Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(19,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("216.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.p (of order \(6\), degree \(2\), not 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: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.6 | ||
Character | \(\chi\) | \(=\) | 216.19 |
Dual form | 216.3.p.b.91.6 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35259 | − | 1.47326i | −0.676296 | − | 0.736630i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.340985 | + | 3.98544i | −0.0852462 | + | 0.996360i | ||||
\(5\) | −0.0166003 | + | 0.00958419i | −0.00332006 | + | 0.00191684i | −0.501659 | − | 0.865065i | \(-0.667277\pi\) |
0.498339 | + | 0.866982i | \(0.333943\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.07208 | − | 2.35102i | −0.581726 | − | 0.335860i | 0.180093 | − | 0.983650i | \(-0.442360\pi\) |
−0.761819 | + | 0.647790i | \(0.775694\pi\) | |||||||
\(8\) | 6.33280 | − | 4.88832i | 0.791600 | − | 0.611040i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.0365734 | + | 0.0114930i | 0.00365734 | + | 0.00114930i | ||||
\(11\) | −2.84945 | + | 4.93540i | −0.259041 | + | 0.448673i | −0.965985 | − | 0.258597i | \(-0.916740\pi\) |
0.706944 | + | 0.707269i | \(0.250073\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.0617 | + | 5.80910i | −0.773974 | + | 0.446854i | −0.834290 | − | 0.551325i | \(-0.814122\pi\) |
0.0603167 | + | 0.998179i | \(0.480789\pi\) | |||||||
\(14\) | 2.04421 | + | 9.17921i | 0.146015 | + | 0.655658i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.7675 | − | 2.71795i | −0.985466 | − | 0.169872i | ||||
\(17\) | 0.376814 | 0.0221655 | 0.0110828 | − | 0.999939i | \(-0.496472\pi\) | ||||
0.0110828 | + | 0.999939i | \(0.496472\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −15.0519 | −0.792207 | −0.396103 | − | 0.918206i | \(-0.629638\pi\) | ||||
−0.396103 | + | 0.918206i | \(0.629638\pi\) | |||||||
\(20\) | −0.0325368 | − | 0.0694276i | −0.00162684 | − | 0.00347138i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.1253 | − | 2.47760i | 0.505694 | − | 0.112618i | ||||
\(23\) | −39.1821 | + | 22.6218i | −1.70357 | + | 0.983556i | −0.761484 | + | 0.648184i | \(0.775529\pi\) |
−0.942086 | + | 0.335372i | \(0.891138\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.4998 | + | 21.6503i | −0.499993 | + | 0.866013i | ||||
\(26\) | 22.1676 | + | 6.96608i | 0.852601 | + | 0.267926i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.7584 | − | 15.4274i | 0.384227 | − | 0.550978i | ||||
\(29\) | 32.0010 | + | 18.4758i | 1.10348 | + | 0.637096i | 0.937134 | − | 0.348971i | \(-0.113469\pi\) |
0.166349 | + | 0.986067i | \(0.446802\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.3839 | − | 15.2328i | 0.851094 | − | 0.491379i | −0.00992571 | − | 0.999951i | \(-0.503160\pi\) |
0.861020 | + | 0.508571i | \(0.169826\pi\) | |||||||
\(32\) | 17.3227 | + | 26.9058i | 0.541335 | + | 0.840807i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.509675 | − | 0.555144i | −0.0149905 | − | 0.0163278i | ||||
\(35\) | 0.0901304 | 0.00257515 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 53.4253i | 1.44393i | 0.691931 | + | 0.721964i | \(0.256760\pi\) | ||||
−0.691931 | + | 0.721964i | \(0.743240\pi\) | |||||||
\(38\) | 20.3591 | + | 22.1754i | 0.535767 | + | 0.583563i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0582758 | + | 0.141842i | −0.00145689 | + | 0.00354606i | ||||
\(41\) | −29.0192 | − | 50.2628i | −0.707786 | − | 1.22592i | −0.965677 | − | 0.259747i | \(-0.916361\pi\) |
0.257891 | − | 0.966174i | \(-0.416973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −23.0516 | + | 39.9265i | −0.536083 | + | 0.928524i | 0.463027 | + | 0.886344i | \(0.346763\pi\) |
−0.999110 | + | 0.0421794i | \(0.986570\pi\) | |||||||
\(44\) | −18.6981 | − | 13.0392i | −0.424957 | − | 0.296346i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 86.3252 | + | 27.1273i | 1.87663 | + | 0.589724i | ||||
\(47\) | −34.2487 | − | 19.7735i | −0.728695 | − | 0.420712i | 0.0892497 | − | 0.996009i | \(-0.471553\pi\) |
−0.817944 | + | 0.575297i | \(0.804886\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.4454 | − | 23.2882i | −0.274396 | − | 0.475268i | ||||
\(50\) | 48.8037 | − | 10.8686i | 0.976074 | − | 0.217372i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.7209 | − | 42.0809i | −0.379249 | − | 0.809249i | ||||
\(53\) | − | 0.989874i | − | 0.0186769i | −0.999956 | − | 0.00933844i | \(-0.997027\pi\) | ||
0.999956 | − | 0.00933844i | \(-0.00297256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.109239i | − | 0.00198616i | ||||||
\(56\) | −37.2802 | + | 5.01711i | −0.665718 | + | 0.0895913i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −16.0647 | − | 72.1360i | −0.276978 | − | 1.24372i | ||||
\(59\) | −29.4331 | − | 50.9797i | −0.498866 | − | 0.864062i | 0.501133 | − | 0.865370i | \(-0.332917\pi\) |
−0.999999 | + | 0.00130851i | \(0.999583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 75.1051 | + | 43.3619i | 1.23123 | + | 0.710851i | 0.967286 | − | 0.253687i | \(-0.0816432\pi\) |
0.263944 | + | 0.964538i | \(0.414977\pi\) | |||||||
\(62\) | −58.1285 | − | 18.2666i | −0.937557 | − | 0.294623i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 16.2087 | − | 61.9135i | 0.253261 | − | 0.967398i | ||||
\(65\) | 0.111351 | − | 0.192866i | 0.00171309 | − | 0.00296716i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −34.1445 | − | 59.1400i | −0.509620 | − | 0.882687i | −0.999938 | − | 0.0111436i | \(-0.996453\pi\) |
0.490318 | − | 0.871543i | \(-0.336881\pi\) | |||||||
\(68\) | −0.128488 | + | 1.50177i | −0.00188953 | + | 0.0220848i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.121910 | − | 0.132785i | −0.00174157 | − | 0.00189694i | ||||
\(71\) | − | 42.3565i | − | 0.596571i | −0.954477 | − | 0.298285i | \(-0.903585\pi\) | ||
0.954477 | − | 0.298285i | \(-0.0964147\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 26.6644 | 0.365266 | 0.182633 | − | 0.983181i | \(-0.441538\pi\) | ||||
0.182633 | + | 0.983181i | \(0.441538\pi\) | |||||||
\(74\) | 78.7093 | − | 72.2627i | 1.06364 | − | 0.976523i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.13248 | − | 59.9886i | 0.0675326 | − | 0.789323i | ||||
\(77\) | 23.2064 | − | 13.3982i | 0.301382 | − | 0.174003i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −121.208 | − | 69.9797i | −1.53428 | − | 0.885819i | −0.999157 | − | 0.0410462i | \(-0.986931\pi\) |
−0.535126 | − | 0.844772i | \(-0.679736\pi\) | |||||||
\(80\) | 0.287794 | − | 0.106000i | 0.00359742 | − | 0.00132499i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −34.7989 | + | 110.738i | −0.424377 | + | 1.35046i | ||||
\(83\) | −40.9931 | + | 71.0021i | −0.493892 | + | 0.855447i | −0.999975 | − | 0.00703820i | \(-0.997760\pi\) |
0.506083 | + | 0.862485i | \(0.331093\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.00625522 | + | 0.00361145i | −7.35908e−5 | + | 4.24877e-5i | ||||
\(86\) | 90.0015 | − | 20.0434i | 1.04653 | − | 0.233062i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.08078 | + | 45.1839i | 0.0690998 | + | 0.513454i | ||||
\(89\) | 42.6370 | 0.479068 | 0.239534 | − | 0.970888i | \(-0.423005\pi\) | ||||
0.239534 | + | 0.970888i | \(0.423005\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 54.6292 | 0.600321 | ||||||||
\(92\) | −76.7973 | − | 163.872i | −0.834753 | − | 1.78121i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17.1930 | + | 77.2026i | 0.182905 | + | 0.821304i | ||||
\(95\) | 0.249867 | − | 0.144261i | 0.00263017 | − | 0.00151853i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 55.9278 | − | 96.8698i | 0.576576 | − | 0.998658i | −0.419293 | − | 0.907851i | \(-0.637722\pi\) |
0.995868 | − | 0.0908072i | \(-0.0289447\pi\) | |||||||
\(98\) | −16.1233 | + | 51.3080i | −0.164523 | + | 0.523551i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −82.0238 | − | 57.1997i | −0.820238 | − | 0.571997i | ||||
\(101\) | 92.9636 | + | 53.6726i | 0.920432 | + | 0.531412i | 0.883773 | − | 0.467916i | \(-0.154995\pi\) |
0.0366592 | + | 0.999328i | \(0.488328\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 44.0704 | − | 25.4441i | 0.427868 | − | 0.247030i | −0.270570 | − | 0.962700i | \(-0.587212\pi\) |
0.698438 | + | 0.715671i | \(0.253879\pi\) | |||||||
\(104\) | −35.3217 | + | 85.9724i | −0.339632 | + | 0.826658i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.45834 | + | 1.33890i | −0.0137579 | + | 0.0126311i | ||||
\(107\) | 49.7181 | 0.464656 | 0.232328 | − | 0.972638i | \(-0.425366\pi\) | ||||
0.232328 | + | 0.972638i | \(0.425366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 40.3370i | − | 0.370064i | −0.982732 | − | 0.185032i | \(-0.940761\pi\) | ||
0.982732 | − | 0.185032i | \(-0.0592389\pi\) | |||||||
\(110\) | −0.160937 | + | 0.147756i | −0.00146306 | + | 0.00134323i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 57.8165 | + | 48.1373i | 0.516218 | + | 0.429797i | ||||
\(113\) | 12.9411 | + | 22.4146i | 0.114523 | + | 0.198360i | 0.917589 | − | 0.397530i | \(-0.130133\pi\) |
