Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,3,Mod(34,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.34");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.953680925261\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.3 | ||
Root | \(-1.58114 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.34 |
Dual form | 35.3.c.c.34.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000i | 1.50000i | 0.661438 | + | 0.750000i | \(0.269947\pi\) | ||||
−0.661438 | + | 0.750000i | \(0.730053\pi\) | |||||||
\(3\) | −3.16228 | −1.05409 | −0.527046 | − | 0.849837i | \(-0.676701\pi\) | ||||
−0.527046 | + | 0.849837i | \(0.676701\pi\) | |||||||
\(4\) | −5.00000 | −1.25000 | ||||||||
\(5\) | 1.58114 | + | 4.74342i | 0.316228 | + | 0.948683i | ||||
\(6\) | − | 9.48683i | − | 1.58114i | ||||||
\(7\) | 6.32456 | − | 3.00000i | 0.903508 | − | 0.428571i | ||||
\(8\) | − | 3.00000i | − | 0.375000i | ||||||
\(9\) | 1.00000 | 0.111111 | ||||||||
\(10\) | −14.2302 | + | 4.74342i | −1.42302 | + | 0.474342i | ||||
\(11\) | 14.0000 | 1.27273 | 0.636364 | − | 0.771389i | \(-0.280438\pi\) | ||||
0.636364 | + | 0.771389i | \(0.280438\pi\) | |||||||
\(12\) | 15.8114 | 1.31762 | ||||||||
\(13\) | 3.16228 | 0.243252 | 0.121626 | − | 0.992576i | \(-0.461189\pi\) | ||||
0.121626 | + | 0.992576i | \(0.461189\pi\) | |||||||
\(14\) | 9.00000 | + | 18.9737i | 0.642857 | + | 1.35526i | ||||
\(15\) | −5.00000 | − | 15.0000i | −0.333333 | − | 1.00000i | ||||
\(16\) | −11.0000 | −0.687500 | ||||||||
\(17\) | −6.32456 | −0.372033 | −0.186016 | − | 0.982547i | \(-0.559558\pi\) | ||||
−0.186016 | + | 0.982547i | \(0.559558\pi\) | |||||||
\(18\) | 3.00000i | 0.166667i | ||||||||
\(19\) | − | 28.4605i | − | 1.49792i | −0.662615 | − | 0.748960i | \(-0.730553\pi\) | ||
0.662615 | − | 0.748960i | \(-0.269447\pi\) | |||||||
\(20\) | −7.90569 | − | 23.7171i | −0.395285 | − | 1.18585i | ||||
\(21\) | −20.0000 | + | 9.48683i | −0.952381 | + | 0.451754i | ||||
\(22\) | 42.0000i | 1.90909i | ||||||||
\(23\) | − | 12.0000i | − | 0.521739i | −0.965374 | − | 0.260870i | \(-0.915991\pi\) | ||
0.965374 | − | 0.260870i | \(-0.0840093\pi\) | |||||||
\(24\) | 9.48683i | 0.395285i | ||||||||
\(25\) | −20.0000 | + | 15.0000i | −0.800000 | + | 0.600000i | ||||
\(26\) | 9.48683i | 0.364878i | ||||||||
\(27\) | 25.2982 | 0.936971 | ||||||||
\(28\) | −31.6228 | + | 15.0000i | −1.12938 | + | 0.535714i | ||||
\(29\) | 14.0000 | 0.482759 | 0.241379 | − | 0.970431i | \(-0.422400\pi\) | ||||
0.241379 | + | 0.970431i | \(0.422400\pi\) | |||||||
\(30\) | 45.0000 | − | 15.0000i | 1.50000 | − | 0.500000i | ||||
\(31\) | 37.9473i | 1.22411i | 0.790816 | + | 0.612054i | \(0.209656\pi\) | ||||
−0.790816 | + | 0.612054i | \(0.790344\pi\) | |||||||
\(32\) | − | 45.0000i | − | 1.40625i | ||||||
\(33\) | −44.2719 | −1.34157 | ||||||||
\(34\) | − | 18.9737i | − | 0.558049i | ||||||
\(35\) | 24.2302 | + | 25.2566i | 0.692293 | + | 0.721617i | ||||
\(36\) | −5.00000 | −0.138889 | ||||||||
\(37\) | 18.0000i | 0.486486i | 0.969965 | + | 0.243243i | \(0.0782113\pi\) | ||||
−0.969965 | + | 0.243243i | \(0.921789\pi\) | |||||||
\(38\) | 85.3815 | 2.24688 | ||||||||
\(39\) | −10.0000 | −0.256410 | ||||||||
\(40\) | 14.2302 | − | 4.74342i | 0.355756 | − | 0.118585i | ||||
\(41\) | − | 18.9737i | − | 0.462772i | −0.972862 | − | 0.231386i | \(-0.925674\pi\) | ||
0.972862 | − | 0.231386i | \(-0.0743261\pi\) | |||||||
\(42\) | −28.4605 | − | 60.0000i | −0.677631 | − | 1.42857i | ||||
\(43\) | − | 42.0000i | − | 0.976744i | −0.872635 | − | 0.488372i | \(-0.837591\pi\) | ||
0.872635 | − | 0.488372i | \(-0.162409\pi\) | |||||||
\(44\) | −70.0000 | −1.59091 | ||||||||
\(45\) | 1.58114 | + | 4.74342i | 0.0351364 | + | 0.105409i | ||||
\(46\) | 36.0000 | 0.782609 | ||||||||
\(47\) | −44.2719 | −0.941955 | −0.470978 | − | 0.882145i | \(-0.656099\pi\) | ||||
−0.470978 | + | 0.882145i | \(0.656099\pi\) | |||||||
\(48\) | 34.7851 | 0.724689 | ||||||||
\(49\) | 31.0000 | − | 37.9473i | 0.632653 | − | 0.774435i | ||||
\(50\) | −45.0000 | − | 60.0000i | −0.900000 | − | 1.20000i | ||||
\(51\) | 20.0000 | 0.392157 | ||||||||
\(52\) | −15.8114 | −0.304065 | ||||||||
\(53\) | 54.0000i | 1.01887i | 0.860510 | + | 0.509434i | \(0.170145\pi\) | ||||
−0.860510 | + | 0.509434i | \(0.829855\pi\) | |||||||
\(54\) | 75.8947i | 1.40546i | ||||||||
\(55\) | 22.1359 | + | 66.4078i | 0.402472 | + | 1.20742i | ||||
\(56\) | −9.00000 | − | 18.9737i | −0.160714 | − | 0.338815i | ||||
\(57\) | 90.0000i | 1.57895i | ||||||||
\(58\) | 42.0000i | 0.724138i | ||||||||
\(59\) | 9.48683i | 0.160794i | 0.996763 | + | 0.0803969i | \(0.0256188\pi\) | ||||
−0.996763 | + | 0.0803969i | \(0.974381\pi\) | |||||||
\(60\) | 25.0000 | + | 75.0000i | 0.416667 | + | 1.25000i | ||||
\(61\) | − | 66.4078i | − | 1.08865i | −0.838873 | − | 0.544326i | \(-0.816785\pi\) | ||
0.838873 | − | 0.544326i | \(-0.183215\pi\) | |||||||
\(62\) | −113.842 | −1.83616 | ||||||||
\(63\) | 6.32456 | − | 3.00000i | 0.100390 | − | 0.0476190i | ||||
\(64\) | 91.0000 | 1.42188 | ||||||||
\(65\) | 5.00000 | + | 15.0000i | 0.0769231 | + | 0.230769i | ||||
\(66\) | − | 132.816i | − | 2.01236i | ||||||
\(67\) | − | 102.000i | − | 1.52239i | −0.648524 | − | 0.761194i | \(-0.724613\pi\) | ||
0.648524 | − | 0.761194i | \(-0.275387\pi\) | |||||||
\(68\) | 31.6228 | 0.465041 | ||||||||
\(69\) | 37.9473i | 0.549961i | ||||||||
\(70\) | −75.7698 | + | 72.6907i | −1.08243 | + | 1.03844i | ||||
\(71\) | −16.0000 | −0.225352 | −0.112676 | − | 0.993632i | \(-0.535942\pi\) | ||||
−0.112676 | + | 0.993632i | \(0.535942\pi\) | |||||||
\(72\) | − | 3.00000i | − | 0.0416667i | ||||||
\(73\) | −63.2456 | −0.866377 | −0.433189 | − | 0.901303i | \(-0.642612\pi\) | ||||
−0.433189 | + | 0.901303i | \(0.642612\pi\) | |||||||
\(74\) | −54.0000 | −0.729730 | ||||||||
\(75\) | 63.2456 | − | 47.4342i | 0.843274 | − | 0.632456i | ||||
\(76\) | 142.302i | 1.87240i | ||||||||
\(77\) | 88.5438 | − | 42.0000i | 1.14992 | − | 0.545455i | ||||
\(78\) | − | 30.0000i | − | 0.384615i | ||||||
\(79\) | −76.0000 | −0.962025 | −0.481013 | − | 0.876714i | \(-0.659731\pi\) | ||||
−0.481013 | + | 0.876714i | \(0.659731\pi\) | |||||||
\(80\) | −17.3925 | − | 52.1776i | −0.217407 | − | 0.652220i | ||||
\(81\) | −89.0000 | −1.09877 | ||||||||
\(82\) | 56.9210 | 0.694159 | ||||||||
\(83\) | −72.7324 | −0.876294 | −0.438147 | − | 0.898903i | \(-0.644365\pi\) | ||||
−0.438147 | + | 0.898903i | \(0.644365\pi\) | |||||||
\(84\) | 100.000 | − | 47.4342i | 1.19048 | − | 0.564692i | ||||
\(85\) | −10.0000 | − | 30.0000i | −0.117647 | − | 0.352941i | ||||
\(86\) | 126.000 | 1.46512 | ||||||||
\(87\) | −44.2719 | −0.508872 | ||||||||
\(88\) | − | 42.0000i | − | 0.477273i | ||||||
\(89\) | 56.9210i | 0.639562i | 0.947492 | + | 0.319781i | \(0.103609\pi\) | ||||
−0.947492 | + | 0.319781i | \(0.896391\pi\) | |||||||
\(90\) | −14.2302 | + | 4.74342i | −0.158114 | + | 0.0527046i | ||||
\(91\) | 20.0000 | − | 9.48683i | 0.219780 | − | 0.104251i | ||||
\(92\) | 60.0000i | 0.652174i | ||||||||
\(93\) | − | 120.000i | − | 1.29032i | ||||||
\(94\) | − | 132.816i | − | 1.41293i | ||||||
\(95\) | 135.000 | − | 45.0000i | 1.42105 | − | 0.473684i | ||||
\(96\) | 142.302i | 1.48232i | ||||||||
\(97\) | 69.5701 | 0.717218 | 0.358609 | − | 0.933488i | \(-0.383251\pi\) | ||||
0.358609 | + | 0.933488i | \(0.383251\pi\) | |||||||
\(98\) | 113.842 | + | 93.0000i | 1.16165 | + | 0.948980i | ||||
\(99\) | 14.0000 | 0.141414 | ||||||||
\(100\) | 100.000 | − | 75.0000i | 1.00000 | − | 0.750000i | ||||
\(101\) | 104.355i | 1.03322i | 0.856221 | + | 0.516610i | \(0.172806\pi\) | ||||
−0.856221 | + | 0.516610i | \(0.827194\pi\) | |||||||
\(102\) | 60.0000i | 0.588235i | ||||||||
\(103\) | 88.5438 | 0.859648 | 0.429824 | − | 0.902913i | \(-0.358576\pi\) | ||||
0.429824 | + | 0.902913i | \(0.358576\pi\) | |||||||
\(104\) | − | 9.48683i | − | 0.0912195i | ||||||
\(105\) | −76.6228 | − | 79.8683i | −0.729741 | − | 0.760651i | ||||
\(106\) | −162.000 | −1.52830 | ||||||||
\(107\) | 54.0000i | 0.504673i | 0.967640 | + | 0.252336i | \(0.0811990\pi\) | ||||
−0.967640 | + | 0.252336i | \(0.918801\pi\) | |||||||
\(108\) | −126.491 | −1.17121 | ||||||||
\(109\) | 74.0000 | 0.678899 | 0.339450 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339450 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(110\) | −199.223 | + | 66.4078i | −1.81112 | + | 0.603708i | ||||
\(111\) | − | 56.9210i | − | 0.512802i | ||||||
\(112\) | −69.5701 | + | 33.0000i | −0.621162 | + | 0.294643i | ||||
\(113\) | 78.0000i | 0.690265i | 0.938554 | + | 0.345133i | \(0.112166\pi\) | ||||
−0.938554 | + | 0.345133i | \(0.887834\pi\) | |||||||
