Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,3,Mod(7,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, 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("15.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(0.408720396540\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.13 |
Dual form | 15.3.f.a.7.2 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.224745 | − | 0.224745i | 0.112372 | − | 0.112372i | −0.648685 | − | 0.761057i | \(-0.724681\pi\) |
0.761057 | + | 0.648685i | \(0.224681\pi\) | |||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 3.89898i | 0.974745i | ||||||||
\(5\) | −4.67423 | − | 1.77526i | −0.934847 | − | 0.355051i | ||||
\(6\) | −0.550510 | −0.0917517 | ||||||||
\(7\) | 3.44949 | − | 3.44949i | 0.492784 | − | 0.492784i | −0.416398 | − | 0.909182i | \(-0.636708\pi\) |
0.909182 | + | 0.416398i | \(0.136708\pi\) | |||||||
\(8\) | 1.77526 | + | 1.77526i | 0.221907 | + | 0.221907i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | −1.44949 | + | 0.651531i | −0.144949 | + | 0.0651531i | ||||
\(11\) | 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 | \(-0.347624\pi\) |
−0.887592 | + | 0.460630i | \(0.847624\pi\) | |||||||
\(14\) | − | 1.55051i | − | 0.110751i | ||||||
\(15\) | 3.55051 | + | 7.89898i | 0.236701 | + | 0.526599i | ||||
\(16\) | −14.7980 | −0.924872 | ||||||||
\(17\) | −17.3485 | + | 17.3485i | −1.02050 | + | 1.02050i | −0.0207127 | + | 0.999785i | \(0.506594\pi\) |
−0.999785 | + | 0.0207127i | \(0.993406\pi\) | |||||||
\(18\) | 0.674235 | + | 0.674235i | 0.0374575 | + | 0.0374575i | ||||
\(19\) | − | 8.69694i | − | 0.457734i | −0.973458 | − | 0.228867i | \(-0.926498\pi\) | ||
0.973458 | − | 0.228867i | \(-0.0735020\pi\) | |||||||
\(20\) | 6.92168 | − | 18.2247i | 0.346084 | − | 0.911237i | ||||
\(21\) | −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 | \(-0.134445\pi\) |
−0.409924 | + | 0.912120i | \(0.634445\pi\) | |||||||
\(24\) | − | 4.34847i | − | 0.181186i | ||||||
\(25\) | 18.6969 | + | 16.5959i | 0.747878 | + | 0.663837i | ||||
\(26\) | −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 | \(-0.792784\pi\) | ||
0.795485 | − | 0.605973i | \(-0.207216\pi\) | |||||||
\(30\) | 2.57321 | + | 0.977296i | 0.0857738 | + | 0.0325765i | ||||
\(31\) | 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 | ||||||||
\(35\) | −22.2474 | + | 10.0000i | −0.635641 | + | 0.285714i | ||||
\(36\) | −11.6969 | −0.324915 | ||||||||
\(37\) | −6.04541 | + | 6.04541i | −0.163389 | + | 0.163389i | −0.784066 | − | 0.620677i | \(-0.786858\pi\) |
0.620677 | + | 0.784066i | \(0.286858\pi\) | |||||||
\(38\) | −1.95459 | − | 1.95459i | −0.0514366 | − | 0.0514366i | ||||
\(39\) | 13.5959i | 0.348613i | ||||||||
\(40\) | −5.14643 | − | 11.4495i | −0.128661 | − | 0.286237i | ||||
\(41\) | 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 | \(-0.393496\pi\) |
−0.944544 | + | 0.328384i | \(0.893496\pi\) | |||||||
\(44\) | 44.2474i | 1.00562i | ||||||||
\(45\) | 5.32577 | − | 14.0227i | 0.118350 | − | 0.311616i | ||||
\(46\) | 5.19184 | 0.112866 | ||||||||
\(47\) | 44.2474 | − | 44.2474i | 0.941435 | − | 0.941435i | −0.0569424 | − | 0.998377i | \(-0.518135\pi\) |
0.998377 | + | 0.0569424i | \(0.0181351\pi\) | |||||||
\(48\) | 18.1237 | + | 18.1237i | 0.377578 | + | 0.377578i | ||||
\(49\) | 25.2020i | 0.514327i | ||||||||
\(50\) | 7.93189 | − | 0.472194i | 0.158638 | − | 0.00944387i | ||||
\(51\) | 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 | \(-0.252960\pi\) |
−0.713651 | + | 0.700501i | \(0.752960\pi\) | |||||||
\(54\) | − | 1.65153i | − | 0.0305839i | ||||||
\(55\) | −53.0454 | − | 20.1464i | −0.964462 | − | 0.366299i | ||||
\(56\) | 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 | \(0.109894\pi\) | ||||
−0.940993 | + | 0.338425i | \(0.890106\pi\) | |||||||
\(60\) | −30.7980 | + | 13.8434i | −0.513299 | + | 0.230723i | ||||
\(61\) | 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 | ||||||
\(65\) | 16.0908 | + | 35.7980i | 0.247551 | + | 0.550738i | ||||
\(66\) | −6.24745 | −0.0946583 | ||||||||
\(67\) | −45.1010 | + | 45.1010i | −0.673150 | + | 0.673150i | −0.958441 | − | 0.285291i | \(-0.907910\pi\) |
0.285291 | + | 0.958441i | \(0.407910\pi\) | |||||||
\(68\) | −67.6413 | − | 67.6413i | −0.994725 | − | 0.994725i | ||||
\(69\) | − | 28.2929i | − | 0.410041i | ||||||
\(70\) | −2.75255 | + | 7.24745i | −0.0393222 | + | 0.103535i | ||||
\(71\) | −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 | 0.997693 | + | 0.0678931i | \(0.0216277\pi\) |
0.0678931 | + | 0.997693i | \(0.478372\pi\) | |||||||
\(74\) | 2.71735i | 0.0367209i | ||||||||
\(75\) | −2.57321 | − | 43.2247i | −0.0343095 | − | 0.576330i | ||||
\(76\) | 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 | \(0.0495477\pi\) | ||||
−0.987910 | + | 0.155031i | \(0.950452\pi\) | |||||||
\(80\) | 69.1691 | + | 26.2702i | 0.864614 | + | 0.328377i | ||||
\(81\) | −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 | \(-0.214275\pi\) |
−0.623463 | + | 0.781853i | \(0.714275\pi\) | |||||||
\(84\) | − | 32.9444i | − | 0.392195i | ||||||
\(85\) | 111.889 | − | 50.2929i | 1.31634 | − | 0.591681i | ||||
\(86\) | −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 | \(-0.847242\pi\) | ||
0.887039 | − | 0.461695i | \(-0.152758\pi\) | |||||||
\(90\) | −1.95459 | − | 4.34847i | −0.0217177 | − | 0.0483163i | ||||
\(91\) | −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 | ||||||
\(95\) | −15.4393 | + | 40.6515i | −0.162519 | + | 0.427911i | ||||
\(96\) | 25.5403 | 0.266045 | ||||||||
\(97\) | −24.5959 | + | 24.5959i | −0.253566 | + | 0.253566i | −0.822431 | − | 0.568865i | \(-0.807383\pi\) |
0.568865 | + | 0.822431i | \(0.307383\pi\) | |||||||
\(98\) | 5.66403 | + | 5.66403i | 0.0577962 | + | 0.0577962i | ||||
\(99\) | 34.0454i | 0.343893i | ||||||||
\(100\) | −64.7071 | + | 72.8990i | −0.647071 | + | 0.728990i | ||||
\(101\) | −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 | \(-0.459914\pi\) |
−0.992081 | + | 0.125601i | \(0.959914\pi\) | |||||||
\(104\) | − | 19.7071i | − | 0.189492i | ||||||
\(105\) | 39.4949 | + | 15.0000i | 0.376142 | + | 0.142857i | ||||
\(106\) | −0.313267 | −0.00295535 | ||||||||
\(107\) | 68.7423 | − | 68.7423i | 0.642452 | − | 0.642452i | −0.308706 | − | 0.951158i | \(-0.599896\pi\) |
0.951158 | + | 0.308706i | \(0.0998958\pi\) | |||||||
