Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(739,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1110.739");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} - 3018 x^{7} + 658 x^{6} - 1584 x^{5} + 16372 x^{4} - 18840 x^{3} + 10952 x^{2} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 739.9 | ||
Root | \(-2.20888 - 2.20888i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.739 |
Dual form | 1110.2.e.d.739.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.20888 | + | 0.347650i | −0.987840 | + | 0.155474i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | − | 2.08112i | − | 0.786591i | −0.919412 | − | 0.393295i | \(-0.871335\pi\) | ||
0.919412 | − | 0.393295i | \(-0.128665\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.20888 | + | 0.347650i | −0.698508 | + | 0.109936i | ||||
\(11\) | 6.52056 | 1.96602 | 0.983011 | − | 0.183545i | \(-0.0587573\pi\) | ||||
0.983011 | + | 0.183545i | \(0.0587573\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −1.53583 | −0.425963 | −0.212981 | − | 0.977056i | \(-0.568317\pi\) | ||||
−0.212981 | + | 0.977056i | \(0.568317\pi\) | |||||||
\(14\) | − | 2.08112i | − | 0.556204i | ||||||
\(15\) | −0.347650 | − | 2.20888i | −0.0897627 | − | 0.570330i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.28561 | 1.28195 | 0.640974 | − | 0.767562i | \(-0.278530\pi\) | ||||
0.640974 | + | 0.767562i | \(0.278530\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | − | 4.07548i | − | 0.934979i | −0.883998 | − | 0.467490i | \(-0.845158\pi\) | ||
0.883998 | − | 0.467490i | \(-0.154842\pi\) | |||||||
\(20\) | −2.20888 | + | 0.347650i | −0.493920 | + | 0.0777368i | ||||
\(21\) | 2.08112 | 0.454138 | ||||||||
\(22\) | 6.52056 | 1.39019 | ||||||||
\(23\) | −1.43562 | −0.299347 | −0.149673 | − | 0.988736i | \(-0.547822\pi\) | ||||
−0.149673 | + | 0.988736i | \(0.547822\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 4.75828 | − | 1.53583i | 0.951656 | − | 0.307166i | ||||
\(26\) | −1.53583 | −0.301201 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 2.08112i | − | 0.393295i | ||||||
\(29\) | 6.89042i | 1.27952i | 0.768575 | + | 0.639760i | \(0.220966\pi\) | ||||
−0.768575 | + | 0.639760i | \(0.779034\pi\) | |||||||
\(30\) | −0.347650 | − | 2.20888i | −0.0634718 | − | 0.403284i | ||||
\(31\) | 8.19513i | 1.47189i | 0.677042 | + | 0.735944i | \(0.263261\pi\) | ||||
−0.677042 | + | 0.735944i | \(0.736739\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.52056i | 1.13508i | ||||||||
\(34\) | 5.28561 | 0.906475 | ||||||||
\(35\) | 0.723502 | + | 4.59695i | 0.122294 | + | 0.777026i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.927865 | + | 6.01158i | 0.152540 | + | 0.988297i | ||||
\(38\) | − | 4.07548i | − | 0.661130i | ||||||
\(39\) | − | 1.53583i | − | 0.245930i | ||||||
\(40\) | −2.20888 | + | 0.347650i | −0.349254 | + | 0.0549682i | ||||
\(41\) | 6.76262 | 1.05614 | 0.528072 | − | 0.849200i | \(-0.322915\pi\) | ||||
0.528072 | + | 0.849200i | \(0.322915\pi\) | |||||||
\(42\) | 2.08112 | 0.321124 | ||||||||
\(43\) | 4.46572 | 0.681016 | 0.340508 | − | 0.940242i | \(-0.389401\pi\) | ||||
0.340508 | + | 0.940242i | \(0.389401\pi\) | |||||||
\(44\) | 6.52056 | 0.983011 | ||||||||
\(45\) | 2.20888 | − | 0.347650i | 0.329280 | − | 0.0518245i | ||||
\(46\) | −1.43562 | −0.211670 | ||||||||
\(47\) | − | 9.83376i | − | 1.43440i | −0.696867 | − | 0.717201i | \(-0.745423\pi\) | ||
0.696867 | − | 0.717201i | \(-0.254577\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 2.66892 | 0.381275 | ||||||||
\(50\) | 4.75828 | − | 1.53583i | 0.672922 | − | 0.217199i | ||||
\(51\) | 5.28561i | 0.740133i | ||||||||
\(52\) | −1.53583 | −0.212981 | ||||||||
\(53\) | − | 6.51769i | − | 0.895273i | −0.894216 | − | 0.447637i | \(-0.852266\pi\) | ||
0.894216 | − | 0.447637i | \(-0.147734\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | −14.4031 | + | 2.26687i | −1.94212 | + | 0.305665i | ||||
\(56\) | − | 2.08112i | − | 0.278102i | ||||||
\(57\) | 4.07548 | 0.539811 | ||||||||
\(58\) | 6.89042i | 0.904757i | ||||||||
\(59\) | − | 11.0304i | − | 1.43603i | −0.696027 | − | 0.718016i | \(-0.745051\pi\) | ||
0.696027 | − | 0.718016i | \(-0.254949\pi\) | |||||||
\(60\) | −0.347650 | − | 2.20888i | −0.0448814 | − | 0.285165i | ||||
\(61\) | − | 4.91211i | − | 0.628931i | −0.949269 | − | 0.314465i | \(-0.898175\pi\) | ||
0.949269 | − | 0.314465i | \(-0.101825\pi\) | |||||||
\(62\) | 8.19513i | 1.04078i | ||||||||
\(63\) | 2.08112i | 0.262197i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.39246 | − | 0.533931i | 0.420783 | − | 0.0662260i | ||||
\(66\) | 6.52056i | 0.802625i | ||||||||
\(67\) | 11.8535i | 1.44813i | 0.689731 | + | 0.724066i | \(0.257729\pi\) | ||||
−0.689731 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(68\) | 5.28561 | 0.640974 | ||||||||
\(69\) | − | 1.43562i | − | 0.172828i | ||||||
\(70\) | 0.723502 | + | 4.59695i | 0.0864750 | + | 0.549440i | ||||
\(71\) | −6.07887 | −0.721430 | −0.360715 | − | 0.932676i | \(-0.617467\pi\) | ||||
−0.360715 | + | 0.932676i | \(0.617467\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 13.6398i | 1.59642i | 0.602379 | + | 0.798211i | \(0.294220\pi\) | ||||
−0.602379 | + | 0.798211i | \(0.705780\pi\) | |||||||
\(74\) | 0.927865 | + | 6.01158i | 0.107862 | + | 0.698832i | ||||
\(75\) | 1.53583 | + | 4.75828i | 0.177342 | + | 0.549439i | ||||
\(76\) | − | 4.07548i | − | 0.467490i | ||||||
\(77\) | − | 13.5701i | − | 1.54646i | ||||||
\(78\) | − | 1.53583i | − | 0.173899i | ||||||
\(79\) | 2.76246i | 0.310801i | 0.987852 | + | 0.155400i | \(0.0496667\pi\) | ||||
−0.987852 | + | 0.155400i | \(0.950333\pi\) | |||||||
\(80\) | −2.20888 | + | 0.347650i | −0.246960 | + | 0.0388684i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.76262 | 0.746806 | ||||||||
\(83\) | − | 15.8823i | − | 1.74331i | −0.490117 | − | 0.871657i | \(-0.663046\pi\) | ||
0.490117 | − | 0.871657i | \(-0.336954\pi\) | |||||||
\(84\) | 2.08112 | 0.227069 | ||||||||
\(85\) | −11.6753 | + | 1.83754i | −1.26636 | + | 0.199309i | ||||
\(86\) | 4.46572 | 0.481551 | ||||||||
\(87\) | −6.89042 | −0.738731 | ||||||||
\(88\) | 6.52056 | 0.695094 | ||||||||
\(89\) | 7.15877i | 0.758828i | 0.925227 | + | 0.379414i | \(0.123874\pi\) | ||||
−0.925227 | + | 0.379414i | \(0.876126\pi\) | |||||||
\(90\) | 2.20888 | − | 0.347650i | 0.232836 | − | 0.0366455i | ||||
\(91\) | 3.19625i | 0.335058i | ||||||||
\(92\) | −1.43562 | −0.149673 | ||||||||
\(93\) | −8.19513 | −0.849795 | ||||||||
\(94\) | − | 9.83376i | − | 1.01427i | ||||||
\(95\) | 1.41684 | + | 9.00224i | 0.145365 | + | 0.923610i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −19.0806 | −1.93734 | −0.968671 | − | 0.248348i | \(-0.920112\pi\) | ||||
−0.968671 | + | 0.248348i | \(0.920112\pi\) | |||||||
\(98\) | 2.66892 | 0.269602 | ||||||||
\(99\) | −6.52056 | −0.655341 | ||||||||
\(100\) | 4.75828 | − | 1.53583i | 0.475828 | − | 0.153583i | ||||
\(101\) | 1.62639 | 0.161832 | 0.0809161 | − | 0.996721i | \(-0.474215\pi\) | ||||
0.0809161 | + | 0.996721i | \(0.474215\pi\) | |||||||
\(102\) | 5.28561i | 0.523353i | ||||||||
\(103\) | 3.70274 | 0.364842 | 0.182421 | − | 0.983220i | \(-0.441607\pi\) | ||||
0.182421 | + | 0.983220i | \(0.441607\pi\) | |||||||
\(104\) | −1.53583 | −0.150601 | ||||||||
\(105\) | −4.59695 | + | 0.723502i | −0.448616 | + | 0.0706065i | ||||
\(106\) | − | 6.51769i | − | 0.633054i | ||||||
\(107\) | 6.80165i | 0.657541i | 0.944410 | + | 0.328770i | \(0.106634\pi\) | ||||
−0.944410 | + | 0.328770i | \(0.893366\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | − | 17.9512i | − | 1.71941i | −0.510792 | − | 0.859704i | \(-0.670648\pi\) | ||
0.510792 | − | 0.859704i | \(-0.329352\pi\) | |||||||
\(110\) | −14.4031 | + | 2.26687i | −1.37328 | + | 0.216138i | ||||
\(111\) | −6.01158 | + | 0.927865i | −0.570594 | + | 0.0880690i | ||||
\(112\) | − | 2.08112i | − | 0.196648i | ||||||
\(113\) | −15.6346 | −1.47078 | −0.735392 | − | 0.677642i | \(-0.763002\pi\) | ||||
−0.735392 | + | 0.677642i | \(0.763002\pi\) | |||||||
\(114\) | 4.07548 | 0.381704 | ||||||||
\(115\) | 3.17110 | − | 0.499091i | 0.295707 | − | 0.0465405i | ||||