\(114\) | −270.000 | −2.36842 | ||||||||
\(115\) | 56.9210 | − | 18.9737i | 0.494965 | − | 0.164988i | ||||
\(116\) | −70.0000 | −0.603448 | ||||||||
\(117\) | 3.16228 | 0.0270280 | ||||||||
\(118\) | −28.4605 | −0.241191 | ||||||||
\(119\) | −40.0000 | + | 18.9737i | −0.336134 | + | 0.159443i | ||||
\(120\) | −45.0000 | + | 15.0000i | −0.375000 | + | 0.125000i | ||||
\(121\) | 75.0000 | 0.619835 | ||||||||
\(122\) | 199.223 | 1.63298 | ||||||||
\(123\) | 60.0000i | 0.487805i | ||||||||
\(124\) | − | 189.737i | − | 1.53013i | ||||||
\(125\) | −102.774 | − | 71.1512i | −0.822192 | − | 0.569210i | ||||
\(126\) | 9.00000 | + | 18.9737i | 0.0714286 | + | 0.150585i | ||||
\(127\) | − | 72.0000i | − | 0.566929i | −0.958983 | − | 0.283465i | \(-0.908516\pi\) | ||
0.958983 | − | 0.283465i | \(-0.0914838\pi\) | |||||||
\(128\) | 93.0000i | 0.726562i | ||||||||
\(129\) | 132.816i | 1.02958i | ||||||||
\(130\) | −45.0000 | + | 15.0000i | −0.346154 | + | 0.115385i | ||||
\(131\) | − | 47.4342i | − | 0.362093i | −0.983475 | − | 0.181046i | \(-0.942052\pi\) | ||
0.983475 | − | 0.181046i | \(-0.0579484\pi\) | |||||||
\(132\) | 221.359 | 1.67697 | ||||||||
\(133\) | −85.3815 | − | 180.000i | −0.641966 | − | 1.35338i | ||||
\(134\) | 306.000 | 2.28358 | ||||||||
\(135\) | 40.0000 | + | 120.000i | 0.296296 | + | 0.888889i | ||||
\(136\) | 18.9737i | 0.139512i | ||||||||
\(137\) | 84.0000i | 0.613139i | 0.951848 | + | 0.306569i | \(0.0991811\pi\) | ||||
−0.951848 | + | 0.306569i | \(0.900819\pi\) | |||||||
\(138\) | −113.842 | −0.824942 | ||||||||
\(139\) | 123.329i | 0.887258i | 0.896211 | + | 0.443629i | \(0.146309\pi\) | ||||
−0.896211 | + | 0.443629i | \(0.853691\pi\) | |||||||
\(140\) | −121.151 | − | 126.283i | −0.865366 | − | 0.902021i | ||||
\(141\) | 140.000 | 0.992908 | ||||||||
\(142\) | − | 48.0000i | − | 0.338028i | ||||||
\(143\) | 44.2719 | 0.309594 | ||||||||
\(144\) | −11.0000 | −0.0763889 | ||||||||
\(145\) | 22.1359 | + | 66.4078i | 0.152662 | + | 0.457985i | ||||
\(146\) | − | 189.737i | − | 1.29957i | ||||||
\(147\) | −98.0306 | + | 120.000i | −0.666875 | + | 0.816327i | ||||
\(148\) | − | 90.0000i | − | 0.608108i | ||||||
\(149\) | −46.0000 | −0.308725 | −0.154362 | − | 0.988014i | \(-0.549332\pi\) | ||||
−0.154362 | + | 0.988014i | \(0.549332\pi\) | |||||||
\(150\) | 142.302 | + | 189.737i | 0.948683 | + | 1.26491i | ||||
\(151\) | 14.0000 | 0.0927152 | 0.0463576 | − | 0.998925i | \(-0.485239\pi\) | ||||
0.0463576 | + | 0.998925i | \(0.485239\pi\) | |||||||
\(152\) | −85.3815 | −0.561720 | ||||||||
\(153\) | −6.32456 | −0.0413370 | ||||||||
\(154\) | 126.000 | + | 265.631i | 0.818182 | + | 1.72488i | ||||
\(155\) | −180.000 | + | 60.0000i | −1.16129 | + | 0.387097i | ||||
\(156\) | 50.0000 | 0.320513 | ||||||||
\(157\) | 117.004 | 0.745250 | 0.372625 | − | 0.927982i | \(-0.378458\pi\) | ||||
0.372625 | + | 0.927982i | \(0.378458\pi\) | |||||||
\(158\) | − | 228.000i | − | 1.44304i | ||||||
\(159\) | − | 170.763i | − | 1.07398i | ||||||
\(160\) | 213.454 | − | 71.1512i | 1.33409 | − | 0.444695i | ||||
\(161\) | −36.0000 | − | 75.8947i | −0.223602 | − | 0.471395i | ||||
\(162\) | − | 267.000i | − | 1.64815i | ||||||
\(163\) | 54.0000i | 0.331288i | 0.986186 | + | 0.165644i | \(0.0529703\pi\) | ||||
−0.986186 | + | 0.165644i | \(0.947030\pi\) | |||||||
\(164\) | 94.8683i | 0.578465i | ||||||||
\(165\) | −70.0000 | − | 210.000i | −0.424242 | − | 1.27273i | ||||
\(166\) | − | 218.197i | − | 1.31444i | ||||||
\(167\) | −139.140 | −0.833175 | −0.416587 | − | 0.909096i | \(-0.636774\pi\) | ||||
−0.416587 | + | 0.909096i | \(0.636774\pi\) | |||||||
\(168\) | 28.4605 | + | 60.0000i | 0.169408 | + | 0.357143i | ||||
\(169\) | −159.000 | −0.940828 | ||||||||
\(170\) | 90.0000 | − | 30.0000i | 0.529412 | − | 0.176471i | ||||
\(171\) | − | 28.4605i | − | 0.166436i | ||||||
\(172\) | 210.000i | 1.22093i | ||||||||
\(173\) | 211.873 | 1.22470 | 0.612349 | − | 0.790588i | \(-0.290225\pi\) | ||||
0.612349 | + | 0.790588i | \(0.290225\pi\) | |||||||
\(174\) | − | 132.816i | − | 0.763308i | ||||||
\(175\) | −81.4911 | + | 154.868i | −0.465663 | + | 0.884962i | ||||
\(176\) | −154.000 | −0.875000 | ||||||||
\(177\) | − | 30.0000i | − | 0.169492i | ||||||
\(178\) | −170.763 | −0.959343 | ||||||||
\(179\) | −178.000 | −0.994413 | −0.497207 | − | 0.867632i | \(-0.665641\pi\) | ||||
−0.497207 | + | 0.867632i | \(0.665641\pi\) | |||||||
\(180\) | −7.90569 | − | 23.7171i | −0.0439205 | − | 0.131762i | ||||
\(181\) | − | 28.4605i | − | 0.157240i | −0.996905 | − | 0.0786202i | \(-0.974949\pi\) | ||
0.996905 | − | 0.0786202i | \(-0.0250514\pi\) | |||||||
\(182\) | 28.4605 | + | 60.0000i | 0.156376 | + | 0.329670i | ||||
\(183\) | 210.000i | 1.14754i | ||||||||
\(184\) | −36.0000 | −0.195652 | ||||||||
\(185\) | −85.3815 | + | 28.4605i | −0.461522 | + | 0.153841i | ||||
\(186\) | 360.000 | 1.93548 | ||||||||
\(187\) | −88.5438 | −0.473496 | ||||||||
\(188\) | 221.359 | 1.17744 | ||||||||
\(189\) | 160.000 | − | 75.8947i | 0.846561 | − | 0.401559i | ||||
\(190\) | 135.000 | + | 405.000i | 0.710526 | + | 2.13158i | ||||
\(191\) | −148.000 | −0.774869 | −0.387435 | − | 0.921897i | \(-0.626639\pi\) | ||||
−0.387435 | + | 0.921897i | \(0.626639\pi\) | |||||||
\(192\) | −287.767 | −1.49879 | ||||||||
\(193\) | 258.000i | 1.33679i | 0.743808 | + | 0.668394i | \(0.233018\pi\) | ||||
−0.743808 | + | 0.668394i | \(0.766982\pi\) | |||||||
\(194\) | 208.710i | 1.07583i | ||||||||
\(195\) | −15.8114 | − | 47.4342i | −0.0810840 | − | 0.243252i | ||||
\(196\) | −155.000 | + | 189.737i | −0.790816 | + | 0.968044i | ||||
\(197\) | − | 342.000i | − | 1.73604i | −0.496529 | − | 0.868020i | \(-0.665392\pi\) | ||
0.496529 | − | 0.868020i | \(-0.334608\pi\) | |||||||
\(198\) | 42.0000i | 0.212121i | ||||||||
\(199\) | − | 56.9210i | − | 0.286035i | −0.989720 | − | 0.143018i | \(-0.954319\pi\) | ||
0.989720 | − | 0.143018i | \(-0.0456805\pi\) | |||||||
\(200\) | 45.0000 | + | 60.0000i | 0.225000 | + | 0.300000i | ||||
\(201\) | 322.552i | 1.60474i | ||||||||
\(202\) | −313.065 | −1.54983 | ||||||||
\(203\) | 88.5438 | − | 42.0000i | 0.436176 | − | 0.206897i | ||||
\(204\) | −100.000 | −0.490196 | ||||||||
\(205\) | 90.0000 | − | 30.0000i | 0.439024 | − | 0.146341i | ||||
\(206\) | 265.631i | 1.28947i | ||||||||
\(207\) | − | 12.0000i | − | 0.0579710i | ||||||
\(208\) | −34.7851 | −0.167236 | ||||||||
\(209\) | − | 398.447i | − | 1.90644i | ||||||
\(210\) | 239.605 | − | 229.868i | 1.14098 | − | 1.09461i | ||||
\(211\) | 242.000 | 1.14692 | 0.573460 | − | 0.819234i | \(-0.305601\pi\) | ||||
0.573460 | + | 0.819234i | \(0.305601\pi\) | |||||||
\(212\) | − | 270.000i | − | 1.27358i | ||||||
\(213\) | 50.5964 | 0.237542 | ||||||||
\(214\) | −162.000 | −0.757009 | ||||||||
\(215\) | 199.223 | − | 66.4078i | 0.926621 | − | 0.308874i | ||||
\(216\) | − | 75.8947i | − | 0.351364i | ||||||
\(217\) | 113.842 | + | 240.000i | 0.524617 | + | 1.10599i | ||||
\(218\) | 222.000i | 1.01835i | ||||||||
\(219\) | 200.000 | 0.913242 | ||||||||
\(220\) | −110.680 | − | 332.039i | −0.503090 | − | 1.50927i | ||||
\(221\) | −20.0000 | −0.0904977 | ||||||||
\(222\) | 170.763 | 0.769203 | ||||||||
\(223\) | −44.2719 | −0.198529 | −0.0992643 | − | 0.995061i | \(-0.531649\pi\) | ||||
−0.0992643 | + | 0.995061i | \(0.531649\pi\) | |||||||
\(224\) | −135.000 | − | 284.605i | −0.602679 | − | 1.27056i | ||||
\(225\) | −20.0000 | + | 15.0000i | −0.0888889 | + | 0.0666667i | ||||
\(226\) | −234.000 | −1.03540 | ||||||||
\(227\) | −357.337 | −1.57417 | −0.787087 | − | 0.616842i | \(-0.788412\pi\) | ||||
−0.787087 | + | 0.616842i | \(0.788412\pi\) | |||||||
\(228\) | − | 450.000i | − | 1.97368i | ||||||
\(229\) | 237.171i | 1.03568i | 0.855477 | + | 0.517840i | \(0.173264\pi\) | ||||
−0.855477 | + | 0.517840i | \(0.826736\pi\) | |||||||
\(230\) | 56.9210 | + | 170.763i | 0.247483 | + | 0.742448i | ||||
\(231\) | −280.000 | + | 132.816i | −1.21212 | + | 0.574960i | ||||
\(232\) | − | 42.0000i | − | 0.181034i | ||||||
\(233\) | − | 252.000i | − | 1.08155i | −0.841169 | − | 0.540773i | \(-0.818132\pi\) | ||
0.841169 | − | 0.540773i | \(-0.181868\pi\) | |||||||
\(234\) | 9.48683i | 0.0405420i | ||||||||
\(235\) | −70.0000 | − | 210.000i | −0.297872 | − | 0.893617i | ||||
\(236\) | − | 47.4342i | − | 0.200992i | ||||||
\(237\) | 240.333 | 1.01406 | ||||||||
\(238\) | −56.9210 | − | 120.000i | −0.239164 | − | 0.504202i | ||||
\(239\) | 242.000 | 1.01255 | 0.506276 | − | 0.862371i | \(-0.331022\pi\) | ||||
0.506276 | + | 0.862371i | \(0.331022\pi\) | |||||||
\(240\) | 55.0000 | + | 165.000i | 0.229167 | + | 0.687500i | ||||
