Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(37,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.p (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: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 570) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1063.10 | ||
Root | \(0.339574 + 0.339574i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1063 |
Dual form | 1710.2.p.c.37.10 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.29975 | + | 1.81952i | 0.581266 | + | 0.813714i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.728588 | + | 0.728588i | −0.275380 | + | 0.275380i | −0.831262 | − | 0.555881i | \(-0.812381\pi\) |
0.555881 | + | 0.831262i | \(0.312381\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.367533 | + | 2.20566i | −0.116224 | + | 0.697490i | ||||
\(11\) | 4.80832 | 1.44976 | 0.724881 | − | 0.688874i | \(-0.241895\pi\) | ||||
0.724881 | + | 0.688874i | \(0.241895\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.531491 | + | 0.531491i | −0.147409 | + | 0.147409i | −0.776960 | − | 0.629550i | \(-0.783239\pi\) |
0.629550 | + | 0.776960i | \(0.283239\pi\) | |||||||
\(14\) | −1.03038 | −0.275380 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.72984 | − | 3.72984i | 0.904619 | − | 0.904619i | −0.0912125 | − | 0.995831i | \(-0.529074\pi\) |
0.995831 | + | 0.0912125i | \(0.0290743\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.90517 | − | 3.24961i | 0.666493 | − | 0.745511i | ||||
\(20\) | −1.81952 | + | 1.29975i | −0.406857 | + | 0.290633i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.39999 | + | 3.39999i | 0.724881 | + | 0.724881i | ||||
\(23\) | 4.07973 | + | 4.07973i | 0.850682 | + | 0.850682i | 0.990217 | − | 0.139535i | \(-0.0445607\pi\) |
−0.139535 | + | 0.990217i | \(0.544561\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.62130 | + | 4.72984i | −0.324260 | + | 0.945968i | ||||
\(26\) | −0.751642 | −0.147409 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.728588 | − | 0.728588i | −0.137690 | − | 0.137690i | ||||
\(29\) | 0.494819 | 0.0918856 | 0.0459428 | − | 0.998944i | \(-0.485371\pi\) | ||||
0.0459428 | + | 0.998944i | \(0.485371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.62312i | 1.54876i | 0.632722 | + | 0.774379i | \(0.281938\pi\) | ||||
−0.632722 | + | 0.774379i | \(0.718062\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.27479 | 0.904619 | ||||||||
\(35\) | −2.27266 | − | 0.378698i | −0.384150 | − | 0.0640117i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.47836 | − | 5.47836i | −0.900637 | − | 0.900637i | 0.0948538 | − | 0.995491i | \(-0.469762\pi\) |
−0.995491 | + | 0.0948538i | \(0.969762\pi\) | |||||||
\(38\) | 4.35209 | − | 0.243552i | 0.706002 | − | 0.0395093i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.20566 | − | 0.367533i | −0.348745 | − | 0.0581120i | ||||
\(41\) | 5.82553i | 0.909794i | 0.890544 | + | 0.454897i | \(0.150324\pi\) | ||||
−0.890544 | + | 0.454897i | \(0.849676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.04079 | − | 3.04079i | −0.463716 | − | 0.463716i | 0.436155 | − | 0.899871i | \(-0.356340\pi\) |
−0.899871 | + | 0.436155i | \(0.856340\pi\) | |||||||
\(44\) | 4.80832i | 0.724881i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.76961i | 0.850682i | ||||||||
\(47\) | −0.910451 | + | 0.910451i | −0.132803 | + | 0.132803i | −0.770384 | − | 0.637581i | \(-0.779935\pi\) |
0.637581 | + | 0.770384i | \(0.279935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.93832i | 0.848331i | ||||||||
\(50\) | −4.49094 | + | 2.19807i | −0.635114 | + | 0.310854i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.531491 | − | 0.531491i | −0.0737046 | − | 0.0737046i | ||||
\(53\) | 3.53266 | − | 3.53266i | 0.485248 | − | 0.485248i | −0.421555 | − | 0.906803i | \(-0.638516\pi\) |
0.906803 | + | 0.421555i | \(0.138516\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.24961 | + | 8.74883i | 0.842697 | + | 1.17969i | ||||
\(56\) | − | 1.03038i | − | 0.137690i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.349890 | + | 0.349890i | 0.0459428 | + | 0.0459428i | ||||
\(59\) | −12.1307 | −1.57928 | −0.789641 | − | 0.613569i | \(-0.789733\pi\) | ||||
−0.789641 | + | 0.613569i | \(0.789733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.32419 | −0.681692 | −0.340846 | − | 0.940119i | \(-0.610713\pi\) | ||||
−0.340846 | + | 0.940119i | \(0.610713\pi\) | |||||||
\(62\) | −6.09747 | + | 6.09747i | −0.774379 | + | 0.774379i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −1.65786 | − | 0.276253i | −0.205633 | − | 0.0342650i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.19128 | − | 9.19128i | −1.12289 | − | 1.12289i | −0.991304 | − | 0.131590i | \(-0.957992\pi\) |
−0.131590 | − | 0.991304i | \(-0.542008\pi\) | |||||||
\(68\) | 3.72984 | + | 3.72984i | 0.452309 | + | 0.452309i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.33924 | − | 1.87480i | −0.160069 | − | 0.224081i | ||||
\(71\) | 2.06076i | 0.244567i | 0.992495 | + | 0.122284i | \(0.0390217\pi\) | ||||
−0.992495 | + | 0.122284i | \(0.960978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.31160 | + | 3.31160i | 0.387594 | + | 0.387594i | 0.873828 | − | 0.486235i | \(-0.161630\pi\) |
−0.486235 | + | 0.873828i | \(0.661630\pi\) | |||||||
\(74\) | − | 7.74758i | − | 0.900637i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.24961 | + | 2.90517i | 0.372756 | + | 0.333246i | ||||
\(77\) | −3.50328 | + | 3.50328i | −0.399236 | + | 0.399236i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.77074 | −0.311733 | −0.155866 | − | 0.987778i | \(-0.549817\pi\) | ||||
−0.155866 | + | 0.987778i | \(0.549817\pi\) | |||||||
\(80\) | −1.29975 | − | 1.81952i | −0.145316 | − | 0.203428i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.11927 | + | 4.11927i | −0.454897 | + | 0.454897i | ||||
\(83\) | 3.57770 | + | 3.57770i | 0.392703 | + | 0.392703i | 0.875650 | − | 0.482947i | \(-0.160433\pi\) |
−0.482947 | + | 0.875650i | \(0.660433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.6344 | + | 1.93866i | 1.26192 | + | 0.210277i | ||||
\(86\) | − | 4.30033i | − | 0.463716i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.39999 | + | 3.39999i | −0.362441 | + | 0.362441i | ||||
\(89\) | 1.08630 | 0.115147 | 0.0575736 | − | 0.998341i | \(-0.481664\pi\) | ||||
0.0575736 | + | 0.998341i | \(0.481664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.774476i | − | 0.0811872i | ||||||
\(92\) | −4.07973 | + | 4.07973i | −0.425341 | + | 0.425341i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.28757 | −0.132803 | ||||||||
\(95\) | 9.68873 | + | 1.06234i | 0.994042 | + | 0.108994i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.81665 | − | 2.81665i | −0.285988 | − | 0.285988i | 0.549503 | − | 0.835491i | \(-0.314817\pi\) |
−0.835491 | + | 0.549503i | \(0.814817\pi\) | |||||||
\(98\) | −4.19903 | + | 4.19903i | −0.424166 | + | 0.424166i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.72984 | − | 1.62130i | −0.472984 | − | 0.162130i | ||||
\(101\) | 14.0592 | 1.39894 | 0.699470 | − | 0.714662i | \(-0.253419\pi\) | ||||
0.699470 | + | 0.714662i | \(0.253419\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.63327 | − | 6.63327i | 0.653596 | − | 0.653596i | −0.300261 | − | 0.953857i | \(-0.597074\pi\) |
0.953857 | + | 0.300261i | \(0.0970739\pi\) | |||||||
\(104\) | − | 0.751642i | − | 0.0737046i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.99593 | 0.485248 | ||||||||
\(107\) | 1.54262 | + | 1.54262i | 0.149131 | + | 0.149131i | 0.777730 | − | 0.628599i | \(-0.216371\pi\) |
−0.628599 | + | 0.777730i | \(0.716371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.4286 | 1.76514 | 0.882569 | − | 0.470183i | \(-0.155812\pi\) | ||||
0.882569 | + | 0.470183i | \(0.155812\pi\) | |||||||
\(110\) | −1.76721 | + | 10.6055i | −0.168497 | + | 1.01119i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.728588 | − | 0.728588i | 0.0688451 | − | 0.0688451i | ||||
\(113\) | −5.25913 | + | 5.25913i | −0.494738 | + | 0.494738i | −0.909795 | − | 0.415058i | \(-0.863761\pi\) |
0.415058 | + | 0.909795i | \(0.363761\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.12052 | + | 12.7258i | −0.197740 | + | 1.18668i | ||||
