Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (of order \(12\), degree \(4\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Character | \(\chi\) | \(=\) | 210.193 |
Dual form | 210.3.v.b.37.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.683013 | + | 0.183013i | ||||
\(3\) | −1.67303 | + | 0.448288i | −0.557678 | + | 0.149429i | ||||
\(4\) | 1.73205 | + | 1.00000i | 0.433013 | + | 0.250000i | ||||
\(5\) | −4.95862 | − | 0.641960i | −0.991724 | − | 0.128392i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 2.95853 | + | 6.34406i | 0.422648 | + | 0.906294i | ||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 2.59808 | − | 1.50000i | 0.288675 | − | 0.166667i | ||||
\(10\) | −6.53862 | − | 2.69191i | −0.653862 | − | 0.269191i | ||||
\(11\) | −9.98405 | + | 17.2929i | −0.907641 | + | 1.57208i | −0.0903080 | + | 0.995914i | \(0.528785\pi\) |
−0.817333 | + | 0.576166i | \(0.804548\pi\) | |||||||
\(12\) | −3.34607 | − | 0.896575i | −0.278839 | − | 0.0747146i | ||||
\(13\) | −13.3742 | − | 13.3742i | −1.02879 | − | 1.02879i | −0.999573 | − | 0.0292138i | \(-0.990700\pi\) |
−0.0292138 | − | 0.999573i | \(-0.509300\pi\) | |||||||
\(14\) | 1.71935 | + | 9.74904i | 0.122810 | + | 0.696360i | ||||
\(15\) | 8.58371 | − | 1.14887i | 0.572247 | − | 0.0765912i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | 5.85604 | + | 21.8551i | 0.344473 | + | 1.28559i | 0.893227 | + | 0.449607i | \(0.148436\pi\) |
−0.548753 | + | 0.835984i | \(0.684897\pi\) | |||||||
\(18\) | 4.09808 | − | 1.09808i | 0.227671 | − | 0.0610042i | ||||
\(19\) | −14.8761 | + | 8.58869i | −0.782950 | + | 0.452037i | −0.837475 | − | 0.546476i | \(-0.815969\pi\) |
0.0545246 | + | 0.998512i | \(0.482636\pi\) | |||||||
\(20\) | −7.94662 | − | 6.07052i | −0.397331 | − | 0.303526i | ||||
\(21\) | −7.79369 | − | 9.28754i | −0.371128 | − | 0.442264i | ||||
\(22\) | −19.9681 | + | 19.9681i | −0.907641 | + | 0.907641i | ||||
\(23\) | −5.43036 | + | 20.2664i | −0.236103 | + | 0.881147i | 0.741546 | + | 0.670902i | \(0.234093\pi\) |
−0.977649 | + | 0.210245i | \(0.932574\pi\) | |||||||
\(24\) | −4.24264 | − | 2.44949i | −0.176777 | − | 0.102062i | ||||
\(25\) | 24.1758 | + | 6.36646i | 0.967031 | + | 0.254659i | ||||
\(26\) | −13.3742 | − | 23.1648i | −0.514394 | − | 0.890956i | ||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | −1.21973 | + | 13.9468i | −0.0435617 | + | 0.498099i | ||||
\(29\) | − | 23.1996i | − | 0.799987i | −0.916518 | − | 0.399994i | \(-0.869012\pi\) | ||
0.916518 | − | 0.399994i | \(-0.130988\pi\) | |||||||
\(30\) | 12.1461 | + | 1.57247i | 0.404869 | + | 0.0524158i | ||||
\(31\) | 27.7400 | − | 48.0470i | 0.894837 | − | 1.54990i | 0.0608318 | − | 0.998148i | \(-0.480625\pi\) |
0.834006 | − | 0.551756i | \(-0.186042\pi\) | |||||||
\(32\) | 1.46410 | + | 5.46410i | 0.0457532 | + | 0.170753i | ||||
\(33\) | 8.95145 | − | 33.4073i | 0.271256 | − | 1.01234i | ||||
\(34\) | 31.9980i | 0.941118i | ||||||||
\(35\) | −10.5976 | − | 33.3570i | −0.302789 | − | 0.953058i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 22.2866 | + | 5.97166i | 0.602339 | + | 0.161396i | 0.547087 | − | 0.837076i | \(-0.315737\pi\) |
0.0552528 | + | 0.998472i | \(0.482404\pi\) | |||||||
\(38\) | −23.4647 | + | 6.28736i | −0.617493 | + | 0.165457i | ||||
\(39\) | 28.3710 | + | 16.3800i | 0.727462 | + | 0.420001i | ||||
\(40\) | −8.63332 | − | 11.2012i | −0.215833 | − | 0.280029i | ||||
\(41\) | −21.6302 | −0.527565 | −0.263783 | − | 0.964582i | \(-0.584970\pi\) | ||||
−0.263783 | + | 0.964582i | \(0.584970\pi\) | |||||||
\(42\) | −7.24690 | − | 15.5397i | −0.172545 | − | 0.369993i | ||||
\(43\) | 14.6809 | + | 14.6809i | 0.341417 | + | 0.341417i | 0.856900 | − | 0.515483i | \(-0.172387\pi\) |
−0.515483 | + | 0.856900i | \(0.672387\pi\) | |||||||
\(44\) | −34.5858 | + | 19.9681i | −0.786040 | + | 0.453820i | ||||
\(45\) | −13.8458 | + | 5.77007i | −0.307685 | + | 0.128224i | ||||
\(46\) | −14.8360 | + | 25.6967i | −0.322522 | + | 0.558625i | ||||
\(47\) | 73.1609 | + | 19.6034i | 1.55662 | + | 0.417094i | 0.931590 | − | 0.363511i | \(-0.118422\pi\) |
0.625025 | + | 0.780604i | \(0.285089\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | −31.4942 | + | 37.5382i | −0.642738 | + | 0.766086i | ||||
\(50\) | 30.6944 | + | 17.5457i | 0.613889 | + | 0.350914i | ||||
\(51\) | −19.5947 | − | 33.9390i | −0.384210 | − | 0.665471i | ||||
\(52\) | −9.79062 | − | 36.5391i | −0.188281 | − | 0.702675i | ||||
\(53\) | 4.01743 | − | 1.07647i | 0.0758005 | − | 0.0203107i | −0.220719 | − | 0.975337i | \(-0.570841\pi\) |
0.296520 | + | 0.955027i | \(0.404174\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 60.6084 | − | 79.3394i | 1.10197 | − | 1.44253i | ||||
\(56\) | −6.77105 | + | 18.6052i | −0.120912 | + | 0.332235i | ||||
\(57\) | 21.0379 | − | 21.0379i | 0.369086 | − | 0.369086i | ||||
\(58\) | 8.49165 | − | 31.6913i | 0.146408 | − | 0.546401i | ||||
\(59\) | −26.7900 | − | 15.4672i | −0.454069 | − | 0.262157i | 0.255478 | − | 0.966815i | \(-0.417767\pi\) |
−0.709547 | + | 0.704658i | \(0.751100\pi\) | |||||||
\(60\) | 16.0163 | + | 6.59381i | 0.266938 | + | 0.109897i | ||||
\(61\) | −1.75837 | − | 3.04558i | −0.0288257 | − | 0.0499275i | 0.851253 | − | 0.524756i | \(-0.175843\pi\) |
−0.880078 | + | 0.474828i | \(0.842510\pi\) | |||||||
\(62\) | 55.4799 | − | 55.4799i | 0.894837 | − | 0.894837i | ||||
\(63\) | 17.2026 | + | 12.0445i | 0.273057 | + | 0.191183i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 57.7320 | + | 74.9034i | 0.888184 | + | 1.15236i | ||||
\(66\) | 24.4558 | − | 42.3587i | 0.370543 | − | 0.641799i | ||||
\(67\) | 0.764309 | + | 2.85244i | 0.0114076 | + | 0.0425737i | 0.971395 | − | 0.237469i | \(-0.0763179\pi\) |
−0.959987 | + | 0.280043i | \(0.909651\pi\) | |||||||
\(68\) | −11.7121 | + | 43.7101i | −0.172237 | + | 0.642796i | ||||
\(69\) | − | 36.3407i | − | 0.526676i | ||||||
\(70\) | −2.26709 | − | 49.4455i | −0.0323870 | − | 0.706365i | ||||
\(71\) | −11.8938 | −0.167518 | −0.0837592 | − | 0.996486i | \(-0.526693\pi\) | ||||
−0.0837592 | + | 0.996486i | \(0.526693\pi\) | |||||||
\(72\) | 8.19615 | + | 2.19615i | 0.113835 | + | 0.0305021i | ||||
\(73\) | 21.0889 | − | 5.65075i | 0.288889 | − | 0.0774075i | −0.111464 | − | 0.993768i | \(-0.535554\pi\) |
0.400353 | + | 0.916361i | \(0.368887\pi\) | |||||||
\(74\) | 28.2582 | + | 16.3149i | 0.381868 | + | 0.220472i | ||||
\(75\) | −43.3009 | + | 0.186402i | −0.577345 | + | 0.00248536i | ||||
\(76\) | −34.3548 | −0.452037 | ||||||||
\(77\) | −139.245 | − | 12.1778i | −1.80838 | − | 0.158153i | ||||
\(78\) | 32.7600 | + | 32.7600i | 0.420001 | + | 0.420001i | ||||
\(79\) | 65.5559 | − | 37.8487i | 0.829821 | − | 0.479097i | −0.0239704 | − | 0.999713i | \(-0.507631\pi\) |
0.853791 | + | 0.520615i | \(0.174297\pi\) | |||||||
\(80\) | −7.69342 | − | 18.4611i | −0.0961678 | − | 0.230763i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −29.5474 | − | 7.91720i | −0.360334 | − | 0.0965512i | ||||
\(83\) | 28.2864 | + | 28.2864i | 0.340800 | + | 0.340800i | 0.856668 | − | 0.515868i | \(-0.172531\pi\) |
−0.515868 | + | 0.856668i | \(0.672531\pi\) | |||||||
\(84\) | −4.21152 | − | 23.8802i | −0.0501372 | − | 0.284288i | ||||
\(85\) | −15.0078 | − | 112.130i | −0.176563 | − | 1.31918i | ||||
\(86\) | 14.6809 | + | 25.4281i | 0.170709 | + | 0.295676i | ||||
\(87\) | 10.4001 | + | 38.8137i | 0.119541 | + | 0.446135i | ||||
\(88\) | −54.5539 | + | 14.6177i | −0.619930 | + | 0.166110i | ||||
\(89\) | −124.644 | + | 71.9632i | −1.40049 | + | 0.808575i | −0.994443 | − | 0.105276i | \(-0.966427\pi\) |
−0.406050 | + | 0.913851i | \(0.633094\pi\) | |||||||
\(90\) | −21.0257 | + | 2.81414i | −0.233619 | + | 0.0312682i | ||||
\(91\) | 45.2788 | − | 124.415i | 0.497569 | − | 1.36720i | ||||
\(92\) | −29.6720 | + | 29.6720i | −0.322522 | + | 0.322522i | ||||
\(93\) | −24.8710 | + | 92.8197i | −0.267430 | + | 0.998061i | ||||
\(94\) | 92.7643 | + | 53.5575i | 0.986855 | + | 0.569761i | ||||
\(95\) | 79.2783 | − | 33.0382i | 0.834508 | − | 0.347771i | ||||
\(96\) | −4.89898 | − | 8.48528i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 56.0616 | − | 56.0616i | 0.577954 | − | 0.577954i | −0.356385 | − | 0.934339i | \(-0.615991\pi\) |
0.934339 | + | 0.356385i | \(0.115991\pi\) | |||||||
\(98\) | −56.7618 | + | 39.7505i | −0.579202 | + | 0.405617i | ||||
\(99\) | 59.9043i | 0.605094i | ||||||||
\(100\) | 35.5072 | + | 35.2028i | 0.355072 | + | 0.352028i | ||||
\(101\) | −56.4634 | + | 97.7974i | −0.559043 | + | 0.968291i | 0.438533 | + | 0.898715i | \(0.355498\pi\) |
−0.997577 | + | 0.0695765i | \(0.977835\pi\) | |||||||
\(102\) | −14.3443 | − | 53.5337i | −0.140631 | − | 0.524840i | ||||
\(103\) | −50.9322 | + | 190.082i | −0.494488 | + | 1.84545i | 0.0383934 | + | 0.999263i | \(0.487776\pi\) |
−0.532881 | + | 0.846190i | \(0.678891\pi\) | |||||||
\(104\) | − | 53.4969i | − | 0.514394i | ||||||
\(105\) | 32.6837 | + | 51.0566i | 0.311273 | + | 0.486253i | ||||
\(106\) | 5.88192 | 0.0554898 | ||||||||
\(107\) | 157.308 | + | 42.1506i | 1.47017 | + | 0.393931i | 0.902990 | − | 0.429662i | \(-0.141367\pi\) |
0.567181 | + | 0.823593i | \(0.308034\pi\) | |||||||
\(108\) | −10.0382 | + | 2.68973i | −0.0929463 | + | 0.0249049i | ||||
\(109\) | 50.7768 | + | 29.3160i | 0.465843 | + | 0.268954i | 0.714498 | − | 0.699638i | \(-0.246655\pi\) |
−0.248655 | + | 0.968592i | \(0.579989\pi\) | |||||||
\(110\) | 111.833 | − | 86.1954i | 1.01666 | − | 0.783595i | ||||
\(111\) | −39.9632 | −0.360028 | ||||||||
\(112\) | −16.0594 | + | 22.9368i | −0.143387 | + | 0.204793i | ||||
\(113\) | −69.9728 | − | 69.9728i | −0.619229 | − | 0.619229i | 0.326105 | − | 0.945334i | \(-0.394264\pi\) |
−0.945334 | + | 0.326105i | \(0.894264\pi\) | |||||||
\(114\) | 36.4387 | − | 21.0379i | 0.319638 | − | 0.184543i | ||||
\(115\) | 39.9373 | − | 97.0071i | 0.347281 | − | 0.843540i | ||||
\(116\) | 23.1996 | − | 40.1829i | 0.199997 | − | 0.346405i | ||||
\(117\) | −54.8086 | − | 14.6859i | −0.468450 | − | 0.125521i | ||||
\(118\) | −30.9345 | − | 30.9345i | −0.262157 | − | 0.262157i | ||||
\(119\) | −121.324 | + | 101.810i | −1.01953 | + | 0.855546i | ||||