\(108\) | 14.3258 | + | 14.3258i | 0.132646 | + | 0.132646i | ||||
\(109\) | − | 68.6969i | − | 0.630247i | −0.949051 | − | 0.315124i | \(-0.897954\pi\) | ||
0.949051 | − | 0.315124i | \(-0.102046\pi\) | |||||||
\(110\) | −16.4495 | + | 7.39388i | −0.149541 | + | 0.0672171i | ||||
\(111\) | 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 | \(-0.0407681\pi\) |
−0.127727 | + | 0.991809i | \(0.540768\pi\) | |||||||
\(114\) | 4.78775i | 0.0419978i | ||||||||
\(115\) | −33.4847 | − | 74.4949i | −0.291171 | − | 0.647782i | ||||
\(116\) | 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 | ||||||||
\(120\) | −7.71964 | + | 20.3258i | −0.0643304 | + | 0.169381i | ||||
\(121\) | 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 | ||||||||
\(125\) | −57.9319 | − | 110.765i | −0.463455 | − | 0.886120i | ||||
\(126\) | 4.65153 | 0.0369169 | ||||||||
\(127\) | 164.621 | − | 164.621i | 1.29623 | − | 1.29623i | 0.365362 | − | 0.930865i | \(-0.380945\pi\) |
0.930865 | − | 0.365362i | \(-0.119055\pi\) | |||||||
\(128\) | −53.9569 | − | 53.9569i | −0.421538 | − | 0.421538i | ||||
\(129\) | 64.8990i | 0.503093i | ||||||||
\(130\) | 11.6617 | + | 4.42908i | 0.0897057 | + | 0.0340698i | ||||
\(131\) | 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 | ||||||||
\(135\) | −23.6969 | + | 10.6515i | −0.175533 | + | 0.0789002i | ||||
\(136\) | −61.5959 | −0.452911 | ||||||||
\(137\) | −166.631 | + | 166.631i | −1.21629 | + | 1.21629i | −0.247363 | + | 0.968923i | \(0.579564\pi\) |
−0.968923 | + | 0.247363i | \(0.920436\pi\) | |||||||
\(138\) | −6.35867 | − | 6.35867i | −0.0460774 | − | 0.0460774i | ||||
\(139\) | 191.171i | 1.37533i | 0.726026 | + | 0.687667i | \(0.241365\pi\) | ||||
−0.726026 | + | 0.687667i | \(0.758635\pi\) | |||||||
\(140\) | −38.9898 | − | 86.7423i | −0.278499 | − | 0.619588i | ||||
\(141\) | −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 | ||||||
\(145\) | −62.3939 | + | 164.283i | −0.430303 | + | 1.13298i | ||||
\(146\) | 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 | \(-0.908092\pi\) | ||
0.958604 | − | 0.284744i | \(-0.0919084\pi\) | |||||||
\(150\) | −10.2929 | − | 9.13622i | −0.0686190 | − | 0.0609082i | ||||
\(151\) | 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 | ||||||
\(155\) | −50.0000 | − | 18.9898i | −0.322581 | − | 0.122515i | ||||
\(156\) | −53.0102 | −0.339809 | ||||||||
\(157\) | 16.8536 | − | 16.8536i | 0.107348 | − | 0.107348i | −0.651393 | − | 0.758741i | \(-0.725815\pi\) |
0.758741 | + | 0.651393i | \(0.225815\pi\) | |||||||
\(158\) | 5.50510 | + | 5.50510i | 0.0348424 | + | 0.0348424i | ||||
\(159\) | 1.70714i | 0.0107368i | ||||||||
\(160\) | 67.2474 | − | 30.2270i | 0.420297 | − | 0.188919i | ||||
\(161\) | 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 | \(-0.0582664\pi\) |
−0.182029 | + | 0.983293i | \(0.558266\pi\) | |||||||
\(164\) | 2.71735i | 0.0165692i | ||||||||
\(165\) | 40.2929 | + | 89.6413i | 0.244199 | + | 0.543281i | ||||
\(166\) | 5.90918 | 0.0355975 | ||||||||
\(167\) | −45.0352 | + | 45.0352i | −0.269672 | + | 0.269672i | −0.828968 | − | 0.559296i | \(-0.811071\pi\) |
0.559296 | + | 0.828968i | \(0.311071\pi\) | |||||||
\(168\) | −15.0000 | − | 15.0000i | −0.0892857 | − | 0.0892857i | ||||
\(169\) | − | 107.384i | − | 0.635406i | ||||||
\(170\) | 13.8434 | − | 36.4495i | 0.0814316 | − | 0.214409i | ||||
\(171\) | 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 | \(-0.0454343\pi\) |
−0.142252 | + | 0.989831i | \(0.545434\pi\) | |||||||
\(174\) | 19.3485i | 0.111198i | ||||||||
\(175\) | 121.742 | − | 7.24745i | 0.695671 | − | 0.0414140i | ||||
\(176\) | −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 | \(-0.828474\pi\) | ||
0.858292 | − | 0.513161i | \(-0.171526\pi\) | |||||||
\(180\) | 54.6742 | + | 20.7650i | 0.303746 | + | 0.115361i | ||||
\(181\) | −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 | ||||||||
\(185\) | 38.9898 | − | 17.5255i | 0.210756 | − | 0.0947325i | ||||
\(186\) | −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 | ||||||
\(190\) | 5.66632 | + | 12.6061i | 0.0298228 | + | 0.0663480i | ||||
\(191\) | 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 | −0.910364 | − | 0.413809i | \(-0.864198\pi\) |
−0.413809 | − | 0.910364i | \(-0.635802\pi\) | |||||||
\(194\) | 11.0556i | 0.0569877i | ||||||||
\(195\) | 24.1362 | − | 63.5505i | 0.123776 | − | 0.325900i | ||||
\(196\) | −98.2622 | −0.501338 | ||||||||
\(197\) | −96.6969 | + | 96.6969i | −0.490847 | + | 0.490847i | −0.908573 | − | 0.417726i | \(-0.862827\pi\) |
0.417726 | + | 0.908573i | \(0.362827\pi\) | |||||||
\(198\) | 7.65153 | + | 7.65153i | 0.0386441 | + | 0.0386441i | ||||
\(199\) | − | 192.606i | − | 0.967870i | −0.875104 | − | 0.483935i | \(-0.839207\pi\) | ||
0.875104 | − | 0.483935i | \(-0.160793\pi\) | |||||||
\(200\) | 3.72985 | + | 62.6538i | 0.0186492 | + | 0.313269i | ||||
\(201\) | 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 | ||||||||
\(205\) | −3.25765 | − | 1.23724i | −0.0158910 | − | 0.00603533i | ||||
\(206\) | −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 | ||||||
\(210\) | 12.2474 | − | 5.50510i | 0.0583212 | − | 0.0262148i | ||||
\(211\) | 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 | ||||||
\(215\) | 76.8082 | + | 170.879i | 0.357247 | + | 0.794784i | ||||
\(216\) | 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 | ||||||
\(220\) | 78.5505 | − | 206.823i | 0.357048 | − | 0.940104i | ||||
\(221\) | 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 | \(-0.0718548\pi\) |
−0.223826 | + | 0.974629i | \(0.571855\pi\) | |||||||
\(224\) | 71.9342i | 0.321135i | ||||||||
\(225\) | −49.7878 | + | 56.0908i | −0.221279 | + | 0.249293i | ||||
\(226\) | 43.8888 | 0.194198 | ||||||||
\(227\) | 253.171 | − | 253.171i | 1.11529 | − | 1.11529i | 0.122870 | − | 0.992423i | \(-0.460790\pi\) |
0.992423 | − | 0.122870i | \(-0.0392098\pi\) | |||||||
\(228\) | −41.5301 | − | 41.5301i | −0.182150 | − | 0.182150i | ||||
\(229\) | 224.202i | 0.979048i | 0.871990 | + | 0.489524i | \(0.162829\pi\) | ||||
−0.871990 | + | 0.489524i | \(0.837171\pi\) | |||||||
\(230\) | −24.2679 | − | 9.21683i | −0.105512 | − | 0.0400732i | ||||
\(231\) | −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 | \(-0.464613\pi\) |
−0.993827 | + | 0.110944i | \(0.964613\pi\) | |||||||
