Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,3,Mod(15,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.c (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: | \(0.762944740209\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1539727.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{3} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 15.1 | ||
Root | \(0.841985 - 1.13625i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 28.15 |
Dual form | 28.3.c.a.15.2 |
$q$-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 \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.92411 | − | 0.545716i | −0.962054 | − | 0.272858i | ||||
\(3\) | 4.54500i | 1.51500i | 0.652836 | + | 0.757499i | \(0.273579\pi\) | ||||
−0.652836 | + | 0.757499i | \(0.726421\pi\) | |||||||
\(4\) | 3.40439 | + | 2.10003i | 0.851097 | + | 0.525009i | ||||
\(5\) | 1.36794 | 0.273588 | 0.136794 | − | 0.990600i | \(-0.456320\pi\) | ||||
0.136794 | + | 0.990600i | \(0.456320\pi\) | |||||||
\(6\) | 2.48028 | − | 8.74507i | 0.413380 | − | 1.45751i | ||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | −5.40439 | − | 5.89853i | −0.675548 | − | 0.737316i | ||||
\(9\) | −11.6570 | −1.29522 | ||||||||
\(10\) | −2.63206 | − | 0.746506i | −0.263206 | − | 0.0746506i | ||||
\(11\) | − | 15.3073i | − | 1.39157i | −0.718250 | − | 0.695785i | \(-0.755057\pi\) | ||
0.718250 | − | 0.695785i | \(-0.244943\pi\) | |||||||
\(12\) | −9.54465 | + | 15.4729i | −0.795388 | + | 1.28941i | ||||
\(13\) | 19.9460 | 1.53431 | 0.767156 | − | 0.641461i | \(-0.221671\pi\) | ||||
0.767156 | + | 0.641461i | \(0.221671\pi\) | |||||||
\(14\) | 1.44383 | − | 5.09071i | 0.103131 | − | 0.363622i | ||||
\(15\) | 6.21727i | 0.414485i | ||||||||
\(16\) | 7.17971 | + | 14.2987i | 0.448732 | + | 0.893667i | ||||
\(17\) | −4.73588 | −0.278581 | −0.139290 | − | 0.990252i | \(-0.544482\pi\) | ||||
−0.139290 | + | 0.990252i | \(0.544482\pi\) | |||||||
\(18\) | 22.4293 | + | 6.36141i | 1.24607 | + | 0.353412i | ||||
\(19\) | − | 13.2765i | − | 0.698761i | −0.936981 | − | 0.349380i | \(-0.886392\pi\) | ||
0.936981 | − | 0.349380i | \(-0.113608\pi\) | |||||||
\(20\) | 4.65699 | + | 2.87272i | 0.232850 | + | 0.143636i | ||||
\(21\) | −12.0249 | −0.572616 | ||||||||
\(22\) | −8.35343 | + | 29.4528i | −0.379701 | + | 1.33877i | ||||
\(23\) | 14.9487i | 0.649945i | 0.945723 | + | 0.324973i | \(0.105355\pi\) | ||||
−0.945723 | + | 0.324973i | \(0.894645\pi\) | |||||||
\(24\) | 26.8088 | − | 24.5629i | 1.11703 | − | 1.02346i | ||||
\(25\) | −23.1287 | −0.925150 | ||||||||
\(26\) | −38.3784 | − | 10.8849i | −1.47609 | − | 0.418649i | ||||
\(27\) | − | 12.0760i | − | 0.447260i | ||||||
\(28\) | −5.55617 | + | 9.00716i | −0.198435 | + | 0.321684i | ||||
\(29\) | 6.20763 | 0.214056 | 0.107028 | − | 0.994256i | \(-0.465867\pi\) | ||||
0.107028 | + | 0.994256i | \(0.465867\pi\) | |||||||
\(30\) | 3.39287 | − | 11.9627i | 0.113096 | − | 0.398757i | ||||
\(31\) | − | 18.5385i | − | 0.598017i | −0.954251 | − | 0.299008i | \(-0.903344\pi\) | ||
0.954251 | − | 0.299008i | \(-0.0966558\pi\) | |||||||
\(32\) | −6.01152 | − | 31.4303i | −0.187860 | − | 0.982196i | ||||
\(33\) | 69.5715 | 2.10823 | ||||||||
\(34\) | 9.11234 | + | 2.58445i | 0.268010 | + | 0.0760131i | ||||
\(35\) | 3.61922i | 0.103406i | ||||||||
\(36\) | −39.6849 | − | 24.4801i | −1.10236 | − | 0.680003i | ||||
\(37\) | −27.5216 | −0.743827 | −0.371914 | − | 0.928267i | \(-0.621298\pi\) | ||||
−0.371914 | + | 0.928267i | \(0.621298\pi\) | |||||||
\(38\) | −7.24518 | + | 25.5453i | −0.190663 | + | 0.672246i | ||||
\(39\) | 90.6547i | 2.32448i | ||||||||
\(40\) | −7.39287 | − | 8.06882i | −0.184822 | − | 0.201720i | ||||
\(41\) | −11.1064 | −0.270887 | −0.135443 | − | 0.990785i | \(-0.543246\pi\) | ||||
−0.135443 | + | 0.990785i | \(0.543246\pi\) | |||||||
\(42\) | 23.1373 | + | 6.56220i | 0.550887 | + | 0.156243i | ||||
\(43\) | − | 27.0248i | − | 0.628483i | −0.949343 | − | 0.314241i | \(-0.898250\pi\) | ||
0.949343 | − | 0.314241i | \(-0.101750\pi\) | |||||||
\(44\) | 32.1458 | − | 52.1119i | 0.730586 | − | 1.18436i | ||||
\(45\) | −15.9460 | −0.354357 | ||||||||
\(46\) | 8.15777 | − | 28.7630i | 0.177343 | − | 0.625282i | ||||
\(47\) | 30.9731i | 0.659001i | 0.944155 | + | 0.329501i | \(0.106880\pi\) | ||||
−0.944155 | + | 0.329501i | \(0.893120\pi\) | |||||||
\(48\) | −64.9874 | + | 32.6317i | −1.35390 | + | 0.679828i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 44.5022 | + | 12.6217i | 0.890044 | + | 0.252435i | ||||
\(51\) | − | 21.5245i | − | 0.422050i | ||||||
\(52\) | 67.9041 | + | 41.8874i | 1.30585 | + | 0.805527i | ||||
\(53\) | −12.7857 | −0.241240 | −0.120620 | − | 0.992699i | \(-0.538488\pi\) | ||||
−0.120620 | + | 0.992699i | \(0.538488\pi\) | |||||||
\(54\) | −6.59008 | + | 23.2356i | −0.122039 | + | 0.430288i | ||||
\(55\) | − | 20.9394i | − | 0.380716i | ||||||
\(56\) | 15.6060 | − | 14.2987i | 0.278679 | − | 0.255333i | ||||
\(57\) | 60.3415 | 1.05862 | ||||||||
\(58\) | −11.9442 | − | 3.38760i | −0.205934 | − | 0.0584070i | ||||
\(59\) | 28.8289i | 0.488626i | 0.969696 | + | 0.244313i | \(0.0785625\pi\) | ||||
−0.969696 | + | 0.244313i | \(0.921438\pi\) | |||||||
\(60\) | −13.0565 | + | 21.1660i | −0.217608 | + | 0.352767i | ||||
\(61\) | 6.52415 | 0.106953 | 0.0534767 | − | 0.998569i | \(-0.482970\pi\) | ||||
0.0534767 | + | 0.998569i | \(0.482970\pi\) | |||||||
\(62\) | −10.1168 | + | 35.6701i | −0.163174 | + | 0.575324i | ||||
\(63\) | − | 30.8415i | − | 0.489548i | ||||||
\(64\) | −5.58519 | + | 63.7558i | −0.0872687 | + | 0.996185i | ||||
\(65\) | 27.2850 | 0.419769 | ||||||||
\(66\) | −133.863 | − | 37.9663i | −2.02823 | − | 0.575247i | ||||
\(67\) | − | 102.863i | − | 1.53526i | −0.640891 | − | 0.767632i | \(-0.721435\pi\) | ||
0.640891 | − | 0.767632i | \(-0.278565\pi\) | |||||||
\(68\) | −16.1228 | − | 9.94551i | −0.237099 | − | 0.146257i | ||||
\(69\) | −67.9420 | −0.984666 | ||||||||
\(70\) | 1.97507 | − | 6.96378i | 0.0282153 | − | 0.0994826i | ||||
\(71\) | − | 45.8085i | − | 0.645190i | −0.946537 | − | 0.322595i | \(-0.895445\pi\) | ||
0.946537 | − | 0.322595i | \(-0.104555\pi\) | |||||||
\(72\) | 62.9989 | + | 68.7591i | 0.874985 | + | 0.954987i | ||||
\(73\) | −70.0997 | −0.960270 | −0.480135 | − | 0.877195i | \(-0.659412\pi\) | ||||
−0.480135 | + | 0.877195i | \(0.659412\pi\) | |||||||
\(74\) | 52.9546 | + | 15.0190i | 0.715602 | + | 0.202959i | ||||
\(75\) | − | 105.120i | − | 1.40160i | ||||||
\(76\) | 27.8810 | − | 45.1982i | 0.366856 | − | 0.594713i | ||||
\(77\) | 40.4992 | 0.525964 | ||||||||
\(78\) | 49.4718 | − | 174.429i | 0.634253 | − | 2.23628i | ||||
\(79\) | 33.3739i | 0.422455i | 0.977437 | + | 0.211228i | \(0.0677461\pi\) | ||||
−0.977437 | + | 0.211228i | \(0.932254\pi\) | |||||||
\(80\) | 9.82140 | + | 19.5597i | 0.122767 | + | 0.244496i | ||||
\(81\) | −50.0275 | −0.617623 | ||||||||
\(82\) | 21.3698 | + | 6.06092i | 0.260608 | + | 0.0739136i | ||||
\(83\) | 159.301i | 1.91930i | 0.281206 | + | 0.959648i | \(0.409266\pi\) | ||||
−0.281206 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(84\) | −40.9375 | − | 25.2528i | −0.487351 | − | 0.300628i | ||||
\(85\) | −6.47839 | −0.0762163 | ||||||||
\(86\) | −14.7478 | + | 51.9986i | −0.171487 | + | 0.604634i | ||||
\(87\) | 28.2137i | 0.324295i | ||||||||
\(88\) | −90.2903 | + | 82.7264i | −1.02603 | + | 0.940073i | ||||
\(89\) | −50.0417 | −0.562266 | −0.281133 | − | 0.959669i | \(-0.590710\pi\) | ||||
−0.281133 | + | 0.959669i | \(0.590710\pi\) | |||||||
\(90\) | 30.6819 | + | 8.70202i | 0.340910 | + | 0.0966891i | ||||
\(91\) | 52.7723i | 0.579915i | ||||||||
\(92\) | −31.3929 | + | 50.8913i | −0.341227 | + | 0.553166i | ||||
\(93\) | 84.2575 | 0.905995 | ||||||||
\(94\) | 16.9025 | − | 59.5955i | 0.179814 | − | 0.633995i | ||||
\(95\) | − | 18.1614i | − | 0.191172i | ||||||
\(96\) | 142.850 | − | 27.3223i | 1.48803 | − | 0.284608i | ||||
\(97\) | 89.7343 | 0.925096 | 0.462548 | − | 0.886594i | \(-0.346935\pi\) | ||||
0.462548 | + | 0.886594i | \(0.346935\pi\) | |||||||
\(98\) | 13.4688 | + | 3.82001i | 0.137436 | + | 0.0389797i | ||||
\(99\) | 178.437i | 1.80239i | ||||||||
\(100\) | −78.7392 | − | 48.5712i | −0.787392 | − | 0.485712i | ||||
\(101\) | 162.881 | 1.61269 | 0.806343 | − | 0.591448i | \(-0.201443\pi\) | ||||
0.806343 | + | 0.591448i | \(0.201443\pi\) | |||||||
\(102\) | −11.7463 | + | 41.4156i | −0.115160 | + | 0.406035i | ||||
\(103\) | 86.1212i | 0.836129i | 0.908417 | + | 0.418064i | \(0.137291\pi\) | ||||
−0.908417 | + | 0.418064i | \(0.862709\pi\) | |||||||
\(104\) | −107.796 | − | 117.652i | −1.03650 | − | 1.13127i | ||||
\(105\) | −16.4494 | −0.156661 | ||||||||
\(106\) | 24.6011 | + | 6.97739i | 0.232086 | + | 0.0658244i | ||||
\(107\) | − | 102.146i | − | 0.954632i | −0.878732 | − | 0.477316i | \(-0.841610\pi\) | ||
0.878732 | − | 0.477316i | \(-0.158390\pi\) | |||||||
\(108\) | 25.3601 | − | 41.1114i | 0.234815 | − | 0.380662i | ||||
\(109\) | 152.037 | 1.39483 | 0.697416 | − | 0.716667i | \(-0.254333\pi\) | ||||
0.697416 | + | 0.716667i | \(0.254333\pi\) | |||||||
\(110\) | −11.4270 | + | 40.2897i | −0.103882 | + | 0.366270i | ||||
\(111\) | − | 125.086i | − | 1.12690i | ||||||