\(116\) | 6.89042i | 0.639760i | ||||||||
\(117\) | 1.53583 | 0.141988 | ||||||||
\(118\) | − | 11.0304i | − | 1.01543i | ||||||
\(119\) | − | 11.0000i | − | 1.00837i | ||||||
\(120\) | −0.347650 | − | 2.20888i | −0.0317359 | − | 0.201642i | ||||
\(121\) | 31.5177 | 2.86524 | ||||||||
\(122\) | − | 4.91211i | − | 0.444721i | ||||||
\(123\) | 6.76262i | 0.609765i | ||||||||
\(124\) | 8.19513i | 0.735944i | ||||||||
\(125\) | −9.97653 | + | 5.04668i | −0.892328 | + | 0.451388i | ||||
\(126\) | 2.08112i | 0.185401i | ||||||||
\(127\) | 0.759690i | 0.0674116i | 0.999432 | + | 0.0337058i | \(0.0107309\pi\) | ||||
−0.999432 | + | 0.0337058i | \(0.989269\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.46572i | 0.393185i | ||||||||
\(130\) | 3.39246 | − | 0.533931i | 0.297539 | − | 0.0468288i | ||||
\(131\) | − | 17.8737i | − | 1.56163i | −0.624763 | − | 0.780815i | \(-0.714804\pi\) | ||
0.624763 | − | 0.780815i | \(-0.285196\pi\) | |||||||
\(132\) | 6.52056i | 0.567542i | ||||||||
\(133\) | −8.48158 | −0.735446 | ||||||||
\(134\) | 11.8535i | 1.02398i | ||||||||
\(135\) | 0.347650 | + | 2.20888i | 0.0299209 | + | 0.190110i | ||||
\(136\) | 5.28561 | 0.453237 | ||||||||
\(137\) | − | 7.88841i | − | 0.673952i | −0.941513 | − | 0.336976i | \(-0.890596\pi\) | ||
0.941513 | − | 0.336976i | \(-0.109404\pi\) | |||||||
\(138\) | − | 1.43562i | − | 0.122208i | ||||||
\(139\) | −17.6834 | −1.49989 | −0.749943 | − | 0.661502i | \(-0.769919\pi\) | ||||
−0.749943 | + | 0.661502i | \(0.769919\pi\) | |||||||
\(140\) | 0.723502 | + | 4.59695i | 0.0611471 | + | 0.388513i | ||||
\(141\) | 9.83376 | 0.828152 | ||||||||
\(142\) | −6.07887 | −0.510128 | ||||||||
\(143\) | −10.0145 | −0.837452 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −2.39545 | − | 15.2201i | −0.198932 | − | 1.26396i | ||||
\(146\) | 13.6398i | 1.12884i | ||||||||
\(147\) | 2.66892i | 0.220129i | ||||||||
\(148\) | 0.927865 | + | 6.01158i | 0.0762700 | + | 0.494149i | ||||
\(149\) | −0.543289 | −0.0445080 | −0.0222540 | − | 0.999752i | \(-0.507084\pi\) | ||||
−0.0222540 | + | 0.999752i | \(0.507084\pi\) | |||||||
\(150\) | 1.53583 | + | 4.75828i | 0.125400 | + | 0.388512i | ||||
\(151\) | 7.98733 | 0.650000 | 0.325000 | − | 0.945714i | \(-0.394636\pi\) | ||||
0.325000 | + | 0.945714i | \(0.394636\pi\) | |||||||
\(152\) | − | 4.07548i | − | 0.330565i | ||||||
\(153\) | −5.28561 | −0.427316 | ||||||||
\(154\) | − | 13.5701i | − | 1.09351i | ||||||
\(155\) | −2.84903 | − | 18.1020i | −0.228840 | − | 1.45399i | ||||
\(156\) | − | 1.53583i | − | 0.122965i | ||||||
\(157\) | − | 11.2296i | − | 0.896216i | −0.893979 | − | 0.448108i | \(-0.852098\pi\) | ||
0.893979 | − | 0.448108i | \(-0.147902\pi\) | |||||||
\(158\) | 2.76246i | 0.219769i | ||||||||
\(159\) | 6.51769 | 0.516886 | ||||||||
\(160\) | −2.20888 | + | 0.347650i | −0.174627 | + | 0.0274841i | ||||
\(161\) | 2.98769i | 0.235463i | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.05362 | 0.630808 | 0.315404 | − | 0.948957i | \(-0.397860\pi\) | ||||
0.315404 | + | 0.948957i | \(0.397860\pi\) | |||||||
\(164\) | 6.76262 | 0.528072 | ||||||||
\(165\) | −2.26687 | − | 14.4031i | −0.176476 | − | 1.12128i | ||||
\(166\) | − | 15.8823i | − | 1.23271i | ||||||
\(167\) | 12.7129 | 0.983753 | 0.491876 | − | 0.870665i | \(-0.336311\pi\) | ||||
0.491876 | + | 0.870665i | \(0.336311\pi\) | |||||||
\(168\) | 2.08112 | 0.160562 | ||||||||
\(169\) | −10.6412 | −0.818556 | ||||||||
\(170\) | −11.6753 | + | 1.83754i | −0.895452 | + | 0.140933i | ||||
\(171\) | 4.07548i | 0.311660i | ||||||||
\(172\) | 4.46572 | 0.340508 | ||||||||
\(173\) | 1.56245i | 0.118791i | 0.998235 | + | 0.0593955i | \(0.0189173\pi\) | ||||
−0.998235 | + | 0.0593955i | \(0.981083\pi\) | |||||||
\(174\) | −6.89042 | −0.522362 | ||||||||
\(175\) | −3.19625 | − | 9.90257i | −0.241614 | − | 0.748564i | ||||
\(176\) | 6.52056 | 0.491506 | ||||||||
\(177\) | 11.0304 | 0.829093 | ||||||||
\(178\) | 7.15877i | 0.536572i | ||||||||
\(179\) | 12.2571i | 0.916135i | 0.888917 | + | 0.458067i | \(0.151458\pi\) | ||||
−0.888917 | + | 0.458067i | \(0.848542\pi\) | |||||||
\(180\) | 2.20888 | − | 0.347650i | 0.164640 | − | 0.0259123i | ||||
\(181\) | −18.8971 | −1.40461 | −0.702305 | − | 0.711876i | \(-0.747846\pi\) | ||||
−0.702305 | + | 0.711876i | \(0.747846\pi\) | |||||||
\(182\) | 3.19625i | 0.236922i | ||||||||
\(183\) | 4.91211 | 0.363113 | ||||||||
\(184\) | −1.43562 | −0.105835 | ||||||||
\(185\) | −4.13946 | − | 12.9563i | −0.304339 | − | 0.952564i | ||||
\(186\) | −8.19513 | −0.600896 | ||||||||
\(187\) | 34.4651 | 2.52034 | ||||||||
\(188\) | − | 9.83376i | − | 0.717201i | ||||||
\(189\) | −2.08112 | −0.151379 | ||||||||
\(190\) | 1.41684 | + | 9.00224i | 0.102788 | + | 0.653091i | ||||
\(191\) | 8.66659i | 0.627093i | 0.949573 | + | 0.313546i | \(0.101517\pi\) | ||||
−0.949573 | + | 0.313546i | \(0.898483\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | −14.0122 | −1.00862 | −0.504311 | − | 0.863522i | \(-0.668253\pi\) | ||||
−0.504311 | + | 0.863522i | \(0.668253\pi\) | |||||||
\(194\) | −19.0806 | −1.36991 | ||||||||
\(195\) | 0.533931 | + | 3.39246i | 0.0382356 | + | 0.242939i | ||||
\(196\) | 2.66892 | 0.190637 | ||||||||
\(197\) | 20.7652i | 1.47946i | 0.672903 | + | 0.739731i | \(0.265047\pi\) | ||||
−0.672903 | + | 0.739731i | \(0.734953\pi\) | |||||||
\(198\) | −6.52056 | −0.463396 | ||||||||
\(199\) | 18.3572i | 1.30131i | 0.759373 | + | 0.650655i | \(0.225506\pi\) | ||||
−0.759373 | + | 0.650655i | \(0.774494\pi\) | |||||||
\(200\) | 4.75828 | − | 1.53583i | 0.336461 | − | 0.108600i | ||||
\(201\) | −11.8535 | −0.836080 | ||||||||
\(202\) | 1.62639 | 0.114433 | ||||||||
\(203\) | 14.3398 | 1.00646 | ||||||||
\(204\) | 5.28561i | 0.370067i | ||||||||
\(205\) | −14.9378 | + | 2.35102i | −1.04330 | + | 0.164202i | ||||
\(206\) | 3.70274 | 0.257982 | ||||||||
\(207\) | 1.43562 | 0.0997822 | ||||||||
\(208\) | −1.53583 | −0.106491 | ||||||||
\(209\) | − | 26.5744i | − | 1.83819i | ||||||
\(210\) | −4.59695 | + | 0.723502i | −0.317220 | + | 0.0499264i | ||||
\(211\) | −1.37092 | −0.0943781 | −0.0471891 | − | 0.998886i | \(-0.515026\pi\) | ||||
−0.0471891 | + | 0.998886i | \(0.515026\pi\) | |||||||
\(212\) | − | 6.51769i | − | 0.447637i | ||||||
\(213\) | − | 6.07887i | − | 0.416518i | ||||||
\(214\) | 6.80165i | 0.464952i | ||||||||
\(215\) | −9.86422 | + | 1.55250i | −0.672735 | + | 0.105880i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 17.0551 | 1.15777 | ||||||||
\(218\) | − | 17.9512i | − | 1.21581i | ||||||
\(219\) | −13.6398 | −0.921694 | ||||||||
\(220\) | −14.4031 | + | 2.26687i | −0.971058 | + | 0.152832i | ||||
\(221\) | −8.11780 | −0.546062 | ||||||||
\(222\) | −6.01158 | + | 0.927865i | −0.403471 | + | 0.0622742i | ||||
\(223\) | 10.4991i | 0.703073i | 0.936174 | + | 0.351537i | \(0.114341\pi\) | ||||
−0.936174 | + | 0.351537i | \(0.885659\pi\) | |||||||
\(224\) | − | 2.08112i | − | 0.139051i | ||||||
\(225\) | −4.75828 | + | 1.53583i | −0.317219 | + | 0.102389i | ||||
\(226\) | −15.6346 | −1.04000 | ||||||||
\(227\) | 23.4274 | 1.55493 | 0.777465 | − | 0.628927i | \(-0.216505\pi\) | ||||
0.777465 | + | 0.628927i | \(0.216505\pi\) | |||||||
\(228\) | 4.07548 | 0.269905 | ||||||||
\(229\) | −17.8860 | −1.18194 | −0.590969 | − | 0.806694i | \(-0.701254\pi\) | ||||
−0.590969 | + | 0.806694i | \(0.701254\pi\) | |||||||
\(230\) | 3.17110 | − | 0.499091i | 0.209096 | − | 0.0329091i | ||||
\(231\) | 13.5701 | 0.892846 | ||||||||
\(232\) | 6.89042i | 0.452379i | ||||||||
\(233\) | 4.01113i | 0.262778i | 0.991331 | + | 0.131389i | \(0.0419437\pi\) | ||||
−0.991331 | + | 0.131389i | \(0.958056\pi\) | |||||||
\(234\) | 1.53583 | 0.100400 | ||||||||
\(235\) | 3.41870 | + | 21.7216i | 0.223012 | + | 1.41696i | ||||
\(236\) | − | 11.0304i | − | 0.718016i | ||||||
\(237\) | −2.76246 | −0.179441 | ||||||||
\(238\) | − | 11.0000i | − | 0.713025i | ||||||
\(239\) | 8.70690i | 0.563203i | 0.959532 | + | 0.281601i | \(0.0908655\pi\) | ||||
−0.959532 | + | 0.281601i | \(0.909134\pi\) | |||||||
\(240\) | −0.347650 | − | 2.20888i | −0.0224407 | − | 0.142582i | ||||
\(241\) | − | 15.6443i | − | 1.00774i | −0.863781 | − | 0.503868i | \(-0.831910\pi\) | ||
