Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(43,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.l (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.4 | ||
Root | \(-0.323042 + 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.43 |
Dual form | 1050.3.l.e.757.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 1.87083 | − | 1.87083i | 0.267261 | − | 0.267261i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.6727 | −1.78843 | −0.894214 | − | 0.447640i | \(-0.852265\pi\) | ||||
−0.894214 | + | 0.447640i | \(0.852265\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.204124 | − | 0.204124i | ||||
\(13\) | 0.747104 | + | 0.747104i | 0.0574696 | + | 0.0574696i | 0.735257 | − | 0.677788i | \(-0.237061\pi\) |
−0.677788 | + | 0.735257i | \(0.737061\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −20.6127 | + | 20.6127i | −1.21251 | + | 1.21251i | −0.242315 | + | 0.970198i | \(0.577907\pi\) |
−0.970198 | + | 0.242315i | \(0.922093\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | 13.7100i | 0.721581i | 0.932647 | + | 0.360791i | \(0.117493\pi\) | ||||
−0.932647 | + | 0.360791i | \(0.882507\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58258 | 0.218218 | ||||||||
\(22\) | −19.6727 | + | 19.6727i | −0.894214 | + | 0.894214i | ||||
\(23\) | 15.2514 | + | 15.2514i | 0.663103 | + | 0.663103i | 0.956110 | − | 0.293007i | \(-0.0946561\pi\) |
−0.293007 | + | 0.956110i | \(0.594656\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.49421 | 0.0574696 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | −3.74166 | − | 3.74166i | −0.133631 | − | 0.133631i | ||||
\(29\) | 52.0555i | 1.79502i | 0.440999 | + | 0.897508i | \(0.354624\pi\) | ||||
−0.440999 | + | 0.897508i | \(0.645376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.68480 | 0.215639 | 0.107819 | − | 0.994171i | \(-0.465613\pi\) | ||||
0.107819 | + | 0.994171i | \(0.465613\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | −24.0940 | − | 24.0940i | −0.730122 | − | 0.730122i | ||||
\(34\) | 41.2254i | 1.21251i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 34.0530 | − | 34.0530i | 0.920352 | − | 0.920352i | −0.0767024 | − | 0.997054i | \(-0.524439\pi\) |
0.997054 | + | 0.0767024i | \(0.0244391\pi\) | |||||||
\(38\) | 13.7100 | + | 13.7100i | 0.360791 | + | 0.360791i | ||||
\(39\) | 1.83002i | 0.0469237i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.98842 | −0.0728882 | −0.0364441 | − | 0.999336i | \(-0.511603\pi\) | ||||
−0.0364441 | + | 0.999336i | \(0.511603\pi\) | |||||||
\(42\) | 4.58258 | − | 4.58258i | 0.109109 | − | 0.109109i | ||||
\(43\) | 16.2459 | + | 16.2459i | 0.377812 | + | 0.377812i | 0.870312 | − | 0.492500i | \(-0.163917\pi\) |
−0.492500 | + | 0.870312i | \(0.663917\pi\) | |||||||
\(44\) | 39.3454i | 0.894214i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 30.5027 | 0.663103 | ||||||||
\(47\) | −62.2607 | + | 62.2607i | −1.32470 | + | 1.32470i | −0.414768 | + | 0.909927i | \(0.636137\pi\) |
−0.909927 | + | 0.414768i | \(0.863863\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −50.4906 | −0.990012 | ||||||||
\(52\) | 1.49421 | − | 1.49421i | 0.0287348 | − | 0.0287348i | ||||
\(53\) | −21.3454 | − | 21.3454i | −0.402743 | − | 0.402743i | 0.476455 | − | 0.879199i | \(-0.341921\pi\) |
−0.879199 | + | 0.476455i | \(0.841921\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.48331 | −0.133631 | ||||||||
\(57\) | −16.7913 | + | 16.7913i | −0.294584 | + | 0.294584i | ||||
\(58\) | 52.0555 | + | 52.0555i | 0.897508 | + | 0.897508i | ||||
\(59\) | − | 95.6898i | − | 1.62186i | −0.585142 | − | 0.810931i | \(-0.698961\pi\) | ||
0.585142 | − | 0.810931i | \(-0.301039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31.9859 | −0.524359 | −0.262180 | − | 0.965019i | \(-0.584441\pi\) | ||||
−0.262180 | + | 0.965019i | \(0.584441\pi\) | |||||||
\(62\) | 6.68480 | − | 6.68480i | 0.107819 | − | 0.107819i | ||||
\(63\) | 5.61249 | + | 5.61249i | 0.0890871 | + | 0.0890871i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −48.1881 | −0.730122 | ||||||||
\(67\) | −41.4927 | + | 41.4927i | −0.619294 | + | 0.619294i | −0.945350 | − | 0.326057i | \(-0.894280\pi\) |
0.326057 | + | 0.945350i | \(0.394280\pi\) | |||||||
\(68\) | 41.2254 | + | 41.2254i | 0.606256 | + | 0.606256i | ||||
\(69\) | 37.3581i | 0.541421i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 108.124 | 1.52287 | 0.761433 | − | 0.648243i | \(-0.224496\pi\) | ||||
0.761433 | + | 0.648243i | \(0.224496\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −79.9477 | − | 79.9477i | −1.09517 | − | 1.09517i | −0.994967 | − | 0.100207i | \(-0.968049\pi\) |
−0.100207 | − | 0.994967i | \(-0.531951\pi\) | |||||||
\(74\) | − | 68.1060i | − | 0.920352i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 27.4201 | 0.360791 | ||||||||
\(77\) | −36.8043 | + | 36.8043i | −0.477977 | + | 0.477977i | ||||
\(78\) | 1.83002 | + | 1.83002i | 0.0234619 | + | 0.0234619i | ||||
\(79\) | 87.2930i | 1.10497i | 0.833521 | + | 0.552487i | \(0.186321\pi\) | ||||
−0.833521 | + | 0.552487i | \(0.813679\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −2.98842 | + | 2.98842i | −0.0364441 | + | 0.0364441i | ||||
\(83\) | 17.3000 | + | 17.3000i | 0.208434 | + | 0.208434i | 0.803601 | − | 0.595168i | \(-0.202914\pi\) |
−0.595168 | + | 0.803601i | \(0.702914\pi\) | |||||||
\(84\) | − | 9.16515i | − | 0.109109i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 32.4918 | 0.377812 | ||||||||
\(87\) | −63.7546 | + | 63.7546i | −0.732812 | + | 0.732812i | ||||
\(88\) | 39.3454 | + | 39.3454i | 0.447107 | + | 0.447107i | ||||
\(89\) | 60.6056i | 0.680962i | 0.940251 | + | 0.340481i | \(0.110590\pi\) | ||||
−0.940251 | + | 0.340481i | \(0.889410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.79541 | 0.0307188 | ||||||||
\(92\) | 30.5027 | − | 30.5027i | 0.331551 | − | 0.331551i | ||||
\(93\) | 8.18717 | + | 8.18717i | 0.0880341 | + | 0.0880341i | ||||
\(94\) | 124.521i | 1.32470i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −49.0544 | + | 49.0544i | −0.505715 | + | 0.505715i | −0.913208 | − | 0.407493i | \(-0.866403\pi\) |
0.407493 | + | 0.913208i | \(0.366403\pi\) | |||||||
\(98\) | −7.00000 | − | 7.00000i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | − | 59.0181i | − | 0.596142i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 175.572 | 1.73834 | 0.869168 | − | 0.494517i | \(-0.164655\pi\) | ||||
0.869168 | + | 0.494517i | \(0.164655\pi\) | |||||||
\(102\) | −50.4906 | + | 50.4906i | −0.495006 | + | 0.495006i | ||||
\(103\) | −79.3766 | − | 79.3766i | −0.770646 | − | 0.770646i | 0.207573 | − | 0.978219i | \(-0.433443\pi\) |
−0.978219 | + | 0.207573i | \(0.933443\pi\) | |||||||
\(104\) | − | 2.98842i | − | 0.0287348i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −42.6908 | −0.402743 | ||||||||
\(107\) | −95.4608 | + | 95.4608i | −0.892157 | + | 0.892157i | −0.994726 | − | 0.102569i | \(-0.967294\pi\) |
0.102569 | + | 0.994726i | \(0.467294\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 31.6515i | − | 0.290381i | −0.989404 | − | 0.145191i | \(-0.953620\pi\) | ||
0.989404 | − | 0.145191i | \(-0.0463795\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 83.4125 | 0.751464 | ||||||||
\(112\) | −7.48331 | + | 7.48331i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | −69.4727 | − | 69.4727i | −0.614803 | − | 0.614803i | 0.329391 | − | 0.944194i | \(-0.393157\pi\) |
−0.944194 | + | 0.329391i | \(0.893157\pi\) | |||||||
\(114\) | 33.5826i | 0.294584i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 104.111 | 0.897508 | ||||||||
\(117\) | −2.24131 | + | 2.24131i | −0.0191565 | + | 0.0191565i | ||||
\(118\) | −95.6898 | − | 95.6898i | −0.810931 | − | 0.810931i | ||||
\(119\) | 77.1257i | 0.648115i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 266.015 | 2.19847 | ||||||||
\(122\) | −31.9859 | + | 31.9859i | −0.262180 | + | 0.262180i | ||||
\(123\) | −3.66005 | − | 3.66005i | −0.0297565 | − | 0.0297565i | ||||
\(124\) | − | 13.3696i | − | 0.107819i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 11.2250 | 0.0890871 | ||||||||
\(127\) | −2.37293 | + | 2.37293i | −0.0186845 | + | 0.0186845i | −0.716387 | − | 0.697703i | \(-0.754206\pi\) |
