Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1261,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, 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("1710.1261");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.l (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: | \(13.6544187456\) |
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: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1261.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1261 |
Dual form | 1710.2.l.f.1531.1 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −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 | 0 | ||||||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 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 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | + | 1.73205i | 0.917663 | + | 0.397360i | ||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.500000 | − | 0.866025i | 0.0944911 | − | 0.163663i | ||||
\(29\) | −5.00000 | + | 8.66025i | −0.928477 | + | 1.60817i | −0.142605 | + | 0.989780i | \(0.545548\pi\) |
−0.785872 | + | 0.618389i | \(0.787786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | + | 3.46410i | −0.342997 | + | 0.594089i | ||||
\(35\) | 0.500000 | + | 0.866025i | 0.0845154 | + | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −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 | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 1.00000 | + | 1.73205i | 0.156174 | + | 0.270501i | 0.933486 | − | 0.358614i | \(-0.116751\pi\) |
−0.777312 | + | 0.629115i | \(0.783417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 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 | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.50000 | + | 2.59808i | 0.208013 | + | 0.360288i | ||||
\(53\) | −6.00000 | + | 10.3923i | −0.824163 | + | 1.42749i | 0.0783936 | + | 0.996922i | \(0.475021\pi\) |
−0.902557 | + | 0.430570i | \(0.858312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | + | 1.73205i | 0.134840 | + | 0.233550i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.0000 | −1.31306 | ||||||||
\(59\) | −1.00000 | − | 1.73205i | −0.130189 | − | 0.225494i | 0.793560 | − | 0.608492i | \(-0.208225\pi\) |
−0.923749 | + | 0.382998i | \(0.874892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −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 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −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 | 0 | ||||||||
\(73\) | −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 | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.50000 | + | 2.59808i | −0.401478 | + | 0.298020i | ||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 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 | 0 | ||||||||
\(82\) | −1.00000 | + | 1.73205i | −0.110432 | + | 0.191273i | ||||
\(83\) | −2.00000 | −0.219529 | −0.109764 | − | 0.993958i | \(-0.535010\pi\) | ||||
−0.109764 | + | 0.993958i | \(0.535010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | − | 3.46410i | 0.216930 | − | 0.375735i | ||||
\(86\) | −2.50000 | + | 4.33013i | −0.269582 | + | 0.466930i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50000 | + | 2.59808i | −0.157243 | + | 0.272352i | ||||
\(92\) | −3.00000 | − | 5.19615i | −0.312772 | − | 0.541736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.500000 | − | 4.33013i | −0.0512989 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 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 | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 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 | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | + | 0.866025i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | 0.559503 | ||||||||
\(116\) | −5.00000 | − | 8.66025i | −0.464238 | − | 0.804084i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.00000 | − | 1.73205i | 0.0920575 | − | 0.159448i | ||||
\(119\) | −2.00000 | − | 3.46410i | −0.183340 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −5.00000 | −0.452679 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.500000 | + | 0.866025i | −0.0449013 | + | 0.0777714i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.50000 | − | 2.59808i | −0.131559 | − | 0.227866i | ||||
\(131\) | −3.00000 | − | 5.19615i | −0.262111 | − | 0.453990i | 0.704692 | − | 0.709514i | \(-0.251085\pi\) |
−0.966803 | + | 0.255524i | \(0.917752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | − | 1.73205i | −0.346844 | − | 0.150188i | ||||
\(134\) | 5.00000 | 0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | − | 3.46410i | −0.171499 | − | 0.297044i | ||||
\(137\) | −1.00000 | + | 1.73205i | −0.0854358 | + | 0.147979i | −0.905577 | − | 0.424182i | \(-0.860562\pi\) |
0.820141 | + | 0.572161i | \(0.193895\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 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 | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 5.50000 | − | 9.52628i | 0.455183 | − | 0.788400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.50000 | − | 4.33013i | 0.205499 | − | 0.355934i | ||||
