Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [528,2,Mod(133,528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(528, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("528.133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 528 = 2^{4} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 528.t (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.21610122672\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 397.19 | ||
Character | \(\chi\) | \(=\) | 528.397 |
Dual form | 528.2.t.b.133.19 |
$q$-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 \(\left(\mathbb{Z}/528\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(145\) | \(353\) | \(463\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40742 | + | 0.138462i | 0.995196 | + | 0.0979072i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.96166 | + | 0.389747i | 0.980828 | + | 0.194874i | ||||
\(5\) | 0.582740 | − | 0.582740i | 0.260609 | − | 0.260609i | −0.564692 | − | 0.825302i | \(-0.691005\pi\) |
0.825302 | + | 0.564692i | \(0.191005\pi\) | |||||||
\(6\) | 0.897288 | + | 1.09310i | 0.366316 | + | 0.446257i | ||||
\(7\) | − | 4.89753i | − | 1.85109i | −0.378637 | − | 0.925545i | \(-0.623607\pi\) | ||
0.378637 | − | 0.925545i | \(-0.376393\pi\) | |||||||
\(8\) | 2.70691 | + | 0.820152i | 0.957037 | + | 0.289967i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.900847 | − | 0.739473i | 0.284873 | − | 0.233842i | ||||
\(11\) | −0.707107 | + | 0.707107i | −0.213201 | + | 0.213201i | ||||
\(12\) | 1.11151 | + | 1.66269i | 0.320865 | + | 0.479978i | ||||
\(13\) | 1.72543 | + | 1.72543i | 0.478549 | + | 0.478549i | 0.904667 | − | 0.426119i | \(-0.140119\pi\) |
−0.426119 | + | 0.904667i | \(0.640119\pi\) | |||||||
\(14\) | 0.678119 | − | 6.89287i | 0.181235 | − | 1.84220i | ||||
\(15\) | 0.824119 | 0.212787 | ||||||||
\(16\) | 3.69619 | + | 1.52910i | 0.924049 | + | 0.382275i | ||||
\(17\) | −2.20698 | −0.535271 | −0.267635 | − | 0.963520i | \(-0.586242\pi\) | ||||
−0.267635 | + | 0.963520i | \(0.586242\pi\) | |||||||
\(18\) | −0.138462 | + | 1.40742i | −0.0326357 | + | 0.331732i | ||||
\(19\) | −4.64217 | − | 4.64217i | −1.06499 | − | 1.06499i | −0.997736 | − | 0.0672519i | \(-0.978577\pi\) |
−0.0672519 | − | 0.997736i | \(-0.521423\pi\) | |||||||
\(20\) | 1.37026 | − | 0.916015i | 0.306399 | − | 0.204827i | ||||
\(21\) | 3.46307 | − | 3.46307i | 0.755705 | − | 0.755705i | ||||
\(22\) | −1.09310 | + | 0.897288i | −0.233050 | + | 0.191303i | ||||
\(23\) | 8.23649i | 1.71743i | 0.512456 | + | 0.858714i | \(0.328736\pi\) | ||||
−0.512456 | + | 0.858714i | \(0.671264\pi\) | |||||||
\(24\) | 1.33414 | + | 2.49401i | 0.272330 | + | 0.509087i | ||||
\(25\) | 4.32083i | 0.864166i | ||||||||
\(26\) | 2.18950 | + | 2.66731i | 0.429396 | + | 0.523103i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 1.90880 | − | 9.60726i | 0.360729 | − | 1.81560i | ||||
\(29\) | −4.49302 | − | 4.49302i | −0.834333 | − | 0.834333i | 0.153773 | − | 0.988106i | \(-0.450858\pi\) |
−0.988106 | + | 0.153773i | \(0.950858\pi\) | |||||||
\(30\) | 1.15988 | + | 0.114109i | 0.211764 | + | 0.0208333i | ||||
\(31\) | 3.82276 | 0.686588 | 0.343294 | − | 0.939228i | \(-0.388457\pi\) | ||||
0.343294 | + | 0.939228i | \(0.388457\pi\) | |||||||
\(32\) | 4.99037 | + | 2.66387i | 0.882182 | + | 0.470909i | ||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −3.10614 | − | 0.305582i | −0.532699 | − | 0.0524068i | ||||
\(35\) | −2.85399 | − | 2.85399i | −0.482412 | − | 0.482412i | ||||
\(36\) | −0.389747 | + | 1.96166i | −0.0649579 | + | 0.326943i | ||||
\(37\) | −4.65242 | + | 4.65242i | −0.764853 | + | 0.764853i | −0.977195 | − | 0.212342i | \(-0.931891\pi\) |
0.212342 | + | 0.977195i | \(0.431891\pi\) | |||||||
\(38\) | −5.89072 | − | 7.17625i | −0.955601 | − | 1.16414i | ||||
\(39\) | 2.44013i | 0.390733i | ||||||||
\(40\) | 2.05536 | − | 1.09949i | 0.324981 | − | 0.173844i | ||||
\(41\) | 10.2041i | 1.59361i | 0.604234 | + | 0.796807i | \(0.293479\pi\) | ||||
−0.604234 | + | 0.796807i | \(0.706521\pi\) | |||||||
\(42\) | 5.35350 | − | 4.39449i | 0.826063 | − | 0.678085i | ||||
\(43\) | −1.22055 | + | 1.22055i | −0.186131 | + | 0.186131i | −0.794021 | − | 0.607890i | \(-0.792016\pi\) |
0.607890 | + | 0.794021i | \(0.292016\pi\) | |||||||
\(44\) | −1.66269 | + | 1.11151i | −0.250660 | + | 0.167566i | ||||
\(45\) | 0.582740 | + | 0.582740i | 0.0868698 | + | 0.0868698i | ||||
\(46\) | −1.14044 | + | 11.5922i | −0.168148 | + | 1.70918i | ||||
\(47\) | 9.80364 | 1.43001 | 0.715004 | − | 0.699120i | \(-0.246425\pi\) | ||||
0.715004 | + | 0.699120i | \(0.246425\pi\) | |||||||
\(48\) | 1.53237 | + | 3.69484i | 0.221178 | + | 0.533304i | ||||
\(49\) | −16.9858 | −2.42654 | ||||||||
\(50\) | −0.598269 | + | 6.08122i | −0.0846080 | + | 0.860014i | ||||
\(51\) | −1.56057 | − | 1.56057i | −0.218523 | − | 0.218523i | ||||
\(52\) | 2.71222 | + | 4.05719i | 0.376118 | + | 0.562631i | ||||
\(53\) | −1.14015 | + | 1.14015i | −0.156611 | + | 0.156611i | −0.781063 | − | 0.624452i | \(-0.785322\pi\) |
0.624452 | + | 0.781063i | \(0.285322\pi\) | |||||||
\(54\) | −1.09310 | + | 0.897288i | −0.148752 | + | 0.122105i | ||||
\(55\) | 0.824119i | 0.111124i | ||||||||
\(56\) | 4.01671 | − | 13.2572i | 0.536756 | − | 1.77156i | ||||
\(57\) | − | 6.56503i | − | 0.869559i | ||||||
\(58\) | −5.70145 | − | 6.94567i | −0.748637 | − | 0.912012i | ||||
\(59\) | 2.17677 | − | 2.17677i | 0.283392 | − | 0.283392i | −0.551068 | − | 0.834460i | \(-0.685780\pi\) |
0.834460 | + | 0.551068i | \(0.185780\pi\) | |||||||
\(60\) | 1.61664 | + | 0.321198i | 0.208707 | + | 0.0414665i | ||||
\(61\) | 2.35153 | + | 2.35153i | 0.301082 | + | 0.301082i | 0.841437 | − | 0.540355i | \(-0.181710\pi\) |
−0.540355 | + | 0.841437i | \(0.681710\pi\) | |||||||
\(62\) | 5.38023 | + | 0.529306i | 0.683289 | + | 0.0672219i | ||||
\(63\) | 4.89753 | 0.617030 | ||||||||
\(64\) | 6.65470 | + | 4.44015i | 0.831838 | + | 0.555019i | ||||
\(65\) | 2.01096 | 0.249429 | ||||||||
\(66\) | −1.40742 | − | 0.138462i | −0.173241 | − | 0.0170435i | ||||
\(67\) | −8.69638 | − | 8.69638i | −1.06243 | − | 1.06243i | −0.997917 | − | 0.0645155i | \(-0.979450\pi\) |
−0.0645155 | − | 0.997917i | \(-0.520550\pi\) | |||||||
\(68\) | −4.32933 | − | 0.860163i | −0.525009 | − | 0.104310i | ||||
\(69\) | −5.82408 | + | 5.82408i | −0.701137 | + | 0.701137i | ||||
\(70\) | −3.62159 | − | 4.41192i | −0.432862 | − | 0.527325i | ||||
\(71\) | − | 9.44670i | − | 1.12112i | −0.828115 | − | 0.560559i | \(-0.810586\pi\) | ||
0.828115 | − | 0.560559i | \(-0.189414\pi\) | |||||||
\(72\) | −0.820152 | + | 2.70691i | −0.0966558 | + | 0.319012i | ||||
\(73\) | − | 14.2278i | − | 1.66524i | −0.553843 | − | 0.832621i | \(-0.686839\pi\) | ||
0.553843 | − | 0.832621i | \(-0.313161\pi\) | |||||||
\(74\) | −7.19209 | + | 5.90373i | −0.836063 | + | 0.686294i | ||||
\(75\) | −3.05529 | + | 3.05529i | −0.352794 | + | 0.352794i | ||||
\(76\) | −7.29708 | − | 10.9156i | −0.837032 | − | 1.25211i | ||||
\(77\) | 3.46307 | + | 3.46307i | 0.394654 | + | 0.394654i | ||||
\(78\) | −0.337864 | + | 3.43429i | −0.0382556 | + | 0.388856i | ||||
\(79\) | −1.80715 | −0.203320 | −0.101660 | − | 0.994819i | \(-0.532415\pi\) | ||||
−0.101660 | + | 0.994819i | \(0.532415\pi\) | |||||||
\(80\) | 3.04499 | − | 1.26285i | 0.340440 | − | 0.141191i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −1.41288 | + | 14.3615i | −0.156026 | + | 1.58596i | ||||
\(83\) | −3.24879 | − | 3.24879i | −0.356601 | − | 0.356601i | 0.505958 | − | 0.862558i | \(-0.331139\pi\) |
−0.862558 | + | 0.505958i | \(0.831139\pi\) | |||||||
\(84\) | 8.14309 | − | 5.44364i | 0.888483 | − | 0.593950i | ||||
\(85\) | −1.28609 | + | 1.28609i | −0.139497 | + | 0.139497i | ||||
\(86\) | −1.88682 | + | 1.54882i | −0.203461 | + | 0.167014i | ||||
\(87\) | − | 6.35409i | − | 0.681230i | ||||||
\(88\) | −2.49401 | + | 1.33414i | −0.265862 | + | 0.142220i | ||||
\(89\) | − | 5.30085i | − | 0.561889i | −0.959724 | − | 0.280945i | \(-0.909352\pi\) | ||
0.959724 | − | 0.280945i | \(-0.0906477\pi\) | |||||||
\(90\) | 0.739473 | + | 0.900847i | 0.0779473 | + | 0.0949576i | ||||
\(91\) | 8.45035 | − | 8.45035i | 0.885837 | − | 0.885837i | ||||
\(92\) | −3.21015 | + | 16.1572i | −0.334681 | + | 1.68450i | ||||
\(93\) | 2.70310 | + | 2.70310i | 0.280298 | + | 0.280298i | ||||
\(94\) | 13.7978 | + | 1.35743i | 1.42314 | + | 0.140008i | ||||
\(95\) | −5.41036 | −0.555092 | ||||||||
\(96\) | 1.64509 | + | 5.41236i | 0.167901 | + | 0.552397i | ||||
\(97\) | 7.23833 | 0.734942 | 0.367471 | − | 0.930035i | \(-0.380224\pi\) | ||||
0.367471 | + | 0.930035i | \(0.380224\pi\) | |||||||
\(98\) | −23.9061 | − | 2.35188i | −2.41488 | − | 0.237575i | ||||
\(99\) | −0.707107 | − | 0.707107i | −0.0710669 | − | 0.0710669i | ||||
\(100\) | −1.68403 | + | 8.47598i | −0.168403 | + | 0.847598i | ||||
\(101\) | −7.36735 | + | 7.36735i | −0.733078 | + | 0.733078i | −0.971228 | − | 0.238150i | \(-0.923459\pi\) |
0.238150 | + | 0.971228i | \(0.423459\pi\) | |||||||
\(102\) | −1.98030 | − | 2.41245i | −0.196078 | − | 0.238868i | ||||
\(103\) | − | 7.81962i | − | 0.770490i | −0.922814 | − | 0.385245i | \(-0.874117\pi\) | ||
0.922814 | − | 0.385245i | \(-0.125883\pi\) | |||||||
\(104\) | 3.25547 | + | 6.08570i | 0.319225 | + | 0.596752i | ||||
\(105\) | − | 4.03614i | − | 0.393887i | ||||||
\(106\) | −1.76253 | + | 1.44680i | −0.171192 | + | 0.140525i | ||||
\(107\) | 1.94604 | − | 1.94604i | 0.188131 | − | 0.188131i | −0.606757 | − | 0.794887i | \(-0.707530\pi\) |
0.794887 | + | 0.606757i | \(0.207530\pi\) | |||||||
\(108\) | −1.66269 | + | 1.11151i | −0.159993 | + | 0.106955i | ||||
\(109\) | −0.638617 | − | 0.638617i | −0.0611684 | − | 0.0611684i | 0.675861 | − | 0.737029i | \(-0.263772\pi\) |
−0.737029 | + | 0.675861i | \(0.763772\pi\) | |||||||
\(110\) | −0.114109 | + | 1.15988i | −0.0108799 | + | 0.110590i | ||||
