Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [228,2,Mod(191,228)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(228, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("228.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 228 = 2^{2} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 228.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: | \(1.82058916609\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.35 | ||
Character | \(\chi\) | \(=\) | 228.191 |
Dual form | 228.2.c.a.191.36 |
$q$-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 \(\left(\mathbb{Z}/228\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) | \(115\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41330 | − | 0.0507215i | 0.999357 | − | 0.0358655i | ||||
\(3\) | 0.756793 | + | 1.55797i | 0.436935 | + | 0.899493i | ||||
\(4\) | 1.99485 | − | 0.143370i | 0.997427 | − | 0.0716848i | ||||
\(5\) | 0.762708i | 0.341093i | 0.985350 | + | 0.170547i | \(0.0545534\pi\) | ||||
−0.985350 | + | 0.170547i | \(0.945447\pi\) | |||||||
\(6\) | 1.14860 | + | 2.16350i | 0.468914 | + | 0.883244i | ||||
\(7\) | − | 3.87706i | − | 1.46539i | −0.680556 | − | 0.732696i | \(-0.738262\pi\) | ||
0.680556 | − | 0.732696i | \(-0.261738\pi\) | |||||||
\(8\) | 2.81206 | − | 0.303807i | 0.994215 | − | 0.107412i | ||||
\(9\) | −1.85453 | + | 2.35812i | −0.618176 | + | 0.786039i | ||||
\(10\) | 0.0386857 | + | 1.07794i | 0.0122335 | + | 0.340874i | ||||
\(11\) | −5.11004 | −1.54073 | −0.770367 | − | 0.637601i | \(-0.779927\pi\) | ||||
−0.770367 | + | 0.637601i | \(0.779927\pi\) | |||||||
\(12\) | 1.73306 | + | 2.99942i | 0.500290 | + | 0.865858i | ||||
\(13\) | −0.587034 | −0.162814 | −0.0814070 | − | 0.996681i | \(-0.525941\pi\) | ||||
−0.0814070 | + | 0.996681i | \(0.525941\pi\) | |||||||
\(14\) | −0.196650 | − | 5.47947i | −0.0525570 | − | 1.46445i | ||||
\(15\) | −1.18828 | + | 0.577212i | −0.306811 | + | 0.149036i | ||||
\(16\) | 3.95889 | − | 0.572003i | 0.989723 | − | 0.143001i | ||||
\(17\) | 1.64637i | 0.399303i | 0.979867 | + | 0.199651i | \(0.0639809\pi\) | ||||
−0.979867 | + | 0.199651i | \(0.936019\pi\) | |||||||
\(18\) | −2.50141 | + | 3.42680i | −0.589587 | + | 0.807705i | ||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0.109349 | + | 1.52149i | 0.0244512 | + | 0.340216i | ||||
\(21\) | 6.04034 | − | 2.93413i | 1.31811 | − | 0.640280i | ||||
\(22\) | −7.22203 | + | 0.259189i | −1.53974 | + | 0.0552592i | ||||
\(23\) | −4.13228 | −0.861640 | −0.430820 | − | 0.902438i | \(-0.641776\pi\) | ||||
−0.430820 | + | 0.902438i | \(0.641776\pi\) | |||||||
\(24\) | 2.60147 | + | 4.15119i | 0.531023 | + | 0.847357i | ||||
\(25\) | 4.41828 | 0.883655 | ||||||||
\(26\) | −0.829657 | + | 0.0297752i | −0.162709 | + | 0.00583940i | ||||
\(27\) | −5.07737 | − | 1.10469i | −0.977140 | − | 0.212598i | ||||
\(28\) | −0.555853 | − | 7.73417i | −0.105046 | − | 1.46162i | ||||
\(29\) | 0.844401i | 0.156801i | 0.996922 | + | 0.0784007i | \(0.0249813\pi\) | ||||
−0.996922 | + | 0.0784007i | \(0.975019\pi\) | |||||||
\(30\) | −1.65012 | + | 0.876047i | −0.301269 | + | 0.159944i | ||||
\(31\) | − | 8.95324i | − | 1.60805i | −0.594596 | − | 0.804025i | \(-0.702688\pi\) | ||
0.594596 | − | 0.804025i | \(-0.297312\pi\) | |||||||
\(32\) | 5.56610 | − | 1.00921i | 0.983957 | − | 0.178406i | ||||
\(33\) | −3.86724 | − | 7.96127i | −0.673200 | − | 1.38588i | ||||
\(34\) | 0.0835061 | + | 2.32682i | 0.0143212 | + | 0.399046i | ||||
\(35\) | 2.95707 | 0.499835 | ||||||||
\(36\) | −3.36143 | + | 4.96999i | −0.560239 | + | 0.828331i | ||||
\(37\) | −1.82868 | −0.300633 | −0.150316 | − | 0.988638i | \(-0.548029\pi\) | ||||
−0.150316 | + | 0.988638i | \(0.548029\pi\) | |||||||
\(38\) | 0.0507215 | + | 1.41330i | 0.00822811 | + | 0.229268i | ||||
\(39\) | −0.444263 | − | 0.914580i | −0.0711390 | − | 0.146450i | ||||
\(40\) | 0.231716 | + | 2.14478i | 0.0366375 | + | 0.339120i | ||||
\(41\) | − | 4.99332i | − | 0.779826i | −0.920852 | − | 0.389913i | \(-0.872505\pi\) | ||
0.920852 | − | 0.389913i | \(-0.127495\pi\) | |||||||
\(42\) | 8.38801 | − | 4.45319i | 1.29430 | − | 0.687143i | ||||
\(43\) | 8.79674i | 1.34149i | 0.741688 | + | 0.670745i | \(0.234025\pi\) | ||||
−0.741688 | + | 0.670745i | \(0.765975\pi\) | |||||||
\(44\) | −10.1938 | + | 0.732624i | −1.53677 | + | 0.110447i | ||||
\(45\) | −1.79856 | − | 1.41446i | −0.268113 | − | 0.210856i | ||||
\(46\) | −5.84017 | + | 0.209595i | −0.861085 | + | 0.0309031i | ||||
\(47\) | 10.6216 | 1.54933 | 0.774663 | − | 0.632374i | \(-0.217919\pi\) | ||||
0.774663 | + | 0.632374i | \(0.217919\pi\) | |||||||
\(48\) | 3.88722 | + | 5.73494i | 0.561072 | + | 0.827767i | ||||
\(49\) | −8.03161 | −1.14737 | ||||||||
\(50\) | 6.24437 | − | 0.224101i | 0.883087 | − | 0.0316927i | ||||
\(51\) | −2.56499 | + | 1.24596i | −0.359170 | + | 0.174469i | ||||
\(52\) | −1.17105 | + | 0.0841628i | −0.162395 | + | 0.0116713i | ||||
\(53\) | 10.3008i | 1.41493i | 0.706750 | + | 0.707463i | \(0.250161\pi\) | ||||
−0.706750 | + | 0.707463i | \(0.749839\pi\) | |||||||
\(54\) | −7.23189 | − | 1.30373i | −0.984136 | − | 0.177415i | ||||
\(55\) | − | 3.89747i | − | 0.525534i | ||||||
\(56\) | −1.17788 | − | 10.9025i | −0.157401 | − | 1.45691i | ||||
\(57\) | −1.55797 | + | 0.756793i | −0.206358 | + | 0.100240i | ||||
\(58\) | 0.0428293 | + | 1.19340i | 0.00562376 | + | 0.156700i | ||||
\(59\) | −7.90462 | −1.02909 | −0.514547 | − | 0.857462i | \(-0.672040\pi\) | ||||
−0.514547 | + | 0.857462i | \(0.672040\pi\) | |||||||
\(60\) | −2.28768 | + | 1.32182i | −0.295338 | + | 0.170646i | ||||
\(61\) | 3.61610 | 0.462994 | 0.231497 | − | 0.972836i | \(-0.425638\pi\) | ||||
0.231497 | + | 0.972836i | \(0.425638\pi\) | |||||||
\(62\) | −0.454122 | − | 12.6537i | −0.0576735 | − | 1.60702i | ||||
\(63\) | 9.14257 | + | 7.19012i | 1.15186 | + | 0.905870i | ||||
\(64\) | 7.81540 | − | 1.70865i | 0.976925 | − | 0.213581i | ||||
\(65\) | − | 0.447736i | − | 0.0555348i | ||||||
\(66\) | −5.86939 | − | 11.0555i | −0.722472 | − | 1.36084i | ||||
\(67\) | − | 8.43168i | − | 1.03009i | −0.857162 | − | 0.515047i | \(-0.827775\pi\) | ||
0.857162 | − | 0.515047i | \(-0.172225\pi\) | |||||||
\(68\) | 0.236039 | + | 3.28426i | 0.0286239 | + | 0.398275i | ||||
\(69\) | −3.12728 | − | 6.43796i | −0.376480 | − | 0.775039i | ||||
\(70\) | 4.17923 | − | 0.149987i | 0.499514 | − | 0.0179268i | ||||
\(71\) | 5.12574 | 0.608313 | 0.304156 | − | 0.952622i | \(-0.401625\pi\) | ||||
0.304156 | + | 0.952622i | \(0.401625\pi\) | |||||||
\(72\) | −4.49864 | + | 7.19460i | −0.530170 | + | 0.847891i | ||||
\(73\) | −7.37979 | −0.863739 | −0.431869 | − | 0.901936i | \(-0.642146\pi\) | ||||
−0.431869 | + | 0.901936i | \(0.642146\pi\) | |||||||
\(74\) | −2.58448 | + | 0.0927532i | −0.300439 | + | 0.0107823i | ||||
\(75\) | 3.34372 | + | 6.88353i | 0.386100 | + | 0.794842i | ||||
\(76\) | 0.143370 | + | 1.99485i | 0.0164456 | + | 0.228826i | ||||
\(77\) | 19.8119i | 2.25778i | ||||||||
\(78\) | −0.674267 | − | 1.27005i | −0.0763458 | − | 0.143804i | ||||
\(79\) | 13.4309i | 1.51110i | 0.655093 | + | 0.755549i | \(0.272630\pi\) | ||||
−0.655093 | + | 0.755549i | \(0.727370\pi\) | |||||||
\(80\) | 0.436272 | + | 3.01948i | 0.0487766 | + | 0.337588i | ||||
\(81\) | −2.12144 | − | 8.74640i | −0.235716 | − | 0.971822i | ||||
\(82\) | −0.253269 | − | 7.05708i | −0.0279688 | − | 0.779325i | ||||
\(83\) | 6.07788 | 0.667134 | 0.333567 | − | 0.942726i | \(-0.391748\pi\) | ||||
0.333567 | + | 0.942726i | \(0.391748\pi\) | |||||||
\(84\) | 11.6289 | − | 6.71917i | 1.26882 | − | 0.733121i | ||||
\(85\) | −1.25570 | −0.136199 | ||||||||
\(86\) | 0.446183 | + | 12.4325i | 0.0481132 | + | 1.34063i | ||||
\(87\) | −1.31555 | + | 0.639037i | −0.141042 | + | 0.0685119i | ||||
\(88\) | −14.3697 | + | 1.55246i | −1.53182 | + | 0.165493i | ||||
\(89\) | 9.06338i | 0.960716i | 0.877073 | + | 0.480358i | \(0.159493\pi\) | ||||
−0.877073 | + | 0.480358i | \(0.840507\pi\) | |||||||
\(90\) | −2.61365 | − | 1.90784i | −0.275503 | − | 0.201104i | ||||
\(91\) | 2.27597i | 0.238586i | ||||||||
\(92\) | −8.24330 | + | 0.592443i | −0.859423 | + | 0.0617665i | ||||
\(93\) | 13.9489 | − | 6.77575i | 1.44643 | − | 0.702613i | ||||
\(94\) | 15.0116 | − | 0.538745i | 1.54833 | − | 0.0555673i | ||||
\(95\) | −0.762708 | −0.0782522 | ||||||||
\(96\) | 5.78471 | + | 7.90804i | 0.590400 | + | 0.807111i | ||||
\(97\) | −4.70298 | −0.477515 | −0.238758 | − | 0.971079i | \(-0.576740\pi\) | ||||
−0.238758 | + | 0.971079i | \(0.576740\pi\) | |||||||
\(98\) | −11.3511 | + | 0.407375i | −1.14663 | + | 0.0411511i | ||||
\(99\) | 9.47671 | − | 12.0501i | 0.952445 | − | 1.21108i | ||||
\(100\) | 8.81382 | − | 0.633447i | 0.881382 | − | 0.0633447i | ||||
\(101\) | − | 8.33215i | − | 0.829080i | −0.910031 | − | 0.414540i | \(-0.863943\pi\) | ||
0.910031 | − | 0.414540i | \(-0.136057\pi\) | |||||||
\(102\) | −3.56191 | + | 1.89102i | −0.352681 | + | 0.187239i | ||||
\(103\) | − | 2.15168i | − | 0.212011i | −0.994366 | − | 0.106006i | \(-0.966194\pi\) | ||
0.994366 | − | 0.106006i | \(-0.0338061\pi\) | |||||||
\(104\) | −1.65078 | + | 0.178345i | −0.161872 | + | 0.0174882i | ||||
\(105\) | 2.23789 | + | 4.60702i | 0.218395 | + | 0.449599i | ||||
\(106\) | 0.522473 | + | 14.5582i | 0.0507470 | + | 1.41402i | ||||
\(107\) | −10.5723 | −1.02207 | −0.511033 | − | 0.859561i | \(-0.670737\pi\) | ||||
−0.511033 | + | 0.859561i | \(0.670737\pi\) | |||||||
\(108\) | −10.2870 | − | 1.47576i | −0.989866 | − | 0.142005i | ||||
\(109\) | 13.0704 | 1.25192 | 0.625960 | − | 0.779855i | \(-0.284707\pi\) | ||||
0.625960 | + | 0.779855i | \(0.284707\pi\) | |||||||
