Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(139,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("420.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.i (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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.19 | ||
Character | \(\chi\) | \(=\) | 420.139 |
Dual form | 420.2.i.a.139.18 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.654401 | + | 1.25370i | −0.462731 | + | 0.886499i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.14352 | − | 1.64084i | −0.571759 | − | 0.820421i | ||||
\(5\) | 0.206931 | + | 2.22647i | 0.0925425 | + | 0.995709i | ||||
\(6\) | 1.25370 | + | 0.654401i | 0.511820 | + | 0.267158i | ||||
\(7\) | −0.859661 | − | 2.50220i | −0.324921 | − | 0.945741i | ||||
\(8\) | 2.80544 | − | 0.359858i | 0.991873 | − | 0.127229i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.92674 | − | 1.19758i | −0.925517 | − | 0.378707i | ||||
\(11\) | 4.14562i | 1.24995i | 0.780644 | + | 0.624976i | \(0.214891\pi\) | ||||
−0.780644 | + | 0.624976i | \(0.785109\pi\) | |||||||
\(12\) | −1.64084 | + | 1.14352i | −0.473671 | + | 0.330105i | ||||
\(13\) | 3.35349 | 0.930089 | 0.465045 | − | 0.885287i | \(-0.346038\pi\) | ||||
0.465045 | + | 0.885287i | \(0.346038\pi\) | |||||||
\(14\) | 3.69956 | + | 0.559684i | 0.988749 | + | 0.149582i | ||||
\(15\) | 2.22647 | − | 0.206931i | 0.574873 | − | 0.0534294i | ||||
\(16\) | −1.38473 | + | 3.75267i | −0.346183 | + | 0.938167i | ||||
\(17\) | 3.18809 | 0.773224 | 0.386612 | − | 0.922242i | \(-0.373645\pi\) | ||||
0.386612 | + | 0.922242i | \(0.373645\pi\) | |||||||
\(18\) | 0.654401 | − | 1.25370i | 0.154244 | − | 0.295500i | ||||
\(19\) | 6.52098 | 1.49602 | 0.748008 | − | 0.663690i | \(-0.231011\pi\) | ||||
0.748008 | + | 0.663690i | \(0.231011\pi\) | |||||||
\(20\) | 3.41666 | − | 2.88555i | 0.763989 | − | 0.645229i | ||||
\(21\) | −2.50220 | + | 0.859661i | −0.546024 | + | 0.187593i | ||||
\(22\) | −5.19736 | − | 2.71290i | −1.10808 | − | 0.578392i | ||||
\(23\) | −1.42902 | −0.297972 | −0.148986 | − | 0.988839i | \(-0.547601\pi\) | ||||
−0.148986 | + | 0.988839i | \(0.547601\pi\) | |||||||
\(24\) | −0.359858 | − | 2.80544i | −0.0734556 | − | 0.572658i | ||||
\(25\) | −4.91436 | + | 0.921454i | −0.982872 | + | 0.184291i | ||||
\(26\) | −2.19452 | + | 4.20426i | −0.430382 | + | 0.824523i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −3.12267 | + | 4.27188i | −0.590129 | + | 0.807309i | ||||
\(29\) | 8.88452 | 1.64981 | 0.824907 | − | 0.565268i | \(-0.191227\pi\) | ||||
0.824907 | + | 0.565268i | \(0.191227\pi\) | |||||||
\(30\) | −1.19758 | + | 2.92674i | −0.218647 | + | 0.534347i | ||||
\(31\) | 2.93809 | 0.527696 | 0.263848 | − | 0.964564i | \(-0.415008\pi\) | ||||
0.263848 | + | 0.964564i | \(0.415008\pi\) | |||||||
\(32\) | −3.79854 | − | 4.19179i | −0.671494 | − | 0.741010i | ||||
\(33\) | 4.14562 | 0.721660 | ||||||||
\(34\) | −2.08629 | + | 3.99690i | −0.357795 | + | 0.685462i | ||||
\(35\) | 5.39318 | − | 2.43179i | 0.911614 | − | 0.411048i | ||||
\(36\) | 1.14352 | + | 1.64084i | 0.190586 | + | 0.273474i | ||||
\(37\) | 9.54315i | 1.56888i | 0.620202 | + | 0.784442i | \(0.287050\pi\) | ||||
−0.620202 | + | 0.784442i | \(0.712950\pi\) | |||||||
\(38\) | −4.26734 | + | 8.17534i | −0.692253 | + | 1.32622i | ||||
\(39\) | − | 3.35349i | − | 0.536987i | ||||||
\(40\) | 1.38175 | + | 6.17177i | 0.218473 | + | 0.975843i | ||||
\(41\) | 3.55466i | 0.555145i | 0.960705 | + | 0.277573i | \(0.0895299\pi\) | ||||
−0.960705 | + | 0.277573i | \(0.910470\pi\) | |||||||
\(42\) | 0.559684 | − | 3.69956i | 0.0863611 | − | 0.570855i | ||||
\(43\) | −0.667790 | −0.101837 | −0.0509185 | − | 0.998703i | \(-0.516215\pi\) | ||||
−0.0509185 | + | 0.998703i | \(0.516215\pi\) | |||||||
\(44\) | 6.80232 | − | 4.74060i | 1.02549 | − | 0.714672i | ||||
\(45\) | −0.206931 | − | 2.22647i | −0.0308475 | − | 0.331903i | ||||
\(46\) | 0.935154 | − | 1.79156i | 0.137881 | − | 0.264152i | ||||
\(47\) | − | 0.693941i | − | 0.101222i | −0.998718 | − | 0.0506109i | \(-0.983883\pi\) | ||
0.998718 | − | 0.0506109i | \(-0.0161168\pi\) | |||||||
\(48\) | 3.75267 | + | 1.38473i | 0.541651 | + | 0.199869i | ||||
\(49\) | −5.52197 | + | 4.30208i | −0.788852 | + | 0.614583i | ||||
\(50\) | 2.06074 | − | 6.76412i | 0.291432 | − | 0.956591i | ||||
\(51\) | − | 3.18809i | − | 0.446421i | ||||||
\(52\) | −3.83477 | − | 5.50254i | −0.531787 | − | 0.763065i | ||||
\(53\) | − | 4.18410i | − | 0.574731i | −0.957821 | − | 0.287365i | \(-0.907221\pi\) | ||
0.957821 | − | 0.287365i | \(-0.0927794\pi\) | |||||||
\(54\) | −1.25370 | − | 0.654401i | −0.170607 | − | 0.0890527i | ||||
\(55\) | −9.23012 | + | 0.857859i | −1.24459 | + | 0.115674i | ||||
\(56\) | −3.31216 | − | 6.71041i | −0.442606 | − | 0.896716i | ||||
\(57\) | − | 6.52098i | − | 0.863725i | ||||||
\(58\) | −5.81404 | + | 11.1385i | −0.763421 | + | 1.46256i | ||||
\(59\) | −5.96025 | −0.775959 | −0.387980 | − | 0.921668i | \(-0.626827\pi\) | ||||
−0.387980 | + | 0.921668i | \(0.626827\pi\) | |||||||
\(60\) | −2.88555 | − | 3.41666i | −0.372523 | − | 0.441089i | ||||
\(61\) | − | 10.3947i | − | 1.33091i | −0.746439 | − | 0.665454i | \(-0.768238\pi\) | ||
0.746439 | − | 0.665454i | \(-0.231762\pi\) | |||||||
\(62\) | −1.92269 | + | 3.68347i | −0.244182 | + | 0.467802i | ||||
\(63\) | 0.859661 | + | 2.50220i | 0.108307 | + | 0.315247i | ||||
\(64\) | 7.74101 | − | 2.01912i | 0.967626 | − | 0.252390i | ||||
\(65\) | 0.693941 | + | 7.46644i | 0.0860728 | + | 0.926098i | ||||
\(66\) | −2.71290 | + | 5.19736i | −0.333935 | + | 0.639751i | ||||
\(67\) | −7.05912 | −0.862409 | −0.431204 | − | 0.902254i | \(-0.641911\pi\) | ||||
−0.431204 | + | 0.902254i | \(0.641911\pi\) | |||||||
\(68\) | −3.64563 | − | 5.23115i | −0.442098 | − | 0.634370i | ||||
\(69\) | 1.42902i | 0.172034i | ||||||||
\(70\) | −0.480565 | + | 8.35279i | −0.0574385 | + | 0.998349i | ||||
\(71\) | 9.50299i | 1.12780i | 0.825844 | + | 0.563899i | \(0.190699\pi\) | ||||
−0.825844 | + | 0.563899i | \(0.809301\pi\) | |||||||
\(72\) | −2.80544 | + | 0.359858i | −0.330624 | + | 0.0424096i | ||||
\(73\) | 7.52091 | 0.880256 | 0.440128 | − | 0.897935i | \(-0.354933\pi\) | ||||
0.440128 | + | 0.897935i | \(0.354933\pi\) | |||||||
\(74\) | −11.9642 | − | 6.24505i | −1.39081 | − | 0.725972i | ||||
\(75\) | 0.921454 | + | 4.91436i | 0.106400 | + | 0.567461i | ||||
\(76\) | −7.45686 | − | 10.6999i | −0.855361 | − | 1.22736i | ||||
\(77\) | 10.3732 | − | 3.56383i | 1.18213 | − | 0.406136i | ||||
\(78\) | 4.20426 | + | 2.19452i | 0.476038 | + | 0.248481i | ||||
\(79\) | − | 12.1118i | − | 1.36269i | −0.731964 | − | 0.681343i | \(-0.761396\pi\) | ||
0.731964 | − | 0.681343i | \(-0.238604\pi\) | |||||||
\(80\) | −8.64176 | − | 2.30652i | −0.966178 | − | 0.257877i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.45647 | − | 2.32618i | −0.492135 | − | 0.256883i | ||||
\(83\) | − | 5.25464i | − | 0.576772i | −0.957514 | − | 0.288386i | \(-0.906881\pi\) | ||
0.957514 | − | 0.288386i | \(-0.0931186\pi\) | |||||||
\(84\) | 4.27188 | + | 3.12267i | 0.466100 | + | 0.340711i | ||||
\(85\) | 0.659715 | + | 7.09818i | 0.0715561 | + | 0.769906i | ||||
\(86\) | 0.437003 | − | 0.837208i | 0.0471232 | − | 0.0902784i | ||||
\(87\) | − | 8.88452i | − | 0.952521i | ||||||
\(88\) | 1.49183 | + | 11.6303i | 0.159030 | + | 1.23979i | ||||
\(89\) | − | 2.83667i | − | 0.300686i | −0.988634 | − | 0.150343i | \(-0.951962\pi\) | ||
0.988634 | − | 0.150343i | \(-0.0480378\pi\) | |||||||
\(90\) | 2.92674 | + | 1.19758i | 0.308506 | + | 0.126236i | ||||
\(91\) | −2.88286 | − | 8.39108i | −0.302206 | − | 0.879624i | ||||
\(92\) | 1.63411 | + | 2.34480i | 0.170368 | + | 0.244463i | ||||
\(93\) | − | 2.93809i | − | 0.304665i | ||||||
\(94\) | 0.869993 | + | 0.454116i | 0.0897329 | + | 0.0468385i | ||||
\(95\) | 1.34940 | + | 14.5188i | 0.138445 | + | 1.48960i | ||||
\(96\) | −4.19179 | + | 3.79854i | −0.427822 | + | 0.387687i | ||||
\(97\) | −15.9682 | −1.62133 | −0.810663 | − | 0.585513i | \(-0.800893\pi\) | ||||
−0.810663 | + | 0.585513i | \(0.800893\pi\) | |||||||
\(98\) | −1.77993 | − | 9.73816i | −0.179800 | − | 0.983703i | ||||
\(99\) | − | 4.14562i | − | 0.416651i | ||||||
\(100\) | 7.13162 | + | 7.00999i | 0.713162 | + | 0.700999i | ||||
\(101\) | − | 1.19853i | − | 0.119258i | −0.998221 | − | 0.0596292i | \(-0.981008\pi\) | ||
0.998221 | − | 0.0596292i | \(-0.0189918\pi\) | |||||||
\(102\) | 3.99690 | + | 2.08629i | 0.395752 | + | 0.206573i | ||||
\(103\) | − | 6.82433i | − | 0.672421i | −0.941787 | − | 0.336210i | \(-0.890855\pi\) | ||
0.941787 | − | 0.336210i | \(-0.109145\pi\) | |||||||
\(104\) | 9.40801 | − | 1.20678i | 0.922531 | − | 0.118334i | ||||
\(105\) | −2.43179 | − | 5.39318i | −0.237319 | − | 0.526320i | ||||
\(106\) | 5.24560 | + | 2.73808i | 0.509498 | + | 0.265946i | ||||
\(107\) | −5.09970 | −0.493007 | −0.246503 | − | 0.969142i | \(-0.579282\pi\) | ||||
−0.246503 | + | 0.969142i | \(0.579282\pi\) | |||||||
\(108\) | 1.64084 | − | 1.14352i | 0.157890 | − | 0.110035i | ||||
\(109\) | 14.9107 | 1.42819 | 0.714093 | − | 0.700051i | \(-0.246840\pi\) | ||||
0.714093 | + | 0.700051i | \(0.246840\pi\) | |||||||
\(110\) | 4.96470 | − | 12.1332i | 0.473366 | − | 1.15685i | ||||
\(111\) | 9.54315 | 0.905795 | ||||||||
\(112\) | 10.5803 | + | 0.238845i | 0.999745 | + | 0.0225688i | ||||
\(113\) | − | 15.0357i | − | 1.41444i | −0.706993 | − | 0.707220i | \(-0.749949\pi\) | ||
0.706993 | − | 0.707220i | \(-0.250051\pi\) | |||||||
\(114\) | 8.17534 | + | 4.26734i | 0.765691 | + | 0.399673i | ||||