0.697703 | + | 0.716387i | \(0.254206\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 39.7942i | 0.308482i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −174.743 | −1.33392 | −0.666958 | − | 0.745095i | \(-0.732404\pi\) | ||||
−0.666958 | + | 0.745095i | \(0.732404\pi\) | |||||||
\(132\) | −48.1881 | + | 48.1881i | −0.365061 | + | 0.365061i | ||||
\(133\) | 25.6491 | + | 25.6491i | 0.192851 | + | 0.192851i | ||||
\(134\) | 82.9854i | 0.619294i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 82.4509 | 0.606256 | ||||||||
\(137\) | 17.9658 | − | 17.9658i | 0.131137 | − | 0.131137i | −0.638492 | − | 0.769629i | \(-0.720441\pi\) |
0.769629 | + | 0.638492i | \(0.220441\pi\) | |||||||
\(138\) | 37.3581 | + | 37.3581i | 0.270711 | + | 0.270711i | ||||
\(139\) | 159.897i | 1.15034i | 0.818036 | + | 0.575168i | \(0.195063\pi\) | ||||
−0.818036 | + | 0.575168i | \(0.804937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −152.507 | −1.08161 | ||||||||
\(142\) | 108.124 | − | 108.124i | 0.761433 | − | 0.761433i | ||||
\(143\) | −14.6976 | − | 14.6976i | −0.102780 | − | 0.102780i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −159.895 | −1.09517 | ||||||||
\(147\) | 8.57321 | − | 8.57321i | 0.0583212 | − | 0.0583212i | ||||
\(148\) | −68.1060 | − | 68.1060i | −0.460176 | − | 0.460176i | ||||
\(149\) | 21.0923i | 0.141559i | 0.997492 | + | 0.0707797i | \(0.0225487\pi\) | ||||
−0.997492 | + | 0.0707797i | \(0.977451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −118.298 | −0.783433 | −0.391717 | − | 0.920086i | \(-0.628119\pi\) | ||||
−0.391717 | + | 0.920086i | \(0.628119\pi\) | |||||||
\(152\) | 27.4201 | − | 27.4201i | 0.180395 | − | 0.180395i | ||||
\(153\) | −61.8381 | − | 61.8381i | −0.404171 | − | 0.404171i | ||||
\(154\) | 73.6085i | 0.477977i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.66005 | 0.0234619 | ||||||||
\(157\) | −61.1533 | + | 61.1533i | −0.389512 | + | 0.389512i | −0.874513 | − | 0.485002i | \(-0.838819\pi\) |
0.485002 | + | 0.874513i | \(0.338819\pi\) | |||||||
\(158\) | 87.2930 | + | 87.2930i | 0.552487 | + | 0.552487i | ||||
\(159\) | − | 52.2853i | − | 0.328839i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 57.0654 | 0.354443 | ||||||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | −126.626 | − | 126.626i | −0.776849 | − | 0.776849i | 0.202444 | − | 0.979294i | \(-0.435111\pi\) |
−0.979294 | + | 0.202444i | \(0.935111\pi\) | |||||||
\(164\) | 5.97683i | 0.0364441i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 34.6000 | 0.208434 | ||||||||
\(167\) | 8.09971 | − | 8.09971i | 0.0485013 | − | 0.0485013i | −0.682440 | − | 0.730941i | \(-0.739081\pi\) |
0.730941 | + | 0.682440i | \(0.239081\pi\) | |||||||
\(168\) | −9.16515 | − | 9.16515i | −0.0545545 | − | 0.0545545i | ||||
\(169\) | − | 167.884i | − | 0.993394i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −41.1301 | −0.240527 | ||||||||
\(172\) | 32.4918 | − | 32.4918i | 0.188906 | − | 0.188906i | ||||
\(173\) | 42.9027 | + | 42.9027i | 0.247993 | + | 0.247993i | 0.820146 | − | 0.572154i | \(-0.193892\pi\) |
−0.572154 | + | 0.820146i | \(0.693892\pi\) | |||||||
\(174\) | 127.509i | 0.732812i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 78.6908 | 0.447107 | ||||||||
\(177\) | 117.196 | − | 117.196i | 0.662122 | − | 0.662122i | ||||
\(178\) | 60.6056 | + | 60.6056i | 0.340481 | + | 0.340481i | ||||
\(179\) | − | 226.474i | − | 1.26522i | −0.774471 | − | 0.632610i | \(-0.781984\pi\) | ||
0.774471 | − | 0.632610i | \(-0.218016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 248.088 | 1.37065 | 0.685326 | − | 0.728236i | \(-0.259660\pi\) | ||||
0.685326 | + | 0.728236i | \(0.259660\pi\) | |||||||
\(182\) | 2.79541 | − | 2.79541i | 0.0153594 | − | 0.0153594i | ||||
\(183\) | −39.1746 | − | 39.1746i | −0.214069 | − | 0.214069i | ||||
\(184\) | − | 61.0055i | − | 0.331551i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.3743 | 0.0880341 | ||||||||
\(187\) | 405.508 | − | 405.508i | 2.16849 | − | 2.16849i | ||||
\(188\) | 124.521 | + | 124.521i | 0.662348 | + | 0.662348i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 175.069 | 0.916592 | 0.458296 | − | 0.888800i | \(-0.348460\pi\) | ||||
0.458296 | + | 0.888800i | \(0.348460\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −175.104 | − | 175.104i | −0.907276 | − | 0.907276i | 0.0887761 | − | 0.996052i | \(-0.471704\pi\) |
−0.996052 | + | 0.0887761i | \(0.971704\pi\) | |||||||
\(194\) | 98.1088i | 0.505715i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −241.786 | + | 241.786i | −1.22734 | + | 1.22734i | −0.262373 | + | 0.964967i | \(0.584505\pi\) |
−0.964967 | + | 0.262373i | \(0.915495\pi\) | |||||||
\(198\) | −59.0181 | − | 59.0181i | −0.298071 | − | 0.298071i | ||||
\(199\) | 21.7782i | 0.109438i | 0.998502 | + | 0.0547192i | \(0.0174264\pi\) | ||||
−0.998502 | + | 0.0547192i | \(0.982574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −101.636 | −0.505651 | ||||||||
\(202\) | 175.572 | − | 175.572i | 0.869168 | − | 0.869168i | ||||
\(203\) | 97.3868 | + | 97.3868i | 0.479738 | + | 0.479738i | ||||
\(204\) | 100.981i | 0.495006i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −158.753 | −0.770646 | ||||||||
\(207\) | −45.7541 | + | 45.7541i | −0.221034 | + | 0.221034i | ||||
\(208\) | −2.98842 | − | 2.98842i | −0.0143674 | − | 0.0143674i | ||||
\(209\) | − | 269.714i | − | 1.29050i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 187.826 | 0.890172 | 0.445086 | − | 0.895488i | \(-0.353173\pi\) | ||||
0.445086 | + | 0.895488i | \(0.353173\pi\) | |||||||
\(212\) | −42.6908 | + | 42.6908i | −0.201372 | + | 0.201372i | ||||
\(213\) | 132.424 | + | 132.424i | 0.621708 | + | 0.621708i | ||||
\(214\) | 190.922i | 0.892157i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 12.5061 | − | 12.5061i | 0.0576319 | − | 0.0576319i | ||||
\(218\) | −31.6515 | − | 31.6515i | −0.145191 | − | 0.145191i | ||||
\(219\) | − | 195.831i | − | 0.894206i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.7997 | −0.139365 | ||||||||
\(222\) | 83.4125 | − | 83.4125i | 0.375732 | − | 0.375732i | ||||
\(223\) | −112.060 | − | 112.060i | −0.502509 | − | 0.502509i | 0.409708 | − | 0.912217i | \(-0.365631\pi\) |
−0.912217 | + | 0.409708i | \(0.865631\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −138.945 | −0.614803 | ||||||||
\(227\) | −25.7399 | + | 25.7399i | −0.113392 | + | 0.113392i | −0.761526 | − | 0.648134i | \(-0.775550\pi\) |
0.648134 | + | 0.761526i | \(0.275550\pi\) | |||||||
\(228\) | 33.5826 | + | 33.5826i | 0.147292 | + | 0.147292i | ||||
\(229\) | 283.393i | 1.23752i | 0.785579 | + | 0.618762i | \(0.212365\pi\) | ||||
−0.785579 | + | 0.618762i | \(0.787635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −90.1516 | −0.390267 | ||||||||
\(232\) | 104.111 | − | 104.111i | 0.448754 | − | 0.448754i | ||||
\(233\) | −1.16854 | − | 1.16854i | −0.00501519 | − | 0.00501519i | 0.704595 | − | 0.709610i | \(-0.251129\pi\) |
−0.709610 | + | 0.704595i | \(0.751129\pi\) | |||||||
\(234\) | 4.48263i | 0.0191565i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −191.380 | −0.810931 | ||||||||
\(237\) | −106.912 | + | 106.912i | −0.451104 | + | 0.451104i | ||||
\(238\) | 77.1257 | + | 77.1257i | 0.324058 | + | 0.324058i | ||||
\(239\) | − | 86.0324i | − | 0.359968i | −0.983670 | − | 0.179984i | \(-0.942395\pi\) | ||
0.983670 | − | 0.179984i | \(-0.0576046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 153.724 | 0.637859 | 0.318930 | − | 0.947778i | \(-0.396677\pi\) | ||||
0.318930 | + | 0.947778i | \(0.396677\pi\) | |||||||
\(242\) | 266.015 | − | 266.015i | 1.09924 | − | 1.09924i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 63.9718i | 0.262180i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.32010 | −0.0297565 | ||||||||
\(247\) | −10.2428 | + | 10.2428i | −0.0414690 | + | 0.0414690i | ||||
\(248\) | −13.3696 | − | 13.3696i | −0.0539097 | − | 0.0539097i | ||||
\(249\) | 42.3762i | 0.170185i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 37.9703 | 0.151276 | 0.0756380 | − | 0.997135i | \(-0.475901\pi\) | ||||
0.0756380 | + | 0.997135i | \(0.475901\pi\) | |||||||