−0.803066 | + | 0.595890i | \(0.796799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.433623 | − | 0.751057i | 0.00377063 | − | 0.00653093i | ||||
\(116\) | −84.5460 | + | 121.238i | −0.728845 | + | 1.04516i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −35.2952 | + | 112.317i | −0.299112 | + | 0.951842i | ||||
\(119\) | −1.53442 | − | 0.885896i | −0.0128943 | − | 0.00744450i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 44.2612 | + | 76.6627i | 0.365795 | + | 0.633576i | ||||
\(122\) | −37.7032 | − | 169.300i | −0.309043 | − | 1.38771i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 51.7127 | + | 110.346i | 0.417038 | + | 0.889884i | ||||
\(125\) | − | 0.958412i | − | 0.00766729i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 38.2335i | − | 0.301051i | −0.988606 | − | 0.150526i | \(-0.951903\pi\) | ||
0.988606 | − | 0.150526i | \(-0.0480966\pi\) | |||||||
\(128\) | −113.138 | + | 59.8641i | −0.883893 | + | 0.467689i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.434754 | + | 0.0968198i | −0.00334426 | + | 0.000744767i | ||||
\(131\) | 61.9020 | + | 107.217i | 0.472534 | + | 0.818453i | 0.999506 | − | 0.0314294i | \(-0.0100059\pi\) |
−0.526972 | + | 0.849883i | \(0.676673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 61.2927 | + | 35.3874i | 0.460848 | + | 0.266070i | ||||
\(134\) | −40.9450 | + | 130.296i | −0.305559 | + | 0.972359i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.38628 | − | 1.84198i | 0.0175462 | − | 0.0135440i | ||||
\(137\) | −56.1949 | + | 97.3324i | −0.410182 | + | 0.710456i | −0.994909 | − | 0.100774i | \(-0.967868\pi\) |
0.584728 | + | 0.811230i | \(0.301201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 56.1874 | + | 97.3194i | 0.404226 | + | 0.700140i | 0.994231 | − | 0.107260i | \(-0.0342077\pi\) |
−0.590005 | + | 0.807399i | \(0.700874\pi\) | |||||||
\(140\) | −0.0307331 | + | 0.359209i | −0.000219522 | + | 0.00256578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −62.4021 | + | 57.2911i | −0.439452 | + | 0.403459i | ||||
\(143\) | − | 66.2111i | − | 0.463014i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.708302 | −0.00488484 | ||||||||
\(146\) | −36.0661 | − | 39.2836i | −0.247028 | − | 0.269066i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −212.923 | − | 18.2172i | −1.43867 | − | 0.123089i | ||||
\(149\) | −0.193825 | + | 0.111905i | −0.00130084 | + | 0.000751040i | −0.500650 | − | 0.865650i | \(-0.666906\pi\) |
0.499349 | + | 0.866401i | \(0.333572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −106.870 | − | 61.7013i | −0.707747 | − | 0.408618i | 0.102479 | − | 0.994735i | \(-0.467323\pi\) |
−0.810226 | + | 0.586117i | \(0.800656\pi\) | |||||||
\(152\) | −95.3209 | + | 73.5786i | −0.627111 | + | 0.484070i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −51.1279 | − | 16.0667i | −0.332000 | − | 0.104329i | ||||
\(155\) | −0.291987 | + | 0.505737i | −0.00188379 | + | 0.00326282i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −169.459 | + | 97.8372i | −1.07936 | + | 0.623167i | −0.930723 | − | 0.365726i | \(-0.880821\pi\) |
−0.148634 | + | 0.988892i | \(0.547488\pi\) | |||||||
\(158\) | 60.8474 | + | 273.225i | 0.385110 | + | 1.72927i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.545433 | − | 0.280621i | −0.00340895 | − | 0.00175388i | ||||
\(161\) | 212.737 | 1.32135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 36.1007 | 0.221477 | 0.110738 | − | 0.993850i | \(-0.464678\pi\) | ||||
0.110738 | + | 0.993850i | \(0.464678\pi\) | |||||||
\(164\) | 210.214 | − | 98.5155i | 1.28179 | − | 0.600704i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 160.051 | − | 35.6435i | 0.964165 | − | 0.214720i | ||||
\(167\) | −89.8711 | + | 51.8871i | −0.538150 | + | 0.310701i | −0.744329 | − | 0.667813i | \(-0.767230\pi\) |
0.206179 | + | 0.978514i | \(0.433897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.0087 | + | 29.4600i | −0.100643 | + | 0.174319i | ||||
\(170\) | 0.0137814 | + | 0.00433073i | 8.10669e−5 | + | 2.54749e-5i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −151.265 | − | 105.485i | −0.879445 | − | 0.613285i | ||||
\(173\) | −53.5978 | − | 30.9447i | −0.309814 | − | 0.178871i | 0.337029 | − | 0.941494i | \(-0.390578\pi\) |
−0.646843 | + | 0.762623i | \(0.723911\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 101.801 | − | 58.7746i | 0.581718 | − | 0.335855i | ||||
\(176\) | 58.3428 | − | 70.0740i | 0.331493 | − | 0.398148i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −57.6705 | − | 62.8154i | −0.323992 | − | 0.352895i | ||||
\(179\) | 235.967 | 1.31825 | 0.659125 | − | 0.752033i | \(-0.270927\pi\) | ||||
0.659125 | + | 0.752033i | \(0.270927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 274.398i | − | 1.51601i | −0.652250 | − | 0.758004i | \(-0.726175\pi\) | ||
0.652250 | − | 0.758004i | \(-0.273825\pi\) | |||||||
\(182\) | −73.8911 | − | 80.4830i | −0.405995 | − | 0.442214i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −137.550 | + | 334.794i | −0.747553 | + | 1.81953i | ||||
\(185\) | −0.512038 | − | 0.886876i | −0.00276777 | − | 0.00479392i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.07371 | + | 1.85973i | −0.00574178 | + | 0.00994506i | ||||
\(188\) | 90.4842 | − | 129.753i | 0.481299 | − | 0.690178i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.550501 | − | 0.172992i | −0.00289737 | − | 0.000910486i | ||||
\(191\) | 75.3616 | + | 43.5100i | 0.394563 | + | 0.227801i | 0.684135 | − | 0.729355i | \(-0.260180\pi\) |
−0.289572 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 51.8130 | + | 89.7428i | 0.268461 | + | 0.464989i | 0.968465 | − | 0.249151i | \(-0.0801515\pi\) |
−0.700003 | + | 0.714140i | \(0.746818\pi\) | |||||||
\(194\) | −218.362 | + | 48.6293i | −1.12558 | + | 0.250666i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 97.3982 | − | 45.6450i | 0.496930 | − | 0.232883i | ||||
\(197\) | − | 200.158i | − | 1.01603i | −0.861349 | − | 0.508014i | \(-0.830380\pi\) | ||
0.861349 | − | 0.508014i | \(-0.169620\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 178.871i | 0.898847i | 0.893319 | + | 0.449424i | \(0.148371\pi\) | ||||
−0.893319 | + | 0.449424i | \(0.851629\pi\) | |||||||
\(200\) | 26.6748 | + | 198.210i | 0.133374 | + | 0.991051i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −46.6683 | − | 209.557i | −0.231031 | − | 1.03741i | ||||
\(203\) | −86.8738 | − | 150.470i | −0.427950 | − | 0.741231i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.963456 | + | 0.556251i | 0.00469978 | + | 0.00271342i | ||||
\(206\) | −97.0951 | − | 30.5117i | −0.471335 | − | 0.148115i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 174.436 | − | 64.2477i | 0.838633 | − | 0.308883i | ||||
\(209\) | 42.8898 | − | 74.2873i | 0.205214 | − | 0.355442i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −95.3087 | − | 165.079i | −0.451700 | − | 0.782367i | 0.546792 | − | 0.837269i | \(-0.315849\pi\) |
−0.998492 | + | 0.0549013i | \(0.982516\pi\) | |||||||
\(212\) | 3.94508 | + | 0.337532i | 0.0186089 | + | 0.00159213i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −67.2484 | − | 73.2477i | −0.314245 | − | 0.342279i | ||||
\(215\) | − | 0.883723i | − | 0.00411034i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −143.250 | −0.660139 | ||||||||
\(218\) | −59.4269 | + | 54.5596i | −0.272600 | + | 0.250273i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.435365 | + | 0.0372488i | 0.00197893 | + | 0.000169313i | ||||
\(221\) | −3.79137 | + | 2.18895i | −0.0171555 | + | 0.00990474i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 188.439 | + | 108.795i | 0.845018 | + | 0.487871i | 0.858967 | − | 0.512031i | \(-0.171107\pi\) |
−0.0139487 | + | 0.999903i | \(0.504440\pi\) | |||||||
\(224\) | −7.28342 | − | 150.289i | −0.0325153 | − | 0.670932i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.5185 | − | 49.3835i | 0.0686661 | − | 0.218511i | ||||
\(227\) | −68.5871 | + | 118.796i | −0.302146 | + | 0.523332i | −0.976622 | − | 0.214965i | \(-0.931036\pi\) |
0.674476 | + | 0.738297i | \(0.264370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −222.151 | + | 128.259i | −0.970090 | + | 0.560082i | −0.899264 | − | 0.437407i | \(-0.855897\pi\) |
−0.0708262 | + | 0.997489i | \(0.522564\pi\) | |||||||
\(230\) | −1.69302 | + | 0.377035i | −0.00736094 | + | 0.00163928i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 292.971 | − | 39.4276i | 1.26281 | − | 0.169947i | ||||
\(233\) | −305.481 | −1.31108 | −0.655538 | − | 0.755162i | \(-0.727558\pi\) | ||||
−0.655538 | + | 0.755162i | \(0.727558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.758051 | 0.00322575 | ||||||||
\(236\) | 213.213 | − | 99.9206i | 0.903443 | − | 0.423392i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.770287 | + | 3.45885i | 0.00323650 | + | 0.0145330i | ||||
\(239\) | 68.4669 | − | 39.5294i | 0.286472 | − | 0.165395i | −0.349878 | − | 0.936795i | \(-0.613777\pi\) |
0.636350 | + | 0.771401i | \(0.280443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 111.403 | − | 192.956i | 0.462254 | − | 0.800647i | −0.536819 | − | 0.843697i | \(-0.680374\pi\) |