\(115\) | −0.295710 | − | 3.18168i | −0.0275751 | − | 0.296693i | ||||
\(116\) | −10.1596 | − | 14.5781i | −0.943297 | − | 1.35354i | ||||
\(117\) | −3.35349 | −0.310030 | ||||||||
\(118\) | 3.90040 | − | 7.47236i | 0.359061 | − | 0.687887i | ||||
\(119\) | −2.74067 | − | 7.97721i | −0.251237 | − | 0.731270i | ||||
\(120\) | 6.17177 | − | 1.38175i | 0.563403 | − | 0.126136i | ||||
\(121\) | −6.18619 | −0.562381 | ||||||||
\(122\) | 13.0318 | + | 6.80232i | 1.17985 | + | 0.615853i | ||||
\(123\) | 3.55466 | 0.320513 | ||||||||
\(124\) | −3.35976 | − | 4.82094i | −0.301715 | − | 0.432933i | ||||
\(125\) | −3.06853 | − | 10.7510i | −0.274457 | − | 0.961599i | ||||
\(126\) | −3.69956 | − | 0.559684i | −0.329583 | − | 0.0498606i | ||||
\(127\) | 15.9750 | 1.41755 | 0.708774 | − | 0.705435i | \(-0.249248\pi\) | ||||
0.708774 | + | 0.705435i | \(0.249248\pi\) | |||||||
\(128\) | −2.53436 | + | 11.0262i | −0.224008 | + | 0.974587i | ||||
\(129\) | 0.667790i | 0.0587957i | ||||||||
\(130\) | −9.81478 | − | 4.01606i | −0.860813 | − | 0.352231i | ||||
\(131\) | −4.17978 | −0.365189 | −0.182595 | − | 0.983188i | \(-0.558450\pi\) | ||||
−0.182595 | + | 0.983188i | \(0.558450\pi\) | |||||||
\(132\) | −4.74060 | − | 6.80232i | −0.412616 | − | 0.592066i | ||||
\(133\) | −5.60583 | − | 16.3168i | −0.486087 | − | 1.41484i | ||||
\(134\) | 4.61950 | − | 8.85001i | 0.399064 | − | 0.764524i | ||||
\(135\) | −2.22647 | + | 0.206931i | −0.191624 | + | 0.0178098i | ||||
\(136\) | 8.94399 | − | 1.14726i | 0.766941 | − | 0.0983764i | ||||
\(137\) | 18.3094i | 1.56428i | 0.623105 | + | 0.782139i | \(0.285871\pi\) | ||||
−0.623105 | + | 0.782139i | \(0.714129\pi\) | |||||||
\(138\) | −1.79156 | − | 0.935154i | −0.152508 | − | 0.0796056i | ||||
\(139\) | −8.23037 | −0.698091 | −0.349046 | − | 0.937106i | \(-0.613494\pi\) | ||||
−0.349046 | + | 0.937106i | \(0.613494\pi\) | |||||||
\(140\) | −10.1574 | − | 6.06856i | −0.858456 | − | 0.512887i | ||||
\(141\) | −0.693941 | −0.0584404 | ||||||||
\(142\) | −11.9139 | − | 6.21877i | −0.999791 | − | 0.521868i | ||||
\(143\) | 13.9023i | 1.16257i | ||||||||
\(144\) | 1.38473 | − | 3.75267i | 0.115394 | − | 0.312722i | ||||
\(145\) | 1.83849 | + | 19.7811i | 0.152678 | + | 1.64273i | ||||
\(146\) | −4.92169 | + | 9.42895i | −0.407322 | + | 0.780346i | ||||
\(147\) | 4.30208 | + | 5.52197i | 0.354830 | + | 0.455444i | ||||
\(148\) | 15.6588 | − | 10.9128i | 1.28715 | − | 0.897024i | ||||
\(149\) | −2.87574 | −0.235590 | −0.117795 | − | 0.993038i | \(-0.537583\pi\) | ||||
−0.117795 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(150\) | −6.76412 | − | 2.06074i | −0.552288 | − | 0.168258i | ||||
\(151\) | 7.47598i | 0.608386i | 0.952610 | + | 0.304193i | \(0.0983868\pi\) | ||||
−0.952610 | + | 0.304193i | \(0.901613\pi\) | |||||||
\(152\) | 18.2942 | − | 2.34662i | 1.48386 | − | 0.190336i | ||||
\(153\) | −3.18809 | −0.257741 | ||||||||
\(154\) | −2.32024 | + | 15.3370i | −0.186970 | + | 1.23589i | ||||
\(155\) | 0.607982 | + | 6.54157i | 0.0488343 | + | 0.525432i | ||||
\(156\) | −5.50254 | + | 3.83477i | −0.440556 | + | 0.307027i | ||||
\(157\) | −1.28235 | −0.102343 | −0.0511715 | − | 0.998690i | \(-0.516296\pi\) | ||||
−0.0511715 | + | 0.998690i | \(0.516296\pi\) | |||||||
\(158\) | 15.1846 | + | 7.92599i | 1.20802 | + | 0.630558i | ||||
\(159\) | −4.18410 | −0.331821 | ||||||||
\(160\) | 8.54686 | − | 9.32476i | 0.675688 | − | 0.737187i | ||||
\(161\) | 1.22848 | + | 3.57569i | 0.0968174 | + | 0.281804i | ||||
\(162\) | −0.654401 | + | 1.25370i | −0.0514146 | + | 0.0984998i | ||||
\(163\) | −21.3376 | −1.67129 | −0.835646 | − | 0.549269i | \(-0.814906\pi\) | ||||
−0.835646 | + | 0.549269i | \(0.814906\pi\) | |||||||
\(164\) | 5.83264 | − | 4.06482i | 0.455453 | − | 0.317409i | ||||
\(165\) | 0.857859 | + | 9.23012i | 0.0667843 | + | 0.718564i | ||||
\(166\) | 6.58774 | + | 3.43864i | 0.511308 | + | 0.266891i | ||||
\(167\) | 14.6737i | 1.13549i | 0.823206 | + | 0.567743i | \(0.192183\pi\) | ||||
−0.823206 | + | 0.567743i | \(0.807817\pi\) | |||||||
\(168\) | −6.71041 | + | 3.31216i | −0.517719 | + | 0.255539i | ||||
\(169\) | −1.75414 | −0.134934 | ||||||||
\(170\) | −9.33070 | − | 3.81798i | −0.715632 | − | 0.292825i | ||||
\(171\) | −6.52098 | −0.498672 | ||||||||
\(172\) | 0.763631 | + | 1.09574i | 0.0582263 | + | 0.0835493i | ||||
\(173\) | −20.6733 | −1.57176 | −0.785882 | − | 0.618376i | \(-0.787791\pi\) | ||||
−0.785882 | + | 0.618376i | \(0.787791\pi\) | |||||||
\(174\) | 11.1385 | + | 5.81404i | 0.844408 | + | 0.440761i | ||||
\(175\) | 6.53034 | + | 11.5045i | 0.493647 | + | 0.869662i | ||||
\(176\) | −15.5571 | − | 5.74057i | −1.17266 | − | 0.432712i | ||||
\(177\) | 5.96025i | 0.448000i | ||||||||
\(178\) | 3.55633 | + | 1.85632i | 0.266558 | + | 0.139137i | ||||
\(179\) | 19.0127i | 1.42108i | 0.703659 | + | 0.710538i | \(0.251548\pi\) | ||||
−0.703659 | + | 0.710538i | \(0.748452\pi\) | |||||||
\(180\) | −3.41666 | + | 2.88555i | −0.254663 | + | 0.215076i | ||||
\(181\) | − | 15.7892i | − | 1.17360i | −0.809732 | − | 0.586800i | \(-0.800387\pi\) | ||
0.809732 | − | 0.586800i | \(-0.199613\pi\) | |||||||
\(182\) | 12.4064 | + | 1.87689i | 0.919625 | + | 0.139124i | ||||
\(183\) | −10.3947 | −0.768400 | ||||||||
\(184\) | −4.00904 | + | 0.514245i | −0.295550 | + | 0.0379106i | ||||
\(185\) | −21.2476 | + | 1.97478i | −1.56215 | + | 0.145188i | ||||
\(186\) | 3.68347 | + | 1.92269i | 0.270085 | + | 0.140978i | ||||
\(187\) | 13.2166i | 0.966494i | ||||||||
\(188\) | −1.13865 | + | 0.793534i | −0.0830445 | + | 0.0578744i | ||||
\(189\) | 2.50220 | − | 0.859661i | 0.182008 | − | 0.0625312i | ||||
\(190\) | −19.0852 | − | 7.80937i | −1.38459 | − | 0.566551i | ||||
\(191\) | − | 1.96830i | − | 0.142421i | −0.997461 | − | 0.0712106i | \(-0.977314\pi\) | ||
0.997461 | − | 0.0712106i | \(-0.0226862\pi\) | |||||||
\(192\) | −2.01912 | − | 7.74101i | −0.145717 | − | 0.558659i | ||||
\(193\) | − | 7.34732i | − | 0.528871i | −0.964403 | − | 0.264436i | \(-0.914814\pi\) | ||
0.964403 | − | 0.264436i | \(-0.0851857\pi\) | |||||||
\(194\) | 10.4496 | − | 20.0193i | 0.750239 | − | 1.43730i | ||||
\(195\) | 7.46644 | − | 0.693941i | 0.534683 | − | 0.0496942i | ||||
\(196\) | 13.3735 | + | 4.14117i | 0.955251 | + | 0.295798i | ||||
\(197\) | − | 4.05059i | − | 0.288593i | −0.989535 | − | 0.144296i | \(-0.953908\pi\) | ||
0.989535 | − | 0.144296i | \(-0.0460918\pi\) | |||||||
\(198\) | 5.19736 | + | 2.71290i | 0.369360 | + | 0.192797i | ||||
\(199\) | 23.8673 | 1.69191 | 0.845954 | − | 0.533256i | \(-0.179032\pi\) | ||||
0.845954 | + | 0.533256i | \(0.179032\pi\) | |||||||
\(200\) | −13.4554 | + | 4.35355i | −0.951437 | + | 0.307843i | ||||
\(201\) | 7.05912i | 0.497912i | ||||||||
\(202\) | 1.50260 | + | 0.784320i | 0.105722 | + | 0.0551846i | ||||
\(203\) | −7.63768 | − | 22.2308i | −0.536060 | − | 1.56030i | ||||
\(204\) | −5.23115 | + | 3.64563i | −0.366254 | + | 0.255245i | ||||
\(205\) | −7.91436 | + | 0.735571i | −0.552763 | + | 0.0513745i | ||||
\(206\) | 8.55565 | + | 4.46585i | 0.596100 | + | 0.311150i | ||||
\(207\) | 1.42902 | 0.0993240 | ||||||||
\(208\) | −4.64368 | + | 12.5845i | −0.321981 | + | 0.872579i | ||||
\(209\) | 27.0335i | 1.86995i | ||||||||
\(210\) | 8.35279 | + | 0.480565i | 0.576397 | + | 0.0331622i | ||||
\(211\) | 6.23257i | 0.429068i | 0.976717 | + | 0.214534i | \(0.0688233\pi\) | ||||
−0.976717 | + | 0.214534i | \(0.931177\pi\) | |||||||
\(212\) | −6.86546 | + | 4.78460i | −0.471522 | + | 0.328608i | ||||
\(213\) | 9.50299 | 0.651134 | ||||||||
\(214\) | 3.33725 | − | 6.39349i | 0.228130 | − | 0.437050i | ||||
\(215\) | −0.138187 | − | 1.48682i | −0.00942426 | − | 0.101400i | ||||
\(216\) | 0.359858 | + | 2.80544i | 0.0244852 | + | 0.190886i | ||||
\(217\) | −2.52576 | − | 7.35167i | −0.171460 | − | 0.499064i | ||||
\(218\) | −9.75757 | + | 18.6935i | −0.660866 | + | 1.26608i | ||||
\(219\) | − | 7.52091i | − | 0.508216i | ||||||
\(220\) | 11.9624 | + | 14.1642i | 0.806506 | + | 0.954950i | ||||
\(221\) | 10.6912 | 0.719168 | ||||||||
\(222\) | −6.24505 | + | 11.9642i | −0.419140 | + | 0.802986i | ||||
\(223\) | 10.0483i | 0.672885i | 0.941704 | + | 0.336443i | \(0.109224\pi\) | ||||
−0.941704 | + | 0.336443i | \(0.890776\pi\) | |||||||
\(224\) | −7.22321 | + | 13.1082i | −0.482621 | + | 0.875829i | ||||
\(225\) | 4.91436 | − | 0.921454i | 0.327624 | − | 0.0614303i | ||||
\(226\) | 18.8502 | + | 9.83938i | 1.25390 | + | 0.654506i | ||||
\(227\) | 12.9107i | 0.856913i | 0.903562 | + | 0.428456i | \(0.140942\pi\) | ||||
−0.903562 | + | 0.428456i | \(0.859058\pi\) | |||||||
\(228\) | −10.6999 | + | 7.45686i | −0.708619 | + | 0.493843i | ||||
\(229\) | − | 20.2148i | − | 1.33583i | −0.744235 | − | 0.667917i | \(-0.767186\pi\) | ||
0.744235 | − | 0.667917i | \(-0.232814\pi\) | |||||||
\(230\) | 4.18238 | + | 1.71136i | 0.275778 | + | 0.112844i | ||||
\(231\) | −3.56383 | − | 10.3732i | −0.234483 | − | 0.682504i | ||||
\(232\) | 24.9250 | − | 3.19716i | 1.63641 | − | 0.209904i | ||||
\(233\) | − | 11.8552i | − | 0.776658i | −0.921521 | − | 0.388329i | \(-0.873052\pi\) | ||
0.921521 | − | 0.388329i | \(-0.126948\pi\) | |||||||
\(234\) | 2.19452 | − | 4.20426i | 0.143461 | − | 0.274841i | ||||
\(235\) | 1.54504 | − | 0.143598i | 0.100787 | − | 0.00936731i | ||||
\(236\) | 6.81566 | + | 9.77984i | 0.443662 | + | 0.636613i | ||||
\(237\) | −12.1118 | −0.786747 | ||||||||
\(238\) | 11.7945 | + | 1.78432i | 0.764525 | + | 0.115660i | ||||
\(239\) | − | 3.95455i | − | 0.255799i | −0.991787 | − | 0.127899i | \(-0.959177\pi\) | ||
0.991787 | − | 0.127899i | \(-0.0408234\pi\) | |||||||
