Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(7,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.f (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: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.7 |
Dual form | 75.3.f.c.43.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.224745 | − | 0.224745i | −0.112372 | − | 0.112372i | 0.648685 | − | 0.761057i | \(-0.275319\pi\) |
−0.761057 | + | 0.648685i | \(0.775319\pi\) | |||||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | − | 3.89898i | − | 0.974745i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.550510 | −0.0917517 | ||||||||
\(7\) | −3.44949 | − | 3.44949i | −0.492784 | − | 0.492784i | 0.416398 | − | 0.909182i | \(-0.363292\pi\) |
−0.909182 | + | 0.416398i | \(0.863292\pi\) | |||||||
\(8\) | −1.77526 | + | 1.77526i | −0.221907 | + | 0.221907i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.3485 | 1.03168 | 0.515840 | − | 0.856685i | \(-0.327480\pi\) | ||||
0.515840 | + | 0.856685i | \(0.327480\pi\) | |||||||
\(12\) | −4.77526 | − | 4.77526i | −0.397938 | − | 0.397938i | ||||
\(13\) | 5.55051 | − | 5.55051i | 0.426962 | − | 0.426962i | −0.460630 | − | 0.887592i | \(-0.652376\pi\) |
0.887592 | + | 0.460630i | \(0.152376\pi\) | |||||||
\(14\) | 1.55051i | 0.110751i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.7980 | −0.924872 | ||||||||
\(17\) | 17.3485 | + | 17.3485i | 1.02050 | + | 1.02050i | 0.999785 | + | 0.0207127i | \(0.00659354\pi\) |
0.0207127 | + | 0.999785i | \(0.493406\pi\) | |||||||
\(18\) | −0.674235 | + | 0.674235i | −0.0374575 | + | 0.0374575i | ||||
\(19\) | 8.69694i | 0.457734i | 0.973458 | + | 0.228867i | \(0.0735020\pi\) | ||||
−0.973458 | + | 0.228867i | \(0.926498\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.44949 | −0.402357 | ||||||||
\(22\) | −2.55051 | − | 2.55051i | −0.115932 | − | 0.115932i | ||||
\(23\) | −11.5505 | + | 11.5505i | −0.502196 | + | 0.502196i | −0.912120 | − | 0.409924i | \(-0.865555\pi\) |
0.409924 | + | 0.912120i | \(0.365555\pi\) | |||||||
\(24\) | 4.34847i | 0.181186i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.49490 | −0.0959576 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | −13.4495 | + | 13.4495i | −0.480339 | + | 0.480339i | ||||
\(29\) | 35.1464i | 1.21195i | 0.795485 | + | 0.605973i | \(0.207216\pi\) | ||||
−0.795485 | + | 0.605973i | \(0.792784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6969 | 0.345063 | 0.172531 | − | 0.985004i | \(-0.444805\pi\) | ||||
0.172531 | + | 0.985004i | \(0.444805\pi\) | |||||||
\(32\) | 10.4268 | + | 10.4268i | 0.325837 | + | 0.325837i | ||||
\(33\) | 13.8990 | − | 13.8990i | 0.421181 | − | 0.421181i | ||||
\(34\) | − | 7.79796i | − | 0.229352i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.6969 | −0.324915 | ||||||||
\(37\) | 6.04541 | + | 6.04541i | 0.163389 | + | 0.163389i | 0.784066 | − | 0.620677i | \(-0.213142\pi\) |
−0.620677 | + | 0.784066i | \(0.713142\pi\) | |||||||
\(38\) | 1.95459 | − | 1.95459i | 0.0514366 | − | 0.0514366i | ||||
\(39\) | − | 13.5959i | − | 0.348613i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.696938 | 0.0169985 | 0.00849925 | − | 0.999964i | \(-0.497295\pi\) | ||||
0.00849925 | + | 0.999964i | \(0.497295\pi\) | |||||||
\(42\) | 1.89898 | + | 1.89898i | 0.0452138 | + | 0.0452138i | ||||
\(43\) | 26.4949 | − | 26.4949i | 0.616160 | − | 0.616160i | −0.328384 | − | 0.944544i | \(-0.606504\pi\) |
0.944544 | + | 0.328384i | \(0.106504\pi\) | |||||||
\(44\) | − | 44.2474i | − | 1.00562i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.19184 | 0.112866 | ||||||||
\(47\) | −44.2474 | − | 44.2474i | −0.941435 | − | 0.941435i | 0.0569424 | − | 0.998377i | \(-0.481865\pi\) |
−0.998377 | + | 0.0569424i | \(0.981865\pi\) | |||||||
\(48\) | −18.1237 | + | 18.1237i | −0.377578 | + | 0.377578i | ||||
\(49\) | − | 25.2020i | − | 0.514327i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42.4949 | 0.833233 | ||||||||
\(52\) | −21.6413 | − | 21.6413i | −0.416179 | − | 0.416179i | ||||
\(53\) | 0.696938 | − | 0.696938i | 0.0131498 | − | 0.0131498i | −0.700501 | − | 0.713651i | \(-0.747040\pi\) |
0.713651 | + | 0.700501i | \(0.247040\pi\) | |||||||
\(54\) | 1.65153i | 0.0305839i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.2474 | 0.218704 | ||||||||
\(57\) | 10.6515 | + | 10.6515i | 0.186869 | + | 0.186869i | ||||
\(58\) | 7.89898 | − | 7.89898i | 0.136189 | − | 0.136189i | ||||
\(59\) | − | 39.9342i | − | 0.676851i | −0.940993 | − | 0.338425i | \(-0.890106\pi\) | ||
0.940993 | − | 0.338425i | \(-0.109894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.90918 | 0.0968719 | 0.0484359 | − | 0.998826i | \(-0.484576\pi\) | ||||
0.0484359 | + | 0.998826i | \(0.484576\pi\) | |||||||
\(62\) | −2.40408 | − | 2.40408i | −0.0387755 | − | 0.0387755i | ||||
\(63\) | −10.3485 | + | 10.3485i | −0.164261 | + | 0.164261i | ||||
\(64\) | 54.5051i | 0.851642i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.24745 | −0.0946583 | ||||||||
\(67\) | 45.1010 | + | 45.1010i | 0.673150 | + | 0.673150i | 0.958441 | − | 0.285291i | \(-0.0920903\pi\) |
−0.285291 | + | 0.958441i | \(0.592090\pi\) | |||||||
\(68\) | 67.6413 | − | 67.6413i | 0.994725 | − | 0.994725i | ||||
\(69\) | 28.2929i | 0.410041i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −68.0000 | −0.957746 | −0.478873 | − | 0.877884i | \(-0.658955\pi\) | ||||
−0.478873 | + | 0.877884i | \(0.658955\pi\) | |||||||
\(72\) | 5.32577 | + | 5.32577i | 0.0739690 | + | 0.0739690i | ||||
\(73\) | −77.7878 | + | 77.7878i | −1.06559 | + | 1.06559i | −0.0678931 | + | 0.997693i | \(0.521628\pi\) |
−0.997693 | + | 0.0678931i | \(0.978372\pi\) | |||||||
\(74\) | − | 2.71735i | − | 0.0367209i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 33.9092 | 0.446173 | ||||||||
\(77\) | −39.1464 | − | 39.1464i | −0.508395 | − | 0.508395i | ||||
\(78\) | −3.05561 | + | 3.05561i | −0.0391745 | + | 0.0391745i | ||||
\(79\) | − | 24.4949i | − | 0.310062i | −0.987910 | − | 0.155031i | \(-0.950452\pi\) | ||
0.987910 | − | 0.155031i | \(-0.0495477\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −0.156633 | − | 0.156633i | −0.00191016 | − | 0.00191016i | ||||
\(83\) | −13.1464 | + | 13.1464i | −0.158391 | + | 0.158391i | −0.781853 | − | 0.623463i | \(-0.785725\pi\) |
0.623463 | + | 0.781853i | \(0.285725\pi\) | |||||||
\(84\) | 32.9444i | 0.392195i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.9092 | −0.138479 | ||||||||
\(87\) | 43.0454 | + | 43.0454i | 0.494775 | + | 0.494775i | ||||
\(88\) | −20.1464 | + | 20.1464i | −0.228937 | + | 0.228937i | ||||
\(89\) | 82.1816i | 0.923389i | 0.887039 | + | 0.461695i | \(0.152758\pi\) | ||||
−0.887039 | + | 0.461695i | \(0.847242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −38.2929 | −0.420801 | ||||||||
\(92\) | 45.0352 | + | 45.0352i | 0.489513 | + | 0.489513i | ||||
\(93\) | 13.1010 | − | 13.1010i | 0.140871 | − | 0.140871i | ||||
\(94\) | 19.8888i | 0.211583i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 25.5403 | 0.266045 | ||||||||
\(97\) | 24.5959 | + | 24.5959i | 0.253566 | + | 0.253566i | 0.822431 | − | 0.568865i | \(-0.192617\pi\) |
−0.568865 | + | 0.822431i | \(0.692617\pi\) | |||||||
\(98\) | −5.66403 | + | 5.66403i | −0.0577962 | + | 0.0577962i | ||||
\(99\) | − | 34.0454i | − | 0.343893i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −105.621 | −1.04575 | −0.522876 | − | 0.852409i | \(-0.675141\pi\) | ||||
−0.522876 | + | 0.852409i | \(0.675141\pi\) | |||||||
\(102\) | −9.55051 | − | 9.55051i | −0.0936325 | − | 0.0936325i | ||||
\(103\) | 89.2474 | − | 89.2474i | 0.866480 | − | 0.866480i | −0.125601 | − | 0.992081i | \(-0.540086\pi\) |
0.992081 | + | 0.125601i | \(0.0400858\pi\) | |||||||
\(104\) | 19.7071i | 0.189492i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.313267 | −0.00295535 | ||||||||
\(107\) | −68.7423 | − | 68.7423i | −0.642452 | − | 0.642452i | 0.308706 | − | 0.951158i | \(-0.400104\pi\) |
−0.951158 | + | 0.308706i | \(0.900104\pi\) | |||||||
\(108\) | −14.3258 | + | 14.3258i | −0.132646 | + | 0.132646i | ||||
\(109\) | 68.6969i | 0.630247i | 0.949051 | + | 0.315124i | \(0.102046\pi\) | ||||
−0.949051 | + | 0.315124i | \(0.897954\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.8082 | 0.133407 | ||||||||
\(112\) | 51.0454 | + | 51.0454i | 0.455763 | + | 0.455763i | ||||
\(113\) | −97.6413 | + | 97.6413i | −0.864083 | + | 0.864083i | −0.991809 | − | 0.127727i | \(-0.959232\pi\) |
0.127727 | + | 0.991809i | \(0.459232\pi\) | |||||||
\(114\) | − | 4.78775i | − | 0.0419978i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 137.035 | 1.18134 | ||||||||
\(117\) | −16.6515 | − | 16.6515i | −0.142321 | − | 0.142321i | ||||
