804i | ||||
\(556\) | 4.50000 | + | 7.79423i | 0.190843 | + | 0.330549i | ||||
\(557\) | 6.00000 | − | 10.3923i | 0.254228 | − | 0.440336i | −0.710457 | − | 0.703740i | \(-0.751512\pi\) |
0.964686 | + | 0.263404i | \(0.0848453\pi\) | |||||||
\(558\) | 1.00000 | 0.0423334 | ||||||||
\(559\) | 15.0000 | 0.634432 | ||||||||
\(560\) | −0.500000 | + | 0.866025i | −0.0211289 | + | 0.0365963i | ||||
\(561\) | −4.00000 | + | 6.92820i | −0.168880 | + | 0.292509i | ||||
\(562\) | −30.0000 | −1.26547 | ||||||||
\(563\) | 22.0000 | 0.927189 | 0.463595 | − | 0.886047i | \(-0.346559\pi\) | ||||
0.463595 | + | 0.886047i | \(0.346559\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.00000 | + | 12.1244i | 0.294492 | + | 0.510075i | ||||
\(566\) | −4.00000 | + | 6.92820i | −0.168133 | + | 0.291214i | ||||
\(567\) | 0.500000 | + | 0.866025i | 0.0209980 | + | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | −4.00000 | − | 1.73205i | −0.167542 | − | 0.0725476i | ||||
\(571\) | 39.0000 | 1.63210 | 0.816050 | − | 0.577982i | \(-0.196160\pi\) | ||||
0.816050 | + | 0.577982i | \(0.196160\pi\) | |||||||
\(572\) | 3.00000 | + | 5.19615i | 0.125436 | + | 0.217262i | ||||
\(573\) | −8.00000 | − | 13.8564i | −0.334205 | − | 0.578860i | ||||
\(574\) | 1.00000 | − | 1.73205i | 0.0417392 | − | 0.0722944i | ||||
\(575\) | 3.00000 | + | 5.19615i | 0.125109 | + | 0.216695i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −12.5000 | + | 21.6506i | −0.519482 | + | 0.899770i | ||||
\(580\) | −5.00000 | + | 8.66025i | −0.207614 | + | 0.359597i | ||||
\(581\) | −2.00000 | −0.0829740 | ||||||||
\(582\) | −2.00000 | −0.0829027 | ||||||||
\(583\) | 12.0000 | − | 20.7846i | 0.496989 | − | 0.860811i | ||||
\(584\) | −5.50000 | − | 9.52628i | −0.227592 | − | 0.394200i | ||||
\(585\) | −1.50000 | + | 2.59808i | −0.0620174 | + | 0.107417i | ||||
\(586\) | 13.0000 | + | 22.5167i | 0.537025 | + | 0.930155i | ||||
\(587\) | −9.00000 | − | 15.5885i | −0.371470 | − | 0.643404i | 0.618322 | − | 0.785925i | \(-0.287813\pi\) |
−0.989792 | + | 0.142520i | \(0.954479\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | 4.00000 | + | 1.73205i | 0.164817 | + | 0.0713679i | ||||
\(590\) | 2.00000 | 0.0823387 | ||||||||
\(591\) | 9.00000 | + | 15.5885i | 0.370211 | + | 0.641223i | ||||
\(592\) | 2.50000 | + | 4.33013i | 0.102749 | + | 0.177967i | ||||
\(593\) | −14.0000 | + | 24.2487i | −0.574911 | + | 0.995775i | 0.421140 | + | 0.906996i | \(0.361630\pi\) |
−0.996051 | + | 0.0887797i | \(0.971703\pi\) | |||||||
\(594\) | −1.00000 | − | 1.73205i | −0.0410305 | − | 0.0710669i | ||||
\(595\) | −2.00000 | + | 3.46410i | −0.0819920 | + | 0.142014i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 5.00000 | 0.204636 | ||||||||
\(598\) | −9.00000 | + | 15.5885i | −0.368037 | + | 0.637459i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 7.00000 | 0.285536 | 0.142768 | − | 0.989756i | \(-0.454400\pi\) | ||||
0.142768 | + | 0.989756i | \(0.454400\pi\) | |||||||
\(602\) | −2.50000 | + | 4.33013i | −0.101892 | + | 0.176483i | ||||
\(603\) | 2.50000 | + | 4.33013i | 0.101808 | + | 0.176336i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.50000 | − | 6.06218i | −0.142295 | − | 0.246463i | ||||
\(606\) | −3.00000 | − | 5.19615i | −0.121867 | − | 0.211079i | ||||
\(607\) | −9.00000 | −0.365299 | −0.182649 | − | 0.983178i | \(-0.558467\pi\) | ||||
−0.182649 | + | 0.983178i | \(0.558467\pi\) | |||||||
\(608\) | −3.50000 | + | 2.59808i | −0.141944 | + | 0.105366i | ||||
\(609\) | 10.0000 | 0.405220 | ||||||||
\(610\) | 2.50000 | + | 4.33013i | 0.101222 | + | 0.175322i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.00000 | + | 3.46410i | −0.0808452 | + | 0.140028i | ||||