\(240\) | −2.30652 | + | 8.64176i | −0.148885 | + | 0.557823i | ||||
\(241\) | 21.4716i | 1.38311i | 0.722324 | + | 0.691555i | \(0.243074\pi\) | ||||
−0.722324 | + | 0.691555i | \(0.756926\pi\) | |||||||
\(242\) | 4.04825 | − | 7.75562i | 0.260231 | − | 0.498550i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −17.0561 | + | 11.8866i | −1.09191 | + | 0.760959i | ||||
\(245\) | −10.7211 | − | 11.4043i | −0.684948 | − | 0.728592i | ||||
\(246\) | −2.32618 | + | 4.45647i | −0.148312 | + | 0.284134i | ||||
\(247\) | 21.8680 | 1.39143 | ||||||||
\(248\) | 8.24263 | − | 1.05729i | 0.523408 | − | 0.0671382i | ||||
\(249\) | −5.25464 | −0.333000 | ||||||||
\(250\) | 15.4866 | + | 3.18846i | 0.979456 | + | 0.201656i | ||||
\(251\) | 24.2390 | 1.52995 | 0.764975 | − | 0.644060i | \(-0.222751\pi\) | ||||
0.764975 | + | 0.644060i | \(0.222751\pi\) | |||||||
\(252\) | 3.12267 | − | 4.27188i | 0.196710 | − | 0.269103i | ||||
\(253\) | − | 5.92419i | − | 0.372451i | ||||||
\(254\) | −10.4540 | + | 20.0278i | −0.655944 | + | 1.25665i | ||||
\(255\) | 7.09818 | − | 0.659715i | 0.444506 | − | 0.0413129i | ||||
\(256\) | −12.1650 | − | 10.3929i | −0.760315 | − | 0.649555i | ||||
\(257\) | −6.84349 | −0.426885 | −0.213443 | − | 0.976956i | \(-0.568468\pi\) | ||||
−0.213443 | + | 0.976956i | \(0.568468\pi\) | |||||||
\(258\) | −0.837208 | − | 0.437003i | −0.0521223 | − | 0.0272066i | ||||
\(259\) | 23.8788 | − | 8.20387i | 1.48376 | − | 0.509764i | ||||
\(260\) | 11.4577 | − | 9.67666i | 0.710578 | − | 0.600121i | ||||
\(261\) | −8.88452 | −0.549938 | ||||||||
\(262\) | 2.73526 | − | 5.24019i | 0.168985 | − | 0.323740i | ||||
\(263\) | −26.0905 | −1.60881 | −0.804403 | − | 0.594083i | \(-0.797515\pi\) | ||||
−0.804403 | + | 0.594083i | \(0.797515\pi\) | |||||||
\(264\) | 11.6303 | − | 1.49183i | 0.715796 | − | 0.0918160i | ||||
\(265\) | 9.31579 | − | 0.865822i | 0.572265 | − | 0.0531870i | ||||
\(266\) | 24.1248 | + | 3.64969i | 1.47918 | + | 0.223777i | ||||
\(267\) | −2.83667 | −0.173601 | ||||||||
\(268\) | 8.07223 | + | 11.5829i | 0.493090 | + | 0.707539i | ||||
\(269\) | − | 8.74121i | − | 0.532961i | −0.963840 | − | 0.266481i | \(-0.914139\pi\) | ||
0.963840 | − | 0.266481i | \(-0.0858608\pi\) | |||||||
\(270\) | 1.19758 | − | 2.92674i | 0.0728822 | − | 0.178116i | ||||
\(271\) | −14.8967 | −0.904911 | −0.452456 | − | 0.891787i | \(-0.649452\pi\) | ||||
−0.452456 | + | 0.891787i | \(0.649452\pi\) | |||||||
\(272\) | −4.41464 | + | 11.9638i | −0.267677 | + | 0.725414i | ||||
\(273\) | −8.39108 | + | 2.88286i | −0.507851 | + | 0.174479i | ||||
\(274\) | −22.9545 | − | 11.9817i | −1.38673 | − | 0.723840i | ||||
\(275\) | −3.82000 | − | 20.3731i | −0.230355 | − | 1.22854i | ||||
\(276\) | 2.34480 | − | 1.63411i | 0.141140 | − | 0.0983621i | ||||
\(277\) | − | 8.86971i | − | 0.532929i | −0.963845 | − | 0.266465i | \(-0.914144\pi\) | ||
0.963845 | − | 0.266465i | \(-0.0858555\pi\) | |||||||
\(278\) | 5.38597 | − | 10.3184i | 0.323029 | − | 0.618857i | ||||
\(279\) | −2.93809 | −0.175899 | ||||||||
\(280\) | 14.2551 | − | 8.76303i | 0.851908 | − | 0.523691i | ||||
\(281\) | −7.14815 | −0.426423 | −0.213211 | − | 0.977006i | \(-0.568392\pi\) | ||||
−0.213211 | + | 0.977006i | \(0.568392\pi\) | |||||||
\(282\) | 0.454116 | − | 0.869993i | 0.0270422 | − | 0.0518073i | ||||
\(283\) | − | 2.57635i | − | 0.153148i | −0.997064 | − | 0.0765742i | \(-0.975602\pi\) | ||
0.997064 | − | 0.0765742i | \(-0.0243982\pi\) | |||||||
\(284\) | 15.5929 | − | 10.8668i | 0.925270 | − | 0.644829i | ||||
\(285\) | 14.5188 | − | 1.34940i | 0.860018 | − | 0.0799313i | ||||
\(286\) | −17.4293 | − | 9.09767i | −1.03061 | − | 0.537957i | ||||
\(287\) | 8.89446 | − | 3.05581i | 0.525023 | − | 0.180379i | ||||
\(288\) | 3.79854 | + | 4.19179i | 0.223831 | + | 0.247003i | ||||
\(289\) | −6.83611 | −0.402124 | ||||||||
\(290\) | −26.0027 | − | 10.6399i | −1.52693 | − | 0.624796i | ||||
\(291\) | 15.9682i | 0.936073i | ||||||||
\(292\) | −8.60030 | − | 12.3406i | −0.503294 | − | 0.722181i | ||||
\(293\) | 25.4873 | 1.48898 | 0.744491 | − | 0.667633i | \(-0.232692\pi\) | ||||
0.744491 | + | 0.667633i | \(0.232692\pi\) | |||||||
\(294\) | −9.73816 | + | 1.77993i | −0.567941 | + | 0.103808i | ||||
\(295\) | −1.23336 | − | 13.2703i | −0.0718092 | − | 0.772629i | ||||
\(296\) | 3.43417 | + | 26.7727i | 0.199607 | + | 1.55613i | ||||
\(297\) | −4.14562 | −0.240553 | ||||||||
\(298\) | 1.88189 | − | 3.60531i | 0.109015 | − | 0.208850i | ||||
\(299\) | −4.79221 | −0.277140 | ||||||||
\(300\) | 7.00999 | − | 7.13162i | 0.404722 | − | 0.411744i | ||||
\(301\) | 0.574074 | + | 1.67094i | 0.0330891 | + | 0.0963115i | ||||
\(302\) | −9.37262 | − | 4.89229i | −0.539334 | − | 0.281520i | ||||
\(303\) | −1.19853 | −0.0688538 | ||||||||
\(304\) | −9.02981 | + | 24.4711i | −0.517895 | + | 1.40351i | ||||
\(305\) | 23.1436 | − | 2.15099i | 1.32520 | − | 0.123166i | ||||
\(306\) | 2.08629 | − | 3.99690i | 0.119265 | − | 0.228487i | ||||
\(307\) | − | 19.5890i | − | 1.11800i | −0.829167 | − | 0.559001i | \(-0.811185\pi\) | ||
0.829167 | − | 0.559001i | \(-0.188815\pi\) | |||||||
\(308\) | −17.7096 | − | 12.9454i | −1.00910 | − | 0.737634i | ||||
\(309\) | −6.82433 | −0.388222 | ||||||||
\(310\) | −8.59902 | − | 3.51858i | −0.488391 | − | 0.199842i | ||||
\(311\) | −25.9353 | −1.47066 | −0.735329 | − | 0.677710i | \(-0.762972\pi\) | ||||
−0.735329 | + | 0.677710i | \(0.762972\pi\) | |||||||
\(312\) | −1.20678 | − | 9.40801i | −0.0683203 | − | 0.532623i | ||||
\(313\) | 8.23386 | 0.465405 | 0.232703 | − | 0.972548i | \(-0.425243\pi\) | ||||
0.232703 | + | 0.972548i | \(0.425243\pi\) | |||||||
\(314\) | 0.839174 | − | 1.60769i | 0.0473573 | − | 0.0907269i | ||||
\(315\) | −5.39318 | + | 2.43179i | −0.303871 | + | 0.137016i | ||||
\(316\) | −19.8736 | + | 13.8501i | −1.11798 | + | 0.779128i | ||||
\(317\) | 27.9672i | 1.57080i | 0.618992 | + | 0.785398i | \(0.287541\pi\) | ||||
−0.618992 | + | 0.785398i | \(0.712459\pi\) | |||||||
\(318\) | 2.73808 | − | 5.24560i | 0.153544 | − | 0.294159i | ||||
\(319\) | 36.8319i | 2.06219i | ||||||||
\(320\) | 6.09737 | + | 16.8173i | 0.340853 | + | 0.940117i | ||||
\(321\) | 5.09970i | 0.284638i | ||||||||
\(322\) | −5.28676 | − | 0.799801i | −0.294619 | − | 0.0445712i | ||||
\(323\) | 20.7894 | 1.15676 | ||||||||
\(324\) | −1.14352 | − | 1.64084i | −0.0635288 | − | 0.0911579i | ||||
\(325\) | −16.4802 | + | 3.09008i | −0.914159 | + | 0.171407i | ||||
\(326\) | 13.9634 | − | 26.7509i | 0.773359 | − | 1.48160i | ||||
\(327\) | − | 14.9107i | − | 0.824563i | ||||||
\(328\) | 1.27917 | + | 9.97240i | 0.0706305 | + | 0.550634i | ||||
\(329\) | −1.73638 | + | 0.596554i | −0.0957295 | + | 0.0328891i | ||||
\(330\) | −12.1332 | − | 4.96470i | −0.667909 | − | 0.273298i | ||||
\(331\) | − | 23.3019i | − | 1.28079i | −0.768046 | − | 0.640395i | \(-0.778771\pi\) | ||
0.768046 | − | 0.640395i | \(-0.221229\pi\) | |||||||
\(332\) | −8.62205 | + | 6.00878i | −0.473196 | + | 0.329775i | ||||
\(333\) | − | 9.54315i | − | 0.522961i | ||||||
\(334\) | −18.3964 | − | 9.60249i | −1.00661 | − | 0.525425i | ||||
\(335\) | −1.46075 | − | 15.7169i | −0.0798095 | − | 0.858708i | ||||
\(336\) | 0.238845 | − | 10.5803i | 0.0130301 | − | 0.577203i | ||||
\(337\) | − | 1.27455i | − | 0.0694292i | −0.999397 | − | 0.0347146i | \(-0.988948\pi\) | ||
0.999397 | − | 0.0347146i | \(-0.0110522\pi\) | |||||||
\(338\) | 1.14791 | − | 2.19916i | 0.0624381 | − | 0.119619i | ||||
\(339\) | −15.0357 | −0.816627 | ||||||||
\(340\) | 10.8926 | − | 9.19939i | 0.590735 | − | 0.498907i | ||||
\(341\) | 12.1802i | 0.659595i | ||||||||
\(342\) | 4.26734 | − | 8.17534i | 0.230751 | − | 0.442072i | ||||
\(343\) | 15.5117 | + | 10.1187i | 0.837551 | + | 0.546359i | ||||
\(344\) | −1.87345 | + | 0.240309i | −0.101010 | + | 0.0129566i | ||||
\(345\) | −3.18168 | + | 0.295710i | −0.171296 | + | 0.0159205i | ||||
\(346\) | 13.5286 | − | 25.9181i | 0.727305 | − | 1.39337i | ||||
\(347\) | 22.6794 | 1.21750 | 0.608748 | − | 0.793363i | \(-0.291672\pi\) | ||||
0.608748 | + | 0.793363i | \(0.291672\pi\) | |||||||
\(348\) | −14.5781 | + | 10.1596i | −0.781469 | + | 0.544613i | ||||
\(349\) | − | 14.8204i | − | 0.793317i | −0.917966 | − | 0.396658i | \(-0.870170\pi\) | ||
0.917966 | − | 0.396658i | \(-0.129830\pi\) | |||||||
\(350\) | −18.6967 | + | 0.658488i | −0.999380 | + | 0.0351977i | ||||
\(351\) | 3.35349i | 0.178996i | ||||||||
\(352\) | 17.3776 | − | 15.7473i | 0.926227 | − | 0.839336i | ||||
\(353\) | 15.4022 | 0.819778 | 0.409889 | − | 0.912135i | \(-0.365567\pi\) | ||||
0.409889 | + | 0.912135i | \(0.365567\pi\) | |||||||
\(354\) | −7.47236 | − | 3.90040i | −0.397151 | − | 0.207304i | ||||
\(355\) | −21.1582 | + | 1.96647i | −1.12296 | + | 0.104369i | ||||
\(356\) | −4.65453 | + | 3.24378i | −0.246689 | + | 0.171920i | ||||
\(357\) | −7.97721 | + | 2.74067i | −0.422199 | + | 0.145052i | ||||
\(358\) | −23.8362 | − | 12.4419i | −1.25978 | − | 0.657576i | ||||
\(359\) | − | 6.40783i | − | 0.338192i | −0.985600 | − | 0.169096i | \(-0.945915\pi\) | ||
0.985600 | − | 0.169096i | \(-0.0540848\pi\) | |||||||
\(360\) | −1.38175 | − | 6.17177i | −0.0728244 | − | 0.325281i | ||||
\(361\) | 23.5232 | 1.23806 | ||||||||
\(362\) | 19.7949 | + | 10.3325i | 1.04040 | + | 0.543062i | ||||
\(363\) | 6.18619i | 0.324691i | ||||||||
\(364\) | −10.4718 | + | 14.3257i | −0.548873 | + | 0.750869i | ||||
\(365\) | 1.55631 | + | 16.7451i | 0.0814611 | + | 0.876479i | ||||
\(366\) | 6.80232 | − | 13.0318i | 0.355563 | − | 0.681185i | ||||
\(367\) | − | 20.1613i | − | 1.05241i | −0.850357 | − | 0.526206i | \(-0.823614\pi\) | ||