\(116\) | 0.494819i | 0.0459428i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.57770 | − | 8.57770i | −0.789641 | − | 0.789641i | ||||
\(119\) | 5.43503i | 0.498229i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.1199 | 1.10181 | ||||||||
\(122\) | −3.76477 | − | 3.76477i | −0.340846 | − | 0.340846i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.62312 | −0.774379 | ||||||||
\(125\) | −10.7133 | + | 3.19762i | −0.958229 | + | 0.286004i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.35800 | − | 9.35800i | −0.830388 | − | 0.830388i | 0.157181 | − | 0.987570i | \(-0.449759\pi\) |
−0.987570 | + | 0.157181i | \(0.949759\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.976946 | − | 1.36763i | −0.0856839 | − | 0.119949i | ||||
\(131\) | −12.6267 | −1.10320 | −0.551601 | − | 0.834108i | \(-0.685983\pi\) | ||||
−0.551601 | + | 0.834108i | \(0.685983\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.250951 | + | 4.48430i | 0.0217602 | + | 0.388838i | ||||
\(134\) | − | 12.9984i | − | 1.12289i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.27479i | 0.452309i | ||||||||
\(137\) | −0.378698 | + | 0.378698i | −0.0323544 | + | 0.0323544i | −0.723099 | − | 0.690745i | \(-0.757283\pi\) |
0.690745 | + | 0.723099i | \(0.257283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 22.7942i | − | 1.93338i | −0.255957 | − | 0.966688i | \(-0.582391\pi\) | ||
0.255957 | − | 0.966688i | \(-0.417609\pi\) | |||||||
\(140\) | 0.378698 | − | 2.27266i | 0.0320058 | − | 0.192075i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.45718 | + | 1.45718i | −0.122284 | + | 0.122284i | ||||
\(143\) | −2.55558 | + | 2.55558i | −0.213708 | + | 0.213708i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.643141 | + | 0.900333i | 0.0534100 | + | 0.0747686i | ||||
\(146\) | 4.68331i | 0.387594i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.47836 | − | 5.47836i | 0.450319 | − | 0.450319i | ||||
\(149\) | 15.8801i | 1.30095i | 0.759529 | + | 0.650473i | \(0.225429\pi\) | ||||
−0.759529 | + | 0.650473i | \(0.774571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.3507i | − | 1.08646i | −0.839583 | − | 0.543231i | \(-0.817201\pi\) | ||
0.839583 | − | 0.543231i | \(-0.182799\pi\) | |||||||
\(152\) | 0.243552 | + | 4.35209i | 0.0197547 | + | 0.353001i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.95439 | −0.399236 | ||||||||
\(155\) | −15.6899 | + | 11.2079i | −1.26025 | + | 0.900240i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7372 | − | 11.7372i | 0.936727 | − | 0.936727i | −0.0613870 | − | 0.998114i | \(-0.519552\pi\) |
0.998114 | + | 0.0613870i | \(0.0195524\pi\) | |||||||
\(158\) | −1.95921 | − | 1.95921i | −0.155866 | − | 0.155866i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.367533 | − | 2.20566i | 0.0290560 | − | 0.174372i | ||||
\(161\) | −5.94489 | −0.468523 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.988668 | − | 0.988668i | −0.0774384 | − | 0.0774384i | 0.667327 | − | 0.744765i | \(-0.267438\pi\) |
−0.744765 | + | 0.667327i | \(0.767438\pi\) | |||||||
\(164\) | −5.82553 | −0.454897 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.05963i | 0.392703i | ||||||||
\(167\) | 7.42584 | + | 7.42584i | 0.574629 | + | 0.574629i | 0.933418 | − | 0.358790i | \(-0.116811\pi\) |
−0.358790 | + | 0.933418i | \(0.616811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4350i | 0.956541i | ||||||||
\(170\) | 6.85591 | + | 9.59758i | 0.525824 | + | 0.736101i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.04079 | − | 3.04079i | 0.231858 | − | 0.231858i | ||||
\(173\) | 11.0462 | − | 11.0462i | 0.839825 | − | 0.839825i | −0.149011 | − | 0.988836i | \(-0.547609\pi\) |
0.988836 | + | 0.149011i | \(0.0476090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.26484 | − | 4.62737i | −0.171206 | − | 0.349796i | ||||
\(176\) | −4.80832 | −0.362441 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.768128 | + | 0.768128i | 0.0575736 | + | 0.0575736i | ||||
\(179\) | −19.0425 | −1.42330 | −0.711652 | − | 0.702532i | \(-0.752053\pi\) | ||||
−0.711652 | + | 0.702532i | \(0.752053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.78110i | 0.132388i | 0.997807 | + | 0.0661941i | \(0.0210857\pi\) | ||||
−0.997807 | + | 0.0661941i | \(0.978914\pi\) | |||||||
\(182\) | 0.547637 | − | 0.547637i | 0.0405936 | − | 0.0405936i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.76961 | −0.425341 | ||||||||
\(185\) | 2.84749 | − | 17.0885i | 0.209351 | − | 1.25637i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.9343 | − | 17.9343i | 1.31148 | − | 1.31148i | ||||
\(188\) | −0.910451 | − | 0.910451i | −0.0664014 | − | 0.0664014i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.09977 | + | 7.60215i | 0.442524 | + | 0.551518i | ||||
\(191\) | 14.8650 | 1.07559 | 0.537797 | − | 0.843075i | \(-0.319257\pi\) | ||||
0.537797 | + | 0.843075i | \(0.319257\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.04632 | + | 5.04632i | −0.363242 | + | 0.363242i | −0.865005 | − | 0.501763i | \(-0.832685\pi\) |
0.501763 | + | 0.865005i | \(0.332685\pi\) | |||||||
\(194\) | − | 3.98335i | − | 0.285988i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.93832 | −0.424166 | ||||||||
\(197\) | 7.66209 | − | 7.66209i | 0.545901 | − | 0.545901i | −0.379351 | − | 0.925253i | \(-0.623853\pi\) |
0.925253 | + | 0.379351i | \(0.123853\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.9302i | − | 1.48370i | −0.670565 | − | 0.741851i | \(-0.733948\pi\) | ||
0.670565 | − | 0.741851i | \(-0.266052\pi\) | |||||||
\(200\) | −2.19807 | − | 4.49094i | −0.155427 | − | 0.317557i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.94134 | + | 9.94134i | 0.699470 | + | 0.699470i | ||||
\(203\) | −0.360520 | + | 0.360520i | −0.0253035 | + | 0.0253035i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.5997 | + | 7.57173i | −0.740312 | + | 0.528832i | ||||
\(206\) | 9.38086 | 0.653596 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.531491 | − | 0.531491i | 0.0368523 | − | 0.0368523i | ||||
\(209\) | 13.9690 | − | 15.6252i | 0.966256 | − | 1.08081i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.6388i | 1.90273i | 0.308062 | + | 0.951366i | \(0.400319\pi\) | ||||
−0.308062 | + | 0.951366i | \(0.599681\pi\) | |||||||
\(212\) | 3.53266 | + | 3.53266i | 0.242624 | + | 0.242624i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.18160i | 0.149131i | ||||||||
\(215\) | 1.58051 | − | 9.48504i | 0.107790 | − | 0.646875i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.28270 | − | 6.28270i | −0.426498 | − | 0.426498i | ||||
\(218\) | 13.0310 | + | 13.0310i | 0.882569 | + | 0.882569i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.74883 | + | 6.24961i | −0.589846 | + | 0.421349i | ||||
\(221\) | 3.96475i | 0.266698i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.04571 | − | 8.04571i | 0.538781 | − | 0.538781i | −0.384390 | − | 0.923171i | \(-0.625588\pi\) |
0.923171 | + | 0.384390i | \(0.125588\pi\) | |||||||
\(224\) | 1.03038 | 0.0688451 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.43754 | −0.494738 | ||||||||
\(227\) | −1.98330 | − | 1.98330i | −0.131636 | − | 0.131636i | 0.638219 | − | 0.769855i | \(-0.279671\pi\) |
−0.769855 | + | 0.638219i | \(0.779671\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6443i | 1.29813i | 0.760732 | + | 0.649066i | \(0.224840\pi\) | ||||
−0.760732 | + | 0.649066i | \(0.775160\pi\) | |||||||
\(230\) | −10.4979 | + | 7.49905i | −0.692212 | + | 0.494473i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.349890 | + | 0.349890i | −0.0229714 | + | 0.0229714i | ||||
\(233\) | 4.73992 | + | 4.73992i | 0.310523 | + | 0.310523i | 0.845112 | − | 0.534589i | \(-0.179534\pi\) |
−0.534589 | + | 0.845112i | \(0.679534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.83994 | − | 0.473225i | −0.185257 | − | 0.0308698i | ||||
\(236\) | − | 12.1307i | − | 0.789641i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.84315 | + | 3.84315i | −0.249114 | + | 0.249114i | ||||
\(239\) | − | 21.1851i | − | 1.37035i | −0.728378 | − | 0.685176i | \(-0.759725\pi\) | ||
0.728378 | − | 0.685176i | \(-0.240275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2784i | 1.04859i | 0.851538 | + | 0.524293i | \(0.175671\pi\) | ||||
