Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,3,Mod(2,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([9]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.f (of order \(14\), degree \(6\), 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: | \(1.17166513675\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{14})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{14}]$ |
Embedding invariants
Embedding label | 8.1 | ||
Character | \(\chi\) | \(=\) | 43.8 |
Dual form | 43.3.f.a.27.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{13}{14}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.53859 | − | 0.807660i | −1.76930 | − | 0.403830i | −0.791128 | − | 0.611650i | \(-0.790506\pi\) |
−0.978167 | + | 0.207820i | \(0.933363\pi\) | |||||||
\(3\) | 1.86243 | − | 0.425087i | 0.620809 | − | 0.141696i | 0.0994635 | − | 0.995041i | \(-0.468287\pi\) |
0.521346 | + | 0.853346i | \(0.325430\pi\) | |||||||
\(4\) | 8.26544 | + | 3.98042i | 2.06636 | + | 0.995106i | ||||
\(5\) | −5.65332 | − | 4.50837i | −1.13066 | − | 0.901674i | −0.134652 | − | 0.990893i | \(-0.542992\pi\) |
−0.996012 | + | 0.0892188i | \(0.971563\pi\) | |||||||
\(6\) | −6.93370 | −1.15562 | ||||||||
\(7\) | − | 11.0869i | − | 1.58384i | −0.610623 | − | 0.791921i | \(-0.709081\pi\) | ||
0.610623 | − | 0.791921i | \(-0.290919\pi\) | |||||||
\(8\) | −14.6823 | − | 11.7087i | −1.83528 | − | 1.46359i | ||||
\(9\) | −4.82078 | + | 2.32157i | −0.535643 | + | 0.257952i | ||||
\(10\) | 16.3636 | + | 20.5192i | 1.63636 | + | 2.05192i | ||||
\(11\) | 8.18301 | − | 3.94073i | 0.743910 | − | 0.358248i | −0.0232278 | − | 0.999730i | \(-0.507394\pi\) |
0.767138 | + | 0.641482i | \(0.221680\pi\) | |||||||
\(12\) | 17.0858 | + | 3.89972i | 1.42382 | + | 0.324977i | ||||
\(13\) | 3.48338 | − | 4.36802i | 0.267952 | − | 0.336001i | −0.629592 | − | 0.776926i | \(-0.716778\pi\) |
0.897544 | + | 0.440925i | \(0.145349\pi\) | |||||||
\(14\) | −8.95445 | + | 39.2320i | −0.639603 | + | 2.80229i | ||||
\(15\) | −12.4453 | − | 5.99336i | −0.829690 | − | 0.399557i | ||||
\(16\) | 19.6184 | + | 24.6007i | 1.22615 | + | 1.53754i | ||||
\(17\) | 7.68404 | + | 9.63548i | 0.452003 | + | 0.566793i | 0.954662 | − | 0.297691i | \(-0.0962166\pi\) |
−0.502660 | + | 0.864484i | \(0.667645\pi\) | |||||||
\(18\) | 18.9338 | − | 4.32152i | 1.05188 | − | 0.240084i | ||||
\(19\) | −4.17143 | + | 8.66206i | −0.219549 | + | 0.455898i | −0.981430 | − | 0.191819i | \(-0.938561\pi\) |
0.761882 | + | 0.647716i | \(0.224276\pi\) | |||||||
\(20\) | −28.7819 | − | 59.7663i | −1.43910 | − | 2.98831i | ||||
\(21\) | −4.71290 | − | 20.6485i | −0.224424 | − | 0.983264i | ||||
\(22\) | −32.1391 | + | 7.33554i | −1.46087 | + | 0.333434i | ||||
\(23\) | 23.3617 | − | 11.2504i | 1.01573 | − | 0.489149i | 0.149481 | − | 0.988765i | \(-0.452240\pi\) |
0.866247 | + | 0.499616i | \(0.166525\pi\) | |||||||
\(24\) | −32.3218 | − | 15.5654i | −1.34674 | − | 0.648557i | ||||
\(25\) | 6.07158 | + | 26.6013i | 0.242863 | + | 1.06405i | ||||
\(26\) | −15.8541 | + | 12.6432i | −0.609774 | + | 0.486278i | ||||
\(27\) | −21.4334 | + | 17.0926i | −0.793831 | + | 0.633059i | ||||
\(28\) | 44.1306 | − | 91.6381i | 1.57609 | − | 3.27279i | ||||
\(29\) | 17.3222 | + | 3.95367i | 0.597316 | + | 0.136333i | 0.510481 | − | 0.859889i | \(-0.329467\pi\) |
0.0868353 | + | 0.996223i | \(0.472325\pi\) | |||||||
\(30\) | 39.1984 | + | 31.2597i | 1.30661 | + | 1.04199i | ||||
\(31\) | −4.39761 | + | 19.2672i | −0.141858 | + | 0.621523i | 0.853144 | + | 0.521675i | \(0.174693\pi\) |
−0.995003 | + | 0.0998476i | \(0.968164\pi\) | |||||||
\(32\) | −16.9603 | − | 35.2185i | −0.530010 | − | 1.10058i | ||||
\(33\) | 13.5651 | − | 10.8178i | 0.411064 | − | 0.327813i | ||||
\(34\) | −19.4085 | − | 40.3021i | −0.570838 | − | 1.18536i | ||||
\(35\) | −49.9839 | + | 62.6778i | −1.42811 | + | 1.79079i | ||||
\(36\) | −49.0867 | −1.36352 | ||||||||
\(37\) | − | 16.3680i | − | 0.442380i | −0.975231 | − | 0.221190i | \(-0.929006\pi\) | ||
0.975231 | − | 0.221190i | \(-0.0709940\pi\) | |||||||
\(38\) | 21.7570 | − | 27.2824i | 0.572552 | − | 0.717957i | ||||
\(39\) | 4.63075 | − | 9.61585i | 0.118737 | − | 0.246560i | ||||
\(40\) | 30.2163 | + | 132.386i | 0.755406 | + | 3.30965i | ||||
\(41\) | 10.5206 | − | 46.0940i | 0.256601 | − | 1.12424i | −0.668257 | − | 0.743931i | \(-0.732959\pi\) |
0.924858 | − | 0.380313i | \(-0.124184\pi\) | |||||||
\(42\) | 76.8732i | 1.83031i | ||||||||
\(43\) | 38.8262 | − | 18.4804i | 0.902935 | − | 0.429777i | ||||
\(44\) | 83.3220 | 1.89368 | ||||||||
\(45\) | 37.7199 | + | 8.60932i | 0.838220 | + | 0.191318i | ||||
\(46\) | −91.7542 | + | 20.9423i | −1.99466 | + | 0.455267i | ||||
\(47\) | 12.0673 | + | 5.81130i | 0.256751 | + | 0.123645i | 0.557832 | − | 0.829954i | \(-0.311633\pi\) |
−0.301081 | + | 0.953598i | \(0.597348\pi\) | |||||||
\(48\) | 46.9953 | + | 37.4775i | 0.979068 | + | 0.780780i | ||||
\(49\) | −73.9193 | −1.50856 | ||||||||
\(50\) | − | 99.0350i | − | 1.98070i | ||||||
\(51\) | 18.4069 | + | 14.6790i | 0.360919 | + | 0.287824i | ||||
\(52\) | 46.1782 | − | 22.2382i | 0.888042 | − | 0.427659i | ||||
\(53\) | −48.3246 | − | 60.5972i | −0.911786 | − | 1.14334i | −0.989233 | − | 0.146347i | \(-0.953248\pi\) |
0.0774476 | − | 0.996996i | \(-0.475323\pi\) | |||||||
\(54\) | 89.6492 | − | 43.1728i | 1.66017 | − | 0.799496i | ||||
\(55\) | −64.0275 | − | 14.6139i | −1.16414 | − | 0.265706i | ||||
\(56\) | −129.813 | + | 162.781i | −2.31809 | + | 2.90680i | ||||
\(57\) | −4.08685 | + | 17.9057i | −0.0716992 | + | 0.314135i | ||||
\(58\) | −58.1028 | − | 27.9809i | −1.00177 | − | 0.482429i | ||||
\(59\) | 33.9563 | + | 42.5798i | 0.575530 | + | 0.721692i | 0.981343 | − | 0.192264i | \(-0.0615831\pi\) |
−0.405813 | + | 0.913956i | \(0.633012\pi\) | |||||||
\(60\) | −79.0101 | − | 99.0755i | −1.31683 | − | 1.65126i | ||||
\(61\) | 89.1648 | − | 20.3513i | 1.46172 | − | 0.333628i | 0.583588 | − | 0.812050i | \(-0.301648\pi\) |
0.878130 | + | 0.478422i | \(0.158791\pi\) | |||||||
\(62\) | 31.1227 | − | 64.6270i | 0.501979 | − | 1.04237i | ||||
\(63\) | 25.7390 | + | 53.4475i | 0.408555 | + | 0.848374i | ||||
\(64\) | 3.56420 | + | 15.6158i | 0.0556906 | + | 0.243996i | ||||
\(65\) | −39.3853 | + | 8.98943i | −0.605927 | + | 0.138299i | ||||
\(66\) | −56.7385 | + | 27.3238i | −0.859675 | + | 0.413997i | ||||
\(67\) | −53.0202 | − | 25.5332i | −0.791347 | − | 0.381093i | −0.00586940 | − | 0.999983i | \(-0.501868\pi\) |
−0.785478 | + | 0.618890i | \(0.787583\pi\) | |||||||
\(68\) | 25.1586 | + | 110.227i | 0.369980 | + | 1.62099i | ||||
\(69\) | 38.7271 | − | 30.8839i | 0.561263 | − | 0.447592i | ||||
\(70\) | 227.495 | − | 181.421i | 3.24993 | − | 2.59173i | ||||
\(71\) | −47.5663 | + | 98.7724i | −0.669948 | + | 1.39116i | 0.237663 | + | 0.971348i | \(0.423619\pi\) |
−0.907611 | + | 0.419813i | \(0.862096\pi\) | |||||||
\(72\) | 97.9625 | + | 22.3593i | 1.36059 | + | 0.310546i | ||||
\(73\) | 54.6728 | + | 43.6001i | 0.748943 | + | 0.597262i | 0.921791 | − | 0.387687i | \(-0.126726\pi\) |
−0.172849 | + | 0.984948i | \(0.555297\pi\) | |||||||
\(74\) | −13.2198 | + | 57.9198i | −0.178646 | + | 0.782700i | ||||
\(75\) | 22.6157 | + | 46.9621i | 0.301543 | + | 0.626161i | ||||
\(76\) | −68.9573 | + | 54.9916i | −0.907333 | + | 0.723574i | ||||
\(77\) | −43.6905 | − | 90.7243i | −0.567409 | − | 1.17824i | ||||
\(78\) | −24.1527 | + | 30.2865i | −0.309650 | + | 0.388288i | ||||
\(79\) | −33.1652 | −0.419813 | −0.209906 | − | 0.977721i | \(-0.567316\pi\) | ||||
−0.209906 | + | 0.977721i | \(0.567316\pi\) | |||||||
\(80\) | − | 227.522i | − | 2.84403i | ||||||
\(81\) | −2.62763 | + | 3.29495i | −0.0324399 | + | 0.0406784i | ||||
\(82\) | −74.4565 | + | 154.611i | −0.908007 | + | 1.88550i | ||||
\(83\) | 3.02602 | + | 13.2578i | 0.0364580 | + | 0.159733i | 0.989880 | − | 0.141906i | \(-0.0453232\pi\) |
−0.953422 | + | 0.301640i | \(0.902466\pi\) | |||||||
\(84\) | 43.2358 | − | 189.429i | 0.514712 | − | 2.25510i | ||||
\(85\) | − | 89.1150i | − | 1.04841i | ||||||
\(86\) | −152.316 | + | 34.0363i | −1.77112 | + | 0.395771i | ||||
\(87\) | 33.9419 | 0.390137 | ||||||||
\(88\) | −166.286 | − | 37.9537i | −1.88961 | − | 0.431292i | ||||
\(89\) | 9.70773 | − | 2.21573i | 0.109076 | − | 0.0248958i | −0.167635 | − | 0.985849i | \(-0.553613\pi\) |
0.276710 | + | 0.960953i | \(0.410756\pi\) | |||||||
\(90\) | −126.522 | − | 60.9297i | −1.40580 | − | 0.676997i | ||||
\(91\) | −48.4278 | − | 38.6198i | −0.532173 | − | 0.424394i | ||||
\(92\) | 237.876 | 2.58561 | ||||||||
\(93\) | 37.7531i | 0.405948i | ||||||||
\(94\) | −38.0076 | − | 30.3101i | −0.404336 | − | 0.322448i | ||||
\(95\) | 62.6342 | − | 30.1630i | 0.659307 | − | 0.317505i | ||||
\(96\) | −46.5583 | − | 58.3822i | −0.484982 | − | 0.608148i | ||||
\(97\) | 29.5117 | − | 14.2121i | 0.304245 | − | 0.146517i | −0.275532 | − | 0.961292i | \(-0.588854\pi\) |
0.579777 | + | 0.814775i | \(0.303140\pi\) | |||||||
\(98\) | 261.570 | + | 59.7017i | 2.66908 | + | 0.609201i | ||||
\(99\) | −30.2999 | + | 37.9948i | −0.306059 | + | 0.383786i | ||||
\(100\) | −55.7003 | + | 244.039i | −0.557003 | + | 2.44039i | ||||
\(101\) | 144.898 | + | 69.7792i | 1.43463 | + | 0.690883i | 0.979853 | − | 0.199721i | \(-0.0640034\pi\) |
0.454780 | + | 0.890604i | \(0.349718\pi\) | |||||||
\(102\) | −53.2788 | − | 66.8095i | −0.522341 | − | 0.654995i | ||||
\(103\) | −46.8835 | − | 58.7901i | −0.455180 | − | 0.570777i | 0.500293 | − | 0.865856i | \(-0.333226\pi\) |
−0.955473 | + | 0.295079i | \(0.904654\pi\) | |||||||
\(104\) | −102.288 | + | 23.3465i | −0.983535 | + | 0.224485i | ||||
\(105\) | −66.4478 | + | 137.980i | −0.632836 | + | 1.31410i | ||||
\(106\) | 122.059 | + | 253.459i | 1.15150 | + | 2.39112i | ||||
\(107\) | −13.7355 | − | 60.1791i | −0.128369 | − | 0.562422i | −0.997675 | − | 0.0681477i | \(-0.978291\pi\) |
0.869306 | − | 0.494274i | \(-0.164566\pi\) | |||||||
\(108\) | −245.193 | + | 55.9636i | −2.27030 | + | 0.518182i | ||||
\(109\) | 58.1442 | − | 28.0008i | 0.533433 | − | 0.256888i | −0.147719 | − | 0.989029i | \(-0.547193\pi\) |
0.681153 | + | 0.732141i | \(0.261479\pi\) | |||||||
