Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,4,Mod(3,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.f (of order \(6\), 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: | \(1.65205348016\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + 5376 x^{11} - 41472 x^{10} + 43008 x^{9} - 28672 x^{8} + 180224 x^{7} + \cdots + 1073741824 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.9 | ||
Root | \(-2.26510 + 1.69390i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 28.19 |
Dual form | 28.4.f.a.3.9 |
$q$-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 \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59951 | + | 1.11469i | 0.919067 | + | 0.394102i | ||||
\(3\) | 1.67134 | + | 2.89484i | 0.321649 | + | 0.557112i | 0.980828 | − | 0.194873i | \(-0.0624296\pi\) |
−0.659179 | + | 0.751986i | \(0.729096\pi\) | |||||||
\(4\) | 5.51494 | + | 5.79529i | 0.689368 | + | 0.724411i | ||||
\(5\) | −15.9583 | − | 9.21354i | −1.42736 | − | 0.824084i | −0.430444 | − | 0.902617i | \(-0.641643\pi\) |
−0.996911 | + | 0.0785333i | \(0.974976\pi\) | |||||||
\(6\) | 1.11782 | + | 9.38820i | 0.0760581 | + | 0.638786i | ||||
\(7\) | 15.4841 | − | 10.1609i | 0.836061 | − | 0.548636i | ||||
\(8\) | 7.87623 | + | 21.2124i | 0.348084 | + | 0.937463i | ||||
\(9\) | 7.91327 | − | 13.7062i | 0.293084 | − | 0.507636i | ||||
\(10\) | −31.2137 | − | 41.7393i | −0.987062 | − | 1.31991i | ||||
\(11\) | −35.6274 | + | 20.5695i | −0.976551 | + | 0.563812i | −0.901227 | − | 0.433347i | \(-0.857332\pi\) |
−0.0753237 | + | 0.997159i | \(0.523999\pi\) | |||||||
\(12\) | −7.55911 | + | 25.6508i | −0.181844 | + | 0.617062i | ||||
\(13\) | − | 24.8455i | − | 0.530069i | −0.964239 | − | 0.265035i | \(-0.914617\pi\) | ||
0.964239 | − | 0.265035i | \(-0.0853834\pi\) | |||||||
\(14\) | 51.5773 | − | 9.15348i | 0.984614 | − | 0.174741i | ||||
\(15\) | − | 61.5957i | − | 1.06026i | ||||||
\(16\) | −3.17079 | + | 63.9214i | −0.0495436 | + | 0.998772i | ||||
\(17\) | −41.3826 | + | 23.8923i | −0.590398 | + | 0.340866i | −0.765255 | − | 0.643728i | \(-0.777387\pi\) |
0.174857 | + | 0.984594i | \(0.444054\pi\) | |||||||
\(18\) | 35.8487 | − | 26.8086i | 0.469424 | − | 0.351047i | ||||
\(19\) | −30.9150 | + | 53.5464i | −0.373284 | + | 0.646547i | −0.990069 | − | 0.140585i | \(-0.955102\pi\) |
0.616785 | + | 0.787132i | \(0.288435\pi\) | |||||||
\(20\) | −34.6141 | − | 143.295i | −0.386997 | − | 1.60209i | ||||
\(21\) | 55.2933 | + | 27.8416i | 0.574570 | + | 0.289312i | ||||
\(22\) | −115.542 | + | 13.7572i | −1.11971 | + | 0.133321i | ||||
\(23\) | 64.3994 | + | 37.1810i | 0.583835 | + | 0.337077i | 0.762656 | − | 0.646804i | \(-0.223895\pi\) |
−0.178821 | + | 0.983882i | \(0.557228\pi\) | |||||||
\(24\) | −48.2426 | + | 58.2535i | −0.410312 | + | 0.495456i | ||||
\(25\) | 107.279 | + | 185.812i | 0.858229 | + | 1.48650i | ||||
\(26\) | 27.6950 | − | 64.5862i | 0.208901 | − | 0.487169i | ||||
\(27\) | 143.155 | 1.02038 | ||||||||
\(28\) | 144.279 | + | 33.6979i | 0.973792 | + | 0.227440i | ||||
\(29\) | 28.8513 | 0.184743 | 0.0923715 | − | 0.995725i | \(-0.470555\pi\) | ||||
0.0923715 | + | 0.995725i | \(0.470555\pi\) | |||||||
\(30\) | 68.6600 | − | 160.119i | 0.417851 | − | 0.974453i | ||||
\(31\) | −11.5660 | − | 20.0328i | −0.0670099 | − | 0.116065i | 0.830574 | − | 0.556908i | \(-0.188013\pi\) |
−0.897584 | + | 0.440844i | \(0.854679\pi\) | |||||||
\(32\) | −79.4949 | + | 162.630i | −0.439151 | + | 0.898413i | ||||
\(33\) | −119.091 | − | 68.7571i | −0.628213 | − | 0.362699i | ||||
\(34\) | −134.207 | + | 15.9796i | −0.676951 | + | 0.0806023i | ||||
\(35\) | −340.717 | + | 19.4877i | −1.64548 | + | 0.0941147i | ||||
\(36\) | 123.072 | − | 29.7291i | 0.569780 | − | 0.137635i | ||||
\(37\) | 51.8900 | − | 89.8761i | 0.230558 | − | 0.399339i | −0.727414 | − | 0.686199i | \(-0.759278\pi\) |
0.957973 | + | 0.286860i | \(0.0926114\pi\) | |||||||
\(38\) | −140.052 | + | 104.734i | −0.597878 | + | 0.447108i | ||||
\(39\) | 71.9237 | − | 41.5252i | 0.295308 | − | 0.170496i | ||||
\(40\) | 69.7496 | − | 411.082i | 0.275710 | − | 1.62494i | ||||
\(41\) | − | 96.1780i | − | 0.366353i | −0.983080 | − | 0.183177i | \(-0.941362\pi\) | ||
0.983080 | − | 0.183177i | \(-0.0586380\pi\) | |||||||
\(42\) | 112.701 | + | 134.009i | 0.414050 | + | 0.492336i | ||||
\(43\) | − | 195.747i | − | 0.694213i | −0.937826 | − | 0.347107i | \(-0.887164\pi\) | ||
0.937826 | − | 0.347107i | \(-0.112836\pi\) | |||||||
\(44\) | −315.689 | − | 93.0315i | −1.08163 | − | 0.318751i | ||||
\(45\) | −252.565 | + | 145.818i | −0.836670 | + | 0.483052i | ||||
\(46\) | 125.962 | + | 168.438i | 0.403741 | + | 0.539887i | ||||
\(47\) | −89.8186 | + | 155.570i | −0.278753 | + | 0.482815i | −0.971075 | − | 0.238774i | \(-0.923254\pi\) |
0.692322 | + | 0.721589i | \(0.256588\pi\) | |||||||
\(48\) | −190.342 | + | 97.6553i | −0.572364 | + | 0.293653i | ||||
\(49\) | 136.513 | − | 314.664i | 0.397996 | − | 0.917387i | ||||
\(50\) | 71.7499 | + | 602.603i | 0.202939 | + | 1.70442i | ||||
\(51\) | −138.329 | − | 79.8641i | −0.379802 | − | 0.219279i | ||||
\(52\) | 143.987 | − | 137.021i | 0.383988 | − | 0.365413i | ||||
\(53\) | −218.681 | − | 378.767i | −0.566758 | − | 0.981654i | −0.996884 | − | 0.0788851i | \(-0.974864\pi\) |
0.430125 | − | 0.902769i | \(-0.358469\pi\) | |||||||
\(54\) | 372.134 | + | 159.573i | 0.937796 | + | 0.402133i | ||||
\(55\) | 758.071 | 1.85851 | ||||||||
\(56\) | 337.493 | + | 248.424i | 0.805346 | + | 0.592805i | ||||
\(57\) | −206.678 | −0.480266 | ||||||||
\(58\) | 74.9993 | + | 32.1601i | 0.169791 | + | 0.0728075i | ||||
\(59\) | 286.640 | + | 496.475i | 0.632497 | + | 1.09552i | 0.987040 | + | 0.160477i | \(0.0513034\pi\) |
−0.354542 | + | 0.935040i | \(0.615363\pi\) | |||||||
\(60\) | 356.965 | − | 339.697i | 0.768067 | − | 0.730911i | ||||
\(61\) | 368.470 | + | 212.736i | 0.773405 | + | 0.446526i | 0.834088 | − | 0.551632i | \(-0.185995\pi\) |
−0.0606829 | + | 0.998157i | \(0.519328\pi\) | |||||||
\(62\) | −7.73553 | − | 64.9681i | −0.0158454 | − | 0.133080i | ||||
\(63\) | −16.7374 | − | 292.633i | −0.0334717 | − | 0.585211i | ||||
\(64\) | −387.930 | + | 334.147i | −0.757675 | + | 0.652631i | ||||
\(65\) | −228.915 | + | 396.492i | −0.436822 | + | 0.756597i | ||||
\(66\) | −232.935 | − | 311.484i | −0.434430 | − | 0.580924i | ||||
\(67\) | −728.093 | + | 420.365i | −1.32762 | + | 0.766504i | −0.984932 | − | 0.172944i | \(-0.944672\pi\) |
−0.342692 | + | 0.939448i | \(0.611339\pi\) | |||||||
\(68\) | −366.686 | − | 108.060i | −0.653929 | − | 0.192709i | ||||
\(69\) | 248.568i | 0.433682i | ||||||||
\(70\) | −907.422 | − | 329.135i | −1.54940 | − | 0.561988i | ||||
\(71\) | − | 1179.04i | − | 1.97079i | −0.170279 | − | 0.985396i | \(-0.554467\pi\) | ||
0.170279 | − | 0.985396i | \(-0.445533\pi\) | |||||||
\(72\) | 353.067 | + | 59.9061i | 0.577908 | + | 0.0980556i | ||||
\(73\) | 716.185 | − | 413.489i | 1.14826 | − | 0.662949i | 0.199798 | − | 0.979837i | \(-0.435971\pi\) |
0.948463 | + | 0.316888i | \(0.102638\pi\) | |||||||
\(74\) | 235.072 | − | 175.793i | 0.369279 | − | 0.276156i | ||||
\(75\) | −358.597 | + | 621.109i | −0.552097 | + | 0.956260i | ||||
\(76\) | −480.812 | + | 116.144i | −0.725696 | + | 0.175297i | ||||
\(77\) | −342.652 | + | 680.505i | −0.507128 | + | 1.00715i | ||||
\(78\) | 233.254 | − | 27.7728i | 0.338601 | − | 0.0403160i | ||||
\(79\) | 282.007 | + | 162.817i | 0.401623 | + | 0.231877i | 0.687184 | − | 0.726483i | \(-0.258847\pi\) |
−0.285561 | + | 0.958361i | \(0.592180\pi\) | |||||||
\(80\) | 639.543 | − | 990.864i | 0.893788 | − | 1.38477i | ||||
\(81\) | 25.6023 | + | 44.3445i | 0.0351198 | + | 0.0608292i | ||||
\(82\) | 107.208 | − | 250.016i | 0.144380 | − | 0.336703i | ||||
\(83\) | −507.854 | −0.671617 | −0.335808 | − | 0.941930i | \(-0.609009\pi\) | ||||
−0.335808 | + | 0.941930i | \(0.609009\pi\) | |||||||
\(84\) | 143.589 | + | 473.986i | 0.186510 | + | 0.615667i | ||||
\(85\) | 880.530 | 1.12361 | ||||||||
\(86\) | 218.197 | − | 508.848i | 0.273591 | − | 0.638029i | ||||
\(87\) | 48.2202 | + | 83.5198i | 0.0594224 | + | 0.102923i | ||||
\(88\) | −716.937 | − | 593.731i | −0.868474 | − | 0.719227i | ||||
\(89\) | −176.826 | − | 102.090i | −0.210601 | − | 0.121590i | 0.390990 | − | 0.920395i | \(-0.372133\pi\) |
−0.601591 | + | 0.798805i | \(0.705466\pi\) | |||||||
\(90\) | −819.088 | + | 97.5260i | −0.959327 | + | 0.114224i | ||||
\(91\) | −252.452 | − | 384.709i | −0.290815 | − | 0.443170i | ||||
\(92\) | 139.684 | + | 578.264i | 0.158295 | + | 0.655307i | ||||
\(93\) | 38.6612 | − | 66.9632i | 0.0431074 | − | 0.0746641i | ||||
\(94\) | −406.897 | + | 304.288i | −0.446471 | + | 0.333882i | ||||
\(95\) | 986.704 | − | 569.674i | 1.06562 | − | 0.615235i | ||||
\(96\) | −603.651 | + | 41.6847i | −0.641770 | + | 0.0443170i | ||||
\(97\) | 1116.33i | 1.16852i | 0.811566 | + | 0.584261i | \(0.198615\pi\) | ||||
−0.811566 | + | 0.584261i | \(0.801385\pi\) | |||||||
\(98\) | 705.618 | − | 665.804i | 0.727329 | − | 0.686289i | ||||
\(99\) | 651.087i | 0.660977i | ||||||||
\(100\) | −485.199 | + | 1646.45i | −0.485199 | + | 1.64645i | ||||
\(101\) | −3.43081 | + | 1.98078i | −0.00337999 | + | 0.00195144i | −0.501689 | − | 0.865048i | \(-0.667288\pi\) |
0.498309 | + | 0.866999i | \(0.333954\pi\) | |||||||
\(102\) | −270.564 | − | 361.801i | −0.262645 | − | 0.351212i | ||||
\(103\) | −179.406 | + | 310.741i | −0.171626 | + | 0.297264i | −0.938988 | − | 0.343949i | \(-0.888235\pi\) |
0.767363 | + | 0.641213i | \(0.221569\pi\) | |||||||
\(104\) | 527.032 | − | 195.689i | 0.496920 | − | 0.184508i | ||||
\(105\) | −625.867 | − | 953.752i | −0.581699 | − | 0.886445i | ||||
\(106\) | −146.258 | − | 1228.37i | −0.134017 | − | 1.12557i | ||||
\(107\) | 803.472 | + | 463.885i | 0.725931 | + | 0.419116i | 0.816932 | − | 0.576735i | \(-0.195673\pi\) |
−0.0910010 | + | 0.995851i | \(0.529007\pi\) | |||||||
\(108\) | 789.493 | + | 829.626i | 0.703416 | + | 0.739174i | ||||
\(109\) | −594.270 | − | 1029.31i | −0.522209 | − | 0.904492i | −0.999666 | − | 0.0258371i | \(-0.991775\pi\) |
0.477458 | − | 0.878655i | \(-0.341558\pi\) | |||||||
\(110\) | 1970.62 | + | 845.012i | 1.70810 | + | 0.732443i | ||||
\(111\) | 346.903 | 0.296635 | ||||||||
\(112\) | 600.402 | + | 1021.98i | 0.506541 | + | 0.862216i | ||||