\(234\) | − | 7.48469i | − | 0.0319859i | ||||||
\(235\) | −285.373 | + | 128.272i | −1.21436 | + | 0.545840i | ||||
\(236\) | −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 | \(0.257434\pi\) | ||||
−0.690401 | + | 0.723427i | \(0.742566\pi\) | |||||||
\(240\) | −52.5403 | − | 116.889i | −0.218918 | − | 0.487037i | ||||
\(241\) | 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 | ||||||||
\(245\) | 44.7401 | − | 117.800i | 0.182612 | − | 0.480817i | ||||
\(246\) | −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 | ||||||
\(250\) | −37.9138 | − | 11.8740i | −0.151655 | − | 0.0474959i | ||||
\(251\) | −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 | ||||||
\(255\) | −198.631 | − | 75.4393i | −0.778946 | − | 0.295840i | ||||
\(256\) | 193.767 | 0.756904 | ||||||||
\(257\) | 33.2372 | − | 33.2372i | 0.129328 | − | 0.129328i | −0.639480 | − | 0.768808i | \(-0.720850\pi\) |
0.768808 | + | 0.639480i | \(0.220850\pi\) | |||||||
\(258\) | 14.5857 | + | 14.5857i | 0.0565338 | + | 0.0565338i | ||||
\(259\) | 41.7071i | 0.161031i | ||||||||
\(260\) | −139.576 | + | 62.7378i | −0.536829 | + | 0.241299i | ||||
\(261\) | 105.439 | 0.403982 | ||||||||
\(262\) | 23.8536 | − | 23.8536i | 0.0910442 | − | 0.0910442i | ||||
\(263\) | −278.157 | − | 278.157i | −1.05763 | − | 1.05763i | −0.998235 | − | 0.0593952i | \(-0.981083\pi\) |
−0.0593952 | − | 0.998235i | \(-0.518917\pi\) | |||||||
\(264\) | − | 49.3485i | − | 0.186926i | ||||||
\(265\) | 2.02041 | + | 4.49490i | 0.00762419 | + | 0.0169619i | ||||
\(266\) | −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 | \(0.362385\pi\) | ||||
−0.418988 | + | 0.907992i | \(0.637615\pi\) | |||||||
\(270\) | −2.93189 | + | 7.71964i | −0.0108588 | + | 0.0285913i | ||||
\(271\) | 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 | ||||||||
\(275\) | 212.182 | + | 188.338i | 0.771570 | + | 0.684866i | ||||
\(276\) | 110.313 | 0.399686 | ||||||||
\(277\) | 101.510 | − | 101.510i | 0.366461 | − | 0.366461i | −0.499724 | − | 0.866185i | \(-0.666565\pi\) |
0.866185 | + | 0.499724i | \(0.166565\pi\) | |||||||
\(278\) | 42.9648 | + | 42.9648i | 0.154550 | + | 0.154550i | ||||
\(279\) | 32.0908i | 0.115021i | ||||||||
\(280\) | −57.2474 | − | 21.7423i | −0.204455 | − | 0.0776512i | ||||
\(281\) | 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 | \(-0.249052\pi\) |
−0.704998 | + | 0.709209i | \(0.749052\pi\) | |||||||
\(284\) | − | 265.131i | − | 0.933558i | ||||||
\(285\) | 68.6969 | − | 30.8786i | 0.241042 | − | 0.108346i | ||||
\(286\) | −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 | ||||||
\(290\) | 22.8990 | + | 50.9444i | 0.0789620 | + | 0.175670i | ||||
\(291\) | 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 | \(-0.175131\pi\) |
−0.522850 | + | 0.852425i | \(0.675131\pi\) | |||||||
\(294\) | − | 13.8740i | − | 0.0471904i | ||||||
\(295\) | 70.8934 | − | 186.662i | 0.240316 | − | 0.632752i | ||||
\(296\) | −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 | ||||||
\(300\) | 168.532 | − | 10.0329i | 0.561775 | − | 0.0334430i | ||||
\(301\) | −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 | ||||||||
\(305\) | −27.6209 | − | 10.4903i | −0.0905604 | − | 0.0343945i | ||||
\(306\) | −23.3939 | −0.0764506 | ||||||||
\(307\) | −124.969 | + | 124.969i | −0.407066 | + | 0.407066i | −0.880714 | − | 0.473648i | \(-0.842937\pi\) |
0.473648 | + | 0.880714i | \(0.342937\pi\) | |||||||
\(308\) | 152.631 | + | 152.631i | 0.495556 | + | 0.495556i | ||||
\(309\) | 218.611i | 0.707478i | ||||||||
\(310\) | −15.5051 | + | 6.96938i | −0.0500165 | + | 0.0224819i | ||||
\(311\) | −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 | \(-0.324290\pi\) |
−0.851472 | + | 0.524400i | \(0.824290\pi\) | |||||||
\(314\) | − | 7.57551i | − | 0.0241258i | ||||||
\(315\) | −30.0000 | − | 66.7423i | −0.0952381 | − | 0.211880i | ||||
\(316\) | −95.5051 | −0.302231 | ||||||||
\(317\) | −108.783 | + | 108.783i | −0.343165 | + | 0.343165i | −0.857556 | − | 0.514391i | \(-0.828018\pi\) |
0.514391 | + | 0.857556i | \(0.328018\pi\) | |||||||
\(318\) | 0.383672 | + | 0.383672i | 0.00120651 | + | 0.00120651i | ||||
\(319\) | − | 398.858i | − | 1.25034i | ||||||
\(320\) | −96.7605 | + | 254.770i | −0.302376 | + | 0.796155i | ||||
\(321\) | −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 | ||||||
\(325\) | −11.6617 | − | 195.893i | −0.0358823 | − | 0.602749i | ||||
\(326\) | 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 | ||||||
\(330\) | 29.2020 | + | 11.0908i | 0.0884910 | + | 0.0336085i | ||||
\(331\) | −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 | ||||||||
\(335\) | 290.879 | − | 130.747i | 0.868294 | − | 0.390289i | ||||
\(336\) | 125.035 | 0.372129 | ||||||||
\(337\) | 213.808 | − | 213.808i | 0.634446 | − | 0.634446i | −0.314734 | − | 0.949180i | \(-0.601915\pi\) |
0.949180 | + | 0.314734i | \(0.101915\pi\) | |||||||
\(338\) | −24.1339 | − | 24.1339i | −0.0714022 | − | 0.0714022i | ||||
\(339\) | − | 239.171i | − | 0.705520i | ||||||
\(340\) | 196.091 | + | 436.252i | 0.576738 | + | 1.28309i | ||||
\(341\) | 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 | ||||||
\(345\) | −50.2270 | + | 132.247i | −0.145586 | + | 0.383326i | ||||
\(346\) | 65.9092 | 0.190489 | ||||||||
\(347\) | −160.050 | + | 160.050i | −0.461239 | + | 0.461239i | −0.899062 | − | 0.437822i | \(-0.855750\pi\) |
0.437822 | + | 0.899062i | \(0.355750\pi\) | |||||||
\(348\) | −167.833 | − | 167.833i | −0.482279 | − | 0.482279i | ||||
\(349\) | 298.009i | 0.853894i | 0.904277 | + | 0.426947i | \(0.140411\pi\) | ||||
−0.904277 | + | 0.426947i | \(0.859589\pi\) | |||||||
\(350\) | 25.7321 | − | 28.9898i | 0.0735204 | − | 0.0828280i | ||||
\(351\) | −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 | \(-0.264364\pi\) |
−0.738285 | + | 0.674489i | \(0.764364\pi\) | |||||||
\(354\) | − | 21.9842i | − | 0.0621022i | ||||||
\(355\) | 317.848 | + | 120.717i | 0.895346 | + | 0.340049i | ||||
\(356\) | 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 | \(-0.978583\pi\) | ||
0.997737 | − | 0.0672318i | \(-0.0214167\pi\) | |||||||
\(360\) | 34.3485 | − | 15.4393i | 0.0954124 | − | 0.0428869i | ||||
\(361\) | 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 | ||||||
\(365\) | −225.505 | − | 501.691i | −0.617822 | − | 1.37450i | ||||