\(149\) | 9.00000 | + | 15.5885i | 0.737309 | + | 1.27706i | 0.953703 | + | 0.300750i | \(0.0972370\pi\) |
−0.216394 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | −4.00000 | − | 1.73205i | −0.324443 | − | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | + | 1.73205i | 0.0805823 | + | 0.139573i | ||||
\(155\) | −0.500000 | − | 0.866025i | −0.0401610 | − | 0.0695608i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 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 | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 3.00000 | − | 5.19615i | 0.236433 | − | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.0000 | −1.33154 | −0.665771 | − | 0.746156i | \(-0.731897\pi\) | ||||
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.00000 | − | 1.73205i | −0.0776151 | − | 0.134433i | ||||
\(167\) | 7.00000 | − | 12.1244i | 0.541676 | − | 0.938211i | −0.457132 | − | 0.889399i | \(-0.651123\pi\) |
0.998808 | − | 0.0488118i | \(-0.0155435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.00000 | + | 3.46410i | 0.153846 | + | 0.266469i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.00000 | −0.381246 | ||||||||
\(173\) | −13.0000 | − | 22.5167i | −0.988372 | − | 1.71191i | −0.625871 | − | 0.779926i | \(-0.715256\pi\) |
−0.362500 | − | 0.931984i | \(-0.618077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | 1.00000 | + | 1.73205i | 0.0753778 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | − | 5.19615i | 0.221163 | − | 0.383065i | ||||
\(185\) | 2.50000 | + | 4.33013i | 0.183804 | + | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | − | 6.92820i | −0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.50000 | − | 2.59808i | 0.253917 | − | 0.188484i | ||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −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 | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −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 | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 5.00000 | − | 8.66025i | 0.350931 | − | 0.607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00000 | − | 1.73205i | 0.0698430 | − | 0.120972i | ||||
\(206\) | 9.50000 | + | 16.4545i | 0.661896 | + | 1.14644i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | −0.208013 | ||||||||
\(209\) | −8.00000 | − | 3.46410i | −0.553372 | − | 0.239617i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 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 | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.00000 | −0.0678844 | ||||||||
\(218\) | −9.00000 | + | 15.5885i | −0.609557 | + | 1.05578i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 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 | 0 | ||||||||
\(226\) | −7.00000 | − | 12.1244i | −0.465633 | − | 0.806500i | ||||
\(227\) | 18.0000 | 1.19470 | 0.597351 | − | 0.801980i | \(-0.296220\pi\) | ||||
0.597351 | + | 0.801980i | \(0.296220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −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 | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.00000 | − | 8.66025i | 0.328266 | − | 0.568574i | ||||
\(233\) | −2.00000 | − | 3.46410i | −0.131024 | − | 0.226941i | 0.793047 | − | 0.609160i | \(-0.208493\pi\) |
−0.924072 | + | 0.382219i | \(0.875160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.00000 | 0.130189 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.00000 | − | 3.46410i | 0.129641 | − | 0.224544i | ||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −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 | 0 | ||||||||
\(244\) | −2.50000 | − | 4.33013i | −0.160046 | − | 0.277208i | ||||
\(245\) | 3.00000 | + | 5.19615i | 0.191663 | + | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.5000 | − | 7.79423i | 0.668099 | − | 0.495935i | ||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −1.00000 | + | 1.73205i | −0.0631194 | + | 0.109326i | −0.895858 | − | 0.444340i | \(-0.853438\pi\) |
0.832739 | + | 0.553666i | \(0.186772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 10.3923i | 0.377217 | − | 0.653359i | ||||
\(254\) | −16.0000 | −1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.00000 | + | 5.19615i | −0.187135 | + | 0.324127i | −0.944294 | − | 0.329104i | \(-0.893253\pi\) |
0.757159 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | 0.310685 | ||||||||
\(260\) | 1.50000 | − | 2.59808i | 0.0930261 | − | 0.161126i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.00000 | − | 5.19615i | 0.185341 | − | 0.321019i | ||||
\(263\) | −5.00000 | − | 8.66025i | −0.308313 | − | 0.534014i | 0.669680 | − | 0.742650i | \(-0.266431\pi\) |
−0.977993 | + | 0.208635i | \(0.933098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 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 | 0.977229 | − | 0.212187i | \(-0.0680585\pi\) |