\(112\) | −37.8307 | + | 18.9957i | −0.337774 | + | 0.169605i | ||||
\(113\) | −168.112 | −1.48772 | −0.743860 | − | 0.668335i | \(-0.767007\pi\) | ||||
−0.743860 | + | 0.668335i | \(0.767007\pi\) | |||||||
\(114\) | −116.104 | − | 32.9293i | −1.01845 | − | 0.288854i | ||||
\(115\) | 20.4489i | 0.177817i | ||||||||
\(116\) | 21.1332 | + | 13.0362i | 0.182183 | + | 0.112381i | ||||
\(117\) | −232.511 | −1.98727 | ||||||||
\(118\) | 15.7324 | − | 55.4700i | 0.133326 | − | 0.470085i | ||||
\(119\) | − | 12.5300i | − | 0.105294i | ||||||
\(120\) | 36.6727 | − | 33.6006i | 0.305606 | − | 0.280005i | ||||
\(121\) | −113.312 | −0.936466 | ||||||||
\(122\) | −12.5532 | − | 3.56034i | −0.102895 | − | 0.0291831i | ||||
\(123\) | − | 50.4783i | − | 0.410393i | ||||||
\(124\) | 38.9315 | − | 63.1123i | 0.313964 | − | 0.508970i | ||||
\(125\) | −65.8372 | −0.526697 | ||||||||
\(126\) | −16.8307 | + | 59.3424i | −0.133577 | + | 0.470971i | ||||
\(127\) | − | 87.8953i | − | 0.692089i | −0.938218 | − | 0.346044i | \(-0.887525\pi\) | ||
0.938218 | − | 0.346044i | \(-0.112475\pi\) | |||||||
\(128\) | 45.5391 | − | 119.625i | 0.355774 | − | 0.934572i | ||||
\(129\) | 122.827 | 0.952150 | ||||||||
\(130\) | −52.4992 | − | 14.8898i | −0.403840 | − | 0.114537i | ||||
\(131\) | 140.141i | 1.06978i | 0.844923 | + | 0.534888i | \(0.179646\pi\) | ||||
−0.844923 | + | 0.534888i | \(0.820354\pi\) | |||||||
\(132\) | 236.848 | + | 146.103i | 1.79430 | + | 1.10684i | ||||
\(133\) | 35.1262 | 0.264107 | ||||||||
\(134\) | −56.1338 | + | 197.919i | −0.418909 | + | 1.47701i | ||||
\(135\) | − | 16.5192i | − | 0.122365i | ||||||
\(136\) | 25.5945 | + | 27.9347i | 0.188195 | + | 0.205402i | ||||
\(137\) | 118.725 | 0.866603 | 0.433301 | − | 0.901249i | \(-0.357349\pi\) | ||||
0.433301 | + | 0.901249i | \(0.357349\pi\) | |||||||
\(138\) | 130.728 | + | 37.0770i | 0.947302 | + | 0.268674i | ||||
\(139\) | − | 72.1046i | − | 0.518738i | −0.965778 | − | 0.259369i | \(-0.916485\pi\) | ||
0.965778 | − | 0.259369i | \(-0.0835147\pi\) | |||||||
\(140\) | −7.60050 | + | 12.3212i | −0.0542893 | + | 0.0880089i | ||||
\(141\) | −140.772 | −0.998386 | ||||||||
\(142\) | −24.9984 | + | 88.1405i | −0.176045 | + | 0.620708i | ||||
\(143\) | − | 305.319i | − | 2.13510i | ||||||
\(144\) | −83.6938 | − | 166.679i | −0.581207 | − | 1.15750i | ||||
\(145\) | 8.49165 | 0.0585631 | ||||||||
\(146\) | 134.879 | + | 38.2546i | 0.923832 | + | 0.262018i | ||||
\(147\) | − | 31.8150i | − | 0.216428i | ||||||
\(148\) | −93.6942 | − | 57.7963i | −0.633069 | − | 0.390516i | ||||
\(149\) | 218.299 | 1.46510 | 0.732548 | − | 0.680716i | \(-0.238331\pi\) | ||||
0.732548 | + | 0.680716i | \(0.238331\pi\) | |||||||
\(150\) | −57.3657 | + | 202.262i | −0.382438 | + | 1.34842i | ||||
\(151\) | 180.946i | 1.19832i | 0.800629 | + | 0.599160i | \(0.204499\pi\) | ||||
−0.800629 | + | 0.599160i | \(0.795501\pi\) | |||||||
\(152\) | −78.3115 | + | 71.7511i | −0.515207 | + | 0.472047i | ||||
\(153\) | 55.2061 | 0.360824 | ||||||||
\(154\) | −77.9249 | − | 22.1011i | −0.506006 | − | 0.143514i | ||||
\(155\) | − | 25.3595i | − | 0.163610i | ||||||
\(156\) | −190.378 | + | 308.624i | −1.22037 | + | 1.97836i | ||||
\(157\) | −191.081 | −1.21708 | −0.608538 | − | 0.793525i | \(-0.708244\pi\) | ||||
−0.608538 | + | 0.793525i | \(0.708244\pi\) | |||||||
\(158\) | 18.2127 | − | 64.2151i | 0.115270 | − | 0.406425i | ||||
\(159\) | − | 58.1111i | − | 0.365479i | ||||||
\(160\) | −8.22339 | − | 42.9947i | −0.0513962 | − | 0.268717i | ||||
\(161\) | −39.5506 | −0.245656 | ||||||||
\(162\) | 96.2583 | + | 27.3008i | 0.594187 | + | 0.168524i | ||||
\(163\) | 287.743i | 1.76530i | 0.470035 | + | 0.882648i | \(0.344241\pi\) | ||||
−0.470035 | + | 0.882648i | \(0.655759\pi\) | |||||||
\(164\) | −37.8103 | − | 23.3237i | −0.230551 | − | 0.142218i | ||||
\(165\) | 95.1695 | 0.576785 | ||||||||
\(166\) | 86.9334 | − | 306.513i | 0.523695 | − | 1.84647i | ||||
\(167\) | − | 124.859i | − | 0.747659i | −0.927497 | − | 0.373829i | \(-0.878045\pi\) | ||
0.927497 | − | 0.373829i | \(-0.121955\pi\) | |||||||
\(168\) | 64.9874 | + | 70.9294i | 0.386830 | + | 0.422199i | ||||
\(169\) | 228.845 | 1.35411 | ||||||||
\(170\) | 12.4651 | + | 3.53536i | 0.0733242 | + | 0.0207962i | ||||
\(171\) | 154.764i | 0.905050i | ||||||||
\(172\) | 56.7529 | − | 92.0027i | 0.329959 | − | 0.534900i | ||||
\(173\) | −275.207 | −1.59079 | −0.795396 | − | 0.606090i | \(-0.792737\pi\) | ||||
−0.795396 | + | 0.606090i | \(0.792737\pi\) | |||||||
\(174\) | 15.3967 | − | 54.2861i | 0.0884865 | − | 0.311989i | ||||
\(175\) | − | 61.1929i | − | 0.349674i | ||||||
\(176\) | 218.873 | − | 109.902i | 1.24360 | − | 0.624441i | ||||
\(177\) | −131.027 | −0.740268 | ||||||||
\(178\) | 96.2856 | + | 27.3086i | 0.540930 | + | 0.153419i | ||||
\(179\) | − | 7.42479i | − | 0.0414792i | −0.999785 | − | 0.0207396i | \(-0.993398\pi\) | ||
0.999785 | − | 0.0207396i | \(-0.00660210\pi\) | |||||||
\(180\) | −54.2865 | − | 33.4873i | −0.301592 | − | 0.186040i | ||||
\(181\) | 99.5623 | 0.550068 | 0.275034 | − | 0.961435i | \(-0.411311\pi\) | ||||
0.275034 | + | 0.961435i | \(0.411311\pi\) | |||||||
\(182\) | 28.7987 | − | 101.540i | 0.158235 | − | 0.557910i | ||||
\(183\) | 29.6522i | 0.162034i | ||||||||
\(184\) | 88.1755 | − | 80.7888i | 0.479215 | − | 0.439069i | ||||
\(185\) | −37.6479 | −0.203502 | ||||||||
\(186\) | −162.121 | − | 45.9807i | −0.871616 | − | 0.247208i | ||||
\(187\) | 72.4933i | 0.387665i | ||||||||
\(188\) | −65.0445 | + | 105.444i | −0.345981 | + | 0.560874i | ||||
\(189\) | 31.9501 | 0.169048 | ||||||||
\(190\) | −9.91096 | + | 34.9445i | −0.0521629 | + | 0.183918i | ||||
\(191\) | − | 58.2058i | − | 0.304743i | −0.988323 | − | 0.152371i | \(-0.951309\pi\) | ||
0.988323 | − | 0.152371i | \(-0.0486909\pi\) | |||||||
\(192\) | −289.770 | − | 25.3847i | −1.50922 | − | 0.132212i | ||||
\(193\) | −103.881 | −0.538246 | −0.269123 | − | 0.963106i | \(-0.586734\pi\) | ||||
−0.269123 | + | 0.963106i | \(0.586734\pi\) | |||||||
\(194\) | −172.659 | − | 48.9695i | −0.889993 | − | 0.252420i | ||||
\(195\) | 124.010i | 0.635949i | ||||||||
\(196\) | −23.8307 | − | 14.7002i | −0.121585 | − | 0.0750012i | ||||
\(197\) | −181.201 | −0.919802 | −0.459901 | − | 0.887970i | \(-0.652115\pi\) | ||||
−0.459901 | + | 0.887970i | \(0.652115\pi\) | |||||||
\(198\) | 97.3758 | − | 343.332i | 0.491797 | − | 1.73400i | ||||
\(199\) | 217.919i | 1.09507i | 0.836783 | + | 0.547535i | \(0.184434\pi\) | ||||
−0.836783 | + | 0.547535i | \(0.815566\pi\) | |||||||
\(200\) | 124.997 | + | 136.425i | 0.624983 | + | 0.682127i | ||||
\(201\) | 467.510 | 2.32592 | ||||||||
\(202\) | −313.401 | − | 88.8870i | −1.55149 | − | 0.440035i | ||||
\(203\) | 16.4238i | 0.0809056i | ||||||||
\(204\) | 45.2023 | − | 73.2779i | 0.221580 | − | 0.359205i | ||||
\(205\) | −15.1928 | −0.0741113 | ||||||||
\(206\) | 46.9978 | − | 165.707i | 0.228145 | − | 0.804401i | ||||
\(207\) | − | 174.257i | − | 0.841823i | ||||||
\(208\) | 143.207 | + | 285.202i | 0.688494 | + | 1.37116i | ||||
\(209\) | −203.226 | −0.972375 | ||||||||
\(210\) | 31.6504 | + | 8.97669i | 0.150716 | + | 0.0427461i | ||||
\(211\) | − | 107.401i | − | 0.509007i | −0.967072 | − | 0.254504i | \(-0.918088\pi\) | ||
0.967072 | − | 0.254504i | \(-0.0819121\pi\) | |||||||
\(212\) | −43.5276 | − | 26.8505i | −0.205319 | − | 0.126653i | ||||
\(213\) | 208.199 | 0.977462 | ||||||||
\(214\) | −55.7425 | + | 196.539i | −0.260479 | + | 0.918407i | ||||
\(215\) | − | 36.9682i | − | 0.171945i | ||||||
\(216\) | −71.2307 | + | 65.2635i | −0.329772 | + | 0.302146i | ||||
\(217\) | 49.0483 | 0.226029 | ||||||||
\(218\) | −292.535 | − | 82.9689i | −1.34190 | − | 0.380591i | ||||
\(219\) | − | 318.603i | − | 1.45481i | ||||||
\(220\) | 43.9735 | − | 71.2858i | 0.199879 | − | 0.324026i | ||||
\(221\) | −94.4620 | −0.427430 | ||||||||
\(222\) | −68.2613 | + | 240.678i | −0.307483 | + | 1.08414i | ||||
\(223\) | 349.685i | 1.56809i | 0.620702 | + | 0.784047i | \(0.286848\pi\) | ||||
−0.620702 | + | 0.784047i | \(0.713152\pi\) | |||||||
\(224\) | 83.1567 | − | 15.9050i | 0.371235 | − | 0.0710044i | ||||
\(225\) | 269.612 | 1.19827 | ||||||||
\(226\) | 323.466 | + | 91.7417i | 1.43127 | + | 0.405937i | ||||
\(227\) | − | 18.3421i | − | 0.0808020i | −0.999184 | − | 0.0404010i | \(-0.987136\pi\) | ||
0.999184 | − | 0.0404010i | \(-0.0128635\pi\) | |||||||
\(228\) | 205.426 | + | 126.719i | 0.900990 | + | 0.555786i | ||||
\(229\) | 68.5444 | 0.299320 | 0.149660 | − | 0.988737i | \(-0.452182\pi\) | ||||
0.149660 | + | 0.988737i | \(0.452182\pi\) | |||||||
\(230\) | 11.1593 | − | 39.3460i | 0.0485188 | − | 0.171070i | ||||
\(231\) | 184.069i | 0.796835i | ||||||||
\(232\) | −33.5484 | − | 36.6159i | −0.144605 | − | 0.157827i | ||||
\(233\) | 61.4788 | 0.263858 | 0.131929 | − | 0.991259i | \(-0.457883\pi\) | ||||
0.131929 | + | 0.991259i | \(0.457883\pi\) | |||||||
\(234\) | 447.376 | + | 126.885i | 1.91186 | + | 0.542244i | ||||
\(235\) | 42.3692i | 0.180295i | ||||||||
\(236\) | −60.5418 | + | 98.1449i | −0.256533 | + | 0.415868i | ||||
\(237\) | −151.684 | −0.640019 | ||||||||
\(238\) | −6.83780 | + | 24.1090i | −0.0287302 | + | 0.101298i | ||||
\(239\) | 204.645i | 0.856256i | 0.903718 | + | 0.428128i | \(0.140827\pi\) | ||||