\(252\) | 11.2250 | − | 11.2250i | 0.0445435 | − | 0.0445435i | ||||
\(253\) | −300.036 | − | 300.036i | −1.18591 | − | 1.18591i | ||||
\(254\) | 4.74587i | 0.0186845i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −208.411 | + | 208.411i | −0.810938 | + | 0.810938i | −0.984774 | − | 0.173837i | \(-0.944383\pi\) |
0.173837 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(258\) | 39.7942 | + | 39.7942i | 0.154241 | + | 0.154241i | ||||
\(259\) | − | 127.415i | − | 0.491949i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −156.166 | −0.598339 | ||||||||
\(262\) | −174.743 | + | 174.743i | −0.666958 | + | 0.666958i | ||||
\(263\) | 261.981 | + | 261.981i | 0.996126 | + | 0.996126i | 0.999993 | − | 0.00386674i | \(-0.00123082\pi\) |
−0.00386674 | + | 0.999993i | \(0.501231\pi\) | |||||||
\(264\) | 96.3762i | 0.365061i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 51.2983 | 0.192851 | ||||||||
\(267\) | −74.2264 | + | 74.2264i | −0.278002 | + | 0.278002i | ||||
\(268\) | 82.9854 | + | 82.9854i | 0.309647 | + | 0.309647i | ||||
\(269\) | 165.758i | 0.616202i | 0.951354 | + | 0.308101i | \(0.0996935\pi\) | ||||
−0.951354 | + | 0.308101i | \(0.900306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −134.063 | −0.494697 | −0.247349 | − | 0.968927i | \(-0.579559\pi\) | ||||
−0.247349 | + | 0.968927i | \(0.579559\pi\) | |||||||
\(272\) | 82.4509 | − | 82.4509i | 0.303128 | − | 0.303128i | ||||
\(273\) | 3.42366 | + | 3.42366i | 0.0125409 | + | 0.0125409i | ||||
\(274\) | − | 35.9315i | − | 0.131137i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 74.7161 | 0.270711 | ||||||||
\(277\) | 369.296 | − | 369.296i | 1.33320 | − | 1.33320i | 0.430707 | − | 0.902492i | \(-0.358264\pi\) |
0.902492 | − | 0.430707i | \(-0.141736\pi\) | |||||||
\(278\) | 159.897 | + | 159.897i | 0.575168 | + | 0.575168i | ||||
\(279\) | 20.0544i | 0.0718796i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −106.023 | −0.377306 | −0.188653 | − | 0.982044i | \(-0.560412\pi\) | ||||
−0.188653 | + | 0.982044i | \(0.560412\pi\) | |||||||
\(282\) | −152.507 | + | 152.507i | −0.540804 | + | 0.540804i | ||||
\(283\) | −19.9037 | − | 19.9037i | −0.0703312 | − | 0.0703312i | 0.671066 | − | 0.741397i | \(-0.265837\pi\) |
−0.741397 | + | 0.671066i | \(0.765837\pi\) | |||||||
\(284\) | − | 216.247i | − | 0.761433i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.3951 | −0.102780 | ||||||||
\(287\) | −5.59082 | + | 5.59082i | −0.0194802 | + | 0.0194802i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 560.768i | − | 1.94037i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −120.158 | −0.412915 | ||||||||
\(292\) | −159.895 | + | 159.895i | −0.547587 | + | 0.547587i | ||||
\(293\) | 177.763 | + | 177.763i | 0.606700 | + | 0.606700i | 0.942082 | − | 0.335382i | \(-0.108865\pi\) |
−0.335382 | + | 0.942082i | \(0.608865\pi\) | |||||||
\(294\) | − | 17.1464i | − | 0.0583212i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −136.212 | −0.460176 | ||||||||
\(297\) | 72.2821 | − | 72.2821i | 0.243374 | − | 0.243374i | ||||
\(298\) | 21.0923 | + | 21.0923i | 0.0707797 | + | 0.0707797i | ||||
\(299\) | 22.7887i | 0.0762165i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 60.7867 | 0.201949 | ||||||||
\(302\) | −118.298 | + | 118.298i | −0.391717 | + | 0.391717i | ||||
\(303\) | 215.031 | + | 215.031i | 0.709672 | + | 0.709672i | ||||
\(304\) | − | 54.8402i | − | 0.180395i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −123.676 | −0.404171 | ||||||||
\(307\) | −21.5926 | + | 21.5926i | −0.0703342 | + | 0.0703342i | −0.741399 | − | 0.671065i | \(-0.765837\pi\) |
0.671065 | + | 0.741399i | \(0.265837\pi\) | |||||||
\(308\) | 73.6085 | + | 73.6085i | 0.238989 | + | 0.238989i | ||||
\(309\) | − | 194.432i | − | 0.629230i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −293.552 | −0.943896 | −0.471948 | − | 0.881626i | \(-0.656449\pi\) | ||||
−0.471948 | + | 0.881626i | \(0.656449\pi\) | |||||||
\(312\) | 3.66005 | − | 3.66005i | 0.0117309 | − | 0.0117309i | ||||
\(313\) | 330.603 | + | 330.603i | 1.05624 | + | 1.05624i | 0.998321 | + | 0.0579193i | \(0.0184466\pi\) |
0.0579193 | + | 0.998321i | \(0.481553\pi\) | |||||||
\(314\) | 122.307i | 0.389512i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 174.586 | 0.552487 | ||||||||
\(317\) | 416.093 | − | 416.093i | 1.31260 | − | 1.31260i | 0.393099 | − | 0.919496i | \(-0.371403\pi\) |
0.919496 | − | 0.393099i | \(-0.128597\pi\) | |||||||
\(318\) | −52.2853 | − | 52.2853i | −0.164419 | − | 0.164419i | ||||
\(319\) | − | 1024.07i | − | 3.21026i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −233.830 | −0.728443 | ||||||||
\(322\) | 57.0654 | − | 57.0654i | 0.177222 | − | 0.177222i | ||||
\(323\) | −282.601 | − | 282.601i | −0.874926 | − | 0.874926i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −253.253 | −0.776849 | ||||||||
\(327\) | 38.7651 | − | 38.7651i | 0.118548 | − | 0.118548i | ||||
\(328\) | 5.97683 | + | 5.97683i | 0.0182221 | + | 0.0182221i | ||||
\(329\) | 232.958i | 0.708079i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 70.3912 | 0.212662 | 0.106331 | − | 0.994331i | \(-0.466090\pi\) | ||||
0.106331 | + | 0.994331i | \(0.466090\pi\) | |||||||
\(332\) | 34.6000 | − | 34.6000i | 0.104217 | − | 0.104217i | ||||
\(333\) | 102.159 | + | 102.159i | 0.306784 | + | 0.306784i | ||||
\(334\) | − | 16.1994i | − | 0.0485013i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −18.3303 | −0.0545545 | ||||||||
\(337\) | 133.492 | − | 133.492i | 0.396119 | − | 0.396119i | −0.480742 | − | 0.876862i | \(-0.659633\pi\) |
0.876862 | + | 0.480742i | \(0.159633\pi\) | |||||||
\(338\) | −167.884 | − | 167.884i | −0.496697 | − | 0.496697i | ||||
\(339\) | − | 170.173i | − | 0.501984i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −131.508 | −0.385654 | ||||||||
\(342\) | −41.1301 | + | 41.1301i | −0.120264 | + | 0.120264i | ||||
\(343\) | −13.0958 | − | 13.0958i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 64.9837i | − | 0.188906i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 85.8054 | 0.247993 | ||||||||
\(347\) | −6.42770 | + | 6.42770i | −0.0185236 | + | 0.0185236i | −0.716308 | − | 0.697784i | \(-0.754169\pi\) |
0.697784 | + | 0.716308i | \(0.254169\pi\) | |||||||
\(348\) | 127.509 | + | 127.509i | 0.366406 | + | 0.366406i | ||||
\(349\) | 569.588i | 1.63206i | 0.578011 | + | 0.816029i | \(0.303829\pi\) | ||||
−0.578011 | + | 0.816029i | \(0.696171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.49007 | −0.0156412 | ||||||||
\(352\) | 78.6908 | − | 78.6908i | 0.223553 | − | 0.223553i | ||||
\(353\) | −274.162 | − | 274.162i | −0.776664 | − | 0.776664i | 0.202598 | − | 0.979262i | \(-0.435062\pi\) |
−0.979262 | + | 0.202598i | \(0.935062\pi\) | |||||||
\(354\) | − | 234.391i | − | 0.662122i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 121.211 | 0.340481 | ||||||||
\(357\) | −94.4593 | + | 94.4593i | −0.264592 | + | 0.264592i | ||||
\(358\) | −226.474 | − | 226.474i | −0.632610 | − | 0.632610i | ||||
\(359\) | 54.6096i | 0.152116i | 0.997103 | + | 0.0760580i | \(0.0242334\pi\) | ||||
−0.997103 | + | 0.0760580i | \(0.975767\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 173.035 | 0.479320 | ||||||||
\(362\) | 248.088 | − | 248.088i | 0.685326 | − | 0.685326i | ||||
\(363\) | 325.801 | + | 325.801i | 0.897523 | + | 0.897523i | ||||
\(364\) | − | 5.59082i | − | 0.0153594i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −78.3492 | −0.214069 | ||||||||
\(367\) | 56.6291 | − | 56.6291i | 0.154303 | − | 0.154303i | −0.625734 | − | 0.780037i | \(-0.715200\pi\) |
0.780037 | + | 0.625734i | \(0.215200\pi\) | |||||||
\(368\) | −61.0055 | − | 61.0055i | −0.165776 | − | 0.165776i | ||||
\(369\) | − | 8.96525i | − | 0.0242961i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −79.8672 | −0.215275 | ||||||||
\(372\) | 16.3743 | − | 16.3743i | 0.0440171 | − | 0.0440171i | ||||
\(373\) | 378.196 | + | 378.196i | 1.01393 | + | 1.01393i | 0.999902 | + | 0.0140288i | \(0.00446566\pi\) |
0.0140288 | + | 0.999902i | \(0.495534\pi\) | |||||||
\(374\) | − | 811.016i | − | 2.16849i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 249.043 | 0.662348 | ||||||||