−0.851538 | + | 0.524293i | \(0.824329\pi\) | |||||||
\(242\) | 8.57008 | + | 8.57008i | 0.550905 | + | 0.550905i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5.32419i | − | 0.340846i | ||||||
\(245\) | −10.8049 | + | 7.71833i | −0.690299 | + | 0.493106i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.183064 | + | 3.27121i | 0.0116481 | + | 0.208142i | ||||
\(248\) | −6.09747 | − | 6.09747i | −0.387190 | − | 0.387190i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.83652 | − | 5.31441i | −0.622116 | − | 0.336113i | ||||
\(251\) | −5.24992 | −0.331372 | −0.165686 | − | 0.986179i | \(-0.552984\pi\) | ||||
−0.165686 | + | 0.986179i | \(0.552984\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.6166 | + | 19.6166i | 1.23329 | + | 1.23329i | ||||
\(254\) | − | 13.2342i | − | 0.830388i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.0320 | − | 16.0320i | −1.00005 | − | 1.00005i | −1.00000 | 4.94079e-5i | \(-0.999984\pi\) | |
−4.94079e−5 | − | 1.00000i | \(-0.500016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.98294 | 0.496036 | ||||||||
\(260\) | 0.276253 | − | 1.65786i | 0.0171325 | − | 0.102816i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.92844 | − | 8.92844i | −0.551601 | − | 0.551601i | ||||
\(263\) | 5.94999 | + | 5.94999i | 0.366892 | + | 0.366892i | 0.866342 | − | 0.499450i | \(-0.166465\pi\) |
−0.499450 | + | 0.866342i | \(0.666465\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0193 | + | 1.83617i | 0.676911 | + | 0.112795i | ||||
\(266\) | −2.99343 | + | 3.34833i | −0.183539 | + | 0.205299i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.19128 | − | 9.19128i | 0.561447 | − | 0.561447i | ||||
\(269\) | 26.2880 | 1.60281 | 0.801404 | − | 0.598123i | \(-0.204087\pi\) | ||||
0.801404 | + | 0.598123i | \(0.204087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.9318 | −0.724802 | −0.362401 | − | 0.932022i | \(-0.618043\pi\) | ||||
−0.362401 | + | 0.932022i | \(0.618043\pi\) | |||||||
\(272\) | −3.72984 | + | 3.72984i | −0.226155 | + | 0.226155i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.535560 | −0.0323544 | ||||||||
\(275\) | −7.79573 | + | 22.7426i | −0.470100 | + | 1.37143i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1943 | + | 13.1943i | −0.792771 | + | 0.792771i | −0.981944 | − | 0.189173i | \(-0.939419\pi\) |
0.189173 | + | 0.981944i | \(0.439419\pi\) | |||||||
\(278\) | 16.1179 | − | 16.1179i | 0.966688 | − | 0.966688i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.87480 | − | 1.33924i | 0.112040 | − | 0.0800346i | ||||
\(281\) | − | 25.4814i | − | 1.52009i | −0.649870 | − | 0.760045i | \(-0.725177\pi\) | ||
0.649870 | − | 0.760045i | \(-0.274823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.9451 | − | 14.9451i | −0.888392 | − | 0.888392i | 0.105977 | − | 0.994369i | \(-0.466203\pi\) |
−0.994369 | + | 0.105977i | \(0.966203\pi\) | |||||||
\(284\) | −2.06076 | −0.122284 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.61413 | −0.213708 | ||||||||
\(287\) | −4.24441 | − | 4.24441i | −0.250540 | − | 0.250540i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 10.8234i | − | 0.636671i | ||||||
\(290\) | −0.181862 | + | 1.09140i | −0.0106793 | + | 0.0640893i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.31160 | + | 3.31160i | −0.193797 | + | 0.193797i | ||||
\(293\) | 19.3388 | − | 19.3388i | 1.12978 | − | 1.12978i | 0.139570 | − | 0.990212i | \(-0.455428\pi\) |
0.990212 | − | 0.139570i | \(-0.0445719\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.7669 | − | 22.0720i | −0.917982 | − | 1.28508i | ||||
\(296\) | 7.74758 | 0.450319 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.2289 | + | 11.2289i | −0.650473 | + | 0.650473i | ||||
\(299\) | −4.33668 | −0.250797 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.43097 | 0.255397 | ||||||||
\(302\) | 9.44035 | − | 9.44035i | 0.543231 | − | 0.543231i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.90517 | + | 3.24961i | −0.166623 | + | 0.186378i | ||||
\(305\) | −6.92011 | − | 9.68746i | −0.396244 | − | 0.554702i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.00353863 | − | 0.00353863i | −0.000201960 | − | 0.000201960i | 0.707006 | − | 0.707208i | \(-0.250045\pi\) |
−0.707208 | + | 0.707006i | \(0.750045\pi\) | |||||||
\(308\) | −3.50328 | − | 3.50328i | −0.199618 | − | 0.199618i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.0196 | − | 3.16928i | −1.08024 | − | 0.180003i | ||||
\(311\) | 11.6925 | 0.663019 | 0.331509 | − | 0.943452i | \(-0.392442\pi\) | ||||
0.331509 | + | 0.943452i | \(0.392442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.6688 | − | 16.6688i | −0.942174 | − | 0.942174i | 0.0562432 | − | 0.998417i | \(-0.482088\pi\) |
−0.998417 | + | 0.0562432i | \(0.982088\pi\) | |||||||
\(314\) | 16.5988 | 0.936727 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 2.77074i | − | 0.155866i | ||||||
\(317\) | −6.96737 | − | 6.96737i | −0.391327 | − | 0.391327i | 0.483834 | − | 0.875160i | \(-0.339244\pi\) |
−0.875160 | + | 0.483834i | \(0.839244\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.37925 | 0.133212 | ||||||||
\(320\) | 1.81952 | − | 1.29975i | 0.101714 | − | 0.0726582i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.20367 | − | 4.20367i | −0.234261 | − | 0.234261i | ||||
\(323\) | −1.28468 | − | 22.9564i | −0.0714818 | − | 1.27733i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.65216 | − | 3.37558i | −0.0916454 | − | 0.187243i | ||||
\(326\) | − | 1.39819i | − | 0.0774384i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.11927 | − | 4.11927i | −0.227449 | − | 0.227449i | ||||
\(329\) | − | 1.32669i | − | 0.0731426i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 12.2381i | − | 0.672669i | −0.941743 | − | 0.336335i | \(-0.890813\pi\) | ||
0.941743 | − | 0.336335i | \(-0.109187\pi\) | |||||||
\(332\) | −3.57770 | + | 3.57770i | −0.196352 | + | 0.196352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.5017i | 0.574629i | ||||||||
\(335\) | 4.77735 | − | 28.6701i | 0.261015 | − | 1.56641i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9918 | + | 18.9918i | 1.03455 | + | 1.03455i | 0.999381 | + | 0.0351664i | \(0.0111961\pi\) |
0.0351664 | + | 0.999381i | \(0.488804\pi\) | |||||||
\(338\) | −8.79290 | + | 8.79290i | −0.478271 | + | 0.478271i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.93866 | + | 11.6344i | −0.105138 | + | 0.630962i | ||||
\(341\) | 41.4627i | 2.24533i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.42671 | − | 9.42671i | −0.508994 | − | 0.508994i | ||||
\(344\) | 4.30033 | 0.231858 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.6216 | 0.839825 | ||||||||
\(347\) | −1.51527 | + | 1.51527i | −0.0813438 | + | 0.0813438i | −0.746608 | − | 0.665264i | \(-0.768319\pi\) |
0.665264 | + | 0.746608i | \(0.268319\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 21.3136i | − | 1.14089i | −0.821336 | − | 0.570444i | \(-0.806771\pi\) | ||
0.821336 | − | 0.570444i | \(-0.193229\pi\) | |||||||
\(350\) | 1.67056 | − | 4.87353i | 0.0892950 | − | 0.260501i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.39999 | − | 3.39999i | −0.181220 | − | 0.181220i | ||||
\(353\) | −9.37463 | − | 9.37463i | −0.498961 | − | 0.498961i | 0.412153 | − | 0.911115i | \(-0.364777\pi\) |
−0.911115 | + | 0.412153i | \(0.864777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.74959 | + | 2.67847i | −0.199008 | + | 0.142158i | ||||
\(356\) | 1.08630i | 0.0575736i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.4651 | − | 13.4651i | −0.711652 | − | 0.711652i | ||||
\(359\) | − | 30.1209i | − | 1.58972i | −0.606792 | − | 0.794861i | \(-0.707544\pi\) | ||
0.606792 | − | 0.794861i | \(-0.292456\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.11992 | − | 18.8814i | −0.111575 | − | 0.993756i | ||||
\(362\) | −1.25943 | + | 1.25943i | −0.0661941 | + | 0.0661941i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.774476 | 0.0405936 | ||||||||
\(365\) | −1.72127 | + | 10.3298i | −0.0900954 | + | 0.540685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0986 | + | 10.0986i | −0.527140 | + | 0.527140i | −0.919719 | − | 0.392578i | \(-0.871583\pi\) |
0.392578 | + | 0.919719i | \(0.371583\pi\) | |||||||