\(366\) | −3.25307 | −0.00888816 | ||||||||
\(367\) | 146.510 | − | 146.510i | 0.399209 | − | 0.399209i | −0.478745 | − | 0.877954i | \(-0.658908\pi\) |
0.877954 | + | 0.478745i | \(0.158908\pi\) | |||||||
\(368\) | −170.924 | − | 170.924i | −0.464467 | − | 0.464467i | ||||
\(369\) | 2.09082i | 0.00566617i | ||||||||
\(370\) | 4.82399 | − | 12.7015i | 0.0130378 | − | 0.0343284i | ||||
\(371\) | −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 | \(-0.197746\pi\) |
−0.582042 | + | 0.813159i | \(0.697746\pi\) | |||||||
\(374\) | 88.4949i | 0.236617i | ||||||||
\(375\) | −64.7071 | + | 206.611i | −0.172552 | + | 0.550962i | ||||
\(376\) | 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 | \(0.0893551\pi\) | ||||
−0.960857 | + | 0.277045i | \(0.910645\pi\) | |||||||
\(380\) | −158.499 | − | 60.1975i | −0.417104 | − | 0.158414i | ||||
\(381\) | −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 | \(-0.256248\pi\) |
−0.720849 | + | 0.693092i | \(0.756248\pi\) | |||||||
\(384\) | 132.167i | 0.344184i | ||||||||
\(385\) | −252.474 | + | 113.485i | −0.655778 | + | 0.294765i | ||||
\(386\) | −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 | \(0.241552\pi\) | ||||
−0.725621 | + | 0.688094i | \(0.758448\pi\) | |||||||
\(390\) | −8.85816 | − | 19.7071i | −0.0227132 | − | 0.0505311i | ||||
\(391\) | −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 | ||||||||
\(395\) | 43.4847 | − | 114.495i | 0.110088 | − | 0.289860i | ||||
\(396\) | −132.742 | −0.335208 | ||||||||
\(397\) | 118.742 | − | 118.742i | 0.299099 | − | 0.299099i | −0.541562 | − | 0.840661i | \(-0.682167\pi\) |
0.840661 | + | 0.541562i | \(0.182167\pi\) | |||||||
\(398\) | −43.2872 | − | 43.2872i | −0.108762 | − | 0.108762i | ||||
\(399\) | 73.4847i | 0.184172i | ||||||||
\(400\) | −276.677 | − | 245.586i | −0.691691 | − | 0.613964i | ||||
\(401\) | 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 | ||||||
\(405\) | 42.0681 | + | 15.9773i | 0.103872 | + | 0.0394501i | ||||
\(406\) | −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 | \(0.216830\pi\) | ||||
−0.776823 | + | 0.629719i | \(0.783170\pi\) | |||||||
\(410\) | −1.01021 | + | 0.454077i | −0.00246391 | + | 0.00110750i | ||||
\(411\) | 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 | ||||||||
\(415\) | −38.1112 | − | 84.7878i | −0.0918343 | − | 0.204308i | ||||
\(416\) | 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 | \(0.0337178\pi\) | ||||
−0.994395 | + | 0.105730i | \(0.966282\pi\) | |||||||
\(420\) | −58.4847 | + | 153.990i | −0.139249 | + | 0.366642i | ||||
\(421\) | −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 | ||||||
\(425\) | −612.277 | + | 36.4495i | −1.44065 | + | 0.0857635i | ||||
\(426\) | 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 | ||||||||
\(430\) | 55.6663 | + | 21.1418i | 0.129457 | + | 0.0491671i | ||||
\(431\) | 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 | \(-0.440411\pi\) |
−0.982528 | + | 0.186113i | \(0.940411\pi\) | |||||||
\(434\) | − | 16.5857i | − | 0.0382159i | ||||||
\(435\) | 277.621 | − | 124.788i | 0.638209 | − | 0.286868i | ||||
\(436\) | 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 | \(-0.835869\pi\) | ||
0.869981 | − | 0.493085i | \(-0.164131\pi\) | |||||||
\(440\) | −58.4041 | − | 129.934i | −0.132737 | − | 0.295305i | ||||
\(441\) | −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 | \(-0.122035\pi\) |
−0.374062 | + | 0.927404i | \(0.622035\pi\) | |||||||
\(444\) | 57.7367i | 0.130038i | ||||||||
\(445\) | −145.893 | + | 384.136i | −0.327850 | + | 0.863227i | ||||
\(446\) | 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 | \(-0.858533\pi\) | ||
0.902855 | − | 0.429945i | \(-0.141467\pi\) | |||||||
\(450\) | 1.41658 | + | 23.7957i | 0.00314796 | + | 0.0528793i | ||||
\(451\) | 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 | ||||||
\(455\) | 178.990 | + | 67.9796i | 0.393384 | + | 0.149406i | ||||
\(456\) | −37.8184 | −0.0829350 | ||||||||
\(457\) | −223.747 | + | 223.747i | −0.489599 | + | 0.489599i | −0.908180 | − | 0.418580i | \(-0.862528\pi\) |
0.418580 | + | 0.908180i | \(0.362528\pi\) | |||||||
\(458\) | 50.3883 | + | 50.3883i | 0.110018 | + | 0.110018i | ||||
\(459\) | 127.485i | 0.277744i | ||||||||
\(460\) | 290.454 | − | 130.556i | 0.631422 | − | 0.283818i | ||||
\(461\) | −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 | \(-0.313472\pi\) |
−0.833162 | + | 0.553029i | \(0.813472\pi\) | |||||||
\(464\) | 520.095i | 1.12090i | ||||||||
\(465\) | 37.9796 | + | 84.4949i | 0.0816765 | + | 0.181709i | ||||
\(466\) | −92.4653 | −0.198423 | ||||||||
\(467\) | 415.258 | − | 415.258i | 0.889203 | − | 0.889203i | −0.105244 | − | 0.994446i | \(-0.533562\pi\) |
0.994446 | + | 0.105244i | \(0.0335623\pi\) | |||||||
\(468\) | 64.9240 | + | 64.9240i | 0.138726 | + | 0.138726i | ||||
\(469\) | 311.151i | 0.663435i | ||||||||
\(470\) | −35.3076 | + | 92.9648i | −0.0751227 | + | 0.197797i | ||||
\(471\) | −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 | ||||||
\(475\) | 144.334 | − | 162.606i | 0.303860 | − | 0.342329i | ||||
\(476\) | −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 | \(-0.896882\pi\) | ||
0.947984 | − | 0.318318i | \(-0.103118\pi\) | |||||||
\(480\) | −119.381 | − | 45.3406i | −0.248711 | − | 0.0944595i | ||||
\(481\) | 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 | ||||||||
\(485\) | 158.631 | − | 71.3031i | 0.327074 | − | 0.147017i | ||||
\(486\) | 4.95459 | 0.0101946 | ||||||||
\(487\) | −429.318 | + | 429.318i | −0.881556 | + | 0.881556i | −0.993693 | − | 0.112137i | \(-0.964231\pi\) |
0.112137 | + | 0.993693i | \(0.464231\pi\) | |||||||
\(488\) | 10.4903 | + | 10.4903i | 0.0214965 | + | 0.0214965i | ||||
\(489\) | − | 319.918i | − | 0.654230i | ||||||
\(490\) | −16.4199 | − | 36.5301i | −0.0335100 | − | 0.0745512i | ||||
\(491\) | −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 | ||||||||
\(495\) | 60.4393 | − | 159.136i | 0.122100 | − | 0.321487i | ||||
\(496\) | −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 | \(-0.879933\pi\) | ||
0.929699 | − | 0.368321i | \(-0.120067\pi\) | |||||||
\(500\) | 431.871 | − | 225.875i | 0.863741 | − | 0.451750i | ||||
\(501\) | 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 | \(-0.254292\pi\) |
−0.716577 | + | 0.697508i | \(0.754292\pi\) | |||||||