\(113\) | −662.367 | −0.551418 | −0.275709 | − | 0.961241i | \(-0.588913\pi\) | ||||
−0.275709 | + | 0.961241i | \(0.588913\pi\) | |||||||
\(114\) | −537.262 | − | 230.381i | −0.441396 | − | 0.189273i | ||||
\(115\) | −685.137 | − | 1186.69i | −0.555560 | − | 0.962258i | ||||
\(116\) | 159.113 | + | 167.201i | 0.127356 | + | 0.133830i | ||||
\(117\) | −340.537 | − | 196.609i | −0.269082 | − | 0.155355i | ||||
\(118\) | 191.710 | + | 1610.11i | 0.149562 | + | 1.25612i | ||||
\(119\) | −398.005 | + | 790.434i | −0.306597 | + | 0.608899i | ||||
\(120\) | 1306.59 | − | 485.142i | 0.993958 | − | 0.369060i | ||||
\(121\) | 180.707 | − | 312.993i | 0.135768 | − | 0.235156i | ||||
\(122\) | 720.708 | + | 963.739i | 0.534835 | + | 0.715187i | ||||
\(123\) | 278.420 | − | 160.746i | 0.204100 | − | 0.117837i | ||||
\(124\) | 52.3105 | − | 177.508i | 0.0378840 | − | 0.128554i | ||||
\(125\) | − | 1650.28i | − | 1.18084i | ||||||
\(126\) | 282.685 | − | 779.361i | 0.199870 | − | 0.551040i | ||||
\(127\) | 1496.04i | 1.04529i | 0.852549 | + | 0.522647i | \(0.175055\pi\) | ||||
−0.852549 | + | 0.522647i | \(0.824945\pi\) | |||||||
\(128\) | −1380.90 | + | 436.200i | −0.953558 | + | 0.301211i | ||||
\(129\) | 566.657 | − | 327.160i | 0.386755 | − | 0.223293i | ||||
\(130\) | −1037.03 | + | 775.518i | −0.699644 | + | 0.523211i | ||||
\(131\) | 984.794 | − | 1705.71i | 0.656808 | − | 1.13762i | −0.324630 | − | 0.945841i | \(-0.605240\pi\) |
0.981437 | − | 0.191783i | \(-0.0614270\pi\) | |||||||
\(132\) | −258.311 | − | 1069.36i | −0.170327 | − | 0.705118i | ||||
\(133\) | 65.3887 | + | 1143.24i | 0.0426310 | + | 0.745350i | ||||
\(134\) | −2361.26 | + | 281.148i | −1.52225 | + | 0.181250i | ||||
\(135\) | −2284.52 | − | 1318.97i | −1.45644 | − | 0.840878i | ||||
\(136\) | −832.751 | − | 689.643i | −0.525058 | − | 0.434826i | ||||
\(137\) | 896.791 | + | 1553.29i | 0.559256 | + | 0.968660i | 0.997559 | + | 0.0698322i | \(0.0222464\pi\) |
−0.438303 | + | 0.898827i | \(0.644420\pi\) | |||||||
\(138\) | −277.076 | + | 646.156i | −0.170915 | + | 0.398583i | ||||
\(139\) | −306.409 | −0.186973 | −0.0934867 | − | 0.995621i | \(-0.529801\pi\) | ||||
−0.0934867 | + | 0.995621i | \(0.529801\pi\) | |||||||
\(140\) | −1991.97 | − | 1867.08i | −1.20252 | − | 1.12712i | ||||
\(141\) | −600.469 | −0.358643 | ||||||||
\(142\) | 1314.26 | − | 3064.93i | 0.776692 | − | 1.81129i | ||||
\(143\) | 511.059 | + | 885.180i | 0.298859 | + | 0.517639i | ||||
\(144\) | 851.027 | + | 549.286i | 0.492492 | + | 0.317874i | ||||
\(145\) | −460.418 | − | 265.822i | −0.263694 | − | 0.152244i | ||||
\(146\) | 2322.64 | − | 276.549i | 1.31660 | − | 0.156763i | ||||
\(147\) | 1139.06 | − | 130.727i | 0.639103 | − | 0.0733481i | ||||
\(148\) | 807.028 | − | 194.944i | 0.448225 | − | 0.108272i | ||||
\(149\) | 714.928 | − | 1238.29i | 0.393082 | − | 0.680838i | −0.599773 | − | 0.800171i | \(-0.704742\pi\) |
0.992854 | + | 0.119333i | \(0.0380756\pi\) | |||||||
\(150\) | −1624.52 | + | 1214.86i | −0.884277 | + | 0.661285i | ||||
\(151\) | −1079.16 | + | 623.054i | −0.581595 | + | 0.335784i | −0.761767 | − | 0.647851i | \(-0.775668\pi\) |
0.180172 | + | 0.983635i | \(0.442335\pi\) | |||||||
\(152\) | −1379.34 | − | 234.037i | −0.736048 | − | 0.124888i | ||||
\(153\) | 756.264i | 0.399610i | ||||||||
\(154\) | −1649.28 | + | 1387.03i | −0.863005 | + | 0.725780i | ||||
\(155\) | 426.254i | 0.220887i | ||||||||
\(156\) | 637.306 | + | 187.810i | 0.327085 | + | 0.0963899i | ||||
\(157\) | −2201.64 | + | 1271.12i | −1.11917 | + | 0.646154i | −0.941189 | − | 0.337880i | \(-0.890290\pi\) |
−0.177982 | + | 0.984034i | \(0.556957\pi\) | |||||||
\(158\) | 551.591 | + | 737.594i | 0.277736 | + | 0.371391i | ||||
\(159\) | 730.980 | − | 1266.10i | 0.364594 | − | 0.631496i | ||||
\(160\) | 2767.00 | − | 1862.87i | 1.36719 | − | 0.920457i | ||||
\(161\) | 1374.96 | − | 78.6420i | 0.673054 | − | 0.0384960i | ||||
\(162\) | 17.1233 | + | 143.813i | 0.00830453 | + | 0.0697469i | ||||
\(163\) | 637.434 | + | 368.022i | 0.306305 | + | 0.176845i | 0.645272 | − | 0.763953i | \(-0.276744\pi\) |
−0.338967 | + | 0.940798i | \(0.610078\pi\) | |||||||
\(164\) | 557.379 | − | 530.416i | 0.265390 | − | 0.252552i | ||||
\(165\) | 1266.99 | + | 2194.49i | 0.597789 | + | 1.03540i | ||||
\(166\) | −1320.17 | − | 566.098i | −0.617261 | − | 0.264685i | ||||
\(167\) | −3110.82 | −1.44145 | −0.720726 | − | 0.693220i | \(-0.756191\pi\) | ||||
−0.720726 | + | 0.693220i | \(0.756191\pi\) | |||||||
\(168\) | −155.085 | + | 1392.19i | −0.0712204 | + | 0.639343i | ||||
\(169\) | 1579.70 | 0.719027 | ||||||||
\(170\) | 2288.95 | + | 981.515i | 1.03267 | + | 0.442816i | ||||
\(171\) | 489.278 | + | 847.454i | 0.218807 | + | 0.378985i | ||||
\(172\) | 1134.41 | − | 1079.54i | 0.502896 | − | 0.478569i | ||||
\(173\) | 2719.50 | + | 1570.10i | 1.19514 | + | 0.690015i | 0.959468 | − | 0.281817i | \(-0.0909370\pi\) |
0.235674 | + | 0.971832i | \(0.424270\pi\) | |||||||
\(174\) | 32.2506 | + | 270.861i | 0.0140512 | + | 0.118011i | ||||
\(175\) | 3549.12 | + | 1787.08i | 1.53308 | + | 0.771946i | ||||
\(176\) | −1201.86 | − | 2342.57i | −0.514738 | − | 1.00328i | ||||
\(177\) | −958.144 | + | 1659.55i | −0.406884 | + | 0.704744i | ||||
\(178\) | −345.862 | − | 462.491i | −0.145637 | − | 0.194748i | ||||
\(179\) | 206.742 | − | 119.362i | 0.0863274 | − | 0.0498411i | −0.456215 | − | 0.889870i | \(-0.650795\pi\) |
0.542542 | + | 0.840028i | \(0.317462\pi\) | |||||||
\(180\) | −2237.94 | − | 659.506i | −0.926701 | − | 0.273093i | ||||
\(181\) | − | 1947.09i | − | 0.799591i | −0.916604 | − | 0.399796i | \(-0.869081\pi\) | ||
0.916604 | − | 0.399796i | \(-0.130919\pi\) | |||||||
\(182\) | −227.423 | − | 1281.46i | −0.0926247 | − | 0.521914i | ||||
\(183\) | 1422.21i | 0.574498i | ||||||||
\(184\) | −281.473 | + | 1658.91i | −0.112774 | + | 0.664655i | ||||
\(185\) | −1656.15 | + | 956.181i | −0.658177 | + | 0.379999i | ||||
\(186\) | 175.143 | − | 130.977i | 0.0690438 | − | 0.0516327i | ||||
\(187\) | 982.903 | − | 1702.44i | 0.384369 | − | 0.665746i | ||||
\(188\) | −1396.92 | + | 337.437i | −0.541920 | + | 0.130905i | ||||
\(189\) | 2216.62 | − | 1454.58i | 0.853099 | − | 0.559817i | ||||
\(190\) | 3199.96 | − | 381.008i | 1.22184 | − | 0.145480i | ||||
\(191\) | −393.391 | − | 227.124i | −0.149030 | − | 0.0860427i | 0.423631 | − | 0.905835i | \(-0.360755\pi\) |
−0.572661 | + | 0.819792i | \(0.694089\pi\) | |||||||
\(192\) | −1615.66 | − | 564.522i | −0.607295 | − | 0.212192i | ||||
\(193\) | −1605.08 | − | 2780.08i | −0.598634 | − | 1.03686i | −0.993023 | − | 0.117921i | \(-0.962377\pi\) |
0.394389 | − | 0.918944i | \(-0.370956\pi\) | |||||||
\(194\) | −1244.36 | + | 2901.93i | −0.460516 | + | 1.07395i | ||||
\(195\) | −1530.38 | −0.562013 | ||||||||
\(196\) | 2576.43 | − | 944.223i | 0.938931 | − | 0.344105i | ||||
\(197\) | −4173.52 | −1.50940 | −0.754698 | − | 0.656073i | \(-0.772216\pi\) | ||||
−0.754698 | + | 0.656073i | \(0.772216\pi\) | |||||||
\(198\) | −725.758 | + | 1692.51i | −0.260492 | + | 0.607482i | ||||
\(199\) | −2639.30 | − | 4571.40i | −0.940176 | − | 1.62843i | −0.765134 | − | 0.643871i | \(-0.777327\pi\) |
−0.175042 | − | 0.984561i | \(-0.556006\pi\) | |||||||
\(200\) | −3096.56 | + | 3739.13i | −1.09480 | + | 1.32198i | ||||
\(201\) | −2433.78 | − | 1405.14i | −0.854057 | − | 0.493090i | ||||
\(202\) | −11.1264 | + | 1.32478i | −0.00387550 | + | 0.000461443i | ||||
\(203\) | 446.735 | − | 293.155i | 0.154456 | − | 0.101357i | ||||
\(204\) | −300.039 | − | 1242.10i | −0.102975 | − | 0.426296i | ||||
\(205\) | −886.140 | + | 1534.84i | −0.301906 | + | 0.522916i | ||||
\(206\) | −812.748 | + | 607.793i | −0.274888 | + | 0.205568i | ||||
\(207\) | 1019.22 | − | 588.446i | 0.342225 | − | 0.197584i | ||||
\(208\) | 1588.16 | + | 78.7798i | 0.529418 | + | 0.0262615i | ||||
\(209\) | − | 2543.62i | − | 0.841848i | ||||||
\(210\) | −563.815 | − | 3176.94i | −0.185271 | − | 1.04395i | ||||
\(211\) | 871.583i | 0.284371i | 0.989840 | + | 0.142185i | \(0.0454130\pi\) | ||||
−0.989840 | + | 0.142185i | \(0.954587\pi\) | |||||||
\(212\) | 989.051 | − | 3356.20i | 0.320416 | − | 1.08729i | ||||
\(213\) | 3413.13 | − | 1970.57i | 1.09795 | − | 0.633903i | ||||
\(214\) | 1571.55 | + | 2101.49i | 0.502004 | + | 0.671286i | ||||
\(215\) | −1803.53 | + | 3123.80i | −0.572090 | + | 0.990889i | ||||
\(216\) | 1127.52 | + | 3036.66i | 0.355177 | + | 0.956568i | ||||
\(217\) | −382.640 | − | 192.669i | −0.119702 | − | 0.0602730i | ||||
\(218\) | −397.459 | − | 3338.12i | −0.123483 | − | 1.03709i | ||||
\(219\) | 2393.97 | + | 1382.16i | 0.738674 | + | 0.426474i | ||||
\(220\) | 4180.72 | + | 4393.24i | 1.28120 | + | 1.34633i | ||||
\(221\) | 593.615 | + | 1028.17i | 0.180683 | + | 0.312952i | ||||
\(222\) | 901.778 | + | 386.688i | 0.272628 | + | 0.116904i | ||||
\(223\) | −1930.21 | −0.579624 | −0.289812 | − | 0.957084i | \(-0.593593\pi\) | ||||
−0.289812 | + | 0.957084i | \(0.593593\pi\) | |||||||
\(224\) | 421.563 | + | 3325.91i | 0.125745 | + | 0.992063i | ||||
\(225\) | 3395.70 | 1.00613 | ||||||||
\(226\) | −1721.83 | − | 738.333i | −0.506790 | − | 0.217315i | ||||
\(227\) | −988.231 | − | 1711.67i | −0.288948 | − | 0.500473i | 0.684611 | − | 0.728909i | \(-0.259972\pi\) |
−0.973559 | + | 0.228436i | \(0.926639\pi\) | |||||||
\(228\) | −1139.82 | − | 1197.76i | −0.331080 | − | 0.347910i | ||||
\(229\) | −2237.66 | − | 1291.92i | −0.645716 | − | 0.372804i | 0.141097 | − | 0.989996i | \(-0.454937\pi\) |
−0.786813 | + | 0.617192i | \(0.788270\pi\) | |||||||
\(230\) | −458.233 | − | 3848.54i | −0.131369 | − | 1.10333i | ||||
\(231\) | −2542.64 | + | 145.429i | −0.724214 | + | 0.0414221i | ||||
\(232\) | 227.239 | + | 612.004i | 0.0643060 | + | 0.173190i | ||||
\(233\) | 1724.22 | − | 2986.43i | 0.484795 | − | 0.839690i | −0.515052 | − | 0.857159i | \(-0.672227\pi\) |
0.999847 | + | 0.0174686i | \(0.00556071\pi\) | |||||||
\(234\) | −666.072 | − | 890.680i | −0.186079 | − | 0.248827i | ||||
\(235\) | 2866.71 | − | 1655.10i | 0.795759 | − | 0.459432i | ||||
\(236\) | −1296.41 | + | 4399.19i | −0.357582 | + | 1.21340i | ||||
\(237\) | 1088.49i | 0.298333i | ||||||||
\(238\) | −1915.71 | + | 1611.09i | −0.521751 | + | 0.438788i | ||||
\(239\) | 3647.94i | 0.987304i | 0.869659 | + | 0.493652i | \(0.164338\pi\) | ||||