0.863781 | − | 0.503868i | \(-0.168090\pi\) | |||||||
\(242\) | 31.5177 | 2.02603 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | − | 4.91211i | − | 0.314465i | ||||||
\(245\) | −5.89533 | + | 0.927850i | −0.376639 | + | 0.0592782i | ||||
\(246\) | 6.76262i | 0.431169i | ||||||||
\(247\) | 6.25925i | 0.398266i | ||||||||
\(248\) | 8.19513i | 0.520391i | ||||||||
\(249\) | 15.8823 | 1.00650 | ||||||||
\(250\) | −9.97653 | + | 5.04668i | −0.630971 | + | 0.319180i | ||||
\(251\) | − | 9.35179i | − | 0.590280i | −0.955454 | − | 0.295140i | \(-0.904634\pi\) | ||
0.955454 | − | 0.295140i | \(-0.0953662\pi\) | |||||||
\(252\) | 2.08112i | 0.131098i | ||||||||
\(253\) | −9.36102 | −0.588522 | ||||||||
\(254\) | 0.759690i | 0.0476672i | ||||||||
\(255\) | −1.83754 | − | 11.6753i | −0.115071 | − | 0.731133i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.5996 | −0.723565 | −0.361782 | − | 0.932263i | \(-0.617832\pi\) | ||||
−0.361782 | + | 0.932263i | \(0.617832\pi\) | |||||||
\(258\) | 4.46572i | 0.278023i | ||||||||
\(259\) | 12.5108 | − | 1.93100i | 0.777386 | − | 0.119987i | ||||
\(260\) | 3.39246 | − | 0.533931i | 0.210392 | − | 0.0331130i | ||||
\(261\) | − | 6.89042i | − | 0.426507i | ||||||
\(262\) | − | 17.8737i | − | 1.10424i | ||||||
\(263\) | − | 1.31327i | − | 0.0809797i | −0.999180 | − | 0.0404898i | \(-0.987108\pi\) | ||
0.999180 | − | 0.0404898i | \(-0.0128918\pi\) | |||||||
\(264\) | 6.52056i | 0.401313i | ||||||||
\(265\) | 2.26587 | + | 14.3968i | 0.139191 | + | 0.884387i | ||||
\(266\) | −8.48158 | −0.520039 | ||||||||
\(267\) | −7.15877 | −0.438109 | ||||||||
\(268\) | 11.8535i | 0.724066i | ||||||||
\(269\) | −16.7383 | −1.02055 | −0.510277 | − | 0.860010i | \(-0.670457\pi\) | ||||
−0.510277 | + | 0.860010i | \(0.670457\pi\) | |||||||
\(270\) | 0.347650 | + | 2.20888i | 0.0211573 | + | 0.134428i | ||||
\(271\) | −27.8757 | −1.69333 | −0.846663 | − | 0.532130i | \(-0.821392\pi\) | ||||
−0.846663 | + | 0.532130i | \(0.821392\pi\) | |||||||
\(272\) | 5.28561 | 0.320487 | ||||||||
\(273\) | −3.19625 | −0.193446 | ||||||||
\(274\) | − | 7.88841i | − | 0.476556i | ||||||
\(275\) | 31.0266 | − | 10.0145i | 1.87098 | − | 0.603896i | ||||
\(276\) | − | 1.43562i | − | 0.0864139i | ||||||
\(277\) | 18.0505 | 1.08455 | 0.542275 | − | 0.840201i | \(-0.317563\pi\) | ||||
0.542275 | + | 0.840201i | \(0.317563\pi\) | |||||||
\(278\) | −17.6834 | −1.06058 | ||||||||
\(279\) | − | 8.19513i | − | 0.490629i | ||||||
\(280\) | 0.723502 | + | 4.59695i | 0.0432375 | + | 0.274720i | ||||
\(281\) | − | 3.12679i | − | 0.186528i | −0.995641 | − | 0.0932642i | \(-0.970270\pi\) | ||
0.995641 | − | 0.0932642i | \(-0.0297301\pi\) | |||||||
\(282\) | 9.83376 | 0.585592 | ||||||||
\(283\) | −13.1469 | −0.781502 | −0.390751 | − | 0.920496i | \(-0.627785\pi\) | ||||
−0.390751 | + | 0.920496i | \(0.627785\pi\) | |||||||
\(284\) | −6.07887 | −0.360715 | ||||||||
\(285\) | −9.00224 | + | 1.41684i | −0.533247 | + | 0.0839263i | ||||
\(286\) | −10.0145 | −0.592168 | ||||||||
\(287\) | − | 14.0738i | − | 0.830753i | ||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 10.9377 | 0.643392 | ||||||||
\(290\) | −2.39545 | − | 15.2201i | −0.140666 | − | 0.893755i | ||||
\(291\) | − | 19.0806i | − | 1.11852i | ||||||
\(292\) | 13.6398i | 0.798211i | ||||||||
\(293\) | − | 17.8889i | − | 1.04508i | −0.852615 | − | 0.522540i | \(-0.824985\pi\) | ||
0.852615 | − | 0.522540i | \(-0.175015\pi\) | |||||||
\(294\) | 2.66892i | 0.155655i | ||||||||
\(295\) | 3.83470 | + | 24.3647i | 0.223265 | + | 1.41857i | ||||
\(296\) | 0.927865 | + | 6.01158i | 0.0539310 | + | 0.349416i | ||||
\(297\) | − | 6.52056i | − | 0.378361i | ||||||
\(298\) | −0.543289 | −0.0314719 | ||||||||
\(299\) | 2.20486 | 0.127510 | ||||||||
\(300\) | 1.53583 | + | 4.75828i | 0.0886712 | + | 0.274719i | ||||
\(301\) | − | 9.29371i | − | 0.535681i | ||||||
\(302\) | 7.98733 | 0.459619 | ||||||||
\(303\) | 1.62639i | 0.0934338i | ||||||||
\(304\) | − | 4.07548i | − | 0.233745i | ||||||
\(305\) | 1.70769 | + | 10.8502i | 0.0977821 | + | 0.621283i | ||||
\(306\) | −5.28561 | −0.302158 | ||||||||
\(307\) | 21.1435i | 1.20672i | 0.797467 | + | 0.603362i | \(0.206173\pi\) | ||||
−0.797467 | + | 0.603362i | \(0.793827\pi\) | |||||||
\(308\) | − | 13.5701i | − | 0.773228i | ||||||
\(309\) | 3.70274i | 0.210642i | ||||||||
\(310\) | −2.84903 | − | 18.1020i | −0.161814 | − | 1.02813i | ||||
\(311\) | 25.3383i | 1.43680i | 0.695629 | + | 0.718401i | \(0.255126\pi\) | ||||
−0.695629 | + | 0.718401i | \(0.744874\pi\) | |||||||
\(312\) | − | 1.53583i | − | 0.0869493i | ||||||
\(313\) | −15.2774 | −0.863532 | −0.431766 | − | 0.901986i | \(-0.642109\pi\) | ||||
−0.431766 | + | 0.901986i | \(0.642109\pi\) | |||||||
\(314\) | − | 11.2296i | − | 0.633720i | ||||||
\(315\) | −0.723502 | − | 4.59695i | −0.0407647 | − | 0.259009i | ||||
\(316\) | 2.76246i | 0.155400i | ||||||||
\(317\) | 26.3718i | 1.48119i | 0.671954 | + | 0.740593i | \(0.265455\pi\) | ||||
−0.671954 | + | 0.740593i | \(0.734545\pi\) | |||||||
\(318\) | 6.51769 | 0.365494 | ||||||||
\(319\) | 44.9294i | 2.51556i | ||||||||
\(320\) | −2.20888 | + | 0.347650i | −0.123480 | + | 0.0194342i | ||||
\(321\) | −6.80165 | −0.379631 | ||||||||
\(322\) | 2.98769i | 0.166498i | ||||||||
\(323\) | − | 21.5414i | − | 1.19860i | ||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −7.30791 | + | 2.35878i | −0.405370 | + | 0.130841i | ||||
\(326\) | 8.05362 | 0.446049 | ||||||||
\(327\) | 17.9512 | 0.992701 | ||||||||
\(328\) | 6.76262 | 0.373403 | ||||||||
\(329\) | −20.4653 | −1.12829 | ||||||||
\(330\) | −2.26687 | − | 14.4031i | −0.124787 | − | 0.792865i | ||||
\(331\) | − | 8.98662i | − | 0.493950i | −0.969022 | − | 0.246975i | \(-0.920564\pi\) | ||
0.969022 | − | 0.246975i | \(-0.0794365\pi\) | |||||||
\(332\) | − | 15.8823i | − | 0.871657i | ||||||
\(333\) | −0.927865 | − | 6.01158i | −0.0508467 | − | 0.329432i | ||||
\(334\) | 12.7129 | 0.695618 | ||||||||
\(335\) | −4.12085 | − | 26.1829i | −0.225146 | − | 1.43052i | ||||
\(336\) | 2.08112 | 0.113535 | ||||||||
\(337\) | − | 5.68375i | − | 0.309614i | −0.987945 | − | 0.154807i | \(-0.950524\pi\) | ||
0.987945 | − | 0.154807i | \(-0.0494755\pi\) | |||||||
\(338\) | −10.6412 | −0.578806 | ||||||||
\(339\) | − | 15.6346i | − | 0.849157i | ||||||
\(340\) | −11.6753 | + | 1.83754i | −0.633180 | + | 0.0996546i | ||||
\(341\) | 53.4368i | 2.89377i | ||||||||
\(342\) | 4.07548i | 0.220377i | ||||||||
\(343\) | − | 20.1222i | − | 1.08650i | ||||||
\(344\) | 4.46572 | 0.240775 | ||||||||
\(345\) | 0.499091 | + | 3.17110i | 0.0268702 | + | 0.170726i | ||||
\(346\) | 1.56245i | 0.0839979i | ||||||||
\(347\) | 11.6758 | 0.626788 | 0.313394 | − | 0.949623i | \(-0.398534\pi\) | ||||
0.313394 | + | 0.949623i | \(0.398534\pi\) | |||||||
\(348\) | −6.89042 | −0.369366 | ||||||||
\(349\) | −0.886357 | −0.0474456 | −0.0237228 | − | 0.999719i | \(-0.507552\pi\) | ||||
−0.0237228 | + | 0.999719i | \(0.507552\pi\) | |||||||
\(350\) | −3.19625 | − | 9.90257i | −0.170847 | − | 0.529315i | ||||
\(351\) | 1.53583i | 0.0819766i | ||||||||
\(352\) | 6.52056 | 0.347547 | ||||||||
\(353\) | 24.8083 | 1.32042 | 0.660208 | − | 0.751083i | \(-0.270468\pi\) | ||||
0.660208 | + | 0.751083i | \(0.270468\pi\) | |||||||
\(354\) | 11.0304 | 0.586257 | ||||||||
\(355\) | 13.4275 | − | 2.11332i | 0.712657 | − | 0.112163i | ||||
\(356\) | 7.15877i | 0.379414i | ||||||||
\(357\) | 11.0000 | 0.582182 | ||||||||
\(358\) | 12.2571i | 0.647805i | ||||||||
\(359\) | −5.29404 | −0.279409 | −0.139704 | − | 0.990193i | \(-0.544615\pi\) | ||||
−0.139704 | + | 0.990193i | \(0.544615\pi\) | |||||||
\(360\) | 2.20888 | − | 0.347650i | 0.116418 | − | 0.0183227i | ||||
\(361\) | 2.39045 | 0.125813 | ||||||||
\(362\) | −18.8971 | −0.993209 | ||||||||
\(363\) | 31.5177i | 1.65425i | ||||||||
\(364\) | 3.19625i | 0.167529i | ||||||||
\(365\) | −4.74188 | − | 30.1287i | −0.248201 | − | 1.57701i | ||||
\(366\) | 4.91211 | 0.256760 | ||||||||
\(367\) | 0.716886i | 0.0374211i | 0.999825 | + | 0.0187106i | \(0.00595610\pi\) | ||||
−0.999825 | + | 0.0187106i | \(0.994044\pi\) | |||||||
\(368\) | −1.43562 | −0.0748366 | ||||||||