0.850357 | − | 0.526206i | \(-0.176386\pi\) | |||||||
\(368\) | 1.97881 | − | 5.36265i | 0.103153 | − | 0.279547i | ||||
\(369\) | − | 3.55466i | − | 0.185048i | ||||||
\(370\) | 11.4286 | − | 27.9303i | 0.594147 | − | 1.45203i | ||||
\(371\) | −10.4694 | + | 3.59691i | −0.543547 | + | 0.186742i | ||||
\(372\) | −4.82094 | + | 3.35976i | −0.249954 | + | 0.174195i | ||||
\(373\) | − | 6.48276i | − | 0.335664i | −0.985816 | − | 0.167832i | \(-0.946323\pi\) | ||
0.985816 | − | 0.167832i | \(-0.0536767\pi\) | |||||||
\(374\) | −16.5696 | − | 8.64896i | −0.856795 | − | 0.447227i | ||||
\(375\) | −10.7510 | + | 3.06853i | −0.555180 | + | 0.158458i | ||||
\(376\) | −0.249720 | − | 1.94681i | −0.0128783 | − | 0.100399i | ||||
\(377\) | 29.7941 | 1.53448 | ||||||||
\(378\) | −0.559684 | + | 3.69956i | −0.0287870 | + | 0.190285i | ||||
\(379\) | 23.4767i | 1.20592i | 0.797773 | + | 0.602958i | \(0.206011\pi\) | ||||
−0.797773 | + | 0.602958i | \(0.793989\pi\) | |||||||
\(380\) | 22.2800 | − | 18.8166i | 1.14294 | − | 0.965273i | ||||
\(381\) | − | 15.9750i | − | 0.818422i | ||||||
\(382\) | 2.46765 | + | 1.28806i | 0.126256 | + | 0.0659027i | ||||
\(383\) | − | 11.2009i | − | 0.572342i | −0.958179 | − | 0.286171i | \(-0.907617\pi\) | ||
0.958179 | − | 0.286171i | \(-0.0923825\pi\) | |||||||
\(384\) | 11.0262 | + | 2.53436i | 0.562678 | + | 0.129331i | ||||
\(385\) | 10.0813 | + | 22.3581i | 0.513791 | + | 1.13947i | ||||
\(386\) | 9.21132 | + | 4.80809i | 0.468844 | + | 0.244725i | ||||
\(387\) | 0.667790 | 0.0339457 | ||||||||
\(388\) | 18.2599 | + | 26.2013i | 0.927008 | + | 1.33017i | ||||
\(389\) | 3.23587 | 0.164065 | 0.0820326 | − | 0.996630i | \(-0.473859\pi\) | ||||
0.0820326 | + | 0.996630i | \(0.473859\pi\) | |||||||
\(390\) | −4.01606 | + | 9.81478i | −0.203361 | + | 0.496991i | ||||
\(391\) | −4.55585 | −0.230399 | ||||||||
\(392\) | −13.9434 | + | 14.0564i | −0.704249 | + | 0.709953i | ||||
\(393\) | 4.17978i | 0.210842i | ||||||||
\(394\) | 5.07822 | + | 2.65071i | 0.255837 | + | 0.133541i | ||||
\(395\) | 26.9666 | − | 2.50631i | 1.35684 | − | 0.126106i | ||||
\(396\) | −6.80232 | + | 4.74060i | −0.341829 | + | 0.238224i | ||||
\(397\) | 26.5118 | 1.33059 | 0.665295 | − | 0.746581i | \(-0.268306\pi\) | ||||
0.665295 | + | 0.746581i | \(0.268306\pi\) | |||||||
\(398\) | −15.6188 | + | 29.9224i | −0.782899 | + | 1.49987i | ||||
\(399\) | −16.3168 | + | 5.60583i | −0.816860 | + | 0.280643i | ||||
\(400\) | 3.34716 | − | 19.7179i | 0.167358 | − | 0.985896i | ||||
\(401\) | −4.93093 | −0.246239 | −0.123119 | − | 0.992392i | \(-0.539290\pi\) | ||||
−0.123119 | + | 0.992392i | \(0.539290\pi\) | |||||||
\(402\) | −8.85001 | − | 4.61950i | −0.441398 | − | 0.230400i | ||||
\(403\) | 9.85283 | 0.490805 | ||||||||
\(404\) | −1.96660 | + | 1.37054i | −0.0978421 | + | 0.0681870i | ||||
\(405\) | 0.206931 | + | 2.22647i | 0.0102825 | + | 0.110634i | ||||
\(406\) | 32.8688 | + | 4.97252i | 1.63125 | + | 0.246782i | ||||
\(407\) | −39.5623 | −1.96103 | ||||||||
\(408\) | −1.14726 | − | 8.94399i | −0.0567977 | − | 0.442793i | ||||
\(409\) | − | 12.8675i | − | 0.636256i | −0.948048 | − | 0.318128i | \(-0.896946\pi\) | ||
0.948048 | − | 0.318128i | \(-0.103054\pi\) | |||||||
\(410\) | 4.25698 | − | 10.4036i | 0.210237 | − | 0.513796i | ||||
\(411\) | 18.3094 | 0.903136 | ||||||||
\(412\) | −11.1976 | + | 7.80374i | −0.551669 | + | 0.384463i | ||||
\(413\) | 5.12380 | + | 14.9137i | 0.252126 | + | 0.733856i | ||||
\(414\) | −0.935154 | + | 1.79156i | −0.0459603 | + | 0.0880505i | ||||
\(415\) | 11.6993 | − | 1.08735i | 0.574297 | − | 0.0533759i | ||||
\(416\) | −12.7384 | − | 14.0571i | −0.624549 | − | 0.689206i | ||||
\(417\) | 8.23037i | 0.403043i | ||||||||
\(418\) | −33.8919 | − | 17.6908i | −1.65771 | − | 0.865284i | ||||
\(419\) | −5.88793 | −0.287644 | −0.143822 | − | 0.989604i | \(-0.545939\pi\) | ||||
−0.143822 | + | 0.989604i | \(0.545939\pi\) | |||||||
\(420\) | −6.06856 | + | 10.1574i | −0.296115 | + | 0.495630i | ||||
\(421\) | −13.8287 | −0.673970 | −0.336985 | − | 0.941510i | \(-0.609407\pi\) | ||||
−0.336985 | + | 0.941510i | \(0.609407\pi\) | |||||||
\(422\) | −7.81376 | − | 4.07860i | −0.380368 | − | 0.198543i | ||||
\(423\) | 0.693941i | 0.0337406i | ||||||||
\(424\) | −1.50568 | − | 11.7383i | −0.0731223 | − | 0.570060i | ||||
\(425\) | −15.6674 | + | 2.93767i | −0.759980 | + | 0.142498i | ||||
\(426\) | −6.21877 | + | 11.9139i | −0.301300 | + | 0.577230i | ||||
\(427\) | −26.0096 | + | 8.93594i | −1.25869 | + | 0.432440i | ||||
\(428\) | 5.83160 | + | 8.36781i | 0.281881 | + | 0.404474i | ||||
\(429\) | 13.9023 | 0.671209 | ||||||||
\(430\) | 1.95445 | + | 0.799730i | 0.0942519 | + | 0.0385664i | ||||
\(431\) | − | 26.3127i | − | 1.26744i | −0.773563 | − | 0.633719i | \(-0.781527\pi\) | ||
0.773563 | − | 0.633719i | \(-0.218473\pi\) | |||||||
\(432\) | −3.75267 | − | 1.38473i | −0.180550 | − | 0.0666229i | ||||
\(433\) | 1.12270 | 0.0539536 | 0.0269768 | − | 0.999636i | \(-0.491412\pi\) | ||||
0.0269768 | + | 0.999636i | \(0.491412\pi\) | |||||||
\(434\) | 10.8696 | + | 1.64440i | 0.521759 | + | 0.0789337i | ||||
\(435\) | 19.7811 | − | 1.83849i | 0.948433 | − | 0.0881487i | ||||
\(436\) | −17.0507 | − | 24.4661i | −0.816578 | − | 1.17171i | ||||
\(437\) | −9.31863 | −0.445771 | ||||||||
\(438\) | 9.42895 | + | 4.92169i | 0.450533 | + | 0.235168i | ||||
\(439\) | 7.08181 | 0.337996 | 0.168998 | − | 0.985616i | \(-0.445947\pi\) | ||||
0.168998 | + | 0.985616i | \(0.445947\pi\) | |||||||
\(440\) | −25.5858 | + | 5.72820i | −1.21976 | + | 0.273081i | ||||
\(441\) | 5.52197 | − | 4.30208i | 0.262951 | − | 0.204861i | ||||
\(442\) | −6.99633 | + | 13.4035i | −0.332782 | + | 0.637541i | ||||
\(443\) | 13.4718 | 0.640066 | 0.320033 | − | 0.947406i | \(-0.396306\pi\) | ||||
0.320033 | + | 0.947406i | \(0.396306\pi\) | |||||||
\(444\) | −10.9128 | − | 15.6588i | −0.517897 | − | 0.743134i | ||||
\(445\) | 6.31576 | − | 0.586995i | 0.299396 | − | 0.0278263i | ||||
\(446\) | −12.5976 | − | 6.57563i | −0.596512 | − | 0.311365i | ||||
\(447\) | 2.87574i | 0.136018i | ||||||||
\(448\) | −11.7069 | − | 17.6338i | −0.553098 | − | 0.833116i | ||||
\(449\) | −21.1302 | −0.997195 | −0.498598 | − | 0.866834i | \(-0.666151\pi\) | ||||
−0.498598 | + | 0.866834i | \(0.666151\pi\) | |||||||
\(450\) | −2.06074 | + | 6.76412i | −0.0971441 | + | 0.318864i | ||||
\(451\) | −14.7363 | −0.693905 | ||||||||
\(452\) | −24.6712 | + | 17.1936i | −1.16044 | + | 0.808719i | ||||
\(453\) | 7.47598 | 0.351252 | ||||||||
\(454\) | −16.1861 | − | 8.44877i | −0.759652 | − | 0.396520i | ||||
\(455\) | 18.0859 | − | 8.15499i | 0.847882 | − | 0.382312i | ||||
\(456\) | −2.34662 | − | 18.2942i | −0.109891 | − | 0.856706i | ||||
\(457\) | − | 6.69819i | − | 0.313328i | −0.987652 | − | 0.156664i | \(-0.949926\pi\) | ||
0.987652 | − | 0.156664i | \(-0.0500740\pi\) | |||||||
\(458\) | 25.3433 | + | 13.2286i | 1.18422 | + | 0.618133i | ||||
\(459\) | 3.18809i | 0.148807i | ||||||||
\(460\) | −4.88249 | + | 4.12352i | −0.227647 | + | 0.192260i | ||||
\(461\) | − | 38.8726i | − | 1.81048i | −0.424904 | − | 0.905238i | \(-0.639692\pi\) | ||
0.424904 | − | 0.905238i | \(-0.360308\pi\) | |||||||
\(462\) | 15.3370 | + | 2.32024i | 0.713541 | + | 0.107947i | ||||
\(463\) | −14.6394 | −0.680350 | −0.340175 | − | 0.940362i | \(-0.610486\pi\) | ||||
−0.340175 | + | 0.940362i | \(0.610486\pi\) | |||||||
\(464\) | −12.3027 | + | 33.3407i | −0.571138 | + | 1.54780i | ||||
\(465\) | 6.54157 | − | 0.607982i | 0.303358 | − | 0.0281945i | ||||
\(466\) | 14.8628 | + | 7.75804i | 0.688506 | + | 0.359384i | ||||
\(467\) | 24.6710i | 1.14164i | 0.821077 | + | 0.570818i | \(0.193374\pi\) | ||||
−0.821077 | + | 0.570818i | \(0.806626\pi\) | |||||||
\(468\) | 3.83477 | + | 5.50254i | 0.177262 | + | 0.254355i | ||||
\(469\) | 6.06845 | + | 17.6633i | 0.280215 | + | 0.815615i | ||||
\(470\) | −0.831048 | + | 2.03099i | −0.0383334 | + | 0.0936824i | ||||
\(471\) | 1.28235i | 0.0590878i | ||||||||
\(472\) | −16.7211 | + | 2.14484i | −0.769653 | + | 0.0987244i | ||||
\(473\) | − | 2.76841i | − | 0.127292i | ||||||
\(474\) | 7.92599 | − | 15.1846i | 0.364053 | − | 0.697450i | ||||
\(475\) | −32.0464 | + | 6.00878i | −1.47039 | + | 0.275702i | ||||
\(476\) | −9.95534 | + | 13.6191i | −0.456302 | + | 0.624231i | ||||
\(477\) | 4.18410i | 0.191577i | ||||||||
\(478\) | 4.95781 | + | 2.58786i | 0.226765 | + | 0.118366i | ||||
\(479\) | −10.2736 | −0.469411 | −0.234705 | − | 0.972067i | \(-0.575413\pi\) | ||||
−0.234705 | + | 0.972067i | \(0.575413\pi\) | |||||||
\(480\) | −9.32476 | − | 8.54686i | −0.425615 | − | 0.390109i | ||||
\(481\) | 32.0028i | 1.45920i | ||||||||
\(482\) | −26.9190 | − | 14.0511i | −1.22613 | − | 0.640009i | ||||
\(483\) | 3.57569 | − | 1.22848i | 0.162700 | − | 0.0558976i | ||||
\(484\) | 7.07402 | + | 10.1506i | 0.321547 | + | 0.461389i | ||||
\(485\) | −3.30432 | − | 35.5528i | −0.150042 | − | 1.61437i | ||||
\(486\) | 1.25370 | + | 0.654401i | 0.0568689 | + | 0.0296842i | ||||
\(487\) | −15.3745 | −0.696683 | −0.348342 | − | 0.937368i | \(-0.613255\pi\) | ||||
−0.348342 | + | 0.937368i | \(0.613255\pi\) | |||||||
\(488\) | −3.74062 | − | 29.1618i | −0.169330 | − | 1.32009i | ||||
\(489\) | 21.3376i | 0.964920i | ||||||||
\(490\) | 21.3134 | − | 5.97810i | 0.962843 | − | 0.270063i | ||||
\(491\) | − | 14.8168i | − | 0.668671i | −0.942454 | − | 0.334336i | \(-0.891488\pi\) | ||
0.942454 | − | 0.334336i | \(-0.108512\pi\) | |||||||
\(492\) | −4.06482 | − | 5.83264i | −0.183256 | − | 0.262956i | ||||
