Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(187,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.187");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.bn (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(112\) |
Relative dimension: | \(56\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 187.5 | ||
Character | \(\chi\) | \(=\) | 624.187 |
Dual form | 624.2.bn.a.307.5 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33764 | − | 0.459045i | −0.945853 | − | 0.324594i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 1.57856 | + | 1.22807i | 0.789278 | + | 0.614037i | ||||
\(5\) | −2.59977 | −1.16265 | −0.581327 | − | 0.813670i | \(-0.697466\pi\) | ||||
−0.581327 | + | 0.813670i | \(0.697466\pi\) | |||||||
\(6\) | 0.621260 | + | 1.27045i | 0.253628 | + | 0.518658i | ||||
\(7\) | 0.312171 | + | 0.312171i | 0.117989 | + | 0.117989i | 0.763636 | − | 0.645647i | \(-0.223412\pi\) |
−0.645647 | + | 0.763636i | \(0.723412\pi\) | |||||||
\(8\) | −1.54780 | − | 2.36735i | −0.547228 | − | 0.836983i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 3.47756 | + | 1.19341i | 1.09970 | + | 0.377391i | ||||
\(11\) | 3.08083 | 0.928904 | 0.464452 | − | 0.885598i | \(-0.346251\pi\) | ||||
0.464452 | + | 0.885598i | \(0.346251\pi\) | |||||||
\(12\) | −0.247828 | − | 1.98459i | −0.0715418 | − | 0.572901i | ||||
\(13\) | 3.18261 | + | 1.69440i | 0.882697 | + | 0.469943i | ||||
\(14\) | −0.274271 | − | 0.560872i | −0.0733021 | − | 0.149899i | ||||
\(15\) | 1.83832 | + | 1.83832i | 0.474652 | + | 0.474652i | ||||
\(16\) | 0.983672 | + | 3.87716i | 0.245918 | + | 0.969291i | ||||
\(17\) | − | 6.87394i | − | 1.66718i | −0.552387 | − | 0.833588i | \(-0.686283\pi\) | ||
0.552387 | − | 0.833588i | \(-0.313717\pi\) | |||||||
\(18\) | 0.459045 | − | 1.33764i | 0.108198 | − | 0.315284i | ||||
\(19\) | −5.01779 | −1.15116 | −0.575580 | − | 0.817746i | \(-0.695224\pi\) | ||||
−0.575580 | + | 0.817746i | \(0.695224\pi\) | |||||||
\(20\) | −4.10389 | − | 3.19271i | −0.917657 | − | 0.713912i | ||||
\(21\) | − | 0.441476i | − | 0.0963380i | ||||||
\(22\) | −4.12103 | − | 1.41424i | −0.878607 | − | 0.301517i | ||||
\(23\) | − | 1.76637i | − | 0.368314i | −0.982897 | − | 0.184157i | \(-0.941044\pi\) | ||
0.982897 | − | 0.184157i | \(-0.0589555\pi\) | |||||||
\(24\) | −0.579510 | + | 2.76842i | −0.118292 | + | 0.565102i | ||||
\(25\) | 1.75882 | 0.351765 | ||||||||
\(26\) | −3.47937 | − | 3.72746i | −0.682361 | − | 0.731015i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0.109410 | + | 0.876147i | 0.0206766 | + | 0.165576i | ||||
\(29\) | −5.32160 | + | 5.32160i | −0.988196 | + | 0.988196i | −0.999931 | − | 0.0117353i | \(-0.996264\pi\) |
0.0117353 | + | 0.999931i | \(0.496264\pi\) | |||||||
\(30\) | −1.61513 | − | 3.30288i | −0.294882 | − | 0.603020i | ||||
\(31\) | −1.73409 | − | 1.73409i | −0.311453 | − | 0.311453i | 0.534020 | − | 0.845472i | \(-0.320681\pi\) |
−0.845472 | + | 0.534020i | \(0.820681\pi\) | |||||||
\(32\) | 0.463995 | − | 5.63779i | 0.0820234 | − | 0.996630i | ||||
\(33\) | −2.17847 | − | 2.17847i | −0.379224 | − | 0.379224i | ||||
\(34\) | −3.15545 | + | 9.19485i | −0.541155 | + | 1.57690i | ||||
\(35\) | −0.811573 | − | 0.811573i | −0.137181 | − | 0.137181i | ||||
\(36\) | −1.22807 | + | 1.57856i | −0.204679 | + | 0.263093i | ||||
\(37\) | − | 6.43566i | − | 1.05802i | −0.848617 | − | 0.529008i | \(-0.822564\pi\) | ||
0.848617 | − | 0.529008i | \(-0.177436\pi\) | |||||||
\(38\) | 6.71199 | + | 2.30339i | 1.08883 | + | 0.373659i | ||||
\(39\) | −1.05232 | − | 3.44857i | −0.168506 | − | 0.552213i | ||||
\(40\) | 4.02392 | + | 6.15457i | 0.636237 | + | 0.973122i | ||||
\(41\) | −7.29029 | − | 7.29029i | −1.13855 | − | 1.13855i | −0.988710 | − | 0.149842i | \(-0.952124\pi\) |
−0.149842 | − | 0.988710i | \(-0.547876\pi\) | |||||||
\(42\) | −0.202657 | + | 0.590536i | −0.0312707 | + | 0.0911216i | ||||
\(43\) | 1.90101 | + | 1.90101i | 0.289901 | + | 0.289901i | 0.837041 | − | 0.547140i | \(-0.184284\pi\) |
−0.547140 | + | 0.837041i | \(0.684284\pi\) | |||||||
\(44\) | 4.86325 | + | 3.78348i | 0.733163 | + | 0.570381i | ||||
\(45\) | − | 2.59977i | − | 0.387551i | ||||||
\(46\) | −0.810845 | + | 2.36277i | −0.119553 | + | 0.348371i | ||||
\(47\) | 1.14377 | − | 1.14377i | 0.166836 | − | 0.166836i | −0.618751 | − | 0.785587i | \(-0.712361\pi\) |
0.785587 | + | 0.618751i | \(0.212361\pi\) | |||||||
\(48\) | 2.04601 | − | 3.43713i | 0.295316 | − | 0.496107i | ||||
\(49\) | − | 6.80510i | − | 0.972157i | ||||||
\(50\) | −2.35267 | − | 0.807380i | −0.332718 | − | 0.114181i | ||||
\(51\) | −4.86061 | + | 4.86061i | −0.680622 | + | 0.680622i | ||||
\(52\) | 2.94307 | + | 6.58318i | 0.408131 | + | 0.912923i | ||||
\(53\) | 4.08570 | + | 4.08570i | 0.561214 | + | 0.561214i | 0.929652 | − | 0.368438i | \(-0.120107\pi\) |
−0.368438 | + | 0.929652i | \(0.620107\pi\) | |||||||
\(54\) | −1.27045 | + | 0.621260i | −0.172886 | + | 0.0845427i | ||||
\(55\) | −8.00945 | −1.07999 | ||||||||
\(56\) | 0.255840 | − | 1.22219i | 0.0341880 | − | 0.163322i | ||||
\(57\) | 3.54811 | + | 3.54811i | 0.469959 | + | 0.469959i | ||||
\(58\) | 9.56123 | − | 4.67552i | 1.25545 | − | 0.613926i | ||||
\(59\) | −13.7329 | −1.78788 | −0.893938 | − | 0.448192i | \(-0.852068\pi\) | ||||
−0.893938 | + | 0.448192i | \(0.852068\pi\) | |||||||
\(60\) | 0.644297 | + | 5.15947i | 0.0831784 | + | 0.666085i | ||||
\(61\) | 5.28947 | − | 5.28947i | 0.677248 | − | 0.677248i | −0.282129 | − | 0.959377i | \(-0.591041\pi\) |
0.959377 | + | 0.282129i | \(0.0910406\pi\) | |||||||
\(62\) | 1.52356 | + | 3.11562i | 0.193493 | + | 0.395684i | ||||
\(63\) | −0.312171 | + | 0.312171i | −0.0393298 | + | 0.0393298i | ||||
\(64\) | −3.20866 | + | 7.32834i | −0.401082 | + | 0.916042i | ||||
\(65\) | −8.27406 | − | 4.40506i | −1.02627 | − | 0.546381i | ||||
\(66\) | 1.91399 | + | 3.91403i | 0.235596 | + | 0.481784i | ||||
\(67\) | −15.7618 | −1.92561 | −0.962804 | − | 0.270200i | \(-0.912910\pi\) | ||||
−0.962804 | + | 0.270200i | \(0.912910\pi\) | |||||||
\(68\) | 8.44170 | − | 10.8509i | 1.02371 | − | 1.31586i | ||||
\(69\) | −1.24901 | + | 1.24901i | −0.150364 | + | 0.150364i | ||||
\(70\) | 0.713043 | + | 1.45814i | 0.0852250 | + | 0.174281i | ||||
\(71\) | −11.1059 | + | 11.1059i | −1.31802 | + | 1.31802i | −0.402684 | + | 0.915339i | \(0.631923\pi\) |
−0.915339 | + | 0.402684i | \(0.868077\pi\) | |||||||
\(72\) | 2.36735 | − | 1.54780i | 0.278994 | − | 0.182409i | ||||
\(73\) | 0.621805 | − | 0.621805i | 0.0727768 | − | 0.0727768i | −0.669781 | − | 0.742558i | \(-0.733612\pi\) |
0.742558 | + | 0.669781i | \(0.233612\pi\) | |||||||
\(74\) | −2.95426 | + | 8.60858i | −0.343425 | + | 1.00073i | ||||
\(75\) | −1.24368 | − | 1.24368i | −0.143607 | − | 0.143607i | ||||
\(76\) | −7.92085 | − | 6.16221i | −0.908584 | − | 0.706854i | ||||
\(77\) | 0.961744 | + | 0.961744i | 0.109601 | + | 0.109601i | ||||
\(78\) | −0.175424 | + | 5.09600i | −0.0198628 | + | 0.577008i | ||||
\(79\) | − | 16.7040i | − | 1.87935i | −0.342066 | − | 0.939676i | \(-0.611127\pi\) | ||
0.342066 | − | 0.939676i | \(-0.388873\pi\) | |||||||
\(80\) | −2.55733 | − | 10.0797i | −0.285918 | − | 1.12695i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 6.40520 | + | 13.0983i | 0.707336 | + | 1.44647i | ||||
\(83\) | −7.48177 | −0.821231 | −0.410615 | − | 0.911809i | \(-0.634686\pi\) | ||||
−0.410615 | + | 0.911809i | \(0.634686\pi\) | |||||||
\(84\) | 0.542165 | − | 0.696894i | 0.0591551 | − | 0.0760374i | ||||
\(85\) | 17.8707i | 1.93835i | ||||||||
\(86\) | −1.67021 | − | 3.41551i | −0.180104 | − | 0.368304i | ||||
\(87\) | 7.52588 | 0.806859 | ||||||||
\(88\) | −4.76849 | − | 7.29338i | −0.508323 | − | 0.777477i | ||||
\(89\) | 11.0906 | − | 11.0906i | 1.17560 | − | 1.17560i | 0.194745 | − | 0.980854i | \(-0.437612\pi\) |
0.980854 | − | 0.194745i | \(-0.0623881\pi\) | |||||||
\(90\) | −1.19341 | + | 3.47756i | −0.125797 | + | 0.366567i | ||||
\(91\) | 0.464574 | + | 1.52246i | 0.0487006 | + | 0.159597i | ||||
\(92\) | 2.16924 | − | 2.78832i | 0.226158 | − | 0.290702i | ||||
\(93\) | 2.45238i | 0.254300i | ||||||||
\(94\) | −2.05499 | + | 1.00491i | −0.211956 | + | 0.103648i | ||||
\(95\) | 13.0451 | 1.33840 | ||||||||
\(96\) | −4.31462 | + | 3.65843i | −0.440359 | + | 0.373387i | ||||
\(97\) | 7.33233 | − | 7.33233i | 0.744486 | − | 0.744486i | −0.228952 | − | 0.973438i | \(-0.573530\pi\) |
0.973438 | + | 0.228952i | \(0.0735299\pi\) | |||||||
\(98\) | −3.12385 | + | 9.10276i | −0.315556 | + | 0.919518i | ||||
\(99\) | 3.08083i | 0.309635i | ||||||||
\(100\) | 2.77640 | + | 2.15997i | 0.277640 | + | 0.215997i | ||||
\(101\) | 4.68560 | − | 4.68560i | 0.466234 | − | 0.466234i | −0.434458 | − | 0.900692i | \(-0.643060\pi\) |
0.900692 | + | 0.434458i | \(0.143060\pi\) | |||||||
\(102\) | 8.73298 | − | 4.27050i | 0.864694 | − | 0.422843i | ||||
\(103\) | 0.250872i | 0.0247192i | 0.999924 | + | 0.0123596i | \(0.00393428\pi\) | ||||
−0.999924 | + | 0.0123596i | \(0.996066\pi\) | |||||||
\(104\) | −0.914789 | − | 10.1569i | −0.0897024 | − | 0.995969i | ||||
\(105\) | 1.14774i | 0.112008i | ||||||||
\(106\) | −3.58967 | − | 7.34072i | −0.348660 | − | 0.712993i | ||||
\(107\) | 1.84416 | − | 1.84416i | 0.178282 | − | 0.178282i | −0.612325 | − | 0.790606i | \(-0.709766\pi\) |
0.790606 | + | 0.612325i | \(0.209766\pi\) | |||||||
\(108\) | 1.98459 | − | 0.247828i | 0.190967 | − | 0.0238473i | ||||
\(109\) | 0.584695i | 0.0560036i | 0.999608 | + | 0.0280018i | \(0.00891442\pi\) | ||||
−0.999608 | + | 0.0280018i | \(0.991086\pi\) | |||||||
\(110\) | 10.7138 | + | 3.67670i | 1.02152 | + | 0.350560i | ||||
\(111\) | −4.55070 | + | 4.55070i | −0.431933 | + | 0.431933i | ||||
\(112\) | −0.903263 | + | 1.51741i | −0.0853503 | + | 0.143382i | ||||
\(113\) | 9.43859 | 0.887908 | 0.443954 | − | 0.896050i | \(-0.353575\pi\) | ||||
0.443954 | + | 0.896050i | \(0.353575\pi\) | |||||||
