Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(29,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.i (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.08720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 29.14 | ||
Character | \(\chi\) | \(=\) | 150.29 |
Dual form | 150.3.i.a.119.14 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.437016 | − | 1.34500i | 0.218508 | − | 0.672499i | ||||
\(3\) | −1.51513 | + | 2.58928i | −0.505043 | + | 0.863094i | ||||
\(4\) | −1.61803 | − | 1.17557i | −0.404508 | − | 0.293893i | ||||
\(5\) | −2.92277 | + | 4.05678i | −0.584554 | + | 0.811355i | ||||
\(6\) | 2.82044 | + | 3.16940i | 0.470074 | + | 0.528233i | ||||
\(7\) | − | 10.3258i | − | 1.47511i | −0.675285 | − | 0.737557i | \(-0.735979\pi\) | ||
0.675285 | − | 0.737557i | \(-0.264021\pi\) | |||||||
\(8\) | −2.28825 | + | 1.66251i | −0.286031 | + | 0.207813i | ||||
\(9\) | −4.40877 | − | 7.84619i | −0.489864 | − | 0.871799i | ||||
\(10\) | 4.17905 | + | 5.70399i | 0.417905 | + | 0.570399i | ||||
\(11\) | −15.3878 | − | 4.99979i | −1.39889 | − | 0.454526i | −0.490057 | − | 0.871690i | \(-0.663024\pi\) |
−0.908831 | + | 0.417164i | \(0.863024\pi\) | |||||||
\(12\) | 5.49541 | − | 2.40841i | 0.457951 | − | 0.200701i | ||||
\(13\) | −12.4481 | + | 4.04463i | −0.957545 | + | 0.311125i | −0.745778 | − | 0.666195i | \(-0.767922\pi\) |
−0.211767 | + | 0.977320i | \(0.567922\pi\) | |||||||
\(14\) | −13.8882 | − | 4.51254i | −0.992012 | − | 0.322324i | ||||
\(15\) | −6.07577 | − | 13.7144i | −0.405051 | − | 0.914294i | ||||
\(16\) | 1.23607 | + | 3.80423i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −1.44783 | + | 1.05191i | −0.0851666 | + | 0.0618772i | −0.629554 | − | 0.776957i | \(-0.716762\pi\) |
0.544387 | + | 0.838834i | \(0.316762\pi\) | |||||||
\(18\) | −12.4798 | + | 2.50088i | −0.693323 | + | 0.138938i | ||||
\(19\) | 7.67604 | − | 5.57697i | 0.404002 | − | 0.293525i | −0.367167 | − | 0.930155i | \(-0.619672\pi\) |
0.771169 | + | 0.636630i | \(0.219672\pi\) | |||||||
\(20\) | 9.49816 | − | 3.12808i | 0.474908 | − | 0.156404i | ||||
\(21\) | 26.7364 | + | 15.6449i | 1.27316 | + | 0.744995i | ||||
\(22\) | −13.4494 | + | 18.5115i | −0.611337 | + | 0.841433i | ||||
\(23\) | −10.8632 | + | 33.4335i | −0.472313 | + | 1.45363i | 0.377236 | + | 0.926117i | \(0.376875\pi\) |
−0.849548 | + | 0.527511i | \(0.823125\pi\) | |||||||
\(24\) | −0.837719 | − | 8.44383i | −0.0349049 | − | 0.351826i | ||||
\(25\) | −7.91485 | − | 23.7140i | −0.316594 | − | 0.948561i | ||||
\(26\) | 18.5102i | 0.711931i | ||||||||
\(27\) | 26.9959 | + | 0.472415i | 0.999847 | + | 0.0174969i | ||||
\(28\) | −12.1387 | + | 16.7075i | −0.433525 | + | 0.596696i | ||||
\(29\) | 3.88473 | − | 5.34688i | 0.133956 | − | 0.184375i | −0.736769 | − | 0.676144i | \(-0.763650\pi\) |
0.870726 | + | 0.491769i | \(0.163650\pi\) | |||||||
\(30\) | −21.1010 | + | 2.17848i | −0.703368 | + | 0.0726159i | ||||
\(31\) | 32.4553 | − | 23.5802i | 1.04695 | − | 0.760651i | 0.0753170 | − | 0.997160i | \(-0.476003\pi\) |
0.971629 | + | 0.236509i | \(0.0760031\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 36.2603 | − | 32.2680i | 1.09880 | − | 0.977817i | ||||
\(34\) | 0.782093 | + | 2.40703i | 0.0230027 | + | 0.0707951i | ||||
\(35\) | 41.8894 | + | 30.1799i | 1.19684 | + | 0.862283i | ||||
\(36\) | −2.09020 | + | 17.8782i | −0.0580612 | + | 0.496617i | ||||
\(37\) | −52.7078 | + | 17.1258i | −1.42454 | + | 0.462860i | −0.917040 | − | 0.398795i | \(-0.869429\pi\) |
−0.507495 | + | 0.861655i | \(0.669429\pi\) | |||||||
\(38\) | −4.14646 | − | 12.7615i | −0.109117 | − | 0.335828i | ||||
\(39\) | 8.38775 | − | 38.3598i | 0.215071 | − | 0.983583i | ||||
\(40\) | −0.0564076 | − | 14.1420i | −0.00141019 | − | 0.353551i | ||||
\(41\) | −43.7419 | + | 14.2126i | −1.06688 | + | 0.346649i | −0.789270 | − | 0.614046i | \(-0.789541\pi\) |
−0.277605 | + | 0.960695i | \(0.589541\pi\) | |||||||
\(42\) | 32.7266 | − | 29.1233i | 0.779204 | − | 0.693412i | ||||
\(43\) | 8.12640i | 0.188986i | 0.995526 | + | 0.0944930i | \(0.0301230\pi\) | ||||
−0.995526 | + | 0.0944930i | \(0.969877\pi\) | |||||||
\(44\) | 19.0203 | + | 26.1792i | 0.432280 | + | 0.594983i | ||||
\(45\) | 44.7161 | + | 5.04719i | 0.993690 | + | 0.112160i | ||||
\(46\) | 40.2205 | + | 29.2219i | 0.874359 | + | 0.635259i | ||||
\(47\) | −17.8973 | − | 13.0031i | −0.380793 | − | 0.276663i | 0.380879 | − | 0.924625i | \(-0.375621\pi\) |
−0.761672 | + | 0.647962i | \(0.775621\pi\) | |||||||
\(48\) | −11.7230 | − | 2.56336i | −0.244230 | − | 0.0534033i | ||||
\(49\) | −57.6220 | −1.17596 | ||||||||
\(50\) | −35.3542 | + | 0.282036i | −0.707084 | + | 0.00564071i | ||||
\(51\) | −0.530046 | − | 5.34263i | −0.0103931 | − | 0.104757i | ||||
\(52\) | 24.8962 | + | 8.08926i | 0.478773 | + | 0.155563i | ||||
\(53\) | 25.5573 | + | 18.5685i | 0.482213 | + | 0.350348i | 0.802182 | − | 0.597080i | \(-0.203672\pi\) |
−0.319969 | + | 0.947428i | \(0.603672\pi\) | |||||||
\(54\) | 12.4330 | − | 36.1029i | 0.230241 | − | 0.668572i | ||||
\(55\) | 65.2579 | − | 47.8115i | 1.18651 | − | 0.869300i | ||||
\(56\) | 17.1667 | + | 23.6280i | 0.306548 | + | 0.421928i | ||||
\(57\) | 2.81017 | + | 28.3253i | 0.0493013 | + | 0.496935i | ||||
\(58\) | −5.49384 | − | 7.56162i | −0.0947214 | − | 0.130373i | ||||