\(118\) | −8.97500 | + | 8.97500i | −0.0760593 | + | 0.0760593i | ||||
\(119\) | − | 119.687i | − | 1.00577i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.78775 | 0.0643616 | ||||||||
\(122\) | −1.32806 | − | 1.32806i | −0.0108857 | − | 0.0108857i | ||||
\(123\) | 0.853572 | − | 0.853572i | 0.00693961 | − | 0.00693961i | ||||
\(124\) | − | 41.7071i | − | 0.336348i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.65153 | 0.0369169 | ||||||||
\(127\) | −164.621 | − | 164.621i | −1.29623 | − | 1.29623i | −0.930865 | − | 0.365362i | \(-0.880945\pi\) |
−0.365362 | − | 0.930865i | \(-0.619055\pi\) | |||||||
\(128\) | 53.9569 | − | 53.9569i | 0.421538 | − | 0.421538i | ||||
\(129\) | − | 64.8990i | − | 0.503093i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 106.136 | 0.810200 | 0.405100 | − | 0.914272i | \(-0.367237\pi\) | ||||
0.405100 | + | 0.914272i | \(0.367237\pi\) | |||||||
\(132\) | −54.1918 | − | 54.1918i | −0.410544 | − | 0.410544i | ||||
\(133\) | 30.0000 | − | 30.0000i | 0.225564 | − | 0.225564i | ||||
\(134\) | − | 20.2724i | − | 0.151287i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −61.5959 | −0.452911 | ||||||||
\(137\) | 166.631 | + | 166.631i | 1.21629 | + | 1.21629i | 0.968923 | + | 0.247363i | \(0.0795639\pi\) |
0.247363 | + | 0.968923i | \(0.420436\pi\) | |||||||
\(138\) | 6.35867 | − | 6.35867i | 0.0460774 | − | 0.0460774i | ||||
\(139\) | − | 191.171i | − | 1.37533i | −0.726026 | − | 0.687667i | \(-0.758635\pi\) | ||
0.726026 | − | 0.687667i | \(-0.241365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −108.384 | −0.768679 | ||||||||
\(142\) | 15.2827 | + | 15.2827i | 0.107624 | + | 0.107624i | ||||
\(143\) | 62.9898 | − | 62.9898i | 0.440488 | − | 0.440488i | ||||
\(144\) | 44.3939i | 0.308291i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 34.9648 | 0.239485 | ||||||||
\(147\) | −30.8661 | − | 30.8661i | −0.209973 | − | 0.209973i | ||||
\(148\) | 23.5709 | − | 23.5709i | 0.159263 | − | 0.159263i | ||||
\(149\) | 84.8536i | 0.569487i | 0.958604 | + | 0.284744i | \(0.0919084\pi\) | ||||
−0.958604 | + | 0.284744i | \(0.908092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 148.969 | 0.986552 | 0.493276 | − | 0.869873i | \(-0.335799\pi\) | ||||
0.493276 | + | 0.869873i | \(0.335799\pi\) | |||||||
\(152\) | −15.4393 | − | 15.4393i | −0.101574 | − | 0.101574i | ||||
\(153\) | 52.0454 | − | 52.0454i | 0.340166 | − | 0.340166i | ||||
\(154\) | 17.5959i | 0.114259i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −53.0102 | −0.339809 | ||||||||
\(157\) | −16.8536 | − | 16.8536i | −0.107348 | − | 0.107348i | 0.651393 | − | 0.758741i | \(-0.274185\pi\) |
−0.758741 | + | 0.651393i | \(0.774185\pi\) | |||||||
\(158\) | −5.50510 | + | 5.50510i | −0.0348424 | + | 0.0348424i | ||||
\(159\) | − | 1.70714i | − | 0.0107368i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 79.6867 | 0.494949 | ||||||||
\(162\) | 2.02270 | + | 2.02270i | 0.0124858 | + | 0.0124858i | ||||
\(163\) | −130.606 | + | 130.606i | −0.801265 | + | 0.801265i | −0.983293 | − | 0.182029i | \(-0.941734\pi\) |
0.182029 | + | 0.983293i | \(0.441734\pi\) | |||||||
\(164\) | − | 2.71735i | − | 0.0165692i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.90918 | 0.0355975 | ||||||||
\(167\) | 45.0352 | + | 45.0352i | 0.269672 | + | 0.269672i | 0.828968 | − | 0.559296i | \(-0.188929\pi\) |
−0.559296 | + | 0.828968i | \(0.688929\pi\) | |||||||
\(168\) | 15.0000 | − | 15.0000i | 0.0892857 | − | 0.0892857i | ||||
\(169\) | 107.384i | 0.635406i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.0908 | 0.152578 | ||||||||
\(172\) | −103.303 | − | 103.303i | −0.600599 | − | 0.600599i | ||||
\(173\) | −146.631 | + | 146.631i | −0.847579 | + | 0.847579i | −0.989831 | − | 0.142252i | \(-0.954566\pi\) |
0.142252 | + | 0.989831i | \(0.454566\pi\) | |||||||
\(174\) | − | 19.3485i | − | 0.111198i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −167.934 | −0.954171 | ||||||||
\(177\) | −48.9092 | − | 48.9092i | −0.276323 | − | 0.276323i | ||||
\(178\) | 18.4699 | − | 18.4699i | 0.103763 | − | 0.103763i | ||||
\(179\) | 183.712i | 1.02632i | 0.858292 | + | 0.513161i | \(0.171526\pi\) | ||||
−0.858292 | + | 0.513161i | \(0.828474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −286.272 | −1.58162 | −0.790808 | − | 0.612064i | \(-0.790339\pi\) | ||||
−0.790808 | + | 0.612064i | \(0.790339\pi\) | |||||||
\(182\) | 8.60612 | + | 8.60612i | 0.0472864 | + | 0.0472864i | ||||
\(183\) | 7.23724 | − | 7.23724i | 0.0395478 | − | 0.0395478i | ||||
\(184\) | − | 41.0102i | − | 0.222882i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.88877 | −0.0316601 | ||||||||
\(187\) | 196.879 | + | 196.879i | 1.05283 | + | 1.05283i | ||||
\(188\) | −172.520 | + | 172.520i | −0.917659 | + | 0.917659i | ||||
\(189\) | 25.3485i | 0.134119i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 48.0908 | 0.251784 | 0.125892 | − | 0.992044i | \(-0.459821\pi\) | ||||
0.125892 | + | 0.992044i | \(0.459821\pi\) | |||||||
\(192\) | 66.7548 | + | 66.7548i | 0.347681 | + | 0.347681i | ||||
\(193\) | 255.565 | − | 255.565i | 1.32417 | − | 1.32417i | 0.413809 | − | 0.910364i | \(-0.364198\pi\) |
0.910364 | − | 0.413809i | \(-0.135802\pi\) | |||||||
\(194\) | − | 11.0556i | − | 0.0569877i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −98.2622 | −0.501338 | ||||||||
\(197\) | 96.6969 | + | 96.6969i | 0.490847 | + | 0.490847i | 0.908573 | − | 0.417726i | \(-0.137173\pi\) |
−0.417726 | + | 0.908573i | \(0.637173\pi\) | |||||||
\(198\) | −7.65153 | + | 7.65153i | −0.0386441 | + | 0.0386441i | ||||
\(199\) | 192.606i | 0.967870i | 0.875104 | + | 0.483935i | \(0.160793\pi\) | ||||
−0.875104 | + | 0.483935i | \(0.839207\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 110.474 | 0.549624 | ||||||||
\(202\) | 23.7378 | + | 23.7378i | 0.117514 | + | 0.117514i | ||||
\(203\) | 121.237 | − | 121.237i | 0.597228 | − | 0.597228i | ||||
\(204\) | − | 165.687i | − | 0.812190i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −40.1158 | −0.194737 | ||||||||
\(207\) | 34.6515 | + | 34.6515i | 0.167399 | + | 0.167399i | ||||
\(208\) | −82.1362 | + | 82.1362i | −0.394886 | + | 0.394886i | ||||
\(209\) | 98.6969i | 0.472234i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 147.212 | 0.697688 | 0.348844 | − | 0.937181i | \(-0.386574\pi\) | ||||
0.348844 | + | 0.937181i | \(0.386574\pi\) | |||||||
\(212\) | −2.71735 | − | 2.71735i | −0.0128177 | − | 0.0128177i | ||||
\(213\) | −83.2827 | + | 83.2827i | −0.390998 | + | 0.390998i | ||||
\(214\) | 30.8990i | 0.144388i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.0454 | 0.0603954 | ||||||||
\(217\) | −36.8990 | − | 36.8990i | −0.170041 | − | 0.170041i | ||||
\(218\) | 15.4393 | − | 15.4393i | 0.0708224 | − | 0.0708224i | ||||
\(219\) | 190.540i | 0.870047i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 192.586 | 0.871429 | ||||||||
\(222\) | −3.32806 | − | 3.32806i | −0.0149913 | − | 0.0149913i | ||||
\(223\) | −167.429 | + | 167.429i | −0.750803 | + | 0.750803i | −0.974629 | − | 0.223826i | \(-0.928145\pi\) |
0.223826 | + | 0.974629i | \(0.428145\pi\) | |||||||
\(224\) | − | 71.9342i | − | 0.321135i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 43.8888 | 0.194198 | ||||||||
\(227\) | −253.171 | − | 253.171i | −1.11529 | − | 1.11529i | −0.992423 | − | 0.122870i | \(-0.960790\pi\) |
−0.122870 | − | 0.992423i | \(-0.539210\pi\) | |||||||
\(228\) | 41.5301 | − | 41.5301i | 0.182150 | − | 0.182150i | ||||
\(229\) | − | 224.202i | − | 0.979048i | −0.871990 | − | 0.489524i | \(-0.837171\pi\) | ||
0.871990 | − | 0.489524i | \(-0.162829\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −95.8888 | −0.415103 | ||||||||
\(232\) | −62.3939 | − | 62.3939i | −0.268939 | − | 0.268939i | ||||
\(233\) | 205.712 | − | 205.712i | 0.882883 | − | 0.882883i | −0.110944 | − | 0.993827i | \(-0.535387\pi\) |
0.993827 | + | 0.110944i | \(0.0353873\pi\) | |||||||
\(234\) | 7.48469i | 0.0319859i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −155.703 | −0.659757 | ||||||||
\(237\) | −30.0000 | − | 30.0000i | −0.126582 | − | 0.126582i | ||||
\(238\) | −26.8990 | + | 26.8990i | −0.113021 | + | 0.113021i | ||||
\(239\) | − | 345.798i | − | 1.44685i | −0.690401 | − | 0.723427i | \(-0.742566\pi\) | ||
0.690401 | − | 0.723427i | \(-0.257434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 101.576 | 0.421475 | 0.210738 | − | 0.977543i | \(-0.432413\pi\) | ||||
0.210738 | + | 0.977543i | \(0.432413\pi\) | |||||||
\(242\) | −1.75026 | − | 1.75026i | −0.00723247 | − | 0.00723247i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 23.0398i | − | 0.0944254i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.383672 | −0.00155964 | ||||||||