0.999073 | + | 0.0430503i | \(0.0137076\pi\) | |||||||
\(242\) | 53.0766 | − | 168.902i | 0.219325 | − | 0.697941i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −198.426 | + | 284.541i | −0.813221 | + | 1.16615i | ||||
\(245\) | 0.446396 | + | 0.257727i | 0.00182202 | + | 0.00105195i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 151.447 | − | 87.4382i | 0.613147 | − | 0.354001i | ||||
\(248\) | 92.6215 | − | 225.439i | 0.373474 | − | 0.909028i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.41199 | + | 1.29634i | −0.00564795 | + | 0.00518536i | ||||
\(251\) | −393.373 | −1.56722 | −0.783611 | − | 0.621252i | \(-0.786624\pi\) | ||||
−0.783611 | + | 0.621252i | \(0.786624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 257.839i | − | 1.01913i | ||||||
\(254\) | −56.3279 | + | 51.7144i | −0.221763 | + | 0.203600i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 241.226 | + | 85.7103i | 0.942287 | + | 0.334806i | ||||
\(257\) | −89.6613 | − | 155.298i | −0.348877 | − | 0.604272i | 0.637173 | − | 0.770720i | \(-0.280103\pi\) |
−0.986050 | + | 0.166448i | \(0.946770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 125.604 | − | 217.552i | 0.484957 | − | 0.839970i | ||||
\(260\) | 0.730685 | + | 0.509547i | 0.00281033 | + | 0.00195980i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 74.2308 | − | 236.219i | 0.283324 | − | 0.901600i | ||||
\(263\) | 241.721 | + | 139.558i | 0.919092 | + | 0.530638i | 0.883345 | − | 0.468723i | \(-0.155286\pi\) |
0.0357465 | + | 0.999361i | \(0.488619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.00948714 | + | 0.0164322i | 3.58005e−5 | + | 6.20083e-5i | ||||
\(266\) | −30.7693 | − | 138.165i | −0.115674 | − | 0.519416i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 247.342 | − | 115.915i | 0.922917 | − | 0.432519i | ||||
\(269\) | 112.462i | 0.418076i | 0.977908 | + | 0.209038i | \(0.0670332\pi\) | ||||
−0.977908 | + | 0.209038i | \(0.932967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 500.279i | 1.84605i | 0.384740 | + | 0.923025i | \(0.374291\pi\) | ||||
−0.384740 | + | 0.923025i | \(0.625709\pi\) | |||||||
\(272\) | −5.94139 | − | 1.02416i | −0.0218434 | − | 0.00376529i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 219.405 | − | 48.8615i | 0.800747 | − | 0.178327i | ||||
\(275\) | −71.2353 | − | 123.383i | −0.259037 | − | 0.448666i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 222.630 | + | 128.535i | 0.803718 | + | 0.464027i | 0.844770 | − | 0.535130i | \(-0.179737\pi\) |
−0.0410514 | + | 0.999157i | \(0.513071\pi\) | |||||||
\(278\) | 67.3780 | − | 214.412i | 0.242367 | − | 0.771267i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.570778 | − | 0.440586i | 0.00203849 | − | 0.00157352i | ||||
\(281\) | −139.228 | + | 241.150i | −0.495474 | + | 0.858187i | −0.999986 | − | 0.00521797i | \(-0.998339\pi\) |
0.504512 | + | 0.863405i | \(0.331672\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 93.9509 | + | 162.728i | 0.331982 | + | 0.575009i | 0.982900 | − | 0.184138i | \(-0.0589494\pi\) |
−0.650919 | + | 0.759148i | \(0.725616\pi\) | |||||||
\(284\) | 168.809 | + | 14.4429i | 0.594399 | + | 0.0508554i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −97.5460 | + | 89.5566i | −0.341070 | + | 0.313135i | ||||
\(287\) | 272.899i | 0.950868i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.858 | −0.999509 | ||||||||
\(290\) | 0.958044 | + | 1.04351i | 0.00330360 | + | 0.00359832i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.09216 | + | 106.269i | −0.0311375 | + | 0.363936i | ||||
\(293\) | −442.987 | + | 255.759i | −1.51190 | + | 0.872897i | −0.511999 | + | 0.858986i | \(0.671095\pi\) |
−0.999903 | + | 0.0139109i | \(0.995572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.977197 | + | 0.564185i | 0.00331253 | + | 0.00191249i | ||||
\(296\) | 261.160 | + | 338.332i | 0.882297 | + | 1.14301i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.427031 | + | 0.134193i | 0.00143299 | + | 0.000450311i | ||||
\(299\) | 262.825 | − | 455.225i | 0.879012 | − | 1.52249i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 187.736 | − | 108.389i | 0.623708 | − | 0.360098i | ||||
\(302\) | 53.6494 | + | 240.904i | 0.177647 | + | 0.797695i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 237.331 | + | 40.9104i | 0.780693 | + | 0.134574i | ||||
\(305\) | −1.66236 | −0.00545035 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −195.885 | −0.638061 | −0.319031 | − | 0.947744i | \(-0.603357\pi\) | ||||
−0.319031 | + | 0.947744i | \(0.603357\pi\) | |||||||
\(308\) | 45.4848 | + | 97.0564i | 0.147678 | + | 0.315118i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.14002 | − | 0.253883i | 0.00367749 | − | 0.000818978i | ||||
\(311\) | 395.492 | − | 228.338i | 1.27168 | − | 0.734205i | 0.296376 | − | 0.955071i | \(-0.404222\pi\) |
0.975304 | + | 0.220867i | \(0.0708886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −185.314 | + | 320.973i | −0.592058 | + | 1.02547i | 0.401897 | + | 0.915685i | \(0.368351\pi\) |
−0.993955 | + | 0.109789i | \(0.964982\pi\) | |||||||
\(314\) | 373.348 | + | 117.323i | 1.18901 | + | 0.373640i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 320.230 | − | 459.207i | 1.01339 | − | 1.45319i | ||||
\(317\) | −435.393 | − | 251.374i | −1.37348 | − | 0.792979i | −0.382115 | − | 0.924115i | \(-0.624804\pi\) |
−0.991364 | + | 0.131136i | \(0.958138\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −182.371 | + | 105.292i | −0.571695 | + | 0.330068i | ||||
\(320\) | 0.324321 | + | 1.18313i | 0.00101350 | + | 0.00369728i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −287.747 | − | 313.417i | −0.893623 | − | 0.973344i | ||||
\(323\) | −5.67177 | −0.0175597 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 290.451i | − | 0.893695i | ||||||
\(326\) | −48.8296 | − | 53.1858i | −0.149784 | − | 0.163146i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −429.473 | − | 176.449i | −1.30937 | − | 0.537954i | ||||
\(329\) | 92.9756 | + | 161.038i | 0.282601 | + | 0.489479i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −187.810 | + | 325.297i | −0.567402 | + | 0.982769i | 0.429420 | + | 0.903105i | \(0.358718\pi\) |
−0.996822 | + | 0.0796642i | \(0.974615\pi\) | |||||||
\(332\) | −268.996 | − | 187.586i | −0.810230 | − | 0.565018i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 198.002 | + | 62.2213i | 0.592821 | + | 0.186291i | ||||
\(335\) | 1.13362 | + | 0.654495i | 0.00338394 | + | 0.00195372i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −161.252 | − | 279.296i | −0.478492 | − | 0.828772i | 0.521204 | − | 0.853432i | \(-0.325483\pi\) |
−0.999696 | + | 0.0246599i | \(0.992150\pi\) | |||||||
\(338\) | 66.4080 | − | 14.7891i | 0.196473 | − | 0.0437547i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.0122603 | − | 0.0261612i | −3.60597e−5 | − | 7.69448e-5i | ||||
\(341\) | 173.620i | 0.509150i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 356.842i | 1.04035i | ||||||||
\(344\) | 49.1925 | + | 365.530i | 0.143001 | + | 1.06259i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26.9064 | + | 120.819i | 0.0777642 | + | 0.349188i | ||||
\(347\) | 42.4458 | + | 73.5183i | 0.122322 | + | 0.211868i | 0.920683 | − | 0.390311i | \(-0.127633\pi\) |
−0.798361 | + | 0.602179i | \(0.794299\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.4597 | − | 20.4727i | −0.101604 | − | 0.0586610i | 0.448337 | − | 0.893865i | \(-0.352016\pi\) |
−0.549941 | + | 0.835204i | \(0.685350\pi\) | |||||||
\(350\) | −224.285 | − | 70.4806i | −0.640814 | − | 0.201373i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −182.151 | + | 8.82757i | −0.517475 | + | 0.0250783i | ||||
\(353\) | 272.714 | − | 472.355i | 0.772561 | − | 1.33812i | −0.163593 | − | 0.986528i | \(-0.552309\pi\) |
0.936155 | − | 0.351588i | \(-0.114358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.405953 | + | 0.703131i | 0.00114353 | + | 0.00198065i | ||||
\(356\) | −14.5386 | + | 169.927i | −0.0408387 | + | 0.477324i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −319.167 | − | 347.640i | −0.891528 | − | 0.971062i | ||||
\(359\) | − | 24.1503i | − | 0.0672710i | −0.999434 | − | 0.0336355i | \(-0.989291\pi\) | ||
0.999434 | − | 0.0336355i | \(-0.0107085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −134.439 | −0.372408 | ||||||||
\(362\) | −404.259 | + | 371.148i | −1.11674 | + | 1.02527i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18.6277 | + | 217.721i | −0.0511751 | + | 0.598136i | ||||
\(365\) | −0.442637 | + | 0.255557i | −0.00121270 | + | 0.000700155i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −227.281 | − | 131.221i | −0.619295 | − | 0.357550i | 0.157299 | − | 0.987551i | \(-0.449721\pi\) |
−0.776595 | + | 0.630001i | \(0.783055\pi\) | |||||||
\(368\) | 679.287 | − | 250.193i | 1.84589 | − | 0.679873i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.614019 | + | 1.95395i | −0.00165951 | + | 0.00528094i | ||||
