Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(539,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.539");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 539.35 | ||
Character | \(\chi\) | \(=\) | 1080.539 |
Dual form | 1080.2.m.c.539.33 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.957850 | + | 1.04044i | 0.677302 | + | 0.735705i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.165046 | + | 1.99318i | −0.0825231 | + | 0.996589i | ||||
\(5\) | −0.214370 | − | 2.22577i | −0.0958692 | − | 0.995394i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.80642 | −1.06073 | −0.530363 | − | 0.847770i | \(-0.677945\pi\) | ||||
−0.530363 | + | 0.847770i | \(0.677945\pi\) | |||||||
\(8\) | −2.23188 | + | 1.73744i | −0.789089 | + | 0.614279i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.11045 | − | 2.35499i | 0.667384 | − | 0.744714i | ||||
\(11\) | 2.27115i | 0.684777i | 0.939559 | + | 0.342388i | \(0.111236\pi\) | ||||
−0.939559 | + | 0.342388i | \(0.888764\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.91324 | −1.08534 | −0.542669 | − | 0.839946i | \(-0.682586\pi\) | ||||
−0.542669 | + | 0.839946i | \(0.682586\pi\) | |||||||
\(14\) | −2.68813 | − | 2.91992i | −0.718433 | − | 0.780382i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.94552 | − | 0.657933i | −0.986380 | − | 0.164483i | ||||
\(17\) | −1.00493 | −0.243731 | −0.121866 | − | 0.992547i | \(-0.538888\pi\) | ||||
−0.121866 | + | 0.992547i | \(0.538888\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.82621 | 0.418961 | 0.209481 | − | 0.977813i | \(-0.432823\pi\) | ||||
0.209481 | + | 0.977813i | \(0.432823\pi\) | |||||||
\(20\) | 4.47173 | − | 0.0599231i | 0.999910 | − | 0.0133992i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.36300 | + | 2.17542i | −0.503794 | + | 0.463801i | ||||
\(23\) | − | 1.93778i | − | 0.404054i | −0.979380 | − | 0.202027i | \(-0.935247\pi\) | ||
0.979380 | − | 0.202027i | \(-0.0647529\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.90809 | + | 0.954277i | −0.981618 | + | 0.190855i | ||||
\(26\) | −3.74830 | − | 4.07151i | −0.735102 | − | 0.798489i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.463189 | − | 5.59370i | 0.0875345 | − | 1.05711i | ||||
\(29\) | −7.74448 | −1.43811 | −0.719057 | − | 0.694951i | \(-0.755426\pi\) | ||||
−0.719057 | + | 0.694951i | \(0.755426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.94024i | − | 0.707689i | −0.935304 | − | 0.353844i | \(-0.884874\pi\) | ||
0.935304 | − | 0.353844i | \(-0.115126\pi\) | |||||||
\(32\) | −3.09467 | − | 4.73529i | −0.547066 | − | 0.837089i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.962571 | − | 1.04557i | −0.165080 | − | 0.179314i | ||||
\(35\) | 0.601613 | + | 6.24644i | 0.101691 | + | 1.05584i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.82415 | −1.45068 | −0.725341 | − | 0.688390i | \(-0.758318\pi\) | ||||
−0.725341 | + | 0.688390i | \(0.758318\pi\) | |||||||
\(38\) | 1.74923 | + | 1.90007i | 0.283763 | + | 0.308232i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.34560 | + | 4.59519i | 0.687099 | + | 0.726563i | ||||
\(41\) | 2.23967i | 0.349778i | 0.984588 | + | 0.174889i | \(0.0559566\pi\) | ||||
−0.984588 | + | 0.174889i | \(0.944043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.7263i | − | 1.78824i | −0.447829 | − | 0.894119i | \(-0.647803\pi\) | ||
0.447829 | − | 0.894119i | \(-0.352197\pi\) | |||||||
\(44\) | −4.52680 | − | 0.374844i | −0.682441 | − | 0.0565099i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.01615 | − | 1.85610i | 0.297265 | − | 0.273667i | ||||
\(47\) | 6.26994i | 0.914564i | 0.889322 | + | 0.457282i | \(0.151177\pi\) | ||||
−0.889322 | + | 0.457282i | \(0.848823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.875992 | 0.125142 | ||||||||
\(50\) | −5.69409 | − | 4.19254i | −0.805265 | − | 0.592914i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.645866 | − | 7.79979i | 0.0895655 | − | 1.08164i | ||||
\(53\) | 6.73830i | 0.925576i | 0.886469 | + | 0.462788i | \(0.153151\pi\) | ||||
−0.886469 | + | 0.462788i | \(0.846849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.05505 | − | 0.486866i | 0.681623 | − | 0.0656490i | ||||
\(56\) | 6.26359 | − | 4.87600i | 0.837008 | − | 0.651583i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.41805 | − | 8.05769i | −0.974038 | − | 1.05803i | ||||
\(59\) | 11.4611i | 1.49211i | 0.665885 | + | 0.746055i | \(0.268054\pi\) | ||||
−0.665885 | + | 0.746055i | \(0.731946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.08558i | 0.523105i | 0.965189 | + | 0.261553i | \(0.0842345\pi\) | ||||
−0.965189 | + | 0.261553i | \(0.915765\pi\) | |||||||
\(62\) | 4.09960 | − | 3.77416i | 0.520650 | − | 0.479319i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.96257 | − | 7.75553i | 0.245321 | − | 0.969442i | ||||
\(65\) | 0.838883 | + | 8.70998i | 0.104051 | + | 1.08034i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.94219i | − | 0.848123i | −0.905633 | − | 0.424062i | \(-0.860604\pi\) | ||
0.905633 | − | 0.424062i | \(-0.139396\pi\) | |||||||
\(68\) | 0.165860 | − | 2.00300i | 0.0201135 | − | 0.242900i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.92282 | + | 6.60910i | −0.707912 | + | 0.789938i | ||||
\(71\) | 7.36200 | 0.873709 | 0.436854 | − | 0.899532i | \(-0.356092\pi\) | ||||
0.436854 | + | 0.899532i | \(0.356092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.13736i | − | 0.601283i | −0.953737 | − | 0.300641i | \(-0.902799\pi\) | ||
0.953737 | − | 0.300641i | \(-0.0972007\pi\) | |||||||
\(74\) | −8.45222 | − | 9.18104i | −0.982550 | − | 1.06727i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.301409 | + | 3.63996i | −0.0345740 | + | 0.417532i | ||||
\(77\) | − | 6.37379i | − | 0.726361i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.14620i | 0.466484i | 0.972419 | + | 0.233242i | \(0.0749335\pi\) | ||||
−0.972419 | + | 0.233242i | \(0.925066\pi\) | |||||||
\(80\) | −0.618605 | + | 8.92285i | −0.0691622 | + | 0.997605i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.33025 | + | 2.14527i | −0.257333 | + | 0.236905i | ||||
\(83\) | −14.8166 | −1.62633 | −0.813167 | − | 0.582031i | \(-0.802258\pi\) | ||||
−0.813167 | + | 0.582031i | \(0.802258\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.215427 | + | 2.23674i | 0.0233663 | + | 0.242608i | ||||
\(86\) | 12.2005 | − | 11.2320i | 1.31562 | − | 1.21118i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.94599 | − | 5.06893i | −0.420644 | − | 0.540350i | ||||
\(89\) | 4.82493i | 0.511442i | 0.966751 | + | 0.255721i | \(0.0823128\pi\) | ||||
−0.966751 | + | 0.255721i | \(0.917687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9822 | 1.15125 | ||||||||
\(92\) | 3.86233 | + | 0.319823i | 0.402676 | + | 0.0333438i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.52352 | + | 6.00566i | −0.672849 | + | 0.619437i | ||||
\(95\) | −0.391485 | − | 4.06472i | −0.0401655 | − | 0.417031i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9168i | 1.51457i | 0.653084 | + | 0.757285i | \(0.273475\pi\) | ||||
−0.653084 | + | 0.757285i | \(0.726525\pi\) | |||||||
\(98\) | 0.839069 | + | 0.911421i | 0.0847588 | + | 0.0920674i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.09198 | − | 9.94020i | −0.109198 | − | 0.994020i | ||||
\(101\) | 14.9650 | 1.48907 | 0.744534 | − | 0.667584i | \(-0.232672\pi\) | ||||
0.744534 | + | 0.667584i | \(0.232672\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5719 | 1.04168 | 0.520839 | − | 0.853655i | \(-0.325619\pi\) | ||||
0.520839 | + | 0.853655i | \(0.325619\pi\) | |||||||
\(104\) | 8.73389 | − | 6.79905i | 0.856428 | − | 0.666701i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.01082 | + | 6.45428i | −0.680951 | + | 0.626895i | ||||
\(107\) | 15.5918 | 1.50731 | 0.753657 | − | 0.657268i | \(-0.228288\pi\) | ||||
0.753657 | + | 0.657268i | \(0.228288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.9241i | − | 1.04634i | −0.852227 | − | 0.523172i | \(-0.824749\pi\) | ||
0.852227 | − | 0.523172i | \(-0.175251\pi\) | |||||||
\(110\) | 5.34854 | + | 4.79315i | 0.509963 | + | 0.457009i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.0728 | + | 1.84644i | 1.04628 | + | 0.174472i | ||||
\(113\) | 12.8613 | 1.20989 | 0.604943 | − | 0.796269i | \(-0.293196\pi\) | ||||