\(241\) | − | 265.631i | − | 1.10220i | −0.834438 | − | 0.551102i | \(-0.814207\pi\) | ||
0.834438 | − | 0.551102i | \(-0.185793\pi\) | |||||||
\(242\) | 225.000i | 0.929752i | ||||||||
\(243\) | 53.7587 | 0.221229 | ||||||||
\(244\) | 332.039i | 1.36082i | ||||||||
\(245\) | 229.015 | + | 87.0459i | 0.934756 | + | 0.355289i | ||||
\(246\) | −180.000 | −0.731707 | ||||||||
\(247\) | − | 90.0000i | − | 0.364372i | ||||||
\(248\) | 113.842 | 0.459040 | ||||||||
\(249\) | 230.000 | 0.923695 | ||||||||
\(250\) | 213.454 | − | 308.322i | 0.853815 | − | 1.23329i | ||||
\(251\) | 483.828i | 1.92760i | 0.266620 | + | 0.963802i | \(0.414093\pi\) | ||||
−0.266620 | + | 0.963802i | \(0.585907\pi\) | |||||||
\(252\) | −31.6228 | + | 15.0000i | −0.125487 | + | 0.0595238i | ||||
\(253\) | − | 168.000i | − | 0.664032i | ||||||
\(254\) | 216.000 | 0.850394 | ||||||||
\(255\) | 31.6228 | + | 94.8683i | 0.124011 | + | 0.372033i | ||||
\(256\) | 85.0000 | 0.332031 | ||||||||
\(257\) | −82.2192 | −0.319919 | −0.159960 | − | 0.987124i | \(-0.551136\pi\) | ||||
−0.159960 | + | 0.987124i | \(0.551136\pi\) | |||||||
\(258\) | −398.447 | −1.54437 | ||||||||
\(259\) | 54.0000 | + | 113.842i | 0.208494 | + | 0.439544i | ||||
\(260\) | −25.0000 | − | 75.0000i | −0.0961538 | − | 0.288462i | ||||
\(261\) | 14.0000 | 0.0536398 | ||||||||
\(262\) | 142.302 | 0.543139 | ||||||||
\(263\) | 318.000i | 1.20913i | 0.796558 | + | 0.604563i | \(0.206652\pi\) | ||||
−0.796558 | + | 0.604563i | \(0.793348\pi\) | |||||||
\(264\) | 132.816i | 0.503090i | ||||||||
\(265\) | −256.144 | + | 85.3815i | −0.966583 | + | 0.322194i | ||||
\(266\) | 540.000 | − | 256.144i | 2.03008 | − | 0.962949i | ||||
\(267\) | − | 180.000i | − | 0.674157i | ||||||
\(268\) | 510.000i | 1.90299i | ||||||||
\(269\) | − | 256.144i | − | 0.952210i | −0.879388 | − | 0.476105i | \(-0.842048\pi\) | ||
0.879388 | − | 0.476105i | \(-0.157952\pi\) | |||||||
\(270\) | −360.000 | + | 120.000i | −1.33333 | + | 0.444444i | ||||
\(271\) | − | 341.526i | − | 1.26024i | −0.776496 | − | 0.630122i | \(-0.783005\pi\) | ||
0.776496 | − | 0.630122i | \(-0.216995\pi\) | |||||||
\(272\) | 69.5701 | 0.255772 | ||||||||
\(273\) | −63.2456 | + | 30.0000i | −0.231669 | + | 0.109890i | ||||
\(274\) | −252.000 | −0.919708 | ||||||||
\(275\) | −280.000 | + | 210.000i | −1.01818 | + | 0.763636i | ||||
\(276\) | − | 189.737i | − | 0.687452i | ||||||
\(277\) | − | 6.00000i | − | 0.0216606i | −0.999941 | − | 0.0108303i | \(-0.996553\pi\) | ||
0.999941 | − | 0.0108303i | \(-0.00344747\pi\) | |||||||
\(278\) | −369.986 | −1.33089 | ||||||||
\(279\) | 37.9473i | 0.136012i | ||||||||
\(280\) | 75.7698 | − | 72.6907i | 0.270606 | − | 0.259610i | ||||
\(281\) | 14.0000 | 0.0498221 | 0.0249110 | − | 0.999690i | \(-0.492070\pi\) | ||||
0.0249110 | + | 0.999690i | \(0.492070\pi\) | |||||||
\(282\) | 420.000i | 1.48936i | ||||||||
\(283\) | 515.451 | 1.82138 | 0.910691 | − | 0.413088i | \(-0.135550\pi\) | ||||
0.910691 | + | 0.413088i | \(0.135550\pi\) | |||||||
\(284\) | 80.0000 | 0.281690 | ||||||||
\(285\) | −426.907 | + | 142.302i | −1.49792 | + | 0.499307i | ||||
\(286\) | 132.816i | 0.464390i | ||||||||
\(287\) | −56.9210 | − | 120.000i | −0.198331 | − | 0.418118i | ||||
\(288\) | − | 45.0000i | − | 0.156250i | ||||||
\(289\) | −249.000 | −0.861592 | ||||||||
\(290\) | −199.223 | + | 66.4078i | −0.686978 | + | 0.228993i | ||||
\(291\) | −220.000 | −0.756014 | ||||||||
\(292\) | 316.228 | 1.08297 | ||||||||
\(293\) | 458.530 | 1.56495 | 0.782475 | − | 0.622682i | \(-0.213957\pi\) | ||||
0.782475 | + | 0.622682i | \(0.213957\pi\) | |||||||
\(294\) | −360.000 | − | 294.092i | −1.22449 | − | 1.00031i | ||||
\(295\) | −45.0000 | + | 15.0000i | −0.152542 | + | 0.0508475i | ||||
\(296\) | 54.0000 | 0.182432 | ||||||||
\(297\) | 354.175 | 1.19251 | ||||||||
\(298\) | − | 138.000i | − | 0.463087i | ||||||
\(299\) | − | 37.9473i | − | 0.126914i | ||||||
\(300\) | −316.228 | + | 237.171i | −1.05409 | + | 0.790569i | ||||
\(301\) | −126.000 | − | 265.631i | −0.418605 | − | 0.882496i | ||||
\(302\) | 42.0000i | 0.139073i | ||||||||
\(303\) | − | 330.000i | − | 1.08911i | ||||||
\(304\) | 313.065i | 1.02982i | ||||||||
\(305\) | 315.000 | − | 105.000i | 1.03279 | − | 0.344262i | ||||
\(306\) | − | 18.9737i | − | 0.0620054i | ||||||
\(307\) | −91.7061 | −0.298717 | −0.149358 | − | 0.988783i | \(-0.547721\pi\) | ||||
−0.149358 | + | 0.988783i | \(0.547721\pi\) | |||||||
\(308\) | −442.719 | + | 210.000i | −1.43740 | + | 0.681818i | ||||
\(309\) | −280.000 | −0.906149 | ||||||||
\(310\) | −180.000 | − | 540.000i | −0.580645 | − | 1.74194i | ||||
\(311\) | − | 360.500i | − | 1.15916i | −0.814914 | − | 0.579581i | \(-0.803216\pi\) | ||
0.814914 | − | 0.579581i | \(-0.196784\pi\) | |||||||
\(312\) | 30.0000i | 0.0961538i | ||||||||
\(313\) | −556.561 | −1.77815 | −0.889075 | − | 0.457762i | \(-0.848651\pi\) | ||||
−0.889075 | + | 0.457762i | \(0.848651\pi\) | |||||||
\(314\) | 351.013i | 1.11788i | ||||||||
\(315\) | 24.2302 | + | 25.2566i | 0.0769214 | + | 0.0801796i | ||||
\(316\) | 380.000 | 1.20253 | ||||||||
\(317\) | 318.000i | 1.00315i | 0.865113 | + | 0.501577i | \(0.167247\pi\) | ||||
−0.865113 | + | 0.501577i | \(0.832753\pi\) | |||||||
\(318\) | 512.289 | 1.61097 | ||||||||
\(319\) | 196.000 | 0.614420 | ||||||||
\(320\) | 143.884 | + | 431.651i | 0.449636 | + | 1.34891i | ||||
\(321\) | − | 170.763i | − | 0.531972i | ||||||
\(322\) | 227.684 | − | 108.000i | 0.707093 | − | 0.335404i | ||||
\(323\) | 180.000i | 0.557276i | ||||||||
\(324\) | 445.000 | 1.37346 | ||||||||
\(325\) | −63.2456 | + | 47.4342i | −0.194602 | + | 0.145951i | ||||
\(326\) | −162.000 | −0.496933 | ||||||||
\(327\) | −234.009 | −0.715622 | ||||||||
\(328\) | −56.9210 | −0.173540 | ||||||||
\(329\) | −280.000 | + | 132.816i | −0.851064 | + | 0.403695i | ||||
\(330\) | 630.000 | − | 210.000i | 1.90909 | − | 0.636364i | ||||
\(331\) | 374.000 | 1.12991 | 0.564955 | − | 0.825122i | \(-0.308894\pi\) | ||||
0.564955 | + | 0.825122i | \(0.308894\pi\) | |||||||
\(332\) | 363.662 | 1.09537 | ||||||||
\(333\) | 18.0000i | 0.0540541i | ||||||||
\(334\) | − | 417.421i | − | 1.24976i | ||||||
\(335\) | 483.828 | − | 161.276i | 1.44426 | − | 0.481421i | ||||
\(336\) | 220.000 | − | 104.355i | 0.654762 | − | 0.310581i | ||||
\(337\) | 654.000i | 1.94065i | 0.241799 | + | 0.970326i | \(0.422263\pi\) | ||||
−0.241799 | + | 0.970326i | \(0.577737\pi\) | |||||||
\(338\) | − | 477.000i | − | 1.41124i | ||||||
\(339\) | − | 246.658i | − | 0.727604i | ||||||
\(340\) | 50.0000 | + | 150.000i | 0.147059 | + | 0.441176i | ||||
\(341\) | 531.263i | 1.55795i | ||||||||
\(342\) | 85.3815 | 0.249653 | ||||||||
\(343\) | 82.2192 | − | 333.000i | 0.239706 | − | 0.970845i | ||||
\(344\) | −126.000 | −0.366279 | ||||||||
\(345\) | −180.000 | + | 60.0000i | −0.521739 | + | 0.173913i | ||||
\(346\) | 635.618i | 1.83705i | ||||||||
\(347\) | − | 282.000i | − | 0.812680i | −0.913722 | − | 0.406340i | \(-0.866805\pi\) | ||
0.913722 | − | 0.406340i | \(-0.133195\pi\) | |||||||
\(348\) | 221.359 | 0.636090 | ||||||||
\(349\) | 161.276i | 0.462109i | 0.972941 | + | 0.231055i | \(0.0742176\pi\) | ||||
−0.972941 | + | 0.231055i | \(0.925782\pi\) | |||||||
\(350\) | −464.605 | − | 244.473i | −1.32744 | − | 0.698495i | ||||
\(351\) | 80.0000 | 0.227920 | ||||||||
\(352\) | − | 630.000i | − | 1.78977i | ||||||
\(353\) | −613.482 | −1.73791 | −0.868954 | − | 0.494892i | \(-0.835208\pi\) | ||||
−0.868954 | + | 0.494892i | \(0.835208\pi\) | |||||||
\(354\) | 90.0000 | 0.254237 | ||||||||
\(355\) | −25.2982 | − | 75.8947i | −0.0712626 | − | 0.213788i | ||||
\(356\) | − | 284.605i | − | 0.799452i | ||||||
\(357\) | 126.491 | − | 60.0000i | 0.354317 | − | 0.168067i | ||||
\(358\) | − | 534.000i | − | 1.49162i | ||||||
\(359\) | 254.000 | 0.707521 | 0.353760 | − | 0.935336i | \(-0.384903\pi\) | ||||
0.353760 | + | 0.935336i | \(0.384903\pi\) | |||||||
\(360\) | 14.2302 | − | 4.74342i | 0.0395285 | − | 0.0131762i | ||||
\(361\) | −449.000 | −1.24377 | ||||||||
\(362\) | 85.3815 | 0.235860 | ||||||||
\(363\) | −237.171 | −0.653363 | ||||||||
\(364\) | −100.000 | + | 47.4342i | −0.274725 | + | 0.130314i | ||||
\(365\) | −100.000 | − | 300.000i | −0.273973 | − | 0.821918i | ||||
\(366\) | −630.000 | −1.72131 | ||||||||
\(367\) | 69.5701 | 0.189564 | 0.0947822 | − | 0.995498i | \(-0.469785\pi\) | ||||
0.0947822 | + | 0.995498i | \(0.469785\pi\) | |||||||
\(368\) | 132.000i | 0.358696i | ||||||||
\(369\) | − | 18.9737i | − | 0.0514191i | ||||||
\(370\) | −85.3815 | − | 256.144i | −0.230761 | − | 0.692282i | ||||
\(371\) | 162.000 | + | 341.526i | 0.436658 | + | 0.920555i | ||||