\(111\) | −6.57952 | −0.624500 | ||||||||
\(112\) | 7.48881 | − | 18.1022i | 0.707626 | − | 1.71050i | ||||
\(113\) | 0.698357 | 0.0656959 | 0.0328480 | − | 0.999460i | \(-0.489542\pi\) | ||||
0.0328480 | + | 0.999460i | \(0.489542\pi\) | |||||||
\(114\) | 0.909004 | − | 9.23974i | 0.0851361 | − | 0.865381i | ||||
\(115\) | 4.79974 | + | 4.79974i | 0.447578 | + | 0.447578i | ||||
\(116\) | −7.06262 | − | 10.5649i | −0.655748 | − | 0.980927i | ||||
\(117\) | −1.72543 | + | 1.72543i | −0.159516 | + | 0.159516i | ||||
\(118\) | 3.36503 | − | 2.76223i | 0.309776 | − | 0.254284i | ||||
\(119\) | 10.8087i | 0.990835i | ||||||||
\(120\) | 2.23081 | + | 0.675903i | 0.203645 | + | 0.0617012i | ||||
\(121\) | − | 1.00000i | − | 0.0909091i | ||||||
\(122\) | 2.98399 | + | 3.63518i | 0.270158 | + | 0.329114i | ||||
\(123\) | −7.21539 | + | 7.21539i | −0.650590 | + | 0.650590i | ||||
\(124\) | 7.49894 | + | 1.48991i | 0.673425 | + | 0.133798i | ||||
\(125\) | 5.43162 | + | 5.43162i | 0.485819 | + | 0.485819i | ||||
\(126\) | 6.89287 | + | 0.678119i | 0.614066 | + | 0.0604117i | ||||
\(127\) | −10.8716 | −0.964696 | −0.482348 | − | 0.875980i | \(-0.660216\pi\) | ||||
−0.482348 | + | 0.875980i | \(0.660216\pi\) | |||||||
\(128\) | 8.75116 | + | 7.17057i | 0.773501 | + | 0.633795i | ||||
\(129\) | −1.72611 | −0.151976 | ||||||||
\(130\) | 2.83026 | + | 0.278441i | 0.248230 | + | 0.0244208i | ||||
\(131\) | 10.4734 | + | 10.4734i | 0.915062 | + | 0.915062i | 0.996665 | − | 0.0816027i | \(-0.0260038\pi\) |
−0.0816027 | + | 0.996665i | \(0.526004\pi\) | |||||||
\(132\) | −1.96166 | − | 0.389747i | −0.170740 | − | 0.0339231i | ||||
\(133\) | −22.7352 | + | 22.7352i | −1.97139 | + | 1.97139i | ||||
\(134\) | −11.0353 | − | 13.4436i | −0.953308 | − | 1.16135i | ||||
\(135\) | 0.824119i | 0.0709289i | ||||||||
\(136\) | −5.97408 | − | 1.81006i | −0.512274 | − | 0.155211i | ||||
\(137\) | 18.9181i | 1.61628i | 0.588992 | + | 0.808139i | \(0.299525\pi\) | ||||
−0.588992 | + | 0.808139i | \(0.700475\pi\) | |||||||
\(138\) | −9.00333 | + | 7.39051i | −0.766415 | + | 0.629122i | ||||
\(139\) | 3.03763 | − | 3.03763i | 0.257649 | − | 0.257649i | −0.566449 | − | 0.824097i | \(-0.691683\pi\) |
0.824097 | + | 0.566449i | \(0.191683\pi\) | |||||||
\(140\) | −4.48621 | − | 6.71087i | −0.379154 | − | 0.567172i | ||||
\(141\) | 6.93222 | + | 6.93222i | 0.583799 | + | 0.583799i | ||||
\(142\) | 1.30801 | − | 13.2955i | 0.109765 | − | 1.11573i | ||||
\(143\) | −2.44013 | −0.204054 | ||||||||
\(144\) | −1.52910 | + | 3.69619i | −0.127425 | + | 0.308016i | ||||
\(145\) | −5.23653 | −0.434870 | ||||||||
\(146\) | 1.97001 | − | 20.0245i | 0.163039 | − | 1.65724i | ||||
\(147\) | −12.0107 | − | 12.0107i | −0.990630 | − | 0.990630i | ||||
\(148\) | −10.9397 | + | 7.31319i | −0.899240 | + | 0.601140i | ||||
\(149\) | 11.8476 | − | 11.8476i | 0.970592 | − | 0.970592i | −0.0289874 | − | 0.999580i | \(-0.509228\pi\) |
0.999580 | + | 0.0289874i | \(0.00922828\pi\) | |||||||
\(150\) | −4.72311 | + | 3.87703i | −0.385640 | + | 0.316558i | ||||
\(151\) | − | 14.6279i | − | 1.19040i | −0.803578 | − | 0.595200i | \(-0.797073\pi\) | ||
0.803578 | − | 0.595200i | \(-0.202927\pi\) | |||||||
\(152\) | −8.75865 | − | 16.3732i | −0.710421 | − | 1.32804i | ||||
\(153\) | − | 2.20698i | − | 0.178424i | ||||||
\(154\) | 4.39449 | + | 5.35350i | 0.354118 | + | 0.431397i | ||||
\(155\) | 2.22768 | − | 2.22768i | 0.178931 | − | 0.178931i | ||||
\(156\) | −0.951034 | + | 4.78670i | −0.0761436 | + | 0.383242i | ||||
\(157\) | 0.217412 | + | 0.217412i | 0.0173514 | + | 0.0173514i | 0.715729 | − | 0.698378i | \(-0.246094\pi\) |
−0.698378 | + | 0.715729i | \(0.746094\pi\) | |||||||
\(158\) | −2.54342 | − | 0.250221i | −0.202344 | − | 0.0199065i | ||||
\(159\) | −1.61241 | −0.127873 | ||||||||
\(160\) | 4.46043 | − | 1.35575i | 0.352628 | − | 0.107181i | ||||
\(161\) | 40.3384 | 3.17911 | ||||||||
\(162\) | −1.40742 | − | 0.138462i | −0.110577 | − | 0.0108786i | ||||
\(163\) | −17.0683 | − | 17.0683i | −1.33689 | − | 1.33689i | −0.899053 | − | 0.437841i | \(-0.855743\pi\) |
−0.437841 | − | 0.899053i | \(-0.644257\pi\) | |||||||
\(164\) | −3.97702 | + | 20.0170i | −0.310553 | + | 1.56306i | ||||
\(165\) | −0.582740 | + | 0.582740i | −0.0453663 | + | 0.0453663i | ||||
\(166\) | −4.12257 | − | 5.02224i | −0.319974 | − | 0.389801i | ||||
\(167\) | 4.03060i | 0.311897i | 0.987765 | + | 0.155948i | \(0.0498434\pi\) | ||||
−0.987765 | + | 0.155948i | \(0.950157\pi\) | |||||||
\(168\) | 12.2145 | − | 6.53398i | 0.942367 | − | 0.504107i | ||||
\(169\) | − | 7.04577i | − | 0.541982i | ||||||
\(170\) | −1.98815 | + | 1.63200i | −0.152484 | + | 0.125169i | ||||
\(171\) | 4.64217 | − | 4.64217i | 0.354996 | − | 0.354996i | ||||
\(172\) | −2.87000 | + | 1.91859i | −0.218835 | + | 0.146291i | ||||
\(173\) | 6.86259 | + | 6.86259i | 0.521753 | + | 0.521753i | 0.918101 | − | 0.396347i | \(-0.129722\pi\) |
−0.396347 | + | 0.918101i | \(0.629722\pi\) | |||||||
\(174\) | 0.879798 | − | 8.94287i | 0.0666973 | − | 0.677957i | ||||
\(175\) | 21.1614 | 1.59965 | ||||||||
\(176\) | −3.69484 | + | 1.53237i | −0.278509 | + | 0.115507i | ||||
\(177\) | 3.07842 | 0.231388 | ||||||||
\(178\) | 0.733965 | − | 7.46052i | 0.0550130 | − | 0.559190i | ||||
\(179\) | −4.44665 | − | 4.44665i | −0.332358 | − | 0.332358i | 0.521123 | − | 0.853481i | \(-0.325513\pi\) |
−0.853481 | + | 0.521123i | \(0.825513\pi\) | |||||||
\(180\) | 0.916015 | + | 1.37026i | 0.0682757 | + | 0.102133i | ||||
\(181\) | −12.2861 | + | 12.2861i | −0.913218 | + | 0.913218i | −0.996524 | − | 0.0833059i | \(-0.973452\pi\) |
0.0833059 | + | 0.996524i | \(0.473452\pi\) | |||||||
\(182\) | 13.0632 | − | 10.7231i | 0.968311 | − | 0.794852i | ||||
\(183\) | 3.32556i | 0.245833i | ||||||||
\(184\) | −6.75517 | + | 22.2954i | −0.497998 | + | 1.64364i | ||||
\(185\) | 5.42231i | 0.398656i | ||||||||
\(186\) | 3.43012 | + | 4.17867i | 0.251509 | + | 0.306395i | ||||
\(187\) | 1.56057 | − | 1.56057i | 0.114120 | − | 0.114120i | ||||
\(188\) | 19.2314 | + | 3.82094i | 1.40259 | + | 0.278671i | ||||
\(189\) | 3.46307 | + | 3.46307i | 0.251902 | + | 0.251902i | ||||
\(190\) | −7.61465 | − | 0.749128i | −0.552425 | − | 0.0543475i | ||||
\(191\) | 21.9781 | 1.59028 | 0.795140 | − | 0.606426i | \(-0.207397\pi\) | ||||
0.795140 | + | 0.606426i | \(0.207397\pi\) | |||||||
\(192\) | 1.56592 | + | 7.84525i | 0.113011 | + | 0.566182i | ||||
\(193\) | 7.33803 | 0.528203 | 0.264102 | − | 0.964495i | \(-0.414925\pi\) | ||||
0.264102 | + | 0.964495i | \(0.414925\pi\) | |||||||
\(194\) | 10.1874 | + | 1.00223i | 0.731411 | + | 0.0719560i | ||||
\(195\) | 1.42196 | + | 1.42196i | 0.101829 | + | 0.101829i | ||||
\(196\) | −33.3202 | − | 6.62015i | −2.38002 | − | 0.472868i | ||||
\(197\) | −5.33250 | + | 5.33250i | −0.379925 | + | 0.379925i | −0.871075 | − | 0.491150i | \(-0.836577\pi\) |
0.491150 | + | 0.871075i | \(0.336577\pi\) | |||||||
\(198\) | −0.897288 | − | 1.09310i | −0.0637675 | − | 0.0776834i | ||||
\(199\) | 21.9645i | 1.55702i | 0.627630 | + | 0.778511i | \(0.284025\pi\) | ||||
−0.627630 | + | 0.778511i | \(0.715975\pi\) | |||||||
\(200\) | −3.54373 | + | 11.6961i | −0.250580 | + | 0.827038i | ||||
\(201\) | − | 12.2985i | − | 0.867472i | ||||||
\(202\) | −11.3890 | + | 9.34885i | −0.801330 | + | 0.657783i | ||||
\(203\) | −22.0047 | + | 22.0047i | −1.54443 | + | 1.54443i | ||||
\(204\) | −2.45307 | − | 3.66953i | −0.171749 | − | 0.256918i | ||||
\(205\) | 5.94634 | + | 5.94634i | 0.415311 | + | 0.415311i | ||||
\(206\) | 1.08272 | − | 11.0055i | 0.0754365 | − | 0.766788i | ||||
\(207\) | −8.23649 | −0.572476 | ||||||||
\(208\) | 3.73917 | + | 9.01589i | 0.259265 | + | 0.625140i | ||||
\(209\) | 6.56503 | 0.454112 | ||||||||
\(210\) | 0.558851 | − | 5.68055i | 0.0385644 | − | 0.391995i | ||||
\(211\) | 8.27179 | + | 8.27179i | 0.569453 | + | 0.569453i | 0.931975 | − | 0.362522i | \(-0.118084\pi\) |
−0.362522 | + | 0.931975i | \(0.618084\pi\) | |||||||
\(212\) | −2.68095 | + | 1.79221i | −0.184128 | + | 0.123089i | ||||
\(213\) | 6.67983 | − | 6.67983i | 0.457694 | − | 0.457694i | ||||
\(214\) | 3.00834 | − | 2.46944i | 0.205646 | − | 0.168807i | ||||
\(215\) | 1.42252i | 0.0970152i | ||||||||
\(216\) | −2.49401 | + | 1.33414i | −0.169696 | + | 0.0907766i | ||||
\(217\) | − | 18.7221i | − | 1.27094i | ||||||
\(218\) | −0.810378 | − | 0.987226i | −0.0548857 | − | 0.0668634i | ||||
\(219\) | 10.0606 | − | 10.0606i | 0.679832 | − | 0.679832i | ||||
\(220\) | −0.321198 | + | 1.61664i | −0.0216552 | + | 0.108994i | ||||
\(221\) | −3.80799 | − | 3.80799i | −0.256153 | − | 0.256153i | ||||
\(222\) | −9.26014 | − | 0.911011i | −0.621500 | − | 0.0611430i | ||||
\(223\) | 24.9613 | 1.67153 | 0.835767 | − | 0.549084i | \(-0.185023\pi\) | ||||
0.835767 | + | 0.549084i | \(0.185023\pi\) | |||||||
\(224\) | 13.0464 | − | 24.4405i | 0.871696 | − | 1.63300i | ||||
\(225\) | −4.32083 | −0.288055 | ||||||||
\(226\) | 0.982881 | + | 0.0966957i | 0.0653803 | + | 0.00643210i | ||||
\(227\) | −15.9235 | − | 15.9235i | −1.05688 | − | 1.05688i | −0.998282 | − | 0.0585975i | \(-0.981337\pi\) |
−0.0585975 | − | 0.998282i | \(-0.518663\pi\) | |||||||
\(228\) | 2.55870 | − | 12.8783i | 0.169454 | − | 0.852888i | ||||
\(229\) | 11.5279 | − | 11.5279i | 0.761788 | − | 0.761788i | −0.214857 | − | 0.976645i | \(-0.568929\pi\) |
0.976645 | + | 0.214857i | \(0.0689286\pi\) | |||||||
\(230\) | 6.09066 | + | 7.41982i | 0.401606 | + | 0.489248i | ||||
\(231\) | 4.89753i | 0.322234i | ||||||||
\(232\) | −8.47724 | − | 15.8472i | −0.556558 | − | 1.04042i | ||||
\(233\) | 5.87804i | 0.385083i | 0.981289 | + | 0.192542i | \(0.0616731\pi\) | ||||
−0.981289 | + | 0.192542i | \(0.938327\pi\) | |||||||
\(234\) | −2.66731 | + | 2.18950i | −0.174368 | + | 0.143132i | ||||
\(235\) | 5.71298 | − | 5.71298i | 0.372674 | − | 0.372674i | ||||