\(114\) | −3.11735 | − | 6.37483i | −0.291966 | − | 0.597058i | ||||
\(115\) | 4.59217i | 0.428222i | ||||||||
\(116\) | −14.9357 | + | 1.86512i | −1.38675 | + | 0.173172i | ||||
\(117\) | −1.69440 | + | 3.18261i | −0.156648 | + | 0.294232i | ||||
\(118\) | 18.3697 | + | 6.30403i | 1.69107 | + | 0.580333i | ||||
\(119\) | 2.14584 | − | 2.14584i | 0.196709 | − | 0.196709i | ||||
\(120\) | 1.50660 | − | 7.19727i | 0.137533 | − | 0.657018i | ||||
\(121\) | −1.50851 | −0.137137 | ||||||||
\(122\) | −9.50351 | + | 4.64730i | −0.860408 | + | 0.420747i | ||||
\(123\) | 10.3100i | 0.929624i | ||||||||
\(124\) | −0.607769 | − | 4.86696i | −0.0545792 | − | 0.437066i | ||||
\(125\) | 8.42632 | 0.753673 | ||||||||
\(126\) | 0.560872 | − | 0.274271i | 0.0499665 | − | 0.0244340i | ||||
\(127\) | −5.82313 | −0.516719 | −0.258360 | − | 0.966049i | \(-0.583182\pi\) | ||||
−0.258360 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(128\) | 7.65606 | − | 8.32975i | 0.676707 | − | 0.736253i | ||||
\(129\) | − | 2.68843i | − | 0.236703i | ||||||
\(130\) | 9.04559 | + | 9.69055i | 0.793350 | + | 0.849918i | ||||
\(131\) | 6.85011 | + | 6.85011i | 0.598497 | + | 0.598497i | 0.939912 | − | 0.341415i | \(-0.110906\pi\) |
−0.341415 | + | 0.939912i | \(0.610906\pi\) | |||||||
\(132\) | −0.763515 | − | 6.11417i | −0.0664555 | − | 0.532170i | ||||
\(133\) | −1.56641 | − | 1.56641i | −0.135825 | − | 0.135825i | ||||
\(134\) | 21.0836 | + | 7.23537i | 1.82134 | + | 0.625041i | ||||
\(135\) | −1.83832 | + | 1.83832i | −0.158217 | + | 0.158217i | ||||
\(136\) | −16.2730 | + | 10.6395i | −1.39540 | + | 0.912326i | ||||
\(137\) | −0.237416 | + | 0.237416i | −0.0202838 | + | 0.0202838i | −0.717176 | − | 0.696892i | \(-0.754566\pi\) |
0.696892 | + | 0.717176i | \(0.254566\pi\) | |||||||
\(138\) | 2.24408 | − | 1.09738i | 0.191029 | − | 0.0934148i | ||||
\(139\) | 2.78720 | − | 2.78720i | 0.236407 | − | 0.236407i | −0.578953 | − | 0.815361i | \(-0.696539\pi\) |
0.815361 | + | 0.578953i | \(0.196539\pi\) | |||||||
\(140\) | −0.284442 | − | 2.27778i | −0.0240397 | − | 0.192508i | ||||
\(141\) | −1.61753 | −0.136221 | ||||||||
\(142\) | 19.9537 | − | 9.75754i | 1.67448 | − | 0.818834i | ||||
\(143\) | 9.80507 | + | 5.22016i | 0.819941 | + | 0.436532i | ||||
\(144\) | −3.87716 | + | 0.983672i | −0.323097 | + | 0.0819727i | ||||
\(145\) | 13.8350 | − | 13.8350i | 1.14893 | − | 1.14893i | ||||
\(146\) | −1.11719 | + | 0.546314i | −0.0924591 | + | 0.0452133i | ||||
\(147\) | −4.81193 | + | 4.81193i | −0.396881 | + | 0.396881i | ||||
\(148\) | 7.90346 | − | 10.1590i | 0.649660 | − | 0.835068i | ||||
\(149\) | −15.1865 | −1.24413 | −0.622064 | − | 0.782966i | \(-0.713706\pi\) | ||||
−0.622064 | + | 0.782966i | \(0.713706\pi\) | |||||||
\(150\) | 1.09269 | + | 2.23449i | 0.0892175 | + | 0.182446i | ||||
\(151\) | 12.1513 | + | 12.1513i | 0.988862 | + | 0.988862i | 0.999939 | − | 0.0110764i | \(-0.00352578\pi\) |
−0.0110764 | + | 0.999939i | \(0.503526\pi\) | |||||||
\(152\) | 7.76651 | + | 11.8788i | 0.629947 | + | 0.963501i | ||||
\(153\) | 6.87394 | 0.555725 | ||||||||
\(154\) | −0.844982 | − | 1.72795i | −0.0680906 | − | 0.139242i | ||||
\(155\) | 4.50825 | + | 4.50825i | 0.362112 | + | 0.362112i | ||||
\(156\) | 2.57395 | − | 6.73608i | 0.206081 | − | 0.539318i | ||||
\(157\) | 4.75195 | − | 4.75195i | 0.379247 | − | 0.379247i | −0.491583 | − | 0.870831i | \(-0.663582\pi\) |
0.870831 | + | 0.491583i | \(0.163582\pi\) | |||||||
\(158\) | −7.66791 | + | 22.3440i | −0.610026 | + | 1.77759i | ||||
\(159\) | − | 5.77806i | − | 0.458230i | ||||||
\(160\) | −1.20628 | + | 14.6570i | −0.0953649 | + | 1.15874i | ||||
\(161\) | 0.551410 | − | 0.551410i | 0.0434572 | − | 0.0434572i | ||||
\(162\) | 1.33764 | + | 0.459045i | 0.105095 | + | 0.0360660i | ||||
\(163\) | − | 7.87339i | − | 0.616692i | −0.951274 | − | 0.308346i | \(-0.900225\pi\) | ||
0.951274 | − | 0.308346i | \(-0.0997754\pi\) | |||||||
\(164\) | −2.55511 | − | 20.4611i | −0.199521 | − | 1.59775i | ||||
\(165\) | 5.66354 | + | 5.66354i | 0.440906 | + | 0.440906i | ||||
\(166\) | 10.0079 | + | 3.43447i | 0.776764 | + | 0.266567i | ||||
\(167\) | −1.90835 | − | 1.90835i | −0.147672 | − | 0.147672i | 0.629405 | − | 0.777077i | \(-0.283299\pi\) |
−0.777077 | + | 0.629405i | \(0.783299\pi\) | |||||||
\(168\) | −1.04513 | + | 0.683315i | −0.0806333 | + | 0.0527189i | ||||
\(169\) | 7.25800 | + | 10.7852i | 0.558308 | + | 0.829634i | ||||
\(170\) | 8.20345 | − | 23.9045i | 0.629176 | − | 1.83339i | ||||
\(171\) | − | 5.01779i | − | 0.383720i | ||||||
\(172\) | 0.666268 | + | 5.33542i | 0.0508025 | + | 0.406822i | ||||
\(173\) | −0.0223126 | − | 0.0223126i | −0.00169639 | − | 0.00169639i | 0.706258 | − | 0.707954i | \(-0.250382\pi\) |
−0.707954 | + | 0.706258i | \(0.750382\pi\) | |||||||
\(174\) | −10.0669 | − | 3.45472i | −0.763170 | − | 0.261901i | ||||
\(175\) | 0.549054 | + | 0.549054i | 0.0415045 | + | 0.0415045i | ||||
\(176\) | 3.03052 | + | 11.9449i | 0.228434 | + | 0.900378i | ||||
\(177\) | 9.71065 | + | 9.71065i | 0.729897 | + | 0.729897i | ||||
\(178\) | −19.9263 | + | 9.74411i | −1.49354 | + | 0.730352i | ||||
\(179\) | 3.42532 | − | 3.42532i | 0.256021 | − | 0.256021i | −0.567413 | − | 0.823434i | \(-0.692056\pi\) |
0.823434 | + | 0.567413i | \(0.192056\pi\) | |||||||
\(180\) | 3.19271 | − | 4.10389i | 0.237971 | − | 0.305886i | ||||
\(181\) | −4.71779 | + | 4.71779i | −0.350671 | + | 0.350671i | −0.860359 | − | 0.509688i | \(-0.829761\pi\) |
0.509688 | + | 0.860359i | \(0.329761\pi\) | |||||||
\(182\) | 0.0774453 | − | 2.24976i | 0.00574063 | − | 0.166764i | ||||
\(183\) | −7.48044 | −0.552970 | ||||||||
\(184\) | −4.18162 | + | 2.73398i | −0.308273 | + | 0.201552i | ||||
\(185\) | 16.7312i | 1.23011i | ||||||||
\(186\) | 1.12575 | − | 3.28040i | 0.0825442 | − | 0.240530i | ||||
\(187\) | − | 21.1774i | − | 1.54865i | ||||||
\(188\) | 3.21014 | − | 0.400870i | 0.234123 | − | 0.0292365i | ||||
\(189\) | 0.441476 | 0.0321127 | ||||||||
\(190\) | −17.4496 | − | 5.98830i | −1.26593 | − | 0.434437i | ||||
\(191\) | 2.24769i | 0.162637i | 0.996688 | + | 0.0813185i | \(0.0259131\pi\) | ||||
−0.996688 | + | 0.0813185i | \(0.974087\pi\) | |||||||
\(192\) | 7.45078 | − | 2.91305i | 0.537714 | − | 0.210231i | ||||
\(193\) | −6.35227 | − | 6.35227i | −0.457246 | − | 0.457246i | 0.440504 | − | 0.897751i | \(-0.354800\pi\) |
−0.897751 | + | 0.440504i | \(0.854800\pi\) | |||||||
\(194\) | −13.1739 | + | 6.44214i | −0.945830 | + | 0.462519i | ||||
\(195\) | 2.73580 | + | 8.96550i | 0.195914 | + | 0.642033i | ||||
\(196\) | 8.35716 | − | 10.7422i | 0.596940 | − | 0.767302i | ||||
\(197\) | 5.77122 | 0.411182 | 0.205591 | − | 0.978638i | \(-0.434088\pi\) | ||||
0.205591 | + | 0.978638i | \(0.434088\pi\) | |||||||
\(198\) | 1.41424 | − | 4.12103i | 0.100506 | − | 0.292869i | ||||
\(199\) | 11.5493i | 0.818709i | 0.912375 | + | 0.409355i | \(0.134246\pi\) | ||||
−0.912375 | + | 0.409355i | \(0.865754\pi\) | |||||||
\(200\) | −2.72230 | − | 4.16375i | −0.192496 | − | 0.294421i | ||||
\(201\) | 11.1453 | + | 11.1453i | 0.786126 | + | 0.786126i | ||||
\(202\) | −8.41854 | + | 4.11674i | −0.592326 | + | 0.289653i | ||||
\(203\) | −3.32249 | −0.233193 | ||||||||
\(204\) | −13.6419 | + | 1.70356i | −0.955126 | + | 0.119273i | ||||
\(205\) | 18.9531 | + | 18.9531i | 1.32374 | + | 1.32374i | ||||
\(206\) | 0.115162 | − | 0.335576i | 0.00802369 | − | 0.0233807i | ||||
\(207\) | 1.76637 | 0.122771 | ||||||||
\(208\) | −3.43883 | + | 14.0062i | −0.238440 | + | 0.971157i | ||||
\(209\) | −15.4589 | −1.06932 | ||||||||
\(210\) | 0.526864 | − | 1.53526i | 0.0363570 | − | 0.105943i | ||||
\(211\) | 1.67957 | + | 1.67957i | 0.115627 | + | 0.115627i | 0.762553 | − | 0.646926i | \(-0.223946\pi\) |
−0.646926 | + | 0.762553i | \(0.723946\pi\) | |||||||
\(212\) | 1.43196 | + | 11.4670i | 0.0983477 | + | 0.787560i | ||||
\(213\) | 15.7061 | 1.07616 | ||||||||
\(214\) | −3.31337 | + | 1.62027i | −0.226497 | + | 0.110759i | ||||
\(215\) | −4.94219 | − | 4.94219i | −0.337054 | − | 0.337054i | ||||
\(216\) | −2.76842 | − | 0.579510i | −0.188367 | − | 0.0394307i | ||||
\(217\) | − | 1.08267i | − | 0.0734962i | ||||||
\(218\) | 0.268402 | − | 0.782111i | 0.0181784 | − | 0.0529712i | ||||
\(219\) | −0.879366 | −0.0594220 | ||||||||
\(220\) | −12.6434 | − | 9.83620i | −0.852415 | − | 0.663156i | ||||
\(221\) | 11.6472 | − | 21.8771i | 0.783477 | − | 1.47161i | ||||
\(222\) | 8.17616 | − | 3.99821i | 0.548748 | − | 0.268342i | ||||
\(223\) | 3.12370 | + | 3.12370i | 0.209179 | + | 0.209179i | 0.803918 | − | 0.594740i | \(-0.202745\pi\) |
−0.594740 | + | 0.803918i | \(0.702745\pi\) | |||||||
\(224\) | 1.90480 | − | 1.61511i | 0.127270 | − | 0.107914i | ||||
\(225\) | 1.75882i | 0.117255i | ||||||||
\(226\) | −12.6254 | − | 4.33274i | −0.839831 | − | 0.288210i | ||||
\(227\) | 16.0224 | 1.06344 | 0.531721 | − | 0.846919i | \(-0.321545\pi\) | ||||
0.531721 | + | 0.846919i | \(0.321545\pi\) | |||||||
\(228\) | 1.24355 | + | 9.95823i | 0.0823560 | + | 0.659500i | ||||
\(229\) | − | 6.51126i | − | 0.430276i | −0.976584 | − | 0.215138i | \(-0.930980\pi\) | ||
0.976584 | − | 0.215138i | \(-0.0690202\pi\) | |||||||
\(230\) | 2.10801 | − | 6.14266i | 0.138998 | − | 0.405035i | ||||
\(231\) | − | 1.36011i | − | 0.0894888i | ||||||
\(232\) | 20.8348 | + | 4.36132i | 1.36787 | + | 0.286335i | ||||
\(233\) | −13.2251 | −0.866405 | −0.433202 | − | 0.901297i | \(-0.642617\pi\) | ||||
−0.433202 | + | 0.901297i | \(0.642617\pi\) | |||||||
\(234\) | 3.72746 | − | 3.47937i | 0.243672 | − | 0.227454i | ||||
\(235\) | −2.97354 | + | 2.97354i | −0.193973 | + | 0.193973i | ||||
\(236\) | −21.6782 | − | 16.8650i | −1.41113 | − | 1.09782i | ||||
\(237\) | −11.8115 | + | 11.8115i | −0.767242 | + | 0.767242i | ||||
\(238\) | −3.85540 | + | 1.88532i | −0.249909 | + | 0.122207i | ||||
\(239\) | 1.81466 | + | 1.81466i | 0.117381 | + | 0.117381i | 0.763357 | − | 0.645977i | \(-0.223550\pi\) |