\(613\) | 11.0000 | + | 19.0526i | 0.444286 | + | 0.769526i | 0.998002 | − | 0.0631797i | \(-0.0201241\pi\) |
−0.553716 | + | 0.832705i | \(0.686791\pi\) | |||||||
\(614\) | −2.00000 | + | 3.46410i | −0.0807134 | + | 0.139800i | ||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | −12.0000 | + | 20.7846i | −0.483102 | + | 0.836757i | −0.999812 | − | 0.0194037i | \(-0.993823\pi\) |
0.516710 | + | 0.856161i | \(0.327157\pi\) | |||||||
\(618\) | −9.50000 | + | 16.4545i | −0.382146 | + | 0.661896i | ||||
\(619\) | −29.0000 | −1.16561 | −0.582804 | − | 0.812613i | \(-0.698045\pi\) | ||||
−0.582804 | + | 0.812613i | \(0.698045\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | 3.00000 | − | 5.19615i | 0.120386 | − | 0.208514i | ||||
\(622\) | 5.00000 | + | 8.66025i | 0.200482 | + | 0.347245i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.50000 | + | 2.59808i | 0.0600481 | + | 0.104006i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 18.0000 | 0.719425 | ||||||||
\(627\) | −1.00000 | − | 8.66025i | −0.0399362 | − | 0.345857i | ||||
\(628\) | −13.0000 | −0.518756 | ||||||||
\(629\) | 10.0000 | + | 17.3205i | 0.398726 | + | 0.690614i | ||||
\(630\) | −0.500000 | − | 0.866025i | −0.0199205 | − | 0.0345033i | ||||
\(631\) | 21.5000 | − | 37.2391i | 0.855901 | − | 1.48246i | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) |
0.875806 | − | 0.482663i | \(-0.160330\pi\) | |||||||
\(632\) | 5.50000 | + | 9.52628i | 0.218778 | + | 0.378935i | ||||
\(633\) | 2.50000 | − | 4.33013i | 0.0993661 | − | 0.172107i | ||||
\(634\) | 30.0000 | 1.19145 | ||||||||
\(635\) | −16.0000 | −0.634941 | ||||||||
\(636\) | 6.00000 | − | 10.3923i | 0.237915 | − | 0.412082i | ||||
\(637\) | −9.00000 | + | 15.5885i | −0.356593 | + | 0.617637i | ||||
\(638\) | −20.0000 | −0.791808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −12.0000 | − | 20.7846i | −0.473972 | − | 0.820943i | 0.525584 | − | 0.850741i | \(-0.323847\pi\) |
−0.999556 | + | 0.0297987i | \(0.990513\pi\) | |||||||
\(642\) | 2.00000 | − | 3.46410i | 0.0789337 | − | 0.136717i | ||||
\(643\) | −20.5000 | − | 35.5070i | −0.808441 | − | 1.40026i | −0.913943 | − | 0.405842i | \(-0.866978\pi\) |
0.105502 | − | 0.994419i | \(-0.466355\pi\) | |||||||
\(644\) | −3.00000 | − | 5.19615i | −0.118217 | − | 0.204757i | ||||
\(645\) | 5.00000 | 0.196875 | ||||||||
\(646\) | −14.0000 | + | 10.3923i | −0.550823 | + | 0.408880i | ||||
\(647\) | 46.0000 | 1.80845 | 0.904223 | − | 0.427060i | \(-0.140451\pi\) | ||||
0.904223 | + | 0.427060i | \(0.140451\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 2.00000 | + | 3.46410i | 0.0785069 | + | 0.135978i | ||||
\(650\) | 1.50000 | − | 2.59808i | 0.0588348 | − | 0.101905i | ||||
\(651\) | 0.500000 | + | 0.866025i | 0.0195965 | + | 0.0339422i | ||||
\(652\) | 8.50000 | − | 14.7224i | 0.332886 | − | 0.576575i | ||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | −18.0000 | −0.703856 | ||||||||
\(655\) | −3.00000 | + | 5.19615i | −0.117220 | + | 0.203030i | ||||
\(656\) | −1.00000 | + | 1.73205i | −0.0390434 | + | 0.0676252i | ||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.00000 | + | 15.5885i | −0.350590 | + | 0.607240i | −0.986353 | − | 0.164644i | \(-0.947352\pi\) |
0.635763 | + | 0.771885i | \(0.280686\pi\) | |||||||
\(660\) | 1.00000 | + | 1.73205i | 0.0389249 | + | 0.0674200i | ||||
\(661\) | −23.0000 | + | 39.8372i | −0.894596 | + | 1.54949i | −0.0602929 | + | 0.998181i | \(0.519203\pi\) |
−0.834303 | + | 0.551306i | \(0.814130\pi\) | |||||||
\(662\) | −2.50000 | − | 4.33013i | −0.0971653 | − | 0.168295i | ||||
\(663\) | 6.00000 | + | 10.3923i | 0.233021 | + | 0.403604i | ||||
\(664\) | 2.00000 | 0.0776151 | ||||||||
\(665\) | −0.500000 | − | 4.33013i | −0.0193892 | − | 0.167915i | ||||