\(504\) | 36.7423i | 0.0729015i | ||||||||
\(505\) | 493.697 | + | 187.504i | 0.977618 | + | 0.371295i | ||||
\(506\) | 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 | \(-0.723360\pi\) | ||
0.645522 | − | 0.763742i | \(-0.276640\pi\) | |||||||
\(510\) | −61.5959 | + | 27.6867i | −0.120776 | + | 0.0542877i | ||||
\(511\) | 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 | ||||||
\(515\) | 258.727 | + | 575.601i | 0.502382 | + | 1.11767i | ||||
\(516\) | −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 | ||||||
\(520\) | −34.9852 | + | 92.1158i | −0.0672792 | + | 0.177146i | ||||
\(521\) | 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 | −0.992649 | − | 0.121030i | \(-0.961380\pi\) |
−0.121030 | − | 0.992649i | \(-0.538620\pi\) | |||||||
\(524\) | 413.823i | 0.789738i | ||||||||
\(525\) | −157.980 | − | 140.227i | −0.300914 | − | 0.267099i | ||||
\(526\) | −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 | ||||||
\(530\) | 1.46428 | + | 0.556128i | 0.00276280 | + | 0.00104930i | ||||
\(531\) | −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 | ||||||||
\(535\) | −443.353 | + | 199.283i | −0.828697 | + | 0.372491i | ||||
\(536\) | −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 | ||||||||
\(540\) | −41.5301 | − | 92.3939i | −0.0769076 | − | 0.171100i | ||||
\(541\) | 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 | ||||||
\(545\) | −121.955 | + | 321.106i | −0.223770 | + | 0.589185i | ||||
\(546\) | 21.0806 | 0.0386092 | ||||||||
\(547\) | −661.778 | + | 661.778i | −1.20983 | + | 1.20983i | −0.238750 | + | 0.971081i | \(0.576738\pi\) |
−0.971081 | + | 0.238750i | \(0.923262\pi\) | |||||||
\(548\) | −649.691 | − | 649.691i | −1.18557 | − | 1.18557i | ||||
\(549\) | 17.7276i | 0.0322906i | ||||||||
\(550\) | 90.0148 | − | 5.35867i | 0.163663 | − | 0.00974304i | ||||
\(551\) | −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 | ||||||
\(555\) | −69.2168 | − | 26.2883i | −0.124715 | − | 0.0473663i | ||||
\(556\) | −745.373 | −1.34060 | ||||||||
\(557\) | 125.909 | − | 125.909i | 0.226049 | − | 0.226049i | −0.584991 | − | 0.811040i | \(-0.698902\pi\) |
0.811040 | + | 0.584991i | \(0.198902\pi\) | |||||||
\(558\) | 7.21225 | + | 7.21225i | 0.0129252 | + | 0.0129252i | ||||
\(559\) | 294.120i | 0.526155i | ||||||||
\(560\) | 329.217 | − | 147.980i | 0.587887 | − | 0.264249i | ||||
\(561\) | 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 | \(-0.330826\pi\) |
−0.862061 | + | 0.506805i | \(0.830826\pi\) | |||||||
\(564\) | − | 422.586i | − | 0.749265i | ||||||
\(565\) | −283.060 | − | 629.737i | −0.500992 | − | 1.11458i | ||||
\(566\) | 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 | \(0.176720\pi\) | ||||
−0.849804 | + | 0.527099i | \(0.823280\pi\) | |||||||
\(570\) | 8.49948 | − | 22.3791i | 0.0149114 | − | 0.0392616i | ||||
\(571\) | −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 | ||||||
\(575\) | 24.2679 | + | 407.650i | 0.0422050 | + | 0.708957i | ||||
\(576\) | 163.515 | 0.283881 | ||||||||
\(577\) | −292.121 | + | 292.121i | −0.506276 | + | 0.506276i | −0.913381 | − | 0.407105i | \(-0.866538\pi\) |
0.407105 | + | 0.913381i | \(0.366538\pi\) | |||||||
\(578\) | −70.3314 | − | 70.3314i | −0.121681 | − | 0.121681i | ||||
\(579\) | 626.005i | 1.08118i | ||||||||
\(580\) | −640.535 | − | 243.272i | −1.10437 | − | 0.419435i | ||||
\(581\) | 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 | ||||||||
\(585\) | −107.394 | + | 48.2724i | −0.183579 | + | 0.0825170i | ||||
\(586\) | 43.4051 | 0.0740702 | ||||||||
\(587\) | 611.217 | − | 611.217i | 1.04126 | − | 1.04126i | 0.0421437 | − | 0.999112i | \(-0.486581\pi\) |
0.999112 | − | 0.0421437i | \(-0.0134187\pi\) | |||||||
\(588\) | 120.346 | + | 120.346i | 0.204670 | + | 0.204670i | ||||
\(589\) | − | 93.0306i | − | 0.157947i | ||||||
\(590\) | −26.0183 | − | 57.8842i | −0.0440989 | − | 0.0981088i | ||||
\(591\) | 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 | \(-0.0348074\pi\) |
−0.109133 | + | 0.994027i | \(0.534807\pi\) | |||||||
\(594\) | − | 18.7423i | − | 0.0315528i | ||||||
\(595\) | 212.474 | − | 559.444i | 0.357100 | − | 0.940242i | ||||
\(596\) | 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 | \(0.0996245\pi\) | ||||
−0.951420 | + | 0.307895i | \(0.900375\pi\) | |||||||
\(600\) | 72.1668 | − | 81.3031i | 0.120278 | − | 0.135505i | ||||
\(601\) | 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 | ||||||||
\(605\) | −36.4018 | − | 13.8252i | −0.0601682 | − | 0.0228517i | ||||
\(606\) | 58.1454 | 0.0959495 | ||||||||
\(607\) | 513.611 | − | 513.611i | 0.846146 | − | 0.846146i | −0.143504 | − | 0.989650i | \(-0.545837\pi\) |
0.989650 | + | 0.143504i | \(0.0458369\pi\) | |||||||
\(608\) | 90.6811 | + | 90.6811i | 0.149147 | + | 0.149147i | ||||
\(609\) | 296.969i | 0.487634i | ||||||||
\(610\) | −8.56530 | + | 3.85002i | −0.0140415 | + | 0.00631150i | ||||
\(611\) | −491.192 | −0.803915 | ||||||||
\(612\) | 202.924 | − | 202.924i | 0.331575 | − | 0.331575i | ||||
\(613\) | −615.287 | − | 615.287i | −1.00373 | − | 1.00373i | −0.999993 | − | 0.00373821i | \(-0.998810\pi\) |
−0.00373821 | − | 0.999993i | \(-0.501190\pi\) | |||||||
\(614\) | 56.1725i | 0.0914861i | ||||||||
\(615\) | 2.47449 | + | 5.50510i | 0.00402356 | + | 0.00895139i | ||||
\(616\) | 138.990 | 0.225633 | ||||||||
\(617\) | 546.752 | − | 546.752i | 0.886145 | − | 0.886145i | −0.108005 | − | 0.994150i | \(-0.534446\pi\) |
0.994150 | + | 0.108005i | \(0.0344463\pi\) | |||||||
\(618\) | 49.1316 | + | 49.1316i | 0.0795010 | + | 0.0795010i | ||||
\(619\) | − | 152.869i | − | 0.246962i | −0.992347 | − | 0.123481i | \(-0.960594\pi\) | ||
0.992347 | − | 0.123481i | \(-0.0394058\pi\) | |||||||
\(620\) | 74.0408 | − | 194.949i | 0.119421 | − | 0.314434i | ||||
\(621\) | 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 | ||||||
\(625\) | 74.1510 | + | 620.586i | 0.118642 | + | 0.992937i | ||||
\(626\) | −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 | ||||||
\(630\) | −21.7423 | − | 8.25765i | −0.0345117 | − | 0.0131074i | ||||
\(631\) | −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 | ||||||||
\(635\) | −1061.72 | + | 477.233i | −1.67200 | + | 0.751547i | ||||
\(636\) | −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 | ||||||
\(640\) | 156.420 | + | 347.994i | 0.244406 | + | 0.543741i | ||||