\(369\) | −6.76262 | −0.352048 | ||||||||
\(370\) | −4.13946 | − | 12.9563i | −0.215200 | − | 0.673564i | ||||
\(371\) | −13.5641 | −0.704214 | ||||||||
\(372\) | −8.19513 | −0.424897 | ||||||||
\(373\) | 1.21732i | 0.0630305i | 0.999503 | + | 0.0315153i | \(0.0100333\pi\) | ||||
−0.999503 | + | 0.0315153i | \(0.989967\pi\) | |||||||
\(374\) | 34.4651 | 1.78215 | ||||||||
\(375\) | −5.04668 | − | 9.97653i | −0.260609 | − | 0.515186i | ||||
\(376\) | − | 9.83376i | − | 0.507137i | ||||||
\(377\) | − | 10.5825i | − | 0.545028i | ||||||
\(378\) | −2.08112 | −0.107041 | ||||||||
\(379\) | −33.1425 | −1.70241 | −0.851207 | − | 0.524830i | \(-0.824129\pi\) | ||||
−0.851207 | + | 0.524830i | \(0.824129\pi\) | |||||||
\(380\) | 1.41684 | + | 9.00224i | 0.0726823 | + | 0.461805i | ||||
\(381\) | −0.759690 | −0.0389201 | ||||||||
\(382\) | 8.66659i | 0.443421i | ||||||||
\(383\) | −8.54131 | −0.436440 | −0.218220 | − | 0.975900i | \(-0.570025\pi\) | ||||
−0.218220 | + | 0.975900i | \(0.570025\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 4.71764 | + | 29.9747i | 0.240433 | + | 1.52765i | ||||
\(386\) | −14.0122 | −0.713204 | ||||||||
\(387\) | −4.46572 | −0.227005 | ||||||||
\(388\) | −19.0806 | −0.968671 | ||||||||
\(389\) | − | 23.0234i | − | 1.16733i | −0.811994 | − | 0.583666i | \(-0.801618\pi\) | ||
0.811994 | − | 0.583666i | \(-0.198382\pi\) | |||||||
\(390\) | 0.533931 | + | 3.39246i | 0.0270366 | + | 0.171784i | ||||
\(391\) | −7.58810 | −0.383747 | ||||||||
\(392\) | 2.66892 | 0.134801 | ||||||||
\(393\) | 17.8737 | 0.901607 | ||||||||
\(394\) | 20.7652i | 1.04614i | ||||||||
\(395\) | −0.960367 | − | 6.10193i | −0.0483213 | − | 0.307021i | ||||
\(396\) | −6.52056 | −0.327670 | ||||||||
\(397\) | − | 16.8160i | − | 0.843973i | −0.906602 | − | 0.421987i | \(-0.861333\pi\) | ||
0.906602 | − | 0.421987i | \(-0.138667\pi\) | |||||||
\(398\) | 18.3572i | 0.920166i | ||||||||
\(399\) | − | 8.48158i | − | 0.424610i | ||||||
\(400\) | 4.75828 | − | 1.53583i | 0.237914 | − | 0.0767915i | ||||
\(401\) | − | 19.6354i | − | 0.980543i | −0.871570 | − | 0.490271i | \(-0.836898\pi\) | ||
0.871570 | − | 0.490271i | \(-0.163102\pi\) | |||||||
\(402\) | −11.8535 | −0.591197 | ||||||||
\(403\) | − | 12.5863i | − | 0.626970i | ||||||
\(404\) | 1.62639 | 0.0809161 | ||||||||
\(405\) | −2.20888 | + | 0.347650i | −0.109760 | + | 0.0172748i | ||||
\(406\) | 14.3398 | 0.711674 | ||||||||
\(407\) | 6.05020 | + | 39.1988i | 0.299897 | + | 1.94301i | ||||
\(408\) | 5.28561i | 0.261677i | ||||||||
\(409\) | 32.0465i | 1.58460i | 0.610134 | + | 0.792298i | \(0.291116\pi\) | ||||
−0.610134 | + | 0.792298i | \(0.708884\pi\) | |||||||
\(410\) | −14.9378 | + | 2.35102i | −0.737725 | + | 0.116109i | ||||
\(411\) | 7.88841 | 0.389106 | ||||||||
\(412\) | 3.70274 | 0.182421 | ||||||||
\(413\) | −22.9556 | −1.12957 | ||||||||
\(414\) | 1.43562 | 0.0705567 | ||||||||
\(415\) | 5.52149 | + | 35.0822i | 0.271039 | + | 1.72212i | ||||
\(416\) | −1.53583 | −0.0753003 | ||||||||
\(417\) | − | 17.6834i | − | 0.865960i | ||||||
\(418\) | − | 26.5744i | − | 1.29980i | ||||||
\(419\) | 3.81945 | 0.186592 | 0.0932962 | − | 0.995638i | \(-0.470260\pi\) | ||||
0.0932962 | + | 0.995638i | \(0.470260\pi\) | |||||||
\(420\) | −4.59695 | + | 0.723502i | −0.224308 | + | 0.0353033i | ||||
\(421\) | 10.0113i | 0.487920i | 0.969785 | + | 0.243960i | \(0.0784466\pi\) | ||||
−0.969785 | + | 0.243960i | \(0.921553\pi\) | |||||||
\(422\) | −1.37092 | −0.0667354 | ||||||||
\(423\) | 9.83376i | 0.478134i | ||||||||
\(424\) | − | 6.51769i | − | 0.316527i | ||||||
\(425\) | 25.1504 | − | 8.11780i | 1.21997 | − | 0.393771i | ||||
\(426\) | − | 6.07887i | − | 0.294522i | ||||||
\(427\) | −10.2227 | −0.494711 | ||||||||
\(428\) | 6.80165i | 0.328770i | ||||||||
\(429\) | − | 10.0145i | − | 0.483503i | ||||||
\(430\) | −9.86422 | + | 1.55250i | −0.475695 | + | 0.0748684i | ||||
\(431\) | 5.28491i | 0.254565i | 0.991866 | + | 0.127283i | \(0.0406255\pi\) | ||||
−0.991866 | + | 0.127283i | \(0.959374\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 23.3433i | 1.12181i | 0.827881 | + | 0.560904i | \(0.189546\pi\) | ||||
−0.827881 | + | 0.560904i | \(0.810454\pi\) | |||||||
\(434\) | 17.0551 | 0.818670 | ||||||||
\(435\) | 15.2201 | − | 2.39545i | 0.729748 | − | 0.114853i | ||||
\(436\) | − | 17.9512i | − | 0.859704i | ||||||
\(437\) | 5.85082i | 0.279883i | ||||||||
\(438\) | −13.6398 | −0.651736 | ||||||||
\(439\) | 20.3738i | 0.972388i | 0.873851 | + | 0.486194i | \(0.161615\pi\) | ||||
−0.873851 | + | 0.486194i | \(0.838385\pi\) | |||||||
\(440\) | −14.4031 | + | 2.26687i | −0.686642 | + | 0.108069i | ||||
\(441\) | −2.66892 | −0.127092 | ||||||||
\(442\) | −8.11780 | −0.386124 | ||||||||
\(443\) | 4.11658i | 0.195585i | 0.995207 | + | 0.0977924i | \(0.0311781\pi\) | ||||
−0.995207 | + | 0.0977924i | \(0.968822\pi\) | |||||||
\(444\) | −6.01158 | + | 0.927865i | −0.285297 | + | 0.0440345i | ||||
\(445\) | −2.48874 | − | 15.8128i | −0.117978 | − | 0.749600i | ||||
\(446\) | 10.4991i | 0.497148i | ||||||||
\(447\) | − | 0.543289i | − | 0.0256967i | ||||||
\(448\) | − | 2.08112i | − | 0.0983239i | ||||||
\(449\) | 13.0977i | 0.618117i | 0.951043 | + | 0.309058i | \(0.100014\pi\) | ||||
−0.951043 | + | 0.309058i | \(0.899986\pi\) | |||||||
\(450\) | −4.75828 | + | 1.53583i | −0.224307 | + | 0.0723998i | ||||
\(451\) | 44.0961 | 2.07640 | ||||||||
\(452\) | −15.6346 | −0.735392 | ||||||||
\(453\) | 7.98733i | 0.375278i | ||||||||
\(454\) | 23.4274 | 1.09950 | ||||||||
\(455\) | −1.11118 | − | 7.06013i | −0.0520927 | − | 0.330984i | ||||
\(456\) | 4.07548 | 0.190852 | ||||||||
\(457\) | 12.4923 | 0.584365 | 0.292183 | − | 0.956363i | \(-0.405618\pi\) | ||||
0.292183 | + | 0.956363i | \(0.405618\pi\) | |||||||
\(458\) | −17.8860 | −0.835756 | ||||||||
\(459\) | − | 5.28561i | − | 0.246711i | ||||||
\(460\) | 3.17110 | − | 0.499091i | 0.147853 | − | 0.0232702i | ||||
\(461\) | − | 1.72410i | − | 0.0802995i | −0.999194 | − | 0.0401497i | \(-0.987217\pi\) | ||
0.999194 | − | 0.0401497i | \(-0.0127835\pi\) | |||||||
\(462\) | 13.5701 | 0.631338 | ||||||||
\(463\) | 17.2119 | 0.799903 | 0.399952 | − | 0.916536i | \(-0.369027\pi\) | ||||
0.399952 | + | 0.916536i | \(0.369027\pi\) | |||||||
\(464\) | 6.89042i | 0.319880i | ||||||||
\(465\) | 18.1020 | − | 2.84903i | 0.839461 | − | 0.132121i | ||||
\(466\) | 4.01113i | 0.185812i | ||||||||
\(467\) | 0.918102 | 0.0424847 | 0.0212423 | − | 0.999774i | \(-0.493238\pi\) | ||||
0.0212423 | + | 0.999774i | \(0.493238\pi\) | |||||||
\(468\) | 1.53583 | 0.0709938 | ||||||||
\(469\) | 24.6685 | 1.13909 | ||||||||
\(470\) | 3.41870 | + | 21.7216i | 0.157693 | + | 1.00194i | ||||
\(471\) | 11.2296 | 0.517430 | ||||||||
\(472\) | − | 11.0304i | − | 0.507714i | ||||||
\(473\) | 29.1190 | 1.33889 | ||||||||
\(474\) | −2.76246 | −0.126884 | ||||||||
\(475\) | −6.25925 | − | 19.3923i | −0.287194 | − | 0.889779i | ||||
\(476\) | − | 11.0000i | − | 0.504185i | ||||||
\(477\) | 6.51769i | 0.298424i | ||||||||
\(478\) | 8.70690i | 0.398244i | ||||||||
\(479\) | − | 16.4565i | − | 0.751918i | −0.926636 | − | 0.375959i | \(-0.877313\pi\) | ||
0.926636 | − | 0.375959i | \(-0.122687\pi\) | |||||||
\(480\) | −0.347650 | − | 2.20888i | −0.0158680 | − | 0.100821i | ||||
\(481\) | −1.42504 | − | 9.23277i | −0.0649764 | − | 0.420978i | ||||
\(482\) | − | 15.6443i | − | 0.712577i | ||||||
\(483\) | −2.98769 | −0.135945 | ||||||||
\(484\) | 31.5177 | 1.43262 | ||||||||
\(485\) | 42.1467 | − | 6.63336i | 1.91378 | − | 0.301206i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −0.244062 | −0.0110595 | −0.00552975 | − | 0.999985i | \(-0.501760\pi\) | ||||
−0.00552975 | + | 0.999985i | \(0.501760\pi\) | |||||||
\(488\) | − | 4.91211i | − | 0.222361i | ||||||
\(489\) | 8.05362i | 0.364197i | ||||||||
\(490\) | −5.89533 | + | 0.927850i | −0.266324 | + | 0.0419160i | ||||
\(491\) | 10.1056 | 0.456060 | 0.228030 | − | 0.973654i | \(-0.426772\pi\) | ||||
0.228030 | + | 0.973654i | \(0.426772\pi\) | |||||||
\(492\) | 6.76262i | 0.304882i | ||||||||
\(493\) | 36.4201i | 1.64028i | ||||||||
\(494\) | 6.25925i | 0.281617i | ||||||||