\(110\) | 214.764 | + | 103.425i | 1.95240 | + | 0.940226i | ||||
\(111\) | −6.95784 | − | 30.4843i | −0.0626833 | − | 0.274633i | ||||
\(112\) | 272.745 | − | 217.507i | 2.43523 | − | 1.94203i | ||||
\(113\) | −42.7493 | + | 34.0914i | −0.378312 | + | 0.301694i | −0.794123 | − | 0.607757i | \(-0.792069\pi\) |
0.415811 | + | 0.909451i | \(0.363498\pi\) | |||||||
\(114\) | 28.9234 | − | 60.0601i | 0.253714 | − | 0.526843i | ||||
\(115\) | −182.792 | − | 41.7212i | −1.58950 | − | 0.362793i | ||||
\(116\) | 127.438 | + | 101.628i | 1.09860 | + | 0.876107i | ||||
\(117\) | −6.65196 | + | 29.1441i | −0.0568544 | + | 0.249095i | ||||
\(118\) | −85.7673 | − | 178.098i | −0.726841 | − | 1.50930i | ||||
\(119\) | 106.828 | − | 85.1922i | 0.897711 | − | 0.715901i | ||||
\(120\) | 112.551 | + | 233.715i | 0.937926 | + | 1.94762i | ||||
\(121\) | −24.0099 | + | 30.1075i | −0.198429 | + | 0.248822i | ||||
\(122\) | −331.955 | −2.72094 | ||||||||
\(123\) | − | 90.3189i | − | 0.734300i | ||||||
\(124\) | −113.040 | + | 141.747i | −0.911612 | + | 1.14312i | ||||
\(125\) | 7.17018 | − | 14.8890i | 0.0573615 | − | 0.119112i | ||||
\(126\) | −47.9123 | − | 209.917i | −0.380256 | − | 1.66601i | ||||
\(127\) | −37.3496 | + | 163.639i | −0.294091 | + | 1.28850i | 0.584683 | + | 0.811262i | \(0.301219\pi\) |
−0.878775 | + | 0.477237i | \(0.841638\pi\) | |||||||
\(128\) | 98.2218i | 0.767357i | ||||||||
\(129\) | 64.4552 | − | 50.9230i | 0.499653 | − | 0.394752i | ||||
\(130\) | 146.629 | 1.12791 | ||||||||
\(131\) | 70.1378 | + | 16.0085i | 0.535403 | + | 0.122202i | 0.481669 | − | 0.876353i | \(-0.340031\pi\) |
0.0537339 | + | 0.998555i | \(0.482888\pi\) | |||||||
\(132\) | 155.181 | − | 35.4191i | 1.17561 | − | 0.268326i | ||||
\(133\) | 96.0353 | + | 46.2482i | 0.722070 | + | 0.347731i | ||||
\(134\) | 166.995 | + | 133.174i | 1.24623 | + | 0.993835i | ||||
\(135\) | 198.230 | 1.46837 | ||||||||
\(136\) | − | 231.441i | − | 1.70177i | ||||||
\(137\) | −104.933 | − | 83.6816i | −0.765937 | − | 0.610814i | 0.160599 | − | 0.987020i | \(-0.448657\pi\) |
−0.926536 | + | 0.376205i | \(0.877229\pi\) | |||||||
\(138\) | −161.983 | + | 78.0070i | −1.17379 | + | 0.565268i | ||||
\(139\) | 6.94309 | + | 8.70635i | 0.0499503 | + | 0.0626356i | 0.806179 | − | 0.591672i | \(-0.201532\pi\) |
−0.756229 | + | 0.654307i | \(0.772960\pi\) | |||||||
\(140\) | −662.623 | + | 319.102i | −4.73302 | + | 2.27930i | ||||
\(141\) | 24.9447 | + | 5.69347i | 0.176913 | + | 0.0403793i | ||||
\(142\) | 248.092 | − | 311.098i | 1.74713 | − | 2.19083i | ||||
\(143\) | 11.2913 | − | 49.4706i | 0.0789604 | − | 0.345948i | ||||
\(144\) | −151.688 | − | 73.0491i | −1.05339 | − | 0.507286i | ||||
\(145\) | −80.1031 | − | 100.446i | −0.552435 | − | 0.692732i | ||||
\(146\) | −158.251 | − | 198.440i | −1.08391 | − | 1.35918i | ||||
\(147\) | −137.669 | + | 31.4221i | −0.936527 | + | 0.213756i | ||||
\(148\) | 65.1518 | − | 135.289i | 0.440215 | − | 0.914115i | ||||
\(149\) | −100.687 | − | 209.079i | −0.675754 | − | 1.40322i | −0.903112 | − | 0.429406i | \(-0.858723\pi\) |
0.227358 | − | 0.973811i | \(-0.426991\pi\) | |||||||
\(150\) | −42.0985 | − | 184.445i | −0.280656 | − | 1.22964i | ||||
\(151\) | 101.814 | − | 23.2384i | 0.674266 | − | 0.153897i | 0.128340 | − | 0.991730i | \(-0.459035\pi\) |
0.545926 | + | 0.837833i | \(0.316178\pi\) | |||||||
\(152\) | 162.667 | − | 78.3365i | 1.07018 | − | 0.515372i | ||||
\(153\) | −59.4125 | − | 28.6116i | −0.388317 | − | 0.187004i | ||||
\(154\) | 81.3284 | + | 356.323i | 0.528107 | + | 2.31379i | ||||
\(155\) | 111.725 | − | 89.0976i | 0.720805 | − | 0.574823i | ||||
\(156\) | 76.5503 | − | 61.0469i | 0.490707 | − | 0.391326i | ||||
\(157\) | −102.045 | + | 211.899i | −0.649968 | + | 1.34967i | 0.271958 | + | 0.962309i | \(0.412329\pi\) |
−0.921927 | + | 0.387364i | \(0.873386\pi\) | |||||||
\(158\) | 117.358 | + | 26.7862i | 0.742773 | + | 0.169533i | ||||
\(159\) | −115.760 | − | 92.3157i | −0.728052 | − | 0.580602i | ||||
\(160\) | −62.8958 | + | 275.565i | −0.393099 | + | 1.72228i | ||||
\(161\) | −124.732 | − | 259.009i | −0.774735 | − | 1.60875i | ||||
\(162\) | 11.9593 | − | 9.53724i | 0.0738229 | − | 0.0588718i | ||||
\(163\) | −14.5755 | − | 30.2663i | −0.0894201 | − | 0.185683i | 0.851463 | − | 0.524415i | \(-0.175716\pi\) |
−0.940883 | + | 0.338733i | \(0.890002\pi\) | |||||||
\(164\) | 270.431 | − | 339.110i | 1.64897 | − | 2.06774i | ||||
\(165\) | −125.459 | −0.760356 | ||||||||
\(166\) | − | 49.3581i | − | 0.297338i | ||||||
\(167\) | −153.423 | + | 192.386i | −0.918700 | + | 1.15201i | 0.0693052 | + | 0.997596i | \(0.477922\pi\) |
−0.988006 | + | 0.154418i | \(0.950650\pi\) | |||||||
\(168\) | −172.572 | + | 358.349i | −1.02721 | + | 2.13303i | ||||
\(169\) | 30.6604 | + | 134.332i | 0.181422 | + | 0.794863i | ||||
\(170\) | −71.9746 | + | 315.341i | −0.423380 | + | 1.85495i | ||||
\(171\) | − | 51.4421i | − | 0.300831i | ||||||
\(172\) | 394.475 | + | 1.79603i | 2.29346 | + | 0.0104420i | ||||
\(173\) | −60.3821 | −0.349030 | −0.174515 | − | 0.984655i | \(-0.555836\pi\) | ||||
−0.174515 | + | 0.984655i | \(0.555836\pi\) | |||||||
\(174\) | −120.107 | − | 27.4136i | −0.690268 | − | 0.157549i | ||||
\(175\) | 294.926 | − | 67.3150i | 1.68529 | − | 0.384657i | ||||
\(176\) | 257.482 | + | 123.997i | 1.46297 | + | 0.704528i | ||||
\(177\) | 81.3412 | + | 64.8674i | 0.459555 | + | 0.366483i | ||||
\(178\) | −36.1413 | −0.203041 | ||||||||
\(179\) | 100.540i | 0.561674i | 0.959755 | + | 0.280837i | \(0.0906121\pi\) | ||||
−0.959755 | + | 0.280837i | \(0.909388\pi\) | |||||||
\(180\) | 277.503 | + | 221.301i | 1.54168 | + | 1.22945i | ||||
\(181\) | 193.035 | − | 92.9607i | 1.06649 | − | 0.513595i | 0.183517 | − | 0.983017i | \(-0.441252\pi\) |
0.882974 | + | 0.469422i | \(0.155538\pi\) | |||||||
\(182\) | 140.174 | + | 175.773i | 0.770188 | + | 0.965786i | ||||
\(183\) | 157.412 | − | 75.8056i | 0.860174 | − | 0.414238i | ||||
\(184\) | −474.731 | − | 108.354i | −2.58006 | − | 0.588882i | ||||
\(185\) | −73.7932 | + | 92.5338i | −0.398882 | + | 0.500183i | ||||
\(186\) | 30.4917 | − | 133.593i | 0.163934 | − | 0.718241i | ||||
\(187\) | 100.849 | + | 48.5666i | 0.539302 | + | 0.259714i | ||||
\(188\) | 76.6099 | + | 96.0658i | 0.407500 | + | 0.510988i | ||||
\(189\) | 189.504 | + | 237.630i | 1.00267 | + | 1.25730i | ||||
\(190\) | −245.998 | + | 56.1475i | −1.29473 | + | 0.295513i | ||||
\(191\) | −76.2443 | + | 158.323i | −0.399185 | + | 0.828916i | 0.600389 | + | 0.799708i | \(0.295013\pi\) |
−0.999573 | + | 0.0292073i | \(0.990702\pi\) | |||||||
\(192\) | 13.2761 | + | 27.5681i | 0.0691464 | + | 0.143584i | ||||
\(193\) | 51.6500 | + | 226.293i | 0.267617 | + | 1.17250i | 0.912777 | + | 0.408458i | \(0.133933\pi\) |
−0.645161 | + | 0.764047i | \(0.723210\pi\) | |||||||
\(194\) | −115.909 | + | 26.4554i | −0.597467 | + | 0.136368i | ||||
\(195\) | −69.5309 | + | 33.4843i | −0.356569 | + | 0.171715i | ||||
\(196\) | −610.976 | − | 294.230i | −3.11722 | − | 1.50118i | ||||
\(197\) | −25.2236 | − | 110.512i | −0.128039 | − | 0.560974i | −0.997728 | − | 0.0673739i | \(-0.978538\pi\) |
0.869689 | − | 0.493600i | \(-0.164319\pi\) | |||||||
\(198\) | 137.906 | − | 109.976i | 0.696494 | − | 0.555435i | ||||
\(199\) | 100.763 | − | 80.3556i | 0.506345 | − | 0.403797i | −0.336723 | − | 0.941604i | \(-0.609319\pi\) |
0.843068 | + | 0.537807i | \(0.180747\pi\) | |||||||
\(200\) | 222.323 | − | 461.658i | 1.11161 | − | 2.30829i | ||||
\(201\) | −109.600 | − | 25.0155i | −0.545275 | − | 0.124455i | ||||
\(202\) | −456.377 | − | 363.948i | −2.25929 | − | 1.80172i | ||||
\(203\) | 43.8340 | − | 192.049i | 0.215931 | − | 0.946055i | ||||
\(204\) | 93.7123 | + | 194.596i | 0.459374 | + | 0.953900i | ||||
\(205\) | −267.285 | + | 213.153i | −1.30383 | + | 1.03977i | ||||
\(206\) | 118.419 | + | 245.900i | 0.574851 | + | 1.19369i | ||||
\(207\) | −86.5033 | + | 108.472i | −0.417890 | + | 0.524018i | ||||
\(208\) | 175.794 | 0.845165 | ||||||||
\(209\) | 87.3202i | 0.417800i | ||||||||
\(210\) | 346.573 | − | 434.589i | 1.65035 | − | 2.06947i | ||||
\(211\) | 6.17150 | − | 12.8152i | 0.0292488 | − | 0.0607358i | −0.885833 | − | 0.464005i | \(-0.846412\pi\) |
0.915081 | + | 0.403269i | \(0.132126\pi\) | |||||||
\(212\) | −158.222 | − | 693.215i | −0.746329 | − | 3.26988i | ||||
\(213\) | −46.6019 | + | 204.176i | −0.218788 | + | 0.958574i | ||||
\(214\) | 224.043i | 1.04693i | ||||||||
\(215\) | −302.813 | − | 70.5672i | −1.40843 | − | 0.328220i | ||||
\(216\) | 514.824 | 2.38344 | ||||||||
\(217\) | 213.614 | + | 48.7559i | 0.984394 | + | 0.224682i | ||||
\(218\) | −228.364 | + | 52.1225i | −1.04754 | + | 0.239094i | ||||
\(219\) | 120.358 | + | 57.9613i | 0.549580 | + | 0.264664i | ||||
\(220\) | −471.046 | − | 375.646i | −2.14112 | − | 1.70748i | ||||
\(221\) | 68.8544 | 0.311558 | ||||||||
\(222\) | 113.491i | 0.511221i | ||||||||
\(223\) | 188.473 | + | 150.302i | 0.845169 | + | 0.674000i | 0.947152 | − | 0.320786i | \(-0.103947\pi\) |
−0.101982 | + | 0.994786i | \(0.532518\pi\) | |||||||
\(224\) | −390.464 | + | 188.037i | −1.74314 | + | 0.839453i | ||||
\(225\) | −91.0265 | − | 114.144i | −0.404562 | − | 0.507305i | ||||
\(226\) | 178.806 | − | 86.1087i | 0.791179 | − | 0.381012i | ||||
\(227\) | 191.912 | + | 43.8027i | 0.845427 | + | 0.192963i | 0.623230 | − | 0.782039i | \(-0.285820\pi\) |
0.222197 | + | 0.975002i | \(0.428677\pi\) | |||||||
\(228\) | −105.052 | + | 131.731i | −0.460753 | + | 0.577766i | ||||
\(229\) | 15.1913 | − | 66.5573i | 0.0663375 | − | 0.290643i | −0.930868 | − | 0.365357i | \(-0.880947\pi\) |
0.997205 | + | 0.0747133i | \(0.0238042\pi\) | |||||||
\(230\) | 613.131 | + | 295.268i | 2.66579 | + | 1.28378i | ||||
\(231\) | −119.936 | − | 150.395i | −0.519204 | − | 0.651061i | ||||
\(232\) | −208.036 | − | 260.869i | −0.896707 | − | 1.12443i | ||||
\(233\) | −124.112 | + | 28.3278i | −0.532670 | + | 0.121578i | −0.480391 | − | 0.877054i | \(-0.659505\pi\) |
−0.0522782 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(234\) | 47.0771 | − | 97.7567i | 0.201184 | − | 0.417764i | ||||