−0.672374 | + | 0.740212i | \(0.734725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 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 | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 1.00000 | − | 1.73205i | 0.0603023 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −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 | 0 | ||||||||
\(280\) | −0.500000 | − | 0.866025i | −0.0298807 | − | 0.0517549i | ||||
\(281\) | −15.0000 | + | 25.9808i | −0.894825 | + | 1.54988i | −0.0608039 | + | 0.998150i | \(0.519366\pi\) |
−0.834021 | + | 0.551733i | \(0.813967\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | −1.00000 | − | 1.73205i | −0.0590281 | − | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 5.00000 | + | 8.66025i | 0.293610 | + | 0.508548i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.0000 | 0.643726 | ||||||||
\(293\) | 26.0000 | 1.51894 | 0.759468 | − | 0.650545i | \(-0.225459\pi\) | ||||
0.759468 | + | 0.650545i | \(0.225459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.00000 | + | 1.73205i | −0.0582223 | + | 0.100844i | ||||
\(296\) | 5.00000 | 0.290619 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.00000 | + | 15.5885i | −0.521356 | + | 0.903015i | ||||
\(299\) | 9.00000 | + | 15.5885i | 0.520483 | + | 0.901504i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | − | 4.33013i | −0.144098 | − | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.500000 | − | 4.33013i | −0.0286770 | − | 0.248350i | ||||
\(305\) | 5.00000 | 0.286299 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −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 | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.500000 | − | 0.866025i | 0.0283981 | − | 0.0491869i | ||||
\(311\) | 10.0000 | 0.567048 | 0.283524 | − | 0.958965i | \(-0.408496\pi\) | ||||
0.283524 | + | 0.958965i | \(0.408496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −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 | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.0000 | −0.618798 | ||||||||
\(317\) | 15.0000 | − | 25.9808i | 0.842484 | − | 1.45922i | −0.0453045 | − | 0.998973i | \(-0.514426\pi\) |
0.887788 | − | 0.460252i | \(-0.152241\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.0000 | − | 17.3205i | 0.559893 | − | 0.969762i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.00000 | 0.334367 | ||||||||
\(323\) | 2.00000 | + | 17.3205i | 0.111283 | + | 0.963739i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.50000 | + | 2.59808i | 0.0832050 | + | 0.144115i | ||||
\(326\) | −8.50000 | − | 14.7224i | −0.470771 | − | 0.815400i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.00000 | − | 1.73205i | −0.0552158 | − | 0.0956365i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 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 | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.0000 | 0.766046 | ||||||||
\(335\) | −5.00000 | −0.273179 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −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 | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.00000 | + | 3.46410i | 0.108465 | + | 0.187867i | ||||
\(341\) | −2.00000 | −0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −2.50000 | − | 4.33013i | −0.134791 | − | 0.233465i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.0000 | − | 22.5167i | 0.698884 | − | 1.21050i | ||||
\(347\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0000 | 0.909989 | 0.454995 | − | 0.890494i | \(-0.349641\pi\) | ||||
0.454995 | + | 0.890494i | \(0.349641\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | + | 1.73205i | −0.0533002 | + | 0.0923186i | ||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.00000 | + | 8.66025i | 0.264258 | + | 0.457709i | ||||
\(359\) | −1.00000 | − | 1.73205i | −0.0527780 | − | 0.0914141i | 0.838429 | − | 0.545010i | \(-0.183474\pi\) |
−0.891207 | + | 0.453596i | \(0.850141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 6.00000 | 0.315353 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.50000 | − | 2.59808i | −0.0786214 | − | 0.136176i | ||||
\(365\) | −5.50000 | + | 9.52628i | −0.287883 | + | 0.498628i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 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 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.50000 | + | 4.33013i | −0.129969 | + | 0.225113i | ||||
\(371\) | 6.00000 | − | 10.3923i | 0.311504 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −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 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.0000 | + | 25.9808i | 0.772539 | + | 1.33808i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.00000 | − | 13.8564i | −0.409316 | − | 0.708955i | ||||
\(383\) | −18.0000 | − | 31.1769i | −0.919757 | − | 1.59307i | −0.799783 | − | 0.600289i | \(-0.795052\pi\) |
−0.119974 | − | 0.992777i | \(-0.538281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | − | 1.73205i | −0.0509647 | − | 0.0882735i | ||||
\(386\) | 12.5000 | − | 21.6506i | 0.636233 | − | 1.10199i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.00000 | −0.101535 | ||||||||
\(389\) | −5.00000 | + | 8.66025i | −0.253510 | + | 0.439092i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) |