\(368\) | −4.07973 | − | 4.07973i | −0.212671 | − | 0.212671i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.0969 | − | 10.0699i | 0.732861 | − | 0.523510i | ||||
\(371\) | 5.14771i | 0.267256i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5759 | − | 11.5759i | 0.599377 | − | 0.599377i | −0.340770 | − | 0.940147i | \(-0.610688\pi\) |
0.940147 | + | 0.340770i | \(0.110688\pi\) | |||||||
\(374\) | 25.3629 | 1.31148 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 1.28757i | − | 0.0664014i | ||||||
\(377\) | −0.262992 | + | 0.262992i | −0.0135448 | + | 0.0135448i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.6895 | 1.57641 | 0.788206 | − | 0.615412i | \(-0.211010\pi\) | ||||
0.788206 | + | 0.615412i | \(0.211010\pi\) | |||||||
\(380\) | −1.06234 | + | 9.68873i | −0.0544971 | + | 0.497021i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.5111 | + | 10.5111i | 0.537797 | + | 0.537797i | ||||
\(383\) | 6.71232 | − | 6.71232i | 0.342983 | − | 0.342983i | −0.514504 | − | 0.857488i | \(-0.672024\pi\) |
0.857488 | + | 0.514504i | \(0.172024\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.9277 | − | 1.82090i | −0.556926 | − | 0.0928017i | ||||
\(386\) | −7.13657 | −0.363242 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.81665 | − | 2.81665i | 0.142994 | − | 0.142994i | ||||
\(389\) | 1.69598i | 0.0859894i | 0.999075 | + | 0.0429947i | \(0.0136899\pi\) | ||||
−0.999075 | + | 0.0429947i | \(0.986310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.4335 | 1.53909 | ||||||||
\(392\) | −4.19903 | − | 4.19903i | −0.212083 | − | 0.212083i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.8358 | 0.545901 | ||||||||
\(395\) | −3.60127 | − | 5.04142i | −0.181199 | − | 0.253661i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.6346 | + | 17.6346i | −0.885057 | + | 0.885057i | −0.994043 | − | 0.108986i | \(-0.965240\pi\) |
0.108986 | + | 0.994043i | \(0.465240\pi\) | |||||||
\(398\) | 14.7999 | − | 14.7999i | 0.741851 | − | 0.741851i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.62130 | − | 4.72984i | 0.0810651 | − | 0.236492i | ||||
\(401\) | − | 1.30146i | − | 0.0649918i | −0.999472 | − | 0.0324959i | \(-0.989654\pi\) | ||
0.999472 | − | 0.0324959i | \(-0.0103456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.58311 | − | 4.58311i | −0.228301 | − | 0.228301i | ||||
\(404\) | 14.0592i | 0.699470i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.509852 | −0.0253035 | ||||||||
\(407\) | −26.3417 | − | 26.3417i | −1.30571 | − | 1.30571i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.8682 | 0.932971 | 0.466485 | − | 0.884529i | \(-0.345520\pi\) | ||||
0.466485 | + | 0.884529i | \(0.345520\pi\) | |||||||
\(410\) | −12.8491 | − | 2.14107i | −0.634572 | − | 0.105740i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.63327 | + | 6.63327i | 0.326798 | + | 0.326798i | ||||
\(413\) | 8.83828 | − | 8.83828i | 0.434903 | − | 0.434903i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.85958 | + | 11.1598i | −0.0912831 | + | 0.547813i | ||||
\(416\) | 0.751642 | 0.0368523 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.9262 | − | 1.17107i | 1.02354 | − | 0.0572791i | ||||
\(419\) | 20.1568i | 0.984725i | 0.870390 | + | 0.492363i | \(0.163867\pi\) | ||||
−0.870390 | + | 0.492363i | \(0.836133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.85286i | − | 0.431462i | −0.976453 | − | 0.215731i | \(-0.930787\pi\) | ||
0.976453 | − | 0.215731i | \(-0.0692134\pi\) | |||||||
\(422\) | −19.5436 | + | 19.5436i | −0.951366 | + | 0.951366i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.99593i | 0.242624i | ||||||||
\(425\) | 11.5943 | + | 23.6887i | 0.562408 | + | 1.14907i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.87914 | − | 3.87914i | 0.187725 | − | 0.187725i | ||||
\(428\) | −1.54262 | + | 1.54262i | −0.0745656 | + | 0.0745656i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.82453 | − | 5.58935i | 0.377332 | − | 0.269542i | ||||
\(431\) | 25.3047i | 1.21889i | 0.792830 | + | 0.609443i | \(0.208607\pi\) | ||||
−0.792830 | + | 0.609443i | \(0.791393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.00560 | − | 6.00560i | 0.288611 | − | 0.288611i | −0.547920 | − | 0.836531i | \(-0.684580\pi\) |
0.836531 | + | 0.547920i | \(0.184580\pi\) | |||||||
\(434\) | − | 8.88509i | − | 0.426498i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.4286i | 0.882569i | ||||||||
\(437\) | 25.1099 | − | 1.40520i | 1.20117 | − | 0.0672198i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.4260 | −1.83397 | −0.916986 | − | 0.398919i | \(-0.869386\pi\) | ||||
−0.916986 | + | 0.398919i | \(0.869386\pi\) | |||||||
\(440\) | −10.6055 | − | 1.76721i | −0.505597 | − | 0.0842486i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.80350 | + | 2.80350i | −0.133349 | + | 0.133349i | ||||
\(443\) | −27.7457 | − | 27.7457i | −1.31824 | − | 1.31824i | −0.915171 | − | 0.403066i | \(-0.867945\pi\) |
−0.403066 | − | 0.915171i | \(-0.632055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.41191 | + | 1.97654i | 0.0669311 | + | 0.0936969i | ||||
\(446\) | 11.3784 | 0.538781 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.728588 | + | 0.728588i | 0.0344226 | + | 0.0344226i | ||||
\(449\) | −28.1598 | −1.32894 | −0.664472 | − | 0.747313i | \(-0.731344\pi\) | ||||
−0.664472 | + | 0.747313i | \(0.731344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.0110i | 1.31899i | ||||||||
\(452\) | −5.25913 | − | 5.25913i | −0.247369 | − | 0.247369i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2.80480i | − | 0.131636i | ||||||
\(455\) | 1.40917 | − | 1.00663i | 0.0660631 | − | 0.0471913i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.5575 | + | 19.5575i | −0.914859 | + | 0.914859i | −0.996650 | − | 0.0817904i | \(-0.973936\pi\) |
0.0817904 | + | 0.996650i | \(0.473936\pi\) | |||||||
\(458\) | −13.8906 | + | 13.8906i | −0.649066 | + | 0.649066i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.7258 | − | 2.12052i | −0.593342 | − | 0.0988698i | ||||
\(461\) | −9.61570 | −0.447848 | −0.223924 | − | 0.974607i | \(-0.571887\pi\) | ||||
−0.223924 | + | 0.974607i | \(0.571887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6735 | + | 16.6735i | 0.774882 | + | 0.774882i | 0.978956 | − | 0.204074i | \(-0.0654182\pi\) |
−0.204074 | + | 0.978956i | \(0.565418\pi\) | |||||||
\(464\) | −0.494819 | −0.0229714 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.70326i | 0.310523i | ||||||||
\(467\) | 17.1190 | − | 17.1190i | 0.792171 | − | 0.792171i | −0.189676 | − | 0.981847i | \(-0.560744\pi\) |
0.981847 | + | 0.189676i | \(0.0607437\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.3933 | 0.618446 | ||||||||
\(470\) | −1.67352 | − | 2.34276i | −0.0771938 | − | 0.108064i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.57770 | − | 8.57770i | 0.394820 | − | 0.394820i | ||||
\(473\) | −14.6211 | − | 14.6211i | −0.672278 | − | 0.672278i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.6600 | + | 19.0096i | 0.489113 | + | 0.872221i | ||||
\(476\) | −5.43503 | −0.249114 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.9801 | − | 14.9801i | 0.685176 | − | 0.685176i | ||||
\(479\) | 14.2801i | 0.652474i | 0.945288 | + | 0.326237i | \(0.105781\pi\) | ||||
−0.945288 | + | 0.326237i | \(0.894219\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.82340 | 0.265524 | ||||||||
\(482\) | −11.5106 | + | 11.5106i | −0.524293 | + | 0.524293i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.1199i | 0.550905i | ||||||||
\(485\) | 1.46401 | − | 8.78590i | 0.0664774 | − | 0.398947i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.6790 | − | 13.6790i | −0.619856 | − | 0.619856i | 0.325639 | − | 0.945494i | \(-0.394421\pi\) |
−0.945494 | + | 0.325639i | \(0.894421\pi\) | |||||||
\(488\) | 3.76477 | − | 3.76477i | 0.170423 | − | 0.170423i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.0979 | − | 2.18253i | −0.591702 | − | 0.0985965i | ||||
\(491\) | −6.60655 | −0.298150 | −0.149075 | − | 0.988826i | \(-0.547630\pi\) | ||||
−0.149075 | + | 0.988826i | \(0.547630\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.84560 | − | 1.84560i | 0.0831215 | − | 0.0831215i | ||||