\(377\) | −38.8909 | + | 38.8909i | −0.103159 | + | 0.103159i | ||||
\(378\) | 13.7477 | + | 13.7477i | 0.0363696 | + | 0.0363696i | ||||
\(379\) | − | 469.010i | − | 1.23749i | −0.785590 | − | 0.618747i | \(-0.787641\pi\) | ||
0.785590 | − | 0.618747i | \(-0.212359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.81247 | −0.0152558 | ||||||||
\(382\) | 175.069 | − | 175.069i | 0.458296 | − | 0.458296i | ||||
\(383\) | −222.284 | − | 222.284i | −0.580377 | − | 0.580377i | 0.354630 | − | 0.935007i | \(-0.384607\pi\) |
−0.935007 | + | 0.354630i | \(0.884607\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −350.208 | −0.907276 | ||||||||
\(387\) | −48.7377 | + | 48.7377i | −0.125937 | + | 0.125937i | ||||
\(388\) | 98.1088 | + | 98.1088i | 0.252858 | + | 0.252858i | ||||
\(389\) | − | 84.3841i | − | 0.216926i | −0.994100 | − | 0.108463i | \(-0.965407\pi\) | ||
0.994100 | − | 0.108463i | \(-0.0345929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −628.744 | −1.60804 | ||||||||
\(392\) | −14.0000 | + | 14.0000i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | −214.016 | − | 214.016i | −0.544569 | − | 0.544569i | ||||
\(394\) | 483.572i | 1.22734i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −118.036 | −0.298071 | ||||||||
\(397\) | 218.706 | − | 218.706i | 0.550898 | − | 0.550898i | −0.375802 | − | 0.926700i | \(-0.622633\pi\) |
0.926700 | + | 0.375802i | \(0.122633\pi\) | |||||||
\(398\) | 21.7782 | + | 21.7782i | 0.0547192 | + | 0.0547192i | ||||
\(399\) | 62.8273i | 0.157462i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 120.115 | 0.299538 | 0.149769 | − | 0.988721i | \(-0.452147\pi\) | ||||
0.149769 | + | 0.988721i | \(0.452147\pi\) | |||||||
\(402\) | −101.636 | + | 101.636i | −0.252826 | + | 0.252826i | ||||
\(403\) | 4.99424 | + | 4.99424i | 0.0123927 | + | 0.0123927i | ||||
\(404\) | − | 351.144i | − | 0.869168i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 194.774 | 0.479738 | ||||||||
\(407\) | −669.915 | + | 669.915i | −1.64598 | + | 1.64598i | ||||
\(408\) | 100.981 | + | 100.981i | 0.247503 | + | 0.247503i | ||||
\(409\) | − | 122.453i | − | 0.299397i | −0.988732 | − | 0.149698i | \(-0.952170\pi\) | ||
0.988732 | − | 0.149698i | \(-0.0478302\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 44.0069 | 0.107073 | ||||||||
\(412\) | −158.753 | + | 158.753i | −0.385323 | + | 0.385323i | ||||
\(413\) | −179.019 | − | 179.019i | −0.433461 | − | 0.433461i | ||||
\(414\) | 91.5082i | 0.221034i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.97683 | −0.0143674 | ||||||||
\(417\) | −195.833 | + | 195.833i | −0.469622 | + | 0.469622i | ||||
\(418\) | −269.714 | − | 269.714i | −0.645248 | − | 0.645248i | ||||
\(419\) | 705.901i | 1.68473i | 0.538909 | + | 0.842364i | \(0.318837\pi\) | ||||
−0.538909 | + | 0.842364i | \(0.681163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.19359 | −0.00521042 | −0.00260521 | − | 0.999997i | \(-0.500829\pi\) | ||||
−0.00260521 | + | 0.999997i | \(0.500829\pi\) | |||||||
\(422\) | 187.826 | − | 187.826i | 0.445086 | − | 0.445086i | ||||
\(423\) | −186.782 | − | 186.782i | −0.441565 | − | 0.441565i | ||||
\(424\) | 85.3816i | 0.201372i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 264.848 | 0.621708 | ||||||||
\(427\) | −59.8402 | + | 59.8402i | −0.140141 | + | 0.140141i | ||||
\(428\) | 190.922 | + | 190.922i | 0.446079 | + | 0.446079i | ||||
\(429\) | − | 36.0015i | − | 0.0839196i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −295.381 | −0.685338 | −0.342669 | − | 0.939456i | \(-0.611331\pi\) | ||||
−0.342669 | + | 0.939456i | \(0.611331\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 159.430 | + | 159.430i | 0.368198 | + | 0.368198i | 0.866820 | − | 0.498622i | \(-0.166160\pi\) |
−0.498622 | + | 0.866820i | \(0.666160\pi\) | |||||||
\(434\) | − | 25.0122i | − | 0.0576319i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −63.3031 | −0.145191 | ||||||||
\(437\) | −209.097 | + | 209.097i | −0.478483 | + | 0.478483i | ||||
\(438\) | −195.831 | − | 195.831i | −0.447103 | − | 0.447103i | ||||
\(439\) | − | 337.545i | − | 0.768896i | −0.923147 | − | 0.384448i | \(-0.874392\pi\) | ||
0.923147 | − | 0.384448i | \(-0.125608\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −30.7997 | + | 30.7997i | −0.0696826 | + | 0.0696826i | ||||
\(443\) | 511.393 | + | 511.393i | 1.15439 | + | 1.15439i | 0.985664 | + | 0.168723i | \(0.0539643\pi\) |
0.168723 | + | 0.985664i | \(0.446036\pi\) | |||||||
\(444\) | − | 166.825i | − | 0.375732i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −224.119 | −0.502509 | ||||||||
\(447\) | −25.8327 | + | 25.8327i | −0.0577914 | + | 0.0577914i | ||||
\(448\) | 14.9666 | + | 14.9666i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | − | 628.997i | − | 1.40088i | −0.713709 | − | 0.700442i | \(-0.752986\pi\) | ||
0.713709 | − | 0.700442i | \(-0.247014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 58.7902 | 0.130355 | ||||||||
\(452\) | −138.945 | + | 138.945i | −0.307401 | + | 0.307401i | ||||
\(453\) | −144.885 | − | 144.885i | −0.319835 | − | 0.319835i | ||||
\(454\) | 51.4798i | 0.113392i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 67.1652 | 0.147292 | ||||||||
\(457\) | 120.705 | − | 120.705i | 0.264124 | − | 0.264124i | −0.562603 | − | 0.826727i | \(-0.690200\pi\) |
0.826727 | + | 0.562603i | \(0.190200\pi\) | |||||||
\(458\) | 283.393 | + | 283.393i | 0.618762 | + | 0.618762i | ||||
\(459\) | − | 151.472i | − | 0.330004i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −53.6000 | −0.116269 | −0.0581345 | − | 0.998309i | \(-0.518515\pi\) | ||||
−0.0581345 | + | 0.998309i | \(0.518515\pi\) | |||||||
\(462\) | −90.1516 | + | 90.1516i | −0.195133 | + | 0.195133i | ||||
\(463\) | −186.045 | − | 186.045i | −0.401825 | − | 0.401825i | 0.477051 | − | 0.878876i | \(-0.341706\pi\) |
−0.878876 | + | 0.477051i | \(0.841706\pi\) | |||||||
\(464\) | − | 208.222i | − | 0.448754i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.33708 | −0.00501519 | ||||||||
\(467\) | 333.349 | − | 333.349i | 0.713810 | − | 0.713810i | −0.253520 | − | 0.967330i | \(-0.581588\pi\) |
0.967330 | + | 0.253520i | \(0.0815884\pi\) | |||||||
\(468\) | 4.48263 | + | 4.48263i | 0.00957826 | + | 0.00957826i | ||||
\(469\) | 155.251i | 0.331026i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −149.794 | −0.318035 | ||||||||
\(472\) | −191.380 | + | 191.380i | −0.405465 | + | 0.405465i | ||||
\(473\) | −319.601 | − | 319.601i | −0.675689 | − | 0.675689i | ||||
\(474\) | 213.823i | 0.451104i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 154.251 | 0.324058 | ||||||||
\(477\) | 64.0362 | − | 64.0362i | 0.134248 | − | 0.134248i | ||||
\(478\) | −86.0324 | − | 86.0324i | −0.179984 | − | 0.179984i | ||||
\(479\) | − | 52.6561i | − | 0.109929i | −0.998488 | − | 0.0549647i | \(-0.982495\pi\) | ||
0.998488 | − | 0.0549647i | \(-0.0175046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.8823 | 0.105784 | ||||||||
\(482\) | 153.724 | − | 153.724i | 0.318930 | − | 0.318930i | ||||
\(483\) | 69.8905 | + | 69.8905i | 0.144701 | + | 0.144701i | ||||
\(484\) | − | 532.030i | − | 1.09924i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −6.34879 | + | 6.34879i | −0.0130365 | + | 0.0130365i | −0.713595 | − | 0.700558i | \(-0.752934\pi\) |
0.700558 | + | 0.713595i | \(0.252934\pi\) | |||||||
\(488\) | 63.9718 | + | 63.9718i | 0.131090 | + | 0.131090i | ||||
\(489\) | − | 310.170i | − | 0.634295i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −899.419 | −1.83181 | −0.915905 | − | 0.401394i | \(-0.868526\pi\) | ||||
−0.915905 | + | 0.401394i | \(0.868526\pi\) | |||||||
\(492\) | −7.32010 | + | 7.32010i | −0.0148782 | + | 0.0148782i | ||||
\(493\) | −1073.00 | − | 1073.00i | −2.17648 | − | 2.17648i | ||||
\(494\) | 20.4857i | 0.0414690i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −26.7392 | −0.0539097 | ||||||||
\(497\) | 202.281 | − | 202.281i | 0.407003 | − | 0.407003i | ||||
\(498\) | 42.3762 | + | 42.3762i | 0.0850927 | + | 0.0850927i | ||||
\(499\) | 895.648i | 1.79489i | 0.441130 | + | 0.897443i | \(0.354578\pi\) | ||||