0.710980 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | 6.00000 | 0.303046 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | 5.50000 | − | 9.52628i | 0.276735 | − | 0.479319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 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 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −19.0000 | − | 32.9090i | −0.948815 | − | 1.64340i | −0.747927 | − | 0.663781i | \(-0.768951\pi\) |
−0.200888 | − | 0.979614i | \(-0.564383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.50000 | − | 2.59808i | 0.0747203 | − | 0.129419i | ||||
\(404\) | 3.00000 | + | 5.19615i | 0.149256 | + | 0.258518i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.0000 | 0.496292 | ||||||||
\(407\) | 10.0000 | 0.495682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.50000 | + | 16.4545i | −0.468031 | + | 0.810654i | ||||
\(413\) | 1.00000 | + | 1.73205i | 0.0492068 | + | 0.0852286i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.00000 | + | 1.73205i | 0.0490881 | + | 0.0850230i | ||||
\(416\) | −1.50000 | − | 2.59808i | −0.0735436 | − | 0.127381i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.00000 | − | 8.66025i | −0.0489116 | − | 0.423587i | ||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.00000 | 0.241121 | ||||||||
\(431\) | −10.0000 | + | 17.3205i | −0.481683 | + | 0.834300i | −0.999779 | − | 0.0210230i | \(-0.993308\pi\) |
0.518096 | + | 0.855323i | \(0.326641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −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 | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.0000 | −0.862044 | ||||||||
\(437\) | −21.0000 | + | 15.5885i | −1.00457 | + | 0.745697i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 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 | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.00000 | + | 10.3923i | 0.285391 | + | 0.494312i | ||||
\(443\) | 6.00000 | − | 10.3923i | 0.285069 | − | 0.493753i | −0.687557 | − | 0.726130i | \(-0.741317\pi\) |
0.972626 | + | 0.232377i | \(0.0746503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.500000 | + | 0.866025i | −0.0236757 | + | 0.0410075i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −28.0000 | −1.32140 | −0.660701 | − | 0.750649i | \(-0.729741\pi\) | ||||
−0.660701 | + | 0.750649i | \(0.729741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −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 | 0 | ||||||||
\(457\) | 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 | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.00000 | + | 5.19615i | −0.139876 | + | 0.242272i | ||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 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 | 0 | ||||||||
\(466\) | 2.00000 | − | 3.46410i | 0.0926482 | − | 0.160471i | ||||
\(467\) | −30.0000 | −1.38823 | −0.694117 | − | 0.719862i | \(-0.744205\pi\) | ||||
−0.694117 | + | 0.719862i | \(0.744205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.50000 | + | 4.33013i | −0.115439 | + | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.00000 | + | 1.73205i | 0.0460287 | + | 0.0797241i | ||||
\(473\) | −5.00000 | − | 8.66025i | −0.229900 | − | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50000 | + | 2.59808i | −0.160591 | + | 0.119208i | ||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.00000 | + | 15.5885i | 0.411650 | + | 0.712999i | ||||
\(479\) | 21.0000 | − | 36.3731i | 0.959514 | − | 1.66193i | 0.235833 | − | 0.971794i | \(-0.424218\pi\) |
0.723681 | − | 0.690134i | \(-0.242449\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.50000 | + | 12.9904i | −0.341971 | + | 0.592310i | ||||
\(482\) | −5.00000 | −0.227744 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 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 | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.00000 | + | 5.19615i | −0.135526 | + | 0.234738i | ||||
\(491\) | 14.0000 | + | 24.2487i | 0.631811 | + | 1.09433i | 0.987181 | + | 0.159603i | \(0.0510215\pi\) |
−0.355370 | + | 0.934726i | \(0.615645\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.0000 | −1.80151 | ||||||||
\(494\) | 12.0000 | + | 5.19615i | 0.539906 | + | 0.233786i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.500000 | − | 0.866025i | −0.0224507 | − | 0.0388857i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.00000 | −0.0892644 | ||||||||
\(503\) | 22.0000 | − | 38.1051i | 0.980932 | − | 1.69902i | 0.322151 | − | 0.946688i | \(-0.395594\pi\) |
0.658781 | − | 0.752335i | \(-0.271072\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.00000 | − | 13.8564i | −0.354943 | − | 0.614779i | ||||
\(509\) | −4.00000 | + | 6.92820i | −0.177297 | + | 0.307087i | −0.940954 | − | 0.338535i | \(-0.890069\pi\) |
0.763657 | + | 0.645622i | \(0.223402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.50000 | + | 9.52628i | 0.243306 | + | 0.421418i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | −9.50000 | − | 16.4545i | −0.418620 | − | 0.725071i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.50000 | + | 4.33013i | 0.109844 | + | 0.190255i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | 0.131559 | ||||||||