\(666\) | −5.00000 | −0.193746 | ||||||||
\(667\) | −30.0000 | − | 51.9615i | −1.16160 | − | 2.01196i | ||||
\(668\) | −7.00000 | − | 12.1244i | −0.270838 | − | 0.469105i | ||||
\(669\) | 0.500000 | − | 0.866025i | 0.0193311 | − | 0.0334825i | ||||
\(670\) | −2.50000 | − | 4.33013i | −0.0965834 | − | 0.167287i | ||||
\(671\) | −5.00000 | + | 8.66025i | −0.193023 | + | 0.334325i | ||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −23.0000 | −0.886585 | −0.443292 | − | 0.896377i | \(-0.646190\pi\) | ||||
−0.443292 | + | 0.896377i | \(0.646190\pi\) | |||||||
\(674\) | −11.5000 | + | 19.9186i | −0.442963 | + | 0.767235i | ||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | 48.0000 | 1.84479 | 0.922395 | − | 0.386248i | \(-0.126229\pi\) | ||||
0.922395 | + | 0.386248i | \(0.126229\pi\) | |||||||
\(678\) | −7.00000 | + | 12.1244i | −0.268833 | + | 0.465633i | ||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | 2.00000 | − | 3.46410i | 0.0766965 | − | 0.132842i | ||||
\(681\) | 9.00000 | + | 15.5885i | 0.344881 | + | 0.597351i | ||||
\(682\) | −1.00000 | − | 1.73205i | −0.0382920 | − | 0.0663237i | ||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | −0.500000 | − | 4.33013i | −0.0191180 | − | 0.165567i | ||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | −6.50000 | − | 11.2583i | −0.248171 | − | 0.429845i | ||||
\(687\) | 2.50000 | + | 4.33013i | 0.0953809 | + | 0.165205i | ||||
\(688\) | 2.50000 | − | 4.33013i | 0.0953116 | − | 0.165085i | ||||
\(689\) | −18.0000 | − | 31.1769i | −0.685745 | − | 1.18775i | ||||
\(690\) | −3.00000 | + | 5.19615i | −0.114208 | + | 0.197814i | ||||
\(691\) | 4.00000 | 0.152167 | 0.0760836 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760836 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(692\) | −26.0000 | −0.988372 | ||||||||
\(693\) | 1.00000 | − | 1.73205i | 0.0379869 | − | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.00000 | 0.341389 | ||||||||
\(696\) | −10.0000 | −0.379049 | ||||||||
\(697\) | −4.00000 | + | 6.92820i | −0.151511 | + | 0.262424i | ||||
\(698\) | −8.50000 | − | 14.7224i | −0.321730 | − | 0.557252i | ||||
\(699\) | 2.00000 | − | 3.46410i | 0.0756469 | − | 0.131024i | ||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | −14.0000 | − | 24.2487i | −0.528773 | − | 0.915861i | −0.999437 | − | 0.0335489i | \(-0.989319\pi\) |
0.470664 | − | 0.882312i | \(-0.344014\pi\) | |||||||
\(702\) | −3.00000 | −0.113228 | ||||||||
\(703\) | −20.0000 | − | 8.66025i | −0.754314 | − | 0.326628i | ||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.00000 | + | 5.19615i | 0.112906 | + | 0.195560i | ||||
\(707\) | 3.00000 | − | 5.19615i | 0.112827 | − | 0.195421i | ||||
\(708\) | 1.00000 | + | 1.73205i | 0.0375823 | + | 0.0650945i | ||||
\(709\) | −9.50000 | + | 16.4545i | −0.356780 | + | 0.617961i | −0.987421 | − | 0.158114i | \(-0.949459\pi\) |
0.630641 | + | 0.776075i | \(0.282792\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.0000 | −0.412532 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00000 | − | 5.19615i | 0.112351 | − | 0.194597i | ||||
\(714\) | −4.00000 | −0.149696 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | 5.00000 | − | 8.66025i | 0.186859 | − | 0.323649i | ||||
\(717\) | 9.00000 | + | 15.5885i | 0.336111 | + | 0.582162i | ||||
\(718\) | 1.00000 | − | 1.73205i | 0.0373197 | − | 0.0646396i | ||||
\(719\) | −13.0000 | − | 22.5167i | −0.484818 | − | 0.839730i | 0.515030 | − | 0.857172i | \(-0.327781\pi\) |
−0.999848 | + | 0.0174426i | \(0.994448\pi\) | |||||||
\(720\) | 0.500000 | + | 0.866025i | 0.0186339 | + | 0.0322749i | ||||
\(721\) | −19.0000 | −0.707597 | ||||||||
\(722\) | 5.50000 | − | 18.1865i | 0.204689 | − | 0.676833i | ||||
\(723\) | 5.00000 | 0.185952 | ||||||||