\(494\) | −2.18365 | + | 2.44254i | −0.0982471 | + | 0.109895i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.62312i | − | 0.387190i | ||||||
\(497\) | −1.50144 | − | 1.50144i | −0.0673490 | − | 0.0673490i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 35.7269i | − | 1.59935i | −0.600430 | − | 0.799677i | \(-0.705004\pi\) | ||
0.600430 | − | 0.799677i | \(-0.294996\pi\) | |||||||
\(500\) | −3.19762 | − | 10.7133i | −0.143002 | − | 0.479114i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.71225 | − | 3.71225i | −0.165686 | − | 0.165686i | ||||
\(503\) | 8.52003 | + | 8.52003i | 0.379889 | + | 0.379889i | 0.871062 | − | 0.491173i | \(-0.163432\pi\) |
−0.491173 | + | 0.871062i | \(0.663432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.2734 | + | 25.5809i | 0.813156 | + | 1.13834i | ||||
\(506\) | 27.7421i | 1.23329i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.35800 | − | 9.35800i | 0.415194 | − | 0.415194i | ||||
\(509\) | 13.4408 | 0.595753 | 0.297877 | − | 0.954604i | \(-0.403722\pi\) | ||||
0.297877 | + | 0.954604i | \(0.403722\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.82559 | −0.213471 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 22.6727i | − | 1.00005i | ||||||
\(515\) | 20.6910 | + | 3.44777i | 0.911752 | + | 0.151927i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.37774 | + | 4.37774i | −0.192533 | + | 0.192533i | ||||
\(518\) | 5.64479 | + | 5.64479i | 0.248018 | + | 0.248018i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.36763 | − | 0.976946i | 0.0599744 | − | 0.0428419i | ||||
\(521\) | 13.5544i | 0.593831i | 0.954904 | + | 0.296916i | \(0.0959580\pi\) | ||||
−0.954904 | + | 0.296916i | \(0.904042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.40357 | − | 5.40357i | 0.236282 | − | 0.236282i | −0.579027 | − | 0.815308i | \(-0.696567\pi\) |
0.815308 | + | 0.579027i | \(0.196567\pi\) | |||||||
\(524\) | − | 12.6267i | − | 0.551601i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.41456i | 0.366892i | ||||||||
\(527\) | 32.1629 | + | 32.1629i | 1.40104 | + | 1.40104i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.2884i | 0.447321i | ||||||||
\(530\) | 6.49346 | + | 9.09020i | 0.282058 | + | 0.394853i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.48430 | + | 0.250951i | −0.194419 | + | 0.0108801i | ||||
\(533\) | −3.09622 | − | 3.09622i | −0.134112 | − | 0.134112i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.801810 | + | 4.81186i | −0.0346653 | + | 0.208035i | ||||
\(536\) | 12.9984 | 0.561447 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.5884 | + | 18.5884i | 0.801404 | + | 0.801404i | ||||
\(539\) | 28.5533i | 1.22988i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.68488 | 0.330399 | 0.165200 | − | 0.986260i | \(-0.447173\pi\) | ||||
0.165200 | + | 0.986260i | \(0.447173\pi\) | |||||||
\(542\) | −8.43702 | − | 8.43702i | −0.362401 | − | 0.362401i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.27479 | −0.226155 | ||||||||
\(545\) | 23.9525 | + | 33.5312i | 1.02601 | + | 1.43632i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8604 | − | 17.8604i | −0.763656 | − | 0.763656i | 0.213325 | − | 0.976981i | \(-0.431571\pi\) |
−0.976981 | + | 0.213325i | \(0.931571\pi\) | |||||||
\(548\) | −0.378698 | − | 0.378698i | −0.0161772 | − | 0.0161772i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21.5938 | + | 10.5690i | −0.920765 | + | 0.450664i | ||||
\(551\) | 1.43754 | − | 1.60797i | 0.0612411 | − | 0.0685018i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.01873 | − | 2.01873i | 0.0858451 | − | 0.0858451i | ||||
\(554\) | −18.6596 | −0.792771 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.7942 | 0.966688 | ||||||||
\(557\) | −12.5198 | + | 12.5198i | −0.530480 | + | 0.530480i | −0.920715 | − | 0.390235i | \(-0.872394\pi\) |
0.390235 | + | 0.920715i | \(0.372394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.23231 | 0.136712 | ||||||||
\(560\) | 2.27266 | + | 0.378698i | 0.0960375 | + | 0.0160029i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0180 | − | 18.0180i | 0.760045 | − | 0.760045i | ||||
\(563\) | −11.0759 | + | 11.0759i | −0.466791 | + | 0.466791i | −0.900873 | − | 0.434082i | \(-0.857073\pi\) |
0.434082 | + | 0.900873i | \(0.357073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.4046 | − | 2.73354i | −0.690149 | − | 0.115001i | ||||
\(566\) | − | 21.1355i | − | 0.888392i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.45718 | − | 1.45718i | −0.0611418 | − | 0.0611418i | ||||
\(569\) | 43.4414 | 1.82116 | 0.910579 | − | 0.413336i | \(-0.135636\pi\) | ||||
0.910579 | + | 0.413336i | \(0.135636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6768 | 0.656052 | 0.328026 | − | 0.944669i | \(-0.393617\pi\) | ||||
0.328026 | + | 0.944669i | \(0.393617\pi\) | |||||||
\(572\) | −2.55558 | − | 2.55558i | −0.106854 | − | 0.106854i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 6.00250i | − | 0.250540i | ||||||
\(575\) | −25.9109 | + | 12.6820i | −1.08056 | + | 0.528876i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.59569 | − | 6.59569i | 0.274582 | − | 0.274582i | −0.556359 | − | 0.830942i | \(-0.687802\pi\) |
0.830942 | + | 0.556359i | \(0.187802\pi\) | |||||||
\(578\) | 7.65330 | − | 7.65330i | 0.318335 | − | 0.318335i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.900333 | + | 0.643141i | −0.0373843 | + | 0.0267050i | ||||
\(581\) | −5.21334 | −0.216286 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.9861 | − | 16.9861i | 0.703494 | − | 0.703494i | ||||
\(584\) | −4.68331 | −0.193797 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.3491 | 1.12978 | ||||||||
\(587\) | 23.8623 | − | 23.8623i | 0.984904 | − | 0.984904i | −0.0149835 | − | 0.999888i | \(-0.504770\pi\) |
0.999888 | + | 0.0149835i | \(0.00476957\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0218 | + | 25.0517i | 1.15462 | + | 1.03224i | ||||
\(590\) | 4.45843 | − | 26.7561i | 0.183551 | − | 1.10153i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.47836 | + | 5.47836i | 0.225159 | + | 0.225159i | ||||
\(593\) | −22.7988 | − | 22.7988i | −0.936236 | − | 0.936236i | 0.0618495 | − | 0.998085i | \(-0.480300\pi\) |
−0.998085 | + | 0.0618495i | \(0.980300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.88915 | + | 7.06418i | −0.405416 | + | 0.289603i | ||||
\(596\) | −15.8801 | −0.650473 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.06650 | − | 3.06650i | −0.125398 | − | 0.125398i | ||||
\(599\) | 11.4248 | 0.466805 | 0.233402 | − | 0.972380i | \(-0.425014\pi\) | ||||
0.233402 | + | 0.972380i | \(0.425014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.14156i | 0.291310i | 0.989335 | + | 0.145655i | \(0.0465290\pi\) | ||||
−0.989335 | + | 0.145655i | \(0.953471\pi\) | |||||||
\(602\) | 3.13317 | + | 3.13317i | 0.127698 | + | 0.127698i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.3507 | 0.543231 | ||||||||
\(605\) | 15.7529 | + | 22.0524i | 0.640445 | + | 0.896559i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.44190 | + | 6.44190i | 0.261469 | + | 0.261469i | 0.825651 | − | 0.564182i | \(-0.190808\pi\) |
−0.564182 | + | 0.825651i | \(0.690808\pi\) | |||||||
\(608\) | −4.35209 | + | 0.243552i | −0.176501 | + | 0.00987733i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.95681 | − | 11.7433i | 0.0792290 | − | 0.475473i | ||||
\(611\) | − | 0.967793i | − | 0.0391527i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.1379 | − | 21.1379i | −0.853752 | − | 0.853752i | 0.136841 | − | 0.990593i | \(-0.456305\pi\) |
−0.990593 | + | 0.136841i | \(0.956305\pi\) | |||||||
\(614\) | − | 0.00500438i | − | 0.000201960i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 4.95439i | − | 0.199618i | ||||||
\(617\) | 9.52678 | − | 9.52678i | 0.383534 | − | 0.383534i | −0.488840 | − | 0.872373i | \(-0.662580\pi\) |
0.872373 | + | 0.488840i | \(0.162580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.57762i | 0.264377i | 0.991225 | + | 0.132188i | \(0.0422004\pi\) | ||||
−0.991225 | + | 0.132188i | \(0.957800\pi\) | |||||||
\(620\) | −11.2079 | − | 15.6899i | −0.450120 | − | 0.630123i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.26782 | + | 8.26782i | 0.331509 | + | 0.331509i | ||||