\(493\) | 28.3246 | 1.27568 | ||||||||
\(494\) | −14.3104 | + | 27.4159i | −0.643858 | + | 1.23350i | ||||
\(495\) | 9.23012 | − | 0.857859i | 0.414863 | − | 0.0385579i | ||||
\(496\) | −4.06846 | + | 11.0257i | −0.182679 | + | 0.495067i | ||||
\(497\) | 23.7784 | − | 8.16936i | 1.06660 | − | 0.366446i | ||||
\(498\) | 3.43864 | − | 6.58774i | 0.154089 | − | 0.295204i | ||||
\(499\) | 17.7914i | 0.796453i | 0.917287 | + | 0.398226i | \(0.130374\pi\) | ||||
−0.917287 | + | 0.398226i | \(0.869626\pi\) | |||||||
\(500\) | −14.1318 | + | 17.3289i | −0.631993 | + | 0.774974i | ||||
\(501\) | 14.6737 | 0.655573 | ||||||||
\(502\) | −15.8620 | + | 30.3883i | −0.707956 | + | 1.35630i | ||||
\(503\) | − | 9.60325i | − | 0.428188i | −0.976813 | − | 0.214094i | \(-0.931320\pi\) | ||
0.976813 | − | 0.214094i | \(-0.0686798\pi\) | |||||||
\(504\) | 3.31216 | + | 6.71041i | 0.147535 | + | 0.298905i | ||||
\(505\) | 2.66850 | − | 0.248014i | 0.118747 | − | 0.0110365i | ||||
\(506\) | 7.42715 | + | 3.87680i | 0.330177 | + | 0.172345i | ||||
\(507\) | 1.75414i | 0.0779040i | ||||||||
\(508\) | −18.2677 | − | 26.2124i | −0.810496 | − | 1.16299i | ||||
\(509\) | − | 26.5301i | − | 1.17593i | −0.808887 | − | 0.587964i | \(-0.799930\pi\) | ||
0.808887 | − | 0.587964i | \(-0.200070\pi\) | |||||||
\(510\) | −3.81798 | + | 9.33070i | −0.169063 | + | 0.413170i | ||||
\(511\) | −6.46543 | − | 18.8188i | −0.286014 | − | 0.832494i | ||||
\(512\) | 20.9903 | − | 8.45018i | 0.927651 | − | 0.373449i | ||||
\(513\) | 6.52098i | 0.287908i | ||||||||
\(514\) | 4.47839 | − | 8.57967i | 0.197533 | − | 0.378433i | ||||
\(515\) | 15.1942 | − | 1.41217i | 0.669535 | − | 0.0622275i | ||||
\(516\) | 1.09574 | − | 0.763631i | 0.0482372 | − | 0.0336170i | ||||
\(517\) | 2.87682 | 0.126522 | ||||||||
\(518\) | −5.34114 | + | 35.3055i | −0.234676 | + | 1.55123i | ||||
\(519\) | 20.6733i | 0.907458i | ||||||||
\(520\) | 4.63367 | + | 20.6969i | 0.203200 | + | 0.907621i | ||||
\(521\) | − | 0.626926i | − | 0.0274661i | −0.999906 | − | 0.0137331i | \(-0.995628\pi\) | ||
0.999906 | − | 0.0137331i | \(-0.00437150\pi\) | |||||||
\(522\) | 5.81404 | − | 11.1385i | 0.254474 | − | 0.487519i | ||||
\(523\) | − | 20.3037i | − | 0.887818i | −0.896072 | − | 0.443909i | \(-0.853591\pi\) | ||
0.896072 | − | 0.443909i | \(-0.146409\pi\) | |||||||
\(524\) | 4.77966 | + | 6.85837i | 0.208800 | + | 0.299609i | ||||
\(525\) | 11.5045 | − | 6.53034i | 0.502100 | − | 0.285007i | ||||
\(526\) | 17.0736 | − | 32.7096i | 0.744446 | − | 1.42620i | ||||
\(527\) | 9.36687 | 0.408027 | ||||||||
\(528\) | −5.74057 | + | 15.5571i | −0.249826 | + | 0.677038i | ||||
\(529\) | −20.9579 | −0.911213 | ||||||||
\(530\) | −5.01079 | + | 12.2458i | −0.217655 | + | 0.531923i | ||||
\(531\) | 5.96025 | 0.258653 | ||||||||
\(532\) | −20.3629 | + | 27.8568i | −0.882843 | + | 1.20775i | ||||
\(533\) | 11.9205i | 0.516335i | ||||||||
\(534\) | 1.85632 | − | 3.55633i | 0.0803308 | − | 0.153897i | ||||
\(535\) | −1.05529 | − | 11.3543i | −0.0456241 | − | 0.490891i | ||||
\(536\) | −19.8040 | + | 2.54028i | −0.855400 | + | 0.109723i | ||||
\(537\) | 19.0127 | 0.820458 | ||||||||
\(538\) | 10.9588 | + | 5.72026i | 0.472469 | + | 0.246618i | ||||
\(539\) | −17.8348 | − | 22.8920i | −0.768200 | − | 0.986028i | ||||
\(540\) | 2.88555 | + | 3.41666i | 0.124174 | + | 0.147030i | ||||
\(541\) | 0.543665 | 0.0233740 | 0.0116870 | − | 0.999932i | \(-0.496280\pi\) | ||||
0.0116870 | + | 0.999932i | \(0.496280\pi\) | |||||||
\(542\) | 9.74843 | − | 18.6760i | 0.418731 | − | 0.802202i | ||||
\(543\) | −15.7892 | −0.677579 | ||||||||
\(544\) | −12.1101 | − | 13.3638i | −0.519215 | − | 0.572967i | ||||
\(545\) | 3.08549 | + | 33.1982i | 0.132168 | + | 1.42206i | ||||
\(546\) | 1.87689 | − | 12.4064i | 0.0803235 | − | 0.530946i | ||||
\(547\) | −4.59239 | −0.196357 | −0.0981783 | − | 0.995169i | \(-0.531302\pi\) | ||||
−0.0981783 | + | 0.995169i | \(0.531302\pi\) | |||||||
\(548\) | 30.0428 | − | 20.9371i | 1.28337 | − | 0.894390i | ||||
\(549\) | 10.3947i | 0.443636i | ||||||||
\(550\) | 28.0415 | + | 8.54304i | 1.19569 | + | 0.364276i | ||||
\(551\) | 57.9358 | 2.46815 | ||||||||
\(552\) | 0.514245 | + | 4.00904i | 0.0218877 | + | 0.170636i | ||||
\(553\) | −30.3061 | + | 10.4121i | −1.28875 | + | 0.442766i | ||||
\(554\) | 11.1199 | + | 5.80435i | 0.472441 | + | 0.246603i | ||||
\(555\) | 1.97478 | + | 21.2476i | 0.0838246 | + | 0.901908i | ||||
\(556\) | 9.41158 | + | 13.5047i | 0.399140 | + | 0.572729i | ||||
\(557\) | − | 26.7881i | − | 1.13505i | −0.823357 | − | 0.567523i | \(-0.807902\pi\) | ||
0.823357 | − | 0.567523i | \(-0.192098\pi\) | |||||||
\(558\) | 1.92269 | − | 3.68347i | 0.0813939 | − | 0.155934i | ||||
\(559\) | −2.23943 | −0.0947176 | ||||||||
\(560\) | 1.65762 | + | 23.6062i | 0.0700470 | + | 0.997544i | ||||
\(561\) | 13.2166 | 0.558005 | ||||||||
\(562\) | 4.67776 | − | 8.96162i | 0.197319 | − | 0.378023i | ||||
\(563\) | 17.7277i | 0.747135i | 0.927603 | + | 0.373567i | \(0.121866\pi\) | ||||
−0.927603 | + | 0.373567i | \(0.878134\pi\) | |||||||
\(564\) | 0.793534 | + | 1.13865i | 0.0334138 | + | 0.0479457i | ||||
\(565\) | 33.4766 | − | 3.11136i | 1.40837 | − | 0.130896i | ||||
\(566\) | 3.22997 | + | 1.68597i | 0.135766 | + | 0.0708666i | ||||
\(567\) | −0.859661 | − | 2.50220i | −0.0361024 | − | 0.105082i | ||||
\(568\) | 3.41972 | + | 26.6601i | 0.143488 | + | 1.11863i | ||||
\(569\) | −42.8231 | −1.79524 | −0.897620 | − | 0.440770i | \(-0.854705\pi\) | ||||
−0.897620 | + | 0.440770i | \(0.854705\pi\) | |||||||
\(570\) | −7.80937 | + | 19.0852i | −0.327099 | + | 0.799392i | ||||
\(571\) | 29.5932i | 1.23844i | 0.785219 | + | 0.619219i | \(0.212551\pi\) | ||||
−0.785219 | + | 0.619219i | \(0.787449\pi\) | |||||||
\(572\) | 22.8115 | − | 15.8975i | 0.953795 | − | 0.664709i | ||||
\(573\) | −1.96830 | −0.0822269 | ||||||||
\(574\) | −1.98949 | + | 13.1507i | −0.0830396 | + | 0.548899i | ||||
\(575\) | 7.02273 | − | 1.31678i | 0.292868 | − | 0.0549135i | ||||
\(576\) | −7.74101 | + | 2.01912i | −0.322542 | + | 0.0841299i | ||||
\(577\) | −19.1483 | −0.797152 | −0.398576 | − | 0.917135i | \(-0.630496\pi\) | ||||
−0.398576 | + | 0.917135i | \(0.630496\pi\) | |||||||
\(578\) | 4.47356 | − | 8.57042i | 0.186076 | − | 0.356483i | ||||
\(579\) | −7.34732 | −0.305344 | ||||||||
\(580\) | 30.3554 | − | 25.6368i | 1.26044 | − | 1.06451i | ||||
\(581\) | −13.1481 | + | 4.51721i | −0.545477 | + | 0.187406i | ||||
\(582\) | −20.0193 | − | 10.4496i | −0.829827 | − | 0.433150i | ||||
\(583\) | 17.3457 | 0.718386 | ||||||||
\(584\) | 21.0995 | − | 2.70646i | 0.873102 | − | 0.111994i | ||||
\(585\) | −0.693941 | − | 7.46644i | −0.0286909 | − | 0.308699i | ||||
\(586\) | −16.6789 | + | 31.9533i | −0.688999 | + | 1.31998i | ||||
\(587\) | − | 35.7778i | − | 1.47671i | −0.674413 | − | 0.738355i | \(-0.735603\pi\) | ||
0.674413 | − | 0.738355i | \(-0.264397\pi\) | |||||||
\(588\) | 4.14117 | − | 13.3735i | 0.170779 | − | 0.551514i | ||||
\(589\) | 19.1592 | 0.789441 | ||||||||
\(590\) | 17.4441 | + | 7.13786i | 0.718163 | + | 0.293861i | ||||
\(591\) | −4.05059 | −0.166619 | ||||||||
\(592\) | −35.8123 | − | 13.2147i | −1.47188 | − | 0.543121i | ||||
\(593\) | −43.1401 | −1.77155 | −0.885775 | − | 0.464115i | \(-0.846372\pi\) | ||||
−0.885775 | + | 0.464115i | \(0.846372\pi\) | |||||||
\(594\) | 2.71290 | − | 5.19736i | 0.111312 | − | 0.213250i | ||||
\(595\) | 17.1939 | − | 7.75277i | 0.704882 | − | 0.317833i | ||||
\(596\) | 3.28846 | + | 4.71864i | 0.134701 | + | 0.193283i | ||||
\(597\) | − | 23.8673i | − | 0.976823i | ||||||
\(598\) | 3.13603 | − | 6.00798i | 0.128242 | − | 0.245685i | ||||
\(599\) | − | 0.774502i | − | 0.0316453i | −0.999875 | − | 0.0158227i | \(-0.994963\pi\) | ||
0.999875 | − | 0.0158227i | \(-0.00503672\pi\) | |||||||
\(600\) | 4.35355 | + | 13.4554i | 0.177733 | + | 0.549313i | ||||
\(601\) | − | 12.2670i | − | 0.500381i | −0.968197 | − | 0.250190i | \(-0.919507\pi\) | ||
0.968197 | − | 0.250190i | \(-0.0804932\pi\) | |||||||
\(602\) | −2.47053 | − | 0.373751i | −0.100691 | − | 0.0152330i | ||||
\(603\) | 7.05912 | 0.287470 | ||||||||
\(604\) | 12.2669 | − | 8.54892i | 0.499133 | − | 0.347851i | ||||
\(605\) | −1.28012 | − | 13.7734i | −0.0520441 | − | 0.559968i | ||||
\(606\) | 0.784320 | − | 1.50260i | 0.0318608 | − | 0.0610388i | ||||
\(607\) | − | 24.9016i | − | 1.01072i | −0.862908 | − | 0.505362i | \(-0.831359\pi\) | ||
0.862908 | − | 0.505362i | \(-0.168641\pi\) | |||||||
\(608\) | −24.7702 | − | 27.3346i | −1.00457 | − | 1.10856i | ||||
\(609\) | −22.2308 | + | 7.63768i | −0.900838 | + | 0.309494i | ||||
\(610\) | −12.4485 | + | 30.4227i | −0.504024 | + | 1.23178i | ||||
\(611\) | − | 2.32712i | − | 0.0941452i | ||||||
\(612\) | 3.64563 | + | 5.23115i | 0.147366 | + | 0.211457i | ||||
\(613\) | 46.8111i | 1.89068i | 0.326085 | + | 0.945340i | \(0.394270\pi\) | ||||
−0.326085 | + | 0.945340i | \(0.605730\pi\) | |||||||
\(614\) | 24.5587 | + | 12.8191i | 0.991107 | + | 0.517335i | ||||
\(615\) | 0.735571 | + | 7.91436i | 0.0296611 | + | 0.319138i | ||||
\(616\) | 27.8188 | − | 13.7310i | 1.12085 | − | 0.553237i | ||||
\(617\) | 14.9253i | 0.600868i | 0.953803 | + | 0.300434i | \(0.0971315\pi\) | ||||
−0.953803 | + | 0.300434i | \(0.902868\pi\) | |||||||
\(618\) | 4.46585 | − | 8.55565i | 0.179643 | − | 0.344159i | ||||
\(619\) | 36.9017 | 1.48321 | 0.741603 | − | 0.670839i | \(-0.234066\pi\) | ||||
0.741603 | + | 0.670839i | \(0.234066\pi\) | |||||||
\(620\) | 10.0385 | − | 8.47801i | 0.403154 | − | 0.340485i | ||||
\(621\) | − | 1.42902i | − | 0.0573447i | ||||||