\(372\) | 600.000i | 1.61290i | ||||||||
\(373\) | 618.000i | 1.65684i | 0.560110 | + | 0.828418i | \(0.310759\pi\) | ||||
−0.560110 | + | 0.828418i | \(0.689241\pi\) | |||||||
\(374\) | − | 265.631i | − | 0.710244i | ||||||
\(375\) | 325.000 | + | 225.000i | 0.866667 | + | 0.600000i | ||||
\(376\) | 132.816i | 0.353233i | ||||||||
\(377\) | 44.2719 | 0.117432 | ||||||||
\(378\) | 227.684 | + | 480.000i | 0.602339 | + | 1.26984i | ||||
\(379\) | −466.000 | −1.22955 | −0.614776 | − | 0.788702i | \(-0.710753\pi\) | ||||
−0.614776 | + | 0.788702i | \(0.710753\pi\) | |||||||
\(380\) | −675.000 | + | 225.000i | −1.77632 | + | 0.592105i | ||||
\(381\) | 227.684i | 0.597596i | ||||||||
\(382\) | − | 444.000i | − | 1.16230i | ||||||
\(383\) | 31.6228 | 0.0825660 | 0.0412830 | − | 0.999147i | \(-0.486855\pi\) | ||||
0.0412830 | + | 0.999147i | \(0.486855\pi\) | |||||||
\(384\) | − | 294.092i | − | 0.765864i | ||||||
\(385\) | 339.223 | + | 353.592i | 0.881100 | + | 0.918421i | ||||
\(386\) | −774.000 | −2.00518 | ||||||||
\(387\) | − | 42.0000i | − | 0.108527i | ||||||
\(388\) | −347.851 | −0.896522 | ||||||||
\(389\) | 14.0000 | 0.0359897 | 0.0179949 | − | 0.999838i | \(-0.494272\pi\) | ||||
0.0179949 | + | 0.999838i | \(0.494272\pi\) | |||||||
\(390\) | 142.302 | − | 47.4342i | 0.364878 | − | 0.121626i | ||||
\(391\) | 75.8947i | 0.194104i | ||||||||
\(392\) | −113.842 | − | 93.0000i | −0.290413 | − | 0.237245i | ||||
\(393\) | 150.000i | 0.381679i | ||||||||
\(394\) | 1026.00 | 2.60406 | ||||||||
\(395\) | −120.167 | − | 360.500i | −0.304219 | − | 0.912657i | ||||
\(396\) | −70.0000 | −0.176768 | ||||||||
\(397\) | 79.0569 | 0.199136 | 0.0995679 | − | 0.995031i | \(-0.468254\pi\) | ||||
0.0995679 | + | 0.995031i | \(0.468254\pi\) | |||||||
\(398\) | 170.763 | 0.429053 | ||||||||
\(399\) | 270.000 | + | 569.210i | 0.676692 | + | 1.42659i | ||||
\(400\) | 220.000 | − | 165.000i | 0.550000 | − | 0.412500i | ||||
\(401\) | 404.000 | 1.00748 | 0.503741 | − | 0.863855i | \(-0.331957\pi\) | ||||
0.503741 | + | 0.863855i | \(0.331957\pi\) | |||||||
\(402\) | −967.657 | −2.40711 | ||||||||
\(403\) | 120.000i | 0.297767i | ||||||||
\(404\) | − | 521.776i | − | 1.29152i | ||||||
\(405\) | −140.721 | − | 422.164i | −0.347460 | − | 1.04238i | ||||
\(406\) | 126.000 | + | 265.631i | 0.310345 | + | 0.654264i | ||||
\(407\) | 252.000i | 0.619165i | ||||||||
\(408\) | − | 60.0000i | − | 0.147059i | ||||||
\(409\) | 208.710i | 0.510294i | 0.966902 | + | 0.255147i | \(0.0821239\pi\) | ||||
−0.966902 | + | 0.255147i | \(0.917876\pi\) | |||||||
\(410\) | 90.0000 | + | 270.000i | 0.219512 | + | 0.658537i | ||||
\(411\) | − | 265.631i | − | 0.646305i | ||||||
\(412\) | −442.719 | −1.07456 | ||||||||
\(413\) | 28.4605 | + | 60.0000i | 0.0689116 | + | 0.145278i | ||||
\(414\) | 36.0000 | 0.0869565 | ||||||||
\(415\) | −115.000 | − | 345.000i | −0.277108 | − | 0.831325i | ||||
\(416\) | − | 142.302i | − | 0.342073i | ||||||
\(417\) | − | 390.000i | − | 0.935252i | ||||||
\(418\) | 1195.34 | 2.85967 | ||||||||
\(419\) | 237.171i | 0.566040i | 0.959114 | + | 0.283020i | \(0.0913363\pi\) | ||||
−0.959114 | + | 0.283020i | \(0.908664\pi\) | |||||||
\(420\) | 383.114 | + | 399.342i | 0.912176 | + | 0.950813i | ||||
\(421\) | 554.000 | 1.31591 | 0.657957 | − | 0.753055i | \(-0.271421\pi\) | ||||
0.657957 | + | 0.753055i | \(0.271421\pi\) | |||||||
\(422\) | 726.000i | 1.72038i | ||||||||
\(423\) | −44.2719 | −0.104662 | ||||||||
\(424\) | 162.000 | 0.382075 | ||||||||
\(425\) | 126.491 | − | 94.8683i | 0.297626 | − | 0.223220i | ||||
\(426\) | 151.789i | 0.356313i | ||||||||
\(427\) | −199.223 | − | 420.000i | −0.466566 | − | 0.983607i | ||||
\(428\) | − | 270.000i | − | 0.630841i | ||||||
\(429\) | −140.000 | −0.326340 | ||||||||
\(430\) | 199.223 | + | 597.670i | 0.463310 | + | 1.38993i | ||||
\(431\) | −358.000 | −0.830626 | −0.415313 | − | 0.909678i | \(-0.636328\pi\) | ||||
−0.415313 | + | 0.909678i | \(0.636328\pi\) | |||||||
\(432\) | −278.280 | −0.644168 | ||||||||
\(433\) | 107.517 | 0.248308 | 0.124154 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124154 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(434\) | −720.000 | + | 341.526i | −1.65899 | + | 0.786926i | ||||
\(435\) | −70.0000 | − | 210.000i | −0.160920 | − | 0.482759i | ||||
\(436\) | −370.000 | −0.848624 | ||||||||
\(437\) | −341.526 | −0.781524 | ||||||||
\(438\) | 600.000i | 1.36986i | ||||||||
\(439\) | 18.9737i | 0.0432202i | 0.999766 | + | 0.0216101i | \(0.00687924\pi\) | ||||
−0.999766 | + | 0.0216101i | \(0.993121\pi\) | |||||||
\(440\) | 199.223 | − | 66.4078i | 0.452781 | − | 0.150927i | ||||
\(441\) | 31.0000 | − | 37.9473i | 0.0702948 | − | 0.0860484i | ||||
\(442\) | − | 60.0000i | − | 0.135747i | ||||||
\(443\) | − | 366.000i | − | 0.826185i | −0.910689 | − | 0.413093i | \(-0.864449\pi\) | ||
0.910689 | − | 0.413093i | \(-0.135551\pi\) | |||||||
\(444\) | 284.605i | 0.641002i | ||||||||
\(445\) | −270.000 | + | 90.0000i | −0.606742 | + | 0.202247i | ||||
\(446\) | − | 132.816i | − | 0.297793i | ||||||
\(447\) | 145.465 | 0.325425 | ||||||||
\(448\) | 575.535 | − | 273.000i | 1.28468 | − | 0.609375i | ||||
\(449\) | 74.0000 | 0.164811 | 0.0824053 | − | 0.996599i | \(-0.473740\pi\) | ||||
0.0824053 | + | 0.996599i | \(0.473740\pi\) | |||||||
\(450\) | −45.0000 | − | 60.0000i | −0.100000 | − | 0.133333i | ||||
\(451\) | − | 265.631i | − | 0.588983i | ||||||
\(452\) | − | 390.000i | − | 0.862832i | ||||||
\(453\) | −44.2719 | −0.0977304 | ||||||||
\(454\) | − | 1072.01i | − | 2.36126i | ||||||
\(455\) | 76.6228 | + | 79.8683i | 0.168402 | + | 0.175535i | ||||
\(456\) | 270.000 | 0.592105 | ||||||||
\(457\) | 138.000i | 0.301969i | 0.988536 | + | 0.150985i | \(0.0482444\pi\) | ||||
−0.988536 | + | 0.150985i | \(0.951756\pi\) | |||||||
\(458\) | −711.512 | −1.55352 | ||||||||
\(459\) | −160.000 | −0.348584 | ||||||||
\(460\) | −284.605 | + | 94.8683i | −0.618706 | + | 0.206235i | ||||
\(461\) | − | 692.539i | − | 1.50225i | −0.660158 | − | 0.751127i | \(-0.729511\pi\) | ||
0.660158 | − | 0.751127i | \(-0.270489\pi\) | |||||||
\(462\) | −398.447 | − | 840.000i | −0.862439 | − | 1.81818i | ||||
\(463\) | − | 606.000i | − | 1.30886i | −0.756125 | − | 0.654428i | \(-0.772910\pi\) | ||
0.756125 | − | 0.654428i | \(-0.227090\pi\) | |||||||
\(464\) | −154.000 | −0.331897 | ||||||||
\(465\) | 569.210 | − | 189.737i | 1.22411 | − | 0.408036i | ||||
\(466\) | 756.000 | 1.62232 | ||||||||
\(467\) | 534.425 | 1.14438 | 0.572189 | − | 0.820121i | \(-0.306094\pi\) | ||||
0.572189 | + | 0.820121i | \(0.306094\pi\) | |||||||
\(468\) | −15.8114 | −0.0337850 | ||||||||
\(469\) | −306.000 | − | 645.105i | −0.652452 | − | 1.37549i | ||||
\(470\) | 630.000 | − | 210.000i | 1.34043 | − | 0.446809i | ||||
\(471\) | −370.000 | −0.785563 | ||||||||
\(472\) | 28.4605 | 0.0602977 | ||||||||
\(473\) | − | 588.000i | − | 1.24313i | ||||||
\(474\) | 720.999i | 1.52110i | ||||||||
\(475\) | 426.907 | + | 569.210i | 0.898753 | + | 1.19834i | ||||
\(476\) | 200.000 | − | 94.8683i | 0.420168 | − | 0.199303i | ||||
\(477\) | 54.0000i | 0.113208i | ||||||||
\(478\) | 726.000i | 1.51883i | ||||||||
\(479\) | 531.263i | 1.10911i | 0.832148 | + | 0.554554i | \(0.187111\pi\) | ||||
−0.832148 | + | 0.554554i | \(0.812889\pi\) | |||||||
\(480\) | −675.000 | + | 225.000i | −1.40625 | + | 0.468750i | ||||
\(481\) | 56.9210i | 0.118339i | ||||||||
\(482\) | 796.894 | 1.65331 | ||||||||
\(483\) | 113.842 | + | 240.000i | 0.235698 | + | 0.496894i | ||||
\(484\) | −375.000 | −0.774793 | ||||||||
\(485\) | 110.000 | + | 330.000i | 0.226804 | + | 0.680412i | ||||
\(486\) | 161.276i | 0.331844i | ||||||||
\(487\) | 108.000i | 0.221766i | 0.993833 | + | 0.110883i | \(0.0353679\pi\) | ||||
−0.993833 | + | 0.110883i | \(0.964632\pi\) | |||||||
\(488\) | −199.223 | −0.408245 | ||||||||
\(489\) | − | 170.763i | − | 0.349209i | ||||||
\(490\) | −261.138 | + | 687.046i | −0.532934 | + | 1.40213i | ||||
\(491\) | 674.000 | 1.37271 | 0.686354 | − | 0.727267i | \(-0.259210\pi\) | ||||
0.686354 | + | 0.727267i | \(0.259210\pi\) | |||||||
\(492\) | − | 300.000i | − | 0.609756i | ||||||
\(493\) | −88.5438 | −0.179602 | ||||||||
\(494\) | 270.000 | 0.546559 | ||||||||
\(495\) | 22.1359 | + | 66.4078i | 0.0447191 | + | 0.134157i | ||||
\(496\) | − | 417.421i | − | 0.841574i | ||||||
\(497\) | −101.193 | + | 48.0000i | −0.203607 | + | 0.0965795i | ||||
\(498\) | 690.000i | 1.38554i | ||||||||
\(499\) | 62.0000 | 0.124248 | 0.0621242 | − | 0.998068i | \(-0.480212\pi\) | ||||
0.0621242 | + | 0.998068i | \(0.480212\pi\) | |||||||