\(495\) | 14.4031 | − | 2.26687i | 0.647372 | − | 0.101888i | ||||
\(496\) | 8.19513i | 0.367972i | ||||||||
\(497\) | 12.6509i | 0.567470i | ||||||||
\(498\) | 15.8823 | 0.711705 | ||||||||
\(499\) | − | 4.16552i | − | 0.186474i | −0.995644 | − | 0.0932370i | \(-0.970279\pi\) | ||
0.995644 | − | 0.0932370i | \(-0.0297214\pi\) | |||||||
\(500\) | −9.97653 | + | 5.04668i | −0.446164 | + | 0.225694i | ||||
\(501\) | 12.7129i | 0.567970i | ||||||||
\(502\) | − | 9.35179i | − | 0.417391i | ||||||
\(503\) | 30.4289 | 1.35676 | 0.678379 | − | 0.734712i | \(-0.262683\pi\) | ||||
0.678379 | + | 0.734712i | \(0.262683\pi\) | |||||||
\(504\) | 2.08112i | 0.0927006i | ||||||||
\(505\) | −3.59250 | + | 0.565415i | −0.159864 | + | 0.0251606i | ||||
\(506\) | −9.36102 | −0.416148 | ||||||||
\(507\) | − | 10.6412i | − | 0.472593i | ||||||
\(508\) | 0.759690i | 0.0337058i | ||||||||
\(509\) | −11.3764 | −0.504249 | −0.252125 | − | 0.967695i | \(-0.581129\pi\) | ||||
−0.252125 | + | 0.967695i | \(0.581129\pi\) | |||||||
\(510\) | −1.83754 | − | 11.6753i | −0.0813676 | − | 0.516989i | ||||
\(511\) | 28.3862 | 1.25573 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.07548 | −0.179937 | ||||||||
\(514\) | −11.5996 | −0.511637 | ||||||||
\(515\) | −8.17891 | + | 1.28726i | −0.360406 | + | 0.0567233i | ||||
\(516\) | 4.46572i | 0.196592i | ||||||||
\(517\) | − | 64.1216i | − | 2.82007i | ||||||
\(518\) | 12.5108 | − | 1.93100i | 0.549695 | − | 0.0848433i | ||||
\(519\) | −1.56245 | −0.0685840 | ||||||||
\(520\) | 3.39246 | − | 0.533931i | 0.148769 | − | 0.0234144i | ||||
\(521\) | −12.3545 | −0.541259 | −0.270630 | − | 0.962684i | \(-0.587232\pi\) | ||||
−0.270630 | + | 0.962684i | \(0.587232\pi\) | |||||||
\(522\) | − | 6.89042i | − | 0.301586i | ||||||
\(523\) | −2.03723 | −0.0890820 | −0.0445410 | − | 0.999008i | \(-0.514183\pi\) | ||||
−0.0445410 | + | 0.999008i | \(0.514183\pi\) | |||||||
\(524\) | − | 17.8737i | − | 0.780815i | ||||||
\(525\) | 9.90257 | − | 3.19625i | 0.432184 | − | 0.139496i | ||||
\(526\) | − | 1.31327i | − | 0.0572613i | ||||||
\(527\) | 43.3162i | 1.88688i | ||||||||
\(528\) | 6.52056i | 0.283771i | ||||||||
\(529\) | −20.9390 | −0.910392 | ||||||||
\(530\) | 2.26587 | + | 14.3968i | 0.0984232 | + | 0.625356i | ||||
\(531\) | 11.0304i | 0.478677i | ||||||||
\(532\) | −8.48158 | −0.367723 | ||||||||
\(533\) | −10.3862 | −0.449878 | ||||||||
\(534\) | −7.15877 | −0.309790 | ||||||||
\(535\) | −2.36459 | − | 15.0240i | −0.102230 | − | 0.649545i | ||||
\(536\) | 11.8535i | 0.511992i | ||||||||
\(537\) | −12.2571 | −0.528931 | ||||||||
\(538\) | −16.7383 | −0.721641 | ||||||||
\(539\) | 17.4029 | 0.749595 | ||||||||
\(540\) | 0.347650 | + | 2.20888i | 0.0149605 | + | 0.0950550i | ||||
\(541\) | − | 18.9129i | − | 0.813129i | −0.913622 | − | 0.406564i | \(-0.866727\pi\) | ||
0.913622 | − | 0.406564i | \(-0.133273\pi\) | |||||||
\(542\) | −27.8757 | −1.19736 | ||||||||
\(543\) | − | 18.8971i | − | 0.810952i | ||||||
\(544\) | 5.28561 | 0.226619 | ||||||||
\(545\) | 6.24071 | + | 39.6519i | 0.267323 | + | 1.69850i | ||||
\(546\) | −3.19625 | −0.136787 | ||||||||
\(547\) | −14.2804 | −0.610588 | −0.305294 | − | 0.952258i | \(-0.598755\pi\) | ||||
−0.305294 | + | 0.952258i | \(0.598755\pi\) | |||||||
\(548\) | − | 7.88841i | − | 0.336976i | ||||||
\(549\) | 4.91211i | 0.209644i | ||||||||
\(550\) | 31.0266 | − | 10.0145i | 1.32298 | − | 0.427019i | ||||
\(551\) | 28.0818 | 1.19632 | ||||||||
\(552\) | − | 1.43562i | − | 0.0611039i | ||||||
\(553\) | 5.74901 | 0.244473 | ||||||||
\(554\) | 18.0505 | 0.766893 | ||||||||
\(555\) | 12.9563 | − | 4.13946i | 0.549963 | − | 0.175710i | ||||
\(556\) | −17.6834 | −0.749943 | ||||||||
\(557\) | −2.04249 | −0.0865433 | −0.0432716 | − | 0.999063i | \(-0.513778\pi\) | ||||
−0.0432716 | + | 0.999063i | \(0.513778\pi\) | |||||||
\(558\) | − | 8.19513i | − | 0.346927i | ||||||
\(559\) | −6.85859 | −0.290087 | ||||||||
\(560\) | 0.723502 | + | 4.59695i | 0.0305735 | + | 0.194256i | ||||
\(561\) | 34.4651i | 1.45512i | ||||||||
\(562\) | − | 3.12679i | − | 0.131896i | ||||||
\(563\) | −5.77225 | −0.243271 | −0.121636 | − | 0.992575i | \(-0.538814\pi\) | ||||
−0.121636 | + | 0.992575i | \(0.538814\pi\) | |||||||
\(564\) | 9.83376 | 0.414076 | ||||||||
\(565\) | 34.5350 | − | 5.43538i | 1.45290 | − | 0.228668i | ||||
\(566\) | −13.1469 | −0.552606 | ||||||||
\(567\) | − | 2.08112i | − | 0.0873990i | ||||||
\(568\) | −6.07887 | −0.255064 | ||||||||
\(569\) | − | 16.6017i | − | 0.695978i | −0.937499 | − | 0.347989i | \(-0.886865\pi\) | ||
0.937499 | − | 0.347989i | \(-0.113135\pi\) | |||||||
\(570\) | −9.00224 | + | 1.41684i | −0.377062 | + | 0.0593449i | ||||
\(571\) | −7.10926 | −0.297513 | −0.148757 | − | 0.988874i | \(-0.547527\pi\) | ||||
−0.148757 | + | 0.988874i | \(0.547527\pi\) | |||||||
\(572\) | −10.0145 | −0.418726 | ||||||||
\(573\) | −8.66659 | −0.362052 | ||||||||
\(574\) | − | 14.0738i | − | 0.587431i | ||||||
\(575\) | −6.83106 | + | 2.20486i | −0.284875 | + | 0.0919491i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −25.8359 | −1.07556 | −0.537782 | − | 0.843084i | \(-0.680738\pi\) | ||||
−0.537782 | + | 0.843084i | \(0.680738\pi\) | |||||||
\(578\) | 10.9377 | 0.454947 | ||||||||
\(579\) | − | 14.0122i | − | 0.582328i | ||||||
\(580\) | −2.39545 | − | 15.2201i | −0.0994658 | − | 0.631980i | ||||
\(581\) | −33.0531 | −1.37127 | ||||||||
\(582\) | − | 19.0806i | − | 0.790916i | ||||||
\(583\) | − | 42.4990i | − | 1.76013i | ||||||
\(584\) | 13.6398i | 0.564420i | ||||||||
\(585\) | −3.39246 | + | 0.533931i | −0.140261 | + | 0.0220753i | ||||
\(586\) | − | 17.8889i | − | 0.738983i | ||||||
\(587\) | −8.21612 | −0.339116 | −0.169558 | − | 0.985520i | \(-0.554234\pi\) | ||||
−0.169558 | + | 0.985520i | \(0.554234\pi\) | |||||||
\(588\) | 2.66892i | 0.110065i | ||||||||
\(589\) | 33.3991 | 1.37619 | ||||||||
\(590\) | 3.83470 | + | 24.3647i | 0.157872 | + | 1.00308i | ||||
\(591\) | −20.7652 | −0.854167 | ||||||||
\(592\) | 0.927865 | + | 6.01158i | 0.0381350 | + | 0.247074i | ||||
\(593\) | − | 26.1388i | − | 1.07339i | −0.843776 | − | 0.536696i | \(-0.819672\pi\) | ||
0.843776 | − | 0.536696i | \(-0.180328\pi\) | |||||||
\(594\) | − | 6.52056i | − | 0.267542i | ||||||
\(595\) | 3.82415 | + | 24.2977i | 0.156775 | + | 0.996107i | ||||
\(596\) | −0.543289 | −0.0222540 | ||||||||
\(597\) | −18.3572 | −0.751312 | ||||||||
\(598\) | 2.20486 | 0.0901635 | ||||||||
\(599\) | 15.3216 | 0.626024 | 0.313012 | − | 0.949749i | \(-0.398662\pi\) | ||||
0.313012 | + | 0.949749i | \(0.398662\pi\) | |||||||
\(600\) | 1.53583 | + | 4.75828i | 0.0627000 | + | 0.194256i | ||||
\(601\) | −31.7252 | −1.29410 | −0.647049 | − | 0.762449i | \(-0.723997\pi\) | ||||
−0.647049 | + | 0.762449i | \(0.723997\pi\) | |||||||
\(602\) | − | 9.29371i | − | 0.378783i | ||||||
\(603\) | − | 11.8535i | − | 0.482711i | ||||||
\(604\) | 7.98733 | 0.325000 | ||||||||
\(605\) | −69.6187 | + | 10.9571i | −2.83040 | + | 0.445470i | ||||
\(606\) | 1.62639i | 0.0660677i | ||||||||
\(607\) | 10.9926 | 0.446176 | 0.223088 | − | 0.974798i | \(-0.428386\pi\) | ||||
0.223088 | + | 0.974798i | \(0.428386\pi\) | |||||||
\(608\) | − | 4.07548i | − | 0.165283i | ||||||
\(609\) | 14.3398i | 0.581079i | ||||||||
\(610\) | 1.70769 | + | 10.8502i | 0.0691424 | + | 0.439313i | ||||
\(611\) | 15.1030i | 0.611002i | ||||||||
\(612\) | −5.28561 | −0.213658 | ||||||||
\(613\) | − | 1.14926i | − | 0.0464181i | −0.999731 | − | 0.0232091i | \(-0.992612\pi\) | ||
0.999731 | − | 0.0232091i | \(-0.00738834\pi\) | |||||||
\(614\) | 21.1435i | 0.853283i | ||||||||
\(615\) | −2.35102 | − | 14.9378i | −0.0948023 | − | 0.602350i | ||||
\(616\) | − | 13.5701i | − | 0.546755i | ||||||
\(617\) | − | 18.8902i | − | 0.760491i | −0.924886 | − | 0.380245i | \(-0.875840\pi\) | ||
0.924886 | − | 0.380245i | \(-0.124160\pi\) | |||||||
\(618\) | 3.70274i | 0.148946i | ||||||||
\(619\) | −44.0915 | −1.77219 | −0.886093 | − | 0.463507i | \(-0.846591\pi\) | ||||
−0.886093 | + | 0.463507i | \(0.846591\pi\) | |||||||
\(620\) | −2.84903 | − | 18.1020i | −0.114420 | − | 0.726995i | ||||
\(621\) | 1.43562i | 0.0576093i | ||||||||