0.604943 | + | 0.796269i | \(0.293196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.31304 | + | 0.415401i | −0.402193 | + | 0.0387364i | ||||
\(116\) | 1.27820 | − | 15.4361i | 0.118678 | − | 1.43321i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.9246 | + | 10.9780i | −1.09775 | + | 1.01061i | ||||
\(119\) | 2.82025 | 0.258532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.84189 | 0.531081 | ||||||||
\(122\) | −4.25082 | + | 3.91338i | −0.384851 | + | 0.354301i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.85361 | + | 0.650323i | 0.705275 | + | 0.0584007i | ||||
\(125\) | 3.17615 | + | 10.7197i | 0.284083 | + | 0.958800i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.75296 | 0.510493 | 0.255246 | − | 0.966876i | \(-0.417843\pi\) | ||||
0.255246 | + | 0.966876i | \(0.417843\pi\) | |||||||
\(128\) | 9.94905 | − | 5.38669i | 0.879380 | − | 0.476121i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.25872 | + | 9.21566i | −0.724337 | + | 0.808267i | ||||
\(131\) | − | 5.24118i | − | 0.457924i | −0.973435 | − | 0.228962i | \(-0.926467\pi\) | ||
0.973435 | − | 0.228962i | \(-0.0735332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.12511 | −0.444403 | ||||||||
\(134\) | 7.22296 | − | 6.64958i | 0.623968 | − | 0.574436i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.24288 | − | 1.74601i | 0.192325 | − | 0.149719i | ||||
\(137\) | −20.3736 | −1.74063 | −0.870317 | − | 0.492493i | \(-0.836086\pi\) | ||||
−0.870317 | + | 0.492493i | \(0.836086\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.3603 | −1.64212 | −0.821058 | − | 0.570844i | \(-0.806616\pi\) | ||||
−0.821058 | + | 0.570844i | \(0.806616\pi\) | |||||||
\(140\) | −12.5496 | + | 0.168170i | −1.06063 | + | 0.0142129i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.05169 | + | 7.65975i | 0.591765 | + | 0.642792i | ||||
\(143\) | − | 8.88755i | − | 0.743215i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.66019 | + | 17.2374i | 0.137871 | + | 1.43149i | ||||
\(146\) | 5.34514 | − | 4.92082i | 0.442367 | − | 0.407250i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.45639 | − | 17.5881i | 0.119715 | − | 1.44573i | ||||
\(149\) | 3.99973 | 0.327671 | 0.163835 | − | 0.986488i | \(-0.447613\pi\) | ||||
0.163835 | + | 0.986488i | \(0.447613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.5259i | 1.26348i | 0.775179 | + | 0.631741i | \(0.217659\pi\) | ||||
−0.775179 | + | 0.631741i | \(0.782341\pi\) | |||||||
\(152\) | −4.07588 | + | 3.17294i | −0.330597 | + | 0.257359i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.63157 | − | 6.10514i | 0.534387 | − | 0.491966i | ||||
\(155\) | −8.77007 | + | 0.844671i | −0.704429 | + | 0.0678456i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.6637 | −1.32991 | −0.664953 | − | 0.746885i | \(-0.731549\pi\) | ||||
−0.664953 | + | 0.746885i | \(0.731549\pi\) | |||||||
\(158\) | −4.31389 | + | 3.97144i | −0.343195 | + | 0.315951i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.87626 | + | 7.90313i | −0.780787 | + | 0.624798i | ||||
\(161\) | 5.43821i | 0.428591i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.3943i | − | 1.20578i | −0.797826 | − | 0.602888i | \(-0.794017\pi\) | ||
0.797826 | − | 0.602888i | \(-0.205983\pi\) | |||||||
\(164\) | −4.46406 | − | 0.369649i | −0.348585 | − | 0.0288648i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.1921 | − | 15.4158i | −1.10152 | − | 1.19650i | ||||
\(167\) | 6.44853i | 0.499002i | 0.968374 | + | 0.249501i | \(0.0802667\pi\) | ||||
−0.968374 | + | 0.249501i | \(0.919733\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.31348 | 0.177960 | ||||||||
\(170\) | −2.12085 | + | 2.36660i | −0.162662 | + | 0.181510i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 23.3725 | + | 1.93538i | 1.78214 | + | 0.147571i | ||||
\(173\) | − | 7.88649i | − | 0.599599i | −0.954002 | − | 0.299799i | \(-0.903080\pi\) | ||
0.954002 | − | 0.299799i | \(-0.0969198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.7742 | − | 2.67810i | 1.04123 | − | 0.202445i | ||||
\(176\) | 1.49426 | − | 8.96086i | 0.112634 | − | 0.675450i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.02007 | + | 4.62156i | −0.376270 | + | 0.346401i | ||||
\(179\) | 14.3041i | 1.06914i | 0.845124 | + | 0.534571i | \(0.179527\pi\) | ||||
−0.845124 | + | 0.534571i | \(0.820473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.0087i | − | 1.63589i | −0.575293 | − | 0.817947i | \(-0.695112\pi\) | ||
0.575293 | − | 0.817947i | \(-0.304888\pi\) | |||||||
\(182\) | 10.5193 | + | 11.4264i | 0.779743 | + | 0.846979i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.36678 | + | 4.32488i | 0.248202 | + | 0.318835i | ||||
\(185\) | 1.89164 | + | 19.6405i | 0.139076 | + | 1.44400i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.28234i | − | 0.166901i | ||||||
\(188\) | −12.4971 | − | 1.03483i | −0.911445 | − | 0.0754727i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.85413 | − | 4.30071i | 0.279608 | − | 0.312006i | ||||
\(191\) | −3.10330 | −0.224547 | −0.112273 | − | 0.993677i | \(-0.535813\pi\) | ||||
−0.112273 | + | 0.993677i | \(0.535813\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.0217i | 1.36921i | 0.728912 | + | 0.684607i | \(0.240026\pi\) | ||||
−0.728912 | + | 0.684607i | \(0.759974\pi\) | |||||||
\(194\) | −15.5201 | + | 14.2880i | −1.11428 | + | 1.02582i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.144579 | + | 1.74601i | −0.0103271 | + | 0.124715i | ||||
\(197\) | − | 11.6269i | − | 0.828382i | −0.910190 | − | 0.414191i | \(-0.864065\pi\) | ||
0.910190 | − | 0.414191i | \(-0.135935\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.80420i | 0.411449i | 0.978610 | + | 0.205725i | \(0.0659551\pi\) | ||||
−0.978610 | + | 0.205725i | \(0.934045\pi\) | |||||||
\(200\) | 9.29626 | − | 10.6574i | 0.657345 | − | 0.753590i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.3342 | + | 15.5702i | 1.00855 | + | 1.09552i | ||||
\(203\) | 21.7343 | 1.52545 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.98499 | − | 0.480119i | 0.348167 | − | 0.0335329i | ||||
\(206\) | 10.1263 | + | 10.9994i | 0.705531 | + | 0.766367i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.4398 | + | 2.57465i | 1.07056 | + | 0.178520i | ||||
\(209\) | 4.14759i | 0.286895i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.88390 | −0.611593 | −0.305797 | − | 0.952097i | \(-0.598923\pi\) | ||||
−0.305797 | + | 0.952097i | \(0.598923\pi\) | |||||||
\(212\) | −13.4306 | − | 1.11213i | −0.922419 | − | 0.0763814i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.9346 | + | 16.2224i | 1.02091 | + | 1.10894i | ||||
\(215\) | −26.1000 | + | 2.51376i | −1.78000 | + | 0.171437i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.0580i | 0.750665i | ||||||||
\(218\) | 11.3660 | − | 10.4637i | 0.769800 | − | 0.708691i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.136094 | + | 10.1560i | 0.00917548 | + | 0.684715i | ||||
\(221\) | 3.93253 | 0.264531 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6483 | 1.18182 | 0.590909 | − | 0.806738i | \(-0.298769\pi\) | ||||
0.590909 | + | 0.806738i | \(0.298769\pi\) | |||||||
\(224\) | 8.68495 | + | 13.2892i | 0.580288 | + | 0.887923i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.3192 | + | 13.3814i | 0.819458 | + | 0.890119i | ||||
\(227\) | −13.0114 | −0.863599 | −0.431799 | − | 0.901970i | \(-0.642121\pi\) | ||||
−0.431799 | + | 0.901970i | \(0.642121\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.6611i | 1.36532i | 0.730735 | + | 0.682662i | \(0.239178\pi\) | ||||
−0.730735 | + | 0.682662i | \(0.760822\pi\) | |||||||
\(230\) | −4.56345 | − | 4.08958i | −0.300905 | − | 0.269659i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.2847 | − | 13.4556i | 1.13480 | − | 0.883404i | ||||
\(233\) | −8.92752 | −0.584861 | −0.292431 | − | 0.956287i | \(-0.594464\pi\) | ||||
−0.292431 | + | 0.956287i | \(0.594464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9554 | − | 1.34409i | 0.910352 | − | 0.0876786i | ||||
\(236\) | −22.8440 | − | 1.89161i | −1.48702 | − | 0.123134i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.70138 | + | 2.93431i | 0.175104 | + | 0.190203i | ||||
\(239\) | 3.02879 | 0.195916 | 0.0979580 | − | 0.995191i | \(-0.468769\pi\) | ||||
0.0979580 | + | 0.995191i | \(0.468769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.1141 | −1.10242 | −0.551209 | − | 0.834367i | \(-0.685833\pi\) | ||||