\(724\) | 3.00000 | + | 5.19615i | 0.111494 | + | 0.193113i | ||||
\(725\) | 5.00000 | + | 8.66025i | 0.185695 | + | 0.321634i | ||||
\(726\) | 3.50000 | − | 6.06218i | 0.129897 | − | 0.224989i | ||||
\(727\) | 22.5000 | + | 38.9711i | 0.834479 | + | 1.44536i | 0.894454 | + | 0.447160i | \(0.147564\pi\) |
−0.0599753 | + | 0.998200i | \(0.519102\pi\) | |||||||
\(728\) | −1.50000 | + | 2.59808i | −0.0555937 | + | 0.0962911i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.0000 | −0.407128 | ||||||||
\(731\) | 10.0000 | − | 17.3205i | 0.369863 | − | 0.640622i | ||||
\(732\) | −2.50000 | + | 4.33013i | −0.0924027 | + | 0.160046i | ||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | −7.00000 | −0.258375 | ||||||||
\(735\) | −3.00000 | + | 5.19615i | −0.110657 | + | 0.191663i | ||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | 5.00000 | − | 8.66025i | 0.184177 | − | 0.319005i | ||||
\(738\) | −1.00000 | − | 1.73205i | −0.0368105 | − | 0.0637577i | ||||
\(739\) | −0.500000 | − | 0.866025i | −0.0183928 | − | 0.0318573i | 0.856683 | − | 0.515844i | \(-0.172522\pi\) |
−0.875075 | + | 0.483987i | \(0.839188\pi\) | |||||||
\(740\) | 5.00000 | 0.183804 | ||||||||
\(741\) | −12.0000 | − | 5.19615i | −0.440831 | − | 0.190885i | ||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | −0.500000 | − | 0.866025i | −0.0183309 | − | 0.0317500i | ||||
\(745\) | 9.00000 | − | 15.5885i | 0.329734 | − | 0.571117i | ||||
\(746\) | 11.0000 | + | 19.0526i | 0.402739 | + | 0.697564i | ||||
\(747\) | −1.00000 | + | 1.73205i | −0.0365881 | + | 0.0633724i | ||||
\(748\) | 8.00000 | 0.292509 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0.500000 | − | 0.866025i | 0.0182574 | − | 0.0316228i | ||||
\(751\) | 23.5000 | − | 40.7032i | 0.857527 | − | 1.48528i | −0.0167534 | − | 0.999860i | \(-0.505333\pi\) |
0.874281 | − | 0.485421i | \(-0.161334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.00000 | −0.0728841 | ||||||||
\(754\) | −15.0000 | + | 25.9808i | −0.546268 | + | 0.946164i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.500000 | − | 0.866025i | 0.0181848 | − | 0.0314970i | ||||
\(757\) | 3.50000 | + | 6.06218i | 0.127210 | + | 0.220334i | 0.922595 | − | 0.385771i | \(-0.126065\pi\) |
−0.795385 | + | 0.606105i | \(0.792731\pi\) | |||||||
\(758\) | 5.50000 | + | 9.52628i | 0.199769 | + | 0.346010i | ||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | 0.500000 | + | 4.33013i | 0.0181369 | + | 0.157070i | ||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | −8.00000 | − | 13.8564i | −0.289809 | − | 0.501965i | ||||
\(763\) | −9.00000 | − | 15.5885i | −0.325822 | − | 0.564340i | ||||
\(764\) | −8.00000 | + | 13.8564i | −0.289430 | + | 0.501307i | ||||
\(765\) | 2.00000 | + | 3.46410i | 0.0723102 | + | 0.125245i | ||||
\(766\) | 18.0000 | − | 31.1769i | 0.650366 | − | 1.12647i | ||||
\(767\) | 6.00000 | 0.216647 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 16.5000 | − | 28.5788i | 0.595005 | − | 1.03058i | −0.398541 | − | 0.917151i | \(-0.630483\pi\) |
0.993546 | − | 0.113429i | \(-0.0361834\pi\) | |||||||
\(770\) | −1.00000 | + | 1.73205i | −0.0360375 | + | 0.0624188i | ||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 25.0000 | 0.899770 | ||||||||
\(773\) | 3.00000 | − | 5.19615i | 0.107903 | − | 0.186893i | −0.807018 | − | 0.590527i | \(-0.798920\pi\) |
0.914920 | + | 0.403634i | \(0.132253\pi\) | |||||||
\(774\) | 2.50000 | + | 4.33013i | 0.0898606 | + | 0.155643i | ||||
\(775\) | −0.500000 | + | 0.866025i | −0.0179605 | + | 0.0311086i | ||||
\(776\) | 1.00000 | + | 1.73205i | 0.0358979 | + | 0.0621770i | ||||
\(777\) | −2.50000 | − | 4.33013i | −0.0896870 | − | 0.155342i | ||||
\(778\) | −10.0000 | −0.358517 | ||||||||