\(641\) | 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 | \(-0.0810234\pi\) |
−0.251803 | + | 0.967779i | \(0.581023\pi\) | |||||||
\(644\) | 310.697i | 0.482449i | ||||||||
\(645\) | 115.212 | − | 303.353i | 0.178624 | − | 0.470315i | ||||
\(646\) | 67.8184 | 0.104982 | ||||||||
\(647\) | −281.287 | + | 281.287i | −0.434756 | + | 0.434756i | −0.890243 | − | 0.455487i | \(-0.849465\pi\) |
0.455487 | + | 0.890243i | \(0.349465\pi\) | |||||||
\(648\) | −15.9773 | − | 15.9773i | −0.0246563 | − | 0.0246563i | ||||
\(649\) | 453.192i | 0.698293i | ||||||||
\(650\) | −46.6469 | − | 41.4051i | −0.0717645 | − | 0.0637002i | ||||
\(651\) | −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 | \(-0.218990\pi\) |
−0.634977 | + | 0.772531i | \(0.718990\pi\) | |||||||
\(654\) | 37.8184i | 0.0578263i | ||||||||
\(655\) | −496.106 | − | 188.419i | −0.757413 | − | 0.287662i | ||||
\(656\) | −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 | \(-0.693772\pi\) | ||
0.571844 | − | 0.820362i | \(-0.306228\pi\) | |||||||
\(660\) | −349.510 | + | 157.101i | −0.529560 | + | 0.238032i | ||||
\(661\) | −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 | ||||||||
\(665\) | 86.9694 | + | 193.485i | 0.130781 | + | 0.290954i | ||||
\(666\) | −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 | ||||||
\(670\) | 35.9888 | − | 94.7582i | 0.0537146 | − | 0.141430i | ||||
\(671\) | 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 | \(-0.171174\pi\) |
−0.512213 | + | 0.858859i | \(0.671174\pi\) | |||||||
\(674\) | − | 96.1046i | − | 0.142588i | ||||||
\(675\) | 129.674 | − | 7.71964i | 0.192110 | − | 0.0114365i | ||||
\(676\) | 418.687 | 0.619359 | ||||||||
\(677\) | −48.3883 | + | 48.3883i | −0.0714745 | + | 0.0714745i | −0.741940 | − | 0.670466i | \(-0.766094\pi\) |
0.670466 | + | 0.741940i | \(0.266094\pi\) | |||||||
\(678\) | −53.7526 | − | 53.7526i | −0.0792810 | − | 0.0792810i | ||||
\(679\) | 169.687i | 0.249907i | ||||||||
\(680\) | 287.914 | + | 109.348i | 0.423403 | + | 0.160807i | ||||
\(681\) | −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 | \(-0.179087\pi\) |
−0.533402 | + | 0.845862i | \(0.679087\pi\) | |||||||
\(684\) | 101.728i | 0.148724i | ||||||||
\(685\) | 1074.69 | − | 483.060i | 1.56888 | − | 0.705197i | ||||
\(686\) | 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 | ||||||||
\(690\) | 18.4337 | + | 41.0102i | 0.0267155 | + | 0.0594351i | ||||
\(691\) | 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 | ||||||||
\(695\) | 339.378 | − | 893.580i | 0.488314 | − | 1.28573i | ||||
\(696\) | −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 | ||||||||
\(700\) | 28.2577 | + | 474.671i | 0.0403681 | + | 0.678101i | ||||
\(701\) | −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 | ||||||
\(705\) | 506.611 | + | 192.409i | 0.718597 | + | 0.272920i | ||||
\(706\) | −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 | \(-0.830722\pi\) | ||
0.861895 | − | 0.507087i | \(-0.169278\pi\) | |||||||
\(710\) | 98.5653 | − | 44.3041i | 0.138824 | − | 0.0624001i | ||||
\(711\) | −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 | ||||||
\(715\) | 182.606 | + | 406.252i | 0.255393 | + | 0.568185i | ||||
\(716\) | 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 | \(0.138290\pi\) | ||||
−0.907101 | + | 0.420912i | \(0.861710\pi\) | |||||||
\(720\) | −78.8105 | + | 207.507i | −0.109459 | + | 0.288205i | ||||
\(721\) | −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 | ||||||
\(725\) | 583.287 | − | 657.131i | 0.804534 | − | 0.906387i | ||||
\(726\) | −4.28724 | −0.00590529 | ||||||||
\(727\) | −246.126 | + | 246.126i | −0.338550 | + | 0.338550i | −0.855821 | − | 0.517271i | \(-0.826948\pi\) |
0.517271 | + | 0.855821i | \(0.326948\pi\) | |||||||
\(728\) | −67.9796 | − | 67.9796i | −0.0933786 | − | 0.0933786i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −163.434 | − | 62.0714i | −0.223882 | − | 0.0850294i | ||||
\(731\) | 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 | \(-0.334118\pi\) |
−0.867255 | + | 0.497865i | \(0.834118\pi\) | |||||||
\(734\) | − | 65.8546i | − | 0.0897202i | ||||||
\(735\) | −199.070 | + | 89.4801i | −0.270844 | + | 0.121742i | ||||
\(736\) | −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 | \(0.113443\pi\) | ||||
−0.937162 | + | 0.348895i | \(0.886557\pi\) | |||||||
\(740\) | 68.3316 | + | 152.020i | 0.0923400 | + | 0.205433i | ||||
\(741\) | 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 | \(-0.118879\pi\) |
−0.364847 | + | 0.931067i | \(0.618879\pi\) | |||||||
\(744\) | − | 46.5153i | − | 0.0625206i | ||||||
\(745\) | −150.637 | + | 396.626i | −0.202197 | + | 0.532383i | ||||
\(746\) | 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 | ||||||
\(750\) | 31.8921 | + | 60.9773i | 0.0425228 | + | 0.0813031i | ||||
\(751\) | −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 | ||||||||
\(755\) | −696.318 | − | 264.459i | −0.922275 | − | 0.350276i | ||||
\(756\) | 98.8332 | 0.130732 | ||||||||
\(757\) | −956.075 | + | 956.075i | −1.26298 | + | 1.26298i | −0.313337 | + | 0.949642i | \(0.601447\pi\) |
−0.949642 | + | 0.313337i | \(0.898553\pi\) | |||||||
\(758\) | 47.1964 | + | 47.1964i | 0.0622644 | + | 0.0622644i | ||||
\(759\) | − | 321.081i | − | 0.423031i | ||||||
\(760\) | −99.5755 | + | 44.7582i | −0.131020 | + | 0.0588923i | ||||
\(761\) | −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 | ||||||||
\(765\) | 150.879 | + | 335.666i | 0.197227 | + | 0.438780i | ||||
\(766\) | −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 | \(-0.851354\pi\) | ||
0.892930 | − | 0.450196i | \(-0.148646\pi\) | |||||||
\(770\) | −31.2372 | + | 82.2474i | −0.0405678 | + | 0.106815i | ||||
\(771\) | −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 | \(-0.138475\pi\) |
−0.421441 | + | 0.906856i | \(0.638475\pi\) | |||||||
\(774\) | − | 35.7276i | − | 0.0461596i | ||||||
\(775\) | 200.000 | + | 177.526i | 0.258065 | + | 0.229065i | ||||
\(776\) | −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 | ||||||
\(780\) | 247.782 | + | 94.1066i | 0.317669 | + | 0.120650i | ||||
\(781\) | −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 | ||||||
\(785\) | −108.697 | + | 48.8582i | −0.138467 | + | 0.0622397i | ||||
\(786\) | −58.4291 | −0.0743373 | ||||||||