\(110\) | −0.197685 | − | 5.50830i | −0.0188485 | − | 0.525196i | ||||
\(111\) | −1.38393 | − | 2.84902i | −0.131357 | − | 0.270417i | ||||
\(112\) | −2.21769 | − | 15.3489i | −0.209552 | − | 1.45033i | ||||
\(113\) | − | 3.59199i | − | 0.337906i | −0.985624 | − | 0.168953i | \(-0.945961\pi\) | ||
0.985624 | − | 0.168953i | \(-0.0540386\pi\) | |||||||
\(114\) | −2.16350 | + | 1.14860i | −0.202630 | + | 0.107576i | ||||
\(115\) | − | 3.15172i | − | 0.293900i | ||||||
\(116\) | 0.121061 | + | 1.68446i | 0.0112403 | + | 0.156398i | ||||
\(117\) | 1.08867 | − | 1.38430i | 0.100648 | − | 0.127978i | ||||
\(118\) | −11.1716 | + | 0.400934i | −1.02843 | + | 0.0369089i | ||||
\(119\) | 6.38306 | 0.585135 | ||||||||
\(120\) | −3.16614 | + | 1.98416i | −0.289028 | + | 0.181128i | ||||
\(121\) | 15.1125 | 1.37386 | ||||||||
\(122\) | 5.11065 | − | 0.183414i | 0.462696 | − | 0.0166055i | ||||
\(123\) | 7.77944 | − | 3.77891i | 0.701449 | − | 0.340733i | ||||
\(124\) | −1.28362 | − | 17.8604i | −0.115273 | − | 1.60391i | ||||
\(125\) | 7.18340i | 0.642503i | ||||||||
\(126\) | 13.2859 | + | 9.69810i | 1.18360 | + | 0.863976i | ||||
\(127\) | 10.8930i | 0.966598i | 0.875455 | + | 0.483299i | \(0.160562\pi\) | ||||
−0.875455 | + | 0.483299i | \(0.839438\pi\) | |||||||
\(128\) | 10.9589 | − | 2.81125i | 0.968637 | − | 0.248481i | ||||
\(129\) | −13.7050 | + | 6.65731i | −1.20666 | + | 0.586143i | ||||
\(130\) | −0.0227098 | − | 0.632786i | −0.00199178 | − | 0.0554990i | ||||
\(131\) | 8.00545 | 0.699439 | 0.349720 | − | 0.936854i | \(-0.386277\pi\) | ||||
0.349720 | + | 0.936854i | \(0.386277\pi\) | |||||||
\(132\) | −8.85599 | − | 15.3271i | −0.770815 | − | 1.33406i | ||||
\(133\) | 3.87706 | 0.336184 | ||||||||
\(134\) | −0.427667 | − | 11.9165i | −0.0369448 | − | 1.02943i | ||||
\(135\) | 0.842556 | − | 3.87255i | 0.0725157 | − | 0.333296i | ||||
\(136\) | 0.500177 | + | 4.62969i | 0.0428899 | + | 0.396992i | ||||
\(137\) | − | 20.8200i | − | 1.77878i | −0.457154 | − | 0.889388i | \(-0.651131\pi\) | ||
0.457154 | − | 0.889388i | \(-0.348869\pi\) | |||||||
\(138\) | −4.74634 | − | 8.94017i | −0.404035 | − | 0.761038i | ||||
\(139\) | 16.7117i | 1.41747i | 0.705477 | + | 0.708733i | \(0.250733\pi\) | ||||
−0.705477 | + | 0.708733i | \(0.749267\pi\) | |||||||
\(140\) | 5.89892 | − | 0.423954i | 0.498550 | − | 0.0358306i | ||||
\(141\) | 8.03839 | + | 16.5482i | 0.676954 | + | 1.39361i | ||||
\(142\) | 7.24422 | − | 0.259985i | 0.607922 | − | 0.0218174i | ||||
\(143\) | 2.99976 | 0.250853 | ||||||||
\(144\) | −5.99303 | + | 10.3963i | −0.499419 | + | 0.866361i | ||||
\(145\) | −0.644032 | −0.0534839 | ||||||||
\(146\) | −10.4299 | + | 0.374314i | −0.863183 | + | 0.0309784i | ||||
\(147\) | −6.07826 | − | 12.5130i | −0.501327 | − | 1.03205i | ||||
\(148\) | −3.64795 | + | 0.262177i | −0.299859 | + | 0.0215508i | ||||
\(149\) | 4.00704i | 0.328269i | 0.986438 | + | 0.164135i | \(0.0524832\pi\) | ||||
−0.986438 | + | 0.164135i | \(0.947517\pi\) | |||||||
\(150\) | 5.07483 | + | 9.55892i | 0.414359 | + | 0.780483i | ||||
\(151\) | 12.0050i | 0.976951i | 0.872578 | + | 0.488476i | \(0.162447\pi\) | ||||
−0.872578 | + | 0.488476i | \(0.837553\pi\) | |||||||
\(152\) | 0.303807 | + | 2.81206i | 0.0246420 | + | 0.228088i | ||||
\(153\) | −3.88233 | − | 3.05323i | −0.313868 | − | 0.246839i | ||||
\(154\) | 1.00489 | + | 28.0003i | 0.0809763 | + | 2.25633i | ||||
\(155\) | 6.82871 | 0.548495 | ||||||||
\(156\) | −1.01736 | − | 1.76076i | −0.0814542 | − | 0.140974i | ||||
\(157\) | 4.28650 | 0.342100 | 0.171050 | − | 0.985262i | \(-0.445284\pi\) | ||||
0.171050 | + | 0.985262i | \(0.445284\pi\) | |||||||
\(158\) | 0.681236 | + | 18.9820i | 0.0541962 | + | 1.51012i | ||||
\(159\) | −16.0484 | + | 7.79559i | −1.27272 | + | 0.618230i | ||||
\(160\) | 0.769736 | + | 4.24531i | 0.0608530 | + | 0.335621i | ||||
\(161\) | 16.0211i | 1.26264i | ||||||||
\(162\) | −3.44187 | − | 12.2537i | −0.270419 | − | 0.962743i | ||||
\(163\) | 13.6584i | 1.06981i | 0.844913 | + | 0.534904i | \(0.179652\pi\) | ||||
−0.844913 | + | 0.534904i | \(0.820348\pi\) | |||||||
\(164\) | −0.715891 | − | 9.96096i | −0.0559017 | − | 0.777820i | ||||
\(165\) | 6.07213 | − | 2.94958i | 0.472715 | − | 0.229624i | ||||
\(166\) | 8.58989 | − | 0.308279i | 0.666705 | − | 0.0239271i | ||||
\(167\) | −13.2030 | −1.02168 | −0.510838 | − | 0.859677i | \(-0.670665\pi\) | ||||
−0.510838 | + | 0.859677i | \(0.670665\pi\) | |||||||
\(168\) | 16.0944 | − | 10.0861i | 1.24171 | − | 0.778157i | ||||
\(169\) | −12.6554 | −0.973492 | ||||||||
\(170\) | −1.77468 | + | 0.0636908i | −0.136112 | + | 0.00488486i | ||||
\(171\) | −2.35812 | − | 1.85453i | −0.180330 | − | 0.141819i | ||||
\(172\) | 1.26118 | + | 17.5482i | 0.0961645 | + | 1.33804i | ||||
\(173\) | − | 21.5437i | − | 1.63794i | −0.573837 | − | 0.818970i | \(-0.694546\pi\) | ||
0.573837 | − | 0.818970i | \(-0.305454\pi\) | |||||||
\(174\) | −1.82686 | + | 0.969880i | −0.138494 | + | 0.0735264i | ||||
\(175\) | − | 17.1299i | − | 1.29490i | ||||||
\(176\) | −20.2301 | + | 2.92296i | −1.52490 | + | 0.220326i | ||||
\(177\) | −5.98216 | − | 12.3151i | −0.449646 | − | 0.925663i | ||||
\(178\) | 0.459708 | + | 12.8093i | 0.0344565 | + | 0.960098i | ||||
\(179\) | 18.3784 | 1.37367 | 0.686834 | − | 0.726814i | \(-0.259000\pi\) | ||||
0.686834 | + | 0.726814i | \(0.259000\pi\) | |||||||
\(180\) | −3.79065 | − | 2.56379i | −0.282538 | − | 0.191094i | ||||
\(181\) | 0.662077 | 0.0492118 | 0.0246059 | − | 0.999697i | \(-0.492167\pi\) | ||||
0.0246059 | + | 0.999697i | \(0.492167\pi\) | |||||||
\(182\) | 0.115440 | + | 3.21663i | 0.00855701 | + | 0.238433i | ||||
\(183\) | 2.73664 | + | 5.63377i | 0.202298 | + | 0.416460i | ||||
\(184\) | −11.6202 | + | 1.25541i | −0.856655 | + | 0.0925504i | ||||
\(185\) | − | 1.39475i | − | 0.102544i | ||||||
\(186\) | 19.3703 | − | 10.2837i | 1.42030 | − | 0.754037i | ||||
\(187\) | − | 8.41299i | − | 0.615219i | ||||||
\(188\) | 21.1886 | − | 1.52282i | 1.54534 | − | 0.111063i | ||||
\(189\) | −4.28295 | + | 19.6853i | −0.311539 | + | 1.43189i | ||||
\(190\) | −1.07794 | + | 0.0386857i | −0.0782019 | + | 0.00280655i | ||||
\(191\) | −14.0483 | −1.01650 | −0.508250 | − | 0.861210i | \(-0.669707\pi\) | ||||
−0.508250 | + | 0.861210i | \(0.669707\pi\) | |||||||
\(192\) | 8.57666 | + | 10.8831i | 0.618967 | + | 0.785417i | ||||
\(193\) | 2.46211 | 0.177227 | 0.0886134 | − | 0.996066i | \(-0.471756\pi\) | ||||
0.0886134 | + | 0.996066i | \(0.471756\pi\) | |||||||
\(194\) | −6.64674 | + | 0.238542i | −0.477208 | + | 0.0171263i | ||||
\(195\) | 0.697558 | − | 0.338843i | 0.0499531 | − | 0.0242651i | ||||
\(196\) | −16.0219 | + | 1.15149i | −1.14442 | + | 0.0822492i | ||||
\(197\) | − | 20.5990i | − | 1.46762i | −0.679357 | − | 0.733808i | \(-0.737741\pi\) | ||
0.679357 | − | 0.733808i | \(-0.262259\pi\) | |||||||
\(198\) | 12.7823 | − | 17.5111i | 0.908397 | − | 1.24446i | ||||
\(199\) | − | 12.8363i | − | 0.909940i | −0.890507 | − | 0.454970i | \(-0.849650\pi\) | ||
0.890507 | − | 0.454970i | \(-0.150350\pi\) | |||||||
\(200\) | 12.4245 | − | 1.34230i | 0.878543 | − | 0.0949151i | ||||
\(201\) | 13.1363 | − | 6.38103i | 0.926562 | − | 0.450084i | ||||
\(202\) | −0.422619 | − | 11.7759i | −0.0297354 | − | 0.828546i | ||||
\(203\) | 3.27380 | 0.229775 | ||||||||
\(204\) | −4.93814 | + | 2.85325i | −0.345739 | + | 0.199767i | ||||
\(205\) | 3.80845 | 0.265994 | ||||||||
\(206\) | −0.109136 | − | 3.04098i | −0.00760388 | − | 0.211875i | ||||
\(207\) | 7.66343 | − | 9.74440i | 0.532645 | − | 0.677283i | ||||
\(208\) | −2.32400 | + | 0.335785i | −0.161141 | + | 0.0232825i | ||||
\(209\) | − | 5.11004i | − | 0.353469i | ||||||
\(210\) | 3.39649 | + | 6.39760i | 0.234380 | + | 0.441477i | ||||
\(211\) | − | 1.23795i | − | 0.0852242i | −0.999092 | − | 0.0426121i | \(-0.986432\pi\) | ||
0.999092 | − | 0.0426121i | \(-0.0135680\pi\) | |||||||
\(212\) | 1.47682 | + | 20.5486i | 0.101429 | + | 1.41129i | ||||
\(213\) | 3.87912 | + | 7.98573i | 0.265793 | + | 0.547173i | ||||
\(214\) | −14.9419 | + | 0.536244i | −1.02141 | + | 0.0366569i | ||||
\(215\) | −6.70934 | −0.457573 | ||||||||
\(216\) | −14.6135 | − | 1.56392i | −0.994322 | − | 0.106411i | ||||
\(217\) | −34.7123 | −2.35642 | ||||||||
\(218\) | 18.4725 | − | 0.662951i | 1.25111 | − | 0.0449007i | ||||
\(219\) | −5.58497 | − | 11.4975i | −0.377397 | − | 0.776927i | ||||
\(220\) | −0.558778 | − | 7.77488i | −0.0376728 | − | 0.524182i | ||||
\(221\) | − | 0.966473i | − | 0.0650120i | ||||||
\(222\) | −2.10042 | − | 3.95634i | −0.140971 | − | 0.265532i | ||||
\(223\) | − | 20.5448i | − | 1.37578i | −0.725816 | − | 0.687889i | \(-0.758537\pi\) | ||
0.725816 | − | 0.687889i | \(-0.241463\pi\) | |||||||
\(224\) | −3.91279 | − | 21.5801i | −0.261434 | − | 1.44188i | ||||
\(225\) | −8.19382 | + | 10.4188i | −0.546255 | + | 0.694588i | ||||
\(226\) | −0.182191 | − | 5.07657i | −0.0121192 | − | 0.337689i | ||||
\(227\) | −25.6172 | −1.70027 | −0.850137 | − | 0.526562i | \(-0.823481\pi\) | ||||
−0.850137 | + | 0.526562i | \(0.823481\pi\) | |||||||
\(228\) | −2.99942 | + | 1.73306i | −0.198641 | + | 0.114775i | ||||
\(229\) | −18.7952 | −1.24202 | −0.621012 | − | 0.783801i | \(-0.713278\pi\) | ||||
−0.621012 | + | 0.783801i | \(0.713278\pi\) | |||||||
\(230\) | −0.159860 | − | 4.45434i | −0.0105409 | − | 0.293711i | ||||
\(231\) | −30.8664 | + | 14.9935i | −2.03086 | + | 0.986502i | ||||
\(232\) | 0.256535 | + | 2.37451i | 0.0168423 | + | 0.155894i | ||||
\(233\) | 13.5571i | 0.888153i | 0.895989 | + | 0.444077i | \(0.146468\pi\) | ||||
−0.895989 | + | 0.444077i | \(0.853532\pi\) | |||||||
\(234\) | 1.46841 | − | 2.01165i | 0.0959930 | − | 0.131506i | ||||