\(247\) | 48.2724 | + | 48.2724i | 0.195435 | + | 0.195435i | ||||
\(248\) | −18.9898 | + | 18.9898i | −0.0765718 | + | 0.0765718i | ||||
\(249\) | 32.2020i | 0.129325i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −331.258 | −1.31975 | −0.659876 | − | 0.751375i | \(-0.729391\pi\) | ||||
−0.659876 | + | 0.751375i | \(0.729391\pi\) | |||||||
\(252\) | 40.3485 | + | 40.3485i | 0.160113 | + | 0.160113i | ||||
\(253\) | −131.081 | + | 131.081i | −0.518105 | + | 0.518105i | ||||
\(254\) | 73.9954i | 0.291321i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 193.767 | 0.756904 | ||||||||
\(257\) | −33.2372 | − | 33.2372i | −0.129328 | − | 0.129328i | 0.639480 | − | 0.768808i | \(-0.279150\pi\) |
−0.768808 | + | 0.639480i | \(0.779150\pi\) | |||||||
\(258\) | −14.5857 | + | 14.5857i | −0.0565338 | + | 0.0565338i | ||||
\(259\) | − | 41.7071i | − | 0.161031i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 105.439 | 0.403982 | ||||||||
\(262\) | −23.8536 | − | 23.8536i | −0.0910442 | − | 0.0910442i | ||||
\(263\) | 278.157 | − | 278.157i | 1.05763 | − | 1.05763i | 0.0593952 | − | 0.998235i | \(-0.481083\pi\) |
0.998235 | − | 0.0593952i | \(-0.0189172\pi\) | |||||||
\(264\) | 49.3485i | 0.186926i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −13.4847 | −0.0506943 | ||||||||
\(267\) | 100.652 | + | 100.652i | 0.376972 | + | 0.376972i | ||||
\(268\) | 175.848 | − | 175.848i | 0.656149 | − | 0.656149i | ||||
\(269\) | − | 488.499i | − | 1.81598i | −0.418988 | − | 0.907992i | \(-0.637615\pi\) | ||
0.418988 | − | 0.907992i | \(-0.362385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 131.576 | 0.485518 | 0.242759 | − | 0.970087i | \(-0.421947\pi\) | ||||
0.242759 | + | 0.970087i | \(0.421947\pi\) | |||||||
\(272\) | −256.722 | − | 256.722i | −0.943831 | − | 0.943831i | ||||
\(273\) | −46.8990 | + | 46.8990i | −0.171791 | + | 0.171791i | ||||
\(274\) | − | 74.8990i | − | 0.273354i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 110.313 | 0.399686 | ||||||||
\(277\) | −101.510 | − | 101.510i | −0.366461 | − | 0.366461i | 0.499724 | − | 0.866185i | \(-0.333435\pi\) |
−0.866185 | + | 0.499724i | \(0.833435\pi\) | |||||||
\(278\) | −42.9648 | + | 42.9648i | −0.154550 | + | 0.154550i | ||||
\(279\) | − | 32.0908i | − | 0.115021i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 343.303 | 1.22172 | 0.610860 | − | 0.791739i | \(-0.290824\pi\) | ||||
0.610860 | + | 0.791739i | \(0.290824\pi\) | |||||||
\(282\) | 24.3587 | + | 24.3587i | 0.0863783 | + | 0.0863783i | ||||
\(283\) | −1.19184 | + | 1.19184i | −0.00421143 | + | 0.00421143i | −0.709209 | − | 0.704998i | \(-0.750948\pi\) |
0.704998 | + | 0.709209i | \(0.250948\pi\) | |||||||
\(284\) | 265.131i | 0.933558i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.3133 | −0.0989974 | ||||||||
\(287\) | −2.40408 | − | 2.40408i | −0.00837659 | − | 0.00837659i | ||||
\(288\) | 31.2804 | − | 31.2804i | 0.108612 | − | 0.108612i | ||||
\(289\) | 312.939i | 1.08283i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 60.2474 | 0.207036 | ||||||||
\(292\) | 303.293 | + | 303.293i | 1.03867 | + | 1.03867i | ||||
\(293\) | −96.5653 | + | 96.5653i | −0.329574 | + | 0.329574i | −0.852425 | − | 0.522850i | \(-0.824869\pi\) |
0.522850 | + | 0.852425i | \(0.324869\pi\) | |||||||
\(294\) | 13.8740i | 0.0471904i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21.4643 | −0.0725145 | ||||||||
\(297\) | −41.6969 | − | 41.6969i | −0.140394 | − | 0.140394i | ||||
\(298\) | 19.0704 | − | 19.0704i | 0.0639946 | − | 0.0639946i | ||||
\(299\) | 128.222i | 0.428838i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −182.788 | −0.607268 | ||||||||
\(302\) | −33.4801 | − | 33.4801i | −0.110861 | − | 0.110861i | ||||
\(303\) | −129.359 | + | 129.359i | −0.426926 | + | 0.426926i | ||||
\(304\) | − | 128.697i | − | 0.423345i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −23.3939 | −0.0764506 | ||||||||
\(307\) | 124.969 | + | 124.969i | 0.407066 | + | 0.407066i | 0.880714 | − | 0.473648i | \(-0.157063\pi\) |
−0.473648 | + | 0.880714i | \(0.657063\pi\) | |||||||
\(308\) | −152.631 | + | 152.631i | −0.495556 | + | 0.495556i | ||||
\(309\) | − | 218.611i | − | 0.707478i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −586.302 | −1.88522 | −0.942608 | − | 0.333902i | \(-0.891635\pi\) | ||||
−0.942608 | + | 0.333902i | \(0.891635\pi\) | |||||||
\(312\) | 24.1362 | + | 24.1362i | 0.0773597 | + | 0.0773597i | ||||
\(313\) | 102.373 | − | 102.373i | 0.327072 | − | 0.327072i | −0.524400 | − | 0.851472i | \(-0.675710\pi\) |
0.851472 | + | 0.524400i | \(0.175710\pi\) | |||||||
\(314\) | 7.57551i | 0.0241258i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −95.5051 | −0.302231 | ||||||||
\(317\) | 108.783 | + | 108.783i | 0.343165 | + | 0.343165i | 0.857556 | − | 0.514391i | \(-0.171982\pi\) |
−0.514391 | + | 0.857556i | \(0.671982\pi\) | |||||||
\(318\) | −0.383672 | + | 0.383672i | −0.00120651 | + | 0.00120651i | ||||
\(319\) | 398.858i | 1.25034i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −168.384 | −0.524560 | ||||||||
\(322\) | −17.9092 | − | 17.9092i | −0.0556186 | − | 0.0556186i | ||||
\(323\) | −150.879 | + | 150.879i | −0.467116 | + | 0.467116i | ||||
\(324\) | 35.0908i | 0.108305i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 58.7061 | 0.180080 | ||||||||
\(327\) | 84.1362 | + | 84.1362i | 0.257297 | + | 0.257297i | ||||
\(328\) | −1.23724 | + | 1.23724i | −0.00377208 | + | 0.00377208i | ||||
\(329\) | 305.262i | 0.927849i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −245.423 | −0.741461 | −0.370730 | − | 0.928741i | \(-0.620893\pi\) | ||||
−0.370730 | + | 0.928741i | \(0.620893\pi\) | |||||||
\(332\) | 51.2577 | + | 51.2577i | 0.154391 | + | 0.154391i | ||||
\(333\) | 18.1362 | − | 18.1362i | 0.0544631 | − | 0.0544631i | ||||
\(334\) | − | 20.2429i | − | 0.0606074i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 125.035 | 0.372129 | ||||||||
\(337\) | −213.808 | − | 213.808i | −0.634446 | − | 0.634446i | 0.314734 | − | 0.949180i | \(-0.398085\pi\) |
−0.949180 | + | 0.314734i | \(0.898085\pi\) | |||||||
\(338\) | 24.1339 | − | 24.1339i | 0.0714022 | − | 0.0714022i | ||||
\(339\) | 239.171i | 0.705520i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 121.394 | 0.355994 | ||||||||
\(342\) | −5.86378 | − | 5.86378i | −0.0171455 | − | 0.0171455i | ||||
\(343\) | −255.959 | + | 255.959i | −0.746237 | + | 0.746237i | ||||
\(344\) | 94.0704i | 0.273460i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 65.9092 | 0.190489 | ||||||||
\(347\) | 160.050 | + | 160.050i | 0.461239 | + | 0.461239i | 0.899062 | − | 0.437822i | \(-0.144250\pi\) |
−0.437822 | + | 0.899062i | \(0.644250\pi\) | |||||||
\(348\) | 167.833 | − | 167.833i | 0.482279 | − | 0.482279i | ||||
\(349\) | − | 298.009i | − | 0.853894i | −0.904277 | − | 0.426947i | \(-0.859589\pi\) | ||
0.904277 | − | 0.426947i | \(-0.140411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −40.7878 | −0.116204 | ||||||||
\(352\) | 118.328 | + | 118.328i | 0.336159 | + | 0.336159i | ||||
\(353\) | 22.5199 | − | 22.5199i | 0.0637957 | − | 0.0637957i | −0.674489 | − | 0.738285i | \(-0.735636\pi\) |
0.738285 | + | 0.674489i | \(0.235636\pi\) | |||||||
\(354\) | 21.9842i | 0.0621022i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 320.424 | 0.900069 | ||||||||
\(357\) | −146.586 | − | 146.586i | −0.410604 | − | 0.410604i | ||||
\(358\) | 41.2883 | − | 41.2883i | 0.115330 | − | 0.115330i | ||||
\(359\) | 48.2724i | 0.134464i | 0.997737 | + | 0.0672318i | \(0.0214167\pi\) | ||||
−0.997737 | + | 0.0672318i | \(0.978583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 285.363 | 0.790480 | ||||||||
\(362\) | 64.3383 | + | 64.3383i | 0.177730 | + | 0.177730i | ||||
\(363\) | 9.53801 | − | 9.53801i | 0.0262755 | − | 0.0262755i | ||||
\(364\) | 149.303i | 0.410173i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.25307 | −0.00888816 | ||||||||
\(367\) | −146.510 | − | 146.510i | −0.399209 | − | 0.399209i | 0.478745 | − | 0.877954i | \(-0.341092\pi\) |
−0.877954 | + | 0.478745i | \(0.841092\pi\) | |||||||
\(368\) | 170.924 | − | 170.924i | 0.464467 | − | 0.464467i | ||||
\(369\) | − | 2.09082i | − | 0.00566617i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.80816 | −0.0129600 | ||||||||
\(372\) | −51.0806 | − | 51.0806i | −0.137313 | − | 0.137313i | ||||
\(373\) | −86.2066 | + | 86.2066i | −0.231117 | + | 0.231117i | −0.813159 | − | 0.582042i | \(-0.802254\pi\) |
0.582042 | + | 0.813159i | \(0.302254\pi\) | |||||||