\(120\) | 19.4652 | + | 14.8697i | 0.162210 | + | 0.123914i | ||||
\(121\) | −138.862 | − | 240.517i | −1.14762 | − | 1.98774i | ||||
\(122\) | −1.28721 | − | 4.80395i | −0.0105509 | − | 0.0393766i | ||||
\(123\) | 36.1880 | − | 9.69654i | 0.294211 | − | 0.0788337i | ||||
\(124\) | 96.0940 | − | 55.4799i | 0.774952 | − | 0.447419i | ||||
\(125\) | −115.791 | − | 47.0887i | −0.926331 | − | 0.376710i | ||||
\(126\) | 19.0906 | + | 22.7497i | 0.151512 | + | 0.180553i | ||||
\(127\) | −43.1314 | + | 43.1314i | −0.339617 | + | 0.339617i | −0.856223 | − | 0.516606i | \(-0.827195\pi\) |
0.516606 | + | 0.856223i | \(0.327195\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.0228766 | + | 0.0853766i | ||||
\(129\) | −31.1430 | − | 17.9804i | −0.241418 | − | 0.139383i | ||||
\(130\) | 51.4468 | + | 123.451i | 0.395745 | + | 0.949626i | ||||
\(131\) | −29.3082 | − | 50.7632i | −0.223727 | − | 0.387506i | 0.732210 | − | 0.681079i | \(-0.238489\pi\) |
−0.955937 | + | 0.293573i | \(0.905156\pi\) | |||||||
\(132\) | 48.9116 | − | 48.9116i | 0.370543 | − | 0.370543i | ||||
\(133\) | −98.4985 | − | 68.9646i | −0.740590 | − | 0.518531i | ||||
\(134\) | 4.17626i | 0.0311661i | ||||||||
\(135\) | 20.5778 | − | 15.8604i | 0.152428 | − | 0.117485i | ||||
\(136\) | −31.9980 | + | 55.4222i | −0.235280 | + | 0.407516i | ||||
\(137\) | 20.8036 | + | 77.6400i | 0.151851 | + | 0.566716i | 0.999354 | + | 0.0359258i | \(0.0114380\pi\) |
−0.847503 | + | 0.530790i | \(0.821895\pi\) | |||||||
\(138\) | 13.3016 | − | 49.6423i | 0.0963885 | − | 0.359727i | ||||
\(139\) | 15.1273i | 0.108830i | 0.998518 | + | 0.0544149i | \(0.0173294\pi\) | ||||
−0.998518 | + | 0.0544149i | \(0.982671\pi\) | |||||||
\(140\) | 15.0014 | − | 68.3737i | 0.107153 | − | 0.488383i | ||||
\(141\) | −131.189 | −0.930416 | ||||||||
\(142\) | −16.2472 | − | 4.35343i | −0.114417 | − | 0.0306580i | ||||
\(143\) | 364.808 | − | 97.7500i | 2.55110 | − | 0.683566i | ||||
\(144\) | 10.3923 | + | 6.00000i | 0.0721688 | + | 0.0416667i | ||||
\(145\) | −14.8932 | + | 115.038i | −0.102712 | + | 0.793366i | ||||
\(146\) | 30.8763 | 0.211481 | ||||||||
\(147\) | 35.8628 | − | 76.9211i | 0.243965 | − | 0.523273i | ||||
\(148\) | 32.6298 | + | 32.6298i | 0.220472 | + | 0.220472i | ||||
\(149\) | 28.5019 | − | 16.4556i | 0.191288 | − | 0.110440i | −0.401297 | − | 0.915948i | \(-0.631441\pi\) |
0.592585 | + | 0.805508i | \(0.298107\pi\) | |||||||
\(150\) | −59.2183 | − | 15.5946i | −0.394789 | − | 0.103964i | ||||
\(151\) | −142.183 | + | 246.269i | −0.941611 | + | 1.63092i | −0.179211 | + | 0.983811i | \(0.557355\pi\) |
−0.762399 | + | 0.647107i | \(0.775979\pi\) | |||||||
\(152\) | −46.9295 | − | 12.5747i | −0.308747 | − | 0.0827284i | ||||
\(153\) | 47.9970 | + | 47.9970i | 0.313706 | + | 0.313706i | ||||
\(154\) | −185.755 | − | 67.6025i | −1.20620 | − | 0.438977i | ||||
\(155\) | −168.396 | + | 220.439i | −1.08643 | + | 1.42219i | ||||
\(156\) | 32.7600 | + | 56.7421i | 0.210000 | + | 0.363731i | ||||
\(157\) | 45.7477 | + | 170.733i | 0.291387 | + | 1.08747i | 0.944045 | + | 0.329817i | \(0.106987\pi\) |
−0.652658 | + | 0.757652i | \(0.726346\pi\) | |||||||
\(158\) | 103.405 | − | 27.7072i | 0.654459 | − | 0.175362i | ||||
\(159\) | −6.23872 | + | 3.60193i | −0.0392372 | + | 0.0226536i | ||||
\(160\) | −3.75219 | − | 28.0343i | −0.0234512 | − | 0.175214i | ||||
\(161\) | −144.637 | + | 25.5083i | −0.898366 | + | 0.158436i | ||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 19.4477 | − | 72.5798i | 0.119311 | − | 0.445275i | −0.880262 | − | 0.474487i | \(-0.842633\pi\) |
0.999573 | + | 0.0292129i | \(0.00930008\pi\) | |||||||
\(164\) | −37.4646 | − | 21.6302i | −0.228443 | − | 0.131891i | ||||
\(165\) | −65.8329 | + | 159.907i | −0.398988 | + | 0.969136i | ||||
\(166\) | 28.2864 | + | 48.9935i | 0.170400 | + | 0.295141i | ||||
\(167\) | 115.501 | − | 115.501i | 0.691625 | − | 0.691625i | −0.270964 | − | 0.962589i | \(-0.587343\pi\) |
0.962589 | + | 0.270964i | \(0.0873426\pi\) | |||||||
\(168\) | 2.98771 | − | 34.1625i | 0.0177840 | − | 0.203348i | ||||
\(169\) | 188.740i | 1.11681i | ||||||||
\(170\) | 20.5414 | − | 158.666i | 0.120832 | − | 0.933329i | ||||
\(171\) | −25.7661 | + | 44.6282i | −0.150679 | + | 0.260983i | ||||
\(172\) | 10.7472 | + | 40.1091i | 0.0624837 | + | 0.233192i | ||||
\(173\) | −51.8207 | + | 193.397i | −0.299541 | + | 1.11790i | 0.638002 | + | 0.770035i | \(0.279761\pi\) |
−0.937543 | + | 0.347869i | \(0.886905\pi\) | |||||||
\(174\) | 56.8272i | 0.326593i | ||||||||
\(175\) | 31.1356 | + | 172.208i | 0.177918 | + | 0.984045i | ||||
\(176\) | −79.8724 | −0.453820 | ||||||||
\(177\) | 51.7544 | + | 13.8675i | 0.292398 | + | 0.0783477i | ||||
\(178\) | −196.607 | + | 52.6807i | −1.10453 | + | 0.295959i | ||||
\(179\) | −103.999 | − | 60.0438i | −0.580999 | − | 0.335440i | 0.180531 | − | 0.983569i | \(-0.442218\pi\) |
−0.761530 | + | 0.648129i | \(0.775552\pi\) | |||||||
\(180\) | −29.7517 | − | 3.85176i | −0.165287 | − | 0.0213987i | ||||
\(181\) | 217.830 | 1.20348 | 0.601741 | − | 0.798691i | \(-0.294474\pi\) | ||||
0.601741 | + | 0.798691i | \(0.294474\pi\) | |||||||
\(182\) | 107.391 | − | 153.381i | 0.590061 | − | 0.842752i | ||||
\(183\) | 4.30710 | + | 4.30710i | 0.0235361 | + | 0.0235361i | ||||
\(184\) | −51.3935 | + | 29.6720i | −0.279312 | + | 0.161261i | ||||
\(185\) | −106.677 | − | 43.9183i | −0.576632 | − | 0.237396i | ||||
\(186\) | −67.9487 | + | 117.691i | −0.365316 | + | 0.632746i | ||||
\(187\) | −436.404 | − | 116.934i | −2.33371 | − | 0.625316i | ||||
\(188\) | 107.115 | + | 107.115i | 0.569761 | + | 0.569761i | ||||
\(189\) | −34.1799 | − | 12.4392i | −0.180846 | − | 0.0658159i | ||||
\(190\) | 120.389 | − | 16.1132i | 0.633626 | − | 0.0848063i | ||||
\(191\) | −56.1666 | − | 97.2834i | −0.294066 | − | 0.509337i | 0.680701 | − | 0.732561i | \(-0.261675\pi\) |
−0.974767 | + | 0.223224i | \(0.928342\pi\) | |||||||
\(192\) | −3.58630 | − | 13.3843i | −0.0186787 | − | 0.0697097i | ||||
\(193\) | −5.59533 | + | 1.49926i | −0.0289913 | + | 0.00776820i | −0.273286 | − | 0.961933i | \(-0.588110\pi\) |
0.244294 | + | 0.969701i | \(0.421444\pi\) | |||||||
\(194\) | 97.1015 | − | 56.0616i | 0.500523 | − | 0.288977i | ||||
\(195\) | −130.166 | − | 99.4353i | −0.667517 | − | 0.509925i | ||||
\(196\) | −92.0877 | + | 33.5240i | −0.469835 | + | 0.171041i | ||||
\(197\) | −40.3068 | + | 40.3068i | −0.204603 | + | 0.204603i | −0.801969 | − | 0.597366i | \(-0.796214\pi\) |
0.597366 | + | 0.801969i | \(0.296214\pi\) | |||||||
\(198\) | −21.9265 | + | 81.8308i | −0.110740 | + | 0.413287i | ||||
\(199\) | −85.5804 | − | 49.4099i | −0.430052 | − | 0.248291i | 0.269317 | − | 0.963052i | \(-0.413202\pi\) |
−0.699369 | + | 0.714761i | \(0.746536\pi\) | |||||||
\(200\) | 35.6186 | + | 61.0845i | 0.178093 | + | 0.305422i | ||||
\(201\) | −2.55743 | − | 4.42960i | −0.0127235 | − | 0.0220378i | ||||
\(202\) | −112.927 | + | 112.927i | −0.559043 | + | 0.559043i | ||||
\(203\) | 147.180 | − | 68.6369i | 0.725024 | − | 0.338113i | ||||
\(204\) | − | 78.3788i | − | 0.384210i | ||||||
\(205\) | 107.256 | + | 13.8857i | 0.523199 | + | 0.0677351i | ||||
\(206\) | −139.149 | + | 241.014i | −0.675483 | + | 1.16997i | ||||
\(207\) | 16.2911 | + | 60.7991i | 0.0787009 | + | 0.293716i | ||||
\(208\) | 19.5812 | − | 73.0782i | 0.0941405 | − | 0.351337i | ||||
\(209\) | − | 343.000i | − | 1.64115i | ||||||
\(210\) | 25.9587 | + | 81.7077i | 0.123613 | + | 0.389084i | ||||
\(211\) | 344.348 | 1.63198 | 0.815991 | − | 0.578064i | \(-0.196192\pi\) | ||||
0.815991 | + | 0.578064i | \(0.196192\pi\) | |||||||
\(212\) | 8.03485 | + | 2.15293i | 0.0379003 | + | 0.0101553i | ||||
\(213\) | 19.8987 | − | 5.33185i | 0.0934212 | − | 0.0250321i | ||||
\(214\) | 199.459 | + | 115.158i | 0.932051 | + | 0.538120i | ||||
\(215\) | −63.3726 | − | 82.2217i | −0.294756 | − | 0.382427i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 386.883 | + | 33.8352i | 1.78287 | + | 0.155922i | ||||
\(218\) | 58.6321 | + | 58.6321i | 0.268954 | + | 0.268954i | ||||
\(219\) | −32.7492 | + | 18.9078i | −0.149540 | + | 0.0863369i | ||||
\(220\) | 184.316 | − | 76.8115i | 0.837801 | − | 0.349143i | ||||
\(221\) | 213.974 | − | 370.615i | 0.968210 | − | 1.67699i | ||||
\(222\) | −54.5907 | − | 14.6275i | −0.245904 | − | 0.0658898i | ||||
\(223\) | 34.8821 | + | 34.8821i | 0.156422 | + | 0.156422i | 0.780979 | − | 0.624557i | \(-0.214721\pi\) |
−0.624557 | + | 0.780979i | \(0.714721\pi\) | |||||||
\(224\) | −30.3330 | + | 25.4541i | −0.135415 | + | 0.113634i | ||||
\(225\) | 72.3602 | − | 19.7231i | 0.321601 | − | 0.0876582i | ||||
\(226\) | −69.9728 | − | 121.197i | −0.309614 | − | 0.536268i | ||||
\(227\) | 44.6847 | + | 166.766i | 0.196849 | + | 0.734651i | 0.991780 | + | 0.127951i | \(0.0408402\pi\) |
−0.794931 | + | 0.606699i | \(0.792493\pi\) | |||||||
\(228\) | 57.4767 | − | 15.4008i | 0.252091 | − | 0.0675475i | ||||
\(229\) | −18.1914 | + | 10.5028i | −0.0794382 | + | 0.0458637i | −0.539193 | − | 0.842182i | \(-0.681271\pi\) |
0.459755 | + | 0.888046i | \(0.347937\pi\) | |||||||
\(230\) | 90.0624 | − | 117.896i | 0.391576 | − | 0.512592i | ||||
\(231\) | 238.421 | − | 42.0480i | 1.03213 | − | 0.182026i | ||||
\(232\) | 46.3993 | − | 46.3993i | 0.199997 | − | 0.199997i | ||||
\(233\) | 51.8914 | − | 193.661i | 0.222710 | − | 0.831164i | −0.760599 | − | 0.649221i | \(-0.775095\pi\) |
0.983309 | − | 0.181943i | \(-0.0582385\pi\) | |||||||
\(234\) | −69.4945 | − | 40.1227i | −0.296985 | − | 0.171465i | ||||
\(235\) | −350.192 | − | 144.172i | −1.49018 | − | 0.613499i | ||||
\(236\) | −30.9345 | − | 53.5801i | −0.131078 | − | 0.227034i | ||||
\(237\) | −92.7100 | + | 92.7100i | −0.391181 | + | 0.391181i | ||||
\(238\) | −202.997 | + | 94.6672i | −0.852930 | + | 0.397761i | ||||
\(239\) | − | 282.776i | − | 1.18316i | −0.806245 | − | 0.591581i | \(-0.798504\pi\) | ||
0.806245 | − | 0.591581i | \(-0.201496\pi\) | |||||||
\(240\) | 21.1472 | + | 27.4371i | 0.0881134 | + | 0.114321i | ||||
\(241\) | 45.5745 | − | 78.9374i | 0.189106 | − | 0.327541i | −0.755846 | − | 0.654749i | \(-0.772774\pi\) |
0.944952 | + | 0.327208i | \(0.106108\pi\) | |||||||