\(235\) | 8.10122i | 0.528465i | ||||||||
\(236\) | −15.7686 | + | 1.13328i | −1.02645 | + | 0.0737704i | ||||
\(237\) | −20.9250 | + | 10.1644i | −1.35922 | + | 0.660251i | ||||
\(238\) | 9.02121 | − | 0.323758i | 0.584758 | − | 0.0209861i | ||||
\(239\) | 11.3716 | 0.735569 | 0.367785 | − | 0.929911i | \(-0.380116\pi\) | ||||
0.367785 | + | 0.929911i | \(0.380116\pi\) | |||||||
\(240\) | −4.37408 | + | 2.96482i | −0.282346 | + | 0.191378i | ||||
\(241\) | −12.0622 | −0.776992 | −0.388496 | − | 0.921450i | \(-0.627005\pi\) | ||||
−0.388496 | + | 0.921450i | \(0.627005\pi\) | |||||||
\(242\) | 21.3585 | − | 0.766527i | 1.37298 | − | 0.0492742i | ||||
\(243\) | 12.0211 | − | 9.92435i | 0.771155 | − | 0.636648i | ||||
\(244\) | 7.21359 | − | 0.518439i | 0.461803 | − | 0.0331896i | ||||
\(245\) | − | 6.12577i | − | 0.391361i | ||||||
\(246\) | 10.8030 | − | 5.73534i | 0.688777 | − | 0.365672i | ||||
\(247\) | − | 0.587034i | − | 0.0373521i | ||||||
\(248\) | −2.72006 | − | 25.1771i | −0.172724 | − | 1.59875i | ||||
\(249\) | 4.59970 | + | 9.46915i | 0.291494 | + | 0.600083i | ||||
\(250\) | 0.364352 | + | 10.1523i | 0.0230437 | + | 0.642089i | ||||
\(251\) | 0.536967 | 0.0338931 | 0.0169465 | − | 0.999856i | \(-0.494605\pi\) | ||||
0.0169465 | + | 0.999856i | \(0.494605\pi\) | |||||||
\(252\) | 19.2689 | + | 13.0325i | 1.21383 | + | 0.820969i | ||||
\(253\) | 21.1161 | 1.32756 | ||||||||
\(254\) | 0.552509 | + | 15.3951i | 0.0346675 | + | 0.965976i | ||||
\(255\) | −0.950303 | − | 1.95634i | −0.0595103 | − | 0.122511i | ||||
\(256\) | 15.3456 | − | 4.52900i | 0.959102 | − | 0.283062i | ||||
\(257\) | − | 19.8858i | − | 1.24044i | −0.784427 | − | 0.620221i | \(-0.787043\pi\) | ||
0.784427 | − | 0.620221i | \(-0.212957\pi\) | |||||||
\(258\) | −19.0317 | + | 10.1039i | −1.18486 | + | 0.629044i | ||||
\(259\) | 7.08990i | 0.440545i | ||||||||
\(260\) | −0.0641917 | − | 0.893167i | −0.00398100 | − | 0.0553919i | ||||
\(261\) | −1.99120 | − | 1.56597i | −0.123252 | − | 0.0969309i | ||||
\(262\) | 11.3141 | − | 0.406048i | 0.698989 | − | 0.0250857i | ||||
\(263\) | −13.4752 | −0.830919 | −0.415459 | − | 0.909612i | \(-0.636379\pi\) | ||||
−0.415459 | + | 0.909612i | \(0.636379\pi\) | |||||||
\(264\) | −13.2936 | − | 21.2127i | −0.818165 | − | 1.30555i | ||||
\(265\) | −7.85652 | −0.482622 | ||||||||
\(266\) | 5.47947 | − | 0.196650i | 0.335968 | − | 0.0120574i | ||||
\(267\) | −14.1205 | + | 6.85910i | −0.864158 | + | 0.419770i | ||||
\(268\) | −1.20885 | − | 16.8200i | −0.0738421 | − | 1.02744i | ||||
\(269\) | − | 14.5106i | − | 0.884728i | −0.896836 | − | 0.442364i | \(-0.854140\pi\) | ||
0.896836 | − | 0.442364i | \(-0.145860\pi\) | |||||||
\(270\) | 0.994366 | − | 5.51582i | 0.0605152 | − | 0.335682i | ||||
\(271\) | 1.76652i | 0.107308i | 0.998560 | + | 0.0536541i | \(0.0170868\pi\) | ||||
−0.998560 | + | 0.0536541i | \(0.982913\pi\) | |||||||
\(272\) | 0.941727 | + | 6.51778i | 0.0571006 | + | 0.395199i | ||||
\(273\) | −3.54588 | + | 1.72244i | −0.214607 | + | 0.104247i | ||||
\(274\) | −1.05602 | − | 29.4250i | −0.0637966 | − | 1.77763i | ||||
\(275\) | −22.5776 | −1.36148 | ||||||||
\(276\) | −7.16148 | − | 12.3944i | −0.431070 | − | 0.746057i | ||||
\(277\) | 4.01710 | 0.241364 | 0.120682 | − | 0.992691i | \(-0.461492\pi\) | ||||
0.120682 | + | 0.992691i | \(0.461492\pi\) | |||||||
\(278\) | 0.847640 | + | 23.6187i | 0.0508381 | + | 1.41655i | ||||
\(279\) | 21.1128 | + | 16.6041i | 1.26399 | + | 0.994058i | ||||
\(280\) | 8.31546 | − | 0.898377i | 0.496944 | − | 0.0536883i | ||||
\(281\) | 21.6108i | 1.28919i | 0.764524 | + | 0.644596i | \(0.222974\pi\) | ||||
−0.764524 | + | 0.644596i | \(0.777026\pi\) | |||||||
\(282\) | 12.2000 | + | 22.9799i | 0.726501 | + | 1.36843i | ||||
\(283\) | − | 17.6039i | − | 1.04644i | −0.852198 | − | 0.523220i | \(-0.824731\pi\) | ||
0.852198 | − | 0.523220i | \(-0.175269\pi\) | |||||||
\(284\) | 10.2251 | − | 0.734875i | 0.606748 | − | 0.0436068i | ||||
\(285\) | −0.577212 | − | 1.18828i | −0.0341911 | − | 0.0703873i | ||||
\(286\) | 4.23958 | − | 0.152152i | 0.250692 | − | 0.00899696i | ||||
\(287\) | −19.3594 | −1.14275 | ||||||||
\(288\) | −7.94265 | + | 14.9971i | −0.468025 | + | 0.883715i | ||||
\(289\) | 14.2895 | 0.840557 | ||||||||
\(290\) | −0.910212 | + | 0.0326662i | −0.0534495 | + | 0.00191823i | ||||
\(291\) | −3.55918 | − | 7.32709i | −0.208643 | − | 0.429522i | ||||
\(292\) | −14.7216 | + | 1.05804i | −0.861517 | + | 0.0619170i | ||||
\(293\) | 11.6431i | 0.680199i | 0.940390 | + | 0.340099i | \(0.110461\pi\) | ||||
−0.940390 | + | 0.340099i | \(0.889539\pi\) | |||||||
\(294\) | −9.22511 | − | 17.3763i | −0.538019 | − | 1.01341i | ||||
\(295\) | − | 6.02892i | − | 0.351017i | ||||||
\(296\) | −5.14236 | + | 0.555565i | −0.298894 | + | 0.0322915i | ||||
\(297\) | 25.9455 | + | 5.64501i | 1.50551 | + | 0.327557i | ||||
\(298\) | 0.203243 | + | 5.66316i | 0.0117735 | + | 0.328058i | ||||
\(299\) | 2.42579 | 0.140287 | ||||||||
\(300\) | 7.65712 | + | 13.2523i | 0.442084 | + | 0.765120i | ||||
\(301\) | 34.1055 | 1.96581 | ||||||||
\(302\) | 0.608910 | + | 16.9667i | 0.0350388 | + | 0.976322i | ||||
\(303\) | 12.9812 | − | 6.30571i | 0.745752 | − | 0.362254i | ||||
\(304\) | 0.572003 | + | 3.95889i | 0.0328066 | + | 0.227058i | ||||
\(305\) | 2.75803i | 0.157924i | ||||||||
\(306\) | −5.64177 | − | 4.11823i | −0.322519 | − | 0.235424i | ||||
\(307\) | 5.09802i | 0.290960i | 0.989361 | + | 0.145480i | \(0.0464726\pi\) | ||||
−0.989361 | + | 0.145480i | \(0.953527\pi\) | |||||||
\(308\) | 2.84043 | + | 39.5219i | 0.161848 | + | 2.25197i | ||||
\(309\) | 3.35225 | − | 1.62837i | 0.190703 | − | 0.0926350i | ||||
\(310\) | 9.65104 | − | 0.346362i | 0.548142 | − | 0.0196721i | ||||
\(311\) | 12.0774 | 0.684849 | 0.342424 | − | 0.939545i | \(-0.388752\pi\) | ||||
0.342424 | + | 0.939545i | \(0.388752\pi\) | |||||||
\(312\) | −1.52715 | − | 2.43689i | −0.0864579 | − | 0.137962i | ||||
\(313\) | 21.0857 | 1.19184 | 0.595918 | − | 0.803045i | \(-0.296788\pi\) | ||||
0.595918 | + | 0.803045i | \(0.296788\pi\) | |||||||
\(314\) | 6.05813 | − | 0.217418i | 0.341880 | − | 0.0122696i | ||||
\(315\) | −5.48397 | + | 6.97311i | −0.308986 | + | 0.392890i | ||||
\(316\) | 1.92559 | + | 26.7927i | 0.108323 | + | 1.50721i | ||||
\(317\) | − | 9.77428i | − | 0.548978i | −0.961590 | − | 0.274489i | \(-0.911491\pi\) | ||
0.961590 | − | 0.274489i | \(-0.0885087\pi\) | |||||||
\(318\) | −22.2858 | + | 11.8315i | −1.24972 | + | 0.663479i | ||||
\(319\) | − | 4.31492i | − | 0.241589i | ||||||
\(320\) | 1.30320 | + | 5.96087i | 0.0728511 | + | 0.333223i | ||||
\(321\) | −8.00107 | − | 16.4714i | −0.446576 | − | 0.919342i | ||||
\(322\) | 0.812613 | + | 22.6427i | 0.0452852 | + | 1.26183i | ||||
\(323\) | −1.64637 | −0.0916063 | ||||||||
\(324\) | −5.48594 | − | 17.1436i | −0.304774 | − | 0.952425i | ||||
\(325\) | −2.59368 | −0.143871 | ||||||||
\(326\) | 0.692774 | + | 19.3035i | 0.0383692 | + | 1.06912i | ||||
\(327\) | 9.89160 | + | 20.3633i | 0.547007 | + | 1.12609i | ||||
\(328\) | −1.51701 | − | 14.0415i | −0.0837626 | − | 0.775315i | ||||
\(329\) | − | 41.1808i | − | 2.27037i | ||||||
\(330\) | 8.43216 | − | 4.47663i | 0.464175 | − | 0.246431i | ||||
\(331\) | − | 1.42855i | − | 0.0785204i | −0.999229 | − | 0.0392602i | \(-0.987500\pi\) | ||
0.999229 | − | 0.0392602i | \(-0.0125001\pi\) | |||||||
\(332\) | 12.1245 | − | 0.871384i | 0.665418 | − | 0.0478234i | ||||
\(333\) | 3.39134 | − | 4.31224i | 0.185844 | − | 0.236309i | ||||
\(334\) | −18.6598 | + | 0.669674i | −1.02102 | + | 0.0366429i | ||||
\(335\) | 6.43091 | 0.351358 | ||||||||
\(336\) | 22.2347 | − | 15.0710i | 1.21300 | − | 0.822191i | ||||
\(337\) | 0.0498717 | 0.00271668 | 0.00135834 | − | 0.999999i | \(-0.499568\pi\) | ||||
0.00135834 | + | 0.999999i | \(0.499568\pi\) | |||||||
\(338\) | −17.8859 | + | 0.641900i | −0.972865 | + | 0.0349147i | ||||
\(339\) | 5.59621 | − | 2.71839i | 0.303944 | − | 0.147643i | ||||
\(340\) | −2.50493 | + | 0.180029i | −0.135849 | + | 0.00976344i | ||||
\(341\) | 45.7514i | 2.47758i | ||||||||
\(342\) | −3.42680 | − | 2.50141i | −0.185300 | − | 0.135261i | ||||
\(343\) | 3.99960i | 0.215958i | ||||||||
\(344\) | 2.67251 | + | 24.7370i | 0.144092 | + | 1.33373i | ||||
\(345\) | 4.91028 | − | 2.38520i | 0.264361 | − | 0.128415i | ||||
\(346\) | −1.09273 | − | 30.4478i | −0.0587455 | − | 1.63689i | ||||
\(347\) | 11.2205 | 0.602346 | 0.301173 | − | 0.953569i | \(-0.402622\pi\) | ||||
0.301173 | + | 0.953569i | \(0.402622\pi\) | |||||||
\(348\) | −2.53271 | + | 1.46340i | −0.135768 | + | 0.0784462i | ||||
\(349\) | −13.0436 | −0.698207 | −0.349104 | − | 0.937084i | \(-0.613514\pi\) | ||||
−0.349104 | + | 0.937084i | \(0.613514\pi\) | |||||||
\(350\) | −0.868855 | − | 24.2098i | −0.0464422 | − | 1.29407i | ||||
\(351\) | 2.98059 | + | 0.648491i | 0.159092 | + | 0.0346139i | ||||
\(352\) | −28.4430 | + | 5.15713i | −1.51602 | + | 0.274876i | ||||
\(353\) | − | 20.2748i | − | 1.07912i | −0.841947 | − | 0.539560i | \(-0.818590\pi\) | ||
0.841947 | − | 0.539560i | \(-0.181410\pi\) | |||||||
\(354\) | −9.07925 | − | 17.1016i | −0.482556 | − | 0.908940i | ||||
\(355\) | 3.90944i | 0.207492i | ||||||||
\(356\) | 1.29941 | + | 18.0801i | 0.0688688 | + | 0.958244i | ||||
\(357\) | 4.83066 | + | 9.94461i | 0.255666 | + | 0.526325i | ||||
\(358\) | 25.9743 | − | 0.932180i | 1.37278 | − | 0.0492673i | ||||
\(359\) | 5.33549 | 0.281597 | 0.140798 | − | 0.990038i | \(-0.455033\pi\) | ||||
0.140798 | + | 0.990038i | \(0.455033\pi\) | |||||||
\(360\) | −5.48738 | − | 3.43115i | −0.289210 | − | 0.180838i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0.935716 | − | 0.0335815i | 0.0491802 | − | 0.00176501i | ||||