\(235\) | −42.0207 | − | 87.2569i | −0.178812 | − | 0.371306i | ||||
\(236\) | 111.178 | + | 487.101i | 0.471092 | + | 2.06399i | ||||
\(237\) | −61.7678 | + | 14.0981i | −0.260624 | + | 0.0594856i | ||||
\(238\) | −446.826 | + | 215.180i | −1.87742 | + | 0.904117i | ||||
\(239\) | −238.606 | − | 114.907i | −0.998353 | − | 0.480782i | −0.137974 | − | 0.990436i | \(-0.544059\pi\) |
−0.860379 | + | 0.509654i | \(0.829773\pi\) | |||||||
\(240\) | −96.7168 | − | 423.744i | −0.402987 | − | 1.76560i | ||||
\(241\) | −326.311 | + | 260.224i | −1.35399 | + | 1.07977i | −0.365121 | + | 0.930960i | \(0.618972\pi\) |
−0.988866 | + | 0.148808i | \(0.952456\pi\) | |||||||
\(242\) | 109.278 | − | 87.1462i | 0.451562 | − | 0.360108i | ||||
\(243\) | 103.559 | − | 215.042i | 0.426168 | − | 0.884947i | ||||
\(244\) | 817.993 | + | 186.702i | 3.35243 | + | 0.765170i | ||||
\(245\) | 417.890 | + | 333.256i | 1.70567 | + | 1.36023i | ||||
\(246\) | −72.9470 | + | 319.602i | −0.296532 | + | 1.29919i | ||||
\(247\) | 23.3053 | + | 48.3941i | 0.0943536 | + | 0.195927i | ||||
\(248\) | 290.161 | − | 231.396i | 1.17000 | − | 0.933047i | ||||
\(249\) | 11.2715 | + | 23.4054i | 0.0452669 | + | 0.0939978i | ||||
\(250\) | −37.3976 | + | 46.8951i | −0.149591 | + | 0.187581i | ||||
\(251\) | 276.471 | 1.10148 | 0.550739 | − | 0.834678i | \(-0.314346\pi\) | ||||
0.550739 | + | 0.834678i | \(0.314346\pi\) | |||||||
\(252\) | 544.219i | 2.15960i | ||||||||
\(253\) | 146.835 | − | 184.125i | 0.580374 | − | 0.727766i | ||||
\(254\) | 264.330 | − | 548.887i | 1.04067 | − | 2.16097i | ||||
\(255\) | −37.8816 | − | 165.970i | −0.148555 | − | 0.650863i | ||||
\(256\) | 93.5866 | − | 410.030i | 0.365573 | − | 1.60168i | ||||
\(257\) | 121.871i | 0.474206i | 0.971485 | + | 0.237103i | \(0.0761978\pi\) | ||||
−0.971485 | + | 0.237103i | \(0.923802\pi\) | |||||||
\(258\) | −269.209 | + | 128.138i | −1.04345 | + | 0.496657i | ||||
\(259\) | −181.471 | −0.700660 | ||||||||
\(260\) | −361.318 | − | 82.4685i | −1.38969 | − | 0.317187i | ||||
\(261\) | −92.6851 | + | 21.1548i | −0.355115 | + | 0.0810528i | ||||
\(262\) | −235.260 | − | 113.295i | −0.897938 | − | 0.432424i | ||||
\(263\) | −364.495 | − | 290.675i | −1.38591 | − | 1.10523i | −0.981672 | − | 0.190577i | \(-0.938964\pi\) |
−0.404241 | − | 0.914652i | \(-0.632464\pi\) | |||||||
\(264\) | −325.829 | −1.23420 | ||||||||
\(265\) | 560.441i | 2.11487i | ||||||||
\(266\) | −302.477 | − | 241.217i | −1.13713 | − | 0.906832i | ||||
\(267\) | 17.1381 | − | 8.25326i | 0.0641875 | − | 0.0309111i | ||||
\(268\) | −336.602 | − | 422.086i | −1.25598 | − | 1.57495i | ||||
\(269\) | 76.0369 | − | 36.6174i | 0.282665 | − | 0.136124i | −0.287180 | − | 0.957877i | \(-0.592718\pi\) |
0.569845 | + | 0.821752i | \(0.307003\pi\) | |||||||
\(270\) | −701.455 | − | 160.102i | −2.59798 | − | 0.592972i | ||||
\(271\) | 15.2184 | − | 19.0832i | 0.0561563 | − | 0.0704177i | −0.752960 | − | 0.658066i | \(-0.771375\pi\) |
0.809116 | + | 0.587648i | \(0.199946\pi\) | |||||||
\(272\) | −86.2909 | + | 378.065i | −0.317246 | + | 1.38995i | ||||
\(273\) | −106.610 | − | 51.3407i | −0.390513 | − | 0.188061i | ||||
\(274\) | 303.730 | + | 380.865i | 1.10850 | + | 1.39002i | ||||
\(275\) | 154.512 | + | 193.753i | 0.561864 | + | 0.704555i | ||||
\(276\) | 443.028 | − | 101.118i | 1.60517 | − | 0.366370i | ||||
\(277\) | 192.181 | − | 399.067i | 0.693793 | − | 1.44068i | −0.194267 | − | 0.980949i | \(-0.562233\pi\) |
0.888060 | − | 0.459727i | \(-0.152053\pi\) | |||||||
\(278\) | −17.5370 | − | 36.4159i | −0.0630826 | − | 0.130992i | ||||
\(279\) | −23.5302 | − | 103.092i | −0.0843375 | − | 0.369507i | ||||
\(280\) | 1467.75 | − | 335.005i | 5.24197 | − | 1.19644i | ||||
\(281\) | 417.971 | − | 201.284i | 1.48744 | − | 0.716315i | 0.498816 | − | 0.866708i | \(-0.333768\pi\) |
0.988626 | + | 0.150393i | \(0.0480540\pi\) | |||||||
\(282\) | −83.6708 | − | 40.2938i | −0.296705 | − | 0.142886i | ||||
\(283\) | 63.9676 | + | 280.260i | 0.226034 | + | 0.990319i | 0.952839 | + | 0.303475i | \(0.0981470\pi\) |
−0.726805 | + | 0.686843i | \(0.758996\pi\) | |||||||
\(284\) | −786.312 | + | 627.063i | −2.76870 | + | 2.20797i | ||||
\(285\) | 103.830 | − | 82.8014i | 0.364315 | − | 0.290531i | ||||
\(286\) | −79.9109 | + | 165.937i | −0.279409 | + | 0.580198i | ||||
\(287\) | −511.039 | − | 116.641i | −1.78062 | − | 0.406416i | ||||
\(288\) | 163.524 | + | 130.406i | 0.567792 | + | 0.452799i | ||||
\(289\) | 30.5105 | − | 133.675i | 0.105573 | − | 0.462544i | ||||
\(290\) | 202.326 | + | 420.134i | 0.697675 | + | 1.44874i | ||||
\(291\) | 48.9221 | − | 39.0141i | 0.168117 | − | 0.134069i | ||||
\(292\) | 278.348 | + | 577.995i | 0.953246 | + | 1.97943i | ||||
\(293\) | 189.051 | − | 237.063i | 0.645226 | − | 0.809088i | −0.346420 | − | 0.938080i | \(-0.612603\pi\) |
0.991646 | + | 0.128992i | \(0.0411741\pi\) | |||||||
\(294\) | 512.534 | 1.74331 | ||||||||
\(295\) | − | 393.805i | − | 1.33493i | ||||||
\(296\) | −191.649 | + | 240.320i | −0.647462 | + | 0.811891i | ||||
\(297\) | −108.033 | + | 224.332i | −0.363747 | + | 0.755328i | ||||
\(298\) | 187.426 | + | 821.167i | 0.628947 | + | 2.75559i | ||||
\(299\) | 32.2357 | − | 141.234i | 0.107812 | − | 0.472354i | ||||
\(300\) | 478.182i | 1.59394i | ||||||||
\(301\) | −204.891 | − | 430.462i | −0.680700 | − | 1.43011i | ||||
\(302\) | −379.048 | −1.25512 | ||||||||
\(303\) | 299.524 | + | 68.3644i | 0.988529 | + | 0.225625i | ||||
\(304\) | −294.929 | + | 67.3156i | −0.970162 | + | 0.221433i | ||||
\(305\) | −595.828 | − | 286.936i | −1.95353 | − | 0.940773i | ||||
\(306\) | 187.128 | + | 149.230i | 0.611530 | + | 0.487679i | ||||
\(307\) | −294.750 | −0.960097 | −0.480049 | − | 0.877242i | \(-0.659381\pi\) | ||||
−0.480049 | + | 0.877242i | \(0.659381\pi\) | |||||||
\(308\) | − | 923.782i | − | 2.99929i | ||||||
\(309\) | −112.308 | − | 89.5627i | −0.363456 | − | 0.289847i | ||||
\(310\) | −467.309 | + | 225.044i | −1.50745 | + | 0.725949i | ||||
\(311\) | 146.441 | + | 183.631i | 0.470870 | + | 0.590452i | 0.959384 | − | 0.282104i | \(-0.0910323\pi\) |
−0.488514 | + | 0.872556i | \(0.662461\pi\) | |||||||
\(312\) | −180.579 | + | 86.9623i | −0.578779 | + | 0.278725i | ||||
\(313\) | −110.395 | − | 25.1969i | −0.352699 | − | 0.0805012i | 0.0425008 | − | 0.999096i | \(-0.486467\pi\) |
−0.395200 | + | 0.918595i | \(0.629325\pi\) | |||||||
\(314\) | 532.238 | − | 667.405i | 1.69502 | − | 2.12549i | ||||
\(315\) | 95.4507 | − | 418.197i | 0.303018 | − | 1.32761i | ||||
\(316\) | −274.125 | − | 132.012i | −0.867484 | − | 0.417758i | ||||
\(317\) | 58.6493 | + | 73.5439i | 0.185014 | + | 0.232000i | 0.865685 | − | 0.500589i | \(-0.166883\pi\) |
−0.680671 | + | 0.732589i | \(0.738312\pi\) | |||||||
\(318\) | 335.068 | + | 420.162i | 1.05367 | + | 1.32127i | ||||
\(319\) | 157.328 | − | 35.9091i | 0.493191 | − | 0.112568i | ||||
\(320\) | 50.2521 | − | 104.350i | 0.157038 | − | 0.326093i | ||||
\(321\) | −51.1627 | − | 106.240i | −0.159385 | − | 0.330967i | ||||
\(322\) | 232.185 | + | 1017.27i | 0.721072 | + | 3.15922i | ||||
\(323\) | −115.517 | + | 26.3659i | −0.357636 | + | 0.0816281i | ||||
\(324\) | −34.8338 | + | 16.7751i | −0.107512 | + | 0.0517750i | ||||
\(325\) | 137.345 | + | 66.1417i | 0.422599 | + | 0.203513i | ||||
\(326\) | 27.1318 | + | 118.872i | 0.0832263 | + | 0.364638i | ||||
\(327\) | 96.3867 | − | 76.8658i | 0.294760 | − | 0.235064i | ||||
\(328\) | −694.167 | + | 553.580i | −2.11636 | + | 1.68774i | ||||
\(329\) | 64.4293 | − | 133.789i | 0.195834 | − | 0.406653i | ||||
\(330\) | 443.947 | + | 101.328i | 1.34529 | + | 0.307055i | ||||
\(331\) | 320.751 | + | 255.791i | 0.969037 | + | 0.772782i | 0.973847 | − | 0.227207i | \(-0.0729593\pi\) |
−0.00480903 | + | 0.999988i | \(0.501531\pi\) | |||||||
\(332\) | −27.7605 | + | 121.627i | −0.0836160 | + | 0.366345i | ||||
\(333\) | 37.9995 | + | 78.9068i | 0.114113 | + | 0.236957i | ||||
\(334\) | 698.284 | − | 556.863i | 2.09067 | − | 1.66725i | ||||
\(335\) | 184.627 | + | 383.382i | 0.551126 | + | 1.14442i | ||||
\(336\) | 415.509 | − | 521.032i | 1.23663 | − | 1.55069i | ||||
\(337\) | −318.775 | −0.945921 | −0.472960 | − | 0.881084i | \(-0.656815\pi\) | ||||
−0.472960 | + | 0.881084i | \(0.656815\pi\) | |||||||
\(338\) | − | 500.109i | − | 1.47961i | ||||||
\(339\) | −65.1256 | + | 81.6649i | −0.192111 | + | 0.240900i | ||||
\(340\) | 354.715 | − | 736.574i | 1.04328 | − | 2.16639i | ||||
\(341\) | 39.9411 | + | 174.994i | 0.117129 | + | 0.513178i | ||||
\(342\) | −41.5478 | + | 182.033i | −0.121485 | + | 0.532259i | ||||
\(343\) | 276.278i | 0.805476i | ||||||||
\(344\) | −786.438 | − | 183.270i | −2.28616 | − | 0.532763i | ||||
\(345\) | −358.173 | −1.03818 | ||||||||
\(346\) | 213.668 | + | 48.7683i | 0.617537 | + | 0.140949i | ||||
\(347\) | 91.8179 | − | 20.9568i | 0.264605 | − | 0.0603943i | −0.0881600 | − | 0.996106i | \(-0.528099\pi\) |
0.352765 | + | 0.935712i | \(0.385242\pi\) | |||||||
\(348\) | 280.545 | + | 135.103i | 0.806163 | + | 0.388228i | ||||
\(349\) | −510.018 | − | 406.725i | −1.46137 | − | 1.16540i | −0.952492 | − | 0.304563i | \(-0.901490\pi\) |
−0.508876 | − | 0.860840i | \(-0.669939\pi\) | |||||||
\(350\) | −1097.99 | −3.13712 | ||||||||
\(351\) | 153.162i | 0.436358i | ||||||||
\(352\) | −277.573 | − | 221.357i | −0.788560 | − | 0.628856i | ||||
\(353\) | 275.129 | − | 132.495i | 0.779401 | − | 0.375340i | −0.00149626 | − | 0.999999i | \(-0.500476\pi\) |
0.780898 | + | 0.624659i | \(0.214762\pi\) | |||||||
\(354\) | −235.442 | − | 295.235i | −0.665091 | − | 0.833998i | ||||
\(355\) | 714.210 | − | 343.945i | 2.01186 | − | 0.968860i | ||||
\(356\) | 89.0582 | + | 20.3269i | 0.250163 | + | 0.0570982i | ||||
\(357\) | 162.745 | − | 204.075i | 0.455867 | − | 0.571640i | ||||
\(358\) | 81.2020 | − | 355.769i | 0.226821 | − | 0.993768i | ||||
\(359\) | −106.443 | − | 51.2602i | −0.296498 | − | 0.142786i | 0.279721 | − | 0.960081i | \(-0.409758\pi\) |
−0.576219 | + | 0.817295i | \(0.695472\pi\) | |||||||
\(360\) | −453.009 | − | 568.055i | −1.25836 | − | 1.57793i | ||||
\(361\) | 167.449 | + | 209.975i | 0.463849 | + | 0.581648i | ||||