\(371\) | −2.32721 | + | 4.03085i | −0.00627281 | + | 0.0108648i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −97.0579 | + | 56.0364i | −0.260209 | + | 0.150232i | −0.624430 | − | 0.781081i | \(-0.714669\pi\) |
0.364221 | + | 0.931313i | \(0.381335\pi\) | |||||||
\(374\) | 4.19215 | − | 0.933594i | 0.0112090 | − | 0.00249624i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −313.549 | + | 42.1969i | −0.833907 | + | 0.112226i | ||||
\(377\) | −429.311 | −1.13876 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 305.554 | 0.806210 | 0.403105 | − | 0.915154i | \(-0.367931\pi\) | ||||
0.403105 | + | 0.915154i | \(0.367931\pi\) | |||||||
\(380\) | 0.489741 | + | 1.04502i | 0.00128879 | + | 0.00275005i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −37.8320 | − | 169.878i | −0.0990366 | − | 0.444708i | ||||
\(383\) | −50.9660 | + | 29.4252i | −0.133070 | + | 0.0768283i | −0.565057 | − | 0.825052i | \(-0.691146\pi\) |
0.431987 | + | 0.901880i | \(0.357813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.256823 | + | 0.444830i | −0.000667071 | + | 0.00115540i | ||||
\(386\) | 62.1325 | − | 197.719i | 0.160965 | − | 0.512227i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 366.998 | + | 255.928i | 0.945872 | + | 0.659609i | ||||
\(389\) | −417.667 | − | 241.140i | −1.07369 | − | 0.619897i | −0.144505 | − | 0.989504i | \(-0.546159\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.7643 | + | 8.52420i | −0.0377605 | + | 0.0218010i | ||||
\(392\) | −198.987 | − | 81.7537i | −0.507620 | − | 0.208555i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −294.884 | + | 270.732i | −0.748436 | + | 0.687136i | ||||
\(395\) | 2.68279 | 0.00679188 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 74.8863i | 0.188631i | 0.995542 | + | 0.0943153i | \(0.0300662\pi\) | ||||
−0.995542 | + | 0.0943153i | \(0.969934\pi\) | |||||||
\(398\) | 263.523 | − | 241.939i | 0.662117 | − | 0.607887i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 255.935 | − | 307.397i | 0.639837 | − | 0.768492i | ||||
\(401\) | 299.864 | + | 519.380i | 0.747791 | + | 1.29521i | 0.948879 | + | 0.315639i | \(0.102219\pi\) |
−0.201088 | + | 0.979573i | \(0.564448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −176.977 | + | 306.534i | −0.439150 | + | 0.760629i | ||||
\(404\) | −245.608 | + | 352.199i | −0.607941 | + | 0.871781i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −104.176 | + | 331.512i | −0.256592 | + | 0.816533i | ||||
\(407\) | −263.675 | − | 152.233i | −0.647851 | − | 0.374037i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 274.176 | + | 474.886i | 0.670356 | + | 1.16109i | 0.977803 | + | 0.209526i | \(0.0671921\pi\) |
−0.307447 | + | 0.951565i | \(0.599475\pi\) | |||||||
\(410\) | −0.483661 | − | 2.17180i | −0.00117966 | − | 0.00529708i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 86.3785 | + | 184.316i | 0.209656 | + | 0.447369i | ||||
\(413\) | 276.791i | 0.670197i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.57154i | − | 0.00378685i | ||||||
\(416\) | −330.594 | − | 170.088i | −0.794697 | − | 0.408865i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −167.457 | + | 37.2927i | −0.400614 | + | 0.0892170i | ||||
\(419\) | 134.464 | + | 232.899i | 0.320917 | + | 0.555845i | 0.980677 | − | 0.195631i | \(-0.0626756\pi\) |
−0.659761 | + | 0.751476i | \(0.729342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −235.498 | − | 135.965i | −0.559378 | − | 0.322957i | 0.193518 | − | 0.981097i | \(-0.438010\pi\) |
−0.752896 | + | 0.658140i | \(0.771344\pi\) | |||||||
\(422\) | −114.291 | + | 363.700i | −0.270832 | + | 0.861848i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.83882 | − | 6.26867i | −0.0114123 | − | 0.0147846i | ||||
\(425\) | −4.71010 | + | 8.15813i | −0.0110826 | + | 0.0191956i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −203.889 | − | 353.147i | −0.477493 | − | 0.827042i | ||||
\(428\) | −16.9531 | + | 198.149i | −0.0396101 | + | 0.462964i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.30195 | + | 1.19532i | −0.00302780 | + | 0.00277981i | ||||
\(431\) | 140.920i | 0.326960i | 0.986547 | + | 0.163480i | \(0.0522719\pi\) | ||||
−0.986547 | + | 0.163480i | \(0.947728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 649.144 | 1.49918 | 0.749589 | − | 0.661903i | \(-0.230251\pi\) | ||||
0.749589 | + | 0.661903i | \(0.230251\pi\) | |||||||
\(434\) | 193.759 | + | 211.044i | 0.446449 | + | 0.486278i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 160.761 | + | 13.7543i | 0.368717 | + | 0.0315466i | ||||
\(437\) | 589.766 | − | 340.502i | 1.34958 | − | 0.779180i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −135.712 | − | 78.3535i | −0.309140 | − | 0.178482i | 0.337402 | − | 0.941361i | \(-0.390452\pi\) |
−0.646541 | + | 0.762879i | \(0.723785\pi\) | |||||||
\(440\) | −0.533994 | − | 0.691787i | −0.00121362 | − | 0.00157224i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.35307 | + | 2.62491i | 0.0188983 | + | 0.00593872i | ||||
\(443\) | −6.92104 | + | 11.9876i | −0.0156231 | + | 0.0270600i | −0.873731 | − | 0.486409i | \(-0.838307\pi\) |
0.858108 | + | 0.513469i | \(0.171640\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.707787 | + | 0.408641i | −0.00159053 | + | 0.000918295i | ||||
\(446\) | −94.5976 | − | 424.775i | −0.212102 | − | 0.952411i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −211.563 | + | 214.010i | −0.472239 | + | 0.477701i | ||||
\(449\) | 682.313 | 1.51963 | 0.759814 | − | 0.650140i | \(-0.225290\pi\) | ||||
0.759814 | + | 0.650140i | \(0.225290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 330.756 | 0.733383 | ||||||||
\(452\) | −93.7449 | + | 43.9329i | −0.207400 | + | 0.0971967i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 267.788 | − | 59.6365i | 0.589842 | − | 0.131358i | ||||
\(455\) | −0.906861 | + | 0.523577i | −0.00199310 | + | 0.00115072i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −140.879 | + | 244.010i | −0.308270 | + | 0.533938i | −0.977984 | − | 0.208680i | \(-0.933083\pi\) |
0.669714 | + | 0.742619i | \(0.266417\pi\) | |||||||
\(458\) | 489.438 | + | 153.804i | 1.06864 | + | 0.335816i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.84543 | + | 1.98428i | 0.00618573 | + | 0.00431365i | ||||
\(461\) | 556.528 | + | 321.312i | 1.20722 | + | 0.696989i | 0.962151 | − | 0.272517i | \(-0.0878561\pi\) |
0.245069 | + | 0.969506i | \(0.421189\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 528.367 | − | 305.053i | 1.14118 | − | 0.658861i | 0.194458 | − | 0.980911i | \(-0.437705\pi\) |
0.946723 | + | 0.322050i | \(0.104372\pi\) | |||||||
\(464\) | −454.358 | − | 378.293i | −0.979220 | − | 0.815287i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 413.191 | + | 450.052i | 0.886676 | + | 0.965777i | ||||
\(467\) | −289.260 | −0.619400 | −0.309700 | − | 0.950834i | \(-0.600229\pi\) | ||||
−0.309700 | + | 0.950834i | \(0.600229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 321.098i | 0.684643i | ||||||||
\(470\) | −1.02533 | − | 1.11680i | −0.00218156 | − | 0.00237618i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −435.599 | − | 178.965i | −0.922879 | − | 0.379164i | ||||
\(473\) | −131.369 | − | 227.538i | −0.277736 | − | 0.481052i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 188.146 | − | 325.879i | 0.396098 | − | 0.686061i | ||||
\(476\) | 4.05390 | − | 5.81325i | 0.00851659 | − | 0.0122127i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −150.845 | − | 47.4023i | −0.315575 | − | 0.0991680i | ||||
\(479\) | −115.068 | − | 66.4346i | −0.240226 | − | 0.138694i | 0.375055 | − | 0.927003i | \(-0.377624\pi\) |
−0.615281 | + | 0.788308i | \(0.710957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −310.353 | − | 537.547i | −0.645224 | − | 1.11756i | ||||
\(482\) | −434.957 | + | 96.8651i | −0.902401 | + | 0.200965i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −320.627 | + | 150.260i | −0.662452 | + | 0.310454i | ||||
\(485\) | 2.14409i | 0.00442081i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 800.882i | − | 1.64452i | −0.569111 | − | 0.822261i | \(-0.692713\pi\) | ||
0.569111 | − | 0.822261i | \(-0.307287\pi\) | |||||||
\(488\) | 687.592 | − | 92.5351i | 1.40900 | − | 0.189621i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.224094 | − | 1.00626i | −0.000457334 | − | 0.00205358i | ||||
\(491\) | 416.975 | + | 722.222i | 0.849236 | + | 1.47092i | 0.881891 | + | 0.471454i | \(0.156270\pi\) |
−0.0326547 | + | 0.999467i | \(0.510396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0584 | + | 6.96193i | 0.0244593 | + | 0.0141216i | ||||
\(494\) | −333.666 | − | 104.853i | −0.675437 | − | 0.212253i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −457.409 | + | 168.472i | −0.922196 | + | 0.339661i | ||||
\(497\) | −99.5810 | + | 172.479i | −0.200364 | + | 0.347041i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −62.9732 | − | 109.073i | −0.126199 | − | 0.218583i | 0.796002 | − | 0.605294i | \(-0.206944\pi\) |
−0.922201 | + | 0.386711i | \(0.873611\pi\) | |||||||