\(363\) | 11.4370 | + | 23.5448i | 0.600288 | + | 1.23578i | ||||
\(364\) | 0.326304 | + | 4.54022i | 0.0171030 | + | 0.237972i | ||||
\(365\) | − | 5.62862i | − | 0.294616i | ||||||
\(366\) | 4.15345 | + | 7.82342i | 0.217104 | + | 0.408937i | ||||
\(367\) | − | 14.9149i | − | 0.778551i | −0.921121 | − | 0.389276i | \(-0.872725\pi\) | ||
0.921121 | − | 0.389276i | \(-0.127275\pi\) | |||||||
\(368\) | −16.3592 | + | 2.36368i | −0.852784 | + | 0.123215i | ||||
\(369\) | 11.7749 | + | 9.26027i | 0.612974 | + | 0.482070i | ||||
\(370\) | −0.0707436 | − | 1.97120i | −0.00367779 | − | 0.102478i | ||||
\(371\) | 39.9369 | 2.07342 | ||||||||
\(372\) | 26.8545 | − | 15.5165i | 1.39234 | − | 0.804492i | ||||
\(373\) | −9.47842 | −0.490774 | −0.245387 | − | 0.969425i | \(-0.578915\pi\) | ||||
−0.245387 | + | 0.969425i | \(0.578915\pi\) | |||||||
\(374\) | −0.426719 | − | 11.8901i | −0.0220651 | − | 0.614823i | ||||
\(375\) | −11.1915 | + | 5.43634i | −0.577927 | + | 0.280732i | ||||
\(376\) | 29.8687 | − | 3.22693i | 1.54036 | − | 0.166416i | ||||
\(377\) | − | 0.495692i | − | 0.0255294i | ||||||
\(378\) | −5.05465 | + | 28.0385i | −0.259983 | + | 1.44214i | ||||
\(379\) | 5.01719i | 0.257716i | 0.991663 | + | 0.128858i | \(0.0411311\pi\) | ||||
−0.991663 | + | 0.128858i | \(0.958869\pi\) | |||||||
\(380\) | −1.52149 | + | 0.109349i | −0.0780509 | + | 0.00560950i | ||||
\(381\) | −16.9710 | + | 8.24375i | −0.869448 | + | 0.422340i | ||||
\(382\) | −19.8545 | + | 0.712551i | −1.01585 | + | 0.0364573i | ||||
\(383\) | 20.5573 | 1.05043 | 0.525215 | − | 0.850970i | \(-0.323985\pi\) | ||||
0.525215 | + | 0.850970i | \(0.323985\pi\) | |||||||
\(384\) | 12.6734 | + | 14.9460i | 0.646738 | + | 0.762712i | ||||
\(385\) | −15.1107 | −0.770114 | ||||||||
\(386\) | 3.47971 | − | 0.124882i | 0.177113 | − | 0.00635633i | ||||
\(387\) | −20.7437 | − | 16.3138i | −1.05446 | − | 0.829277i | ||||
\(388\) | −9.38176 | + | 0.674264i | −0.476287 | + | 0.0342306i | ||||
\(389\) | − | 19.0560i | − | 0.966179i | −0.875571 | − | 0.483089i | \(-0.839515\pi\) | ||
0.875571 | − | 0.483089i | \(-0.160485\pi\) | |||||||
\(390\) | 0.968674 | − | 0.514269i | 0.0490507 | − | 0.0260410i | ||||
\(391\) | − | 6.80325i | − | 0.344055i | ||||||
\(392\) | −22.5854 | + | 2.44006i | −1.14073 | + | 0.123241i | ||||
\(393\) | 6.05847 | + | 12.4722i | 0.305609 | + | 0.629141i | ||||
\(394\) | −1.04481 | − | 29.1126i | −0.0526367 | − | 1.46667i | ||||
\(395\) | −10.2439 | −0.515425 | ||||||||
\(396\) | 17.1771 | − | 25.3968i | 0.863179 | − | 1.27624i | ||||
\(397\) | 35.2791 | 1.77061 | 0.885304 | − | 0.465012i | \(-0.153950\pi\) | ||||
0.885304 | + | 0.465012i | \(0.153950\pi\) | |||||||
\(398\) | −0.651075 | − | 18.1416i | −0.0326355 | − | 0.909355i | ||||
\(399\) | 2.93413 | + | 6.04034i | 0.146890 | + | 0.302395i | ||||
\(400\) | 17.4915 | − | 2.52727i | 0.874574 | − | 0.126363i | ||||
\(401\) | 18.4215i | 0.919928i | 0.887938 | + | 0.459964i | \(0.152138\pi\) | ||||
−0.887938 | + | 0.459964i | \(0.847862\pi\) | |||||||
\(402\) | 18.2419 | − | 9.68463i | 0.909824 | − | 0.483026i | ||||
\(403\) | 5.25586i | 0.261813i | ||||||||
\(404\) | −1.19458 | − | 16.6214i | −0.0594324 | − | 0.826947i | ||||
\(405\) | 6.67095 | − | 1.61804i | 0.331482 | − | 0.0804012i | ||||
\(406\) | 4.62687 | − | 0.166052i | 0.229628 | − | 0.00824101i | ||||
\(407\) | 9.34461 | 0.463195 | ||||||||
\(408\) | −6.83437 | + | 4.28297i | −0.338352 | + | 0.212039i | ||||
\(409\) | −5.91166 | −0.292313 | −0.146156 | − | 0.989261i | \(-0.546690\pi\) | ||||
−0.146156 | + | 0.989261i | \(0.546690\pi\) | |||||||
\(410\) | 5.38250 | − | 0.193170i | 0.265823 | − | 0.00953999i | ||||
\(411\) | 32.4369 | − | 15.7565i | 1.60000 | − | 0.777208i | ||||
\(412\) | −0.308485 | − | 4.29229i | −0.0151980 | − | 0.211466i | ||||
\(413\) | 30.6467i | 1.50802i | ||||||||
\(414\) | 10.3365 | − | 14.1605i | 0.508012 | − | 0.695951i | ||||
\(415\) | 4.63565i | 0.227555i | ||||||||
\(416\) | −3.26749 | + | 0.592443i | −0.160202 | + | 0.0290469i | ||||
\(417\) | −26.0363 | + | 12.6473i | −1.27500 | + | 0.619340i | ||||
\(418\) | −0.259189 | − | 7.22203i | −0.0126773 | − | 0.353241i | ||||
\(419\) | 34.7614 | 1.69821 | 0.849104 | − | 0.528226i | \(-0.177143\pi\) | ||||
0.849104 | + | 0.528226i | \(0.177143\pi\) | |||||||
\(420\) | 5.12477 | + | 8.86948i | 0.250063 | + | 0.432786i | ||||
\(421\) | 17.4241 | 0.849198 | 0.424599 | − | 0.905381i | \(-0.360415\pi\) | ||||
0.424599 | + | 0.905381i | \(0.360415\pi\) | |||||||
\(422\) | −0.0627908 | − | 1.74960i | −0.00305661 | − | 0.0851693i | ||||
\(423\) | −19.6982 | + | 25.0471i | −0.957757 | + | 1.21783i | ||||
\(424\) | 3.12946 | + | 28.9666i | 0.151980 | + | 1.40674i | ||||
\(425\) | 7.27410i | 0.352846i | ||||||||
\(426\) | 5.88742 | + | 11.0895i | 0.285247 | + | 0.537289i | ||||
\(427\) | − | 14.0198i | − | 0.678467i | ||||||
\(428\) | −21.0903 | + | 1.51575i | −1.01944 | + | 0.0732666i | ||||
\(429\) | 2.27020 | + | 4.67354i | 0.109606 | + | 0.225641i | ||||
\(430\) | −9.48234 | + | 0.340308i | −0.457279 | + | 0.0164111i | ||||
\(431\) | −26.1850 | −1.26129 | −0.630644 | − | 0.776072i | \(-0.717209\pi\) | ||||
−0.630644 | + | 0.776072i | \(0.717209\pi\) | |||||||
\(432\) | −20.7326 | − | 1.46908i | −0.997499 | − | 0.0706810i | ||||
\(433\) | −33.3944 | −1.60483 | −0.802417 | − | 0.596764i | \(-0.796453\pi\) | ||||
−0.802417 | + | 0.596764i | \(0.796453\pi\) | |||||||
\(434\) | −49.0590 | + | 1.76066i | −2.35491 | + | 0.0845142i | ||||
\(435\) | −0.487399 | − | 1.00338i | −0.0233690 | − | 0.0481084i | ||||
\(436\) | 26.0736 | − | 1.87390i | 1.24870 | − | 0.0897436i | ||||
\(437\) | − | 4.13228i | − | 0.197674i | ||||||
\(438\) | −8.47643 | − | 15.9661i | −0.405019 | − | 0.762892i | ||||
\(439\) | 11.6628i | 0.556636i | 0.960489 | + | 0.278318i | \(0.0897770\pi\) | ||||
−0.960489 | + | 0.278318i | \(0.910223\pi\) | |||||||
\(440\) | −1.18408 | − | 10.9599i | −0.0564487 | − | 0.522494i | ||||
\(441\) | 14.8948 | − | 18.9395i | 0.709278 | − | 0.901880i | ||||
\(442\) | −0.0490209 | − | 1.36592i | −0.00233169 | − | 0.0649702i | ||||
\(443\) | −22.5598 | −1.07185 | −0.535924 | − | 0.844266i | \(-0.680037\pi\) | ||||
−0.535924 | + | 0.844266i | \(0.680037\pi\) | |||||||
\(444\) | −3.16920 | − | 5.48497i | −0.150404 | − | 0.260305i | ||||
\(445\) | −6.91271 | −0.327694 | ||||||||
\(446\) | −1.04206 | − | 29.0360i | −0.0493430 | − | 1.37489i | ||||
\(447\) | −6.24284 | + | 3.03250i | −0.295276 | + | 0.143432i | ||||
\(448\) | −6.62453 | − | 30.3008i | −0.312980 | − | 1.43158i | ||||
\(449\) | − | 5.11285i | − | 0.241290i | −0.992696 | − | 0.120645i | \(-0.961504\pi\) | ||
0.992696 | − | 0.120645i | \(-0.0384963\pi\) | |||||||
\(450\) | −11.0519 | + | 15.1406i | −0.520992 | + | 0.713733i | ||||
\(451\) | 25.5161i | 1.20151i | ||||||||
\(452\) | −0.514982 | − | 7.16550i | −0.0242227 | − | 0.337037i | ||||
\(453\) | −18.7034 | + | 9.08528i | −0.878761 | + | 0.426864i | ||||
\(454\) | −36.2049 | + | 1.29934i | −1.69918 | + | 0.0609811i | ||||
\(455\) | −1.73590 | −0.0813802 | ||||||||
\(456\) | −4.15119 | + | 2.60147i | −0.194397 | + | 0.121825i | ||||
\(457\) | 20.6806 | 0.967398 | 0.483699 | − | 0.875235i | \(-0.339293\pi\) | ||||
0.483699 | + | 0.875235i | \(0.339293\pi\) | |||||||
\(458\) | −26.5634 | + | 0.953322i | −1.24122 | + | 0.0445458i | ||||
\(459\) | 1.81872 | − | 8.35921i | 0.0848908 | − | 0.390174i | ||||
\(460\) | −0.451861 | − | 6.28723i | −0.0210681 | − | 0.293144i | ||||
\(461\) | 2.97037i | 0.138344i | 0.997605 | + | 0.0691720i | \(0.0220357\pi\) | ||||
−0.997605 | + | 0.0691720i | \(0.977964\pi\) | |||||||
\(462\) | −42.8630 | + | 22.7560i | −1.99417 | + | 1.05870i | ||||
\(463\) | − | 19.0211i | − | 0.883984i | −0.897019 | − | 0.441992i | \(-0.854272\pi\) | ||
0.897019 | − | 0.441992i | \(-0.145728\pi\) | |||||||
\(464\) | 0.483000 | + | 3.34289i | 0.0224227 | + | 0.155190i | ||||
\(465\) | 5.16792 | + | 10.6389i | 0.239657 | + | 0.493368i | ||||
\(466\) | 0.687634 | + | 19.1603i | 0.0318541 | + | 0.887582i | ||||
\(467\) | −9.90799 | −0.458487 | −0.229243 | − | 0.973369i | \(-0.573625\pi\) | ||||
−0.229243 | + | 0.973369i | \(0.573625\pi\) | |||||||
\(468\) | 1.97328 | − | 2.91755i | 0.0912147 | − | 0.134864i | ||||
\(469\) | −32.6901 | −1.50949 | ||||||||
\(470\) | 0.410906 | + | 11.4495i | 0.0189537 | + | 0.528125i | ||||
\(471\) | 3.24400 | + | 6.67824i | 0.149475 | + | 0.307717i | ||||
\(472\) | −22.2283 | + | 2.40148i | −1.02314 | + | 0.110537i | ||||
\(473\) | − | 44.9517i | − | 2.06688i | ||||||
\(474\) | −29.0578 | + | 15.4268i | −1.33467 | + | 0.708575i | ||||
\(475\) | 4.41828i | 0.202724i | ||||||||
\(476\) | 12.7333 | − | 0.915138i | 0.583629 | − | 0.0419453i | ||||
\(477\) | −24.2906 | − | 19.1032i | −1.11219 | − | 0.874674i | ||||
\(478\) | 16.0716 | − | 0.576785i | 0.735096 | − | 0.0263815i | ||||
\(479\) | −3.29331 | −0.150475 | −0.0752376 | − | 0.997166i | \(-0.523972\pi\) | ||||
−0.0752376 | + | 0.997166i | \(0.523972\pi\) | |||||||
\(480\) | −6.03153 | + | 4.41205i | −0.275300 | + | 0.201381i | ||||
\(481\) | 1.07350 | 0.0489472 | ||||||||
\(482\) | −17.0475 | + | 0.611810i | −0.776492 | + | 0.0278672i | ||||
\(483\) | −24.9604 | + | 12.1247i | −1.13574 | + | 0.551691i | ||||
\(484\) | 30.1472 | − | 2.16667i | 1.37033 | − | 0.0984850i | ||||
\(485\) | − | 3.58700i | − | 0.162877i | ||||||
\(486\) | 16.4861 | − | 14.6359i | 0.747825 | − | 0.663896i | ||||
\(487\) | 3.51432i | 0.159249i | 0.996825 | + | 0.0796246i | \(0.0253722\pi\) | ||||
−0.996825 | + | 0.0796246i | \(0.974628\pi\) | |||||||