\(374\) | − | 88.4949i | − | 0.236617i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 157.101 | 0.417822 | ||||||||
\(377\) | 195.081 | + | 195.081i | 0.517455 | + | 0.517455i | ||||
\(378\) | 5.69694 | − | 5.69694i | 0.0150713 | − | 0.0150713i | ||||
\(379\) | − | 210.000i | − | 0.554090i | −0.960857 | − | 0.277045i | \(-0.910645\pi\) | ||
0.960857 | − | 0.277045i | \(-0.0893551\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −403.237 | −1.05837 | ||||||||
\(382\) | −10.8082 | − | 10.8082i | −0.0282936 | − | 0.0282936i | ||||
\(383\) | 10.6311 | − | 10.6311i | 0.0277575 | − | 0.0277575i | −0.693092 | − | 0.720849i | \(-0.743752\pi\) |
0.720849 | + | 0.693092i | \(0.243752\pi\) | |||||||
\(384\) | − | 132.167i | − | 0.344184i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −114.874 | −0.297601 | ||||||||
\(387\) | −79.4847 | − | 79.4847i | −0.205387 | − | 0.205387i | ||||
\(388\) | 95.8990 | − | 95.8990i | 0.247162 | − | 0.247162i | ||||
\(389\) | − | 535.337i | − | 1.37619i | −0.725621 | − | 0.688094i | \(-0.758448\pi\) | ||
0.725621 | − | 0.688094i | \(-0.241552\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −400.767 | −1.02498 | ||||||||
\(392\) | 44.7401 | + | 44.7401i | 0.114133 | + | 0.114133i | ||||
\(393\) | 129.990 | − | 129.990i | 0.330763 | − | 0.330763i | ||||
\(394\) | − | 43.4643i | − | 0.110315i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −132.742 | −0.335208 | ||||||||
\(397\) | −118.742 | − | 118.742i | −0.299099 | − | 0.299099i | 0.541562 | − | 0.840661i | \(-0.317833\pi\) |
−0.840661 | + | 0.541562i | \(0.817833\pi\) | |||||||
\(398\) | 43.2872 | − | 43.2872i | 0.108762 | − | 0.108762i | ||||
\(399\) | − | 73.4847i | − | 0.184172i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 420.302 | 1.04813 | 0.524067 | − | 0.851677i | \(-0.324414\pi\) | ||||
0.524067 | + | 0.851677i | \(0.324414\pi\) | |||||||
\(402\) | −24.8286 | − | 24.8286i | −0.0617626 | − | 0.0617626i | ||||
\(403\) | 59.3735 | − | 59.3735i | 0.147329 | − | 0.147329i | ||||
\(404\) | 411.814i | 1.01934i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −54.4949 | −0.134224 | ||||||||
\(407\) | 68.6061 | + | 68.6061i | 0.168565 | + | 0.168565i | ||||
\(408\) | −75.4393 | + | 75.4393i | −0.184900 | + | 0.184900i | ||||
\(409\) | − | 515.110i | − | 1.25944i | −0.776823 | − | 0.629719i | \(-0.783170\pi\) | ||
0.776823 | − | 0.629719i | \(-0.216830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 408.161 | 0.993093 | ||||||||
\(412\) | −347.974 | − | 347.974i | −0.844597 | − | 0.844597i | ||||
\(413\) | −137.753 | + | 137.753i | −0.333541 | + | 0.333541i | ||||
\(414\) | − | 15.5755i | − | 0.0376220i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 115.748 | 0.278240 | ||||||||
\(417\) | −234.136 | − | 234.136i | −0.561478 | − | 0.561478i | ||||
\(418\) | 22.1816 | − | 22.1816i | 0.0530661 | − | 0.0530661i | ||||
\(419\) | − | 88.6015i | − | 0.211460i | −0.994395 | − | 0.105730i | \(-0.966282\pi\) | ||
0.994395 | − | 0.105730i | \(-0.0337178\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −257.151 | −0.610810 | −0.305405 | − | 0.952223i | \(-0.598792\pi\) | ||||
−0.305405 | + | 0.952223i | \(0.598792\pi\) | |||||||
\(422\) | −33.0852 | − | 33.0852i | −0.0784009 | − | 0.0784009i | ||||
\(423\) | −132.742 | + | 132.742i | −0.313812 | + | 0.313812i | ||||
\(424\) | 2.47449i | 0.00583605i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 37.4347 | 0.0878749 | ||||||||
\(427\) | −20.3837 | − | 20.3837i | −0.0477369 | − | 0.0477369i | ||||
\(428\) | −268.025 | + | 268.025i | −0.626227 | + | 0.626227i | ||||
\(429\) | − | 154.293i | − | 0.359657i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 804.636 | 1.86690 | 0.933452 | − | 0.358702i | \(-0.116781\pi\) | ||||
0.933452 | + | 0.358702i | \(0.116781\pi\) | |||||||
\(432\) | 54.3712 | + | 54.3712i | 0.125859 | + | 0.125859i | ||||
\(433\) | 344.848 | − | 344.848i | 0.796416 | − | 0.796416i | −0.186113 | − | 0.982528i | \(-0.559589\pi\) |
0.982528 | + | 0.186113i | \(0.0595890\pi\) | |||||||
\(434\) | 16.5857i | 0.0382159i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 267.848 | 0.614330 | ||||||||
\(437\) | −100.454 | − | 100.454i | −0.229872 | − | 0.229872i | ||||
\(438\) | 42.8230 | − | 42.8230i | 0.0977693 | − | 0.0977693i | ||||
\(439\) | 432.929i | 0.986170i | 0.869981 | + | 0.493085i | \(0.164131\pi\) | ||||
−0.869981 | + | 0.493085i | \(0.835869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −75.6061 | −0.171442 | ||||||||
\(442\) | −43.2827 | − | 43.2827i | −0.0979246 | − | 0.0979246i | ||||
\(443\) | −245.131 | + | 245.131i | −0.553342 | + | 0.553342i | −0.927404 | − | 0.374062i | \(-0.877965\pi\) |
0.374062 | + | 0.927404i | \(0.377965\pi\) | |||||||
\(444\) | − | 57.7367i | − | 0.130038i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 75.2577 | 0.168739 | ||||||||
\(447\) | 103.924 | + | 103.924i | 0.232492 | + | 0.232492i | ||||
\(448\) | 188.015 | − | 188.015i | 0.419676 | − | 0.419676i | ||||
\(449\) | 386.091i | 0.859890i | 0.902855 | + | 0.429945i | \(0.141467\pi\) | ||||
−0.902855 | + | 0.429945i | \(0.858533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.90918 | 0.0175370 | ||||||||
\(452\) | 380.702 | + | 380.702i | 0.842260 | + | 0.842260i | ||||
\(453\) | 182.449 | − | 182.449i | 0.402758 | − | 0.402758i | ||||
\(454\) | 113.798i | 0.250656i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −37.8184 | −0.0829350 | ||||||||
\(457\) | 223.747 | + | 223.747i | 0.489599 | + | 0.489599i | 0.908180 | − | 0.418580i | \(-0.137472\pi\) |
−0.418580 | + | 0.908180i | \(0.637472\pi\) | |||||||
\(458\) | −50.3883 | + | 50.3883i | −0.110018 | + | 0.110018i | ||||
\(459\) | − | 127.485i | − | 0.277744i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −722.620 | −1.56751 | −0.783753 | − | 0.621073i | \(-0.786697\pi\) | ||||
−0.783753 | + | 0.621073i | \(0.786697\pi\) | |||||||
\(462\) | 21.5505 | + | 21.5505i | 0.0466461 | + | 0.0466461i | ||||
\(463\) | 129.702 | − | 129.702i | 0.280133 | − | 0.280133i | −0.553029 | − | 0.833162i | \(-0.686528\pi\) |
0.833162 | + | 0.553029i | \(0.186528\pi\) | |||||||
\(464\) | − | 520.095i | − | 1.12090i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −92.4653 | −0.198423 | ||||||||
\(467\) | −415.258 | − | 415.258i | −0.889203 | − | 0.889203i | 0.105244 | − | 0.994446i | \(-0.466438\pi\) |
−0.994446 | + | 0.105244i | \(0.966438\pi\) | |||||||
\(468\) | −64.9240 | + | 64.9240i | −0.138726 | + | 0.138726i | ||||
\(469\) | − | 311.151i | − | 0.663435i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −41.2827 | −0.0876489 | ||||||||
\(472\) | 70.8934 | + | 70.8934i | 0.150198 | + | 0.150198i | ||||
\(473\) | 300.677 | − | 300.677i | 0.635680 | − | 0.635680i | ||||
\(474\) | 13.4847i | 0.0284487i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −466.656 | −0.980370 | ||||||||
\(477\) | −2.09082 | − | 2.09082i | −0.00438326 | − | 0.00438326i | ||||
\(478\) | −77.7163 | + | 77.7163i | −0.162586 | + | 0.162586i | ||||
\(479\) | 304.949i | 0.636637i | 0.947984 | + | 0.318318i | \(0.103118\pi\) | ||||
−0.947984 | + | 0.318318i | \(0.896882\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 67.1102 | 0.139522 | ||||||||
\(482\) | −22.8286 | − | 22.8286i | −0.0473622 | − | 0.0473622i | ||||
\(483\) | 97.5959 | − | 97.5959i | 0.202062 | − | 0.202062i | ||||
\(484\) | − | 30.3643i | − | 0.0627361i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.95459 | 0.0101946 | ||||||||
\(487\) | 429.318 | + | 429.318i | 0.881556 | + | 0.881556i | 0.993693 | − | 0.112137i | \(-0.0357694\pi\) |
−0.112137 | + | 0.993693i | \(0.535769\pi\) | |||||||
\(488\) | −10.4903 | + | 10.4903i | −0.0214965 | + | 0.0214965i | ||||
\(489\) | 319.918i | 0.654230i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −414.318 | −0.843825 | −0.421912 | − | 0.906637i | \(-0.638641\pi\) | ||||
−0.421912 | + | 0.906637i | \(0.638641\pi\) | |||||||
\(492\) | −3.32806 | − | 3.32806i | −0.00676435 | − | 0.00676435i | ||||
\(493\) | −609.737 | + | 609.737i | −1.23679 | + | 1.23679i | ||||
\(494\) | − | 21.6980i | − | 0.0439230i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −158.293 | −0.319139 | ||||||||
\(497\) | 234.565 | + | 234.565i | 0.471962 | + | 0.471962i | ||||
\(498\) | 7.23724 | − | 7.23724i | 0.0145326 | − | 0.0145326i | ||||
\(499\) | 367.585i | 0.736643i | 0.929699 | + | 0.368321i | \(0.120067\pi\) | ||||
−0.929699 | + | 0.368321i | \(0.879933\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 110.313 | 0.220186 | ||||||||
\(502\) | 74.4485 | + | 74.4485i | 0.148304 | + | 0.148304i | ||||
\(503\) | 9.59133 | − | 9.59133i | 0.0190683 | − | 0.0190683i | −0.697508 | − | 0.716577i | \(-0.745708\pi\) |