\(521\) | −8.00000 | −0.350486 | −0.175243 | − | 0.984525i | \(-0.556071\pi\) | ||||
−0.175243 | + | 0.984525i | \(0.556071\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 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 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.00000 | − | 8.66025i | 0.218010 | − | 0.377605i | ||||
\(527\) | 2.00000 | + | 3.46410i | 0.0871214 | + | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 6.00000 | + | 10.3923i | 0.260623 | + | 0.451413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.00000 | + | 8.66025i | −0.215565 | + | 0.373370i | ||||
\(539\) | 12.0000 | 0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 9.00000 | − | 15.5885i | 0.385518 | − | 0.667736i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 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 | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.00000 | 0.0852803 | ||||||||
\(551\) | −35.0000 | + | 25.9808i | −1.49105 | + | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.50000 | − | 9.52628i | −0.233884 | − | 0.405099i | ||||
\(554\) | −5.00000 | − | 8.66025i | −0.212430 | − | 0.367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.50000 | + | 7.79423i | 0.190843 | + | 0.330549i | ||||
\(557\) | −6.00000 | + | 10.3923i | −0.254228 | + | 0.440336i | −0.964686 | − | 0.263404i | \(-0.915155\pi\) |
0.710457 | + | 0.703740i | \(0.248488\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.0000 | 0.634432 | ||||||||
\(560\) | 0.500000 | − | 0.866025i | 0.0211289 | − | 0.0365963i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.0000 | −1.26547 | ||||||||
\(563\) | −22.0000 | −0.927189 | −0.463595 | − | 0.886047i | \(-0.653441\pi\) | ||||
−0.463595 | + | 0.886047i | \(0.653441\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.00000 | + | 12.1244i | 0.294492 | + | 0.510075i | ||||
\(566\) | 4.00000 | − | 6.92820i | 0.168133 | − | 0.291214i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.00000 | − | 1.73205i | 0.0417392 | − | 0.0722944i | ||||
\(575\) | −3.00000 | − | 5.19615i | −0.125109 | − | 0.216695i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.00000 | + | 8.66025i | −0.207614 | + | 0.359597i | ||||
\(581\) | 2.00000 | 0.0829740 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | − | 20.7846i | 0.496989 | − | 0.860811i | ||||
\(584\) | 5.50000 | + | 9.52628i | 0.227592 | + | 0.394200i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.0000 | + | 22.5167i | 0.537025 | + | 0.930155i | ||||
\(587\) | 9.00000 | + | 15.5885i | 0.371470 | + | 0.643404i | 0.989792 | − | 0.142520i | \(-0.0455206\pi\) |
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | + | 1.73205i | 0.164817 | + | 0.0713679i | ||||
\(590\) | −2.00000 | −0.0823387 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.50000 | + | 4.33013i | 0.102749 | + | 0.177967i | ||||
\(593\) | 14.0000 | − | 24.2487i | 0.574911 | − | 0.995775i | −0.421140 | − | 0.906996i | \(-0.638370\pi\) |
0.996051 | − | 0.0887797i | \(-0.0282967\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | + | 3.46410i | −0.0819920 | + | 0.142014i | ||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.00000 | + | 15.5885i | −0.368037 | + | 0.637459i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.50000 | + | 6.06218i | 0.142295 | + | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −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 | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.50000 | + | 4.33013i | 0.101222 | + | 0.175322i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 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 | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | 12.0000 | − | 20.7846i | 0.483102 | − | 0.836757i | −0.516710 | − | 0.856161i | \(-0.672843\pi\) |
0.999812 | + | 0.0194037i | \(0.00617676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.0000 | −1.16561 | −0.582804 | − | 0.812613i | \(-0.698045\pi\) | ||||
−0.582804 | + | 0.812613i | \(0.698045\pi\) | |||||||
\(620\) | 1.00000 | 0.0401610 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.00000 | + | 8.66025i | 0.200482 | + | 0.347245i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −18.0000 | −0.719425 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.0000 | −0.518756 | ||||||||
\(629\) | −10.0000 | − | 17.3205i | −0.398726 | − | 0.690614i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.0000 | 1.19145 | ||||||||
\(635\) | 16.0000 | 0.634941 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −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 | 0.999556 | − | 0.0297987i | \(-0.00948663\pi\) |
−0.525584 | + | 0.850741i | \(0.676153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −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 | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.0000 | + | 10.3923i | −0.550823 | + | 0.408880i | ||||