−0.441130 | + | 0.897443i | \(0.645422\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.8402 | 0.0396011 | ||||||||
\(502\) | 37.9703 | − | 37.9703i | 0.0756380 | − | 0.0756380i | ||||
\(503\) | 251.261 | + | 251.261i | 0.499526 | + | 0.499526i | 0.911290 | − | 0.411764i | \(-0.135087\pi\) |
−0.411764 | + | 0.911290i | \(0.635087\pi\) | |||||||
\(504\) | − | 22.4499i | − | 0.0445435i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −600.071 | −1.18591 | ||||||||
\(507\) | 205.615 | − | 205.615i | 0.405552 | − | 0.405552i | ||||
\(508\) | 4.74587 | + | 4.74587i | 0.00934225 | + | 0.00934225i | ||||
\(509\) | 117.566i | 0.230975i | 0.993309 | + | 0.115487i | \(0.0368429\pi\) | ||||
−0.993309 | + | 0.115487i | \(0.963157\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −299.137 | −0.585395 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −50.3739 | − | 50.3739i | −0.0981948 | − | 0.0981948i | ||||
\(514\) | 416.822i | 0.810938i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 79.5884 | 0.154241 | ||||||||
\(517\) | 1224.84 | − | 1224.84i | 2.36912 | − | 2.36912i | ||||
\(518\) | −127.415 | − | 127.415i | −0.245974 | − | 0.245974i | ||||
\(519\) | 105.090i | 0.202485i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 814.948 | 1.56420 | 0.782100 | − | 0.623153i | \(-0.214149\pi\) | ||||
0.782100 | + | 0.623153i | \(0.214149\pi\) | |||||||
\(522\) | −156.166 | + | 156.166i | −0.299169 | + | 0.299169i | ||||
\(523\) | 532.145 | + | 532.145i | 1.01749 | + | 1.01749i | 0.999844 | + | 0.0176417i | \(0.00561582\pi\) |
0.0176417 | + | 0.999844i | \(0.494384\pi\) | |||||||
\(524\) | 349.486i | 0.666958i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 523.962 | 0.996126 | ||||||||
\(527\) | −137.792 | + | 137.792i | −0.261465 | + | 0.261465i | ||||
\(528\) | 96.3762 | + | 96.3762i | 0.182531 | + | 0.182531i | ||||
\(529\) | − | 63.7918i | − | 0.120589i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 287.070 | 0.540621 | ||||||||
\(532\) | 51.2983 | − | 51.2983i | 0.0964254 | − | 0.0964254i | ||||
\(533\) | −2.23266 | − | 2.23266i | −0.00418885 | − | 0.00418885i | ||||
\(534\) | 148.453i | 0.278002i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 165.971 | 0.309647 | ||||||||
\(537\) | 277.373 | − | 277.373i | 0.516524 | − | 0.516524i | ||||
\(538\) | 165.758 | + | 165.758i | 0.308101 | + | 0.308101i | ||||
\(539\) | 137.709i | 0.255490i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 210.363 | 0.388841 | 0.194420 | − | 0.980918i | \(-0.437717\pi\) | ||||
0.194420 | + | 0.980918i | \(0.437717\pi\) | |||||||
\(542\) | −134.063 | + | 134.063i | −0.247349 | + | 0.247349i | ||||
\(543\) | 303.845 | + | 303.845i | 0.559567 | + | 0.559567i | ||||
\(544\) | − | 164.902i | − | 0.303128i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.84732 | 0.0125409 | ||||||||
\(547\) | −285.880 | + | 285.880i | −0.522633 | + | 0.522633i | −0.918366 | − | 0.395733i | \(-0.870491\pi\) |
0.395733 | + | 0.918366i | \(0.370491\pi\) | |||||||
\(548\) | −35.9315 | − | 35.9315i | −0.0655684 | − | 0.0655684i | ||||
\(549\) | − | 95.9578i | − | 0.174786i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −713.683 | −1.29525 | ||||||||
\(552\) | 74.7161 | − | 74.7161i | 0.135355 | − | 0.135355i | ||||
\(553\) | 163.310 | + | 163.310i | 0.295317 | + | 0.295317i | ||||
\(554\) | − | 738.592i | − | 1.33320i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 319.793 | 0.575168 | ||||||||
\(557\) | −107.372 | + | 107.372i | −0.192769 | + | 0.192769i | −0.796892 | − | 0.604122i | \(-0.793524\pi\) |
0.604122 | + | 0.796892i | \(0.293524\pi\) | |||||||
\(558\) | 20.0544 | + | 20.0544i | 0.0359398 | + | 0.0359398i | ||||
\(559\) | 24.2748i | 0.0434254i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 993.287 | 1.77057 | ||||||||
\(562\) | −106.023 | + | 106.023i | −0.188653 | + | 0.188653i | ||||
\(563\) | −622.633 | − | 622.633i | −1.10592 | − | 1.10592i | −0.993681 | − | 0.112238i | \(-0.964198\pi\) |
−0.112238 | − | 0.993681i | \(-0.535802\pi\) | |||||||
\(564\) | 305.014i | 0.540804i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −39.8075 | −0.0703312 | ||||||||
\(567\) | −16.8375 | + | 16.8375i | −0.0296957 | + | 0.0296957i | ||||
\(568\) | −216.247 | − | 216.247i | −0.380717 | − | 0.380717i | ||||
\(569\) | 406.703i | 0.714768i | 0.933957 | + | 0.357384i | \(0.116331\pi\) | ||||
−0.933957 | + | 0.357384i | \(0.883669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −467.047 | −0.817945 | −0.408973 | − | 0.912547i | \(-0.634113\pi\) | ||||
−0.408973 | + | 0.912547i | \(0.634113\pi\) | |||||||
\(572\) | −29.3951 | + | 29.3951i | −0.0513901 | + | 0.0513901i | ||||
\(573\) | 214.415 | + | 214.415i | 0.374197 | + | 0.374197i | ||||
\(574\) | 11.1816i | 0.0194802i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −110.180 | + | 110.180i | −0.190953 | + | 0.190953i | −0.796108 | − | 0.605155i | \(-0.793111\pi\) |
0.605155 | + | 0.796108i | \(0.293111\pi\) | |||||||
\(578\) | −560.768 | − | 560.768i | −0.970187 | − | 0.970187i | ||||
\(579\) | − | 428.916i | − | 0.740787i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 64.7307 | 0.111412 | ||||||||
\(582\) | −120.158 | + | 120.158i | −0.206457 | + | 0.206457i | ||||
\(583\) | 419.922 | + | 419.922i | 0.720278 | + | 0.720278i | ||||
\(584\) | 319.791i | 0.547587i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 355.526 | 0.606700 | ||||||||
\(587\) | −746.351 | + | 746.351i | −1.27147 | + | 1.27147i | −0.326148 | + | 0.945319i | \(0.605751\pi\) |
−0.945319 | + | 0.326148i | \(0.894249\pi\) | |||||||
\(588\) | −17.1464 | − | 17.1464i | −0.0291606 | − | 0.0291606i | ||||
\(589\) | 91.6489i | 0.155601i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −592.252 | −1.00212 | ||||||||
\(592\) | −136.212 | + | 136.212i | −0.230088 | + | 0.230088i | ||||
\(593\) | 482.746 | + | 482.746i | 0.814075 | + | 0.814075i | 0.985242 | − | 0.171167i | \(-0.0547538\pi\) |
−0.171167 | + | 0.985242i | \(0.554754\pi\) | |||||||
\(594\) | − | 144.564i | − | 0.243374i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 42.1847 | 0.0707797 | ||||||||
\(597\) | −26.6728 | + | 26.6728i | −0.0446780 | + | 0.0446780i | ||||
\(598\) | 22.7887 | + | 22.7887i | 0.0381082 | + | 0.0381082i | ||||
\(599\) | 772.324i | 1.28936i | 0.764454 | + | 0.644678i | \(0.223008\pi\) | ||||
−0.764454 | + | 0.644678i | \(0.776992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 138.790 | 0.230932 | 0.115466 | − | 0.993311i | \(-0.463164\pi\) | ||||
0.115466 | + | 0.993311i | \(0.463164\pi\) | |||||||
\(602\) | 60.7867 | − | 60.7867i | 0.100975 | − | 0.100975i | ||||
\(603\) | −124.478 | − | 124.478i | −0.206431 | − | 0.206431i | ||||
\(604\) | 236.597i | 0.391717i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 430.062 | 0.709672 | ||||||||
\(607\) | 207.780 | − | 207.780i | 0.342307 | − | 0.342307i | −0.514927 | − | 0.857234i | \(-0.672181\pi\) |
0.857234 | + | 0.514927i | \(0.172181\pi\) | |||||||
\(608\) | −54.8402 | − | 54.8402i | −0.0901977 | − | 0.0901977i | ||||
\(609\) | 238.548i | 0.391705i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −93.0304 | −0.152259 | ||||||||
\(612\) | −123.676 | + | 123.676i | −0.202085 | + | 0.202085i | ||||
\(613\) | −98.1205 | − | 98.1205i | −0.160066 | − | 0.160066i | 0.622530 | − | 0.782596i | \(-0.286105\pi\) |
−0.782596 | + | 0.622530i | \(0.786105\pi\) | |||||||
\(614\) | 43.1852i | 0.0703342i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 147.217 | 0.238989 | ||||||||
\(617\) | −102.775 | + | 102.775i | −0.166572 | + | 0.166572i | −0.785471 | − | 0.618899i | \(-0.787579\pi\) |
0.618899 | + | 0.785471i | \(0.287579\pi\) | |||||||
\(618\) | −194.432 | − | 194.432i | −0.314615 | − | 0.314615i | ||||
\(619\) | 599.871i | 0.969098i | 0.874764 | + | 0.484549i | \(0.161016\pi\) | ||||
−0.874764 | + | 0.484549i | \(0.838984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −112.074 | −0.180474 | ||||||||
\(622\) | −293.552 | + | 293.552i | −0.471948 | + | 0.471948i | ||||
\(623\) | 113.383 | + | 113.383i | 0.181995 | + | 0.181995i | ||||
\(624\) | − | 7.32010i | − | 0.0117309i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 661.207 | 1.05624 | ||||||||