0.716577 | + | 0.697508i | \(0.245708\pi\) | |||||||
\(504\) | − | 36.7423i | − | 0.0729015i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 58.9194 | 0.116441 | ||||||||
\(507\) | 131.518 | + | 131.518i | 0.259404 | + | 0.259404i | ||||
\(508\) | −641.854 | + | 641.854i | −1.26349 | + | 1.26349i | ||||
\(509\) | 777.489i | 1.52748i | 0.645522 | + | 0.763742i | \(0.276640\pi\) | ||||
−0.645522 | + | 0.763742i | \(0.723360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 536.656 | 1.05021 | ||||||||
\(512\) | −259.376 | − | 259.376i | −0.506593 | − | 0.506593i | ||||
\(513\) | 31.9546 | − | 31.9546i | 0.0622897 | − | 0.0622897i | ||||
\(514\) | 14.9398i | 0.0290658i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −253.040 | −0.490387 | ||||||||
\(517\) | −502.141 | − | 502.141i | −0.971259 | − | 0.971259i | ||||
\(518\) | −9.37347 | + | 9.37347i | −0.0180955 | + | 0.0180955i | ||||
\(519\) | 359.171i | 0.692045i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 321.605 | 0.617284 | 0.308642 | − | 0.951178i | \(-0.400125\pi\) | ||||
0.308642 | + | 0.951178i | \(0.400125\pi\) | |||||||
\(522\) | −23.6969 | − | 23.6969i | −0.0453964 | − | 0.0453964i | ||||
\(523\) | 582.454 | − | 582.454i | 1.11368 | − | 1.11368i | 0.121030 | − | 0.992649i | \(-0.461380\pi\) |
0.992649 | − | 0.121030i | \(-0.0386198\pi\) | |||||||
\(524\) | − | 413.823i | − | 0.789738i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −125.029 | −0.237697 | ||||||||
\(527\) | 185.576 | + | 185.576i | 0.352136 | + | 0.352136i | ||||
\(528\) | −205.677 | + | 205.677i | −0.389539 | + | 0.389539i | ||||
\(529\) | 262.171i | 0.495598i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −119.803 | −0.225617 | ||||||||
\(532\) | −116.969 | − | 116.969i | −0.219867 | − | 0.219867i | ||||
\(533\) | 3.86836 | − | 3.86836i | 0.00725772 | − | 0.00725772i | ||||
\(534\) | − | 45.2418i | − | 0.0847225i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −160.132 | −0.298753 | ||||||||
\(537\) | 225.000 | + | 225.000i | 0.418994 | + | 0.418994i | ||||
\(538\) | −109.788 | + | 109.788i | −0.204066 | + | 0.204066i | ||||
\(539\) | − | 286.005i | − | 0.530621i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 460.697 | 0.851566 | 0.425783 | − | 0.904825i | \(-0.359999\pi\) | ||||
0.425783 | + | 0.904825i | \(0.359999\pi\) | |||||||
\(542\) | −29.5709 | − | 29.5709i | −0.0545589 | − | 0.0545589i | ||||
\(543\) | −350.611 | + | 350.611i | −0.645692 | + | 0.645692i | ||||
\(544\) | 361.778i | 0.665032i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 21.0806 | 0.0386092 | ||||||||
\(547\) | 661.778 | + | 661.778i | 1.20983 | + | 1.20983i | 0.971081 | + | 0.238750i | \(0.0767376\pi\) |
0.238750 | + | 0.971081i | \(0.423262\pi\) | |||||||
\(548\) | 649.691 | − | 649.691i | 1.18557 | − | 1.18557i | ||||
\(549\) | − | 17.7276i | − | 0.0322906i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −305.666 | −0.554748 | ||||||||
\(552\) | −50.2270 | − | 50.2270i | −0.0909910 | − | 0.0909910i | ||||
\(553\) | −84.4949 | + | 84.4949i | −0.152794 | + | 0.152794i | ||||
\(554\) | 45.6276i | 0.0823602i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −745.373 | −1.34060 | ||||||||
\(557\) | −125.909 | − | 125.909i | −0.226049 | − | 0.226049i | 0.584991 | − | 0.811040i | \(-0.301098\pi\) |
−0.811040 | + | 0.584991i | \(0.801098\pi\) | |||||||
\(558\) | −7.21225 | + | 7.21225i | −0.0129252 | + | 0.0129252i | ||||
\(559\) | − | 294.120i | − | 0.526155i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 482.252 | 0.859629 | ||||||||
\(562\) | −77.1556 | − | 77.1556i | −0.137288 | − | 0.137288i | ||||
\(563\) | 200.009 | − | 200.009i | 0.355256 | − | 0.355256i | −0.506805 | − | 0.862061i | \(-0.669174\pi\) |
0.862061 | + | 0.506805i | \(0.169174\pi\) | |||||||
\(564\) | 422.586i | 0.749265i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.535718 | 0.000946498 | ||||||||
\(567\) | 31.0454 | + | 31.0454i | 0.0547538 | + | 0.0547538i | ||||
\(568\) | 120.717 | − | 120.717i | 0.212531 | − | 0.212531i | ||||
\(569\) | − | 599.839i | − | 1.05420i | −0.849804 | − | 0.527099i | \(-0.823280\pi\) | ||
0.849804 | − | 0.527099i | \(-0.176720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −247.970 | −0.434274 | −0.217137 | − | 0.976141i | \(-0.569672\pi\) | ||||
−0.217137 | + | 0.976141i | \(0.569672\pi\) | |||||||
\(572\) | −245.596 | − | 245.596i | −0.429363 | − | 0.429363i | ||||
\(573\) | 58.8990 | − | 58.8990i | 0.102791 | − | 0.102791i | ||||
\(574\) | 1.08061i | 0.00188260i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 163.515 | 0.283881 | ||||||||
\(577\) | 292.121 | + | 292.121i | 0.506276 | + | 0.506276i | 0.913381 | − | 0.407105i | \(-0.133462\pi\) |
−0.407105 | + | 0.913381i | \(0.633462\pi\) | |||||||
\(578\) | 70.3314 | − | 70.3314i | 0.121681 | − | 0.121681i | ||||
\(579\) | − | 626.005i | − | 1.08118i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 90.6969 | 0.156105 | ||||||||
\(582\) | −13.5403 | − | 13.5403i | −0.0232651 | − | 0.0232651i | ||||
\(583\) | 7.90918 | − | 7.90918i | 0.0135664 | − | 0.0135664i | ||||
\(584\) | − | 276.186i | − | 0.472922i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.4051 | 0.0740702 | ||||||||
\(587\) | −611.217 | − | 611.217i | −1.04126 | − | 1.04126i | −0.999112 | − | 0.0421437i | \(-0.986581\pi\) |
−0.0421437 | − | 0.999112i | \(-0.513419\pi\) | |||||||
\(588\) | −120.346 | + | 120.346i | −0.204670 | + | 0.204670i | ||||
\(589\) | 93.0306i | 0.157947i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 236.858 | 0.400775 | ||||||||
\(592\) | −89.4597 | − | 89.4597i | −0.151114 | − | 0.151114i | ||||
\(593\) | −524.742 | + | 524.742i | −0.884894 | + | 0.884894i | −0.994027 | − | 0.109133i | \(-0.965193\pi\) |
0.109133 | + | 0.994027i | \(0.465193\pi\) | |||||||
\(594\) | 18.7423i | 0.0315528i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 330.842 | 0.555105 | ||||||||
\(597\) | 235.893 | + | 235.893i | 0.395131 | + | 0.395131i | ||||
\(598\) | 28.8173 | − | 28.8173i | 0.0481895 | − | 0.0481895i | ||||
\(599\) | − | 368.858i | − | 0.615790i | −0.951420 | − | 0.307895i | \(-0.900375\pi\) | ||
0.951420 | − | 0.307895i | \(-0.0996245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 932.484 | 1.55155 | 0.775777 | − | 0.631007i | \(-0.217358\pi\) | ||||
0.775777 | + | 0.631007i | \(0.217358\pi\) | |||||||
\(602\) | 41.0806 | + | 41.0806i | 0.0682402 | + | 0.0682402i | ||||
\(603\) | 135.303 | − | 135.303i | 0.224383 | − | 0.224383i | ||||
\(604\) | − | 580.829i | − | 0.961637i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 58.1454 | 0.0959495 | ||||||||
\(607\) | −513.611 | − | 513.611i | −0.846146 | − | 0.846146i | 0.143504 | − | 0.989650i | \(-0.454163\pi\) |
−0.989650 | + | 0.143504i | \(0.954163\pi\) | |||||||
\(608\) | −90.6811 | + | 90.6811i | −0.149147 | + | 0.149147i | ||||
\(609\) | − | 296.969i | − | 0.487634i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −491.192 | −0.803915 | ||||||||
\(612\) | −202.924 | − | 202.924i | −0.331575 | − | 0.331575i | ||||
\(613\) | 615.287 | − | 615.287i | 1.00373 | − | 1.00373i | 0.00373821 | − | 0.999993i | \(-0.498810\pi\) |
0.999993 | − | 0.00373821i | \(-0.00118991\pi\) | |||||||
\(614\) | − | 56.1725i | − | 0.0914861i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 138.990 | 0.225633 | ||||||||
\(617\) | −546.752 | − | 546.752i | −0.886145 | − | 0.886145i | 0.108005 | − | 0.994150i | \(-0.465554\pi\) |
−0.994150 | + | 0.108005i | \(0.965554\pi\) | |||||||
\(618\) | −49.1316 | + | 49.1316i | −0.0795010 | + | 0.0795010i | ||||
\(619\) | 152.869i | 0.246962i | 0.992347 | + | 0.123481i | \(0.0394058\pi\) | ||||
−0.992347 | + | 0.123481i | \(0.960594\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 84.8786 | 0.136680 | ||||||||
\(622\) | 131.768 | + | 131.768i | 0.211846 | + | 0.211846i | ||||
\(623\) | 283.485 | − | 283.485i | 0.455032 | − | 0.455032i | ||||
\(624\) | 201.192i | 0.322423i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −46.0158 | −0.0735077 | ||||||||
\(627\) | 120.879 | + | 120.879i | 0.192789 | + | 0.192789i | ||||
\(628\) | −65.7117 | + | 65.7117i | −0.104637 | + | 0.104637i | ||||
\(629\) | 209.757i | 0.333477i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.4847 | −0.0657444 | −0.0328722 | − | 0.999460i | \(-0.510465\pi\) | ||||
−0.0328722 | + | 0.999460i | \(0.510465\pi\) | |||||||
\(632\) | 43.4847 | + | 43.4847i | 0.0688049 | + | 0.0688049i | ||||
\(633\) | 180.297 | − | 180.297i | 0.284830 | − | 0.284830i | ||||
\(634\) | − | 48.8969i | − | 0.0771245i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.65612 | −0.0104656 | ||||||||