\(362\) | −758.152 | + | 173.043i | −2.09434 | + | 0.478020i | ||||
\(363\) | −31.9184 | + | 66.2793i | −0.0879296 | + | 0.182588i | ||||
\(364\) | −246.553 | − | 511.973i | −0.677344 | − | 1.40652i | ||||
\(365\) | −112.517 | − | 492.971i | −0.308267 | − | 1.35060i | ||||
\(366\) | −618.242 | + | 141.110i | −1.68918 | + | 0.385545i | ||||
\(367\) | −313.419 | + | 150.934i | −0.854002 | + | 0.411265i | −0.809061 | − | 0.587724i | \(-0.800024\pi\) |
−0.0449402 | + | 0.998990i | \(0.514310\pi\) | |||||||
\(368\) | 735.088 | + | 354.000i | 1.99752 | + | 0.961955i | ||||
\(369\) | 56.2925 | + | 246.633i | 0.152554 | + | 0.668383i | ||||
\(370\) | 335.860 | − | 267.839i | 0.907730 | − | 0.723890i | ||||
\(371\) | −671.835 | + | 535.770i | −1.81088 | + | 1.44413i | ||||
\(372\) | −150.274 | + | 312.046i | −0.403961 | + | 0.838834i | ||||
\(373\) | 613.063 | + | 139.928i | 1.64360 | + | 0.375141i | 0.941520 | − | 0.336957i | \(-0.109398\pi\) |
0.702080 | + | 0.712098i | \(0.252255\pi\) | |||||||
\(374\) | −317.640 | − | 253.309i | −0.849304 | − | 0.677298i | ||||
\(375\) | 7.02481 | − | 30.7777i | 0.0187328 | − | 0.0820739i | ||||
\(376\) | −109.132 | − | 226.615i | −0.290245 | − | 0.602700i | ||||
\(377\) | 77.6093 | − | 61.8914i | 0.205860 | − | 0.164168i | ||||
\(378\) | −478.652 | − | 993.932i | −1.26628 | − | 2.62945i | ||||
\(379\) | −179.127 | + | 224.618i | −0.472629 | + | 0.592659i | −0.959813 | − | 0.280641i | \(-0.909453\pi\) |
0.487183 | + | 0.873300i | \(0.338024\pi\) | |||||||
\(380\) | 637.760 | 1.67832 | ||||||||
\(381\) | 320.643i | 0.841583i | ||||||||
\(382\) | 397.669 | − | 498.661i | 1.04102 | − | 1.30539i | ||||
\(383\) | −94.6602 | + | 196.564i | −0.247154 | + | 0.513222i | −0.987230 | − | 0.159302i | \(-0.949076\pi\) |
0.740075 | + | 0.672524i | \(0.234790\pi\) | |||||||
\(384\) | 41.7528 | + | 182.931i | 0.108731 | + | 0.476383i | ||||
\(385\) | −162.022 | + | 709.866i | −0.420837 | + | 1.84381i | ||||
\(386\) | − | 842.475i | − | 2.18258i | ||||||
\(387\) | −144.269 | + | 179.228i | −0.372789 | + | 0.463121i | ||||
\(388\) | 300.498 | 0.774479 | ||||||||
\(389\) | 211.232 | + | 48.2124i | 0.543013 | + | 0.123939i | 0.485225 | − | 0.874390i | \(-0.338738\pi\) |
0.0577888 | + | 0.998329i | \(0.481595\pi\) | |||||||
\(390\) | 273.085 | − | 62.3300i | 0.700219 | − | 0.159820i | ||||
\(391\) | 287.916 | + | 138.653i | 0.736358 | + | 0.354611i | ||||
\(392\) | 1085.30 | + | 865.500i | 2.76863 | + | 2.20791i | ||||
\(393\) | 137.432 | 0.349699 | ||||||||
\(394\) | 411.428i | 1.04423i | ||||||||
\(395\) | 187.494 | + | 149.521i | 0.474667 | + | 0.378534i | ||||
\(396\) | −401.677 | + | 193.438i | −1.01434 | + | 0.488479i | ||||
\(397\) | −6.48080 | − | 8.12667i | −0.0163244 | − | 0.0204702i | 0.773602 | − | 0.633671i | \(-0.218453\pi\) |
−0.789927 | + | 0.613201i | \(0.789881\pi\) | |||||||
\(398\) | −421.458 | + | 202.964i | −1.05894 | + | 0.509959i | ||||
\(399\) | 198.518 | + | 45.3105i | 0.497540 | + | 0.113560i | ||||
\(400\) | −535.296 | + | 671.240i | −1.33824 | + | 1.67810i | ||||
\(401\) | −118.641 | + | 519.801i | −0.295863 | + | 1.29626i | 0.580361 | + | 0.814359i | \(0.302911\pi\) |
−0.876224 | + | 0.481903i | \(0.839946\pi\) | |||||||
\(402\) | 367.626 | + | 177.039i | 0.914493 | + | 0.440397i | ||||
\(403\) | 68.8409 | + | 86.3238i | 0.170821 | + | 0.214203i | ||||
\(404\) | 919.894 | + | 1153.51i | 2.27697 | + | 2.85522i | ||||
\(405\) | 29.7097 | − | 6.78104i | 0.0733573 | − | 0.0167433i | ||||
\(406\) | −310.221 | + | 644.180i | −0.764091 | + | 1.58665i | ||||
\(407\) | −64.5021 | − | 133.940i | −0.158482 | − | 0.329091i | ||||
\(408\) | −98.3824 | − | 431.042i | −0.241133 | − | 1.05647i | ||||
\(409\) | −17.3967 | + | 3.97068i | −0.0425347 | + | 0.00970827i | −0.243735 | − | 0.969842i | \(-0.578373\pi\) |
0.201201 | + | 0.979550i | \(0.435516\pi\) | |||||||
\(410\) | 1117.97 | − | 538.385i | 2.72675 | − | 1.31313i | ||||
\(411\) | −231.003 | − | 111.245i | −0.562050 | − | 0.270669i | ||||
\(412\) | −153.503 | − | 672.542i | −0.372581 | − | 1.63238i | ||||
\(413\) | 472.078 | − | 376.470i | 1.14305 | − | 0.911549i | ||||
\(414\) | 393.708 | − | 313.972i | 0.950986 | − | 0.758386i | ||||
\(415\) | 42.6642 | − | 88.5932i | 0.102805 | − | 0.213478i | ||||
\(416\) | −212.914 | − | 48.5962i | −0.511813 | − | 0.116818i | ||||
\(417\) | 16.6319 | + | 13.2635i | 0.0398848 | + | 0.0318070i | ||||
\(418\) | 70.5251 | − | 308.990i | 0.168720 | − | 0.739212i | ||||
\(419\) | 277.631 | + | 576.507i | 0.662605 | + | 1.37591i | 0.913076 | + | 0.407789i | \(0.133700\pi\) |
−0.250472 | + | 0.968124i | \(0.580586\pi\) | |||||||
\(420\) | −1098.44 | + | 875.977i | −2.61533 | + | 2.08566i | ||||
\(421\) | −277.767 | − | 576.789i | −0.659780 | − | 1.37005i | −0.915115 | − | 0.403194i | \(-0.867900\pi\) |
0.255335 | − | 0.966853i | \(-0.417814\pi\) | |||||||
\(422\) | −32.1888 | + | 40.3635i | −0.0762767 | + | 0.0956480i | ||||
\(423\) | −71.6651 | −0.169421 | ||||||||
\(424\) | 1455.52i | 3.43283i | ||||||||
\(425\) | −209.662 | + | 262.908i | −0.493323 | + | 0.618608i | ||||
\(426\) | 329.810 | − | 684.858i | 0.774202 | − | 1.60765i | ||||
\(427\) | −225.633 | − | 988.561i | −0.528414 | − | 2.31513i | ||||
\(428\) | 126.009 | − | 552.080i | 0.294413 | − | 1.28991i | ||||
\(429\) | − | 96.9352i | − | 0.225956i | ||||||
\(430\) | 1014.54 | + | 494.279i | 2.35939 | + | 1.14949i | ||||
\(431\) | 90.4497 | 0.209860 | 0.104930 | − | 0.994480i | \(-0.466538\pi\) | ||||
0.104930 | + | 0.994480i | \(0.466538\pi\) | |||||||
\(432\) | −840.979 | − | 191.948i | −1.94671 | − | 0.444324i | ||||
\(433\) | −388.048 | + | 88.5694i | −0.896184 | + | 0.204548i | −0.645717 | − | 0.763577i | \(-0.723441\pi\) |
−0.250467 | + | 0.968125i | \(0.580584\pi\) | |||||||
\(434\) | −716.513 | − | 345.054i | −1.65095 | − | 0.795056i | ||||
\(435\) | −191.885 | − | 153.023i | −0.441114 | − | 0.351777i | ||||
\(436\) | 592.043 | 1.35790 | ||||||||
\(437\) | 249.291i | 0.570460i | ||||||||
\(438\) | −379.085 | − | 302.310i | −0.865490 | − | 0.690205i | ||||
\(439\) | −742.597 | + | 357.616i | −1.69156 | + | 0.814615i | −0.696263 | + | 0.717786i | \(0.745155\pi\) |
−0.995301 | + | 0.0968282i | \(0.969130\pi\) | |||||||
\(440\) | 768.958 | + | 964.243i | 1.74763 | + | 2.19146i | ||||
\(441\) | 356.349 | − | 171.609i | 0.808048 | − | 0.389135i | ||||
\(442\) | −243.647 | − | 55.6109i | −0.551239 | − | 0.125817i | ||||
\(443\) | 270.689 | − | 339.433i | 0.611035 | − | 0.766214i | −0.376017 | − | 0.926613i | \(-0.622707\pi\) |
0.987052 | + | 0.160399i | \(0.0512780\pi\) | |||||||
\(444\) | 63.8309 | − | 279.661i | 0.143763 | − | 0.629868i | ||||
\(445\) | −64.8702 | − | 31.2399i | −0.145776 | − | 0.0702019i | ||||
\(446\) | −545.535 | − | 684.079i | −1.22317 | − | 1.53381i | ||||
\(447\) | −276.400 | − | 346.594i | −0.618344 | − | 0.775378i | ||||
\(448\) | 173.130 | − | 39.5159i | 0.386452 | − | 0.0882051i | ||||
\(449\) | −154.251 | + | 320.306i | −0.343544 | + | 0.713376i | −0.999128 | − | 0.0417461i | \(-0.986708\pi\) |
0.655585 | + | 0.755122i | \(0.272422\pi\) | |||||||
\(450\) | 229.916 | + | 477.426i | 0.510925 | + | 1.06095i | ||||
\(451\) | −95.5534 | − | 418.647i | −0.211870 | − | 0.928263i | ||||
\(452\) | −489.040 | + | 111.620i | −1.08195 | + | 0.246947i | ||||
\(453\) | 179.743 | − | 86.5598i | 0.396784 | − | 0.191081i | ||||
\(454\) | −643.720 | − | 309.999i | −1.41789 | − | 0.682818i | ||||
\(455\) | 99.6649 | + | 436.661i | 0.219044 | + | 0.959694i | ||||
\(456\) | 269.656 | − | 215.044i | 0.591352 | − | 0.471587i | ||||
\(457\) | 404.830 | − | 322.841i | 0.885842 | − | 0.706435i | −0.0708657 | − | 0.997486i | \(-0.522576\pi\) |
0.956708 | + | 0.291050i | \(0.0940047\pi\) | |||||||
\(458\) | −107.511 | + | 223.250i | −0.234741 | + | 0.487445i | ||||
\(459\) | −329.391 | − | 75.1814i | −0.717628 | − | 0.163794i | ||||
\(460\) | −1344.79 | − | 1072.44i | −2.92346 | − | 2.33138i | ||||
\(461\) | 75.1765 | − | 329.370i | 0.163073 | − | 0.714468i | −0.825585 | − | 0.564278i | \(-0.809154\pi\) |
0.988657 | − | 0.150190i | \(-0.0479884\pi\) | |||||||
\(462\) | 302.937 | + | 629.054i | 0.655707 | + | 1.36159i | ||||
\(463\) | 163.105 | − | 130.072i | 0.352278 | − | 0.280932i | −0.431322 | − | 0.902198i | \(-0.641953\pi\) |
0.783600 | + | 0.621266i | \(0.213381\pi\) | |||||||
\(464\) | 242.570 | + | 503.702i | 0.522780 | + | 1.08556i | ||||
\(465\) | 170.205 | − | 213.431i | 0.366033 | − | 0.458990i | ||||
\(466\) | 462.061 | 0.991547 | ||||||||
\(467\) | − | 127.080i | − | 0.272121i | −0.990701 | − | 0.136060i | \(-0.956556\pi\) | ||
0.990701 | − | 0.136060i | \(-0.0434442\pi\) | |||||||
\(468\) | −170.987 | + | 214.411i | −0.365358 | + | 0.458144i | ||||
\(469\) | −283.084 | + | 587.830i | −0.603591 | + | 1.25337i | ||||
\(470\) | 78.2202 | + | 342.705i | 0.166426 | + | 0.729159i | ||||
\(471\) | −99.9761 | + | 438.024i | −0.212263 | + | 0.929987i | ||||
\(472\) | − | 1022.75i | − | 2.16685i | ||||||
\(473\) | 244.889 | − | 304.229i | 0.517736 | − | 0.643191i | ||||
\(474\) | 229.957 | 0.485142 | ||||||||
\(475\) | −255.749 | − | 58.3731i | −0.538419 | − | 0.122891i | ||||
\(476\) | 1222.08 | − | 278.931i | 2.56739 | − | 0.585990i | ||||
\(477\) | 373.643 | + | 179.937i | 0.783319 | + | 0.377226i | ||||
\(478\) | 751.525 | + | 599.321i | 1.57223 | + | 1.25381i | ||||
\(479\) | 543.915 | 1.13552 | 0.567761 | − | 0.823194i | \(-0.307810\pi\) | ||||
0.567761 | + | 0.823194i | \(0.307810\pi\) | |||||||
\(480\) | 539.955i | 1.12491i | ||||||||
\(481\) | −71.4959 | − | 57.0161i | −0.148640 | − | 0.118537i | ||||
\(482\) | 1364.85 | − | 657.279i | 2.83165 | − | 1.36365i | ||||
\(483\) | −342.406 | − | 429.364i | −0.708916 | − | 0.888952i | ||||
\(484\) | −318.293 | + | 153.282i | −0.657630 | + | 0.316698i | ||||
\(485\) | −230.913 | − | 52.7043i | −0.476109 | − | 0.108669i | ||||
\(486\) | −540.134 | + | 677.306i | −1.11139 | + | 1.39363i | ||||
\(487\) | −56.0260 | + | 245.466i | −0.115043 | + | 0.504037i | 0.884270 | + | 0.466976i | \(0.154657\pi\) |
−0.999313 | + | 0.0370606i | \(0.988201\pi\) | |||||||