\(242\) | −101.654 | − | 379.379i | −0.420059 | − | 1.56768i | ||||
\(243\) | −4.03459 | + | 15.0573i | −0.0166032 | + | 0.0619642i | ||||
\(244\) | − | 7.03346i | − | 0.0288257i | ||||||
\(245\) | 180.265 | − | 165.920i | 0.735777 | − | 0.677223i | ||||
\(246\) | 52.9829 | 0.215378 | ||||||||
\(247\) | 313.823 | + | 84.0886i | 1.27054 | + | 0.340440i | ||||
\(248\) | 151.574 | − | 40.6141i | 0.611185 | − | 0.163767i | ||||
\(249\) | −60.0045 | − | 34.6436i | −0.240982 | − | 0.139131i | ||||
\(250\) | −140.938 | − | 106.707i | −0.563753 | − | 0.426828i | ||||
\(251\) | 278.796 | 1.11074 | 0.555371 | − | 0.831603i | \(-0.312576\pi\) | ||||
0.555371 | + | 0.831603i | \(0.312576\pi\) | |||||||
\(252\) | 17.7512 | + | 38.0643i | 0.0704413 | + | 0.151049i | ||||
\(253\) | −296.247 | − | 296.247i | −1.17094 | − | 1.17094i | ||||
\(254\) | −74.7058 | + | 43.1314i | −0.294117 | + | 0.169809i | ||||
\(255\) | 75.3752 | + | 180.870i | 0.295589 | + | 0.709293i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 93.6352 | + | 25.0895i | 0.364339 | + | 0.0976244i | 0.436344 | − | 0.899780i | \(-0.356273\pi\) |
−0.0720049 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(258\) | −35.9608 | − | 35.9608i | −0.139383 | − | 0.139383i | ||||
\(259\) | 28.0509 | + | 159.055i | 0.108305 | + | 0.614110i | ||||
\(260\) | 25.0913 | + | 187.468i | 0.0965050 | + | 0.721033i | ||||
\(261\) | −34.7994 | − | 60.2744i | −0.133331 | − | 0.230936i | ||||
\(262\) | −21.4551 | − | 80.0714i | −0.0818896 | − | 0.305616i | ||||
\(263\) | 201.551 | − | 54.0055i | 0.766354 | − | 0.205344i | 0.145594 | − | 0.989344i | \(-0.453491\pi\) |
0.620760 | + | 0.784000i | \(0.286824\pi\) | |||||||
\(264\) | 84.7175 | − | 48.9116i | 0.320899 | − | 0.185271i | ||||
\(265\) | −20.6119 | + | 2.75876i | −0.0777809 | + | 0.0104104i | ||||
\(266\) | −109.309 | − | 130.260i | −0.410935 | − | 0.489701i | ||||
\(267\) | 176.273 | − | 176.273i | 0.660199 | − | 0.660199i | ||||
\(268\) | −1.52862 | + | 5.70488i | −0.00570380 | + | 0.0212869i | ||||
\(269\) | 177.916 | + | 102.720i | 0.661397 | + | 0.381858i | 0.792809 | − | 0.609470i | \(-0.208618\pi\) |
−0.131412 | + | 0.991328i | \(0.541951\pi\) | |||||||
\(270\) | 33.9152 | − | 14.1337i | 0.125612 | − | 0.0523471i | ||||
\(271\) | −55.2715 | − | 95.7331i | −0.203954 | − | 0.353259i | 0.745845 | − | 0.666120i | \(-0.232046\pi\) |
−0.949799 | + | 0.312861i | \(0.898713\pi\) | |||||||
\(272\) | −63.9960 | + | 63.9960i | −0.235280 | + | 0.235280i | ||||
\(273\) | −19.9792 | + | 228.448i | −0.0731837 | + | 0.836807i | ||||
\(274\) | 113.673i | 0.414865i | ||||||||
\(275\) | −351.467 | + | 354.506i | −1.27806 | + | 1.28911i | ||||
\(276\) | 36.3407 | − | 62.9439i | 0.131669 | − | 0.228058i | ||||
\(277\) | 18.2366 | + | 68.0599i | 0.0658361 | + | 0.245704i | 0.991000 | − | 0.133865i | \(-0.0427390\pi\) |
−0.925163 | + | 0.379569i | \(0.876072\pi\) | |||||||
\(278\) | −5.53699 | + | 20.6643i | −0.0199172 | + | 0.0743321i | ||||
\(279\) | − | 166.440i | − | 0.596558i | ||||||
\(280\) | 45.5188 | − | 87.9093i | 0.162567 | − | 0.313962i | ||||
\(281\) | 172.628 | 0.614336 | 0.307168 | − | 0.951655i | \(-0.400619\pi\) | ||||
0.307168 | + | 0.951655i | \(0.400619\pi\) | |||||||
\(282\) | −179.207 | − | 48.0184i | −0.635486 | − | 0.170278i | ||||
\(283\) | −27.2132 | + | 7.29175i | −0.0961597 | + | 0.0257659i | −0.306578 | − | 0.951846i | \(-0.599184\pi\) |
0.210418 | + | 0.977611i | \(0.432517\pi\) | |||||||
\(284\) | −20.6007 | − | 11.8938i | −0.0725376 | − | 0.0418796i | ||||
\(285\) | −117.824 | + | 90.8135i | −0.413419 | + | 0.318644i | ||||
\(286\) | 534.116 | 1.86754 | ||||||||
\(287\) | −63.9936 | − | 137.223i | −0.222974 | − | 0.478129i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | −193.069 | + | 111.468i | −0.668058 | + | 0.385703i | ||||
\(290\) | −62.4514 | + | 151.694i | −0.215350 | + | 0.523082i | ||||
\(291\) | −68.6611 | + | 118.925i | −0.235949 | + | 0.408675i | ||||
\(292\) | 42.1778 | + | 11.3015i | 0.144444 | + | 0.0387038i | ||||
\(293\) | −78.8568 | − | 78.8568i | −0.269136 | − | 0.269136i | 0.559616 | − | 0.828752i | \(-0.310949\pi\) |
−0.828752 | + | 0.559616i | \(0.810949\pi\) | |||||||
\(294\) | 77.1446 | − | 91.9495i | 0.262397 | − | 0.312753i | ||||
\(295\) | 122.912 | + | 93.8943i | 0.416652 | + | 0.318286i | ||||
\(296\) | 32.6298 | + | 56.5164i | 0.110236 | + | 0.190934i | ||||
\(297\) | −26.8544 | − | 100.222i | −0.0904187 | − | 0.337447i | ||||
\(298\) | 44.9575 | − | 12.0463i | 0.150864 | − | 0.0404239i | ||||
\(299\) | 343.674 | − | 198.420i | 1.14941 | − | 0.663613i | ||||
\(300\) | −75.1857 | − | 42.9780i | −0.250619 | − | 0.143260i | ||||
\(301\) | −49.7027 | + | 136.571i | −0.165125 | + | 0.453724i | ||||
\(302\) | −284.366 | + | 284.366i | −0.941611 | + | 0.941611i | ||||
\(303\) | 50.6237 | − | 188.930i | 0.167075 | − | 0.623532i | ||||
\(304\) | −59.5042 | − | 34.3548i | −0.195738 | − | 0.113009i | ||||
\(305\) | 6.76393 | + | 16.2307i | 0.0221768 | + | 0.0532153i | ||||
\(306\) | 47.9970 | + | 83.1333i | 0.156853 | + | 0.271677i | ||||
\(307\) | 21.8398 | − | 21.8398i | 0.0711395 | − | 0.0711395i | −0.670642 | − | 0.741781i | \(-0.733981\pi\) |
0.741781 | + | 0.670642i | \(0.233981\pi\) | |||||||
\(308\) | −229.002 | − | 160.338i | −0.743513 | − | 0.520577i | ||||
\(309\) | − | 340.845i | − | 1.10306i | ||||||
\(310\) | −310.720 | + | 239.488i | −1.00232 | + | 0.772541i | ||||
\(311\) | −85.0972 | + | 147.393i | −0.273624 | + | 0.473931i | −0.969787 | − | 0.243953i | \(-0.921556\pi\) |
0.696163 | + | 0.717884i | \(0.254889\pi\) | |||||||
\(312\) | 23.9820 | + | 89.5021i | 0.0768654 | + | 0.286866i | ||||
\(313\) | 101.548 | − | 378.982i | 0.324434 | − | 1.21080i | −0.590446 | − | 0.807077i | \(-0.701048\pi\) |
0.914880 | − | 0.403727i | \(-0.132285\pi\) | |||||||
\(314\) | 249.970i | 0.796083i | ||||||||
\(315\) | −77.5689 | − | 70.7677i | −0.246251 | − | 0.224659i | ||||
\(316\) | 151.395 | 0.479097 | ||||||||
\(317\) | −137.832 | − | 36.9318i | −0.434800 | − | 0.116504i | 0.0347786 | − | 0.999395i | \(-0.488927\pi\) |
−0.469578 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(318\) | −9.84065 | + | 2.63679i | −0.0309454 | + | 0.00829180i | ||||
\(319\) | 401.188 | + | 231.626i | 1.25764 | + | 0.726101i | ||||
\(320\) | 5.13568 | − | 39.6689i | 0.0160490 | − | 0.123965i | ||||
\(321\) | −282.078 | −0.878746 | ||||||||
\(322\) | −206.914 | − | 18.0959i | −0.642592 | − | 0.0561984i | ||||
\(323\) | −274.821 | − | 274.821i | −0.850840 | − | 0.850840i | ||||
\(324\) | 15.5885 | − | 9.00000i | 0.0481125 | − | 0.0277778i | ||||
\(325\) | −238.186 | − | 408.479i | −0.732880 | − | 1.25686i | ||||
\(326\) | 53.1321 | − | 92.0274i | 0.162982 | − | 0.282293i | ||||
\(327\) | −98.0933 | − | 26.2840i | −0.299980 | − | 0.0803793i | ||||
\(328\) | −43.2604 | − | 43.2604i | −0.131891 | − | 0.131891i | ||||
\(329\) | 92.0839 | + | 522.135i | 0.279890 | + | 1.58704i | ||||
\(330\) | −148.460 | + | 194.341i | −0.449878 | + | 0.588912i | ||||
\(331\) | −11.5185 | − | 19.9506i | −0.0347990 | − | 0.0602736i | 0.848101 | − | 0.529834i | \(-0.177746\pi\) |
−0.882900 | + | 0.469560i | \(0.844412\pi\) | |||||||
\(332\) | 20.7071 | + | 77.2798i | 0.0623707 | + | 0.232771i | ||||
\(333\) | 66.8597 | − | 17.9150i | 0.200780 | − | 0.0537988i | ||||
\(334\) | 200.054 | − | 115.501i | 0.598965 | − | 0.345812i | ||||
\(335\) | −1.95877 | − | 14.6348i | −0.00584706 | − | 0.0436860i | ||||
\(336\) | 16.5856 | − | 45.5732i | 0.0493619 | − | 0.135635i | ||||
\(337\) | −438.660 | + | 438.660i | −1.30166 | + | 1.30166i | −0.374391 | + | 0.927271i | \(0.622148\pi\) |
−0.927271 | + | 0.374391i | \(0.877852\pi\) | |||||||
\(338\) | −69.0837 | + | 257.824i | −0.204390 | + | 0.762792i | ||||
\(339\) | 148.435 | + | 85.6989i | 0.437861 | + | 0.252799i | ||||
\(340\) | 86.1359 | − | 209.223i | 0.253341 | − | 0.615362i | ||||
\(341\) | 553.914 | + | 959.408i | 1.62438 | + | 2.81351i | ||||
\(342\) | −51.5322 | + | 51.5322i | −0.150679 | + | 0.150679i | ||||
\(343\) | −331.321 | − | 88.7426i | −0.965951 | − | 0.258725i | ||||
\(344\) | 58.7238i | 0.170709i | ||||||||
\(345\) | −23.3292 | + | 180.200i | −0.0676210 | + | 0.522317i | ||||
\(346\) | −141.577 | + | 245.218i | −0.409181 | + | 0.708723i | ||||
\(347\) | −118.344 | − | 441.664i | −0.341048 | − | 1.27281i | −0.897162 | − | 0.441702i | \(-0.854375\pi\) |
0.556114 | − | 0.831106i | \(-0.312292\pi\) | |||||||
\(348\) | −20.8002 | + | 77.6275i | −0.0597707 | + | 0.223067i | ||||
\(349\) | 70.3408i | 0.201549i | 0.994909 | + | 0.100775i | \(0.0321321\pi\) | ||||
−0.994909 | + | 0.100775i | \(0.967868\pi\) | |||||||
\(350\) | −20.5004 | + | 246.637i | −0.0585726 | + | 0.704677i | ||||
\(351\) | 98.2801 | 0.280000 | ||||||||
\(352\) | −109.108 | − | 29.2353i | −0.309965 | − | 0.0830549i | ||||
\(353\) | −161.135 | + | 43.1761i | −0.456474 | + | 0.122312i | −0.479727 | − | 0.877418i | \(-0.659264\pi\) |
0.0232531 | + | 0.999730i | \(0.492598\pi\) | |||||||
\(354\) | 65.6219 | + | 37.8868i | 0.185373 | + | 0.107025i | ||||
\(355\) | 58.9768 | + | 7.63534i | 0.166132 | + | 0.0215080i | ||||
\(356\) | −287.853 | −0.808575 | ||||||||
\(357\) | 157.340 | − | 224.720i | 0.440727 | − | 0.629467i | ||||
\(358\) | −120.088 | − | 120.088i | −0.335440 | − | 0.335440i | ||||
\(359\) | 446.981 | − | 258.064i | 1.24507 | − | 0.718842i | 0.274949 | − | 0.961459i | \(-0.411339\pi\) |
0.970122 | + | 0.242616i | \(0.0780056\pi\) | |||||||
\(360\) | −39.2317 | − | 16.1515i | −0.108977 | − | 0.0448652i | ||||
\(361\) | −32.9687 | + | 57.1034i | −0.0913260 | + | 0.158181i | ||||
\(362\) | 297.562 | + | 79.7314i | 0.821994 | + | 0.220253i | ||||
\(363\) | 340.142 | + | 340.142i | 0.937031 | + | 0.937031i | ||||
\(364\) | 202.840 | − | 170.214i | 0.557253 | − | 0.467622i | ||||
\(365\) | −108.199 | + | 14.4817i | −0.296436 | + | 0.0396759i | ||||
\(366\) | 4.30710 | + | 7.46012i | 0.0117680 | + | 0.0203828i | ||||
\(367\) | 130.270 | + | 486.174i | 0.354959 | + | 1.32472i | 0.880536 | + | 0.473979i | \(0.157183\pi\) |
−0.525577 | + | 0.850746i | \(0.676151\pi\) | |||||||
\(368\) | −81.0655 | + | 21.7214i | −0.220287 | + | 0.0590256i | ||||