\(236\) | 5.11847 | − | 3.42169i | 0.333184 | − | 0.222733i | ||||
\(237\) | −1.27785 | − | 1.27785i | −0.0830052 | − | 0.0830052i | ||||
\(238\) | −1.49659 | + | 15.2124i | −0.0970098 | + | 0.986074i | ||||
\(239\) | −0.0664988 | −0.00430145 | −0.00215072 | − | 0.999998i | \(-0.500685\pi\) | ||||
−0.00215072 | + | 0.999998i | \(0.500685\pi\) | |||||||
\(240\) | 3.04610 | + | 1.26016i | 0.196625 | + | 0.0813430i | ||||
\(241\) | −23.1161 | −1.48904 | −0.744520 | − | 0.667600i | \(-0.767322\pi\) | ||||
−0.744520 | + | 0.667600i | \(0.767322\pi\) | |||||||
\(242\) | 0.138462 | − | 1.40742i | 0.00890065 | − | 0.0904723i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 3.69639 | + | 5.52939i | 0.236637 | + | 0.353983i | ||||
\(245\) | −9.89829 | + | 9.89829i | −0.632378 | + | 0.632378i | ||||
\(246\) | −11.1541 | + | 9.15603i | −0.711162 | + | 0.583767i | ||||
\(247\) | − | 16.0195i | − | 1.01930i | ||||||
\(248\) | 10.3479 | + | 3.13524i | 0.657090 | + | 0.199088i | ||||
\(249\) | − | 4.59448i | − | 0.291163i | ||||||
\(250\) | 6.89250 | + | 8.39664i | 0.435920 | + | 0.531050i | ||||
\(251\) | −7.72118 | + | 7.72118i | −0.487356 | + | 0.487356i | −0.907471 | − | 0.420115i | \(-0.861990\pi\) |
0.420115 | + | 0.907471i | \(0.361990\pi\) | |||||||
\(252\) | 9.60726 | + | 1.90880i | 0.605201 | + | 0.120243i | ||||
\(253\) | −5.82408 | − | 5.82408i | −0.366157 | − | 0.366157i | ||||
\(254\) | −15.3009 | − | 1.50530i | −0.960061 | − | 0.0944506i | ||||
\(255\) | −1.81881 | −0.113898 | ||||||||
\(256\) | 11.3237 | + | 11.3037i | 0.707732 | + | 0.706481i | ||||
\(257\) | −1.47156 | −0.0917932 | −0.0458966 | − | 0.998946i | \(-0.514614\pi\) | ||||
−0.0458966 | + | 0.998946i | \(0.514614\pi\) | |||||||
\(258\) | −2.42936 | − | 0.239000i | −0.151246 | − | 0.0148795i | ||||
\(259\) | 22.7854 | + | 22.7854i | 1.41581 | + | 1.41581i | ||||
\(260\) | 3.94481 | + | 0.783765i | 0.244647 | + | 0.0486070i | ||||
\(261\) | 4.49302 | − | 4.49302i | 0.278111 | − | 0.278111i | ||||
\(262\) | 13.2903 | + | 16.1906i | 0.821075 | + | 1.00026i | ||||
\(263\) | − | 19.5129i | − | 1.20322i | −0.798790 | − | 0.601610i | \(-0.794526\pi\) | ||
0.798790 | − | 0.601610i | \(-0.205474\pi\) | |||||||
\(264\) | −2.70691 | − | 0.820152i | −0.166599 | − | 0.0504768i | ||||
\(265\) | 1.32882i | 0.0816287i | ||||||||
\(266\) | −35.1459 | + | 28.8500i | −2.15493 | + | 1.76890i | ||||
\(267\) | 3.74827 | − | 3.74827i | 0.229390 | − | 0.229390i | ||||
\(268\) | −13.6699 | − | 20.4487i | −0.835024 | − | 1.24910i | ||||
\(269\) | 5.88616 | + | 5.88616i | 0.358886 | + | 0.358886i | 0.863402 | − | 0.504517i | \(-0.168329\pi\) |
−0.504517 | + | 0.863402i | \(0.668329\pi\) | |||||||
\(270\) | −0.114109 | + | 1.15988i | −0.00694445 | + | 0.0705881i | ||||
\(271\) | 13.3108 | 0.808571 | 0.404286 | − | 0.914633i | \(-0.367520\pi\) | ||||
0.404286 | + | 0.914633i | \(0.367520\pi\) | |||||||
\(272\) | −8.15742 | − | 3.37469i | −0.494616 | − | 0.204621i | ||||
\(273\) | 11.9506 | 0.723283 | ||||||||
\(274\) | −2.61942 | + | 26.6256i | −0.158245 | + | 1.60851i | ||||
\(275\) | −3.05529 | − | 3.05529i | −0.184241 | − | 0.184241i | ||||
\(276\) | −13.6948 | + | 9.15493i | −0.824328 | + | 0.551062i | ||||
\(277\) | −0.343580 | + | 0.343580i | −0.0206438 | + | 0.0206438i | −0.717353 | − | 0.696710i | \(-0.754647\pi\) |
0.696710 | + | 0.717353i | \(0.254647\pi\) | |||||||
\(278\) | 4.69582 | − | 3.85463i | 0.281636 | − | 0.231185i | ||||
\(279\) | 3.82276i | 0.228863i | ||||||||
\(280\) | −5.38478 | − | 10.0662i | −0.321802 | − | 0.601569i | ||||
\(281\) | − | 0.183598i | − | 0.0109525i | −0.999985 | − | 0.00547627i | \(-0.998257\pi\) | ||
0.999985 | − | 0.00547627i | \(-0.00174316\pi\) | |||||||
\(282\) | 8.79670 | + | 10.7164i | 0.523836 | + | 0.638152i | ||||
\(283\) | 12.3011 | − | 12.3011i | 0.731225 | − | 0.731225i | −0.239637 | − | 0.970863i | \(-0.577029\pi\) |
0.970863 | + | 0.239637i | \(0.0770285\pi\) | |||||||
\(284\) | 3.68183 | − | 18.5312i | 0.218476 | − | 1.09962i | ||||
\(285\) | −3.82571 | − | 3.82571i | −0.226615 | − | 0.226615i | ||||
\(286\) | −3.43429 | − | 0.337864i | −0.203074 | − | 0.0199783i | ||||
\(287\) | 49.9749 | 2.94992 | ||||||||
\(288\) | −2.66387 | + | 4.99037i | −0.156970 | + | 0.294061i | ||||
\(289\) | −12.1293 | −0.713485 | ||||||||
\(290\) | −7.36999 | − | 0.725058i | −0.432781 | − | 0.0425769i | ||||
\(291\) | 5.11828 | + | 5.11828i | 0.300039 | + | 0.300039i | ||||
\(292\) | 5.54526 | − | 27.9101i | 0.324512 | − | 1.63332i | ||||
\(293\) | 2.19204 | − | 2.19204i | 0.128060 | − | 0.128060i | −0.640172 | − | 0.768232i | \(-0.721137\pi\) |
0.768232 | + | 0.640172i | \(0.221137\pi\) | |||||||
\(294\) | −15.2411 | − | 18.5672i | −0.888880 | − | 1.08286i | ||||
\(295\) | − | 2.53699i | − | 0.147709i | ||||||
\(296\) | −16.4094 | + | 8.77799i | −0.953775 | + | 0.510210i | ||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | 18.3150 | − | 15.0341i | 1.06096 | − | 0.870901i | ||||
\(299\) | −14.2115 | + | 14.2115i | −0.821873 | + | 0.821873i | ||||
\(300\) | −7.18421 | + | 4.80263i | −0.414781 | + | 0.277280i | ||||
\(301\) | 5.97765 | + | 5.97765i | 0.344546 | + | 0.344546i | ||||
\(302\) | 2.02540 | − | 20.5876i | 0.116549 | − | 1.18468i | ||||
\(303\) | −10.4190 | −0.598556 | ||||||||
\(304\) | −10.0600 | − | 24.2567i | −0.576982 | − | 1.39122i | ||||
\(305\) | 2.74066 | 0.156930 | ||||||||
\(306\) | 0.305582 | − | 3.10614i | 0.0174689 | − | 0.177566i | ||||
\(307\) | 4.73919 | + | 4.73919i | 0.270480 | + | 0.270480i | 0.829293 | − | 0.558814i | \(-0.188743\pi\) |
−0.558814 | + | 0.829293i | \(0.688743\pi\) | |||||||
\(308\) | 5.44364 | + | 8.14309i | 0.310180 | + | 0.463995i | ||||
\(309\) | 5.52930 | − | 5.52930i | 0.314551 | − | 0.314551i | ||||
\(310\) | 3.44372 | − | 2.82683i | 0.195590 | − | 0.160553i | ||||
\(311\) | − | 1.86379i | − | 0.105686i | −0.998603 | − | 0.0528431i | \(-0.983172\pi\) | ||
0.998603 | − | 0.0528431i | \(-0.0168283\pi\) | |||||||
\(312\) | −2.00128 | + | 6.60521i | −0.113300 | + | 0.373946i | ||||
\(313\) | 2.88059i | 0.162821i | 0.996681 | + | 0.0814103i | \(0.0259424\pi\) | ||||
−0.996681 | + | 0.0814103i | \(0.974058\pi\) | |||||||
\(314\) | 0.275887 | + | 0.336093i | 0.0155692 | + | 0.0189669i | ||||
\(315\) | 2.85399 | − | 2.85399i | 0.160804 | − | 0.160804i | ||||
\(316\) | −3.54501 | − | 0.704332i | −0.199422 | − | 0.0396218i | ||||
\(317\) | −10.6057 | − | 10.6057i | −0.595673 | − | 0.595673i | 0.343485 | − | 0.939158i | \(-0.388393\pi\) |
−0.939158 | + | 0.343485i | \(0.888393\pi\) | |||||||
\(318\) | −2.26934 | − | 0.223257i | −0.127258 | − | 0.0125196i | ||||
\(319\) | 6.35409 | 0.355761 | ||||||||
\(320\) | 6.46542 | − | 1.29051i | 0.361428 | − | 0.0721416i | ||||
\(321\) | 2.75211 | 0.153608 | ||||||||
\(322\) | 56.7731 | + | 5.58533i | 3.16384 | + | 0.311258i | ||||
\(323\) | 10.2452 | + | 10.2452i | 0.570057 | + | 0.570057i | ||||
\(324\) | −1.96166 | − | 0.389747i | −0.108981 | − | 0.0216526i | ||||
\(325\) | −7.45530 | + | 7.45530i | −0.413545 | + | 0.413545i | ||||
\(326\) | −21.6590 | − | 26.3856i | −1.19958 | − | 1.46136i | ||||
\(327\) | − | 0.903141i | − | 0.0499438i | ||||||
\(328\) | −8.36891 | + | 27.6216i | −0.462096 | + | 1.52515i | ||||
\(329\) | − | 48.0136i | − | 2.64708i | ||||||
\(330\) | −0.900847 | + | 0.739473i | −0.0495900 | + | 0.0407066i | ||||
\(331\) | −9.01783 | + | 9.01783i | −0.495665 | + | 0.495665i | −0.910085 | − | 0.414421i | \(-0.863984\pi\) |
0.414421 | + | 0.910085i | \(0.363984\pi\) | |||||||
\(332\) | −5.10680 | − | 7.63921i | −0.280272 | − | 0.419256i | ||||
\(333\) | −4.65242 | − | 4.65242i | −0.254951 | − | 0.254951i | ||||
\(334\) | −0.558083 | + | 5.67274i | −0.0305369 | + | 0.310398i | ||||
\(335\) | −10.1355 | −0.553760 | ||||||||
\(336\) | 18.0956 | − | 7.50481i | 0.987195 | − | 0.409421i | ||||
\(337\) | 19.9937 | 1.08913 | 0.544563 | − | 0.838720i | \(-0.316695\pi\) | ||||
0.544563 | + | 0.838720i | \(0.316695\pi\) | |||||||
\(338\) | 0.975568 | − | 9.91635i | 0.0530639 | − | 0.539378i | ||||
\(339\) | 0.493813 | + | 0.493813i | 0.0268202 | + | 0.0268202i | ||||
\(340\) | −3.02413 | + | 2.02162i | −0.164006 | + | 0.109638i | ||||
\(341\) | −2.70310 | + | 2.70310i | −0.146381 | + | 0.146381i | ||||
\(342\) | 7.17625 | − | 5.89072i | 0.388047 | − | 0.318534i | ||||
\(343\) | 48.9055i | 2.64065i | ||||||||
\(344\) | −4.30494 | + | 2.30287i | −0.232107 | + | 0.124163i | ||||
\(345\) | 6.78785i | 0.365446i | ||||||||
\(346\) | 8.70833 | + | 10.6087i | 0.468163 | + | 0.570330i | ||||
\(347\) | −14.4537 | + | 14.4537i | −0.775916 | + | 0.775916i | −0.979134 | − | 0.203217i | \(-0.934860\pi\) |
0.203217 | + | 0.979134i | \(0.434860\pi\) | |||||||
\(348\) | 2.47649 | − | 12.4645i | 0.132754 | − | 0.668170i | ||||
\(349\) | 20.2751 | + | 20.2751i | 1.08530 | + | 1.08530i | 0.996005 | + | 0.0892971i | \(0.0284621\pi\) |
0.0892971 | + | 0.996005i | \(0.471538\pi\) | |||||||
\(350\) | 29.7829 | + | 2.93004i | 1.59196 | + | 0.156617i | ||||
\(351\) | −2.44013 | −0.130244 | ||||||||
\(352\) | −5.41236 | + | 1.64509i | −0.288480 | + | 0.0876835i | ||||
\(353\) | 10.2789 | 0.547090 | 0.273545 | − | 0.961859i | \(-0.411804\pi\) | ||||
0.273545 | + | 0.961859i | \(0.411804\pi\) | |||||||
\(354\) | 4.33263 | + | 0.426243i | 0.230277 | + | 0.0226546i | ||||
\(355\) | −5.50497 | − | 5.50497i | −0.292174 | − | 0.292174i | ||||
\(356\) | 2.06599 | − | 10.3985i | 0.109497 | − | 0.551117i | ||||
\(357\) | −7.64293 | + | 7.64293i | −0.404507 | + | 0.404507i | ||||
\(358\) | −5.64261 | − | 6.87399i | −0.298221 | − | 0.363302i | ||||
\(359\) | 11.6208i | 0.613324i | 0.951818 | + | 0.306662i | \(0.0992121\pi\) | ||||
−0.951818 | + | 0.306662i | \(0.900788\pi\) | |||||||
\(360\) | 1.09949 | + | 2.05536i | 0.0579482 | + | 0.108327i | ||||
\(361\) | 24.0996i | 1.26840i | ||||||||
\(362\) | −18.9928 | + | 15.5905i | −0.998241 | + | 0.819420i | ||||