\(59\) | 46.0547 | − | 14.9641i | 0.780588 | − | 0.253628i | 0.108497 | − | 0.994097i | \(-0.465396\pi\) |
0.672091 | + | 0.740469i | \(0.265396\pi\) | |||||||
\(60\) | −6.29145 | + | 29.3329i | −0.104857 | + | 0.488881i | ||||
\(61\) | 10.2167 | − | 31.4437i | 0.167487 | − | 0.515471i | −0.831724 | − | 0.555189i | \(-0.812646\pi\) |
0.999211 | + | 0.0397180i | \(0.0126460\pi\) | |||||||
\(62\) | −17.5318 | − | 53.9573i | −0.282771 | − | 0.870278i | ||||
\(63\) | −81.0181 | + | 45.5241i | −1.28600 | + | 0.722605i | ||||
\(64\) | 2.47214 | − | 7.60845i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 19.9747 | − | 62.3206i | 0.307304 | − | 0.958778i | ||||
\(66\) | −27.5540 | − | 62.8716i | −0.417485 | − | 0.952601i | ||||
\(67\) | 67.3796 | + | 92.7400i | 1.00567 | + | 1.38418i | 0.921784 | + | 0.387704i | \(0.126732\pi\) |
0.0838815 | + | 0.996476i | \(0.473268\pi\) | |||||||
\(68\) | 3.57924 | 0.0526359 | ||||||||
\(69\) | −70.1096 | − | 78.7838i | −1.01608 | − | 1.14179i | ||||
\(70\) | 58.8982 | − | 43.1520i | 0.841403 | − | 0.616458i | ||||
\(71\) | 60.0004 | − | 82.5835i | 0.845077 | − | 1.16315i | −0.139849 | − | 0.990173i | \(-0.544662\pi\) |
0.984926 | − | 0.172976i | \(-0.0553382\pi\) | |||||||
\(72\) | 23.1327 | + | 10.6244i | 0.321288 | + | 0.147561i | ||||
\(73\) | −37.7781 | − | 12.2749i | −0.517509 | − | 0.168149i | 0.0386056 | − | 0.999255i | \(-0.487708\pi\) |
−0.556114 | + | 0.831106i | \(0.687708\pi\) | |||||||
\(74\) | 78.3761i | 1.05914i | ||||||||
\(75\) | 73.3943 | + | 15.4360i | 0.978591 | + | 0.205813i | ||||
\(76\) | −18.9762 | −0.249687 | ||||||||
\(77\) | −51.6268 | + | 158.891i | −0.670478 | + | 2.06352i | ||||
\(78\) | −47.9282 | − | 28.0453i | −0.614464 | − | 0.359556i | ||||
\(79\) | −78.8234 | − | 57.2685i | −0.997764 | − | 0.724918i | −0.0361567 | − | 0.999346i | \(-0.511512\pi\) |
−0.961608 | + | 0.274428i | \(0.911512\pi\) | |||||||
\(80\) | −19.0456 | − | 6.10442i | −0.238070 | − | 0.0763053i | ||||
\(81\) | −42.1254 | + | 69.1842i | −0.520067 | + | 0.854126i | ||||
\(82\) | 65.0438i | 0.793218i | ||||||||
\(83\) | −25.4310 | + | 18.4767i | −0.306398 | + | 0.222611i | −0.730349 | − | 0.683074i | \(-0.760643\pi\) |
0.423952 | + | 0.905685i | \(0.360643\pi\) | |||||||
\(84\) | −24.8687 | − | 56.7445i | −0.296056 | − | 0.675530i | ||||
\(85\) | −0.0356906 | − | 8.94803i | −0.000419889 | − | 0.105271i | ||||
\(86\) | 10.9300 | + | 3.55137i | 0.127093 | + | 0.0412950i | ||||
\(87\) | 7.95871 | + | 18.1599i | 0.0914794 | + | 0.208734i | ||||
\(88\) | 43.5232 | − | 14.1415i | 0.494582 | − | 0.160699i | ||||
\(89\) | −93.5800 | − | 30.4060i | −1.05146 | − | 0.341640i | −0.268219 | − | 0.963358i | \(-0.586435\pi\) |
−0.783242 | + | 0.621718i | \(0.786435\pi\) | |||||||
\(90\) | 26.3301 | − | 57.9373i | 0.292557 | − | 0.643747i | ||||
\(91\) | 41.7640 | + | 128.536i | 0.458945 | + | 1.41249i | ||||
\(92\) | 56.8804 | − | 41.3260i | 0.618265 | − | 0.449196i | ||||
\(93\) | 11.8818 | + | 119.763i | 0.127761 | + | 1.28777i | ||||
\(94\) | −25.3106 | + | 18.3892i | −0.269262 | + | 0.195630i | ||||
\(95\) | 0.189222 | + | 47.4402i | 0.00199181 | + | 0.499370i | ||||
\(96\) | −8.57086 | + | 14.6472i | −0.0892798 | + | 0.152575i | ||||
\(97\) | −43.1136 | + | 59.3408i | −0.444470 | + | 0.611761i | −0.971198 | − | 0.238273i | \(-0.923419\pi\) |
0.526728 | + | 0.850034i | \(0.323419\pi\) | |||||||
\(98\) | −25.1818 | + | 77.5015i | −0.256957 | + | 0.790831i | ||||
\(99\) | 28.6119 | + | 142.778i | 0.289009 | + | 1.44221i | ||||
\(100\) | −15.0710 | + | 47.6746i | −0.150710 | + | 0.476746i | ||||
\(101\) | − | 23.0113i | − | 0.227835i | −0.993490 | − | 0.113917i | \(-0.963660\pi\) | ||
0.993490 | − | 0.113917i | \(-0.0363399\pi\) | |||||||
\(102\) | −7.41746 | − | 1.62190i | −0.0727202 | − | 0.0159010i | ||||
\(103\) | 56.8534 | − | 78.2520i | 0.551975 | − | 0.759729i | −0.438303 | − | 0.898827i | \(-0.644420\pi\) |
0.990279 | + | 0.139098i | \(0.0444205\pi\) | |||||||
\(104\) | 21.7601 | − | 29.9501i | 0.209231 | − | 0.287982i | ||||
\(105\) | −141.612 | + | 62.7372i | −1.34869 | + | 0.597497i | ||||
\(106\) | 36.1435 | − | 26.2598i | 0.340976 | − | 0.247734i | ||||
\(107\) | −139.734 | −1.30593 | −0.652965 | − | 0.757388i | \(-0.726475\pi\) | ||||
−0.652965 | + | 0.757388i | \(0.726475\pi\) | |||||||
\(108\) | −43.1249 | − | 32.4999i | −0.399304 | − | 0.300925i | ||||
\(109\) | 13.5680 | + | 41.7581i | 0.124477 | + | 0.383102i | 0.993806 | − | 0.111133i | \(-0.0354481\pi\) |
−0.869328 | + | 0.494235i | \(0.835448\pi\) | |||||||
\(110\) | −35.7876 | − | 108.666i | −0.325342 | − | 0.987874i | ||||
\(111\) | 35.5155 | − | 162.423i | 0.319960 | − | 1.46327i | ||||
\(112\) | 39.2817 | − | 12.7634i | 0.350729 | − | 0.113959i | ||||
\(113\) | −57.7727 | − | 177.806i | −0.511263 | − | 1.57351i | −0.789980 | − | 0.613133i | \(-0.789909\pi\) |
0.278716 | − | 0.960373i | \(-0.410091\pi\) | |||||||
\(114\) | 39.3255 | + | 8.59892i | 0.344960 | + | 0.0754292i | ||||
\(115\) | −103.881 | − | 141.788i | −0.903317 | − | 1.23294i | ||||
\(116\) | −12.5713 | + | 4.08465i | −0.108373 | + | 0.0352125i | ||||
\(117\) | 86.6157 | + | 79.8382i | 0.740305 | + | 0.682378i | ||||
\(118\) | − | 68.4829i | − | 0.580364i | ||||||
\(119\) | 10.8618 | + | 14.9500i | 0.0912759 | + | 0.125630i | ||||
\(120\) | 36.7032 | + | 21.2809i | 0.305860 | + | 0.177341i | ||||