\(622\) | 25.3383i | 1.01597i | ||||||||
\(623\) | 14.8983 | 0.596887 | ||||||||
\(624\) | − | 1.53583i | − | 0.0614824i | ||||||
\(625\) | 20.2824 | − | 14.6158i | 0.811298 | − | 0.584633i | ||||
\(626\) | −15.2774 | −0.610610 | ||||||||
\(627\) | 26.5744 | 1.06128 | ||||||||
\(628\) | − | 11.2296i | − | 0.448108i | ||||||
\(629\) | 4.90433 | + | 31.7749i | 0.195548 | + | 1.26695i | ||||
\(630\) | −0.723502 | − | 4.59695i | −0.0288250 | − | 0.183147i | ||||
\(631\) | − | 25.3338i | − | 1.00852i | −0.863552 | − | 0.504261i | \(-0.831765\pi\) | ||
0.863552 | − | 0.504261i | \(-0.168235\pi\) | |||||||
\(632\) | 2.76246i | 0.109885i | ||||||||
\(633\) | − | 1.37092i | − | 0.0544892i | ||||||
\(634\) | 26.3718i | 1.04736i | ||||||||
\(635\) | −0.264106 | − | 1.67806i | −0.0104807 | − | 0.0665919i | ||||
\(636\) | 6.51769 | 0.258443 | ||||||||
\(637\) | −4.09901 | −0.162409 | ||||||||
\(638\) | 44.9294i | 1.77877i | ||||||||
\(639\) | 6.07887 | 0.240477 | ||||||||
\(640\) | −2.20888 | + | 0.347650i | −0.0873135 | + | 0.0137421i | ||||
\(641\) | 24.8092 | 0.979904 | 0.489952 | − | 0.871749i | \(-0.337014\pi\) | ||||
0.489952 | + | 0.871749i | \(0.337014\pi\) | |||||||
\(642\) | −6.80165 | −0.268440 | ||||||||
\(643\) | −7.91150 | −0.311999 | −0.156000 | − | 0.987757i | \(-0.549860\pi\) | ||||
−0.156000 | + | 0.987757i | \(0.549860\pi\) | |||||||
\(644\) | 2.98769i | 0.117732i | ||||||||
\(645\) | −1.55250 | − | 9.86422i | −0.0611298 | − | 0.388403i | ||||
\(646\) | − | 21.5414i | − | 0.847535i | ||||||
\(647\) | 7.28378 | 0.286355 | 0.143177 | − | 0.989697i | \(-0.454268\pi\) | ||||
0.143177 | + | 0.989697i | \(0.454268\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | − | 71.9242i | − | 2.82327i | ||||||
\(650\) | −7.30791 | + | 2.35878i | −0.286640 | + | 0.0925188i | ||||
\(651\) | 17.0551i | 0.668441i | ||||||||
\(652\) | 8.05362 | 0.315404 | ||||||||
\(653\) | −10.3228 | −0.403961 | −0.201980 | − | 0.979390i | \(-0.564738\pi\) | ||||
−0.201980 | + | 0.979390i | \(0.564738\pi\) | |||||||
\(654\) | 17.9512 | 0.701946 | ||||||||
\(655\) | 6.21377 | + | 39.4807i | 0.242792 | + | 1.54264i | ||||
\(656\) | 6.76262 | 0.264036 | ||||||||
\(657\) | − | 13.6398i | − | 0.532140i | ||||||
\(658\) | −20.4653 | −0.797819 | ||||||||
\(659\) | −37.2866 | −1.45248 | −0.726240 | − | 0.687442i | \(-0.758734\pi\) | ||||
−0.726240 | + | 0.687442i | \(0.758734\pi\) | |||||||
\(660\) | −2.26687 | − | 14.4031i | −0.0882378 | − | 0.560641i | ||||
\(661\) | − | 38.1635i | − | 1.48439i | −0.670184 | − | 0.742195i | \(-0.733785\pi\) | ||
0.670184 | − | 0.742195i | \(-0.266215\pi\) | |||||||
\(662\) | − | 8.98662i | − | 0.349275i | ||||||
\(663\) | − | 8.11780i | − | 0.315269i | ||||||
\(664\) | − | 15.8823i | − | 0.616355i | ||||||
\(665\) | 18.7348 | − | 2.94862i | 0.726503 | − | 0.114342i | ||||
\(666\) | −0.927865 | − | 6.01158i | −0.0359540 | − | 0.232944i | ||||
\(667\) | − | 9.89200i | − | 0.383020i | ||||||
\(668\) | 12.7129 | 0.491876 | ||||||||
\(669\) | −10.4991 | −0.405919 | ||||||||
\(670\) | −4.12085 | − | 26.1829i | −0.159203 | − | 1.01153i | ||||
\(671\) | − | 32.0297i | − | 1.23649i | ||||||
\(672\) | 2.08112 | 0.0802811 | ||||||||
\(673\) | 36.4380i | 1.40458i | 0.711890 | + | 0.702291i | \(0.247840\pi\) | ||||
−0.711890 | + | 0.702291i | \(0.752160\pi\) | |||||||
\(674\) | − | 5.68375i | − | 0.218930i | ||||||
\(675\) | −1.53583 | − | 4.75828i | −0.0591141 | − | 0.183146i | ||||
\(676\) | −10.6412 | −0.409278 | ||||||||
\(677\) | 11.3104i | 0.434694i | 0.976094 | + | 0.217347i | \(0.0697403\pi\) | ||||
−0.976094 | + | 0.217347i | \(0.930260\pi\) | |||||||
\(678\) | − | 15.6346i | − | 0.600445i | ||||||
\(679\) | 39.7091i | 1.52390i | ||||||||
\(680\) | −11.6753 | + | 1.83754i | −0.447726 | + | 0.0704664i | ||||
\(681\) | 23.4274i | 0.897739i | ||||||||
\(682\) | 53.4368i | 2.04620i | ||||||||
\(683\) | −1.49065 | −0.0570380 | −0.0285190 | − | 0.999593i | \(-0.509079\pi\) | ||||
−0.0285190 | + | 0.999593i | \(0.509079\pi\) | |||||||
\(684\) | 4.07548i | 0.155830i | ||||||||
\(685\) | 2.74240 | + | 17.4245i | 0.104782 | + | 0.665757i | ||||
\(686\) | − | 20.1222i | − | 0.768270i | ||||||
\(687\) | − | 17.8860i | − | 0.682392i | ||||||
\(688\) | 4.46572 | 0.170254 | ||||||||
\(689\) | 10.0101i | 0.381353i | ||||||||
\(690\) | 0.499091 | + | 3.17110i | 0.0190001 | + | 0.120722i | ||||
\(691\) | 41.8658 | 1.59265 | 0.796325 | − | 0.604869i | \(-0.206775\pi\) | ||||
0.796325 | + | 0.604869i | \(0.206775\pi\) | |||||||
\(692\) | 1.56245i | 0.0593955i | ||||||||
\(693\) | 13.5701i | 0.515485i | ||||||||
\(694\) | 11.6758 | 0.443206 | ||||||||
\(695\) | 39.0605 | − | 6.14763i | 1.48165 | − | 0.233193i | ||||
\(696\) | −6.89042 | −0.261181 | ||||||||
\(697\) | 35.7446 | 1.35392 | ||||||||
\(698\) | −0.886357 | −0.0335491 | ||||||||
\(699\) | −4.01113 | −0.151715 | ||||||||
\(700\) | −3.19625 | − | 9.90257i | −0.120807 | − | 0.374282i | ||||
\(701\) | − | 18.0848i | − | 0.683052i | −0.939872 | − | 0.341526i | \(-0.889056\pi\) | ||
0.939872 | − | 0.341526i | \(-0.110944\pi\) | |||||||
\(702\) | 1.53583i | 0.0579662i | ||||||||
\(703\) | 24.5001 | − | 3.78149i | 0.924038 | − | 0.142622i | ||||
\(704\) | 6.52056 | 0.245753 | ||||||||
\(705\) | −21.7216 | + | 3.41870i | −0.818082 | + | 0.128756i | ||||
\(706\) | 24.8083 | 0.933674 | ||||||||
\(707\) | − | 3.38473i | − | 0.127296i | ||||||
\(708\) | 11.0304 | 0.414547 | ||||||||
\(709\) | 30.5559i | 1.14755i | 0.819013 | + | 0.573775i | \(0.194522\pi\) | ||||
−0.819013 | + | 0.573775i | \(0.805478\pi\) | |||||||
\(710\) | 13.4275 | − | 2.11332i | 0.503925 | − | 0.0793114i | ||||
\(711\) | − | 2.76246i | − | 0.103600i | ||||||
\(712\) | 7.15877i | 0.268286i | ||||||||
\(713\) | − | 11.7651i | − | 0.440605i | ||||||
\(714\) | 11.0000 | 0.411665 | ||||||||
\(715\) | 22.1207 | − | 3.48153i | 0.827269 | − | 0.130202i | ||||
\(716\) | 12.2571i | 0.458067i | ||||||||
\(717\) | −8.70690 | −0.325165 | ||||||||
\(718\) | −5.29404 | −0.197572 | ||||||||
\(719\) | 42.0288 | 1.56741 | 0.783704 | − | 0.621134i | \(-0.213328\pi\) | ||||
0.783704 | + | 0.621134i | \(0.213328\pi\) | |||||||
\(720\) | 2.20888 | − | 0.347650i | 0.0823200 | − | 0.0129561i | ||||
\(721\) | − | 7.70587i | − | 0.286982i | ||||||
\(722\) | 2.39045 | 0.0889635 | ||||||||
\(723\) | 15.6443 | 0.581816 | ||||||||
\(724\) | −18.8971 | −0.702305 | ||||||||
\(725\) | 10.5825 | + | 32.7866i | 0.393025 | + | 1.21766i | ||||
\(726\) | 31.5177i | 1.16973i | ||||||||
\(727\) | 43.0285 | 1.59584 | 0.797919 | − | 0.602765i | \(-0.205934\pi\) | ||||
0.797919 | + | 0.602765i | \(0.205934\pi\) | |||||||
\(728\) | 3.19625i | 0.118461i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −4.74188 | − | 30.1287i | −0.175505 | − | 1.11511i | ||||
\(731\) | 23.6040 | 0.873027 | ||||||||
\(732\) | 4.91211 | 0.181557 | ||||||||
\(733\) | 34.2793i | 1.26613i | 0.774097 | + | 0.633067i | \(0.218204\pi\) | ||||
−0.774097 | + | 0.633067i | \(0.781796\pi\) | |||||||
\(734\) | 0.716886i | 0.0264607i | ||||||||
\(735\) | −0.927850 | − | 5.89533i | −0.0342243 | − | 0.217452i | ||||
\(736\) | −1.43562 | −0.0529175 | ||||||||
\(737\) | 77.2913i | 2.84706i | ||||||||
\(738\) | −6.76262 | −0.248935 | ||||||||
\(739\) | 8.98532 | 0.330530 | 0.165265 | − | 0.986249i | \(-0.447152\pi\) | ||||
0.165265 | + | 0.986249i | \(0.447152\pi\) | |||||||
\(740\) | −4.13946 | − | 12.9563i | −0.152170 | − | 0.476282i | ||||
\(741\) | −6.25925 | −0.229939 | ||||||||
\(742\) | −13.5641 | −0.497954 | ||||||||
\(743\) | 3.60771i | 0.132354i | 0.997808 | + | 0.0661771i | \(0.0210802\pi\) | ||||
−0.997808 | + | 0.0661771i | \(0.978920\pi\) | |||||||
\(744\) | −8.19513 | −0.300448 | ||||||||
\(745\) | 1.20006 | − | 0.188874i | 0.0439668 | − | 0.00691982i | ||||
\(746\) | 1.21732i | 0.0445693i | ||||||||
\(747\) | 15.8823i | 0.581105i | ||||||||
\(748\) | 34.4651 | 1.26017 | ||||||||
\(749\) | 14.1551 | 0.517216 | ||||||||
\(750\) | −5.04668 | − | 9.97653i | −0.184279 | − | 0.364291i | ||||
\(751\) | 13.5278 | 0.493635 | 0.246817 | − | 0.969062i | \(-0.420615\pi\) | ||||
0.246817 | + | 0.969062i | \(0.420615\pi\) | |||||||
\(752\) | − | 9.83376i | − | 0.358600i | ||||||