\(622\) | 16.9721 | − | 32.5151i | 0.680520 | − | 1.30374i | ||||
\(623\) | −7.09790 | + | 2.43857i | −0.284371 | + | 0.0976994i | ||||
\(624\) | 12.5845 | + | 4.64368i | 0.503784 | + | 0.185896i | ||||
\(625\) | 23.3018 | − | 9.05671i | 0.932074 | − | 0.362268i | ||||
\(626\) | −5.38825 | + | 10.3228i | −0.215358 | + | 0.412581i | ||||
\(627\) | 27.0335 | 1.07962 | ||||||||
\(628\) | 1.46640 | + | 2.10414i | 0.0585156 | + | 0.0839644i | ||||
\(629\) | 30.4244i | 1.21310i | ||||||||
\(630\) | 0.480565 | − | 8.35279i | 0.0191462 | − | 0.332783i | ||||
\(631\) | 2.54553i | 0.101336i | 0.998716 | + | 0.0506679i | \(0.0161350\pi\) | ||||
−0.998716 | + | 0.0506679i | \(0.983865\pi\) | |||||||
\(632\) | −4.35853 | − | 33.9790i | −0.173373 | − | 1.35161i | ||||
\(633\) | 6.23257 | 0.247723 | ||||||||
\(634\) | −35.0624 | − | 18.3018i | −1.39251 | − | 0.726856i | ||||
\(635\) | 3.30572 | + | 35.5678i | 0.131183 | + | 1.41147i | ||||
\(636\) | 4.78460 | + | 6.86546i | 0.189722 | + | 0.272233i | ||||
\(637\) | −18.5178 | + | 14.4270i | −0.733703 | + | 0.571617i | ||||
\(638\) | −46.1761 | − | 24.1028i | −1.82813 | − | 0.954240i | ||||
\(639\) | − | 9.50299i | − | 0.375933i | ||||||
\(640\) | −25.0740 | − | 3.36101i | −0.991135 | − | 0.132856i | ||||
\(641\) | −19.2685 | −0.761062 | −0.380531 | − | 0.924768i | \(-0.624259\pi\) | ||||
−0.380531 | + | 0.924768i | \(0.624259\pi\) | |||||||
\(642\) | −6.39349 | − | 3.33725i | −0.252331 | − | 0.131711i | ||||
\(643\) | − | 8.44962i | − | 0.333220i | −0.986023 | − | 0.166610i | \(-0.946718\pi\) | ||
0.986023 | − | 0.166610i | \(-0.0532821\pi\) | |||||||
\(644\) | 4.46237 | − | 6.10461i | 0.175842 | − | 0.240555i | ||||
\(645\) | −1.48682 | + | 0.138187i | −0.0585434 | + | 0.00544110i | ||||
\(646\) | −13.6046 | + | 26.0637i | −0.535267 | + | 1.02546i | ||||
\(647\) | − | 2.73522i | − | 0.107532i | −0.998554 | − | 0.0537662i | \(-0.982877\pi\) | ||
0.998554 | − | 0.0537662i | \(-0.0171226\pi\) | |||||||
\(648\) | 2.80544 | − | 0.359858i | 0.110208 | − | 0.0141365i | ||||
\(649\) | − | 24.7090i | − | 0.969912i | ||||||
\(650\) | 6.91065 | − | 22.6834i | 0.271058 | − | 0.889716i | ||||
\(651\) | −7.35167 | + | 2.52576i | −0.288135 | + | 0.0989923i | ||||
\(652\) | 24.4000 | + | 35.0117i | 0.955576 | + | 1.37116i | ||||
\(653\) | − | 11.3268i | − | 0.443253i | −0.975132 | − | 0.221627i | \(-0.928863\pi\) | ||
0.975132 | − | 0.221627i | \(-0.0711366\pi\) | |||||||
\(654\) | 18.6935 | + | 9.75757i | 0.730974 | + | 0.381551i | ||||
\(655\) | −0.864928 | − | 9.30617i | −0.0337955 | − | 0.363622i | ||||
\(656\) | −13.3395 | − | 4.92225i | −0.520819 | − | 0.192182i | ||||
\(657\) | −7.52091 | −0.293419 | ||||||||
\(658\) | 0.388388 | − | 2.56728i | 0.0151409 | − | 0.100083i | ||||
\(659\) | − | 29.0409i | − | 1.13127i | −0.824654 | − | 0.565637i | \(-0.808630\pi\) | ||
0.824654 | − | 0.565637i | \(-0.191370\pi\) | |||||||
\(660\) | 14.1642 | − | 11.9624i | 0.551340 | − | 0.465637i | ||||
\(661\) | 40.7524i | 1.58508i | 0.609818 | + | 0.792541i | \(0.291242\pi\) | ||||
−0.609818 | + | 0.792541i | \(0.708758\pi\) | |||||||
\(662\) | 29.2136 | + | 15.2488i | 1.13542 | + | 0.592662i | ||||
\(663\) | − | 10.6912i | − | 0.415212i | ||||||
\(664\) | −1.89092 | − | 14.7416i | −0.0733820 | − | 0.572085i | ||||
\(665\) | 35.1688 | − | 15.8577i | 1.36379 | − | 0.614935i | ||||
\(666\) | 11.9642 | + | 6.24505i | 0.463604 | + | 0.241991i | ||||
\(667\) | −12.6962 | −0.491598 | ||||||||
\(668\) | 24.0772 | − | 16.7796i | 0.931576 | − | 0.649224i | ||||
\(669\) | 10.0483 | 0.388491 | ||||||||
\(670\) | 20.6602 | + | 8.45384i | 0.798174 | + | 0.326600i | ||||
\(671\) | 43.0926 | 1.66357 | ||||||||
\(672\) | 13.1082 | + | 7.22321i | 0.505660 | + | 0.278641i | ||||
\(673\) | 35.8470i | 1.38180i | 0.722950 | + | 0.690901i | \(0.242786\pi\) | ||||
−0.722950 | + | 0.690901i | \(0.757214\pi\) | |||||||
\(674\) | 1.59790 | + | 0.834068i | 0.0615489 | + | 0.0321271i | ||||
\(675\) | −0.921454 | − | 4.91436i | −0.0354668 | − | 0.189154i | ||||
\(676\) | 2.00589 | + | 2.87827i | 0.0771496 | + | 0.110703i | ||||
\(677\) | −20.0017 | −0.768726 | −0.384363 | − | 0.923182i | \(-0.625579\pi\) | ||||
−0.384363 | + | 0.923182i | \(0.625579\pi\) | |||||||
\(678\) | 9.83938 | − | 18.8502i | 0.377879 | − | 0.723939i | ||||
\(679\) | 13.7273 | + | 39.9556i | 0.526804 | + | 1.53335i | ||||
\(680\) | 4.40513 | + | 19.6761i | 0.168929 | + | 0.754545i | ||||
\(681\) | 12.9107 | 0.494739 | ||||||||
\(682\) | −15.2703 | − | 7.97074i | −0.584730 | − | 0.305215i | ||||
\(683\) | 11.9025 | 0.455438 | 0.227719 | − | 0.973727i | \(-0.426873\pi\) | ||||
0.227719 | + | 0.973727i | \(0.426873\pi\) | |||||||
\(684\) | 7.45686 | + | 10.6999i | 0.285120 | + | 0.409121i | ||||
\(685\) | −40.7654 | + | 3.78879i | −1.55756 | + | 0.144762i | ||||
\(686\) | −22.8367 | + | 12.8253i | −0.871907 | + | 0.489671i | ||||
\(687\) | −20.2148 | −0.771245 | ||||||||
\(688\) | 0.924710 | − | 2.50600i | 0.0352543 | − | 0.0955402i | ||||
\(689\) | − | 14.0313i | − | 0.534551i | ||||||
\(690\) | 1.71136 | − | 4.18238i | 0.0651505 | − | 0.159220i | ||||
\(691\) | 10.6264 | 0.404246 | 0.202123 | − | 0.979360i | \(-0.435216\pi\) | ||||
0.202123 | + | 0.979360i | \(0.435216\pi\) | |||||||
\(692\) | 23.6403 | + | 33.9217i | 0.898671 | + | 1.28951i | ||||
\(693\) | −10.3732 | + | 3.56383i | −0.394044 | + | 0.135379i | ||||
\(694\) | −14.8415 | + | 28.4332i | −0.563374 | + | 1.07931i | ||||
\(695\) | −1.70312 | − | 18.3247i | −0.0646031 | − | 0.695095i | ||||
\(696\) | −3.19716 | − | 24.9250i | −0.121188 | − | 0.944780i | ||||
\(697\) | 11.3326i | 0.429252i | ||||||||
\(698\) | 18.5803 | + | 9.69848i | 0.703274 | + | 0.367093i | ||||
\(699\) | −11.8552 | −0.448404 | ||||||||
\(700\) | 11.4096 | − | 23.8709i | 0.431242 | − | 0.902236i | ||||
\(701\) | 13.4641 | 0.508532 | 0.254266 | − | 0.967134i | \(-0.418166\pi\) | ||||
0.254266 | + | 0.967134i | \(0.418166\pi\) | |||||||
\(702\) | −4.20426 | − | 2.19452i | −0.158679 | − | 0.0828270i | ||||
\(703\) | 62.2307i | 2.34707i | ||||||||
\(704\) | 8.37050 | + | 32.0913i | 0.315475 | + | 1.20949i | ||||
\(705\) | −0.143598 | − | 1.54504i | −0.00540822 | − | 0.0581896i | ||||
\(706\) | −10.0792 | + | 19.3097i | −0.379337 | + | 0.726732i | ||||
\(707\) | −2.99896 | + | 1.03033i | −0.112787 | + | 0.0387496i | ||||
\(708\) | 9.77984 | − | 6.81566i | 0.367549 | − | 0.256148i | ||||
\(709\) | 30.2783 | 1.13713 | 0.568563 | − | 0.822639i | \(-0.307499\pi\) | ||||
0.568563 | + | 0.822639i | \(0.307499\pi\) | |||||||
\(710\) | 11.3806 | − | 27.8128i | 0.427105 | − | 1.04380i | ||||
\(711\) | 12.1118i | 0.454229i | ||||||||
\(712\) | −1.02080 | − | 7.95811i | −0.0382560 | − | 0.298243i | ||||
\(713\) | −4.19859 | −0.157239 | ||||||||
\(714\) | 1.78432 | − | 11.7945i | 0.0667765 | − | 0.441399i | ||||
\(715\) | −30.9531 | + | 2.87682i | −1.15758 | + | 0.107587i | ||||
\(716\) | 31.1969 | − | 21.7414i | 1.16588 | − | 0.812513i | ||||
\(717\) | −3.95455 | −0.147685 | ||||||||
\(718\) | 8.03348 | + | 4.19329i | 0.299807 | + | 0.156492i | ||||
\(719\) | −16.9891 | −0.633586 | −0.316793 | − | 0.948495i | \(-0.602606\pi\) | ||||
−0.316793 | + | 0.948495i | \(0.602606\pi\) | |||||||
\(720\) | 8.64176 | + | 2.30652i | 0.322059 | + | 0.0859590i | ||||
\(721\) | −17.0758 | + | 5.86661i | −0.635936 | + | 0.218484i | ||||
\(722\) | −15.3936 | + | 29.4910i | −0.572890 | + | 1.09754i | ||||
\(723\) | 21.4716 | 0.798539 | ||||||||
\(724\) | −25.9076 | + | 18.0552i | −0.962847 | + | 0.671017i | ||||
\(725\) | −43.6617 | + | 8.18668i | −1.62156 | + | 0.304046i | ||||
\(726\) | −7.75562 | − | 4.04825i | −0.287838 | − | 0.150245i | ||||
\(727\) | 36.5682i | 1.35624i | 0.734951 | + | 0.678120i | \(0.237205\pi\) | ||||
−0.734951 | + | 0.678120i | \(0.762795\pi\) | |||||||
\(728\) | −11.1073 | − | 22.5033i | −0.411664 | − | 0.834026i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −22.0118 | − | 9.00687i | −0.814691 | − | 0.333359i | ||||
\(731\) | −2.12897 | −0.0787429 | ||||||||
\(732\) | 11.8866 | + | 17.0561i | 0.439340 | + | 0.630412i | ||||
\(733\) | −38.7859 | −1.43259 | −0.716295 | − | 0.697797i | \(-0.754164\pi\) | ||||
−0.716295 | + | 0.697797i | \(0.754164\pi\) | |||||||
\(734\) | 25.2762 | + | 13.1936i | 0.932962 | + | 0.486984i | ||||
\(735\) | −11.4043 | + | 10.7211i | −0.420653 | + | 0.395455i | ||||
\(736\) | 5.42821 | + | 5.99016i | 0.200086 | + | 0.220800i | ||||
\(737\) | − | 29.2645i | − | 1.07797i | ||||||
\(738\) | 4.45647 | + | 2.32618i | 0.164045 | + | 0.0856277i | ||||
\(739\) | − | 41.8959i | − | 1.54116i | −0.637341 | − | 0.770582i | \(-0.719966\pi\) | ||
0.637341 | − | 0.770582i | \(-0.280034\pi\) | |||||||
\(740\) | 27.5373 | + | 32.6057i | 1.01229 | + | 1.19861i | ||||
\(741\) | − | 21.8680i | − | 0.803341i | ||||||
\(742\) | 2.34178 | − | 15.4794i | 0.0859693 | − | 0.568265i | ||||
\(743\) | 13.4718 | 0.494233 | 0.247117 | − | 0.968986i | \(-0.420517\pi\) | ||||
0.247117 | + | 0.968986i | \(0.420517\pi\) | |||||||
\(744\) | −1.05729 | − | 8.24263i | −0.0387622 | − | 0.302190i | ||||
\(745\) | −0.595081 | − | 6.40276i | −0.0218021 | − | 0.234579i | ||||
\(746\) | 8.12742 | + | 4.24232i | 0.297566 | + | 0.155322i | ||||
\(747\) | 5.25464i | 0.192257i | ||||||||
\(748\) | 21.6864 | − | 15.1134i | 0.792932 | − | 0.552602i | ||||
\(749\) | 4.38402 | + | 12.7605i | 0.160189 | + | 0.466257i | ||||
\(750\) | 3.18846 | − | 15.4866i | 0.116426 | − | 0.565489i | ||||
\(751\) | 21.3020i | 0.777320i | 0.921381 | + | 0.388660i | \(0.127062\pi\) | ||||
−0.921381 | + | 0.388660i | \(0.872938\pi\) | |||||||