−0.869659 | + | 0.493652i | \(0.835662\pi\) | |||||||
\(240\) | 3937.28 | + | 195.307i | 1.05896 | + | 0.0525292i | ||||
\(241\) | −2194.49 | + | 1266.99i | −0.586553 | + | 0.338646i | −0.763733 | − | 0.645532i | \(-0.776636\pi\) |
0.177180 | + | 0.984178i | \(0.443302\pi\) | |||||||
\(242\) | 818.639 | − | 612.198i | 0.217455 | − | 0.162618i | ||||
\(243\) | 1847.01 | − | 3199.12i | 0.487597 | − | 0.844542i | ||||
\(244\) | 799.222 | + | 3308.62i | 0.209692 | + | 0.868084i | ||||
\(245\) | −5077.68 | + | 3763.74i | −1.32409 | + | 0.981455i | ||||
\(246\) | 902.938 | − | 107.510i | 0.234021 | − | 0.0278641i | ||||
\(247\) | 1330.39 | + | 768.099i | 0.342714 | + | 0.197866i | ||||
\(248\) | 333.848 | − | 403.125i | 0.0854813 | − | 0.103220i | ||||
\(249\) | −848.795 | − | 1470.16i | −0.216025 | − | 0.374166i | ||||
\(250\) | 1839.54 | − | 4289.92i | 0.465372 | − | 1.08527i | ||||
\(251\) | 5658.23 | 1.42289 | 0.711443 | − | 0.702744i | \(-0.248042\pi\) | ||||
0.711443 | + | 0.702744i | \(0.248042\pi\) | |||||||
\(252\) | 1603.59 | − | 1710.85i | 0.400859 | − | 0.427673i | ||||
\(253\) | −3059.18 | −0.760193 | ||||||||
\(254\) | −1667.62 | + | 3888.98i | −0.411952 | + | 0.960695i | ||||
\(255\) | 1471.66 | + | 2548.99i | 0.361408 | + | 0.625977i | ||||
\(256\) | −4075.89 | − | 405.362i | −0.995091 | − | 0.0989655i | ||||
\(257\) | 4328.82 | + | 2499.25i | 1.05068 | + | 0.606610i | 0.922840 | − | 0.385185i | \(-0.125862\pi\) |
0.127840 | + | 0.991795i | \(0.459196\pi\) | |||||||
\(258\) | 1837.71 | − | 218.810i | 0.443454 | − | 0.0528006i | ||||
\(259\) | −109.753 | − | 1918.90i | −0.0263310 | − | 0.460364i | ||||
\(260\) | −3560.24 | + | 860.004i | −0.849218 | + | 0.205135i | ||||
\(261\) | 228.308 | − | 395.441i | 0.0541452 | − | 0.0937822i | ||||
\(262\) | 4461.32 | − | 3336.29i | 1.05199 | − | 0.786704i | ||||
\(263\) | −1646.99 | + | 950.892i | −0.386152 | + | 0.222945i | −0.680491 | − | 0.732756i | \(-0.738234\pi\) |
0.294340 | + | 0.955701i | \(0.404900\pi\) | |||||||
\(264\) | 520.514 | − | 3067.74i | 0.121346 | − | 0.715176i | ||||
\(265\) | 8059.32i | 1.86823i | ||||||||
\(266\) | −1104.38 | + | 3044.76i | −0.254563 | + | 0.701827i | ||||
\(267\) | − | 682.509i | − | 0.156438i | ||||||
\(268\) | −6451.53 | − | 1901.22i | −1.47048 | − | 0.433342i | ||||
\(269\) | 6976.20 | − | 4027.71i | 1.58121 | − | 0.912913i | 0.586530 | − | 0.809928i | \(-0.300494\pi\) |
0.994683 | − | 0.102986i | \(-0.0328395\pi\) | |||||||
\(270\) | −4468.39 | − | 5975.19i | −1.00718 | − | 1.34681i | ||||
\(271\) | −2189.04 | + | 3791.53i | −0.490682 | + | 0.849886i | −0.999942 | − | 0.0107264i | \(-0.996586\pi\) |
0.509261 | + | 0.860612i | \(0.329919\pi\) | |||||||
\(272\) | −1396.01 | − | 2720.99i | −0.311197 | − | 0.606560i | ||||
\(273\) | 691.739 | − | 1373.79i | 0.153355 | − | 0.304562i | ||||
\(274\) | 599.791 | + | 5037.44i | 0.132243 | + | 1.11067i | ||||
\(275\) | −7644.11 | − | 4413.33i | −1.67621 | − | 0.967759i | ||||
\(276\) | −1440.52 | + | 1370.84i | −0.314164 | + | 0.298967i | ||||
\(277\) | 1602.26 | + | 2775.19i | 0.347547 | + | 0.601968i | 0.985813 | − | 0.167847i | \(-0.0536815\pi\) |
−0.638266 | + | 0.769815i | \(0.720348\pi\) | |||||||
\(278\) | −796.515 | − | 341.551i | −0.171841 | − | 0.0736865i | ||||
\(279\) | −366.098 | −0.0785581 | ||||||||
\(280\) | −3096.95 | − | 7073.94i | −0.660993 | − | 1.50982i | ||||
\(281\) | 6258.33 | 1.32861 | 0.664307 | − | 0.747460i | \(-0.268727\pi\) | ||||
0.664307 | + | 0.747460i | \(0.268727\pi\) | |||||||
\(282\) | −1560.93 | − | 669.335i | −0.329617 | − | 0.141342i | ||||
\(283\) | 3029.37 | + | 5247.02i | 0.636316 | + | 1.10213i | 0.986235 | + | 0.165351i | \(0.0528759\pi\) |
−0.349919 | + | 0.936780i | \(0.613791\pi\) | |||||||
\(284\) | 6832.87 | − | 6502.33i | 1.42766 | − | 1.35860i | ||||
\(285\) | 3298.23 | + | 1904.23i | 0.685510 | + | 0.395779i | ||||
\(286\) | 341.806 | + | 2870.71i | 0.0706692 | + | 0.593526i | ||||
\(287\) | −977.254 | − | 1489.23i | −0.200995 | − | 0.306294i | ||||
\(288\) | 1599.97 | + | 2376.51i | 0.327359 | + | 0.486240i | ||||
\(289\) | −1314.82 | + | 2277.33i | −0.267620 | + | 0.463532i | ||||
\(290\) | −900.554 | − | 1204.23i | −0.182353 | − | 0.243844i | ||||
\(291\) | −3231.61 | + | 1865.77i | −0.650998 | + | 0.375854i | ||||
\(292\) | 6346.01 | + | 1870.13i | 1.27182 | + | 0.374798i | ||||
\(293\) | − | 457.644i | − | 0.0912486i | −0.998959 | − | 0.0456243i | \(-0.985472\pi\) | ||
0.998959 | − | 0.0456243i | \(-0.0145277\pi\) | |||||||
\(294\) | 3106.72 | + | 929.870i | 0.616285 | + | 0.184460i | ||||
\(295\) | − | 10563.9i | − | 2.08492i | ||||||
\(296\) | 2315.18 | + | 392.825i | 0.454619 | + | 0.0771367i | ||||
\(297\) | −5100.24 | + | 2944.63i | −0.996451 | + | 0.575301i | ||||
\(298\) | 3238.77 | − | 2422.03i | 0.629588 | − | 0.470821i | ||||
\(299\) | 923.780 | − | 1600.03i | 0.178674 | − | 0.309473i | ||||
\(300\) | −5577.15 | + | 1347.20i | −1.07332 | + | 0.259270i | ||||
\(301\) | −1988.97 | − | 3030.96i | −0.380871 | − | 0.580405i | ||||
\(302\) | −3499.80 | + | 416.710i | −0.666858 | + | 0.0794005i | ||||
\(303\) | −11.4681 | − | 6.62110i | −0.00217434 | − | 0.00125535i | ||||
\(304\) | −3324.74 | − | 2145.92i | −0.627259 | − | 0.404858i | ||||
\(305\) | −3920.10 | − | 6789.82i | −0.735949 | − | 1.27470i | ||||
\(306\) | −842.997 | + | 1965.92i | −0.157487 | + | 0.367268i | ||||
\(307\) | −4195.62 | −0.779989 | −0.389995 | − | 0.920817i | \(-0.627523\pi\) | ||||
−0.389995 | + | 0.920817i | \(0.627523\pi\) | |||||||
\(308\) | −5833.43 | + | 1767.18i | −1.07919 | + | 0.326929i | ||||
\(309\) | −1199.39 | −0.220813 | ||||||||
\(310\) | −475.140 | + | 1108.05i | −0.0870520 | + | 0.203010i | ||||
\(311\) | 3254.20 | + | 5636.44i | 0.593341 | + | 1.02770i | 0.993779 | + | 0.111372i | \(0.0355246\pi\) |
−0.400438 | + | 0.916324i | \(0.631142\pi\) | |||||||
\(312\) | 1447.34 | + | 1198.61i | 0.262626 | + | 0.217494i | ||||
\(313\) | −7481.59 | − | 4319.50i | −1.35107 | − | 0.780040i | −0.362670 | − | 0.931918i | \(-0.618135\pi\) |
−0.988399 | + | 0.151878i | \(0.951468\pi\) | |||||||
\(314\) | −7140.09 | + | 850.146i | −1.28324 | + | 0.152792i | ||||
\(315\) | −2429.09 | + | 4824.14i | −0.434487 | + | 0.862888i | ||||
\(316\) | 611.682 | + | 2532.24i | 0.108892 | + | 0.450789i | ||||
\(317\) | −463.165 | + | 802.226i | −0.0820629 | + | 0.142137i | −0.904136 | − | 0.427245i | \(-0.859484\pi\) |
0.822073 | + | 0.569382i | \(0.192818\pi\) | |||||||
\(318\) | 3311.49 | − | 2476.42i | 0.583960 | − | 0.436700i | ||||
\(319\) | −1027.90 | + | 593.455i | −0.180411 | + | 0.104160i | ||||
\(320\) | 9269.39 | − | 1758.22i | 1.61930 | − | 0.307149i | ||||
\(321\) | 3101.23i | 0.539233i | ||||||||
\(322\) | 3661.88 | + | 1328.22i | 0.633753 | + | 0.229871i | ||||
\(323\) | − | 2954.52i | − | 0.508960i | ||||||
\(324\) | −115.794 | + | 392.930i | −0.0198549 | + | 0.0673749i | ||||
\(325\) | 4616.59 | − | 2665.39i | 0.787946 | − | 0.454921i | ||||
\(326\) | 1246.79 | + | 1667.22i | 0.211820 | + | 0.283248i | ||||
\(327\) | 1986.45 | − | 3440.63i | 0.335936 | − | 0.581858i | ||||
\(328\) | 2040.16 | − | 757.520i | 0.343443 | − | 0.127522i | ||||
\(329\) | 189.976 | + | 3321.50i | 0.0318351 | + | 0.556596i | ||||
\(330\) | 847.387 | + | 7116.92i | 0.141355 | + | 1.18719i | ||||
\(331\) | 8260.72 | + | 4769.33i | 1.37175 | + | 0.791982i | 0.991149 | − | 0.132756i | \(-0.0423828\pi\) |
0.380604 | + | 0.924738i | \(0.375716\pi\) | |||||||
\(332\) | −2800.79 | − | 2943.16i | −0.462991 | − | 0.486527i | ||||
\(333\) | −821.238 | − | 1422.43i | −0.135146 | − | 0.234080i | ||||
\(334\) | −8086.62 | − | 3467.59i | −1.32479 | − | 0.568078i | ||||
\(335\) | 15492.2 | 2.52665 | ||||||||
\(336\) | −1955.00 | + | 3446.14i | −0.317423 | + | 0.559531i | ||||
\(337\) | 4736.32 | 0.765589 | 0.382795 | − | 0.923833i | \(-0.374962\pi\) | ||||
0.382795 | + | 0.923833i | \(0.374962\pi\) | |||||||
\(338\) | 4106.46 | + | 1760.87i | 0.660834 | + | 0.283370i | ||||
\(339\) | −1107.04 | − | 1917.45i | −0.177363 | − | 0.307202i | ||||
\(340\) | 4856.07 | + | 5102.92i | 0.774581 | + | 0.813956i | ||||
\(341\) | 824.130 | + | 475.812i | 0.130877 | + | 0.0755620i | ||||
\(342\) | 327.238 | + | 2748.36i | 0.0517398 | + | 0.434545i | ||||
\(343\) | −1083.49 | − | 6259.36i | −0.170563 | − | 0.985347i | ||||
\(344\) | 4152.26 | − | 1541.75i | 0.650800 | − | 0.241644i | ||||
\(345\) | 2290.19 | − | 3966.73i | 0.357391 | − | 0.619019i | ||||
\(346\) | 5319.20 | + | 7112.89i | 0.826479 | + | 1.10518i | ||||
\(347\) | −1694.40 | + | 978.260i | −0.262133 | + | 0.151342i | −0.625307 | − | 0.780379i | \(-0.715026\pi\) |
0.363174 | + | 0.931721i | \(0.381693\pi\) | |||||||
\(348\) | −218.090 | + | 740.057i | −0.0335944 | + | 0.113998i | ||||
\(349\) | − | 9739.50i | − | 1.49382i | −0.664924 | − | 0.746911i | \(-0.731536\pi\) | ||
0.664924 | − | 0.746911i | \(-0.268464\pi\) | |||||||
\(350\) | 7233.96 | + | 8601.70i | 1.10478 | + | 1.31366i | ||||
\(351\) | − | 3556.76i | − | 0.540871i | ||||||
\(352\) | −513.022 | − | 7429.25i | −0.0776823 | − | 1.12494i | ||||
\(353\) | −2590.09 | + | 1495.39i | −0.390528 | + | 0.225471i | −0.682389 | − | 0.730989i | \(-0.739059\pi\) |
0.291861 | + | 0.956461i | \(0.405726\pi\) | |||||||
\(354\) | −4340.59 | + | 3246.00i | −0.651695 | + | 0.487353i | ||||
\(355\) | −10863.1 | + | 18815.5i | −1.62410 | + | 2.81302i | ||||
\(356\) | −383.540 | − | 1587.78i | −0.0571000 | − | 0.236382i | ||||
\(357\) | −2953.38 | + | 168.921i | −0.437842 | + | 0.0250428i | ||||
\(358\) | 670.480 | − | 79.8318i | 0.0989831 | − | 0.0117856i | ||||
\(359\) | 1144.24 | + | 660.628i | 0.168219 | + | 0.0971215i | 0.581746 | − | 0.813371i | \(-0.302370\pi\) |
−0.413527 | + | 0.910492i | \(0.635703\pi\) | |||||||
\(360\) | −5082.41 | − | 4209.00i | −0.744074 | − | 0.616205i | ||||
\(361\) | 1518.02 | + | 2629.29i | 0.221318 | + | 0.383334i | ||||
\(362\) | 2170.40 | − | 5061.49i | 0.315120 | − | 0.734878i | ||||
\(363\) | 1208.09 | 0.174678 | ||||||||
\(364\) | 837.241 | − | 3584.68i | 0.120559 | − | 0.516177i | ||||
\(365\) | −15238.8 | −2.18530 | ||||||||
\(366\) | −1585.32 | + | 3697.07i | −0.226411 | + | 0.528002i | ||||
\(367\) | −3367.76 | − | 5833.14i | −0.479008 | − | 0.829666i | 0.520703 | − | 0.853738i | \(-0.325670\pi\) |
−0.999710 | + | 0.0240726i | \(0.992337\pi\) | |||||||