−0.551209 | + | 0.834367i | \(0.685833\pi\) | |||||||
\(242\) | 5.59565 | + | 6.07816i | 0.359702 | + | 0.390719i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.14330 | − | 0.674310i | −0.521321 | − | 0.0431683i | ||||
\(245\) | −0.187787 | − | 1.94976i | −0.0119972 | − | 0.124565i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.14640 | −0.454715 | ||||||||
\(248\) | 6.84596 | + | 8.79415i | 0.434719 | + | 0.558429i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.11098 | + | 13.5725i | −0.512983 | + | 0.858399i | ||||
\(251\) | − | 24.5888i | − | 1.55203i | −0.630713 | − | 0.776016i | \(-0.717237\pi\) | ||
0.630713 | − | 0.776016i | \(-0.282763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.40098 | 0.276687 | ||||||||
\(254\) | 5.51047 | + | 5.98563i | 0.345758 | + | 0.375572i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.1342 | + | 5.19178i | 0.945890 | + | 0.324486i | ||||
\(257\) | 9.91878 | 0.618716 | 0.309358 | − | 0.950946i | \(-0.399886\pi\) | ||||
0.309358 | + | 0.950946i | \(0.399886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.7643 | 1.53878 | ||||||||
\(260\) | −17.4990 | + | 0.234494i | −1.08524 | + | 0.0145427i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.45315 | − | 5.02027i | 0.336897 | − | 0.310153i | ||||
\(263\) | 3.87555i | 0.238977i | 0.992836 | + | 0.119488i | \(0.0381254\pi\) | ||||
−0.992836 | + | 0.119488i | \(0.961875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.9979 | − | 1.44449i | 0.921313 | − | 0.0887343i | ||||
\(266\) | −4.90909 | − | 5.33239i | −0.300995 | − | 0.326950i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.8370 | + | 1.14578i | 0.845230 | + | 0.0699898i | ||||
\(269\) | −22.5216 | −1.37317 | −0.686585 | − | 0.727050i | \(-0.740891\pi\) | ||||
−0.686585 | + | 0.727050i | \(0.740891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.5544i | − | 1.12710i | −0.826081 | − | 0.563551i | \(-0.809435\pi\) | ||
0.826081 | − | 0.563551i | \(-0.190565\pi\) | |||||||
\(272\) | 3.96497 | + | 0.661176i | 0.240411 | + | 0.0400897i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.5148 | − | 21.1976i | −1.17893 | − | 1.28059i | ||||
\(275\) | −2.16730 | − | 11.1470i | −0.130693 | − | 0.672189i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.9192 | −1.43717 | −0.718584 | − | 0.695440i | \(-0.755209\pi\) | ||||
−0.718584 | + | 0.695440i | \(0.755209\pi\) | |||||||
\(278\) | −18.5442 | − | 20.1433i | −1.11221 | − | 1.20811i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.1956 | − | 12.8960i | −0.728825 | − | 0.770685i | ||||
\(281\) | − | 23.9246i | − | 1.42722i | −0.700541 | − | 0.713612i | \(-0.747058\pi\) | ||
0.700541 | − | 0.713612i | \(-0.252942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.86207i | − | 0.170132i | −0.996375 | − | 0.0850662i | \(-0.972890\pi\) | ||
0.996375 | − | 0.0850662i | \(-0.0271102\pi\) | |||||||
\(284\) | −1.21507 | + | 14.6738i | −0.0721012 | + | 0.870729i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.24700 | − | 8.51295i | 0.546787 | − | 0.503381i | ||||
\(287\) | − | 6.28546i | − | 0.371019i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9901 | −0.940595 | ||||||||
\(290\) | −16.3444 | + | 18.2382i | −0.959774 | + | 1.07098i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.2397 | + | 0.847902i | 0.599232 | + | 0.0496197i | ||||
\(293\) | 17.3345i | 1.01269i | 0.862330 | + | 0.506347i | \(0.169004\pi\) | ||||
−0.862330 | + | 0.506347i | \(0.830996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.5098 | − | 2.45692i | 1.48524 | − | 0.143047i | ||||
\(296\) | 19.6944 | − | 15.3315i | 1.14472 | − | 0.891124i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.83114 | + | 4.16150i | 0.221932 | + | 0.241069i | ||||
\(299\) | 7.58299i | 0.438536i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.9088i | 1.89683i | ||||||||
\(302\) | −16.1539 | + | 14.8715i | −0.929550 | + | 0.855759i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.20534 | − | 1.20152i | −0.413255 | − | 0.0689121i | ||||
\(305\) | 9.09356 | − | 0.875827i | 0.520696 | − | 0.0501497i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.51078i | 0.257444i | 0.991681 | + | 0.128722i | \(0.0410875\pi\) | ||||
−0.991681 | + | 0.128722i | \(0.958913\pi\) | |||||||
\(308\) | 12.7041 | + | 1.05197i | 0.723884 | + | 0.0599416i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.27925 | − | 8.31570i | −0.527026 | − | 0.472300i | ||||
\(311\) | −1.96277 | −0.111299 | −0.0556493 | − | 0.998450i | \(-0.517723\pi\) | ||||
−0.0556493 | + | 0.998450i | \(0.517723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.22881i | − | 0.182503i | −0.995828 | − | 0.0912516i | \(-0.970913\pi\) | ||
0.995828 | − | 0.0912516i | \(-0.0290867\pi\) | |||||||
\(314\) | −15.9613 | − | 17.3376i | −0.900749 | − | 0.978419i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.26412 | − | 0.684316i | −0.464893 | − | 0.0384958i | ||||
\(317\) | 17.6637i | 0.992091i | 0.868296 | + | 0.496046i | \(0.165215\pi\) | ||||
−0.868296 | + | 0.496046i | \(0.834785\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 17.5889i | − | 0.984787i | ||||||
\(320\) | −17.6827 | − | 2.70567i | −0.988495 | − | 0.151252i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.65815 | + | 5.20899i | −0.315317 | + | 0.290286i | ||||
\(323\) | −1.83521 | −0.102114 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.2066 | − | 3.73432i | 1.06539 | − | 0.207143i | ||||
\(326\) | 16.0169 | − | 14.7454i | 0.887095 | − | 0.816674i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.89130 | − | 4.99868i | −0.214861 | − | 0.276006i | ||||
\(329\) | − | 17.5961i | − | 0.970103i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3298 | −0.622741 | −0.311371 | − | 0.950289i | \(-0.600788\pi\) | ||||
−0.311371 | + | 0.950289i | \(0.600788\pi\) | |||||||
\(332\) | 2.44542 | − | 29.5321i | 0.134210 | − | 1.62079i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.70934 | + | 6.17673i | −0.367119 | + | 0.337976i | ||||
\(335\) | −15.4517 | + | 1.48820i | −0.844217 | + | 0.0813089i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.3805i | 0.783355i | 0.920103 | + | 0.391677i | \(0.128105\pi\) | ||||
−0.920103 | + | 0.391677i | \(0.871895\pi\) | |||||||
\(338\) | 2.21597 | + | 2.40704i | 0.120533 | + | 0.130926i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.49378 | + | 0.0602185i | −0.243709 | + | 0.00326581i | ||||
\(341\) | 8.94888 | 0.484609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1865 | 0.927986 | ||||||||
\(344\) | 20.3737 | + | 26.1716i | 1.09848 | + | 1.41108i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.20545 | − | 7.55408i | 0.441128 | − | 0.406110i | ||||
\(347\) | 6.09377 | 0.327131 | 0.163565 | − | 0.986533i | \(-0.447701\pi\) | ||||
0.163565 | + | 0.986533i | \(0.447701\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 18.3257i | − | 0.980954i | −0.871454 | − | 0.490477i | \(-0.836823\pi\) | ||
0.871454 | − | 0.490477i | \(-0.163177\pi\) | |||||||
\(350\) | 15.9800 | + | 11.7660i | 0.854167 | + | 0.628920i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.7545 | − | 7.02846i | 0.573219 | − | 0.374618i | ||||
\(353\) | −27.9785 | −1.48915 | −0.744573 | − | 0.667541i | \(-0.767347\pi\) | ||||
−0.744573 | + | 0.667541i | \(0.767347\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.57819 | − | 16.3861i | −0.0837618 | − | 0.869684i | ||||
\(356\) | −9.61695 | − | 0.796337i | −0.509697 | − | 0.0422058i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.8826 | + | 13.7012i | −0.786572 | + | 0.724132i | ||||
\(359\) | 25.5787 | 1.34999 | 0.674996 | − | 0.737822i | \(-0.264145\pi\) | ||||
0.674996 | + | 0.737822i | \(0.264145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6650 | −0.824472 | ||||||||
\(362\) | 22.8988 | − | 21.0810i | 1.20354 | − | 1.10799i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.81257 | + | 21.8895i | −0.0950046 | + | 1.14732i | ||||
\(365\) | −11.4346 | + | 1.10130i | −0.598513 | + | 0.0576445i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7018 | −0.767426 | −0.383713 | − | 0.923452i | \(-0.625355\pi\) | ||||
−0.383713 | + | 0.923452i | \(0.625355\pi\) | |||||||
\(368\) | −1.27493 | + | 7.64553i | −0.0664602 | + | 0.398551i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −18.6230 | + | 20.7808i | −0.968162 | + | 1.08034i | ||||