\(753\) | 9.35179 | 0.340798 | ||||||||
\(754\) | − | 10.5825i | − | 0.385393i | ||||||
\(755\) | −17.6430 | + | 2.77679i | −0.642096 | + | 0.101058i | ||||
\(756\) | −2.08112 | −0.0756897 | ||||||||
\(757\) | −11.9133 | −0.432995 | −0.216497 | − | 0.976283i | \(-0.569463\pi\) | ||||
−0.216497 | + | 0.976283i | \(0.569463\pi\) | |||||||
\(758\) | −33.1425 | −1.20379 | ||||||||
\(759\) | − | 9.36102i | − | 0.339783i | ||||||
\(760\) | 1.41684 | + | 9.00224i | 0.0513942 | + | 0.326546i | ||||
\(761\) | 32.0203 | 1.16074 | 0.580368 | − | 0.814354i | \(-0.302909\pi\) | ||||
0.580368 | + | 0.814354i | \(0.302909\pi\) | |||||||
\(762\) | −0.759690 | −0.0275207 | ||||||||
\(763\) | −37.3586 | −1.35247 | ||||||||
\(764\) | 8.66659i | 0.313546i | ||||||||
\(765\) | 11.6753 | − | 1.83754i | 0.422120 | − | 0.0664364i | ||||
\(766\) | −8.54131 | −0.308610 | ||||||||
\(767\) | 16.9408i | 0.611696i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 34.1223i | 1.23048i | 0.788339 | + | 0.615241i | \(0.210941\pi\) | ||||
−0.788339 | + | 0.615241i | \(0.789059\pi\) | |||||||
\(770\) | 4.71764 | + | 29.9747i | 0.170012 | + | 1.08021i | ||||
\(771\) | − | 11.5996i | − | 0.417750i | ||||||
\(772\) | −14.0122 | −0.504311 | ||||||||
\(773\) | − | 48.7174i | − | 1.75224i | −0.482090 | − | 0.876122i | \(-0.660122\pi\) | ||
0.482090 | − | 0.876122i | \(-0.339878\pi\) | |||||||
\(774\) | −4.46572 | −0.160517 | ||||||||
\(775\) | 12.5863 | + | 38.9947i | 0.452114 | + | 1.40073i | ||||
\(776\) | −19.0806 | −0.684954 | ||||||||
\(777\) | 1.93100 | + | 12.5108i | 0.0692743 | + | 0.448824i | ||||
\(778\) | − | 23.0234i | − | 0.825429i | ||||||
\(779\) | − | 27.5609i | − | 0.987473i | ||||||
\(780\) | 0.533931 | + | 3.39246i | 0.0191178 | + | 0.121470i | ||||
\(781\) | −39.6377 | −1.41835 | ||||||||
\(782\) | −7.58810 | −0.271350 | ||||||||
\(783\) | 6.89042 | 0.246244 | ||||||||
\(784\) | 2.66892 | 0.0953187 | ||||||||
\(785\) | 3.90395 | + | 24.8047i | 0.139338 | + | 0.885318i | ||||
\(786\) | 17.8737 | 0.637532 | ||||||||
\(787\) | 9.85605i | 0.351330i | 0.984450 | + | 0.175665i | \(0.0562076\pi\) | ||||
−0.984450 | + | 0.175665i | \(0.943792\pi\) | |||||||
\(788\) | 20.7652i | 0.739731i | ||||||||
\(789\) | 1.31327 | 0.0467536 | ||||||||
\(790\) | −0.960367 | − | 6.10193i | −0.0341683 | − | 0.217097i | ||||
\(791\) | 32.5376i | 1.15690i | ||||||||
\(792\) | −6.52056 | −0.231698 | ||||||||
\(793\) | 7.54416i | 0.267901i | ||||||||
\(794\) | − | 16.8160i | − | 0.596779i | ||||||
\(795\) | −14.3968 | + | 2.26587i | −0.510601 | + | 0.0803622i | ||||
\(796\) | 18.3572i | 0.650655i | ||||||||
\(797\) | −40.2825 | −1.42688 | −0.713439 | − | 0.700717i | \(-0.752863\pi\) | ||||
−0.713439 | + | 0.700717i | \(0.752863\pi\) | |||||||
\(798\) | − | 8.48158i | − | 0.300245i | ||||||
\(799\) | − | 51.9774i | − | 1.83883i | ||||||
\(800\) | 4.75828 | − | 1.53583i | 0.168231 | − | 0.0542998i | ||||
\(801\) | − | 7.15877i | − | 0.252943i | ||||||
\(802\) | − | 19.6354i | − | 0.693349i | ||||||
\(803\) | 88.9393i | 3.13860i | ||||||||
\(804\) | −11.8535 | −0.418040 | ||||||||
\(805\) | −1.03867 | − | 6.59945i | −0.0366083 | − | 0.232600i | ||||
\(806\) | − | 12.5863i | − | 0.443334i | ||||||
\(807\) | − | 16.7383i | − | 0.589217i | ||||||
\(808\) | 1.62639 | 0.0572163 | ||||||||
\(809\) | 10.5881i | 0.372257i | 0.982525 | + | 0.186128i | \(0.0595940\pi\) | ||||
−0.982525 | + | 0.186128i | \(0.940406\pi\) | |||||||
\(810\) | −2.20888 | + | 0.347650i | −0.0776120 | + | 0.0122152i | ||||
\(811\) | 14.1487 | 0.496829 | 0.248414 | − | 0.968654i | \(-0.420091\pi\) | ||||
0.248414 | + | 0.968654i | \(0.420091\pi\) | |||||||
\(812\) | 14.3398 | 0.503229 | ||||||||
\(813\) | − | 27.8757i | − | 0.977642i | ||||||
\(814\) | 6.05020 | + | 39.1988i | 0.212059 | + | 1.37392i | ||||
\(815\) | −17.7895 | + | 2.79984i | −0.623138 | + | 0.0980740i | ||||
\(816\) | 5.28561i | 0.185033i | ||||||||
\(817\) | − | 18.1999i | − | 0.636736i | ||||||
\(818\) | 32.0465i | 1.12048i | ||||||||
\(819\) | − | 3.19625i | − | 0.111686i | ||||||
\(820\) | −14.9378 | + | 2.35102i | −0.521650 | + | 0.0821012i | ||||
\(821\) | −52.6633 | −1.83796 | −0.918981 | − | 0.394301i | \(-0.870987\pi\) | ||||
−0.918981 | + | 0.394301i | \(0.870987\pi\) | |||||||
\(822\) | 7.88841 | 0.275140 | ||||||||
\(823\) | − | 2.21515i | − | 0.0772153i | −0.999254 | − | 0.0386077i | \(-0.987708\pi\) | ||
0.999254 | − | 0.0386077i | \(-0.0122923\pi\) | |||||||
\(824\) | 3.70274 | 0.128991 | ||||||||
\(825\) | 10.0145 | + | 31.0266i | 0.348659 | + | 1.08021i | ||||
\(826\) | −22.9556 | −0.798726 | ||||||||
\(827\) | 34.6262 | 1.20407 | 0.602036 | − | 0.798469i | \(-0.294356\pi\) | ||||
0.602036 | + | 0.798469i | \(0.294356\pi\) | |||||||
\(828\) | 1.43562 | 0.0498911 | ||||||||
\(829\) | − | 21.2800i | − | 0.739084i | −0.929214 | − | 0.369542i | \(-0.879515\pi\) | ||
0.929214 | − | 0.369542i | \(-0.120485\pi\) | |||||||
\(830\) | 5.52149 | + | 35.0822i | 0.191654 | + | 1.21772i | ||||
\(831\) | 18.0505i | 0.626165i | ||||||||
\(832\) | −1.53583 | −0.0532453 | ||||||||
\(833\) | 14.1069 | 0.488775 | ||||||||
\(834\) | − | 17.6834i | − | 0.612326i | ||||||
\(835\) | −28.0812 | + | 4.41963i | −0.971790 | + | 0.152948i | ||||
\(836\) | − | 26.5744i | − | 0.919095i | ||||||
\(837\) | 8.19513 | 0.283265 | ||||||||
\(838\) | 3.81945 | 0.131941 | ||||||||
\(839\) | −30.1498 | −1.04089 | −0.520443 | − | 0.853896i | \(-0.674233\pi\) | ||||
−0.520443 | + | 0.853896i | \(0.674233\pi\) | |||||||
\(840\) | −4.59695 | + | 0.723502i | −0.158610 | + | 0.0249632i | ||||
\(841\) | −18.4780 | −0.637171 | ||||||||
\(842\) | 10.0113i | 0.345012i | ||||||||
\(843\) | 3.12679 | 0.107692 | ||||||||
\(844\) | −1.37092 | −0.0471891 | ||||||||
\(845\) | 23.5052 | − | 3.69942i | 0.808602 | − | 0.127264i | ||||
\(846\) | 9.83376i | 0.338092i | ||||||||
\(847\) | − | 65.5922i | − | 2.25378i | ||||||
\(848\) | − | 6.51769i | − | 0.223818i | ||||||
\(849\) | − | 13.1469i | − | 0.451201i | ||||||
\(850\) | 25.1504 | − | 8.11780i | 0.862652 | − | 0.278438i | ||||
\(851\) | −1.33206 | − | 8.63032i | −0.0456623 | − | 0.295843i | ||||
\(852\) | − | 6.07887i | − | 0.208259i | ||||||
\(853\) | 48.4265 | 1.65809 | 0.829046 | − | 0.559180i | \(-0.188884\pi\) | ||||
0.829046 | + | 0.559180i | \(0.188884\pi\) | |||||||
\(854\) | −10.2227 | −0.349814 | ||||||||
\(855\) | −1.41684 | − | 9.00224i | −0.0484549 | − | 0.307870i | ||||
\(856\) | 6.80165i | 0.232476i | ||||||||
\(857\) | 1.36575 | 0.0466531 | 0.0233265 | − | 0.999728i | \(-0.492574\pi\) | ||||
0.0233265 | + | 0.999728i | \(0.492574\pi\) | |||||||
\(858\) | − | 10.0145i | − | 0.341889i | ||||||
\(859\) | − | 24.4949i | − | 0.835754i | −0.908504 | − | 0.417877i | \(-0.862774\pi\) | ||
0.908504 | − | 0.417877i | \(-0.137226\pi\) | |||||||
\(860\) | −9.86422 | + | 1.55250i | −0.336367 | + | 0.0529400i | ||||
\(861\) | 14.0738 | 0.479635 | ||||||||
\(862\) | 5.28491i | 0.180005i | ||||||||
\(863\) | 24.3928i | 0.830341i | 0.909744 | + | 0.415170i | \(0.136278\pi\) | ||||
−0.909744 | + | 0.415170i | \(0.863722\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | −0.543186 | − | 3.45126i | −0.0184689 | − | 0.117347i | ||||
\(866\) | 23.3433i | 0.793238i | ||||||||
\(867\) | 10.9377i | 0.371463i | ||||||||
\(868\) | 17.0551 | 0.578887 | ||||||||
\(869\) | 18.0128i | 0.611041i | ||||||||
\(870\) | 15.2201 | − | 2.39545i | 0.516010 | − | 0.0812135i | ||||
\(871\) | − | 18.2049i | − | 0.616850i | ||||||
\(872\) | − | 17.9512i | − | 0.607903i | ||||||
\(873\) | 19.0806 | 0.645781 | ||||||||
\(874\) | 5.85082i | 0.197907i | ||||||||
\(875\) | 10.5028 | + | 20.7624i | 0.355058 | + | 0.701897i | ||||
\(876\) | −13.6398 | −0.460847 | ||||||||
\(877\) | 1.49594i | 0.0505142i | 0.999681 | + | 0.0252571i | \(0.00804045\pi\) | ||||
−0.999681 | + | 0.0252571i | \(0.991960\pi\) | |||||||
\(878\) | 20.3738i | 0.687582i | ||||||||
\(879\) | 17.8889 | 0.603377 | ||||||||
\(880\) | −14.4031 | + | 2.26687i | −0.485529 | + | 0.0764162i | ||||
\(881\) | −19.4185 | −0.654224 | −0.327112 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327112 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(882\) | −2.66892 | −0.0898673 | ||||||||