\(368\) | −2580.86 | + | 3998.61i | −0.365589 | + | 0.566418i | ||||
\(369\) | −1318.23 | − | 761.082i | −0.185974 | − | 0.107372i | ||||
\(370\) | −5371.04 | + | 639.511i | −0.754667 | + | 0.0898557i | ||||
\(371\) | −7234.69 | − | 3642.86i | −1.01242 | − | 0.509779i | ||||
\(372\) | 601.286 | − | 145.245i | 0.0838044 | − | 0.0202436i | ||||
\(373\) | −104.742 | + | 181.419i | −0.0145398 | + | 0.0251837i | −0.873204 | − | 0.487355i | \(-0.837962\pi\) |
0.858664 | + | 0.512539i | \(0.171295\pi\) | |||||||
\(374\) | 4452.76 | − | 3329.88i | 0.615632 | − | 0.460385i | ||||
\(375\) | 4777.29 | − | 2758.17i | 0.657862 | − | 0.379817i | ||||
\(376\) | −4007.45 | − | 679.957i | −0.549650 | − | 0.0932610i | ||||
\(377\) | − | 716.824i | − | 0.0979265i | ||||||
\(378\) | 7383.55 | − | 1310.37i | 1.00468 | − | 0.178302i | ||||
\(379\) | − | 1205.99i | − | 0.163450i | −0.996655 | − | 0.0817250i | \(-0.973957\pi\) | ||
0.996655 | − | 0.0817250i | \(-0.0260429\pi\) | |||||||
\(380\) | 8743.04 | + | 2576.52i | 1.18029 | + | 0.347822i | ||||
\(381\) | −4330.81 | + | 2500.39i | −0.582346 | + | 0.336218i | ||||
\(382\) | −769.453 | − | 1028.92i | −0.103059 | − | 0.137812i | ||||
\(383\) | 1590.45 | − | 2754.73i | 0.212188 | − | 0.367520i | −0.740211 | − | 0.672375i | \(-0.765274\pi\) |
0.952399 | + | 0.304854i | \(0.0986078\pi\) | |||||||
\(384\) | −3570.68 | − | 3268.44i | −0.474519 | − | 0.434354i | ||||
\(385\) | 11738.0 | − | 7702.67i | 1.55383 | − | 1.01965i | ||||
\(386\) | −1073.51 | − | 9016.03i | −0.141555 | − | 1.18887i | ||||
\(387\) | −2682.95 | − | 1549.00i | −0.352408 | − | 0.203463i | ||||
\(388\) | −6469.48 | + | 6156.52i | −0.846490 | + | 0.805541i | ||||
\(389\) | 4006.02 | + | 6938.63i | 0.522142 | + | 0.904377i | 0.999668 | + | 0.0257595i | \(0.00820040\pi\) |
−0.477526 | + | 0.878618i | \(0.658466\pi\) | |||||||
\(390\) | −3978.23 | − | 1705.89i | −0.516527 | − | 0.221490i | ||||
\(391\) | −3553.36 | −0.459593 | ||||||||
\(392\) | 7749.97 | + | 417.391i | 0.998553 | + | 0.0537792i | ||||
\(393\) | 6583.69 | 0.845046 | ||||||||
\(394\) | −10849.1 | − | 4652.17i | −1.38724 | − | 0.594855i | ||||
\(395\) | −3000.24 | − | 5196.56i | −0.382173 | − | 0.661943i | ||||
\(396\) | −3773.24 | + | 3590.71i | −0.478819 | + | 0.455656i | ||||
\(397\) | 10496.5 | + | 6060.15i | 1.32696 | + | 0.766121i | 0.984828 | − | 0.173531i | \(-0.0555177\pi\) |
0.342132 | + | 0.939652i | \(0.388851\pi\) | |||||||
\(398\) | −1765.21 | − | 14825.4i | −0.222317 | − | 1.86716i | ||||
\(399\) | −3200.21 | + | 2100.03i | −0.401531 | + | 0.263491i | ||||
\(400\) | −12217.5 | + | 6268.23i | −1.52719 | + | 0.783529i | ||||
\(401\) | −5497.13 | + | 9521.31i | −0.684573 | + | 1.18571i | 0.288998 | + | 0.957330i | \(0.406678\pi\) |
−0.973571 | + | 0.228385i | \(0.926655\pi\) | |||||||
\(402\) | −4760.35 | − | 6365.59i | −0.590608 | − | 0.789768i | ||||
\(403\) | −497.726 | + | 287.362i | −0.0615223 | + | 0.0355199i | ||||
\(404\) | −30.3999 | − | 8.95866i | −0.00374370 | − | 0.00110324i | ||||
\(405\) | − | 943.552i | − | 0.115767i | ||||||
\(406\) | 1488.07 | − | 264.090i | 0.181901 | − | 0.0322821i | ||||
\(407\) | 4269.40i | 0.519966i | ||||||||
\(408\) | 604.598 | − | 3563.31i | 0.0733629 | − | 0.432377i | ||||
\(409\) | −1739.78 | + | 1004.46i | −0.210333 | + | 0.121436i | −0.601466 | − | 0.798898i | \(-0.705417\pi\) |
0.391133 | + | 0.920334i | \(0.372083\pi\) | |||||||
\(410\) | −4014.40 | + | 3002.07i | −0.483554 | + | 0.361613i | ||||
\(411\) | −2997.68 | + | 5192.14i | −0.359768 | + | 0.623137i | ||||
\(412\) | −2790.25 | + | 674.007i | −0.333655 | + | 0.0805969i | ||||
\(413\) | 9482.98 | + | 4774.93i | 1.12985 | + | 0.568908i | ||||
\(414\) | 3305.41 | − | 393.564i | 0.392396 | − | 0.0467213i | ||||
\(415\) | 8104.49 | + | 4679.13i | 0.958636 | + | 0.553469i | ||||
\(416\) | 4040.63 | + | 1975.09i | 0.476221 | + | 0.232781i | ||||
\(417\) | −512.113 | − | 887.006i | −0.0601398 | − | 0.104165i | ||||
\(418\) | 2835.35 | − | 6612.18i | 0.331773 | − | 0.773714i | ||||
\(419\) | 6662.83 | 0.776850 | 0.388425 | − | 0.921480i | \(-0.373019\pi\) | ||||
0.388425 | + | 0.921480i | \(0.373019\pi\) | |||||||
\(420\) | 2075.65 | − | 8886.97i | 0.241146 | − | 1.03248i | ||||
\(421\) | 5859.67 | 0.678344 | 0.339172 | − | 0.940724i | \(-0.389853\pi\) | ||||
0.339172 | + | 0.940724i | \(0.389853\pi\) | |||||||
\(422\) | −971.543 | + | 2265.69i | −0.112071 | + | 0.261356i | ||||
\(423\) | 1421.52 | + | 2462.14i | 0.163396 | + | 0.283010i | ||||
\(424\) | 6312.17 | − | 7622.01i | 0.722986 | − | 0.873013i | ||||
\(425\) | −8878.94 | − | 5126.26i | −1.01339 | − | 0.585083i | ||||
\(426\) | 11069.1 | − | 1317.95i | 1.25891 | − | 0.149895i | ||||
\(427\) | 7867.00 | − | 449.960i | 0.891594 | − | 0.0509956i | ||||
\(428\) | 1742.76 | + | 7214.65i | 0.196821 | + | 0.814798i | ||||
\(429\) | −1708.30 | + | 2958.87i | −0.192256 | + | 0.332996i | ||||
\(430\) | −8170.35 | + | 6109.99i | −0.916300 | + | 0.685232i | ||||
\(431\) | −3178.02 | + | 1834.83i | −0.355174 | + | 0.205060i | −0.666962 | − | 0.745092i | \(-0.732406\pi\) |
0.311788 | + | 0.950152i | \(0.399072\pi\) | |||||||
\(432\) | −453.915 | + | 9150.68i | −0.0505532 | + | 1.01913i | ||||
\(433\) | 8282.34i | 0.919224i | 0.888120 | + | 0.459612i | \(0.152011\pi\) | ||||
−0.888120 | + | 0.459612i | \(0.847989\pi\) | |||||||
\(434\) | −779.911 | − | 927.370i | −0.0862602 | − | 0.102570i | ||||
\(435\) | − | 1777.11i | − | 0.195876i | ||||||
\(436\) | 2687.76 | − | 9120.53i | 0.295230 | − | 1.00182i | ||||
\(437\) | −3981.82 | + | 2298.90i | −0.435872 | + | 0.251651i | ||||
\(438\) | 4682.49 | + | 6261.47i | 0.510817 | + | 0.683070i | ||||
\(439\) | 4840.93 | − | 8384.73i | 0.526298 | − | 0.911575i | −0.473233 | − | 0.880938i | \(-0.656913\pi\) |
0.999531 | − | 0.0306374i | \(-0.00975370\pi\) | |||||||
\(440\) | 5970.74 | + | 16080.5i | 0.646918 | + | 1.74229i | ||||
\(441\) | −3232.58 | − | 4361.08i | −0.349053 | − | 0.470909i | ||||
\(442\) | 397.021 | + | 3334.44i | 0.0427248 | + | 0.358831i | ||||
\(443\) | −7154.34 | − | 4130.56i | −0.767298 | − | 0.443000i | 0.0646117 | − | 0.997910i | \(-0.479419\pi\) |
−0.831910 | + | 0.554911i | \(0.812752\pi\) | |||||||
\(444\) | 1913.15 | + | 2010.40i | 0.204491 | + | 0.214886i | ||||
\(445\) | 1881.23 | + | 3258.38i | 0.200402 | + | 0.347106i | ||||
\(446\) | −5017.60 | − | 2151.58i | −0.532713 | − | 0.228431i | ||||
\(447\) | 4779.54 | 0.505737 | ||||||||
\(448\) | −2611.50 | + | 9115.67i | −0.275405 | + | 0.961328i | ||||
\(449\) | −73.1562 | −0.00768921 | −0.00384461 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384461 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(450\) | 8827.16 | + | 3785.14i | 0.924703 | + | 0.396518i | ||||
\(451\) | 1978.33 | + | 3426.57i | 0.206554 | + | 0.357762i | ||||
\(452\) | −3652.92 | − | 3838.61i | −0.380130 | − | 0.399454i | ||||
\(453\) | −3607.28 | − | 2082.67i | −0.374139 | − | 0.216009i | ||||
\(454\) | −660.948 | − | 5551.07i | −0.0683256 | − | 0.573843i | ||||
\(455\) | 484.180 | + | 8465.29i | 0.0498873 | + | 0.872217i | ||||
\(456\) | −1627.84 | − | 4384.13i | −0.167173 | − | 0.450231i | ||||
\(457\) | 6586.17 | − | 11407.6i | 0.674153 | − | 1.16767i | −0.302563 | − | 0.953129i | \(-0.597842\pi\) |
0.976716 | − | 0.214538i | \(-0.0688245\pi\) | |||||||
\(458\) | −4376.75 | − | 5852.65i | −0.446533 | − | 0.597110i | ||||
\(459\) | −5924.14 | + | 3420.30i | −0.602429 | + | 0.347813i | ||||
\(460\) | 3098.74 | − | 10515.1i | 0.314085 | − | 1.06580i | ||||
\(461\) | − | 12655.0i | − | 1.27853i | −0.768985 | − | 0.639267i | \(-0.779238\pi\) | ||
0.768985 | − | 0.639267i | \(-0.220762\pi\) | |||||||
\(462\) | −6771.74 | − | 2456.21i | −0.681926 | − | 0.247344i | ||||
\(463\) | 852.596i | 0.0855799i | 0.999084 | + | 0.0427899i | \(0.0136246\pi\) | ||||
−0.999084 | + | 0.0427899i | \(0.986375\pi\) | |||||||
\(464\) | −91.4813 | + | 1844.21i | −0.00915283 | + | 0.184516i | ||||
\(465\) | −1233.94 | + | 712.414i | −0.123059 | + | 0.0710482i | ||||
\(466\) | 7811.07 | − | 5841.31i | 0.776483 | − | 0.580673i | ||||
\(467\) | 5462.60 | − | 9461.49i | 0.541282 | − | 0.937528i | −0.457549 | − | 0.889185i | \(-0.651272\pi\) |
0.998831 | − | 0.0483436i | \(-0.0153942\pi\) | |||||||
\(468\) | −738.635 | − | 3057.80i | −0.0729560 | − | 0.302023i | ||||
\(469\) | −7002.56 | + | 13907.0i | −0.689442 | + | 1.36923i | ||||
\(470\) | 9296.96 | − | 1106.96i | 0.912419 | − | 0.108639i | ||||
\(471\) | −7359.36 | − | 4248.93i | −0.719961 | − | 0.415669i | ||||
\(472\) | −8273.77 | + | 9990.67i | −0.806846 | + | 0.974275i | ||||
\(473\) | 4026.42 | + | 6973.96i | 0.391406 | + | 0.677935i | ||||
\(474\) | −1213.32 | + | 2829.54i | −0.117573 | + | 0.274188i | ||||
\(475\) | −13266.1 | −1.28145 | ||||||||
\(476\) | −6775.77 | + | 2052.65i | −0.652451 | + | 0.197653i | ||||
\(477\) | −6921.93 | −0.664431 | ||||||||
\(478\) | −4066.32 | + | 9482.88i | −0.389098 | + | 0.907399i | ||||
\(479\) | 5330.56 | + | 9232.81i | 0.508475 | + | 0.880705i | 0.999952 | + | 0.00981425i | \(0.00312402\pi\) |
−0.491477 | + | 0.870891i | \(0.663543\pi\) | |||||||
\(480\) | 10017.3 | + | 4896.55i | 0.952554 | + | 0.465616i | ||||
\(481\) | −2233.01 | − | 1289.23i | −0.211677 | − | 0.122212i | ||||
\(482\) | −7116.89 | + | 847.384i | −0.672542 | + | 0.0800774i | ||||
\(483\) | 2525.67 | + | 3848.84i | 0.237934 | + | 0.362585i | ||||
\(484\) | 2810.47 | − | 678.892i | 0.263944 | − | 0.0637577i | ||||
\(485\) | 10285.4 | − | 17814.8i | 0.962960 | − | 1.66789i | ||||
\(486\) | 8367.36 | − | 6257.32i | 0.780969 | − | 0.584028i | ||||
\(487\) | 46.9282 | − | 27.0940i | 0.00436657 | − | 0.00252104i | −0.497815 | − | 0.867283i | \(-0.665864\pi\) |
0.502182 | + | 0.864762i | \(0.332531\pi\) | |||||||
\(488\) | −1610.48 | + | 9491.68i | −0.149392 | + | 0.880467i | ||||
\(489\) | 2460.36i | 0.227528i | ||||||||
\(490\) | −17394.9 | + | 4123.87i | −1.60372 | + | 0.380199i | ||||
\(491\) | − | 5628.07i | − | 0.517294i | −0.965972 | − | 0.258647i | \(-0.916723\pi\) | ||
0.965972 | − | 0.258647i | \(-0.0832766\pi\) | |||||||
\(492\) | 2467.04 | + | 727.020i | 0.226062 | + | 0.0666191i | ||||
\(493\) | −1193.94 | + | 689.322i | −0.109072 | + | 0.0629727i | ||||
\(494\) | 2602.17 | + | 3479.65i | 0.236998 | + | 0.316917i | ||||