\(488\) | 10.1687 | − | 1.09860i | 0.460315 | − | 0.0497311i | ||||
\(489\) | −21.2793 | + | 10.3366i | −0.962285 | + | 0.467436i | ||||
\(490\) | −0.310708 | − | 8.65758i | −0.0140364 | − | 0.391109i | ||||
\(491\) | 27.3945 | 1.23630 | 0.618149 | − | 0.786061i | \(-0.287883\pi\) | ||||
0.618149 | + | 0.786061i | \(0.287883\pi\) | |||||||
\(492\) | 14.9771 | − | 8.65372i | 0.675219 | − | 0.390140i | ||||
\(493\) | −1.39019 | −0.0626112 | ||||||||
\(494\) | −0.0297752 | − | 0.829657i | −0.00133965 | − | 0.0373280i | ||||
\(495\) | 9.19069 | + | 7.22797i | 0.413091 | + | 0.324873i | ||||
\(496\) | −5.12128 | − | 35.4449i | −0.229952 | − | 1.59152i | ||||
\(497\) | − | 19.8728i | − | 0.891417i | ||||||
\(498\) | 6.98106 | + | 13.1495i | 0.312829 | + | 0.589242i | ||||
\(499\) | − | 22.7931i | − | 1.02036i | −0.860068 | − | 0.510179i | \(-0.829579\pi\) | ||
0.860068 | − | 0.510179i | \(-0.170421\pi\) | |||||||
\(500\) | 1.02988 | + | 14.3298i | 0.0460577 | + | 0.640850i | ||||
\(501\) | −9.99191 | − | 20.5698i | −0.446406 | − | 0.918991i | ||||
\(502\) | 0.758898 | − | 0.0272358i | 0.0338713 | − | 0.00121559i | ||||
\(503\) | 11.0608 | 0.493177 | 0.246588 | − | 0.969120i | \(-0.420690\pi\) | ||||
0.246588 | + | 0.969120i | \(0.420690\pi\) | |||||||
\(504\) | 27.8939 | + | 17.4415i | 1.24249 | + | 0.776907i | ||||
\(505\) | 6.35500 | 0.282794 | ||||||||
\(506\) | 29.8435 | − | 1.07104i | 1.32670 | − | 0.0476135i | ||||
\(507\) | −9.57751 | − | 19.7167i | −0.425352 | − | 0.875649i | ||||
\(508\) | 1.56173 | + | 21.7300i | 0.0692904 | + | 0.964111i | ||||
\(509\) | − | 16.9182i | − | 0.749887i | −0.927048 | − | 0.374944i | \(-0.877662\pi\) | ||
0.927048 | − | 0.374944i | \(-0.122338\pi\) | |||||||
\(510\) | −1.44229 | − | 2.71670i | −0.0638659 | − | 0.120297i | ||||
\(511\) | 28.6119i | 1.26572i | ||||||||
\(512\) | 21.4583 | − | 7.17920i | 0.948332 | − | 0.317279i | ||||
\(513\) | 1.10469 | − | 5.07737i | 0.0487733 | − | 0.224171i | ||||
\(514\) | −1.00864 | − | 28.1047i | −0.0444891 | − | 1.23964i | ||||
\(515\) | 1.64110 | 0.0723156 | ||||||||
\(516\) | −26.3851 | + | 15.2452i | −1.16154 | + | 0.671135i | ||||
\(517\) | −54.2770 | −2.38710 | ||||||||
\(518\) | 0.359610 | + | 10.0202i | 0.0158004 | + | 0.440261i | ||||
\(519\) | 33.5644 | − | 16.3041i | 1.47332 | − | 0.715672i | ||||
\(520\) | −0.136025 | − | 1.25906i | −0.00596509 | − | 0.0552135i | ||||
\(521\) | 32.2873i | 1.41453i | 0.706948 | + | 0.707265i | \(0.250071\pi\) | ||||
−0.706948 | + | 0.707265i | \(0.749929\pi\) | |||||||
\(522\) | −2.89360 | − | 2.11219i | −0.126649 | − | 0.0924480i | ||||
\(523\) | 16.7639i | 0.733034i | 0.930411 | + | 0.366517i | \(0.119450\pi\) | ||||
−0.930411 | + | 0.366517i | \(0.880550\pi\) | |||||||
\(524\) | 15.9697 | − | 1.14774i | 0.697640 | − | 0.0501392i | ||||
\(525\) | 26.6879 | − | 12.9638i | 1.16475 | − | 0.565787i | ||||
\(526\) | −19.0446 | + | 0.683484i | −0.830384 | + | 0.0298013i | ||||
\(527\) | 14.7403 | 0.642098 | ||||||||
\(528\) | −19.8639 | − | 29.3057i | −0.864463 | − | 1.27537i | ||||
\(529\) | −5.92427 | −0.257577 | ||||||||
\(530\) | −11.1036 | + | 0.398494i | −0.482312 | + | 0.0173095i | ||||
\(531\) | 14.6593 | − | 18.6400i | 0.636161 | − | 0.808908i | ||||
\(532\) | 7.73417 | − | 0.555853i | 0.335319 | − | 0.0240993i | ||||
\(533\) | 2.93125i | 0.126967i | ||||||||
\(534\) | −19.6086 | + | 10.4102i | −0.848546 | + | 0.450493i | ||||
\(535\) | − | 8.06361i | − | 0.348620i | ||||||
\(536\) | −2.56160 | − | 23.7104i | −0.110644 | − | 1.02413i | ||||
\(537\) | 13.9087 | + | 28.6330i | 0.600203 | + | 1.23560i | ||||
\(538\) | −0.736000 | − | 20.5079i | −0.0317312 | − | 0.884159i | ||||
\(539\) | 41.0418 | 1.76780 | ||||||||
\(540\) | 1.12557 | − | 7.84597i | 0.0484369 | − | 0.337637i | ||||
\(541\) | −3.18983 | −0.137141 | −0.0685707 | − | 0.997646i | \(-0.521844\pi\) | ||||
−0.0685707 | + | 0.997646i | \(0.521844\pi\) | |||||||
\(542\) | 0.0896003 | + | 2.49662i | 0.00384866 | + | 0.107239i | ||||
\(543\) | 0.501055 | + | 1.03150i | 0.0215023 | + | 0.0442657i | ||||
\(544\) | 1.66154 | + | 9.16384i | 0.0712378 | + | 0.392897i | ||||
\(545\) | 9.96892i | 0.427022i | ||||||||
\(546\) | −4.92405 | + | 2.61418i | −0.210730 | + | 0.111876i | ||||
\(547\) | 37.9635i | 1.62320i | 0.584211 | + | 0.811602i | \(0.301404\pi\) | ||||
−0.584211 | + | 0.811602i | \(0.698596\pi\) | |||||||
\(548\) | −2.98496 | − | 41.5329i | −0.127511 | − | 1.77420i | ||||
\(549\) | −6.70616 | + | 8.52719i | −0.286212 | + | 0.363932i | ||||
\(550\) | −31.9089 | + | 1.14517i | −1.36060 | + | 0.0488301i | ||||
\(551\) | −0.844401 | −0.0359727 | ||||||||
\(552\) | −10.7500 | − | 17.1539i | −0.457551 | − | 0.730117i | ||||
\(553\) | 52.0725 | 2.21435 | ||||||||
\(554\) | 5.67739 | − | 0.203753i | 0.241209 | − | 0.00865665i | ||||
\(555\) | 2.17297 | − | 1.05554i | 0.0922375 | − | 0.0448050i | ||||
\(556\) | 2.39595 | + | 33.3374i | 0.101611 | + | 1.41382i | ||||
\(557\) | − | 3.37117i | − | 0.142841i | −0.997446 | − | 0.0714204i | \(-0.977247\pi\) | ||
0.997446 | − | 0.0714204i | \(-0.0227532\pi\) | |||||||
\(558\) | 30.6810 | + | 22.3957i | 1.29883 | + | 0.948085i | ||||
\(559\) | − | 5.16398i | − | 0.218413i | ||||||
\(560\) | 11.7067 | − | 1.69145i | 0.494698 | − | 0.0714769i | ||||
\(561\) | 13.1072 | − | 6.36689i | 0.553385 | − | 0.268810i | ||||
\(562\) | 1.09613 | + | 30.5426i | 0.0462375 | + | 1.28836i | ||||
\(563\) | −26.3977 | −1.11253 | −0.556265 | − | 0.831005i | \(-0.687766\pi\) | ||||
−0.556265 | + | 0.831005i | \(0.687766\pi\) | |||||||
\(564\) | 18.4079 | + | 31.8588i | 0.775113 | + | 1.34150i | ||||
\(565\) | 2.73964 | 0.115258 | ||||||||
\(566\) | −0.892893 | − | 24.8796i | −0.0375311 | − | 1.04577i | ||||
\(567\) | −33.9103 | + | 8.22497i | −1.42410 | + | 0.345416i | ||||
\(568\) | 14.4139 | − | 1.55723i | 0.604794 | − | 0.0653401i | ||||
\(569\) | 27.7716i | 1.16425i | 0.813101 | + | 0.582123i | \(0.197778\pi\) | ||||
−0.813101 | + | 0.582123i | \(0.802222\pi\) | |||||||
\(570\) | −0.876047 | − | 1.65012i | −0.0366936 | − | 0.0691158i | ||||
\(571\) | − | 0.846452i | − | 0.0354229i | −0.999843 | − | 0.0177115i | \(-0.994362\pi\) | ||
0.999843 | − | 0.0177115i | \(-0.00563803\pi\) | |||||||
\(572\) | 5.98410 | − | 0.430075i | 0.250208 | − | 0.0179823i | ||||
\(573\) | −10.6317 | − | 21.8868i | −0.444144 | − | 0.914335i | ||||
\(574\) | −27.3608 | + | 0.981938i | −1.14202 | + | 0.0409853i | ||||
\(575\) | −18.2575 | −0.761392 | ||||||||
\(576\) | −10.4647 | + | 21.5984i | −0.436029 | + | 0.899933i | ||||
\(577\) | 18.5211 | 0.771045 | 0.385523 | − | 0.922698i | \(-0.374021\pi\) | ||||
0.385523 | + | 0.922698i | \(0.374021\pi\) | |||||||
\(578\) | 20.1954 | − | 0.724783i | 0.840017 | − | 0.0301470i | ||||
\(579\) | 1.86331 | + | 3.83589i | 0.0774365 | + | 0.159414i | ||||
\(580\) | −1.28475 | + | 0.0923346i | −0.0533463 | + | 0.00383399i | ||||
\(581\) | − | 23.5643i | − | 0.977613i | ||||||
\(582\) | −5.40184 | − | 10.1749i | −0.223914 | − | 0.421762i | ||||
\(583\) | − | 52.6376i | − | 2.18003i | ||||||
\(584\) | −20.7524 | + | 2.24203i | −0.858742 | + | 0.0927758i | ||||
\(585\) | 1.05581 | + | 0.830339i | 0.0436525 | + | 0.0343303i | ||||
\(586\) | 0.590556 | + | 16.4553i | 0.0243956 | + | 0.679761i | ||||
\(587\) | −38.1358 | −1.57403 | −0.787017 | − | 0.616931i | \(-0.788376\pi\) | ||||
−0.787017 | + | 0.616931i | \(0.788376\pi\) | |||||||
\(588\) | −13.9192 | − | 24.0901i | −0.574019 | − | 0.993461i | ||||
\(589\) | 8.95324 | 0.368912 | ||||||||
\(590\) | −0.305795 | − | 8.52069i | −0.0125894 | − | 0.350791i | ||||
\(591\) | 32.0925 | − | 15.5891i | 1.32011 | − | 0.641252i | ||||
\(592\) | −7.23954 | + | 1.04601i | −0.297543 | + | 0.0429907i | ||||
\(593\) | 6.09379i | 0.250242i | 0.992142 | + | 0.125121i | \(0.0399319\pi\) | ||||
−0.992142 | + | 0.125121i | \(0.960068\pi\) | |||||||
\(594\) | 36.9552 | + | 6.66211i | 1.51629 | + | 0.273350i | ||||
\(595\) | 4.86842i | 0.199586i | ||||||||
\(596\) | 0.574487 | + | 7.99346i | 0.0235319 | + | 0.327425i | ||||
\(597\) | 19.9985 | − | 9.71441i | 0.818485 | − | 0.397584i | ||||
\(598\) | 3.42837 | − | 0.123039i | 0.140197 | − | 0.00503146i | ||||
\(599\) | −37.7702 | −1.54325 | −0.771625 | − | 0.636078i | \(-0.780556\pi\) | ||||
−0.771625 | + | 0.636078i | \(0.780556\pi\) | |||||||
\(600\) | 11.4940 | + | 18.3411i | 0.469241 | + | 0.748772i | ||||
\(601\) | −21.2157 | −0.865405 | −0.432702 | − | 0.901537i | \(-0.642440\pi\) | ||||
−0.432702 | + | 0.901537i | \(0.642440\pi\) | |||||||
\(602\) | 48.2014 | − | 1.72988i | 1.96454 | − | 0.0705046i | ||||
\(603\) | 19.8829 | + | 15.6368i | 0.809694 | + | 0.636780i | ||||
\(604\) | 1.72115 | + | 23.9482i | 0.0700326 | + | 0.974438i | ||||
\(605\) | 11.5264i | 0.468615i | ||||||||
\(606\) | 18.0266 | − | 9.57031i | 0.732280 | − | 0.388767i | ||||
\(607\) | − | 17.2749i | − | 0.701168i | −0.936531 | − | 0.350584i | \(-0.885983\pi\) | ||
0.936531 | − | 0.350584i | \(-0.114017\pi\) | |||||||
\(608\) | 1.00921 | + | 5.56610i | 0.0409291 | + | 0.225735i | ||||
\(609\) | 2.47758 | + | 5.10047i | 0.100397 | + | 0.206681i | ||||
\(610\) | 0.139891 | + | 3.89793i | 0.00566403 | + | 0.157823i | ||||
\(611\) | −6.23527 | −0.252252 | ||||||||
\(612\) | −8.18242 | − | 5.53415i | −0.330755 | − | 0.223705i | ||||
\(613\) | −28.0989 | −1.13490 | −0.567452 | − | 0.823406i | \(-0.692071\pi\) | ||||
−0.567452 | + | 0.823406i | \(0.692071\pi\) | |||||||
\(614\) | 0.258579 | + | 7.20506i | 0.0104354 | + | 0.290772i | ||||
\(615\) | 2.88221 | + | 5.93344i | 0.116222 | + | 0.239260i | ||||
\(616\) | 6.01900 | + | 55.7124i | 0.242512 | + | 2.24472i | ||||