\(488\) | −1547.43 | − | 745.202i | −3.17096 | − | 1.52705i | ||||
\(489\) | −40.0116 | − | 50.1729i | −0.0818233 | − | 0.102603i | ||||
\(490\) | −1209.58 | − | 1516.77i | −2.46854 | − | 3.09545i | ||||
\(491\) | −50.5810 | + | 11.5448i | −0.103016 | + | 0.0235128i | −0.273718 | − | 0.961810i | \(-0.588254\pi\) |
0.170702 | + | 0.985323i | \(0.445396\pi\) | |||||||
\(492\) | 359.507 | − | 746.525i | 0.730706 | − | 1.51733i | ||||
\(493\) | 95.0087 | + | 197.288i | 0.192715 | + | 0.400178i | ||||
\(494\) | −43.3821 | − | 190.070i | −0.0878181 | − | 0.384756i | ||||
\(495\) | 342.590 | − | 78.1938i | 0.692100 | − | 0.157967i | ||||
\(496\) | −560.260 | + | 269.807i | −1.12956 | + | 0.543966i | ||||
\(497\) | 1095.08 | + | 527.363i | 2.20338 | + | 1.06109i | ||||
\(498\) | −20.9815 | − | 91.9258i | −0.0421315 | − | 0.184590i | ||||
\(499\) | −396.319 | + | 316.054i | −0.794227 | + | 0.633375i | −0.934188 | − | 0.356782i | \(-0.883874\pi\) |
0.139961 | + | 0.990157i | \(0.455302\pi\) | |||||||
\(500\) | 118.529 | − | 94.5240i | 0.237059 | − | 0.189048i | ||||
\(501\) | −203.958 | + | 423.524i | −0.407102 | + | 0.845357i | ||||
\(502\) | −978.318 | − | 223.295i | −1.94884 | − | 0.444810i | ||||
\(503\) | 559.050 | + | 445.827i | 1.11143 | + | 0.886336i | 0.994283 | − | 0.106778i | \(-0.0340535\pi\) |
0.117148 | + | 0.993115i | \(0.462625\pi\) | |||||||
\(504\) | 247.895 | − | 1086.10i | 0.491856 | − | 2.15496i | ||||
\(505\) | −504.564 | − | 1047.74i | −0.999136 | − | 2.07473i | ||||
\(506\) | −668.298 | + | 532.950i | −1.32075 | + | 1.05326i | ||||
\(507\) | 114.205 | + | 237.150i | 0.225257 | + | 0.467752i | ||||
\(508\) | −960.065 | + | 1203.88i | −1.88989 | + | 2.36985i | ||||
\(509\) | −426.880 | −0.838664 | −0.419332 | − | 0.907833i | \(-0.637736\pi\) | ||||
−0.419332 | + | 0.907833i | \(0.637736\pi\) | |||||||
\(510\) | 617.896i | 1.21156i | ||||||||
\(511\) | 483.390 | − | 606.152i | 0.945969 | − | 1.18621i | ||||
\(512\) | −491.862 | + | 1021.36i | −0.960668 | + | 1.99485i | ||||
\(513\) | −58.6490 | − | 256.958i | −0.114326 | − | 0.500893i | ||||
\(514\) | 98.4302 | − | 431.251i | 0.191499 | − | 0.839010i | ||||
\(515\) | 543.727i | 1.05578i | ||||||||
\(516\) | 735.445 | − | 164.341i | 1.42528 | − | 0.318491i | ||||
\(517\) | 121.647 | 0.235295 | ||||||||
\(518\) | 642.151 | + | 146.567i | 1.23967 | + | 0.282948i | ||||
\(519\) | −112.457 | + | 25.6677i | −0.216681 | + | 0.0494560i | ||||
\(520\) | 683.519 | + | 329.165i | 1.31446 | + | 0.633010i | ||||
\(521\) | −579.975 | − | 462.515i | −1.11320 | − | 0.887744i | −0.118743 | − | 0.992925i | \(-0.537886\pi\) |
−0.994453 | + | 0.105181i | \(0.966458\pi\) | |||||||
\(522\) | 345.061 | 0.661036 | ||||||||
\(523\) | 486.520i | 0.930248i | 0.885245 | + | 0.465124i | \(0.153990\pi\) | ||||
−0.885245 | + | 0.465124i | \(0.846010\pi\) | |||||||
\(524\) | 515.999 | + | 411.496i | 0.984731 | + | 0.785297i | ||||
\(525\) | 520.664 | − | 250.738i | 0.991741 | − | 0.477597i | ||||
\(526\) | 1055.03 | + | 1322.97i | 2.00577 | + | 2.51515i | ||||
\(527\) | −219.440 | + | 105.677i | −0.416395 | + | 0.200525i | ||||
\(528\) | 532.251 | + | 121.483i | 1.00805 | + | 0.230081i | ||||
\(529\) | 89.3729 | − | 112.070i | 0.168947 | − | 0.211853i | ||||
\(530\) | 452.646 | − | 1983.17i | 0.854048 | − | 3.74183i | ||||
\(531\) | −262.548 | − | 126.436i | −0.494440 | − | 0.238110i | ||||
\(532\) | 609.687 | + | 764.523i | 1.14603 | + | 1.43707i | ||||
\(533\) | −164.692 | − | 206.517i | −0.308990 | − | 0.387462i | ||||
\(534\) | −67.3105 | + | 15.3632i | −0.126050 | + | 0.0287700i | ||||
\(535\) | −193.659 | + | 402.136i | −0.361979 | + | 0.751657i | ||||
\(536\) | 479.496 | + | 995.683i | 0.894582 | + | 1.85762i | ||||
\(537\) | 42.7381 | + | 187.248i | 0.0795868 | + | 0.348693i | ||||
\(538\) | −298.638 | + | 68.1622i | −0.555089 | + | 0.126695i | ||||
\(539\) | −604.883 | + | 291.296i | −1.12223 | + | 0.540438i | ||||
\(540\) | 1638.46 | + | 789.039i | 3.03418 | + | 1.46118i | ||||
\(541\) | −160.412 | − | 702.810i | −0.296510 | − | 1.29909i | −0.875285 | − | 0.483607i | \(-0.839326\pi\) |
0.578775 | − | 0.815487i | \(-0.303531\pi\) | |||||||
\(542\) | −69.2643 | + | 55.2364i | −0.127794 | + | 0.101912i | ||||
\(543\) | 319.997 | − | 255.189i | 0.589313 | − | 0.469961i | ||||
\(544\) | 209.023 | − | 434.041i | 0.384234 | − | 0.797870i | ||||
\(545\) | −454.946 | − | 103.838i | −0.834763 | − | 0.190529i | ||||
\(546\) | 335.783 | + | 267.778i | 0.614988 | + | 0.490436i | ||||
\(547\) | 175.322 | − | 768.134i | 0.320515 | − | 1.40427i | −0.516125 | − | 0.856513i | \(-0.672626\pi\) |
0.836640 | − | 0.547754i | \(-0.184517\pi\) | |||||||
\(548\) | −534.232 | − | 1109.34i | −0.974876 | − | 2.02435i | ||||
\(549\) | −382.597 | + | 305.111i | −0.696898 | + | 0.555758i | ||||
\(550\) | −390.270 | − | 810.405i | −0.709582 | − | 1.47346i | ||||
\(551\) | −106.505 | + | 133.553i | −0.193294 | + | 0.242383i | ||||
\(552\) | −930.212 | −1.68517 | ||||||||
\(553\) | 367.699i | 0.664918i | ||||||||
\(554\) | −1002.36 | + | 1256.92i | −1.80931 | + | 2.26881i | ||||
\(555\) | −98.0997 | + | 203.706i | −0.176756 | + | 0.367038i | ||||
\(556\) | 22.7326 | + | 99.5982i | 0.0408861 | + | 0.179134i | ||||
\(557\) | 49.3092 | − | 216.038i | 0.0885264 | − | 0.387859i | −0.911182 | − | 0.412004i | \(-0.864829\pi\) |
0.999708 | + | 0.0241445i | \(0.00768617\pi\) | |||||||
\(558\) | 383.806i | 0.687824i | ||||||||
\(559\) | 54.5235 | − | 233.968i | 0.0975376 | − | 0.418547i | ||||
\(560\) | −2522.52 | −4.50450 | ||||||||
\(561\) | 208.470 | + | 47.5819i | 0.371604 | + | 0.0848162i | ||||
\(562\) | −1641.60 | + | 374.684i | −2.92099 | + | 0.666698i | ||||
\(563\) | 193.185 | + | 93.0328i | 0.343134 | + | 0.165245i | 0.597511 | − | 0.801860i | \(-0.296156\pi\) |
−0.254377 | + | 0.967105i | \(0.581871\pi\) | |||||||
\(564\) | 183.517 | + | 146.350i | 0.325384 | + | 0.259485i | ||||
\(565\) | 395.372 | 0.699773 | ||||||||
\(566\) | − | 1043.39i | − | 1.84345i | ||||||
\(567\) | 36.5307 | + | 29.1323i | 0.0644281 | + | 0.0513797i | ||||
\(568\) | 1854.88 | − | 893.262i | 3.26563 | − | 1.57264i | ||||
\(569\) | −592.360 | − | 742.796i | −1.04106 | − | 1.30544i | −0.950895 | − | 0.309514i | \(-0.899833\pi\) |
−0.0901603 | − | 0.995927i | \(-0.528738\pi\) | |||||||
\(570\) | −434.286 | + | 209.141i | −0.761906 | + | 0.366914i | ||||
\(571\) | 996.896 | + | 227.535i | 1.74588 | + | 0.398485i | 0.972025 | − | 0.234879i | \(-0.0754694\pi\) |
0.773854 | + | 0.633364i | \(0.218327\pi\) | |||||||
\(572\) | 290.242 | − | 363.952i | 0.507416 | − | 0.636279i | ||||
\(573\) | −74.6985 | + | 327.275i | −0.130364 | + | 0.571161i | ||||
\(574\) | 1714.15 | + | 825.492i | 2.98633 | + | 1.43814i | ||||
\(575\) | 441.119 | + | 553.145i | 0.767163 | + | 0.961992i | ||||
\(576\) | −53.4353 | − | 67.0057i | −0.0927695 | − | 0.116329i | ||||
\(577\) | 986.398 | − | 225.139i | 1.70953 | − | 0.390189i | 0.747743 | − | 0.663989i | \(-0.231138\pi\) |
0.961787 | + | 0.273800i | \(0.0882806\pi\) | |||||||
\(578\) | −215.928 | + | 448.380i | −0.373578 | + | 0.775744i | ||||
\(579\) | 192.389 | + | 399.499i | 0.332278 | + | 0.689982i | ||||
\(580\) | −262.269 | − | 1149.08i | −0.452188 | − | 1.98116i | ||||
\(581\) | 146.988 | − | 33.5491i | 0.252992 | − | 0.0577438i | ||||
\(582\) | −204.625 | + | 98.5424i | −0.351590 | + | 0.169317i | ||||
\(583\) | −634.238 | − | 305.433i | −1.08789 | − | 0.523899i | ||||
\(584\) | −292.219 | − | 1280.30i | −0.500375 | − | 2.19229i | ||||
\(585\) | 168.998 | − | 134.772i | 0.288886 | − | 0.230379i | ||||
\(586\) | −860.441 | + | 686.179i | −1.46833 | + | 1.17095i | ||||
\(587\) | −368.008 | + | 764.177i | −0.626930 | + | 1.30183i | 0.309473 | + | 0.950908i | \(0.399847\pi\) |
−0.936403 | + | 0.350926i | \(0.885867\pi\) | |||||||
\(588\) | −1262.97 | − | 288.265i | −2.14791 | − | 0.490246i | ||||
\(589\) | −148.549 | − | 118.464i | −0.252206 | − | 0.201127i | ||||
\(590\) | −318.060 | + | 1393.51i | −0.539085 | + | 2.36189i | ||||
\(591\) | −93.9542 | − | 195.098i | −0.158975 | − | 0.330115i | ||||
\(592\) | 402.665 | − | 321.115i | 0.680178 | − | 0.542424i | ||||
\(593\) | 172.295 | + | 357.775i | 0.290549 | + | 0.603331i | 0.994240 | − | 0.107175i | \(-0.0341805\pi\) |
−0.703691 | + | 0.710506i | \(0.748466\pi\) | |||||||
\(594\) | 563.468 | − | 706.567i | 0.948600 | − | 1.18951i | ||||
\(595\) | −988.009 | −1.66052 | ||||||||
\(596\) | − | 2128.91i | − | 3.57200i | ||||||
\(597\) | 153.505 | − | 192.489i | 0.257128 | − | 0.322428i | ||||
\(598\) | −228.138 | + | 473.734i | −0.381502 | + | 0.792197i | ||||
\(599\) | −8.60496 | − | 37.7008i | −0.0143655 | − | 0.0629395i | 0.967237 | − | 0.253875i | \(-0.0817051\pi\) |
−0.981603 | + | 0.190935i | \(0.938848\pi\) | |||||||
\(600\) | 217.815 | − | 954.310i | 0.363025 | − | 1.59052i | ||||
\(601\) | − | 561.024i | − | 0.933485i | −0.884393 | − | 0.466742i | \(-0.845428\pi\) | ||
0.884393 | − | 0.466742i | \(-0.154572\pi\) | |||||||
\(602\) | 377.357 | + | 1688.71i | 0.626838 | + | 2.80517i | ||||
\(603\) | 314.876 | 0.522183 | ||||||||
\(604\) | 934.037 | + | 213.188i | 1.54642 | + | 0.352960i | ||||
\(605\) | 271.471 | − | 61.9616i | 0.448713 | − | 0.102416i | ||||
\(606\) | −1004.68 | − | 483.828i | −1.65789 | − | 0.798395i | ||||
\(607\) | 198.596 | + | 158.375i | 0.327176 | + | 0.260914i | 0.773277 | − | 0.634069i | \(-0.218616\pi\) |
−0.446101 | + | 0.894983i | \(0.647188\pi\) | |||||||
\(608\) | 375.813 | 0.618114 | ||||||||
\(609\) | − | 376.311i | − | 0.617916i | ||||||
\(610\) | 1876.65 | + | 1496.57i | 3.07647 | + | 2.45340i | ||||
\(611\) | 67.4187 | − | 32.4671i | 0.110342 | − | 0.0531377i | ||||
\(612\) | −377.184 | − | 472.974i | −0.616314 | − | 0.772833i | ||||
\(613\) | −770.564 | + | 371.084i | −1.25704 | + | 0.605358i | −0.939390 | − | 0.342851i | \(-0.888607\pi\) |
−0.317648 | + | 0.948209i | \(0.602893\pi\) | |||||||
\(614\) | 1043.00 | + | 238.058i | 1.69870 | + | 0.387716i | ||||
\(615\) | −407.191 | + | 510.601i | −0.662099 | + | 0.830246i | ||||
\(616\) | −420.789 | + | 1843.60i | −0.683098 | + | 2.99285i | ||||
\(617\) | 678.741 | + | 326.865i | 1.10007 | + | 0.529764i | 0.893679 | − | 0.448706i | \(-0.148115\pi\) |