\(495\) | 5998.81 | − | 10390.3i | 0.544700 | − | 0.943449i | ||||
\(496\) | 1317.20 | − | 675.793i | 0.119242 | − | 0.0611774i | ||||
\(497\) | −11980.1 | − | 18256.3i | −1.08125 | − | 1.64770i | ||||
\(498\) | −567.690 | − | 4767.83i | −0.0510819 | − | 0.429019i | ||||
\(499\) | −536.728 | − | 309.880i | −0.0481508 | − | 0.0277999i | 0.475731 | − | 0.879591i | \(-0.342183\pi\) |
−0.523882 | + | 0.851791i | \(0.675517\pi\) | |||||||
\(500\) | 9563.84 | − | 9101.19i | 0.855416 | − | 0.814035i | ||||
\(501\) | −5199.23 | − | 9005.33i | −0.463641 | − | 0.803050i | ||||
\(502\) | 14708.7 | + | 6307.16i | 1.30773 | + | 0.560762i | ||||
\(503\) | −18680.1 | −1.65587 | −0.827935 | − | 0.560823i | \(-0.810485\pi\) | ||||
−0.827935 | + | 0.560823i | \(0.810485\pi\) | |||||||
\(504\) | 6075.62 | − | 2659.89i | 0.536963 | − | 0.235081i | ||||
\(505\) | 73.0000 | 0.00643259 | ||||||||
\(506\) | −7952.37 | − | 3410.02i | −0.698668 | − | 0.299593i | ||||
\(507\) | 2640.21 | + | 4572.98i | 0.231274 | + | 0.400579i | ||||
\(508\) | −8670.00 | + | 8250.59i | −0.757223 | + | 0.720592i | ||||
\(509\) | 3084.16 | + | 1780.64i | 0.268572 | + | 0.155060i | 0.628238 | − | 0.778021i | \(-0.283776\pi\) |
−0.359667 | + | 0.933081i | \(0.617110\pi\) | |||||||
\(510\) | 984.275 | + | 8266.58i | 0.0854596 | + | 0.717746i | ||||
\(511\) | 6888.03 | − | 13679.6i | 0.596298 | − | 1.18424i | ||||
\(512\) | −10143.5 | − | 5597.09i | −0.875553 | − | 0.483123i | ||||
\(513\) | −4425.65 | + | 7665.44i | −0.380891 | + | 0.659722i | ||||
\(514\) | 8466.96 | + | 11322.1i | 0.726579 | + | 0.971590i | ||||
\(515\) | 5726.05 | − | 3305.93i | 0.489941 | − | 0.282868i | ||||
\(516\) | 5021.07 | + | 1479.68i | 0.428372 | + | 0.126239i | ||||
\(517\) | − | 7390.09i | − | 0.628657i | ||||||
\(518\) | 1853.66 | − | 5110.54i | 0.157230 | − | 0.433483i | ||||
\(519\) | 10496.7i | 0.887771i | ||||||||
\(520\) | −10213.5 | − | 1732.96i | −0.861333 | − | 0.146145i | ||||
\(521\) | 10004.0 | − | 5775.82i | 0.841235 | − | 0.485687i | −0.0164486 | − | 0.999865i | \(-0.505236\pi\) |
0.857684 | + | 0.514177i | \(0.171903\pi\) | |||||||
\(522\) | 1034.28 | − | 773.462i | 0.0867228 | − | 0.0648534i | ||||
\(523\) | −2135.62 | + | 3699.00i | −0.178554 | + | 0.309265i | −0.941386 | − | 0.337332i | \(-0.890475\pi\) |
0.762831 | + | 0.646598i | \(0.223809\pi\) | |||||||
\(524\) | 15316.2 | − | 3699.74i | 1.27689 | − | 0.308443i | ||||
\(525\) | 758.474 | + | 13261.0i | 0.0630524 | + | 1.10239i | ||||
\(526\) | −5341.33 | + | 635.974i | −0.442762 | + | 0.0527182i | ||||
\(527\) | 957.260 | + | 552.674i | 0.0791250 | + | 0.0456829i | ||||
\(528\) | 4772.66 | − | 7394.43i | 0.393377 | − | 0.609472i | ||||
\(529\) | −3318.65 | − | 5748.06i | −0.272758 | − | 0.472431i | ||||
\(530\) | −8983.62 | + | 20950.3i | −0.736271 | + | 1.71702i | ||||
\(531\) | 9073.03 | 0.741499 | ||||||||
\(532\) | −6264.79 | + | 6683.85i | −0.510551 | + | 0.544703i | ||||
\(533\) | −2389.59 | −0.194192 | ||||||||
\(534\) | 760.785 | − | 1774.19i | 0.0616524 | − | 0.143777i | ||||
\(535\) | −8548.04 | − | 14805.6i | −0.690774 | − | 1.19646i | ||||
\(536\) | −14651.6 | − | 12133.7i | −1.18069 | − | 0.977791i | ||||
\(537\) | 691.070 | + | 398.990i | 0.0555342 | + | 0.0320627i | ||||
\(538\) | 22624.4 | − | 2693.81i | 1.81302 | − | 0.215870i | ||||
\(539\) | 1608.88 | + | 14018.6i | 0.128570 | + | 1.12027i | ||||
\(540\) | −4955.18 | − | 20513.5i | −0.394884 | − | 1.63474i | ||||
\(541\) | −4878.48 | + | 8449.78i | −0.387694 | + | 0.671505i | −0.992139 | − | 0.125142i | \(-0.960061\pi\) |
0.604445 | + | 0.796647i | \(0.293395\pi\) | |||||||
\(542\) | −9916.82 | + | 7416.04i | −0.785911 | + | 0.587724i | ||||
\(543\) | 5636.51 | − | 3254.24i | 0.445462 | − | 0.257188i | ||||
\(544\) | −595.896 | − | 8629.38i | −0.0469647 | − | 0.680113i | ||||
\(545\) | 21901.3i | 1.72138i | ||||||||
\(546\) | 3329.53 | − | 2800.11i | 0.260972 | − | 0.219475i | ||||
\(547\) | 19891.0i | 1.55480i | 0.629005 | + | 0.777401i | \(0.283463\pi\) | ||||
−0.629005 | + | 0.777401i | \(0.716537\pi\) | |||||||
\(548\) | −4056.00 | + | 13763.5i | −0.316175 | + | 1.07289i | ||||
\(549\) | 5831.60 | − | 3366.87i | 0.453345 | − | 0.261739i | ||||
\(550\) | −14951.5 | − | 19993.3i | −1.15915 | − | 1.55003i | ||||
\(551\) | −891.938 | + | 1544.88i | −0.0689616 | + | 0.119445i | ||||
\(552\) | −5272.72 | + | 1957.78i | −0.406561 | + | 0.150958i | ||||
\(553\) | 6020.98 | − | 344.376i | 0.462998 | − | 0.0264816i | ||||
\(554\) | 1071.62 | + | 9000.17i | 0.0821819 | + | 0.690218i | ||||
\(555\) | −5535.98 | − | 3196.20i | −0.423404 | − | 0.244453i | ||||
\(556\) | −1689.83 | − | 1775.73i | −0.128893 | − | 0.135446i | ||||
\(557\) | −3043.39 | − | 5271.30i | −0.231513 | − | 0.400992i | 0.726741 | − | 0.686912i | \(-0.241034\pi\) |
−0.958253 | + | 0.285920i | \(0.907701\pi\) | |||||||
\(558\) | −951.677 | − | 408.085i | −0.0722002 | − | 0.0309599i | ||||
\(559\) | −4863.44 | −0.367981 | ||||||||
\(560\) | −165.336 | − | 21840.9i | −0.0124763 | − | 1.64812i | ||||
\(561\) | 6571.05 | 0.494527 | ||||||||
\(562\) | 16268.6 | + | 6976.08i | 1.22108 | + | 0.523609i | ||||
\(563\) | −4067.94 | − | 7045.87i | −0.304517 | − | 0.527439i | 0.672637 | − | 0.739973i | \(-0.265162\pi\) |
−0.977154 | + | 0.212534i | \(0.931828\pi\) | |||||||
\(564\) | −3311.55 | − | 3479.89i | −0.247237 | − | 0.259805i | ||||
\(565\) | 10570.3 | + | 6102.75i | 0.787070 | + | 0.454415i | ||||
\(566\) | 2026.10 | + | 17016.5i | 0.150465 | + | 1.26371i | ||||
\(567\) | 847.008 | + | 426.491i | 0.0627354 | + | 0.0315890i | ||||
\(568\) | 25010.2 | − | 9286.39i | 1.84755 | − | 0.686000i | ||||
\(569\) | −11495.9 | + | 19911.5i | −0.846985 | + | 1.46702i | 0.0369008 | + | 0.999319i | \(0.488251\pi\) |
−0.883886 | + | 0.467702i | \(0.845082\pi\) | |||||||
\(570\) | 6451.17 | + | 8626.58i | 0.474052 | + | 0.633908i | ||||
\(571\) | 16493.6 | − | 9522.59i | 1.20882 | − | 0.697912i | 0.246318 | − | 0.969189i | \(-0.420779\pi\) |
0.962501 | + | 0.271277i | \(0.0874459\pi\) | |||||||
\(572\) | −2311.41 | + | 7843.45i | −0.168960 | + | 0.573341i | ||||
\(573\) | − | 1518.41i | − | 0.110702i | ||||||
\(574\) | −880.363 | − | 4960.60i | −0.0640168 | − | 0.360717i | ||||
\(575\) | 15954.9i | 1.15716i | ||||||||
\(576\) | 1510.09 | + | 7961.23i | 0.109237 | + | 0.575899i | ||||
\(577\) | 13902.1 | − | 8026.36i | 1.00303 | − | 0.579102i | 0.0938892 | − | 0.995583i | \(-0.470070\pi\) |
0.909144 | + | 0.416481i | \(0.136737\pi\) | |||||||
\(578\) | −5956.40 | + | 4454.35i | −0.428640 | + | 0.320547i | ||||
\(579\) | 5365.27 | − | 9292.92i | 0.385100 | − | 0.667013i | ||||
\(580\) | −998.660 | − | 4134.25i | −0.0714950 | − | 0.295975i | ||||
\(581\) | −7863.64 | + | 5160.25i | −0.561513 | + | 0.368473i | ||||
\(582\) | −10480.4 | + | 1247.86i | −0.746435 | + | 0.0888755i | ||||
\(583\) | 15582.1 | + | 8996.32i | 1.10694 | + | 0.639090i | ||||
\(584\) | 14411.9 | + | 11935.2i | 1.02118 | + | 0.845691i | ||||
\(585\) | 3622.93 | + | 6275.10i | 0.256051 | + | 0.443493i | ||||
\(586\) | 510.130 | − | 1189.65i | 0.0359612 | − | 0.0838635i | ||||
\(587\) | −21155.6 | −1.48754 | −0.743770 | − | 0.668436i | \(-0.766964\pi\) | ||||
−0.743770 | + | 0.668436i | \(0.766964\pi\) | |||||||
\(588\) | 7039.45 | + | 5880.23i | 0.493711 | + | 0.412409i | ||||
\(589\) | 1430.25 | 0.100055 | ||||||||
\(590\) | 11775.4 | − | 27460.9i | 0.821672 | − | 1.91618i | ||||
\(591\) | −6975.36 | − | 12081.7i | −0.485495 | − | 0.840903i | ||||
\(592\) | 5580.47 | + | 3601.86i | 0.387426 | + | 0.250060i | ||||
\(593\) | −1240.18 | − | 716.018i | −0.0858821 | − | 0.0495840i | 0.456444 | − | 0.889752i | \(-0.349123\pi\) |
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(594\) | −16540.5 | + | 1969.42i | −1.14253 | + | 0.136038i | ||||
\(595\) | 13634.2 | − | 8946.96i | 0.939406 | − | 0.616453i | ||||
\(596\) | 11119.0 | − | 2685.89i | 0.764184 | − | 0.184595i | ||||
\(597\) | 8822.32 | − | 15280.7i | 0.604813 | − | 1.04757i | ||||
\(598\) | 4184.92 | − | 3129.59i | 0.286177 | − | 0.214010i | ||||
\(599\) | −4611.09 | + | 2662.21i | −0.314531 | + | 0.181595i | −0.648952 | − | 0.760829i | \(-0.724793\pi\) |
0.334421 | + | 0.942424i | \(0.391459\pi\) | |||||||
\(600\) | −15999.6 | − | 2714.70i | −1.08863 | − | 0.184712i | ||||
\(601\) | 8711.39i | 0.591256i | 0.955303 | + | 0.295628i | \(0.0955289\pi\) | ||||
−0.955303 | + | 0.295628i | \(0.904471\pi\) | |||||||
\(602\) | −1791.77 | − | 10096.1i | −0.121307 | − | 0.683533i | ||||
\(603\) | 13305.8i | 0.898599i | ||||||||
\(604\) | −9562.29 | − | 2817.94i | −0.644179 | − | 0.189835i | ||||
\(605\) | −5767.55 | + | 3329.90i | −0.387577 | + | 0.223768i | ||||
\(606\) | −22.4310 | − | 29.9950i | −0.00150363 | − | 0.00201067i | ||||
\(607\) | −12379.6 | + | 21442.1i | −0.827796 | + | 1.43378i | 0.0719681 | + | 0.997407i | \(0.477072\pi\) |
−0.899764 | + | 0.436377i | \(0.856261\pi\) | |||||||
\(608\) | −6250.67 | − | 9284.38i | −0.416938 | − | 0.619295i | ||||
\(609\) | 1595.28 | + | 803.266i | 0.106148 | + | 0.0534483i | ||||
\(610\) | −2621.84 | − | 22019.9i | −0.174025 | − | 1.46157i | ||||
\(611\) | 3865.22 | + | 2231.59i | 0.255925 | + | 0.147758i | ||||
\(612\) | −4382.77 | + | 4170.75i | −0.289482 | + | 0.275478i | ||||
\(613\) | −3167.74 | − | 5486.69i | −0.208717 | − | 0.361509i | 0.742593 | − | 0.669743i | \(-0.233596\pi\) |
−0.951311 | + | 0.308233i | \(0.900262\pi\) | |||||||
\(614\) | −10906.6 | − | 4676.81i | −0.716862 | − | 0.307395i | ||||
\(615\) | −5924.15 | −0.388431 | ||||||||
\(616\) | −17133.9 | − | 1908.66i | −1.12069 | − | 0.124841i | ||||
\(617\) | 12720.7 | 0.830013 | 0.415006 | − | 0.909819i | \(-0.363779\pi\) | ||||
0.415006 | + | 0.909819i | \(0.363779\pi\) | |||||||
\(618\) | −3117.84 | − | 1336.95i | −0.202942 | − | 0.0870226i | ||||
\(619\) | −11135.8 | − | 19287.7i | −0.723077 | − | 1.25241i | −0.959761 | − | 0.280820i | \(-0.909394\pi\) |
0.236683 | − | 0.971587i | \(-0.423940\pi\) | |||||||
\(620\) | −2470.26 | + | 2350.77i | −0.160013 | + | 0.152273i | ||||
\(621\) | 9219.10 | + | 5322.65i | 0.595733 | + | 0.343946i | ||||
\(622\) | 2176.47 | + | 18279.4i | 0.140303 | + | 1.17836i | ||||
\(623\) | −3775.31 | + | 215.932i | −0.242784 | + | 0.0138863i | ||||
\(624\) | 2426.29 | + | 4729.13i | 0.155656 | + | 0.303392i | ||||