−0.645977 | + | 0.763357i | \(0.723550\pi\) | |||||||
\(240\) | −5.31915 | + | 8.93576i | −0.343350 | + | 0.576801i | ||||
\(241\) | −12.3236 | − | 12.3236i | −0.793834 | − | 0.793834i | 0.188281 | − | 0.982115i | \(-0.439708\pi\) |
−0.982115 | + | 0.188281i | \(0.939708\pi\) | |||||||
\(242\) | 2.01784 | + | 0.692472i | 0.129711 | + | 0.0445138i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 14.8456 | − | 1.85386i | 0.950391 | − | 0.118681i | ||||
\(245\) | 17.6917i | 1.13028i | ||||||||
\(246\) | 4.73277 | − | 13.7911i | 0.301750 | − | 0.879288i | ||||
\(247\) | −15.9697 | − | 8.50215i | −1.01612 | − | 0.540979i | ||||
\(248\) | −1.42118 | + | 6.78923i | −0.0902450 | + | 0.431116i | ||||
\(249\) | 5.29041 | + | 5.29041i | 0.335266 | + | 0.335266i | ||||
\(250\) | −11.2714 | − | 3.86806i | −0.712865 | − | 0.244638i | ||||
\(251\) | −8.97239 | − | 8.97239i | −0.566332 | − | 0.566332i | 0.364767 | − | 0.931099i | \(-0.381149\pi\) |
−0.931099 | + | 0.364767i | \(0.881149\pi\) | |||||||
\(252\) | −0.876147 | + | 0.109410i | −0.0551921 | + | 0.00689219i | ||||
\(253\) | − | 5.44189i | − | 0.342129i | ||||||
\(254\) | 7.78925 | + | 2.67308i | 0.488741 | + | 0.167724i | ||||
\(255\) | 12.6365 | − | 12.6365i | 0.791328 | − | 0.791328i | ||||
\(256\) | −14.0648 | + | 7.62771i | −0.879049 | + | 0.476732i | ||||
\(257\) | − | 1.97467i | − | 0.123176i | −0.998102 | − | 0.0615881i | \(-0.980383\pi\) | ||
0.998102 | − | 0.0615881i | \(-0.0196165\pi\) | |||||||
\(258\) | −1.23411 | + | 3.59615i | −0.0768324 | + | 0.223886i | ||||
\(259\) | 2.00902 | − | 2.00902i | 0.124835 | − | 0.124835i | ||||
\(260\) | −7.65132 | − | 17.1148i | −0.474515 | − | 1.06141i | ||||
\(261\) | −5.32160 | − | 5.32160i | −0.329399 | − | 0.329399i | ||||
\(262\) | −6.01846 | − | 12.3075i | −0.371822 | − | 0.760359i | ||||
\(263\) | 20.1922 | 1.24510 | 0.622551 | − | 0.782579i | \(-0.286096\pi\) | ||||
0.622551 | + | 0.782579i | \(0.286096\pi\) | |||||||
\(264\) | −1.78537 | + | 8.52903i | −0.109882 | + | 0.524926i | ||||
\(265\) | −10.6219 | − | 10.6219i | −0.652498 | − | 0.652498i | ||||
\(266\) | 1.37623 | + | 2.81434i | 0.0843824 | + | 0.172558i | ||||
\(267\) | −15.6845 | −0.959873 | ||||||||
\(268\) | −24.8808 | − | 19.3566i | −1.51984 | − | 1.18239i | ||||
\(269\) | −18.9916 | + | 18.9916i | −1.15794 | + | 1.15794i | −0.173020 | + | 0.984918i | \(0.555353\pi\) |
−0.984918 | + | 0.173020i | \(0.944647\pi\) | |||||||
\(270\) | 3.30288 | − | 1.61513i | 0.201007 | − | 0.0982939i | ||||
\(271\) | −5.60706 | + | 5.60706i | −0.340605 | + | 0.340605i | −0.856595 | − | 0.515990i | \(-0.827424\pi\) |
0.515990 | + | 0.856595i | \(0.327424\pi\) | |||||||
\(272\) | 26.6514 | − | 6.76170i | 1.61598 | − | 0.409989i | ||||
\(273\) | 0.748038 | − | 1.40505i | 0.0452733 | − | 0.0850372i | ||||
\(274\) | 0.426562 | − | 0.208592i | 0.0257696 | − | 0.0126015i | ||||
\(275\) | 5.41863 | 0.326756 | ||||||||
\(276\) | −3.50552 | + | 0.437757i | −0.211007 | + | 0.0263499i | ||||
\(277\) | 7.97084 | − | 7.97084i | 0.478922 | − | 0.478922i | −0.425865 | − | 0.904787i | \(-0.640030\pi\) |
0.904787 | + | 0.425865i | \(0.140030\pi\) | |||||||
\(278\) | −5.00772 | + | 2.44882i | −0.300343 | + | 0.146870i | ||||
\(279\) | 1.73409 | − | 1.73409i | 0.103818 | − | 0.103818i | ||||
\(280\) | −0.665126 | + | 3.17742i | −0.0397489 | + | 0.189887i | ||||
\(281\) | −8.08671 | + | 8.08671i | −0.482413 | + | 0.482413i | −0.905901 | − | 0.423489i | \(-0.860805\pi\) |
0.423489 | + | 0.905901i | \(0.360805\pi\) | |||||||
\(282\) | 2.16368 | + | 0.742521i | 0.128845 | + | 0.0442165i | ||||
\(283\) | −22.7352 | − | 22.7352i | −1.35147 | − | 1.35147i | −0.884022 | − | 0.467445i | \(-0.845174\pi\) |
−0.467445 | − | 0.884022i | \(-0.654826\pi\) | |||||||
\(284\) | −31.1700 | + | 3.89240i | −1.84960 | + | 0.230972i | ||||
\(285\) | −9.22429 | − | 9.22429i | −0.546400 | − | 0.546400i | ||||
\(286\) | −10.7193 | − | 11.4837i | −0.633848 | − | 0.679043i | ||||
\(287\) | − | 4.55163i | − | 0.268674i | ||||||
\(288\) | 5.63779 | + | 0.463995i | 0.332210 | + | 0.0273411i | ||||
\(289\) | −30.2511 | −1.77947 | ||||||||
\(290\) | −24.8570 | + | 12.1553i | −1.45966 | + | 0.713784i | ||||
\(291\) | −10.3695 | −0.607870 | ||||||||
\(292\) | 1.74518 | − | 0.217932i | 0.102129 | − | 0.0127535i | ||||
\(293\) | 7.84277i | 0.458180i | 0.973405 | + | 0.229090i | \(0.0735750\pi\) | ||||
−0.973405 | + | 0.229090i | \(0.926425\pi\) | |||||||
\(294\) | 8.64552 | − | 4.22773i | 0.504217 | − | 0.246566i | ||||
\(295\) | 35.7025 | 2.07868 | ||||||||
\(296\) | −15.2354 | + | 9.96108i | −0.885541 | + | 0.578976i | ||||
\(297\) | 2.17847 | − | 2.17847i | 0.126408 | − | 0.126408i | ||||
\(298\) | 20.3141 | + | 6.97130i | 1.17676 | + | 0.403837i | ||||
\(299\) | 2.99295 | − | 5.62167i | 0.173087 | − | 0.325110i | ||||
\(300\) | −0.435886 | − | 3.49054i | −0.0251659 | − | 0.201526i | ||||
\(301\) | 1.18688i | 0.0684105i | ||||||||
\(302\) | −10.6761 | − | 21.8321i | −0.614340 | − | 1.25630i | ||||
\(303\) | −6.62644 | −0.380679 | ||||||||
\(304\) | −4.93586 | − | 19.4548i | −0.283091 | − | 1.11581i | ||||
\(305\) | −13.7514 | + | 13.7514i | −0.787405 | + | 0.787405i | ||||
\(306\) | −9.19485 | − | 3.15545i | −0.525635 | − | 0.180385i | ||||
\(307\) | 19.3002i | 1.10152i | 0.834664 | + | 0.550760i | \(0.185662\pi\) | ||||
−0.834664 | + | 0.550760i | \(0.814338\pi\) | |||||||
\(308\) | 0.337074 | + | 2.69926i | 0.0192066 | + | 0.153805i | ||||
\(309\) | 0.177393 | − | 0.177393i | 0.0100916 | − | 0.0100916i | ||||
\(310\) | −3.96092 | − | 8.09991i | −0.224965 | − | 0.460044i | ||||
\(311\) | 25.4700i | 1.44427i | 0.691750 | + | 0.722137i | \(0.256840\pi\) | ||||
−0.691750 | + | 0.722137i | \(0.743160\pi\) | |||||||
\(312\) | −6.53518 | + | 7.82889i | −0.369982 | + | 0.443223i | ||||
\(313\) | 0.779174i | 0.0440415i | 0.999758 | + | 0.0220208i | \(0.00700999\pi\) | ||||
−0.999758 | + | 0.0220208i | \(0.992990\pi\) | |||||||
\(314\) | −8.53776 | + | 4.17504i | −0.481814 | + | 0.235611i | ||||
\(315\) | 0.811573 | − | 0.811573i | 0.0457270 | − | 0.0457270i | ||||
\(316\) | 20.5138 | − | 26.3683i | 1.15399 | − | 1.48333i | ||||
\(317\) | − | 7.53592i | − | 0.423259i | −0.977350 | − | 0.211630i | \(-0.932123\pi\) | ||
0.977350 | − | 0.211630i | \(-0.0678771\pi\) | |||||||
\(318\) | −2.65239 | + | 7.72895i | −0.148739 | + | 0.433418i | ||||
\(319\) | −16.3949 | + | 16.3949i | −0.917939 | + | 0.917939i | ||||
\(320\) | 8.34179 | − | 19.0520i | 0.466320 | − | 1.06504i | ||||
\(321\) | −2.60803 | −0.145566 | ||||||||
\(322\) | −0.990709 | + | 0.484465i | −0.0552101 | + | 0.0269982i | ||||
\(323\) | 34.4920i | 1.91918i | ||||||||
\(324\) | −1.57856 | − | 1.22807i | −0.0876975 | − | 0.0682263i | ||||
\(325\) | 5.59765 | + | 2.98016i | 0.310502 | + | 0.165309i | ||||
\(326\) | −3.61424 | + | 10.5318i | −0.200174 | + | 0.583300i | ||||
\(327\) | 0.413442 | − | 0.413442i | 0.0228634 | − | 0.0228634i | ||||
\(328\) | −5.97476 | + | 28.5425i | −0.329901 | + | 1.57600i | ||||
\(329\) | 0.714103 | 0.0393698 | ||||||||
\(330\) | −4.97595 | − | 10.1756i | −0.273917 | − | 0.560148i | ||||
\(331\) | 13.2622i | 0.728959i | 0.931211 | + | 0.364480i | \(0.118753\pi\) | ||||
−0.931211 | + | 0.364480i | \(0.881247\pi\) | |||||||
\(332\) | −11.8104 | − | 9.18816i | −0.648179 | − | 0.504266i | ||||
\(333\) | 6.43566 | 0.352672 | ||||||||
\(334\) | 1.67666 | + | 3.42869i | 0.0917428 | + | 0.187610i | ||||
\(335\) | 40.9771 | 2.23882 | ||||||||
\(336\) | 1.71167 | − | 0.434268i | 0.0933795 | − | 0.0236912i | ||||
\(337\) | − | 3.21855i | − | 0.175326i | −0.996150 | − | 0.0876629i | \(-0.972060\pi\) | ||
0.996150 | − | 0.0876629i | \(-0.0279398\pi\) | |||||||
\(338\) | −4.75767 | − | 17.7585i | −0.258783 | − | 0.965935i | ||||
\(339\) | −6.67409 | − | 6.67409i | −0.362487 | − | 0.362487i | ||||
\(340\) | −21.9465 | + | 28.2099i | −1.19022 | + | 1.52990i | ||||
\(341\) | −5.34244 | − | 5.34244i | −0.289310 | − | 0.289310i | ||||
\(342\) | −2.30339 | + | 6.71199i | −0.124553 | + | 0.362943i | ||||
\(343\) | 4.30955 | − | 4.30955i | 0.232694 | − | 0.232694i | ||||
\(344\) | 1.55797 | − | 7.44271i | 0.0840002 | − | 0.401284i | ||||
\(345\) | 3.24715 | − | 3.24715i | 0.174821 | − | 0.174821i | ||||
\(346\) | 0.0196037 | + | 0.0400887i | 0.00105390 | + | 0.00215518i | ||||
\(347\) | −6.19697 | + | 6.19697i | −0.332671 | + | 0.332671i | −0.853600 | − | 0.520929i | \(-0.825586\pi\) |
0.520929 | + | 0.853600i | \(0.325586\pi\) | |||||||
\(348\) | 11.8800 | + | 9.24233i | 0.636835 | + | 0.495441i | ||||
\(349\) | 25.9541 | 1.38929 | 0.694646 | − | 0.719351i | \(-0.255561\pi\) | ||||
0.694646 | + | 0.719351i | \(0.255561\pi\) | |||||||
\(350\) | −0.482395 | − | 0.986476i | −0.0257851 | − | 0.0527293i | ||||
\(351\) | 3.44857 | − | 1.05232i | 0.184071 | − | 0.0561687i | ||||
\(352\) | 1.42949 | − | 17.3691i | 0.0761919 | − | 0.925774i | ||||
\(353\) | 23.8028 | − | 23.8028i | 1.26689 | − | 1.26689i | 0.319208 | − | 0.947685i | \(-0.396583\pi\) |
0.947685 | − | 0.319208i | \(-0.103417\pi\) | |||||||
\(354\) | −8.53171 | − | 17.4470i | −0.453455 | − | 0.927296i | ||||
\(355\) | 28.8727 | − | 28.8727i | 1.53241 | − | 1.53241i | ||||
\(356\) | 31.1271 | − | 3.88705i | 1.64974 | − | 0.206013i | ||||
\(357\) | −3.03468 | −0.160612 | ||||||||
\(358\) | −6.15422 | + | 3.00947i | −0.325261 | + | 0.159055i | ||||
\(359\) | −20.6184 | − | 20.6184i | −1.08820 | − | 1.08820i | −0.995714 | − | 0.0924811i | \(-0.970520\pi\) |
−0.0924811 | − | 0.995714i | \(-0.529480\pi\) | |||||||
\(360\) | −6.15457 | + | 4.02392i | −0.324374 | + | 0.212079i | ||||
\(361\) | 6.17818 | 0.325168 | ||||||||
\(362\) | 8.47638 | − | 4.14502i | 0.445509 | − | 0.217858i | ||||
\(363\) | 1.06667 | + | 1.06667i | 0.0559859 | + | 0.0559859i | ||||
\(364\) | −1.13634 | + | 2.97382i | −0.0595602 | + | 0.155870i | ||||
\(365\) | −1.61655 | + | 1.61655i | −0.0846143 | + | 0.0846143i | ||||