\(369\) | −56.1969 | + | 32.4453i | −0.152295 | + | 0.0879276i | ||||
\(370\) | −129.648 | − | 99.0399i | −0.350401 | − | 0.267676i | ||||
\(371\) | 18.7149 | + | 22.3020i | 0.0504444 | + | 0.0601133i | ||||
\(372\) | −135.897 | + | 135.897i | −0.365316 | + | 0.365316i | ||||
\(373\) | 99.5820 | − | 371.645i | 0.266976 | − | 0.996368i | −0.694054 | − | 0.719923i | \(-0.744177\pi\) |
0.961030 | − | 0.276445i | \(-0.0891563\pi\) | |||||||
\(374\) | −553.338 | − | 319.470i | −1.47951 | − | 0.854197i | ||||
\(375\) | 214.832 | + | 26.8731i | 0.572886 | + | 0.0716616i | ||||
\(376\) | 107.115 | + | 185.529i | 0.284880 | + | 0.493427i | ||||
\(377\) | −310.277 | + | 310.277i | −0.823016 | + | 0.823016i | ||||
\(378\) | −42.1376 | − | 29.5030i | −0.111475 | − | 0.0780502i | ||||
\(379\) | − | 352.609i | − | 0.930366i | −0.885214 | − | 0.465183i | \(-0.845988\pi\) | ||
0.885214 | − | 0.465183i | \(-0.154012\pi\) | |||||||
\(380\) | 170.352 | + | 22.0544i | 0.448295 | + | 0.0580378i | ||||
\(381\) | 52.8250 | − | 91.4955i | 0.138648 | − | 0.240146i | ||||
\(382\) | −41.1168 | − | 153.450i | −0.107636 | − | 0.401701i | ||||
\(383\) | 15.6711 | − | 58.4854i | 0.0409167 | − | 0.152703i | −0.942445 | − | 0.334361i | \(-0.891480\pi\) |
0.983362 | + | 0.181658i | \(0.0581462\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 682.646 | + | 149.775i | 1.77311 | + | 0.389026i | ||||
\(386\) | −8.19212 | −0.0212231 | ||||||||
\(387\) | 60.1636 | + | 16.1208i | 0.155462 | + | 0.0416558i | ||||
\(388\) | 153.163 | − | 41.0399i | 0.394750 | − | 0.105773i | ||||
\(389\) | −623.238 | − | 359.827i | −1.60215 | − | 0.925004i | −0.991056 | − | 0.133450i | \(-0.957395\pi\) |
−0.611099 | − | 0.791554i | \(-0.709272\pi\) | |||||||
\(390\) | −141.414 | − | 183.475i | −0.362600 | − | 0.470449i | ||||
\(391\) | −474.723 | −1.21413 | ||||||||
\(392\) | −138.065 | + | 12.0882i | −0.352206 | + | 0.0308371i | ||||
\(393\) | 71.7901 | + | 71.7901i | 0.182672 | + | 0.182672i | ||||
\(394\) | −69.8135 | + | 40.3068i | −0.177192 | + | 0.102302i | ||||
\(395\) | −349.364 | + | 145.593i | −0.884465 | + | 0.368590i | ||||
\(396\) | −59.9043 | + | 103.757i | −0.151273 | + | 0.262013i | ||||
\(397\) | 93.8233 | + | 25.1399i | 0.236331 | + | 0.0633246i | 0.375040 | − | 0.927008i | \(-0.377629\pi\) |
−0.138710 | + | 0.990333i | \(0.544295\pi\) | |||||||
\(398\) | −98.8197 | − | 98.8197i | −0.248291 | − | 0.248291i | ||||
\(399\) | 195.707 | + | 71.2244i | 0.490494 | + | 0.178507i | ||||
\(400\) | 26.2975 | + | 96.4803i | 0.0657437 | + | 0.241201i | ||||
\(401\) | −74.7359 | − | 129.446i | −0.186374 | − | 0.322809i | 0.757665 | − | 0.652644i | \(-0.226340\pi\) |
−0.944039 | + | 0.329835i | \(0.893007\pi\) | |||||||
\(402\) | −1.87217 | − | 6.98702i | −0.00465713 | − | 0.0173807i | ||||
\(403\) | −1013.59 | + | 271.591i | −2.51512 | + | 0.673924i | ||||
\(404\) | −195.595 | + | 112.927i | −0.484146 | + | 0.279522i | ||||
\(405\) | −27.3174 | + | 35.7598i | −0.0674503 | + | 0.0882958i | ||||
\(406\) | 226.174 | − | 39.8882i | 0.557079 | − | 0.0982468i | ||||
\(407\) | −325.777 | + | 325.777i | −0.800436 | + | 0.800436i | ||||
\(408\) | 28.6886 | − | 107.067i | 0.0703153 | − | 0.262420i | ||||
\(409\) | 316.278 | + | 182.603i | 0.773295 | + | 0.446462i | 0.834049 | − | 0.551690i | \(-0.186017\pi\) |
−0.0607535 | + | 0.998153i | \(0.519350\pi\) | |||||||
\(410\) | 141.432 | + | 58.2266i | 0.344955 | + | 0.142016i | ||||
\(411\) | −69.6102 | − | 120.568i | −0.169368 | − | 0.293354i | ||||
\(412\) | −278.299 | + | 278.299i | −0.675483 | + | 0.675483i | ||||
\(413\) | 18.8658 | − | 215.718i | 0.0456799 | − | 0.522320i | ||||
\(414\) | 89.0161i | 0.215015i | ||||||||
\(415\) | −122.103 | − | 158.420i | −0.294223 | − | 0.381735i | ||||
\(416\) | 53.4969 | − | 92.6594i | 0.128598 | − | 0.222739i | ||||
\(417\) | −6.78140 | − | 25.3085i | −0.0162624 | − | 0.0606919i | ||||
\(418\) | 125.547 | − | 468.546i | 0.300351 | − | 1.12092i | ||||
\(419\) | 373.960i | 0.892507i | 0.894907 | + | 0.446254i | \(0.147242\pi\) | ||||
−0.894907 | + | 0.446254i | \(0.852758\pi\) | |||||||
\(420\) | 5.55321 | + | 121.116i | 0.0132219 | + | 0.288372i | ||||
\(421\) | 414.109 | 0.983631 | 0.491816 | − | 0.870699i | \(-0.336333\pi\) | ||||
0.491816 | + | 0.870699i | \(0.336333\pi\) | |||||||
\(422\) | 470.389 | + | 126.040i | 1.11467 | + | 0.298674i | ||||
\(423\) | 219.483 | − | 58.8102i | 0.518872 | − | 0.139031i | ||||
\(424\) | 10.1878 | + | 5.88192i | 0.0240278 | + | 0.0138725i | ||||
\(425\) | 2.43500 | + | 565.645i | 0.00572941 | + | 1.33093i | ||||
\(426\) | 29.1338 | 0.0683891 | ||||||||
\(427\) | 14.1191 | − | 20.1656i | 0.0330659 | − | 0.0472263i | ||||
\(428\) | 230.315 | + | 230.315i | 0.538120 | + | 0.538120i | ||||
\(429\) | −566.515 | + | 327.078i | −1.32055 | + | 0.762419i | ||||
\(430\) | −56.4733 | − | 135.513i | −0.131333 | − | 0.315146i | ||||
\(431\) | −258.753 | + | 448.173i | −0.600355 | + | 1.03985i | 0.392412 | + | 0.919789i | \(0.371641\pi\) |
−0.992767 | + | 0.120056i | \(0.961693\pi\) | |||||||
\(432\) | −20.0764 | − | 5.37945i | −0.0464731 | − | 0.0124524i | ||||
\(433\) | −28.4380 | − | 28.4380i | −0.0656767 | − | 0.0656767i | 0.673506 | − | 0.739182i | \(-0.264788\pi\) |
−0.739182 | + | 0.673506i | \(0.764788\pi\) | |||||||
\(434\) | 516.107 | + | 187.829i | 1.18919 | + | 0.432785i | ||||
\(435\) | −26.6533 | − | 199.139i | −0.0612720 | − | 0.457791i | ||||
\(436\) | 58.6321 | + | 101.554i | 0.134477 | + | 0.232921i | ||||
\(437\) | −93.2794 | − | 348.123i | −0.213454 | − | 0.796621i | ||||
\(438\) | −51.6570 | + | 13.8415i | −0.117938 | + | 0.0316015i | ||||
\(439\) | −241.933 | + | 139.680i | −0.551100 | + | 0.318178i | −0.749565 | − | 0.661930i | \(-0.769738\pi\) |
0.198466 | + | 0.980108i | \(0.436404\pi\) | |||||||
\(440\) | 279.896 | − | 37.4620i | 0.636126 | − | 0.0851410i | ||||
\(441\) | −25.5169 | + | 144.768i | −0.0578614 | + | 0.328273i | ||||
\(442\) | 427.949 | − | 427.949i | 0.968210 | − | 0.968210i | ||||
\(443\) | −152.194 | + | 567.996i | −0.343553 | + | 1.28216i | 0.550740 | + | 0.834677i | \(0.314346\pi\) |
−0.894293 | + | 0.447482i | \(0.852321\pi\) | |||||||
\(444\) | −69.2182 | − | 39.9632i | −0.155897 | − | 0.0900071i | ||||
\(445\) | 664.259 | − | 276.821i | 1.49272 | − | 0.622071i | ||||
\(446\) | 34.8821 | + | 60.4175i | 0.0782109 | + | 0.135465i | ||||
\(447\) | −40.3078 | + | 40.3078i | −0.0901739 | + | 0.0901739i | ||||
\(448\) | −50.7525 | + | 23.6683i | −0.113287 | + | 0.0528310i | ||||
\(449\) | − | 515.916i | − | 1.14903i | −0.818493 | − | 0.574517i | \(-0.805190\pi\) | ||
0.818493 | − | 0.574517i | \(-0.194810\pi\) | |||||||
\(450\) | 106.065 | − | 0.456591i | 0.235700 | − | 0.00101465i | ||||
\(451\) | 215.957 | − | 374.048i | 0.478840 | − | 0.829375i | ||||
\(452\) | −51.2237 | − | 191.169i | −0.113327 | − | 0.422941i | ||||
\(453\) | 127.478 | − | 475.754i | 0.281408 | − | 1.05023i | ||||
\(454\) | 244.162i | 0.537802i | ||||||||
\(455\) | −304.390 | + | 587.859i | −0.668988 | + | 1.29200i | ||||
\(456\) | 84.1517 | 0.184543 | ||||||||
\(457\) | −281.008 | − | 75.2958i | −0.614896 | − | 0.164761i | −0.0620898 | − | 0.998071i | \(-0.519777\pi\) |
−0.552807 | + | 0.833310i | \(0.686443\pi\) | |||||||
\(458\) | −28.6941 | + | 7.68857i | −0.0626510 | + | 0.0167873i | ||||
\(459\) | −101.817 | − | 58.7841i | −0.221824 | − | 0.128070i | ||||
\(460\) | 166.181 | − | 128.084i | 0.361262 | − | 0.278444i | ||||
\(461\) | 431.271 | 0.935511 | 0.467756 | − | 0.883858i | \(-0.345063\pi\) | ||||
0.467756 | + | 0.883858i | \(0.345063\pi\) | |||||||
\(462\) | 341.080 | + | 29.8294i | 0.738268 | + | 0.0645659i | ||||
\(463\) | 81.4930 | + | 81.4930i | 0.176011 | + | 0.176011i | 0.789614 | − | 0.613603i | \(-0.210281\pi\) |
−0.613603 | + | 0.789614i | \(0.710281\pi\) | |||||||
\(464\) | 80.3659 | − | 46.3993i | 0.173202 | − | 0.0999984i | ||||
\(465\) | 182.912 | − | 444.291i | 0.393359 | − | 0.955465i | ||||
\(466\) | 141.770 | − | 245.553i | 0.304227 | − | 0.526937i | ||||
\(467\) | −213.017 | − | 57.0779i | −0.456140 | − | 0.122222i | 0.0234309 | − | 0.999725i | \(-0.492541\pi\) |
−0.479571 | + | 0.877503i | \(0.659208\pi\) | |||||||
\(468\) | −80.2454 | − | 80.2454i | −0.171465 | − | 0.171465i | ||||
\(469\) | −15.8348 | + | 13.2879i | −0.0337629 | + | 0.0283323i | ||||
\(470\) | −425.601 | − | 325.122i | −0.905534 | − | 0.691749i | ||||
\(471\) | −153.075 | − | 265.133i | −0.324999 | − | 0.562916i | ||||
\(472\) | −22.6456 | − | 84.5146i | −0.0479780 | − | 0.179056i | ||||
\(473\) | −400.451 | + | 107.301i | −0.846619 | + | 0.226851i | ||||
\(474\) | −160.578 | + | 92.7100i | −0.338773 | + | 0.195591i | ||||
\(475\) | −414.320 | + | 112.930i | −0.872252 | + | 0.237748i | ||||
\(476\) | −311.950 | + | 55.0157i | −0.655357 | + | 0.115579i | ||||
\(477\) | 8.82288 | − | 8.82288i | 0.0184966 | − | 0.0184966i | ||||
\(478\) | 103.503 | − | 386.279i | 0.216534 | − | 0.808115i | ||||
\(479\) | 322.538 | + | 186.218i | 0.673357 | + | 0.388763i | 0.797348 | − | 0.603520i | \(-0.206236\pi\) |
−0.123990 | + | 0.992283i | \(0.539569\pi\) | |||||||
\(480\) | 18.8450 | + | 45.2202i | 0.0392603 | + | 0.0942088i | ||||
\(481\) | −218.199 | − | 377.932i | −0.453636 | − | 0.785721i | ||||
\(482\) | 91.1491 | − | 91.1491i | 0.189106 | − | 0.189106i | ||||
\(483\) | 230.547 | − | 107.515i | 0.477324 | − | 0.222599i | ||||
\(484\) | − | 555.450i | − | 1.14762i | ||||||
\(485\) | −313.977 | + | 241.999i | −0.647376 | + | 0.498966i | ||||
\(486\) | −11.0227 | + | 19.0919i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −95.0398 | − | 354.693i | −0.195154 | − | 0.728323i | −0.992227 | − | 0.124441i | \(-0.960286\pi\) |
0.797073 | − | 0.603882i | \(-0.206380\pi\) | |||||||
\(488\) | 2.57443 | − | 9.60789i | 0.00527546 | − | 0.0196883i | ||||
\(489\) | 130.146i | 0.266148i | ||||||||
\(490\) | 306.978 | − | 160.669i | 0.626486 | − | 0.327896i | ||||
\(491\) | 8.71393 | 0.0177473 | 0.00887366 | − | 0.999961i | \(-0.497175\pi\) | ||||
0.00887366 | + | 0.999961i | \(0.497175\pi\) | |||||||
\(492\) | 72.3760 | + | 19.3931i | 0.147106 | + | 0.0394168i | ||||
\(493\) | 507.029 | − | 135.858i | 1.02846 | − | 0.275574i | ||||