\(625\) | −1795.08 | + | 3109.16i | −0.114885 | + | 0.198987i | ||||
\(626\) | −14633.6 | − | 19568.2i | −0.934308 | − | 1.24937i | ||||
\(627\) | 7363.39 | − | 4251.25i | 0.469004 | − | 0.270779i | ||||
\(628\) | −19508.4 | − | 5749.00i | −1.23960 | − | 0.365303i | ||||
\(629\) | 4959.08i | 0.314358i | ||||||||
\(630\) | −11691.9 | + | 9832.76i | −0.739388 | + | 0.621820i | ||||
\(631\) | − | 7895.30i | − | 0.498110i | −0.968489 | − | 0.249055i | \(-0.919880\pi\) | ||
0.968489 | − | 0.249055i | \(-0.0801199\pi\) | |||||||
\(632\) | −1232.58 | + | 7264.42i | −0.0775780 | + | 0.457220i | ||||
\(633\) | −2523.10 | + | 1456.71i | −0.158427 | + | 0.0914676i | ||||
\(634\) | −2098.23 | + | 1569.11i | −0.131438 | + | 0.0982924i | ||||
\(635\) | 13783.8 | − | 23874.3i | 0.861410 | − | 1.49201i | ||||
\(636\) | 11368.7 | − | 2746.20i | 0.708803 | − | 0.171217i | ||||
\(637\) | −7817.98 | − | 3391.72i | −0.486279 | − | 0.210965i | ||||
\(638\) | −3333.54 | + | 396.914i | −0.206859 | + | 0.0246301i | ||||
\(639\) | −16160.1 | − | 9330.05i | −1.00045 | − | 0.577607i | ||||
\(640\) | 26055.8 | + | 5761.95i | 1.60929 | + | 0.355876i | ||||
\(641\) | −4213.92 | − | 7298.73i | −0.259657 | − | 0.449739i | 0.706493 | − | 0.707720i | \(-0.250276\pi\) |
−0.966150 | + | 0.257981i | \(0.916943\pi\) | |||||||
\(642\) | −3456.90 | + | 8061.69i | −0.212513 | + | 0.495591i | ||||
\(643\) | 12838.8 | 0.787424 | 0.393712 | − | 0.919234i | \(-0.371191\pi\) | ||||
0.393712 | + | 0.919234i | \(0.371191\pi\) | |||||||
\(644\) | 8038.56 | + | 7534.57i | 0.491869 | + | 0.461030i | ||||
\(645\) | −12057.2 | −0.736049 | ||||||||
\(646\) | 3293.37 | − | 7680.32i | 0.200582 | − | 0.467768i | ||||
\(647\) | 11376.3 | + | 19704.4i | 0.691267 | + | 1.19731i | 0.971423 | + | 0.237355i | \(0.0762805\pi\) |
−0.280156 | + | 0.959955i | \(0.590386\pi\) | |||||||
\(648\) | −739.003 | + | 892.354i | −0.0448006 | + | 0.0540972i | ||||
\(649\) | −20424.5 | − | 11792.1i | −1.23533 | − | 0.713219i | ||||
\(650\) | 14972.0 | − | 1782.66i | 0.903460 | − | 0.107572i | ||||
\(651\) | −81.7728 | − | 1429.70i | −0.00492309 | − | 0.0860740i | ||||
\(652\) | 1382.61 | + | 5723.74i | 0.0830480 | + | 0.343802i | ||||
\(653\) | −430.103 | + | 744.961i | −0.0257753 | + | 0.0446441i | −0.878625 | − | 0.477512i | \(-0.841539\pi\) |
0.852850 | + | 0.522156i | \(0.174872\pi\) | |||||||
\(654\) | 8999.04 | − | 6729.70i | 0.538058 | − | 0.402373i | ||||
\(655\) | −31431.3 | + | 18146.9i | −1.87500 | + | 1.08253i | ||||
\(656\) | 6147.83 | + | 304.960i | 0.365903 | + | 0.0181504i | ||||
\(657\) | − | 13088.2i | − | 0.777199i | ||||||
\(658\) | −3208.59 | + | 8846.05i | −0.190097 | + | 0.524096i | ||||
\(659\) | − | 19262.8i | − | 1.13865i | −0.822111 | − | 0.569327i | \(-0.807204\pi\) | ||
0.822111 | − | 0.569327i | \(-0.192796\pi\) | |||||||
\(660\) | −5730.34 | + | 19445.1i | −0.337959 | + | 1.14682i | ||||
\(661\) | 3499.64 | − | 2020.52i | 0.205931 | − | 0.118894i | −0.393488 | − | 0.919330i | \(-0.628732\pi\) |
0.599419 | + | 0.800436i | \(0.295398\pi\) | |||||||
\(662\) | 16157.5 | + | 21606.1i | 0.948611 | + | 1.26849i | ||||
\(663\) | −1984.26 | + | 3436.84i | −0.116233 | + | 0.201321i | ||||
\(664\) | −3999.98 | − | 10772.8i | −0.233779 | − | 0.629616i | ||||
\(665\) | 9489.80 | − | 18846.7i | 0.553381 | − | 1.09901i | ||||
\(666\) | −549.259 | − | 4613.04i | −0.0319570 | − | 0.268396i | ||||
\(667\) | 1858.00 | + | 1072.72i | 0.107859 | + | 0.0622727i | ||||
\(668\) | −17156.0 | − | 18028.1i | −0.993691 | − | 1.04420i | ||||
\(669\) | −3226.03 | − | 5587.64i | −0.186435 | − | 0.322916i | ||||
\(670\) | 40272.2 | + | 17269.0i | 2.32216 | + | 0.995758i | ||||
\(671\) | −17503.5 | −1.00703 | ||||||||
\(672\) | −8923.42 | + | 6779.08i | −0.512245 | + | 0.389150i | ||||
\(673\) | −30094.8 | −1.72373 | −0.861863 | − | 0.507141i | \(-0.830702\pi\) | ||||
−0.861863 | + | 0.507141i | \(0.830702\pi\) | |||||||
\(674\) | 12312.1 | + | 5279.51i | 0.703628 | + | 0.301720i | ||||
\(675\) | 15357.5 | + | 26599.9i | 0.875718 | + | 1.51679i | ||||
\(676\) | 8711.97 | + | 9154.83i | 0.495674 | + | 0.520871i | ||||
\(677\) | 16898.8 | + | 9756.55i | 0.959343 | + | 0.553877i | 0.895971 | − | 0.444113i | \(-0.146481\pi\) |
0.0633724 | + | 0.997990i | \(0.479814\pi\) | |||||||
\(678\) | −740.408 | − | 6218.43i | −0.0419398 | − | 0.352238i | ||||
\(679\) | 11342.9 | + | 17285.4i | 0.641093 | + | 0.976955i | ||||
\(680\) | 6935.26 | + | 18678.1i | 0.391110 | + | 1.05334i | ||||
\(681\) | 3303.34 | − | 5721.55i | 0.185880 | − | 0.321953i | ||||
\(682\) | 1611.96 | + | 2155.53i | 0.0905058 | + | 0.121025i | ||||
\(683\) | 19594.6 | − | 11312.9i | 1.09775 | − | 0.633788i | 0.162123 | − | 0.986771i | \(-0.448166\pi\) |
0.935630 | + | 0.352982i | \(0.114832\pi\) | |||||||
\(684\) | −2212.90 | + | 7509.17i | −0.123702 | + | 0.419766i | ||||
\(685\) | − | 33050.5i | − | 1.84350i | ||||||
\(686\) | 4160.68 | − | 17479.1i | 0.231568 | − | 0.972819i | ||||
\(687\) | − | 8636.90i | − | 0.479648i | ||||||
\(688\) | 12512.4 | + | 620.673i | 0.693361 | + | 0.0343938i | ||||
\(689\) | −9410.66 | + | 5433.24i | −0.520345 | + | 0.300421i | ||||
\(690\) | 10375.0 | − | 7758.71i | 0.572422 | − | 0.428071i | ||||
\(691\) | 102.478 | − | 177.498i | 0.00564177 | − | 0.00977182i | −0.863191 | − | 0.504878i | \(-0.831537\pi\) |
0.868833 | + | 0.495106i | \(0.164871\pi\) | |||||||
\(692\) | 5898.67 | + | 24419.3i | 0.324037 | + | 1.34145i | ||||
\(693\) | 6615.62 | + | 10081.5i | 0.362636 | + | 0.552617i | ||||
\(694\) | −5495.06 | + | 654.279i | −0.300562 | + | 0.0357869i | ||||
\(695\) | 4889.78 | + | 2823.11i | 0.266877 | + | 0.154082i | ||||
\(696\) | −1391.86 | + | 1680.69i | −0.0758022 | + | 0.0915320i | ||||
\(697\) | 2297.91 | + | 3980.10i | 0.124877 | + | 0.216294i | ||||
\(698\) | 10856.5 | − | 25318.0i | 0.588717 | − | 1.37292i | ||||
\(699\) | 11527.0 | 0.623736 | ||||||||
\(700\) | 9216.58 | + | 30423.9i | 0.497649 | + | 1.64273i | ||||
\(701\) | 9946.71 | 0.535923 | 0.267962 | − | 0.963430i | \(-0.413650\pi\) | ||||
0.267962 | + | 0.963430i | \(0.413650\pi\) | |||||||
\(702\) | 3964.67 | − | 9245.84i | 0.213158 | − | 0.497097i | ||||
\(703\) | 3208.36 | + | 5557.04i | 0.172127 | + | 0.298133i | ||||
\(704\) | 6947.69 | − | 19884.3i | 0.371947 | − | 1.06451i | ||||
\(705\) | 9582.47 | + | 5532.44i | 0.511910 | + | 0.295552i | ||||
\(706\) | −8399.85 | + | 1000.14i | −0.447780 | + | 0.0533157i | ||||
\(707\) | −32.9964 | + | 65.5307i | −0.00175525 | + | 0.00348590i | ||||
\(708\) | −14901.7 | + | 3599.62i | −0.791018 | + | 0.191076i | ||||
\(709\) | −14432.4 | + | 24997.6i | −0.764484 | + | 1.32412i | 0.176035 | + | 0.984384i | \(0.443673\pi\) |
−0.940519 | + | 0.339741i | \(0.889661\pi\) | |||||||
\(710\) | −49212.2 | + | 36802.1i | −2.60127 | + | 1.94529i | ||||
\(711\) | 4463.19 | − | 2576.82i | 0.235419 | − | 0.135919i | ||||
\(712\) | 772.858 | − | 4554.98i | 0.0406799 | − | 0.239754i | ||||
\(713\) | − | 1720.14i | − | 0.0903501i | ||||||
\(714\) | −7865.65 | − | 2852.98i | −0.412275 | − | 0.149538i | ||||
\(715\) | − | 18834.6i | − | 0.985141i | ||||||
\(716\) | 1831.91 | + | 539.852i | 0.0956168 | + | 0.0281777i | ||||
\(717\) | −10560.2 | + | 6096.94i | −0.550039 | + | 0.317565i | ||||
\(718\) | 2238.08 | + | 2992.78i | 0.116329 | + | 0.155557i | ||||
\(719\) | 3063.07 | − | 5305.39i | 0.158878 | − | 0.275185i | −0.775586 | − | 0.631241i | \(-0.782546\pi\) |
0.934464 | + | 0.356057i | \(0.115879\pi\) | |||||||
\(720\) | −8520.09 | − | 16606.7i | −0.441007 | − | 0.859574i | ||||
\(721\) | 379.464 | + | 6634.46i | 0.0196005 | + | 0.342691i | ||||
\(722\) | 1015.28 | + | 8527.00i | 0.0523336 | + | 0.439532i | ||||
\(723\) | −7335.45 | − | 4235.12i | −0.377328 | − | 0.217851i | ||||
\(724\) | 11283.9 | − | 10738.1i | 0.579233 | − | 0.551213i | ||||
\(725\) | 3095.12 | + | 5360.91i | 0.158552 | + | 0.274620i | ||||
\(726\) | 3140.44 | + | 1346.64i | 0.160541 | + | 0.0688409i | ||||
\(727\) | 20742.9 | 1.05820 | 0.529101 | − | 0.848559i | \(-0.322529\pi\) | ||||
0.529101 | + | 0.848559i | \(0.322529\pi\) | |||||||
\(728\) | 6172.22 | − | 8385.17i | 0.314228 | − | 0.426889i | ||||
\(729\) | 13730.5 | 0.697579 | ||||||||
\(730\) | −39613.5 | − | 16986.5i | −2.00844 | − | 0.861231i | ||||
\(731\) | 4676.85 | + | 8100.54i | 0.236634 | + | 0.409862i | ||||
\(732\) | −8242.15 | + | 7843.43i | −0.416173 | + | 0.396040i | ||||
\(733\) | −15694.9 | − | 9061.44i | −0.790864 | − | 0.456606i | 0.0494026 | − | 0.998779i | \(-0.484268\pi\) |
−0.840267 | + | 0.542173i | \(0.817602\pi\) | |||||||
\(734\) | −2252.42 | − | 18917.3i | −0.113268 | − | 0.951296i | ||||
\(735\) | −19381.9 | − | 8408.59i | −0.972672 | − | 0.421980i | ||||
\(736\) | −11166.2 | + | 7517.58i | −0.559227 | + | 0.376497i | ||||
\(737\) | 17293.4 | − | 29953.0i | 0.864328 | − | 1.49706i | ||||
\(738\) | −2578.40 | − | 3447.86i | −0.128607 | − | 0.171975i | ||||
\(739\) | −32754.4 | + | 18910.8i | −1.63043 | + | 0.941332i | −0.646476 | + | 0.762934i | \(0.723758\pi\) |
−0.983958 | + | 0.178398i | \(0.942909\pi\) | |||||||
\(740\) | −14674.9 | − | 4324.61i | −0.729002 | − | 0.214832i | ||||
\(741\) | 5135.01i | 0.254574i | ||||||||
\(742\) | −14746.0 | − | 17534.1i | −0.729573 | − | 0.867515i | ||||
\(743\) | 4974.35i | 0.245614i | 0.992431 | + | 0.122807i | \(0.0391896\pi\) | ||||
−0.992431 | + | 0.122807i | \(0.960810\pi\) | |||||||
\(744\) | 1724.95 | + | 292.679i | 0.0849999 | + | 0.0144222i | ||||
\(745\) | −22818.1 | + | 13174.0i | −1.12213 | + | 0.647865i | ||||
\(746\) | −474.504 | + | 354.846i | −0.0232880 | + | 0.0174153i | ||||
\(747\) | −4018.78 | + | 6960.73i | −0.196840 | + | 0.340937i | ||||
\(748\) | 15286.8 | − | 3692.64i | 0.747246 | − | 0.180503i | ||||
\(749\) | 17154.5 | − | 981.168i | 0.836865 | − | 0.0478653i | ||||
\(750\) | 15493.1 | − | 1844.72i | 0.754306 | − | 0.0898127i | ||||
\(751\) | −19034.7 | − | 10989.7i | −0.924884 | − | 0.533982i | −0.0396939 | − | 0.999212i | \(-0.512638\pi\) |
−0.885190 | + | 0.465230i | \(0.845972\pi\) | |||||||
\(752\) | −9659.49 | − | 6234.61i | −0.468411 | − | 0.302331i | ||||
\(753\) | 9456.81 | + | 16379.7i | 0.457670 | + | 0.792707i | ||||
\(754\) | 799.035 | − | 1863.39i | 0.0385930 | − | 0.0900011i | ||||
\(755\) | 22962.1 | 1.10686 | ||||||||
\(756\) | 20654.3 | + | 4824.03i | 0.993637 | + | 0.232075i | ||||