\(121\) | 113.895 | + | 82.7492i | 0.941277 | + | 0.683878i | ||||
\(122\) | −37.8269 | − | 27.4828i | −0.310056 | − | 0.225269i | ||||
\(123\) | 29.4741 | − | 134.794i | 0.239627 | − | 1.09589i | ||||
\(124\) | −80.2340 | −0.647048 | ||||||||
\(125\) | 119.336 | + | 37.2019i | 0.954686 | + | 0.297615i | ||||
\(126\) | 25.8236 | + | 128.864i | 0.204949 | + | 1.02273i | ||||
\(127\) | −172.285 | − | 55.9788i | −1.35657 | − | 0.440778i | −0.461677 | − | 0.887048i | \(-0.652752\pi\) |
−0.894898 | + | 0.446270i | \(0.852752\pi\) | |||||||
\(128\) | −9.15298 | − | 6.65003i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | −21.0416 | − | 12.3125i | −0.163113 | − | 0.0954460i | ||||
\(130\) | −75.0917 | − | 54.1011i | −0.577629 | − | 0.416162i | ||||
\(131\) | −138.827 | − | 191.079i | −1.05975 | − | 1.45862i | −0.880039 | − | 0.474901i | \(-0.842484\pi\) |
−0.179711 | − | 0.983719i | \(-0.557516\pi\) | |||||||
\(132\) | −96.6037 | + | 9.58413i | −0.731846 | + | 0.0726070i | ||||
\(133\) | −57.5867 | − | 79.2612i | −0.432982 | − | 0.595949i | ||||
\(134\) | 154.181 | − | 50.0965i | 1.15060 | − | 0.373854i | ||||
\(135\) | −80.8192 | + | 108.135i | −0.598660 | + | 0.801003i | ||||
\(136\) | 1.56419 | − | 4.81407i | 0.0115014 | − | 0.0353975i | ||||
\(137\) | 19.5096 | + | 60.0444i | 0.142406 | + | 0.438280i | 0.996668 | − | 0.0815619i | \(-0.0259908\pi\) |
−0.854262 | + | 0.519842i | \(0.825991\pi\) | |||||||
\(138\) | −136.603 | + | 59.8674i | −0.989877 | + | 0.433821i | ||||
\(139\) | −25.0594 | + | 77.1249i | −0.180283 | + | 0.554855i | −0.999835 | − | 0.0181497i | \(-0.994222\pi\) |
0.819552 | + | 0.573005i | \(0.194222\pi\) | |||||||
\(140\) | −32.2999 | − | 98.0761i | −0.230714 | − | 0.700543i | ||||
\(141\) | 60.7855 | − | 26.6397i | 0.431103 | − | 0.188934i | ||||
\(142\) | −84.8534 | − | 116.791i | −0.597559 | − | 0.822470i | ||||
\(143\) | 211.771 | 1.48091 | ||||||||
\(144\) | 24.3991 | − | 26.4704i | 0.169438 | − | 0.183822i | ||||
\(145\) | 10.3369 | + | 31.3872i | 0.0712890 | + | 0.216463i | ||||
\(146\) | −33.0193 | + | 45.4472i | −0.226160 | + | 0.311282i | ||||
\(147\) | 87.3047 | − | 149.200i | 0.593910 | − | 1.01496i | ||||
\(148\) | 105.416 | + | 34.2516i | 0.712268 | + | 0.231430i | ||||
\(149\) | 73.8699i | 0.495771i | 0.968789 | + | 0.247885i | \(0.0797357\pi\) | ||||
−0.968789 | + | 0.247885i | \(0.920264\pi\) | |||||||
\(150\) | 52.8359 | − | 91.9694i | 0.352239 | − | 0.613129i | ||||
\(151\) | 59.9849 | 0.397251 | 0.198625 | − | 0.980075i | \(-0.436352\pi\) | ||||
0.198625 | + | 0.980075i | \(0.436352\pi\) | |||||||
\(152\) | −8.29291 | + | 25.5230i | −0.0545586 | + | 0.167914i | ||||
\(153\) | 14.6367 | + | 6.72233i | 0.0956645 | + | 0.0439368i | ||||
\(154\) | 191.146 | + | 138.876i | 1.24121 | + | 0.901791i | ||||
\(155\) | 0.800057 | + | 200.583i | 0.00516166 | + | 1.29409i | ||||
\(156\) | −58.6663 | + | 52.2070i | −0.376066 | + | 0.334660i | ||||
\(157\) | − | 122.502i | − | 0.780268i | −0.920758 | − | 0.390134i | \(-0.872429\pi\) | ||
0.920758 | − | 0.390134i | \(-0.127571\pi\) | |||||||
\(158\) | −111.473 | + | 80.9900i | −0.705526 | + | 0.512595i | ||||
\(159\) | −86.8016 | + | 38.0415i | −0.545922 | + | 0.239255i | ||||
\(160\) | −16.5337 | + | 22.9486i | −0.103335 | + | 0.143429i | ||||
\(161\) | 345.227 | + | 112.171i | 2.14427 | + | 0.696715i | ||||
\(162\) | 74.6430 | + | 86.8931i | 0.460759 | + | 0.536377i | ||||
\(163\) | 97.4427 | − | 31.6610i | 0.597808 | − | 0.194240i | 0.00554531 | − | 0.999985i | \(-0.498235\pi\) |
0.592262 | + | 0.805745i | \(0.298235\pi\) | |||||||
\(164\) | 87.4838 | + | 28.4252i | 0.533438 | + | 0.173324i | ||||
\(165\) | 24.9234 | + | 241.412i | 0.151051 | + | 1.46310i | ||||
\(166\) | 13.7374 | + | 42.2793i | 0.0827552 | + | 0.254694i | ||||
\(167\) | 216.705 | − | 157.446i | 1.29764 | − | 0.942788i | 0.297706 | − | 0.954658i | \(-0.403778\pi\) |
0.999930 | + | 0.0118699i | \(0.00377839\pi\) | |||||||
\(168\) | −87.1892 | + | 8.65011i | −0.518984 | + | 0.0514888i | ||||
\(169\) | 1.87198 | − | 1.36007i | 0.0110768 | − | 0.00804775i | ||||
\(170\) | −12.0507 | − | 3.86243i | −0.0708863 | − | 0.0227202i | ||||
\(171\) | −77.5999 | − | 35.6401i | −0.453801 | − | 0.208422i | ||||
\(172\) | 9.55316 | − | 13.1488i | 0.0555416 | − | 0.0764465i | ||||
\(173\) | 11.6248 | − | 35.7773i | 0.0671951 | − | 0.206805i | −0.911821 | − | 0.410588i | \(-0.865324\pi\) |
0.979016 | + | 0.203782i | \(0.0653235\pi\) | |||||||
\(174\) | 27.9031 | − | 2.76828i | 0.160362 | − | 0.0159097i | ||||
\(175\) | −244.866 | + | 81.7271i | −1.39924 | + | 0.467012i | ||||
\(176\) | − | 64.7186i | − | 0.367720i | ||||||
\(177\) | −31.0325 | + | 141.921i | −0.175325 | + | 0.801814i | ||||
\(178\) | −81.7919 | + | 112.577i | −0.459505 | + | 0.632455i | ||||
\(179\) | 105.036 | − | 144.570i | 0.586795 | − | 0.807655i | −0.407624 | − | 0.913150i | \(-0.633643\pi\) |
0.994420 | + | 0.105495i | \(0.0336427\pi\) | |||||||
\(180\) | −66.4188 | − | 60.7334i | −0.368993 | − | 0.337408i | ||||
\(181\) | −63.1666 | + | 45.8932i | −0.348987 | + | 0.253554i | −0.748444 | − | 0.663198i | \(-0.769199\pi\) |
0.399457 | + | 0.916752i | \(0.369199\pi\) | |||||||
\(182\) | 191.133 | 1.05018 | ||||||||
\(183\) | 65.9371 | + | 74.0952i | 0.360312 | + | 0.404892i | ||||
\(184\) | −30.7257 | − | 94.5641i | −0.166988 | − | 0.513935i | ||||