\(627\) | 330.330 | − | 330.330i | 0.526843 | − | 0.526843i | ||||
\(628\) | 122.307 | + | 122.307i | 0.194756 | + | 0.194756i | ||||
\(629\) | 1403.85i | 2.23188i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1024.65 | 1.62384 | 0.811922 | − | 0.583766i | \(-0.198421\pi\) | ||||
0.811922 | + | 0.583766i | \(0.198421\pi\) | |||||||
\(632\) | 174.586 | − | 174.586i | 0.276244 | − | 0.276244i | ||||
\(633\) | 230.039 | + | 230.039i | 0.363411 | + | 0.363411i | ||||
\(634\) | − | 832.185i | − | 1.31260i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −104.571 | −0.164419 | ||||||||
\(637\) | 5.22973 | − | 5.22973i | 0.00820994 | − | 0.00820994i | ||||
\(638\) | −1024.07 | − | 1024.07i | −1.60513 | − | 1.60513i | ||||
\(639\) | 324.371i | 0.507622i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1025.12 | 1.59925 | 0.799625 | − | 0.600499i | \(-0.205032\pi\) | ||||
0.799625 | + | 0.600499i | \(0.205032\pi\) | |||||||
\(642\) | −233.830 | + | 233.830i | −0.364222 | + | 0.364222i | ||||
\(643\) | 654.943 | + | 654.943i | 1.01857 | + | 1.01857i | 0.999824 | + | 0.0187492i | \(0.00596839\pi\) |
0.0187492 | + | 0.999824i | \(0.494032\pi\) | |||||||
\(644\) | − | 114.131i | − | 0.177222i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −565.203 | −0.874926 | ||||||||
\(647\) | 151.482 | − | 151.482i | 0.234131 | − | 0.234131i | −0.580284 | − | 0.814414i | \(-0.697058\pi\) |
0.814414 | + | 0.580284i | \(0.197058\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | 1882.48i | 2.90058i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.6336 | 0.0470562 | ||||||||
\(652\) | −253.253 | + | 253.253i | −0.388425 | + | 0.388425i | ||||
\(653\) | 27.1000 | + | 27.1000i | 0.0415007 | + | 0.0415007i | 0.727553 | − | 0.686052i | \(-0.240658\pi\) |
−0.686052 | + | 0.727553i | \(0.740658\pi\) | |||||||
\(654\) | − | 77.5301i | − | 0.118548i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.9537 | 0.0182221 | ||||||||
\(657\) | 239.843 | − | 239.843i | 0.365058 | − | 0.365058i | ||||
\(658\) | 232.958 | + | 232.958i | 0.354040 | + | 0.354040i | ||||
\(659\) | 781.056i | 1.18521i | 0.805492 | + | 0.592607i | \(0.201901\pi\) | ||||
−0.805492 | + | 0.592607i | \(0.798099\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 813.674 | 1.23097 | 0.615487 | − | 0.788147i | \(-0.288959\pi\) | ||||
0.615487 | + | 0.788147i | \(0.288959\pi\) | |||||||
\(662\) | 70.3912 | − | 70.3912i | 0.106331 | − | 0.106331i | ||||
\(663\) | −37.7218 | − | 37.7218i | −0.0568956 | − | 0.0568956i | ||||
\(664\) | − | 69.2000i | − | 0.104217i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 204.318 | 0.306784 | ||||||||
\(667\) | −793.917 | + | 793.917i | −1.19028 | + | 1.19028i | ||||
\(668\) | −16.1994 | − | 16.1994i | −0.0242506 | − | 0.0242506i | ||||
\(669\) | − | 274.489i | − | 0.410297i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 629.250 | 0.937779 | ||||||||
\(672\) | −18.3303 | + | 18.3303i | −0.0272772 | + | 0.0272772i | ||||
\(673\) | 404.915 | + | 404.915i | 0.601656 | + | 0.601656i | 0.940752 | − | 0.339096i | \(-0.110121\pi\) |
−0.339096 | + | 0.940752i | \(0.610121\pi\) | |||||||
\(674\) | − | 266.984i | − | 0.396119i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −335.767 | −0.496697 | ||||||||
\(677\) | 288.937 | − | 288.937i | 0.426790 | − | 0.426790i | −0.460743 | − | 0.887533i | \(-0.652417\pi\) |
0.887533 | + | 0.460743i | \(0.152417\pi\) | |||||||
\(678\) | −170.173 | − | 170.173i | −0.250992 | − | 0.250992i | ||||
\(679\) | 183.545i | 0.270316i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −63.0496 | −0.0925839 | ||||||||
\(682\) | −131.508 | + | 131.508i | −0.192827 | + | 0.192827i | ||||
\(683\) | −513.975 | − | 513.975i | −0.752526 | − | 0.752526i | 0.222424 | − | 0.974950i | \(-0.428603\pi\) |
−0.974950 | + | 0.222424i | \(0.928603\pi\) | |||||||
\(684\) | 82.2603i | 0.120264i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.1916 | −0.0381802 | ||||||||
\(687\) | −347.084 | + | 347.084i | −0.505217 | + | 0.505217i | ||||
\(688\) | −64.9837 | − | 64.9837i | −0.0944530 | − | 0.0944530i | ||||
\(689\) | − | 31.8945i | − | 0.0462910i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 905.116 | 1.30986 | 0.654932 | − | 0.755688i | \(-0.272697\pi\) | ||||
0.654932 | + | 0.755688i | \(0.272697\pi\) | |||||||
\(692\) | 85.8054 | − | 85.8054i | 0.123996 | − | 0.123996i | ||||
\(693\) | −110.413 | − | 110.413i | −0.159326 | − | 0.159326i | ||||
\(694\) | 12.8554i | 0.0185236i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 255.019 | 0.366406 | ||||||||
\(697\) | 61.5994 | − | 61.5994i | 0.0883779 | − | 0.0883779i | ||||
\(698\) | 569.588 | + | 569.588i | 0.816029 | + | 0.816029i | ||||
\(699\) | − | 2.86232i | − | 0.00409489i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1395.60 | 1.99088 | 0.995438 | − | 0.0954091i | \(-0.0304159\pi\) | ||||
0.995438 | + | 0.0954091i | \(0.0304159\pi\) | |||||||
\(702\) | −5.49007 | + | 5.49007i | −0.00782062 | + | 0.00782062i | ||||
\(703\) | 466.868 | + | 466.868i | 0.664109 | + | 0.664109i | ||||
\(704\) | − | 157.382i | − | 0.223553i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −548.325 | −0.776664 | ||||||||
\(707\) | 328.465 | − | 328.465i | 0.464590 | − | 0.464590i | ||||
\(708\) | −234.391 | − | 234.391i | −0.331061 | − | 0.331061i | ||||
\(709\) | − | 896.236i | − | 1.26408i | −0.774934 | − | 0.632042i | \(-0.782217\pi\) | ||
0.774934 | − | 0.632042i | \(-0.217783\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −261.879 | −0.368325 | ||||||||
\(712\) | 121.211 | − | 121.211i | 0.170241 | − | 0.170241i | ||||
\(713\) | 101.952 | + | 101.952i | 0.142991 | + | 0.142991i | ||||
\(714\) | 188.919i | 0.264592i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −452.948 | −0.632610 | ||||||||
\(717\) | 105.368 | − | 105.368i | 0.146956 | − | 0.146956i | ||||
\(718\) | 54.6096 | + | 54.6096i | 0.0760580 | + | 0.0760580i | ||||
\(719\) | 737.704i | 1.02601i | 0.858384 | + | 0.513007i | \(0.171469\pi\) | ||||
−0.858384 | + | 0.513007i | \(0.828531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −297.000 | −0.411928 | ||||||||
\(722\) | 173.035 | − | 173.035i | 0.239660 | − | 0.239660i | ||||
\(723\) | 188.273 | + | 188.273i | 0.260405 | + | 0.260405i | ||||
\(724\) | − | 496.176i | − | 0.685326i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 651.602 | 0.897523 | ||||||||
\(727\) | −256.607 | + | 256.607i | −0.352967 | + | 0.352967i | −0.861212 | − | 0.508245i | \(-0.830294\pi\) |
0.508245 | + | 0.861212i | \(0.330294\pi\) | |||||||
\(728\) | −5.59082 | − | 5.59082i | −0.00767969 | − | 0.00767969i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −669.745 | −0.916204 | ||||||||
\(732\) | −78.3492 | + | 78.3492i | −0.107034 | + | 0.107034i | ||||
\(733\) | −574.332 | − | 574.332i | −0.783537 | − | 0.783537i | 0.196889 | − | 0.980426i | \(-0.436916\pi\) |
−0.980426 | + | 0.196889i | \(0.936916\pi\) | |||||||
\(734\) | − | 113.258i | − | 0.154303i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −122.011 | −0.165776 | ||||||||
\(737\) | 816.273 | − | 816.273i | 1.10756 | − | 1.10756i | ||||
\(738\) | −8.96525 | − | 8.96525i | −0.0121480 | − | 0.0121480i | ||||
\(739\) | 847.046i | 1.14621i | 0.819484 | + | 0.573103i | \(0.194260\pi\) | ||||
−0.819484 | + | 0.573103i | \(0.805740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.0897 | −0.0338593 | ||||||||
\(742\) | −79.8672 | + | 79.8672i | −0.107638 | + | 0.107638i | ||||
\(743\) | −582.140 | − | 582.140i | −0.783500 | − | 0.783500i | 0.196920 | − | 0.980420i | \(-0.436906\pi\) |
−0.980420 | + | 0.196920i | \(0.936906\pi\) | |||||||
\(744\) | − | 32.7487i | − | 0.0440171i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 756.392 | 1.01393 | ||||||||
\(747\) | −51.9000 | + | 51.9000i | −0.0694779 | + | 0.0694779i | ||||
\(748\) | −811.016 | − | 811.016i | −1.08425 | − | 1.08425i | ||||
\(749\) | 357.182i | 0.476878i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 763.660 | 1.01686 | 0.508429 | − | 0.861104i | \(-0.330227\pi\) | ||||
0.508429 | + | 0.861104i | \(0.330227\pi\) | |||||||
\(752\) | 249.043 | − | 249.043i | 0.331174 | − | 0.331174i | ||||