\(494\) | 397.912 | + | 229.734i | 0.805489 | + | 0.465049i | ||||
\(495\) | 38.4561 | − | 297.042i | 0.0776892 | − | 0.600086i | ||||
\(496\) | 221.920 | 0.447419 | ||||||||
\(497\) | −35.1882 | − | 75.4550i | −0.0708013 | − | 0.151821i | ||||
\(498\) | −69.2872 | − | 69.2872i | −0.139131 | − | 0.139131i | ||||
\(499\) | −233.352 | + | 134.726i | −0.467640 | + | 0.269992i | −0.715251 | − | 0.698867i | \(-0.753688\pi\) |
0.247611 | + | 0.968860i | \(0.420354\pi\) | |||||||
\(500\) | −153.468 | − | 197.351i | −0.306936 | − | 0.394703i | ||||
\(501\) | −141.460 | + | 245.015i | −0.282355 | + | 0.489053i | ||||
\(502\) | 380.843 | + | 102.047i | 0.758651 | + | 0.203280i | ||||
\(503\) | 308.184 | + | 308.184i | 0.612693 | + | 0.612693i | 0.943647 | − | 0.330954i | \(-0.107371\pi\) |
−0.330954 | + | 0.943647i | \(0.607371\pi\) | |||||||
\(504\) | 10.3161 | + | 58.4943i | 0.0204684 | + | 0.116060i | ||||
\(505\) | 342.762 | − | 448.693i | 0.678737 | − | 0.888501i | ||||
\(506\) | −296.247 | − | 513.115i | −0.585468 | − | 1.01406i | ||||
\(507\) | −84.6099 | − | 315.768i | −0.166883 | − | 0.622817i | ||||
\(508\) | −117.837 | + | 31.5744i | −0.231963 | + | 0.0621543i | ||||
\(509\) | 568.117 | − | 328.003i | 1.11614 | − | 0.644406i | 0.175730 | − | 0.984438i | \(-0.443771\pi\) |
0.940414 | + | 0.340032i | \(0.110438\pi\) | |||||||
\(510\) | 36.7615 | + | 274.662i | 0.0720814 | + | 0.538552i | ||||
\(511\) | 98.2409 | + | 117.071i | 0.192252 | + | 0.229102i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 23.1012 | − | 86.2150i | 0.0450317 | − | 0.168060i | ||||
\(514\) | 118.725 | + | 68.5457i | 0.230982 | + | 0.133357i | ||||
\(515\) | 374.578 | − | 909.846i | 0.727336 | − | 1.76669i | ||||
\(516\) | −35.9608 | − | 62.2860i | −0.0696915 | − | 0.120709i | ||||
\(517\) | −1069.44 | + | 1069.44i | −2.06855 | + | 2.06855i | ||||
\(518\) | −19.8997 | + | 227.540i | −0.0384164 | + | 0.439266i | ||||
\(519\) | − | 346.791i | − | 0.668190i | ||||||
\(520\) | −34.3429 | + | 265.271i | −0.0660440 | + | 0.510136i | ||||
\(521\) | 91.8665 | − | 159.117i | 0.176327 | − | 0.305408i | −0.764293 | − | 0.644870i | \(-0.776912\pi\) |
0.940620 | + | 0.339462i | \(0.110245\pi\) | |||||||
\(522\) | −25.4750 | − | 95.0738i | −0.0488026 | − | 0.182134i | ||||
\(523\) | −213.259 | + | 795.892i | −0.407760 | + | 1.52178i | 0.391147 | + | 0.920328i | \(0.372078\pi\) |
−0.798908 | + | 0.601454i | \(0.794588\pi\) | |||||||
\(524\) | − | 117.233i | − | 0.223727i | ||||||
\(525\) | −129.290 | − | 274.152i | −0.246266 | − | 0.522194i | ||||
\(526\) | 295.091 | 0.561010 | ||||||||
\(527\) | 1212.52 | + | 324.893i | 2.30079 | + | 0.616495i | ||||
\(528\) | 133.629 | − | 35.8058i | 0.253085 | − | 0.0678140i | ||||
\(529\) | 76.8901 | + | 44.3925i | 0.145350 | + | 0.0839179i | ||||
\(530\) | −29.1662 | − | 3.77596i | −0.0550306 | − | 0.00712445i | ||||
\(531\) | −92.8034 | −0.174771 | ||||||||
\(532\) | −101.640 | − | 217.949i | −0.191052 | − | 0.409678i | ||||
\(533\) | 289.287 | + | 289.287i | 0.542752 | + | 0.542752i | ||||
\(534\) | 305.314 | − | 176.273i | 0.571749 | − | 0.330099i | ||||
\(535\) | −752.973 | − | 309.994i | −1.40743 | − | 0.579429i | ||||
\(536\) | −4.17626 | + | 7.23350i | −0.00779154 | + | 0.0134953i | ||||
\(537\) | 200.910 | + | 53.8338i | 0.374135 | + | 0.100249i | ||||
\(538\) | 205.439 | + | 205.439i | 0.381858 | + | 0.381858i | ||||
\(539\) | −334.705 | − | 919.408i | −0.620974 | − | 1.70577i | ||||
\(540\) | 51.5023 | − | 6.89321i | 0.0953746 | − | 0.0127652i | ||||
\(541\) | 190.462 | + | 329.891i | 0.352056 | + | 0.609779i | 0.986610 | − | 0.163100i | \(-0.0521493\pi\) |
−0.634553 | + | 0.772879i | \(0.718816\pi\) | |||||||
\(542\) | −40.4616 | − | 151.005i | −0.0746524 | − | 0.278606i | ||||
\(543\) | −364.437 | + | 97.6506i | −0.671155 | + | 0.179835i | ||||
\(544\) | −110.844 | + | 63.9960i | −0.203758 | + | 0.117640i | ||||
\(545\) | −232.963 | − | 177.964i | −0.427456 | − | 0.326539i | ||||
\(546\) | −110.910 | + | 304.753i | −0.203132 | + | 0.558156i | ||||
\(547\) | 231.815 | − | 231.815i | 0.423794 | − | 0.423794i | −0.462714 | − | 0.886508i | \(-0.653124\pi\) |
0.886508 | + | 0.462714i | \(0.153124\pi\) | |||||||
\(548\) | −41.6072 | + | 155.280i | −0.0759255 | + | 0.283358i | ||||
\(549\) | −9.13674 | − | 5.27510i | −0.0166425 | − | 0.00960856i | ||||
\(550\) | −609.870 | + | 355.618i | −1.10886 | + | 0.646578i | ||||
\(551\) | 199.254 | + | 345.119i | 0.361623 | + | 0.626350i | ||||
\(552\) | 72.6814 | − | 72.6814i | 0.131669 | − | 0.131669i | ||||
\(553\) | 434.064 | + | 303.914i | 0.784925 | + | 0.549572i | ||||
\(554\) | 99.6466i | 0.179867i | ||||||||
\(555\) | 198.162 | + | 25.6547i | 0.357049 | + | 0.0462247i | ||||
\(556\) | −15.1273 | + | 26.2013i | −0.0272075 | + | 0.0471247i | ||||
\(557\) | −255.272 | − | 952.690i | −0.458299 | − | 1.71039i | −0.678204 | − | 0.734873i | \(-0.737242\pi\) |
0.219906 | − | 0.975521i | \(-0.429425\pi\) | |||||||
\(558\) | 60.9212 | − | 227.361i | 0.109178 | − | 0.407457i | ||||
\(559\) | − | 392.693i | − | 0.702491i | ||||||
\(560\) | 94.3569 | − | 103.425i | 0.168494 | − | 0.184688i | ||||
\(561\) | 782.538 | 1.39490 | ||||||||
\(562\) | 235.815 | + | 63.1864i | 0.419599 | + | 0.112431i | ||||
\(563\) | −24.4993 | + | 6.56455i | −0.0435155 | + | 0.0116600i | −0.280511 | − | 0.959851i | \(-0.590504\pi\) |
0.236996 | + | 0.971511i | \(0.423837\pi\) | |||||||
\(564\) | −227.225 | − | 131.189i | −0.402882 | − | 0.232604i | ||||
\(565\) | 302.049 | + | 391.888i | 0.534600 | + | 0.693608i | ||||
\(566\) | −39.8429 | −0.0703938 | ||||||||
\(567\) | 62.7604 | + | 5.48877i | 0.110689 | + | 0.00968037i | ||||
\(568\) | −23.7876 | − | 23.7876i | −0.0418796 | − | 0.0418796i | ||||
\(569\) | −731.187 | + | 422.151i | −1.28504 | + | 0.741917i | −0.977765 | − | 0.209704i | \(-0.932750\pi\) |
−0.307273 | + | 0.951621i | \(0.599417\pi\) | |||||||
\(570\) | −194.191 | + | 80.9268i | −0.340686 | + | 0.141977i | ||||
\(571\) | −442.183 | + | 765.884i | −0.774402 | + | 1.34130i | 0.160728 | + | 0.986999i | \(0.448616\pi\) |
−0.935130 | + | 0.354304i | \(0.884718\pi\) | |||||||
\(572\) | 729.616 | + | 195.500i | 1.27555 | + | 0.341783i | ||||
\(573\) | 137.579 | + | 137.579i | 0.240104 | + | 0.240104i | ||||
\(574\) | −37.1898 | − | 210.874i | −0.0647905 | − | 0.367376i | ||||
\(575\) | −260.308 | + | 455.383i | −0.452710 | + | 0.791971i | ||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −202.316 | − | 755.053i | −0.350634 | − | 1.30858i | −0.885891 | − | 0.463894i | \(-0.846452\pi\) |
0.535257 | − | 0.844689i | \(-0.320215\pi\) | |||||||
\(578\) | −304.537 | + | 81.6004i | −0.526881 | + | 0.141177i | ||||
\(579\) | 8.68906 | − | 5.01663i | 0.0150070 | − | 0.00866430i | ||||
\(580\) | −140.834 | + | 184.359i | −0.242817 | + | 0.317860i | ||||
\(581\) | −95.7642 | + | 263.137i | −0.164827 | + | 0.452903i | ||||
\(582\) | −137.322 | + | 137.322i | −0.235949 | + | 0.235949i | ||||
\(583\) | −21.4950 | + | 80.2204i | −0.0368696 | + | 0.137599i | ||||
\(584\) | 53.4793 | + | 30.8763i | 0.0915741 | + | 0.0528703i | ||||
\(585\) | 262.347 | + | 108.007i | 0.448457 | + | 0.184627i | ||||
\(586\) | −78.8568 | − | 136.584i | −0.134568 | − | 0.233078i | ||||
\(587\) | −198.669 | + | 198.669i | −0.338449 | + | 0.338449i | −0.855783 | − | 0.517334i | \(-0.826924\pi\) |
0.517334 | + | 0.855783i | \(0.326924\pi\) | |||||||
\(588\) | 139.037 | − | 97.3685i | 0.236458 | − | 0.165593i | ||||
\(589\) | 953.000i | 1.61800i | ||||||||
\(590\) | 133.534 | + | 173.251i | 0.226328 | + | 0.293646i | ||||
\(591\) | 49.3656 | − | 85.5037i | 0.0835289 | − | 0.144676i | ||||
\(592\) | 23.8867 | + | 89.1462i | 0.0403491 | + | 0.150585i | ||||
\(593\) | 162.343 | − | 605.873i | 0.273766 | − | 1.02171i | −0.682898 | − | 0.730514i | \(-0.739281\pi\) |
0.956664 | − | 0.291194i | \(-0.0940526\pi\) | |||||||
\(594\) | − | 146.735i | − | 0.247029i | ||||||
\(595\) | 666.959 | − | 426.951i | 1.12094 | − | 0.717565i | ||||
\(596\) | 65.8223 | 0.110440 | ||||||||
\(597\) | 165.329 | + | 44.2997i | 0.276932 | + | 0.0742038i | ||||
\(598\) | 542.094 | − | 145.254i | 0.906512 | − | 0.242899i | ||||
\(599\) | 335.297 | + | 193.584i | 0.559762 | + | 0.323179i | 0.753050 | − | 0.657963i | \(-0.228582\pi\) |
−0.193288 | + | 0.981142i | \(0.561915\pi\) | |||||||
\(600\) | −86.9745 | − | 86.2289i | −0.144958 | − | 0.143715i | ||||
\(601\) | 267.104 | 0.444433 | 0.222217 | − | 0.974997i | \(-0.428671\pi\) | ||||
0.222217 | + | 0.974997i | \(0.428671\pi\) | |||||||
\(602\) | −117.884 | + | 168.367i | −0.195820 | + | 0.279679i | ||||
\(603\) | 6.26439 | + | 6.26439i | 0.0103887 | + | 0.0103887i | ||||
\(604\) | −492.537 | + | 284.366i | −0.815459 | + | 0.470805i | ||||
\(605\) | 534.164 | + | 1281.77i | 0.882915 | + | 2.11864i | ||||
\(606\) | 138.306 | − | 239.554i | 0.228228 | − | 0.395303i | ||||
\(607\) | −335.219 | − | 89.8215i | −0.552255 | − | 0.147976i | −0.0281090 | − | 0.999605i | \(-0.508949\pi\) |
−0.524146 | + | 0.851629i | \(0.675615\pi\) | |||||||
\(608\) | −68.7096 | − | 68.7096i | −0.113009 | − | 0.113009i | ||||
\(609\) | −215.468 | + | 180.811i | −0.353805 | + | 0.296898i | ||||
\(610\) | 3.29886 | + | 24.6473i | 0.00540797 | + | 0.0404054i | ||||
\(611\) | −716.291 | − | 1240.65i | −1.17233 | − | 2.03053i | ||||
\(612\) | 35.1363 | + | 131.130i | 0.0574122 | + | 0.214265i | ||||
\(613\) | 399.843 | − | 107.138i | 0.652272 | − | 0.174776i | 0.0825161 | − | 0.996590i | \(-0.473704\pi\) |
0.569756 | + | 0.821814i | \(0.307038\pi\) | |||||||
\(614\) | 37.8277 | − | 21.8398i | 0.0616086 | − | 0.0355698i | ||||
\(615\) | −185.667 | + | 24.8502i | −0.301898 | + | 0.0404069i | ||||
\(616\) | −254.135 | − | 302.846i | −0.412556 | − | 0.491633i | ||||
\(617\) | 637.339 | − | 637.339i | 1.03297 | − | 1.03297i | 0.0335273 | − | 0.999438i | \(-0.489326\pi\) |
0.999438 | − | 0.0335273i | \(-0.0106741\pi\) | |||||||
\(618\) | 124.758 | − | 465.603i | 0.201874 | − | 0.753403i | ||||
\(619\) | −956.137 | − | 552.026i | −1.54465 | − | 0.891803i | −0.998536 | − | 0.0540914i | \(-0.982774\pi\) |
−0.546113 | − | 0.837712i | \(-0.683893\pi\) | |||||||