\(366\) | 10.0061 | + | 3.43386i | 0.523029 | + | 0.179491i | ||||
\(367\) | − | 30.9160i | − | 1.61380i | −0.590687 | − | 0.806901i | \(-0.701143\pi\) | ||
0.590687 | − | 0.806901i | \(-0.298857\pi\) | |||||||
\(368\) | 6.84851 | − | 1.73753i | 0.357003 | − | 0.0905751i | ||||
\(369\) | 7.29029 | − | 7.29029i | 0.379517 | − | 0.379517i | ||||
\(370\) | 7.68040 | − | 22.3804i | 0.399285 | − | 1.16350i | ||||
\(371\) | 2.55087i | 0.132435i | ||||||||
\(372\) | −3.01170 | + | 3.87122i | −0.156149 | + | 0.200713i | ||||
\(373\) | 7.25450 | + | 7.25450i | 0.375624 | + | 0.375624i | 0.869521 | − | 0.493897i | \(-0.164428\pi\) |
−0.493897 | + | 0.869521i | \(0.664428\pi\) | |||||||
\(374\) | −9.72139 | + | 28.3277i | −0.502681 | + | 1.46479i | ||||
\(375\) | −5.95831 | − | 5.95831i | −0.307686 | − | 0.307686i | ||||
\(376\) | −4.47802 | − | 0.937378i | −0.230936 | − | 0.0483416i | ||||
\(377\) | −25.9535 | + | 7.91963i | −1.33667 | + | 0.407882i | ||||
\(378\) | −0.590536 | − | 0.202657i | −0.0303739 | − | 0.0104236i | ||||
\(379\) | − | 4.56879i | − | 0.234683i | −0.993092 | − | 0.117341i | \(-0.962563\pi\) | ||
0.993092 | − | 0.117341i | \(-0.0374372\pi\) | |||||||
\(380\) | 20.5924 | + | 16.0204i | 1.05637 | + | 0.821827i | ||||
\(381\) | 4.11758 | + | 4.11758i | 0.210950 | + | 0.210950i | ||||
\(382\) | 1.03179 | − | 3.00660i | 0.0527910 | − | 0.153831i | ||||
\(383\) | 25.0640 | + | 25.0640i | 1.28071 | + | 1.28071i | 0.940262 | + | 0.340451i | \(0.110580\pi\) |
0.340451 | + | 0.940262i | \(0.389420\pi\) | |||||||
\(384\) | −11.3037 | + | 0.476366i | −0.576838 | + | 0.0243095i | ||||
\(385\) | −2.50032 | − | 2.50032i | −0.127428 | − | 0.127428i | ||||
\(386\) | 5.58107 | + | 11.4130i | 0.284069 | + | 0.580908i | ||||
\(387\) | −1.90101 | + | 1.90101i | −0.0966336 | + | 0.0966336i | ||||
\(388\) | 20.5791 | − | 2.56985i | 1.04475 | − | 0.130464i | ||||
\(389\) | −9.29703 | + | 9.29703i | −0.471378 | + | 0.471378i | −0.902360 | − | 0.430982i | \(-0.858167\pi\) |
0.430982 | + | 0.902360i | \(0.358167\pi\) | |||||||
\(390\) | 0.456061 | − | 13.2485i | 0.0230936 | − | 0.670861i | ||||
\(391\) | −12.1419 | −0.614044 | ||||||||
\(392\) | −16.1100 | + | 10.5329i | −0.813679 | + | 0.531992i | ||||
\(393\) | − | 9.68752i | − | 0.488671i | ||||||
\(394\) | −7.71981 | − | 2.64925i | −0.388918 | − | 0.133467i | ||||
\(395\) | 43.4267i | 2.18504i | ||||||||
\(396\) | −3.78348 | + | 4.86325i | −0.190127 | + | 0.244388i | ||||
\(397\) | −9.42160 | −0.472856 | −0.236428 | − | 0.971649i | \(-0.575977\pi\) | ||||
−0.236428 | + | 0.971649i | \(0.575977\pi\) | |||||||
\(398\) | 5.30166 | − | 15.4488i | 0.265748 | − | 0.774379i | ||||
\(399\) | 2.21523i | 0.110900i | ||||||||
\(400\) | 1.73011 | + | 6.81925i | 0.0865053 | + | 0.340962i | ||||
\(401\) | 22.1391 | + | 22.1391i | 1.10557 | + | 1.10557i | 0.993725 | + | 0.111849i | \(0.0356772\pi\) |
0.111849 | + | 0.993725i | \(0.464323\pi\) | |||||||
\(402\) | −9.79216 | − | 20.0245i | −0.488388 | − | 0.998732i | ||||
\(403\) | −2.58069 | − | 8.45720i | −0.128553 | − | 0.421283i | ||||
\(404\) | 13.1507 | − | 1.64222i | 0.654273 | − | 0.0817034i | ||||
\(405\) | 2.59977 | 0.129184 | ||||||||
\(406\) | 4.44430 | + | 1.52517i | 0.220567 | + | 0.0756932i | ||||
\(407\) | − | 19.8271i | − | 0.982795i | ||||||
\(408\) | 19.0300 | + | 3.98352i | 0.942124 | + | 0.197214i | ||||
\(409\) | 6.68243 | + | 6.68243i | 0.330425 | + | 0.330425i | 0.852748 | − | 0.522323i | \(-0.174934\pi\) |
−0.522323 | + | 0.852748i | \(0.674934\pi\) | |||||||
\(410\) | −16.6521 | − | 34.0527i | −0.822387 | − | 1.68174i | ||||
\(411\) | 0.335757 | 0.0165617 | ||||||||
\(412\) | −0.308089 | + | 0.396016i | −0.0151785 | + | 0.0195103i | ||||
\(413\) | −4.28702 | − | 4.28702i | −0.210950 | − | 0.210950i | ||||
\(414\) | −2.36277 | − | 0.810845i | −0.116124 | − | 0.0398509i | ||||
\(415\) | 19.4509 | 0.954808 | ||||||||
\(416\) | 11.0294 | − | 17.1567i | 0.540761 | − | 0.841176i | ||||
\(417\) | −3.94170 | −0.193026 | ||||||||
\(418\) | 20.6785 | + | 7.09635i | 1.01142 | + | 0.347094i | ||||
\(419\) | 8.15845 | + | 8.15845i | 0.398567 | + | 0.398567i | 0.877727 | − | 0.479161i | \(-0.159059\pi\) |
−0.479161 | + | 0.877727i | \(0.659059\pi\) | |||||||
\(420\) | −1.40951 | + | 1.81177i | −0.0687769 | + | 0.0884052i | ||||
\(421\) | −24.2088 | −1.17987 | −0.589933 | − | 0.807452i | \(-0.700846\pi\) | ||||
−0.589933 | + | 0.807452i | \(0.700846\pi\) | |||||||
\(422\) | −1.47566 | − | 3.01766i | −0.0718341 | − | 0.146898i | ||||
\(423\) | 1.14377 | + | 1.14377i | 0.0556120 | + | 0.0556120i | ||||
\(424\) | 3.34844 | − | 15.9961i | 0.162615 | − | 0.776839i | ||||
\(425\) | − | 12.0901i | − | 0.586454i | ||||||
\(426\) | −21.0090 | − | 7.20979i | −1.01789 | − | 0.349316i | ||||
\(427\) | 3.30244 | 0.159816 | ||||||||
\(428\) | 5.17587 | − | 0.646344i | 0.250185 | − | 0.0312422i | ||||
\(429\) | −3.24202 | − | 10.6244i | −0.156526 | − | 0.512953i | ||||
\(430\) | 4.34217 | + | 8.87955i | 0.209398 | + | 0.428210i | ||||
\(431\) | −0.871986 | − | 0.871986i | −0.0420021 | − | 0.0420021i | 0.685794 | − | 0.727796i | \(-0.259455\pi\) |
−0.727796 | + | 0.685794i | \(0.759455\pi\) | |||||||
\(432\) | 3.43713 | + | 2.04601i | 0.165369 | + | 0.0984385i | ||||
\(433\) | 6.16927i | 0.296476i | 0.988952 | + | 0.148238i | \(0.0473602\pi\) | ||||
−0.988952 | + | 0.148238i | \(0.952640\pi\) | |||||||
\(434\) | −0.496993 | + | 1.44822i | −0.0238564 | + | 0.0695167i | ||||
\(435\) | −19.5656 | −0.938098 | ||||||||
\(436\) | −0.718049 | + | 0.922974i | −0.0343883 | + | 0.0442024i | ||||
\(437\) | 8.86328i | 0.423988i | ||||||||
\(438\) | 1.17627 | + | 0.403669i | 0.0562045 | + | 0.0192880i | ||||
\(439\) | 13.5607i | 0.647217i | 0.946191 | + | 0.323608i | \(0.104896\pi\) | ||||
−0.946191 | + | 0.323608i | \(0.895104\pi\) | |||||||
\(440\) | 12.3970 | + | 18.9612i | 0.591004 | + | 0.903937i | ||||
\(441\) | 6.80510 | 0.324052 | ||||||||
\(442\) | −25.6223 | + | 23.9170i | −1.21873 | + | 1.13762i | ||||
\(443\) | 7.44734 | − | 7.44734i | 0.353834 | − | 0.353834i | −0.507700 | − | 0.861534i | \(-0.669504\pi\) |
0.861534 | + | 0.507700i | \(0.169504\pi\) | |||||||
\(444\) | −12.7721 | + | 1.59494i | −0.606138 | + | 0.0756923i | ||||
\(445\) | −28.8330 | + | 28.8330i | −1.36682 | + | 1.36682i | ||||
\(446\) | −2.74447 | − | 5.61231i | −0.129954 | − | 0.265751i | ||||
\(447\) | 10.7385 | + | 10.7385i | 0.507913 | + | 0.507913i | ||||
\(448\) | −3.28934 | + | 1.28604i | −0.155407 | + | 0.0607598i | ||||
\(449\) | 15.0382 | + | 15.0382i | 0.709697 | + | 0.709697i | 0.966471 | − | 0.256775i | \(-0.0826598\pi\) |
−0.256775 | + | 0.966471i | \(0.582660\pi\) | |||||||
\(450\) | 0.807380 | − | 2.35267i | 0.0380602 | − | 0.110906i | ||||
\(451\) | −22.4601 | − | 22.4601i | −1.05761 | − | 1.05761i | ||||
\(452\) | 14.8993 | + | 11.5913i | 0.700806 | + | 0.545208i | ||||
\(453\) | − | 17.1846i | − | 0.807403i | ||||||
\(454\) | −21.4322 | − | 7.35500i | −1.00586 | − | 0.345187i | ||||
\(455\) | −1.20779 | − | 3.95805i | −0.0566220 | − | 0.185556i | ||||
\(456\) | 2.90786 | − | 13.8914i | 0.136173 | − | 0.650522i | ||||
\(457\) | −28.0523 | − | 28.0523i | −1.31223 | − | 1.31223i | −0.919769 | − | 0.392460i | \(-0.871624\pi\) |
−0.392460 | − | 0.919769i | \(-0.628376\pi\) | |||||||
\(458\) | −2.98896 | + | 8.70972i | −0.139665 | + | 0.406978i | ||||
\(459\) | −4.86061 | − | 4.86061i | −0.226874 | − | 0.226874i | ||||
\(460\) | −5.63952 | + | 7.24899i | −0.262944 | + | 0.337986i | ||||
\(461\) | 17.7812i | 0.828155i | 0.910242 | + | 0.414078i | \(0.135896\pi\) | ||||
−0.910242 | + | 0.414078i | \(0.864104\pi\) | |||||||
\(462\) | −0.624353 | + | 1.81934i | −0.0290475 | + | 0.0846433i | ||||
\(463\) | −5.04088 | + | 5.04088i | −0.234270 | + | 0.234270i | −0.814472 | − | 0.580203i | \(-0.802973\pi\) |
0.580203 | + | 0.814472i | \(0.302973\pi\) | |||||||
\(464\) | −25.8674 | − | 15.3980i | −1.20086 | − | 0.714834i | ||||
\(465\) | − | 6.37563i | − | 0.295663i | ||||||
\(466\) | 17.6904 | + | 6.07092i | 0.819492 | + | 0.281230i | ||||
\(467\) | −23.4380 | + | 23.4380i | −1.08458 | + | 1.08458i | −0.0885031 | + | 0.996076i | \(0.528208\pi\) |
−0.996076 | + | 0.0885031i | \(0.971792\pi\) | |||||||
\(468\) | −6.58318 | + | 2.94307i | −0.304308 | + | 0.136044i | ||||
\(469\) | −4.92037 | − | 4.92037i | −0.227201 | − | 0.227201i | ||||
\(470\) | 5.34252 | − | 2.61254i | 0.246432 | − | 0.120507i | ||||
\(471\) | −6.72028 | −0.309654 | ||||||||
\(472\) | 21.2558 | + | 32.5106i | 0.978376 | + | 1.49642i | ||||
\(473\) | 5.85667 | + | 5.85667i | 0.269290 | + | 0.269290i | ||||
\(474\) | 21.2216 | − | 10.3775i | 0.974741 | − | 0.476656i | ||||
\(475\) | −8.82541 | −0.404937 | ||||||||
\(476\) | 6.02258 | − | 0.752079i | 0.276045 | − | 0.0344715i | ||||
\(477\) | −4.08570 | + | 4.08570i | −0.187071 | + | 0.187071i | ||||
\(478\) | −1.59435 | − | 3.26037i | −0.0729239 | − | 0.149126i | ||||
\(479\) | 2.83070 | − | 2.83070i | 0.129338 | − | 0.129338i | −0.639474 | − | 0.768812i | \(-0.720848\pi\) |
0.768812 | + | 0.639474i | \(0.220848\pi\) | |||||||
\(480\) | 11.2170 | − | 9.51109i | 0.511985 | − | 0.434120i | ||||
\(481\) | 10.9046 | − | 20.4822i | 0.497207 | − | 0.933907i | ||||
\(482\) | 10.8275 | + | 22.1417i | 0.493177 | + | 1.00852i | ||||
\(483\) | −0.779811 | −0.0354826 | ||||||||
\(484\) | −2.38126 | − | 1.85256i | −0.108239 | − | 0.0842071i | ||||
\(485\) | −19.0624 | + | 19.0624i | −0.865579 | + | 0.865579i | ||||
\(486\) | −0.621260 | − | 1.27045i | −0.0281809 | − | 0.0576287i | ||||
\(487\) | −15.2061 | + | 15.2061i | −0.689053 | + | 0.689053i | −0.962023 | − | 0.272970i | \(-0.911994\pi\) |
0.272970 | + | 0.962023i | \(0.411994\pi\) | |||||||
\(488\) | −20.7090 | − | 4.33499i | −0.937454 | − | 0.196236i | ||||
\(489\) | −5.56733 | + | 5.56733i | −0.251763 | + | 0.251763i | ||||
\(490\) | 8.12130 | − | 23.6651i | 0.366883 | − | 1.06908i | ||||