0.206388 | + | 0.978470i | \(0.433829\pi\) | |||||||
\(618\) | 325.076 | + | 407.632i | 0.526013 | + | 0.659600i | ||||
\(619\) | 202.593 | + | 254.043i | 0.327290 | + | 0.410409i | 0.918066 | − | 0.396426i | \(-0.129750\pi\) |
−0.590776 | + | 0.806835i | \(0.701178\pi\) | |||||||
\(620\) | 1278.10 | − | 291.718i | 2.06145 | − | 0.470513i | ||||
\(621\) | −308.424 | + | 640.448i | −0.496657 | + | 1.03132i | ||||
\(622\) | −369.882 | − | 768.068i | −0.594666 | − | 1.23484i | ||||
\(623\) | −24.5655 | − | 107.629i | −0.0394310 | − | 0.172759i | ||||
\(624\) | 327.404 | − | 74.7279i | 0.524686 | − | 0.119756i | ||||
\(625\) | 506.922 | − | 244.121i | 0.811076 | − | 0.390593i | ||||
\(626\) | 370.291 | + | 178.323i | 0.591520 | + | 0.284861i | ||||
\(627\) | 37.1187 | + | 162.628i | 0.0592004 | + | 0.259374i | ||||
\(628\) | −1686.89 | + | 1345.25i | −2.68614 | + | 2.14212i | ||||
\(629\) | 157.714 | − | 125.773i | 0.250738 | − | 0.199957i | ||||
\(630\) | −675.522 | + | 1402.74i | −1.07226 | + | 2.22656i | ||||
\(631\) | −490.091 | − | 111.860i | −0.776689 | − | 0.177274i | −0.184239 | − | 0.982881i | \(-0.558982\pi\) |
−0.592450 | + | 0.805607i | \(0.701839\pi\) | |||||||
\(632\) | 486.940 | + | 388.322i | 0.770475 | + | 0.614433i | ||||
\(633\) | 6.04637 | − | 26.4909i | 0.00955193 | − | 0.0418498i | ||||
\(634\) | −148.137 | − | 307.611i | −0.233655 | − | 0.485190i | ||||
\(635\) | 948.896 | − | 756.720i | 1.49432 | − | 1.19168i | ||||
\(636\) | −589.353 | − | 1223.80i | −0.926656 | − | 1.92422i | ||||
\(637\) | −257.489 | + | 322.881i | −0.404221 | + | 0.506877i | ||||
\(638\) | −585.721 | −0.918059 | ||||||||
\(639\) | − | 586.589i | − | 0.917979i | ||||||
\(640\) | 442.820 | − | 555.279i | 0.691906 | − | 0.867623i | ||||
\(641\) | 16.8968 | − | 35.0865i | 0.0263600 | − | 0.0547371i | −0.887373 | − | 0.461052i | \(-0.847472\pi\) |
0.913733 | + | 0.406315i | \(0.133186\pi\) | |||||||
\(642\) | 95.2377 | + | 417.264i | 0.148345 | + | 0.649943i | ||||
\(643\) | −12.4460 | + | 54.5296i | −0.0193562 | + | 0.0848050i | −0.983683 | − | 0.179908i | \(-0.942420\pi\) |
0.964327 | + | 0.264713i | \(0.0852772\pi\) | |||||||
\(644\) | − | 2637.31i | − | 4.09521i | ||||||
\(645\) | −593.965 | − | 2.70430i | −0.920877 | − | 0.00419271i | ||||
\(646\) | 430.060 | 0.665728 | ||||||||
\(647\) | −912.741 | − | 208.327i | −1.41073 | − | 0.321989i | −0.551753 | − | 0.834007i | \(-0.686041\pi\) |
−0.858975 | + | 0.512018i | \(0.828898\pi\) | |||||||
\(648\) | 77.1591 | − | 17.6111i | 0.119073 | − | 0.0271776i | ||||
\(649\) | 445.660 | + | 214.619i | 0.686687 | + | 0.330691i | ||||
\(650\) | −432.586 | − | 344.976i | −0.665517 | − | 0.530732i | ||||
\(651\) | 418.565 | 0.642957 | ||||||||
\(652\) | − | 308.181i | − | 0.472670i | ||||||
\(653\) | −769.287 | − | 613.486i | −1.17808 | − | 0.939489i | −0.179065 | − | 0.983837i | \(-0.557307\pi\) |
−0.999016 | + | 0.0443486i | \(0.985879\pi\) | |||||||
\(654\) | −403.154 | + | 194.149i | −0.616444 | + | 0.296864i | ||||
\(655\) | −324.339 | − | 406.709i | −0.495174 | − | 0.620929i | ||||
\(656\) | 1340.34 | − | 645.474i | 2.04320 | − | 0.983955i | ||||
\(657\) | −364.786 | − | 83.2601i | −0.555230 | − | 0.126728i | ||||
\(658\) | −336.045 | + | 421.387i | −0.510706 | + | 0.640405i | ||||
\(659\) | −70.0648 | + | 306.974i | −0.106320 | + | 0.465818i | 0.893539 | + | 0.448987i | \(0.148215\pi\) |
−0.999858 | + | 0.0168311i | \(0.994642\pi\) | |||||||
\(660\) | −1036.97 | − | 499.379i | −1.57117 | − | 0.756634i | ||||
\(661\) | −14.3813 | − | 18.0336i | −0.0217569 | − | 0.0272823i | 0.770834 | − | 0.637036i | \(-0.219840\pi\) |
−0.792591 | + | 0.609754i | \(0.791268\pi\) | |||||||
\(662\) | −928.416 | − | 1164.20i | −1.40244 | − | 1.75861i | ||||
\(663\) | 128.236 | − | 29.2691i | 0.193418 | − | 0.0441464i | ||||
\(664\) | 110.803 | − | 230.086i | 0.166873 | − | 0.346515i | ||||
\(665\) | −334.414 | − | 694.419i | −0.502879 | − | 1.04424i | ||||
\(666\) | −70.7349 | − | 309.910i | −0.106208 | − | 0.465330i | ||||
\(667\) | 449.156 | − | 102.517i | 0.673398 | − | 0.153699i | ||||
\(668\) | −2033.89 | + | 979.468i | −3.04474 | + | 1.46627i | ||||
\(669\) | 414.908 | + | 199.809i | 0.620192 | + | 0.298669i | ||||
\(670\) | −343.677 | − | 1505.75i | −0.512951 | − | 2.24739i | ||||
\(671\) | 649.438 | − | 517.909i | 0.967866 | − | 0.771847i | ||||
\(672\) | −647.278 | + | 516.187i | −0.963211 | + | 0.768135i | ||||
\(673\) | 429.761 | − | 892.407i | 0.638574 | − | 1.32601i | −0.290768 | − | 0.956794i | \(-0.593911\pi\) |
0.929342 | − | 0.369220i | \(-0.120375\pi\) | |||||||
\(674\) | 1128.02 | + | 257.462i | 1.67361 | + | 0.381991i | ||||
\(675\) | −584.821 | − | 466.379i | −0.866401 | − | 0.690932i | ||||
\(676\) | −281.277 | + | 1232.35i | −0.416090 | + | 1.82301i | ||||
\(677\) | 434.321 | + | 901.876i | 0.641537 | + | 1.33217i | 0.927463 | + | 0.373914i | \(0.121985\pi\) |
−0.285926 | + | 0.958252i | \(0.592301\pi\) | |||||||
\(678\) | 296.410 | − | 236.379i | 0.437184 | − | 0.348642i | ||||
\(679\) | −157.568 | − | 327.194i | −0.232059 | − | 0.481876i | ||||
\(680\) | −1043.42 | + | 1308.41i | −1.53444 | + | 1.92413i | ||||
\(681\) | 376.042 | 0.552191 | ||||||||
\(682\) | − | 651.490i | − | 0.955263i | ||||||
\(683\) | −719.357 | + | 902.045i | −1.05323 | + | 1.32071i | −0.108056 | + | 0.994145i | \(0.534463\pi\) |
−0.945175 | + | 0.326565i | \(0.894109\pi\) | |||||||
\(684\) | 204.762 | − | 425.192i | 0.299359 | − | 0.621625i | ||||
\(685\) | 215.954 | + | 946.157i | 0.315262 | + | 1.38125i | ||||
\(686\) | 223.139 | − | 977.635i | 0.325275 | − | 1.42512i | ||||
\(687\) | − | 130.416i | − | 0.189834i | ||||||
\(688\) | 1216.34 | + | 592.595i | 1.76793 | + | 0.861330i | ||||
\(689\) | −433.022 | −0.628480 | ||||||||
\(690\) | 1267.43 | + | 289.282i | 1.83685 | + | 0.419249i | ||||
\(691\) | 225.043 | − | 51.3647i | 0.325678 | − | 0.0743338i | −0.0565562 | − | 0.998399i | \(-0.518012\pi\) |
0.382234 | + | 0.924066i | \(0.375155\pi\) | |||||||
\(692\) | −499.085 | − | 240.347i | −0.721221 | − | 0.347322i | ||||
\(693\) | 421.245 | + | 335.932i | 0.607857 | + | 0.484750i | ||||
\(694\) | −341.832 | −0.492553 | ||||||||
\(695\) | − | 80.5218i | − | 0.115859i | ||||||
\(696\) | −498.344 | − | 397.416i | −0.716011 | − | 0.571000i | ||||
\(697\) | 524.979 | − | 252.817i | 0.753198 | − | 0.362721i | ||||
\(698\) | 1476.25 | + | 1851.16i | 2.11497 | + | 2.65209i | ||||
\(699\) | −219.108 | + | 105.517i | −0.313459 | + | 0.150954i | ||||
\(700\) | 2705.64 | + | 617.544i | 3.86519 | + | 0.882205i | ||||
\(701\) | −411.060 | + | 515.453i | −0.586391 | + | 0.735311i | −0.983188 | − | 0.182596i | \(-0.941550\pi\) |
0.396797 | + | 0.917906i | \(0.370122\pi\) | |||||||
\(702\) | 123.703 | − | 541.976i | 0.176214 | − | 0.772046i | ||||
\(703\) | 141.781 | + | 68.2781i | 0.201680 | + | 0.0971239i | ||||
\(704\) | 90.7034 | + | 113.738i | 0.128840 | + | 0.161560i | ||||
\(705\) | −115.352 | − | 144.647i | −0.163620 | − | 0.205173i | ||||
\(706\) | −1080.58 | + | 246.635i | −1.53057 | + | 0.349342i | ||||
\(707\) | 773.635 | − | 1606.47i | 1.09425 | − | 2.27223i | ||||
\(708\) | 414.120 | + | 859.930i | 0.584916 | + | 1.21459i | ||||
\(709\) | −43.1041 | − | 188.851i | −0.0607956 | − | 0.266363i | 0.935391 | − | 0.353616i | \(-0.115048\pi\) |
−0.996186 | + | 0.0872534i | \(0.972191\pi\) | |||||||
\(710\) | −2805.09 | + | 640.243i | −3.95083 | + | 0.901751i | ||||
\(711\) | 159.882 | − | 76.9953i | 0.224870 | − | 0.108291i | ||||
\(712\) | −168.475 | − | 81.1331i | −0.236622 | − | 0.113951i | ||||
\(713\) | 114.028 | + | 499.590i | 0.159927 | + | 0.700688i | ||||
\(714\) | −740.710 | + | 590.697i | −1.03741 | + | 0.827306i | ||||
\(715\) | −286.865 | + | 228.767i | −0.401210 | + | 0.319954i | ||||
\(716\) | −400.191 | + | 831.005i | −0.558926 | + | 1.16062i | ||||
\(717\) | −493.233 | − | 112.577i | −0.687911 | − | 0.157011i | ||||
\(718\) | 335.257 | + | 267.358i | 0.466932 | + | 0.372366i | ||||
\(719\) | 158.708 | − | 695.345i | 0.220734 | − | 0.967100i | −0.736193 | − | 0.676772i | \(-0.763378\pi\) |
0.956927 | − | 0.290328i | \(-0.0937645\pi\) | |||||||
\(720\) | 528.209 | + | 1096.84i | 0.733623 | + | 1.52338i | ||||
\(721\) | −651.800 | + | 519.793i | −0.904022 | + | 0.720933i | ||||
\(722\) | −422.947 | − | 878.258i | −0.585799 | − | 1.21642i | ||||
\(723\) | −497.112 | + | 623.359i | −0.687569 | + | 0.862184i | ||||
\(724\) | 1965.54 | 2.71483 | ||||||||
\(725\) | 484.798i | 0.668686i | ||||||||
\(726\) | 166.477 | − | 208.756i | 0.229308 | − | 0.287543i | ||||
\(727\) | 423.494 | − | 879.395i | 0.582523 | − | 1.20962i | −0.376533 | − | 0.926403i | \(-0.622884\pi\) |
0.959056 | − | 0.283218i | \(-0.0914020\pi\) | |||||||
\(728\) | 258.840 | + | 1134.05i | 0.355550 | + | 1.55776i | ||||
\(729\) | 109.899 | − | 481.501i | 0.150754 | − | 0.660495i | ||||
\(730\) | 1835.30i | 2.51411i | ||||||||
\(731\) | 476.410 | + | 232.105i | 0.651724 | + | 0.317517i | ||||
\(732\) | 1602.82 | 2.18964 | ||||||||
\(733\) | −522.196 | − | 119.188i | −0.712409 | − | 0.162603i | −0.149068 | − | 0.988827i | \(-0.547627\pi\) |
−0.563341 | + | 0.826224i | \(0.690484\pi\) | |||||||
\(734\) | 1230.96 | − | 280.959i | 1.67706 | − | 0.382779i | ||||
\(735\) | 919.952 | + | 443.025i | 1.25163 | + | 0.602756i | ||||
\(736\) | −792.445 | − | 631.954i | −1.07669 | − | 0.858633i | ||||
\(737\) | −534.485 | −0.725217 | ||||||||
\(738\) | − | 918.200i | − | 1.24417i | ||||||
\(739\) | −515.544 | − | 411.133i | −0.697624 | − | 0.556336i | 0.209186 | − | 0.977876i | \(-0.432918\pi\) |
−0.906810 | + | 0.421539i | \(0.861490\pi\) | |||||||
\(740\) | −978.257 | + | 471.104i | −1.32197 | + | 0.636627i | ||||
\(741\) | 63.9762 | + | 80.2236i | 0.0863377 | + | 0.108264i | ||||
\(742\) | 2810.07 | − | 1353.26i | 3.78716 | − | 1.82380i | ||||
\(743\) | −53.3684 | − | 12.1810i | −0.0718282 | − | 0.0163943i | 0.186456 | − | 0.982463i | \(-0.440300\pi\) |
−0.258284 | + | 0.966069i | \(0.583157\pi\) | |||||||
\(744\) | 442.040 | − | 554.301i | 0.594140 | − | 0.745028i | ||||
\(745\) | −373.390 | + | 1635.93i | −0.501194 | + | 2.19588i | ||||