\(371\) | − | 18.9105i | − | 0.981783i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1670 | 0.526428 | 0.263214 | − | 0.964737i | \(-0.415217\pi\) | ||||
0.263214 | + | 0.964737i | \(0.415217\pi\) | |||||||
\(374\) | 2.37465 | − | 2.18614i | 0.122790 | − | 0.113043i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.8937 | − | 13.9937i | −0.561798 | − | 0.721672i | ||||
\(377\) | 30.3060 | 1.56084 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2106 | 1.08951 | 0.544757 | − | 0.838594i | \(-0.316622\pi\) | ||||
0.544757 | + | 0.838594i | \(0.316622\pi\) | |||||||
\(380\) | 8.16632 | − | 0.109432i | 0.418923 | − | 0.00561375i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.97250 | − | 3.22881i | −0.152086 | − | 0.165200i | ||||
\(383\) | 25.4830i | 1.30212i | 0.759026 | + | 0.651060i | \(0.225676\pi\) | ||||
−0.759026 | + | 0.651060i | \(0.774324\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.1866 | + | 1.36635i | −0.723016 | + | 0.0696357i | ||||
\(386\) | −19.7910 | + | 18.2200i | −1.00734 | + | 0.927372i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −29.7318 | − | 2.46196i | −1.50940 | − | 0.124987i | ||||
\(389\) | −9.85609 | −0.499723 | −0.249862 | − | 0.968282i | \(-0.580385\pi\) | ||||
−0.249862 | + | 0.968282i | \(0.580385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.94733i | 0.0984806i | ||||||||
\(392\) | −1.95511 | + | 1.52199i | −0.0987479 | + | 0.0768720i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0971 | − | 11.1368i | 0.609444 | − | 0.561065i | ||||
\(395\) | 9.22849 | − | 0.888822i | 0.464336 | − | 0.0447215i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.5167 | −1.53159 | −0.765795 | − | 0.643085i | \(-0.777654\pi\) | ||||
−0.765795 | + | 0.643085i | \(0.777654\pi\) | |||||||
\(398\) | −6.03895 | + | 5.55956i | −0.302705 | + | 0.278675i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.9928 | − | 0.535921i | 0.999641 | − | 0.0267960i | ||||
\(401\) | − | 23.8072i | − | 1.18888i | −0.804142 | − | 0.594438i | \(-0.797375\pi\) | ||
0.804142 | − | 0.594438i | \(-0.202625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.4191i | 0.768082i | ||||||||
\(404\) | −2.46991 | + | 29.8278i | −0.122883 | + | 1.48399i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.8182 | + | 22.6133i | 1.03319 | + | 1.12228i | ||||
\(407\) | − | 20.0410i | − | 0.993393i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7023 | 0.529197 | 0.264598 | − | 0.964359i | \(-0.414761\pi\) | ||||
0.264598 | + | 0.964359i | \(0.414761\pi\) | |||||||
\(410\) | 5.27441 | + | 4.72672i | 0.260484 | + | 0.233436i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.74485 | + | 21.0716i | −0.0859625 | + | 1.03812i | ||||
\(413\) | − | 32.1647i | − | 1.58272i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.17624 | + | 32.9783i | 0.155915 | + | 1.61884i | ||||
\(416\) | 12.1102 | + | 18.5304i | 0.593752 | + | 0.908525i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.31533 | + | 3.97277i | −0.211070 | + | 0.194315i | ||||
\(419\) | 10.4707i | 0.511525i | 0.966740 | + | 0.255762i | \(0.0823265\pi\) | ||||
−0.966740 | + | 0.255762i | \(0.917674\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.935700i | 0.0456033i | 0.999740 | + | 0.0228016i | \(0.00725861\pi\) | ||||
−0.999740 | + | 0.0228016i | \(0.992741\pi\) | |||||||
\(422\) | −8.50945 | − | 9.24320i | −0.414233 | − | 0.449952i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.7074 | − | 15.0391i | −0.568562 | − | 0.730361i | ||||
\(425\) | 4.93228 | − | 0.958980i | 0.239251 | − | 0.0465174i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 11.4659i | − | 0.554872i | ||||||
\(428\) | −2.57336 | + | 31.0772i | −0.124388 | + | 1.50217i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −27.6153 | − | 24.7477i | −1.33173 | − | 1.19344i | ||||
\(431\) | 12.1803 | 0.586703 | 0.293351 | − | 0.956005i | \(-0.405229\pi\) | ||||
0.293351 | + | 0.956005i | \(0.405229\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.5905i | 0.989514i | 0.869031 | + | 0.494757i | \(0.164743\pi\) | ||||
−0.869031 | + | 0.494757i | \(0.835257\pi\) | |||||||
\(434\) | −11.5052 | + | 10.5919i | −0.552268 | + | 0.508427i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.7738 | + | 1.80299i | 1.04277 | + | 0.0863475i | ||||
\(437\) | − | 3.53878i | − | 0.169283i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 12.3535i | − | 0.589598i | −0.955559 | − | 0.294799i | \(-0.904747\pi\) | ||
0.955559 | − | 0.294799i | \(-0.0952527\pi\) | |||||||
\(440\) | −10.4364 | + | 9.86949i | −0.497534 | + | 0.470510i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.76678 | + | 4.09158i | 0.179167 | + | 0.194617i | ||||
\(443\) | −20.4381 | −0.971043 | −0.485521 | − | 0.874225i | \(-0.661370\pi\) | ||||
−0.485521 | + | 0.874225i | \(0.661370\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.7392 | − | 1.03432i | 0.509086 | − | 0.0490315i | ||||
\(446\) | 16.9044 | + | 18.3621i | 0.800448 | + | 0.869469i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.50780 | + | 21.7653i | −0.260219 | + | 1.02831i | ||||
\(449\) | − | 40.9555i | − | 1.93281i | −0.257029 | − | 0.966404i | \(-0.582744\pi\) | ||
0.257029 | − | 0.966404i | \(-0.417256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.08662 | −0.239520 | ||||||||
\(452\) | −2.12270 | + | 25.6348i | −0.0998435 | + | 1.20576i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.4630 | − | 13.5377i | −0.584917 | − | 0.635354i | ||||
\(455\) | −2.35426 | − | 24.4438i | −0.110369 | − | 1.14595i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.1652i | − | 0.802953i | −0.915869 | − | 0.401476i | \(-0.868497\pi\) | ||
0.915869 | − | 0.401476i | \(-0.131503\pi\) | |||||||
\(458\) | −21.4967 | + | 19.7902i | −1.00447 | + | 0.924736i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.116118 | − | 8.66522i | −0.00541401 | − | 0.404018i | ||||
\(461\) | −4.53444 | −0.211190 | −0.105595 | − | 0.994409i | \(-0.533675\pi\) | ||||
−0.105595 | + | 0.994409i | \(0.533675\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.82358 | 0.131223 | 0.0656114 | − | 0.997845i | \(-0.479100\pi\) | ||||
0.0656114 | + | 0.997845i | \(0.479100\pi\) | |||||||
\(464\) | 30.5560 | + | 5.09535i | 1.41853 | + | 0.236546i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.55122 | − | 9.28858i | −0.396128 | − | 0.430285i | ||||
\(467\) | −18.3153 | −0.847532 | −0.423766 | − | 0.905772i | \(-0.639292\pi\) | ||||
−0.423766 | + | 0.905772i | \(0.639292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.4827i | 0.899627i | ||||||||
\(470\) | 14.7657 | + | 13.2324i | 0.681089 | + | 0.610365i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.9130 | − | 25.5798i | −0.916572 | − | 1.17741i | ||||
\(473\) | 26.6321 | 1.22454 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.96320 | + | 1.74271i | −0.411260 | + | 0.0799609i | ||||
\(476\) | −0.465472 | + | 5.62127i | −0.0213349 | + | 0.257650i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.90113 | + | 3.15128i | 0.132694 | + | 0.144136i | ||||
\(479\) | 34.5811 | 1.58005 | 0.790026 | − | 0.613073i | \(-0.210067\pi\) | ||||
0.790026 | + | 0.613073i | \(0.210067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.5311 | 1.57448 | ||||||||
\(482\) | −16.3928 | − | 17.8063i | −0.746670 | − | 0.811054i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.964182 | + | 11.6439i | −0.0438264 | + | 0.529269i | ||||
\(485\) | 33.2013 | − | 3.19771i | 1.50759 | − | 0.145201i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.1948 | −1.64014 | −0.820072 | − | 0.572260i | \(-0.806067\pi\) | ||||
−0.820072 | + | 0.572260i | \(0.806067\pi\) | |||||||
\(488\) | −7.09848 | − | 9.11853i | −0.321333 | − | 0.412776i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.84874 | − | 2.06296i | 0.0835176 | − | 0.0931948i | ||||
\(491\) | − | 11.9287i | − | 0.538335i | −0.963093 | − | 0.269168i | \(-0.913251\pi\) | ||
0.963093 | − | 0.269168i | \(-0.0867486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.78265 | 0.350513 | ||||||||
\(494\) | −6.84518 | − | 7.43543i | −0.307979 | − | 0.334536i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.59242 | + | 15.5463i | −0.116403 | + | 0.698050i | ||||
\(497\) | −20.6609 | −0.926767 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.7402 | −0.928459 | −0.464230 | − | 0.885715i | \(-0.653669\pi\) | ||||