\(647\) | −46.0000 | −1.80845 | −0.904223 | − | 0.427060i | \(-0.859549\pi\) | ||||
−0.904223 | + | 0.427060i | \(0.859549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.00000 | + | 3.46410i | 0.0785069 | + | 0.135978i | ||||
\(650\) | −1.50000 | + | 2.59808i | −0.0588348 | + | 0.101905i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.50000 | − | 14.7224i | 0.332886 | − | 0.576575i | ||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | + | 5.19615i | −0.117220 | + | 0.203030i | ||||
\(656\) | 1.00000 | − | 1.73205i | 0.0390434 | − | 0.0676252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.00000 | − | 15.5885i | 0.350590 | − | 0.607240i | −0.635763 | − | 0.771885i | \(-0.719314\pi\) |
0.986353 | + | 0.164644i | \(0.0526477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −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 | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.00000 | 0.0776151 | ||||||||
\(665\) | 0.500000 | + | 4.33013i | 0.0193892 | + | 0.167915i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.0000 | − | 51.9615i | −1.16160 | − | 2.01196i | ||||
\(668\) | 7.00000 | + | 12.1244i | 0.270838 | + | 0.469105i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.50000 | − | 4.33013i | −0.0965834 | − | 0.167287i | ||||
\(671\) | 5.00000 | − | 8.66025i | 0.193023 | − | 0.334325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −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 | 0 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | −48.0000 | −1.84479 | −0.922395 | − | 0.386248i | \(-0.873771\pi\) | ||||
−0.922395 | + | 0.386248i | \(0.873771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | −2.00000 | + | 3.46410i | −0.0766965 | + | 0.132842i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.00000 | − | 1.73205i | −0.0382920 | − | 0.0663237i | ||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 6.50000 | + | 11.2583i | 0.248171 | + | 0.429845i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.50000 | − | 4.33013i | 0.0953116 | − | 0.165085i | ||||
\(689\) | 18.0000 | + | 31.1769i | 0.685745 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | 0.152167 | 0.0760836 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760836 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(692\) | 26.0000 | 0.988372 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.00000 | −0.341389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | + | 6.92820i | −0.151511 | + | 0.262424i | ||||
\(698\) | 8.50000 | + | 14.7224i | 0.321730 | + | 0.557252i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.500000 | + | 0.866025i | 0.0188982 | + | 0.0327327i | ||||
\(701\) | 14.0000 | + | 24.2487i | 0.528773 | + | 0.915861i | 0.999437 | + | 0.0335489i | \(0.0106809\pi\) |
−0.470664 | + | 0.882312i | \(0.655986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −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 | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.00000 | + | 5.19615i | −0.112351 | + | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | −5.00000 | + | 8.66025i | −0.186859 | + | 0.323649i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.00000 | − | 1.73205i | 0.0373197 | − | 0.0646396i | ||||
\(719\) | 13.0000 | + | 22.5167i | 0.484818 | + | 0.839730i | 0.999848 | − | 0.0174426i | \(-0.00555244\pi\) |
−0.515030 | + | 0.857172i | \(0.672219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.0000 | −0.707597 | ||||||||
\(722\) | −5.50000 | + | 18.1865i | −0.204689 | + | 0.676833i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.00000 | + | 5.19615i | 0.111494 | + | 0.193113i | ||||
\(725\) | −5.00000 | − | 8.66025i | −0.185695 | − | 0.321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 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 | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.0000 | −0.407128 | ||||||||
\(731\) | −10.0000 | + | 17.3205i | −0.369863 | + | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | 7.00000 | 0.258375 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | −5.00000 | + | 8.66025i | −0.184177 | + | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | 3.00000 | + | 5.19615i | 0.110059 | + | 0.190628i | 0.915794 | − | 0.401648i | \(-0.131563\pi\) |
−0.805735 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 15.5885i | 0.329734 | − | 0.571117i | ||||
\(746\) | −11.0000 | − | 19.0526i | −0.402739 | − | 0.697564i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.00000 | 0.292509 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.0000 | + | 25.9808i | −0.546268 | + | 0.946164i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 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 | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.500000 | + | 4.33013i | 0.0181369 | + | 0.157070i | ||||
\(761\) | −10.0000 | −0.362500 | −0.181250 | − | 0.983437i | \(-0.558014\pi\) | ||||
−0.181250 | + | 0.983437i | \(0.558014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.00000 | − | 15.5885i | −0.325822 | − | 0.564340i | ||||