\(623\) | −0.791463 | + | 0.791463i | −0.0317093 | + | 0.0317093i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.7428 | − | 15.3370i | −0.789710 | − | 0.613480i | ||||
\(626\) | − | 23.5732i | − | 0.942174i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.7372 | + | 11.7372i | 0.468363 | + | 0.468363i | ||||
\(629\) | −40.8668 | −1.62947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.0875 | −0.680241 | −0.340121 | − | 0.940382i | \(-0.610468\pi\) | ||||
−0.340121 | + | 0.940382i | \(0.610468\pi\) | |||||||
\(632\) | 1.95921 | − | 1.95921i | 0.0779332 | − | 0.0779332i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 9.85335i | − | 0.391327i | ||||||
\(635\) | 4.86401 | − | 29.1901i | 0.193022 | − | 1.15837i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.15616 | − | 3.15616i | −0.125052 | − | 0.125052i | ||||
\(638\) | 1.68238 | + | 1.68238i | 0.0666062 | + | 0.0666062i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.20566 | + | 0.367533i | 0.0871862 | + | 0.0145280i | ||||
\(641\) | 46.7376i | 1.84602i | 0.384773 | + | 0.923011i | \(0.374280\pi\) | ||||
−0.384773 | + | 0.923011i | \(0.625720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.16897 | − | 7.16897i | −0.282717 | − | 0.282717i | 0.551475 | − | 0.834191i | \(-0.314065\pi\) |
−0.834191 | + | 0.551475i | \(0.814065\pi\) | |||||||
\(644\) | − | 5.94489i | − | 0.234261i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.3242 | − | 17.1410i | 0.602922 | − | 0.674404i | ||||
\(647\) | 6.19558 | − | 6.19558i | 0.243574 | − | 0.243574i | −0.574753 | − | 0.818327i | \(-0.694902\pi\) |
0.818327 | + | 0.574753i | \(0.194902\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58.3282 | −2.28958 | ||||||||
\(650\) | 1.21864 | − | 3.55515i | 0.0477989 | − | 0.139444i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.988668 | − | 0.988668i | 0.0387192 | − | 0.0387192i | ||||
\(653\) | −17.2336 | − | 17.2336i | −0.674401 | − | 0.674401i | 0.284326 | − | 0.958728i | \(-0.408230\pi\) |
−0.958728 | + | 0.284326i | \(0.908230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.4116 | − | 22.9746i | −0.641253 | − | 0.897690i | ||||
\(656\) | − | 5.82553i | − | 0.227449i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.938110 | − | 0.938110i | 0.0365713 | − | 0.0365713i | ||||
\(659\) | 21.6005 | 0.841436 | 0.420718 | − | 0.907191i | \(-0.361778\pi\) | ||||
0.420718 | + | 0.907191i | \(0.361778\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.49297i | 0.0580696i | 0.999578 | + | 0.0290348i | \(0.00924337\pi\) | ||||
−0.999578 | + | 0.0290348i | \(0.990757\pi\) | |||||||
\(662\) | 8.65367 | − | 8.65367i | 0.336335 | − | 0.336335i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.05963 | −0.196352 | ||||||||
\(665\) | −7.83310 | + | 6.28508i | −0.303755 | + | 0.243725i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.01873 | + | 2.01873i | 0.0781655 | + | 0.0781655i | ||||
\(668\) | −7.42584 | + | 7.42584i | −0.287314 | + | 0.287314i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.6509 | − | 16.8947i | 0.913714 | − | 0.652700i | ||||
\(671\) | −25.6004 | −0.988291 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.49705 | + | 8.49705i | −0.327537 | + | 0.327537i | −0.851649 | − | 0.524112i | \(-0.824397\pi\) |
0.524112 | + | 0.851649i | \(0.324397\pi\) | |||||||
\(674\) | 26.8584i | 1.03455i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4350 | −0.478271 | ||||||||
\(677\) | 5.92660 | + | 5.92660i | 0.227778 | + | 0.227778i | 0.811764 | − | 0.583986i | \(-0.198508\pi\) |
−0.583986 | + | 0.811764i | \(0.698508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.10436 | 0.157511 | ||||||||
\(680\) | −9.59758 | + | 6.85591i | −0.368050 | + | 0.262912i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29.3186 | + | 29.3186i | −1.12267 | + | 1.12267i | ||||
\(683\) | −26.3647 | + | 26.3647i | −1.00882 | + | 1.00882i | −0.00885484 | + | 0.999961i | \(0.502819\pi\) |
−0.999961 | + | 0.00885484i | \(0.997181\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.18126 | − | 0.196836i | −0.0451337 | − | 0.00752071i | ||||
\(686\) | − | 13.3314i | − | 0.508994i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.04079 | + | 3.04079i | 0.115929 | + | 0.115929i | ||||
\(689\) | 3.75515i | 0.143060i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3186 | 0.734913 | 0.367456 | − | 0.930041i | \(-0.380229\pi\) | ||||
0.367456 | + | 0.930041i | \(0.380229\pi\) | |||||||
\(692\) | 11.0462 | + | 11.0462i | 0.419912 | + | 0.419912i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.14291 | −0.0813438 | ||||||||
\(695\) | 41.4744 | − | 29.6267i | 1.57322 | − | 1.12381i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.7283 | + | 21.7283i | 0.823017 | + | 0.823017i | ||||
\(698\) | 15.0710 | − | 15.0710i | 0.570444 | − | 0.570444i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.62737 | − | 2.26484i | 0.174898 | − | 0.0856031i | ||||
\(701\) | −8.82340 | −0.333255 | −0.166628 | − | 0.986020i | \(-0.553288\pi\) | ||||
−0.166628 | + | 0.986020i | \(0.553288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.7181 | + | 1.88694i | −1.27170 | + | 0.0711672i | ||||
\(704\) | − | 4.80832i | − | 0.181220i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 13.2577i | − | 0.498961i | ||||||
\(707\) | −10.2434 | + | 10.2434i | −0.385241 | + | 0.385241i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.20583i | − | 0.0452859i | −0.999744 | − | 0.0226429i | \(-0.992792\pi\) | ||
0.999744 | − | 0.0226429i | \(-0.00720808\pi\) | |||||||
\(710\) | −4.54533 | − | 0.757396i | −0.170583 | − | 0.0284246i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.768128 | + | 0.768128i | −0.0287868 | + | 0.0287868i | ||||
\(713\) | −35.1800 | + | 35.1800i | −1.31750 | + | 1.31750i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.97154 | − | 1.32831i | −0.298119 | − | 0.0496761i | ||||
\(716\) | − | 19.0425i | − | 0.711652i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.2987 | − | 21.2987i | 0.794861 | − | 0.794861i | ||||
\(719\) | 9.38938i | 0.350165i | 0.984554 | + | 0.175082i | \(0.0560192\pi\) | ||||
−0.984554 | + | 0.175082i | \(0.943981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.66585i | 0.359975i | ||||||||
\(722\) | 11.8521 | − | 14.8502i | 0.441091 | − | 0.552665i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.78110 | −0.0661941 | ||||||||
\(725\) | −0.802251 | + | 2.34042i | −0.0297949 | + | 0.0869209i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.4688 | + | 17.4688i | −0.647884 | + | 0.647884i | −0.952481 | − | 0.304597i | \(-0.901478\pi\) |
0.304597 | + | 0.952481i | \(0.401478\pi\) | |||||||
\(728\) | 0.547637 | + | 0.547637i | 0.0202968 | + | 0.0202968i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.52138 | + | 6.08713i | −0.315390 | + | 0.225295i | ||||
\(731\) | −22.6833 | −0.838973 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.1840 | + | 13.1840i | 0.486963 | + | 0.486963i | 0.907347 | − | 0.420383i | \(-0.138104\pi\) |
−0.420383 | + | 0.907347i | \(0.638104\pi\) | |||||||
\(734\) | −14.2815 | −0.527140 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.76961i | − | 0.212671i | ||||||
\(737\) | −44.1946 | − | 44.1946i | −1.62793 | − | 1.62793i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.8710i | 1.76096i | 0.474080 | + | 0.880482i | \(0.342781\pi\) | ||||
−0.474080 | + | 0.880482i | \(0.657219\pi\) | |||||||
\(740\) | 17.0885 | + | 2.84749i | 0.628185 | + | 0.104676i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.63998 | + | 3.63998i | −0.133628 | + | 0.133628i | ||||
\(743\) | −19.4260 | + | 19.4260i | −0.712670 | + | 0.712670i | −0.967093 | − | 0.254423i | \(-0.918114\pi\) |
0.254423 | + | 0.967093i | \(0.418114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.8941 | + | 20.6401i | −1.05860 | + | 0.756196i | ||||
\(746\) | 16.3708 | 0.599377 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.9343 | + | 17.9343i | 0.655741 | + | 0.655741i | ||||
\(749\) | −2.24788 | −0.0821356 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.5009i | 0.857559i | 0.903409 | + | 0.428779i | \(0.141056\pi\) | ||||
−0.903409 | + | 0.428779i | \(0.858944\pi\) | |||||||