\(185\) | 84.5772 | − | 263.878i | 0.457174 | − | 1.42637i | ||||
\(186\) | 166.273 | + | 36.3574i | 0.893943 | + | 0.195470i | ||||
\(187\) | 27.5383 | − | 8.94772i | 0.147263 | − | 0.0478488i | ||||
\(188\) | 13.6723 | + | 42.0791i | 0.0727251 | + | 0.223825i | ||||
\(189\) | 4.87806 | − | 278.754i | 0.0258099 | − | 1.47489i | ||||
\(190\) | 63.8896 | + | 20.4776i | 0.336261 | + | 0.107777i | ||||
\(191\) | −111.878 | + | 36.3514i | −0.585750 | + | 0.190322i | −0.586875 | − | 0.809678i | \(-0.699642\pi\) |
0.00112493 | + | 0.999999i | \(0.499642\pi\) | |||||||
\(192\) | 15.9548 | + | 17.9288i | 0.0830981 | + | 0.0933794i | ||||
\(193\) | 234.366i | 1.21433i | 0.794575 | + | 0.607166i | \(0.207694\pi\) | ||||
−0.794575 | + | 0.607166i | \(0.792306\pi\) | |||||||
\(194\) | 60.9718 | + | 83.9205i | 0.314288 | + | 0.432580i | ||||
\(195\) | 131.101 | + | 146.144i | 0.672315 | + | 0.749456i | ||||
\(196\) | 93.2344 | + | 67.7388i | 0.475686 | + | 0.345606i | ||||
\(197\) | −187.632 | − | 136.323i | −0.952448 | − | 0.691994i | −0.00106335 | − | 0.999999i | \(-0.500338\pi\) |
−0.951385 | + | 0.308006i | \(0.900338\pi\) | |||||||
\(198\) | 204.540 | + | 23.9135i | 1.03303 | + | 0.120775i | ||||
\(199\) | 168.540 | 0.846934 | 0.423467 | − | 0.905912i | \(-0.360813\pi\) | ||||
0.423467 | + | 0.905912i | \(0.360813\pi\) | |||||||
\(200\) | 57.5359 | + | 41.1050i | 0.287679 | + | 0.205525i | ||||
\(201\) | −342.219 | + | 33.9518i | −1.70258 | + | 0.168914i | ||||
\(202\) | −30.9502 | − | 10.0563i | −0.153219 | − | 0.0497837i | ||||
\(203\) | −55.2107 | − | 40.1130i | −0.271974 | − | 0.197601i | ||||
\(204\) | −5.42301 | + | 9.26766i | −0.0265834 | + | 0.0454297i | ||||
\(205\) | 70.1901 | − | 218.991i | 0.342391 | − | 1.06825i | ||||
\(206\) | −80.4029 | − | 110.665i | −0.390305 | − | 0.537209i | ||||
\(207\) | 310.219 | − | 62.1659i | 1.49864 | − | 0.300319i | ||||
\(208\) | −30.7734 | − | 42.3559i | −0.147949 | − | 0.203634i | ||||
\(209\) | −146.001 | + | 47.4386i | −0.698569 | + | 0.226979i | ||||
\(210\) | 22.4945 | + | 217.885i | 0.107117 | + | 1.03755i | ||||
\(211\) | 2.11247 | − | 6.50152i | 0.0100117 | − | 0.0308129i | −0.945926 | − | 0.324383i | \(-0.894843\pi\) |
0.955938 | + | 0.293570i | \(0.0948434\pi\) | |||||||
\(212\) | −19.5240 | − | 60.0888i | −0.0920945 | − | 0.283438i | ||||
\(213\) | 122.924 | + | 280.483i | 0.577107 | + | 1.31682i | ||||
\(214\) | −61.0662 | + | 187.942i | −0.285356 | + | 0.878236i | ||||
\(215\) | −32.9670 | − | 23.7516i | −0.153335 | − | 0.110473i | ||||
\(216\) | −62.5586 | + | 43.7998i | −0.289623 | + | 0.202777i | ||||
\(217\) | −243.484 | − | 335.127i | −1.12205 | − | 1.54436i | ||||
\(218\) | 62.0940 | 0.284835 | ||||||||
\(219\) | 89.0218 | − | 79.2203i | 0.406492 | − | 0.361737i | ||||
\(220\) | −161.795 | + | 0.645345i | −0.735433 | + | 0.00293339i | ||||
\(221\) | 13.7682 | − | 18.9502i | 0.0622993 | − | 0.0857477i | ||||
\(222\) | −202.938 | − | 118.750i | −0.914135 | − | 0.534909i | ||||
\(223\) | 282.966 | + | 91.9413i | 1.26891 | + | 0.412293i | 0.864660 | − | 0.502357i | \(-0.167534\pi\) |
0.404247 | + | 0.914650i | \(0.367534\pi\) | |||||||
\(224\) | − | 58.4115i | − | 0.260766i | ||||||
\(225\) | −151.170 | + | 166.651i | −0.671867 | + | 0.740672i | ||||
\(226\) | −264.396 | −1.16990 | ||||||||
\(227\) | −72.6559 | + | 223.612i | −0.320070 | + | 0.985074i | 0.653547 | + | 0.756886i | \(0.273280\pi\) |
−0.973617 | + | 0.228188i | \(0.926720\pi\) | |||||||
\(228\) | 28.7514 | − | 49.1348i | 0.126103 | − | 0.215504i | ||||
\(229\) | 199.833 | + | 145.187i | 0.872632 | + | 0.634004i | 0.931292 | − | 0.364274i | \(-0.118683\pi\) |
−0.0586602 | + | 0.998278i | \(0.518683\pi\) | |||||||
\(230\) | −236.102 | + | 77.7567i | −1.02653 | + | 0.338073i | ||||
\(231\) | −333.192 | − | 374.417i | −1.44239 | − | 1.62085i | ||||
\(232\) | 18.6934i | 0.0805748i | ||||||||
\(233\) | 48.0579 | − | 34.9161i | 0.206257 | − | 0.149855i | −0.479861 | − | 0.877344i | \(-0.659313\pi\) |
0.686119 | + | 0.727490i | \(0.259313\pi\) | |||||||
\(234\) | 145.235 | − | 81.6073i | 0.620661 | − | 0.348749i | ||||
\(235\) | 105.060 | − | 34.6001i | 0.447066 | − | 0.147234i | ||||
\(236\) | −92.1093 | − | 29.9281i | −0.390294 | − | 0.126814i | ||||
\(237\) | 267.712 | − | 117.327i | 1.12959 | − | 0.495050i | ||||
\(238\) | 24.8545 | − | 8.07573i | 0.104431 | − | 0.0339316i | ||||
\(239\) | −295.152 | − | 95.9006i | −1.23494 | − | 0.401258i | −0.382441 | − | 0.923980i | \(-0.624917\pi\) |
−0.852503 | + | 0.522722i | \(0.824917\pi\) | |||||||
\(240\) | 44.6626 | − | 40.0655i | 0.186094 | − | 0.166940i | ||||
\(241\) | −85.6491 | − | 263.601i | −0.355391 | − | 1.09378i | −0.955783 | − | 0.294074i | \(-0.904989\pi\) |
0.600392 | − | 0.799706i | \(-0.295011\pi\) | |||||||
\(242\) | 161.071 | − | 117.025i | 0.665584 | − | 0.483575i | ||||
\(243\) | −115.312 | − | 213.897i | −0.474535 | − | 0.880237i | ||||
\(244\) | −53.4953 | + | 38.8666i | −0.219243 | + | 0.159289i | ||||
\(245\) | 168.416 | − | 233.760i | 0.687412 | − | 0.954121i | ||||
\(246\) | −168.417 | − | 98.5497i | −0.684622 | − | 0.400609i | ||||
\(247\) | −72.9953 | + | 100.469i | −0.295527 | + | 0.406759i | ||||
\(248\) | −35.0635 | + | 107.915i | −0.141385 | + | 0.435139i | ||||
\(249\) | −9.31020 | − | 93.8427i | −0.0373904 | − | 0.376878i | ||||