\(500\) | 3.81969 | + | 0.326804i | 0.00763938 | + | 0.000653608i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 532.073 | + | 579.540i | 1.05991 | + | 1.15446i | ||||
\(503\) | 321.537i | 0.639239i | 0.947546 | + | 0.319619i | \(0.103555\pi\) | ||||
−0.947546 | + | 0.319619i | \(0.896445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.05763 | −0.00407452 | ||||||||
\(506\) | −379.864 | + | 348.751i | −0.750719 | + | 0.689232i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 152.377 | + | 13.0370i | 0.299955 | + | 0.0256635i | ||||
\(509\) | 473.601 | − | 273.434i | 0.930455 | − | 0.537198i | 0.0434992 | − | 0.999053i | \(-0.486149\pi\) |
0.886955 | + | 0.461855i | \(0.152816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −108.580 | − | 62.6885i | −0.212485 | − | 0.122678i | ||||
\(512\) | −200.006 | − | 471.319i | −0.390638 | − | 0.920545i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −107.519 | + | 342.149i | −0.209181 | + | 0.665660i | ||||
\(515\) | −0.487722 | + | 0.844758i | −0.000947032 | + | 0.00164031i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 195.180 | − | 112.687i | 0.377524 | − | 0.217964i | ||||
\(518\) | −490.402 | + | 109.213i | −0.946722 | + | 0.210835i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.237625 | − | 1.76570i | −0.000456971 | − | 0.00339557i | ||||
\(521\) | −774.144 | −1.48588 | −0.742940 | − | 0.669358i | \(-0.766569\pi\) | ||||
−0.742940 | + | 0.669358i | \(0.766569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 126.448 | 0.241774 | 0.120887 | − | 0.992666i | \(-0.461426\pi\) | ||||
0.120887 | + | 0.992666i | \(0.461426\pi\) | |||||||
\(524\) | −448.416 | + | 210.147i | −0.855756 | + | 0.401044i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −121.346 | − | 544.883i | −0.230695 | − | 1.03590i | ||||
\(527\) | 9.94182 | − | 5.73991i | 0.0188649 | − | 0.0108917i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 758.991 | − | 1314.61i | 1.43477 | − | 2.48509i | ||||
\(530\) | 0.0113767 | − | 0.0362031i | 2.14654e−5 | − | 6.83077e-5i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −161.934 | + | 232.212i | −0.304387 | + | 0.436489i | ||||
\(533\) | 583.963 | + | 337.151i | 1.09562 | + | 0.632554i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.825336 | + | 0.476508i | −0.00154268 | + | 0.000890669i | ||||
\(536\) | −505.326 | − | 207.613i | −0.942772 | − | 0.387337i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 165.686 | − | 152.116i | 0.307967 | − | 0.282743i | ||||
\(539\) | 153.248 | 0.284320 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 323.091i | 0.597210i | 0.954377 | + | 0.298605i | \(0.0965213\pi\) | ||||
−0.954377 | + | 0.298605i | \(0.903479\pi\) | |||||||
\(542\) | 737.041 | − | 676.674i | 1.35985 | − | 1.24848i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.52743 | + | 10.1385i | 0.0119990 | + | 0.0186369i | ||||
\(545\) | 0.386598 | + | 0.669607i | 0.000709353 | + | 0.00122864i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.9079 | − | 74.3187i | 0.0784423 | − | 0.135866i | −0.824136 | − | 0.566392i | \(-0.808339\pi\) |
0.902578 | + | 0.430526i | \(0.141672\pi\) | |||||||
\(548\) | −368.751 | − | 257.150i | −0.672903 | − | 0.469252i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −85.4230 | + | 271.835i | −0.155315 | + | 0.494246i | ||||
\(551\) | −481.677 | − | 278.096i | −0.874187 | − | 0.504712i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 329.047 | + | 569.926i | 0.595022 | + | 1.03061i | ||||
\(554\) | −111.762 | − | 501.848i | −0.201736 | − | 0.905863i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −407.020 | + | 190.747i | −0.732050 | + | 0.343070i | ||||
\(557\) | − | 666.623i | − | 1.19681i | −0.801194 | − | 0.598405i | \(-0.795801\pi\) | ||
0.801194 | − | 0.598405i | \(-0.204199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 535.636i | − | 0.958204i | ||||||
\(560\) | −1.42113 | − | 0.244970i | −0.00253773 | − | 0.000437446i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 543.596 | − | 121.059i | 0.967253 | − | 0.215408i | ||||
\(563\) | −234.690 | − | 406.495i | −0.416856 | − | 0.722016i | 0.578765 | − | 0.815494i | \(-0.303535\pi\) |
−0.995621 | + | 0.0934780i | \(0.970202\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.429652 | − | 0.248060i | −0.000760446 | − | 0.000439044i | ||||
\(566\) | 112.663 | − | 358.518i | 0.199051 | − | 0.633424i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −207.052 | − | 268.235i | −0.364528 | − | 0.472245i | ||||
\(569\) | 129.732 | − | 224.702i | 0.228000 | − | 0.394907i | −0.729215 | − | 0.684284i | \(-0.760115\pi\) |
0.957215 | + | 0.289377i | \(0.0934481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.3743 | + | 66.4663i | 0.0672055 | + | 0.116403i | 0.897670 | − | 0.440668i | \(-0.145258\pi\) |
−0.830465 | + | 0.557071i | \(0.811925\pi\) | |||||||
\(572\) | 263.880 | + | 22.5770i | 0.461329 | + | 0.0394702i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 402.051 | − | 369.121i | 0.700437 | − | 0.643068i | ||||
\(575\) | − | 1131.07i | − | 1.96708i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 289.811 | 0.502272 | 0.251136 | − | 0.967952i | \(-0.419196\pi\) | ||||
0.251136 | + | 0.967952i | \(0.419196\pi\) | |||||||
\(578\) | 390.707 | + | 425.563i | 0.675964 | + | 0.736268i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.241520 | − | 2.82289i | 0.000416414 | − | 0.00486706i | ||||
\(581\) | 333.854 | − | 192.751i | 0.574620 | − | 0.331757i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.88542 | + | 2.82060i | 0.00837980 | + | 0.00483808i | ||||
\(584\) | 168.860 | − | 130.344i | 0.289144 | − | 0.223192i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 975.981 | + | 306.697i | 1.66550 | + | 0.523375i | ||||
\(587\) | −136.875 | + | 237.074i | −0.233177 | + | 0.403874i | −0.958741 | − | 0.284280i | \(-0.908245\pi\) |
0.725565 | + | 0.688154i | \(0.241579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −397.129 | + | 229.282i | −0.674243 | + | 0.389274i | ||||
\(590\) | −0.490559 | − | 2.20278i | −0.000831456 | − | 0.00373352i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 145.207 | − | 842.381i | 0.245282 | − | 1.42294i | ||||
\(593\) | 461.865 | 0.778861 | 0.389431 | − | 0.921056i | \(-0.372672\pi\) | ||||
0.389431 | + | 0.921056i | \(0.372672\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0339624 | 5.70796e−5 | ||||||||
\(596\) | −0.379899 | − | 0.810636i | −0.000637414 | − | 0.00136013i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1026.16 | + | 228.526i | −1.71599 | + | 0.382151i | ||||
\(599\) | −551.557 | + | 318.442i | −0.920797 | + | 0.531622i | −0.883889 | − | 0.467696i | \(-0.845084\pi\) |
−0.0369077 | + | 0.999319i | \(0.511751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −456.737 | + | 791.092i | −0.759962 | + | 1.31629i | 0.182908 | + | 0.983130i | \(0.441449\pi\) |
−0.942869 | + | 0.333162i | \(0.891884\pi\) | |||||||
\(602\) | −413.616 | − | 129.977i | −0.687070 | − | 0.215909i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 282.348 | − | 404.884i | 0.467464 | − | 0.670338i | ||||
\(605\) | −1.46950 | − | 0.848416i | −0.00242892 | − | 0.00140234i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −108.688 | + | 62.7511i | −0.179058 | + | 0.103379i | −0.586850 | − | 0.809696i | \(-0.699632\pi\) |
0.407792 | + | 0.913075i | \(0.366299\pi\) | |||||||
\(608\) | −260.740 | − | 404.985i | −0.428849 | − | 0.666093i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.24849 | + | 2.44908i | 0.00368605 | + | 0.00401489i | ||||
\(611\) | 459.464 | 0.751987 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 929.305i | 1.51600i | 0.652257 | + | 0.757998i | \(0.273822\pi\) | ||||
−0.652257 | + | 0.757998i | \(0.726178\pi\) | |||||||
\(614\) | 264.952 | + | 288.589i | 0.431519 | + | 0.470015i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 81.4668 | − | 198.289i | 0.132251 | − | 0.321897i | ||||
\(617\) | −9.42520 | − | 16.3249i | −0.0152759 | − | 0.0264585i | 0.858286 | − | 0.513171i | \(-0.171529\pi\) |
−0.873562 | + | 0.486712i | \(0.838196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 158.239 | − | 274.079i | 0.255637 | − | 0.442777i | −0.709431 | − | 0.704775i | \(-0.751048\pi\) |
0.965068 | + | 0.261998i | \(0.0843814\pi\) | |||||||
\(620\) | −1.91602 | − | 1.33615i | −0.00309036 | − | 0.00215507i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −871.341 | − | 273.815i | −1.40087 | − | 0.440217i | ||||
\(623\) | −173.622 | − | 100.240i | −0.278686 | − | 0.160900i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.486 | − | 541.242i | −0.499978 | − | 0.865987i | ||||
\(626\) | 723.532 | − | 161.131i | 1.15580 | − | 0.257397i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −332.141 | − | 708.729i | −0.528887 | − | 1.12855i | ||||
\(629\) | 20.1314i | 0.0320054i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 254.226i | − | 0.402893i | −0.979499 | − | 0.201447i | \(-0.935436\pi\) | ||
0.979499 | − | 0.201447i | \(-0.0645643\pi\) | |||||||
\(632\) | −1109.67 | + | 149.338i | −1.75581 | + | 0.236294i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 218.570 | + | 981.454i | 0.344748 | + | 1.54803i | ||||