\(363\) | 0.707107 | − | 0.707107i | 0.0371135 | − | 0.0371135i | ||||
\(364\) | 19.8702 | − | 13.2832i | 1.04148 | − | 0.696228i | ||||
\(365\) | −8.29113 | − | 8.29113i | −0.433978 | − | 0.433978i | ||||
\(366\) | −0.460463 | + | 4.68046i | −0.0240688 | + | 0.244652i | ||||
\(367\) | −0.813135 | −0.0424453 | −0.0212226 | − | 0.999775i | \(-0.506756\pi\) | ||||
−0.0212226 | + | 0.999775i | \(0.506756\pi\) | |||||||
\(368\) | −12.5944 | + | 30.4437i | −0.656530 | + | 1.58699i | ||||
\(369\) | −10.2041 | −0.531205 | ||||||||
\(370\) | −0.750782 | + | 7.63146i | −0.0390313 | + | 0.396741i | ||||
\(371\) | 5.58390 | + | 5.58390i | 0.289902 | + | 0.289902i | ||||
\(372\) | 4.24903 | + | 6.35608i | 0.220302 | + | 0.329547i | ||||
\(373\) | 22.8768 | − | 22.8768i | 1.18451 | − | 1.18451i | 0.205953 | − | 0.978562i | \(-0.433971\pi\) |
0.978562 | − | 0.205953i | \(-0.0660294\pi\) | |||||||
\(374\) | 2.41245 | − | 1.98030i | 0.124745 | − | 0.102399i | ||||
\(375\) | 7.68147i | 0.396670i | ||||||||
\(376\) | 26.5376 | + | 8.04048i | 1.36857 | + | 0.414656i | ||||
\(377\) | − | 15.5048i | − | 0.798538i | ||||||
\(378\) | 4.39449 | + | 5.35350i | 0.226028 | + | 0.275354i | ||||
\(379\) | −3.21310 | + | 3.21310i | −0.165046 | + | 0.165046i | −0.784798 | − | 0.619752i | \(-0.787233\pi\) |
0.619752 | + | 0.784798i | \(0.287233\pi\) | |||||||
\(380\) | −10.6133 | − | 2.10867i | −0.544450 | − | 0.108173i | ||||
\(381\) | −7.68736 | − | 7.68736i | −0.393835 | − | 0.393835i | ||||
\(382\) | 30.9324 | + | 3.04312i | 1.58264 | + | 0.155700i | ||||
\(383\) | 9.08904 | 0.464428 | 0.232214 | − | 0.972665i | \(-0.425403\pi\) | ||||
0.232214 | + | 0.972665i | \(0.425403\pi\) | |||||||
\(384\) | 1.11765 | + | 11.2584i | 0.0570347 | + | 0.574526i | ||||
\(385\) | 4.03614 | 0.205701 | ||||||||
\(386\) | 10.3277 | + | 1.01604i | 0.525666 | + | 0.0517149i | ||||
\(387\) | −1.22055 | − | 1.22055i | −0.0620438 | − | 0.0620438i | ||||
\(388\) | 14.1991 | + | 2.82112i | 0.720852 | + | 0.143221i | ||||
\(389\) | 8.32569 | − | 8.32569i | 0.422129 | − | 0.422129i | −0.463807 | − | 0.885936i | \(-0.653517\pi\) |
0.885936 | + | 0.463807i | \(0.153517\pi\) | |||||||
\(390\) | 1.80441 | + | 2.19818i | 0.0913698 | + | 0.111309i | ||||
\(391\) | − | 18.1778i | − | 0.919288i | ||||||
\(392\) | −45.9789 | − | 13.9309i | −2.32228 | − | 0.703617i | ||||
\(393\) | 14.8116i | 0.747145i | ||||||||
\(394\) | −8.24340 | + | 6.76671i | −0.415297 | + | 0.340902i | ||||
\(395\) | −1.05310 | + | 1.05310i | −0.0529872 | + | 0.0529872i | ||||
\(396\) | −1.11151 | − | 1.66269i | −0.0558554 | − | 0.0835535i | ||||
\(397\) | −15.4784 | − | 15.4784i | −0.776840 | − | 0.776840i | 0.202452 | − | 0.979292i | \(-0.435109\pi\) |
−0.979292 | + | 0.202452i | \(0.935109\pi\) | |||||||
\(398\) | −3.04124 | + | 30.9133i | −0.152444 | + | 1.54954i | ||||
\(399\) | −32.1524 | −1.60963 | ||||||||
\(400\) | −6.60698 | + | 15.9706i | −0.330349 | + | 0.798531i | ||||
\(401\) | 8.52766 | 0.425851 | 0.212926 | − | 0.977068i | \(-0.431701\pi\) | ||||
0.212926 | + | 0.977068i | \(0.431701\pi\) | |||||||
\(402\) | 1.70288 | − | 17.3092i | 0.0849318 | − | 0.863305i | ||||
\(403\) | 6.59591 | + | 6.59591i | 0.328566 | + | 0.328566i | ||||
\(404\) | −17.3236 | + | 11.5808i | −0.861882 | + | 0.576166i | ||||
\(405\) | −0.582740 | + | 0.582740i | −0.0289566 | + | 0.0289566i | ||||
\(406\) | −34.0166 | + | 27.9230i | −1.68822 | + | 1.38580i | ||||
\(407\) | − | 6.57952i | − | 0.326135i | ||||||
\(408\) | −2.94441 | − | 5.50422i | −0.145770 | − | 0.272499i | ||||
\(409\) | − | 0.959341i | − | 0.0474364i | −0.999719 | − | 0.0237182i | \(-0.992450\pi\) | ||
0.999719 | − | 0.0237182i | \(-0.00755044\pi\) | |||||||
\(410\) | 7.54566 | + | 9.19234i | 0.372653 | + | 0.453977i | ||||
\(411\) | −13.3771 | + | 13.3771i | −0.659843 | + | 0.659843i | ||||
\(412\) | 3.04767 | − | 15.3394i | 0.150148 | − | 0.755718i | ||||
\(413\) | −10.6608 | − | 10.6608i | −0.524584 | − | 0.524584i | ||||
\(414\) | −11.5922 | − | 1.14044i | −0.569725 | − | 0.0560495i | ||||
\(415\) | −3.78640 | −0.185867 | ||||||||
\(416\) | 4.01423 | + | 13.2069i | 0.196814 | + | 0.647520i | ||||
\(417\) | 4.29586 | 0.210369 | ||||||||
\(418\) | 9.23974 | + | 0.909004i | 0.451931 | + | 0.0444609i | ||||
\(419\) | −15.9502 | − | 15.9502i | −0.779216 | − | 0.779216i | 0.200481 | − | 0.979697i | \(-0.435749\pi\) |
−0.979697 | + | 0.200481i | \(0.935749\pi\) | |||||||
\(420\) | 1.57308 | − | 7.91753i | 0.0767582 | − | 0.386336i | ||||
\(421\) | 6.78917 | − | 6.78917i | 0.330884 | − | 0.330884i | −0.522038 | − | 0.852922i | \(-0.674828\pi\) |
0.852922 | + | 0.522038i | \(0.174828\pi\) | |||||||
\(422\) | 10.4965 | + | 12.7872i | 0.510964 | + | 0.622471i | ||||
\(423\) | 9.80364i | 0.476669i | ||||||||
\(424\) | −4.02137 | + | 2.15118i | −0.195295 | + | 0.104471i | ||||
\(425\) | − | 9.53597i | − | 0.462562i | ||||||
\(426\) | 10.3262 | − | 8.47642i | 0.500307 | − | 0.410684i | ||||
\(427\) | 11.5167 | − | 11.5167i | 0.557331 | − | 0.557331i | ||||
\(428\) | 4.57592 | − | 3.05899i | 0.221185 | − | 0.147862i | ||||
\(429\) | −1.72543 | − | 1.72543i | −0.0833047 | − | 0.0833047i | ||||
\(430\) | −0.196965 | + | 2.00208i | −0.00949848 | + | 0.0965491i | ||||
\(431\) | −5.46458 | −0.263219 | −0.131610 | − | 0.991302i | \(-0.542015\pi\) | ||||
−0.131610 | + | 0.991302i | \(0.542015\pi\) | |||||||
\(432\) | −3.69484 | + | 1.53237i | −0.177768 | + | 0.0737260i | ||||
\(433\) | 33.8187 | 1.62522 | 0.812611 | − | 0.582806i | \(-0.198045\pi\) | ||||
0.812611 | + | 0.582806i | \(0.198045\pi\) | |||||||
\(434\) | 2.59229 | − | 26.3498i | 0.124434 | − | 1.26483i | ||||
\(435\) | −3.70278 | − | 3.70278i | −0.177535 | − | 0.177535i | ||||
\(436\) | −1.00385 | − | 1.50165i | −0.0480756 | − | 0.0719158i | ||||
\(437\) | 38.2352 | − | 38.2352i | 1.82904 | − | 1.82904i | ||||
\(438\) | 15.5525 | − | 12.7665i | 0.743127 | − | 0.610006i | ||||
\(439\) | 20.8628i | 0.995729i | 0.867255 | + | 0.497864i | \(0.165882\pi\) | ||||
−0.867255 | + | 0.497864i | \(0.834118\pi\) | |||||||
\(440\) | −0.675903 | + | 2.23081i | −0.0322224 | + | 0.106350i | ||||
\(441\) | − | 16.9858i | − | 0.808846i | ||||||
\(442\) | −4.83218 | − | 5.88670i | −0.229843 | − | 0.280002i | ||||
\(443\) | −23.9878 | + | 23.9878i | −1.13970 | + | 1.13970i | −0.151191 | + | 0.988505i | \(0.548311\pi\) |
−0.988505 | + | 0.151191i | \(0.951689\pi\) | |||||||
\(444\) | −12.9068 | − | 2.56435i | −0.612528 | − | 0.121699i | ||||
\(445\) | −3.08902 | − | 3.08902i | −0.146434 | − | 0.146434i | ||||
\(446\) | 35.1311 | + | 3.45619i | 1.66350 | + | 0.163655i | ||||
\(447\) | 16.7550 | 0.792485 | ||||||||
\(448\) | 21.7458 | − | 32.5916i | 1.02739 | − | 1.53981i | ||||
\(449\) | −23.6534 | −1.11627 | −0.558135 | − | 0.829750i | \(-0.688483\pi\) | ||||
−0.558135 | + | 0.829750i | \(0.688483\pi\) | |||||||
\(450\) | −6.08122 | − | 0.598269i | −0.286671 | − | 0.0282027i | ||||
\(451\) | −7.21539 | − | 7.21539i | −0.339760 | − | 0.339760i | ||||
\(452\) | 1.36994 | + | 0.272183i | 0.0644364 | + | 0.0128024i | ||||
\(453\) | 10.3435 | − | 10.3435i | 0.485979 | − | 0.485979i | ||||
\(454\) | −20.2062 | − | 24.6158i | −0.948325 | − | 1.15528i | ||||
\(455\) | − | 9.84872i | − | 0.461715i | ||||||
\(456\) | 5.38432 | − | 17.7709i | 0.252144 | − | 0.832200i | ||||
\(457\) | − | 0.845965i | − | 0.0395726i | −0.999804 | − | 0.0197863i | \(-0.993701\pi\) | ||
0.999804 | − | 0.0197863i | \(-0.00629858\pi\) | |||||||
\(458\) | 17.8208 | − | 14.6285i | 0.832713 | − | 0.683544i | ||||
\(459\) | 1.56057 | − | 1.56057i | 0.0728411 | − | 0.0728411i | ||||
\(460\) | 7.54475 | + | 11.2861i | 0.351776 | + | 0.526218i | ||||
\(461\) | −7.70908 | − | 7.70908i | −0.359047 | − | 0.359047i | 0.504414 | − | 0.863462i | \(-0.331708\pi\) |
−0.863462 | + | 0.504414i | \(0.831708\pi\) | |||||||
\(462\) | −0.678119 | + | 6.89287i | −0.0315490 | + | 0.320685i | ||||
\(463\) | −29.6331 | −1.37717 | −0.688584 | − | 0.725156i | \(-0.741767\pi\) | ||||
−0.688584 | + | 0.725156i | \(0.741767\pi\) | |||||||
\(464\) | −9.73680 | − | 23.4774i | −0.452020 | − | 1.08991i | ||||
\(465\) | 3.15041 | 0.146097 | ||||||||
\(466\) | −0.813883 | + | 8.27287i | −0.0377024 | + | 0.383233i | ||||
\(467\) | −22.1239 | − | 22.1239i | −1.02377 | − | 1.02377i | −0.999710 | − | 0.0240610i | \(-0.992340\pi\) |
−0.0240610 | − | 0.999710i | \(-0.507660\pi\) | |||||||
\(468\) | −4.05719 | + | 2.71222i | −0.187544 | + | 0.125373i | ||||
\(469\) | −42.5908 | + | 42.5908i | −1.96666 | + | 1.96666i | ||||
\(470\) | 8.83158 | − | 7.24953i | 0.407371 | − | 0.334396i | ||||
\(471\) | 0.307467i | 0.0141674i | ||||||||
\(472\) | 7.67761 | − | 4.10704i | 0.353391 | − | 0.189042i | ||||
\(473\) | − | 1.72611i | − | 0.0793667i | ||||||
\(474\) | −1.62154 | − | 1.97540i | −0.0744796 | − | 0.0907332i | ||||
\(475\) | 20.0580 | − | 20.0580i | 0.920326 | − | 0.920326i | ||||
\(476\) | −4.21267 | + | 21.2030i | −0.193087 | + | 0.971839i | ||||
\(477\) | −1.14015 | − | 1.14015i | −0.0522037 | − | 0.0522037i | ||||
\(478\) | −0.0935916 | − | 0.00920753i | −0.00428078 | − | 0.000421142i | ||||
\(479\) | 10.8545 | 0.495953 | 0.247976 | − | 0.968766i | \(-0.420234\pi\) | ||||
0.247976 | + | 0.968766i | \(0.420234\pi\) | |||||||
\(480\) | 4.11266 | + | 2.19534i | 0.187716 | + | 0.100203i | ||||
\(481\) | −16.0549 | −0.732039 | ||||||||
\(482\) | −32.5341 | − | 3.20070i | −1.48189 | − | 0.145788i | ||||
\(483\) | 28.5236 | + | 28.5236i | 1.29787 | + | 1.29787i | ||||
\(484\) | 0.389747 | − | 1.96166i | 0.0177158 | − | 0.0891662i | ||||
\(485\) | 4.21807 | − | 4.21807i | 0.191533 | − | 0.191533i | ||||
\(486\) | −0.897288 | − | 1.09310i | −0.0407018 | − | 0.0495841i | ||||
\(487\) | − | 6.22316i | − | 0.281999i | −0.990010 | − | 0.140999i | \(-0.954968\pi\) | ||
0.990010 | − | 0.140999i | \(-0.0450315\pi\) | |||||||