−0.464230 | + | 0.885715i | \(0.653669\pi\) | |||||||
\(500\) | −21.8905 | + | 4.56138i | −0.978973 | + | 0.203991i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.5833 | − | 23.5524i | 1.14184 | − | 1.05120i | ||||
\(503\) | 3.89107i | 0.173494i | 0.996230 | + | 0.0867471i | \(0.0276472\pi\) | ||||
−0.996230 | + | 0.0867471i | \(0.972353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.20804 | − | 33.3085i | −0.142756 | − | 1.48221i | ||||
\(506\) | 4.21547 | + | 4.57897i | 0.187401 | + | 0.203560i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.949504 | + | 11.4667i | −0.0421274 | + | 0.508751i | ||||
\(509\) | −44.3736 | −1.96683 | −0.983413 | − | 0.181382i | \(-0.941943\pi\) | ||||
−0.983413 | + | 0.181382i | \(0.941943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.4176i | 0.637797i | ||||||||
\(512\) | 9.09459 | + | 20.7193i | 0.401928 | + | 0.915671i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.50070 | + | 10.3199i | 0.419058 | + | 0.455193i | ||||
\(515\) | −2.26629 | − | 23.5305i | −0.0998648 | − | 1.03688i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.2400 | −0.626273 | ||||||||
\(518\) | 23.7205 | + | 25.7658i | 1.04222 | + | 1.13209i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.0054 | − | 17.9821i | −0.745735 | − | 0.788567i | ||||
\(521\) | 3.66605i | 0.160613i | 0.996770 | + | 0.0803064i | \(0.0255899\pi\) | ||||
−0.996770 | + | 0.0803064i | \(0.974410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.548243i | − | 0.0239730i | −0.999928 | − | 0.0119865i | \(-0.996184\pi\) | ||
0.999928 | − | 0.0119865i | \(-0.00381552\pi\) | |||||||
\(524\) | 10.4466 | + | 0.865037i | 0.456362 | + | 0.0377893i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.03229 | + | 3.71220i | −0.175816 | + | 0.161860i | ||||
\(527\) | 3.95967i | 0.172486i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.2450 | 0.836740 | ||||||||
\(530\) | 15.8686 | + | 14.2209i | 0.689289 | + | 0.617714i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.845880 | − | 10.2153i | 0.0366735 | − | 0.442887i | ||||
\(533\) | − | 8.76438i | − | 0.379627i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.34241 | − | 34.7037i | −0.144505 | − | 1.50037i | ||||
\(536\) | 12.0617 | + | 15.4941i | 0.520985 | + | 0.669244i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.5724 | − | 23.4325i | −0.930051 | − | 1.01025i | ||||
\(539\) | 1.98951i | 0.0856942i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 42.7910i | − | 1.83973i | −0.392238 | − | 0.919864i | \(-0.628299\pi\) | ||
0.392238 | − | 0.919864i | \(-0.371701\pi\) | |||||||
\(542\) | 19.3048 | − | 17.7724i | 0.829214 | − | 0.763388i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.10993 | + | 4.75863i | 0.133337 | + | 0.204025i | ||||
\(545\) | −24.3146 | + | 2.34181i | −1.04152 | + | 0.100312i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 15.6821i | − | 0.670520i | −0.942126 | − | 0.335260i | \(-0.891176\pi\) | ||
0.942126 | − | 0.335260i | \(-0.108824\pi\) | |||||||
\(548\) | 3.36258 | − | 40.6082i | 0.143642 | − | 1.73470i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.52187 | − | 12.9321i | 0.406014 | − | 0.551427i | ||||
\(551\) | −14.1430 | −0.602514 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 11.6360i | − | 0.494813i | ||||||
\(554\) | −22.9110 | − | 24.8866i | −0.973397 | − | 1.05733i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.19534 | − | 38.5885i | 0.135513 | − | 1.63652i | ||||
\(557\) | 12.6435i | 0.535721i | 0.963458 | + | 0.267861i | \(0.0863166\pi\) | ||||
−0.963458 | + | 0.267861i | \(0.913683\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.8877i | 1.94084i | ||||||||
\(560\) | 1.73607 | − | 25.0413i | 0.0733622 | − | 1.05819i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.8922 | − | 22.9162i | 1.05002 | − | 0.966663i | ||||
\(563\) | 46.3326 | 1.95268 | 0.976342 | − | 0.216231i | \(-0.0693764\pi\) | ||||
0.976342 | + | 0.216231i | \(0.0693764\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.75707 | − | 28.6262i | −0.115991 | − | 1.20431i | ||||
\(566\) | 2.97782 | − | 2.74144i | 0.125167 | − | 0.115231i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.4311 | + | 12.7911i | −0.689434 | + | 0.536701i | ||||
\(569\) | − | 37.9125i | − | 1.58938i | −0.607018 | − | 0.794688i | \(-0.707634\pi\) | ||
0.607018 | − | 0.794688i | \(-0.292366\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.8483 | −0.956172 | −0.478086 | − | 0.878313i | \(-0.658669\pi\) | ||||
−0.478086 | + | 0.878313i | \(0.658669\pi\) | |||||||
\(572\) | 17.7145 | + | 1.46686i | 0.740680 | + | 0.0613324i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.53966 | − | 6.02053i | 0.272960 | − | 0.251292i | ||||
\(575\) | 1.84917 | + | 9.51078i | 0.0771159 | + | 0.396627i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 34.7210i | − | 1.44545i | −0.691134 | − | 0.722727i | \(-0.742889\pi\) | ||
0.691134 | − | 0.722727i | \(-0.257111\pi\) | |||||||
\(578\) | −15.3161 | − | 16.6368i | −0.637067 | − | 0.692000i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −34.6313 | + | 0.464074i | −1.43798 | + | 0.0192696i | ||||
\(581\) | 41.5816 | 1.72510 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.3037 | −0.633813 | ||||||||
\(584\) | 8.92588 | + | 11.4660i | 0.369356 | + | 0.474465i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0356 | + | 16.6039i | −0.745043 | + | 0.685899i | ||||
\(587\) | 22.3865 | 0.923988 | 0.461994 | − | 0.886883i | \(-0.347134\pi\) | ||||
0.461994 | + | 0.886883i | \(0.347134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.19571i | − | 0.296494i | ||||||
\(590\) | 26.9908 | + | 24.1881i | 1.11119 | + | 0.995809i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 34.8159 | + | 5.80570i | 1.43092 | + | 0.238613i | ||||
\(593\) | −1.73287 | −0.0711603 | −0.0355802 | − | 0.999367i | \(-0.511328\pi\) | ||||
−0.0355802 | + | 0.999367i | \(0.511328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.604578 | − | 6.27723i | −0.0247853 | − | 0.257341i | ||||
\(596\) | −0.660141 | + | 7.97218i | −0.0270404 | + | 0.326553i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.88967 | + | 7.26337i | −0.322633 | + | 0.297021i | ||||
\(599\) | 11.2417 | 0.459325 | 0.229662 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229662 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.09680 | 0.167112 | 0.0835559 | − | 0.996503i | \(-0.473372\pi\) | ||||
0.0835559 | + | 0.996503i | \(0.473372\pi\) | |||||||
\(602\) | −34.2398 | + | 31.5217i | −1.39551 | + | 1.28473i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −30.9459 | − | 2.56250i | −1.25917 | − | 0.104266i | ||||
\(605\) | −1.25233 | − | 13.0027i | −0.0509143 | − | 0.528635i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.4524 | −1.56073 | −0.780366 | − | 0.625323i | \(-0.784967\pi\) | ||||
−0.780366 | + | 0.625323i | \(0.784967\pi\) | |||||||
\(608\) | −5.65152 | − | 8.64763i | −0.229199 | − | 0.350708i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.62152 | + | 8.62243i | 0.389564 | + | 0.349112i | ||||
\(611\) | − | 24.5358i | − | 0.992612i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.08629 | −0.124654 | −0.0623271 | − | 0.998056i | \(-0.519852\pi\) | ||||
−0.0623271 | + | 0.998056i | \(0.519852\pi\) | |||||||
\(614\) | −4.69321 | + | 4.32065i | −0.189403 | + | 0.174367i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.0741 | + | 14.2255i | 0.446189 | + | 0.573163i | ||||
\(617\) | 7.92538 | 0.319064 | 0.159532 | − | 0.987193i | \(-0.449002\pi\) | ||||
0.159532 | + | 0.987193i | \(0.449002\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.1896 | 0.650716 | 0.325358 | − | 0.945591i | \(-0.394515\pi\) | ||||
0.325358 | + | 0.945591i | \(0.394515\pi\) | |||||||
\(620\) | −0.236112 | − | 17.6197i | −0.00948248 | − | 0.707625i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.88004 | − | 2.04215i | −0.0753828 | − | 0.0818829i | ||||
\(623\) | − | 13.5408i | − | 0.542500i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1787 | − | 9.36735i | 0.927148 | − | 0.374694i | ||||
\(626\) | 3.35939 | − | 3.09272i | 0.134268 | − | 0.123610i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.75028 | − | 33.2137i | 0.109748 | − | 1.32537i | ||||