\(635\) | 0.366437 | + | 0.634688i | 0.000577066 | + | 0.000999508i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 270.566 | + | 156.212i | 0.424751 | + | 0.245230i | ||||
\(638\) | 401.796 | + | 126.262i | 0.629774 | + | 0.197904i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.30438 | − | 2.07810i | 0.00203810 | − | 0.00324703i | ||||
\(641\) | 509.350 | − | 882.221i | 0.794618 | − | 1.37632i | −0.128463 | − | 0.991714i | \(-0.541004\pi\) |
0.923081 | − | 0.384605i | \(-0.125662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 302.348 | + | 523.683i | 0.470215 | + | 0.814436i | 0.999420 | − | 0.0340578i | \(-0.0108430\pi\) |
−0.529205 | + | 0.848494i | \(0.677510\pi\) | |||||||
\(644\) | −72.5401 | + | 847.851i | −0.112640 | + | 1.31654i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.67160 | + | 8.35599i | 0.0118755 | + | 0.0129350i | ||||
\(647\) | 86.7767i | 0.134122i | 0.997749 | + | 0.0670608i | \(0.0213622\pi\) | ||||
−0.997749 | + | 0.0670608i | \(0.978638\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 335.473 | 0.516908 | ||||||||
\(650\) | −427.909 | + | 392.862i | −0.658322 | + | 0.604402i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.3098 | + | 143.877i | −0.0188801 | + | 0.220671i | ||||
\(653\) | −346.903 | + | 200.285i | −0.531245 | + | 0.306714i | −0.741523 | − | 0.670927i | \(-0.765896\pi\) |
0.210278 | + | 0.977642i | \(0.432563\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.05518 | − | 1.18656i | −0.00313768 | − | 0.00181154i | ||||
\(656\) | 320.948 | + | 871.389i | 0.489250 | + | 1.32834i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 111.493 | − | 354.797i | 0.169443 | − | 0.539205i | ||||
\(659\) | −28.0360 | + | 48.5597i | −0.0425432 | + | 0.0736870i | −0.886513 | − | 0.462704i | \(-0.846879\pi\) |
0.843970 | + | 0.536391i | \(0.180213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 675.562 | − | 390.036i | 1.02203 | − | 0.590069i | 0.107339 | − | 0.994222i | \(-0.465767\pi\) |
0.914691 | + | 0.404153i | \(0.132434\pi\) | |||||||
\(662\) | 733.277 | − | 163.301i | 1.10767 | − | 0.246678i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 87.4799 | + | 650.029i | 0.131747 | + | 0.978959i | ||||
\(665\) | −1.35664 | −0.00204006 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1671.82 | −2.50648 | ||||||||
\(668\) | −176.148 | − | 375.868i | −0.263695 | − | 0.562677i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.569084 | − | 2.55538i | −0.000849379 | − | 0.00381400i | ||||
\(671\) | −428.017 | + | 247.116i | −0.637879 | + | 0.368280i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −353.998 | + | 613.143i | −0.526001 | + | 0.911060i | 0.473541 | + | 0.880772i | \(0.342976\pi\) |
−0.999541 | + | 0.0302878i | \(0.990358\pi\) | |||||||
\(674\) | −193.368 | + | 615.340i | −0.286896 | + | 0.912967i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −111.611 | − | 77.8326i | −0.165105 | − | 0.115137i | ||||
\(677\) | 503.417 | + | 290.648i | 0.743600 | + | 0.429318i | 0.823377 | − | 0.567495i | \(-0.192087\pi\) |
−0.0797769 | + | 0.996813i | \(0.525421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −455.486 | + | 262.975i | −0.670818 | + | 0.387297i | ||||
\(680\) | −0.0219591 | + | 0.0534481i | −3.22928e−5 | + | 7.86001e-5i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 255.788 | − | 234.838i | 0.375055 | − | 0.344337i | ||||
\(683\) | −558.887 | −0.818282 | −0.409141 | − | 0.912471i | \(-0.634172\pi\) | ||||
−0.409141 | + | 0.912471i | \(0.634172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.15433i | − | 0.00314501i | ||||||
\(686\) | 525.720 | − | 482.661i | 0.766356 | − | 0.703588i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 471.983 | − | 566.887i | 0.686022 | − | 0.823963i | ||||
\(689\) | 5.75028 | + | 9.95977i | 0.00834583 | + | 0.0144554i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −158.856 | + | 275.147i | −0.229893 | + | 0.398187i | −0.957776 | − | 0.287515i | \(-0.907171\pi\) |
0.727883 | + | 0.685701i | \(0.240504\pi\) | |||||||
\(692\) | 141.604 | − | 203.059i | 0.204630 | − | 0.293438i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 50.8996 | − | 161.974i | 0.0733423 | − | 0.233392i | ||||
\(695\) | −1.86545 | − | 1.07702i | −0.00268411 | − | 0.00154967i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.9348 | − | 18.9397i | −0.0156884 | − | 0.0271732i | ||||
\(698\) | 17.8010 | + | 79.9326i | 0.0255029 | + | 0.114517i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 199.530 | + | 425.761i | 0.285043 | + | 0.608231i | ||||
\(701\) | 731.568i | 1.04361i | 0.853066 | + | 0.521803i | \(0.174741\pi\) | ||||
−0.853066 | + | 0.521803i | \(0.825259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 804.154i | − | 1.14389i | ||||||
\(704\) | 259.382 | + | 256.416i | 0.368440 | + | 0.364227i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1064.77 | + | 237.125i | −1.50818 | + | 0.335871i | ||||
\(707\) | −252.371 | − | 437.119i | −0.356960 | − | 0.618272i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 112.277 | + | 64.8230i | 0.158359 | + | 0.0914288i | 0.577085 | − | 0.816684i | \(-0.304190\pi\) |
−0.418726 | + | 0.908113i | \(0.637523\pi\) | |||||||
\(710\) | 0.486805 | − | 1.54912i | 0.000685641 | − | 0.00218186i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 270.012 | − | 208.423i | 0.379230 | − | 0.292729i | ||||
\(713\) | −689.185 | + | 1193.70i | −0.966599 | + | 1.67420i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.634579 | + | 1.09912i | 0.000887523 | + | 0.00153724i | ||||
\(716\) | −80.4611 | + | 940.431i | −0.112376 | + | 1.31345i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −35.5796 | + | 32.6655i | −0.0495538 | + | 0.0454951i | ||||
\(719\) | 726.317i | 1.01018i | 0.863068 | + | 0.505088i | \(0.168540\pi\) | ||||
−0.863068 | + | 0.505088i | \(0.831460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −239.278 | −0.331870 | ||||||||
\(722\) | 181.842 | + | 198.064i | 0.251858 | + | 0.274327i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1093.59 | + | 93.5654i | 1.51049 | + | 0.129234i | ||||
\(725\) | −800.013 | + | 461.888i | −1.10347 | + | 0.637087i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 498.049 | + | 287.549i | 0.685075 | + | 0.395528i | 0.801764 | − | 0.597640i | \(-0.203895\pi\) |
−0.116690 | + | 0.993168i | \(0.537228\pi\) | |||||||
\(728\) | 345.956 | − | 267.045i | 0.475214 | − | 0.366820i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.975209 | + | 0.306455i | 0.00133590 | + | 0.000419801i | ||||
\(731\) | −8.68615 | + | 15.0449i | −0.0118826 | + | 0.0205812i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 113.103 | − | 65.3000i | 0.154301 | − | 0.0890859i | −0.420861 | − | 0.907125i | \(-0.638272\pi\) |
0.575163 | + | 0.818039i | \(0.304939\pi\) | |||||||
\(734\) | 114.097 | + | 512.333i | 0.155445 | + | 0.698001i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1287.40 | − | 662.356i | −1.74918 | − | 0.899940i | ||||
\(737\) | 389.173 | 0.528050 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −61.7030 | −0.0834953 | −0.0417477 | − | 0.999128i | \(-0.513293\pi\) | ||||
−0.0417477 | + | 0.999128i | \(0.513293\pi\) | |||||||
\(740\) | 3.70919 | − | 1.73829i | 0.00501242 | − | 0.00234903i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.08626 | − | 2.02351i | 0.0122456 | − | 0.00272711i | ||||
\(743\) | 368.246 | − | 212.607i | 0.495620 | − | 0.286147i | −0.231283 | − | 0.972887i | \(-0.574292\pi\) |
0.726903 | + | 0.686740i | \(0.240959\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.00214503 | − | 0.00371531i | 2.87924e−6 | − | 4.98699e-6i | ||||
\(746\) | 213.836 | + | 67.1970i | 0.286644 | + | 0.0900764i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.04570 | − | 4.91336i | −0.00941939 | − | 0.00656866i | ||||
\(749\) | −202.456 | − | 116.888i | −0.270302 | − | 0.156059i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1180.47 | + | 681.543i | −1.57186 | + | 0.907514i | −0.575920 | + | 0.817506i | \(0.695356\pi\) |
−0.995941 | + | 0.0900084i | \(0.971311\pi\) | |||||||
\(752\) | 486.271 | + | 404.863i | 0.646637 | + | 0.538382i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 580.683 | + | 632.486i | 0.770136 | + | 0.838841i | ||||
\(755\) | 2.36543 | 0.00313302 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 105.684i | − | 0.139610i | −0.997561 | − | 0.0698048i | \(-0.977762\pi\) | ||
0.997561 | − | 0.0698048i | \(-0.0222376\pi\) | |||||||
\(758\) | −413.290 | − | 450.159i | −0.545237 | − | 0.593878i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.877163 | − | 2.13500i | 0.00115416 | − | 0.00280921i | ||||
\(761\) | −452.651 | − | 784.015i | −0.594811 | − | 1.03024i | −0.993574 | − | 0.113189i | \(-0.963894\pi\) |
0.398763 | − | 0.917054i | \(-0.369440\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −94.8331 | + | 164.256i | −0.124290 | + | 0.215276i | ||||
\(764\) | −199.104 | + | 285.513i | −0.260607 | + | 0.373708i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 112.287 | + | 35.2858i | 0.146589 | + | 0.0460650i | ||||