\(620\) | −512.109 | + | 213.415i | −0.825983 | + | 0.344218i | ||||
\(621\) | −54.5110 | − | 94.4158i | −0.0877794 | − | 0.152038i | ||||
\(622\) | −170.194 | + | 170.194i | −0.273624 | + | 0.273624i | ||||
\(623\) | −825.302 | − | 577.842i | −1.32472 | − | 0.927516i | ||||
\(624\) | 131.040i | 0.210000i | ||||||||
\(625\) | 543.936 | + | 307.828i | 0.870298 | + | 0.492525i | ||||
\(626\) | 277.434 | − | 480.529i | 0.443185 | − | 0.767619i | ||||
\(627\) | 153.763 | + | 573.850i | 0.245235 | + | 0.915231i | ||||
\(628\) | −91.4954 | + | 341.465i | −0.145693 | + | 0.543735i | ||||
\(629\) | 522.044i | 0.829959i | ||||||||
\(630\) | −80.0584 | − | 125.063i | −0.127077 | − | 0.198512i | ||||
\(631\) | −1130.27 | −1.79124 | −0.895618 | − | 0.444824i | \(-0.853266\pi\) | ||||
−0.895618 | + | 0.444824i | \(0.853266\pi\) | |||||||
\(632\) | 206.809 | + | 55.4143i | 0.327230 | + | 0.0876809i | ||||
\(633\) | −576.106 | + | 154.367i | −0.910120 | + | 0.243866i | ||||
\(634\) | −174.763 | − | 100.900i | −0.275652 | − | 0.159148i | ||||
\(635\) | 241.561 | − | 186.184i | 0.380411 | − | 0.293202i | ||||
\(636\) | −14.4077 | −0.0226536 | ||||||||
\(637\) | 923.255 | − | 80.8349i | 1.44938 | − | 0.126899i | ||||
\(638\) | 463.252 | + | 463.252i | 0.726101 | + | 0.726101i | ||||
\(639\) | −30.9010 | + | 17.8407i | −0.0483584 | + | 0.0279197i | ||||
\(640\) | 21.5353 | − | 52.3090i | 0.0336489 | − | 0.0817328i | ||||
\(641\) | 251.753 | − | 436.050i | 0.392751 | − | 0.680265i | −0.600060 | − | 0.799955i | \(-0.704857\pi\) |
0.992811 | + | 0.119690i | \(0.0381901\pi\) | |||||||
\(642\) | −385.325 | − | 103.248i | −0.600195 | − | 0.160822i | ||||
\(643\) | 363.947 | + | 363.947i | 0.566015 | + | 0.566015i | 0.931010 | − | 0.364995i | \(-0.118929\pi\) |
−0.364995 | + | 0.931010i | \(0.618929\pi\) | |||||||
\(644\) | −276.027 | − | 100.455i | −0.428613 | − | 0.155987i | ||||
\(645\) | 142.883 | + | 109.151i | 0.221525 | + | 0.169226i | ||||
\(646\) | −274.821 | − | 476.004i | −0.425420 | − | 0.736849i | ||||
\(647\) | −3.62332 | − | 13.5224i | −0.00560018 | − | 0.0209002i | 0.963069 | − | 0.269254i | \(-0.0867771\pi\) |
−0.968669 | + | 0.248354i | \(0.920110\pi\) | |||||||
\(648\) | 24.5885 | − | 6.58846i | 0.0379452 | − | 0.0101674i | ||||
\(649\) | 534.946 | − | 308.851i | 0.824262 | − | 0.475888i | ||||
\(650\) | −175.854 | − | 645.175i | −0.270545 | − | 0.992576i | ||||
\(651\) | −662.435 | + | 116.827i | −1.01757 | + | 0.179458i | ||||
\(652\) | 106.264 | − | 106.264i | 0.162982 | − | 0.162982i | ||||
\(653\) | 221.348 | − | 826.082i | 0.338971 | − | 1.26506i | −0.560529 | − | 0.828135i | \(-0.689402\pi\) |
0.899500 | − | 0.436921i | \(-0.143931\pi\) | |||||||
\(654\) | −124.377 | − | 71.8093i | −0.190179 | − | 0.109800i | ||||
\(655\) | 112.740 | + | 270.530i | 0.172122 | + | 0.413023i | ||||
\(656\) | −43.2604 | − | 74.9291i | −0.0659457 | − | 0.114221i | ||||
\(657\) | 46.3144 | − | 46.3144i | 0.0704938 | − | 0.0704938i | ||||
\(658\) | −65.3255 | + | 746.954i | −0.0992789 | + | 1.13519i | ||||
\(659\) | 254.644i | 0.386410i | 0.981158 | + | 0.193205i | \(0.0618882\pi\) | ||||
−0.981158 | + | 0.193205i | \(0.938112\pi\) | |||||||
\(660\) | −273.933 | + | 211.135i | −0.415051 | + | 0.319901i | ||||
\(661\) | 2.28118 | − | 3.95112i | 0.00345111 | − | 0.00597749i | −0.864295 | − | 0.502986i | \(-0.832235\pi\) |
0.867746 | + | 0.497008i | \(0.165568\pi\) | |||||||
\(662\) | −8.43210 | − | 31.4690i | −0.0127373 | − | 0.0475363i | ||||
\(663\) | −191.844 | + | 715.972i | −0.289358 | + | 1.07990i | ||||
\(664\) | 113.146i | 0.170400i | ||||||||
\(665\) | 444.144 | + | 405.201i | 0.667885 | + | 0.609325i | ||||
\(666\) | 97.8893 | 0.146981 | ||||||||
\(667\) | 470.172 | + | 125.982i | 0.704906 | + | 0.188879i | ||||
\(668\) | 315.556 | − | 84.5529i | 0.472389 | − | 0.126576i | ||||
\(669\) | −73.9961 | − | 42.7216i | −0.110607 | − | 0.0638590i | ||||
\(670\) | 2.68099 | − | 20.7085i | 0.00400148 | − | 0.0309082i | ||||
\(671\) | 70.2224 | 0.104653 | ||||||||
\(672\) | 39.3373 | − | 56.1834i | 0.0585377 | − | 0.0836063i | ||||
\(673\) | 183.435 | + | 183.435i | 0.272563 | + | 0.272563i | 0.830131 | − | 0.557568i | \(-0.188265\pi\) |
−0.557568 | + | 0.830131i | \(0.688265\pi\) | |||||||
\(674\) | −759.782 | + | 438.660i | −1.12727 | + | 0.650831i | ||||
\(675\) | −112.219 | + | 65.4356i | −0.166251 | + | 0.0969416i | ||||
\(676\) | −188.740 | + | 326.907i | −0.279201 | + | 0.483591i | ||||
\(677\) | −1033.53 | − | 276.933i | −1.52663 | − | 0.409059i | −0.604711 | − | 0.796445i | \(-0.706711\pi\) |
−0.921917 | + | 0.387386i | \(0.873378\pi\) | |||||||
\(678\) | 171.398 | + | 171.398i | 0.252799 | + | 0.252799i | ||||
\(679\) | 521.518 | + | 189.798i | 0.768068 | + | 0.279526i | ||||
\(680\) | 194.245 | − | 254.276i | 0.285654 | − | 0.373935i | ||||
\(681\) | −149.518 | − | 258.973i | −0.219557 | − | 0.380283i | ||||
\(682\) | 405.493 | + | 1513.32i | 0.594565 | + | 2.21895i | ||||
\(683\) | 314.257 | − | 84.2049i | 0.460113 | − | 0.123287i | −0.0213146 | − | 0.999773i | \(-0.506785\pi\) |
0.481427 | + | 0.876486i | \(0.340118\pi\) | |||||||
\(684\) | −89.2563 | + | 51.5322i | −0.130492 | + | 0.0753394i | ||||
\(685\) | −53.3153 | − | 398.342i | −0.0778325 | − | 0.581522i | ||||
\(686\) | −420.111 | − | 242.497i | −0.612407 | − | 0.353494i | ||||
\(687\) | 25.7265 | − | 25.7265i | 0.0374475 | − | 0.0374475i | ||||
\(688\) | −21.4944 | + | 80.2182i | −0.0312418 | + | 0.116596i | ||||
\(689\) | −68.1269 | − | 39.3331i | −0.0988780 | − | 0.0570872i | ||||
\(690\) | −97.8259 | + | 237.618i | −0.141777 | + | 0.344374i | ||||
\(691\) | −391.517 | − | 678.127i | −0.566595 | − | 0.981371i | −0.996899 | − | 0.0786873i | \(-0.974927\pi\) |
0.430304 | − | 0.902684i | \(-0.358406\pi\) | |||||||
\(692\) | −283.153 | + | 283.153i | −0.409181 | + | 0.409181i | ||||
\(693\) | −380.036 | + | 177.229i | −0.548393 | + | 0.255742i | ||||
\(694\) | − | 646.642i | − | 0.931760i | ||||||
\(695\) | 9.71114 | − | 75.0107i | 0.0139729 | − | 0.107929i | ||||
\(696\) | −56.8272 | + | 98.4277i | −0.0816483 | + | 0.141419i | ||||
\(697\) | −126.667 | − | 472.729i | −0.181732 | − | 0.678233i | ||||
\(698\) | −25.7465 | + | 96.0873i | −0.0368861 | + | 0.137661i | ||||
\(699\) | 347.264i | 0.496801i | ||||||||
\(700\) | −118.279 | + | 329.409i | −0.168971 | + | 0.470584i | ||||
\(701\) | −451.488 | −0.644063 | −0.322031 | − | 0.946729i | \(-0.604366\pi\) | ||||
−0.322031 | + | 0.946729i | \(0.604366\pi\) | |||||||
\(702\) | 134.253 | + | 35.9730i | 0.191244 | + | 0.0512436i | ||||
\(703\) | −382.825 | + | 102.578i | −0.544559 | + | 0.145914i | ||||
\(704\) | −138.343 | − | 79.8724i | −0.196510 | − | 0.113455i | ||||
\(705\) | 650.514 | + | 84.2178i | 0.922715 | + | 0.119458i | ||||
\(706\) | −235.918 | −0.334162 | ||||||||
\(707\) | −787.481 | − | 68.8699i | −1.11384 | − | 0.0974114i | ||||
\(708\) | 75.7737 | + | 75.7737i | 0.107025 | + | 0.107025i | ||||
\(709\) | 389.602 | − | 224.937i | 0.549509 | − | 0.317259i | −0.199415 | − | 0.979915i | \(-0.563904\pi\) |
0.748924 | + | 0.662656i | \(0.230571\pi\) | |||||||
\(710\) | 77.7691 | + | 32.0171i | 0.109534 | + | 0.0450945i | ||||
\(711\) | 113.546 | − | 196.668i | 0.159699 | − | 0.276607i | ||||
\(712\) | −393.214 | − | 105.361i | −0.552267 | − | 0.147979i | ||||
\(713\) | 823.101 | + | 823.101i | 1.15442 | + | 1.15442i | ||||
\(714\) | 297.183 | − | 249.383i | 0.416223 | − | 0.349275i | ||||
\(715\) | −1871.69 | + | 250.513i | −2.61775 | + | 0.350368i | ||||
\(716\) | −120.088 | − | 207.998i | −0.167720 | − | 0.290500i | ||||
\(717\) | 126.765 | + | 473.093i | 0.176799 | + | 0.659823i | ||||
\(718\) | 705.045 | − | 188.916i | 0.981957 | − | 0.263115i | ||||
\(719\) | 825.620 | − | 476.672i | 1.14829 | − | 0.662965i | 0.199820 | − | 0.979833i | \(-0.435964\pi\) |
0.948470 | + | 0.316868i | \(0.102631\pi\) | |||||||
\(720\) | −47.6797 | − | 36.4231i | −0.0662218 | − | 0.0505877i | ||||
\(721\) | −1356.57 | + | 239.246i | −1.88152 | + | 0.331825i | ||||
\(722\) | −65.9374 | + | 65.9374i | −0.0913260 | + | 0.0913260i | ||||
\(723\) | −40.8610 | + | 152.495i | −0.0565159 | + | 0.210920i | ||||
\(724\) | 377.293 | + | 217.830i | 0.521123 | + | 0.300871i | ||||
\(725\) | 147.700 | − | 560.869i | 0.203724 | − | 0.773612i | ||||
\(726\) | 340.142 | + | 589.143i | 0.468515 | + | 0.811492i | ||||
\(727\) | 438.595 | − | 438.595i | 0.603295 | − | 0.603295i | −0.337890 | − | 0.941185i | \(-0.609713\pi\) |
0.941185 | + | 0.337890i | \(0.109713\pi\) | |||||||
\(728\) | 339.388 | − | 158.272i | 0.466192 | − | 0.217407i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −153.104 | − | 19.8213i | −0.209731 | − | 0.0271525i | ||||
\(731\) | −234.881 | + | 406.825i | −0.321314 | + | 0.556532i | ||||
\(732\) | 3.15302 | + | 11.7672i | 0.00430740 | + | 0.0160754i | ||||
\(733\) | −196.927 | + | 734.941i | −0.268659 | + | 1.00265i | 0.691314 | + | 0.722554i | \(0.257032\pi\) |
−0.959973 | + | 0.280093i | \(0.909635\pi\) | |||||||
\(734\) | 711.808i | 0.969766i | ||||||||
\(735\) | −227.210 | + | 358.400i | −0.309130 | + | 0.487619i | ||||
\(736\) | −118.688 | −0.161261 | ||||||||
\(737\) | −56.9578 | − | 15.2618i | −0.0772833 | − | 0.0207080i | ||||
\(738\) | −88.6421 | + | 23.7516i | −0.120111 | + | 0.0321837i | ||||
\(739\) | −557.758 | − | 322.022i | −0.754747 | − | 0.435754i | 0.0726593 | − | 0.997357i | \(-0.476851\pi\) |
−0.827407 | + | 0.561603i | \(0.810185\pi\) | |||||||
\(740\) | −140.852 | − | 182.746i | −0.190340 | − | 0.246954i | ||||
\(741\) | −562.732 | −0.759422 | ||||||||
\(742\) | 17.4019 | + | 37.3153i | 0.0234527 | + | 0.0502901i | ||||
\(743\) | −166.104 | − | 166.104i | −0.223558 | − | 0.223558i | 0.586437 | − | 0.809995i | \(-0.300530\pi\) |
−0.809995 | + | 0.586437i | \(0.800530\pi\) | |||||||
\(744\) | −235.381 | + | 135.897i | −0.316373 | + | 0.182658i | ||||
\(745\) | −151.894 | + | 63.2998i | −0.203884 | + | 0.0849662i | ||||
\(746\) | 272.063 | − | 471.227i | 0.364696 | − | 0.631672i | ||||
\(747\) | 115.920 | + | 31.0606i | 0.155180 | + | 0.0415805i | ||||
\(748\) | −638.939 | − | 638.939i | −0.854197 | − | 0.854197i | ||||
\(749\) | 197.996 | + | 1122.68i | 0.264347 | + | 1.49890i | ||||