\(637\) | −139.884 | − | 139.884i | −0.219598 | − | 0.219598i | ||||
\(638\) | 89.6413 | − | 89.6413i | 0.140504 | − | 0.140504i | ||||
\(639\) | 204.000i | 0.319249i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.2122 | 0.0736541 | 0.0368270 | − | 0.999322i | \(-0.488275\pi\) | ||||
0.0368270 | + | 0.999322i | \(0.488275\pi\) | |||||||
\(642\) | 37.8434 | + | 37.8434i | 0.0589461 | + | 0.0589461i | ||||
\(643\) | −460.372 | + | 460.372i | −0.715976 | + | 0.715976i | −0.967779 | − | 0.251803i | \(-0.918977\pi\) |
0.251803 | + | 0.967779i | \(0.418977\pi\) | |||||||
\(644\) | − | 310.697i | − | 0.482449i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 67.8184 | 0.104982 | ||||||||
\(647\) | 281.287 | + | 281.287i | 0.434756 | + | 0.434756i | 0.890243 | − | 0.455487i | \(-0.150535\pi\) |
−0.455487 | + | 0.890243i | \(0.650535\pi\) | |||||||
\(648\) | 15.9773 | − | 15.9773i | 0.0246563 | − | 0.0246563i | ||||
\(649\) | − | 453.192i | − | 0.698293i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −90.3837 | −0.138838 | ||||||||
\(652\) | 509.231 | + | 509.231i | 0.781029 | + | 0.781029i | ||||
\(653\) | −89.8230 | + | 89.8230i | −0.137554 | + | 0.137554i | −0.772531 | − | 0.634977i | \(-0.781010\pi\) |
0.634977 | + | 0.772531i | \(0.281010\pi\) | |||||||
\(654\) | − | 37.8184i | − | 0.0578263i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.3133 | −0.0157214 | ||||||||
\(657\) | 233.363 | + | 233.363i | 0.355195 | + | 0.355195i | ||||
\(658\) | 68.6061 | − | 68.6061i | 0.104265 | − | 0.104265i | ||||
\(659\) | 1081.24i | 1.64072i | 0.571844 | + | 0.820362i | \(0.306228\pi\) | ||||
−0.571844 | + | 0.820362i | \(0.693772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −632.393 | −0.956721 | −0.478361 | − | 0.878163i | \(-0.658769\pi\) | ||||
−0.478361 | + | 0.878163i | \(0.658769\pi\) | |||||||
\(662\) | 55.1577 | + | 55.1577i | 0.0833197 | + | 0.0833197i | ||||
\(663\) | 235.868 | − | 235.868i | 0.355759 | − | 0.355759i | ||||
\(664\) | − | 46.6765i | − | 0.0702960i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.15205 | −0.0122403 | ||||||||
\(667\) | −405.959 | − | 405.959i | −0.608634 | − | 0.608634i | ||||
\(668\) | 175.591 | − | 175.591i | 0.262861 | − | 0.262861i | ||||
\(669\) | 410.116i | 0.613028i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 67.0602 | 0.0999407 | ||||||||
\(672\) | −88.1010 | − | 88.1010i | −0.131103 | − | 0.131103i | ||||
\(673\) | −233.293 | + | 233.293i | −0.346646 | + | 0.346646i | −0.858859 | − | 0.512213i | \(-0.828826\pi\) |
0.512213 | + | 0.858859i | \(0.328826\pi\) | |||||||
\(674\) | 96.1046i | 0.142588i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 418.687 | 0.619359 | ||||||||
\(677\) | 48.3883 | + | 48.3883i | 0.0714745 | + | 0.0714745i | 0.741940 | − | 0.670466i | \(-0.233906\pi\) |
−0.670466 | + | 0.741940i | \(0.733906\pi\) | |||||||
\(678\) | 53.7526 | − | 53.7526i | 0.0792810 | − | 0.0792810i | ||||
\(679\) | − | 169.687i | − | 0.249907i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −620.141 | −0.910633 | ||||||||
\(682\) | −27.2827 | − | 27.2827i | −0.0400039 | − | 0.0400039i | ||||
\(683\) | −213.410 | + | 213.410i | −0.312459 | + | 0.312459i | −0.845862 | − | 0.533402i | \(-0.820913\pi\) |
0.533402 | + | 0.845862i | \(0.320913\pi\) | |||||||
\(684\) | − | 101.728i | − | 0.148724i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 115.051 | 0.167713 | ||||||||
\(687\) | −274.590 | − | 274.590i | −0.399695 | − | 0.399695i | ||||
\(688\) | −392.070 | + | 392.070i | −0.569870 | + | 0.569870i | ||||
\(689\) | − | 7.73673i | − | 0.0112289i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 151.121 | 0.218700 | 0.109350 | − | 0.994003i | \(-0.465123\pi\) | ||||
0.109350 | + | 0.994003i | \(0.465123\pi\) | |||||||
\(692\) | 571.712 | + | 571.712i | 0.826173 | + | 0.826173i | ||||
\(693\) | −117.439 | + | 117.439i | −0.169465 | + | 0.169465i | ||||
\(694\) | − | 71.9408i | − | 0.103661i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −152.833 | −0.219588 | ||||||||
\(697\) | 12.0908 | + | 12.0908i | 0.0173469 | + | 0.0173469i | ||||
\(698\) | −66.9760 | + | 66.9760i | −0.0959542 | + | 0.0959542i | ||||
\(699\) | − | 503.889i | − | 0.720871i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −745.680 | −1.06374 | −0.531869 | − | 0.846827i | \(-0.678510\pi\) | ||||
−0.531869 | + | 0.846827i | \(0.678510\pi\) | |||||||
\(702\) | 9.16684 | + | 9.16684i | 0.0130582 | + | 0.0130582i | ||||
\(703\) | −52.5765 | + | 52.5765i | −0.0747888 | + | 0.0747888i | ||||
\(704\) | 618.549i | 0.878621i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.1225 | −0.0143378 | ||||||||
\(707\) | 364.338 | + | 364.338i | 0.515330 | + | 0.515330i | ||||
\(708\) | −190.696 | + | 190.696i | −0.269345 | + | 0.269345i | ||||
\(709\) | 719.049i | 1.01417i | 0.861895 | + | 0.507087i | \(0.169278\pi\) | ||||
−0.861895 | + | 0.507087i | \(0.830722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −73.4847 | −0.103354 | ||||||||
\(712\) | −145.893 | − | 145.893i | −0.204906 | − | 0.204906i | ||||
\(713\) | −123.555 | + | 123.555i | −0.173289 | + | 0.173289i | ||||
\(714\) | 65.8888i | 0.0922812i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 716.288 | 1.00040 | ||||||||
\(717\) | −423.514 | − | 423.514i | −0.590675 | − | 0.590675i | ||||
\(718\) | 10.8490 | − | 10.8490i | 0.0151100 | − | 0.0151100i | ||||
\(719\) | − | 605.271i | − | 0.841824i | −0.907101 | − | 0.420912i | \(-0.861710\pi\) | ||
0.907101 | − | 0.420912i | \(-0.138290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −615.716 | −0.853975 | ||||||||
\(722\) | −64.1339 | − | 64.1339i | −0.0888282 | − | 0.0888282i | ||||
\(723\) | 124.404 | − | 124.404i | 0.172067 | − | 0.172067i | ||||
\(724\) | 1116.17i | 1.54167i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.28724 | −0.00590529 | ||||||||
\(727\) | 246.126 | + | 246.126i | 0.338550 | + | 0.338550i | 0.855821 | − | 0.517271i | \(-0.173052\pi\) |
−0.517271 | + | 0.855821i | \(0.673052\pi\) | |||||||
\(728\) | 67.9796 | − | 67.9796i | 0.0933786 | − | 0.0933786i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 919.292 | 1.25758 | ||||||||
\(732\) | −28.2179 | − | 28.2179i | −0.0385490 | − | 0.0385490i | ||||
\(733\) | 270.763 | − | 270.763i | 0.369390 | − | 0.369390i | −0.497865 | − | 0.867255i | \(-0.665882\pi\) |
0.867255 | + | 0.497865i | \(0.165882\pi\) | |||||||
\(734\) | 65.8546i | 0.0897202i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −240.869 | −0.327268 | ||||||||
\(737\) | 511.828 | + | 511.828i | 0.694474 | + | 0.694474i | ||||
\(738\) | −0.469900 | + | 0.469900i | −0.000636721 | + | 0.000636721i | ||||
\(739\) | − | 515.666i | − | 0.697789i | −0.937162 | − | 0.348895i | \(-0.886557\pi\) | ||
0.937162 | − | 0.348895i | \(-0.113443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 118.243 | 0.159572 | ||||||||
\(742\) | 1.08061 | + | 1.08061i | 0.00145635 | + | 0.00145635i | ||||
\(743\) | −420.702 | + | 420.702i | −0.566220 | + | 0.566220i | −0.931067 | − | 0.364847i | \(-0.881121\pi\) |
0.364847 | + | 0.931067i | \(0.381121\pi\) | |||||||
\(744\) | 46.5153i | 0.0625206i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 38.7490 | 0.0519424 | ||||||||
\(747\) | 39.4393 | + | 39.4393i | 0.0527969 | + | 0.0527969i | ||||
\(748\) | 767.626 | − | 767.626i | 1.02624 | − | 1.02624i | ||||
\(749\) | 474.252i | 0.633180i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −859.787 | −1.14486 | −0.572428 | − | 0.819955i | \(-0.693998\pi\) | ||||
−0.572428 | + | 0.819955i | \(0.693998\pi\) | |||||||
\(752\) | 654.772 | + | 654.772i | 0.870707 | + | 0.870707i | ||||
\(753\) | −405.706 | + | 405.706i | −0.538786 | + | 0.538786i | ||||
\(754\) | − | 87.6867i | − | 0.116295i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 98.8332 | 0.130732 | ||||||||
\(757\) | 956.075 | + | 956.075i | 1.26298 | + | 1.26298i | 0.949642 | + | 0.313337i | \(0.101447\pi\) |
0.313337 | + | 0.949642i | \(0.398553\pi\) | |||||||
\(758\) | −47.1964 | + | 47.1964i | −0.0622644 | + | 0.0622644i | ||||
\(759\) | 321.081i | 0.423031i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −322.758 | −0.424124 | −0.212062 | − | 0.977256i | \(-0.568018\pi\) | ||||
−0.212062 | + | 0.977256i | \(0.568018\pi\) | |||||||
\(762\) | 90.6255 | + | 90.6255i | 0.118931 | + | 0.118931i | ||||
\(763\) | 236.969 | − | 236.969i | 0.310576 | − | 0.310576i | ||||
\(764\) | − | 187.505i | − | 0.245426i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.77858 | −0.00623835 | ||||||||
\(767\) | −221.655 | − | 221.655i | −0.288990 | − | 0.288990i | ||||
\(768\) | 237.316 | − | 237.316i | 0.309005 | − | 0.309005i | ||||