\(500\) | 513.870 | + | 355.756i | 1.02774 | + | 0.711512i | ||||
\(501\) | 440.000 | 0.878244 | ||||||||
\(502\) | −1451.49 | −2.89141 | ||||||||
\(503\) | −632.456 | −1.25737 | −0.628683 | − | 0.777661i | \(-0.716406\pi\) | ||||
−0.628683 | + | 0.777661i | \(0.716406\pi\) | |||||||
\(504\) | −9.00000 | − | 18.9737i | −0.0178571 | − | 0.0376462i | ||||
\(505\) | −495.000 | + | 165.000i | −0.980198 | + | 0.326733i | ||||
\(506\) | 504.000 | 0.996047 | ||||||||
\(507\) | 502.802 | 0.991720 | ||||||||
\(508\) | 360.000i | 0.708661i | ||||||||
\(509\) | 635.618i | 1.24876i | 0.781122 | + | 0.624379i | \(0.214648\pi\) | ||||
−0.781122 | + | 0.624379i | \(0.785352\pi\) | |||||||
\(510\) | −284.605 | + | 94.8683i | −0.558049 | + | 0.186016i | ||||
\(511\) | −400.000 | + | 189.737i | −0.782779 | + | 0.371305i | ||||
\(512\) | 627.000i | 1.22461i | ||||||||
\(513\) | − | 720.000i | − | 1.40351i | ||||||
\(514\) | − | 246.658i | − | 0.479879i | ||||||
\(515\) | 140.000 | + | 420.000i | 0.271845 | + | 0.815534i | ||||
\(516\) | − | 664.078i | − | 1.28697i | ||||||
\(517\) | −619.806 | −1.19885 | ||||||||
\(518\) | −341.526 | + | 162.000i | −0.659317 | + | 0.312741i | ||||
\(519\) | −670.000 | −1.29094 | ||||||||
\(520\) | 45.0000 | − | 15.0000i | 0.0865385 | − | 0.0288462i | ||||
\(521\) | 398.447i | 0.764773i | 0.924002 | + | 0.382387i | \(0.124898\pi\) | ||||
−0.924002 | + | 0.382387i | \(0.875102\pi\) | |||||||
\(522\) | 42.0000i | 0.0804598i | ||||||||
\(523\) | −262.469 | −0.501853 | −0.250926 | − | 0.968006i | \(-0.580735\pi\) | ||||
−0.250926 | + | 0.968006i | \(0.580735\pi\) | |||||||
\(524\) | 237.171i | 0.452616i | ||||||||
\(525\) | 257.698 | − | 489.737i | 0.490852 | − | 0.932832i | ||||
\(526\) | −954.000 | −1.81369 | ||||||||
\(527\) | − | 240.000i | − | 0.455408i | ||||||
\(528\) | 486.991 | 0.922331 | ||||||||
\(529\) | 385.000 | 0.727788 | ||||||||
\(530\) | −256.144 | − | 768.433i | −0.483291 | − | 1.44987i | ||||
\(531\) | 9.48683i | 0.0178660i | ||||||||
\(532\) | 426.907 | + | 900.000i | 0.802458 | + | 1.69173i | ||||
\(533\) | − | 60.0000i | − | 0.112570i | ||||||
\(534\) | 540.000 | 1.01124 | ||||||||
\(535\) | −256.144 | + | 85.3815i | −0.478775 | + | 0.159592i | ||||
\(536\) | −306.000 | −0.570896 | ||||||||
\(537\) | 562.885 | 1.04820 | ||||||||
\(538\) | 768.433 | 1.42832 | ||||||||
\(539\) | 434.000 | − | 531.263i | 0.805195 | − | 0.985645i | ||||
\(540\) | −200.000 | − | 600.000i | −0.370370 | − | 1.11111i | ||||
\(541\) | −1006.00 | −1.85952 | −0.929760 | − | 0.368167i | \(-0.879985\pi\) | ||||
−0.929760 | + | 0.368167i | \(0.879985\pi\) | |||||||
\(542\) | 1024.58 | 1.89037 | ||||||||
\(543\) | 90.0000i | 0.165746i | ||||||||
\(544\) | 284.605i | 0.523171i | ||||||||
\(545\) | 117.004 | + | 351.013i | 0.214687 | + | 0.644060i | ||||
\(546\) | −90.0000 | − | 189.737i | −0.164835 | − | 0.347503i | ||||
\(547\) | 318.000i | 0.581353i | 0.956821 | + | 0.290676i | \(0.0938803\pi\) | ||||
−0.956821 | + | 0.290676i | \(0.906120\pi\) | |||||||
\(548\) | − | 420.000i | − | 0.766423i | ||||||
\(549\) | − | 66.4078i | − | 0.120961i | ||||||
\(550\) | −630.000 | − | 840.000i | −1.14545 | − | 1.52727i | ||||
\(551\) | − | 398.447i | − | 0.723134i | ||||||
\(552\) | 113.842 | 0.206235 | ||||||||
\(553\) | −480.666 | + | 228.000i | −0.869197 | + | 0.412297i | ||||
\(554\) | 18.0000 | 0.0324910 | ||||||||
\(555\) | 270.000 | − | 90.0000i | 0.486486 | − | 0.162162i | ||||
\(556\) | − | 616.644i | − | 1.10907i | ||||||
\(557\) | 18.0000i | 0.0323160i | 0.999869 | + | 0.0161580i | \(0.00514347\pi\) | ||||
−0.999869 | + | 0.0161580i | \(0.994857\pi\) | |||||||
\(558\) | −113.842 | −0.204018 | ||||||||
\(559\) | − | 132.816i | − | 0.237595i | ||||||
\(560\) | −266.533 | − | 277.822i | −0.475951 | − | 0.496111i | ||||
\(561\) | 280.000 | 0.499109 | ||||||||
\(562\) | 42.0000i | 0.0747331i | ||||||||
\(563\) | 60.0833 | 0.106720 | 0.0533599 | − | 0.998575i | \(-0.483007\pi\) | ||||
0.0533599 | + | 0.998575i | \(0.483007\pi\) | |||||||
\(564\) | −700.000 | −1.24113 | ||||||||
\(565\) | −369.986 | + | 123.329i | −0.654843 | + | 0.218281i | ||||
\(566\) | 1546.35i | 2.73207i | ||||||||
\(567\) | −562.885 | + | 267.000i | −0.992743 | + | 0.470899i | ||||
\(568\) | 48.0000i | 0.0845070i | ||||||||
\(569\) | 464.000 | 0.815466 | 0.407733 | − | 0.913101i | \(-0.366319\pi\) | ||||
0.407733 | + | 0.913101i | \(0.366319\pi\) | |||||||
\(570\) | −426.907 | − | 1280.72i | −0.748960 | − | 2.24688i | ||||
\(571\) | 314.000 | 0.549912 | 0.274956 | − | 0.961457i | \(-0.411337\pi\) | ||||
0.274956 | + | 0.961457i | \(0.411337\pi\) | |||||||
\(572\) | −221.359 | −0.386992 | ||||||||
\(573\) | 468.017 | 0.816784 | ||||||||
\(574\) | 360.000 | − | 170.763i | 0.627178 | − | 0.297497i | ||||
\(575\) | 180.000 | + | 240.000i | 0.313043 | + | 0.417391i | ||||
\(576\) | 91.0000 | 0.157986 | ||||||||
\(577\) | 676.727 | 1.17284 | 0.586419 | − | 0.810008i | \(-0.300537\pi\) | ||||
0.586419 | + | 0.810008i | \(0.300537\pi\) | |||||||
\(578\) | − | 747.000i | − | 1.29239i | ||||||
\(579\) | − | 815.868i | − | 1.40910i | ||||||
\(580\) | −110.680 | − | 332.039i | −0.190827 | − | 0.572481i | ||||
\(581\) | −460.000 | + | 218.197i | −0.791738 | + | 0.375554i | ||||
\(582\) | − | 660.000i | − | 1.13402i | ||||||
\(583\) | 756.000i | 1.29674i | ||||||||
\(584\) | 189.737i | 0.324892i | ||||||||
\(585\) | 5.00000 | + | 15.0000i | 0.00854701 | + | 0.0256410i | ||||
\(586\) | 1375.59i | 2.34742i | ||||||||
\(587\) | −585.021 | −0.996629 | −0.498315 | − | 0.866996i | \(-0.666048\pi\) | ||||
−0.498315 | + | 0.866996i | \(0.666048\pi\) | |||||||
\(588\) | 490.153 | − | 600.000i | 0.833594 | − | 1.02041i | ||||
\(589\) | 1080.00 | 1.83362 | ||||||||
\(590\) | −45.0000 | − | 135.000i | −0.0762712 | − | 0.228814i | ||||
\(591\) | 1081.50i | 1.82995i | ||||||||
\(592\) | − | 198.000i | − | 0.334459i | ||||||
\(593\) | 449.043 | 0.757240 | 0.378620 | − | 0.925552i | \(-0.376399\pi\) | ||||
0.378620 | + | 0.925552i | \(0.376399\pi\) | |||||||
\(594\) | 1062.53i | 1.78876i | ||||||||
\(595\) | −153.246 | − | 159.737i | −0.257556 | − | 0.268465i | ||||
\(596\) | 230.000 | 0.385906 | ||||||||
\(597\) | 180.000i | 0.301508i | ||||||||
\(598\) | 113.842 | 0.190371 | ||||||||
\(599\) | −136.000 | −0.227045 | −0.113523 | − | 0.993535i | \(-0.536213\pi\) | ||||
−0.113523 | + | 0.993535i | \(0.536213\pi\) | |||||||
\(600\) | −142.302 | − | 189.737i | −0.237171 | − | 0.316228i | ||||
\(601\) | 360.500i | 0.599833i | 0.953965 | + | 0.299917i | \(0.0969588\pi\) | ||||
−0.953965 | + | 0.299917i | \(0.903041\pi\) | |||||||
\(602\) | 796.894 | − | 378.000i | 1.32374 | − | 0.627907i | ||||
\(603\) | − | 102.000i | − | 0.169154i | ||||||
\(604\) | −70.0000 | −0.115894 | ||||||||
\(605\) | 118.585 | + | 355.756i | 0.196009 | + | 0.588027i | ||||
\(606\) | 990.000 | 1.63366 | ||||||||
\(607\) | 828.517 | 1.36494 | 0.682468 | − | 0.730915i | \(-0.260906\pi\) | ||||
0.682468 | + | 0.730915i | \(0.260906\pi\) | |||||||
\(608\) | −1280.72 | −2.10645 | ||||||||
\(609\) | −280.000 | + | 132.816i | −0.459770 | + | 0.218088i | ||||
\(610\) | 315.000 | + | 945.000i | 0.516393 | + | 1.54918i | ||||
\(611\) | −140.000 | −0.229133 | ||||||||
\(612\) | 31.6228 | 0.0516712 | ||||||||
\(613\) | 198.000i | 0.323002i | 0.986873 | + | 0.161501i | \(0.0516334\pi\) | ||||
−0.986873 | + | 0.161501i | \(0.948367\pi\) | |||||||
\(614\) | − | 275.118i | − | 0.448075i | ||||||
\(615\) | −284.605 | + | 94.8683i | −0.462772 | + | 0.154257i | ||||
\(616\) | −126.000 | − | 265.631i | −0.204545 | − | 0.431220i | ||||
\(617\) | − | 822.000i | − | 1.33225i | −0.745839 | − | 0.666126i | \(-0.767951\pi\) | ||
0.745839 | − | 0.666126i | \(-0.232049\pi\) | |||||||
\(618\) | − | 840.000i | − | 1.35922i | ||||||
\(619\) | − | 863.302i | − | 1.39467i | −0.716745 | − | 0.697336i | \(-0.754369\pi\) | ||
0.716745 | − | 0.697336i | \(-0.245631\pi\) | |||||||
\(620\) | 900.000 | − | 300.000i | 1.45161 | − | 0.483871i | ||||
\(621\) | − | 303.579i | − | 0.488855i | ||||||
\(622\) | 1081.50 | 1.73874 | ||||||||
\(623\) | 170.763 | + | 360.000i | 0.274098 | + | 0.577849i | ||||
\(624\) | 110.000 | 0.176282 | ||||||||
\(625\) | 175.000 | − | 600.000i | 0.280000 | − | 0.960000i | ||||
\(626\) | − | 1669.68i | − | 2.66722i | ||||||
\(627\) | 1260.00i | 2.00957i | ||||||||
\(628\) | −585.021 | −0.931563 | ||||||||
\(629\) | − | 113.842i | − | 0.180989i | ||||||
\(630\) | −75.7698 | + | 72.6907i | −0.120269 | + | 0.115382i | ||||
\(631\) | −16.0000 | −0.0253566 | −0.0126783 | − | 0.999920i | \(-0.504036\pi\) | ||||
−0.0126783 | + | 0.999920i | \(0.504036\pi\) | |||||||
\(632\) | 228.000i | 0.360759i | ||||||||