\(617\) | 43.2071i | 1.73945i | 0.493535 | + | 0.869726i | \(0.335704\pi\) | ||||
−0.493535 | + | 0.869726i | \(0.664296\pi\) | |||||||
\(618\) | 4.65515 | − | 2.47142i | 0.187258 | − | 0.0994151i | ||||
\(619\) | 4.54698i | 0.182759i | 0.995816 | + | 0.0913793i | \(0.0291276\pi\) | ||||
−0.995816 | + | 0.0913793i | \(0.970872\pi\) | |||||||
\(620\) | 13.6223 | − | 0.979030i | 0.547084 | − | 0.0393188i | ||||
\(621\) | 20.9811 | + | 4.56489i | 0.841942 | + | 0.183183i | ||||
\(622\) | 17.0691 | − | 0.612585i | 0.684408 | − | 0.0245624i | ||||
\(623\) | 35.1393 | 1.40783 | ||||||||
\(624\) | −2.28193 | − | 3.36660i | −0.0913504 | − | 0.134772i | ||||
\(625\) | 16.6125 | 0.664502 | ||||||||
\(626\) | 29.8005 | − | 1.06950i | 1.19107 | − | 0.0427458i | ||||
\(627\) | 7.96127 | − | 3.86724i | 0.317943 | − | 0.154443i | ||||
\(628\) | 8.55095 | − | 0.614554i | 0.341220 | − | 0.0245234i | ||||
\(629\) | − | 3.01067i | − | 0.120043i | ||||||
\(630\) | −7.39682 | + | 10.1333i | −0.294696 | + | 0.403720i | ||||
\(631\) | − | 7.74390i | − | 0.308280i | −0.988049 | − | 0.154140i | \(-0.950739\pi\) | ||
0.988049 | − | 0.154140i | \(-0.0492606\pi\) | |||||||
\(632\) | 4.08041 | + | 37.7686i | 0.162310 | + | 1.50235i | ||||
\(633\) | 1.92869 | − | 0.936874i | 0.0766586 | − | 0.0372374i | ||||
\(634\) | −0.495766 | − | 13.8140i | −0.0196894 | − | 0.548625i | ||||
\(635\) | −8.30818 | −0.329700 | ||||||||
\(636\) | −30.8965 | + | 17.8519i | −1.22512 | + | 0.707874i | ||||
\(637\) | 4.71482 | 0.186808 | ||||||||
\(638\) | −0.218859 | − | 6.09829i | −0.00866471 | − | 0.241434i | ||||
\(639\) | −9.50583 | + | 12.0871i | −0.376045 | + | 0.478158i | ||||
\(640\) | 2.14416 | + | 8.35842i | 0.0847554 | + | 0.330396i | ||||
\(641\) | − | 24.6485i | − | 0.973558i | −0.873525 | − | 0.486779i | \(-0.838172\pi\) | ||
0.873525 | − | 0.486779i | \(-0.161828\pi\) | |||||||
\(642\) | −12.1434 | − | 22.8732i | −0.479261 | − | 0.902734i | ||||
\(643\) | 20.1704i | 0.795441i | 0.917507 | + | 0.397721i | \(0.130199\pi\) | ||||
−0.917507 | + | 0.397721i | \(0.869801\pi\) | |||||||
\(644\) | 2.29694 | + | 31.9598i | 0.0905121 | + | 1.25939i | ||||
\(645\) | −5.07758 | − | 10.4529i | −0.199930 | − | 0.411584i | ||||
\(646\) | −2.32682 | + | 0.0835061i | −0.0915474 | + | 0.00328550i | ||||
\(647\) | −0.822458 | −0.0323342 | −0.0161671 | − | 0.999869i | \(-0.505146\pi\) | ||||
−0.0161671 | + | 0.999869i | \(0.505146\pi\) | |||||||
\(648\) | −8.62285 | − | 23.9509i | −0.338737 | − | 0.940881i | ||||
\(649\) | 40.3929 | 1.58556 | ||||||||
\(650\) | −3.66565 | + | 0.131555i | −0.143779 | + | 0.00516002i | ||||
\(651\) | −26.2700 | − | 54.0806i | −1.02960 | − | 2.11959i | ||||
\(652\) | 1.95820 | + | 27.2465i | 0.0766890 | + | 1.06706i | ||||
\(653\) | 28.7332i | 1.12442i | 0.826995 | + | 0.562209i | \(0.190048\pi\) | ||||
−0.826995 | + | 0.562209i | \(0.809952\pi\) | |||||||
\(654\) | 15.0127 | + | 28.2778i | 0.587043 | + | 1.10575i | ||||
\(655\) | 6.10582i | 0.238574i | ||||||||
\(656\) | −2.85620 | − | 19.7680i | −0.111516 | − | 0.771812i | ||||
\(657\) | 13.6860 | − | 17.4024i | 0.533943 | − | 0.678933i | ||||
\(658\) | −2.08875 | − | 58.2009i | −0.0814279 | − | 2.26891i | ||||
\(659\) | −28.7797 | −1.12110 | −0.560549 | − | 0.828121i | \(-0.689410\pi\) | ||||
−0.560549 | + | 0.828121i | \(0.689410\pi\) | |||||||
\(660\) | 11.6901 | − | 6.75453i | 0.455038 | − | 0.262920i | ||||
\(661\) | −3.76984 | −0.146630 | −0.0733149 | − | 0.997309i | \(-0.523358\pi\) | ||||
−0.0733149 | + | 0.997309i | \(0.523358\pi\) | |||||||
\(662\) | −0.0724583 | − | 2.01898i | −0.00281617 | − | 0.0784699i | ||||
\(663\) | 1.50573 | − | 0.731420i | 0.0584779 | − | 0.0284060i | ||||
\(664\) | 17.0914 | − | 1.84650i | 0.663275 | − | 0.0716582i | ||||
\(665\) | 2.95707i | 0.114670i | ||||||||
\(666\) | 4.57427 | − | 6.26652i | 0.177249 | − | 0.242823i | ||||
\(667\) | − | 3.48930i | − | 0.135106i | ||||||
\(668\) | −26.3380 | + | 1.89290i | −1.01905 | + | 0.0732387i | ||||
\(669\) | 32.0081 | − | 15.5481i | 1.23750 | − | 0.601125i | ||||
\(670\) | 9.08883 | − | 0.326185i | 0.351132 | − | 0.0126016i | ||||
\(671\) | −18.4784 | −0.713351 | ||||||||
\(672\) | 30.6600 | − | 22.4277i | 1.18273 | − | 0.865166i | ||||
\(673\) | −18.6014 | −0.717033 | −0.358516 | − | 0.933523i | \(-0.616717\pi\) | ||||
−0.358516 | + | 0.933523i | \(0.616717\pi\) | |||||||
\(674\) | 0.0704838 | − | 0.00252956i | 0.00271493 | − | 9.74351e-5i | ||||
\(675\) | −22.4332 | − | 4.88083i | −0.863455 | − | 0.187863i | ||||
\(676\) | −25.2457 | + | 1.81440i | −0.970987 | + | 0.0697846i | ||||
\(677\) | − | 30.9430i | − | 1.18923i | −0.804009 | − | 0.594617i | \(-0.797304\pi\) | ||
0.804009 | − | 0.594617i | \(-0.202696\pi\) | |||||||
\(678\) | 7.77126 | − | 4.12576i | 0.298453 | − | 0.158449i | ||||
\(679\) | 18.2337i | 0.699746i | ||||||||
\(680\) | −3.53110 | + | 0.381489i | −0.135412 | + | 0.0146294i | ||||
\(681\) | −19.3869 | − | 39.9108i | −0.742908 | − | 1.52938i | ||||
\(682\) | 2.32058 | + | 64.6606i | 0.0888595 | + | 2.47598i | ||||
\(683\) | −31.2070 | −1.19410 | −0.597052 | − | 0.802203i | \(-0.703661\pi\) | ||||
−0.597052 | + | 0.802203i | \(0.703661\pi\) | |||||||
\(684\) | −4.96999 | − | 3.36143i | −0.190032 | − | 0.128528i | ||||
\(685\) | 15.8796 | 0.606729 | ||||||||
\(686\) | 0.202865 | + | 5.65265i | 0.00774544 | + | 0.215819i | ||||
\(687\) | −14.2241 | − | 29.2824i | −0.542683 | − | 1.11719i | ||||
\(688\) | 5.03176 | + | 34.8253i | 0.191834 | + | 1.32770i | ||||
\(689\) | − | 6.04693i | − | 0.230370i | ||||||
\(690\) | 6.81874 | − | 3.62007i | 0.259585 | − | 0.137814i | ||||
\(691\) | 49.2668i | 1.87420i | 0.349065 | + | 0.937099i | \(0.386499\pi\) | ||||
−0.349065 | + | 0.937099i | \(0.613501\pi\) | |||||||
\(692\) | −3.08872 | − | 42.9766i | −0.117415 | − | 1.63373i | ||||
\(693\) | −46.7189 | − | 36.7418i | −1.77470 | − | 1.39571i | ||||
\(694\) | 15.8579 | − | 0.569118i | 0.601959 | − | 0.0216034i | ||||
\(695\) | −12.7461 | −0.483488 | ||||||||
\(696\) | −3.50527 | + | 2.19668i | −0.132867 | + | 0.0832651i | ||||
\(697\) | 8.22084 | 0.311387 | ||||||||
\(698\) | −18.4345 | + | 0.661590i | −0.697758 | + | 0.0250415i | ||||
\(699\) | −21.1215 | + | 10.2599i | −0.798888 | + | 0.388065i | ||||
\(700\) | −2.45591 | − | 34.1717i | −0.0928247 | − | 1.29157i | ||||
\(701\) | 21.9424i | 0.828753i | 0.910105 | + | 0.414377i | \(0.136000\pi\) | ||||
−0.910105 | + | 0.414377i | \(0.864000\pi\) | |||||||
\(702\) | 4.24537 | + | 0.765334i | 0.160231 | + | 0.0288857i | ||||
\(703\) | − | 1.82868i | − | 0.0689699i | ||||||
\(704\) | −39.9370 | + | 8.73125i | −1.50518 | + | 0.329072i | ||||
\(705\) | −12.6214 | + | 6.13094i | −0.475351 | + | 0.230905i | ||||
\(706\) | −1.02837 | − | 28.6545i | −0.0387032 | − | 1.07843i | ||||
\(707\) | −32.3043 | −1.21493 | ||||||||
\(708\) | −13.6992 | − | 23.7093i | −0.514846 | − | 0.891048i | ||||
\(709\) | 16.0534 | 0.602898 | 0.301449 | − | 0.953482i | \(-0.402530\pi\) | ||||
0.301449 | + | 0.953482i | \(0.402530\pi\) | |||||||
\(710\) | 0.198293 | + | 5.52523i | 0.00744179 | + | 0.207358i | ||||
\(711\) | −31.6717 | − | 24.9080i | −1.18778 | − | 0.934125i | ||||
\(712\) | 2.75352 | + | 25.4868i | 0.103192 | + | 0.955158i | ||||
\(713\) | 36.9973i | 1.38556i | ||||||||
\(714\) | 7.33159 | + | 13.8097i | 0.274378 | + | 0.516816i | ||||
\(715\) | 2.28795i | 0.0855643i | ||||||||
\(716\) | 36.6623 | − | 2.63491i | 1.37013 | − | 0.0984711i | ||||
\(717\) | 8.60596 | + | 17.7166i | 0.321396 | + | 0.661640i | ||||
\(718\) | 7.54067 | − | 0.270624i | 0.281415 | − | 0.0100996i | ||||
\(719\) | 51.9817 | 1.93859 | 0.969294 | − | 0.245904i | \(-0.0790847\pi\) | ||||
0.969294 | + | 0.245904i | \(0.0790847\pi\) | |||||||
\(720\) | −7.92936 | − | 4.57093i | −0.295510 | − | 0.170349i | ||||
\(721\) | −8.34219 | −0.310679 | ||||||||
\(722\) | −1.41330 | + | 0.0507215i | −0.0525977 | + | 0.00188766i | ||||
\(723\) | −9.12855 | − | 18.7925i | −0.339495 | − | 0.698899i | ||||
\(724\) | 1.32075 | − | 0.0949218i | 0.0490852 | − | 0.00352774i | ||||
\(725\) | 3.73080i | 0.138558i | ||||||||
\(726\) | 17.3582 | + | 32.6958i | 0.644223 | + | 1.21345i | ||||
\(727\) | − | 11.3387i | − | 0.420528i | −0.977645 | − | 0.210264i | \(-0.932568\pi\) | ||
0.977645 | − | 0.210264i | \(-0.0674324\pi\) | |||||||
\(728\) | 0.691454 | + | 6.40016i | 0.0256270 | + | 0.237206i | ||||
\(729\) | 24.5593 | + | 11.2178i | 0.909604 | + | 0.415475i | ||||
\(730\) | −0.285492 | − | 7.95496i | −0.0105665 | − | 0.294426i | ||||
\(731\) | −14.4827 | −0.535660 | ||||||||
\(732\) | 6.26691 | + | 10.8462i | 0.231631 | + | 0.400887i | ||||
\(733\) | −19.3407 | −0.714364 | −0.357182 | − | 0.934035i | \(-0.616262\pi\) | ||||
−0.357182 | + | 0.934035i | \(0.616262\pi\) | |||||||
\(734\) | −0.756505 | − | 21.0793i | −0.0279231 | − | 0.778050i | ||||
\(735\) | 9.54376 | − | 4.63594i | 0.352027 | − | 0.170999i | ||||
\(736\) | −23.0007 | + | 4.17036i | −0.847816 | + | 0.153721i | ||||
\(737\) | 43.0862i | 1.58710i | ||||||||
\(738\) | 17.1111 | + | 12.4903i | 0.629870 | + | 0.459775i | ||||
\(739\) | 3.81202i | 0.140227i | 0.997539 | + | 0.0701136i | \(0.0223362\pi\) | ||||
−0.997539 | + | 0.0701136i | \(0.977664\pi\) | |||||||
\(740\) | −0.199964 | − | 2.78232i | −0.00735084 | − | 0.102280i | ||||
\(741\) | 0.914580 | − | 0.444263i | 0.0335979 | − | 0.0163204i | ||||
\(742\) | 56.4430 | − | 2.02566i | 2.07209 | − | 0.0743643i | ||||
\(743\) | 21.1840 | 0.777167 | 0.388583 | − | 0.921414i | \(-0.372965\pi\) | ||||
0.388583 | + | 0.921414i | \(0.372965\pi\) | |||||||
\(744\) | 37.1666 | − | 23.2916i | 1.36259 | − | 0.853912i | ||||
\(745\) | −3.05620 | −0.111971 | ||||||||