\(753\) | 46.5039 | + | 46.5039i | 0.0617582 | + | 0.0617582i | ||||
\(754\) | 77.7817i | 0.103159i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 27.4955 | 0.0363696 | ||||||||
\(757\) | −256.630 | + | 256.630i | −0.339009 | + | 0.339009i | −0.855994 | − | 0.516985i | \(-0.827054\pi\) |
0.516985 | + | 0.855994i | \(0.327054\pi\) | |||||||
\(758\) | −469.010 | − | 469.010i | −0.618747 | − | 0.618747i | ||||
\(759\) | − | 734.934i | − | 0.968292i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −72.6089 | −0.0954125 | −0.0477062 | − | 0.998861i | \(-0.515191\pi\) | ||||
−0.0477062 | + | 0.998861i | \(0.515191\pi\) | |||||||
\(762\) | −5.81247 | + | 5.81247i | −0.00762792 | + | 0.00762792i | ||||
\(763\) | −59.2146 | − | 59.2146i | −0.0776076 | − | 0.0776076i | ||||
\(764\) | − | 350.138i | − | 0.458296i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −444.569 | −0.580377 | ||||||||
\(767\) | 71.4903 | − | 71.4903i | 0.0932077 | − | 0.0932077i | ||||
\(768\) | 19.5959 | + | 19.5959i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 672.338i | − | 0.874302i | −0.899388 | − | 0.437151i | \(-0.855988\pi\) | ||
0.899388 | − | 0.437151i | \(-0.144012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −510.501 | −0.662128 | ||||||||
\(772\) | −350.208 | + | 350.208i | −0.453638 | + | 0.453638i | ||||
\(773\) | −76.4778 | − | 76.4778i | −0.0989364 | − | 0.0989364i | 0.655906 | − | 0.754842i | \(-0.272287\pi\) |
−0.754842 | + | 0.655906i | \(0.772287\pi\) | |||||||
\(774\) | 97.4755i | 0.125937i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 196.218 | 0.252858 | ||||||||
\(777\) | 156.050 | − | 156.050i | 0.200837 | − | 0.200837i | ||||
\(778\) | −84.3841 | − | 84.3841i | −0.108463 | − | 0.108463i | ||||
\(779\) | − | 40.9713i | − | 0.0525948i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2127.08 | −2.72354 | ||||||||
\(782\) | −628.744 | + | 628.744i | −0.804020 | + | 0.804020i | ||||
\(783\) | −191.264 | − | 191.264i | −0.244271 | − | 0.244271i | ||||
\(784\) | 28.0000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −428.031 | −0.544569 | ||||||||
\(787\) | −1036.91 | + | 1036.91i | −1.31755 | + | 1.31755i | −0.401843 | + | 0.915709i | \(0.631630\pi\) |
−0.915709 | + | 0.401843i | \(0.868370\pi\) | |||||||
\(788\) | 483.572 | + | 483.572i | 0.613670 | + | 0.613670i | ||||
\(789\) | 641.720i | 0.813333i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −259.943 | −0.328626 | ||||||||
\(792\) | −118.036 | + | 118.036i | −0.149036 | + | 0.149036i | ||||
\(793\) | −23.8968 | − | 23.8968i | −0.0301347 | − | 0.0301347i | ||||
\(794\) | − | 437.413i | − | 0.550898i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 43.5565 | 0.0547192 | ||||||||
\(797\) | −980.601 | + | 980.601i | −1.23036 | + | 1.23036i | −0.266542 | + | 0.963823i | \(0.585881\pi\) |
−0.963823 | + | 0.266542i | \(0.914119\pi\) | |||||||
\(798\) | 62.8273 | + | 62.8273i | 0.0787310 | + | 0.0787310i | ||||
\(799\) | − | 2566.72i | − | 3.21242i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −181.817 | −0.226987 | ||||||||
\(802\) | 120.115 | − | 120.115i | 0.149769 | − | 0.149769i | ||||
\(803\) | 1572.79 | + | 1572.79i | 1.95864 | + | 1.95864i | ||||
\(804\) | 203.272i | 0.252826i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.98848 | 0.0123927 | ||||||||
\(807\) | −203.012 | + | 203.012i | −0.251564 | + | 0.251564i | ||||
\(808\) | −351.144 | − | 351.144i | −0.434584 | − | 0.434584i | ||||
\(809\) | 462.188i | 0.571308i | 0.958333 | + | 0.285654i | \(0.0922108\pi\) | ||||
−0.958333 | + | 0.285654i | \(0.907789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −827.689 | −1.02058 | −0.510289 | − | 0.860003i | \(-0.670462\pi\) | ||||
−0.510289 | + | 0.860003i | \(0.670462\pi\) | |||||||
\(812\) | 194.774 | − | 194.774i | 0.239869 | − | 0.239869i | ||||
\(813\) | −164.193 | − | 164.193i | −0.201959 | − | 0.201959i | ||||
\(814\) | 1339.83i | 1.64598i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 201.963 | 0.247503 | ||||||||
\(817\) | −222.732 | + | 222.732i | −0.272622 | + | 0.272622i | ||||
\(818\) | −122.453 | − | 122.453i | −0.149698 | − | 0.149698i | ||||
\(819\) | 8.38623i | 0.0102396i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 514.958 | 0.627233 | 0.313616 | − | 0.949550i | \(-0.398459\pi\) | ||||
0.313616 | + | 0.949550i | \(0.398459\pi\) | |||||||
\(822\) | 44.0069 | − | 44.0069i | 0.0535364 | − | 0.0535364i | ||||
\(823\) | 204.979 | + | 204.979i | 0.249064 | + | 0.249064i | 0.820586 | − | 0.571523i | \(-0.193647\pi\) |
−0.571523 | + | 0.820586i | \(0.693647\pi\) | |||||||
\(824\) | 317.506i | 0.385323i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −358.039 | −0.433461 | ||||||||
\(827\) | −727.042 | + | 727.042i | −0.879132 | + | 0.879132i | −0.993445 | − | 0.114313i | \(-0.963533\pi\) |
0.114313 | + | 0.993445i | \(0.463533\pi\) | |||||||
\(828\) | 91.5082 | + | 91.5082i | 0.110517 | + | 0.110517i | ||||
\(829\) | 1216.17i | 1.46703i | 0.679674 | + | 0.733514i | \(0.262121\pi\) | ||||
−0.679674 | + | 0.733514i | \(0.737879\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 904.587 | 1.08855 | ||||||||
\(832\) | −5.97683 | + | 5.97683i | −0.00718370 | + | 0.00718370i | ||||
\(833\) | 144.289 | + | 144.289i | 0.173216 | + | 0.173216i | ||||
\(834\) | 391.665i | 0.469622i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −539.427 | −0.645248 | ||||||||
\(837\) | −24.5615 | + | 24.5615i | −0.0293447 | + | 0.0293447i | ||||
\(838\) | 705.901 | + | 705.901i | 0.842364 | + | 0.842364i | ||||
\(839\) | − | 350.631i | − | 0.417916i | −0.977925 | − | 0.208958i | \(-0.932993\pi\) | ||
0.977925 | − | 0.208958i | \(-0.0670072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1868.77 | −2.22208 | ||||||||
\(842\) | −2.19359 | + | 2.19359i | −0.00260521 | + | 0.00260521i | ||||
\(843\) | −129.851 | − | 129.851i | −0.154035 | − | 0.154035i | ||||
\(844\) | − | 375.653i | − | 0.445086i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −373.564 | −0.441565 | ||||||||
\(847\) | 497.669 | − | 497.669i | 0.587567 | − | 0.587567i | ||||
\(848\) | 85.3816 | + | 85.3816i | 0.100686 | + | 0.100686i | ||||
\(849\) | − | 48.7540i | − | 0.0574252i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1038.71 | 1.22058 | ||||||||
\(852\) | 264.848 | − | 264.848i | 0.310854 | − | 0.310854i | ||||
\(853\) | 503.944 | + | 503.944i | 0.590790 | + | 0.590790i | 0.937845 | − | 0.347055i | \(-0.112818\pi\) |
−0.347055 | + | 0.937845i | \(0.612818\pi\) | |||||||
\(854\) | 119.680i | 0.140141i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 381.843 | 0.446079 | ||||||||
\(857\) | 764.994 | − | 764.994i | 0.892642 | − | 0.892642i | −0.102129 | − | 0.994771i | \(-0.532566\pi\) |
0.994771 | + | 0.102129i | \(0.0325655\pi\) | |||||||
\(858\) | −36.0015 | − | 36.0015i | −0.0419598 | − | 0.0419598i | ||||
\(859\) | 990.406i | 1.15298i | 0.817106 | + | 0.576488i | \(0.195577\pi\) | ||||
−0.817106 | + | 0.576488i | \(0.804423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.6946 | −0.0159055 | ||||||||
\(862\) | −295.381 | + | 295.381i | −0.342669 | + | 0.342669i | ||||
\(863\) | −417.343 | − | 417.343i | −0.483595 | − | 0.483595i | 0.422682 | − | 0.906278i | \(-0.361089\pi\) |
−0.906278 | + | 0.422682i | \(0.861089\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 318.859 | 0.368198 | ||||||||
\(867\) | 686.798 | − | 686.798i | 0.792154 | − | 0.792154i | ||||
\(868\) | −25.0122 | − | 25.0122i | −0.0288159 | − | 0.0288159i | ||||
\(869\) | − | 1717.29i | − | 1.97617i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −61.9987 | −0.0711811 | ||||||||
\(872\) | −63.3031 | + | 63.3031i | −0.0725953 | + | 0.0725953i | ||||
\(873\) | −147.163 | − | 147.163i | −0.168572 | − | 0.168572i | ||||
\(874\) | 418.194i | 0.478483i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −391.662 | −0.447103 | ||||||||
\(877\) | −512.763 | + | 512.763i | −0.584678 | + | 0.584678i | −0.936185 | − | 0.351507i | \(-0.885669\pi\) |
0.351507 | + | 0.936185i | \(0.385669\pi\) | |||||||
\(878\) | −337.545 | − | 337.545i | −0.384448 | − | 0.384448i | ||||