\(633\) | −765.271 | −1.20896 | ||||||||
\(634\) | −954.000 | −1.50473 | ||||||||
\(635\) | 341.526 | − | 113.842i | 0.537836 | − | 0.179279i | ||||
\(636\) | 853.815i | 1.34248i | ||||||||
\(637\) | 98.0306 | − | 120.000i | 0.153894 | − | 0.188383i | ||||
\(638\) | 588.000i | 0.921630i | ||||||||
\(639\) | −16.0000 | −0.0250391 | ||||||||
\(640\) | −441.138 | + | 147.046i | −0.689278 | + | 0.229759i | ||||
\(641\) | −1156.00 | −1.80343 | −0.901716 | − | 0.432329i | \(-0.857692\pi\) | ||||
−0.901716 | + | 0.432329i | \(0.857692\pi\) | |||||||
\(642\) | 512.289 | 0.797958 | ||||||||
\(643\) | −736.811 | −1.14590 | −0.572948 | − | 0.819592i | \(-0.694200\pi\) | ||||
−0.572948 | + | 0.819592i | \(0.694200\pi\) | |||||||
\(644\) | 180.000 | + | 379.473i | 0.279503 | + | 0.589244i | ||||
\(645\) | −630.000 | + | 210.000i | −0.976744 | + | 0.325581i | ||||
\(646\) | −540.000 | −0.835913 | ||||||||
\(647\) | −746.298 | −1.15347 | −0.576737 | − | 0.816930i | \(-0.695674\pi\) | ||||
−0.576737 | + | 0.816930i | \(0.695674\pi\) | |||||||
\(648\) | 267.000i | 0.412037i | ||||||||
\(649\) | 132.816i | 0.204647i | ||||||||
\(650\) | −142.302 | − | 189.737i | −0.218927 | − | 0.291903i | ||||
\(651\) | −360.000 | − | 758.947i | −0.552995 | − | 1.16582i | ||||
\(652\) | − | 270.000i | − | 0.414110i | ||||||
\(653\) | 834.000i | 1.27718i | 0.769546 | + | 0.638591i | \(0.220482\pi\) | ||||
−0.769546 | + | 0.638591i | \(0.779518\pi\) | |||||||
\(654\) | − | 702.026i | − | 1.07343i | ||||||
\(655\) | 225.000 | − | 75.0000i | 0.343511 | − | 0.114504i | ||||
\(656\) | 208.710i | 0.318156i | ||||||||
\(657\) | −63.2456 | −0.0962642 | ||||||||
\(658\) | −398.447 | − | 840.000i | −0.605543 | − | 1.27660i | ||||
\(659\) | −958.000 | −1.45372 | −0.726859 | − | 0.686787i | \(-0.759021\pi\) | ||||
−0.726859 | + | 0.686787i | \(0.759021\pi\) | |||||||
\(660\) | 350.000 | + | 1050.00i | 0.530303 | + | 1.59091i | ||||
\(661\) | − | 104.355i | − | 0.157875i | −0.996880 | − | 0.0789373i | \(-0.974847\pi\) | ||
0.996880 | − | 0.0789373i | \(-0.0251527\pi\) | |||||||
\(662\) | 1122.00i | 1.69486i | ||||||||
\(663\) | 63.2456 | 0.0953930 | ||||||||
\(664\) | 218.197i | 0.328610i | ||||||||
\(665\) | 718.815 | − | 689.605i | 1.08092 | − | 1.03700i | ||||
\(666\) | −54.0000 | −0.0810811 | ||||||||
\(667\) | − | 168.000i | − | 0.251874i | ||||||
\(668\) | 695.701 | 1.04147 | ||||||||
\(669\) | 140.000 | 0.209268 | ||||||||
\(670\) | 483.828 | + | 1451.49i | 0.722132 | + | 2.16640i | ||||
\(671\) | − | 929.710i | − | 1.38556i | ||||||
\(672\) | 426.907 | + | 900.000i | 0.635279 | + | 1.33929i | ||||
\(673\) | − | 456.000i | − | 0.677563i | −0.940865 | − | 0.338782i | \(-0.889985\pi\) | ||
0.940865 | − | 0.338782i | \(-0.110015\pi\) | |||||||
\(674\) | −1962.00 | −2.91098 | ||||||||
\(675\) | −505.964 | + | 379.473i | −0.749577 | + | 0.562183i | ||||
\(676\) | 795.000 | 1.17604 | ||||||||
\(677\) | −243.495 | −0.359668 | −0.179834 | − | 0.983697i | \(-0.557556\pi\) | ||||
−0.179834 | + | 0.983697i | \(0.557556\pi\) | |||||||
\(678\) | 739.973 | 1.09141 | ||||||||
\(679\) | 440.000 | − | 208.710i | 0.648012 | − | 0.307379i | ||||
\(680\) | −90.0000 | + | 30.0000i | −0.132353 | + | 0.0441176i | ||||
\(681\) | 1130.00 | 1.65932 | ||||||||
\(682\) | −1593.79 | −2.33693 | ||||||||
\(683\) | − | 882.000i | − | 1.29136i | −0.763607 | − | 0.645681i | \(-0.776574\pi\) | ||
0.763607 | − | 0.645681i | \(-0.223426\pi\) | |||||||
\(684\) | 142.302i | 0.208045i | ||||||||
\(685\) | −398.447 | + | 132.816i | −0.581674 | + | 0.193891i | ||||
\(686\) | 999.000 | + | 246.658i | 1.45627 | + | 0.359559i | ||||
\(687\) | − | 750.000i | − | 1.09170i | ||||||
\(688\) | 462.000i | 0.671512i | ||||||||
\(689\) | 170.763i | 0.247842i | ||||||||
\(690\) | −180.000 | − | 540.000i | −0.260870 | − | 0.782609i | ||||
\(691\) | 901.249i | 1.30427i | 0.758104 | + | 0.652134i | \(0.226126\pi\) | ||||
−0.758104 | + | 0.652134i | \(0.773874\pi\) | |||||||
\(692\) | −1059.36 | −1.53087 | ||||||||
\(693\) | 88.5438 | − | 42.0000i | 0.127769 | − | 0.0606061i | ||||
\(694\) | 846.000 | 1.21902 | ||||||||
\(695\) | −585.000 | + | 195.000i | −0.841727 | + | 0.280576i | ||||
\(696\) | 132.816i | 0.190827i | ||||||||
\(697\) | 120.000i | 0.172166i | ||||||||
\(698\) | −483.828 | −0.693164 | ||||||||
\(699\) | 796.894i | 1.14005i | ||||||||
\(700\) | 407.456 | − | 774.342i | 0.582079 | − | 1.10620i | ||||
\(701\) | −358.000 | −0.510699 | −0.255350 | − | 0.966849i | \(-0.582191\pi\) | ||||
−0.255350 | + | 0.966849i | \(0.582191\pi\) | |||||||
\(702\) | 240.000i | 0.341880i | ||||||||
\(703\) | 512.289 | 0.728718 | ||||||||
\(704\) | 1274.00 | 1.80966 | ||||||||
\(705\) | 221.359 | + | 664.078i | 0.313985 | + | 0.941955i | ||||
\(706\) | − | 1840.45i | − | 2.60686i | ||||||
\(707\) | 313.065 | + | 660.000i | 0.442808 | + | 0.933522i | ||||
\(708\) | 150.000i | 0.211864i | ||||||||
\(709\) | −238.000 | −0.335684 | −0.167842 | − | 0.985814i | \(-0.553680\pi\) | ||||
−0.167842 | + | 0.985814i | \(0.553680\pi\) | |||||||
\(710\) | 227.684 | − | 75.8947i | 0.320682 | − | 0.106894i | ||||
\(711\) | −76.0000 | −0.106892 | ||||||||
\(712\) | 170.763 | 0.239836 | ||||||||
\(713\) | 455.368 | 0.638665 | ||||||||
\(714\) | 180.000 | + | 379.473i | 0.252101 | + | 0.531475i | ||||
\(715\) | 70.0000 | + | 210.000i | 0.0979021 | + | 0.293706i | ||||
\(716\) | 890.000 | 1.24302 | ||||||||
\(717\) | −765.271 | −1.06732 | ||||||||
\(718\) | 762.000i | 1.06128i | ||||||||
\(719\) | − | 569.210i | − | 0.791669i | −0.918322 | − | 0.395834i | \(-0.870455\pi\) | ||
0.918322 | − | 0.395834i | \(-0.129545\pi\) | |||||||
\(720\) | −17.3925 | − | 52.1776i | −0.0241563 | − | 0.0724689i | ||||
\(721\) | 560.000 | − | 265.631i | 0.776699 | − | 0.368421i | ||||
\(722\) | − | 1347.00i | − | 1.86565i | ||||||
\(723\) | 840.000i | 1.16183i | ||||||||
\(724\) | 142.302i | 0.196550i | ||||||||
\(725\) | −280.000 | + | 210.000i | −0.386207 | + | 0.289655i | ||||
\(726\) | − | 711.512i | − | 0.980045i | ||||||
\(727\) | 1037.23 | 1.42672 | 0.713361 | − | 0.700797i | \(-0.247172\pi\) | ||||
0.713361 | + | 0.700797i | \(0.247172\pi\) | |||||||
\(728\) | −28.4605 | − | 60.0000i | −0.0390941 | − | 0.0824176i | ||||
\(729\) | 631.000 | 0.865569 | ||||||||
\(730\) | 900.000 | − | 300.000i | 1.23288 | − | 0.410959i | ||||
\(731\) | 265.631i | 0.363381i | ||||||||
\(732\) | − | 1050.00i | − | 1.43443i | ||||||
\(733\) | 629.293 | 0.858517 | 0.429259 | − | 0.903182i | \(-0.358775\pi\) | ||||
0.429259 | + | 0.903182i | \(0.358775\pi\) | |||||||
\(734\) | 208.710i | 0.284346i | ||||||||
\(735\) | −724.210 | − | 275.263i | −0.985320 | − | 0.374508i | ||||
\(736\) | −540.000 | −0.733696 | ||||||||
\(737\) | − | 1428.00i | − | 1.93758i | ||||||
\(738\) | 56.9210 | 0.0771287 | ||||||||
\(739\) | −466.000 | −0.630582 | −0.315291 | − | 0.948995i | \(-0.602102\pi\) | ||||
−0.315291 | + | 0.948995i | \(0.602102\pi\) | |||||||
\(740\) | 426.907 | − | 142.302i | 0.576902 | − | 0.192301i | ||||
\(741\) | 284.605i | 0.384082i | ||||||||
\(742\) | −1024.58 | + | 486.000i | −1.38083 | + | 0.654987i | ||||
\(743\) | 924.000i | 1.24361i | 0.783173 | + | 0.621803i | \(0.213600\pi\) | ||||
−0.783173 | + | 0.621803i | \(0.786400\pi\) | |||||||
\(744\) | −360.000 | −0.483871 | ||||||||
\(745\) | −72.7324 | − | 218.197i | −0.0976274 | − | 0.292882i | ||||
\(746\) | −1854.00 | −2.48525 | ||||||||
\(747\) | −72.7324 | −0.0973660 | ||||||||
\(748\) | 442.719 | 0.591870 | ||||||||
\(749\) | 162.000 | + | 341.526i | 0.216288 | + | 0.455976i | ||||
\(750\) | −675.000 | + | 975.000i | −0.900000 | + | 1.30000i | ||||
\(751\) | 1142.00 | 1.52064 | 0.760320 | − | 0.649549i | \(-0.225042\pi\) | ||||
0.760320 | + | 0.649549i | \(0.225042\pi\) | |||||||
\(752\) | 486.991 | 0.647594 | ||||||||
\(753\) | − | 1530.00i | − | 2.03187i | ||||||
\(754\) | 132.816i | 0.176148i | ||||||||
\(755\) | 22.1359 | + | 66.4078i | 0.0293191 | + | 0.0879574i | ||||
\(756\) | −800.000 | + | 379.473i | −1.05820 | + | 0.501949i | ||||
\(757\) | − | 162.000i | − | 0.214003i | −0.994259 | − | 0.107001i | \(-0.965875\pi\) | ||
0.994259 | − | 0.107001i | \(-0.0341249\pi\) | |||||||
\(758\) | − | 1398.00i | − | 1.84433i | ||||||
\(759\) | 531.263i | 0.699951i | ||||||||
\(760\) | −135.000 | − | 405.000i | −0.177632 | − | 0.532895i | ||||
\(761\) | − | 929.710i | − | 1.22169i | −0.791748 | − | 0.610847i | \(-0.790829\pi\) | ||
0.791748 | − | 0.610847i | \(-0.209171\pi\) | |||||||
\(762\) | −683.052 | −0.896394 | ||||||||
\(763\) | 468.017 | − | 222.000i | 0.613391 | − | 0.290957i | ||||
\(764\) | 740.000 | 0.968586 | ||||||||