\(746\) | −2056.36 | − | 990.293i | −2.75652 | − | 1.32747i | ||||
\(747\) | −45.3667 | − | 56.8881i | −0.0607319 | − | 0.0761554i | ||||
\(748\) | 640.250 | + | 802.848i | 0.855949 | + | 1.07333i | ||||
\(749\) | −667.200 | + | 152.284i | −0.890788 | + | 0.203316i | ||||
\(750\) | −49.7159 | + | 103.236i | −0.0662878 | + | 0.137648i | ||||
\(751\) | 78.2859 | + | 162.562i | 0.104242 | + | 0.216461i | 0.946566 | − | 0.322511i | \(-0.104527\pi\) |
−0.842323 | + | 0.538972i | \(0.818813\pi\) | |||||||
\(752\) | 93.7788 | + | 410.872i | 0.124706 | + | 0.546372i | ||||
\(753\) | 514.907 | − | 117.524i | 0.683808 | − | 0.156075i | ||||
\(754\) | −324.615 | + | 156.326i | −0.430524 | + | 0.207329i | ||||
\(755\) | −680.355 | − | 327.642i | −0.901133 | − | 0.433963i | ||||
\(756\) | 620.463 | + | 2718.43i | 0.820718 | + | 3.59580i | ||||
\(757\) | 15.6363 | − | 12.4695i | 0.0206556 | − | 0.0164723i | −0.613108 | − | 0.789999i | \(-0.710081\pi\) |
0.633763 | + | 0.773527i | \(0.281509\pi\) | |||||||
\(758\) | 815.270 | − | 650.156i | 1.07555 | − | 0.857726i | ||||
\(759\) | 195.200 | − | 405.336i | 0.257180 | − | 0.534040i | ||||
\(760\) | −1272.78 | − | 290.504i | −1.67471 | − | 0.382242i | ||||
\(761\) | 61.5912 | + | 49.1173i | 0.0809346 | + | 0.0645432i | 0.663121 | − | 0.748512i | \(-0.269231\pi\) |
−0.582187 | + | 0.813055i | \(0.697803\pi\) | |||||||
\(762\) | 258.971 | − | 1134.63i | 0.339857 | − | 1.48901i | ||||
\(763\) | −310.442 | − | 644.639i | −0.406870 | − | 0.844875i | ||||
\(764\) | −1260.38 | + | 1005.12i | −1.64972 | + | 1.31561i | ||||
\(765\) | 206.886 | + | 429.604i | 0.270440 | + | 0.561574i | ||||
\(766\) | 493.720 | − | 619.106i | 0.644544 | − | 0.808232i | ||||
\(767\) | 304.272 | 0.396704 | ||||||||
\(768\) | − | 803.433i | − | 1.04614i | ||||||
\(769\) | −516.616 | + | 647.816i | −0.671802 | + | 0.842413i | −0.994571 | − | 0.104065i | \(-0.966815\pi\) |
0.322768 | + | 0.946478i | \(0.395386\pi\) | |||||||
\(770\) | 1146.66 | − | 2381.07i | 1.48917 | − | 3.09229i | ||||
\(771\) | 51.8057 | + | 226.976i | 0.0671929 | + | 0.294391i | ||||
\(772\) | −473.834 | + | 2076.00i | −0.613775 | + | 2.68912i | ||||
\(773\) | 748.866i | 0.968779i | 0.874852 | + | 0.484390i | \(0.160958\pi\) | ||||
−0.874852 | + | 0.484390i | \(0.839042\pi\) | |||||||
\(774\) | 655.265 | − | 517.693i | 0.846595 | − | 0.668854i | ||||
\(775\) | −539.233 | −0.695785 | ||||||||
\(776\) | −599.704 | − | 136.879i | −0.772815 | − | 0.176390i | ||||
\(777\) | −337.976 | + | 77.1409i | −0.434976 | + | 0.0992804i | ||||
\(778\) | −708.525 | − | 341.208i | −0.910701 | − | 0.438570i | ||||
\(779\) | 355.382 | + | 283.408i | 0.456203 | + | 0.363810i | ||||
\(780\) | −707.985 | −0.907674 | ||||||||
\(781\) | 995.702i | 1.27491i | ||||||||
\(782\) | −906.832 | − | 723.175i | −1.15963 | − | 0.924776i | ||||
\(783\) | −438.852 | + | 211.340i | −0.560475 | + | 0.269911i | ||||
\(784\) | −1450.18 | − | 1818.47i | −1.84972 | − | 2.31947i | ||||
\(785\) | 1532.21 | − | 737.874i | 1.95186 | − | 0.939967i | ||||
\(786\) | −486.314 | − | 110.998i | −0.618721 | − | 0.141219i | ||||
\(787\) | 199.457 | − | 250.112i | 0.253440 | − | 0.317804i | −0.638793 | − | 0.769378i | \(-0.720566\pi\) |
0.892233 | + | 0.451575i | \(0.149138\pi\) | |||||||
\(788\) | 231.400 | − | 1013.83i | 0.293655 | − | 1.28658i | ||||
\(789\) | −802.408 | − | 386.419i | −1.01699 | − | 0.489759i | ||||
\(790\) | −542.701 | − | 680.525i | −0.686963 | − | 0.861424i | ||||
\(791\) | 377.968 | + | 473.957i | 0.477836 | + | 0.599187i | ||||
\(792\) | 889.740 | − | 203.077i | 1.12341 | − | 0.256411i | ||||
\(793\) | 221.700 | − | 460.364i | 0.279571 | − | 0.580535i | ||||
\(794\) | 16.3693 | + | 33.9912i | 0.0206163 | + | 0.0428101i | ||||
\(795\) | 238.236 | + | 1043.78i | 0.299668 | + | 1.31293i | ||||
\(796\) | 1152.70 | − | 263.096i | 1.44811 | − | 0.330522i | ||||
\(797\) | 415.766 | − | 200.222i | 0.521663 | − | 0.251220i | −0.154472 | − | 0.987997i | \(-0.549368\pi\) |
0.676135 | + | 0.736777i | \(0.263653\pi\) | |||||||
\(798\) | −665.880 | − | 320.671i | −0.834436 | − | 0.401843i | ||||
\(799\) | 36.7308 | + | 160.928i | 0.0459710 | + | 0.201412i | ||||
\(800\) | 833.882 | − | 664.999i | 1.04235 | − | 0.831248i | ||||
\(801\) | −41.6549 | + | 33.2187i | −0.0520036 | + | 0.0414715i | ||||
\(802\) | 839.646 | − | 1743.54i | 1.04694 | − | 2.17399i | ||||
\(803\) | 619.205 | + | 141.329i | 0.771114 | + | 0.176002i | ||||
\(804\) | −806.321 | − | 643.020i | −1.00289 | − | 0.799776i | ||||
\(805\) | −462.559 | + | 2026.60i | −0.574607 | + | 2.51752i | ||||
\(806\) | −173.880 | − | 361.065i | −0.215731 | − | 0.447971i | ||||
\(807\) | 126.048 | − | 100.520i | 0.156193 | − | 0.124560i | ||||
\(808\) | −1310.40 | − | 2721.08i | −1.62179 | − | 3.36768i | ||||
\(809\) | −243.386 | + | 305.196i | −0.300848 | + | 0.377251i | −0.909160 | − | 0.416447i | \(-0.863275\pi\) |
0.608313 | + | 0.793698i | \(0.291847\pi\) | |||||||
\(810\) | −110.607 | −0.136552 | ||||||||
\(811\) | − | 101.122i | − | 0.124688i | −0.998055 | − | 0.0623439i | \(-0.980142\pi\) | ||
0.998055 | − | 0.0623439i | \(-0.0198576\pi\) | |||||||
\(812\) | 1126.74 | − | 1412.89i | 1.38762 | − | 1.74001i | ||||
\(813\) | 20.2311 | − | 42.0102i | 0.0248844 | − | 0.0516731i | ||||
\(814\) | 120.069 | + | 526.055i | 0.147504 | + | 0.646259i | ||||
\(815\) | −54.0519 | + | 236.817i | −0.0663213 | + | 0.290573i | ||||
\(816\) | 740.800i | 0.907844i | ||||||||
\(817\) | −1.88221 | + | 413.404i | −0.00230381 | + | 0.506003i | ||||
\(818\) | 64.7667 | 0.0791769 | ||||||||
\(819\) | 323.118 | + | 73.7496i | 0.394528 | + | 0.0900484i | ||||
\(820\) | −3057.67 | + | 697.893i | −3.72886 | + | 0.851089i | ||||
\(821\) | −328.283 | − | 158.093i | −0.399858 | − | 0.192561i | 0.223137 | − | 0.974787i | \(-0.428370\pi\) |
−0.622995 | + | 0.782226i | \(0.714084\pi\) | |||||||
\(822\) | 727.576 | + | 580.223i | 0.885129 | + | 0.705867i | ||||
\(823\) | −471.027 | −0.572329 | −0.286164 | − | 0.958181i | \(-0.592380\pi\) | ||||
−0.286164 | + | 0.958181i | \(0.592380\pi\) | |||||||
\(824\) | 1412.12i | 1.71373i | ||||||||
\(825\) | 370.130 | + | 295.169i | 0.448642 | + | 0.357780i | ||||
\(826\) | −1974.55 | + | 950.893i | −2.39050 | + | 1.15120i | ||||
\(827\) | 264.259 | + | 331.370i | 0.319539 | + | 0.400689i | 0.915496 | − | 0.402327i | \(-0.131799\pi\) |
−0.595957 | + | 0.803016i | \(0.703227\pi\) | |||||||
\(828\) | −1146.75 | + | 552.246i | −1.38496 | + | 0.666964i | ||||
\(829\) | 328.286 | + | 74.9291i | 0.396002 | + | 0.0903849i | 0.415885 | − | 0.909417i | \(-0.363472\pi\) |
−0.0198824 | + | 0.999802i | \(0.506329\pi\) | |||||||
\(830\) | −222.525 | + | 279.037i | −0.268102 | + | 0.336189i | ||||
\(831\) | 188.284 | − | 824.927i | 0.226576 | − | 0.992692i | ||||
\(832\) | 80.6253 | + | 38.8271i | 0.0969055 | + | 0.0466672i | ||||
\(833\) | −567.999 | − | 712.249i | −0.681872 | − | 0.855040i | ||||
\(834\) | −48.1412 | − | 60.3672i | −0.0577233 | − | 0.0723827i | ||||
\(835\) | 1734.70 | − | 395.933i | 2.07748 | − | 0.474172i | ||||
\(836\) | −347.571 | + | 721.740i | −0.415755 | + | 0.863325i | ||||
\(837\) | −235.071 | − | 488.129i | −0.280849 | − | 0.583189i | ||||
\(838\) | −516.802 | − | 2264.26i | −0.616708 | − | 2.70198i | ||||
\(839\) | −221.701 | + | 50.6018i | −0.264244 | + | 0.0603120i | −0.352590 | − | 0.935778i | \(-0.614699\pi\) |
0.0883459 | + | 0.996090i | \(0.471842\pi\) | |||||||
\(840\) | 2591.17 | − | 1247.84i | 3.08473 | − | 1.48553i | ||||
\(841\) | −473.289 | − | 227.924i | −0.562769 | − | 0.271015i | ||||
\(842\) | 517.054 | + | 2265.36i | 0.614079 | + | 2.69046i | ||||
\(843\) | 692.878 | − | 552.552i | 0.821919 | − | 0.655459i | ||||
\(844\) | 102.020 | − | 81.3584i | 0.120877 | − | 0.0963963i | ||||
\(845\) | 432.285 | − | 897.650i | 0.511580 | − | 1.06231i | ||||
\(846\) | 253.593 | + | 57.8810i | 0.299756 | + | 0.0684173i | ||||
\(847\) | 333.799 | + | 266.196i | 0.394095 | + | 0.314280i | ||||
\(848\) | 542.680 | − | 2377.64i | 0.639953 | − | 2.80382i | ||||
\(849\) | 238.270 | + | 494.773i | 0.280648 | + | 0.582771i | ||||
\(850\) | 954.250 | − | 760.989i | 1.12265 | − | 0.895281i | ||||
\(851\) | −184.147 | − | 382.386i | −0.216390 | − | 0.449337i | ||||
\(852\) | −1197.89 | + | 1502.11i | −1.40598 | + | 1.76304i | ||||
\(853\) | −749.133 | −0.878233 | −0.439116 | − | 0.898430i | \(-0.644708\pi\) | ||||
−0.439116 | + | 0.898430i | \(0.644708\pi\) | |||||||
\(854\) | 3680.35i | 4.30954i | ||||||||
\(855\) | −231.920 | + | 290.819i | −0.271252 | + | 0.340139i | ||||
\(856\) | −502.952 | + | 1044.39i | −0.587560 | + | 1.22008i | ||||
\(857\) | 113.883 | + | 498.952i | 0.132885 | + | 0.582208i | 0.996896 | + | 0.0787339i | \(0.0250877\pi\) |
−0.864011 | + | 0.503474i | \(0.832055\pi\) | |||||||
\(858\) | −78.2907 | + | 343.014i | −0.0912479 | + | 0.399783i | ||||
\(859\) | − | 663.778i | − | 0.772733i | −0.922345 | − | 0.386367i | \(-0.873730\pi\) | ||
0.922345 | − | 0.386367i | \(-0.126270\pi\) | |||||||
\(860\) | −2222.00 | − | 1788.60i | −2.58372 | − | 2.07976i | ||||
\(861\) | −1001.36 | −1.16302 | ||||||||
\(862\) | −320.065 | − | 73.0526i | −0.371305 | − | 0.0847478i | ||||
\(863\) | 1051.97 | − | 240.106i | 1.21897 | − | 0.278222i | 0.435809 | − | 0.900039i | \(-0.356462\pi\) |
0.783163 | + | 0.621817i | \(0.213605\pi\) | |||||||
\(864\) | 965.494 | + | 464.957i | 1.11747 | + | 0.538145i | ||||
\(865\) | 341.359 | + | 272.225i | 0.394635 | + | 0.314711i | ||||
\(866\) | 1444.68 | 1.66822 | ||||||||
\(867\) | − | 261.930i | − | 0.302111i | ||||||
\(868\) | 1571.54 | + | 1253.26i | 1.81053 | + | 1.44385i | ||||
\(869\) | −271.391 | + | 130.695i | −0.312303 | + | 0.150397i | ||||
\(870\) | 555.411 | + | 696.463i | 0.638403 | + | 0.800532i | ||||
\(871\) | −296.219 | + | 142.652i | −0.340091 | + | 0.163779i | ||||
\(872\) | −1181.54 | − | 269.679i | −1.35498 | − | 0.309265i | ||||
\(873\) | −109.275 | + | 137.027i | −0.125172 | + | 0.156961i | ||||
\(874\) | 201.342 | − | 882.139i | 0.230369 | − | 1.00931i | ||||
\(875\) | −165.073 | − | 79.4951i | −0.188655 | − | 0.0908515i | ||||