\(779\) | −1.00000 | − | 8.66025i | −0.0358287 | − | 0.310286i | ||||
\(780\) | 3.00000 | 0.107417 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12.0000 | + | 20.7846i | 0.429119 | + | 0.743256i | ||||
\(783\) | 5.00000 | − | 8.66025i | 0.178685 | − | 0.309492i | ||||
\(784\) | 3.00000 | + | 5.19615i | 0.107143 | + | 0.185577i | ||||
\(785\) | −6.50000 | + | 11.2583i | −0.231995 | + | 0.401827i | ||||
\(786\) | −6.00000 | −0.214013 | ||||||||
\(787\) | −23.0000 | −0.819861 | −0.409931 | − | 0.912117i | \(-0.634447\pi\) | ||||
−0.409931 | + | 0.912117i | \(0.634447\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | 5.00000 | − | 8.66025i | 0.178005 | − | 0.308313i | ||||
\(790\) | 11.0000 | 0.391362 | ||||||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | −1.00000 | + | 1.73205i | −0.0355335 | + | 0.0615457i | ||||
\(793\) | 7.50000 | + | 12.9904i | 0.266333 | + | 0.461302i | ||||
\(794\) | 0.500000 | − | 0.866025i | 0.0177443 | − | 0.0307341i | ||||
\(795\) | −6.00000 | − | 10.3923i | −0.212798 | − | 0.368577i | ||||
\(796\) | −2.50000 | − | 4.33013i | −0.0886102 | − | 0.153477i | ||||
\(797\) | 2.00000 | 0.0708436 | 0.0354218 | − | 0.999372i | \(-0.488723\pi\) | ||||
0.0354218 | + | 0.999372i | \(0.488723\pi\) | |||||||
\(798\) | 3.50000 | − | 2.59808i | 0.123899 | − | 0.0919709i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.0000 | − | 32.9090i | 0.670913 | − | 1.16206i | ||||
\(803\) | −11.0000 | − | 19.0526i | −0.388182 | − | 0.672350i | ||||
\(804\) | 2.50000 | − | 4.33013i | 0.0881682 | − | 0.152712i | ||||
\(805\) | −6.00000 | −0.211472 | ||||||||
\(806\) | −3.00000 | −0.105670 | ||||||||
\(807\) | −5.00000 | + | 8.66025i | −0.176008 | + | 0.304855i | ||||
\(808\) | −3.00000 | + | 5.19615i | −0.105540 | + | 0.182800i | ||||
\(809\) | 50.0000 | 1.75791 | 0.878953 | − | 0.476908i | \(-0.158243\pi\) | ||||
0.878953 | + | 0.476908i | \(0.158243\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 14.0000 | − | 24.2487i | 0.491606 | − | 0.851487i | −0.508347 | − | 0.861152i | \(-0.669743\pi\) |
0.999953 | + | 0.00966502i | \(0.00307652\pi\) | |||||||
\(812\) | −5.00000 | − | 8.66025i | −0.175466 | − | 0.303915i | ||||
\(813\) | 4.00000 | − | 6.92820i | 0.140286 | − | 0.242983i | ||||
\(814\) | 5.00000 | + | 8.66025i | 0.175250 | + | 0.303542i | ||||
\(815\) | −8.50000 | − | 14.7224i | −0.297742 | − | 0.515704i | ||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | 2.50000 | + | 21.6506i | 0.0874639 | + | 0.757460i | ||||
\(818\) | −30.0000 | −1.04893 | ||||||||
\(819\) | −1.50000 | − | 2.59808i | −0.0524142 | − | 0.0907841i | ||||
\(820\) | 1.00000 | + | 1.73205i | 0.0349215 | + | 0.0604858i | ||||
\(821\) | 5.00000 | − | 8.66025i | 0.174501 | − | 0.302245i | −0.765487 | − | 0.643451i | \(-0.777502\pi\) |
0.939989 | + | 0.341206i | \(0.110835\pi\) | |||||||
\(822\) | 1.00000 | + | 1.73205i | 0.0348790 | + | 0.0604122i | ||||
\(823\) | 22.0000 | − | 38.1051i | 0.766872 | − | 1.32826i | −0.172379 | − | 0.985031i | \(-0.555146\pi\) |
0.939251 | − | 0.343230i | \(-0.111521\pi\) | |||||||
\(824\) | 19.0000 | 0.661896 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | −1.00000 | + | 1.73205i | −0.0347945 | + | 0.0602658i | ||||
\(827\) | 11.0000 | − | 19.0526i | 0.382507 | − | 0.662522i | −0.608913 | − | 0.793237i | \(-0.708394\pi\) |
0.991420 | + | 0.130715i | \(0.0417273\pi\) | |||||||
\(828\) | −6.00000 | −0.208514 | ||||||||
\(829\) | 23.0000 | 0.798823 | 0.399412 | − | 0.916772i | \(-0.369214\pi\) | ||||
0.399412 | + | 0.916772i | \(0.369214\pi\) | |||||||
\(830\) | 1.00000 | − | 1.73205i | 0.0347105 | − | 0.0601204i | ||||
\(831\) | 5.00000 | + | 8.66025i | 0.173448 | + | 0.300421i | ||||
\(832\) | 1.50000 | − | 2.59808i | 0.0520031 | − | 0.0900721i | ||||