\(765\) | −10.0000 | − | 30.0000i | −0.0130719 | − | 0.0392157i | ||||
\(766\) | 94.8683i | 0.123849i | ||||||||
\(767\) | 30.0000i | 0.0391134i | ||||||||
\(768\) | −268.794 | −0.349992 | ||||||||
\(769\) | 151.789i | 0.197385i | 0.995118 | + | 0.0986927i | \(0.0314661\pi\) | ||||
−0.995118 | + | 0.0986927i | \(0.968534\pi\) | |||||||
\(770\) | −1060.78 | + | 1017.67i | −1.37763 | + | 1.32165i | ||||
\(771\) | 260.000 | 0.337224 | ||||||||
\(772\) | − | 1290.00i | − | 1.67098i | ||||||
\(773\) | 1274.40 | 1.64864 | 0.824319 | − | 0.566125i | \(-0.191558\pi\) | ||||
0.824319 | + | 0.566125i | \(0.191558\pi\) | |||||||
\(774\) | 126.000 | 0.162791 | ||||||||
\(775\) | −569.210 | − | 758.947i | −0.734464 | − | 0.979286i | ||||
\(776\) | − | 208.710i | − | 0.268957i | ||||||
\(777\) | −170.763 | − | 360.000i | −0.219772 | − | 0.463320i | ||||
\(778\) | 42.0000i | 0.0539846i | ||||||||
\(779\) | −540.000 | −0.693196 | ||||||||
\(780\) | 79.0569 | + | 237.171i | 0.101355 | + | 0.304065i | ||||
\(781\) | −224.000 | −0.286812 | ||||||||
\(782\) | −227.684 | −0.291156 | ||||||||
\(783\) | 354.175 | 0.452331 | ||||||||
\(784\) | −341.000 | + | 417.421i | −0.434949 | + | 0.532424i | ||||
\(785\) | 185.000 | + | 555.000i | 0.235669 | + | 0.707006i | ||||
\(786\) | −450.000 | −0.572519 | ||||||||
\(787\) | 230.846 | 0.293324 | 0.146662 | − | 0.989187i | \(-0.453147\pi\) | ||||
0.146662 | + | 0.989187i | \(0.453147\pi\) | |||||||
\(788\) | 1710.00i | 2.17005i | ||||||||
\(789\) | − | 1005.60i | − | 1.27453i | ||||||
\(790\) | 1081.50 | − | 360.500i | 1.36899 | − | 0.456329i | ||||
\(791\) | 234.000 | + | 493.315i | 0.295828 | + | 0.623660i | ||||
\(792\) | − | 42.0000i | − | 0.0530303i | ||||||
\(793\) | − | 210.000i | − | 0.264817i | ||||||
\(794\) | 237.171i | 0.298704i | ||||||||
\(795\) | 810.000 | − | 270.000i | 1.01887 | − | 0.339623i | ||||
\(796\) | 284.605i | 0.357544i | ||||||||
\(797\) | −1192.18 | −1.49583 | −0.747916 | − | 0.663793i | \(-0.768946\pi\) | ||||
−0.747916 | + | 0.663793i | \(0.768946\pi\) | |||||||
\(798\) | −1707.63 | + | 810.000i | −2.13989 | + | 1.01504i | ||||
\(799\) | 280.000 | 0.350438 | ||||||||
\(800\) | 675.000 | + | 900.000i | 0.843750 | + | 1.12500i | ||||
\(801\) | 56.9210i | 0.0710624i | ||||||||
\(802\) | 1212.00i | 1.51122i | ||||||||
\(803\) | −885.438 | −1.10266 | ||||||||
\(804\) | − | 1612.76i | − | 2.00592i | ||||||
\(805\) | 303.079 | − | 290.763i | 0.376496 | − | 0.361196i | ||||
\(806\) | −360.000 | −0.446650 | ||||||||
\(807\) | 810.000i | 1.00372i | ||||||||
\(808\) | 313.065 | 0.387457 | ||||||||
\(809\) | 1424.00 | 1.76020 | 0.880099 | − | 0.474790i | \(-0.157476\pi\) | ||||
0.880099 | + | 0.474790i | \(0.157476\pi\) | |||||||
\(810\) | 1266.49 | − | 422.164i | 1.56357 | − | 0.521190i | ||||
\(811\) | 1109.96i | 1.36863i | 0.729186 | + | 0.684315i | \(0.239899\pi\) | ||||
−0.729186 | + | 0.684315i | \(0.760101\pi\) | |||||||
\(812\) | −442.719 | + | 210.000i | −0.545220 | + | 0.258621i | ||||
\(813\) | 1080.00i | 1.32841i | ||||||||
\(814\) | −756.000 | −0.928747 | ||||||||
\(815\) | −256.144 | + | 85.3815i | −0.314288 | + | 0.104763i | ||||
\(816\) | −220.000 | −0.269608 | ||||||||
\(817\) | −1195.34 | −1.46309 | ||||||||
\(818\) | −626.131 | −0.765441 | ||||||||
\(819\) | 20.0000 | − | 9.48683i | 0.0244200 | − | 0.0115834i | ||||
\(820\) | −450.000 | + | 150.000i | −0.548780 | + | 0.182927i | ||||
\(821\) | 662.000 | 0.806334 | 0.403167 | − | 0.915126i | \(-0.367909\pi\) | ||||
0.403167 | + | 0.915126i | \(0.367909\pi\) | |||||||
\(822\) | 796.894 | 0.969457 | ||||||||
\(823\) | − | 1182.00i | − | 1.43621i | −0.695935 | − | 0.718104i | \(-0.745010\pi\) | ||
0.695935 | − | 0.718104i | \(-0.254990\pi\) | |||||||
\(824\) | − | 265.631i | − | 0.322368i | ||||||
\(825\) | 885.438 | − | 664.078i | 1.07326 | − | 0.804943i | ||||
\(826\) | −180.000 | + | 85.3815i | −0.217918 | + | 0.103367i | ||||
\(827\) | 18.0000i | 0.0217654i | 0.999941 | + | 0.0108827i | \(0.00346414\pi\) | ||||
−0.999941 | + | 0.0108827i | \(0.996536\pi\) | |||||||
\(828\) | 60.0000i | 0.0724638i | ||||||||
\(829\) | 1166.88i | 1.40758i | 0.710410 | + | 0.703788i | \(0.248509\pi\) | ||||
−0.710410 | + | 0.703788i | \(0.751491\pi\) | |||||||
\(830\) | 1035.00 | − | 345.000i | 1.24699 | − | 0.415663i | ||||
\(831\) | 18.9737i | 0.0228323i | ||||||||
\(832\) | 287.767 | 0.345874 | ||||||||
\(833\) | −196.061 | + | 240.000i | −0.235368 | + | 0.288115i | ||||
\(834\) | 1170.00 | 1.40288 | ||||||||
\(835\) | −220.000 | − | 660.000i | −0.263473 | − | 0.790419i | ||||
\(836\) | 1992.23i | 2.38306i | ||||||||
\(837\) | 960.000i | 1.14695i | ||||||||
\(838\) | −711.512 | −0.849060 | ||||||||
\(839\) | − | 1119.45i | − | 1.33426i | −0.744940 | − | 0.667131i | \(-0.767522\pi\) | ||
0.744940 | − | 0.667131i | \(-0.232478\pi\) | |||||||
\(840\) | −239.605 | + | 229.868i | −0.285244 | + | 0.273653i | ||||
\(841\) | −645.000 | −0.766944 | ||||||||
\(842\) | 1662.00i | 1.97387i | ||||||||
\(843\) | −44.2719 | −0.0525171 | ||||||||
\(844\) | −1210.00 | −1.43365 | ||||||||
\(845\) | −251.401 | − | 754.203i | −0.297516 | − | 0.892548i | ||||
\(846\) | − | 132.816i | − | 0.156993i | ||||||
\(847\) | 474.342 | − | 225.000i | 0.560026 | − | 0.265643i | ||||
\(848\) | − | 594.000i | − | 0.700472i | ||||||
\(849\) | −1630.00 | −1.91991 | ||||||||
\(850\) | 284.605 | + | 379.473i | 0.334829 | + | 0.446439i | ||||
\(851\) | 216.000 | 0.253819 | ||||||||
\(852\) | −252.982 | −0.296927 | ||||||||
\(853\) | 1407.21 | 1.64972 | 0.824861 | − | 0.565335i | \(-0.191253\pi\) | ||||
0.824861 | + | 0.565335i | \(0.191253\pi\) | |||||||
\(854\) | 1260.00 | − | 597.670i | 1.47541 | − | 0.699848i | ||||
\(855\) | 135.000 | − | 45.0000i | 0.157895 | − | 0.0526316i | ||||
\(856\) | 162.000 | 0.189252 | ||||||||
\(857\) | 126.491 | 0.147598 | 0.0737988 | − | 0.997273i | \(-0.476488\pi\) | ||||
0.0737988 | + | 0.997273i | \(0.476488\pi\) | |||||||
\(858\) | − | 420.000i | − | 0.489510i | ||||||
\(859\) | 1546.35i | 1.80018i | 0.435705 | + | 0.900090i | \(0.356499\pi\) | ||||
−0.435705 | + | 0.900090i | \(0.643501\pi\) | |||||||
\(860\) | −996.117 | + | 332.039i | −1.15828 | + | 0.386092i | ||||
\(861\) | 180.000 | + | 379.473i | 0.209059 | + | 0.440736i | ||||
\(862\) | − | 1074.00i | − | 1.24594i | ||||||
\(863\) | − | 162.000i | − | 0.187717i | −0.995586 | − | 0.0938586i | \(-0.970080\pi\) | ||
0.995586 | − | 0.0938586i | \(-0.0299202\pi\) | |||||||
\(864\) | − | 1138.42i | − | 1.31762i | ||||||
\(865\) | 335.000 | + | 1005.00i | 0.387283 | + | 1.16185i | ||||
\(866\) | 322.552i | 0.372462i | ||||||||
\(867\) | 787.407 | 0.908197 | ||||||||
\(868\) | −569.210 | − | 1200.00i | −0.655772 | − | 1.38249i | ||||
\(869\) | −1064.00 | −1.22440 | ||||||||
\(870\) | 630.000 | − | 210.000i | 0.724138 | − | 0.241379i | ||||
\(871\) | − | 322.552i | − | 0.370324i | ||||||
\(872\) | − | 222.000i | − | 0.254587i | ||||||
\(873\) | 69.5701 | 0.0796908 | ||||||||
\(874\) | − | 1024.58i | − | 1.17229i | ||||||
\(875\) | −863.454 | − | 141.678i | −0.986804 | − | 0.161918i | ||||
\(876\) | −1000.00 | −1.14155 | ||||||||
\(877\) | − | 426.000i | − | 0.485747i | −0.970058 | − | 0.242873i | \(-0.921910\pi\) | ||
0.970058 | − | 0.242873i | \(-0.0780900\pi\) | |||||||
\(878\) | −56.9210 | −0.0648303 | ||||||||
\(879\) | −1450.00 | −1.64960 | ||||||||
\(880\) | −243.495 | − | 730.486i | −0.276699 | − | 0.830098i | ||||
\(881\) | 455.368i | 0.516876i | 0.966028 | + | 0.258438i | \(0.0832078\pi\) | ||||
−0.966028 | + | 0.258438i | \(0.916792\pi\) | |||||||
\(882\) | 113.842 | + | 93.0000i | 0.129073 | + | 0.105442i | ||||
\(883\) | − | 342.000i | − | 0.387316i | −0.981069 | − | 0.193658i | \(-0.937965\pi\) | ||
0.981069 | − | 0.193658i | \(-0.0620352\pi\) | |||||||
\(884\) | 100.000 | 0.113122 | ||||||||
\(885\) | 142.302 | − | 47.4342i | 0.160794 | − | 0.0535979i | ||||
\(886\) | 1098.00 | 1.23928 | ||||||||
\(887\) | −139.140 | −0.156866 | −0.0784330 | − | 0.996919i | \(-0.524992\pi\) | ||||
−0.0784330 | + | 0.996919i | \(0.524992\pi\) | |||||||
\(888\) | −170.763 | −0.192301 | ||||||||
\(889\) | −216.000 | − | 455.368i | −0.242970 | − | 0.512225i | ||||
\(890\) | −270.000 | − | 810.000i | −0.303371 | − | 0.910112i | ||||
\(891\) | −1246.00 | −1.39843 | ||||||||
\(892\) | 221.359 | 0.248161 | ||||||||
\(893\) | 1260.00i | 1.41097i | ||||||||
\(894\) | 436.394i | 0.488137i | ||||||||
\(895\) | −281.443 | − | 844.328i | −0.314461 | − | 0.943383i | ||||
\(896\) | 279.000 | + | 588.184i | 0.311384 | + | 0.656455i | ||||
\(897\) | 120.000i | 0.133779i | ||||||||
\(898\) | 222.000i | 0.247216i | ||||||||
\(899\) | 531.263i | 0.590948i | ||||||||