\(491\) | −21.3579 | − | 21.3579i | −0.963868 | − | 0.963868i | 0.0355015 | − | 0.999370i | \(-0.488697\pi\) |
−0.999370 | + | 0.0355015i | \(0.988697\pi\) | |||||||
\(492\) | −12.6615 | + | 16.2749i | −0.570823 | + | 0.733731i | ||||
\(493\) | 36.5803 | + | 36.5803i | 1.64750 | + | 1.64750i | ||||
\(494\) | 17.4588 | + | 18.7036i | 0.785507 | + | 0.841515i | ||||
\(495\) | − | 8.00945i | − | 0.359998i | ||||||
\(496\) | 5.01759 | − | 8.42915i | 0.225296 | − | 0.378480i | ||||
\(497\) | −6.93385 | −0.311026 | ||||||||
\(498\) | −4.64812 | − | 9.50519i | −0.208287 | − | 0.425938i | ||||
\(499\) | 26.9120 | 1.20475 | 0.602374 | − | 0.798214i | \(-0.294222\pi\) | ||||
0.602374 | + | 0.798214i | \(0.294222\pi\) | |||||||
\(500\) | 13.3014 | + | 10.3481i | 0.594857 | + | 0.462783i | ||||
\(501\) | 2.69881i | 0.120574i | ||||||||
\(502\) | 7.88308 | + | 16.1205i | 0.351839 | + | 0.719495i | ||||
\(503\) | 15.6841 | 0.699319 | 0.349660 | − | 0.936877i | \(-0.386297\pi\) | ||||
0.349660 | + | 0.936877i | \(0.386297\pi\) | |||||||
\(504\) | 1.22219 | + | 0.255840i | 0.0544408 | + | 0.0113960i | ||||
\(505\) | −12.1815 | + | 12.1815i | −0.542070 | + | 0.542070i | ||||
\(506\) | −2.49807 | + | 7.27928i | −0.111053 | + | 0.323604i | ||||
\(507\) | 2.49414 | − | 12.7585i | 0.110769 | − | 0.566625i | ||||
\(508\) | −9.19213 | − | 7.15123i | −0.407835 | − | 0.317285i | ||||
\(509\) | − | 34.3940i | − | 1.52449i | −0.647290 | − | 0.762244i | \(-0.724098\pi\) | ||
0.647290 | − | 0.762244i | \(-0.275902\pi\) | |||||||
\(510\) | −22.7038 | + | 11.1023i | −1.00534 | + | 0.491620i | ||||
\(511\) | 0.388219 | 0.0171738 | ||||||||
\(512\) | 22.3151 | − | 3.74676i | 0.986196 | − | 0.165585i | ||||
\(513\) | −3.54811 | + | 3.54811i | −0.156653 | + | 0.156653i | ||||
\(514\) | −0.906460 | + | 2.64139i | −0.0399823 | + | 0.116507i | ||||
\(515\) | − | 0.652211i | − | 0.0287398i | ||||||
\(516\) | 3.30159 | − | 4.24383i | 0.145344 | − | 0.186824i | ||||
\(517\) | 3.52376 | − | 3.52376i | 0.154975 | − | 0.154975i | ||||
\(518\) | −3.60958 | + | 1.76512i | −0.158596 | + | 0.0775547i | ||||
\(519\) | 0.0315548i | 0.00138510i | ||||||||
\(520\) | 2.37824 | + | 26.4057i | 0.104293 | + | 1.15797i | ||||
\(521\) | − | 45.0314i | − | 1.97286i | −0.164183 | − | 0.986430i | \(-0.552499\pi\) | ||
0.164183 | − | 0.986430i | \(-0.447501\pi\) | |||||||
\(522\) | 4.67552 | + | 9.56123i | 0.204642 | + | 0.418484i | ||||
\(523\) | 2.59835 | − | 2.59835i | 0.113618 | − | 0.113618i | −0.648012 | − | 0.761630i | \(-0.724399\pi\) |
0.761630 | + | 0.648012i | \(0.224399\pi\) | |||||||
\(524\) | 2.40084 | + | 19.2257i | 0.104881 | + | 0.839879i | ||||
\(525\) | − | 0.776479i | − | 0.0338883i | ||||||
\(526\) | −27.0098 | − | 9.26912i | −1.17768 | − | 0.404153i | ||||
\(527\) | −11.9201 | + | 11.9201i | −0.519246 | + | 0.519246i | ||||
\(528\) | 6.30339 | − | 10.5892i | 0.274320 | − | 0.460836i | ||||
\(529\) | 19.8799 | 0.864345 | ||||||||
\(530\) | 9.33234 | + | 19.0842i | 0.405371 | + | 0.828965i | ||||
\(531\) | − | 13.7329i | − | 0.595958i | ||||||
\(532\) | −0.548997 | − | 4.39632i | −0.0238020 | − | 0.190605i | ||||
\(533\) | −10.8495 | − | 35.5548i | −0.469942 | − | 1.54005i | ||||
\(534\) | 20.9801 | + | 7.19987i | 0.907899 | + | 0.311569i | ||||
\(535\) | −4.79439 | + | 4.79439i | −0.207280 | + | 0.207280i | ||||
\(536\) | 24.3960 | + | 37.3136i | 1.05375 | + | 1.61170i | ||||
\(537\) | −4.84414 | −0.209040 | ||||||||
\(538\) | 34.1219 | − | 16.6859i | 1.47110 | − | 0.719380i | ||||
\(539\) | − | 20.9653i | − | 0.903041i | ||||||
\(540\) | −5.15947 | + | 0.644297i | −0.222028 | + | 0.0277261i | ||||
\(541\) | 27.3236 | 1.17474 | 0.587368 | − | 0.809320i | \(-0.300164\pi\) | ||||
0.587368 | + | 0.809320i | \(0.300164\pi\) | |||||||
\(542\) | 10.0741 | − | 4.92633i | 0.432720 | − | 0.211604i | ||||
\(543\) | 6.67197 | 0.286322 | ||||||||
\(544\) | −38.7539 | − | 3.18947i | −1.66156 | − | 0.136747i | ||||
\(545\) | − | 1.52008i | − | 0.0651129i | ||||||
\(546\) | −1.64558 | + | 1.53606i | −0.0704245 | + | 0.0657373i | ||||
\(547\) | −4.06928 | − | 4.06928i | −0.173990 | − | 0.173990i | 0.614740 | − | 0.788730i | \(-0.289261\pi\) |
−0.788730 | + | 0.614740i | \(0.789261\pi\) | |||||||
\(548\) | −0.666339 | + | 0.0832101i | −0.0284646 | + | 0.00355456i | ||||
\(549\) | 5.28947 | + | 5.28947i | 0.225749 | + | 0.225749i | ||||
\(550\) | −7.24817 | − | 2.48740i | −0.309063 | − | 0.106063i | ||||
\(551\) | 26.7026 | − | 26.7026i | 1.13757 | − | 1.13757i | ||||
\(552\) | 4.89007 | + | 1.02363i | 0.208135 | + | 0.0435686i | ||||
\(553\) | 5.21451 | − | 5.21451i | 0.221744 | − | 0.221744i | ||||
\(554\) | −14.3211 | + | 7.00313i | −0.608445 | + | 0.297535i | ||||
\(555\) | 11.8308 | − | 11.8308i | 0.502189 | − | 0.502189i | ||||
\(556\) | 7.82264 | − | 0.976863i | 0.331754 | − | 0.0414282i | ||||
\(557\) | −25.7141 | −1.08954 | −0.544771 | − | 0.838585i | \(-0.683383\pi\) | ||||
−0.544771 | + | 0.838585i | \(0.683383\pi\) | |||||||
\(558\) | −3.11562 | + | 1.52356i | −0.131895 | + | 0.0644976i | ||||
\(559\) | 2.82909 | + | 9.27123i | 0.119658 | + | 0.392131i | ||||
\(560\) | 2.34828 | − | 3.94492i | 0.0992329 | − | 0.166703i | ||||
\(561\) | −14.9747 | + | 14.9747i | −0.632232 | + | 0.632232i | ||||
\(562\) | 14.5293 | − | 7.10494i | 0.612880 | − | 0.299704i | ||||
\(563\) | 16.1382 | − | 16.1382i | 0.680143 | − | 0.680143i | −0.279889 | − | 0.960032i | \(-0.590298\pi\) |
0.960032 | + | 0.279889i | \(0.0902977\pi\) | |||||||
\(564\) | −2.55337 | − | 1.98645i | −0.107516 | − | 0.0836447i | ||||
\(565\) | −24.5382 | −1.03233 | ||||||||
\(566\) | 19.9750 | + | 40.8480i | 0.839612 | + | 1.71697i | ||||
\(567\) | −0.312171 | − | 0.312171i | −0.0131099 | − | 0.0131099i | ||||
\(568\) | 43.4810 | + | 9.10182i | 1.82442 | + | 0.381904i | ||||
\(569\) | 37.7402 | 1.58215 | 0.791075 | − | 0.611719i | \(-0.209522\pi\) | ||||
0.791075 | + | 0.611719i | \(0.209522\pi\) | |||||||
\(570\) | 8.10440 | + | 16.5731i | 0.339456 | + | 0.694172i | ||||
\(571\) | 30.6444 | + | 30.6444i | 1.28243 | + | 1.28243i | 0.939282 | + | 0.343147i | \(0.111493\pi\) |
0.343147 | + | 0.939282i | \(0.388507\pi\) | |||||||
\(572\) | 9.06710 | + | 20.2817i | 0.379114 | + | 0.848019i | ||||
\(573\) | 1.58936 | − | 1.58936i | 0.0663963 | − | 0.0663963i | ||||
\(574\) | −2.08940 | + | 6.08844i | −0.0872100 | + | 0.254126i | ||||
\(575\) | − | 3.10674i | − | 0.129560i | ||||||
\(576\) | −7.32834 | − | 3.20866i | −0.305347 | − | 0.133694i | ||||
\(577\) | −1.65091 | + | 1.65091i | −0.0687281 | + | 0.0687281i | −0.740635 | − | 0.671907i | \(-0.765475\pi\) |
0.671907 | + | 0.740635i | \(0.265475\pi\) | |||||||
\(578\) | 40.4650 | + | 13.8866i | 1.68312 | + | 0.577607i | ||||
\(579\) | 8.98347i | 0.373340i | ||||||||
\(580\) | 38.8296 | − | 4.84890i | 1.61231 | − | 0.201340i | ||||
\(581\) | −2.33559 | − | 2.33559i | −0.0968966 | − | 0.0968966i | ||||
\(582\) | 13.8706 | + | 4.76006i | 0.574956 | + | 0.197311i | ||||
\(583\) | 12.5873 | + | 12.5873i | 0.521314 | + | 0.521314i | ||||
\(584\) | −2.43446 | − | 0.509601i | −0.100739 | − | 0.0210875i | ||||
\(585\) | 4.40506 | − | 8.27406i | 0.182127 | − | 0.342090i | ||||
\(586\) | 3.60019 | − | 10.4908i | 0.148722 | − | 0.433371i | ||||
\(587\) | 12.5683i | 0.518747i | 0.965777 | + | 0.259374i | \(0.0835161\pi\) | ||||
−0.965777 | + | 0.259374i | \(0.916484\pi\) | |||||||
\(588\) | −13.5053 | + | 1.68649i | −0.556949 | + | 0.0695499i | ||||
\(589\) | 8.70132 | + | 8.70132i | 0.358532 | + | 0.358532i | ||||
\(590\) | −47.7571 | − | 16.3891i | −1.96613 | − | 0.674727i | ||||
\(591\) | −4.08087 | − | 4.08087i | −0.167865 | − | 0.167865i | ||||
\(592\) | 24.9521 | − | 6.33058i | 1.02552 | − | 0.260185i | ||||
\(593\) | −16.6876 | − | 16.6876i | −0.685276 | − | 0.685276i | 0.275908 | − | 0.961184i | \(-0.411021\pi\) |
−0.961184 | + | 0.275908i | \(0.911021\pi\) | |||||||
\(594\) | −3.91403 | + | 1.91399i | −0.160595 | + | 0.0785321i | ||||
\(595\) | −5.57871 | + | 5.57871i | −0.228705 | + | 0.228705i | ||||
\(596\) | −23.9728 | − | 18.6502i | −0.981963 | − | 0.763940i | ||||
\(597\) | 8.16660 | − | 8.16660i | 0.334237 | − | 0.334237i | ||||
\(598\) | −6.58408 | + | 6.14587i | −0.269243 | + | 0.251323i | ||||
\(599\) | 5.17898 | 0.211607 | 0.105804 | − | 0.994387i | \(-0.466258\pi\) | ||||
0.105804 | + | 0.994387i | \(0.466258\pi\) | |||||||
\(600\) | −1.01926 | + | 4.86917i | −0.0416110 | + | 0.198783i | ||||
\(601\) | 12.7711i | 0.520946i | 0.965481 | + | 0.260473i | \(0.0838784\pi\) | ||||
−0.965481 | + | 0.260473i | \(0.916122\pi\) | |||||||
\(602\) | 0.544830 | − | 1.58761i | 0.0222056 | − | 0.0647063i | ||||
\(603\) | − | 15.7618i | − | 0.641869i | ||||||
\(604\) | 4.25882 | + | 34.1043i | 0.173289 | + | 1.38768i | ||||
\(605\) | 3.92177 | 0.159443 | ||||||||
\(606\) | 8.86378 | + | 3.04183i | 0.360066 | + | 0.123566i | ||||
\(607\) | 5.73009i | 0.232577i | 0.993215 | + | 0.116289i | \(0.0370997\pi\) | ||||
−0.993215 | + | 0.116289i | \(0.962900\pi\) | |||||||
\(608\) | −2.32823 | + | 28.2892i | −0.0944220 | + | 1.14728i | ||||
\(609\) | 2.34936 | + | 2.34936i | 0.0952008 | + | 0.0952008i | ||||
\(610\) | 24.7070 | − | 12.0819i | 1.00036 | − | 0.489183i | ||||
\(611\) | 5.57818 | − | 1.70217i | 0.225669 | − | 0.0688622i | ||||
\(612\) | 10.8509 | + | 8.44170i | 0.438621 | + | 0.341236i | ||||
\(613\) | 38.1340 | 1.54022 | 0.770109 | − | 0.637912i | \(-0.220202\pi\) | ||||
0.770109 | + | 0.637912i | \(0.220202\pi\) | |||||||
\(614\) | 8.85966 | − | 25.8167i | 0.357547 | − | 1.04188i | ||||
\(615\) | − | 26.8037i | − | 1.08083i | ||||||
\(616\) | 0.788198 | − | 3.76536i | 0.0317574 | − | 0.151711i | ||||
\(617\) | −14.6535 | − | 14.6535i | −0.589927 | − | 0.589927i | 0.347685 | − | 0.937611i | \(-0.386968\pi\) |
−0.937611 | + | 0.347685i | \(0.886968\pi\) | |||||||
\(618\) | −0.318720 | + | 0.155857i | −0.0128208 | + | 0.00626948i | ||||