\(764\) | 8.00000 | − | 13.8564i | 0.289430 | − | 0.501307i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0000 | − | 31.1769i | 0.650366 | − | 1.12647i | ||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 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 | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.0000 | 0.899770 | ||||||||
\(773\) | −3.00000 | + | 5.19615i | −0.107903 | + | 0.186893i | −0.914920 | − | 0.403634i | \(-0.867747\pi\) |
0.807018 | + | 0.590527i | \(0.201080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.500000 | + | 0.866025i | −0.0179605 | + | 0.0311086i | ||||
\(776\) | −1.00000 | − | 1.73205i | −0.0358979 | − | 0.0621770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.0000 | −0.358517 | ||||||||
\(779\) | 1.00000 | + | 8.66025i | 0.0358287 | + | 0.310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −12.0000 | − | 20.7846i | −0.429119 | − | 0.743256i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | + | 5.19615i | 0.107143 | + | 0.185577i | ||||
\(785\) | 6.50000 | − | 11.2583i | 0.231995 | − | 0.401827i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −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 | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.0000 | 0.391362 | ||||||||
\(791\) | 14.0000 | 0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.50000 | + | 12.9904i | 0.266333 | + | 0.461302i | ||||
\(794\) | −0.500000 | + | 0.866025i | −0.0177443 | + | 0.0307341i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.50000 | − | 4.33013i | −0.0886102 | − | 0.153477i | ||||
\(797\) | −2.00000 | −0.0708436 | −0.0354218 | − | 0.999372i | \(-0.511277\pi\) | ||||
−0.0354218 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 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 | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.00000 | −0.211472 | ||||||||
\(806\) | 3.00000 | 0.105670 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.00000 | + | 5.19615i | −0.105540 | + | 0.182800i | ||||
\(809\) | −50.0000 | −1.75791 | −0.878953 | − | 0.476908i | \(-0.841757\pi\) | ||||
−0.878953 | + | 0.476908i | \(0.841757\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.00000 | + | 8.66025i | 0.175250 | + | 0.303542i | ||||
\(815\) | 8.50000 | + | 14.7224i | 0.297742 | + | 0.515704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.50000 | + | 21.6506i | 0.0874639 | + | 0.757460i | ||||
\(818\) | 30.0000 | 1.04893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.00000 | + | 1.73205i | 0.0349215 | + | 0.0604858i | ||||
\(821\) | −5.00000 | + | 8.66025i | −0.174501 | + | 0.302245i | −0.939989 | − | 0.341206i | \(-0.889165\pi\) |
0.765487 | + | 0.643451i | \(0.222498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.00000 | + | 1.73205i | −0.0347945 | + | 0.0602658i | ||||
\(827\) | −11.0000 | + | 19.0526i | −0.382507 | + | 0.662522i | −0.991420 | − | 0.130715i | \(-0.958273\pi\) |
0.608913 | + | 0.793237i | \(0.291606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 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 | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.50000 | − | 2.59808i | 0.0520031 | − | 0.0900721i | ||||
\(833\) | −12.0000 | − | 20.7846i | −0.415775 | − | 0.720144i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0000 | −0.484490 | ||||||||
\(836\) | 7.00000 | − | 5.19615i | 0.242100 | − | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | 0 | ||||||||
\(841\) | −35.5000 | − | 61.4878i | −1.22414 | − | 2.12027i | ||||
\(842\) | −7.00000 | + | 12.1244i | −0.241236 | + | 0.417833i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −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 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 12.0000 | + | 20.7846i | 0.409912 | + | 0.709989i | 0.994880 | − | 0.101068i | \(-0.0322260\pi\) |
−0.584967 | + | 0.811057i | \(0.698893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −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 | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.0000 | −0.681203 | ||||||||
\(863\) | −46.0000 | −1.56586 | −0.782929 | − | 0.622111i | \(-0.786275\pi\) | ||||
−0.782929 | + | 0.622111i | \(0.786275\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.0000 | + | 22.5167i | −0.442013 | + | 0.765589i | ||||
\(866\) | −29.0000 | −0.985460 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.500000 | − | 0.866025i | 0.0169711 | − | 0.0293948i | ||||
\(869\) | −11.0000 | − | 19.0526i | −0.373149 | − | 0.646314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.50000 | − | 12.9904i | −0.254128 | − | 0.440162i | ||||
\(872\) | −9.00000 | − | 15.5885i | −0.304778 | − | 0.527892i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.0000 | − | 10.3923i | −0.811812 | − | 0.351525i | ||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −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 | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.00000 | − | 1.73205i | 0.0337100 | − | 0.0583874i | ||||