\(787\) | 910.990 | − | 910.990i | 1.15755 | − | 1.15755i | 0.172546 | − | 0.985001i | \(-0.444801\pi\) |
0.985001 | − | 0.172546i | \(-0.0551993\pi\) | |||||||
\(788\) | −377.019 | − | 377.019i | −0.478451 | − | 0.478451i | ||||
\(789\) | 681.342i | 0.863551i | ||||||||
\(790\) | −15.9592 | − | 35.5051i | −0.0202015 | − | 0.0449432i | ||||
\(791\) | 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 | ||||||
\(795\) | 3.03062 | − | 7.97959i | 0.00381209 | − | 0.0100372i | ||||
\(796\) | 750.967 | 0.943426 | ||||||||
\(797\) | −7.21683 | + | 7.21683i | −0.00905500 | + | 0.00905500i | −0.711620 | − | 0.702565i | \(-0.752038\pi\) |
0.702565 | + | 0.711620i | \(0.252038\pi\) | |||||||
\(798\) | 16.5153 | + | 16.5153i | 0.0206959 | + | 0.0206959i | ||||
\(799\) | 1535.25i | 1.92147i | ||||||||
\(800\) | −367.991 | + | 21.9069i | −0.459989 | + | 0.0273836i | ||||
\(801\) | 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 | ||||||||
\(805\) | −372.474 | − | 141.464i | −0.462701 | − | 0.175732i | ||||
\(806\) | −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 | \(0.0295520\pi\) | ||||
−0.995693 | + | 0.0927070i | \(0.970448\pi\) | |||||||
\(810\) | 13.0454 | − | 5.86378i | 0.0161054 | − | 0.00723923i | ||||
\(811\) | 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 | ||||||||
\(815\) | −378.624 | − | 842.343i | −0.464570 | − | 1.03355i | ||||
\(816\) | −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 | ||||||
\(820\) | 4.82399 | − | 12.7015i | 0.00588291 | − | 0.0154897i | ||||
\(821\) | −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 | \(-0.114198\pi\) |
−0.351117 | + | 0.936331i | \(0.614198\pi\) | |||||||
\(824\) | − | 316.874i | − | 0.384556i | ||||||
\(825\) | −29.2020 | − | 490.535i | −0.0353964 | − | 0.594587i | ||||
\(826\) | 61.9184 | 0.0749617 | ||||||||
\(827\) | 350.756 | − | 350.756i | 0.424131 | − | 0.424131i | −0.462492 | − | 0.886623i | \(-0.653045\pi\) |
0.886623 | + | 0.462492i | \(0.153045\pi\) | |||||||
\(828\) | −135.106 | − | 135.106i | −0.163171 | − | 0.163171i | ||||
\(829\) | 697.423i | 0.841283i | 0.907227 | + | 0.420641i | \(0.138195\pi\) | ||||
−0.907227 | + | 0.420641i | \(0.861805\pi\) | |||||||
\(830\) | −27.6209 | − | 10.4903i | −0.0332782 | − | 0.0126389i | ||||
\(831\) | −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 | ||||||
\(835\) | 290.454 | − | 130.556i | 0.347849 | − | 0.156355i | ||||
\(836\) | 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 | \(-0.986267\pi\) | ||
0.999069 | − | 0.0431302i | \(-0.0137330\pi\) | |||||||
\(840\) | 43.4847 | + | 96.7423i | 0.0517675 | + | 0.115169i | ||||
\(841\) | −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 | ||||||||
\(845\) | −190.633 | + | 501.936i | −0.225602 | + | 0.594008i | ||||
\(846\) | 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 | ||||||
\(850\) | −129.414 | + | 145.798i | −0.152252 | + | 0.171527i | ||||
\(851\) | −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 | \(-0.269689\pi\) |
−0.749465 | + | 0.662044i | \(0.769689\pi\) | |||||||
\(854\) | − | 9.16225i | − | 0.0107286i | ||||||
\(855\) | −121.955 | − | 46.3179i | −0.142637 | − | 0.0541729i | ||||
\(856\) | 244.070 | 0.285129 | ||||||||
\(857\) | −293.176 | + | 293.176i | −0.342096 | + | 0.342096i | −0.857155 | − | 0.515059i | \(-0.827770\pi\) |
0.515059 | + | 0.857155i | \(0.327770\pi\) | |||||||
\(858\) | 34.6765 | + | 34.6765i | 0.0404155 | + | 0.0404155i | ||||
\(859\) | 786.867i | 0.916027i | 0.888945 | + | 0.458014i | \(0.151439\pi\) | ||||
−0.888945 | + | 0.458014i | \(0.848561\pi\) | |||||||
\(860\) | −666.252 | + | 299.473i | −0.774712 | + | 0.348225i | ||||
\(861\) | −5.88877 | −0.00683946 | ||||||||
\(862\) | 180.838 | − | 180.838i | 0.209789 | − | 0.209789i | ||||
\(863\) | −1072.68 | − | 1072.68i | −1.24297 | − | 1.24297i | −0.958764 | − | 0.284204i | \(-0.908271\pi\) |
−0.284204 | − | 0.958764i | \(-0.591729\pi\) | |||||||
\(864\) | 76.6209i | 0.0886816i | ||||||||
\(865\) | −425.081 | − | 945.696i | −0.491423 | − | 1.09329i | ||||
\(866\) | −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 | ||||||||
\(870\) | 34.3485 | − | 90.4393i | 0.0394810 | − | 0.103953i | ||||
\(871\) | 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 | ||||||
\(875\) | −581.918 | − | 182.247i | −0.665050 | − | 0.208283i | ||||
\(876\) | 742.913 | 0.848074 | ||||||||
\(877\) | 239.460 | − | 239.460i | 0.273044 | − | 0.273044i | −0.557280 | − | 0.830324i | \(-0.688155\pi\) |
0.830324 | + | 0.557280i | \(0.188155\pi\) | |||||||
\(878\) | −97.2985 | − | 97.2985i | −0.110818 | − | 0.110818i | ||||
\(879\) | − | 236.536i | − | 0.269096i | ||||||
\(880\) | 784.964 | + | 298.126i | 0.892004 | + | 0.338780i | ||||
\(881\) | 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 | \(-0.290399\pi\) |
−0.790922 | + | 0.611917i | \(0.790399\pi\) | |||||||
\(884\) | 750.888i | 0.849421i | ||||||||
\(885\) | −315.439 | + | 141.787i | −0.356429 | + | 0.160211i | ||||
\(886\) | 110.184 | 0.124361 | ||||||||
\(887\) | 30.2066 | − | 30.2066i | 0.0340548 | − | 0.0340548i | −0.689874 | − | 0.723929i | \(-0.742334\pi\) |
0.723929 | + | 0.689874i | \(0.242334\pi\) | |||||||
\(888\) | 26.2883 | + | 26.2883i | 0.0296039 | + | 0.0296039i | ||||
\(889\) | − | 1135.72i | − | 1.27752i | ||||||
\(890\) | 53.5439 | + | 119.121i | 0.0601616 | + | 0.133844i | ||||
\(891\) | −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 | ||||||||
\(895\) | −326.135 | + | 858.712i | −0.364397 | + | 0.959454i | ||||
\(896\) | −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 | ||||||
\(900\) | −218.697 | − | 194.121i | −0.242997 | − | 0.215690i | ||||
\(901\) | 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 | ||||||||
\(905\) | 1338.10 | + | 508.207i | 1.47857 | + | 0.561554i | ||||
\(906\) | −82.0092 | −0.0905179 | ||||||||
\(907\) | 571.342 | − | 571.342i | 0.629925 | − | 0.629925i | −0.318124 | − | 0.948049i | \(-0.603053\pi\) |
0.948049 | + | 0.318124i | \(0.103053\pi\) | |||||||
\(908\) | 987.110 | + | 987.110i | 1.08713 | + | 1.08713i | ||||
\(909\) | − | 316.863i | − | 0.348584i | ||||||
\(910\) | 55.5051 | − | 24.9490i | 0.0609946 | − | 0.0274165i | ||||
\(911\) | 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 | ||||||||
\(915\) | 20.9806 | + | 46.6765i | 0.0229296 | + | 0.0510126i | ||||
\(916\) | −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 | \(-0.785393\pi\) | ||