\(629\) | 8.86765 | 0.353576 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3661i | 0.691333i | 0.938357 | + | 0.345666i | \(0.112347\pi\) | ||||
−0.938357 | + | 0.345666i | \(0.887653\pi\) | |||||||
\(632\) | −7.20380 | − | 9.25383i | −0.286552 | − | 0.368098i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.3781 | + | 16.9192i | −0.729886 | + | 0.671946i | ||||
\(635\) | −1.23326 | − | 12.8048i | −0.0489405 | − | 0.508141i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.42797 | −0.135821 | ||||||||
\(638\) | 18.3002 | − | 16.8475i | 0.724512 | − | 0.666998i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.1223 | − | 20.9895i | −0.558233 | − | 0.829684i | ||||
\(641\) | 14.3388i | 0.566350i | 0.959068 | + | 0.283175i | \(0.0913878\pi\) | ||||
−0.959068 | + | 0.283175i | \(0.908612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2489i | 0.601357i | 0.953726 | + | 0.300678i | \(0.0972131\pi\) | ||||
−0.953726 | + | 0.300678i | \(0.902787\pi\) | |||||||
\(644\) | −10.8393 | − | 0.897557i | −0.427129 | − | 0.0353687i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.75786 | − | 1.90943i | −0.0691619 | − | 0.0751256i | ||||
\(647\) | 38.3484i | 1.50763i | 0.657087 | + | 0.753815i | \(0.271788\pi\) | ||||
−0.657087 | + | 0.753815i | \(0.728212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.0299 | −1.02176 | ||||||||
\(650\) | 22.2824 | + | 16.4064i | 0.873986 | + | 0.643513i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.6836 | + | 2.54077i | 1.20166 | + | 0.0995043i | ||||
\(653\) | 21.7545i | 0.851319i | 0.904883 | + | 0.425659i | \(0.139958\pi\) | ||||
−0.904883 | + | 0.425659i | \(0.860042\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.6657 | + | 1.12355i | −0.455815 | + | 0.0439008i | ||||
\(656\) | 1.47355 | − | 8.83667i | 0.0575326 | − | 0.345014i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.3077 | − | 16.8544i | 0.713710 | − | 0.657053i | ||||
\(659\) | 8.22885i | 0.320551i | 0.987072 | + | 0.160275i | \(0.0512382\pi\) | ||||
−0.987072 | + | 0.160275i | \(0.948762\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7212i | 0.417007i | 0.978022 | + | 0.208503i | \(0.0668592\pi\) | ||||
−0.978022 | + | 0.208503i | \(0.933141\pi\) | |||||||
\(662\) | −10.8522 | − | 11.7880i | −0.421784 | − | 0.458154i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.0689 | − | 25.7430i | 1.28332 | − | 0.999023i | ||||
\(665\) | 1.09867 | + | 11.4073i | 0.0426046 | + | 0.442356i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0071i | 0.581076i | ||||||||
\(668\) | −12.8531 | − | 1.06431i | −0.497300 | − | 0.0411792i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.3488 | − | 14.6512i | −0.631609 | − | 0.566024i | ||||
\(671\) | −9.27896 | −0.358210 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.76512i | 0.145135i | 0.997364 | + | 0.0725673i | \(0.0231192\pi\) | ||||
−0.997364 | + | 0.0725673i | \(0.976881\pi\) | |||||||
\(674\) | −14.9621 | + | 13.7743i | −0.576318 | + | 0.530568i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.381831 | + | 4.61118i | −0.0146858 | + | 0.177353i | ||||
\(677\) | 36.2409i | 1.39285i | 0.717630 | + | 0.696425i | \(0.245227\pi\) | ||||
−0.717630 | + | 0.696425i | \(0.754773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 41.8628i | − | 1.60655i | ||||||
\(680\) | −4.36702 | − | 4.61784i | −0.167467 | − | 0.177086i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.57168 | + | 9.31080i | 0.328227 | + | 0.356529i | ||||
\(683\) | −20.4976 | −0.784320 | −0.392160 | − | 0.919897i | \(-0.628272\pi\) | ||||
−0.392160 | + | 0.919897i | \(0.628272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.36749 | + | 45.3469i | 0.166873 | + | 1.73262i | ||||
\(686\) | 16.4621 | + | 17.8816i | 0.628527 | + | 0.682724i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.71510 | + | 46.2662i | −0.294135 | + | 1.76388i | ||||
\(689\) | − | 26.3686i | − | 1.00456i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.8335 | 1.78163 | 0.890815 | − | 0.454366i | \(-0.150134\pi\) | ||||
0.890815 | + | 0.454366i | \(0.150134\pi\) | |||||||
\(692\) | 15.7192 | + | 1.30164i | 0.597554 | + | 0.0494808i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.83692 | + | 6.34022i | 0.221566 | + | 0.240672i | ||||
\(695\) | 4.15026 | + | 43.0915i | 0.157428 | + | 1.63455i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.25071i | − | 0.0852517i | ||||||
\(698\) | 19.0669 | − | 17.5533i | 0.721692 | − | 0.664402i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.06456 | + | 27.8964i | 0.115829 | + | 1.05438i | ||||
\(701\) | −37.7416 | −1.42548 | −0.712740 | − | 0.701428i | \(-0.752546\pi\) | ||||
−0.712740 | + | 0.701428i | \(0.752546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.1147 | −0.607779 | ||||||||
\(704\) | 17.6140 | + | 4.45729i | 0.663851 | + | 0.167990i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.7992 | − | 29.1101i | −1.00860 | − | 1.09557i | ||||
\(707\) | −41.9980 | −1.57950 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 7.35664i | − | 0.276285i | −0.990412 | − | 0.138142i | \(-0.955887\pi\) | ||
0.990412 | − | 0.138142i | \(-0.0441131\pi\) | |||||||
\(710\) | 15.5372 | − | 17.3375i | 0.583099 | − | 0.650663i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.38305 | − | 10.7687i | −0.314168 | − | 0.403573i | ||||
\(713\) | −7.63531 | −0.285945 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.7816 | + | 1.90523i | −0.739791 | + | 0.0712514i | ||||
\(716\) | −28.5107 | − | 2.36084i | −1.06549 | − | 0.0882289i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.5005 | + | 26.6132i | 0.914352 | + | 0.993195i | ||||
\(719\) | −29.9929 | −1.11855 | −0.559274 | − | 0.828983i | \(-0.688920\pi\) | ||||
−0.559274 | + | 0.828983i | \(0.688920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.6691 | −1.10494 | ||||||||
\(722\) | −15.0047 | − | 16.2985i | −0.558417 | − | 0.606568i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 43.8673 | + | 3.63245i | 1.63031 | + | 0.134999i | ||||
\(725\) | 38.0106 | − | 7.39038i | 1.41168 | − | 0.274472i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.7756 | −1.03014 | −0.515069 | − | 0.857148i | \(-0.672234\pi\) | ||||
−0.515069 | + | 0.857148i | \(0.672234\pi\) | |||||||
\(728\) | −24.5110 | + | 19.0810i | −0.908437 | + | 0.707188i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.0985 | − | 10.8422i | −0.447784 | − | 0.401286i | ||||
\(731\) | 11.7841i | 0.435849i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.84099 | 0.178806 | 0.0894031 | − | 0.995996i | \(-0.471504\pi\) | ||||
0.0894031 | + | 0.995996i | \(0.471504\pi\) | |||||||
\(734\) | −14.0821 | − | 15.2964i | −0.519780 | − | 0.564599i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.17594 | + | 5.99678i | −0.338229 | + | 0.221044i | ||||
\(737\) | 15.7667 | 0.580775 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.2911 | −1.40856 | −0.704280 | − | 0.709923i | \(-0.748730\pi\) | ||||
−0.704280 | + | 0.709923i | \(0.748730\pi\) | |||||||
\(740\) | −39.4593 | + | 0.528771i | −1.45055 | + | 0.0194380i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.6753 | − | 18.1134i | 0.722303 | − | 0.664964i | ||||
\(743\) | − | 20.4534i | − | 0.750361i | −0.926952 | − | 0.375181i | \(-0.877581\pi\) | ||
0.926952 | − | 0.375181i | \(-0.122419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.857423 | − | 8.90248i | −0.0314136 | − | 0.326162i | ||||
\(746\) | 9.73848 | + | 10.5782i | 0.356551 | + | 0.387296i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.54912 | + | 0.376692i | 0.166332 | + | 0.0137732i | ||||
\(749\) | −43.7571 | −1.59885 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 43.5967i | − | 1.59087i | −0.606041 | − | 0.795433i | \(-0.707243\pi\) | ||
0.606041 | − | 0.795433i | \(-0.292757\pi\) | |||||||
\(752\) | 4.12520 | − | 24.7382i | 0.150431 | − | 0.902108i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29.0286 | + | 31.5317i | 1.05716 | + | 1.14832i | ||||
\(755\) | 34.5571 | − | 3.32830i | 1.25766 | − | 0.121129i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0079 | 0.545472 | 0.272736 | − | 0.962089i | \(-0.412071\pi\) | ||||
0.272736 | + | 0.962089i | \(0.412071\pi\) | |||||||
\(758\) | 20.3165 | + | 22.0684i | 0.737930 | + | 0.801560i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.93597 | + | 8.39178i | 0.287868 | + | 0.304402i | ||||