\(757\) | −10241.5 | −0.491722 | −0.245861 | − | 0.969305i | \(-0.579071\pi\) | ||||
−0.245861 | + | 0.969305i | \(0.579071\pi\) | |||||||
\(758\) | 1344.30 | − | 3134.99i | 0.0644159 | − | 0.150221i | ||||
\(759\) | −5112.91 | − | 8855.83i | −0.244515 | − | 0.423513i | ||||
\(760\) | 19855.6 | + | 16443.4i | 0.947684 | + | 0.784824i | ||||
\(761\) | −18578.2 | − | 10726.2i | −0.884968 | − | 0.510937i | −0.0126751 | − | 0.999920i | \(-0.504035\pi\) |
−0.872293 | + | 0.488983i | \(0.837368\pi\) | |||||||
\(762\) | −14045.1 | + | 1672.31i | −0.667719 | + | 0.0795031i | ||||
\(763\) | −19660.4 | − | 9899.53i | −0.932836 | − | 0.469708i | ||||
\(764\) | −853.278 | − | 3532.39i | −0.0404064 | − | 0.167274i | ||||
\(765\) | 6967.86 | − | 12068.7i | 0.329312 | − | 0.570385i | ||||
\(766\) | 7205.05 | − | 5388.12i | 0.339855 | − | 0.254152i | ||||
\(767\) | 12335.2 | − | 7121.71i | 0.580700 | − | 0.335267i | ||||
\(768\) | −5638.73 | − | 12476.6i | −0.264935 | − | 0.586210i | ||||
\(769\) | 26466.5i | 1.24110i | 0.784166 | + | 0.620551i | \(0.213091\pi\) | ||||
−0.784166 | + | 0.620551i | \(0.786909\pi\) | |||||||
\(770\) | 39099.2 | − | 6938.98i | 1.82992 | − | 0.324758i | ||||
\(771\) | 16708.3i | 0.780462i | ||||||||
\(772\) | 7259.46 | − | 24633.9i | 0.338437 | − | 1.14844i | ||||
\(773\) | 9692.09 | − | 5595.73i | 0.450971 | − | 0.260368i | −0.257269 | − | 0.966340i | \(-0.582823\pi\) |
0.708240 | + | 0.705972i | \(0.249489\pi\) | |||||||
\(774\) | −5247.71 | − | 7017.29i | −0.243701 | − | 0.325880i | ||||
\(775\) | 2481.56 | − | 4298.19i | 0.115020 | − | 0.199220i | ||||
\(776\) | −23680.1 | + | 8792.51i | −1.09545 | + | 0.406743i | ||||
\(777\) | 5371.46 | − | 3524.84i | 0.248005 | − | 0.162745i | ||||
\(778\) | 2679.30 | + | 22502.5i | 0.123467 | + | 1.03696i | ||||
\(779\) | 5149.99 | + | 2973.35i | 0.236864 | + | 0.136754i | ||||
\(780\) | −8439.94 | − | 8868.97i | −0.387434 | − | 0.407128i | ||||
\(781\) | 24252.2 | + | 42006.1i | 1.11116 | + | 1.92458i | ||||
\(782\) | −9237.00 | − | 3960.88i | −0.422397 | − | 0.181126i | ||||
\(783\) | 4130.21 | 0.188508 | ||||||||
\(784\) | 19680.9 | + | 9723.81i | 0.896542 | + | 0.442958i | ||||
\(785\) | 46845.9 | 2.12994 | ||||||||
\(786\) | 17114.4 | + | 7338.75i | 0.776654 | + | 0.333034i | ||||
\(787\) | −15026.0 | − | 26025.7i | −0.680582 | − | 1.17880i | −0.974804 | − | 0.223065i | \(-0.928394\pi\) |
0.294222 | − | 0.955737i | \(-0.404939\pi\) | |||||||
\(788\) | −23016.7 | − | 24186.8i | −1.04053 | − | 1.09342i | ||||
\(789\) | −5505.36 | − | 3178.52i | −0.248411 | − | 0.143420i | ||||
\(790\) | −2006.61 | − | 16852.9i | −0.0903698 | − | 0.758985i | ||||
\(791\) | −10256.1 | + | 6730.24i | −0.461019 | + | 0.302528i | ||||
\(792\) | −13811.1 | + | 5128.11i | −0.619641 | + | 0.230075i | ||||
\(793\) | 5285.53 | − | 9154.81i | 0.236689 | − | 0.409958i | ||||
\(794\) | 20530.6 | + | 27453.7i | 0.917636 | + | 1.22707i | ||||
\(795\) | −23330.4 | + | 13469.8i | −1.04081 | + | 0.600913i | ||||
\(796\) | 11937.0 | − | 40506.5i | 0.531528 | − | 1.80366i | ||||
\(797\) | 26567.8i | 1.18078i | 0.807119 | + | 0.590389i | \(0.201026\pi\) | ||||
−0.807119 | + | 0.590389i | \(0.798974\pi\) | |||||||
\(798\) | −10659.9 | + | 1891.82i | −0.472876 | + | 0.0839219i | ||||
\(799\) | − | 8583.89i | − | 0.380070i | ||||||
\(800\) | −38746.7 | + | 2675.63i | −1.71238 | + | 0.118247i | ||||
\(801\) | −2798.54 | + | 1615.74i | −0.123447 | + | 0.0712724i | ||||
\(802\) | −24903.2 | + | 18623.2i | −1.09646 | + | 0.819960i | ||||
\(803\) | −17010.5 | + | 29463.1i | −0.747557 | + | 1.29481i | ||||
\(804\) | −5278.94 | − | 21853.7i | −0.231560 | − | 0.958609i | ||||
\(805\) | −22666.6 | − | 11413.2i | −0.992412 | − | 0.499706i | ||||
\(806\) | −1614.16 | + | 192.193i | −0.0705415 | + | 0.00839914i | ||||
\(807\) | 23319.1 | + | 13463.3i | 1.01719 | + | 0.587275i | ||||
\(808\) | −69.0390 | − | 57.1746i | −0.00300592 | − | 0.00248935i | ||||
\(809\) | 980.413 | + | 1698.13i | 0.0426075 | + | 0.0737984i | 0.886543 | − | 0.462647i | \(-0.153100\pi\) |
−0.843935 | + | 0.536445i | \(0.819767\pi\) | |||||||
\(810\) | 1051.77 | − | 2452.78i | 0.0456238 | − | 0.106397i | ||||
\(811\) | −2633.82 | −0.114040 | −0.0570198 | − | 0.998373i | \(-0.518160\pi\) | ||||
−0.0570198 | + | 0.998373i | \(0.518160\pi\) | |||||||
\(812\) | 4162.63 | + | 972.228i | 0.179901 | + | 0.0420179i | ||||
\(813\) | −14634.5 | −0.631309 | ||||||||
\(814\) | −4759.04 | + | 11098.4i | −0.204919 | + | 0.477884i | ||||
\(815\) | −6781.58 | − | 11746.0i | −0.291470 | − | 0.504841i | ||||
\(816\) | 5543.63 | − | 8588.93i | 0.237826 | − | 0.368471i | ||||
\(817\) | 10481.6 | + | 6051.53i | 0.448841 | + | 0.259139i | ||||
\(818\) | −5642.23 | + | 671.801i | −0.241169 | + | 0.0287151i | ||||
\(819\) | −7270.61 | + | 415.850i | −0.310202 | + | 0.0177423i | ||||
\(820\) | −13781.8 | + | 3329.11i | −0.586931 | + | 0.141778i | ||||
\(821\) | −5333.16 | + | 9237.30i | −0.226710 | + | 0.392672i | −0.956831 | − | 0.290645i | \(-0.906130\pi\) |
0.730121 | + | 0.683317i | \(0.239463\pi\) | |||||||
\(822\) | −13580.1 | + | 10155.6i | −0.576230 | + | 0.430919i | ||||
\(823\) | 32943.1 | − | 19019.7i | 1.39529 | − | 0.805571i | 0.401395 | − | 0.915905i | \(-0.368525\pi\) |
0.993895 | + | 0.110334i | \(0.0351922\pi\) | |||||||
\(824\) | −8004.60 | − | 1358.17i | −0.338414 | − | 0.0574199i | ||||
\(825\) | − | 29504.6i | − | 1.24512i | ||||||
\(826\) | 19328.6 | + | 22983.1i | 0.814198 | + | 0.968139i | ||||
\(827\) | − | 22277.0i | − | 0.936697i | −0.883544 | − | 0.468349i | \(-0.844849\pi\) | ||
0.883544 | − | 0.468349i | \(-0.155151\pi\) | |||||||
\(828\) | 9031.15 | + | 2661.42i | 0.379051 | + | 0.111704i | ||||
\(829\) | 18752.2 | − | 10826.6i | 0.785633 | − | 0.453585i | −0.0527901 | − | 0.998606i | \(-0.516811\pi\) |
0.838423 | + | 0.545020i | \(0.183478\pi\) | |||||||
\(830\) | 15852.0 | + | 21197.4i | 0.662928 | + | 0.886475i | ||||
\(831\) | −5355.83 | + | 9276.57i | −0.223576 | + | 0.387245i | ||||
\(832\) | 8302.05 | + | 9638.31i | 0.345940 | + | 0.401620i | ||||
\(833\) | 1868.78 | + | 16283.2i | 0.0777304 | + | 0.677287i | ||||
\(834\) | −342.511 | − | 2876.63i | −0.0142208 | − | 0.119436i | ||||
\(835\) | 49643.4 | + | 28661.7i | 2.05746 | + | 1.18788i | ||||
\(836\) | 14741.0 | − | 14027.9i | 0.609844 | − | 0.580343i | ||||
\(837\) | −1655.73 | − | 2867.80i | −0.0683755 | − | 0.118430i | ||||
\(838\) | 17320.1 | + | 7426.97i | 0.713977 | + | 0.306158i | ||||
\(839\) | 47337.4 | 1.94788 | 0.973939 | − | 0.226811i | \(-0.0728299\pi\) | ||||
0.973939 | + | 0.226811i | \(0.0728299\pi\) | |||||||
\(840\) | 15301.9 | − | 20788.1i | 0.628529 | − | 0.853878i | ||||
\(841\) | −23556.6 | −0.965870 | ||||||||
\(842\) | 15232.3 | + | 6531.70i | 0.623443 | + | 0.267336i | ||||
\(843\) | 10459.8 | + | 18116.9i | 0.427347 | + | 0.740187i | ||||
\(844\) | −5051.08 | + | 4806.73i | −0.206002 | + | 0.196036i | ||||
\(845\) | −25209.4 | − | 14554.6i | −1.02631 | − | 0.592538i | ||||
\(846\) | 950.737 | + | 7984.92i | 0.0386371 | + | 0.324500i | ||||
\(847\) | −382.215 | − | 6682.55i | −0.0155054 | − | 0.271092i | ||||
\(848\) | 24904.7 | − | 12777.4i | 1.00853 | − | 0.517428i | ||||
\(849\) | −10126.2 | + | 17539.1i | −0.409341 | + | 0.708999i | ||||
\(850\) | −17366.8 | − | 23223.0i | −0.700794 | − | 0.937110i | ||||
\(851\) | 6683.37 | − | 3858.64i | 0.269216 | − | 0.155432i | ||||
\(852\) | 30243.3 | + | 8912.49i | 1.21610 | + | 0.358377i | ||||
\(853\) | − | 16562.9i | − | 0.664833i | −0.943133 | − | 0.332417i | \(-0.892136\pi\) | ||
0.943133 | − | 0.332417i | \(-0.107864\pi\) | |||||||
\(854\) | 20951.9 | + | 7599.56i | 0.839532 | + | 0.304510i | ||||
\(855\) | − | 18031.9i | − | 0.721261i | ||||||
\(856\) | −3511.76 | + | 20697.2i | −0.140222 | + | 0.826421i | ||||
\(857\) | −28076.8 | + | 16210.2i | −1.11912 | + | 0.646124i | −0.941176 | − | 0.337917i | \(-0.890278\pi\) |
−0.177944 | + | 0.984041i | \(0.556944\pi\) | |||||||
\(858\) | −7738.97 | + | 5787.39i | −0.307930 | + | 0.230278i | ||||
\(859\) | −16065.2 | + | 27825.8i | −0.638112 | + | 1.10524i | 0.347735 | + | 0.937593i | \(0.386951\pi\) |
−0.985847 | + | 0.167649i | \(0.946382\pi\) | |||||||
\(860\) | −28049.7 | + | 6775.61i | −1.11219 | + | 0.268659i | ||||
\(861\) | 2677.75 | − | 5317.99i | 0.105990 | − | 0.210496i | ||||
\(862\) | −10306.6 | + | 1227.17i | −0.407243 | + | 0.0484891i | ||||
\(863\) | −33292.7 | − | 19221.5i | −1.31320 | − | 0.758179i | −0.330579 | − | 0.943778i | \(-0.607244\pi\) |
−0.982625 | + | 0.185600i | \(0.940577\pi\) | |||||||
\(864\) | −11380.1 | + | 23281.3i | −0.448101 | + | 0.916721i | ||||
\(865\) | −28932.4 | − | 50112.4i | −1.13726 | − | 1.96979i | ||||
\(866\) | −9232.22 | + | 21530.1i | −0.362267 | + | 0.844828i | ||||
\(867\) | −8790.02 | −0.344319 | ||||||||
\(868\) | −993.661 | − | 3280.07i | −0.0388561 | − | 0.128264i | ||||
\(869\) | −13396.2 | −0.522941 | ||||||||
\(870\) | 1980.93 | − | 4619.63i | 0.0771951 | − | 0.180023i | ||||
\(871\) | 10444.2 | + | 18089.8i | 0.406300 | + | 0.703732i | ||||
\(872\) | 17153.4 | − | 20712.9i | 0.666156 | − | 0.804390i | ||||
\(873\) | 15300.7 | + | 8833.85i | 0.593184 | + | 0.342475i | ||||
\(874\) | −12913.4 | + | 1537.55i | −0.499772 | + | 0.0595062i | ||||
\(875\) | −16768.3 | − | 25553.0i | −0.647854 | − | 0.987257i | ||||
\(876\) | 5192.60 | + | 21496.3i | 0.200276 | + | 0.829101i | ||||
\(877\) | 10742.3 | − | 18606.2i | 0.413616 | − | 0.716404i | −0.581666 | − | 0.813428i | \(-0.697599\pi\) |
0.995282 | + | 0.0970237i | \(0.0309323\pi\) | |||||||
\(878\) | 21930.4 | − | 16400.1i | 0.842956 | − | 0.630383i | ||||
\(879\) | 1324.81 | − | 764.877i | 0.0508357 | − | 0.0293500i | ||||
\(880\) | −2403.68 | + | 48456.9i | −0.0920774 | + | 1.85623i | ||||
\(881\) | − | 17193.8i | − | 0.657517i | −0.944414 | − | 0.328759i | \(-0.893370\pi\) | ||
0.944414 | − | 0.328759i | \(-0.106630\pi\) | |||||||
\(882\) | −3541.88 | − | 14940.0i | −0.135217 | − | 0.570359i | ||||
\(883\) | − | 16514.2i | − | 0.629384i | −0.949194 | − | 0.314692i | \(-0.898099\pi\) | ||
0.949194 | − | 0.314692i | \(-0.101901\pi\) | |||||||
\(884\) | −2684.80 | + | 9110.48i | −0.102149 | + | 0.346627i | ||||
\(885\) | 30580.7 | − | 17655.8i | 1.16154 | − | 0.670614i | ||||
\(886\) | −13993.5 | − | 18712.3i | −0.530612 | − | 0.709540i | ||||