\(752\) | 0.910451 | − | 0.910451i | 0.0332007 | − | 0.0332007i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.371927 | −0.0135448 | ||||||||
\(755\) | 24.2918 | − | 17.3525i | 0.884069 | − | 0.631523i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.2062 | − | 19.2062i | 0.698060 | − | 0.698060i | −0.265932 | − | 0.963992i | \(-0.585680\pi\) |
0.963992 | + | 0.265932i | \(0.0856796\pi\) | |||||||
\(758\) | 21.7007 | + | 21.7007i | 0.788206 | + | 0.788206i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.60215 | + | 6.09977i | −0.275759 | + | 0.221262i | ||||
\(761\) | 23.7982 | 0.862685 | 0.431343 | − | 0.902188i | \(-0.358040\pi\) | ||||
0.431343 | + | 0.902188i | \(0.358040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.4268 | + | 13.4268i | −0.486084 | + | 0.486084i | ||||
\(764\) | 14.8650i | 0.537797i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.49265 | 0.342983 | ||||||||
\(767\) | 6.44736 | − | 6.44736i | 0.232801 | − | 0.232801i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 28.9884i | − | 1.04535i | −0.852532 | − | 0.522675i | \(-0.824934\pi\) | ||
0.852532 | − | 0.522675i | \(-0.175066\pi\) | |||||||
\(770\) | −6.43947 | − | 9.01461i | −0.232062 | − | 0.324864i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.04632 | − | 5.04632i | −0.181621 | − | 0.181621i | ||||
\(773\) | −29.2365 | + | 29.2365i | −1.05156 | + | 1.05156i | −0.0529667 | + | 0.998596i | \(0.516868\pi\) |
−0.998596 | + | 0.0529667i | \(0.983132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.7860 | − | 13.9807i | −1.46508 | − | 0.502201i | ||||
\(776\) | 3.98335 | 0.142994 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.19924 | + | 1.19924i | −0.0429947 | + | 0.0429947i | ||||
\(779\) | 18.9307 | + | 16.9242i | 0.678262 | + | 0.606371i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.90878i | 0.354564i | ||||||||
\(782\) | 21.5197 | + | 21.5197i | 0.769543 | + | 0.769543i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 5.93832i | − | 0.212083i | ||||||
\(785\) | 36.6113 | + | 6.10062i | 1.30671 | + | 0.217740i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6866 | + | 12.6866i | 0.452228 | + | 0.452228i | 0.896093 | − | 0.443866i | \(-0.146393\pi\) |
−0.443866 | + | 0.896093i | \(0.646393\pi\) | |||||||
\(788\) | 7.66209 | + | 7.66209i | 0.272951 | + | 0.272951i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.01834 | − | 6.11130i | 0.0362308 | − | 0.217430i | ||||
\(791\) | − | 7.66348i | − | 0.272482i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.82976 | − | 2.82976i | 0.100488 | − | 0.100488i | ||||
\(794\) | −24.9391 | −0.885057 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.9302 | 0.741851 | ||||||||
\(797\) | −15.7202 | − | 15.7202i | −0.556838 | − | 0.556838i | 0.371568 | − | 0.928406i | \(-0.378820\pi\) |
−0.928406 | + | 0.371568i | \(0.878820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.79167i | 0.240272i | ||||||||
\(800\) | 4.49094 | − | 2.19807i | 0.158779 | − | 0.0777134i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.920271 | − | 0.920271i | 0.0324959 | − | 0.0324959i | ||||
\(803\) | 15.9232 | + | 15.9232i | 0.561919 | + | 0.561919i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.72686 | − | 10.8168i | −0.272336 | − | 0.381243i | ||||
\(806\) | − | 6.48150i | − | 0.228301i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.94134 | + | 9.94134i | −0.349735 | + | 0.349735i | ||||
\(809\) | 11.4400i | 0.402210i | 0.979570 | + | 0.201105i | \(0.0644533\pi\) | ||||
−0.979570 | + | 0.201105i | \(0.935547\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.5878i | 0.617592i | 0.951128 | + | 0.308796i | \(0.0999260\pi\) | ||||
−0.951128 | + | 0.308796i | \(0.900074\pi\) | |||||||
\(812\) | −0.360520 | − | 0.360520i | −0.0126518 | − | 0.0126518i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 37.2528i | − | 1.30571i | ||||||
\(815\) | 0.513880 | − | 3.08392i | 0.0180004 | − | 0.108025i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.7154 | + | 1.04735i | −0.654769 | + | 0.0366422i | ||||
\(818\) | 13.3418 | + | 13.3418i | 0.466485 | + | 0.466485i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.57173 | − | 10.5997i | −0.264416 | − | 0.370156i | ||||
\(821\) | −13.1354 | −0.458428 | −0.229214 | − | 0.973376i | \(-0.573616\pi\) | ||||
−0.229214 | + | 0.973376i | \(0.573616\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2779 | − | 23.2779i | −0.811417 | − | 0.811417i | 0.173429 | − | 0.984846i | \(-0.444515\pi\) |
−0.984846 | + | 0.173429i | \(0.944515\pi\) | |||||||
\(824\) | 9.38086i | 0.326798i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.4992 | 0.434903 | ||||||||
\(827\) | −33.6240 | − | 33.6240i | −1.16922 | − | 1.16922i | −0.982393 | − | 0.186828i | \(-0.940179\pi\) |
−0.186828 | − | 0.982393i | \(-0.559821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.3434 | −0.776020 | −0.388010 | − | 0.921655i | \(-0.626837\pi\) | ||||
−0.388010 | + | 0.921655i | \(0.626837\pi\) | |||||||
\(830\) | −9.20609 | + | 6.57625i | −0.319548 | + | 0.228265i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.531491 | + | 0.531491i | 0.0184261 | + | 0.0184261i | ||||
\(833\) | 22.1490 | + | 22.1490i | 0.767416 | + | 0.767416i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.85973 | + | 23.1632i | −0.133571 | + | 0.801595i | ||||
\(836\) | 15.6252 | + | 13.9690i | 0.540407 | + | 0.483128i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.2530 | + | 14.2530i | −0.492363 | + | 0.492363i | ||||
\(839\) | 31.3884 | 1.08365 | 0.541824 | − | 0.840492i | \(-0.317734\pi\) | ||||
0.541824 | + | 0.840492i | \(0.317734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7552 | −0.991557 | ||||||||
\(842\) | 6.25992 | − | 6.25992i | 0.215731 | − | 0.215731i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −27.6388 | −0.951366 | ||||||||
\(845\) | −22.6258 | + | 16.1624i | −0.778351 | + | 0.556005i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.83043 | + | 8.83043i | −0.303417 | + | 0.303417i | ||||
\(848\) | −3.53266 | + | 3.53266i | −0.121312 | + | 0.121312i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.55203 | + | 24.9489i | −0.293332 | + | 0.855740i | ||||
\(851\) | − | 44.7005i | − | 1.53231i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.0193 | − | 16.0193i | −0.548490 | − | 0.548490i | 0.377514 | − | 0.926004i | \(-0.376779\pi\) |
−0.926004 | + | 0.377514i | \(0.876779\pi\) | |||||||
\(854\) | 5.48593 | 0.187725 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.18160 | −0.0745656 | ||||||||
\(857\) | 14.3582 | + | 14.3582i | 0.490467 | + | 0.490467i | 0.908453 | − | 0.417986i | \(-0.137264\pi\) |
−0.417986 | + | 0.908453i | \(0.637264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 23.5232i | − | 0.802602i | −0.915946 | − | 0.401301i | \(-0.868558\pi\) | ||
0.915946 | − | 0.401301i | \(-0.131442\pi\) | |||||||
\(860\) | 9.48504 | + | 1.58051i | 0.323437 | + | 0.0538950i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.8931 | + | 17.8931i | −0.609443 | + | 0.609443i | ||||
\(863\) | −34.2060 | + | 34.2060i | −1.16439 | + | 1.16439i | −0.180881 | + | 0.983505i | \(0.557895\pi\) |
−0.983505 | + | 0.180881i | \(0.942105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.4560 | + | 5.74146i | 1.17154 | + | 0.195216i | ||||
\(866\) | 8.49320 | 0.288611 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.28270 | − | 6.28270i | 0.213249 | − | 0.213249i | ||||
\(869\) | −13.3226 | −0.451938 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.77017 | 0.331050 | ||||||||
\(872\) | −13.0310 | + | 13.0310i | −0.441284 | + | 0.441284i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.7490 | + | 16.7617i | 0.634193 | + | 0.566974i | ||||
\(875\) | 5.47585 | − | 10.1353i | 0.185118 | − | 0.342637i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.2759 | + | 34.2759i | 1.15742 | + | 1.15742i | 0.985029 | + | 0.172387i | \(0.0551479\pi\) |
0.172387 | + | 0.985029i | \(0.444852\pi\) | |||||||
\(878\) | −27.1713 | − | 27.1713i | −0.916986 | − | 0.916986i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.24961 | − | 8.74883i | −0.210674 | − | 0.294923i | ||||
\(881\) | 16.2818 | 0.548548 | 0.274274 | − | 0.961652i | \(-0.411562\pi\) | ||||