\(833\) | 12.0000 | + | 20.7846i | 0.415775 | + | 0.720144i | ||||
\(834\) | 4.50000 | + | 7.79423i | 0.155822 | + | 0.269892i | ||||
\(835\) | −14.0000 | −0.484490 | ||||||||
\(836\) | −7.00000 | + | 5.19615i | −0.242100 | + | 0.179713i | ||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 12.0000 | + | 20.7846i | 0.414533 | + | 0.717992i | ||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | −0.500000 | + | 0.866025i | −0.0172516 | + | 0.0298807i | ||||
\(841\) | −35.5000 | − | 61.4878i | −1.22414 | − | 2.12027i | ||||
\(842\) | 7.00000 | − | 12.1244i | 0.241236 | − | 0.417833i | ||||
\(843\) | −30.0000 | −1.03325 | ||||||||
\(844\) | −5.00000 | −0.172107 | ||||||||
\(845\) | −2.00000 | + | 3.46410i | −0.0688021 | + | 0.119169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | 0.240523 | ||||||||
\(848\) | −12.0000 | −0.412082 | ||||||||
\(849\) | −4.00000 | + | 6.92820i | −0.137280 | + | 0.237775i | ||||
\(850\) | −2.00000 | − | 3.46410i | −0.0685994 | − | 0.118818i | ||||
\(851\) | −15.0000 | + | 25.9808i | −0.514193 | + | 0.890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.50000 | + | 14.7224i | 0.291034 | + | 0.504086i | 0.974055 | − | 0.226313i | \(-0.0726672\pi\) |
−0.683020 | + | 0.730400i | \(0.739334\pi\) | |||||||
\(854\) | −5.00000 | −0.171096 | ||||||||
\(855\) | −4.00000 | − | 1.73205i | −0.136797 | − | 0.0592349i | ||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | −12.0000 | − | 20.7846i | −0.409912 | − | 0.709989i | 0.584967 | − | 0.811057i | \(-0.301107\pi\) |
−0.994880 | + | 0.101068i | \(0.967774\pi\) | |||||||
\(858\) | 3.00000 | + | 5.19615i | 0.102418 | + | 0.177394i | ||||
\(859\) | −18.5000 | + | 32.0429i | −0.631212 | + | 1.09329i | 0.356092 | + | 0.934451i | \(0.384109\pi\) |
−0.987304 | + | 0.158840i | \(0.949225\pi\) | |||||||
\(860\) | −2.50000 | − | 4.33013i | −0.0852493 | − | 0.147656i | ||||
\(861\) | 1.00000 | − | 1.73205i | 0.0340799 | − | 0.0590281i | ||||
\(862\) | −20.0000 | −0.681203 | ||||||||
\(863\) | 46.0000 | 1.56586 | 0.782929 | − | 0.622111i | \(-0.213725\pi\) | ||||
0.782929 | + | 0.622111i | \(0.213725\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −13.0000 | + | 22.5167i | −0.442013 | + | 0.765589i | ||||
\(866\) | 29.0000 | 0.985460 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0.500000 | − | 0.866025i | 0.0169711 | − | 0.0293948i | ||||
\(869\) | 11.0000 | + | 19.0526i | 0.373149 | + | 0.646314i | ||||
\(870\) | −5.00000 | + | 8.66025i | −0.169516 | + | 0.293610i | ||||
\(871\) | −7.50000 | − | 12.9904i | −0.254128 | − | 0.440162i | ||||
\(872\) | 9.00000 | + | 15.5885i | 0.304778 | + | 0.527892i | ||||
\(873\) | −2.00000 | −0.0676897 | ||||||||
\(874\) | −24.0000 | − | 10.3923i | −0.811812 | − | 0.351525i | ||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −5.50000 | − | 9.52628i | −0.185828 | − | 0.321863i | ||||
\(877\) | −7.50000 | − | 12.9904i | −0.253257 | − | 0.438654i | 0.711164 | − | 0.703027i | \(-0.248168\pi\) |
−0.964421 | + | 0.264373i | \(0.914835\pi\) | |||||||
\(878\) | 20.5000 | − | 35.5070i | 0.691841 | − | 1.19830i | ||||
\(879\) | 13.0000 | + | 22.5167i | 0.438479 | + | 0.759468i | ||||
\(880\) | 1.00000 | − | 1.73205i | 0.0337100 | − | 0.0583874i | ||||
\(881\) | 34.0000 | 1.14549 | 0.572745 | − | 0.819734i | \(-0.305879\pi\) | ||||
0.572745 | + | 0.819734i | \(0.305879\pi\) | |||||||
\(882\) | −6.00000 | −0.202031 | ||||||||
\(883\) | −15.5000 | + | 26.8468i | −0.521617 | + | 0.903466i | 0.478067 | + | 0.878323i | \(0.341337\pi\) |
−0.999684 | + | 0.0251431i | \(0.991996\pi\) | |||||||
\(884\) | 6.00000 | − | 10.3923i | 0.201802 | − | 0.349531i | ||||
\(885\) | 2.00000 | 0.0672293 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 2.50000 | + | 4.33013i | 0.0838945 | + | 0.145310i | ||||