\(619\) | −12.1900 | −0.489959 | −0.244980 | − | 0.969528i | \(-0.578781\pi\) | ||||
−0.244980 | + | 0.969528i | \(0.578781\pi\) | |||||||
\(620\) | 1.58006 | + | 12.6530i | 0.0634568 | + | 0.508156i | ||||
\(621\) | −1.24901 | − | 1.24901i | −0.0501212 | − | 0.0501212i | ||||
\(622\) | 11.6919 | − | 34.0697i | 0.468803 | − | 1.36607i | ||||
\(623\) | 6.92431 | 0.277417 | ||||||||
\(624\) | 12.3355 | − | 7.47228i | 0.493816 | − | 0.299131i | ||||
\(625\) | −30.7007 | −1.22803 | ||||||||
\(626\) | 0.357676 | − | 1.04225i | 0.0142956 | − | 0.0416568i | ||||
\(627\) | 10.9311 | + | 10.9311i | 0.436547 | + | 0.436547i | ||||
\(628\) | 13.3370 | − | 1.66547i | 0.532203 | − | 0.0664596i | ||||
\(629\) | −44.2383 | −1.76390 | ||||||||
\(630\) | −1.45814 | + | 0.713043i | −0.0580937 | + | 0.0284083i | ||||
\(631\) | 18.8694 | + | 18.8694i | 0.751179 | + | 0.751179i | 0.974699 | − | 0.223520i | \(-0.0717548\pi\) |
−0.223520 | + | 0.974699i | \(0.571755\pi\) | |||||||
\(632\) | −39.5443 | + | 25.8544i | −1.57299 | + | 1.02843i | ||||
\(633\) | − | 2.37528i | − | 0.0944087i | ||||||
\(634\) | −3.45933 | + | 10.0803i | −0.137387 | + | 0.400341i | ||||
\(635\) | 15.1388 | 0.600766 | ||||||||
\(636\) | 7.09588 | − | 9.12098i | 0.281370 | − | 0.361670i | ||||
\(637\) | 11.5306 | − | 21.6580i | 0.456858 | − | 0.858120i | ||||
\(638\) | 29.4565 | − | 14.4045i | 1.16619 | − | 0.570279i | ||||
\(639\) | −11.1059 | − | 11.1059i | −0.439341 | − | 0.439341i | ||||
\(640\) | −19.9040 | + | 21.6555i | −0.786776 | + | 0.856007i | ||||
\(641\) | 43.6031i | 1.72222i | 0.508419 | + | 0.861110i | \(0.330230\pi\) | ||||
−0.508419 | + | 0.861110i | \(0.669770\pi\) | |||||||
\(642\) | 3.48861 | + | 1.19721i | 0.137684 | + | 0.0472499i | ||||
\(643\) | 5.43518 | 0.214342 | 0.107171 | − | 0.994241i | \(-0.465821\pi\) | ||||
0.107171 | + | 0.994241i | \(0.465821\pi\) | |||||||
\(644\) | 1.54760 | − | 0.193259i | 0.0609841 | − | 0.00761548i | ||||
\(645\) | 6.98931i | 0.275204i | ||||||||
\(646\) | 15.8334 | − | 46.1378i | 0.622956 | − | 1.81527i | ||||
\(647\) | − | 20.5427i | − | 0.807618i | −0.914843 | − | 0.403809i | \(-0.867686\pi\) | ||
0.914843 | − | 0.403809i | \(-0.132314\pi\) | |||||||
\(648\) | 1.54780 | + | 2.36735i | 0.0608031 | + | 0.0929982i | ||||
\(649\) | −42.3088 | −1.66076 | ||||||||
\(650\) | −6.11961 | − | 6.55595i | −0.240031 | − | 0.257145i | ||||
\(651\) | −0.765561 | + | 0.765561i | −0.0300047 | + | 0.0300047i | ||||
\(652\) | 9.66910 | − | 12.4286i | 0.378671 | − | 0.486741i | ||||
\(653\) | 22.8348 | − | 22.8348i | 0.893594 | − | 0.893594i | −0.101265 | − | 0.994859i | \(-0.532289\pi\) |
0.994859 | + | 0.101265i | \(0.0322891\pi\) | |||||||
\(654\) | −0.742825 | + | 0.363247i | −0.0290467 | + | 0.0142041i | ||||
\(655\) | −17.8087 | − | 17.8087i | −0.695845 | − | 0.695845i | ||||
\(656\) | 21.0944 | − | 35.4369i | 0.823597 | − | 1.38358i | ||||
\(657\) | 0.621805 | + | 0.621805i | 0.0242589 | + | 0.0242589i | ||||
\(658\) | −0.955212 | − | 0.327805i | −0.0372380 | − | 0.0127792i | ||||
\(659\) | −22.3109 | − | 22.3109i | −0.869111 | − | 0.869111i | 0.123263 | − | 0.992374i | \(-0.460664\pi\) |
−0.992374 | + | 0.123263i | \(0.960664\pi\) | |||||||
\(660\) | 1.98497 | + | 15.8954i | 0.0772647 | + | 0.618729i | ||||
\(661\) | 3.35317i | 0.130423i | 0.997871 | + | 0.0652115i | \(0.0207722\pi\) | ||||
−0.997871 | + | 0.0652115i | \(0.979228\pi\) | |||||||
\(662\) | 6.08797 | − | 17.7401i | 0.236616 | − | 0.689488i | ||||
\(663\) | −23.7053 | + | 7.23359i | −0.920636 | + | 0.280929i | ||||
\(664\) | 11.5802 | + | 17.7119i | 0.449401 | + | 0.687357i | ||||
\(665\) | 4.07230 | + | 4.07230i | 0.157917 | + | 0.157917i | ||||
\(666\) | −8.60858 | − | 2.95426i | −0.333576 | − | 0.114475i | ||||
\(667\) | 9.39993 | + | 9.39993i | 0.363967 | + | 0.363967i | ||||
\(668\) | −0.668841 | − | 5.35602i | −0.0258782 | − | 0.207231i | ||||
\(669\) | − | 4.41759i | − | 0.170794i | ||||||
\(670\) | −54.8125 | − | 18.8103i | −2.11759 | − | 0.726706i | ||||
\(671\) | 16.2960 | − | 16.2960i | 0.629098 | − | 0.629098i | ||||
\(672\) | −2.48895 | − | 0.204843i | −0.0960134 | − | 0.00790197i | ||||
\(673\) | 28.8339i | 1.11147i | 0.831361 | + | 0.555733i | \(0.187562\pi\) | ||||
−0.831361 | + | 0.555733i | \(0.812438\pi\) | |||||||
\(674\) | −1.47746 | + | 4.30526i | −0.0569097 | + | 0.165832i | ||||
\(675\) | 1.24368 | − | 1.24368i | 0.0478691 | − | 0.0478691i | ||||
\(676\) | −1.78792 | + | 25.9385i | −0.0687660 | + | 0.997633i | ||||
\(677\) | 2.94170 | + | 2.94170i | 0.113059 | + | 0.113059i | 0.761373 | − | 0.648314i | \(-0.224526\pi\) |
−0.648314 | + | 0.761373i | \(0.724526\pi\) | |||||||
\(678\) | 5.86381 | + | 11.9912i | 0.225198 | + | 0.460520i | ||||
\(679\) | 4.57788 | 0.175683 | ||||||||
\(680\) | 42.3061 | − | 27.6602i | 1.62237 | − | 1.06072i | ||||
\(681\) | −11.3295 | − | 11.3295i | −0.434149 | − | 0.434149i | ||||
\(682\) | 4.69384 | + | 9.59869i | 0.179736 | + | 0.367553i | ||||
\(683\) | 7.51526 | 0.287563 | 0.143782 | − | 0.989609i | \(-0.454074\pi\) | ||||
0.143782 | + | 0.989609i | \(0.454074\pi\) | |||||||
\(684\) | 6.16221 | − | 7.92085i | 0.235618 | − | 0.302861i | ||||
\(685\) | 0.617229 | − | 0.617229i | 0.0235831 | − | 0.0235831i | ||||
\(686\) | −7.74290 | + | 3.78634i | −0.295625 | + | 0.144563i | ||||
\(687\) | −4.60416 | + | 4.60416i | −0.175660 | + | 0.175660i | ||||
\(688\) | −5.50054 | + | 9.24048i | −0.209706 | + | 0.352290i | ||||
\(689\) | 6.08037 | + | 19.9260i | 0.231644 | + | 0.759121i | ||||
\(690\) | −5.83411 | + | 2.85293i | −0.222101 | + | 0.108609i | ||||
\(691\) | 49.5404 | 1.88461 | 0.942303 | − | 0.334761i | \(-0.108656\pi\) | ||||
0.942303 | + | 0.334761i | \(0.108656\pi\) | |||||||
\(692\) | −0.00782015 | − | 0.0626231i | −0.000297278 | − | 0.00238057i | ||||
\(693\) | −0.961744 | + | 0.961744i | −0.0365336 | + | 0.0365336i | ||||
\(694\) | 11.1340 | − | 5.44462i | 0.422641 | − | 0.206675i | ||||
\(695\) | −7.24609 | + | 7.24609i | −0.274860 | + | 0.274860i | ||||
\(696\) | −11.6485 | − | 17.8164i | −0.441536 | − | 0.675327i | ||||
\(697\) | −50.1130 | + | 50.1130i | −1.89817 | + | 1.89817i | ||||
\(698\) | −34.7172 | − | 11.9141i | −1.31407 | − | 0.450956i | ||||
\(699\) | 9.35156 | + | 9.35156i | 0.353708 | + | 0.353708i | ||||
\(700\) | 0.192433 | + | 1.54099i | 0.00727329 | + | 0.0582439i | ||||
\(701\) | −0.00498862 | − | 0.00498862i | −0.000188418 | − | 0.000188418i | 0.707013 | − | 0.707201i | \(-0.250042\pi\) |
−0.707201 | + | 0.707013i | \(0.750042\pi\) | |||||||
\(702\) | −5.09600 | − | 0.175424i | −0.192336 | − | 0.00662093i | ||||
\(703\) | 32.2927i | 1.21794i | ||||||||
\(704\) | −9.88532 | + | 22.5773i | −0.372567 | + | 0.850915i | ||||
\(705\) | 4.20522 | 0.158378 | ||||||||
\(706\) | −42.7660 | + | 20.9129i | −1.60952 | + | 0.787069i | ||||
\(707\) | 2.92541 | 0.110022 | ||||||||
\(708\) | 3.40341 | + | 27.2542i | 0.127908 | + | 1.02427i | ||||
\(709\) | 9.34496i | 0.350957i | 0.984483 | + | 0.175479i | \(0.0561473\pi\) | ||||
−0.984483 | + | 0.175479i | \(0.943853\pi\) | |||||||
\(710\) | −51.8752 | + | 25.3674i | −1.94684 | + | 0.952021i | ||||
\(711\) | 16.7040 | 0.626451 | ||||||||
\(712\) | −43.4212 | − | 9.08930i | −1.62728 | − | 0.340636i | ||||
\(713\) | −3.06306 | + | 3.06306i | −0.114712 | + | 0.114712i | ||||
\(714\) | 4.05931 | + | 1.39306i | 0.151916 | + | 0.0521338i | ||||
\(715\) | −25.4910 | − | 13.5712i | −0.953308 | − | 0.507536i | ||||
\(716\) | 9.61361 | − | 1.20051i | 0.359278 | − | 0.0448653i | ||||
\(717\) | − | 2.56632i | − | 0.0958410i | ||||||
\(718\) | 18.1152 | + | 37.0447i | 0.676052 | + | 1.38250i | ||||
\(719\) | −4.52247 | −0.168660 | −0.0843299 | − | 0.996438i | \(-0.526875\pi\) | ||||
−0.0843299 | + | 0.996438i | \(0.526875\pi\) | |||||||
\(720\) | 10.0797 | − | 2.55733i | 0.375650 | − | 0.0953059i | ||||
\(721\) | −0.0783150 | + | 0.0783150i | −0.00291660 | + | 0.00291660i | ||||
\(722\) | −8.26418 | − | 2.83607i | −0.307561 | − | 0.105547i | ||||
\(723\) | 17.4282i | 0.648163i | ||||||||
\(724\) | −13.2411 | + | 1.65350i | −0.492101 | + | 0.0614519i | ||||
\(725\) | −9.35976 | + | 9.35976i | −0.347613 | + | 0.347613i | ||||
\(726\) | −0.937174 | − | 1.91648i | −0.0347818 | − | 0.0711271i | ||||
\(727\) | − | 33.8528i | − | 1.25553i | −0.778403 | − | 0.627765i | \(-0.783970\pi\) | ||
0.778403 | − | 0.627765i | \(-0.216030\pi\) | |||||||
\(728\) | 2.88513 | − | 3.45627i | 0.106930 | − | 0.128098i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 2.90444 | − | 1.42029i | 0.107498 | − | 0.0525674i | ||||
\(731\) | 13.0674 | − | 13.0674i | 0.483315 | − | 0.483315i | ||||
\(732\) | −11.8083 | − | 9.18653i | −0.436447 | − | 0.339544i | ||||
\(733\) | 33.7659i | 1.24717i | 0.781755 | + | 0.623585i | \(0.214325\pi\) | ||||
−0.781755 | + | 0.623585i | \(0.785675\pi\) | |||||||
\(734\) | −14.1918 | + | 41.3544i | −0.523830 | + | 1.52642i | ||||
\(735\) | 12.5099 | − | 12.5099i | 0.461436 | − | 0.461436i | ||||
\(736\) | −9.95844 | − | 0.819587i | −0.367073 | − | 0.0302104i | ||||
\(737\) | −48.5593 | −1.78871 | ||||||||
\(738\) | −13.0983 | + | 6.40520i | −0.482157 | + | 0.235779i | ||||
\(739\) | − | 16.0669i | − | 0.591032i | −0.955338 | − | 0.295516i | \(-0.904508\pi\) | ||
0.955338 | − | 0.295516i | \(-0.0954916\pi\) | |||||||
\(740\) | −20.5472 | + | 26.4112i | −0.755330 | + | 0.970895i | ||||
\(741\) | 5.28032 | + | 17.3042i | 0.193977 | + | 0.635685i | ||||
\(742\) | 1.17097 | − | 3.41215i | 0.0429875 | − | 0.125264i | ||||
\(743\) | 30.5825 | − | 30.5825i | 1.12196 | − | 1.12196i | 0.130519 | − | 0.991446i | \(-0.458336\pi\) |
0.991446 | − | 0.130519i | \(-0.0416642\pi\) | |||||||
\(744\) | 5.80563 | − | 3.79578i | 0.212845 | − | 0.139160i | ||||
\(745\) | 39.4815 | 1.44649 | ||||||||
\(746\) | −6.37376 | − | 13.0340i | −0.233360 | − | 0.477210i | ||||
\(747\) | − | 7.48177i | − | 0.273744i | ||||||