0.274274 | + | 0.961652i | \(0.411562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.4556 | − | 16.4556i | −0.553774 | − | 0.553774i | 0.373754 | − | 0.927528i | \(-0.378070\pi\) |
−0.927528 | + | 0.373754i | \(0.878070\pi\) | |||||||
\(884\) | −3.96475 | −0.133349 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 39.2383i | − | 1.31824i | ||||||
\(887\) | 20.1627 | + | 20.1627i | 0.676997 | + | 0.676997i | 0.959320 | − | 0.282322i | \(-0.0911047\pi\) |
−0.282322 | + | 0.959320i | \(0.591105\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.6363 | 0.457345 | ||||||||
\(890\) | −0.399250 | + | 2.39600i | −0.0133829 | + | 0.0803140i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.04571 | + | 8.04571i | 0.269390 | + | 0.269390i | ||||
\(893\) | 0.313590 | + | 5.60363i | 0.0104939 | + | 0.187518i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.7505 | − | 34.6482i | −0.827318 | − | 1.15816i | ||||
\(896\) | 1.03038i | 0.0344226i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.9120 | − | 19.9120i | −0.664472 | − | 0.664472i | ||||
\(899\) | 4.26689i | 0.142309i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 26.3525i | − | 0.877929i | ||||||
\(902\) | −19.8068 | + | 19.8068i | −0.659493 | + | 0.659493i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.43754i | − | 0.247369i | ||||||
\(905\) | −3.24075 | + | 2.31499i | −0.107726 | + | 0.0769527i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.3346 | − | 36.3346i | −1.20647 | − | 1.20647i | −0.972162 | − | 0.234309i | \(-0.924717\pi\) |
−0.234309 | − | 0.972162i | \(-0.575283\pi\) | |||||||
\(908\) | 1.98330 | − | 1.98330i | 0.0658180 | − | 0.0658180i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.70823 | + | 0.284645i | 0.0566272 | + | 0.00943590i | ||||
\(911\) | − | 9.50181i | − | 0.314809i | −0.987534 | − | 0.157405i | \(-0.949687\pi\) | ||
0.987534 | − | 0.157405i | \(-0.0503127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.2027 | + | 17.2027i | 0.569326 | + | 0.569326i | ||||
\(914\) | −27.6584 | −0.914859 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.6443 | −0.649066 | ||||||||
\(917\) | 9.19968 | − | 9.19968i | 0.303800 | − | 0.303800i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.20583i | − | 0.105751i | −0.998601 | − | 0.0528753i | \(-0.983161\pi\) | ||
0.998601 | − | 0.0528753i | \(-0.0168386\pi\) | |||||||
\(920\) | −7.49905 | − | 10.4979i | −0.247236 | − | 0.346106i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.79932 | − | 6.79932i | −0.223924 | − | 0.223924i | ||||
\(923\) | −1.09527 | − | 1.09527i | −0.0360514 | − | 0.0360514i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.7939 | − | 17.0297i | 1.14402 | − | 0.559933i | ||||
\(926\) | 23.5799i | 0.774882i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.349890 | − | 0.349890i | −0.0114857 | − | 0.0114857i | ||||
\(929\) | − | 0.680198i | − | 0.0223166i | −0.999938 | − | 0.0111583i | \(-0.996448\pi\) | ||
0.999938 | − | 0.0111583i | \(-0.00355187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.2972 | + | 17.2519i | 0.632441 | + | 0.565407i | ||||
\(932\) | −4.73992 | + | 4.73992i | −0.155261 | + | 0.155261i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.2099 | 0.792171 | ||||||||
\(935\) | 55.9418 | + | 9.32168i | 1.82949 | + | 0.304852i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6037 | − | 20.6037i | 0.673093 | − | 0.673093i | −0.285335 | − | 0.958428i | \(-0.592105\pi\) |
0.958428 | + | 0.285335i | \(0.0921048\pi\) | |||||||
\(938\) | 9.47051 | + | 9.47051i | 0.309223 | + | 0.309223i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.473225 | − | 2.83994i | 0.0154349 | − | 0.0926286i | ||||
\(941\) | 16.5409i | 0.539220i | 0.962970 | + | 0.269610i | \(0.0868947\pi\) | ||||
−0.962970 | + | 0.269610i | \(0.913105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.7666 | + | 23.7666i | −0.773946 | + | 0.773946i | ||||
\(944\) | 12.1307 | 0.394820 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 20.6773i | − | 0.672278i | ||||||
\(947\) | −21.1699 | + | 21.1699i | −0.687929 | + | 0.687929i | −0.961774 | − | 0.273845i | \(-0.911704\pi\) |
0.273845 | + | 0.961774i | \(0.411704\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.52017 | −0.114270 | ||||||||
\(950\) | −5.90409 | + | 20.9796i | −0.191554 | + | 0.680667i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.84315 | − | 3.84315i | −0.124557 | − | 0.124557i | ||||
\(953\) | 28.1289 | − | 28.1289i | 0.911186 | − | 0.911186i | −0.0851800 | − | 0.996366i | \(-0.527147\pi\) |
0.996366 | + | 0.0851800i | \(0.0271465\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.3208 | + | 27.0471i | 0.625205 | + | 0.875225i | ||||
\(956\) | 21.1851 | 0.685176 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.0976 | + | 10.0976i | −0.326237 | + | 0.326237i | ||||
\(959\) | − | 0.551830i | − | 0.0178195i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −43.3582 | −1.39865 | ||||||||
\(962\) | 4.11777 | + | 4.11777i | 0.132762 | + | 0.132762i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.2784 | −0.524293 | ||||||||
\(965\) | −15.7408 | − | 2.62292i | −0.506715 | − | 0.0844349i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.96462 | + | 2.96462i | −0.0953359 | + | 0.0953359i | −0.753166 | − | 0.657830i | \(-0.771474\pi\) |
0.657830 | + | 0.753166i | \(0.271474\pi\) | |||||||
\(968\) | −8.57008 | + | 8.57008i | −0.275453 | + | 0.275453i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.24778 | − | 5.17736i | 0.232712 | − | 0.166235i | ||||
\(971\) | − | 4.90480i | − | 0.157403i | −0.996898 | − | 0.0787013i | \(-0.974923\pi\) | ||
0.996898 | − | 0.0787013i | \(-0.0250773\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6076 | + | 16.6076i | 0.532414 | + | 0.532414i | ||||
\(974\) | − | 19.3451i | − | 0.619856i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.32419 | 0.170423 | ||||||||
\(977\) | −11.6920 | − | 11.6920i | −0.374061 | − | 0.374061i | 0.494893 | − | 0.868954i | \(-0.335207\pi\) |
−0.868954 | + | 0.494893i | \(0.835207\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.22326 | 0.166936 | ||||||||
\(980\) | −7.71833 | − | 10.8049i | −0.246553 | − | 0.345149i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.67154 | − | 4.67154i | −0.149075 | − | 0.149075i | ||||
\(983\) | −24.4836 | + | 24.4836i | −0.780907 | + | 0.780907i | −0.979984 | − | 0.199077i | \(-0.936206\pi\) |
0.199077 | + | 0.979984i | \(0.436206\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.9001 | + | 3.98252i | 0.761521 | + | 0.126894i | ||||
\(986\) | 2.61007 | 0.0831215 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.27121 | + | 0.183064i | −0.104071 | + | 0.00582404i | ||||
\(989\) | − | 24.8112i | − | 0.788950i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.2681i | 1.78741i | 0.448650 | + | 0.893707i | \(0.351905\pi\) | ||||
−0.448650 | + | 0.893707i | \(0.648095\pi\) | |||||||
\(992\) | 6.09747 | − | 6.09747i | 0.193595 | − | 0.193595i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 2.12336i | − | 0.0673490i | ||||||
\(995\) | 38.0829 | − | 27.2040i | 1.20731 | − | 0.862425i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.01280 | + | 2.01280i | −0.0637459 | + | 0.0637459i | −0.738261 | − | 0.674515i | \(-0.764353\pi\) |
0.674515 | + | 0.738261i | \(0.264353\pi\) | |||||||
\(998\) | 25.2627 | − | 25.2627i | 0.799677 | − | 0.799677i | ||||
\(999\) | 0 | 0 |
(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 | 1710.2.p.c.1063.10 | 20 | ||
3.2 | odd | 2 | 570.2.m.b.493.1 | yes | 20 | ||
5.2 | odd | 4 | inner | 1710.2.p.c.37.5 | 20 | ||
15.2 | even | 4 | 570.2.m.b.37.6 | yes | 20 | ||
19.18 | odd | 2 | inner | 1710.2.p.c.1063.5 | 20 | ||
57.56 | even | 2 | 570.2.m.b.493.6 | yes | 20 | ||
95.37 | even | 4 | inner | 1710.2.p.c.37.10 | 20 | ||
285.227 | odd | 4 | 570.2.m.b.37.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.b.37.1 | ✓ | 20 | 285.227 | odd | 4 | ||
570.2.m.b.37.6 | yes | 20 | 15.2 | even | 4 | ||
570.2.m.b.493.1 | yes | 20 | 3.2 | odd | 2 | ||
570.2.m.b.493.6 | yes | 20 | 57.56 | even | 2 | ||
1710.2.p.c.37.5 | 20 | 5.2 | odd | 4 | inner | ||
1710.2.p.c.37.10 | 20 | 95.37 | even | 4 | inner | ||
1710.2.p.c.1063.5 | 20 | 19.18 | odd | 2 | inner | ||
1710.2.p.c.1063.10 | 20 | 1.1 | even | 1 | trivial |