\(900\) | 100.000 | − | 75.0000i | 0.111111 | − | 0.0833333i | ||||
\(901\) | − | 341.526i | − | 0.379052i | ||||||
\(902\) | 796.894 | 0.883474 | ||||||||
\(903\) | 398.447 | + | 840.000i | 0.441248 | + | 0.930233i | ||||
\(904\) | 234.000 | 0.258850 | ||||||||
\(905\) | 135.000 | − | 45.0000i | 0.149171 | − | 0.0497238i | ||||
\(906\) | − | 132.816i | − | 0.146596i | ||||||
\(907\) | − | 1446.00i | − | 1.59427i | −0.603803 | − | 0.797133i | \(-0.706349\pi\) | ||
0.603803 | − | 0.797133i | \(-0.293651\pi\) | |||||||
\(908\) | 1786.69 | 1.96772 | ||||||||
\(909\) | 104.355i | 0.114802i | ||||||||
\(910\) | −239.605 | + | 229.868i | −0.263302 | + | 0.252603i | ||||
\(911\) | 374.000 | 0.410538 | 0.205269 | − | 0.978706i | \(-0.434193\pi\) | ||||
0.205269 | + | 0.978706i | \(0.434193\pi\) | |||||||
\(912\) | − | 990.000i | − | 1.08553i | ||||||
\(913\) | −1018.25 | −1.11528 | ||||||||
\(914\) | −414.000 | −0.452954 | ||||||||
\(915\) | −996.117 | + | 332.039i | −1.08865 | + | 0.362884i | ||||
\(916\) | − | 1185.85i | − | 1.29460i | ||||||
\(917\) | −142.302 | − | 300.000i | −0.155183 | − | 0.327154i | ||||
\(918\) | − | 480.000i | − | 0.522876i | ||||||
\(919\) | 704.000 | 0.766050 | 0.383025 | − | 0.923738i | \(-0.374882\pi\) | ||||
0.383025 | + | 0.923738i | \(0.374882\pi\) | |||||||
\(920\) | −56.9210 | − | 170.763i | −0.0618706 | − | 0.185612i | ||||
\(921\) | 290.000 | 0.314875 | ||||||||
\(922\) | 2077.62 | 2.25338 | ||||||||
\(923\) | −50.5964 | −0.0548174 | ||||||||
\(924\) | 1400.00 | − | 664.078i | 1.51515 | − | 0.718699i | ||||
\(925\) | −270.000 | − | 360.000i | −0.291892 | − | 0.389189i | ||||
\(926\) | 1818.00 | 1.96328 | ||||||||
\(927\) | 88.5438 | 0.0955165 | ||||||||
\(928\) | − | 630.000i | − | 0.678879i | ||||||
\(929\) | 303.579i | 0.326780i | 0.986562 | + | 0.163390i | \(0.0522429\pi\) | ||||
−0.986562 | + | 0.163390i | \(0.947757\pi\) | |||||||
\(930\) | 569.210 | + | 1707.63i | 0.612054 | + | 1.83616i | ||||
\(931\) | −1080.00 | − | 882.275i | −1.16004 | − | 0.947664i | ||||
\(932\) | 1260.00i | 1.35193i | ||||||||
\(933\) | 1140.00i | 1.22186i | ||||||||
\(934\) | 1603.27i | 1.71657i | ||||||||
\(935\) | −140.000 | − | 420.000i | −0.149733 | − | 0.449198i | ||||
\(936\) | − | 9.48683i | − | 0.0101355i | ||||||
\(937\) | 278.280 | 0.296991 | 0.148495 | − | 0.988913i | \(-0.452557\pi\) | ||||
0.148495 | + | 0.988913i | \(0.452557\pi\) | |||||||
\(938\) | 1935.31 | − | 918.000i | 2.06323 | − | 0.978678i | ||||
\(939\) | 1760.00 | 1.87433 | ||||||||
\(940\) | 350.000 | + | 1050.00i | 0.372340 | + | 1.11702i | ||||
\(941\) | − | 1072.01i | − | 1.13923i | −0.821913 | − | 0.569613i | \(-0.807093\pi\) | ||
0.821913 | − | 0.569613i | \(-0.192907\pi\) | |||||||
\(942\) | − | 1110.00i | − | 1.17834i | ||||||
\(943\) | −227.684 | −0.241446 | ||||||||
\(944\) | − | 104.355i | − | 0.110546i | ||||||
\(945\) | 612.982 | + | 638.947i | 0.648658 | + | 0.676134i | ||||
\(946\) | 1764.00 | 1.86469 | ||||||||
\(947\) | 354.000i | 0.373812i | 0.982378 | + | 0.186906i | \(0.0598460\pi\) | ||||
−0.982378 | + | 0.186906i | \(0.940154\pi\) | |||||||
\(948\) | −1201.67 | −1.26758 | ||||||||
\(949\) | −200.000 | −0.210748 | ||||||||
\(950\) | −1707.63 | + | 1280.72i | −1.79751 | + | 1.34813i | ||||
\(951\) | − | 1005.60i | − | 1.05742i | ||||||
\(952\) | 56.9210 | + | 120.000i | 0.0597910 | + | 0.126050i | ||||
\(953\) | − | 612.000i | − | 0.642183i | −0.947048 | − | 0.321091i | \(-0.895950\pi\) | ||
0.947048 | − | 0.321091i | \(-0.104050\pi\) | |||||||
\(954\) | −162.000 | −0.169811 | ||||||||
\(955\) | −234.009 | − | 702.026i | −0.245035 | − | 0.735105i | ||||
\(956\) | −1210.00 | −1.26569 | ||||||||
\(957\) | −619.806 | −0.647656 | ||||||||
\(958\) | −1593.79 | −1.66366 | ||||||||
\(959\) | 252.000 | + | 531.263i | 0.262774 | + | 0.553976i | ||||
\(960\) | −455.000 | − | 1365.00i | −0.473958 | − | 1.42188i | ||||
\(961\) | −479.000 | −0.498439 | ||||||||
\(962\) | −170.763 | −0.177508 | ||||||||
\(963\) | 54.0000i | 0.0560748i | ||||||||
\(964\) | 1328.16i | 1.37776i | ||||||||
\(965\) | −1223.80 | + | 407.934i | −1.26819 | + | 0.422729i | ||||
\(966\) | −720.000 | + | 341.526i | −0.745342 | + | 0.353547i | ||||
\(967\) | 1644.00i | 1.70010i | 0.526699 | + | 0.850052i | \(0.323429\pi\) | ||||
−0.526699 | + | 0.850052i | \(0.676571\pi\) | |||||||
\(968\) | − | 225.000i | − | 0.232438i | ||||||
\(969\) | − | 569.210i | − | 0.587420i | ||||||
\(970\) | −990.000 | + | 330.000i | −1.02062 | + | 0.340206i | ||||
\(971\) | − | 85.3815i | − | 0.0879315i | −0.999033 | − | 0.0439658i | \(-0.986001\pi\) | ||
0.999033 | − | 0.0439658i | \(-0.0139992\pi\) | |||||||
\(972\) | −268.794 | −0.276537 | ||||||||
\(973\) | 369.986 | + | 780.000i | 0.380253 | + | 0.801644i | ||||
\(974\) | −324.000 | −0.332649 | ||||||||
\(975\) | 200.000 | − | 150.000i | 0.205128 | − | 0.153846i | ||||
\(976\) | 730.486i | 0.748449i | ||||||||
\(977\) | 888.000i | 0.908905i | 0.890771 | + | 0.454452i | \(0.150165\pi\) | ||||
−0.890771 | + | 0.454452i | \(0.849835\pi\) | |||||||
\(978\) | 512.289 | 0.523813 | ||||||||
\(979\) | 796.894i | 0.813988i | ||||||||
\(980\) | −1145.08 | − | 435.230i | −1.16845 | − | 0.444112i | ||||
\(981\) | 74.0000 | 0.0754332 | ||||||||
\(982\) | 2022.00i | 2.05906i | ||||||||
\(983\) | −101.193 | −0.102943 | −0.0514715 | − | 0.998674i | \(-0.516391\pi\) | ||||
−0.0514715 | + | 0.998674i | \(0.516391\pi\) | |||||||
\(984\) | 180.000 | 0.182927 | ||||||||
\(985\) | 1622.25 | − | 540.749i | 1.64695 | − | 0.548984i | ||||
\(986\) | − | 265.631i | − | 0.269403i | ||||||
\(987\) | 885.438 | − | 420.000i | 0.897100 | − | 0.425532i | ||||
\(988\) | 450.000i | 0.455466i | ||||||||
\(989\) | −504.000 | −0.509606 | ||||||||
\(990\) | −199.223 | + | 66.4078i | −0.201236 | + | 0.0670786i | ||||
\(991\) | 1244.00 | 1.25530 | 0.627649 | − | 0.778497i | \(-0.284017\pi\) | ||||
0.627649 | + | 0.778497i | \(0.284017\pi\) | |||||||
\(992\) | 1707.63 | 1.72140 | ||||||||
\(993\) | −1182.69 | −1.19103 | ||||||||
\(994\) | −144.000 | − | 303.579i | −0.144869 | − | 0.305411i | ||||
\(995\) | 270.000 | − | 90.0000i | 0.271357 | − | 0.0904523i | ||||
\(996\) | −1150.00 | −1.15462 | ||||||||
\(997\) | −1211.15 | −1.21480 | −0.607398 | − | 0.794397i | \(-0.707787\pi\) | ||||
−0.607398 | + | 0.794397i | \(0.707787\pi\) | |||||||
\(998\) | 186.000i | 0.186373i | ||||||||
\(999\) | 455.368i | 0.455824i |
(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 | 35.3.c.c.34.3 | yes | 4 | |
3.2 | odd | 2 | 315.3.e.c.244.1 | 4 | |||
4.3 | odd | 2 | 560.3.p.f.209.4 | 4 | |||
5.2 | odd | 4 | 175.3.d.b.76.2 | 2 | |||
5.3 | odd | 4 | 175.3.d.h.76.1 | 2 | |||
5.4 | even | 2 | inner | 35.3.c.c.34.2 | yes | 4 | |
7.2 | even | 3 | 245.3.i.c.129.4 | 8 | |||
7.3 | odd | 6 | 245.3.i.c.19.1 | 8 | |||
7.4 | even | 3 | 245.3.i.c.19.2 | 8 | |||
7.5 | odd | 6 | 245.3.i.c.129.3 | 8 | |||
7.6 | odd | 2 | inner | 35.3.c.c.34.4 | yes | 4 | |
15.14 | odd | 2 | 315.3.e.c.244.4 | 4 | |||
20.19 | odd | 2 | 560.3.p.f.209.2 | 4 | |||
21.20 | even | 2 | 315.3.e.c.244.2 | 4 | |||
28.27 | even | 2 | 560.3.p.f.209.1 | 4 | |||
35.4 | even | 6 | 245.3.i.c.19.3 | 8 | |||
35.9 | even | 6 | 245.3.i.c.129.1 | 8 | |||
35.13 | even | 4 | 175.3.d.h.76.2 | 2 | |||
35.19 | odd | 6 | 245.3.i.c.129.2 | 8 | |||
35.24 | odd | 6 | 245.3.i.c.19.4 | 8 | |||
35.27 | even | 4 | 175.3.d.b.76.1 | 2 | |||
35.34 | odd | 2 | inner | 35.3.c.c.34.1 | ✓ | 4 | |
105.104 | even | 2 | 315.3.e.c.244.3 | 4 | |||
140.139 | even | 2 | 560.3.p.f.209.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.3.c.c.34.1 | ✓ | 4 | 35.34 | odd | 2 | inner | |
35.3.c.c.34.2 | yes | 4 | 5.4 | even | 2 | inner | |
35.3.c.c.34.3 | yes | 4 | 1.1 | even | 1 | trivial | |
35.3.c.c.34.4 | yes | 4 | 7.6 | odd | 2 | inner | |
175.3.d.b.76.1 | 2 | 35.27 | even | 4 | |||
175.3.d.b.76.2 | 2 | 5.2 | odd | 4 | |||
175.3.d.h.76.1 | 2 | 5.3 | odd | 4 | |||
175.3.d.h.76.2 | 2 | 35.13 | even | 4 | |||
245.3.i.c.19.1 | 8 | 7.3 | odd | 6 | |||
245.3.i.c.19.2 | 8 | 7.4 | even | 3 | |||
245.3.i.c.19.3 | 8 | 35.4 | even | 6 | |||
245.3.i.c.19.4 | 8 | 35.24 | odd | 6 | |||
245.3.i.c.129.1 | 8 | 35.9 | even | 6 | |||
245.3.i.c.129.2 | 8 | 35.19 | odd | 6 | |||
245.3.i.c.129.3 | 8 | 7.5 | odd | 6 | |||
245.3.i.c.129.4 | 8 | 7.2 | even | 3 | |||
315.3.e.c.244.1 | 4 | 3.2 | odd | 2 | |||
315.3.e.c.244.2 | 4 | 21.20 | even | 2 | |||
315.3.e.c.244.3 | 4 | 105.104 | even | 2 | |||
315.3.e.c.244.4 | 4 | 15.14 | odd | 2 | |||
560.3.p.f.209.1 | 4 | 28.27 | even | 2 | |||
560.3.p.f.209.2 | 4 | 20.19 | odd | 2 | |||
560.3.p.f.209.3 | 4 | 140.139 | even | 2 | |||
560.3.p.f.209.4 | 4 | 4.3 | odd | 2 |