\(887\) | −10239.6 | + | 17735.5i | −0.387612 | + | 0.671364i | −0.992128 | − | 0.125229i | \(-0.960033\pi\) |
0.604516 | + | 0.796593i | \(0.293367\pi\) | |||||||
\(888\) | 2732.29 | + | 7358.63i | 0.103254 | + | 0.278085i | ||||
\(889\) | 15201.1 | + | 23164.8i | 0.573486 | + | 0.873929i | ||||
\(890\) | 1258.20 | + | 10567.2i | 0.0473876 | + | 0.397992i | ||||
\(891\) | −1824.29 | − | 1053.25i | −0.0685925 | − | 0.0396019i | ||||
\(892\) | −10645.0 | − | 11186.1i | −0.399574 | − | 0.419886i | ||||
\(893\) | −5553.49 | − | 9618.93i | −0.208108 | − | 0.360454i | ||||
\(894\) | 12424.5 | + | 5327.70i | 0.464806 | + | 0.199312i | ||||
\(895\) | −4399.00 | −0.164293 | ||||||||
\(896\) | −16949.7 | + | 20785.3i | −0.631977 | + | 0.774987i | ||||
\(897\) | 6175.79 | 0.229882 | ||||||||
\(898\) | −190.171 | − | 81.5463i | −0.00706690 | − | 0.00303033i | ||||
\(899\) | −333.693 | − | 577.973i | −0.0123796 | − | 0.0214421i | ||||
\(900\) | 18727.1 | + | 19679.0i | 0.693595 | + | 0.728854i | ||||
\(901\) | 18099.2 | + | 10449.6i | 0.669226 | + | 0.386378i | ||||
\(902\) | 1323.14 | + | 11112.6i | 0.0488424 | + | 0.410211i | ||||
\(903\) | 5449.92 | − | 10823.5i | 0.200844 | − | 0.398874i | ||||
\(904\) | −5216.96 | − | 14050.4i | −0.191940 | − | 0.516935i | ||||
\(905\) | −17939.6 | + | 31072.3i | −0.658930 | + | 1.14130i | ||||
\(906\) | −7055.66 | − | 9434.91i | −0.258729 | − | 0.345976i | ||||
\(907\) | −26983.7 | + | 15579.0i | −0.987848 | + | 0.570334i | −0.904630 | − | 0.426197i | \(-0.859853\pi\) |
−0.0832177 | + | 0.996531i | \(0.526520\pi\) | |||||||
\(908\) | 4469.57 | − | 15166.8i | 0.163357 | − | 0.554327i | ||||
\(909\) | 62.6978i | 0.00228774i | ||||||||
\(910\) | −8177.52 | + | 22545.4i | −0.297892 | + | 0.821287i | ||||
\(911\) | 412.348i | 0.0149964i | 0.999972 | + | 0.00749818i | \(0.00238677\pi\) | ||||
−0.999972 | + | 0.00749818i | \(0.997613\pi\) | |||||||
\(912\) | 655.331 | − | 13211.1i | 0.0237941 | − | 0.479676i | ||||
\(913\) | 18093.5 | − | 10446.3i | 0.655868 | − | 0.378666i | ||||
\(914\) | 29836.7 | − | 22312.6i | 1.07977 | − | 0.807480i | ||||
\(915\) | 13103.6 | − | 22696.2i | 0.473435 | − | 0.820013i | ||||
\(916\) | −4853.56 | − | 20092.7i | −0.175072 | − | 0.724763i | ||||
\(917\) | −2082.95 | − | 36417.7i | −0.0750109 | − | 1.31147i | ||||
\(918\) | −19212.4 | + | 2287.56i | −0.690746 | + | 0.0822448i | ||||
\(919\) | 8444.08 | + | 4875.19i | 0.303095 | + | 0.174992i | 0.643832 | − | 0.765166i | \(-0.277343\pi\) |
−0.340737 | + | 0.940159i | \(0.610677\pi\) | |||||||
\(920\) | 19776.3 | − | 23880.1i | 0.708700 | − | 0.855763i | ||||
\(921\) | −7012.30 | − | 12145.7i | −0.250883 | − | 0.434542i | ||||
\(922\) | 14106.4 | − | 32897.0i | 0.503872 | − | 1.17506i | ||||
\(923\) | −29293.8 | −1.04466 | ||||||||
\(924\) | −14865.3 | − | 13933.3i | −0.529257 | − | 0.496074i | ||||
\(925\) | 22266.7 | 0.791487 | ||||||||
\(926\) | −950.378 | + | 2216.33i | −0.0337272 | + | 0.0786536i | ||||
\(927\) | 2839.38 | + | 4917.95i | 0.100601 | + | 0.174247i | ||||
\(928\) | −2293.53 | + | 4692.09i | −0.0811301 | + | 0.165976i | ||||
\(929\) | −19036.4 | − | 10990.7i | −0.672297 | − | 0.388151i | 0.124650 | − | 0.992201i | \(-0.460219\pi\) |
−0.796946 | + | 0.604050i | \(0.793553\pi\) | |||||||
\(930\) | −4001.75 | + | 476.475i | −0.141100 | + | 0.0168003i | ||||
\(931\) | 12628.8 | + | 17037.6i | 0.444568 | + | 0.599769i | ||||
\(932\) | 26816.2 | − | 6477.67i | 0.942484 | − | 0.227664i | ||||
\(933\) | −10877.7 | + | 18840.8i | −0.381695 | + | 0.661115i | ||||
\(934\) | 24746.7 | − | 18506.2i | 0.866956 | − | 0.648331i | ||||
\(935\) | −31371.0 | + | 18112.0i | −1.09726 | + | 0.633505i | ||||
\(936\) | 1488.40 | − | 8772.13i | 0.0519762 | − | 0.306331i | ||||
\(937\) | 19723.5i | 0.687662i | 0.939032 | + | 0.343831i | \(0.111725\pi\) | ||||
−0.939032 | + | 0.343831i | \(0.888275\pi\) | |||||||
\(938\) | −33705.3 | + | 28345.9i | −1.17326 | + | 0.986700i | ||||
\(939\) | − | 28877.4i | − | 1.00360i | ||||||
\(940\) | 25401.5 | + | 7485.65i | 0.881389 | + | 0.259739i | ||||
\(941\) | −9773.15 | + | 5642.53i | −0.338571 | + | 0.195474i | −0.659640 | − | 0.751582i | \(-0.729291\pi\) |
0.321069 | + | 0.947056i | \(0.395958\pi\) | |||||||
\(942\) | −14394.5 | − | 19248.5i | −0.497876 | − | 0.665766i | ||||
\(943\) | 3575.99 | − | 6193.80i | 0.123489 | − | 0.213890i | ||||
\(944\) | −32644.2 | + | 16748.2i | −1.12551 | + | 0.577445i | ||||
\(945\) | −48775.4 | + | 2789.76i | −1.67901 | + | 0.0960327i | ||||
\(946\) | 2692.94 | + | 22617.1i | 0.0925530 | + | 0.777321i | ||||
\(947\) | −26386.0 | − | 15234.0i | −0.905417 | − | 0.522743i | −0.0264635 | − | 0.999650i | \(-0.508425\pi\) |
−0.878954 | + | 0.476907i | \(0.841758\pi\) | |||||||
\(948\) | −6308.10 | + | 6002.94i | −0.216115 | + | 0.205661i | ||||
\(949\) | −10273.3 | − | 17794.0i | −0.351409 | − | 0.608658i | ||||
\(950\) | −34485.4 | − | 14787.5i | −1.17774 | − | 0.505022i | ||||
\(951\) | −3096.42 | −0.105582 | ||||||||
\(952\) | −19901.8 | − | 2216.98i | −0.677542 | − | 0.0754756i | ||||
\(953\) | 11791.2 | 0.400791 | 0.200395 | − | 0.979715i | \(-0.435777\pi\) | ||||
0.200395 | + | 0.979715i | \(0.435777\pi\) | |||||||
\(954\) | −17993.7 | − | 7715.79i | −0.610657 | − | 0.261853i | ||||
\(955\) | 4185.24 | + | 7249.05i | 0.141813 | + | 0.245627i | ||||
\(956\) | −21140.9 | + | 20118.2i | −0.715215 | + | 0.680616i | ||||
\(957\) | −3435.92 | − | 1983.73i | −0.116058 | − | 0.0670061i | ||||
\(958\) | 3565.18 | + | 29942.7i | 0.120236 | + | 1.00982i | ||||
\(959\) | 29668.8 | + | 14939.0i | 0.999014 | + | 0.503030i | ||||
\(960\) | 20582.0 | + | 23894.8i | 0.691961 | + | 0.803335i | ||||
\(961\) | 14628.0 | − | 25336.4i | 0.491019 | − | 0.850470i | ||||
\(962\) | −4367.66 | − | 5840.49i | −0.146382 | − | 0.195743i | ||||
\(963\) | 12716.2 | − | 7341.69i | 0.425517 | − | 0.245672i | ||||
\(964\) | −19445.0 | − | 5730.32i | −0.649670 | − | 0.191454i | ||||
\(965\) | 59154.0i | 1.97330i | ||||||||
\(966\) | 2275.26 | + | 12820.5i | 0.0757819 | + | 0.427010i | ||||
\(967\) | − | 40914.1i | − | 1.36061i | −0.732929 | − | 0.680305i | \(-0.761847\pi\) | ||
0.732929 | − | 0.680305i | \(-0.238153\pi\) | |||||||
\(968\) | 8062.61 | + | 1368.01i | 0.267709 | + | 0.0454230i | ||||
\(969\) | 8552.87 | − | 4938.00i | 0.283548 | − | 0.163706i | ||||
\(970\) | 46595.0 | − | 34844.9i | 1.54234 | − | 1.15340i | ||||
\(971\) | 9276.00 | − | 16066.5i | 0.306572 | − | 0.530997i | −0.671038 | − | 0.741423i | \(-0.734151\pi\) |
0.977610 | + | 0.210425i | \(0.0674848\pi\) | |||||||
\(972\) | 28726.0 | − | 6939.00i | 0.947930 | − | 0.228980i | ||||
\(973\) | −4744.46 | + | 3113.39i | −0.156321 | + | 0.102580i | ||||
\(974\) | 152.192 | − | 18.1210i | 0.00500671 | − | 0.000596133i | ||||
\(975\) | 15431.8 | + | 8909.53i | 0.506884 | + | 0.292650i | ||||
\(976\) | −14766.7 | + | 22878.6i | −0.484294 | + | 0.750333i | ||||
\(977\) | 1455.74 | + | 2521.42i | 0.0476697 | + | 0.0825664i | 0.888876 | − | 0.458148i | \(-0.151487\pi\) |
−0.841206 | + | 0.540715i | \(0.818154\pi\) | |||||||
\(978\) | −2742.53 | + | 6395.74i | −0.0896692 | + | 0.209114i | ||||
\(979\) | 8399.78 | 0.274217 | ||||||||
\(980\) | −49815.1 | − | 8669.81i | −1.62376 | − | 0.282599i | ||||
\(981\) | −18810.5 | −0.612204 | ||||||||
\(982\) | 6273.54 | − | 14630.3i | 0.203866 | − | 0.475428i | ||||
\(983\) | 18251.1 | + | 31611.8i | 0.592186 | + | 1.02570i | 0.993937 | + | 0.109947i | \(0.0350682\pi\) |
−0.401752 | + | 0.915749i | \(0.631598\pi\) | |||||||
\(984\) | 5602.70 | + | 4639.88i | 0.181512 | + | 0.150319i | ||||
\(985\) | 66602.3 | + | 38452.9i | 2.15444 | + | 1.24387i | ||||
\(986\) | −3872.05 | + | 461.032i | −0.125062 | + | 0.0148907i | ||||
\(987\) | −9297.70 | + | 6101.30i | −0.299847 | + | 0.196764i | ||||
\(988\) | 2885.65 | + | 11946.0i | 0.0929198 | + | 0.384669i | ||||
\(989\) | 7278.08 | − | 12606.0i | 0.234004 | − | 0.405306i | ||||
\(990\) | 27175.9 | − | 20322.8i | 0.872431 | − | 0.652425i | ||||
\(991\) | 31879.7 | − | 18405.7i | 1.02189 | − | 0.589987i | 0.107238 | − | 0.994233i | \(-0.465799\pi\) |
0.914650 | + | 0.404246i | \(0.132466\pi\) | |||||||
\(992\) | 4177.38 | − | 288.466i | 0.133701 | − | 0.00923266i | ||||
\(993\) | 31884.6i | 1.01896i | ||||||||
\(994\) | −10792.3 | − | 60811.6i | −0.344378 | − | 1.94047i | ||||
\(995\) | 97269.2i | 3.09914i | ||||||||
\(996\) | 3838.92 | − | 13026.8i | 0.122129 | − | 0.414429i | ||||
\(997\) | −10060.1 | + | 5808.18i | −0.319564 | + | 0.184500i | −0.651198 | − | 0.758908i | \(-0.725733\pi\) |
0.331634 | + | 0.943408i | \(0.392400\pi\) | |||||||
\(998\) | −1049.81 | − | 1403.82i | −0.0332978 | − | 0.0445262i | ||||
\(999\) | 7428.32 | − | 12866.2i | 0.235257 | − | 0.407477i |
(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 | 28.4.f.a.19.9 | yes | 20 | |
4.3 | odd | 2 | inner | 28.4.f.a.19.2 | yes | 20 | |
7.2 | even | 3 | 196.4.d.b.195.9 | 20 | |||
7.3 | odd | 6 | inner | 28.4.f.a.3.2 | ✓ | 20 | |
7.4 | even | 3 | 196.4.f.d.31.2 | 20 | |||
7.5 | odd | 6 | 196.4.d.b.195.10 | 20 | |||
7.6 | odd | 2 | 196.4.f.d.19.9 | 20 | |||
8.3 | odd | 2 | 448.4.p.h.383.7 | 20 | |||
8.5 | even | 2 | 448.4.p.h.383.4 | 20 | |||
28.3 | even | 6 | inner | 28.4.f.a.3.9 | yes | 20 | |
28.11 | odd | 6 | 196.4.f.d.31.9 | 20 | |||
28.19 | even | 6 | 196.4.d.b.195.11 | 20 | |||
28.23 | odd | 6 | 196.4.d.b.195.12 | 20 | |||
28.27 | even | 2 | 196.4.f.d.19.2 | 20 | |||
56.3 | even | 6 | 448.4.p.h.255.4 | 20 | |||
56.45 | odd | 6 | 448.4.p.h.255.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.f.a.3.2 | ✓ | 20 | 7.3 | odd | 6 | inner | |
28.4.f.a.3.9 | yes | 20 | 28.3 | even | 6 | inner | |
28.4.f.a.19.2 | yes | 20 | 4.3 | odd | 2 | inner | |
28.4.f.a.19.9 | yes | 20 | 1.1 | even | 1 | trivial | |
196.4.d.b.195.9 | 20 | 7.2 | even | 3 | |||
196.4.d.b.195.10 | 20 | 7.5 | odd | 6 | |||
196.4.d.b.195.11 | 20 | 28.19 | even | 6 | |||
196.4.d.b.195.12 | 20 | 28.23 | odd | 6 | |||
196.4.f.d.19.2 | 20 | 28.27 | even | 2 | |||
196.4.f.d.19.9 | 20 | 7.6 | odd | 2 | |||
196.4.f.d.31.2 | 20 | 7.4 | even | 3 | |||
196.4.f.d.31.9 | 20 | 28.11 | odd | 6 | |||
448.4.p.h.255.4 | 20 | 56.3 | even | 6 | |||
448.4.p.h.255.7 | 20 | 56.45 | odd | 6 | |||
448.4.p.h.383.4 | 20 | 8.5 | even | 2 | |||
448.4.p.h.383.7 | 20 | 8.3 | odd | 2 |