−0.903718 | + | 0.428128i | \(0.859173\pi\) | |||||||
\(240\) | −88.8987 | + | 44.6382i | −0.370411 | + | 0.185993i | ||||
\(241\) | −389.266 | −1.61521 | −0.807606 | − | 0.589723i | \(-0.799237\pi\) | ||||
−0.807606 | + | 0.589723i | \(0.799237\pi\) | |||||||
\(242\) | 218.025 | + | 61.8364i | 0.900931 | + | 0.255522i | ||||
\(243\) | − | 336.059i | − | 1.38296i | ||||||
\(244\) | 22.2107 | + | 13.7009i | 0.0910276 | + | 0.0561514i | ||||
\(245\) | −9.57557 | −0.0390840 | ||||||||
\(246\) | −27.5469 | + | 97.1258i | −0.111979 | + | 0.394820i | ||||
\(247\) | − | 264.813i | − | 1.07212i | ||||||
\(248\) | −109.350 | + | 100.189i | −0.440927 | + | 0.403989i | ||||
\(249\) | −724.025 | −2.90773 | ||||||||
\(250\) | 126.678 | + | 35.9284i | 0.506711 | + | 0.143714i | ||||
\(251\) | − | 115.082i | − | 0.458494i | −0.973368 | − | 0.229247i | \(-0.926374\pi\) | ||
0.973368 | − | 0.229247i | \(-0.0736264\pi\) | |||||||
\(252\) | 64.7682 | − | 104.996i | 0.257017 | − | 0.416652i | ||||
\(253\) | 228.824 | 0.904444 | ||||||||
\(254\) | −47.9659 | + | 169.120i | −0.188842 | + | 0.665827i | ||||
\(255\) | − | 29.4442i | − | 0.115468i | ||||||
\(256\) | −152.904 | + | 205.320i | −0.597280 | + | 0.802033i | ||||
\(257\) | 337.233 | 1.31219 | 0.656094 | − | 0.754679i | \(-0.272207\pi\) | ||||
0.656094 | + | 0.754679i | \(0.272207\pi\) | |||||||
\(258\) | −236.333 | − | 67.0289i | −0.916020 | − | 0.259802i | ||||
\(259\) | − | 72.8153i | − | 0.281140i | ||||||
\(260\) | 92.8886 | + | 57.2994i | 0.357264 | + | 0.220382i | ||||
\(261\) | −72.3623 | −0.277250 | ||||||||
\(262\) | 76.4770 | − | 269.646i | 0.291897 | − | 1.02918i | ||||
\(263\) | − | 163.729i | − | 0.622543i | −0.950321 | − | 0.311271i | \(-0.899245\pi\) | ||
0.950321 | − | 0.311271i | \(-0.100755\pi\) | |||||||
\(264\) | −375.991 | − | 410.369i | −1.42421 | − | 1.55443i | ||||
\(265\) | −17.4901 | −0.0660004 | ||||||||
\(266\) | −67.5866 | − | 19.1689i | −0.254085 | − | 0.0720637i | ||||
\(267\) | − | 227.439i | − | 0.851832i | ||||||
\(268\) | 216.015 | − | 350.184i | 0.806027 | − | 1.30666i | ||||
\(269\) | 290.784 | 1.08098 | 0.540490 | − | 0.841350i | \(-0.318239\pi\) | ||||
0.540490 | + | 0.841350i | \(0.318239\pi\) | |||||||
\(270\) | −9.01482 | + | 31.7848i | −0.0333882 | + | 0.117722i | ||||
\(271\) | − | 368.628i | − | 1.36025i | −0.733096 | − | 0.680126i | \(-0.761925\pi\) | ||
0.733096 | − | 0.680126i | \(-0.238075\pi\) | |||||||
\(272\) | −34.0022 | − | 67.7167i | −0.125008 | − | 0.248958i | ||||
\(273\) | −239.850 | −0.878571 | ||||||||
\(274\) | −228.439 | − | 64.7899i | −0.833719 | − | 0.236460i | ||||
\(275\) | 354.038i | 1.28741i | ||||||||
\(276\) | −231.301 | − | 142.680i | −0.838046 | − | 0.516958i | ||||
\(277\) | 254.425 | 0.918503 | 0.459252 | − | 0.888306i | \(-0.348118\pi\) | ||||
0.459252 | + | 0.888306i | \(0.348118\pi\) | |||||||
\(278\) | −39.3487 | + | 138.737i | −0.141542 | + | 0.499055i | ||||
\(279\) | 216.103i | 0.774564i | ||||||||
\(280\) | 21.3481 | − | 19.5597i | 0.0762432 | − | 0.0698560i | ||||
\(281\) | 146.631 | 0.521819 | 0.260909 | − | 0.965363i | \(-0.415978\pi\) | ||||
0.260909 | + | 0.965363i | \(0.415978\pi\) | |||||||
\(282\) | 270.862 | + | 76.8218i | 0.960502 | + | 0.272418i | ||||
\(283\) | − | 191.554i | − | 0.676868i | −0.940990 | − | 0.338434i | \(-0.890103\pi\) | ||
0.940990 | − | 0.338434i | \(-0.109897\pi\) | |||||||
\(284\) | 96.1994 | − | 155.950i | 0.338730 | − | 0.549119i | ||||
\(285\) | 82.5434 | 0.289626 | ||||||||
\(286\) | −166.618 | + | 587.468i | −0.582580 | + | 2.05408i | ||||
\(287\) | − | 29.3847i | − | 0.102386i | ||||||
\(288\) | 70.0762 | + | 366.382i | 0.243320 | + | 1.27216i | ||||
\(289\) | −266.571 | −0.922393 | ||||||||
\(290\) | −16.3389 | − | 4.63403i | −0.0563409 | − | 0.0159794i | ||||
\(291\) | 407.842i | 1.40152i | ||||||||
\(292\) | −238.647 | − | 147.212i | −0.817283 | − | 0.504150i | ||||
\(293\) | 315.496 | 1.07678 | 0.538389 | − | 0.842696i | \(-0.319033\pi\) | ||||
0.538389 | + | 0.842696i | \(0.319033\pi\) | |||||||
\(294\) | −17.3620 | + | 61.2155i | −0.0590543 | + | 0.208216i | ||||
\(295\) | 39.4362i | 0.133682i | ||||||||
\(296\) | 148.737 | + | 162.337i | 0.502491 | + | 0.548436i | ||||
\(297\) | −184.851 | −0.622393 | ||||||||
\(298\) | −420.031 | − | 119.129i | −1.40950 | − | 0.399763i | ||||
\(299\) | 298.168i | 0.997218i | ||||||||
\(300\) | 220.756 | − | 357.869i | 0.735853 | − | 1.19290i | ||||
\(301\) | 71.5008 | 0.237544 | ||||||||
\(302\) | 98.7454 | − | 348.161i | 0.326972 | − | 1.15285i | ||||
\(303\) | 740.295i | 2.44322i | ||||||||
\(304\) | 189.836 | − | 95.3211i | 0.624459 | − | 0.313556i | ||||
\(305\) | 8.92464 | 0.0292611 | ||||||||
\(306\) | −106.222 | − | 30.1269i | −0.347132 | − | 0.0984538i | ||||
\(307\) | − | 452.508i | − | 1.47397i | −0.675911 | − | 0.736983i | \(-0.736250\pi\) | ||
0.675911 | − | 0.736983i | \(-0.263750\pi\) | |||||||
\(308\) | 137.875 | + | 85.0498i | 0.447646 | + | 0.276136i | ||||
\(309\) | −391.421 | −1.26673 | ||||||||
\(310\) | −13.8391 | + | 48.7945i | −0.0446423 | + | 0.157402i | ||||
\(311\) | 477.817i | 1.53639i | 0.640217 | + | 0.768194i | \(0.278845\pi\) | ||||
−0.640217 | + | 0.768194i | \(0.721155\pi\) | |||||||
\(312\) | 534.729 | − | 489.933i | 1.71388 | − | 1.57030i | ||||
\(313\) | 209.435 | 0.669122 | 0.334561 | − | 0.942374i | \(-0.391412\pi\) | ||||
0.334561 | + | 0.942374i | \(0.391412\pi\) | |||||||
\(314\) | 367.660 | + | 104.276i | 1.17089 | + | 0.332089i | ||||
\(315\) | − | 42.1893i | − | 0.133934i | ||||||
\(316\) | −70.0865 | + | 113.618i | −0.221793 | + | 0.359550i | ||||
\(317\) | 1.74873 | 0.00551651 | 0.00275825 | − | 0.999996i | \(-0.499122\pi\) | ||||
0.00275825 | + | 0.999996i | \(0.499122\pi\) | |||||||
\(318\) | −31.7122 | + | 111.812i | −0.0997239 | + | 0.351610i | ||||
\(319\) | − | 95.0218i | − | 0.297874i | ||||||
\(320\) | −7.64020 | + | 87.2140i | −0.0238756 | + | 0.272544i | ||||
\(321\) | 464.251 | 1.44627 | ||||||||
\(322\) | 76.0997 | + | 21.5834i | 0.236335 | + | 0.0670293i | ||||
\(323\) | 62.8757i | 0.194662i | ||||||||
\(324\) | −170.313 | − | 105.059i | −0.525657 | − | 0.324258i | ||||
\(325\) | −461.327 | −1.41947 | ||||||||
\(326\) | 157.026 | − | 553.649i | 0.481675 | − | 1.69831i | ||||
\(327\) | 691.006i | 2.11317i | ||||||||
\(328\) | 60.0230 | + | 65.5111i | 0.182997 | + | 0.199729i | ||||
\(329\) | −81.9470 | −0.249079 | ||||||||
\(330\) | −183.116 | − | 51.9355i | −0.554898 | − | 0.157380i | ||||
\(331\) | − | 375.049i | − | 1.13308i | −0.824035 | − | 0.566539i | \(-0.808282\pi\) | ||
0.824035 | − | 0.566539i | \(-0.191718\pi\) | |||||||
\(332\) | −334.539 | + | 542.324i | −1.00765 | + | 1.63351i | ||||
\(333\) | 320.819 | 0.963421 | ||||||||
\(334\) | −68.1376 | + | 240.242i | −0.204005 | + | 0.719288i | ||||
\(335\) | − | 140.710i | − | 0.420029i | ||||||
\(336\) | −86.3355 | − | 171.940i | −0.256951 | − | 0.511728i | ||||
\(337\) | 254.740 | 0.755906 | 0.377953 | − | 0.925825i | \(-0.376628\pi\) | ||||
0.377953 | + | 0.925825i | \(0.376628\pi\) | |||||||
\(338\) | −440.322 | − | 124.884i | −1.30273 | − | 0.369480i | ||||
\(339\) | − | 764.070i | − | 2.25389i | ||||||
\(340\) | −22.0549 | − | 13.6048i | −0.0648675 | − | 0.0400142i | ||||
\(341\) | −283.774 | −0.832182 | ||||||||
\(342\) | 84.4570 | − | 297.782i | 0.246950 | − | 0.870707i | ||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | −159.406 | + | 146.052i | −0.463390 | + | 0.424570i | ||||
\(345\) | −92.9404 | −0.269392 | ||||||||
\(346\) | 529.528 | + | 150.185i | 1.53043 | + | 0.434061i | ||||
\(347\) | 511.422i | 1.47384i | 0.675981 | + | 0.736919i | \(0.263720\pi\) | ||||
−0.675981 | + | 0.736919i | \(0.736280\pi\) | |||||||
\(348\) | −59.2497 | + | 96.0502i | −0.170258 | + | 0.276006i | ||||
\(349\) | −383.129 | −1.09779 | −0.548895 | − | 0.835891i | \(-0.684951\pi\) | ||||
−0.548895 | + | 0.835891i | \(0.684951\pi\) | |||||||
\(350\) | −33.3940 | + | 117.742i | −0.0954113 | + | 0.336405i | ||||
\(351\) | − | 240.869i | − | 0.686236i | ||||||
\(352\) | −481.111 | + | 92.0199i | −1.36679 | + | 0.261420i | ||||
\(353\) | 217.384 | 0.615819 | 0.307909 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307909 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(354\) | 252.111 | + | 71.5038i | 0.712178 | + | 0.201988i | ||||
\(355\) | − | 62.6632i | − | 0.176516i | ||||||
\(356\) | −170.361 | − | 105.089i | −0.478543 | − | 0.295195i | ||||
\(357\) | 56.9486 | 0.159520 | ||||||||
\(358\) | −4.05183 | + | 14.2861i | −0.0113180 | + | 0.0399053i | ||||
\(359\) | − | 483.099i | − | 1.34568i | −0.739788 | − | 0.672840i | \(-0.765074\pi\) | ||
0.739788 | − | 0.672840i | \(-0.234926\pi\) | |||||||
\(360\) | 86.1786 | + | 94.0581i | 0.239385 | + | 0.261273i | ||||
\(361\) | 184.736 | 0.511733 | ||||||||
\(362\) | −191.569 | − | 54.3328i | −0.529195 | − | 0.150091i | ||||
\(363\) | − | 515.005i | − | 1.41875i | ||||||
\(364\) | −110.824 | + | 179.657i | −0.304461 | + | 0.493564i | ||||
\(365\) | −95.8921 | −0.262718 | ||||||||
\(366\) | 16.1817 | − | 57.0541i | 0.0442123 | − | 0.155886i | ||||
\(367\) | 470.944i | 1.28323i | 0.767028 | + | 0.641614i | \(0.221735\pi\) | ||||
−0.767028 | + | 0.641614i | \(0.778265\pi\) | |||||||