\(746\) | −13.3959 | + | 0.480759i | −0.490458 | + | 0.0176018i | ||||
\(747\) | −11.2716 | + | 14.3324i | −0.412407 | + | 0.524394i | ||||
\(748\) | −1.20617 | − | 16.7827i | −0.0441019 | − | 0.613636i | ||||
\(749\) | 40.9896i | 1.49773i | ||||||||
\(750\) | −15.5413 | + | 8.25085i | −0.567486 | + | 0.301279i | ||||
\(751\) | 40.7496i | 1.48697i | 0.668750 | + | 0.743487i | \(0.266830\pi\) | ||||
−0.668750 | + | 0.743487i | \(0.733170\pi\) | |||||||
\(752\) | 42.0499 | − | 6.07562i | 1.53340 | − | 0.221555i | ||||
\(753\) | 0.406373 | + | 0.836578i | 0.0148091 | + | 0.0304866i | ||||
\(754\) | −0.0251422 | − | 0.700563i | −0.000915626 | − | 0.0255130i | ||||
\(755\) | −9.15629 | −0.333232 | ||||||||
\(756\) | −5.72160 | + | 39.8833i | −0.208092 | + | 1.45054i | ||||
\(757\) | −6.39533 | −0.232442 | −0.116221 | − | 0.993223i | \(-0.537078\pi\) | ||||
−0.116221 | + | 0.993223i | \(0.537078\pi\) | |||||||
\(758\) | 0.254479 | + | 7.09082i | 0.00924311 | + | 0.257550i | ||||
\(759\) | 15.9805 | + | 32.8982i | 0.580056 | + | 1.19413i | ||||
\(760\) | −2.14478 | + | 0.231716i | −0.0777995 | + | 0.00840522i | ||||
\(761\) | 18.6783i | 0.677087i | 0.940951 | + | 0.338543i | \(0.109934\pi\) | ||||
−0.940951 | + | 0.338543i | \(0.890066\pi\) | |||||||
\(762\) | −23.5670 | + | 12.5117i | −0.853742 | + | 0.453252i | ||||
\(763\) | − | 50.6748i | − | 1.83455i | ||||||
\(764\) | −28.0243 | + | 2.01410i | −1.01389 | + | 0.0728676i | ||||
\(765\) | 2.32873 | − | 2.96108i | 0.0841953 | − | 0.107058i | ||||
\(766\) | 29.0537 | − | 1.04270i | 1.04975 | − | 0.0376742i | ||||
\(767\) | 4.64028 | 0.167551 | ||||||||
\(768\) | 18.6695 | + | 20.4805i | 0.673677 | + | 0.739026i | ||||
\(769\) | 41.4802 | 1.49582 | 0.747908 | − | 0.663803i | \(-0.231059\pi\) | ||||
0.747908 | + | 0.663803i | \(0.231059\pi\) | |||||||
\(770\) | −21.3560 | + | 0.766438i | −0.769618 | + | 0.0276205i | ||||
\(771\) | 30.9814 | − | 15.0494i | 1.11577 | − | 0.541992i | ||||
\(772\) | 4.91156 | − | 0.352992i | 0.176771 | − | 0.0127045i | ||||
\(773\) | 4.79619i | 0.172507i | 0.996273 | + | 0.0862536i | \(0.0274895\pi\) | ||||
−0.996273 | + | 0.0862536i | \(0.972510\pi\) | |||||||
\(774\) | −30.1447 | − | 22.0042i | −1.08353 | − | 0.790925i | ||||
\(775\) | − | 39.5579i | − | 1.42096i | ||||||
\(776\) | −13.2251 | + | 1.42880i | −0.474752 | + | 0.0512908i | ||||
\(777\) | −11.0458 | + | 5.36558i | −0.396267 | + | 0.192489i | ||||
\(778\) | −0.966549 | − | 26.9320i | −0.0346525 | − | 0.965557i | ||||
\(779\) | 4.99332 | 0.178904 | ||||||||
\(780\) | 1.34295 | − | 0.775951i | 0.0480852 | − | 0.0277835i | ||||
\(781\) | −26.1927 | −0.937248 | ||||||||
\(782\) | −0.345071 | − | 9.61505i | −0.0123397 | − | 0.343834i | ||||
\(783\) | 0.932802 | − | 4.28733i | 0.0333356 | − | 0.153217i | ||||
\(784\) | −31.7962 | + | 4.59410i | −1.13558 | + | 0.164075i | ||||
\(785\) | 3.26935i | 0.116688i | ||||||||
\(786\) | 9.19506 | + | 17.3198i | 0.327977 | + | 0.617775i | ||||
\(787\) | 4.94761i | 0.176363i | 0.996104 | + | 0.0881816i | \(0.0281056\pi\) | ||||
−0.996104 | + | 0.0881816i | \(0.971894\pi\) | |||||||
\(788\) | −2.95327 | − | 41.0919i | −0.105206 | − | 1.46384i | ||||
\(789\) | −10.1980 | − | 20.9940i | −0.363057 | − | 0.747406i | ||||
\(790\) | −14.4777 | + | 0.519584i | −0.515094 | + | 0.0184860i | ||||
\(791\) | −13.9264 | −0.495165 | ||||||||
\(792\) | 22.9882 | − | 36.7647i | 0.816851 | − | 1.30638i | ||||
\(793\) | −2.12277 | −0.0753819 | ||||||||
\(794\) | 49.8601 | − | 1.78941i | 1.76947 | − | 0.0635037i | ||||
\(795\) | −5.94576 | − | 12.2402i | −0.210874 | − | 0.434115i | ||||
\(796\) | −1.84033 | − | 25.6065i | −0.0652289 | − | 0.907599i | ||||
\(797\) | 0.611017i | 0.0216433i | 0.999941 | + | 0.0108217i | \(0.00344471\pi\) | ||||
−0.999941 | + | 0.0108217i | \(0.996555\pi\) | |||||||
\(798\) | 4.45319 | + | 8.38801i | 0.157641 | + | 0.296932i | ||||
\(799\) | 17.4871i | 0.618650i | ||||||||
\(800\) | 24.5926 | − | 4.45899i | 0.869479 | − | 0.157649i | ||||
\(801\) | −21.3725 | − | 16.8083i | −0.755161 | − | 0.593892i | ||||
\(802\) | 0.934368 | + | 26.0352i | 0.0329937 | + | 0.919336i | ||||
\(803\) | 37.7110 | 1.33079 | ||||||||
\(804\) | 25.2901 | − | 14.6126i | 0.891914 | − | 0.515346i | ||||
\(805\) | −12.2194 | −0.430678 | ||||||||
\(806\) | 0.266585 | + | 7.42812i | 0.00939005 | + | 0.261644i | ||||
\(807\) | 22.6071 | − | 10.9815i | 0.795807 | − | 0.386568i | ||||
\(808\) | −2.53136 | − | 23.4305i | −0.0890531 | − | 0.824283i | ||||
\(809\) | 22.0883i | 0.776584i | 0.921536 | + | 0.388292i | \(0.126935\pi\) | ||||
−0.921536 | + | 0.388292i | \(0.873065\pi\) | |||||||
\(810\) | 9.34601 | − | 2.62515i | 0.328385 | − | 0.0922382i | ||||
\(811\) | − | 3.55462i | − | 0.124819i | −0.998051 | − | 0.0624097i | \(-0.980121\pi\) | ||
0.998051 | − | 0.0624097i | \(-0.0198786\pi\) | |||||||
\(812\) | 6.53075 | − | 0.469363i | 0.229184 | − | 0.0164714i | ||||
\(813\) | −2.75218 | + | 1.33689i | −0.0965231 | + | 0.0468867i | ||||
\(814\) | 13.2068 | − | 0.473972i | 0.462897 | − | 0.0166127i | ||||
\(815\) | −10.4174 | −0.364905 | ||||||||
\(816\) | −9.44181 | + | 6.39979i | −0.330529 | + | 0.224038i | ||||
\(817\) | −8.79674 | −0.307759 | ||||||||
\(818\) | −8.35498 | + | 0.299848i | −0.292125 | + | 0.0104839i | ||||
\(819\) | −5.36700 | − | 4.22085i | −0.187538 | − | 0.147488i | ||||
\(820\) | 7.59730 | − | 0.546016i | 0.265309 | − | 0.0190677i | ||||
\(821\) | 3.66352i | 0.127858i | 0.997954 | + | 0.0639289i | \(0.0203631\pi\) | ||||
−0.997954 | + | 0.0639289i | \(0.979637\pi\) | |||||||
\(822\) | 45.0441 | − | 23.9139i | 1.57109 | − | 0.834093i | ||||
\(823\) | − | 23.5512i | − | 0.820942i | −0.911874 | − | 0.410471i | \(-0.865364\pi\) | ||
0.911874 | − | 0.410471i | \(-0.134636\pi\) | |||||||
\(824\) | −0.653695 | − | 6.05066i | −0.0227725 | − | 0.210785i | ||||
\(825\) | −17.0865 | − | 35.1751i | −0.594877 | − | 1.22464i | ||||
\(826\) | 1.55444 | + | 43.3131i | 0.0540860 | + | 1.50705i | ||||
\(827\) | −0.973110 | −0.0338384 | −0.0169192 | − | 0.999857i | \(-0.505386\pi\) | ||||
−0.0169192 | + | 0.999857i | \(0.505386\pi\) | |||||||
\(828\) | 13.8904 | − | 20.5374i | 0.482724 | − | 0.713723i | ||||
\(829\) | −36.6213 | −1.27191 | −0.635955 | − | 0.771727i | \(-0.719393\pi\) | ||||
−0.635955 | + | 0.771727i | \(0.719393\pi\) | |||||||
\(830\) | 0.235127 | + | 6.55158i | 0.00816138 | + | 0.227409i | ||||
\(831\) | 3.04011 | + | 6.25852i | 0.105460 | + | 0.217106i | ||||
\(832\) | −4.58791 | + | 1.00303i | −0.159057 | + | 0.0347740i | ||||
\(833\) | − | 13.2230i | − | 0.458149i | ||||||
\(834\) | −36.1556 | + | 19.1950i | −1.25197 | + | 0.664670i | ||||
\(835\) | − | 10.0700i | − | 0.348487i | ||||||
\(836\) | −0.732624 | − | 10.1938i | −0.0253383 | − | 0.352559i | ||||
\(837\) | −9.89056 | + | 45.4589i | −0.341868 | + | 1.57129i | ||||
\(838\) | 49.1285 | − | 1.76315i | 1.69711 | − | 0.0609070i | ||||
\(839\) | 43.8957 | 1.51545 | 0.757723 | − | 0.652576i | \(-0.226312\pi\) | ||||
0.757723 | + | 0.652576i | \(0.226312\pi\) | |||||||
\(840\) | 7.69272 | + | 12.2753i | 0.265424 | + | 0.423539i | ||||
\(841\) | 28.2870 | 0.975413 | ||||||||
\(842\) | 24.6255 | − | 0.883775i | 0.848652 | − | 0.0304569i | ||||
\(843\) | −33.6689 | + | 16.3549i | −1.15962 | + | 0.563292i | ||||
\(844\) | −0.177485 | − | 2.46954i | −0.00610928 | − | 0.0850049i | ||||
\(845\) | − | 9.65237i | − | 0.332052i | ||||||
\(846\) | −26.5690 | + | 36.3983i | −0.913463 | + | 1.25140i | ||||
\(847\) | − | 58.5920i | − | 2.01325i | ||||||
\(848\) | 5.89210 | + | 40.7798i | 0.202336 | + | 1.40038i | ||||
\(849\) | 27.4262 | − | 13.3225i | 0.941266 | − | 0.457226i | ||||
\(850\) | 0.368953 | + | 10.2805i | 0.0126550 | + | 0.352619i | ||||
\(851\) | 7.55661 | 0.259037 | ||||||||
\(852\) | 8.88319 | + | 15.3742i | 0.304333 | + | 0.526712i | ||||
\(853\) | −4.11172 | −0.140783 | −0.0703913 | − | 0.997519i | \(-0.522425\pi\) | ||||
−0.0703913 | + | 0.997519i | \(0.522425\pi\) | |||||||
\(854\) | −0.711106 | − | 19.8143i | −0.0243336 | − | 0.678031i | ||||
\(855\) | 1.41446 | − | 1.79856i | 0.0483737 | − | 0.0615093i | ||||
\(856\) | −29.7301 | + | 3.21195i | −1.01615 | + | 0.109782i | ||||
\(857\) | 4.47889i | 0.152996i | 0.997070 | + | 0.0764979i | \(0.0243739\pi\) | ||||
−0.997070 | + | 0.0764979i | \(0.975626\pi\) | |||||||
\(858\) | 3.44553 | + | 6.48998i | 0.117629 | + | 0.221564i | ||||
\(859\) | 40.8441i | 1.39358i | 0.717273 | + | 0.696792i | \(0.245390\pi\) | ||||
−0.717273 | + | 0.696792i | \(0.754610\pi\) | |||||||
\(860\) | −13.3842 | + | 0.961916i | −0.456396 | + | 0.0328011i | ||||
\(861\) | −14.6511 | − | 30.1614i | −0.499307 | − | 1.02790i | ||||
\(862\) | −37.0074 | + | 1.32814i | −1.26048 | + | 0.0452367i | ||||
\(863\) | 15.5380 | 0.528920 | 0.264460 | − | 0.964397i | \(-0.414806\pi\) | ||||
0.264460 | + | 0.964397i | \(0.414806\pi\) | |||||||
\(864\) | −29.3760 | − | 1.02466i | −0.999392 | − | 0.0348597i | ||||
\(865\) | 16.4316 | 0.558691 | ||||||||
\(866\) | −47.1965 | + | 1.69381i | −1.60380 | + | 0.0575581i | ||||
\(867\) | 10.8142 | + | 22.2625i | 0.367269 | + | 0.756076i | ||||
\(868\) | −69.2459 | + | 4.97669i | −2.35036 | + | 0.168920i | ||||
\(869\) | − | 68.6325i | − | 2.32820i | ||||||
\(870\) | −0.739735 | − | 1.39336i | −0.0250794 | − | 0.0472393i | ||||
\(871\) | 4.94968i | 0.167714i | ||||||||
\(872\) | 36.7549 | − | 3.97088i | 1.24468 | − | 0.134471i | ||||
\(873\) | 8.72181 | − | 11.0902i | 0.295189 | − | 0.375346i | ||||
\(874\) | −0.209595 | − | 5.84017i | −0.00708966 | − | 0.197547i | ||||
\(875\) | 27.8505 | 0.941518 | ||||||||
\(876\) | −12.7896 | − | 22.1351i | −0.432120 | − | 0.747875i | ||||