\(250\) | 102.188 | − | 144.248i | 0.408752 | − | 0.576994i | ||||
\(251\) | 268.555i | 1.06994i | 0.844870 | + | 0.534971i | \(0.179677\pi\) | ||||
−0.844870 | + | 0.534971i | \(0.820323\pi\) | |||||||
\(252\) | 184.607 | + | 21.5830i | 0.732567 | + | 0.0856468i | ||||
\(253\) | 334.321 | − | 460.153i | 1.32143 | − | 1.81879i | ||||
\(254\) | −150.583 | + | 207.259i | −0.592845 | + | 0.815981i | ||||
\(255\) | 23.2231 | + | 13.4650i | 0.0910708 | + | 0.0528039i | ||||
\(256\) | −12.9443 | + | 9.40456i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | −301.675 | −1.17383 | −0.586917 | − | 0.809647i | \(-0.699658\pi\) | ||||
−0.586917 | + | 0.809647i | \(0.699658\pi\) | |||||||
\(258\) | −25.7558 | + | 22.9201i | −0.0998288 | + | 0.0888374i | ||||
\(259\) | 176.838 | + | 544.250i | 0.682770 | + | 2.10135i | ||||
\(260\) | −105.582 | + | 77.3552i | −0.406085 | + | 0.297520i | ||||
\(261\) | −59.0795 | − | 6.90718i | −0.226358 | − | 0.0264643i | ||||
\(262\) | −317.671 | + | 103.218i | −1.21248 | + | 0.393960i | ||||
\(263\) | 41.6514 | + | 128.190i | 0.158370 | + | 0.487414i | 0.998487 | − | 0.0549921i | \(-0.0175134\pi\) |
−0.840116 | + | 0.542406i | \(0.817513\pi\) | |||||||
\(264\) | −29.3267 | + | 134.120i | −0.111086 | + | 0.508031i | ||||
\(265\) | −150.026 | + | 49.4089i | −0.566136 | + | 0.186449i | ||||
\(266\) | −131.772 | + | 42.8155i | −0.495385 | + | 0.160960i | ||||
\(267\) | 220.515 | − | 196.236i | 0.825900 | − | 0.734967i | ||||
\(268\) | − | 229.266i | − | 0.855470i | ||||||
\(269\) | 53.6367 | + | 73.8246i | 0.199393 | + | 0.274441i | 0.896991 | − | 0.442048i | \(-0.145748\pi\) |
−0.697598 | + | 0.716489i | \(0.745748\pi\) | |||||||
\(270\) | 110.123 | + | 155.958i | 0.407861 | + | 0.577624i | ||||
\(271\) | 35.8686 | + | 26.0601i | 0.132357 | + | 0.0961627i | 0.651994 | − | 0.758224i | \(-0.273933\pi\) |
−0.519637 | + | 0.854387i | \(0.673933\pi\) | |||||||
\(272\) | −5.79133 | − | 4.20765i | −0.0212917 | − | 0.0154693i | ||||
\(273\) | −396.095 | − | 86.6102i | −1.45090 | − | 0.317254i | ||||
\(274\) | 89.2855 | 0.325859 | ||||||||
\(275\) | 3.22670 | + | 404.479i | 0.0117335 | + | 1.47083i | ||||
\(276\) | 20.8237 | + | 209.894i | 0.0754482 | + | 0.760484i | ||||
\(277\) | 50.7112 | + | 16.4771i | 0.183073 | + | 0.0594840i | 0.399119 | − | 0.916899i | \(-0.369316\pi\) |
−0.216046 | + | 0.976383i | \(0.569316\pi\) | |||||||
\(278\) | 92.7814 | + | 67.4096i | 0.333746 | + | 0.242481i | ||||
\(279\) | −328.103 | − | 150.691i | −1.17600 | − | 0.540111i | ||||
\(280\) | −146.028 | + | 0.582453i | −0.521527 | + | 0.00208019i | ||||
\(281\) | 183.355 | + | 252.367i | 0.652510 | + | 0.898103i | 0.999205 | − | 0.0398749i | \(-0.0126959\pi\) |
−0.346695 | + | 0.937978i | \(0.612696\pi\) | |||||||
\(282\) | −9.26612 | − | 93.3983i | −0.0328586 | − | 0.331200i | ||||
\(283\) | −76.2924 | − | 105.007i | −0.269584 | − | 0.371051i | 0.652665 | − | 0.757647i | \(-0.273651\pi\) |
−0.922249 | + | 0.386596i | \(0.873651\pi\) | |||||||
\(284\) | −194.166 | + | 63.0882i | −0.683681 | + | 0.222142i | ||||
\(285\) | −123.123 | − | 71.3880i | −0.432010 | − | 0.250484i | ||||
\(286\) | 92.5472 | − | 284.831i | 0.323591 | − | 0.995912i | ||||
\(287\) | 146.756 | + | 451.670i | 0.511346 | + | 1.57376i | ||||
\(288\) | −24.9398 | − | 44.3848i | −0.0865965 | − | 0.154114i | ||||
\(289\) | −88.3162 | + | 271.809i | −0.305592 | + | 0.940517i | ||||
\(290\) | 46.7330 | − | 0.186402i | 0.161148 | − | 0.000642765i | ||||
\(291\) | −88.3275 | − | 201.542i | −0.303531 | − | 0.692585i | ||||
\(292\) | 46.6964 | + | 64.2720i | 0.159919 | + | 0.220110i | ||||
\(293\) | −506.053 | −1.72714 | −0.863571 | − | 0.504227i | \(-0.831778\pi\) | ||||
−0.863571 | + | 0.504227i | \(0.831778\pi\) | |||||||
\(294\) | −162.520 | − | 182.627i | −0.552788 | − | 0.621181i | ||||
\(295\) | −73.9013 | + | 230.570i | −0.250513 | + | 0.781593i | ||||
\(296\) | 92.1366 | − | 126.815i | 0.311272 | − | 0.428430i | ||||
\(297\) | −413.044 | − | 142.243i | −1.39072 | − | 0.478933i | ||||
\(298\) | 99.3548 | + | 32.2823i | 0.333405 | + | 0.108330i | ||||
\(299\) | − | 460.120i | − | 1.53886i | ||||||
\(300\) | −100.608 | − | 111.256i | −0.335361 | − | 0.370854i | ||||
\(301\) | 83.9116 | 0.278776 | ||||||||
\(302\) | 26.2144 | − | 80.6795i | 0.0868025 | − | 0.267151i | ||||
\(303\) | 59.5828 | + | 34.8651i | 0.196643 | + | 0.115066i | ||||
\(304\) | 30.7042 | + | 22.3079i | 0.101001 | + | 0.0733812i | ||||
\(305\) | 97.6991 | + | 133.350i | 0.320325 | + | 0.437212i | ||||
\(306\) | 15.4380 | − | 16.7485i | 0.0504509 | − | 0.0547337i | ||||
\(307\) | − | 78.0720i | − | 0.254306i | −0.991883 | − | 0.127153i | \(-0.959416\pi\) | ||
0.991883 | − | 0.127153i | \(-0.0405839\pi\) | |||||||
\(308\) | 270.321 | − | 196.400i | 0.877667 | − | 0.637662i | ||||
\(309\) | 116.476 | + | 265.772i | 0.376947 | + | 0.860102i | ||||
\(310\) | 270.134 | + | 86.5821i | 0.871399 | + | 0.279297i | ||||
\(311\) | −65.8087 | − | 21.3826i | −0.211604 | − | 0.0687542i | 0.201297 | − | 0.979530i | \(-0.435484\pi\) |
−0.412901 | + | 0.910776i | \(0.635484\pi\) | |||||||
\(312\) | 44.5801 | + | 101.721i | 0.142885 | + | 0.326030i | ||||
\(313\) | 350.713 | − | 113.954i | 1.12049 | − | 0.364069i | 0.310535 | − | 0.950562i | \(-0.399492\pi\) |
0.809955 | + | 0.586493i | \(0.199492\pi\) | |||||||