\(488\) | 4.43676 | + | 8.29398i | 0.200843 | + | 0.375451i | ||||
\(489\) | − | 24.1382i | − | 1.09157i | ||||||
\(490\) | −15.3016 | + | 12.5605i | −0.691254 | + | 0.567426i | ||||
\(491\) | −26.7116 | + | 26.7116i | −1.20548 | + | 1.20548i | −0.233002 | + | 0.972476i | \(0.574855\pi\) |
−0.972476 | + | 0.233002i | \(0.925145\pi\) | |||||||
\(492\) | −16.9663 | + | 11.3419i | −0.764900 | + | 0.511334i | ||||
\(493\) | 9.91600 | + | 9.91600i | 0.446594 | + | 0.446594i | ||||
\(494\) | 2.21809 | − | 22.5462i | 0.0997965 | − | 1.01440i | ||||
\(495\) | −0.824119 | −0.0370414 | ||||||||
\(496\) | 14.1297 | + | 5.84538i | 0.634441 | + | 0.262465i | ||||
\(497\) | −46.2655 | −2.07529 | ||||||||
\(498\) | 0.636159 | − | 6.46636i | 0.0285070 | − | 0.289764i | ||||
\(499\) | 11.3391 | + | 11.3391i | 0.507607 | + | 0.507607i | 0.913791 | − | 0.406184i | \(-0.133141\pi\) |
−0.406184 | + | 0.913791i | \(0.633141\pi\) | |||||||
\(500\) | 8.53802 | + | 12.7719i | 0.381832 | + | 0.571178i | ||||
\(501\) | −2.85006 | + | 2.85006i | −0.127331 | + | 0.127331i | ||||
\(502\) | −11.9360 | + | 9.79785i | −0.532731 | + | 0.437299i | ||||
\(503\) | − | 28.6656i | − | 1.27814i | −0.769151 | − | 0.639068i | \(-0.779320\pi\) | ||
0.769151 | − | 0.639068i | \(-0.220680\pi\) | |||||||
\(504\) | 13.2572 | + | 4.01671i | 0.590521 | + | 0.178919i | ||||
\(505\) | 8.58650i | 0.382094i | ||||||||
\(506\) | −7.39051 | − | 9.00333i | −0.328548 | − | 0.400247i | ||||
\(507\) | 4.98211 | − | 4.98211i | 0.221263 | − | 0.221263i | ||||
\(508\) | −21.3263 | − | 4.23716i | −0.946201 | − | 0.187994i | ||||
\(509\) | −5.69583 | − | 5.69583i | −0.252463 | − | 0.252463i | 0.569517 | − | 0.821980i | \(-0.307130\pi\) |
−0.821980 | + | 0.569517i | \(0.807130\pi\) | |||||||
\(510\) | −2.55983 | − | 0.251836i | −0.113351 | − | 0.0111515i | ||||
\(511\) | −69.6812 | −3.08251 | ||||||||
\(512\) | 14.3721 | + | 17.4769i | 0.635162 | + | 0.772379i | ||||
\(513\) | 6.56503 | 0.289853 | ||||||||
\(514\) | −2.07110 | − | 0.203754i | −0.0913522 | − | 0.00898722i | ||||
\(515\) | −4.55681 | − | 4.55681i | −0.200797 | − | 0.200797i | ||||
\(516\) | −3.38604 | − | 0.672747i | −0.149062 | − | 0.0296160i | ||||
\(517\) | −6.93222 | + | 6.93222i | −0.304879 | + | 0.304879i | ||||
\(518\) | 28.9136 | + | 35.2234i | 1.27039 | + | 1.54763i | ||||
\(519\) | 9.70517i | 0.426010i | ||||||||
\(520\) | 5.44348 | + | 1.64929i | 0.238712 | + | 0.0723262i | ||||
\(521\) | 3.76148i | 0.164794i | 0.996600 | + | 0.0823968i | \(0.0262575\pi\) | ||||
−0.996600 | + | 0.0823968i | \(0.973743\pi\) | |||||||
\(522\) | 6.94567 | − | 5.70145i | 0.304004 | − | 0.249546i | ||||
\(523\) | −6.40138 | + | 6.40138i | −0.279913 | + | 0.279913i | −0.833074 | − | 0.553161i | \(-0.813421\pi\) |
0.553161 | + | 0.833074i | \(0.313421\pi\) | |||||||
\(524\) | 16.4632 | + | 24.6271i | 0.719198 | + | 1.07584i | ||||
\(525\) | 14.9633 | + | 14.9633i | 0.653054 | + | 0.653054i | ||||
\(526\) | 2.70179 | − | 27.4629i | 0.117804 | − | 1.19744i | ||||
\(527\) | −8.43675 | −0.367510 | ||||||||
\(528\) | −3.69619 | − | 1.52910i | −0.160856 | − | 0.0665455i | ||||
\(529\) | −44.8398 | −1.94956 | ||||||||
\(530\) | −0.183990 | + | 1.87021i | −0.00799203 | + | 0.0812365i | ||||
\(531\) | 2.17677 | + | 2.17677i | 0.0944639 | + | 0.0944639i | ||||
\(532\) | −53.4596 | + | 35.7376i | −2.31777 | + | 1.54942i | ||||
\(533\) | −17.6065 | + | 17.6065i | −0.762622 | + | 0.762622i | ||||
\(534\) | 5.79438 | − | 4.75639i | 0.250747 | − | 0.205829i | ||||
\(535\) | − | 2.26807i | − | 0.0980572i | ||||||
\(536\) | −16.4080 | − | 30.6727i | −0.708716 | − | 1.32486i | ||||
\(537\) | − | 6.28851i | − | 0.271369i | ||||||
\(538\) | 7.46929 | + | 9.09930i | 0.322024 | + | 0.392299i | ||||
\(539\) | 12.0107 | − | 12.0107i | 0.517339 | − | 0.517339i | ||||
\(540\) | −0.321198 | + | 1.61664i | −0.0138222 | + | 0.0695691i | ||||
\(541\) | 7.83193 | + | 7.83193i | 0.336721 | + | 0.336721i | 0.855132 | − | 0.518411i | \(-0.173476\pi\) |
−0.518411 | + | 0.855132i | \(0.673476\pi\) | |||||||
\(542\) | 18.7338 | + | 1.84303i | 0.804687 | + | 0.0791649i | ||||
\(543\) | −17.3752 | −0.745639 | ||||||||
\(544\) | −11.0136 | − | 5.87909i | −0.472206 | − | 0.252064i | ||||
\(545\) | −0.744296 | −0.0318821 | ||||||||
\(546\) | 16.8195 | + | 1.65470i | 0.719808 | + | 0.0708146i | ||||
\(547\) | −9.88804 | − | 9.88804i | −0.422782 | − | 0.422782i | 0.463378 | − | 0.886161i | \(-0.346637\pi\) |
−0.886161 | + | 0.463378i | \(0.846637\pi\) | |||||||
\(548\) | −7.37326 | + | 37.1107i | −0.314970 | + | 1.58529i | ||||
\(549\) | −2.35153 | + | 2.35153i | −0.100361 | + | 0.100361i | ||||
\(550\) | −3.87703 | − | 4.72311i | −0.165317 | − | 0.201394i | ||||
\(551\) | 41.7148i | 1.77711i | ||||||||
\(552\) | −20.5419 | + | 10.9886i | −0.874320 | + | 0.467707i | ||||
\(553\) | 8.85057i | 0.376365i | ||||||||
\(554\) | −0.531134 | + | 0.435989i | −0.0225657 | + | 0.0185234i | ||||
\(555\) | −3.83415 | + | 3.83415i | −0.162751 | + | 0.162751i | ||||
\(556\) | 7.14270 | − | 4.77488i | 0.302918 | − | 0.202500i | ||||
\(557\) | −11.7849 | − | 11.7849i | −0.499342 | − | 0.499342i | 0.411891 | − | 0.911233i | \(-0.364868\pi\) |
−0.911233 | + | 0.411891i | \(0.864868\pi\) | |||||||
\(558\) | −0.529306 | + | 5.38023i | −0.0224073 | + | 0.227763i | ||||
\(559\) | −4.21194 | −0.178146 | ||||||||
\(560\) | −6.18486 | − | 14.9129i | −0.261358 | − | 0.630186i | ||||
\(561\) | 2.20698 | 0.0931787 | ||||||||
\(562\) | 0.0254213 | − | 0.258399i | 0.00107233 | − | 0.0108999i | ||||
\(563\) | −6.86919 | − | 6.86919i | −0.289502 | − | 0.289502i | 0.547381 | − | 0.836883i | \(-0.315625\pi\) |
−0.836883 | + | 0.547381i | \(0.815625\pi\) | |||||||
\(564\) | 10.8968 | + | 16.3005i | 0.458839 | + | 0.686373i | ||||
\(565\) | 0.406961 | − | 0.406961i | 0.0171210 | − | 0.0171210i | ||||
\(566\) | 19.0161 | − | 15.6096i | 0.799304 | − | 0.656120i | ||||
\(567\) | 4.89753i | 0.205677i | ||||||||
\(568\) | 7.74773 | − | 25.5714i | 0.325088 | − | 1.07295i | ||||
\(569\) | 2.65812i | 0.111434i | 0.998447 | + | 0.0557170i | \(0.0177445\pi\) | ||||
−0.998447 | + | 0.0557170i | \(0.982256\pi\) | |||||||
\(570\) | −4.85466 | − | 5.91408i | −0.203339 | − | 0.247714i | ||||
\(571\) | −3.47521 | + | 3.47521i | −0.145433 | + | 0.145433i | −0.776074 | − | 0.630641i | \(-0.782792\pi\) |
0.630641 | + | 0.776074i | \(0.282792\pi\) | |||||||
\(572\) | −4.78670 | − | 0.951034i | −0.200142 | − | 0.0397647i | ||||
\(573\) | 15.5409 | + | 15.5409i | 0.649229 | + | 0.649229i | ||||
\(574\) | 70.3356 | + | 6.91960i | 2.93575 | + | 0.288819i | ||||
\(575\) | −35.5885 | −1.48414 | ||||||||
\(576\) | −4.44015 | + | 6.65470i | −0.185006 | + | 0.277279i | ||||
\(577\) | 20.5740 | 0.856506 | 0.428253 | − | 0.903659i | \(-0.359129\pi\) | ||||
0.428253 | + | 0.903659i | \(0.359129\pi\) | |||||||
\(578\) | −17.0709 | − | 1.67944i | −0.710057 | − | 0.0698553i | ||||
\(579\) | 5.18877 | + | 5.18877i | 0.215638 | + | 0.215638i | ||||
\(580\) | −10.2723 | − | 2.04092i | −0.426533 | − | 0.0847447i | ||||
\(581\) | −15.9110 | + | 15.9110i | −0.660100 | + | 0.660100i | ||||
\(582\) | 6.49487 | + | 7.91224i | 0.269221 | + | 0.327973i | ||||
\(583\) | − | 1.61241i | − | 0.0667792i | ||||||
\(584\) | 11.6690 | − | 38.5134i | 0.482866 | − | 1.59370i | ||||
\(585\) | 2.01096i | 0.0831429i | ||||||||
\(586\) | 3.38863 | − | 2.78160i | 0.139983 | − | 0.114907i | ||||
\(587\) | 3.77592 | − | 3.77592i | 0.155849 | − | 0.155849i | −0.624875 | − | 0.780724i | \(-0.714850\pi\) |
0.780724 | + | 0.624875i | \(0.214850\pi\) | |||||||
\(588\) | −18.8798 | − | 28.2421i | −0.778590 | − | 1.16469i | ||||
\(589\) | −17.7459 | − | 17.7459i | −0.731208 | − | 0.731208i | ||||
\(590\) | 0.351275 | − | 3.57060i | 0.0144618 | − | 0.146999i | ||||
\(591\) | −7.54129 | −0.310207 | ||||||||
\(592\) | −24.3103 | + | 10.0822i | −0.999146 | + | 0.414377i | ||||
\(593\) | 26.4648 | 1.08678 | 0.543390 | − | 0.839481i | \(-0.317141\pi\) | ||||
0.543390 | + | 0.839481i | \(0.317141\pi\) | |||||||
\(594\) | 0.138462 | − | 1.40742i | 0.00568115 | − | 0.0577471i | ||||
\(595\) | 6.29868 | + | 6.29868i | 0.258221 | + | 0.258221i | ||||
\(596\) | 27.8585 | − | 18.6233i | 1.14113 | − | 0.762842i | ||||
\(597\) | −15.5313 | + | 15.5313i | −0.635652 | + | 0.635652i | ||||
\(598\) | −21.9693 | + | 18.0338i | −0.898391 | + | 0.737457i | ||||
\(599\) | 6.53747i | 0.267114i | 0.991041 | + | 0.133557i | \(0.0426399\pi\) | ||||
−0.991041 | + | 0.133557i | \(0.957360\pi\) | |||||||
\(600\) | −10.7762 | + | 5.76458i | −0.439936 | + | 0.235338i | ||||
\(601\) | − | 13.0445i | − | 0.532096i | −0.963960 | − | 0.266048i | \(-0.914282\pi\) | ||
0.963960 | − | 0.266048i | \(-0.0857179\pi\) | |||||||
\(602\) | 7.58539 | + | 9.24074i | 0.309157 | + | 0.376624i | ||||
\(603\) | 8.69638 | − | 8.69638i | 0.354144 | − | 0.354144i | ||||
\(604\) | 5.70117 | − | 28.6949i | 0.231977 | − | 1.16758i | ||||
\(605\) | −0.582740 | − | 0.582740i | −0.0236918 | − | 0.0236918i | ||||
\(606\) | −14.6639 | − | 1.44263i | −0.595680 | − | 0.0586029i | ||||
\(607\) | −10.2549 | −0.416235 | −0.208117 | − | 0.978104i | \(-0.566734\pi\) | ||||
−0.208117 | + | 0.978104i | \(0.566734\pi\) | |||||||
\(608\) | −10.8001 | − | 35.5323i | −0.438000 | − | 1.44103i | ||||
\(609\) | −31.1193 | −1.26102 | ||||||||
\(610\) | 3.85726 | + | 0.379476i | 0.156176 | + | 0.0153645i | ||||
\(611\) | 16.9155 | + | 16.9155i | 0.684329 | + | 0.684329i | ||||
\(612\) | 0.860163 | − | 4.32933i | 0.0347700 | − | 0.175003i | ||||
\(613\) | 6.91080 | − | 6.91080i | 0.279125 | − | 0.279125i | −0.553635 | − | 0.832759i | \(-0.686760\pi\) |
0.832759 | + | 0.553635i | \(0.186760\pi\) | |||||||
\(614\) | 6.01383 | + | 7.32622i | 0.242698 | + | 0.295662i | ||||
\(615\) | 8.40940i | 0.339100i | ||||||||
\(616\) | 6.53398 | + | 12.2145i | 0.263261 | + | 0.492135i | ||||