\(769\) | 692.402i | 0.900393i | 0.892930 | + | 0.450196i | \(0.148646\pi\) | ||||
−0.892930 | + | 0.450196i | \(0.851354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −81.4143 | −0.105596 | ||||||||
\(772\) | −996.444 | − | 996.444i | −1.29073 | − | 1.29073i | ||||
\(773\) | −375.226 | + | 375.226i | −0.485415 | + | 0.485415i | −0.906856 | − | 0.421441i | \(-0.861525\pi\) |
0.421441 | + | 0.906856i | \(0.361525\pi\) | |||||||
\(774\) | 35.7276i | 0.0461596i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −87.3281 | −0.112536 | ||||||||
\(777\) | −51.0806 | − | 51.0806i | −0.0657408 | − | 0.0657408i | ||||
\(778\) | −120.314 | + | 120.314i | −0.154646 | + | 0.154646i | ||||
\(779\) | 6.06123i | 0.00778078i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −771.696 | −0.988087 | ||||||||
\(782\) | 90.0704 | + | 90.0704i | 0.115180 | + | 0.115180i | ||||
\(783\) | 129.136 | − | 129.136i | 0.164925 | − | 0.164925i | ||||
\(784\) | 372.939i | 0.475687i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −58.4291 | −0.0743373 | ||||||||
\(787\) | −910.990 | − | 910.990i | −1.15755 | − | 1.15755i | −0.985001 | − | 0.172546i | \(-0.944801\pi\) |
−0.172546 | − | 0.985001i | \(-0.555199\pi\) | |||||||
\(788\) | 377.019 | − | 377.019i | 0.478451 | − | 0.478451i | ||||
\(789\) | − | 681.342i | − | 0.863551i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 673.626 | 0.851613 | ||||||||
\(792\) | 60.4393 | + | 60.4393i | 0.0763122 | + | 0.0763122i | ||||
\(793\) | 32.7990 | − | 32.7990i | 0.0413606 | − | 0.0413606i | ||||
\(794\) | 53.3735i | 0.0672210i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 750.967 | 0.943426 | ||||||||
\(797\) | 7.21683 | + | 7.21683i | 0.00905500 | + | 0.00905500i | 0.711620 | − | 0.702565i | \(-0.247962\pi\) |
−0.702565 | + | 0.711620i | \(0.747962\pi\) | |||||||
\(798\) | −16.5153 | + | 16.5153i | −0.0206959 | + | 0.0206959i | ||||
\(799\) | − | 1535.25i | − | 1.92147i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 246.545 | 0.307796 | ||||||||
\(802\) | −94.4607 | − | 94.4607i | −0.117781 | − | 0.117781i | ||||
\(803\) | −882.772 | + | 882.772i | −1.09934 | + | 1.09934i | ||||
\(804\) | − | 430.738i | − | 0.535743i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26.6878 | −0.0331114 | ||||||||
\(807\) | −598.287 | − | 598.287i | −0.741372 | − | 0.741372i | ||||
\(808\) | 187.504 | − | 187.504i | 0.232059 | − | 0.232059i | ||||
\(809\) | − | 150.000i | − | 0.185414i | −0.995693 | − | 0.0927070i | \(-0.970448\pi\) | ||
0.995693 | − | 0.0927070i | \(-0.0295520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1336.85 | 1.64839 | 0.824197 | − | 0.566304i | \(-0.191627\pi\) | ||||
0.824197 | + | 0.566304i | \(0.191627\pi\) | |||||||
\(812\) | −472.702 | − | 472.702i | −0.582145 | − | 0.582145i | ||||
\(813\) | 161.146 | − | 161.146i | 0.198212 | − | 0.198212i | ||||
\(814\) | − | 30.8377i | − | 0.0378842i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −628.838 | −0.770634 | ||||||||
\(817\) | 230.424 | + | 230.424i | 0.282037 | + | 0.282037i | ||||
\(818\) | −115.768 | + | 115.768i | −0.141526 | + | 0.141526i | ||||
\(819\) | 114.879i | 0.140267i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.8934 | −0.0412830 | −0.0206415 | − | 0.999787i | \(-0.506571\pi\) | ||||
−0.0206415 | + | 0.999787i | \(0.506571\pi\) | |||||||
\(822\) | −91.7321 | − | 91.7321i | −0.111596 | − | 0.111596i | ||||
\(823\) | −481.631 | + | 481.631i | −0.585214 | + | 0.585214i | −0.936331 | − | 0.351117i | \(-0.885802\pi\) |
0.351117 | + | 0.936331i | \(0.385802\pi\) | |||||||
\(824\) | 316.874i | 0.384556i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 61.9184 | 0.0749617 | ||||||||
\(827\) | −350.756 | − | 350.756i | −0.424131 | − | 0.424131i | 0.462492 | − | 0.886623i | \(-0.346955\pi\) |
−0.886623 | + | 0.462492i | \(0.846955\pi\) | |||||||
\(828\) | 135.106 | − | 135.106i | 0.163171 | − | 0.163171i | ||||
\(829\) | − | 697.423i | − | 0.841283i | −0.907227 | − | 0.420641i | \(-0.861805\pi\) | ||
0.907227 | − | 0.420641i | \(-0.138195\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −248.647 | −0.299214 | ||||||||
\(832\) | 302.531 | + | 302.531i | 0.363619 | + | 0.363619i | ||||
\(833\) | 437.217 | − | 437.217i | 0.524870 | − | 0.524870i | ||||
\(834\) | 105.242i | 0.126189i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 384.817 | 0.460308 | ||||||||
\(837\) | −39.3031 | − | 39.3031i | −0.0469571 | − | 0.0469571i | ||||
\(838\) | −19.9127 | + | 19.9127i | −0.0237622 | + | 0.0237622i | ||||
\(839\) | 72.3724i | 0.0862604i | 0.999069 | + | 0.0431302i | \(0.0137330\pi\) | ||||
−0.999069 | + | 0.0431302i | \(0.986267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −394.271 | −0.468813 | ||||||||
\(842\) | 57.7934 | + | 57.7934i | 0.0686382 | + | 0.0686382i | ||||
\(843\) | 420.459 | − | 420.459i | 0.498765 | − | 0.498765i | ||||
\(844\) | − | 573.978i | − | 0.680068i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 59.6663 | 0.0705276 | ||||||||
\(847\) | −26.8638 | − | 26.8638i | −0.0317164 | − | 0.0317164i | ||||
\(848\) | −10.3133 | + | 10.3133i | −0.0121619 | + | 0.0121619i | ||||
\(849\) | 2.91939i | 0.00343862i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −139.655 | −0.164107 | ||||||||
\(852\) | 324.717 | + | 324.717i | 0.381124 | + | 0.381124i | ||||
\(853\) | 74.5699 | − | 74.5699i | 0.0874207 | − | 0.0874207i | −0.662044 | − | 0.749465i | \(-0.730311\pi\) |
0.749465 | + | 0.662044i | \(0.230311\pi\) | |||||||
\(854\) | 9.16225i | 0.0107286i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 244.070 | 0.285129 | ||||||||
\(857\) | 293.176 | + | 293.176i | 0.342096 | + | 0.342096i | 0.857155 | − | 0.515059i | \(-0.172230\pi\) |
−0.515059 | + | 0.857155i | \(0.672230\pi\) | |||||||
\(858\) | −34.6765 | + | 34.6765i | −0.0404155 | + | 0.0404155i | ||||
\(859\) | − | 786.867i | − | 0.916027i | −0.888945 | − | 0.458014i | \(-0.848561\pi\) | ||
0.888945 | − | 0.458014i | \(-0.151439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.88877 | −0.00683946 | ||||||||
\(862\) | −180.838 | − | 180.838i | −0.209789 | − | 0.209789i | ||||
\(863\) | 1072.68 | − | 1072.68i | 1.24297 | − | 1.24297i | 0.284204 | − | 0.958764i | \(-0.408271\pi\) |
0.958764 | − | 0.284204i | \(-0.0917292\pi\) | |||||||
\(864\) | − | 76.6209i | − | 0.0886816i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −155.006 | −0.178990 | ||||||||
\(867\) | 383.270 | + | 383.270i | 0.442065 | + | 0.442065i | ||||
\(868\) | −143.868 | + | 143.868i | −0.165747 | + | 0.165747i | ||||
\(869\) | − | 277.980i | − | 0.319884i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 500.667 | 0.574819 | ||||||||
\(872\) | −121.955 | − | 121.955i | −0.139856 | − | 0.139856i | ||||
\(873\) | 73.7878 | − | 73.7878i | 0.0845221 | − | 0.0845221i | ||||
\(874\) | 45.1531i | 0.0516626i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 742.913 | 0.848074 | ||||||||
\(877\) | −239.460 | − | 239.460i | −0.273044 | − | 0.273044i | 0.557280 | − | 0.830324i | \(-0.311845\pi\) |
−0.830324 | + | 0.557280i | \(0.811845\pi\) | |||||||
\(878\) | 97.2985 | − | 97.2985i | 0.110818 | − | 0.110818i | ||||
\(879\) | 236.536i | 0.269096i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 62.8490 | 0.0713382 | 0.0356691 | − | 0.999364i | \(-0.488644\pi\) | ||||
0.0356691 | + | 0.999364i | \(0.488644\pi\) | |||||||
\(882\) | 16.9921 | + | 16.9921i | 0.0192654 | + | 0.0192654i | ||||
\(883\) | 158.061 | − | 158.061i | 0.179005 | − | 0.179005i | −0.611917 | − | 0.790922i | \(-0.709601\pi\) |
0.790922 | + | 0.611917i | \(0.209601\pi\) | |||||||
\(884\) | − | 750.888i | − | 0.849421i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 110.184 | 0.124361 | ||||||||
\(887\) | −30.2066 | − | 30.2066i | −0.0340548 | − | 0.0340548i | 0.689874 | − | 0.723929i | \(-0.257666\pi\) |
−0.723929 | + | 0.689874i | \(0.757666\pi\) | |||||||
\(888\) | −26.2883 | + | 26.2883i | −0.0296039 | + | 0.0296039i | ||||
\(889\) | 1135.72i | 1.27752i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −102.136 | −0.114631 | ||||||||
\(892\) | 652.803 | + | 652.803i | 0.731841 | + | 0.731841i | ||||
\(893\) | 384.817 | − | 384.817i | 0.430926 | − | 0.430926i | ||||
\(894\) | − | 46.7128i | − | 0.0522514i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −372.247 | −0.415455 | ||||||||
\(897\) | 157.040 | + | 157.040i | 0.175072 | + | 0.175072i | ||||
\(898\) | 86.7719 | − | 86.7719i | 0.0966280 | − | 0.0966280i | ||||
\(899\) | 375.959i | 0.418197i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.1816 | 0.0268387 | ||||||||
\(902\) | −1.77755 | − | 1.77755i | −0.00197067 | − | 0.00197067i | ||||
\(903\) | −223.868 | + | 223.868i | −0.247916 | + | 0.247916i | ||||