\(750\) | 283.630 | + | 115.343i | 0.378173 | + | 0.153791i | ||||
\(751\) | 560.910 | + | 971.525i | 0.746884 | + | 1.29364i | 0.949309 | + | 0.314344i | \(0.101785\pi\) |
−0.202425 | + | 0.979298i | \(0.564882\pi\) | |||||||
\(752\) | 78.4136 | + | 292.644i | 0.104273 | + | 0.389154i | ||||
\(753\) | −466.435 | + | 124.981i | −0.619436 | + | 0.165977i | ||||
\(754\) | −537.416 | + | 310.277i | −0.712753 | + | 0.411508i | ||||
\(755\) | 863.127 | − | 1129.88i | 1.14321 | − | 1.49652i | ||||
\(756\) | −46.7621 | − | 55.7253i | −0.0618547 | − | 0.0737106i | ||||
\(757\) | 646.859 | − | 646.859i | 0.854504 | − | 0.854504i | −0.136180 | − | 0.990684i | \(-0.543483\pi\) |
0.990684 | + | 0.136180i | \(0.0434827\pi\) | |||||||
\(758\) | 129.064 | − | 481.673i | 0.170269 | − | 0.635452i | ||||
\(759\) | 628.435 | + | 362.827i | 0.827977 | + | 0.478033i | ||||
\(760\) | 224.633 | + | 92.4801i | 0.295570 | + | 0.121684i | ||||
\(761\) | 273.840 | + | 474.305i | 0.359842 | + | 0.623265i | 0.987934 | − | 0.154874i | \(-0.0494971\pi\) |
−0.628092 | + | 0.778139i | \(0.716164\pi\) | |||||||
\(762\) | 105.650 | − | 105.650i | 0.138648 | − | 0.138648i | ||||
\(763\) | −35.7575 | + | 408.864i | −0.0468644 | + | 0.535863i | ||||
\(764\) | − | 224.666i | − | 0.294066i | ||||||
\(765\) | −207.187 | − | 268.811i | −0.270832 | − | 0.351387i | ||||
\(766\) | 42.8143 | − | 74.1565i | 0.0558933 | − | 0.0968101i | ||||
\(767\) | 151.434 | + | 565.159i | 0.197437 | + | 0.736843i | ||||
\(768\) | 7.17260 | − | 26.7685i | 0.00933933 | − | 0.0348548i | ||||
\(769\) | − | 991.204i | − | 1.28895i | −0.764624 | − | 0.644476i | \(-0.777075\pi\) | ||
0.764624 | − | 0.644476i | \(-0.222925\pi\) | |||||||
\(770\) | 877.690 | + | 454.462i | 1.13986 | + | 0.590210i | ||||
\(771\) | −167.902 | −0.217772 | ||||||||
\(772\) | −11.1907 | − | 2.99853i | −0.0144957 | − | 0.00388410i | ||||
\(773\) | 362.154 | − | 97.0389i | 0.468505 | − | 0.125535i | −0.0168403 | − | 0.999858i | \(-0.505361\pi\) |
0.485345 | + | 0.874323i | \(0.338694\pi\) | |||||||
\(774\) | 76.2844 | + | 44.0428i | 0.0985587 | + | 0.0569029i | ||||
\(775\) | 976.525 | − | 984.969i | 1.26003 | − | 1.27093i | ||||
\(776\) | 224.246 | 0.288977 | ||||||||
\(777\) | −118.232 | − | 253.529i | −0.152165 | − | 0.326292i | ||||
\(778\) | −719.653 | − | 719.653i | −0.925004 | − | 0.925004i | ||||
\(779\) | 321.772 | − | 185.775i | 0.413057 | − | 0.238479i | ||||
\(780\) | −126.018 | − | 302.393i | −0.161562 | − | 0.387683i | ||||
\(781\) | 118.748 | − | 205.678i | 0.152047 | − | 0.263352i | ||||
\(782\) | −648.484 | − | 173.761i | −0.829263 | − | 0.222200i | ||||
\(783\) | 85.2409 | + | 85.2409i | 0.108864 | + | 0.108864i | ||||
\(784\) | −193.025 | − | 34.0225i | −0.246205 | − | 0.0433960i | ||||
\(785\) | −117.242 | − | 875.966i | −0.149353 | − | 1.11588i | ||||
\(786\) | 71.7901 | + | 124.344i | 0.0913360 | + | 0.158199i | ||||
\(787\) | 44.0553 | + | 164.417i | 0.0559788 | + | 0.208916i | 0.988250 | − | 0.152843i | \(-0.0488430\pi\) |
−0.932272 | + | 0.361759i | \(0.882176\pi\) | |||||||
\(788\) | −110.120 | + | 29.5067i | −0.139747 | + | 0.0374450i | ||||
\(789\) | −312.992 | + | 180.706i | −0.396694 | + | 0.229031i | ||||
\(790\) | −530.530 | + | 71.0077i | −0.671558 | + | 0.0898832i | ||||
\(791\) | 236.895 | − | 650.929i | 0.299488 | − | 0.822919i | ||||
\(792\) | −119.809 | + | 119.809i | −0.151273 | + | 0.151273i | ||||
\(793\) | −17.2155 | + | 64.2491i | −0.0217093 | + | 0.0810203i | ||||
\(794\) | 118.963 | + | 68.6834i | 0.149828 | + | 0.0865030i | ||||
\(795\) | 33.2477 | − | 13.8556i | 0.0418210 | − | 0.0174284i | ||||
\(796\) | −98.8197 | − | 171.161i | −0.124145 | − | 0.215026i | ||||
\(797\) | −410.228 | + | 410.228i | −0.514715 | + | 0.514715i | −0.915967 | − | 0.401253i | \(-0.868575\pi\) |
0.401253 | + | 0.915967i | \(0.368575\pi\) | |||||||
\(798\) | 241.271 | + | 168.928i | 0.302345 | + | 0.211689i | ||||
\(799\) | 1713.73i | 2.14485i | ||||||||
\(800\) | 0.608787 | + | 141.420i | 0.000760984 | + | 0.176775i | ||||
\(801\) | −215.889 | + | 373.932i | −0.269525 | + | 0.466831i | ||||
\(802\) | −54.7105 | − | 204.182i | −0.0682175 | − | 0.254591i | ||||
\(803\) | −112.835 | + | 421.105i | −0.140516 | + | 0.524415i | ||||
\(804\) | − | 10.2297i | − | 0.0127235i | ||||||
\(805\) | 733.575 | − | 33.6346i | 0.911273 | − | 0.0417821i | ||||
\(806\) | −1484.00 | −1.84119 | ||||||||
\(807\) | −343.707 | − | 92.0960i | −0.425907 | − | 0.114121i | ||||
\(808\) | −308.522 | + | 82.6681i | −0.381834 | + | 0.102312i | ||||
\(809\) | 870.428 | + | 502.542i | 1.07593 | + | 0.621189i | 0.929796 | − | 0.368075i | \(-0.119983\pi\) |
0.146135 | + | 0.989265i | \(0.453317\pi\) | |||||||
\(810\) | −50.4052 | + | 38.8499i | −0.0622286 | + | 0.0479629i | ||||
\(811\) | 971.608 | 1.19804 | 0.599018 | − | 0.800735i | \(-0.295558\pi\) | ||||
0.599018 | + | 0.800735i | \(0.295558\pi\) | |||||||
\(812\) | 323.560 | + | 28.2972i | 0.398473 | + | 0.0348488i | ||||
\(813\) | 135.387 | + | 135.387i | 0.166528 | + | 0.166528i | ||||
\(814\) | −564.263 | + | 325.777i | −0.693198 | + | 0.400218i | ||||
\(815\) | −143.027 | + | 347.411i | −0.175493 | + | 0.426271i | ||||
\(816\) | 78.3788 | − | 135.756i | 0.0960525 | − | 0.166368i | ||||
\(817\) | −344.485 | − | 92.3044i | −0.421646 | − | 0.112980i | ||||
\(818\) | 365.206 | + | 365.206i | 0.446462 | + | 0.446462i | ||||
\(819\) | −68.9848 | − | 391.158i | −0.0842305 | − | 0.477604i | ||||
\(820\) | 171.887 | + | 131.307i | 0.209618 | + | 0.160130i | ||||
\(821\) | 51.5972 | + | 89.3690i | 0.0628468 | + | 0.108854i | 0.895737 | − | 0.444585i | \(-0.146649\pi\) |
−0.832890 | + | 0.553439i | \(0.813315\pi\) | |||||||
\(822\) | −50.9582 | − | 190.178i | −0.0619929 | − | 0.231361i | ||||
\(823\) | 1111.03 | − | 297.701i | 1.34998 | − | 0.361726i | 0.489853 | − | 0.871805i | \(-0.337050\pi\) |
0.860128 | + | 0.510079i | \(0.170384\pi\) | |||||||
\(824\) | −482.028 | + | 278.299i | −0.584985 | + | 0.337741i | ||||
\(825\) | 429.095 | − | 750.658i | 0.520115 | − | 0.909888i | ||||
\(826\) | 104.729 | − | 287.771i | 0.126791 | − | 0.348391i | ||||
\(827\) | −87.7582 | + | 87.7582i | −0.106116 | + | 0.106116i | −0.758172 | − | 0.652055i | \(-0.773907\pi\) |
0.652055 | + | 0.758172i | \(0.273907\pi\) | |||||||
\(828\) | −32.5822 | + | 121.598i | −0.0393504 | + | 0.146858i | ||||
\(829\) | −201.887 | − | 116.559i | −0.243530 | − | 0.140602i | 0.373268 | − | 0.927724i | \(-0.378237\pi\) |
−0.616798 | + | 0.787121i | \(0.711571\pi\) | |||||||
\(830\) | −108.810 | − | 261.099i | −0.131096 | − | 0.314577i | ||||
\(831\) | −61.0208 | − | 105.691i | −0.0734306 | − | 0.127186i | ||||
\(832\) | 106.994 | − | 106.994i | 0.128598 | − | 0.128598i | ||||
\(833\) | −1004.83 | − | 468.481i | −1.20628 | − | 0.562402i | ||||
\(834\) | − | 37.0543i | − | 0.0444296i | ||||||
\(835\) | −646.874 | + | 498.580i | −0.774700 | + | 0.597102i | ||||
\(836\) | 343.000 | − | 594.093i | 0.410287 | − | 0.710638i | ||||
\(837\) | 74.6129 | + | 278.459i | 0.0891433 | + | 0.332687i | ||||
\(838\) | −136.879 | + | 510.839i | −0.163340 | + | 0.609594i | ||||
\(839\) | − | 1438.36i | − | 1.71438i | −0.515002 | − | 0.857189i | \(-0.672209\pi\) | ||
0.515002 | − | 0.857189i | \(-0.327791\pi\) | |||||||
\(840\) | −36.7458 | + | 167.481i | −0.0437450 | + | 0.199382i | ||||
\(841\) | 302.777 | 0.360021 | ||||||||
\(842\) | 565.683 | + | 151.574i | 0.671833 | + | 0.180017i | ||||
\(843\) | −288.813 | + | 77.3872i | −0.342601 | + | 0.0917997i | ||||
\(844\) | 596.429 | + | 344.348i | 0.706669 | + | 0.407996i | ||||
\(845\) | 121.164 | − | 935.890i | 0.143389 | − | 1.10756i | ||||
\(846\) | 321.345 | 0.379841 | ||||||||
\(847\) | 1115.02 | − | 1592.53i | 1.31644 | − | 1.88020i | ||||
\(848\) | 11.7638 | + | 11.7638i | 0.0138725 | + | 0.0138725i | ||||
\(849\) | 42.2598 | − | 24.3987i | 0.0497759 | − | 0.0287381i | ||||
\(850\) | −203.714 | + | 773.577i | −0.239664 | + | 0.910090i | ||||
\(851\) | −242.048 | + | 419.239i | −0.284428 | + | 0.492643i | ||||
\(852\) | 39.7974 | + | 10.6637i | 0.0467106 | + | 0.0125161i | ||||
\(853\) | −878.537 | − | 878.537i | −1.02994 | − | 1.02994i | −0.999538 | − | 0.0304000i | \(-0.990322\pi\) |
−0.0304000 | − | 0.999538i | \(-0.509678\pi\) | |||||||
\(854\) | 26.6682 | − | 22.3788i | 0.0312275 | − | 0.0262047i | ||||
\(855\) | 156.414 | − | 204.753i | 0.182940 | − | 0.239477i | ||||
\(856\) | 230.315 | + | 398.918i | 0.269060 | + | 0.466026i | ||||
\(857\) | −21.8504 | − | 81.5467i | −0.0254964 | − | 0.0951537i | 0.952005 | − | 0.306082i | \(-0.0990181\pi\) |
−0.977502 | + | 0.210928i | \(0.932351\pi\) | |||||||
\(858\) | −893.593 | + | 239.438i | −1.04148 | + | 0.279065i | ||||
\(859\) | −774.281 | + | 447.031i | −0.901375 | + | 0.520409i | −0.877646 | − | 0.479309i | \(-0.840887\pi\) |
−0.0237288 | + | 0.999718i | \(0.507554\pi\) | |||||||
\(860\) | −27.5428 | − | 205.785i | −0.0320265 | − | 0.239285i | ||||
\(861\) | 168.579 | + | 200.891i | 0.195794 | + | 0.233323i | ||||
\(862\) | −517.506 | + | 517.506i | −0.600355 | + | 0.600355i | ||||
\(863\) | −278.137 | + | 1038.02i | −0.322291 | + | 1.20281i | 0.594717 | + | 0.803935i | \(0.297264\pi\) |
−0.917008 | + | 0.398870i | \(0.869403\pi\) | |||||||
\(864\) | −25.4558 | − | 14.6969i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 381.112 | − | 925.717i | 0.440592 | − | 1.07019i | ||||
\(866\) | −28.4380 | − | 49.2561i | −0.0328383 | − | 0.0568777i | ||||
\(867\) | 273.040 | − | 273.040i | 0.314925 | − | 0.314925i | ||||
\(868\) | 636.265 | + | 445.487i | 0.733025 | + | 0.513234i | ||||
\(869\) | 1511.53i | 1.73939i | ||||||||
\(870\) | 36.4808 | − | 281.785i | 0.0419319 | − | 0.323890i | ||||
\(871\) | 27.9272 | − | 48.3712i | 0.0320633 | − | 0.0555353i | ||||
\(872\) | 42.9216 | + | 160.186i | 0.0492221 | + | 0.183699i | ||||
\(873\) | 61.5599 | − | 229.745i | 0.0705153 | − | 0.263167i | ||||
\(874\) | − | 509.688i | − | 0.583167i | ||||||
\(875\) | −43.8392 | − | 873.901i | −0.0501020 | − | 0.998744i | ||||
\(876\) | −75.6311 | −0.0863369 | ||||||||
\(877\) | 1073.72 | + | 287.701i | 1.22430 | + | 0.328051i | 0.812359 | − | 0.583157i | \(-0.198183\pi\) |