\(314\) | −164.765 | − | 53.5353i | −0.524729 | − | 0.170495i | ||||
\(315\) | 52.1163 | − | 461.729i | 0.165448 | − | 1.46581i | ||||
\(316\) | 60.2157 | + | 185.325i | 0.190556 | + | 0.586471i | ||||
\(317\) | 225.873 | − | 164.106i | 0.712532 | − | 0.517685i | −0.171457 | − | 0.985192i | \(-0.554848\pi\) |
0.883990 | + | 0.467507i | \(0.154848\pi\) | |||||||
\(318\) | 13.2320 | + | 133.373i | 0.0416101 | + | 0.419411i | ||||
\(319\) | −86.5106 | + | 62.8537i | −0.271193 | + | 0.197033i | ||||
\(320\) | 23.6403 | + | 32.2666i | 0.0738759 | + | 0.100833i | ||||
\(321\) | 211.716 | − | 361.812i | 0.659550 | − | 1.12714i | ||||
\(322\) | 301.739 | − | 415.309i | 0.937079 | − | 1.28978i | ||||
\(323\) | −5.24714 | + | 16.1490i | −0.0162450 | + | 0.0499970i | ||||
\(324\) | 149.491 | − | 62.4210i | 0.461393 | − | 0.192657i | ||||
\(325\) | 194.439 | + | 263.182i | 0.598274 | + | 0.809790i | ||||
\(326\) | − | 144.896i | − | 0.444468i | ||||||
\(327\) | −128.681 | − | 28.1374i | −0.393520 | − | 0.0860471i | ||||
\(328\) | 76.4636 | − | 105.243i | 0.233121 | − | 0.320863i | ||||
\(329\) | −134.268 | + | 184.804i | −0.408109 | + | 0.561714i | ||||
\(330\) | 335.590 | + | 71.9789i | 1.01694 | + | 0.218118i | ||||
\(331\) | −323.497 | + | 235.034i | −0.977331 | + | 0.710073i | −0.957111 | − | 0.289723i | \(-0.906437\pi\) |
−0.0202205 | + | 0.999796i | \(0.506437\pi\) | |||||||
\(332\) | 62.8689 | 0.189364 | ||||||||
\(333\) | 366.749 | + | 338.052i | 1.10135 | + | 1.01517i | ||||
\(334\) | −117.060 | − | 360.274i | −0.350479 | − | 1.07866i | ||||
\(335\) | −573.160 | + | 2.28614i | −1.71093 | + | 0.00682429i | ||||
\(336\) | −26.4687 | + | 121.049i | −0.0787759 | + | 0.360266i | ||||
\(337\) | 29.8595 | − | 9.70195i | 0.0886040 | − | 0.0287892i | −0.264380 | − | 0.964419i | \(-0.585167\pi\) |
0.352984 | + | 0.935630i | \(0.385167\pi\) | |||||||
\(338\) | −1.01121 | − | 3.11218i | −0.00299174 | − | 0.00920762i | ||||
\(339\) | 547.924 | + | 119.809i | 1.61629 | + | 0.353419i | ||||
\(340\) | −10.4613 | + | 14.5202i | −0.0307685 | + | 0.0427064i | ||||
\(341\) | −617.311 | + | 200.577i | −1.81030 | + | 0.588201i | ||||
\(342\) | −81.8482 | + | 88.7964i | −0.239322 | + | 0.259639i | ||||
\(343\) | 89.0293i | 0.259561i | ||||||||
\(344\) | −13.5102 | − | 18.5952i | −0.0392739 | − | 0.0540558i | ||||
\(345\) | 524.522 | − | 54.1518i | 1.52035 | − | 0.156962i | ||||
\(346\) | −43.0402 | − | 31.2705i | −0.124394 | − | 0.0903772i | ||||
\(347\) | −334.612 | − | 243.110i | −0.964300 | − | 0.700605i | −0.0101544 | − | 0.999948i | \(-0.503232\pi\) |
−0.954145 | + | 0.299344i | \(0.903232\pi\) | |||||||
\(348\) | 8.47075 | − | 38.7393i | 0.0243412 | − | 0.111320i | ||||
\(349\) | −340.865 | −0.976692 | −0.488346 | − | 0.872650i | \(-0.662400\pi\) | ||||
−0.488346 | + | 0.872650i | \(0.662400\pi\) | |||||||
\(350\) | 2.91224 | + | 365.060i | 0.00832069 | + | 1.04303i | ||||
\(351\) | −337.958 | + | 103.308i | −0.962842 | + | 0.294324i | ||||
\(352\) | −87.0464 | − | 28.2831i | −0.247291 | − | 0.0803497i | ||||
\(353\) | 318.377 | + | 231.315i | 0.901919 | + | 0.655282i | 0.938958 | − | 0.344032i | \(-0.111793\pi\) |
−0.0370394 | + | 0.999314i | \(0.511793\pi\) | |||||||
\(354\) | 177.322 | + | 103.760i | 0.500909 | + | 0.293108i | ||||
\(355\) | 159.655 | + | 484.781i | 0.449733 | + | 1.36558i | ||||
\(356\) | 115.671 | + | 159.208i | 0.324919 | + | 0.447213i | ||||
\(357\) | −55.1669 | + | 5.47315i | −0.154529 | + | 0.0153310i | ||||
\(358\) | −148.544 | − | 204.453i | −0.414927 | − | 0.571098i | ||||
\(359\) | 339.591 | − | 110.340i | 0.945937 | − | 0.307354i | 0.204873 | − | 0.978788i | \(-0.434322\pi\) |
0.741064 | + | 0.671435i | \(0.234322\pi\) | |||||||
\(360\) | −110.712 | + | 62.7916i | −0.307534 | + | 0.174421i | ||||
\(361\) | −83.7361 | + | 257.713i | −0.231956 | + | 0.713887i | ||||
\(362\) | 34.1214 | + | 105.015i | 0.0942581 | + | 0.290096i | ||||
\(363\) | −386.826 | + | 169.530i | −1.06564 | + | 0.467024i | ||||
\(364\) | 83.5280 | − | 257.073i | 0.229473 | − | 0.706244i | ||||
\(365\) | 160.213 | − | 117.381i | 0.438940 | − | 0.321591i | ||||
\(366\) | 128.473 | − | 56.3045i | 0.351020 | − | 0.153837i | ||||
\(367\) | 355.767 | + | 489.671i | 0.969392 | + | 1.33425i | 0.942354 | + | 0.334619i | \(0.108608\pi\) |
0.0270383 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(368\) | −140.616 | −0.382109 | ||||||||
\(369\) | 304.363 | + | 280.547i | 0.824832 | + | 0.760290i | ||||
\(370\) | −317.954 | − | 229.075i | −0.859336 | − | 0.619122i | ||||
\(371\) | 191.734 | − | 263.899i | 0.516804 | − | 0.711319i | ||||
\(372\) | 121.565 | − | 207.749i | 0.326787 | − | 0.558464i | ||||
\(373\) | −86.6720 | − | 28.1614i | −0.232365 | − | 0.0754999i | 0.190520 | − | 0.981683i | \(-0.438983\pi\) |
−0.422885 | + | 0.906183i | \(0.638983\pi\) | |||||||
\(374\) | − | 40.9492i | − | 0.109490i | ||||||
\(375\) | −277.135 | + | 252.628i | −0.739027 | + | 0.673676i | ||||
\(376\) | 62.5712 | 0.166413 | ||||||||
\(377\) | −26.7314 | + | 82.2707i | −0.0709055 | + | 0.218225i | ||||
\(378\) | −372.791 | − | 128.381i | −0.986220 | − | 0.339632i | ||||
\(379\) | −251.832 | − | 182.967i | −0.664465 | − | 0.482762i | 0.203703 | − | 0.979033i | \(-0.434702\pi\) |
−0.868168 | + | 0.496271i | \(0.834702\pi\) | |||||||