\(368\) | −213.747 | + | 107.328i | −0.580834 | + | 0.291651i | ||||
\(369\) | 129.467 | 0.350858 | ||||||||
\(370\) | 72.4386 | + | 20.5451i | 0.195780 | + | 0.0555272i | ||||
\(371\) | − | 33.8279i | − | 0.0911803i | ||||||
\(372\) | 286.845 | + | 176.944i | 0.771089 | + | 0.475655i | ||||
\(373\) | −179.535 | −0.481326 | −0.240663 | − | 0.970609i | \(-0.577365\pi\) | ||||
−0.240663 | + | 0.970609i | \(0.577365\pi\) | |||||||
\(374\) | 39.5608 | − | 139.485i | 0.105778 | − | 0.372955i | ||||
\(375\) | − | 299.230i | − | 0.797946i | ||||||
\(376\) | 182.695 | − | 167.390i | 0.485892 | − | 0.445187i | ||||
\(377\) | 123.818 | 0.328429 | ||||||||
\(378\) | −61.4755 | − | 17.4357i | −0.162634 | − | 0.0461262i | ||||
\(379\) | − | 87.8468i | − | 0.231786i | −0.993262 | − | 0.115893i | \(-0.963027\pi\) | ||
0.993262 | − | 0.115893i | \(-0.0369729\pi\) | |||||||
\(380\) | 38.1395 | − | 61.8284i | 0.100367 | − | 0.162706i | ||||
\(381\) | 399.484 | 1.04851 | ||||||||
\(382\) | −31.7639 | + | 111.994i | −0.0831515 | + | 0.293179i | ||||
\(383\) | − | 653.584i | − | 1.70649i | −0.521513 | − | 0.853243i | \(-0.674632\pi\) | ||
0.521513 | − | 0.853243i | \(-0.325368\pi\) | |||||||
\(384\) | 543.696 | + | 206.975i | 1.41588 | + | 0.538998i | ||||
\(385\) | 55.4004 | 0.143897 | ||||||||
\(386\) | 199.879 | + | 56.6898i | 0.517822 | + | 0.146865i | ||||
\(387\) | 315.027i | 0.814024i | ||||||||
\(388\) | 305.490 | + | 188.445i | 0.787346 | + | 0.485684i | ||||
\(389\) | −168.861 | −0.434090 | −0.217045 | − | 0.976162i | \(-0.569642\pi\) | ||||
−0.217045 | + | 0.976162i | \(0.569642\pi\) | |||||||
\(390\) | 67.6743 | − | 238.609i | 0.173524 | − | 0.611817i | ||||
\(391\) | − | 70.7954i | − | 0.181062i | ||||||
\(392\) | 37.8307 | + | 41.2897i | 0.0965069 | + | 0.105331i | ||||
\(393\) | −636.939 | −1.62071 | ||||||||
\(394\) | 348.650 | + | 98.8843i | 0.884899 | + | 0.250975i | ||||
\(395\) | 45.6535i | 0.115578i | ||||||||
\(396\) | −374.723 | + | 607.468i | −0.946271 | + | 1.53401i | ||||
\(397\) | −691.521 | −1.74187 | −0.870934 | − | 0.491401i | \(-0.836485\pi\) | ||||
−0.870934 | + | 0.491401i | \(0.836485\pi\) | |||||||
\(398\) | 118.922 | − | 419.300i | 0.298799 | − | 1.05352i | ||||
\(399\) | 159.648i | 0.400121i | ||||||||
\(400\) | −166.058 | − | 330.710i | −0.415144 | − | 0.826775i | ||||
\(401\) | −399.834 | −0.997091 | −0.498546 | − | 0.866864i | \(-0.666132\pi\) | ||||
−0.498546 | + | 0.866864i | \(0.666132\pi\) | |||||||
\(402\) | −899.541 | − | 255.128i | −2.23766 | − | 0.634647i | ||||
\(403\) | − | 369.770i | − | 0.917544i | ||||||
\(404\) | 554.511 | + | 342.057i | 1.37255 | + | 0.846675i | ||||
\(405\) | −68.4345 | −0.168974 | ||||||||
\(406\) | 8.96276 | − | 31.6013i | 0.0220758 | − | 0.0778356i | ||||
\(407\) | 421.281i | 1.03509i | ||||||||
\(408\) | −126.963 | + | 116.327i | −0.311184 | + | 0.285115i | ||||
\(409\) | 111.079 | 0.271586 | 0.135793 | − | 0.990737i | \(-0.456642\pi\) | ||||
0.135793 | + | 0.990737i | \(0.456642\pi\) | |||||||
\(410\) | 29.2326 | + | 8.29096i | 0.0712990 | + | 0.0202219i | ||||
\(411\) | 539.603i | 1.31290i | ||||||||
\(412\) | −180.858 | + | 293.190i | −0.438975 | + | 0.711626i | ||||
\(413\) | −76.2742 | −0.184683 | ||||||||
\(414\) | −95.0951 | + | 335.290i | −0.229698 | + | 0.809879i | ||||
\(415\) | 217.915i | 0.525095i | ||||||||
\(416\) | −119.906 | − | 626.910i | −0.288236 | − | 1.50699i | ||||
\(417\) | 327.715 | 0.785888 | ||||||||
\(418\) | 391.029 | + | 110.904i | 0.935477 | + | 0.265320i | ||||
\(419\) | 641.986i | 1.53219i | 0.642729 | + | 0.766094i | \(0.277802\pi\) | ||||
−0.642729 | + | 0.766094i | \(0.722198\pi\) | |||||||
\(420\) | −56.0000 | − | 34.5442i | −0.133333 | − | 0.0822482i | ||||
\(421\) | 151.970 | 0.360975 | 0.180487 | − | 0.983577i | \(-0.442233\pi\) | ||||
0.180487 | + | 0.983577i | \(0.442233\pi\) | |||||||
\(422\) | −58.6102 | + | 206.650i | −0.138887 | + | 0.489693i | ||||
\(423\) | − | 361.053i | − | 0.853553i | ||||||
\(424\) | 69.0991 | + | 75.4170i | 0.162970 | + | 0.177870i | ||||
\(425\) | 109.535 | 0.257729 | ||||||||
\(426\) | −400.598 | − | 113.618i | −0.940372 | − | 0.266709i | ||||
\(427\) | 17.2613i | 0.0404246i | ||||||||
\(428\) | 214.509 | − | 347.743i | 0.501190 | − | 0.812484i | ||||
\(429\) | 1387.68 | 3.23468 | ||||||||
\(430\) | −20.1741 | + | 71.1308i | −0.0469166 | + | 0.165421i | ||||
\(431\) | − | 459.854i | − | 1.06695i | −0.845817 | − | 0.533473i | \(-0.820887\pi\) | ||
0.845817 | − | 0.533473i | \(-0.179113\pi\) | |||||||
\(432\) | 172.671 | − | 86.7023i | 0.399701 | − | 0.200700i | ||||
\(433\) | 534.370 | 1.23411 | 0.617056 | − | 0.786919i | \(-0.288325\pi\) | ||||
0.617056 | + | 0.786919i | \(0.288325\pi\) | |||||||
\(434\) | −94.3743 | − | 26.7665i | −0.217452 | − | 0.0616739i | ||||
\(435\) | 38.5945i | 0.0887231i | ||||||||
\(436\) | 517.591 | + | 319.282i | 1.18714 | + | 0.732299i | ||||
\(437\) | 198.466 | 0.454156 | ||||||||
\(438\) | −173.867 | + | 613.027i | −0.396956 | + | 1.39960i | ||||
\(439\) | − | 201.259i | − | 0.458449i | −0.973374 | − | 0.229224i | \(-0.926381\pi\) | ||
0.973374 | − | 0.229224i | \(-0.0736189\pi\) | |||||||
\(440\) | −123.512 | + | 113.165i | −0.280708 | + | 0.257192i | ||||
\(441\) | 81.5989 | 0.185032 | ||||||||
\(442\) | 181.755 | + | 51.5495i | 0.411211 | + | 0.116628i | ||||
\(443\) | − | 73.4928i | − | 0.165898i | −0.996554 | − | 0.0829490i | \(-0.973566\pi\) | ||
0.996554 | − | 0.0829490i | \(-0.0264339\pi\) | |||||||
\(444\) | 262.684 | − | 425.840i | 0.591631 | − | 0.959099i | ||||
\(445\) | −68.4539 | −0.153829 | ||||||||
\(446\) | 190.829 | − | 672.832i | 0.427867 | − | 1.50859i | ||||
\(447\) | 992.169i | 2.21962i | ||||||||
\(448\) | −168.682 | − | 14.7770i | −0.376522 | − | 0.0329845i | ||||
\(449\) | −41.4382 | −0.0922899 | −0.0461450 | − | 0.998935i | \(-0.514694\pi\) | ||||
−0.0461450 | + | 0.998935i | \(0.514694\pi\) | |||||||
\(450\) | −518.762 | − | 147.131i | −1.15280 | − | 0.326959i | ||||
\(451\) | 170.008i | 0.376958i | ||||||||
\(452\) | −572.320 | − | 353.042i | −1.26619 | − | 0.781066i | ||||
\(453\) | −822.401 | −1.81545 | ||||||||
\(454\) | −10.0096 | + | 35.2921i | −0.0220475 | + | 0.0777359i | ||||
\(455\) | 72.1892i | 0.158658i | ||||||||
\(456\) | −326.109 | − | 355.926i | −0.715150 | − | 0.780539i | ||||
\(457\) | 270.205 | 0.591258 | 0.295629 | − | 0.955303i | \(-0.404471\pi\) | ||||
0.295629 | + | 0.955303i | \(0.404471\pi\) | |||||||
\(458\) | −131.887 | − | 37.4058i | −0.287962 | − | 0.0816720i | ||||
\(459\) | 57.1905i | 0.124598i | ||||||||
\(460\) | −42.9435 | + | 69.6161i | −0.0933554 | + | 0.151339i | ||||
\(461\) | −735.133 | −1.59465 | −0.797324 | − | 0.603552i | \(-0.793752\pi\) | ||||
−0.797324 | + | 0.603552i | \(0.793752\pi\) | |||||||
\(462\) | 100.449 | − | 354.168i | 0.217423 | − | 0.766598i | ||||
\(463\) | 742.356i | 1.60336i | 0.597753 | + | 0.801681i | \(0.296060\pi\) | ||||
−0.597753 | + | 0.801681i | \(0.703940\pi\) | |||||||
\(464\) | 44.5690 | + | 88.7608i | 0.0960538 | + | 0.191295i | ||||
\(465\) | 115.259 | 0.247869 | ||||||||
\(466\) | −118.292 | − | 33.5500i | −0.253845 | − | 0.0719957i | ||||
\(467\) | − | 402.152i | − | 0.861140i | −0.902557 | − | 0.430570i | \(-0.858313\pi\) | ||
0.902557 | − | 0.430570i | \(-0.141687\pi\) | |||||||
\(468\) | −791.557 | − | 488.281i | −1.69136 | − | 1.04334i | ||||
\(469\) | 272.149 | 0.580275 | ||||||||
\(470\) | 23.1216 | − | 81.5230i | 0.0491949 | − | 0.173453i | ||||
\(471\) | − | 868.462i | − | 1.84387i | ||||||
\(472\) | 170.048 | − | 155.803i | 0.360272 | − | 0.330091i | ||||
\(473\) | −413.675 | −0.874577 | ||||||||
\(474\) | 291.857 | + | 82.7767i | 0.615733 | + | 0.174634i | ||||
\(475\) | 307.068i | 0.646459i | ||||||||
\(476\) | 26.3133 | − | 42.6568i | 0.0552801 | − | 0.0896151i | ||||
\(477\) | 149.043 | 0.312460 | ||||||||
\(478\) | 111.678 | − | 393.760i | 0.233636 | − | 0.823765i | ||||
\(479\) | − | 356.741i | − | 0.744763i | −0.928080 | − | 0.372381i | \(-0.878541\pi\) | ||
0.928080 | − | 0.372381i | \(-0.121459\pi\) | |||||||
\(480\) | 195.411 | − | 37.3753i | 0.407105 | − | 0.0778651i | ||||
\(481\) | −548.947 | −1.14126 | ||||||||
\(482\) | 748.990 | + | 212.429i | 1.55392 | + | 0.440724i | ||||
\(483\) | − | 179.758i | − | 0.372169i | ||||||
\(484\) | −385.759 | − | 237.960i | −0.797024 | − | 0.491653i | ||||
\(485\) | 122.751 | 0.253095 | ||||||||
\(486\) | −183.393 | + | 646.614i | −0.377351 | + | 1.33048i | ||||
\(487\) | − | 121.123i | − | 0.248713i | −0.992238 | − | 0.124356i | \(-0.960313\pi\) | ||
0.992238 | − | 0.124356i | \(-0.0396866\pi\) | |||||||
\(488\) | −35.2590 | − | 38.4829i | −0.0722521 | − | 0.0788584i | ||||
\(489\) | −1307.79 | −2.67442 | ||||||||
\(490\) | 18.4244 | + | 5.22554i | 0.0376009 | + | 0.0106644i | ||||
\(491\) | − | 18.4535i | − | 0.0375835i | −0.999823 | − | 0.0187917i | \(-0.994018\pi\) | ||
0.999823 | − | 0.0187917i | \(-0.00598195\pi\) | |||||||
\(492\) | 106.006 | − | 171.848i | 0.215460 | − | 0.349284i | ||||
\(493\) | −29.3986 | −0.0596320 | ||||||||
\(494\) | −144.513 | + | 509.529i | −0.292536 | + | 1.03143i | ||||
\(495\) | 244.090i | 0.493112i | ||||||||
\(496\) | 265.076 | − | 133.101i | 0.534427 | − | 0.268349i | ||||