\(767\) | 592.292 | + | 341.960i | 0.772219 | + | 0.445841i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.2383 | − | 28.1255i | −0.0211161 | − | 0.0365741i | 0.855274 | − | 0.518176i | \(-0.173389\pi\) |
−0.876390 | + | 0.481601i | \(0.840055\pi\) | |||||||
\(770\) | 1.00273 | − | 0.223307i | 0.00130224 | − | 0.000290010i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −375.332 | + | 175.897i | −0.486181 | + | 0.227846i | ||||
\(773\) | 367.930i | 0.475976i | 0.971268 | + | 0.237988i | \(0.0764880\pi\) | ||||
−0.971268 | + | 0.237988i | \(0.923512\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 761.627i | 0.982744i | ||||||||
\(776\) | −119.351 | − | 886.850i | −0.153803 | − | 1.14285i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 209.671 | + | 941.496i | 0.269501 | + | 1.21015i | ||||
\(779\) | 436.795 | + | 756.552i | 0.560713 | + | 0.971183i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 209.046 | + | 120.693i | 0.267665 | + | 0.154536i | ||||
\(782\) | 32.5285 | + | 10.2219i | 0.0415966 | + | 0.0130715i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 148.704 | + | 403.739i | 0.189674 | + | 0.514973i | ||||
\(785\) | 1.87538 | − | 3.24825i | 0.00238902 | − | 0.00413790i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 563.311 | + | 975.684i | 0.715770 | + | 1.23975i | 0.962662 | + | 0.270707i | \(0.0872576\pi\) |
−0.246891 | + | 0.969043i | \(0.579409\pi\) | |||||||
\(788\) | 797.716 | + | 68.2507i | 1.01233 | + | 0.0866125i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.62873 | − | 3.95245i | −0.00459333 | − | 0.00500310i | ||||
\(791\) | − | 121.699i | − | 0.153855i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1007.58 | −1.27059 | ||||||||
\(794\) | 110.327 | − | 101.291i | 0.138951 | − | 0.127570i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −712.878 | − | 60.9921i | −0.895575 | − | 0.0766233i | ||||
\(797\) | −297.816 | + | 171.944i | −0.373672 | + | 0.215739i | −0.675061 | − | 0.737762i | \(-0.735883\pi\) |
0.301390 | + | 0.953501i | \(0.402550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.9054 | − | 7.45091i | −0.0161519 | − | 0.00932530i | ||||
\(800\) | −799.050 | + | 38.7242i | −0.998813 | + | 0.0484053i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 359.587 | − | 1144.29i | 0.448363 | − | 1.42679i | ||||
\(803\) | −75.9790 | + | 131.600i | −0.0946189 | + | 0.163885i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.53150 | + | 2.03891i | −0.00438696 | + | 0.00253281i | ||||
\(806\) | 690.982 | − | 153.882i | 0.857297 | − | 0.190920i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 851.089 | − | 114.538i | 1.05333 | − | 0.141755i | ||||
\(809\) | −273.136 | −0.337622 | −0.168811 | − | 0.985648i | \(-0.553993\pi\) | ||||
−0.168811 | + | 0.985648i | \(0.553993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 615.310 | 0.758705 | 0.379352 | − | 0.925252i | \(-0.376147\pi\) | ||||
0.379352 | + | 0.925252i | \(0.376147\pi\) | |||||||
\(812\) | 629.311 | − | 294.923i | 0.775014 | − | 0.363205i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 132.367 | + | 594.371i | 0.162613 | + | 0.730186i | ||||
\(815\) | −0.599283 | + | 0.345996i | −0.000735317 | + | 0.000424535i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 346.971 | − | 600.971i | 0.424689 | − | 0.735583i | ||||
\(818\) | 328.782 | − | 1046.26i | 0.401935 | − | 1.27905i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.54543 | + | 3.65012i | −0.00310418 | + | 0.00445137i | ||||
\(821\) | −1110.25 | − | 641.002i | −1.35231 | − | 0.780757i | −0.363739 | − | 0.931501i | \(-0.618500\pi\) |
−0.988573 | + | 0.150744i | \(0.951833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −241.117 | + | 139.209i | −0.292973 | + | 0.169148i | −0.639282 | − | 0.768972i | \(-0.720768\pi\) |
0.346309 | + | 0.938121i | \(0.387435\pi\) | |||||||
\(824\) | 154.710 | − | 376.562i | 0.187755 | − | 0.456993i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 407.785 | − | 374.386i | 0.493687 | − | 0.453252i | ||||
\(827\) | −88.6450 | −0.107189 | −0.0535943 | − | 0.998563i | \(-0.517068\pi\) | ||||
−0.0535943 | + | 0.998563i | \(0.517068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 673.447i | 0.812361i | 0.913793 | + | 0.406180i | \(0.133140\pi\) | ||||
−0.913793 | + | 0.406180i | \(0.866860\pi\) | |||||||
\(830\) | −2.31529 | + | 2.12566i | −0.00278950 | + | 0.00256103i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 196.575 | + | 717.110i | 0.236268 | + | 0.861911i | ||||
\(833\) | −5.06642 | − | 8.77529i | −0.00608213 | − | 0.0105346i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.994591 | − | 1.72268i | 0.00119113 | − | 0.00206309i | ||||
\(836\) | 281.443 | + | 196.265i | 0.336654 | + | 0.234767i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 161.245 | − | 513.118i | 0.192416 | − | 0.612313i | ||||
\(839\) | −29.6126 | − | 17.0968i | −0.0352951 | − | 0.0203776i | 0.482249 | − | 0.876034i | \(-0.339820\pi\) |
−0.517544 | + | 0.855657i | \(0.673154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 262.209 | + | 454.160i | 0.311783 | + | 0.540024i | ||||
\(842\) | 118.222 | + | 530.855i | 0.140406 | + | 0.630469i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 690.413 | − | 323.557i | 0.818025 | − | 0.383362i | ||||
\(845\) | − | 0.652059i | − | 0.000771667i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 416.236i | − | 0.491424i | ||||||
\(848\) | −2.69043 | + | 15.6078i | −0.00317267 | + | 0.0184054i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.3899 | − | 4.09544i | 0.0216352 | − | 0.00481816i | ||||
\(851\) | −1208.58 | − | 2093.32i | −1.42018 | − | 2.45983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1052.33 | − | 607.564i | −1.23368 | − | 0.712267i | −0.265887 | − | 0.964004i | \(-0.585665\pi\) |
−0.967796 | + | 0.251737i | \(0.918998\pi\) | |||||||
\(854\) | −244.497 | + | 778.046i | −0.286297 | + | 0.911061i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 314.855 | − | 243.038i | 0.367821 | − | 0.283923i | ||||
\(857\) | −462.160 | + | 800.484i | −0.539276 | + | 0.934054i | 0.459667 | + | 0.888091i | \(0.347969\pi\) |
−0.998943 | + | 0.0459627i | \(0.985364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −625.687 | − | 1083.72i | −0.728390 | − | 1.26161i | −0.957563 | − | 0.288223i | \(-0.906936\pi\) |
0.229174 | − | 0.973386i | \(-0.426398\pi\) | |||||||
\(860\) | 3.52202 | + | 0.301336i | 0.00409538 | + | 0.000350391i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 207.611 | − | 190.607i | 0.240848 | − | 0.221122i | ||||
\(863\) | − | 291.210i | − | 0.337439i | −0.985664 | − | 0.168719i | \(-0.946037\pi\) | ||
0.985664 | − | 0.168719i | \(-0.0539632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.18632 | 0.00137147 | ||||||||
\(866\) | −878.028 | − | 956.358i | −1.01389 | − | 1.10434i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 48.8461 | − | 570.914i | 0.0562743 | − | 0.657736i | ||||
\(869\) | 690.755 | − | 398.808i | 0.794885 | − | 0.458927i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 687.101 | + | 396.698i | 0.788864 | + | 0.455451i | ||||
\(872\) | −197.180 | − | 255.446i | −0.226124 | − | 0.292943i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1299.36 | − | 408.318i | −1.48668 | − | 0.467183i | ||||
\(875\) | −2.25324 | + | 3.90273i | −0.00257514 | + | 0.00446027i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 623.417 | − | 359.930i | 0.710851 | − | 0.410410i | −0.100525 | − | 0.994935i | \(-0.532052\pi\) |
0.811376 | + | 0.584524i | \(0.198719\pi\) | |||||||
\(878\) | 68.1284 | + | 305.920i | 0.0775950 | + | 0.348428i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.296905 | + | 1.72242i | −0.000337393 | + | 0.00195729i | ||||
\(881\) | −136.645 | −0.155102 | −0.0775512 | − | 0.996988i | \(-0.524710\pi\) | ||||
−0.0775512 | + | 0.996988i | \(0.524710\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −795.629 | −0.901052 | −0.450526 | − | 0.892763i | \(-0.648764\pi\) | ||||
−0.450526 | + | 0.892763i | \(0.648764\pi\) | |||||||
\(884\) | −7.43112 | − | 15.8567i | −0.00840625 | − | 0.0179374i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.0222 | − | 6.01785i | 0.0304991 | − | 0.00679215i | ||||
\(887\) | −92.9513 | + | 53.6654i | −0.104793 | + | 0.0605022i | −0.551480 | − | 0.834188i | \(-0.685937\pi\) |
0.446688 | + | 0.894690i | \(0.352604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −89.8877 | + | 155.690i | −0.101111 | + | 0.175129i | ||||
\(890\) | 1.55938 | + | 0.490029i | 0.00175212 | + | 0.000550594i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −497.852 | + | 713.915i | −0.558130 | + | 0.800353i | ||||
\(893\) | 515.508 | + | 297.629i | 0.577277 | + | 0.333291i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.91712 | + | 2.26155i | −0.00437667 | + | 0.00252687i | ||||
\(896\) | 601.451 | + | 22.2186i | 0.671262 | + | 0.0247975i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −922.892 | − | 1005.22i | −1.02772 | − | 1.11940i | ||||