\(380\) | 55.4631 | − | 76.9823i | 0.145956 | − | 0.202585i | ||||
\(381\) | 405.979 | − | 361.280i | 1.06556 | − | 0.948241i | ||||
\(382\) | 166.362i | 0.435503i | ||||||||
\(383\) | −12.9876 | + | 9.43603i | −0.0339101 | + | 0.0246372i | −0.604611 | − | 0.796521i | \(-0.706672\pi\) |
0.570701 | + | 0.821158i | \(0.306672\pi\) | |||||||
\(384\) | 31.0868 | − | 13.6240i | 0.0809551 | − | 0.0354792i | ||||
\(385\) | −493.692 | − | 673.840i | −1.28232 | − | 1.75023i | ||||
\(386\) | 315.222 | + | 102.422i | 0.816637 | + | 0.265341i | ||||
\(387\) | 63.7613 | − | 35.8275i | 0.164758 | − | 0.0925775i | ||||
\(388\) | 139.519 | − | 45.3323i | 0.359584 | − | 0.116836i | ||||
\(389\) | 511.741 | + | 166.275i | 1.31553 | + | 0.427442i | 0.880958 | − | 0.473195i | \(-0.156899\pi\) |
0.434573 | + | 0.900637i | \(0.356899\pi\) | |||||||
\(390\) | 253.857 | − | 112.464i | 0.650914 | − | 0.288369i | ||||
\(391\) | −19.4410 | − | 59.8332i | −0.0497212 | − | 0.153026i | ||||
\(392\) | 131.853 | − | 95.7971i | 0.336361 | − | 0.244380i | ||||
\(393\) | 705.099 | − | 69.9535i | 1.79415 | − | 0.177999i | ||||
\(394\) | −265.352 | + | 192.790i | −0.673482 | + | 0.489314i | ||||
\(395\) | 462.708 | − | 152.386i | 1.17141 | − | 0.385787i | ||||
\(396\) | 121.551 | − | 264.656i | 0.306947 | − | 0.668322i | ||||
\(397\) | 26.8549 | − | 36.9626i | 0.0676446 | − | 0.0931048i | −0.773854 | − | 0.633364i | \(-0.781674\pi\) |
0.841499 | + | 0.540259i | \(0.181674\pi\) | |||||||
\(398\) | 73.6546 | − | 226.686i | 0.185062 | − | 0.569562i | ||||
\(399\) | 292.481 | − | 29.0173i | 0.733035 | − | 0.0727250i | ||||
\(400\) | 80.4302 | − | 59.4220i | 0.201076 | − | 0.148555i | ||||
\(401\) | 152.437i | 0.380142i | 0.981770 | + | 0.190071i | \(0.0608718\pi\) | ||||
−0.981770 | + | 0.190071i | \(0.939128\pi\) | |||||||
\(402\) | −103.890 | + | 475.121i | −0.258433 | + | 1.18189i | ||||
\(403\) | −308.634 | + | 424.798i | −0.765841 | + | 1.05409i | ||||
\(404\) | −27.0514 | + | 37.2331i | −0.0669590 | + | 0.0921611i | ||||
\(405\) | −157.542 | − | 373.103i | −0.388992 | − | 0.921241i | ||||
\(406\) | −78.0798 | + | 56.7283i | −0.192315 | + | 0.139725i | ||||
\(407\) | 896.681 | 2.20315 | ||||||||
\(408\) | 10.0950 | + | 11.3440i | 0.0247427 | + | 0.0278040i | ||||
\(409\) | −128.554 | − | 395.647i | −0.314312 | − | 0.967353i | −0.976037 | − | 0.217606i | \(-0.930175\pi\) |
0.661725 | − | 0.749747i | \(-0.269825\pi\) | |||||||
\(410\) | −263.868 | − | 190.108i | −0.643581 | − | 0.463678i | ||||
\(411\) | −185.031 | − | 40.4590i | −0.450198 | − | 0.0984404i | ||||
\(412\) | −183.982 | + | 59.7792i | −0.446557 | + | 0.145095i | ||||
\(413\) | −154.516 | − | 475.551i | −0.374131 | − | 1.15146i | ||||
\(414\) | 51.9575 | − | 444.411i | 0.125501 | − | 1.07346i | ||||
\(415\) | −0.626901 | − | 157.171i | −0.00151060 | − | 0.378725i | ||||
\(416\) | −70.4170 | + | 22.8799i | −0.169272 | + | 0.0549997i | ||||
\(417\) | −161.730 | − | 181.740i | −0.387842 | − | 0.435827i | ||||
\(418\) | 217.102i | 0.519383i | ||||||||
\(419\) | −79.9671 | − | 110.065i | −0.190852 | − | 0.262686i | 0.702858 | − | 0.711330i | \(-0.251907\pi\) |
−0.893710 | + | 0.448645i | \(0.851907\pi\) | |||||||
\(420\) | 302.885 | + | 64.9642i | 0.721155 | + | 0.154677i | ||||
\(421\) | 216.844 | + | 157.547i | 0.515070 | + | 0.374220i | 0.814743 | − | 0.579822i | \(-0.196878\pi\) |
−0.299674 | + | 0.954042i | \(0.596878\pi\) | |||||||
\(422\) | −7.82134 | − | 5.68254i | −0.0185340 | − | 0.0134657i | ||||
\(423\) | −23.1200 | + | 197.753i | −0.0546572 | + | 0.467502i | ||||
\(424\) | −89.3516 | −0.210735 | ||||||||
\(425\) | 36.4045 | + | 26.0082i | 0.0856575 | + | 0.0611958i | ||||
\(426\) | 430.968 | − | 42.7567i | 1.01166 | − | 0.100368i | ||||
\(427\) | −324.681 | − | 105.495i | −0.760378 | − | 0.247062i | ||||
\(428\) | 226.095 | + | 164.268i | 0.528260 | + | 0.383803i | ||||
\(429\) | −320.860 | + | 548.334i | −0.747924 | + | 1.27817i | ||||
\(430\) | −46.3529 | + | 33.9607i | −0.107797 | + | 0.0789783i | ||||
\(431\) | 176.847 | + | 243.410i | 0.410319 | + | 0.564755i | 0.963296 | − | 0.268441i | \(-0.0865084\pi\) |
−0.552977 | + | 0.833196i | \(0.686508\pi\) | |||||||
\(432\) | 31.5716 | + | 103.282i | 0.0730823 | + | 0.239079i | ||||
\(433\) | −137.678 | − | 189.498i | −0.317964 | − | 0.437640i | 0.619880 | − | 0.784696i | \(-0.287181\pi\) |
−0.937844 | + | 0.347057i | \(0.887181\pi\) | |||||||
\(434\) | −557.152 | + | 181.029i | −1.28376 | + | 0.417119i | ||||
\(435\) | −96.9320 | − | 20.7904i | −0.222832 | − | 0.0477941i | ||||
\(436\) | 27.1361 | − | 83.5163i | 0.0622387 | − | 0.191551i | ||||
\(437\) | 103.071 | + | 317.220i | 0.235861 | + | 0.725905i | ||||
\(438\) | −67.6472 | − | 154.355i | −0.154446 | − | 0.352408i | ||||
\(439\) | −1.68162 | + | 5.17549i | −0.00383056 | + | 0.0117893i | −0.952954 | − | 0.303116i | \(-0.901973\pi\) |
0.949123 | + | 0.314906i | \(0.101973\pi\) | |||||||
\(440\) | −69.8392 | + | 217.896i | −0.158725 | + | 0.495219i | ||||
\(441\) | 254.043 | + | 452.113i | 0.576060 | + | 1.02520i | ||||
\(442\) | −19.4711 | − | 26.7997i | −0.0440523 | − | 0.0606328i | ||||
\(443\) | −792.434 | −1.78879 | −0.894395 | − | 0.447277i | \(-0.852394\pi\) | ||||
−0.894395 | + | 0.447277i | \(0.852394\pi\) | |||||||
\(444\) | −248.405 | + | 221.055i | −0.559471 | + | 0.497872i | ||||