\(889\) | 8.00000 | − | 13.8564i | 0.268311 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 18.0000 | 0.602010 | ||||||||
\(895\) | −5.00000 | − | 8.66025i | −0.167132 | − | 0.289480i | ||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | −9.00000 | + | 15.5885i | −0.300501 | + | 0.520483i | ||||
\(898\) | −14.0000 | − | 24.2487i | −0.467186 | − | 0.809190i | ||||
\(899\) | 5.00000 | − | 8.66025i | 0.166759 | − | 0.288836i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −48.0000 | −1.59911 | ||||||||
\(902\) | −2.00000 | + | 3.46410i | −0.0665927 | + | 0.115342i | ||||
\(903\) | −2.50000 | + | 4.33013i | −0.0831948 | + | 0.144098i | ||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(908\) | 9.00000 | − | 15.5885i | 0.298675 | − | 0.517321i | ||||
\(909\) | −3.00000 | − | 5.19615i | −0.0995037 | − | 0.172345i | ||||
\(910\) | 1.50000 | + | 2.59808i | 0.0497245 | + | 0.0861254i | ||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | −3.50000 | + | 2.59808i | −0.115897 | + | 0.0860309i | ||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | −11.5000 | − | 19.9186i | −0.380386 | − | 0.658848i | ||||
\(915\) | 2.50000 | + | 4.33013i | 0.0826475 | + | 0.143150i | ||||
\(916\) | 2.50000 | − | 4.33013i | 0.0826023 | − | 0.143071i | ||||
\(917\) | −3.00000 | − | 5.19615i | −0.0990687 | − | 0.171592i | ||||
\(918\) | −2.00000 | + | 3.46410i | −0.0660098 | + | 0.114332i | ||||
\(919\) | 43.0000 | 1.41844 | 0.709220 | − | 0.704988i | \(-0.249047\pi\) | ||||
0.709220 | + | 0.704988i | \(0.249047\pi\) | |||||||
\(920\) | 6.00000 | 0.197814 | ||||||||
\(921\) | −2.00000 | + | 3.46410i | −0.0659022 | + | 0.114146i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | 2.50000 | − | 4.33013i | 0.0821995 | − | 0.142374i | ||||
\(926\) | −0.500000 | − | 0.866025i | −0.0164310 | − | 0.0284594i | ||||
\(927\) | −9.50000 | + | 16.4545i | −0.312021 | + | 0.540436i | ||||
\(928\) | 5.00000 | + | 8.66025i | 0.164133 | + | 0.284287i | ||||
\(929\) | 24.0000 | + | 41.5692i | 0.787414 | + | 1.36384i | 0.927546 | + | 0.373709i | \(0.121914\pi\) |
−0.140132 | + | 0.990133i | \(0.544753\pi\) | |||||||
\(930\) | −1.00000 | −0.0327913 | ||||||||
\(931\) | −24.0000 | − | 10.3923i | −0.786568 | − | 0.340594i | ||||
\(932\) | −4.00000 | −0.131024 | ||||||||
\(933\) | 5.00000 | + | 8.66025i | 0.163693 | + | 0.283524i | ||||
\(934\) | −15.0000 | − | 25.9808i | −0.490815 | − | 0.850117i | ||||
\(935\) | 4.00000 | − | 6.92820i | 0.130814 | − | 0.226576i | ||||
\(936\) | 1.50000 | + | 2.59808i | 0.0490290 | + | 0.0849208i | ||||
\(937\) | −10.5000 | + | 18.1865i | −0.343020 | + | 0.594128i | −0.984992 | − | 0.172600i | \(-0.944783\pi\) |
0.641972 | + | 0.766728i | \(0.278117\pi\) | |||||||
\(938\) | 5.00000 | 0.163256 | ||||||||
\(939\) | 18.0000 | 0.587408 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.0000 | − | 29.4449i | 0.554184 | − | 0.959875i | −0.443782 | − | 0.896135i | \(-0.646364\pi\) |
0.997967 | − | 0.0637405i | \(-0.0203030\pi\) | |||||||
\(942\) | −13.0000 | −0.423563 | ||||||||
\(943\) | −12.0000 | −0.390774 | ||||||||
\(944\) | 1.00000 | − | 1.73205i | 0.0325472 | − | 0.0563735i | ||||
\(945\) | −0.500000 | − | 0.866025i | −0.0162650 | − | 0.0281718i | ||||
\(946\) | 5.00000 | − | 8.66025i | 0.162564 | − | 0.281569i | ||||
\(947\) | 11.0000 | + | 19.0526i | 0.357452 | + | 0.619125i | 0.987534 | − | 0.157403i | \(-0.0503122\pi\) |
−0.630082 | + | 0.776528i | \(0.716979\pi\) | |||||||
\(948\) | 5.50000 | + | 9.52628i | 0.178632 | + | 0.309399i | ||||
\(949\) | −33.0000 | −1.07123 | ||||||||
\(950\) | 4.00000 | + | 1.73205i | 0.129777 | + | 0.0561951i | ||||
\(951\) | 30.0000 | 0.972817 | ||||||||