\(497\) | 121.198 | 0.243859 | ||||||||
\(498\) | 1393.10 | + | 395.112i | 2.79739 | + | 0.793398i | ||||
\(499\) | 149.571i | 0.299742i | 0.988706 | + | 0.149871i | \(0.0478859\pi\) | ||||
−0.988706 | + | 0.149871i | \(0.952114\pi\) | |||||||
\(500\) | −224.135 | − | 138.260i | −0.448270 | − | 0.276521i | ||||
\(501\) | 567.484 | 1.13270 | ||||||||
\(502\) | −62.8022 | + | 221.430i | −0.125104 | + | 0.441097i | ||||
\(503\) | − | 651.239i | − | 1.29471i | −0.762189 | − | 0.647354i | \(-0.775875\pi\) | ||
0.762189 | − | 0.647354i | \(-0.224125\pi\) | |||||||
\(504\) | −181.919 | + | 166.679i | −0.360951 | + | 0.330713i | ||||
\(505\) | 222.812 | 0.441211 | ||||||||
\(506\) | −440.283 | − | 124.873i | −0.870124 | − | 0.246785i | ||||
\(507\) | 1040.10i | 2.05148i | ||||||||
\(508\) | 184.583 | − | 299.230i | 0.363353 | − | 0.589035i | ||||
\(509\) | 817.972 | 1.60702 | 0.803509 | − | 0.595293i | \(-0.202964\pi\) | ||||
0.803509 | + | 0.595293i | \(0.202964\pi\) | |||||||
\(510\) | −16.0682 | + | 56.6539i | −0.0315063 | + | 0.111086i | ||||
\(511\) | − | 185.466i | − | 0.362948i | ||||||
\(512\) | 406.250 | − | 311.617i | 0.793457 | − | 0.608627i | ||||
\(513\) | −160.327 | −0.312528 | ||||||||
\(514\) | −648.872 | − | 184.033i | −1.26240 | − | 0.358041i | ||||
\(515\) | 117.809i | 0.228754i | ||||||||
\(516\) | 418.152 | + | 257.942i | 0.810372 | + | 0.499887i | ||||
\(517\) | 474.113 | 0.917046 | ||||||||
\(518\) | −39.7365 | + | 140.105i | −0.0767114 | + | 0.270472i | ||||
\(519\) | − | 1250.82i | − | 2.41005i | ||||||
\(520\) | −147.458 | − | 160.941i | −0.283574 | − | 0.309502i | ||||
\(521\) | −173.603 | −0.333211 | −0.166606 | − | 0.986024i | \(-0.553281\pi\) | ||||
−0.166606 | + | 0.986024i | \(0.553281\pi\) | |||||||
\(522\) | 139.233 | + | 39.4893i | 0.266730 | + | 0.0756500i | ||||
\(523\) | 680.630i | 1.30139i | 0.759337 | + | 0.650697i | \(0.225523\pi\) | ||||
−0.759337 | + | 0.650697i | \(0.774477\pi\) | |||||||
\(524\) | −294.300 | + | 477.093i | −0.561642 | + | 0.910483i | ||||
\(525\) | 278.122 | 0.529755 | ||||||||
\(526\) | −89.3494 | + | 315.032i | −0.169866 | + | 0.598920i | ||||
\(527\) | 87.7961i | 0.166596i | ||||||||
\(528\) | 499.503 | + | 994.779i | 0.946028 | + | 1.88405i | ||||
\(529\) | 305.535 | 0.577571 | ||||||||
\(530\) | 33.6528 | + | 9.54463i | 0.0634959 | + | 0.0180087i | ||||
\(531\) | − | 336.059i | − | 0.632879i | ||||||
\(532\) | 119.583 | + | 73.7663i | 0.224780 | + | 0.138658i | ||||
\(533\) | −221.528 | −0.415624 | ||||||||
\(534\) | −124.117 | + | 437.618i | −0.232429 | + | 0.819509i | ||||
\(535\) | − | 139.729i | − | 0.261175i | ||||||
\(536\) | −606.738 | + | 555.910i | −1.13197 | + | 1.03714i | ||||
\(537\) | 33.7456 | 0.0628410 | ||||||||
\(538\) | −559.499 | − | 158.685i | −1.03996 | − | 0.294954i | ||||
\(539\) | 107.151i | 0.198796i | ||||||||
\(540\) | 34.6910 | − | 56.2379i | 0.0642426 | − | 0.104144i | ||||
\(541\) | −313.190 | −0.578909 | −0.289454 | − | 0.957192i | \(-0.593474\pi\) | ||||
−0.289454 | + | 0.957192i | \(0.593474\pi\) | |||||||
\(542\) | −201.166 | + | 709.280i | −0.371156 | + | 1.30864i | ||||
\(543\) | 452.510i | 0.833352i | ||||||||
\(544\) | 28.4698 | + | 148.850i | 0.0523342 | + | 0.273621i | ||||
\(545\) | 207.977 | 0.381609 | ||||||||
\(546\) | 461.497 | + | 130.890i | 0.845233 | + | 0.239725i | ||||
\(547\) | − | 352.784i | − | 0.644944i | −0.946579 | − | 0.322472i | \(-0.895486\pi\) | ||
0.946579 | − | 0.322472i | \(-0.104514\pi\) | |||||||
\(548\) | 404.184 | + | 249.326i | 0.737563 | + | 0.454974i | ||||
\(549\) | −76.0520 | −0.138528 | ||||||||
\(550\) | 193.204 | − | 681.207i | 0.351280 | − | 1.23856i | ||||
\(551\) | − | 82.4153i | − | 0.149574i | ||||||
\(552\) | 367.185 | + | 400.757i | 0.665190 | + | 0.726010i | ||||
\(553\) | −88.2992 | −0.159673 | ||||||||
\(554\) | −489.542 | − | 138.844i | −0.883650 | − | 0.250621i | ||||
\(555\) | − | 171.109i | − | 0.308305i | ||||||
\(556\) | 151.422 | − | 245.472i | 0.272342 | − | 0.441497i | ||||
\(557\) | −135.925 | −0.244030 | −0.122015 | − | 0.992528i | \(-0.538936\pi\) | ||||
−0.122015 | + | 0.992528i | \(0.538936\pi\) | |||||||
\(558\) | 117.931 | − | 415.806i | 0.211346 | − | 0.745173i | ||||
\(559\) | − | 539.037i | − | 0.964288i | ||||||
\(560\) | −51.7501 | + | 25.9850i | −0.0924109 | + | 0.0464017i | ||||
\(561\) | −329.482 | −0.587312 | ||||||||
\(562\) | −282.134 | − | 80.0190i | −0.502018 | − | 0.142383i | ||||
\(563\) | − | 160.363i | − | 0.284836i | −0.989807 | − | 0.142418i | \(-0.954512\pi\) | ||
0.989807 | − | 0.142418i | \(-0.0454878\pi\) | |||||||
\(564\) | −479.244 | − | 295.627i | −0.849723 | − | 0.524162i | ||||
\(565\) | −229.967 | −0.407022 | ||||||||
\(566\) | −104.534 | + | 368.570i | −0.184689 | + | 0.651184i | ||||
\(567\) | − | 132.360i | − | 0.233440i | ||||||
\(568\) | −270.203 | + | 247.567i | −0.475709 | + | 0.435857i | ||||
\(569\) | 611.297 | 1.07434 | 0.537168 | − | 0.843475i | \(-0.319494\pi\) | ||||
0.537168 | + | 0.843475i | \(0.319494\pi\) | |||||||
\(570\) | −158.822 | − | 45.0453i | −0.278636 | − | 0.0790268i | ||||
\(571\) | 286.952i | 0.502542i | 0.967917 | + | 0.251271i | \(0.0808486\pi\) | ||||
−0.967917 | + | 0.251271i | \(0.919151\pi\) | |||||||
\(572\) | 641.182 | − | 1039.43i | 1.12095 | − | 1.81718i | ||||
\(573\) | 264.545 | 0.461685 | ||||||||
\(574\) | −16.0357 | + | 56.5393i | −0.0279367 | + | 0.0985004i | ||||
\(575\) | − | 345.746i | − | 0.601297i | ||||||
\(576\) | 65.1066 | − | 743.201i | 0.113032 | − | 1.29028i | ||||
\(577\) | −530.428 | −0.919286 | −0.459643 | − | 0.888104i | \(-0.652023\pi\) | ||||
−0.459643 | + | 0.888104i | \(0.652023\pi\) | |||||||
\(578\) | 512.912 | + | 145.472i | 0.887392 | + | 0.251682i | ||||
\(579\) | − | 472.141i | − | 0.815442i | ||||||
\(580\) | 28.9089 | + | 17.8328i | 0.0498429 | + | 0.0307462i | ||||
\(581\) | −421.472 | −0.725425 | ||||||||
\(582\) | 222.566 | − | 784.733i | 0.382416 | − | 1.34834i | ||||
\(583\) | 195.715i | 0.335703i | ||||||||
\(584\) | 378.846 | + | 413.485i | 0.648709 | + | 0.708022i | ||||
\(585\) | −318.061 | −0.543693 | ||||||||
\(586\) | −607.049 | − | 172.171i | −1.03592 | − | 0.293808i | ||||
\(587\) | 10.9359i | 0.0186301i | 0.999957 | + | 0.00931506i | \(0.00296512\pi\) | ||||
−0.999957 | + | 0.00931506i | \(0.997035\pi\) | |||||||
\(588\) | 66.8126 | − | 108.310i | 0.113627 | − | 0.184202i | ||||
\(589\) | −246.126 | −0.417871 | ||||||||
\(590\) | 21.5210 | − | 75.8796i | 0.0364763 | − | 0.128609i | ||||
\(591\) | − | 823.558i | − | 1.39350i | ||||||
\(592\) | −197.597 | − | 393.522i | −0.333779 | − | 0.664734i | ||||
\(593\) | 119.459 | 0.201449 | 0.100725 | − | 0.994914i | \(-0.467884\pi\) | ||||
0.100725 | + | 0.994914i | \(0.467884\pi\) | |||||||
\(594\) | 355.673 | + | 100.876i | 0.598776 | + | 0.169825i | ||||
\(595\) | − | 17.1402i | − | 0.0288071i | ||||||
\(596\) | 743.175 | + | 458.436i | 1.24694 | + | 0.769188i | ||||
\(597\) | −990.441 | −1.65903 | ||||||||
\(598\) | 162.715 | − | 573.708i | 0.272099 | − | 0.959378i | ||||
\(599\) | 1020.35i | 1.70342i | 0.524014 | + | 0.851710i | \(0.324434\pi\) | ||||
−0.524014 | + | 0.851710i | \(0.675566\pi\) | |||||||
\(600\) | −620.053 | + | 568.110i | −1.03342 | + | 0.946849i | ||||
\(601\) | −109.785 | −0.182671 | −0.0913356 | − | 0.995820i | \(-0.529114\pi\) | ||||
−0.0913356 | + | 0.995820i | \(0.529114\pi\) | |||||||
\(602\) | −137.575 | − | 39.0191i | −0.228530 | − | 0.0648159i | ||||
\(603\) | 1199.07i | 1.98851i | ||||||||
\(604\) | −379.994 | + | 616.012i | −0.629129 | + | 1.01989i | ||||
\(605\) | −155.004 | −0.256206 | ||||||||
\(606\) | 403.991 | − | 1424.41i | 0.666652 | − | 2.35051i | ||||
\(607\) | 649.557i | 1.07011i | 0.844817 | + | 0.535055i | \(0.179709\pi\) | ||||
−0.844817 | + | 0.535055i | \(0.820291\pi\) | |||||||
\(608\) | −417.283 | + | 79.8117i | −0.686320 | + | 0.131269i | ||||
\(609\) | −74.6463 | −0.122572 | ||||||||
\(610\) | −17.1720 | − | 4.87032i | −0.0281508 | − | 0.00798413i | ||||
\(611\) | 617.790i | 1.01111i | ||||||||
\(612\) | 187.943 | + | 115.935i | 0.307096 | + | 0.189436i | ||||
\(613\) | 802.148 | 1.30856 | 0.654281 | − | 0.756252i | \(-0.272971\pi\) | ||||
0.654281 | + | 0.756252i | \(0.272971\pi\) | |||||||
\(614\) | −246.941 | + | 870.674i | −0.402184 | + | 1.41804i | ||||
\(615\) | − | 69.0513i | − | 0.112278i | ||||||
\(616\) | −218.873 | − | 238.886i | −0.355314 | − | 0.387801i | ||||
\(617\) | 1151.11 | 1.86565 | 0.932825 | − | 0.360329i | \(-0.117336\pi\) | ||||
0.932825 | + | 0.360329i | \(0.117336\pi\) | |||||||
\(618\) | 753.136 | + | 213.605i | 1.21867 | + | 0.345639i | ||||
\(619\) | − | 223.829i | − | 0.361598i | −0.983520 | − | 0.180799i | \(-0.942132\pi\) | ||
0.983520 | − | 0.180799i | \(-0.0578683\pi\) | |||||||
\(620\) | 53.2559 | − | 86.3337i | 0.0858967 | − | 0.139248i | ||||
\(621\) | 180.521 | 0.290694 | ||||||||
\(622\) | 260.752 | − | 919.371i | 0.419216 | − | 1.47809i | ||||
\(623\) | − | 132.398i | − | 0.212517i | ||||||
\(624\) | −1296.24 | + | 650.874i | −2.07731 | + | 1.04307i | ||||
\(625\) | 488.157 | 0.781052 | ||||||||
\(626\) | −402.976 | − | 114.292i | −0.643732 | − | 0.182575i | ||||
\(627\) | − | 923.663i | − | 1.47315i | ||||||