\(617\) | 2.64616i | 0.106531i | 0.998580 | + | 0.0532653i | \(0.0169629\pi\) | ||||
−0.998580 | + | 0.0532653i | \(0.983037\pi\) | |||||||
\(618\) | 8.54765 | − | 7.01645i | 0.343837 | − | 0.282243i | ||||
\(619\) | −19.2581 | + | 19.2581i | −0.774050 | + | 0.774050i | −0.978812 | − | 0.204762i | \(-0.934358\pi\) |
0.204762 | + | 0.978812i | \(0.434358\pi\) | |||||||
\(620\) | 5.23817 | − | 3.50171i | 0.210370 | − | 0.140632i | ||||
\(621\) | −5.82408 | − | 5.82408i | −0.233712 | − | 0.233712i | ||||
\(622\) | 0.258064 | − | 2.62314i | 0.0103474 | − | 0.105178i | ||||
\(623\) | −25.9611 | −1.04011 | ||||||||
\(624\) | −3.73120 | + | 9.01919i | −0.149368 | + | 0.361057i | ||||
\(625\) | −15.2737 | −0.610948 | ||||||||
\(626\) | −0.398851 | + | 4.05420i | −0.0159413 | + | 0.162038i | ||||
\(627\) | 4.64217 | + | 4.64217i | 0.185391 | + | 0.185391i | ||||
\(628\) | 0.341753 | + | 0.511224i | 0.0136374 | + | 0.0204001i | ||||
\(629\) | 10.2678 | − | 10.2678i | 0.409404 | − | 0.409404i | ||||
\(630\) | 4.41192 | − | 3.62159i | 0.175775 | − | 0.144287i | ||||
\(631\) | 14.1966i | 0.565156i | 0.959244 | + | 0.282578i | \(0.0911896\pi\) | ||||
−0.959244 | + | 0.282578i | \(0.908810\pi\) | |||||||
\(632\) | −4.89179 | − | 1.48214i | −0.194585 | − | 0.0589563i | ||||
\(633\) | 11.6981i | 0.464957i | ||||||||
\(634\) | −13.4581 | − | 16.3951i | −0.534491 | − | 0.651132i | ||||
\(635\) | −6.33530 | + | 6.33530i | −0.251409 | + | 0.251409i | ||||
\(636\) | −3.16300 | − | 0.628433i | −0.125421 | − | 0.0249190i | ||||
\(637\) | −29.3078 | − | 29.3078i | −1.16122 | − | 1.16122i | ||||
\(638\) | 8.94287 | + | 0.879798i | 0.354052 | + | 0.0348315i | ||||
\(639\) | 9.44670 | 0.373706 | ||||||||
\(640\) | 9.27824 | − | 0.921074i | 0.366755 | − | 0.0364086i | ||||
\(641\) | −21.6912 | −0.856753 | −0.428376 | − | 0.903600i | \(-0.640914\pi\) | ||||
−0.428376 | + | 0.903600i | \(0.640914\pi\) | |||||||
\(642\) | 3.87338 | + | 0.381062i | 0.152870 | + | 0.0150393i | ||||
\(643\) | 32.7693 | + | 32.7693i | 1.29229 | + | 1.29229i | 0.933365 | + | 0.358930i | \(0.116858\pi\) |
0.358930 | + | 0.933365i | \(0.383142\pi\) | |||||||
\(644\) | 79.1302 | + | 15.7218i | 3.11817 | + | 0.619525i | ||||
\(645\) | −1.00588 | + | 1.00588i | −0.0396063 | + | 0.0396063i | ||||
\(646\) | 13.0007 | + | 15.8378i | 0.511505 | + | 0.623131i | ||||
\(647\) | − | 49.5258i | − | 1.94706i | −0.228563 | − | 0.973529i | \(-0.573403\pi\) | ||
0.228563 | − | 0.973529i | \(-0.426597\pi\) | |||||||
\(648\) | −2.70691 | − | 0.820152i | −0.106337 | − | 0.0322186i | ||||
\(649\) | 3.07842i | 0.120839i | ||||||||
\(650\) | −11.5250 | + | 9.46045i | −0.452048 | + | 0.371069i | ||||
\(651\) | 13.2385 | − | 13.2385i | 0.518858 | − | 0.518858i | ||||
\(652\) | −26.8298 | − | 40.1345i | −1.05074 | − | 1.57179i | ||||
\(653\) | −31.1015 | − | 31.1015i | −1.21710 | − | 1.21710i | −0.968645 | − | 0.248450i | \(-0.920079\pi\) |
−0.248450 | − | 0.968645i | \(-0.579921\pi\) | |||||||
\(654\) | 0.125050 | − | 1.27110i | 0.00488986 | − | 0.0497039i | ||||
\(655\) | 12.2065 | 0.476948 | ||||||||
\(656\) | −15.6031 | + | 37.7164i | −0.609199 | + | 1.47258i | ||||
\(657\) | 14.2278 | 0.555081 | ||||||||
\(658\) | 6.64804 | − | 67.5753i | 0.259168 | − | 2.63436i | ||||
\(659\) | 12.4434 | + | 12.4434i | 0.484727 | + | 0.484727i | 0.906637 | − | 0.421911i | \(-0.138640\pi\) |
−0.421911 | + | 0.906637i | \(0.638640\pi\) | |||||||
\(660\) | −1.37026 | + | 0.916015i | −0.0533372 | + | 0.0356558i | ||||
\(661\) | 22.2673 | − | 22.2673i | 0.866098 | − | 0.866098i | −0.125940 | − | 0.992038i | \(-0.540195\pi\) |
0.992038 | + | 0.125940i | \(0.0401948\pi\) | |||||||
\(662\) | −13.9405 | + | 11.4432i | −0.541812 | + | 0.444754i | ||||
\(663\) | − | 5.38531i | − | 0.209148i | ||||||
\(664\) | −6.12967 | − | 11.4587i | −0.237877 | − | 0.444683i | ||||
\(665\) | 26.4974i | 1.02753i | ||||||||
\(666\) | −5.90373 | − | 7.19209i | −0.228765 | − | 0.278688i | ||||
\(667\) | 37.0067 | − | 37.0067i | 1.43291 | − | 1.43291i | ||||
\(668\) | −1.57091 | + | 7.90665i | −0.0607805 | + | 0.305917i | ||||
\(669\) | 17.6503 | + | 17.6503i | 0.682401 | + | 0.682401i | ||||
\(670\) | −14.2648 | − | 1.40337i | −0.551099 | − | 0.0542170i | ||||
\(671\) | −3.32556 | −0.128382 | ||||||||
\(672\) | 26.5072 | − | 8.05687i | 1.02254 | − | 0.310800i | ||||
\(673\) | 11.8771 | 0.457829 | 0.228914 | − | 0.973447i | \(-0.426482\pi\) | ||||
0.228914 | + | 0.973447i | \(0.426482\pi\) | |||||||
\(674\) | 28.1395 | + | 2.76836i | 1.08389 | + | 0.106633i | ||||
\(675\) | −3.05529 | − | 3.05529i | −0.117598 | − | 0.117598i | ||||
\(676\) | 2.74607 | − | 13.8214i | 0.105618 | − | 0.531591i | ||||
\(677\) | −5.07654 | + | 5.07654i | −0.195107 | + | 0.195107i | −0.797899 | − | 0.602792i | \(-0.794055\pi\) |
0.602792 | + | 0.797899i | \(0.294055\pi\) | |||||||
\(678\) | 0.626628 | + | 0.763376i | 0.0240655 | + | 0.0293173i | ||||
\(679\) | − | 35.4499i | − | 1.36044i | ||||||
\(680\) | −4.53613 | + | 2.42655i | −0.173953 | + | 0.0930538i | ||||
\(681\) | − | 22.5192i | − | 0.862938i | ||||||
\(682\) | −4.17867 | + | 3.43012i | −0.160010 | + | 0.131346i | ||||
\(683\) | −9.91820 | + | 9.91820i | −0.379510 | + | 0.379510i | −0.870925 | − | 0.491416i | \(-0.836480\pi\) |
0.491416 | + | 0.870925i | \(0.336480\pi\) | |||||||
\(684\) | 10.9156 | − | 7.29708i | 0.417369 | − | 0.279011i | ||||
\(685\) | 11.0243 | + | 11.0243i | 0.421217 | + | 0.421217i | ||||
\(686\) | −6.77154 | + | 68.8306i | −0.258539 | + | 2.62796i | ||||
\(687\) | 16.3030 | 0.621998 | ||||||||
\(688\) | −6.37771 | + | 2.64504i | −0.243148 | + | 0.100841i | ||||
\(689\) | −3.93449 | −0.149892 | ||||||||
\(690\) | −0.939857 | + | 9.55335i | −0.0357797 | + | 0.363690i | ||||
\(691\) | −20.2640 | − | 20.2640i | −0.770880 | − | 0.770880i | 0.207380 | − | 0.978260i | \(-0.433506\pi\) |
−0.978260 | + | 0.207380i | \(0.933506\pi\) | |||||||
\(692\) | 10.7874 | + | 16.1367i | 0.410074 | + | 0.613426i | ||||
\(693\) | −3.46307 | + | 3.46307i | −0.131551 | + | 0.131551i | ||||
\(694\) | −22.3437 | + | 18.3412i | −0.848156 | + | 0.696221i | ||||
\(695\) | − | 3.54030i | − | 0.134291i | ||||||
\(696\) | 5.21132 | − | 17.1999i | 0.197535 | − | 0.651962i | ||||
\(697\) | − | 22.5202i | − | 0.853015i | ||||||
\(698\) | 25.7283 | + | 31.3429i | 0.973829 | + | 1.18635i | ||||
\(699\) | −4.15640 | + | 4.15640i | −0.157210 | + | 0.157210i | ||||
\(700\) | 41.5113 | + | 8.24758i | 1.56898 | + | 0.311729i | ||||
\(701\) | 3.05442 | + | 3.05442i | 0.115364 | + | 0.115364i | 0.762432 | − | 0.647068i | \(-0.224005\pi\) |
−0.647068 | + | 0.762432i | \(0.724005\pi\) | |||||||
\(702\) | −3.43429 | − | 0.337864i | −0.129619 | − | 0.0127519i | ||||
\(703\) | 43.1947 | 1.62912 | ||||||||
\(704\) | −7.84525 | + | 1.56592i | −0.295679 | + | 0.0590180i | ||||
\(705\) | 8.07937 | 0.304287 | ||||||||
\(706\) | 14.4667 | + | 1.42323i | 0.544462 | + | 0.0535641i | ||||
\(707\) | 36.0818 | + | 36.0818i | 1.35699 | + | 1.35699i | ||||
\(708\) | 6.03881 | + | 1.19981i | 0.226952 | + | 0.0450915i | ||||
\(709\) | 8.62217 | − | 8.62217i | 0.323812 | − | 0.323812i | −0.526415 | − | 0.850228i | \(-0.676464\pi\) |
0.850228 | + | 0.526415i | \(0.176464\pi\) | |||||||
\(710\) | −6.98558 | − | 8.51003i | −0.262164 | − | 0.319376i | ||||
\(711\) | − | 1.80715i | − | 0.0677735i | ||||||
\(712\) | 4.34750 | − | 14.3489i | 0.162930 | − | 0.537749i | ||||
\(713\) | 31.4861i | 1.17917i | ||||||||
\(714\) | −11.8151 | + | 9.69855i | −0.442167 | + | 0.362959i | ||||
\(715\) | −1.42196 | + | 1.42196i | −0.0531784 | + | 0.0531784i | ||||
\(716\) | −6.98973 | − | 10.4559i | −0.261218 | − | 0.390754i | ||||
\(717\) | −0.0470217 | − | 0.0470217i | −0.00175606 | − | 0.00175606i | ||||
\(718\) | −1.60904 | + | 16.3554i | −0.0600488 | + | 0.610377i | ||||
\(719\) | 24.8479 | 0.926670 | 0.463335 | − | 0.886183i | \(-0.346653\pi\) | ||||
0.463335 | + | 0.886183i | \(0.346653\pi\) | |||||||
\(720\) | 1.26285 | + | 3.04499i | 0.0470638 | + | 0.113480i | ||||
\(721\) | −38.2968 | −1.42625 | ||||||||
\(722\) | −3.33687 | + | 33.9182i | −0.124185 | + | 1.26230i | ||||
\(723\) | −16.3456 | − | 16.3456i | −0.607898 | − | 0.607898i | ||||
\(724\) | −28.8896 | + | 19.3126i | −1.07367 | + | 0.717748i | ||||
\(725\) | 19.4136 | − | 19.4136i | 0.721002 | − | 0.721002i | ||||
\(726\) | 1.09310 | − | 0.897288i | 0.0405688 | − | 0.0333015i | ||||
\(727\) | − | 14.2040i | − | 0.526796i | −0.964687 | − | 0.263398i | \(-0.915157\pi\) | ||
0.964687 | − | 0.263398i | \(-0.0848433\pi\) | |||||||
\(728\) | 29.8049 | − | 15.9437i | 1.10464 | − | 0.590915i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −10.5211 | − | 12.8171i | −0.389403 | − | 0.474382i | ||||
\(731\) | 2.69372 | − | 2.69372i | 0.0996307 | − | 0.0996307i | ||||
\(732\) | −1.29613 | + | 6.52361i | −0.0479063 | + | 0.241120i | ||||
\(733\) | 7.98976 | + | 7.98976i | 0.295109 | + | 0.295109i | 0.839094 | − | 0.543986i | \(-0.183085\pi\) |
−0.543986 | + | 0.839094i | \(0.683085\pi\) | |||||||
\(734\) | −1.14442 | − | 0.112588i | −0.0422414 | − | 0.00415570i | ||||
\(735\) | −13.9983 | −0.516335 | ||||||||
\(736\) | −21.9409 | + | 41.1032i | −0.808753 | + | 1.51508i | ||||
\(737\) | 12.2985 | 0.453023 | ||||||||
\(738\) | −14.3615 | − | 1.41288i | −0.528652 | − | 0.0520087i | ||||
\(739\) | −25.9202 | − | 25.9202i | −0.953489 | − | 0.953489i | 0.0454768 | − | 0.998965i | \(-0.485519\pi\) |
−0.998965 | + | 0.0454768i | \(0.985519\pi\) | |||||||
\(740\) | −2.11333 | + | 10.6367i | −0.0776875 | + | 0.391013i | ||||
\(741\) | 11.3275 | − | 11.3275i | 0.416126 | − | 0.416126i | ||||
\(742\) | 7.08573 | + | 8.63204i | 0.260125 | + | 0.316892i | ||||
\(743\) | 23.5780i | 0.864991i | 0.901636 | + | 0.432496i | \(0.142367\pi\) | ||||
−0.901636 | + | 0.432496i | \(0.857633\pi\) | |||||||
\(744\) | 5.10009 | + | 9.53400i | 0.186978 | + | 0.349533i | ||||
\(745\) | − | 13.8081i | − | 0.505891i | ||||||