\(877\) | −47.0782 | −1.58972 | −0.794859 | − | 0.606794i | \(-0.792455\pi\) | ||||
−0.794859 | + | 0.606794i | \(0.792455\pi\) | |||||||
\(878\) | 0.591556 | + | 16.4831i | 0.0199640 | + | 0.556278i | ||||
\(879\) | −18.1396 | + | 8.81143i | −0.611834 | + | 0.297202i | ||||
\(880\) | −2.22936 | − | 15.4296i | −0.0751518 | − | 0.520133i | ||||
\(881\) | − | 21.9573i | − | 0.739760i | −0.929080 | − | 0.369880i | \(-0.879399\pi\) | ||
0.929080 | − | 0.369880i | \(-0.120601\pi\) | |||||||
\(882\) | 20.0903 | − | 27.5227i | 0.676476 | − | 0.926738i | ||||
\(883\) | 52.0256i | 1.75080i | 0.483399 | + | 0.875400i | \(0.339402\pi\) | ||||
−0.483399 | + | 0.875400i | \(0.660598\pi\) | |||||||
\(884\) | −0.138563 | − | 1.92797i | −0.00466037 | − | 0.0648448i | ||||
\(885\) | 9.39286 | − | 4.56264i | 0.315737 | − | 0.153371i | ||||
\(886\) | −31.8838 | + | 1.14427i | −1.07116 | + | 0.0384424i | ||||
\(887\) | 4.23989 | 0.142362 | 0.0711808 | − | 0.997463i | \(-0.477323\pi\) | ||||
0.0711808 | + | 0.997463i | \(0.477323\pi\) | |||||||
\(888\) | −4.75725 | − | 7.59118i | −0.159643 | − | 0.254743i | ||||
\(889\) | 42.2329 | 1.41644 | ||||||||
\(890\) | −9.76976 | + | 0.350623i | −0.327483 | + | 0.0117529i | ||||
\(891\) | 10.8407 | + | 44.6944i | 0.363176 | + | 1.49732i | ||||
\(892\) | −2.94549 | − | 40.9838i | −0.0986224 | − | 1.37224i | ||||
\(893\) | 10.6216i | 0.355440i | ||||||||
\(894\) | −8.66921 | + | 4.60249i | −0.289942 | + | 0.153930i | ||||
\(895\) | 14.0174i | 0.468549i | ||||||||
\(896\) | −10.8994 | − | 42.4882i | −0.364123 | − | 1.41943i | ||||
\(897\) | 1.83582 | + | 3.77930i | 0.0612962 | + | 0.126187i | ||||
\(898\) | −0.259331 | − | 7.22601i | −0.00865399 | − | 0.241135i | ||||
\(899\) | 7.56013 | 0.252144 | ||||||||
\(900\) | −14.8517 | + | 21.9588i | −0.495058 | + | 0.731959i | ||||
\(901\) | −16.9589 | −0.564984 | ||||||||
\(902\) | 1.29421 | + | 36.0620i | 0.0430926 | + | 1.20073i | ||||
\(903\) | 25.8108 | + | 53.1353i | 0.858929 | + | 1.76823i | ||||
\(904\) | −1.09127 | − | 10.1009i | −0.0362951 | − | 0.335951i | ||||
\(905\) | 0.504972i | 0.0167858i | ||||||||
\(906\) | −25.9727 | + | 13.7889i | −0.862886 | + | 0.458106i | ||||
\(907\) | 5.68483i | 0.188762i | 0.995536 | + | 0.0943808i | \(0.0300871\pi\) | ||||
−0.995536 | + | 0.0943808i | \(0.969913\pi\) | |||||||
\(908\) | −51.1026 | + | 3.67273i | −1.69590 | + | 0.121884i | ||||
\(909\) | 19.6482 | + | 15.4522i | 0.651689 | + | 0.512518i | ||||
\(910\) | −2.45335 | + | 0.0880473i | −0.0813278 | + | 0.00291874i | ||||
\(911\) | −23.2965 | −0.771846 | −0.385923 | − | 0.922531i | \(-0.626117\pi\) | ||||
−0.385923 | + | 0.922531i | \(0.626117\pi\) | |||||||
\(912\) | −5.73494 | + | 3.88722i | −0.189903 | + | 0.128719i | ||||
\(913\) | −31.0582 | −1.02788 | ||||||||
\(914\) | 29.2280 | − | 1.04895i | 0.966775 | − | 0.0346962i | ||||
\(915\) | −4.29692 | + | 2.08726i | −0.142052 | + | 0.0690026i | ||||
\(916\) | −37.4938 | + | 2.69467i | −1.23883 | + | 0.0890343i | ||||
\(917\) | − | 31.0376i | − | 1.02495i | ||||||
\(918\) | 2.14642 | − | 11.9063i | 0.0708424 | − | 0.392968i | ||||
\(919\) | − | 50.5761i | − | 1.66835i | −0.551497 | − | 0.834177i | \(-0.685943\pi\) | ||
0.551497 | − | 0.834177i | \(-0.314057\pi\) | |||||||
\(920\) | −0.957515 | − | 8.86285i | −0.0315683 | − | 0.292199i | ||||
\(921\) | −7.94256 | + | 3.85815i | −0.261716 | + | 0.127130i | ||||
\(922\) | 0.150662 | + | 4.19804i | 0.00496177 | + | 0.138255i | ||||
\(923\) | −3.00898 | −0.0990418 | ||||||||
\(924\) | −59.4243 | + | 34.3352i | −1.95491 | + | 1.12955i | ||||
\(925\) | −8.07960 | −0.265656 | ||||||||
\(926\) | −0.964777 | − | 26.8826i | −0.0317045 | − | 0.883416i | ||||
\(927\) | 5.07391 | + | 3.99035i | 0.166649 | + | 0.131060i | ||||
\(928\) | 0.852182 | + | 4.70002i | 0.0279743 | + | 0.154286i | ||||
\(929\) | − | 7.75818i | − | 0.254538i | −0.991868 | − | 0.127269i | \(-0.959379\pi\) | ||
0.991868 | − | 0.127269i | \(-0.0406211\pi\) | |||||||
\(930\) | 7.84346 | + | 14.7739i | 0.257197 | + | 0.484455i | ||||
\(931\) | − | 8.03161i | − | 0.263225i | ||||||
\(932\) | 1.94367 | + | 27.0444i | 0.0636671 | + | 0.885868i | ||||
\(933\) | 9.14012 | + | 18.8163i | 0.299234 | + | 0.616017i | ||||
\(934\) | −14.0030 | + | 0.502547i | −0.458192 | + | 0.0164439i | ||||
\(935\) | 6.41666 | 0.209847 | ||||||||
\(936\) | 2.64085 | − | 4.22347i | 0.0863190 | − | 0.138049i | ||||
\(937\) | 33.6892 | 1.10058 | 0.550289 | − | 0.834974i | \(-0.314518\pi\) | ||||
0.550289 | + | 0.834974i | \(0.314518\pi\) | |||||||
\(938\) | −46.2011 | + | 1.65809i | −1.50852 | + | 0.0541386i | ||||
\(939\) | 15.9575 | + | 32.8509i | 0.520754 | + | 1.07205i | ||||
\(940\) | 1.16147 | + | 16.1608i | 0.0378829 | + | 0.527106i | ||||
\(941\) | − | 18.8448i | − | 0.614322i | −0.951657 | − | 0.307161i | \(-0.900621\pi\) | ||
0.951657 | − | 0.307161i | \(-0.0993791\pi\) | |||||||
\(942\) | 4.92348 | + | 9.27384i | 0.160416 | + | 0.302158i | ||||
\(943\) | 20.6338i | 0.671929i | ||||||||
\(944\) | −31.2935 | + | 4.52147i | −1.01852 | + | 0.147161i | ||||
\(945\) | −15.0141 | − | 3.26664i | −0.488409 | − | 0.106264i | ||||
\(946\) | −2.28001 | − | 63.5303i | −0.0741296 | − | 2.06555i | ||||
\(947\) | −0.755202 | −0.0245408 | −0.0122704 | − | 0.999925i | \(-0.503906\pi\) | ||||
−0.0122704 | + | 0.999925i | \(0.503906\pi\) | |||||||
\(948\) | −40.2850 | + | 23.2766i | −1.30839 | + | 0.755988i | ||||
\(949\) | 4.33219 | 0.140629 | ||||||||
\(950\) | 0.224101 | + | 6.24437i | 0.00727081 | + | 0.202594i | ||||
\(951\) | 15.2280 | − | 7.39711i | 0.493802 | − | 0.239868i | ||||
\(952\) | 17.9496 | − | 1.93922i | 0.581749 | − | 0.0628504i | ||||
\(953\) | 33.2815i | 1.07809i | 0.842275 | + | 0.539047i | \(0.181216\pi\) | ||||
−0.842275 | + | 0.539047i | \(0.818784\pi\) | |||||||
\(954\) | −35.2989 | − | 25.7665i | −1.14284 | − | 0.834222i | ||||
\(955\) | − | 10.7148i | − | 0.346722i | ||||||
\(956\) | 22.6847 | − | 1.63035i | 0.733677 | − | 0.0527292i | ||||
\(957\) | 6.72251 | − | 3.26550i | 0.217308 | − | 0.105559i | ||||
\(958\) | −4.65445 | + | 0.167041i | −0.150378 | + | 0.00539686i | ||||
\(959\) | −80.7205 | −2.60660 | ||||||||
\(960\) | −8.30060 | + | 6.54149i | −0.267901 | + | 0.211126i | ||||
\(961\) | −49.1606 | −1.58582 | ||||||||
\(962\) | 1.51718 | − | 0.0544493i | 0.0489157 | − | 0.00175552i | ||||
\(963\) | 19.6067 | − | 24.9308i | 0.631817 | − | 0.803384i | ||||
\(964\) | −24.0622 | + | 1.72935i | −0.774993 | + | 0.0556985i | ||||
\(965\) | 1.87787i | 0.0604509i | ||||||||
\(966\) | −34.6616 | + | 18.4018i | −1.11522 | + | 0.592070i | ||||
\(967\) | 2.72533i | 0.0876407i | 0.999039 | + | 0.0438203i | \(0.0139529\pi\) | ||||
−0.999039 | + | 0.0438203i | \(0.986047\pi\) | |||||||
\(968\) | 42.4973 | − | 4.59127i | 1.36591 | − | 0.147569i | ||||
\(969\) | −1.24596 | − | 2.56499i | −0.0400260 | − | 0.0823992i | ||||
\(970\) | −0.181938 | − | 5.06952i | −0.00584167 | − | 0.162772i | ||||
\(971\) | 28.9519 | 0.929110 | 0.464555 | − | 0.885544i | \(-0.346214\pi\) | ||||
0.464555 | + | 0.885544i | \(0.346214\pi\) | |||||||
\(972\) | 22.5575 | − | 21.5211i | 0.723533 | − | 0.690290i | ||||
\(973\) | 64.7922 | 2.07714 | ||||||||
\(974\) | 0.178252 | + | 4.96681i | 0.00571155 | + | 0.159147i | ||||
\(975\) | −1.96288 | − | 4.04087i | −0.0628624 | − | 0.129411i | ||||
\(976\) | 14.3157 | − | 2.06842i | 0.458236 | − | 0.0662085i | ||||
\(977\) | − | 31.1279i | − | 0.995869i | −0.867215 | − | 0.497934i | \(-0.834092\pi\) | ||
0.867215 | − | 0.497934i | \(-0.165908\pi\) | |||||||
\(978\) | −29.5499 | + | 15.6880i | −0.944901 | + | 0.501648i | ||||
\(979\) | − | 46.3142i | − | 1.48021i | ||||||
\(980\) | −0.878250 | − | 12.2200i | −0.0280547 | − | 0.390354i | ||||
\(981\) | −24.2395 | + | 30.8216i | −0.773907 | + | 0.984058i | ||||
\(982\) | 38.7168 | − | 1.38949i | 1.23550 | − | 0.0443404i | ||||
\(983\) | −20.2857 | −0.647014 | −0.323507 | − | 0.946226i | \(-0.604862\pi\) | ||||
−0.323507 | + | 0.946226i | \(0.604862\pi\) | |||||||
\(984\) | 20.7282 | − | 12.9900i | 0.660792 | − | 0.414106i | ||||
\(985\) | 15.7110 | 0.500594 | ||||||||
\(986\) | −1.96477 | + | 0.0705127i | −0.0625709 | + | 0.00224558i | ||||
\(987\) | 64.1583 | − | 31.1653i | 2.04218 | − | 0.992003i | ||||
\(988\) | −0.0841628 | − | 1.17105i | −0.00267758 | − | 0.0372560i | ||||
\(989\) | − | 36.3506i | − | 1.15588i | ||||||
\(990\) | 13.3558 | + | 9.74915i | 0.424477 | + | 0.309848i | ||||
\(991\) | 22.3311i | 0.709371i | 0.934986 | + | 0.354686i | \(0.115412\pi\) | ||||
−0.934986 | + | 0.354686i | \(0.884588\pi\) | |||||||
\(992\) | −9.03575 | − | 49.8347i | −0.286885 | − | 1.58225i | ||||
\(993\) | 2.22564 | − | 1.08112i | 0.0706286 | − | 0.0343083i | ||||
\(994\) | −1.00798 | − | 28.0863i | −0.0319711 | − | 0.890843i | ||||
\(995\) | 9.79034 | 0.310375 | ||||||||
\(996\) | 10.5333 | + | 18.2301i | 0.333761 | + | 0.577643i | ||||
\(997\) | −26.5250 | −0.840055 | −0.420027 | − | 0.907511i | \(-0.637980\pi\) | ||||
−0.420027 | + | 0.907511i | \(0.637980\pi\) | |||||||
\(998\) | −1.15610 | − | 32.2135i | −0.0365956 | − | 1.01970i | ||||
\(999\) | 9.28487 | + | 2.02012i | 0.293760 | + | 0.0639138i |
(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 | 228.2.c.a.191.35 | yes | 36 | |
3.2 | odd | 2 | inner | 228.2.c.a.191.2 | yes | 36 | |
4.3 | odd | 2 | inner | 228.2.c.a.191.1 | ✓ | 36 | |
12.11 | even | 2 | inner | 228.2.c.a.191.36 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.c.a.191.1 | ✓ | 36 | 4.3 | odd | 2 | inner | |
228.2.c.a.191.2 | yes | 36 | 3.2 | odd | 2 | inner | |
228.2.c.a.191.35 | yes | 36 | 1.1 | even | 1 | trivial | |
228.2.c.a.191.36 | yes | 36 | 12.11 | even | 2 | inner |