\(881\) | −34.0000 | −1.14549 | −0.572745 | − | 0.819734i | \(-0.694121\pi\) | ||||
−0.572745 | + | 0.819734i | \(0.694121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −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 | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | − | 13.8564i | 0.268311 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.00000 | − | 8.66025i | −0.167132 | − | 0.289480i | ||||
\(896\) | −0.500000 | − | 0.866025i | −0.0167038 | − | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.0000 | − | 24.2487i | −0.467186 | − | 0.809190i | ||||
\(899\) | −5.00000 | + | 8.66025i | −0.166759 | + | 0.288836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0000 | −1.59911 | ||||||||
\(902\) | 2.00000 | − | 3.46410i | 0.0665927 | − | 0.115342i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.50000 | + | 2.59808i | 0.0497245 | + | 0.0861254i | ||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 11.5000 | + | 19.9186i | 0.380386 | + | 0.658848i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.50000 | − | 4.33013i | 0.0826023 | − | 0.143071i | ||||
\(917\) | 3.00000 | + | 5.19615i | 0.0990687 | + | 0.171592i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.0000 | 1.41844 | 0.709220 | − | 0.704988i | \(-0.249047\pi\) | ||||
0.709220 | + | 0.704988i | \(0.249047\pi\) | |||||||
\(920\) | −6.00000 | −0.197814 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.50000 | − | 4.33013i | 0.0821995 | − | 0.142374i | ||||
\(926\) | 0.500000 | + | 0.866025i | 0.0164310 | + | 0.0284594i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.00000 | + | 8.66025i | 0.164133 | + | 0.284287i | ||||
\(929\) | −24.0000 | − | 41.5692i | −0.787414 | − | 1.36384i | −0.927546 | − | 0.373709i | \(-0.878086\pi\) |
0.140132 | − | 0.990133i | \(-0.455247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0000 | − | 10.3923i | −0.786568 | − | 0.340594i | ||||
\(932\) | 4.00000 | 0.131024 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.0000 | − | 25.9808i | −0.490815 | − | 0.850117i | ||||
\(935\) | −4.00000 | + | 6.92820i | −0.130814 | + | 0.226576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.0000 | + | 29.4449i | −0.554184 | + | 0.959875i | 0.443782 | + | 0.896135i | \(0.353636\pi\) |
−0.997967 | + | 0.0637405i | \(0.979697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0000 | −0.390774 | ||||||||
\(944\) | −1.00000 | + | 1.73205i | −0.0325472 | + | 0.0563735i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.00000 | − | 8.66025i | 0.162564 | − | 0.281569i | ||||
\(947\) | −11.0000 | − | 19.0526i | −0.357452 | − | 0.619125i | 0.630082 | − | 0.776528i | \(-0.283021\pi\) |
−0.987534 | + | 0.157403i | \(0.949688\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.0000 | −1.07123 | ||||||||
\(950\) | −4.00000 | − | 1.73205i | −0.129777 | − | 0.0561951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.00000 | + | 3.46410i | 0.0648204 | + | 0.112272i | ||||
\(953\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | + | 13.8564i | 0.258874 | + | 0.448383i | ||||
\(956\) | −9.00000 | + | 15.5885i | −0.291081 | + | 0.504167i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 42.0000 | 1.35696 | ||||||||
\(959\) | 1.00000 | − | 1.73205i | 0.0322917 | − | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | −15.0000 | −0.483619 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.50000 | − | 4.33013i | −0.0805196 | − | 0.139464i | ||||
\(965\) | −12.5000 | + | 21.6506i | −0.402389 | + | 0.696959i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.00000 | 0.0642161 | ||||||||
\(971\) | −4.00000 | − | 6.92820i | −0.128366 | − | 0.222337i | 0.794678 | − | 0.607032i | \(-0.207640\pi\) |
−0.923044 | + | 0.384695i | \(0.874307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.50000 | + | 7.79423i | −0.144263 | + | 0.249871i | ||||
\(974\) | 8.00000 | + | 13.8564i | 0.256337 | + | 0.443988i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.00000 | 0.160046 | ||||||||
\(977\) | 34.0000 | 1.08776 | 0.543878 | − | 0.839164i | \(-0.316955\pi\) | ||||
0.543878 | + | 0.839164i | \(0.316955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.0000 | + | 24.2487i | −0.446758 | + | 0.773807i | ||||
\(983\) | 12.0000 | + | 20.7846i | 0.382741 | + | 0.662926i | 0.991453 | − | 0.130465i | \(-0.0416470\pi\) |
−0.608712 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −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 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.00000 | 0.158511 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −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 | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1710.2.l.f.1261.1 | 2 | ||
3.2 | odd | 2 | 570.2.i.b.121.1 | ✓ | 2 | ||
19.11 | even | 3 | inner | 1710.2.l.f.1531.1 | 2 | ||
57.11 | odd | 6 | 570.2.i.b.391.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.b.121.1 | ✓ | 2 | 3.2 | odd | 2 | ||
570.2.i.b.391.1 | yes | 2 | 57.11 | odd | 6 | ||
1710.2.l.f.1261.1 | 2 | 1.1 | even | 1 | trivial | ||
1710.2.l.f.1531.1 | 2 | 19.11 | even | 3 | inner |