\(952\) | 2.00000 | + | 3.46410i | 0.0648204 | + | 0.112272i | ||||
\(953\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(954\) | 6.00000 | − | 10.3923i | 0.194257 | − | 0.336463i | ||||
\(955\) | 8.00000 | + | 13.8564i | 0.258874 | + | 0.448383i | ||||
\(956\) | 9.00000 | − | 15.5885i | 0.291081 | − | 0.504167i | ||||
\(957\) | −20.0000 | −0.646508 | ||||||||
\(958\) | 42.0000 | 1.35696 | ||||||||
\(959\) | −1.00000 | + | 1.73205i | −0.0322917 | + | 0.0559308i | ||||
\(960\) | 0.500000 | − | 0.866025i | 0.0161374 | − | 0.0279508i | ||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 15.0000 | 0.483619 | ||||||||
\(963\) | 2.00000 | − | 3.46410i | 0.0644491 | − | 0.111629i | ||||
\(964\) | −2.50000 | − | 4.33013i | −0.0805196 | − | 0.139464i | ||||
\(965\) | 12.5000 | − | 21.6506i | 0.402389 | − | 0.696959i | ||||
\(966\) | −3.00000 | − | 5.19615i | −0.0965234 | − | 0.167183i | ||||
\(967\) | −14.5000 | − | 25.1147i | −0.466289 | − | 0.807635i | 0.532970 | − | 0.846134i | \(-0.321076\pi\) |
−0.999259 | + | 0.0384986i | \(0.987742\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | −14.0000 | + | 10.3923i | −0.449745 | + | 0.333849i | ||||
\(970\) | 2.00000 | 0.0642161 | ||||||||
\(971\) | 4.00000 | + | 6.92820i | 0.128366 | + | 0.222337i | 0.923044 | − | 0.384695i | \(-0.125693\pi\) |
−0.794678 | + | 0.607032i | \(0.792360\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −4.50000 | + | 7.79423i | −0.144263 | + | 0.249871i | ||||
\(974\) | −8.00000 | − | 13.8564i | −0.256337 | − | 0.443988i | ||||
\(975\) | 1.50000 | − | 2.59808i | 0.0480384 | − | 0.0832050i | ||||
\(976\) | 5.00000 | 0.160046 | ||||||||
\(977\) | −34.0000 | −1.08776 | −0.543878 | − | 0.839164i | \(-0.683045\pi\) | ||||
−0.543878 | + | 0.839164i | \(0.683045\pi\) | |||||||
\(978\) | 8.50000 | − | 14.7224i | 0.271800 | − | 0.470771i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.00000 | 0.191663 | ||||||||
\(981\) | −18.0000 | −0.574696 | ||||||||
\(982\) | −14.0000 | + | 24.2487i | −0.446758 | + | 0.773807i | ||||
\(983\) | −12.0000 | − | 20.7846i | −0.382741 | − | 0.662926i | 0.608712 | − | 0.793391i | \(-0.291686\pi\) |
−0.991453 | + | 0.130465i | \(0.958353\pi\) | |||||||
\(984\) | −1.00000 | + | 1.73205i | −0.0318788 | + | 0.0552158i | ||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | 20.0000 | + | 34.6410i | 0.636930 | + | 1.10319i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.50000 | + | 12.9904i | 0.0477214 | + | 0.413279i | ||||
\(989\) | 30.0000 | 0.953945 | ||||||||
\(990\) | 1.00000 | + | 1.73205i | 0.0317821 | + | 0.0550482i | ||||
\(991\) | −11.5000 | − | 19.9186i | −0.365310 | − | 0.632735i | 0.623516 | − | 0.781810i | \(-0.285704\pi\) |
−0.988826 | + | 0.149076i | \(0.952370\pi\) | |||||||
\(992\) | −0.500000 | + | 0.866025i | −0.0158750 | + | 0.0274963i | ||||
\(993\) | −2.50000 | − | 4.33013i | −0.0793351 | − | 0.137412i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.00000 | −0.158511 | ||||||||
\(996\) | 2.00000 | 0.0633724 | ||||||||
\(997\) | −5.50000 | + | 9.52628i | −0.174187 | + | 0.301700i | −0.939880 | − | 0.341506i | \(-0.889063\pi\) |
0.765693 | + | 0.643206i | \(0.222396\pi\) | |||||||
\(998\) | 12.5000 | − | 21.6506i | 0.395681 | − | 0.685339i | ||||
\(999\) | −5.00000 | −0.158193 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 570.2.i.b.121.1 | ✓ | 2 | |
3.2 | odd | 2 | 1710.2.l.f.1261.1 | 2 | |||
19.11 | even | 3 | inner | 570.2.i.b.391.1 | yes | 2 | |
57.11 | odd | 6 | 1710.2.l.f.1531.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.b.121.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
570.2.i.b.391.1 | yes | 2 | 19.11 | even | 3 | inner | |
1710.2.l.f.1261.1 | 2 | 3.2 | odd | 2 | |||
1710.2.l.f.1531.1 | 2 | 57.11 | odd | 6 |