\(876\) | 764.100 | + | 958.152i | 0.872261 | + | 1.09378i | ||||
\(877\) | 537.003 | + | 673.381i | 0.612318 | + | 0.767823i | 0.987241 | − | 0.159233i | \(-0.0509021\pi\) |
−0.374923 | + | 0.927056i | \(0.622331\pi\) | |||||||
\(878\) | 2916.58 | − | 665.690i | 3.32184 | − | 0.758189i | ||||
\(879\) | 251.322 | − | 521.875i | 0.285918 | − | 0.593715i | ||||
\(880\) | −896.605 | − | 1861.82i | −1.01887 | − | 2.11570i | ||||
\(881\) | 3.66727 | + | 16.0674i | 0.00416263 | + | 0.0182377i | 0.976967 | − | 0.213392i | \(-0.0684513\pi\) |
−0.972804 | + | 0.231630i | \(0.925594\pi\) | |||||||
\(882\) | −1399.58 | + | 319.444i | −1.58682 | + | 0.362181i | ||||
\(883\) | −1010.01 | + | 486.394i | −1.14384 | + | 0.550842i | −0.907176 | − | 0.420750i | \(-0.861767\pi\) |
−0.236659 | + | 0.971593i | \(0.576053\pi\) | |||||||
\(884\) | 569.111 | + | 274.070i | 0.643791 | + | 0.310033i | ||||
\(885\) | −167.401 | − | 733.432i | −0.189154 | − | 0.828737i | ||||
\(886\) | −1232.00 | + | 982.489i | −1.39052 | + | 1.10890i | ||||
\(887\) | −1171.09 | + | 933.914i | −1.32028 | + | 1.05289i | −0.326083 | + | 0.945341i | \(0.605729\pi\) |
−0.994200 | + | 0.107550i | \(0.965700\pi\) | |||||||
\(888\) | −254.775 | + | 529.046i | −0.286909 | + | 0.595772i | ||||
\(889\) | 1814.25 | + | 414.091i | 2.04078 | + | 0.465795i | ||||
\(890\) | 204.318 | + | 162.938i | 0.229571 | + | 0.183077i | ||||
\(891\) | −8.51745 | + | 37.3174i | −0.00955943 | + | 0.0418826i | ||||
\(892\) | 959.544 | + | 1992.51i | 1.07572 | + | 2.23376i | ||||
\(893\) | −100.676 | + | 80.2861i | −0.112739 | + | 0.0899060i | ||||
\(894\) | 698.135 | + | 1449.69i | 0.780912 | + | 1.62158i | ||||
\(895\) | 453.270 | − | 568.383i | 0.506447 | − | 0.635065i | ||||
\(896\) | 1088.97 | 1.21537 | ||||||||
\(897\) | − | 276.741i | − | 0.308518i | ||||||
\(898\) | 804.530 | − | 1008.85i | 0.895913 | − | 1.12344i | ||||
\(899\) | −152.352 | + | 316.363i | −0.169469 | + | 0.351905i | ||||
\(900\) | −298.034 | − | 1305.77i | −0.331149 | − | 1.45086i | ||||
\(901\) | 212.555 | − | 931.263i | 0.235910 | − | 1.03359i | ||||
\(902\) | 1558.59i | 1.72793i | ||||||||
\(903\) | −564.578 | − | 714.608i | −0.625224 | − | 0.791371i | ||||
\(904\) | 1026.82 | 1.13586 | ||||||||
\(905\) | −1510.39 | − | 344.736i | −1.66894 | − | 0.380924i | ||||
\(906\) | −705.948 | + | 161.128i | −0.779193 | + | 0.177846i | ||||
\(907\) | −816.659 | − | 393.282i | −0.900396 | − | 0.433608i | −0.0743642 | − | 0.997231i | \(-0.523693\pi\) |
−0.826032 | + | 0.563623i | \(0.809407\pi\) | |||||||
\(908\) | 1411.88 | + | 1125.94i | 1.55494 | + | 1.24002i | ||||
\(909\) | −860.519 | −0.946665 | ||||||||
\(910\) | − | 1625.66i | − | 1.78644i | ||||||
\(911\) | 773.335 | + | 616.714i | 0.848886 | + | 0.676964i | 0.948055 | − | 0.318107i | \(-0.103047\pi\) |
−0.0991693 | + | 0.995071i | \(0.531619\pi\) | |||||||
\(912\) | −520.669 | + | 250.741i | −0.570909 | + | 0.274935i | ||||
\(913\) | 77.0075 | + | 96.5644i | 0.0843456 | + | 0.105766i | ||||
\(914\) | −1693.27 | + | 815.437i | −1.85260 | + | 0.892163i | ||||
\(915\) | −1231.66 | − | 281.118i | −1.34608 | − | 0.307233i | ||||
\(916\) | 390.489 | − | 489.658i | 0.426298 | − | 0.534561i | ||||
\(917\) | 177.485 | − | 777.611i | 0.193549 | − | 0.847995i | ||||
\(918\) | 1104.86 | + | 532.072i | 1.20355 | + | 0.579599i | ||||
\(919\) | 122.826 | + | 154.020i | 0.133652 | + | 0.167595i | 0.844154 | − | 0.536101i | \(-0.180103\pi\) |
−0.710502 | + | 0.703696i | \(0.751532\pi\) | |||||||
\(920\) | 2195.30 | + | 2752.82i | 2.38620 | + | 2.99220i | ||||
\(921\) | −548.950 | + | 125.294i | −0.596037 | + | 0.136042i | ||||
\(922\) | −532.038 | + | 1104.79i | −0.577048 | + | 1.19825i | ||||
\(923\) | 265.748 | + | 551.832i | 0.287918 | + | 0.597868i | ||||
\(924\) | −392.688 | − | 1720.48i | −0.424987 | − | 1.86199i | ||||
\(925\) | 435.412 | − | 99.3799i | 0.470715 | − | 0.107438i | ||||
\(926\) | −682.215 | + | 328.537i | −0.736733 | + | 0.354792i | ||||
\(927\) | 362.500 | + | 174.571i | 0.391047 | + | 0.188318i | ||||
\(928\) | −154.547 | − | 677.116i | −0.166538 | − | 0.729651i | ||||
\(929\) | 79.3250 | − | 63.2596i | 0.0853875 | − | 0.0680943i | −0.579866 | − | 0.814712i | \(-0.696895\pi\) |
0.665253 | + | 0.746618i | \(0.268324\pi\) | |||||||
\(930\) | −774.666 | + | 617.775i | −0.832974 | + | 0.664275i | ||||
\(931\) | 308.349 | − | 640.293i | 0.331202 | − | 0.687748i | ||||
\(932\) | −1138.60 | − | 259.877i | −1.22167 | − | 0.278838i | ||||
\(933\) | 350.794 | + | 279.749i | 0.375985 | + | 0.299838i | ||||
\(934\) | −102.638 | + | 449.686i | −0.109891 | + | 0.481462i | ||||
\(935\) | −351.178 | − | 729.229i | −0.375592 | − | 0.779924i | ||||
\(936\) | 438.906 | − | 350.016i | 0.468917 | − | 0.373949i | ||||
\(937\) | 329.508 | + | 684.231i | 0.351663 | + | 0.730236i | 0.999502 | − | 0.0315411i | \(-0.0100415\pi\) |
−0.647839 | + | 0.761777i | \(0.724327\pi\) | |||||||
\(938\) | 1476.49 | − | 1851.45i | 1.57408 | − | 1.97383i | ||||
\(939\) | −216.313 | −0.230365 | ||||||||
\(940\) | − | 888.477i | − | 0.945188i | ||||||
\(941\) | −344.534 | + | 432.032i | −0.366136 | + | 0.459120i | −0.930439 | − | 0.366448i | \(-0.880574\pi\) |
0.564302 | + | 0.825568i | \(0.309145\pi\) | |||||||
\(942\) | 707.549 | − | 1469.24i | 0.751114 | − | 1.55970i | ||||
\(943\) | −272.796 | − | 1195.20i | −0.289285 | − | 1.26744i | ||||
\(944\) | −381.325 | + | 1670.69i | −0.403946 | + | 1.76980i | ||||
\(945\) | − | 2197.76i | − | 2.32567i | ||||||
\(946\) | −1112.28 | + | 878.756i | −1.17577 | + | 0.928917i | ||||
\(947\) | −374.964 | −0.395949 | −0.197975 | − | 0.980207i | \(-0.563436\pi\) | ||||
−0.197975 | + | 0.980207i | \(0.563436\pi\) | |||||||
\(948\) | −566.654 | − | 129.335i | −0.597737 | − | 0.136429i | ||||
\(949\) | 380.892 | − | 86.9361i | 0.401361 | − | 0.0916081i | ||||
\(950\) | 857.846 | + | 413.117i | 0.902996 | + | 0.434860i | ||||
\(951\) | 140.493 | + | 112.039i | 0.147732 | + | 0.117812i | ||||
\(952\) | −2565.96 | −2.69534 | ||||||||
\(953\) | − | 1123.12i | − | 1.17851i | −0.807946 | − | 0.589256i | \(-0.799421\pi\) | ||
0.807946 | − | 0.589256i | \(-0.200579\pi\) | |||||||
\(954\) | −1176.84 | − | 938.500i | −1.23359 | − | 0.983753i | ||||
\(955\) | 1144.81 | − | 551.312i | 1.19876 | − | 0.577290i | ||||
\(956\) | −1514.81 | − | 1899.51i | −1.58453 | − | 1.98693i | ||||
\(957\) | 277.747 | − | 133.756i | 0.290227 | − | 0.139766i | ||||
\(958\) | −1924.69 | − | 439.298i | −2.00907 | − | 0.458558i | ||||
\(959\) | −927.769 | + | 1163.39i | −0.967434 | + | 1.21312i | ||||
\(960\) | 49.2333 | − | 215.705i | 0.0512847 | − | 0.224693i | ||||
\(961\) | 513.945 | + | 247.503i | 0.534802 | + | 0.257547i | ||||
\(962\) | 206.945 | + | 259.501i | 0.215120 | + | 0.269752i | ||||
\(963\) | 205.926 | + | 258.223i | 0.213838 | + | 0.268144i | ||||
\(964\) | −3732.90 | + | 852.011i | −3.87231 | + | 0.883829i | ||||
\(965\) | 728.221 | − | 1512.17i | 0.754633 | − | 1.56701i | ||||
\(966\) | 864.856 | + | 1795.89i | 0.895296 | + | 1.85910i | ||||
\(967\) | 405.766 | + | 1777.78i | 0.419613 | + | 1.83844i | 0.534636 | + | 0.845082i | \(0.320449\pi\) |
−0.115023 | + | 0.993363i | \(0.536694\pi\) | |||||||
\(968\) | 705.039 | − | 160.921i | 0.728346 | − | 0.166240i | ||||
\(969\) | −203.933 | + | 98.2091i | −0.210458 | + | 0.101351i | ||||
\(970\) | 774.539 | + | 372.998i | 0.798494 | + | 0.384534i | ||||
\(971\) | −386.164 | − | 1691.90i | −0.397697 | − | 1.74243i | −0.636424 | − | 0.771339i | \(-0.719587\pi\) |
0.238727 | − | 0.971087i | \(-0.423270\pi\) | |||||||
\(972\) | 1711.92 | − | 1365.21i | 1.76123 | − | 1.40454i | ||||
\(973\) | 96.5265 | − | 76.9773i | 0.0992050 | − | 0.0791133i | ||||
\(974\) | 396.506 | − | 823.354i | 0.407091 | − | 0.845332i | ||||
\(975\) | 283.910 | + | 64.8007i | 0.291190 | + | 0.0664622i | ||||
\(976\) | 2249.93 | + | 1794.26i | 2.30525 | + | 1.83838i | ||||
\(977\) | 1.75913 | − | 7.70725i | 0.00180054 | − | 0.00788869i | −0.974020 | − | 0.226463i | \(-0.927284\pi\) |
0.975820 | + | 0.218575i | \(0.0701408\pi\) | |||||||
\(978\) | 101.062 | + | 209.857i | 0.103335 | + | 0.214578i | ||||
\(979\) | 70.7069 | − | 56.3869i | 0.0722236 | − | 0.0575964i | ||||
\(980\) | 2127.54 | + | 4417.88i | 2.17096 | + | 4.50804i | ||||
\(981\) | −215.295 | + | 269.971i | −0.219465 | + | 0.275200i | ||||
\(982\) | 188.310 | 0.191761 | ||||||||
\(983\) | − | 1165.48i | − | 1.18563i | −0.805337 | − | 0.592817i | \(-0.798016\pi\) | ||
0.805337 | − | 0.592817i | \(-0.201984\pi\) | |||||||
\(984\) | −1057.52 | + | 1326.08i | −1.07471 | + | 1.34765i | ||||
\(985\) | −355.631 | + | 738.476i | −0.361047 | + | 0.749721i | ||||
\(986\) | −176.856 | − | 774.855i | −0.179367 | − | 0.785857i | ||||
\(987\) | 63.1230 | − | 276.560i | 0.0639544 | − | 0.280202i | ||||
\(988\) | 492.763i | 0.498748i | ||||||||
\(989\) | 699.135 | − | 868.546i | 0.706911 | − | 0.878206i | ||||
\(990\) | −1275.44 | −1.28832 | ||||||||
\(991\) | 1345.16 | + | 307.023i | 1.35737 | + | 0.309811i | 0.838435 | − | 0.545001i | \(-0.183471\pi\) |
0.518937 | + | 0.854813i | \(0.326328\pi\) | |||||||
\(992\) | 753.146 | − | 171.901i | 0.759220 | − | 0.173287i | ||||
\(993\) | 706.110 | + | 340.044i | 0.711087 | + | 0.342442i | ||||
\(994\) | −3449.11 | − | 2750.57i | −3.46993 | − | 2.76718i | ||||
\(995\) | −931.917 | −0.936600 | ||||||||
\(996\) | 238.321i | 0.239279i | ||||||||
\(997\) | −1492.00 | − | 1189.83i | −1.49649 | − | 1.19341i | −0.929027 | − | 0.370012i | \(-0.879353\pi\) |
−0.567463 | − | 0.823399i | \(-0.692075\pi\) | |||||||
\(998\) | 1657.68 | − | 798.295i | 1.66100 | − | 0.799894i | ||||
\(999\) | 279.773 | + | 350.824i | 0.280053 | + | 0.351175i |
(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 | 43.3.f.a.8.1 | ✓ | 42 | |
3.2 | odd | 2 | 387.3.w.b.352.7 | 42 | |||
43.27 | odd | 14 | inner | 43.3.f.a.27.1 | yes | 42 | |
129.113 | even | 14 | 387.3.w.b.199.7 | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.3.f.a.8.1 | ✓ | 42 | 1.1 | even | 1 | trivial | |
43.3.f.a.27.1 | yes | 42 | 43.27 | odd | 14 | inner | |
387.3.w.b.199.7 | 42 | 129.113 | even | 14 | |||
387.3.w.b.352.7 | 42 | 3.2 | odd | 2 |