\(904\) | − | 346.677i | − | 0.383492i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −82.0092 | −0.0905179 | ||||||||
\(907\) | −571.342 | − | 571.342i | −0.629925 | − | 0.629925i | 0.318124 | − | 0.948049i | \(-0.396947\pi\) |
−0.948049 | + | 0.318124i | \(0.896947\pi\) | |||||||
\(908\) | −987.110 | + | 987.110i | −1.08713 | + | 1.08713i | ||||
\(909\) | 316.863i | 0.348584i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 173.362 | 0.190299 | 0.0951494 | − | 0.995463i | \(-0.469667\pi\) | ||||
0.0951494 | + | 0.995463i | \(0.469667\pi\) | |||||||
\(912\) | −157.621 | − | 157.621i | −0.172830 | − | 0.172830i | ||||
\(913\) | −149.192 | + | 149.192i | −0.163408 | + | 0.163408i | ||||
\(914\) | − | 100.572i | − | 0.110035i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −874.159 | −0.954322 | ||||||||
\(917\) | −366.116 | − | 366.116i | −0.399254 | − | 0.399254i | ||||
\(918\) | −28.6515 | + | 28.6515i | −0.0312108 | + | 0.0312108i | ||||
\(919\) | 1147.42i | 1.24856i | 0.781202 | + | 0.624278i | \(0.214607\pi\) | ||||
−0.781202 | + | 0.624278i | \(0.785393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 306.111 | 0.332368 | ||||||||
\(922\) | 162.405 | + | 162.405i | 0.176144 | + | 0.176144i | ||||
\(923\) | −377.435 | + | 377.435i | −0.408922 | + | 0.408922i | ||||
\(924\) | 373.868i | 0.404619i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −58.2995 | −0.0629584 | ||||||||
\(927\) | −267.742 | − | 267.742i | −0.288827 | − | 0.288827i | ||||
\(928\) | −366.464 | + | 366.464i | −0.394897 | + | 0.394897i | ||||
\(929\) | − | 220.293i | − | 0.237129i | −0.992946 | − | 0.118565i | \(-0.962171\pi\) | ||
0.992946 | − | 0.118565i | \(-0.0378292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 219.181 | 0.235425 | ||||||||
\(932\) | −802.066 | − | 802.066i | −0.860586 | − | 0.860586i | ||||
\(933\) | −718.070 | + | 718.070i | −0.769636 | + | 0.769636i | ||||
\(934\) | 186.654i | 0.199844i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 59.1214 | 0.0631639 | ||||||||
\(937\) | 396.090 | + | 396.090i | 0.422721 | + | 0.422721i | 0.886140 | − | 0.463418i | \(-0.153377\pi\) |
−0.463418 | + | 0.886140i | \(0.653377\pi\) | |||||||
\(938\) | −69.9296 | + | 69.9296i | −0.0745518 | + | 0.0745518i | ||||
\(939\) | − | 250.763i | − | 0.267053i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 185.771 | 0.197419 | 0.0987093 | − | 0.995116i | \(-0.468529\pi\) | ||||
0.0987093 | + | 0.995116i | \(0.468529\pi\) | |||||||
\(942\) | 9.27806 | + | 9.27806i | 0.00984932 | + | 0.00984932i | ||||
\(943\) | −8.04999 | + | 8.04999i | −0.00853658 | + | 0.00853658i | ||||
\(944\) | 590.944i | 0.626000i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −135.151 | −0.142866 | ||||||||
\(947\) | 845.190 | + | 845.190i | 0.892492 | + | 0.892492i | 0.994757 | − | 0.102265i | \(-0.0326091\pi\) |
−0.102265 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(948\) | −116.969 | + | 116.969i | −0.123385 | + | 0.123385i | ||||
\(949\) | 863.523i | 0.909930i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 266.463 | 0.280193 | ||||||||
\(952\) | 212.474 | + | 212.474i | 0.223187 | + | 0.223187i | ||||
\(953\) | 630.499 | − | 630.499i | 0.661594 | − | 0.661594i | −0.294161 | − | 0.955756i | \(-0.595040\pi\) |
0.955756 | + | 0.294161i | \(0.0950403\pi\) | |||||||
\(954\) | 0.939800i | 0.000985115i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1348.26 | −1.41031 | ||||||||
\(957\) | 488.499 | + | 488.499i | 0.510449 | + | 0.510449i | ||||
\(958\) | 68.5357 | − | 68.5357i | 0.0715404 | − | 0.0715404i | ||||
\(959\) | − | 1149.58i | − | 1.19873i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −846.576 | −0.880932 | ||||||||
\(962\) | −15.0827 | − | 15.0827i | −0.0156785 | − | 0.0156785i | ||||
\(963\) | −206.227 | + | 206.227i | −0.214151 | + | 0.214151i | ||||
\(964\) | − | 396.041i | − | 0.410831i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −43.8684 | −0.0454124 | ||||||||
\(967\) | 381.690 | + | 381.690i | 0.394716 | + | 0.394716i | 0.876364 | − | 0.481649i | \(-0.159962\pi\) |
−0.481649 | + | 0.876364i | \(0.659962\pi\) | |||||||
\(968\) | −13.8252 | + | 13.8252i | −0.0142823 | + | 0.0142823i | ||||
\(969\) | 369.576i | 0.381399i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1000.44 | −1.03032 | −0.515159 | − | 0.857095i | \(-0.672267\pi\) | ||||
−0.515159 | + | 0.857095i | \(0.672267\pi\) | |||||||
\(972\) | 42.9773 | + | 42.9773i | 0.0442153 | + | 0.0442153i | ||||
\(973\) | −659.444 | + | 659.444i | −0.677743 | + | 0.677743i | ||||
\(974\) | − | 192.974i | − | 0.198125i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −87.4439 | −0.0895941 | ||||||||
\(977\) | −593.662 | − | 593.662i | −0.607637 | − | 0.607637i | 0.334691 | − | 0.942328i | \(-0.391368\pi\) |
−0.942328 | + | 0.334691i | \(0.891368\pi\) | |||||||
\(978\) | 71.9000 | − | 71.9000i | 0.0735174 | − | 0.0735174i | ||||
\(979\) | 932.636i | 0.952641i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 206.091 | 0.210082 | ||||||||
\(982\) | 93.1158 | + | 93.1158i | 0.0948226 | + | 0.0948226i | ||||
\(983\) | 1217.34 | − | 1217.34i | 1.23839 | − | 1.23839i | 0.277731 | − | 0.960659i | \(-0.410418\pi\) |
0.960659 | − | 0.277731i | \(-0.0895824\pi\) | |||||||
\(984\) | 3.03062i | 0.00307989i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 274.070 | 0.277962 | ||||||||
\(987\) | 373.868 | + | 373.868i | 0.378793 | + | 0.378793i | ||||
\(988\) | 188.213 | − | 188.213i | 0.190499 | − | 0.190499i | ||||
\(989\) | 612.059i | 0.618867i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −544.061 | −0.549002 | −0.274501 | − | 0.961587i | \(-0.588513\pi\) | ||||
−0.274501 | + | 0.961587i | \(0.588513\pi\) | |||||||
\(992\) | 111.535 | + | 111.535i | 0.112434 | + | 0.112434i | ||||
\(993\) | −300.581 | + | 300.581i | −0.302700 | + | 0.302700i | ||||
\(994\) | − | 105.435i | − | 0.106071i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 125.555 | 0.126059 | ||||||||
\(997\) | 316.733 | + | 316.733i | 0.317686 | + | 0.317686i | 0.847878 | − | 0.530192i | \(-0.177880\pi\) |
−0.530192 | + | 0.847878i | \(0.677880\pi\) | |||||||
\(998\) | 82.6128 | − | 82.6128i | 0.0827783 | − | 0.0827783i | ||||
\(999\) | − | 44.4245i | − | 0.0444690i |
(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 | 75.3.f.c.7.1 | 4 | ||
3.2 | odd | 2 | 225.3.g.a.82.2 | 4 | |||
4.3 | odd | 2 | 1200.3.bg.k.1057.1 | 4 | |||
5.2 | odd | 4 | 15.3.f.a.13.2 | yes | 4 | ||
5.3 | odd | 4 | inner | 75.3.f.c.43.1 | 4 | ||
5.4 | even | 2 | 15.3.f.a.7.2 | ✓ | 4 | ||
15.2 | even | 4 | 45.3.g.b.28.1 | 4 | |||
15.8 | even | 4 | 225.3.g.a.118.2 | 4 | |||
15.14 | odd | 2 | 45.3.g.b.37.1 | 4 | |||
20.3 | even | 4 | 1200.3.bg.k.193.1 | 4 | |||
20.7 | even | 4 | 240.3.bg.a.193.2 | 4 | |||
20.19 | odd | 2 | 240.3.bg.a.97.2 | 4 | |||
40.19 | odd | 2 | 960.3.bg.h.577.1 | 4 | |||
40.27 | even | 4 | 960.3.bg.h.193.1 | 4 | |||
40.29 | even | 2 | 960.3.bg.i.577.2 | 4 | |||
40.37 | odd | 4 | 960.3.bg.i.193.2 | 4 | |||
45.2 | even | 12 | 405.3.l.f.28.2 | 8 | |||
45.4 | even | 6 | 405.3.l.h.217.1 | 8 | |||
45.7 | odd | 12 | 405.3.l.h.28.1 | 8 | |||
45.14 | odd | 6 | 405.3.l.f.217.2 | 8 | |||
45.22 | odd | 12 | 405.3.l.h.298.2 | 8 | |||
45.29 | odd | 6 | 405.3.l.f.352.1 | 8 | |||
45.32 | even | 12 | 405.3.l.f.298.1 | 8 | |||
45.34 | even | 6 | 405.3.l.h.352.2 | 8 | |||
60.47 | odd | 4 | 720.3.bh.k.433.2 | 4 | |||
60.59 | even | 2 | 720.3.bh.k.577.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.f.a.7.2 | ✓ | 4 | 5.4 | even | 2 | ||
15.3.f.a.13.2 | yes | 4 | 5.2 | odd | 4 | ||
45.3.g.b.28.1 | 4 | 15.2 | even | 4 | |||
45.3.g.b.37.1 | 4 | 15.14 | odd | 2 | |||
75.3.f.c.7.1 | 4 | 1.1 | even | 1 | trivial | ||
75.3.f.c.43.1 | 4 | 5.3 | odd | 4 | inner | ||
225.3.g.a.82.2 | 4 | 3.2 | odd | 2 | |||
225.3.g.a.118.2 | 4 | 15.8 | even | 4 | |||
240.3.bg.a.97.2 | 4 | 20.19 | odd | 2 | |||
240.3.bg.a.193.2 | 4 | 20.7 | even | 4 | |||
405.3.l.f.28.2 | 8 | 45.2 | even | 12 | |||
405.3.l.f.217.2 | 8 | 45.14 | odd | 6 | |||
405.3.l.f.298.1 | 8 | 45.32 | even | 12 | |||
405.3.l.f.352.1 | 8 | 45.29 | odd | 6 | |||
405.3.l.h.28.1 | 8 | 45.7 | odd | 12 | |||
405.3.l.h.217.1 | 8 | 45.4 | even | 6 | |||
405.3.l.h.298.2 | 8 | 45.22 | odd | 12 | |||
405.3.l.h.352.2 | 8 | 45.34 | even | 6 | |||
720.3.bh.k.433.2 | 4 | 60.47 | odd | 4 | |||
720.3.bh.k.577.2 | 4 | 60.59 | even | 2 | |||
960.3.bg.h.193.1 | 4 | 40.27 | even | 4 | |||
960.3.bg.h.577.1 | 4 | 40.19 | odd | 2 | |||
960.3.bg.i.193.2 | 4 | 40.37 | odd | 4 | |||
960.3.bg.i.577.2 | 4 | 40.29 | even | 2 | |||
1200.3.bg.k.193.1 | 4 | 20.3 | even | 4 | |||
1200.3.bg.k.1057.1 | 4 | 4.3 | odd | 2 |