\(883\) | 33.5516 | 1.12910 | 0.564551 | − | 0.825398i | \(-0.309049\pi\) | ||||
0.564551 | + | 0.825398i | \(0.309049\pi\) | |||||||
\(884\) | −8.11780 | −0.273031 | ||||||||
\(885\) | −24.3647 | + | 3.83470i | −0.819011 | + | 0.128902i | ||||
\(886\) | 4.11658i | 0.138299i | ||||||||
\(887\) | 7.43914i | 0.249782i | 0.992170 | + | 0.124891i | \(0.0398581\pi\) | ||||
−0.992170 | + | 0.124891i | \(0.960142\pi\) | |||||||
\(888\) | −6.01158 | + | 0.927865i | −0.201735 | + | 0.0311371i | ||||
\(889\) | 1.58101 | 0.0530254 | ||||||||
\(890\) | −2.48874 | − | 15.8128i | −0.0834228 | − | 0.530048i | ||||
\(891\) | 6.52056 | 0.218447 | ||||||||
\(892\) | 10.4991i | 0.351537i | ||||||||
\(893\) | −40.0773 | −1.34114 | ||||||||
\(894\) | − | 0.543289i | − | 0.0181703i | ||||||
\(895\) | −4.26116 | − | 27.0743i | −0.142435 | − | 0.904995i | ||||
\(896\) | − | 2.08112i | − | 0.0695255i | ||||||
\(897\) | 2.20486i | 0.0736182i | ||||||||
\(898\) | 13.0977i | 0.437075i | ||||||||
\(899\) | −56.4679 | −1.88331 | ||||||||
\(900\) | −4.75828 | + | 1.53583i | −0.158609 | + | 0.0511944i | ||||
\(901\) | − | 34.4500i | − | 1.14769i | ||||||
\(902\) | 44.0961 | 1.46824 | ||||||||
\(903\) | 9.29371 | 0.309275 | ||||||||
\(904\) | −15.6346 | −0.520000 | ||||||||
\(905\) | 41.7414 | − | 6.56957i | 1.38753 | − | 0.218380i | ||||
\(906\) | 7.98733i | 0.265361i | ||||||||
\(907\) | −34.3902 | −1.14191 | −0.570953 | − | 0.820983i | \(-0.693426\pi\) | ||||
−0.570953 | + | 0.820983i | \(0.693426\pi\) | |||||||
\(908\) | 23.4274 | 0.777465 | ||||||||
\(909\) | −1.62639 | −0.0539441 | ||||||||
\(910\) | −1.11118 | − | 7.06013i | −0.0368351 | − | 0.234041i | ||||
\(911\) | − | 0.581529i | − | 0.0192669i | −0.999954 | − | 0.00963346i | \(-0.996934\pi\) | ||
0.999954 | − | 0.00963346i | \(-0.00306647\pi\) | |||||||
\(912\) | 4.07548 | 0.134953 | ||||||||
\(913\) | − | 103.562i | − | 3.42739i | ||||||
\(914\) | 12.4923 | 0.413209 | ||||||||
\(915\) | −10.8502 | + | 1.70769i | −0.358698 | + | 0.0564545i | ||||
\(916\) | −17.8860 | −0.590969 | ||||||||
\(917\) | −37.1973 | −1.22836 | ||||||||
\(918\) | − | 5.28561i | − | 0.174451i | ||||||
\(919\) | − | 0.382311i | − | 0.0126113i | −0.999980 | − | 0.00630564i | \(-0.997993\pi\) | ||
0.999980 | − | 0.00630564i | \(-0.00200716\pi\) | |||||||
\(920\) | 3.17110 | − | 0.499091i | 0.104548 | − | 0.0164545i | ||||
\(921\) | −21.1435 | −0.696702 | ||||||||
\(922\) | − | 1.72410i | − | 0.0567803i | ||||||
\(923\) | 9.33612 | 0.307302 | ||||||||
\(924\) | 13.5701 | 0.446423 | ||||||||
\(925\) | 13.6478 | + | 27.1797i | 0.448737 | + | 0.893664i | ||||
\(926\) | 17.2119 | 0.565617 | ||||||||
\(927\) | −3.70274 | −0.121614 | ||||||||
\(928\) | 6.89042i | 0.226189i | ||||||||
\(929\) | 11.2764 | 0.369967 | 0.184983 | − | 0.982742i | \(-0.440777\pi\) | ||||
0.184983 | + | 0.982742i | \(0.440777\pi\) | |||||||
\(930\) | 18.1020 | − | 2.84903i | 0.593589 | − | 0.0934234i | ||||
\(931\) | − | 10.8771i | − | 0.356484i | ||||||
\(932\) | 4.01113i | 0.131389i | ||||||||
\(933\) | −25.3383 | −0.829538 | ||||||||
\(934\) | 0.918102 | 0.0300412 | ||||||||
\(935\) | −76.1293 | + | 11.9818i | −2.48969 | + | 0.391846i | ||||
\(936\) | 1.53583 | 0.0502002 | ||||||||
\(937\) | 31.5133i | 1.02949i | 0.857342 | + | 0.514747i | \(0.172114\pi\) | ||||
−0.857342 | + | 0.514747i | \(0.827886\pi\) | |||||||
\(938\) | 24.6685 | 0.805457 | ||||||||
\(939\) | − | 15.2774i | − | 0.498561i | ||||||
\(940\) | 3.41870 | + | 21.7216i | 0.111506 | + | 0.708480i | ||||
\(941\) | 28.8572 | 0.940719 | 0.470360 | − | 0.882475i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882475i | \(0.344124\pi\) | |||||||
\(942\) | 11.2296 | 0.365879 | ||||||||
\(943\) | −9.70852 | −0.316153 | ||||||||
\(944\) | − | 11.0304i | − | 0.359008i | ||||||
\(945\) | 4.59695 | − | 0.723502i | 0.149539 | − | 0.0235355i | ||||
\(946\) | 29.1190 | 0.946740 | ||||||||
\(947\) | 4.66293 | 0.151525 | 0.0757625 | − | 0.997126i | \(-0.475861\pi\) | ||||
0.0757625 | + | 0.997126i | \(0.475861\pi\) | |||||||
\(948\) | −2.76246 | −0.0897204 | ||||||||
\(949\) | − | 20.9485i | − | 0.680016i | ||||||
\(950\) | −6.25925 | − | 19.3923i | −0.203077 | − | 0.629169i | ||||
\(951\) | −26.3718 | −0.855163 | ||||||||
\(952\) | − | 11.0000i | − | 0.356512i | ||||||
\(953\) | − | 3.87816i | − | 0.125626i | −0.998025 | − | 0.0628130i | \(-0.979993\pi\) | ||
0.998025 | − | 0.0628130i | \(-0.0200072\pi\) | |||||||
\(954\) | 6.51769i | 0.211018i | ||||||||
\(955\) | −3.01294 | − | 19.1434i | −0.0974964 | − | 0.619467i | ||||
\(956\) | 8.70690i | 0.281601i | ||||||||
\(957\) | −44.9294 | −1.45236 | ||||||||
\(958\) | − | 16.4565i | − | 0.531687i | ||||||
\(959\) | −16.4168 | −0.530125 | ||||||||
\(960\) | −0.347650 | − | 2.20888i | −0.0112203 | − | 0.0712912i | ||||
\(961\) | −36.1601 | −1.16645 | ||||||||
\(962\) | −1.42504 | − | 9.23277i | −0.0459452 | − | 0.297676i | ||||
\(963\) | − | 6.80165i | − | 0.219180i | ||||||
\(964\) | − | 15.6443i | − | 0.503868i | ||||||
\(965\) | 30.9513 | − | 4.87134i | 0.996357 | − | 0.156814i | ||||
\(966\) | −2.98769 | −0.0961275 | ||||||||
\(967\) | 7.25231 | 0.233219 | 0.116609 | − | 0.993178i | \(-0.462797\pi\) | ||||
0.116609 | + | 0.993178i | \(0.462797\pi\) | |||||||
\(968\) | 31.5177 | 1.01302 | ||||||||
\(969\) | 21.5414 | 0.692010 | ||||||||
\(970\) | 42.1467 | − | 6.63336i | 1.35325 | − | 0.212984i | ||||
\(971\) | −25.7900 | −0.827640 | −0.413820 | − | 0.910359i | \(-0.635806\pi\) | ||||
−0.413820 | + | 0.910359i | \(0.635806\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 36.8013i | 1.17980i | ||||||||
\(974\) | −0.244062 | −0.00782025 | ||||||||
\(975\) | −2.35878 | − | 7.30791i | −0.0755413 | − | 0.234040i | ||||
\(976\) | − | 4.91211i | − | 0.157233i | ||||||
\(977\) | −22.9259 | −0.733464 | −0.366732 | − | 0.930327i | \(-0.619523\pi\) | ||||
−0.366732 | + | 0.930327i | \(0.619523\pi\) | |||||||
\(978\) | 8.05362i | 0.257526i | ||||||||
\(979\) | 46.6792i | 1.49187i | ||||||||
\(980\) | −5.89533 | + | 0.927850i | −0.188319 | + | 0.0296391i | ||||
\(981\) | 17.9512i | 0.573136i | ||||||||
\(982\) | 10.1056 | 0.322483 | ||||||||
\(983\) | − | 6.33377i | − | 0.202016i | −0.994886 | − | 0.101008i | \(-0.967793\pi\) | ||
0.994886 | − | 0.101008i | \(-0.0322068\pi\) | |||||||
\(984\) | 6.76262i | 0.215584i | ||||||||
\(985\) | −7.21902 | − | 45.8679i | −0.230017 | − | 1.46147i | ||||
\(986\) | 36.4201i | 1.15985i | ||||||||
\(987\) | − | 20.4653i | − | 0.651417i | ||||||
\(988\) | 6.25925i | 0.199133i | ||||||||
\(989\) | −6.41105 | −0.203860 | ||||||||
\(990\) | 14.4031 | − | 2.26687i | 0.457761 | − | 0.0720458i | ||||
\(991\) | 29.5353i | 0.938219i | 0.883140 | + | 0.469109i | \(0.155425\pi\) | ||||
−0.883140 | + | 0.469109i | \(0.844575\pi\) | |||||||
\(992\) | 8.19513i | 0.260195i | ||||||||
\(993\) | 8.98662 | 0.285182 | ||||||||
\(994\) | 12.6509i | 0.401262i | ||||||||
\(995\) | −6.38189 | − | 40.5489i | −0.202319 | − | 1.28549i | ||||
\(996\) | 15.8823 | 0.503251 | ||||||||
\(997\) | −55.4664 | −1.75664 | −0.878319 | − | 0.478074i | \(-0.841335\pi\) | ||||
−0.878319 | + | 0.478074i | \(0.841335\pi\) | |||||||
\(998\) | − | 4.16552i | − | 0.131857i | ||||||
\(999\) | 6.01158 | − | 0.927865i | 0.190198 | − | 0.0293563i |
(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 | 1110.2.e.d.739.9 | yes | 16 | |
3.2 | odd | 2 | 3330.2.e.e.739.15 | 16 | |||
5.4 | even | 2 | 1110.2.e.c.739.8 | ✓ | 16 | ||
15.14 | odd | 2 | 3330.2.e.f.739.1 | 16 | |||
37.36 | even | 2 | 1110.2.e.c.739.16 | yes | 16 | ||
111.110 | odd | 2 | 3330.2.e.f.739.2 | 16 | |||
185.184 | even | 2 | inner | 1110.2.e.d.739.1 | yes | 16 | |
555.554 | odd | 2 | 3330.2.e.e.739.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.e.c.739.8 | ✓ | 16 | 5.4 | even | 2 | ||
1110.2.e.c.739.16 | yes | 16 | 37.36 | even | 2 | ||
1110.2.e.d.739.1 | yes | 16 | 185.184 | even | 2 | inner | |
1110.2.e.d.739.9 | yes | 16 | 1.1 | even | 1 | trivial | |
3330.2.e.e.739.15 | 16 | 3.2 | odd | 2 | |||
3330.2.e.e.739.16 | 16 | 555.554 | odd | 2 | |||
3330.2.e.f.739.1 | 16 | 15.14 | odd | 2 | |||
3330.2.e.f.739.2 | 16 | 111.110 | odd | 2 |