\(746\) | 35.3648 | − | 29.0297i | 1.29480 | − | 1.06285i | ||||
\(747\) | 3.24879 | − | 3.24879i | 0.118867 | − | 0.118867i | ||||
\(748\) | 3.66953 | − | 2.45307i | 0.134171 | − | 0.0896932i | ||||
\(749\) | −9.53077 | − | 9.53077i | −0.348247 | − | 0.348247i | ||||
\(750\) | −1.06359 | + | 10.8111i | −0.0388368 | + | 0.394764i | ||||
\(751\) | 48.9405 | 1.78586 | 0.892931 | − | 0.450193i | \(-0.148645\pi\) | ||||
0.892931 | + | 0.450193i | \(0.148645\pi\) | |||||||
\(752\) | 36.2362 | + | 14.9908i | 1.32140 | + | 0.546657i | ||||
\(753\) | −10.9194 | −0.397925 | ||||||||
\(754\) | 2.14682 | − | 21.8218i | 0.0781826 | − | 0.794702i | ||||
\(755\) | −8.52425 | − | 8.52425i | −0.310229 | − | 0.310229i | ||||
\(756\) | 5.44364 | + | 8.14309i | 0.197983 | + | 0.296161i | ||||
\(757\) | 14.8100 | − | 14.8100i | 0.538277 | − | 0.538277i | −0.384745 | − | 0.923023i | \(-0.625711\pi\) |
0.923023 | + | 0.384745i | \(0.125711\pi\) | |||||||
\(758\) | −4.96706 | + | 4.07728i | −0.180412 | + | 0.148094i | ||||
\(759\) | − | 8.23649i | − | 0.298966i | ||||||
\(760\) | −14.6454 | − | 4.43732i | −0.531243 | − | 0.160959i | ||||
\(761\) | 13.6678i | 0.495456i | 0.968830 | + | 0.247728i | \(0.0796840\pi\) | ||||
−0.968830 | + | 0.247728i | \(0.920316\pi\) | |||||||
\(762\) | −9.75493 | − | 11.8837i | −0.353384 | − | 0.430503i | ||||
\(763\) | −3.12764 | + | 3.12764i | −0.113228 | + | 0.113228i | ||||
\(764\) | 43.1135 | + | 8.56590i | 1.55979 | + | 0.309903i | ||||
\(765\) | −1.28609 | − | 1.28609i | −0.0464988 | − | 0.0464988i | ||||
\(766\) | 12.7921 | + | 1.25848i | 0.462197 | + | 0.0454709i | ||||
\(767\) | 7.51175 | 0.271234 | ||||||||
\(768\) | 0.0141446 | + | 16.0000i | 0.000510398 | + | 0.577350i | ||||
\(769\) | 7.88350 | 0.284286 | 0.142143 | − | 0.989846i | \(-0.454601\pi\) | ||||
0.142143 | + | 0.989846i | \(0.454601\pi\) | |||||||
\(770\) | 5.68055 | + | 0.558851i | 0.204713 | + | 0.0201396i | ||||
\(771\) | −1.04055 | − | 1.04055i | −0.0374744 | − | 0.0374744i | ||||
\(772\) | 14.3947 | + | 2.85998i | 0.518077 | + | 0.102933i | ||||
\(773\) | 10.1154 | − | 10.1154i | 0.363826 | − | 0.363826i | −0.501393 | − | 0.865220i | \(-0.667179\pi\) |
0.865220 | + | 0.501393i | \(0.167179\pi\) | |||||||
\(774\) | −1.54882 | − | 1.88682i | −0.0556712 | − | 0.0678203i | ||||
\(775\) | 16.5175i | 0.593326i | ||||||||
\(776\) | 19.5935 | + | 5.93653i | 0.703366 | + | 0.213109i | ||||
\(777\) | 32.2234i | 1.15601i | ||||||||
\(778\) | 12.8705 | − | 10.5649i | 0.461431 | − | 0.378772i | ||||
\(779\) | 47.3692 | − | 47.3692i | 1.69718 | − | 1.69718i | ||||
\(780\) | 2.23520 | + | 3.34361i | 0.0800328 | + | 0.119720i | ||||
\(781\) | 6.67983 | + | 6.67983i | 0.239023 | + | 0.239023i | ||||
\(782\) | 2.51692 | − | 25.5837i | 0.0900049 | − | 0.914872i | ||||
\(783\) | 6.35409 | 0.227077 | ||||||||
\(784\) | −62.7827 | − | 25.9729i | −2.24224 | − | 0.927605i | ||||
\(785\) | 0.253390 | 0.00904387 | ||||||||
\(786\) | −2.05084 | + | 20.8461i | −0.0731509 | + | 0.743556i | ||||
\(787\) | −15.5278 | − | 15.5278i | −0.553508 | − | 0.553508i | 0.373943 | − | 0.927452i | \(-0.378005\pi\) |
−0.927452 | + | 0.373943i | \(0.878005\pi\) | |||||||
\(788\) | −12.5389 | + | 8.38220i | −0.446678 | + | 0.298604i | ||||
\(789\) | 13.7977 | − | 13.7977i | 0.491212 | − | 0.491212i | ||||
\(790\) | −1.62797 | + | 1.33634i | −0.0579204 | + | 0.0475448i | ||||
\(791\) | − | 3.42022i | − | 0.121609i | ||||||
\(792\) | −1.33414 | − | 2.49401i | −0.0474065 | − | 0.0886207i | ||||
\(793\) | 8.11480i | 0.288165i | ||||||||
\(794\) | −19.6415 | − | 23.9278i | −0.697050 | − | 0.849166i | ||||
\(795\) | −0.939617 | + | 0.939617i | −0.0333248 | + | 0.0333248i | ||||
\(796\) | −8.56060 | + | 43.0868i | −0.303423 | + | 1.52717i | ||||
\(797\) | 31.0037 | + | 31.0037i | 1.09821 | + | 1.09821i | 0.994620 | + | 0.103586i | \(0.0330317\pi\) |
0.103586 | + | 0.994620i | \(0.466968\pi\) | |||||||
\(798\) | −45.2519 | − | 4.45187i | −1.60190 | − | 0.157595i | ||||
\(799\) | −21.6364 | −0.765442 | ||||||||
\(800\) | −11.5101 | + | 21.5625i | −0.406944 | + | 0.762351i | ||||
\(801\) | 5.30085 | 0.187296 | ||||||||
\(802\) | 12.0020 | + | 1.18075i | 0.423805 | + | 0.0416939i | ||||
\(803\) | 10.0606 | + | 10.0606i | 0.355031 | + | 0.355031i | ||||
\(804\) | 4.79332 | − | 24.1255i | 0.169047 | − | 0.850841i | ||||
\(805\) | 23.5068 | − | 23.5068i | 0.828507 | − | 0.828507i | ||||
\(806\) | 8.36993 | + | 10.1965i | 0.294818 | + | 0.359156i | ||||
\(807\) | 8.32429i | 0.293029i | ||||||||
\(808\) | −25.9851 | + | 13.9004i | −0.914152 | + | 0.489014i | ||||
\(809\) | 31.8240i | 1.11887i | 0.828874 | + | 0.559436i | \(0.188982\pi\) | ||||
−0.828874 | + | 0.559436i | \(0.811018\pi\) | |||||||
\(810\) | −0.900847 | + | 0.739473i | −0.0316525 | + | 0.0259824i | ||||
\(811\) | −27.7285 | + | 27.7285i | −0.973678 | + | 0.973678i | −0.999662 | − | 0.0259841i | \(-0.991728\pi\) |
0.0259841 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(812\) | −51.7419 | + | 34.5894i | −1.81578 | + | 1.21385i | ||||
\(813\) | 9.41213 | + | 9.41213i | 0.330098 | + | 0.330098i | ||||
\(814\) | 0.911011 | − | 9.26014i | 0.0319309 | − | 0.324568i | ||||
\(815\) | −19.8928 | −0.696814 | ||||||||
\(816\) | −3.38190 | − | 8.15443i | −0.118390 | − | 0.285462i | ||||
\(817\) | 11.3320 | 0.396456 | ||||||||
\(818\) | 0.132832 | − | 1.35020i | 0.00464436 | − | 0.0472085i | ||||
\(819\) | 8.45035 | + | 8.45035i | 0.295279 | + | 0.295279i | ||||
\(820\) | 9.34711 | + | 13.9823i | 0.326415 | + | 0.488281i | ||||
\(821\) | 1.84278 | − | 1.84278i | 0.0643133 | − | 0.0643133i | −0.674219 | − | 0.738532i | \(-0.735519\pi\) |
0.738532 | + | 0.674219i | \(0.235519\pi\) | |||||||
\(822\) | −20.6794 | + | 16.9749i | −0.721276 | + | 0.592069i | ||||
\(823\) | 47.7183i | 1.66336i | 0.555259 | + | 0.831678i | \(0.312619\pi\) | ||||
−0.555259 | + | 0.831678i | \(0.687381\pi\) | |||||||
\(824\) | 6.41327 | − | 21.1670i | 0.223417 | − | 0.737387i | ||||
\(825\) | − | 4.32083i | − | 0.150432i | ||||||
\(826\) | −13.5281 | − | 16.4803i | −0.470703 | − | 0.573424i | ||||
\(827\) | 10.0174 | − | 10.0174i | 0.348341 | − | 0.348341i | −0.511151 | − | 0.859491i | \(-0.670781\pi\) |
0.859491 | + | 0.511151i | \(0.170781\pi\) | |||||||
\(828\) | −16.1572 | − | 3.21015i | −0.561500 | − | 0.111560i | ||||
\(829\) | 22.1564 | + | 22.1564i | 0.769524 | + | 0.769524i | 0.978023 | − | 0.208498i | \(-0.0668576\pi\) |
−0.208498 | + | 0.978023i | \(0.566858\pi\) | |||||||
\(830\) | −5.32905 | − | 0.524271i | −0.184974 | − | 0.0181977i | ||||
\(831\) | −0.485896 | −0.0168556 | ||||||||
\(832\) | 3.82106 | + | 19.1434i | 0.132471 | + | 0.663679i | ||||
\(833\) | 37.4872 | 1.29885 | ||||||||
\(834\) | 6.04608 | + | 0.594812i | 0.209358 | + | 0.0205966i | ||||
\(835\) | 2.34879 | + | 2.34879i | 0.0812833 | + | 0.0812833i | ||||
\(836\) | 12.8783 | + | 2.55870i | 0.445406 | + | 0.0884945i | ||||
\(837\) | −2.70310 | + | 2.70310i | −0.0934328 | + | 0.0934328i | ||||
\(838\) | −20.2401 | − | 24.6570i | −0.699181 | − | 0.851763i | ||||
\(839\) | − | 1.68311i | − | 0.0581073i | −0.999578 | − | 0.0290537i | \(-0.990751\pi\) | ||
0.999578 | − | 0.0290537i | \(-0.00924937\pi\) | |||||||
\(840\) | 3.31025 | − | 10.9255i | 0.114215 | − | 0.376965i | ||||
\(841\) | 11.3745i | 0.392223i | ||||||||
\(842\) | 10.4953 | − | 8.61517i | 0.361690 | − | 0.296898i | ||||
\(843\) | 0.129823 | − | 0.129823i | 0.00447135 | − | 0.00447135i | ||||
\(844\) | 13.0025 | + | 19.4503i | 0.447565 | + | 0.669507i | ||||
\(845\) | −4.10585 | − | 4.10585i | −0.141246 | − | 0.141246i | ||||
\(846\) | −1.35743 | + | 13.7978i | −0.0466694 | + | 0.474379i | ||||
\(847\) | −4.89753 | −0.168281 | ||||||||
\(848\) | −5.95760 | + | 2.47081i | −0.204585 | + | 0.0848478i | ||||
\(849\) | 17.3964 | 0.597043 | ||||||||
\(850\) | 1.32037 | − | 13.4211i | 0.0452882 | − | 0.460340i | ||||
\(851\) | −38.3196 | − | 38.3196i | −1.31358 | − | 1.31358i | ||||
\(852\) | 15.7070 | − | 10.5001i | 0.538112 | − | 0.359727i | ||||
\(853\) | −10.3815 | + | 10.3815i | −0.355455 | + | 0.355455i | −0.862134 | − | 0.506680i | \(-0.830873\pi\) |
0.506680 | + | 0.862134i | \(0.330873\pi\) | |||||||
\(854\) | 17.8034 | − | 14.6142i | 0.609220 | − | 0.500086i | ||||
\(855\) | − | 5.41036i | − | 0.185031i | ||||||
\(856\) | 6.86379 | − | 3.67170i | 0.234600 | − | 0.125496i | ||||
\(857\) | 42.3908i | 1.44804i | 0.689777 | + | 0.724022i | \(0.257709\pi\) | ||||
−0.689777 | + | 0.724022i | \(0.742291\pi\) | |||||||
\(858\) | −2.18950 | − | 2.66731i | −0.0747483 | − | 0.0910605i | ||||
\(859\) | 27.7450 | − | 27.7450i | 0.946649 | − | 0.946649i | −0.0519984 | − | 0.998647i | \(-0.516559\pi\) |
0.998647 | + | 0.0519984i | \(0.0165591\pi\) | |||||||
\(860\) | −0.554424 | + | 2.79050i | −0.0189057 | + | 0.0951553i | ||||
\(861\) | 35.3376 | + | 35.3376i | 1.20430 | + | 1.20430i | ||||
\(862\) | −7.69095 | − | 0.756634i | −0.261955 | − | 0.0257711i | ||||
\(863\) | 0.888441 | 0.0302429 | 0.0151214 | − | 0.999886i | \(-0.495187\pi\) | ||||
0.0151214 | + | 0.999886i | \(0.495187\pi\) | |||||||
\(864\) | −5.41236 | + | 1.64509i | −0.184132 | + | 0.0559671i | ||||
\(865\) | 7.99822 | 0.271947 | ||||||||
\(866\) | 47.5971 | + | 4.68259i | 1.61741 | + | 0.159121i | ||||
\(867\) | −8.57668 | − | 8.57668i | −0.291279 | − | 0.291279i | ||||
\(868\) | 7.29687 | − | 36.7263i | 0.247672 | − | 1.24657i | ||||
\(869\) | 1.27785 | − | 1.27785i | 0.0433481 | − | 0.0433481i | ||||
\(870\) | −4.69868 | − | 5.72406i | −0.159300 | − | 0.194064i | ||||
\(871\) | − | 30.0100i | − | 1.01685i | ||||||
\(872\) | −1.20491 | − | 2.25244i | −0.0408036 | − | 0.0762773i | ||||
\(873\) | 7.23833i | 0.244981i | ||||||||
\(874\) | 59.1071 | − | 48.5189i | 1.99933 | − | 1.64118i | ||||
\(875\) | 26.6015 | − | 26.6015i | 0.899295 | − | 0.899295i | ||||