\(752\) | 2.60413 | + | 0.960922i | 0.0949629 | + | 0.0350412i | ||||
\(753\) | − | 24.2390i | − | 0.883317i | ||||||
\(754\) | −19.4973 | + | 37.3528i | −0.710050 | + | 1.36031i | ||||
\(755\) | −16.6451 | + | 1.54701i | −0.605776 | + | 0.0563016i | ||||
\(756\) | −4.27188 | − | 3.12267i | −0.155367 | − | 0.113570i | ||||
\(757\) | − | 12.6260i | − | 0.458898i | −0.973321 | − | 0.229449i | \(-0.926308\pi\) | ||
0.973321 | − | 0.229449i | \(-0.0736925\pi\) | |||||||
\(758\) | −29.4327 | − | 15.3632i | −1.06904 | − | 0.558015i | ||||
\(759\) | −5.92419 | −0.215034 | ||||||||
\(760\) | 9.01034 | + | 40.2460i | 0.326839 | + | 1.45988i | ||||
\(761\) | − | 23.4789i | − | 0.851108i | −0.904933 | − | 0.425554i | \(-0.860079\pi\) | ||
0.904933 | − | 0.425554i | \(-0.139921\pi\) | |||||||
\(762\) | 20.0278 | + | 10.4540i | 0.725530 | + | 0.378710i | ||||
\(763\) | −12.8181 | − | 37.3095i | −0.464048 | − | 1.35069i | ||||
\(764\) | −3.22967 | + | 2.25079i | −0.116845 | + | 0.0814306i | ||||
\(765\) | −0.659715 | − | 7.09818i | −0.0238520 | − | 0.256635i | ||||
\(766\) | 14.0426 | + | 7.32991i | 0.507380 | + | 0.264841i | ||||
\(767\) | −19.9876 | −0.721711 | ||||||||
\(768\) | −10.3929 | + | 12.1650i | −0.375021 | + | 0.438968i | ||||
\(769\) | − | 5.99496i | − | 0.216184i | −0.994141 | − | 0.108092i | \(-0.965526\pi\) | ||
0.994141 | − | 0.108092i | \(-0.0344741\pi\) | |||||||
\(770\) | −34.6275 | − | 1.99224i | −1.24789 | − | 0.0717954i | ||||
\(771\) | 6.84349i | 0.246462i | ||||||||
\(772\) | −12.0558 | + | 8.40179i | −0.433897 | + | 0.302387i | ||||
\(773\) | −4.98453 | −0.179281 | −0.0896406 | − | 0.995974i | \(-0.528572\pi\) | ||||
−0.0896406 | + | 0.995974i | \(0.528572\pi\) | |||||||
\(774\) | −0.437003 | + | 0.837208i | −0.0157077 | + | 0.0300928i | ||||
\(775\) | −14.4388 | + | 2.70731i | −0.518658 | + | 0.0972495i | ||||
\(776\) | −44.7979 | + | 5.74628i | −1.60815 | + | 0.206279i | ||||
\(777\) | −8.20387 | − | 23.8788i | −0.294312 | − | 0.856648i | ||||
\(778\) | −2.11756 | + | 4.05680i | −0.0759181 | + | 0.145444i | ||||
\(779\) | 23.1799i | 0.830506i | ||||||||
\(780\) | −9.67666 | − | 11.4577i | −0.346480 | − | 0.410252i | ||||
\(781\) | −39.3958 | −1.40969 | ||||||||
\(782\) | 2.98135 | − | 5.71166i | 0.106613 | − | 0.204248i | ||||
\(783\) | 8.88452i | 0.317507i | ||||||||
\(784\) | −8.49784 | − | 26.6793i | −0.303494 | − | 0.952833i | ||||
\(785\) | −0.265359 | − | 2.85513i | −0.00947108 | − | 0.101904i | ||||
\(786\) | −5.24019 | − | 2.73526i | −0.186911 | − | 0.0975633i | ||||
\(787\) | 9.43059i | 0.336164i | 0.985773 | + | 0.168082i | \(0.0537573\pi\) | ||||
−0.985773 | + | 0.168082i | \(0.946243\pi\) | |||||||
\(788\) | −6.64638 | + | 4.63192i | −0.236768 | + | 0.165005i | ||||
\(789\) | 26.0905i | 0.928845i | ||||||||
\(790\) | −14.5048 | + | 35.4481i | −0.516059 | + | 1.26119i | ||||
\(791\) | −37.6223 | + | 12.9256i | −1.33769 | + | 0.459582i | ||||
\(792\) | −1.49183 | − | 11.6303i | −0.0530100 | − | 0.413265i | ||||
\(793\) | − | 34.8585i | − | 1.23786i | ||||||
\(794\) | −17.3494 | + | 33.2378i | −0.615706 | + | 1.17957i | ||||
\(795\) | −0.865822 | − | 9.31579i | −0.0307076 | − | 0.330397i | ||||
\(796\) | −27.2927 | − | 39.1625i | −0.967364 | − | 1.38808i | ||||
\(797\) | 20.0949 | 0.711797 | 0.355898 | − | 0.934525i | \(-0.384175\pi\) | ||||
0.355898 | + | 0.934525i | \(0.384175\pi\) | |||||||
\(798\) | 3.64969 | − | 24.1248i | 0.129198 | − | 0.854007i | ||||
\(799\) | − | 2.21234i | − | 0.0782671i | ||||||
\(800\) | 22.5299 | + | 17.0998i | 0.796554 | + | 0.604568i | ||||
\(801\) | 2.83667i | 0.100229i | ||||||||
\(802\) | 3.22681 | − | 6.18190i | 0.113943 | − | 0.218290i | ||||
\(803\) | 31.1789i | 1.10028i | ||||||||
\(804\) | 11.5829 | − | 8.07223i | 0.408498 | − | 0.284686i | ||||
\(805\) | −7.70698 | + | 3.47509i | −0.271635 | + | 0.122481i | ||||
\(806\) | −6.44770 | + | 12.3525i | −0.227111 | + | 0.435097i | ||||
\(807\) | −8.74121 | −0.307705 | ||||||||
\(808\) | −0.431300 | − | 3.36241i | −0.0151731 | − | 0.118289i | ||||
\(809\) | −1.73923 | −0.0611480 | −0.0305740 | − | 0.999533i | \(-0.509734\pi\) | ||||
−0.0305740 | + | 0.999533i | \(0.509734\pi\) | |||||||
\(810\) | −2.92674 | − | 1.19758i | −0.102835 | − | 0.0420786i | ||||
\(811\) | 17.6292 | 0.619044 | 0.309522 | − | 0.950892i | \(-0.399831\pi\) | ||||
0.309522 | + | 0.950892i | \(0.399831\pi\) | |||||||
\(812\) | −27.7434 | + | 37.9536i | −0.973604 | + | 1.33191i | ||||
\(813\) | 14.8967i | 0.522451i | ||||||||
\(814\) | 25.8896 | − | 49.5992i | 0.907430 | − | 1.73845i | ||||
\(815\) | −4.41542 | − | 47.5076i | −0.154665 | − | 1.66412i | ||||
\(816\) | 11.9638 | + | 4.41464i | 0.418818 | + | 0.154543i | ||||
\(817\) | −4.35465 | −0.152350 | ||||||||
\(818\) | 16.1319 | + | 8.42049i | 0.564040 | + | 0.294416i | ||||
\(819\) | 2.88286 | + | 8.39108i | 0.100735 | + | 0.293208i | ||||
\(820\) | 10.2572 | + | 12.1451i | 0.358196 | + | 0.424125i | ||||
\(821\) | 41.3089 | 1.44169 | 0.720846 | − | 0.693095i | \(-0.243753\pi\) | ||||
0.720846 | + | 0.693095i | \(0.243753\pi\) | |||||||
\(822\) | −11.9817 | + | 22.9545i | −0.417909 | + | 0.800629i | ||||
\(823\) | 38.9835 | 1.35888 | 0.679440 | − | 0.733731i | \(-0.262223\pi\) | ||||
0.679440 | + | 0.733731i | \(0.262223\pi\) | |||||||
\(824\) | −2.45579 | − | 19.1452i | −0.0855513 | − | 0.666956i | ||||
\(825\) | −20.3731 | + | 3.82000i | −0.709300 | + | 0.132995i | ||||
\(826\) | −22.0503 | − | 3.33586i | −0.767229 | − | 0.116069i | ||||
\(827\) | 3.65170 | 0.126982 | 0.0634911 | − | 0.997982i | \(-0.479777\pi\) | ||||
0.0634911 | + | 0.997982i | \(0.479777\pi\) | |||||||
\(828\) | −1.63411 | − | 2.34480i | −0.0567894 | − | 0.0814875i | ||||
\(829\) | − | 18.9941i | − | 0.659693i | −0.944035 | − | 0.329846i | \(-0.893003\pi\) | ||
0.944035 | − | 0.329846i | \(-0.106997\pi\) | |||||||
\(830\) | −6.29284 | + | 15.3790i | −0.218428 | + | 0.533812i | ||||
\(831\) | −8.86971 | −0.307687 | ||||||||
\(832\) | 25.9593 | − | 6.77108i | 0.899978 | − | 0.234745i | ||||
\(833\) | −17.6045 | + | 13.7154i | −0.609960 | + | 0.475210i | ||||
\(834\) | −10.3184 | − | 5.38597i | −0.357297 | − | 0.186501i | ||||
\(835\) | −32.6706 | + | 3.03645i | −1.13061 | + | 0.105081i | ||||
\(836\) | 44.3578 | − | 30.9133i | 1.53415 | − | 1.06916i | ||||
\(837\) | 2.93809i | 0.101555i | ||||||||
\(838\) | 3.85306 | − | 7.38168i | 0.133102 | − | 0.254996i | ||||
\(839\) | −36.3049 | −1.25339 | −0.626693 | − | 0.779266i | \(-0.715592\pi\) | ||||
−0.626693 | + | 0.779266i | \(0.715592\pi\) | |||||||
\(840\) | −8.76303 | − | 14.2551i | −0.302353 | − | 0.491849i | ||||
\(841\) | 49.9348 | 1.72189 | ||||||||
\(842\) | 9.04953 | − | 17.3370i | 0.311867 | − | 0.597474i | ||||
\(843\) | 7.14815i | 0.246195i | ||||||||
\(844\) | 10.2267 | − | 7.12706i | 0.352017 | − | 0.245324i | ||||
\(845\) | −0.362986 | − | 3.90554i | −0.0124871 | − | 0.134355i | ||||
\(846\) | −0.869993 | − | 0.454116i | −0.0299110 | − | 0.0156128i | ||||
\(847\) | 5.31803 | + | 15.4791i | 0.182730 | + | 0.531867i | ||||
\(848\) | 15.7016 | + | 5.79386i | 0.539194 | + | 0.198962i | ||||
\(849\) | −2.57635 | −0.0884202 | ||||||||
\(850\) | 6.56980 | − | 21.5646i | 0.225342 | − | 0.739660i | ||||
\(851\) | − | 13.6374i | − | 0.467483i | ||||||
\(852\) | −10.8668 | − | 15.5929i | −0.372292 | − | 0.534205i | ||||
\(853\) | −17.8797 | −0.612189 | −0.306094 | − | 0.952001i | \(-0.599022\pi\) | ||||
−0.306094 | + | 0.952001i | \(0.599022\pi\) | |||||||
\(854\) | 5.81776 | − | 38.4559i | 0.199080 | − | 1.31593i | ||||
\(855\) | −1.34940 | − | 14.5188i | −0.0461483 | − | 0.496532i | ||||
\(856\) | −14.3069 | + | 1.83517i | −0.489000 | + | 0.0627247i | ||||
\(857\) | −36.5307 | −1.24786 | −0.623932 | − | 0.781478i | \(-0.714466\pi\) | ||||
−0.623932 | + | 0.781478i | \(0.714466\pi\) | |||||||
\(858\) | −9.09767 | + | 17.4293i | −0.310589 | + | 0.595025i | ||||
\(859\) | 10.2299 | 0.349038 | 0.174519 | − | 0.984654i | \(-0.444163\pi\) | ||||
0.174519 | + | 0.984654i | \(0.444163\pi\) | |||||||
\(860\) | −2.28161 | + | 1.92695i | −0.0778024 | + | 0.0657083i | ||||
\(861\) | −3.05581 | − | 8.89446i | −0.104142 | − | 0.303122i | ||||
\(862\) | 32.9882 | + | 17.2191i | 1.12358 | + | 0.586484i | ||||
\(863\) | 31.2788 | 1.06474 | 0.532372 | − | 0.846511i | \(-0.321301\pi\) | ||||
0.532372 | + | 0.846511i | \(0.321301\pi\) | |||||||
\(864\) | 4.19179 | − | 3.79854i | 0.142607 | − | 0.129229i | ||||
\(865\) | −4.27796 | − | 46.0286i | −0.145455 | − | 1.56502i | ||||
\(866\) | −0.734697 | + | 1.40753i | −0.0249660 | + | 0.0478298i | ||||
\(867\) | 6.83611i | 0.232167i | ||||||||
\(868\) | −9.17468 | + | 12.5511i | −0.311409 | + | 0.426014i | ||||
\(869\) | 50.2110 | 1.70329 | ||||||||
\(870\) | −10.6399 | + | 26.0027i | −0.360726 | + | 0.881574i | ||||
\(871\) | −23.6727 | −0.802117 | ||||||||
\(872\) | 41.8311 | − | 5.36572i | 1.41658 | − | 0.181706i | ||||
\(873\) | 15.9682 | 0.540442 | ||||||||
\(874\) | 6.09812 | − | 11.6827i | 0.206272 | − | 0.395175i | ||||
\(875\) | −24.2632 | + | 16.9203i | −0.820247 | + | 0.572010i | ||||
\(876\) | −12.3406 | + | 8.60030i | −0.416951 | + | 0.290577i | ||||
\(877\) | 9.19346i | 0.310441i | 0.987880 | + | 0.155220i | \(0.0496088\pi\) | ||||
−0.987880 | + | 0.155220i | \(0.950391\pi\) | |||||||
\(878\) | −4.63434 | + | 8.87845i | −0.156401 | + | 0.299633i | ||||
\(879\) | − | 25.4873i | − | 0.859664i | ||||||
\(880\) | 9.56197 | − | 35.8255i | 0.322334 | − | 1.20768i | ||||
\(881\) | − | 7.56097i | − | 0.254736i | −0.991856 | − | 0.127368i | \(-0.959347\pi\) | ||
0.991856 | − | 0.127368i | \(-0.0406528\pi\) | |||||||