\(748\) | 26.0074 | − | 33.4297i | 0.950926 | − | 1.22231i | ||||
\(749\) | 1.15138 | 0.0420707 | ||||||||
\(750\) | 5.23493 | + | 10.7052i | 0.191153 | + | 0.390899i | ||||
\(751\) | −49.0740 | −1.79074 | −0.895368 | − | 0.445327i | \(-0.853087\pi\) | ||||
−0.895368 | + | 0.445327i | \(0.853087\pi\) | |||||||
\(752\) | 5.55968 | + | 3.30949i | 0.202740 | + | 0.120685i | ||||
\(753\) | 12.6889i | 0.462408i | ||||||||
\(754\) | 38.3519 | + | 1.32022i | 1.39669 | + | 0.0480794i | ||||
\(755\) | −31.5907 | − | 31.5907i | −1.14970 | − | 1.14970i | ||||
\(756\) | 0.696894 | + | 0.542165i | 0.0253458 | + | 0.0197184i | ||||
\(757\) | −19.2872 | − | 19.2872i | −0.701004 | − | 0.701004i | 0.263622 | − | 0.964626i | \(-0.415083\pi\) |
−0.964626 | + | 0.263622i | \(0.915083\pi\) | |||||||
\(758\) | −2.09728 | + | 6.11139i | −0.0761766 | + | 0.221976i | ||||
\(759\) | −3.84800 | + | 3.84800i | −0.139673 | + | 0.139673i | ||||
\(760\) | −20.1912 | − | 30.8823i | −0.732410 | − | 1.12022i | ||||
\(761\) | 13.4163 | − | 13.4163i | 0.486341 | − | 0.486341i | −0.420808 | − | 0.907150i | \(-0.638253\pi\) |
0.907150 | + | 0.420808i | \(0.138253\pi\) | |||||||
\(762\) | −3.61768 | − | 7.39798i | −0.131055 | − | 0.268001i | ||||
\(763\) | −0.182525 | + | 0.182525i | −0.00660784 | + | 0.00660784i | ||||
\(764\) | −2.76033 | + | 3.54810i | −0.0998651 | + | 0.128366i | ||||
\(765\) | −17.8707 | −0.646116 | ||||||||
\(766\) | −22.0211 | − | 45.0322i | −0.795655 | − | 1.62708i | ||||
\(767\) | −43.7065 | − | 23.2691i | −1.57815 | − | 0.840199i | ||||
\(768\) | 15.3389 | + | 4.55169i | 0.553495 | + | 0.164245i | ||||
\(769\) | 37.1538 | − | 37.1538i | 1.33980 | − | 1.33980i | 0.443550 | − | 0.896250i | \(-0.353719\pi\) |
0.896250 | − | 0.443550i | \(-0.146281\pi\) | |||||||
\(770\) | 2.19676 | + | 4.49228i | 0.0791658 | + | 0.161891i | ||||
\(771\) | −1.39630 | + | 1.39630i | −0.0502865 | + | 0.0502865i | ||||
\(772\) | −2.22636 | − | 17.8285i | −0.0801283 | − | 0.641660i | ||||
\(773\) | −19.0516 | −0.685238 | −0.342619 | − | 0.939474i | \(-0.611314\pi\) | ||||
−0.342619 | + | 0.939474i | \(0.611314\pi\) | |||||||
\(774\) | 3.41551 | − | 1.67021i | 0.122768 | − | 0.0600345i | ||||
\(775\) | −3.04997 | − | 3.04997i | −0.109558 | − | 0.109558i | ||||
\(776\) | −28.7071 | − | 6.00922i | −1.03053 | − | 0.215719i | ||||
\(777\) | −2.84119 | −0.101927 | ||||||||
\(778\) | 16.7038 | − | 8.16831i | 0.598861 | − | 0.292848i | ||||
\(779\) | 36.5811 | + | 36.5811i | 1.31065 | + | 1.31065i | ||||
\(780\) | −6.69168 | + | 17.5123i | −0.239601 | + | 0.627041i | ||||
\(781\) | −34.2152 | + | 34.2152i | −1.22432 | + | 1.22432i | ||||
\(782\) | 16.2415 | + | 5.57370i | 0.580796 | + | 0.199315i | ||||
\(783\) | 7.52588i | 0.268953i | ||||||||
\(784\) | 26.3845 | − | 6.69399i | 0.942303 | − | 0.239071i | ||||
\(785\) | −12.3540 | + | 12.3540i | −0.440933 | + | 0.440933i | ||||
\(786\) | −4.44701 | + | 12.9584i | −0.158620 | + | 0.462211i | ||||
\(787\) | − | 30.5115i | − | 1.08762i | −0.839209 | − | 0.543809i | \(-0.816982\pi\) | ||
0.839209 | − | 0.543809i | \(-0.183018\pi\) | |||||||
\(788\) | 9.11019 | + | 7.08748i | 0.324537 | + | 0.252481i | ||||
\(789\) | −14.2780 | − | 14.2780i | −0.508311 | − | 0.508311i | ||||
\(790\) | 19.9348 | − | 58.0893i | 0.709250 | − | 2.06672i | ||||
\(791\) | 2.94645 | + | 2.94645i | 0.104764 | + | 0.104764i | ||||
\(792\) | 7.29338 | − | 4.76849i | 0.259159 | − | 0.169441i | ||||
\(793\) | 25.7968 | − | 7.87183i | 0.916072 | − | 0.279537i | ||||
\(794\) | 12.6027 | + | 4.32494i | 0.447253 | + | 0.153486i | ||||
\(795\) | 15.0216i | 0.532763i | ||||||||
\(796\) | −14.1834 | + | 18.2312i | −0.502718 | + | 0.646189i | ||||
\(797\) | −26.4617 | − | 26.4617i | −0.937323 | − | 0.937323i | 0.0608252 | − | 0.998148i | \(-0.480627\pi\) |
−0.998148 | + | 0.0608252i | \(0.980627\pi\) | |||||||
\(798\) | 1.01689 | − | 2.96318i | 0.0359976 | − | 0.104895i | ||||
\(799\) | −7.86220 | − | 7.86220i | −0.278145 | − | 0.278145i | ||||
\(800\) | 0.816085 | − | 9.91589i | 0.0288530 | − | 0.350580i | ||||
\(801\) | 11.0906 | + | 11.0906i | 0.391866 | + | 0.391866i | ||||
\(802\) | −19.4513 | − | 39.7770i | −0.686848 | − | 1.40457i | ||||
\(803\) | 1.91567 | − | 1.91567i | 0.0676027 | − | 0.0676027i | ||||
\(804\) | 3.90621 | + | 31.2806i | 0.137761 | + | 1.10318i | ||||
\(805\) | −1.43354 | + | 1.43354i | −0.0505257 | + | 0.0505257i | ||||
\(806\) | −0.430205 | + | 12.4973i | −0.0151533 | + | 0.440200i | ||||
\(807\) | 26.8582 | 0.945453 | ||||||||
\(808\) | −18.3448 | − | 3.84009i | −0.645367 | − | 0.135094i | ||||
\(809\) | 19.7169i | 0.693211i | 0.938011 | + | 0.346606i | \(0.112666\pi\) | ||||
−0.938011 | + | 0.346606i | \(0.887334\pi\) | |||||||
\(810\) | −3.47756 | − | 1.19341i | −0.122189 | − | 0.0419323i | ||||
\(811\) | − | 34.0528i | − | 1.19576i | −0.801587 | − | 0.597878i | \(-0.796011\pi\) | ||
0.801587 | − | 0.597878i | \(-0.203989\pi\) | |||||||
\(812\) | −5.24474 | − | 4.08027i | −0.184054 | − | 0.143189i | ||||
\(813\) | 7.92958 | 0.278102 | ||||||||
\(814\) | −9.10155 | + | 26.5216i | −0.319009 | + | 0.929580i | ||||
\(815\) | 20.4690i | 0.716999i | ||||||||
\(816\) | −23.6266 | − | 14.0641i | −0.827097 | − | 0.492343i | ||||
\(817\) | −9.53884 | − | 9.53884i | −0.333722 | − | 0.333722i | ||||
\(818\) | −5.87114 | − | 12.0062i | −0.205280 | − | 0.419787i | ||||
\(819\) | −1.52246 | + | 0.464574i | −0.0531991 | + | 0.0162335i | ||||
\(820\) | 6.64272 | + | 53.1943i | 0.231974 | + | 1.85763i | ||||
\(821\) | 20.9843 | 0.732357 | 0.366179 | − | 0.930545i | \(-0.380666\pi\) | ||||
0.366179 | + | 0.930545i | \(0.380666\pi\) | |||||||
\(822\) | −0.449122 | − | 0.154128i | −0.0156649 | − | 0.00537582i | ||||
\(823\) | 31.0687i | 1.08299i | 0.840705 | + | 0.541494i | \(0.182141\pi\) | ||||
−0.840705 | + | 0.541494i | \(0.817859\pi\) | |||||||
\(824\) | 0.593901 | − | 0.388299i | 0.0206895 | − | 0.0135270i | ||||
\(825\) | −3.83155 | − | 3.83155i | −0.133398 | − | 0.133398i | ||||
\(826\) | 3.76655 | + | 7.70242i | 0.131055 | + | 0.268001i | ||||
\(827\) | 22.0032 | 0.765127 | 0.382563 | − | 0.923929i | \(-0.375041\pi\) | ||||
0.382563 | + | 0.923929i | \(0.375041\pi\) | |||||||
\(828\) | 2.78832 | + | 2.16924i | 0.0969007 | + | 0.0753861i | ||||
\(829\) | −26.4165 | − | 26.4165i | −0.917483 | − | 0.917483i | 0.0793628 | − | 0.996846i | \(-0.474711\pi\) |
−0.996846 | + | 0.0793628i | \(0.974711\pi\) | |||||||
\(830\) | −26.0183 | − | 8.92885i | −0.903108 | − | 0.309925i | ||||
\(831\) | −11.2725 | −0.391038 | ||||||||
\(832\) | −22.6291 | + | 17.8865i | −0.784521 | + | 0.620102i | ||||
\(833\) | −46.7778 | −1.62076 | ||||||||
\(834\) | 5.27257 | + | 1.80942i | 0.182574 | + | 0.0626550i | ||||
\(835\) | 4.96127 | + | 4.96127i | 0.171692 | + | 0.171692i | ||||
\(836\) | −24.4028 | − | 18.9847i | −0.843988 | − | 0.656600i | ||||
\(837\) | −2.45238 | −0.0847667 | ||||||||
\(838\) | −7.16797 | − | 14.6582i | −0.247613 | − | 0.506358i | ||||
\(839\) | −19.9383 | − | 19.9383i | −0.688346 | − | 0.688346i | 0.273520 | − | 0.961866i | \(-0.411812\pi\) |
−0.961866 | + | 0.273520i | \(0.911812\pi\) | |||||||
\(840\) | 2.71709 | − | 1.77646i | 0.0937486 | − | 0.0612938i | ||||
\(841\) | − | 27.6388i | − | 0.953062i | ||||||
\(842\) | 32.3827 | + | 11.1129i | 1.11598 | + | 0.382977i | ||||
\(843\) | 11.4363 | 0.393888 | ||||||||
\(844\) | 0.588660 | + | 4.71394i | 0.0202625 | + | 0.162260i | ||||
\(845\) | −18.8692 | − | 28.0392i | −0.649119 | − | 0.964578i | ||||
\(846\) | −1.00491 | − | 2.05499i | −0.0345495 | − | 0.0706521i | ||||
\(847\) | −0.470911 | − | 0.470911i | −0.0161807 | − | 0.0161807i | ||||
\(848\) | −11.8219 | + | 19.8599i | −0.405967 | + | 0.681993i | ||||
\(849\) | 32.1524i | 1.10347i | ||||||||
\(850\) | −5.54988 | + | 16.1721i | −0.190359 | + | 0.554699i | ||||
\(851\) | −11.3678 | −0.389682 | ||||||||
\(852\) | 24.7929 | + | 19.2882i | 0.849390 | + | 0.660803i | ||||
\(853\) | 36.3083i | 1.24317i | 0.783346 | + | 0.621586i | \(0.213511\pi\) | ||||
−0.783346 | + | 0.621586i | \(0.786489\pi\) | |||||||
\(854\) | −4.41747 | − | 1.51597i | −0.151163 | − | 0.0518754i | ||||
\(855\) | 13.0451i | 0.446133i | ||||||||
\(856\) | −7.22014 | − | 1.51138i | −0.246779 | − | 0.0516580i | ||||
\(857\) | 18.0709 | 0.617289 | 0.308644 | − | 0.951178i | \(-0.400125\pi\) | ||||
0.308644 | + | 0.951178i | \(0.400125\pi\) | |||||||
\(858\) | −0.540449 | + | 15.6999i | −0.0184506 | + | 0.535986i | ||||
\(859\) | −2.21247 | + | 2.21247i | −0.0754885 | + | 0.0754885i | −0.743843 | − | 0.668354i | \(-0.766999\pi\) |
0.668354 | + | 0.743843i | \(0.266999\pi\) | |||||||
\(860\) | −1.73215 | − | 13.8709i | −0.0590657 | − | 0.472993i | ||||
\(861\) | −3.21849 | + | 3.21849i | −0.109686 | + | 0.109686i | ||||
\(862\) | 0.766122 | + | 1.56668i | 0.0260942 | + | 0.0533615i | ||||
\(863\) | −8.59919 | − | 8.59919i | −0.292720 | − | 0.292720i | 0.545434 | − | 0.838154i | \(-0.316365\pi\) |
−0.838154 | + | 0.545434i | \(0.816365\pi\) | |||||||
\(864\) | −3.65843 | − | 4.31462i | −0.124462 | − | 0.146786i | ||||
\(865\) | 0.0580077 | + | 0.0580077i | 0.00197232 | + | 0.00197232i | ||||
\(866\) | 2.83197 | − | 8.25226i | 0.0962344 | − | 0.280423i | ||||
\(867\) | 21.3907 | + | 21.3907i | 0.726467 | + | 0.726467i | ||||
\(868\) | 1.32959 | − | 1.70905i | 0.0451294 | − | 0.0580089i | ||||
\(869\) | − | 51.4623i | − | 1.74574i | ||||||
\(870\) | 26.1717 | + | 8.98148i | 0.887303 | + | 0.304501i | ||||
\(871\) | −50.1636 | − | 26.7068i | −1.69973 | − | 0.904926i | ||||
\(872\) | 1.38418 | − | 0.904989i | 0.0468741 | − | 0.0306468i | ||||
\(873\) | 7.33233 | + | 7.33233i | 0.248162 | + | 0.248162i | ||||
\(874\) | 4.06865 | − | 11.8559i | 0.137624 | − | 0.401031i | ||||
\(875\) | 2.63045 | + | 2.63045i | 0.0889255 | + | 0.0889255i | ||||
\(876\) | −1.38813 | − | 1.07993i | −0.0469005 | − | 0.0364873i | ||||
\(877\) | 24.8875i | 0.840391i | 0.907434 | + | 0.420195i | \(0.138038\pi\) | ||||