\(879\) | 435.429i | 0.495369i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 967.153 | 1.09779 | 0.548895 | − | 0.835891i | \(-0.315049\pi\) | ||||
0.548895 | + | 0.835891i | \(0.315049\pi\) | |||||||
\(882\) | 21.0000 | − | 21.0000i | 0.0238095 | − | 0.0238095i | ||||
\(883\) | −243.337 | − | 243.337i | −0.275579 | − | 0.275579i | 0.555762 | − | 0.831341i | \(-0.312427\pi\) |
−0.831341 | + | 0.555762i | \(0.812427\pi\) | |||||||
\(884\) | 61.5994i | 0.0696826i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1022.79 | 1.15439 | ||||||||
\(887\) | −1081.67 | + | 1081.67i | −1.21947 | + | 1.21947i | −0.251648 | + | 0.967819i | \(0.580972\pi\) |
−0.967819 | + | 0.251648i | \(0.919028\pi\) | |||||||
\(888\) | −166.825 | − | 166.825i | −0.187866 | − | 0.187866i | ||||
\(889\) | 8.87870i | 0.00998729i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 177.054 | 0.198714 | ||||||||
\(892\) | −224.119 | + | 224.119i | −0.251255 | + | 0.251255i | ||||
\(893\) | −853.597 | − | 853.597i | −0.955875 | − | 0.955875i | ||||
\(894\) | 51.6655i | 0.0577914i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333 | 0.0334077 | ||||||||
\(897\) | −27.9104 | + | 27.9104i | −0.0311152 | + | 0.0311152i | ||||
\(898\) | −628.997 | − | 628.997i | −0.700442 | − | 0.700442i | ||||
\(899\) | 347.980i | 0.387075i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 879.973 | 0.976663 | ||||||||
\(902\) | 58.7902 | − | 58.7902i | 0.0651777 | − | 0.0651777i | ||||
\(903\) | 74.4481 | + | 74.4481i | 0.0824453 | + | 0.0824453i | ||||
\(904\) | 277.891i | 0.307401i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −289.771 | −0.319835 | ||||||||
\(907\) | −835.988 | + | 835.988i | −0.921706 | + | 0.921706i | −0.997150 | − | 0.0754436i | \(-0.975963\pi\) |
0.0754436 | + | 0.997150i | \(0.475963\pi\) | |||||||
\(908\) | 51.4798 | + | 51.4798i | 0.0566958 | + | 0.0566958i | ||||
\(909\) | 526.716i | 0.579445i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 807.746 | 0.886658 | 0.443329 | − | 0.896359i | \(-0.353797\pi\) | ||||
0.443329 | + | 0.896359i | \(0.353797\pi\) | |||||||
\(912\) | 67.1652 | − | 67.1652i | 0.0736461 | − | 0.0736461i | ||||
\(913\) | −340.338 | − | 340.338i | −0.372769 | − | 0.372769i | ||||
\(914\) | − | 241.409i | − | 0.264124i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 566.786 | 0.618762 | ||||||||
\(917\) | −326.914 | + | 326.914i | −0.356504 | + | 0.356504i | ||||
\(918\) | −151.472 | − | 151.472i | −0.165002 | − | 0.165002i | ||||
\(919\) | 42.8044i | 0.0465771i | 0.999729 | + | 0.0232885i | \(0.00741365\pi\) | ||||
−0.999729 | + | 0.0232885i | \(0.992586\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −52.8909 | −0.0574277 | ||||||||
\(922\) | −53.6000 | + | 53.6000i | −0.0581345 | + | 0.0581345i | ||||
\(923\) | 80.7796 | + | 80.7796i | 0.0875185 | + | 0.0875185i | ||||
\(924\) | 180.303i | 0.195133i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −372.090 | −0.401825 | ||||||||
\(927\) | 238.130 | − | 238.130i | 0.256882 | − | 0.256882i | ||||
\(928\) | −208.222 | − | 208.222i | −0.224377 | − | 0.224377i | ||||
\(929\) | 1264.62i | 1.36127i | 0.732624 | + | 0.680634i | \(0.238295\pi\) | ||||
−0.732624 | + | 0.680634i | \(0.761705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 95.9703 | 0.103083 | ||||||||
\(932\) | −2.33708 | + | 2.33708i | −0.00250759 | + | 0.00250759i | ||||
\(933\) | −359.526 | − | 359.526i | −0.385344 | − | 0.385344i | ||||
\(934\) | − | 666.698i | − | 0.713810i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.96525 | 0.00957826 | ||||||||
\(937\) | 17.5516 | − | 17.5516i | 0.0187317 | − | 0.0187317i | −0.697679 | − | 0.716411i | \(-0.745784\pi\) |
0.716411 | + | 0.697679i | \(0.245784\pi\) | |||||||
\(938\) | 155.251 | + | 155.251i | 0.165513 | + | 0.165513i | ||||
\(939\) | 809.809i | 0.862417i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −768.243 | −0.816411 | −0.408206 | − | 0.912890i | \(-0.633845\pi\) | ||||
−0.408206 | + | 0.912890i | \(0.633845\pi\) | |||||||
\(942\) | −149.794 | + | 149.794i | −0.159018 | + | 0.159018i | ||||
\(943\) | −45.5774 | − | 45.5774i | −0.0483324 | − | 0.0483324i | ||||
\(944\) | 382.759i | 0.405465i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −639.202 | −0.675689 | ||||||||
\(947\) | 166.556 | − | 166.556i | 0.175878 | − | 0.175878i | −0.613678 | − | 0.789556i | \(-0.710311\pi\) |
0.789556 | + | 0.613678i | \(0.210311\pi\) | |||||||
\(948\) | 213.823 | + | 213.823i | 0.225552 | + | 0.225552i | ||||
\(949\) | − | 119.459i | − | 0.125878i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1019.21 | 1.07173 | ||||||||
\(952\) | 154.251 | − | 154.251i | 0.162029 | − | 0.162029i | ||||
\(953\) | 708.623 | + | 708.623i | 0.743571 | + | 0.743571i | 0.973263 | − | 0.229692i | \(-0.0737719\pi\) |
−0.229692 | + | 0.973263i | \(0.573772\pi\) | |||||||
\(954\) | − | 128.072i | − | 0.134248i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −172.065 | −0.179984 | ||||||||
\(957\) | 1254.23 | − | 1254.23i | 1.31058 | − | 1.31058i | ||||
\(958\) | −52.6561 | − | 52.6561i | −0.0549647 | − | 0.0549647i | ||||
\(959\) | − | 67.2217i | − | 0.0700956i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −916.313 | −0.953500 | ||||||||
\(962\) | 50.8823 | − | 50.8823i | 0.0528922 | − | 0.0528922i | ||||
\(963\) | −286.382 | − | 286.382i | −0.297386 | − | 0.297386i | ||||
\(964\) | − | 307.448i | − | 0.318930i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 139.781 | 0.144701 | ||||||||
\(967\) | −358.885 | + | 358.885i | −0.371132 | + | 0.371132i | −0.867890 | − | 0.496757i | \(-0.834524\pi\) |
0.496757 | + | 0.867890i | \(0.334524\pi\) | |||||||
\(968\) | −532.030 | − | 532.030i | −0.549618 | − | 0.549618i | ||||
\(969\) | − | 692.229i | − | 0.714374i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1694.48 | −1.74509 | −0.872546 | − | 0.488532i | \(-0.837533\pi\) | ||||
−0.872546 | + | 0.488532i | \(0.837533\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 299.139 | + | 299.139i | 0.307440 | + | 0.307440i | ||||
\(974\) | 12.6976i | 0.0130365i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 127.944 | 0.131090 | ||||||||
\(977\) | −614.329 | + | 614.329i | −0.628791 | + | 0.628791i | −0.947764 | − | 0.318973i | \(-0.896662\pi\) |
0.318973 | + | 0.947764i | \(0.396662\pi\) | |||||||
\(978\) | −310.170 | − | 310.170i | −0.317147 | − | 0.317147i | ||||
\(979\) | − | 1192.28i | − | 1.21785i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 94.9546 | 0.0967937 | ||||||||
\(982\) | −899.419 | + | 899.419i | −0.915905 | + | 0.915905i | ||||
\(983\) | −135.511 | − | 135.511i | −0.137854 | − | 0.137854i | 0.634812 | − | 0.772667i | \(-0.281077\pi\) |
−0.772667 | + | 0.634812i | \(0.781077\pi\) | |||||||
\(984\) | 14.6402i | 0.0148782i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2146.01 | −2.17648 | ||||||||
\(987\) | −285.314 | + | 285.314i | −0.289072 | + | 0.289072i | ||||
\(988\) | 20.4857 | + | 20.4857i | 0.0207345 | + | 0.0207345i | ||||
\(989\) | 495.545i | 0.501056i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −984.841 | −0.993785 | −0.496892 | − | 0.867812i | \(-0.665526\pi\) | ||||
−0.496892 | + | 0.867812i | \(0.665526\pi\) | |||||||
\(992\) | −26.7392 | + | 26.7392i | −0.0269548 | + | 0.0269548i | ||||
\(993\) | 86.2113 | + | 86.2113i | 0.0868190 | + | 0.0868190i | ||||
\(994\) | − | 404.561i | − | 0.407003i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 84.7523 | 0.0850927 | ||||||||
\(997\) | −597.756 | + | 597.756i | −0.599555 | + | 0.599555i | −0.940194 | − | 0.340639i | \(-0.889357\pi\) |
0.340639 | + | 0.940194i | \(0.389357\pi\) | |||||||
\(998\) | 895.648 | + | 895.648i | 0.897443 | + | 0.897443i | ||||
\(999\) | 250.237i | 0.250488i |
(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 | 1050.3.l.e.43.4 | yes | 8 | |
5.2 | odd | 4 | inner | 1050.3.l.e.757.4 | yes | 8 | |
5.3 | odd | 4 | 1050.3.l.a.757.1 | yes | 8 | ||
5.4 | even | 2 | 1050.3.l.a.43.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.l.a.43.1 | ✓ | 8 | 5.4 | even | 2 | ||
1050.3.l.a.757.1 | yes | 8 | 5.3 | odd | 4 | ||
1050.3.l.e.43.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1050.3.l.e.757.4 | yes | 8 | 5.2 | odd | 4 | inner |