\(882\) | 1.77993 | + | 9.73816i | 0.0599334 | + | 0.327901i | ||||
\(883\) | −33.5250 | −1.12821 | −0.564103 | − | 0.825705i | \(-0.690778\pi\) | ||||
−0.564103 | + | 0.825705i | \(0.690778\pi\) | |||||||
\(884\) | −12.2256 | − | 17.5426i | −0.411191 | − | 0.590021i | ||||
\(885\) | −13.2703 | + | 1.23336i | −0.446078 | + | 0.0414591i | ||||
\(886\) | −8.81598 | + | 16.8896i | −0.296179 | + | 0.567418i | ||||
\(887\) | 45.8345i | 1.53897i | 0.638663 | + | 0.769486i | \(0.279488\pi\) | ||||
−0.638663 | + | 0.769486i | \(0.720512\pi\) | |||||||
\(888\) | 26.7727 | − | 3.43417i | 0.898434 | − | 0.115243i | ||||
\(889\) | −13.7331 | − | 39.9725i | −0.460592 | − | 1.34063i | ||||
\(890\) | −3.39713 | + | 8.30219i | −0.113872 | + | 0.278290i | ||||
\(891\) | 4.14562i | 0.138884i | ||||||||
\(892\) | 16.4877 | − | 11.4904i | 0.552050 | − | 0.384728i | ||||
\(893\) | − | 4.52518i | − | 0.151429i | ||||||
\(894\) | −3.60531 | − | 1.88189i | −0.120580 | − | 0.0629398i | ||||
\(895\) | −42.3312 | + | 3.93432i | −1.41498 | + | 0.131510i | ||||
\(896\) | 29.7684 | − | 3.13734i | 0.994492 | − | 0.104811i | ||||
\(897\) | 4.79221i | 0.160007i | ||||||||
\(898\) | 13.8276 | − | 26.4909i | 0.461434 | − | 0.884012i | ||||
\(899\) | 26.1035 | 0.870601 | ||||||||
\(900\) | −7.13162 | − | 7.00999i | −0.237721 | − | 0.233666i | ||||
\(901\) | − | 13.3393i | − | 0.444396i | ||||||
\(902\) | 9.64345 | − | 18.4749i | 0.321092 | − | 0.615146i | ||||
\(903\) | 1.67094 | − | 0.574074i | 0.0556055 | − | 0.0191040i | ||||
\(904\) | −5.41071 | − | 42.1818i | −0.179958 | − | 1.40295i | ||||
\(905\) | 35.1542 | − | 3.26728i | 1.16856 | − | 0.108608i | ||||
\(906\) | −4.89229 | + | 9.37262i | −0.162535 | + | 0.311384i | ||||
\(907\) | −10.4401 | −0.346658 | −0.173329 | − | 0.984864i | \(-0.555452\pi\) | ||||
−0.173329 | + | 0.984864i | \(0.555452\pi\) | |||||||
\(908\) | 21.1844 | − | 14.7636i | 0.703030 | − | 0.489948i | ||||
\(909\) | 1.19853i | 0.0397528i | ||||||||
\(910\) | −1.61157 | + | 28.0109i | −0.0534230 | + | 0.928554i | ||||
\(911\) | 7.71906i | 0.255744i | 0.991791 | + | 0.127872i | \(0.0408146\pi\) | ||||
−0.991791 | + | 0.127872i | \(0.959185\pi\) | |||||||
\(912\) | 24.4711 | + | 9.02981i | 0.810318 | + | 0.299007i | ||||
\(913\) | 21.7838 | 0.720938 | ||||||||
\(914\) | 8.39751 | + | 4.38330i | 0.277765 | + | 0.144987i | ||||
\(915\) | −2.15099 | − | 23.1436i | −0.0711096 | − | 0.765102i | ||||
\(916\) | −33.1694 | + | 23.1160i | −1.09595 | + | 0.763776i | ||||
\(917\) | 3.59320 | + | 10.4586i | 0.118658 | + | 0.345375i | ||||
\(918\) | −3.99690 | − | 2.08629i | −0.131917 | − | 0.0688577i | ||||
\(919\) | − | 2.09031i | − | 0.0689530i | −0.999406 | − | 0.0344765i | \(-0.989024\pi\) | ||
0.999406 | − | 0.0344765i | \(-0.0109764\pi\) | |||||||
\(920\) | −1.97455 | − | 8.81960i | −0.0650989 | − | 0.290774i | ||||
\(921\) | −19.5890 | −0.645479 | ||||||||
\(922\) | 48.7345 | + | 25.4383i | 1.60498 | + | 0.837764i | ||||
\(923\) | 31.8681i | 1.04895i | ||||||||
\(924\) | −12.9454 | + | 17.7096i | −0.425873 | + | 0.582603i | ||||
\(925\) | −8.79357 | − | 46.8985i | −0.289131 | − | 1.54201i | ||||
\(926\) | 9.58003 | − | 18.3534i | 0.314819 | − | 0.603129i | ||||
\(927\) | 6.82433i | 0.224140i | ||||||||
\(928\) | −33.7483 | − | 37.2420i | −1.10784 | − | 1.22253i | ||||
\(929\) | 37.8995i | 1.24344i | 0.783238 | + | 0.621722i | \(0.213566\pi\) | ||||
−0.783238 | + | 0.621722i | \(0.786434\pi\) | |||||||
\(930\) | −3.51858 | + | 8.59902i | −0.115379 | + | 0.281973i | ||||
\(931\) | −36.0086 | + | 28.0538i | −1.18014 | + | 0.919426i | ||||
\(932\) | −19.4525 | + | 13.5566i | −0.637187 | + | 0.444061i | ||||
\(933\) | 25.9353i | 0.849085i | ||||||||
\(934\) | −30.9299 | − | 16.1447i | −1.01206 | − | 0.528271i | ||||
\(935\) | −29.4264 | + | 2.73493i | −0.962346 | + | 0.0894417i | ||||
\(936\) | −9.40801 | + | 1.20678i | −0.307510 | + | 0.0394447i | ||||
\(937\) | 6.24587 | 0.204044 | 0.102022 | − | 0.994782i | \(-0.467469\pi\) | ||||
0.102022 | + | 0.994782i | \(0.467469\pi\) | |||||||
\(938\) | −26.1157 | − | 3.95088i | −0.852706 | − | 0.129001i | ||||
\(939\) | − | 8.23386i | − | 0.268702i | ||||||
\(940\) | −2.00240 | − | 2.37096i | −0.0653112 | − | 0.0773323i | ||||
\(941\) | 21.7262i | 0.708253i | 0.935197 | + | 0.354127i | \(0.115222\pi\) | ||||
−0.935197 | + | 0.354127i | \(0.884778\pi\) | |||||||
\(942\) | −1.60769 | − | 0.839174i | −0.0523812 | − | 0.0273418i | ||||
\(943\) | − | 5.07969i | − | 0.165418i | ||||||
\(944\) | 8.25335 | − | 22.3669i | 0.268624 | − | 0.727979i | ||||
\(945\) | 2.43179 | + | 5.39318i | 0.0791063 | + | 0.175440i | ||||
\(946\) | 3.47075 | + | 1.81165i | 0.112844 | + | 0.0589018i | ||||
\(947\) | 11.2143 | 0.364415 | 0.182208 | − | 0.983260i | \(-0.441676\pi\) | ||||
0.182208 | + | 0.983260i | \(0.441676\pi\) | |||||||
\(948\) | 13.8501 | + | 19.8736i | 0.449830 | + | 0.645464i | ||||
\(949\) | 25.2213 | 0.818717 | ||||||||
\(950\) | 13.4380 | − | 44.1087i | 0.435987 | − | 1.43108i | ||||
\(951\) | 27.9672 | 0.906899 | ||||||||
\(952\) | −10.5595 | − | 21.3934i | −0.342234 | − | 0.693363i | ||||
\(953\) | 30.9796i | 1.00353i | 0.865005 | + | 0.501764i | \(0.167315\pi\) | ||||
−0.865005 | + | 0.501764i | \(0.832685\pi\) | |||||||
\(954\) | −5.24560 | − | 2.73808i | −0.169833 | − | 0.0886487i | ||||
\(955\) | 4.38236 | − | 0.407303i | 0.141810 | − | 0.0131800i | ||||
\(956\) | −6.48879 | + | 4.52210i | −0.209863 | + | 0.146255i | ||||
\(957\) | 36.8319 | 1.19061 | ||||||||
\(958\) | 6.72302 | − | 12.8799i | 0.217211 | − | 0.416132i | ||||
\(959\) | 45.8137 | − | 15.7399i | 1.47940 | − | 0.508267i | ||||
\(960\) | 16.8173 | − | 6.09737i | 0.542777 | − | 0.196792i | ||||
\(961\) | −22.3676 | −0.721537 | ||||||||
\(962\) | −40.1219 | − | 20.9427i | −1.29358 | − | 0.675219i | ||||
\(963\) | 5.09970 | 0.164336 | ||||||||
\(964\) | 35.2316 | − | 24.5532i | 1.13473 | − | 0.790806i | ||||
\(965\) | 16.3586 | − | 1.52039i | 0.526602 | − | 0.0489431i | ||||
\(966\) | −0.799801 | + | 5.28676i | −0.0257332 | + | 0.170099i | ||||
\(967\) | 48.5226 | 1.56038 | 0.780190 | − | 0.625542i | \(-0.215122\pi\) | ||||
0.780190 | + | 0.625542i | \(0.215122\pi\) | |||||||
\(968\) | −17.3550 | + | 2.22615i | −0.557811 | + | 0.0715511i | ||||
\(969\) | − | 20.7894i | − | 0.667853i | ||||||
\(970\) | 46.7348 | + | 19.1232i | 1.50056 | + | 0.614008i | ||||
\(971\) | −55.7545 | −1.78925 | −0.894624 | − | 0.446820i | \(-0.852556\pi\) | ||||
−0.894624 | + | 0.446820i | \(0.852556\pi\) | |||||||
\(972\) | −1.64084 | + | 1.14352i | −0.0526301 | + | 0.0366784i | ||||
\(973\) | 7.07533 | + | 20.5940i | 0.226825 | + | 0.660213i | ||||
\(974\) | 10.0611 | − | 19.2749i | 0.322377 | − | 0.617609i | ||||
\(975\) | 3.09008 | + | 16.4802i | 0.0989618 | + | 0.527790i | ||||
\(976\) | 39.0079 | + | 14.3939i | 1.24861 | + | 0.460737i | ||||
\(977\) | − | 15.4305i | − | 0.493667i | −0.969058 | − | 0.246833i | \(-0.920610\pi\) | ||
0.969058 | − | 0.246833i | \(-0.0793900\pi\) | |||||||
\(978\) | −26.7509 | − | 13.9634i | −0.855400 | − | 0.446499i | ||||
\(979\) | 11.7598 | 0.375843 | ||||||||
\(980\) | −6.45280 | + | 30.6327i | −0.206127 | + | 0.978525i | ||||
\(981\) | −14.9107 | −0.476062 | ||||||||
\(982\) | 18.5757 | + | 9.69611i | 0.592776 | + | 0.309415i | ||||
\(983\) | − | 29.4115i | − | 0.938081i | −0.883177 | − | 0.469040i | \(-0.844600\pi\) | ||
0.883177 | − | 0.469040i | \(-0.155400\pi\) | |||||||
\(984\) | 9.97240 | − | 1.27917i | 0.317908 | − | 0.0407785i | ||||
\(985\) | 9.01853 | − | 0.838194i | 0.287354 | − | 0.0267071i | ||||
\(986\) | −18.5357 | + | 35.5105i | −0.590296 | + | 1.13089i | ||||
\(987\) | 0.596554 | + | 1.73638i | 0.0189885 | + | 0.0552695i | ||||
\(988\) | −25.0065 | − | 35.8820i | −0.795562 | − | 1.14156i | ||||
\(989\) | 0.954288 | 0.0303446 | ||||||||
\(990\) | −4.96470 | + | 12.1332i | −0.157789 | + | 0.385617i | ||||
\(991\) | − | 37.8845i | − | 1.20344i | −0.798707 | − | 0.601720i | \(-0.794482\pi\) | ||
0.798707 | − | 0.601720i | \(-0.205518\pi\) | |||||||
\(992\) | −11.1605 | − | 12.3158i | −0.354345 | − | 0.391028i | ||||
\(993\) | −23.3019 | −0.739464 | ||||||||
\(994\) | −5.31867 | + | 35.1569i | −0.168698 | + | 1.11511i | ||||
\(995\) | 4.93889 | + | 53.1399i | 0.156573 | + | 1.68465i | ||||
\(996\) | 6.00878 | + | 8.62205i | 0.190396 | + | 0.273200i | ||||
\(997\) | −3.24991 | −0.102926 | −0.0514629 | − | 0.998675i | \(-0.516388\pi\) | ||||
−0.0514629 | + | 0.998675i | \(0.516388\pi\) | |||||||
\(998\) | −22.3051 | − | 11.6427i | −0.706054 | − | 0.368544i | ||||
\(999\) | −9.54315 | −0.301932 |
(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 | 420.2.i.a.139.19 | yes | 48 | |
4.3 | odd | 2 | inner | 420.2.i.a.139.32 | yes | 48 | |
5.4 | even | 2 | inner | 420.2.i.a.139.30 | yes | 48 | |
7.6 | odd | 2 | inner | 420.2.i.a.139.20 | yes | 48 | |
20.19 | odd | 2 | inner | 420.2.i.a.139.17 | ✓ | 48 | |
28.27 | even | 2 | inner | 420.2.i.a.139.31 | yes | 48 | |
35.34 | odd | 2 | inner | 420.2.i.a.139.29 | yes | 48 | |
140.139 | even | 2 | inner | 420.2.i.a.139.18 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.i.a.139.17 | ✓ | 48 | 20.19 | odd | 2 | inner | |
420.2.i.a.139.18 | yes | 48 | 140.139 | even | 2 | inner | |
420.2.i.a.139.19 | yes | 48 | 1.1 | even | 1 | trivial | |
420.2.i.a.139.20 | yes | 48 | 7.6 | odd | 2 | inner | |
420.2.i.a.139.29 | yes | 48 | 35.34 | odd | 2 | inner | |
420.2.i.a.139.30 | yes | 48 | 5.4 | even | 2 | inner | |
420.2.i.a.139.31 | yes | 48 | 28.27 | even | 2 | inner | |
420.2.i.a.139.32 | yes | 48 | 4.3 | odd | 2 | inner |