−0.907434 | + | 0.420195i | \(0.861962\pi\) | |||||||
\(878\) | 6.22497 | − | 18.1393i | 0.210083 | − | 0.612172i | ||||
\(879\) | 5.54568 | − | 5.54568i | 0.187051 | − | 0.187051i | ||||
\(880\) | −7.87868 | − | 31.0540i | −0.265590 | − | 1.04683i | ||||
\(881\) | 39.7663i | 1.33976i | 0.742469 | + | 0.669880i | \(0.233655\pi\) | ||||
−0.742469 | + | 0.669880i | \(0.766345\pi\) | |||||||
\(882\) | −9.10276 | − | 3.12385i | −0.306506 | − | 0.105185i | ||||
\(883\) | −0.270023 | + | 0.270023i | −0.00908699 | + | 0.00908699i | −0.711636 | − | 0.702549i | \(-0.752045\pi\) |
0.702549 | + | 0.711636i | \(0.252045\pi\) | |||||||
\(884\) | 45.2524 | − | 20.2305i | 1.52200 | − | 0.680426i | ||||
\(885\) | −25.2455 | − | 25.2455i | −0.848618 | − | 0.848618i | ||||
\(886\) | −13.3805 | + | 6.54319i | −0.449527 | + | 0.219823i | ||||
\(887\) | 28.6599 | 0.962304 | 0.481152 | − | 0.876637i | \(-0.340218\pi\) | ||||
0.481152 | + | 0.876637i | \(0.340218\pi\) | |||||||
\(888\) | 17.8166 | + | 3.72953i | 0.597887 | + | 0.125155i | ||||
\(889\) | −1.81781 | − | 1.81781i | −0.0609674 | − | 0.0609674i | ||||
\(890\) | 51.8038 | − | 25.3325i | 1.73647 | − | 0.849147i | ||||
\(891\) | −3.08083 | −0.103212 | ||||||||
\(892\) | 1.09480 | + | 8.76708i | 0.0366567 | + | 0.293543i | ||||
\(893\) | −5.73919 | + | 5.73919i | −0.192055 | + | 0.192055i | ||||
\(894\) | −9.43477 | − | 19.2937i | −0.315546 | − | 0.645277i | ||||
\(895\) | −8.90507 | + | 8.90507i | −0.297664 | + | 0.297664i | ||||
\(896\) | 4.99030 | − | 0.210304i | 0.166714 | − | 0.00702577i | ||||
\(897\) | −6.09146 | + | 1.85879i | −0.203388 | + | 0.0620632i | ||||
\(898\) | −13.2125 | − | 27.0189i | −0.440906 | − | 0.901632i | ||||
\(899\) | 18.4563 | 0.615552 | ||||||||
\(900\) | −2.15997 | + | 2.77640i | −0.0719988 | + | 0.0925467i | ||||
\(901\) | 28.0849 | − | 28.0849i | 0.935643 | − | 0.935643i | ||||
\(902\) | 19.7333 | + | 40.3537i | 0.657047 | + | 1.34363i | ||||
\(903\) | 0.839249 | − | 0.839249i | 0.0279285 | − | 0.0279285i | ||||
\(904\) | −14.6090 | − | 22.3444i | −0.485888 | − | 0.743164i | ||||
\(905\) | 12.2652 | − | 12.2652i | 0.407709 | − | 0.407709i | ||||
\(906\) | −7.88851 | + | 22.9868i | −0.262078 | + | 0.763685i | ||||
\(907\) | 7.92876 | + | 7.92876i | 0.263270 | + | 0.263270i | 0.826381 | − | 0.563111i | \(-0.190396\pi\) |
−0.563111 | + | 0.826381i | \(0.690396\pi\) | |||||||
\(908\) | 25.2922 | + | 19.6767i | 0.839351 | + | 0.652993i | ||||
\(909\) | 4.68560 | + | 4.68560i | 0.155411 | + | 0.155411i | ||||
\(910\) | −0.201340 | + | 5.84887i | −0.00667436 | + | 0.193888i | ||||
\(911\) | − | 0.271475i | − | 0.00899435i | −0.999990 | − | 0.00449718i | \(-0.998568\pi\) | ||
0.999990 | − | 0.00449718i | \(-0.00143150\pi\) | |||||||
\(912\) | −10.2664 | + | 17.2468i | −0.339955 | + | 0.571098i | ||||
\(913\) | −23.0500 | −0.762845 | ||||||||
\(914\) | 24.6465 | + | 50.4010i | 0.815235 | + | 1.66712i | ||||
\(915\) | 19.4475 | 0.642913 | ||||||||
\(916\) | 7.99631 | − | 10.2784i | 0.264205 | − | 0.339607i | ||||
\(917\) | 4.27681i | 0.141233i | ||||||||
\(918\) | 4.27050 | + | 8.73298i | 0.140948 | + | 0.288231i | ||||
\(919\) | −30.8639 | −1.01811 | −0.509054 | − | 0.860735i | \(-0.670005\pi\) | ||||
−0.509054 | + | 0.860735i | \(0.670005\pi\) | |||||||
\(920\) | 10.8713 | − | 7.10774i | 0.358415 | − | 0.234335i | ||||
\(921\) | 13.6473 | − | 13.6473i | 0.449694 | − | 0.449694i | ||||
\(922\) | 8.16239 | − | 23.7849i | 0.268814 | − | 0.783313i | ||||
\(923\) | −54.1634 | + | 16.5278i | −1.78281 | + | 0.544020i | ||||
\(924\) | 1.67032 | − | 2.14701i | 0.0549494 | − | 0.0706315i | ||||
\(925\) | − | 11.3192i | − | 0.372173i | ||||||
\(926\) | 9.05687 | − | 4.42889i | 0.297627 | − | 0.145542i | ||||
\(927\) | −0.250872 | −0.00823972 | ||||||||
\(928\) | 27.5329 | + | 32.4713i | 0.903811 | + | 1.06592i | ||||
\(929\) | 24.5772 | − | 24.5772i | 0.806351 | − | 0.806351i | −0.177728 | − | 0.984080i | \(-0.556875\pi\) |
0.984080 | + | 0.177728i | \(0.0568748\pi\) | |||||||
\(930\) | −2.92670 | + | 8.52829i | −0.0959704 | + | 0.279654i | ||||
\(931\) | 34.1465i | 1.11911i | ||||||||
\(932\) | −20.8765 | − | 16.2414i | −0.683834 | − | 0.532004i | ||||
\(933\) | 18.0100 | − | 18.0100i | 0.589622 | − | 0.589622i | ||||
\(934\) | 42.1106 | − | 20.5924i | 1.37790 | − | 0.673805i | ||||
\(935\) | 55.0565i | 1.80054i | ||||||||
\(936\) | 10.1569 | − | 0.914789i | 0.331990 | − | 0.0299008i | ||||
\(937\) | 38.5662i | 1.25990i | 0.776634 | + | 0.629952i | \(0.216925\pi\) | ||||
−0.776634 | + | 0.629952i | \(0.783075\pi\) | |||||||
\(938\) | 4.32300 | + | 8.84035i | 0.141151 | + | 0.288648i | ||||
\(939\) | 0.550959 | − | 0.550959i | 0.0179799 | − | 0.0179799i | ||||
\(940\) | −8.34563 | + | 1.04217i | −0.272204 | + | 0.0339919i | ||||
\(941\) | 17.9469i | 0.585052i | 0.956258 | + | 0.292526i | \(0.0944958\pi\) | ||||
−0.956258 | + | 0.292526i | \(0.905504\pi\) | |||||||
\(942\) | 8.98930 | + | 3.08491i | 0.292887 | + | 0.100512i | ||||
\(943\) | −12.8774 | + | 12.8774i | −0.419345 | + | 0.419345i | ||||
\(944\) | −13.5087 | − | 53.2448i | −0.439671 | − | 1.73297i | ||||
\(945\) | −1.14774 | −0.0373359 | ||||||||
\(946\) | −5.14563 | − | 10.5226i | −0.167299 | − | 0.342119i | ||||
\(947\) | − | 16.7657i | − | 0.544812i | −0.962182 | − | 0.272406i | \(-0.912181\pi\) | ||
0.962182 | − | 0.272406i | \(-0.0878193\pi\) | |||||||
\(948\) | −33.1506 | + | 4.13973i | −1.07668 | + | 0.134452i | ||||
\(949\) | 3.03255 | − | 0.925375i | 0.0984408 | − | 0.0300389i | ||||
\(950\) | 11.8052 | + | 4.05126i | 0.383011 | + | 0.131440i | ||||
\(951\) | −5.32870 | + | 5.32870i | −0.172795 | + | 0.172795i | ||||
\(952\) | −8.40128 | − | 1.75863i | −0.272287 | − | 0.0569975i | ||||
\(953\) | 44.7508 | 1.44962 | 0.724810 | − | 0.688949i | \(-0.241927\pi\) | ||||
0.724810 | + | 0.688949i | \(0.241927\pi\) | |||||||
\(954\) | 7.34072 | − | 3.58967i | 0.237664 | − | 0.116220i | ||||
\(955\) | − | 5.84348i | − | 0.189091i | ||||||
\(956\) | 0.636006 | + | 5.09308i | 0.0205699 | + | 0.164722i | ||||
\(957\) | 23.1859 | 0.749494 | ||||||||
\(958\) | −5.08587 | + | 2.48703i | −0.164317 | + | 0.0803523i | ||||
\(959\) | −0.148229 | −0.00478656 | ||||||||
\(960\) | −19.3703 | + | 7.57328i | −0.625175 | + | 0.244426i | ||||
\(961\) | − | 24.9858i | − | 0.805995i | ||||||
\(962\) | −23.9886 | + | 22.3920i | −0.773425 | + | 0.721949i | ||||
\(963\) | 1.84416 | + | 1.84416i | 0.0594272 | + | 0.0594272i | ||||
\(964\) | −4.31921 | − | 34.5878i | −0.139112 | − | 1.11400i | ||||
\(965\) | 16.5145 | + | 16.5145i | 0.531620 | + | 0.531620i | ||||
\(966\) | 1.04311 | + | 0.357969i | 0.0335614 | + | 0.0115175i | ||||
\(967\) | −25.6036 | + | 25.6036i | −0.823355 | + | 0.823355i | −0.986588 | − | 0.163233i | \(-0.947808\pi\) |
0.163233 | + | 0.986588i | \(0.447808\pi\) | |||||||
\(968\) | 2.33486 | + | 3.57116i | 0.0750452 | + | 0.114781i | ||||
\(969\) | 24.3895 | − | 24.3895i | 0.783504 | − | 0.783504i | ||||
\(970\) | 34.2491 | − | 16.7481i | 1.09967 | − | 0.537749i | ||||
\(971\) | 6.12175 | − | 6.12175i | 0.196456 | − | 0.196456i | −0.602023 | − | 0.798479i | \(-0.705638\pi\) |
0.798479 | + | 0.602023i | \(0.205638\pi\) | |||||||
\(972\) | 0.247828 | + | 1.98459i | 0.00794909 | + | 0.0636556i | ||||
\(973\) | 1.74017 | 0.0557871 | ||||||||
\(974\) | 27.3205 | − | 13.3600i | 0.875406 | − | 0.428081i | ||||
\(975\) | −1.85085 | − | 6.06543i | −0.0592745 | − | 0.194249i | ||||
\(976\) | 25.7113 | + | 15.3050i | 0.822997 | + | 0.489902i | ||||
\(977\) | 22.5001 | − | 22.5001i | 0.719842 | − | 0.719842i | −0.248730 | − | 0.968573i | \(-0.580013\pi\) |
0.968573 | + | 0.248730i | \(0.0800133\pi\) | |||||||
\(978\) | 10.0027 | − | 4.89142i | 0.319852 | − | 0.156410i | ||||
\(979\) | 34.1682 | − | 34.1682i | 1.09202 | − | 1.09202i | ||||
\(980\) | −21.7267 | + | 27.9274i | −0.694035 | + | 0.892107i | ||||
\(981\) | −0.584695 | −0.0186679 | ||||||||
\(982\) | 18.7649 | + | 38.3734i | 0.598812 | + | 1.22454i | ||||
\(983\) | −38.2746 | − | 38.2746i | −1.22077 | − | 1.22077i | −0.967359 | − | 0.253411i | \(-0.918447\pi\) |
−0.253411 | − | 0.967359i | \(-0.581553\pi\) | |||||||
\(984\) | 24.4074 | − | 15.9578i | 0.778079 | − | 0.508716i | ||||
\(985\) | −15.0039 | −0.478063 | ||||||||
\(986\) | −32.1393 | − | 65.7233i | −1.02352 | − | 2.09306i | ||||
\(987\) | −0.504947 | − | 0.504947i | −0.0160726 | − | 0.0160726i | ||||
\(988\) | −14.7677 | − | 33.0330i | −0.469823 | − | 1.05092i | ||||
\(989\) | 3.35789 | − | 3.35789i | 0.106775 | − | 0.106775i | ||||
\(990\) | −3.67670 | + | 10.7138i | −0.116853 | + | 0.340506i | ||||
\(991\) | 21.6332i | 0.687200i | 0.939116 | + | 0.343600i | \(0.111646\pi\) | ||||
−0.939116 | + | 0.343600i | \(0.888354\pi\) | |||||||
\(992\) | −10.5811 | + | 8.97186i | −0.335950 | + | 0.284857i | ||||
\(993\) | 9.37783 | − | 9.37783i | 0.297596 | − | 0.297596i | ||||
\(994\) | 9.27499 | + | 3.18295i | 0.294185 | + | 0.100957i | ||||
\(995\) | − | 30.0256i | − | 0.951876i | ||||||
\(996\) | 1.85419 | + | 14.8482i | 0.0587523 | + | 0.470484i | ||||
\(997\) | 14.0786 | + | 14.0786i | 0.445873 | + | 0.445873i | 0.893980 | − | 0.448107i | \(-0.147902\pi\) |
−0.448107 | + | 0.893980i | \(0.647902\pi\) | |||||||
\(998\) | −35.9986 | − | 12.3538i | −1.13951 | − | 0.391054i | ||||
\(999\) | −4.55070 | − | 4.55070i | −0.143978 | − | 0.143978i |
(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 | 624.2.bn.a.187.5 | yes | 112 | |
13.8 | odd | 4 | 624.2.r.a.619.33 | yes | 112 | ||
16.3 | odd | 4 | 624.2.r.a.499.33 | ✓ | 112 | ||
208.99 | even | 4 | inner | 624.2.bn.a.307.5 | yes | 112 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
624.2.r.a.499.33 | ✓ | 112 | 16.3 | odd | 4 | ||
624.2.r.a.619.33 | yes | 112 | 13.8 | odd | 4 | ||
624.2.bn.a.187.5 | yes | 112 | 1.1 | even | 1 | trivial | |
624.2.bn.a.307.5 | yes | 112 | 208.99 | even | 4 | inner |