\(899\) | 1125.75 | 1.25222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.372998i | − | 0.000413982i | ||||||
\(902\) | −447.378 | − | 487.289i | −0.495984 | − | 0.540232i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 191.523 | + | 78.6872i | 0.211862 | + | 0.0870434i | ||||
\(905\) | 2.62988 | + | 4.55508i | 0.00290594 | + | 0.00503324i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 686.970 | − | 1189.87i | 0.757409 | − | 1.31187i | −0.186759 | − | 0.982406i | \(-0.559798\pi\) |
0.944168 | − | 0.329465i | \(-0.106868\pi\) | |||||||
\(908\) | −450.068 | − | 313.857i | −0.495670 | − | 0.345658i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.99798 | + | 0.627856i | 0.00219558 | + | 0.000689951i | ||||
\(911\) | −166.832 | − | 96.3207i | −0.183131 | − | 0.105731i | 0.405632 | − | 0.914037i | \(-0.367051\pi\) |
−0.588763 | + | 0.808306i | \(0.700385\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −233.616 | − | 404.634i | −0.255877 | − | 0.443192i | ||||
\(914\) | 550.042 | − | 122.495i | 0.601796 | − | 0.134020i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −435.417 | − | 929.102i | −0.475346 | − | 1.01430i | ||||
\(917\) | − | 582.131i | − | 0.634821i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 818.741i | − | 0.890905i | −0.895306 | − | 0.445452i | \(-0.853043\pi\) | ||
0.895306 | − | 0.445452i | \(-0.146957\pi\) | |||||||
\(920\) | −0.925359 | − | 6.87598i | −0.00100582 | − | 0.00747389i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −279.381 | − | 1254.51i | −0.303016 | − | 1.36064i | ||||
\(923\) | 246.053 | + | 426.177i | 0.266580 | + | 0.461730i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1156.67 | − | 667.807i | −1.25046 | − | 0.721953i | ||||
\(926\) | −1164.09 | − | 365.809i | −1.25711 | − | 0.395042i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 57.2377 | + | 1181.06i | 0.0616786 | + | 1.27270i | ||||
\(929\) | 657.748 | − | 1139.25i | 0.708017 | − | 1.22632i | −0.257575 | − | 0.966258i | \(-0.582923\pi\) |
0.965592 | − | 0.260063i | \(-0.0837434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 202.380 | + | 350.532i | 0.217379 | + | 0.376511i | ||||
\(932\) | 104.164 | − | 1217.47i | 0.111764 | − | 1.30630i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 391.251 | + | 426.155i | 0.418898 | + | 0.456268i | ||||
\(935\) | − | 0.0411627i | − | 4.40242e-5i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −521.572 | −0.556640 | −0.278320 | − | 0.960488i | \(-0.589778\pi\) | ||||
−0.278320 | + | 0.960488i | \(0.589778\pi\) | |||||||
\(938\) | 473.060 | − | 434.314i | 0.504328 | − | 0.463022i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.258484 | + | 3.02116i | −0.000274983 | + | 0.00321401i | ||||
\(941\) | −340.545 | + | 196.614i | −0.361896 | + | 0.208941i | −0.669912 | − | 0.742440i | \(-0.733668\pi\) |
0.308016 | + | 0.951381i | \(0.400335\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2274.07 | + | 1312.93i | 2.41153 | + | 1.39229i | ||||
\(944\) | 325.525 | + | 883.817i | 0.344836 | + | 0.936247i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −157.533 | + | 501.306i | −0.166526 | + | 0.529922i | ||||
\(947\) | −437.860 | + | 758.396i | −0.462366 | + | 0.800841i | −0.999078 | − | 0.0429244i | \(-0.986333\pi\) |
0.536713 | + | 0.843765i | \(0.319666\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −268.288 | + | 154.896i | −0.282706 | + | 0.163220i | ||||
\(950\) | −734.590 | + | 163.593i | −0.773252 | + | 0.172204i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.0477 | + | 1.89052i | −0.0147560 | + | 0.00198584i | ||||
\(953\) | −71.0166 | −0.0745190 | −0.0372595 | − | 0.999306i | \(-0.511863\pi\) | ||||
−0.0372595 | + | 0.999306i | \(0.511863\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.66803 | −0.00174663 | ||||||||
\(956\) | 134.196 | + | 286.349i | 0.140372 | + | 0.299529i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 57.7650 | + | 259.384i | 0.0602974 | + | 0.270756i | ||||
\(959\) | 457.661 | − | 264.231i | 0.477227 | − | 0.275527i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.4259 | + | 28.4504i | −0.0170925 | + | 0.0296050i | ||||
\(962\) | −372.165 | + | 1184.31i | −0.386866 | + | 1.23109i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 731.028 | + | 509.786i | 0.758327 | + | 0.528823i | ||||
\(965\) | −1.72022 | − | 0.993171i | −0.00178261 | − | 0.00102919i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 194.113 | − | 112.071i | 0.200737 | − | 0.115896i | −0.396262 | − | 0.918137i | \(-0.629693\pi\) |
0.596999 | + | 0.802242i | \(0.296359\pi\) | |||||||
\(968\) | 655.049 | + | 269.126i | 0.676704 | + | 0.278023i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.15880 | − | 2.90008i | 0.00325650 | − | 0.00298978i | ||||
\(971\) | −91.8845 | −0.0946287 | −0.0473144 | − | 0.998880i | \(-0.515066\pi\) | ||||
−0.0473144 | + | 0.998880i | \(0.515066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 528.390i | − | 0.543053i | ||||||
\(974\) | −1179.91 | + | 1083.27i | −1.21140 | + | 1.11218i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1066.36 | − | 887.839i | −1.09258 | − | 0.909671i | ||||
\(977\) | −368.517 | − | 638.289i | −0.377192 | − | 0.653316i | 0.613461 | − | 0.789725i | \(-0.289777\pi\) |
−0.990653 | + | 0.136410i | \(0.956444\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −121.492 | + | 210.431i | −0.124098 | + | 0.214945i | ||||
\(980\) | −1.17937 | + | 1.69120i | −0.00120344 | + | 0.00172572i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 500.022 | − | 1591.18i | 0.509188 | − | 1.62035i | ||||
\(983\) | 1534.66 | + | 886.034i | 1.56120 | + | 0.901357i | 0.997136 | + | 0.0756241i | \(0.0240949\pi\) |
0.564061 | + | 0.825733i | \(0.309238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.91835 | + | 3.32267i | 0.00194756 | + | 0.00337327i | ||||
\(986\) | −6.05340 | − | 27.1818i | −0.00613935 | − | 0.0275678i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 296.838 | + | 633.399i | 0.300444 | + | 0.641093i | ||||
\(989\) | − | 2085.87i | − | 2.10907i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1115.19i | 1.12532i | 0.826689 | + | 0.562659i | \(0.190221\pi\) | ||||
−0.826689 | + | 0.562659i | \(0.809779\pi\) | |||||||
\(992\) | 866.891 | + | 446.009i | 0.873882 | + | 0.449605i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 388.799 | − | 86.5857i | 0.391146 | − | 0.0871084i | ||||
\(995\) | −1.71433 | − | 2.96930i | −0.00172294 | − | 0.00298423i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 193.012 | + | 111.435i | 0.193593 | + | 0.111771i | 0.593663 | − | 0.804714i | \(-0.297681\pi\) |
−0.400071 | + | 0.916484i | \(0.631014\pi\) | |||||||
\(998\) | −75.5153 | + | 240.307i | −0.0756666 | + | 0.240788i | ||||
\(999\) | 0 | 0 |
(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 | 216.3.p.b.19.6 | 40 | ||
3.2 | odd | 2 | 72.3.p.b.43.15 | yes | 40 | ||
4.3 | odd | 2 | 864.3.t.b.559.10 | 40 | |||
8.3 | odd | 2 | inner | 216.3.p.b.19.19 | 40 | ||
8.5 | even | 2 | 864.3.t.b.559.11 | 40 | |||
9.2 | odd | 6 | 648.3.b.f.163.11 | 20 | |||
9.4 | even | 3 | inner | 216.3.p.b.91.19 | 40 | ||
9.5 | odd | 6 | 72.3.p.b.67.2 | yes | 40 | ||
9.7 | even | 3 | 648.3.b.e.163.10 | 20 | |||
12.11 | even | 2 | 288.3.t.b.79.2 | 40 | |||
24.5 | odd | 2 | 288.3.t.b.79.1 | 40 | |||
24.11 | even | 2 | 72.3.p.b.43.2 | ✓ | 40 | ||
36.7 | odd | 6 | 2592.3.b.f.1135.10 | 20 | |||
36.11 | even | 6 | 2592.3.b.e.1135.11 | 20 | |||
36.23 | even | 6 | 288.3.t.b.175.1 | 40 | |||
36.31 | odd | 6 | 864.3.t.b.847.11 | 40 | |||
72.5 | odd | 6 | 288.3.t.b.175.2 | 40 | |||
72.11 | even | 6 | 648.3.b.f.163.12 | 20 | |||
72.13 | even | 6 | 864.3.t.b.847.10 | 40 | |||
72.29 | odd | 6 | 2592.3.b.e.1135.10 | 20 | |||
72.43 | odd | 6 | 648.3.b.e.163.9 | 20 | |||
72.59 | even | 6 | 72.3.p.b.67.15 | yes | 40 | ||
72.61 | even | 6 | 2592.3.b.f.1135.11 | 20 | |||
72.67 | odd | 6 | inner | 216.3.p.b.91.6 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.p.b.43.2 | ✓ | 40 | 24.11 | even | 2 | ||
72.3.p.b.43.15 | yes | 40 | 3.2 | odd | 2 | ||
72.3.p.b.67.2 | yes | 40 | 9.5 | odd | 6 | ||
72.3.p.b.67.15 | yes | 40 | 72.59 | even | 6 | ||
216.3.p.b.19.6 | 40 | 1.1 | even | 1 | trivial | ||
216.3.p.b.19.19 | 40 | 8.3 | odd | 2 | inner | ||
216.3.p.b.91.6 | 40 | 72.67 | odd | 6 | inner | ||
216.3.p.b.91.19 | 40 | 9.4 | even | 3 | inner | ||
288.3.t.b.79.1 | 40 | 24.5 | odd | 2 | |||
288.3.t.b.79.2 | 40 | 12.11 | even | 2 | |||
288.3.t.b.175.1 | 40 | 36.23 | even | 6 | |||
288.3.t.b.175.2 | 40 | 72.5 | odd | 6 | |||
648.3.b.e.163.9 | 20 | 72.43 | odd | 6 | |||
648.3.b.e.163.10 | 20 | 9.7 | even | 3 | |||
648.3.b.f.163.11 | 20 | 9.2 | odd | 6 | |||
648.3.b.f.163.12 | 20 | 72.11 | even | 6 | |||
864.3.t.b.559.10 | 40 | 4.3 | odd | 2 | |||
864.3.t.b.559.11 | 40 | 8.5 | even | 2 | |||
864.3.t.b.847.10 | 40 | 72.13 | even | 6 | |||
864.3.t.b.847.11 | 40 | 36.31 | odd | 6 | |||
2592.3.b.e.1135.10 | 20 | 72.29 | odd | 6 | |||
2592.3.b.e.1135.11 | 20 | 36.11 | even | 6 | |||
2592.3.b.f.1135.10 | 20 | 36.7 | odd | 6 | |||
2592.3.b.f.1135.11 | 20 | 72.61 | even | 6 |