\(628\) | −650.513 | − | 401.276i | −1.03585 | − | 0.638975i | ||||
\(629\) | 130.339 | 0.207216 | ||||||||
\(630\) | −23.0234 | + | 81.1767i | −0.0365450 | + | 0.128852i | ||||
\(631\) | 385.557i | 0.611026i | 0.952188 | + | 0.305513i | \(0.0988279\pi\) | ||||
−0.952188 | + | 0.305513i | \(0.901172\pi\) | |||||||
\(632\) | 196.857 | − | 180.366i | 0.311483 | − | 0.285389i | ||||
\(633\) | 488.135 | 0.771146 | ||||||||
\(634\) | −3.36475 | − | 0.954312i | −0.00530718 | − | 0.00150522i | ||||
\(635\) | − | 120.235i | − | 0.189347i | ||||||
\(636\) | 122.035 | − | 197.833i | 0.191880 | − | 0.311058i | ||||
\(637\) | −139.622 | −0.219187 | ||||||||
\(638\) | −51.8550 | + | 182.832i | −0.0812774 | + | 0.286571i | ||||
\(639\) | 533.989i | 0.835664i | ||||||||
\(640\) | 62.2947 | − | 163.640i | 0.0973355 | − | 0.255687i | ||||
\(641\) | −289.861 | −0.452201 | −0.226100 | − | 0.974104i | \(-0.572598\pi\) | ||||
−0.226100 | + | 0.974104i | \(0.572598\pi\) | |||||||
\(642\) | −893.270 | − | 253.350i | −1.39139 | − | 0.394625i | ||||
\(643\) | 525.629i | 0.817463i | 0.912655 | + | 0.408731i | \(0.134029\pi\) | ||||
−0.912655 | + | 0.408731i | \(0.865971\pi\) | |||||||
\(644\) | −134.646 | − | 83.0577i | −0.209077 | − | 0.128972i | ||||
\(645\) | 168.020 | 0.260497 | ||||||||
\(646\) | 34.3123 | − | 120.980i | 0.0531150 | − | 0.187275i | ||||
\(647\) | 95.6042i | 0.147765i | 0.997267 | + | 0.0738827i | \(0.0235390\pi\) | ||||
−0.997267 | + | 0.0738827i | \(0.976461\pi\) | |||||||
\(648\) | 270.368 | + | 295.088i | 0.417234 | + | 0.455383i | ||||
\(649\) | 441.292 | 0.679958 | ||||||||
\(650\) | 887.643 | + | 251.754i | 1.36560 | + | 0.387313i | ||||
\(651\) | 222.924i | 0.342434i | ||||||||
\(652\) | −604.271 | + | 979.589i | −0.926796 | + | 1.50244i | ||||
\(653\) | −627.508 | −0.960962 | −0.480481 | − | 0.877005i | \(-0.659538\pi\) | ||||
−0.480481 | + | 0.877005i | \(0.659538\pi\) | |||||||
\(654\) | 377.093 | − | 1329.57i | 0.576595 | − | 2.03298i | ||||
\(655\) | 191.704i | 0.292677i | ||||||||
\(656\) | −79.7404 | − | 158.806i | −0.121555 | − | 0.242082i | ||||
\(657\) | 817.152 | 1.24376 | ||||||||
\(658\) | 157.675 | + | 44.7198i | 0.239628 | + | 0.0679633i | ||||
\(659\) | − | 220.070i | − | 0.333945i | −0.985962 | − | 0.166972i | \(-0.946601\pi\) | ||
0.985962 | − | 0.166972i | \(-0.0533991\pi\) | |||||||
\(660\) | 323.994 | + | 199.859i | 0.490900 | + | 0.302817i | ||||
\(661\) | 743.710 | 1.12513 | 0.562564 | − | 0.826754i | \(-0.309815\pi\) | ||||
0.562564 | + | 0.826754i | \(0.309815\pi\) | |||||||
\(662\) | −204.670 | + | 721.635i | −0.309170 | + | 1.09008i | ||||
\(663\) | − | 429.329i | − | 0.647556i | ||||||
\(664\) | 939.644 | − | 860.927i | 1.41513 | − | 1.29658i | ||||
\(665\) | 48.0505 | 0.0722564 | ||||||||
\(666\) | −617.291 | − | 175.076i | −0.926863 | − | 0.262877i | ||||
\(667\) | 92.7962i | 0.139125i | ||||||||
\(668\) | 262.208 | − | 425.068i | 0.392527 | − | 0.636330i | ||||
\(669\) | −1589.32 | −2.37566 | ||||||||
\(670\) | −76.7876 | + | 270.741i | −0.114608 | + | 0.404091i | ||||
\(671\) | − | 99.8669i | − | 0.148833i | ||||||
\(672\) | 72.2881 | + | 377.947i | 0.107572 | + | 0.562421i | ||||
\(673\) | −1017.05 | −1.51122 | −0.755610 | − | 0.655022i | \(-0.772659\pi\) | ||||
−0.755610 | + | 0.655022i | \(0.772659\pi\) | |||||||
\(674\) | −490.148 | − | 139.016i | −0.727223 | − | 0.206255i | ||||
\(675\) | 279.303i | 0.413782i | ||||||||
\(676\) | 779.076 | + | 480.582i | 1.15248 | + | 0.710920i | ||||
\(677\) | 861.905 | 1.27312 | 0.636562 | − | 0.771225i | \(-0.280356\pi\) | ||||
0.636562 | + | 0.771225i | \(0.280356\pi\) | |||||||
\(678\) | −416.966 | + | 1470.15i | −0.614993 | + | 2.16837i | ||||
\(679\) | 237.415i | 0.349653i | ||||||||
\(680\) | 35.0117 | + | 38.2129i | 0.0514878 | + | 0.0561955i | ||||
\(681\) | 83.3646 | 0.122415 | ||||||||
\(682\) | 546.012 | + | 154.860i | 0.800604 | + | 0.227068i | ||||
\(683\) | − | 635.790i | − | 0.930879i | −0.885080 | − | 0.465440i | \(-0.845896\pi\) | ||
0.885080 | − | 0.465440i | \(-0.154104\pi\) | |||||||
\(684\) | −325.009 | + | 526.875i | −0.475159 | + | 0.770285i | ||||
\(685\) | 162.408 | 0.237092 | ||||||||
\(686\) | −10.1068 | + | 35.6350i | −0.0147330 | + | 0.0519460i | ||||
\(687\) | 311.534i | 0.453470i | ||||||||
\(688\) | 386.418 | − | 194.030i | 0.561654 | − | 0.282020i | ||||
\(689\) | −255.025 | −0.370138 | ||||||||
\(690\) | 178.827 | + | 50.7191i | 0.259170 | + | 0.0735059i | ||||
\(691\) | − | 214.780i | − | 0.310825i | −0.987850 | − | 0.155412i | \(-0.950329\pi\) | ||
0.987850 | − | 0.155412i | \(-0.0496706\pi\) | |||||||
\(692\) | −936.911 | − | 577.944i | −1.35392 | − | 0.835180i | ||||
\(693\) | −472.099 | −0.681240 | ||||||||
\(694\) | 279.091 | − | 984.031i | 0.402149 | − | 1.41791i | ||||
\(695\) | − | 98.6347i | − | 0.141920i | ||||||
\(696\) | 166.419 | − | 152.478i | 0.239108 | − | 0.219077i | ||||
\(697\) | 52.5983 | 0.0754639 | ||||||||
\(698\) | 737.181 | + | 209.080i | 1.05613 | + | 0.299541i | ||||
\(699\) | 279.421i | 0.399744i | ||||||||
\(700\) | 128.507 | − | 208.324i | 0.183582 | − | 0.297606i | ||||
\(701\) | −271.746 | −0.387655 | −0.193828 | − | 0.981036i | \(-0.562090\pi\) | ||||
−0.193828 | + | 0.981036i | \(0.562090\pi\) | |||||||
\(702\) | −131.446 | + | 463.458i | −0.187245 | + | 0.660196i | ||||
\(703\) | 365.390i | 0.519758i | ||||||||
\(704\) | 975.927 | + | 85.4941i | 1.38626 | + | 0.121440i | ||||
\(705\) | −192.568 | −0.273146 | ||||||||
\(706\) | −418.271 | − | 118.630i | −0.592451 | − | 0.168031i | ||||
\(707\) | 430.944i | 0.609538i | ||||||||
\(708\) | −446.068 | − | 275.162i | −0.630040 | − | 0.388647i | ||||
\(709\) | −616.894 | −0.870090 | −0.435045 | − | 0.900409i | \(-0.643267\pi\) | ||||
−0.435045 | + | 0.900409i | \(0.643267\pi\) | |||||||
\(710\) | −34.1963 | + | 120.571i | −0.0481638 | + | 0.169818i | ||||
\(711\) | − | 389.040i | − | 0.547173i | ||||||
\(712\) | 270.445 | + | 295.172i | 0.379838 | + | 0.414567i | ||||
\(713\) | 277.127 | 0.388678 | ||||||||
\(714\) | −109.575 | − | 31.0778i | −0.153467 | − | 0.0435263i | ||||
\(715\) | − | 417.658i | − | 0.584137i | ||||||
\(716\) | 15.5923 | − | 25.2768i | 0.0217770 | − | 0.0353029i | ||||
\(717\) | −930.112 | −1.29723 | ||||||||
\(718\) | −263.635 | + | 929.536i | −0.367180 | + | 1.29462i | ||||
\(719\) | 55.3428i | 0.0769719i | 0.999259 | + | 0.0384859i | \(0.0122535\pi\) | ||||
−0.999259 | + | 0.0384859i | \(0.987747\pi\) | |||||||
\(720\) | −114.488 | − | 228.007i | −0.159011 | − | 0.316677i | ||||
\(721\) | −227.855 | −0.316027 | ||||||||
\(722\) | −355.451 | − | 100.813i | −0.492315 | − | 0.139631i | ||||
\(723\) | − | 1769.21i | − | 2.44704i | ||||||
\(724\) | 338.949 | + | 209.084i | 0.468161 | + | 0.288790i | ||||
\(725\) | −143.575 | −0.198034 | ||||||||
\(726\) | −281.046 | + | 990.925i | −0.387116 | + | 1.36491i | ||||
\(727\) | − | 1046.07i | − | 1.43888i | −0.694554 | − | 0.719440i | \(-0.744398\pi\) | ||
0.694554 | − | 0.719440i | \(-0.255602\pi\) | |||||||
\(728\) | 311.279 | − | 285.202i | 0.427580 | − | 0.391761i | ||||
\(729\) | 1077.14 | 1.47756 | ||||||||
\(730\) | 184.507 | + | 52.3299i | 0.252749 | + | 0.0716848i | ||||
\(731\) | 127.986i | 0.175083i | ||||||||
\(732\) | −62.2708 | + | 100.948i | −0.0850693 | + | 0.137907i | ||||
\(733\) | 851.328 | 1.16143 | 0.580715 | − | 0.814107i | \(-0.302773\pi\) | ||||
0.580715 | + | 0.814107i | \(0.302773\pi\) | |||||||
\(734\) | 257.002 | − | 906.148i | 0.350139 | − | 1.23453i | ||||
\(735\) | − | 43.5209i | − | 0.0592121i | ||||||
\(736\) | 469.843 | − | 89.8646i | 0.638373 | − | 0.122099i | ||||
\(737\) | −1574.55 | −2.13643 | ||||||||
\(738\) | −249.108 | − | 70.6521i | −0.337545 | − | 0.0957345i | ||||
\(739\) | − | 789.585i | − | 1.06845i | −0.845342 | − | 0.534226i | \(-0.820603\pi\) | ||
0.845342 | − | 0.534226i | \(-0.179397\pi\) | |||||||
\(740\) | −128.168 | − | 79.0618i | −0.173200 | − | 0.106840i | ||||
\(741\) | 1203.57 | 1.62426 | ||||||||
\(742\) | −18.4604 | + | 65.0885i | −0.0248793 | + | 0.0877204i | ||||
\(743\) | − | 892.788i | − | 1.20160i | −0.799400 | − | 0.600799i | \(-0.794849\pi\) | ||
0.799400 | − | 0.600799i | \(-0.205151\pi\) | |||||||
\(744\) | −455.360 | − | 496.995i | −0.612043 | − | 0.668004i | ||||
\(745\) | 298.620 | 0.400832 | ||||||||
\(746\) | 345.444 | + | 97.9751i | 0.463062 | + | 0.131334i | ||||
\(747\) | − | 1856.98i | − | 2.48591i | ||||||
\(748\) | −152.239 | + | 246.795i | −0.203527 | + | 0.329940i | ||||
\(749\) | 270.252 | 0.360817 | ||||||||
\(750\) | −163.294 | + | 575.750i | −0.217726 | + | 0.767667i | ||||
\(751\) | 406.211i | 0.540894i | 0.962735 | + | 0.270447i | \(0.0871715\pi\) | ||||
−0.962735 | + | 0.270447i | \(0.912829\pi\) | |||||||
\(752\) | −442.873 | + | 222.378i | −0.588928 | + | 0.295715i | ||||
\(753\) | 523.048 | 0.694619 | ||||||||
\(754\) | −238.239 | − | 67.5693i | −0.315966 | − | 0.0896145i | ||||
\(755\) | 247.524i | 0.327846i | ||||||||
\(756\) | 108.771 | + | 67.0964i | 0.143877 | + | 0.0887519i | ||||
\(757\) | 89.9062 | 0.118766 | 0.0593832 | − | 0.998235i | \(-0.481087\pi\) | ||||
0.0593832 | + | 0.998235i | \(0.481087\pi\) | |||||||
\(758\) | −47.9394 | + | 169.027i | −0.0632446 | + | 0.222990i | ||||
\(759\) | 1040.01i | 1.37023i | ||||||||