\(761\) | 36.9239i | 1.33849i | 0.743041 | + | 0.669246i | \(0.233383\pi\) | ||||
−0.743041 | + | 0.669246i | \(0.766617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.6577i | 1.10988i | ||||||||
\(764\) | 0.512188 | − | 6.18543i | 0.0185303 | − | 0.223781i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.5136 | + | 24.4089i | −0.957977 | + | 0.881929i | ||||
\(767\) | − | 44.8501i | − | 1.61944i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.84339 | 0.0664745 | 0.0332372 | − | 0.999447i | \(-0.489418\pi\) | ||||
0.0332372 | + | 0.999447i | \(0.489418\pi\) | |||||||
\(770\) | −15.0102 | − | 13.4516i | −0.540931 | − | 0.484762i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −37.9137 | − | 3.13947i | −1.36454 | − | 0.112992i | ||||
\(773\) | − | 1.25203i | − | 0.0450322i | −0.999746 | − | 0.0225161i | \(-0.992832\pi\) | ||
0.999746 | − | 0.0225161i | \(-0.00716771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.76008 | + | 19.3391i | 0.135066 | + | 0.694680i | ||||
\(776\) | −25.9171 | − | 33.2925i | −0.930370 | − | 1.19513i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.44065 | − | 10.2547i | −0.338464 | − | 0.367649i | ||||
\(779\) | 4.09011i | 0.146543i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7202i | 0.598296i | ||||||||
\(782\) | −2.02608 | + | 1.86525i | −0.0724526 | + | 0.0667011i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.45624 | − | 0.576344i | −0.123437 | − | 0.0205837i | ||||
\(785\) | 3.57220 | + | 37.0895i | 0.127497 | + | 1.32378i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.1540i | 1.25310i | 0.779380 | + | 0.626552i | \(0.215534\pi\) | ||||
−0.779380 | + | 0.626552i | \(0.784466\pi\) | |||||||
\(788\) | 23.1745 | + | 1.91897i | 0.825556 | + | 0.0683606i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.76428 | + | 8.75037i | 0.347398 | + | 0.311324i | ||||
\(791\) | −36.0941 | −1.28336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 15.9879i | − | 0.567747i | ||||||
\(794\) | −29.2304 | − | 31.7509i | −1.03735 | − | 1.12680i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.5688 | − | 0.957962i | −0.410046 | − | 0.0339541i | ||||
\(797\) | − | 36.2717i | − | 1.28481i | −0.766366 | − | 0.642404i | \(-0.777937\pi\) | ||
0.766366 | − | 0.642404i | \(-0.222063\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.30084i | − | 0.222908i | ||||||
\(800\) | 19.7077 | + | 20.2881i | 0.696773 | + | 0.717292i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.7701 | − | 22.8037i | 0.874661 | − | 0.805228i | ||||
\(803\) | 11.6677 | 0.411745 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.1042 | − | 1.16579i | 0.426617 | − | 0.0410887i | ||||
\(806\) | −16.0427 | + | 14.7692i | −0.565082 | + | 0.520224i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33.4000 | + | 26.0008i | −1.17501 | + | 0.914704i | ||||
\(809\) | − | 3.68656i | − | 0.129612i | −0.997898 | − | 0.0648062i | \(-0.979357\pi\) | ||
0.997898 | − | 0.0648062i | \(-0.0206429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.1790 | 1.34065 | 0.670323 | − | 0.742070i | \(-0.266156\pi\) | ||||
0.670323 | + | 0.742070i | \(0.266156\pi\) | |||||||
\(812\) | −3.58716 | + | 43.3203i | −0.125885 | + | 1.52024i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.8515 | − | 19.1962i | 0.730844 | − | 0.672828i | ||||
\(815\) | −34.2642 | + | 3.30008i | −1.20022 | + | 0.115597i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 21.4146i | − | 0.749202i | ||||||
\(818\) | 10.2512 | + | 11.1352i | 0.358426 | + | 0.389333i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.134208 | + | 10.0152i | 0.00468675 | + | 0.349746i | ||||
\(821\) | 41.1529 | 1.43624 | 0.718122 | − | 0.695917i | \(-0.245002\pi\) | ||||
0.718122 | + | 0.695917i | \(0.245002\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.17378 | −0.110631 | −0.0553155 | − | 0.998469i | \(-0.517616\pi\) | ||||
−0.0553155 | + | 0.998469i | \(0.517616\pi\) | |||||||
\(824\) | −23.5951 | + | 18.3680i | −0.821976 | + | 0.639881i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.4655 | − | 30.8090i | 1.16442 | − | 1.07198i | ||||
\(827\) | −25.7874 | −0.896715 | −0.448358 | − | 0.893854i | \(-0.647991\pi\) | ||||
−0.448358 | + | 0.893854i | \(0.647991\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.86692i | 0.342692i | 0.985211 | + | 0.171346i | \(0.0548117\pi\) | ||||
−0.985211 | + | 0.171346i | \(0.945188\pi\) | |||||||
\(830\) | −31.2697 | + | 34.8930i | −1.08539 | + | 1.21115i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.68002 | + | 30.3493i | −0.266257 | + | 1.05217i | ||||
\(833\) | −0.880310 | −0.0305009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.3529 | − | 1.38237i | 0.496704 | − | 0.0478390i | ||||
\(836\) | −8.26689 | − | 0.684544i | −0.285916 | − | 0.0236755i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.8941 | + | 10.0293i | −0.376331 | + | 0.346457i | ||||
\(839\) | 9.25026 | 0.319355 | 0.159677 | − | 0.987169i | \(-0.448955\pi\) | ||||
0.159677 | + | 0.987169i | \(0.448955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.9770 | 1.06817 | ||||||||
\(842\) | −0.973544 | + | 0.896261i | −0.0335505 | + | 0.0308872i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.46626 | − | 17.7072i | 0.0504706 | − | 0.609507i | ||||
\(845\) | −0.495941 | − | 5.14927i | −0.0170609 | − | 0.177140i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.3948 | −0.563332 | ||||||||
\(848\) | 4.43335 | − | 26.5861i | 0.152242 | − | 0.912970i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.72215 | + | 4.21320i | 0.196268 | + | 0.144512i | ||||
\(851\) | 17.0992i | 0.586154i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.7095 | 1.63354 | 0.816771 | − | 0.576962i | \(-0.195762\pi\) | ||||
0.816771 | + | 0.576962i | \(0.195762\pi\) | |||||||
\(854\) | 11.9296 | − | 10.9826i | 0.408222 | − | 0.375816i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −34.7990 | + | 27.0899i | −1.18940 | + | 0.925912i | ||||
\(857\) | 24.3588 | 0.832079 | 0.416040 | − | 0.909346i | \(-0.363418\pi\) | ||||
0.416040 | + | 0.909346i | \(0.363418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8902 | −0.678644 | −0.339322 | − | 0.940670i | \(-0.610198\pi\) | ||||
−0.339322 | + | 0.940670i | \(0.610198\pi\) | |||||||
\(860\) | −0.702675 | − | 52.4367i | −0.0239610 | − | 1.78808i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.6669 | + | 12.6729i | 0.397375 | + | 0.431640i | ||||
\(863\) | − | 23.9506i | − | 0.815287i | −0.913141 | − | 0.407643i | \(-0.866351\pi\) | ||
0.913141 | − | 0.407643i | \(-0.133649\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.5535 | + | 1.69063i | −0.596837 | + | 0.0574831i | ||||
\(866\) | −21.4232 | + | 19.7226i | −0.727990 | + | 0.670200i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −22.0405 | − | 1.82508i | −0.748104 | − | 0.0619472i | ||||
\(869\) | −9.41664 | −0.319438 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.1665i | 0.920501i | ||||||||
\(872\) | 18.9801 | + | 24.3814i | 0.642747 | + | 0.825657i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.68190 | − | 3.38962i | 0.124542 | − | 0.114656i | ||||
\(875\) | −8.91360 | − | 30.0840i | −0.301335 | − | 1.01702i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.60517 | 0.324343 | 0.162172 | − | 0.986763i | \(-0.448150\pi\) | ||||
0.162172 | + | 0.986763i | \(0.448150\pi\) | |||||||
\(878\) | 12.8531 | − | 11.8328i | 0.433770 | − | 0.399336i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20.2651 | − | 1.40494i | −0.683137 | − | 0.0473607i | ||||
\(881\) | 54.0320i | 1.82038i | 0.414186 | + | 0.910192i | \(0.364066\pi\) | ||||
−0.414186 | + | 0.910192i | \(0.635934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.1178i | 1.92217i | 0.276260 | + | 0.961083i | \(0.410905\pi\) | ||||
−0.276260 | + | 0.961083i | \(0.589095\pi\) | |||||||
\(884\) | −0.649050 | + | 7.83824i | −0.0218299 | + | 0.263628i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.5766 | − | 21.2647i | −0.657690 | − | 0.714401i | ||||
\(887\) | − | 45.5832i | − | 1.53053i | −0.643712 | − | 0.765267i | \(-0.722607\pi\) | ||
0.643712 | − | 0.765267i | \(-0.277393\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.1452 | −0.541493 | ||||||||
\(890\) | 11.3627 | + | 10.1828i | 0.380878 | + | 0.341328i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.91279 | + | 35.1762i | −0.0975273 | + | 1.17779i | ||||