\(876\) | 23.6565 | − | 15.8144i | 0.799280 | − | 0.534318i | ||||
\(877\) | 21.6802 | + | 21.6802i | 0.732089 | + | 0.732089i | 0.971033 | − | 0.238944i | \(-0.0768014\pi\) |
−0.238944 | + | 0.971033i | \(0.576801\pi\) | |||||||
\(878\) | −2.88870 | + | 29.3628i | −0.0974890 | + | 0.990945i | ||||
\(879\) | 3.10001 | 0.104561 | ||||||||
\(880\) | −1.26016 | + | 3.04610i | −0.0424800 | + | 0.102684i | ||||
\(881\) | 5.60419 | 0.188810 | 0.0944050 | − | 0.995534i | \(-0.469905\pi\) | ||||
0.0944050 | + | 0.995534i | \(0.469905\pi\) | |||||||
\(882\) | 2.35188 | − | 23.9061i | 0.0791918 | − | 0.804960i | ||||
\(883\) | −13.8664 | − | 13.8664i | −0.466641 | − | 0.466641i | 0.434183 | − | 0.900825i | \(-0.357037\pi\) |
−0.900825 | + | 0.434183i | \(0.857037\pi\) | |||||||
\(884\) | −5.98582 | − | 8.95412i | −0.201325 | − | 0.301160i | ||||
\(885\) | 1.79392 | − | 1.79392i | 0.0603020 | − | 0.0603020i | ||||
\(886\) | −37.0823 | + | 30.4395i | −1.24580 | + | 1.02264i | ||||
\(887\) | − | 55.7634i | − | 1.87235i | −0.351533 | − | 0.936176i | \(-0.614339\pi\) | ||
0.351533 | − | 0.936176i | \(-0.385661\pi\) | |||||||
\(888\) | −17.8102 | − | 5.39620i | −0.597670 | − | 0.181085i | ||||
\(889\) | 53.2438i | 1.78574i | ||||||||
\(890\) | −3.91984 | − | 4.77526i | −0.131393 | − | 0.160067i | ||||
\(891\) | 0.707107 | − | 0.707107i | 0.0236890 | − | 0.0236890i | ||||
\(892\) | 48.9656 | + | 9.72861i | 1.63949 | + | 0.325738i | ||||
\(893\) | −45.5102 | − | 45.5102i | −1.52294 | − | 1.52294i | ||||
\(894\) | 23.5813 | + | 2.31993i | 0.788678 | + | 0.0775900i | ||||
\(895\) | −5.18248 | −0.173231 | ||||||||
\(896\) | 35.1181 | − | 42.8591i | 1.17321 | − | 1.43182i | ||||
\(897\) | −20.0981 | −0.671056 | ||||||||
\(898\) | −33.2902 | − | 3.27508i | −1.11091 | − | 0.109291i | ||||
\(899\) | −17.1757 | − | 17.1757i | −0.572843 | − | 0.572843i | ||||
\(900\) | −8.47598 | − | 1.68403i | −0.282533 | − | 0.0561343i | ||||
\(901\) | 2.51628 | − | 2.51628i | 0.0838294 | − | 0.0838294i | ||||
\(902\) | −9.15603 | − | 11.1541i | −0.304862 | − | 0.371392i | ||||
\(903\) | 8.45368i | 0.281321i | ||||||||
\(904\) | 1.89039 | + | 0.572759i | 0.0628734 | + | 0.0190497i | ||||
\(905\) | 14.3192i | 0.475986i | ||||||||
\(906\) | 15.9898 | − | 13.1254i | 0.531225 | − | 0.436063i | ||||
\(907\) | −31.3840 | + | 31.3840i | −1.04209 | + | 1.04209i | −0.0430131 | + | 0.999075i | \(0.513696\pi\) |
−0.999075 | + | 0.0430131i | \(0.986304\pi\) | |||||||
\(908\) | −25.0303 | − | 37.4426i | −0.830659 | − | 1.24257i | ||||
\(909\) | −7.36735 | − | 7.36735i | −0.244359 | − | 0.244359i | ||||
\(910\) | 1.36367 | − | 13.8613i | 0.0452052 | − | 0.459497i | ||||
\(911\) | −24.5585 | −0.813661 | −0.406831 | − | 0.913504i | \(-0.633366\pi\) | ||||
−0.406831 | + | 0.913504i | \(0.633366\pi\) | |||||||
\(912\) | 10.0386 | − | 24.2656i | 0.332411 | − | 0.803515i | ||||
\(913\) | 4.59448 | 0.152055 | ||||||||
\(914\) | 0.117134 | − | 1.19063i | 0.00387444 | − | 0.0393824i | ||||
\(915\) | 1.93794 | + | 1.93794i | 0.0640663 | + | 0.0640663i | ||||
\(916\) | 27.1069 | − | 18.1209i | 0.895636 | − | 0.598731i | ||||
\(917\) | 51.2936 | − | 51.2936i | 1.69386 | − | 1.69386i | ||||
\(918\) | 2.41245 | − | 1.98030i | 0.0796228 | − | 0.0653595i | ||||
\(919\) | 55.9358i | 1.84515i | 0.385815 | + | 0.922576i | \(0.373920\pi\) | ||||
−0.385815 | + | 0.922576i | \(0.626080\pi\) | |||||||
\(920\) | 9.05593 | + | 16.9290i | 0.298565 | + | 0.558131i | ||||
\(921\) | 6.70222i | 0.220846i | ||||||||
\(922\) | −9.78249 | − | 11.9173i | −0.322169 | − | 0.392476i | ||||
\(923\) | 16.2996 | − | 16.2996i | 0.536509 | − | 0.536509i | ||||
\(924\) | −1.90880 | + | 9.60726i | −0.0627948 | + | 0.316056i | ||||
\(925\) | −20.1023 | − | 20.1023i | −0.660960 | − | 0.660960i | ||||
\(926\) | −41.7062 | − | 4.10305i | −1.37055 | − | 0.134835i | ||||
\(927\) | 7.81962 | 0.256830 | ||||||||
\(928\) | −10.4530 | − | 34.3907i | −0.343138 | − | 1.12893i | ||||
\(929\) | 26.9636 | 0.884647 | 0.442324 | − | 0.896856i | \(-0.354154\pi\) | ||||
0.442324 | + | 0.896856i | \(0.354154\pi\) | |||||||
\(930\) | 4.43395 | + | 0.436211i | 0.145395 | + | 0.0143039i | ||||
\(931\) | 78.8509 | + | 78.8509i | 2.58423 | + | 2.58423i | ||||
\(932\) | −2.29095 | + | 11.5307i | −0.0750426 | + | 0.377701i | ||||
\(933\) | 1.31790 | − | 1.31790i | 0.0431462 | − | 0.0431462i | ||||
\(934\) | −28.0743 | − | 34.2009i | −0.918618 | − | 1.11909i | ||||
\(935\) | − | 1.81881i | − | 0.0594815i | ||||||
\(936\) | −6.08570 | + | 3.25547i | −0.198917 | + | 0.106408i | ||||
\(937\) | − | 46.8857i | − | 1.53169i | −0.643027 | − | 0.765844i | \(-0.722322\pi\) | ||
0.643027 | − | 0.765844i | \(-0.277678\pi\) | |||||||
\(938\) | −65.8402 | + | 54.0459i | −2.14976 | + | 1.76466i | ||||
\(939\) | −2.03688 | + | 2.03688i | −0.0664712 | + | 0.0664712i | ||||
\(940\) | 13.4335 | − | 8.98029i | 0.438153 | − | 0.292905i | ||||
\(941\) | −26.1894 | − | 26.1894i | −0.853752 | − | 0.853752i | 0.136841 | − | 0.990593i | \(-0.456305\pi\) |
−0.990593 | + | 0.136841i | \(0.956305\pi\) | |||||||
\(942\) | −0.0425724 | + | 0.432736i | −0.00138709 | + | 0.0140993i | ||||
\(943\) | −84.0460 | −2.73692 | ||||||||
\(944\) | 11.3743 | − | 4.71727i | 0.370201 | − | 0.153534i | ||||
\(945\) | 4.03614 | 0.131296 | ||||||||
\(946\) | 0.239000 | − | 2.42936i | 0.00777057 | − | 0.0789854i | ||||
\(947\) | 30.1063 | + | 30.1063i | 0.978322 | + | 0.978322i | 0.999770 | − | 0.0214476i | \(-0.00682751\pi\) |
−0.0214476 | + | 0.999770i | \(0.506828\pi\) | |||||||
\(948\) | −2.00866 | − | 3.00474i | −0.0652383 | − | 0.0975894i | ||||
\(949\) | 24.5492 | − | 24.5492i | 0.796900 | − | 0.796900i | ||||
\(950\) | 31.0073 | − | 25.4528i | 1.00601 | − | 0.825798i | ||||
\(951\) | − | 14.9987i | − | 0.486365i | ||||||
\(952\) | −8.86480 | + | 29.2582i | −0.287310 | + | 0.948265i | ||||
\(953\) | 34.2473i | 1.10938i | 0.832057 | + | 0.554690i | \(0.187163\pi\) | ||||
−0.832057 | + | 0.554690i | \(0.812837\pi\) | |||||||
\(954\) | −1.44680 | − | 1.76253i | −0.0468418 | − | 0.0570641i | ||||
\(955\) | 12.8075 | − | 12.8075i | 0.414442 | − | 0.414442i | ||||
\(956\) | −0.130448 | − | 0.0259177i | −0.00421898 | − | 0.000838238i | ||||
\(957\) | 4.49302 | + | 4.49302i | 0.145239 | + | 0.145239i | ||||
\(958\) | 15.2768 | + | 1.50293i | 0.493570 | + | 0.0485573i | ||||
\(959\) | 92.6517 | 2.99188 | ||||||||
\(960\) | 5.48427 | + | 3.65921i | 0.177004 | + | 0.118101i | ||||
\(961\) | −16.3865 | −0.528597 | ||||||||
\(962\) | −22.5959 | − | 2.22298i | −0.728522 | − | 0.0716719i | ||||
\(963\) | 1.94604 | + | 1.94604i | 0.0627102 | + | 0.0627102i | ||||
\(964\) | −45.3459 | − | 9.00944i | −1.46049 | − | 0.290174i | ||||
\(965\) | 4.27617 | − | 4.27617i | 0.137655 | − | 0.137655i | ||||
\(966\) | 36.1952 | + | 44.0941i | 1.16456 | + | 1.41870i | ||||
\(967\) | − | 26.2775i | − | 0.845029i | −0.906356 | − | 0.422514i | \(-0.861148\pi\) | ||
0.906356 | − | 0.422514i | \(-0.138852\pi\) | |||||||
\(968\) | 0.820152 | − | 2.70691i | 0.0263607 | − | 0.0870033i | ||||
\(969\) | 14.4889i | 0.465449i | ||||||||
\(970\) | 6.52063 | − | 5.35255i | 0.209365 | − | 0.171860i | ||||
\(971\) | −15.2593 | + | 15.2593i | −0.489695 | + | 0.489695i | −0.908210 | − | 0.418515i | \(-0.862551\pi\) |
0.418515 | + | 0.908210i | \(0.362551\pi\) | |||||||
\(972\) | −1.11151 | − | 1.66269i | −0.0356516 | − | 0.0533309i | ||||
\(973\) | −14.8769 | − | 14.8769i | −0.476931 | − | 0.476931i | ||||
\(974\) | 0.861670 | − | 8.75860i | 0.0276097 | − | 0.280644i | ||||
\(975\) | −10.5434 | −0.337658 | ||||||||
\(976\) | 5.09598 | + | 12.2874i | 0.163118 | + | 0.393311i | ||||
\(977\) | 12.4229 | 0.397445 | 0.198723 | − | 0.980056i | \(-0.436321\pi\) | ||||
0.198723 | + | 0.980056i | \(0.436321\pi\) | |||||||
\(978\) | 3.34222 | − | 33.9726i | 0.106872 | − | 1.08632i | ||||
\(979\) | 3.74827 | + | 3.74827i | 0.119795 | + | 0.119795i | ||||
\(980\) | −23.2749 | + | 15.5592i | −0.743488 | + | 0.497021i | ||||
\(981\) | 0.638617 | − | 0.638617i | 0.0203895 | − | 0.0203895i | ||||
\(982\) | −41.2930 | + | 33.8959i | −1.31771 | + | 1.08166i | ||||
\(983\) | 21.4959i | 0.685613i | 0.939406 | + | 0.342807i | \(0.111378\pi\) | ||||
−0.939406 | + | 0.342807i | \(0.888622\pi\) | |||||||
\(984\) | −25.4491 | + | 13.6137i | −0.811288 | + | 0.433988i | ||||
\(985\) | 6.21492i | 0.198024i | ||||||||
\(986\) | 12.5830 | + | 15.3289i | 0.400724 | + | 0.488173i | ||||
\(987\) | 33.9507 | − | 33.9507i | 1.08066 | − | 1.08066i | ||||
\(988\) | 6.24356 | − | 31.4248i | 0.198634 | − | 0.999756i | ||||
\(989\) | −10.0530 | − | 10.0530i | −0.319667 | − | 0.319667i | ||||
\(990\) | −1.15988 | − | 0.114109i | −0.0368634 | − | 0.00362662i | ||||
\(991\) | 17.3220 | 0.550251 | 0.275126 | − | 0.961408i | \(-0.411281\pi\) | ||||
0.275126 | + | 0.961408i | \(0.411281\pi\) | |||||||
\(992\) | 19.0770 | + | 10.1833i | 0.605695 | + | 0.323321i | ||||
\(993\) | −12.7531 | −0.404708 | ||||||||
\(994\) | −65.1149 | − | 6.40599i | −2.06532 | − | 0.203186i | ||||
\(995\) | 12.7996 | + | 12.7996i | 0.405775 | + | 0.405775i | ||||
\(996\) | 1.79068 | − | 9.01279i | 0.0567400 | − | 0.285581i | ||||
\(997\) | −8.28691 | + | 8.28691i | −0.262449 | + | 0.262449i | −0.826048 | − | 0.563599i | \(-0.809416\pi\) |
0.563599 | + | 0.826048i | \(0.309416\pi\) | |||||||
\(998\) | 14.3888 | + | 17.5289i | 0.455470 | + | 0.554866i | ||||
\(999\) | − | 6.57952i | − | 0.208167i |
(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 | 528.2.t.b.397.19 | yes | 40 | |
4.3 | odd | 2 | 2112.2.t.b.529.5 | 40 | |||
16.5 | even | 4 | inner | 528.2.t.b.133.19 | ✓ | 40 | |
16.11 | odd | 4 | 2112.2.t.b.1585.5 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
528.2.t.b.133.19 | ✓ | 40 | 16.5 | even | 4 | inner | |
528.2.t.b.397.19 | yes | 40 | 1.1 | even | 1 | trivial | |
2112.2.t.b.529.5 | 40 | 4.3 | odd | 2 | |||
2112.2.t.b.1585.5 | 40 | 16.11 | odd | 4 |