\(760\) | −107.125 | + | 98.1511i | −0.140954 | + | 0.129146i | ||||
\(761\) | −261.751 | −0.343956 | −0.171978 | − | 0.985101i | \(-0.555016\pi\) | ||||
−0.171978 | + | 0.985101i | \(0.555016\pi\) | |||||||
\(762\) | −768.650 | − | 218.005i | −1.00873 | − | 0.286096i | ||||
\(763\) | 402.251i | 0.527197i | ||||||||
\(764\) | 122.234 | − | 198.155i | 0.159992 | − | 0.259365i | ||||
\(765\) | 75.5185 | 0.0987170 | ||||||||
\(766\) | −356.672 | + | 1257.57i | −0.465629 | + | 1.64173i | ||||
\(767\) | 575.024i | 0.749705i | ||||||||
\(768\) | −933.181 | − | 694.946i | −1.21508 | − | 0.904878i | ||||
\(769\) | −753.905 | −0.980370 | −0.490185 | − | 0.871618i | \(-0.663071\pi\) | ||||
−0.490185 | + | 0.871618i | \(0.663071\pi\) | |||||||
\(770\) | −106.596 | − | 30.2329i | −0.138437 | − | 0.0392635i | ||||
\(771\) | 1532.72i | 1.98796i | ||||||||
\(772\) | −353.653 | − | 218.155i | −0.458099 | − | 0.282584i | ||||
\(773\) | −463.530 | −0.599650 | −0.299825 | − | 0.953994i | \(-0.596928\pi\) | ||||
−0.299825 | + | 0.953994i | \(0.596928\pi\) | |||||||
\(774\) | 171.916 | − | 606.147i | 0.222113 | − | 0.783135i | ||||
\(775\) | 428.773i | 0.553255i | ||||||||
\(776\) | −484.959 | − | 529.300i | −0.624947 | − | 0.682088i | ||||
\(777\) | 330.945 | 0.425927 | ||||||||
\(778\) | 324.907 | + | 92.1501i | 0.417618 | + | 0.118445i | ||||
\(779\) | 147.453i | 0.189285i | ||||||||
\(780\) | −260.425 | + | 422.178i | −0.333879 | + | 0.541254i | ||||
\(781\) | −701.203 | −0.897827 | ||||||||
\(782\) | −38.6342 | + | 136.218i | −0.0494043 | + | 0.174192i | ||||
\(783\) | − | 74.9634i | − | 0.0957388i | ||||||
\(784\) | −50.2579 | − | 100.091i | −0.0641045 | − | 0.127667i | ||||
\(785\) | −261.387 | −0.332977 | ||||||||
\(786\) | 1225.54 | + | 347.588i | 1.55921 | + | 0.442224i | ||||
\(787\) | − | 618.821i | − | 0.786304i | −0.919473 | − | 0.393152i | \(-0.871385\pi\) | ||
0.919473 | − | 0.393152i | \(-0.128615\pi\) | |||||||
\(788\) | −616.878 | − | 380.528i | −0.782841 | − | 0.482904i | ||||
\(789\) | 744.146 | 0.943151 | ||||||||
\(790\) | 24.9139 | − | 87.8423i | 0.0315365 | − | 0.111193i | ||||
\(791\) | − | 444.784i | − | 0.562305i | ||||||
\(792\) | 1052.51 | − | 964.341i | 1.32893 | − | 1.21760i | ||||
\(793\) | 130.131 | 0.164100 | ||||||||
\(794\) | 1330.56 | + | 377.375i | 1.67577 | + | 0.475283i | ||||
\(795\) | − | 79.4924i | − | 0.0999905i | ||||||
\(796\) | −457.638 | + | 741.881i | −0.574922 | + | 0.932011i | ||||
\(797\) | −441.998 | −0.554577 | −0.277289 | − | 0.960787i | \(-0.589436\pi\) | ||||
−0.277289 | + | 0.960787i | \(0.589436\pi\) | |||||||
\(798\) | 87.1228 | − | 307.181i | 0.109176 | − | 0.384939i | ||||
\(799\) | − | 146.685i | − | 0.183585i | ||||||
\(800\) | 139.039 | + | 726.943i | 0.173799 | + | 0.908678i | ||||
\(801\) | 583.335 | 0.728259 | ||||||||
\(802\) | 769.323 | + | 218.196i | 0.959256 | + | 0.272064i | ||||
\(803\) | 1073.04i | 1.33628i | ||||||||
\(804\) | 1591.59 | + | 981.788i | 1.97958 | + | 1.22113i | ||||
\(805\) | −54.1028 | −0.0672085 | ||||||||
\(806\) | −201.790 | + | 711.478i | −0.250359 | + | 0.882727i | ||||
\(807\) | 1321.61i | 1.63768i | ||||||||
\(808\) | −880.274 | − | 960.760i | −1.08945 | − | 1.18906i | ||||
\(809\) | 311.447 | 0.384978 | 0.192489 | − | 0.981299i | \(-0.438344\pi\) | ||||
0.192489 | + | 0.981299i | \(0.438344\pi\) | |||||||
\(810\) | 131.675 | + | 37.3458i | 0.162562 | + | 0.0461060i | ||||
\(811\) | 965.110i | 1.19002i | 0.803717 | + | 0.595012i | \(0.202853\pi\) | ||||
−0.803717 | + | 0.595012i | \(0.797147\pi\) | |||||||
\(812\) | −34.4906 | + | 55.9131i | −0.0424762 | + | 0.0688585i | ||||
\(813\) | 1675.41 | 2.06078 | ||||||||
\(814\) | 229.900 | − | 810.590i | 0.282432 | − | 0.995811i | ||||
\(815\) | 393.615i | 0.482963i | ||||||||
\(816\) | 307.772 | − | 154.540i | 0.377172 | − | 0.189387i | ||||
\(817\) | −358.793 | −0.439159 | ||||||||
\(818\) | −213.728 | − | 60.6175i | −0.261281 | − | 0.0741045i | ||||
\(819\) | − | 615.166i | − | 0.751118i | ||||||
\(820\) | −51.7222 | − | 31.9054i | −0.0630759 | − | 0.0389091i | ||||
\(821\) | 1464.81 | 1.78417 | 0.892087 | − | 0.451864i | \(-0.149241\pi\) | ||||
0.892087 | + | 0.451864i | \(0.149241\pi\) | |||||||
\(822\) | 294.470 | − | 1038.25i | 0.358236 | − | 1.26308i | ||||
\(823\) | 967.159i | 1.17516i | 0.809165 | + | 0.587581i | \(0.199920\pi\) | ||||
−0.809165 | + | 0.587581i | \(0.800080\pi\) | |||||||
\(824\) | 507.988 | − | 465.433i | 0.616491 | − | 0.564845i | ||||
\(825\) | −1609.10 | −1.95043 | ||||||||
\(826\) | 146.760 | + | 41.6241i | 0.177675 | + | 0.0503924i | ||||
\(827\) | − | 1298.46i | − | 1.57009i | −0.619441 | − | 0.785043i | \(-0.712641\pi\) | ||
0.619441 | − | 0.785043i | \(-0.287359\pi\) | |||||||
\(828\) | 365.946 | − | 593.239i | 0.441964 | − | 0.716473i | ||||
\(829\) | −771.397 | −0.930515 | −0.465258 | − | 0.885175i | \(-0.654038\pi\) | ||||
−0.465258 | + | 0.885175i | \(0.654038\pi\) | |||||||
\(830\) | 118.920 | − | 419.291i | 0.143277 | − | 0.505170i | ||||
\(831\) | 1156.36i | 1.39153i | ||||||||
\(832\) | −111.403 | + | 1271.68i | −0.133897 | + | 1.52846i | ||||
\(833\) | 33.1511 | 0.0397973 | ||||||||
\(834\) | −630.560 | − | 178.840i | −0.756067 | − | 0.214436i | ||||
\(835\) | − | 170.799i | − | 0.204550i | ||||||
\(836\) | −691.861 | − | 426.782i | −0.827585 | − | 0.510505i | ||||
\(837\) | −223.871 | −0.267469 | ||||||||
\(838\) | 350.343 | − | 1235.25i | 0.418070 | − | 1.47405i | ||||
\(839\) | 1088.04i | 1.29683i | 0.761287 | + | 0.648415i | \(0.224568\pi\) | ||||
−0.761287 | + | 0.648415i | \(0.775432\pi\) | |||||||
\(840\) | 88.8987 | + | 97.0270i | 0.105832 | + | 0.115508i | ||||
\(841\) | −802.465 | −0.954180 | ||||||||
\(842\) | −292.407 | − | 82.9327i | −0.347277 | − | 0.0984949i | ||||
\(843\) | 666.438i | 0.790555i | ||||||||
\(844\) | 225.545 | − | 365.633i | 0.267233 | − | 0.433215i | ||||
\(845\) | 313.045 | 0.370468 | ||||||||
\(846\) | −197.032 | + | 694.705i | −0.232899 | + | 0.821164i | ||||
\(847\) | − | 299.797i | − | 0.353951i | ||||||
\(848\) | −91.7978 | − | 182.819i | −0.108252 | − | 0.215588i | ||||
\(849\) | 870.611 | 1.02545 | ||||||||
\(850\) | −210.757 | − | 59.7750i | −0.247949 | − | 0.0703235i | ||||
\(851\) | − | 411.413i | − | 0.483447i | ||||||
\(852\) | 708.792 | + | 437.226i | 0.831915 | + | 0.513176i | ||||
\(853\) | 126.051 | 0.147774 | 0.0738870 | − | 0.997267i | \(-0.476460\pi\) | ||||
0.0738870 | + | 0.997267i | \(0.476460\pi\) | |||||||
\(854\) | 9.41976 | − | 33.2126i | 0.0110302 | − | 0.0388906i | ||||
\(855\) | 211.707i | 0.247611i | ||||||||
\(856\) | −602.508 | + | 552.034i | −0.703865 | + | 0.644900i | ||||
\(857\) | −1135.93 | −1.32547 | −0.662736 | − | 0.748853i | \(-0.730605\pi\) | ||||
−0.662736 | + | 0.748853i | \(0.730605\pi\) | |||||||
\(858\) | −2670.04 | − | 757.277i | −3.11193 | − | 0.882608i | ||||
\(859\) | − | 590.556i | − | 0.687492i | −0.939063 | − | 0.343746i | \(-0.888304\pi\) | ||
0.939063 | − | 0.343746i | \(-0.111696\pi\) | |||||||
\(860\) | 77.6345 | − | 125.854i | 0.0902727 | − | 0.146342i | ||||
\(861\) | 133.553 | 0.155114 | ||||||||
\(862\) | −250.950 | + | 884.809i | −0.291125 | + | 1.02646i | ||||
\(863\) | − | 292.067i | − | 0.338432i | −0.985579 | − | 0.169216i | \(-0.945876\pi\) | ||
0.985579 | − | 0.169216i | \(-0.0541235\pi\) | |||||||
\(864\) | −379.552 | + | 72.5952i | −0.439297 | + | 0.0840222i | ||||
\(865\) | −376.466 | −0.435221 | ||||||||
\(866\) | −1028.19 | − | 291.615i | −1.18728 | − | 0.336737i | ||||
\(867\) | − | 1211.57i | − | 1.39742i | ||||||
\(868\) | 166.979 | + | 103.003i | 0.192373 | + | 0.118667i | ||||
\(869\) | 510.864 | 0.587876 | ||||||||
\(870\) | 21.0617 | − | 74.2601i | 0.0242088 | − | 0.0853564i | ||||
\(871\) | − | 2051.70i | − | 2.35557i | ||||||
\(872\) | −821.665 | − | 896.792i | −0.942276 | − | 1.02843i | ||||
\(873\) | −1046.03 | −1.19820 | ||||||||
\(874\) | −381.871 | − | 108.306i | −0.436923 | − | 0.123920i | ||||
\(875\) | − | 174.189i | − | 0.199073i | ||||||
\(876\) | 669.077 | − | 1084.65i | 0.763787 | − | 1.23818i | ||||
\(877\) | 1087.23 | 1.23971 | 0.619856 | − | 0.784715i | \(-0.287191\pi\) | ||||
0.619856 | + | 0.784715i | \(0.287191\pi\) | |||||||
\(878\) | −109.830 | + | 387.244i | −0.125091 | + | 0.441053i | ||||
\(879\) | 1433.93i | 1.63132i | ||||||||
\(880\) | 299.405 | − | 150.339i | 0.340233 | − | 0.170839i | ||||
\(881\) | 1217.53 | 1.38198 | 0.690991 | − | 0.722863i | \(-0.257174\pi\) | ||||
0.690991 | + | 0.722863i | \(0.257174\pi\) | |||||||
\(882\) | −157.005 | − | 44.5299i | −0.178010 | − | 0.0504874i | ||||
\(883\) | − | 1141.10i | − | 1.29230i | −0.763212 | − | 0.646148i | \(-0.776379\pi\) | ||
0.763212 | − | 0.646148i | \(-0.223621\pi\) | |||||||
\(884\) | −321.585 | − | 198.374i | −0.363784 | − | 0.224404i | ||||
\(885\) | −179.237 | −0.202528 | ||||||||
\(886\) | −40.1062 | + | 141.408i | −0.0452666 | + | 0.159603i | ||||
\(887\) | − | 368.518i | − | 0.415466i | −0.978186 | − | 0.207733i | \(-0.933391\pi\) | ||
0.978186 | − | 0.207733i | \(-0.0666085\pi\) | |||||||
\(888\) | −737.821 | + | 676.011i | −0.830879 | + | 0.761274i | ||||
\(889\) | 232.549 | 0.261585 | ||||||||
\(890\) | 131.713 | + | 37.3564i | 0.147992 | + | 0.0419735i | ||||