0.781202 | − | 0.624278i | \(-0.214607\pi\) | |||||||
\(920\) | 72.8036 | − | 191.691i | 0.0791343 | − | 0.208360i | ||||
\(921\) | 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 | ||||||
\(925\) | −213.360 | + | 12.7015i | −0.230659 | + | 0.0137314i | ||||
\(926\) | −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 | \(0.0378292\pi\) | ||||
−0.992946 | + | 0.118565i | \(0.962171\pi\) | |||||||
\(930\) | 27.5255 | + | 10.4541i | 0.0295973 | + | 0.0112409i | ||||
\(931\) | 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 | ||||||
\(935\) | 1269.77 | − | 570.747i | 1.35804 | − | 0.610425i | ||||
\(936\) | 59.1214 | 0.0631639 | ||||||||
\(937\) | −396.090 | + | 396.090i | −0.422721 | + | 0.422721i | −0.886140 | − | 0.463418i | \(-0.846623\pi\) |
0.463418 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(938\) | 69.9296 | + | 69.9296i | 0.0745518 | + | 0.0745518i | ||||
\(939\) | 250.763i | 0.267053i | ||||||||
\(940\) | −500.132 | − | 1112.67i | −0.532055 | − | 1.18369i | ||||
\(941\) | 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 | ||||||
\(945\) | −45.0000 | + | 118.485i | −0.0476190 | + | 0.125381i | ||||
\(946\) | −135.151 | −0.142866 | ||||||||
\(947\) | −845.190 | + | 845.190i | −0.892492 | + | 0.892492i | −0.994757 | − | 0.102265i | \(-0.967391\pi\) |
0.102265 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(948\) | 116.969 | + | 116.969i | 0.123385 | + | 0.123385i | ||||
\(949\) | − | 863.523i | − | 0.909930i | ||||||
\(950\) | −4.10664 | − | 68.9831i | −0.00432278 | − | 0.0726138i | ||||
\(951\) | 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 | \(-0.404960\pi\) |
−0.955756 | + | 0.294161i | \(0.904960\pi\) | |||||||
\(954\) | − | 0.939800i | − | 0.000985115i | ||||||
\(955\) | −224.788 | − | 85.3735i | −0.235380 | − | 0.0893963i | ||||
\(956\) | −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 | ||||||||
\(960\) | 430.535 | − | 193.521i | 0.448474 | − | 0.201584i | ||||
\(961\) | −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 | ||||||||
\(965\) | 740.879 | + | 1648.27i | 0.767750 | + | 1.70805i | ||||
\(966\) | −43.8684 | −0.0454124 | ||||||||
\(967\) | −381.690 | + | 381.690i | −0.394716 | + | 0.394716i | −0.876364 | − | 0.481649i | \(-0.840038\pi\) |
0.481649 | + | 0.876364i | \(0.340038\pi\) | |||||||
\(968\) | 13.8252 | + | 13.8252i | 0.0142823 | + | 0.0142823i | ||||
\(969\) | − | 369.576i | − | 0.381399i | ||||||
\(970\) | 19.6265 | − | 51.6765i | 0.0202335 | − | 0.0532748i | ||||
\(971\) | −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 | ||||||||
\(975\) | −225.637 | + | 254.202i | −0.231422 | + | 0.260720i | ||||
\(976\) | −87.4439 | −0.0895941 | ||||||||
\(977\) | 593.662 | − | 593.662i | 0.607637 | − | 0.607637i | −0.334691 | − | 0.942328i | \(-0.608632\pi\) |
0.942328 | + | 0.334691i | \(0.108632\pi\) | |||||||
\(978\) | −71.9000 | − | 71.9000i | −0.0735174 | − | 0.0735174i | ||||
\(979\) | − | 932.636i | − | 0.952641i | ||||||
\(980\) | 459.301 | + | 174.441i | 0.468674 | + | 0.178001i | ||||
\(981\) | 206.091 | 0.210082 | ||||||||
\(982\) | −93.1158 | + | 93.1158i | −0.0948226 | + | 0.0948226i | ||||
\(983\) | −1217.34 | − | 1217.34i | −1.23839 | − | 1.23839i | −0.960659 | − | 0.277731i | \(-0.910418\pi\) |
−0.277731 | − | 0.960659i | \(-0.589582\pi\) | |||||||
\(984\) | − | 3.03062i | − | 0.00307989i | ||||||
\(985\) | 623.646 | − | 280.322i | 0.633143 | − | 0.284591i | ||||
\(986\) | 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 | ||||||
\(990\) | −22.1816 | − | 49.3485i | −0.0224057 | − | 0.0498469i | ||||
\(991\) | −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 | ||||||||
\(995\) | −341.925 | + | 900.286i | −0.343643 | + | 0.904810i | ||||
\(996\) | 125.555 | 0.126059 | ||||||||
\(997\) | −316.733 | + | 316.733i | −0.317686 | + | 0.317686i | −0.847878 | − | 0.530192i | \(-0.822120\pi\) |
0.530192 | + | 0.847878i | \(0.322120\pi\) | |||||||
\(998\) | −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 | 15.3.f.a.13.2 | yes | 4 | |
3.2 | odd | 2 | 45.3.g.b.28.1 | 4 | |||
4.3 | odd | 2 | 240.3.bg.a.193.2 | 4 | |||
5.2 | odd | 4 | inner | 15.3.f.a.7.2 | ✓ | 4 | |
5.3 | odd | 4 | 75.3.f.c.7.1 | 4 | |||
5.4 | even | 2 | 75.3.f.c.43.1 | 4 | |||
8.3 | odd | 2 | 960.3.bg.h.193.1 | 4 | |||
8.5 | even | 2 | 960.3.bg.i.193.2 | 4 | |||
9.2 | odd | 6 | 405.3.l.f.28.2 | 8 | |||
9.4 | even | 3 | 405.3.l.h.298.2 | 8 | |||
9.5 | odd | 6 | 405.3.l.f.298.1 | 8 | |||
9.7 | even | 3 | 405.3.l.h.28.1 | 8 | |||
12.11 | even | 2 | 720.3.bh.k.433.2 | 4 | |||
15.2 | even | 4 | 45.3.g.b.37.1 | 4 | |||
15.8 | even | 4 | 225.3.g.a.82.2 | 4 | |||
15.14 | odd | 2 | 225.3.g.a.118.2 | 4 | |||
20.3 | even | 4 | 1200.3.bg.k.1057.1 | 4 | |||
20.7 | even | 4 | 240.3.bg.a.97.2 | 4 | |||
20.19 | odd | 2 | 1200.3.bg.k.193.1 | 4 | |||
40.27 | even | 4 | 960.3.bg.h.577.1 | 4 | |||
40.37 | odd | 4 | 960.3.bg.i.577.2 | 4 | |||
45.2 | even | 12 | 405.3.l.f.352.1 | 8 | |||
45.7 | odd | 12 | 405.3.l.h.352.2 | 8 | |||
45.22 | odd | 12 | 405.3.l.h.217.1 | 8 | |||
45.32 | even | 12 | 405.3.l.f.217.2 | 8 | |||
60.47 | odd | 4 | 720.3.bh.k.577.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.f.a.7.2 | ✓ | 4 | 5.2 | odd | 4 | inner | |
15.3.f.a.13.2 | yes | 4 | 1.1 | even | 1 | trivial | |
45.3.g.b.28.1 | 4 | 3.2 | odd | 2 | |||
45.3.g.b.37.1 | 4 | 15.2 | even | 4 | |||
75.3.f.c.7.1 | 4 | 5.3 | odd | 4 | |||
75.3.f.c.43.1 | 4 | 5.4 | even | 2 | |||
225.3.g.a.82.2 | 4 | 15.8 | even | 4 | |||
225.3.g.a.118.2 | 4 | 15.14 | odd | 2 | |||
240.3.bg.a.97.2 | 4 | 20.7 | even | 4 | |||
240.3.bg.a.193.2 | 4 | 4.3 | odd | 2 | |||
405.3.l.f.28.2 | 8 | 9.2 | odd | 6 | |||
405.3.l.f.217.2 | 8 | 45.32 | even | 12 | |||
405.3.l.f.298.1 | 8 | 9.5 | odd | 6 | |||
405.3.l.f.352.1 | 8 | 45.2 | even | 12 | |||
405.3.l.h.28.1 | 8 | 9.7 | even | 3 | |||
405.3.l.h.217.1 | 8 | 45.22 | odd | 12 | |||
405.3.l.h.298.2 | 8 | 9.4 | even | 3 | |||
405.3.l.h.352.2 | 8 | 45.7 | odd | 12 | |||
720.3.bh.k.433.2 | 4 | 12.11 | even | 2 | |||
720.3.bh.k.577.2 | 4 | 60.47 | odd | 4 | |||
960.3.bg.h.193.1 | 4 | 8.3 | odd | 2 | |||
960.3.bg.h.577.1 | 4 | 40.27 | even | 4 | |||
960.3.bg.i.193.2 | 4 | 8.5 | even | 2 | |||
960.3.bg.i.577.2 | 4 | 40.37 | odd | 4 | |||
1200.3.bg.k.193.1 | 4 | 20.19 | odd | 2 | |||
1200.3.bg.k.1057.1 | 4 | 20.3 | even | 4 |