\(893\) | 11.4502i | 0.383167i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.8377 | − | 3.06638i | 1.06422 | − | 0.102498i | ||||
\(896\) | −27.9212 | + | 15.1173i | −0.932782 | + | 0.505034i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42.6118 | − | 39.2292i | 1.42198 | − | 1.30909i | ||||
\(899\) | 30.5151i | 1.01774i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.77151i | − | 0.225592i | ||||||
\(902\) | −4.87222 | − | 5.29235i | −0.162227 | − | 0.176216i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.7048 | + | 22.3457i | −0.954707 | + | 0.743208i | ||||
\(905\) | −48.9863 | + | 4.71801i | −1.62836 | + | 0.156832i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0428i | 0.831534i | 0.909471 | + | 0.415767i | \(0.136487\pi\) | ||||
−0.909471 | + | 0.415767i | \(0.863513\pi\) | |||||||
\(908\) | 2.14749 | − | 25.9341i | 0.0712669 | − | 0.860653i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 23.1774 | − | 25.8630i | 0.768324 | − | 0.857351i | ||||
\(911\) | −34.0216 | −1.12719 | −0.563593 | − | 0.826053i | \(-0.690581\pi\) | ||||
−0.563593 | + | 0.826053i | \(0.690581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 33.6507i | − | 1.11368i | ||||||
\(914\) | 17.8594 | − | 16.4417i | 0.590736 | − | 0.543842i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −41.1812 | − | 3.41003i | −1.36067 | − | 0.112671i | ||||
\(917\) | 14.7090i | 0.485732i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8359i | 0.489391i | 0.969600 | + | 0.244695i | \(0.0786879\pi\) | ||||
−0.969600 | + | 0.244695i | \(0.921312\pi\) | |||||||
\(920\) | 8.90445 | − | 8.42080i | 0.293571 | − | 0.277625i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.34331 | − | 4.71783i | −0.143039 | − | 0.155373i | ||||
\(923\) | −28.8093 | −0.948270 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.3098 | − | 8.42068i | 1.42402 | − | 0.276870i | ||||
\(926\) | 2.70456 | + | 2.93777i | 0.0888775 | + | 0.0965413i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.9666 | + | 36.6724i | 0.786743 | + | 1.20383i | ||||
\(929\) | 3.53367i | 0.115936i | 0.998318 | + | 0.0579679i | \(0.0184621\pi\) | ||||
−0.998318 | + | 0.0579679i | \(0.981538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.59974 | 0.0524295 | ||||||||
\(932\) | 1.47345 | − | 17.7941i | 0.0482646 | − | 0.582866i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.5433 | − | 19.0561i | −0.574035 | − | 0.623533i | ||||
\(935\) | −5.07997 | + | 0.489266i | −0.166133 | + | 0.0160007i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4410i | 0.961794i | 0.876777 | + | 0.480897i | \(0.159689\pi\) | ||||
−0.876777 | + | 0.480897i | \(0.840311\pi\) | |||||||
\(938\) | −20.2706 | + | 18.6615i | −0.661860 | + | 0.609320i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.375714 | + | 28.0375i | 0.0122545 | + | 0.914482i | ||||
\(941\) | −33.6670 | −1.09751 | −0.548757 | − | 0.835982i | \(-0.684899\pi\) | ||||
−0.548757 | + | 0.835982i | \(0.684899\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.33998 | 0.141329 | ||||||||
\(944\) | 7.54065 | − | 45.2200i | 0.245427 | − | 1.47179i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.5095 | + | 27.7092i | 0.829387 | + | 0.900903i | ||||
\(947\) | 54.4568 | 1.76961 | 0.884804 | − | 0.465963i | \(-0.154292\pi\) | ||||
0.884804 | + | 0.465963i | \(0.154292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.1038i | 0.652595i | ||||||||
\(950\) | −10.3986 | − | 7.65645i | −0.337375 | − | 0.248408i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.29446 | + | 4.90003i | −0.204005 | + | 0.158811i | ||||
\(953\) | −11.0742 | −0.358728 | −0.179364 | − | 0.983783i | \(-0.557404\pi\) | ||||
−0.179364 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.665255 | + | 6.90723i | 0.0215271 | + | 0.223513i | ||||
\(956\) | −0.499890 | + | 6.03692i | −0.0161676 | + | 0.195248i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.1235 | + | 35.9797i | 1.07017 | + | 1.16245i | ||||
\(959\) | 57.1768 | 1.84634 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4745 | 0.499176 | ||||||||
\(962\) | 33.0756 | + | 35.9276i | 1.06640 | + | 1.15835i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.82462 | − | 34.1115i | 0.0909750 | − | 1.09866i | ||||
\(965\) | 42.3380 | − | 4.07769i | 1.36291 | − | 0.131266i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6897 | 0.890442 | 0.445221 | − | 0.895421i | \(-0.353125\pi\) | ||||
0.445221 | + | 0.895421i | \(0.353125\pi\) | |||||||
\(968\) | −13.0384 | + | 10.1500i | −0.419070 | + | 0.326232i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 35.1289 | + | 31.4812i | 1.12792 | + | 1.01080i | ||||
\(971\) | 23.7464i | 0.762058i | 0.924563 | + | 0.381029i | \(0.124430\pi\) | ||||
−0.924563 | + | 0.381029i | \(0.875570\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54.3330 | 1.74184 | ||||||||
\(974\) | −34.6692 | − | 37.6587i | −1.11087 | − | 1.20666i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.68804 | − | 16.1198i | 0.0860421 | − | 0.515981i | ||||
\(977\) | −0.687528 | −0.0219960 | −0.0109980 | − | 0.999940i | \(-0.503501\pi\) | ||||
−0.0109980 | + | 0.999940i | \(0.503501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.9581 | −0.350223 | ||||||||
\(980\) | 3.91720 | − | 0.0524922i | 0.125131 | − | 0.00167680i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.4112 | − | 11.4259i | 0.396056 | − | 0.364616i | ||||
\(983\) | 27.8527i | 0.888363i | 0.895937 | + | 0.444181i | \(0.146505\pi\) | ||||
−0.895937 | + | 0.444181i | \(0.853495\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.8788 | + | 2.49246i | −0.824566 | + | 0.0794163i | ||||
\(986\) | 7.45461 | + | 8.09741i | 0.237403 | + | 0.257874i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.17949 | − | 14.2441i | 0.0375245 | − | 0.453164i | ||||
\(989\) | −22.7229 | −0.722545 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.7921i | − | 1.35934i | −0.733519 | − | 0.679668i | \(-0.762124\pi\) | ||
0.733519 | − | 0.679668i | \(-0.237876\pi\) | |||||||
\(992\) | −18.6582 | + | 12.1938i | −0.592399 | + | 0.387153i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19.7900 | − | 21.4965i | −0.627701 | − | 0.681827i | ||||
\(995\) | 12.9188 | − | 1.24425i | 0.409554 | − | 0.0394453i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.2645 | 0.420091 | 0.210045 | − | 0.977692i | \(-0.432639\pi\) | ||||
0.210045 | + | 0.977692i | \(0.432639\pi\) | |||||||
\(998\) | −19.8660 | − | 21.5790i | −0.628848 | − | 0.683072i | ||||
\(999\) | 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 | 1080.2.m.c.539.35 | yes | 48 | |
3.2 | odd | 2 | inner | 1080.2.m.c.539.14 | yes | 48 | |
4.3 | odd | 2 | 4320.2.m.c.2159.22 | 48 | |||
5.4 | even | 2 | inner | 1080.2.m.c.539.13 | ✓ | 48 | |
8.3 | odd | 2 | inner | 1080.2.m.c.539.34 | yes | 48 | |
8.5 | even | 2 | 4320.2.m.c.2159.27 | 48 | |||
12.11 | even | 2 | 4320.2.m.c.2159.28 | 48 | |||
15.14 | odd | 2 | inner | 1080.2.m.c.539.36 | yes | 48 | |
20.19 | odd | 2 | 4320.2.m.c.2159.23 | 48 | |||
24.5 | odd | 2 | 4320.2.m.c.2159.21 | 48 | |||
24.11 | even | 2 | inner | 1080.2.m.c.539.15 | yes | 48 | |
40.19 | odd | 2 | inner | 1080.2.m.c.539.16 | yes | 48 | |
40.29 | even | 2 | 4320.2.m.c.2159.26 | 48 | |||
60.59 | even | 2 | 4320.2.m.c.2159.25 | 48 | |||
120.29 | odd | 2 | 4320.2.m.c.2159.24 | 48 | |||
120.59 | even | 2 | inner | 1080.2.m.c.539.33 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.m.c.539.13 | ✓ | 48 | 5.4 | even | 2 | inner | |
1080.2.m.c.539.14 | yes | 48 | 3.2 | odd | 2 | inner | |
1080.2.m.c.539.15 | yes | 48 | 24.11 | even | 2 | inner | |
1080.2.m.c.539.16 | yes | 48 | 40.19 | odd | 2 | inner | |
1080.2.m.c.539.33 | yes | 48 | 120.59 | even | 2 | inner | |
1080.2.m.c.539.34 | yes | 48 | 8.3 | odd | 2 | inner | |
1080.2.m.c.539.35 | yes | 48 | 1.1 | even | 1 | trivial | |
1080.2.m.c.539.36 | yes | 48 | 15.14 | odd | 2 | inner | |
4320.2.m.c.2159.21 | 48 | 24.5 | odd | 2 | |||
4320.2.m.c.2159.22 | 48 | 4.3 | odd | 2 | |||
4320.2.m.c.2159.23 | 48 | 20.19 | odd | 2 | |||
4320.2.m.c.2159.24 | 48 | 120.29 | odd | 2 | |||
4320.2.m.c.2159.25 | 48 | 60.59 | even | 2 | |||
4320.2.m.c.2159.26 | 48 | 40.29 | even | 2 | |||
4320.2.m.c.2159.27 | 48 | 8.5 | even | 2 | |||
4320.2.m.c.2159.28 | 48 | 12.11 | even | 2 |