\(891\) | 765.784i | 0.859466i | ||||||||
\(892\) | −734.350 | + | 1190.46i | −0.823263 | + | 1.33460i | ||||
\(893\) | 411.213 | 0.460484 | ||||||||
\(894\) | 541.443 | − | 1909.04i | 0.605641 | − | 2.13539i | ||||
\(895\) | − | 10.1566i | − | 0.0113482i | ||||||
\(896\) | 316.499 | + | 120.485i | 0.353235 | + | 0.134470i | ||||
\(897\) | −1355.17 | −1.51078 | ||||||||
\(898\) | 79.7315 | + | 22.6135i | 0.0887879 | + | 0.0251821i | ||||
\(899\) | − | 115.080i | − | 0.128009i | ||||||
\(900\) | 917.862 | + | 566.194i | 1.01985 | + | 0.629104i | ||||
\(901\) | 60.5517 | 0.0672050 | ||||||||
\(902\) | 92.7761 | − | 327.114i | 0.102856 | − | 0.362654i | ||||
\(903\) | 324.971i | 0.359879i | ||||||||
\(904\) | 908.544 | + | 991.615i | 1.00503 | + | 1.09692i | ||||
\(905\) | 136.195 | 0.150492 | ||||||||
\(906\) | 1582.39 | + | 448.798i | 1.74657 | + | 0.495362i | ||||
\(907\) | 341.525i | 0.376544i | 0.982117 | + | 0.188272i | \(0.0602886\pi\) | ||||
−0.982117 | + | 0.188272i | \(0.939711\pi\) | |||||||
\(908\) | 38.5190 | − | 62.4435i | 0.0424218 | − | 0.0687703i | ||||
\(909\) | −1898.71 | −2.08879 | ||||||||
\(910\) | 39.3948 | − | 138.900i | 0.0432910 | − | 0.152637i | ||||
\(911\) | 536.979i | 0.589439i | 0.955584 | + | 0.294719i | \(0.0952262\pi\) | ||||
−0.955584 | + | 0.294719i | \(0.904774\pi\) | |||||||
\(912\) | 433.234 | + | 862.802i | 0.475037 | + | 0.946055i | ||||
\(913\) | 2438.47 | 2.67083 | ||||||||
\(914\) | −519.904 | − | 147.455i | −0.568823 | − | 0.161330i | ||||
\(915\) | 40.5624i | 0.0443305i | ||||||||
\(916\) | 233.352 | + | 143.946i | 0.254751 | + | 0.157146i | ||||
\(917\) | −370.777 | −0.404337 | ||||||||
\(918\) | 31.2098 | − | 110.041i | 0.0339976 | − | 0.119870i | ||||
\(919\) | − | 987.383i | − | 1.07441i | −0.843452 | − | 0.537205i | \(-0.819480\pi\) | ||
0.843452 | − | 0.537205i | \(-0.180520\pi\) | |||||||
\(920\) | 120.619 | − | 110.514i | 0.131107 | − | 0.120124i | ||||
\(921\) | 2056.65 | 2.23306 | ||||||||
\(922\) | 1414.47 | + | 401.174i | 1.53414 | + | 0.435113i | ||||
\(923\) | − | 913.698i | − | 0.989922i | ||||||
\(924\) | −386.551 | + | 626.642i | −0.418345 | + | 0.678183i | ||||
\(925\) | 636.540 | 0.688152 | ||||||||
\(926\) | 405.116 | − | 1428.37i | 0.437490 | − | 1.54252i | ||||
\(927\) | − | 1003.91i | − | 1.08297i | ||||||
\(928\) | −37.3173 | − | 195.107i | −0.0402126 | − | 0.210245i | ||||
\(929\) | −1285.67 | −1.38393 | −0.691965 | − | 0.721932i | \(-0.743255\pi\) | ||||
−0.691965 | + | 0.721932i | \(0.743255\pi\) | |||||||
\(930\) | −221.771 | − | 62.8987i | −0.238463 | − | 0.0676331i | ||||
\(931\) | 92.9352i | 0.0998230i | ||||||||
\(932\) | 209.298 | + | 129.108i | 0.224568 | + | 0.138527i | ||||
\(933\) | −2171.68 | −2.32763 | ||||||||
\(934\) | −219.461 | + | 773.785i | −0.234969 | + | 0.828463i | ||||
\(935\) | 99.1664i | 0.106060i | ||||||||
\(936\) | 1256.58 | + | 1371.47i | 1.34250 | + | 1.46525i | ||||
\(937\) | −887.657 | −0.947339 | −0.473670 | − | 0.880703i | \(-0.657071\pi\) | ||||
−0.473670 | + | 0.880703i | \(0.657071\pi\) | |||||||
\(938\) | −523.644 | − | 148.516i | −0.558256 | − | 0.158333i | ||||
\(939\) | 951.882i | 1.01372i | ||||||||
\(940\) | −88.9769 | + | 144.241i | −0.0946563 | + | 0.153448i | ||||
\(941\) | 380.526 | 0.404385 | 0.202192 | − | 0.979346i | \(-0.435193\pi\) | ||||
0.202192 | + | 0.979346i | \(0.435193\pi\) | |||||||
\(942\) | −473.934 | + | 1671.01i | −0.503114 | + | 1.77390i | ||||
\(943\) | − | 166.026i | − | 0.176061i | ||||||
\(944\) | −412.215 | + | 206.983i | −0.436669 | + | 0.219262i | ||||
\(945\) | 43.7058 | 0.0462495 | ||||||||
\(946\) | 795.956 | + | 225.749i | 0.841391 | + | 0.238636i | ||||
\(947\) | − | 363.169i | − | 0.383494i | −0.981444 | − | 0.191747i | \(-0.938585\pi\) | ||
0.981444 | − | 0.191747i | \(-0.0614153\pi\) | |||||||
\(948\) | −516.393 | − | 318.543i | −0.544718 | − | 0.336015i | ||||
\(949\) | −1398.21 | −1.47335 | ||||||||
\(950\) | 167.572 | − | 590.832i | 0.176391 | − | 0.621928i | ||||
\(951\) | 7.94799i | 0.00835750i | ||||||||
\(952\) | −73.9082 | + | 67.7167i | −0.0776347 | + | 0.0711310i | ||||
\(953\) | −679.479 | −0.712990 | −0.356495 | − | 0.934297i | \(-0.616028\pi\) | ||||
−0.356495 | + | 0.934297i | \(0.616028\pi\) | |||||||
\(954\) | −286.775 | − | 81.3353i | −0.300603 | − | 0.0852572i | ||||
\(955\) | − | 79.6220i | − | 0.0833738i | ||||||
\(956\) | −429.762 | + | 696.692i | −0.449542 | + | 0.728757i | ||||
\(957\) | 431.874 | 0.451279 | ||||||||
\(958\) | −194.680 | + | 686.409i | −0.203215 | + | 0.716502i | ||||
\(959\) | 314.116i | 0.327545i | ||||||||
\(960\) | −396.387 | − | 34.7247i | −0.412904 | − | 0.0361716i | ||||
\(961\) | 617.323 | 0.642376 | ||||||||
\(962\) | 1056.23 | + | 299.570i | 1.09796 | + | 0.311403i | ||||
\(963\) | 1190.71i | 1.23646i | ||||||||
\(964\) | −1325.21 | − | 817.472i | −1.37470 | − | 0.848000i | ||||
\(965\) | −142.103 | −0.147257 | ||||||||
\(966\) | −98.0966 | + | 345.873i | −0.101549 | + | 0.358047i | ||||
\(967\) | 209.525i | 0.216675i | 0.994114 | + | 0.108337i | \(0.0345527\pi\) | ||||
−0.994114 | + | 0.108337i | \(0.965447\pi\) | |||||||
\(968\) | 612.384 | + | 668.376i | 0.632628 | + | 0.690471i | ||||
\(969\) | −285.770 | −0.294912 | ||||||||
\(970\) | −236.186 | − | 66.9872i | −0.243491 | − | 0.0690590i | ||||
\(971\) | 538.867i | 0.554961i | 0.960731 | + | 0.277481i | \(0.0894994\pi\) | ||||
−0.960731 | + | 0.277481i | \(0.910501\pi\) | |||||||
\(972\) | 705.735 | − | 1144.07i | 0.726065 | − | 1.17703i | ||||
\(973\) | 190.771 | 0.196065 | ||||||||
\(974\) | −66.0989 | + | 233.054i | −0.0678633 | + | 0.239275i | ||||
\(975\) | − | 2096.73i | − | 2.15049i | ||||||
\(976\) | 46.8415 | + | 93.2867i | 0.0479933 | + | 0.0955806i | ||||
\(977\) | 1028.30 | 1.05250 | 0.526252 | − | 0.850329i | \(-0.323597\pi\) | ||||
0.526252 | + | 0.850329i | \(0.323597\pi\) | |||||||
\(978\) | 2516.33 | + | 713.683i | 2.57294 | + | 0.729738i | ||||
\(979\) | 766.001i | 0.782432i | ||||||||
\(980\) | −32.5989 | − | 20.1090i | −0.0332642 | − | 0.0205194i | ||||
\(981\) | −1772.29 | −1.80661 | ||||||||
\(982\) | −10.0704 | + | 35.5065i | −0.0102550 | + | 0.0361574i | ||||
\(983\) | 520.479i | 0.529480i | 0.964320 | + | 0.264740i | \(0.0852862\pi\) | ||||
−0.964320 | + | 0.264740i | \(0.914714\pi\) | |||||||
\(984\) | −297.748 | + | 272.804i | −0.302589 | + | 0.277240i | ||||
\(985\) | −247.872 | −0.251646 | ||||||||
\(986\) | 56.5660 | + | 16.0433i | 0.0573692 | + | 0.0162711i | ||||
\(987\) | − | 372.449i | − | 0.377355i | ||||||
\(988\) | 556.116 | − | 901.525i | 0.562871 | − | 0.912475i | ||||
\(989\) | 403.986 | 0.408479 | ||||||||
\(990\) | 133.204 | − | 469.656i | 0.134550 | − | 0.474400i | ||||
\(991\) | − | 1849.00i | − | 1.86579i | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||
0.360148 | − | 0.932895i | \(-0.382726\pi\) | |||||||
\(992\) | −582.671 | + | 111.445i | −0.587369 | + | 0.112343i | ||||
\(993\) | 1704.60 | 1.71661 | ||||||||
\(994\) | −233.198 | − | 66.1397i | −0.234606 | − | 0.0665389i | ||||
\(995\) | 298.100i | 0.299598i | ||||||||
\(996\) | −2464.86 | − | 1520.48i | −2.47476 | − | 1.52658i | ||||
\(997\) | 1010.23 | 1.01327 | 0.506635 | − | 0.862161i | \(-0.330889\pi\) | ||||
0.506635 | + | 0.862161i | \(0.330889\pi\) | |||||||
\(998\) | 81.6236 | − | 287.792i | 0.0817872 | − | 0.288368i | ||||
\(999\) | 332.351i | 0.332684i |
(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 | 28.3.c.a.15.1 | ✓ | 6 | |
3.2 | odd | 2 | 252.3.g.a.127.6 | 6 | |||
4.3 | odd | 2 | inner | 28.3.c.a.15.2 | yes | 6 | |
7.2 | even | 3 | 196.3.g.k.67.4 | 12 | |||
7.3 | odd | 6 | 196.3.g.j.79.5 | 12 | |||
7.4 | even | 3 | 196.3.g.k.79.5 | 12 | |||
7.5 | odd | 6 | 196.3.g.j.67.4 | 12 | |||
7.6 | odd | 2 | 196.3.c.g.99.1 | 6 | |||
8.3 | odd | 2 | 448.3.d.d.127.6 | 6 | |||
8.5 | even | 2 | 448.3.d.d.127.1 | 6 | |||
12.11 | even | 2 | 252.3.g.a.127.5 | 6 | |||
16.3 | odd | 4 | 1792.3.g.g.127.11 | 12 | |||
16.5 | even | 4 | 1792.3.g.g.127.12 | 12 | |||
16.11 | odd | 4 | 1792.3.g.g.127.2 | 12 | |||
16.13 | even | 4 | 1792.3.g.g.127.1 | 12 | |||
28.3 | even | 6 | 196.3.g.j.79.4 | 12 | |||
28.11 | odd | 6 | 196.3.g.k.79.4 | 12 | |||
28.19 | even | 6 | 196.3.g.j.67.5 | 12 | |||
28.23 | odd | 6 | 196.3.g.k.67.5 | 12 | |||
28.27 | even | 2 | 196.3.c.g.99.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.3.c.a.15.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
28.3.c.a.15.2 | yes | 6 | 4.3 | odd | 2 | inner | |
196.3.c.g.99.1 | 6 | 7.6 | odd | 2 | |||
196.3.c.g.99.2 | 6 | 28.27 | even | 2 | |||
196.3.g.j.67.4 | 12 | 7.5 | odd | 6 | |||
196.3.g.j.67.5 | 12 | 28.19 | even | 6 | |||
196.3.g.j.79.4 | 12 | 28.3 | even | 6 | |||
196.3.g.j.79.5 | 12 | 7.3 | odd | 6 | |||
196.3.g.k.67.4 | 12 | 7.2 | even | 3 | |||
196.3.g.k.67.5 | 12 | 28.23 | odd | 6 | |||
196.3.g.k.79.4 | 12 | 28.11 | odd | 6 | |||
196.3.g.k.79.5 | 12 | 7.4 | even | 3 | |||
252.3.g.a.127.5 | 6 | 12.11 | even | 2 | |||
252.3.g.a.127.6 | 6 | 3.2 | odd | 2 | |||
448.3.d.d.127.1 | 6 | 8.5 | even | 2 | |||
448.3.d.d.127.6 | 6 | 8.3 | odd | 2 | |||
1792.3.g.g.127.1 | 12 | 16.13 | even | 4 | |||
1792.3.g.g.127.2 | 12 | 16.11 | odd | 4 | |||
1792.3.g.g.127.11 | 12 | 16.3 | odd | 4 | |||
1792.3.g.g.127.12 | 12 | 16.5 | even | 4 |