0.411945 | + | 0.911209i | \(0.364849\pi\) | |||||||
\(878\) | −381.613 | + | 102.253i | −0.434639 | + | 0.116461i | ||||
\(879\) | 167.281 | + | 96.5795i | 0.190308 | + | 0.109874i | ||||
\(880\) | 396.057 | + | 51.2748i | 0.450064 | + | 0.0582669i | ||||
\(881\) | −258.843 | −0.293805 | −0.146903 | − | 0.989151i | \(-0.546930\pi\) | ||||
−0.146903 | + | 0.989151i | \(0.546930\pi\) | |||||||
\(882\) | −87.8456 | + | 188.417i | −0.0995982 | + | 0.213625i | ||||
\(883\) | 814.683 | + | 814.683i | 0.922631 | + | 0.922631i | 0.997215 | − | 0.0745837i | \(-0.0237628\pi\) |
−0.0745837 | + | 0.997215i | \(0.523763\pi\) | |||||||
\(884\) | 741.229 | − | 427.949i | 0.838495 | − | 0.484105i | ||||
\(885\) | −247.728 | − | 101.988i | −0.279918 | − | 0.115241i | ||||
\(886\) | −415.802 | + | 720.190i | −0.469303 | + | 0.812856i | ||||
\(887\) | 507.265 | + | 135.921i | 0.571888 | + | 0.153237i | 0.533163 | − | 0.846013i | \(-0.321003\pi\) |
0.0387258 | + | 0.999250i | \(0.487670\pi\) | |||||||
\(888\) | −79.9263 | − | 79.9263i | −0.0900071 | − | 0.0900071i | ||||
\(889\) | −401.234 | − | 146.022i | −0.451332 | − | 0.164255i | ||||
\(890\) | 1008.72 | − | 135.010i | 1.13339 | − | 0.151696i | ||||
\(891\) | 89.8564 | + | 155.636i | 0.100849 | + | 0.174676i | ||||
\(892\) | 25.5355 | + | 95.2996i | 0.0286272 | + | 0.106838i | ||||
\(893\) | −1256.71 | + | 336.735i | −1.40729 | + | 0.377083i | ||||
\(894\) | −69.8151 | + | 40.3078i | −0.0780929 | + | 0.0450870i | ||||
\(895\) | 477.145 | + | 364.497i | 0.533123 | + | 0.407259i | ||||
\(896\) | −77.9923 | + | 13.7548i | −0.0870450 | + | 0.0153513i | ||||
\(897\) | −486.029 | + | 486.029i | −0.541838 | + | 0.541838i | ||||
\(898\) | 188.838 | − | 704.754i | 0.210288 | − | 0.784805i | ||||
\(899\) | −1114.67 | − | 643.557i | −1.23990 | − | 0.715858i | ||||
\(900\) | 145.055 | + | 38.1988i | 0.161172 | + | 0.0424431i | ||||
\(901\) | 47.0525 | + | 81.4972i | 0.0522225 | + | 0.0904520i | ||||
\(902\) | 431.914 | − | 431.914i | 0.478840 | − | 0.478840i | ||||
\(903\) | 21.9312 | − | 250.769i | 0.0242870 | − | 0.277706i | ||||
\(904\) | − | 279.891i | − | 0.309614i | ||||||
\(905\) | −1080.14 | − | 139.838i | −1.19352 | − | 0.154517i | ||||
\(906\) | 348.276 | − | 603.232i | 0.384411 | − | 0.665819i | ||||
\(907\) | 99.0344 | + | 369.601i | 0.109189 | + | 0.407499i | 0.998787 | − | 0.0492462i | \(-0.0156819\pi\) |
−0.889598 | + | 0.456745i | \(0.849015\pi\) | |||||||
\(908\) | −89.3695 | + | 333.531i | −0.0984246 | + | 0.367325i | ||||
\(909\) | 338.780i | 0.372696i | ||||||||
\(910\) | −630.975 | + | 691.617i | −0.693380 | + | 0.760018i | ||||
\(911\) | 505.532 | 0.554920 | 0.277460 | − | 0.960737i | \(-0.410507\pi\) | ||||
0.277460 | + | 0.960737i | \(0.410507\pi\) | |||||||
\(912\) | 114.953 | + | 30.8016i | 0.126045 | + | 0.0337737i | ||||
\(913\) | −771.566 | + | 206.740i | −0.845088 | + | 0.226441i | ||||
\(914\) | −356.303 | − | 205.712i | −0.389829 | − | 0.225068i | ||||
\(915\) | −18.5923 | − | 24.1222i | −0.0203194 | − | 0.0263631i | ||||
\(916\) | −42.0111 | −0.0458637 | ||||||||
\(917\) | 235.336 | − | 336.118i | 0.256637 | − | 0.366540i | ||||
\(918\) | −117.568 | − | 117.568i | −0.128070 | − | 0.128070i | ||||
\(919\) | −90.0279 | + | 51.9776i | −0.0979629 | + | 0.0565589i | −0.548181 | − | 0.836360i | \(-0.684680\pi\) |
0.450218 | + | 0.892919i | \(0.351346\pi\) | |||||||
\(920\) | 273.889 | − | 114.140i | 0.297705 | − | 0.124065i | ||||
\(921\) | −26.7482 | + | 46.3293i | −0.0290426 | + | 0.0503032i | ||||
\(922\) | 589.127 | + | 157.856i | 0.638966 | + | 0.171210i | ||||
\(923\) | 159.070 | + | 159.070i | 0.172341 | + | 0.172341i | ||||
\(924\) | 455.005 | + | 165.592i | 0.492430 | + | 0.179212i | ||||
\(925\) | 500.776 | + | 286.256i | 0.541380 | + | 0.309466i | ||||
\(926\) | 81.4930 | + | 141.150i | 0.0880054 | + | 0.152430i | ||||
\(927\) | 152.797 | + | 570.245i | 0.164829 | + | 0.615151i | ||||
\(928\) | 126.765 | − | 33.9666i | 0.136600 | − | 0.0366020i | ||||
\(929\) | 3.46379 | − | 1.99982i | 0.00372852 | − | 0.00215266i | −0.498135 | − | 0.867100i | \(-0.665981\pi\) |
0.501863 | + | 0.864947i | \(0.332648\pi\) | |||||||
\(930\) | 412.485 | − | 539.963i | 0.443532 | − | 0.580605i | ||||
\(931\) | 146.104 | − | 828.914i | 0.156933 | − | 0.890348i | ||||
\(932\) | 283.540 | − | 283.540i | 0.304227 | − | 0.304227i | ||||
\(933\) | 76.2960 | − | 284.741i | 0.0817750 | − | 0.305188i | ||||
\(934\) | −270.095 | − | 155.940i | −0.289181 | − | 0.166959i | ||||
\(935\) | 2088.89 | + | 859.985i | 2.23411 | + | 0.919770i | ||||
\(936\) | −80.2454 | − | 138.989i | −0.0857323 | − | 0.148493i | ||||
\(937\) | −441.544 | + | 441.544i | −0.471232 | + | 0.471232i | −0.902313 | − | 0.431081i | \(-0.858132\pi\) |
0.431081 | + | 0.902313i | \(0.358132\pi\) | |||||||
\(938\) | −26.4945 | + | 12.3556i | −0.0282457 | + | 0.0131723i | ||||
\(939\) | 679.571i | 0.723718i | ||||||||
\(940\) | −462.379 | − | 599.906i | −0.491893 | − | 0.638198i | ||||
\(941\) | 586.555 | − | 1015.94i | 0.623332 | − | 1.07964i | −0.365529 | − | 0.930800i | \(-0.619112\pi\) |
0.988861 | − | 0.148842i | \(-0.0475546\pi\) | |||||||
\(942\) | −112.058 | − | 418.208i | −0.118958 | − | 0.443958i | ||||
\(943\) | 117.460 | − | 438.365i | 0.124560 | − | 0.464863i | ||||
\(944\) | − | 123.738i | − | 0.131078i | ||||||
\(945\) | 161.500 | + | 83.6234i | 0.170899 | + | 0.0884904i | ||||
\(946\) | −586.301 | −0.619768 | ||||||||
\(947\) | −1145.51 | − | 306.937i | −1.20962 | − | 0.324115i | −0.403004 | − | 0.915198i | \(-0.632034\pi\) |
−0.806611 | + | 0.591083i | \(0.798701\pi\) | |||||||
\(948\) | −253.288 | + | 67.8684i | −0.267182 | + | 0.0715912i | ||||
\(949\) | −357.622 | − | 206.473i | −0.376841 | − | 0.217569i | ||||
\(950\) | −607.307 | + | 2.61434i | −0.639270 | + | 0.00275194i | ||||
\(951\) | 247.153 | 0.259887 | ||||||||
\(952\) | −446.269 | − | 39.0288i | −0.468770 | − | 0.0409967i | ||||
\(953\) | −788.797 | − | 788.797i | −0.827699 | − | 0.827699i | 0.159499 | − | 0.987198i | \(-0.449012\pi\) |
−0.987198 | + | 0.159499i | \(0.949012\pi\) | |||||||
\(954\) | 15.2817 | − | 8.82288i | 0.0160185 | − | 0.00924831i | ||||
\(955\) | 216.057 | + | 518.448i | 0.226237 | + | 0.542877i | ||||
\(956\) | 282.776 | − | 489.782i | 0.295791 | − | 0.512324i | ||||
\(957\) | −775.036 | − | 207.670i | −0.809860 | − | 0.217001i | ||||
\(958\) | 372.435 | + | 372.435i | 0.388763 | + | 0.388763i | ||||
\(959\) | −431.005 | + | 361.680i | −0.449432 | + | 0.377143i | ||||
\(960\) | 9.19095 | + | 68.6697i | 0.00957390 | + | 0.0715309i | ||||
\(961\) | −1058.51 | − | 1833.39i | −1.10147 | − | 1.90780i | ||||
\(962\) | −159.733 | − | 596.131i | −0.166042 | − | 0.619679i | ||||
\(963\) | 471.925 | − | 126.452i | 0.490057 | − | 0.131310i | ||||
\(964\) | 157.875 | − | 91.1491i | 0.163771 | − | 0.0945530i | ||||
\(965\) | 28.7075 | − | 3.84230i | 0.0297487 | − | 0.00398166i | ||||
\(966\) | 354.287 | − | 62.4822i | 0.366757 | − | 0.0646814i | ||||
\(967\) | 437.038 | − | 437.038i | 0.451953 | − | 0.451953i | −0.444050 | − | 0.896002i | \(-0.646459\pi\) |
0.896002 | + | 0.444050i | \(0.146459\pi\) | |||||||
\(968\) | 203.309 | − | 758.758i | 0.210030 | − | 0.783841i | ||||
\(969\) | 582.984 | + | 336.586i | 0.601634 | + | 0.347354i | ||||
\(970\) | −517.478 | + | 215.653i | −0.533483 | + | 0.222322i | ||||
\(971\) | 5.97107 | + | 10.3422i | 0.00614940 | + | 0.0106511i | 0.869084 | − | 0.494665i | \(-0.164709\pi\) |
−0.862934 | + | 0.505316i | \(0.831376\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −95.9687 | + | 44.7548i | −0.0986318 | + | 0.0459967i | ||||
\(974\) | − | 519.307i | − | 0.533170i | ||||||
\(975\) | 581.609 | + | 576.623i | 0.596522 | + | 0.591408i | ||||
\(976\) | 7.03346 | − | 12.1823i | 0.00720642 | − | 0.0124819i | ||||
\(977\) | 366.611 | + | 1368.21i | 0.375242 | + | 1.40042i | 0.852991 | + | 0.521926i | \(0.174786\pi\) |
−0.477749 | + | 0.878496i | \(0.658547\pi\) | |||||||
\(978\) | −47.6369 | + | 177.783i | −0.0487085 | + | 0.181783i | ||||
\(979\) | − | 2873.93i | − | 2.93558i | ||||||
\(980\) | 478.149 | − | 107.116i | 0.487907 | − | 0.109302i | ||||
\(981\) | 175.896 | 0.179303 | ||||||||
\(982\) | 11.9035 | + | 3.18952i | 0.0121216 | + | 0.00324799i | ||||
\(983\) | 1009.31 | − | 270.445i | 1.02677 | − | 0.275122i | 0.294149 | − | 0.955760i | \(-0.404964\pi\) |
0.732620 | + | 0.680638i | \(0.238297\pi\) | |||||||
\(984\) | 91.7691 | + | 52.9829i | 0.0932613 | + | 0.0538444i | ||||
\(985\) | 225.742 | − | 173.991i | 0.229179 | − | 0.176640i | ||||
\(986\) | 742.342 | 0.752882 | ||||||||
\(987\) | −388.126 | − | 832.268i | −0.393238 | − | 0.843230i | ||||
\(988\) | 459.469 | + | 459.469i | 0.465049 | + | 0.465049i | ||||
\(989\) | −377.252 | + | 217.807i | −0.381448 | + | 0.220229i | ||||
\(990\) | 161.257 | − | 391.692i | 0.162886 | − | 0.395648i | ||||
\(991\) | −305.146 | + | 528.528i | −0.307917 | + | 0.533328i | −0.977907 | − | 0.209042i | \(-0.932965\pi\) |
0.669989 | + | 0.742371i | \(0.266299\pi\) | |||||||
\(992\) | 303.148 | + | 81.2282i | 0.305593 | + | 0.0818833i | ||||
\(993\) | 28.2143 | + | 28.2143i | 0.0284132 | + | 0.0284132i | ||||
\(994\) | −20.4496 | − | 115.953i | −0.0205730 | − | 0.116653i | ||||
\(995\) | 392.641 | + | 299.944i | 0.394614 | + | 0.301451i | ||||
\(996\) | −69.2872 | − | 120.009i | −0.0695655 | − | 0.120491i | ||||
\(997\) | −354.588 | − | 1323.34i | −0.355655 | − | 1.32732i | −0.879659 | − | 0.475605i | \(-0.842229\pi\) |
0.524004 | − | 0.851716i | \(-0.324438\pi\) | |||||||
\(998\) | −368.079 | + | 98.6264i | −0.368816 | + | 0.0988240i | ||||
\(999\) | −103.827 | + | 59.9447i | −0.103931 | + | 0.0600047i |
(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 | 210.3.v.b.193.1 | yes | 32 | |
5.2 | odd | 4 | inner | 210.3.v.b.67.8 | yes | 32 | |
7.2 | even | 3 | inner | 210.3.v.b.163.8 | yes | 32 | |
35.2 | odd | 12 | inner | 210.3.v.b.37.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.b.37.1 | ✓ | 32 | 35.2 | odd | 12 | inner | |
210.3.v.b.67.8 | yes | 32 | 5.2 | odd | 4 | inner | |
210.3.v.b.163.8 | yes | 32 | 7.2 | even | 3 | inner | |
210.3.v.b.193.1 | yes | 32 | 1.1 | even | 1 | trivial |