\(445\) | 396.863 | − | 290.763i | 0.891827 | − | 0.653401i | ||||
\(446\) | 247.322 | − | 340.409i | 0.554533 | − | 0.763249i | ||||
\(447\) | −191.270 | − | 111.922i | −0.427897 | − | 0.250385i | ||||
\(448\) | −78.5633 | − | 25.5268i | −0.175365 | − | 0.0569794i | ||||
\(449\) | 71.5381i | 0.159328i | 0.996822 | + | 0.0796638i | \(0.0253847\pi\) | ||||
−0.996822 | + | 0.0796638i | \(0.974615\pi\) | |||||||
\(450\) | 158.082 | + | 276.152i | 0.351293 | + | 0.613672i | ||||
\(451\) | 744.150 | 1.65000 | ||||||||
\(452\) | −115.545 | + | 355.612i | −0.255632 | + | 0.786753i | ||||
\(453\) | −90.8848 | + | 155.318i | −0.200629 | + | 0.342865i | ||||
\(454\) | 269.005 | + | 195.444i | 0.592523 | + | 0.430493i | ||||
\(455\) | −643.510 | − | 206.255i | −1.41431 | − | 0.453308i | ||||
\(456\) | −53.5213 | − | 60.1432i | −0.117371 | − | 0.131893i | ||||
\(457\) | 227.518i | 0.497852i | 0.968522 | + | 0.248926i | \(0.0800776\pi\) | ||||
−0.968522 | + | 0.248926i | \(0.919922\pi\) | |||||||
\(458\) | 282.606 | − | 205.325i | 0.617044 | − | 0.448308i | ||||
\(459\) | −39.5824 | + | 27.7133i | −0.0862363 | + | 0.0603776i | ||||
\(460\) | 1.40216 | + | 351.537i | 0.00304817 | + | 0.764212i | ||||
\(461\) | 849.227 | + | 275.931i | 1.84214 | + | 0.598548i | 0.998055 | + | 0.0623422i | \(0.0198570\pi\) |
0.844087 | + | 0.536206i | \(0.180143\pi\) | |||||||
\(462\) | −649.200 | + | 284.517i | −1.40519 | + | 0.615837i | ||||
\(463\) | −427.284 | + | 138.833i | −0.922859 | + | 0.299855i | −0.731639 | − | 0.681692i | \(-0.761244\pi\) |
−0.191220 | + | 0.981547i | \(0.561244\pi\) | |||||||
\(464\) | 25.1425 | + | 8.16930i | 0.0541865 | + | 0.0176062i | ||||
\(465\) | −520.580 | − | 301.838i | −1.11953 | − | 0.649114i | ||||
\(466\) | −25.9600 | − | 79.8967i | −0.0557082 | − | 0.171452i | ||||
\(467\) | −71.4787 | + | 51.9323i | −0.153059 | + | 0.111204i | −0.661679 | − | 0.749787i | \(-0.730156\pi\) |
0.508620 | + | 0.860991i | \(0.330156\pi\) | |||||||
\(468\) | −46.2918 | − | 231.004i | −0.0989140 | − | 0.493598i | ||||
\(469\) | 957.615 | − | 695.748i | 2.04182 | − | 1.48347i | ||||
\(470\) | −0.623932 | − | 156.427i | −0.00132751 | − | 0.332823i | ||||
\(471\) | 317.192 | + | 185.606i | 0.673445 | + | 0.394068i | ||||
\(472\) | −80.5065 | + | 110.808i | −0.170565 | + | 0.234762i | ||||
\(473\) | 40.6303 | − | 125.047i | 0.0858992 | − | 0.264370i | ||||
\(474\) | −40.8099 | − | 411.346i | −0.0860969 | − | 0.867818i | ||||
\(475\) | −193.007 | − | 137.889i | −0.406331 | − | 0.290293i | ||||
\(476\) | − | 36.9585i | − | 0.0776439i | ||||||
\(477\) | 33.0153 | − | 282.392i | 0.0692145 | − | 0.592016i | ||||
\(478\) | −257.972 | + | 355.068i | −0.539691 | + | 0.742820i | ||||
\(479\) | 454.305 | − | 625.298i | 0.948445 | − | 1.30542i | −0.00376930 | − | 0.999993i | \(-0.501200\pi\) |
0.952215 | − | 0.305430i | \(-0.0988002\pi\) | |||||||
\(480\) | −34.3698 | − | 77.5804i | −0.0716037 | − | 0.161626i | ||||
\(481\) | 586.844 | − | 426.367i | 1.22005 | − | 0.886418i | ||||
\(482\) | −391.972 | −0.813221 | ||||||||
\(483\) | −813.506 | + | 723.937i | −1.68428 | + | 1.49883i | ||||
\(484\) | −87.0077 | − | 267.782i | −0.179768 | − | 0.553269i | ||||
\(485\) | −114.721 | − | 348.341i | −0.236538 | − | 0.718230i | ||||
\(486\) | −338.085 | + | 61.6177i | −0.695648 | + | 0.126785i | ||||
\(487\) | −131.086 | + | 42.5926i | −0.269171 | + | 0.0874591i | −0.440493 | − | 0.897756i | \(-0.645196\pi\) |
0.171322 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(488\) | 28.8971 | + | 88.9363i | 0.0592155 | + | 0.182246i | ||||
\(489\) | −65.6587 | + | 300.277i | −0.134271 | + | 0.614064i | ||||
\(490\) | −240.806 | − | 328.676i | −0.491440 | − | 0.670766i | ||||
\(491\) | −376.626 | + | 122.373i | −0.767059 | + | 0.249233i | −0.666306 | − | 0.745679i | \(-0.732125\pi\) |
−0.100754 | + | 0.994911i | \(0.532125\pi\) | |||||||
\(492\) | −206.150 | + | 183.452i | −0.419004 | + | 0.372871i | ||||
\(493\) | 11.8278i | 0.0239914i | ||||||||
\(494\) | 103.231 | + | 142.085i | 0.208969 | + | 0.287622i | ||||
\(495\) | −662.846 | − | 301.236i | −1.33908 | − | 0.608557i | ||||
\(496\) | 129.821 | + | 94.3207i | 0.261737 | + | 0.190163i | ||||
\(497\) | −852.741 | − | 619.552i | −1.71578 | − | 1.24658i | ||||
\(498\) | −130.287 | − | 28.4886i | −0.261620 | − | 0.0572059i | ||||
\(499\) | −361.889 | −0.725229 | −0.362614 | − | 0.931939i | \(-0.618116\pi\) | ||||
−0.362614 | + | 0.931939i | \(0.618116\pi\) | |||||||
\(500\) | −149.356 | − | 200.481i | −0.298712 | − | 0.400963i | ||||
\(501\) | 79.3350 | + | 799.661i | 0.158353 | + | 1.59613i | ||||
\(502\) | 361.206 | + | 117.363i | 0.719534 | + | 0.233791i | ||||
\(503\) | −617.260 | − | 448.466i | −1.22716 | − | 0.891582i | −0.230483 | − | 0.973076i | \(-0.574031\pi\) |
−0.996674 | + | 0.0814946i | \(0.974031\pi\) | |||||||
\(504\) | 109.705 | − | 238.864i | 0.217669 | − | 0.473936i | ||||
\(505\) | 93.3517 | + | 67.2568i | 0.184855 | + | 0.133182i | ||||
\(506\) | −472.801 | − | 650.754i | −0.934389 | − | 1.28608i | ||||
\(507\) | 0.685324 | + | 6.90776i | 0.00135172 | + | 0.0136248i | ||||
\(508\) | 212.956 | + | 293.109i | 0.419205 | + | 0.576986i | ||||
\(509\) | −668.341 | + | 217.157i | −1.31305 | + | 0.426635i | −0.880102 | − | 0.474785i | \(-0.842526\pi\) |
−0.432946 | + | 0.901420i | \(0.642526\pi\) | |||||||
\(510\) | 28.2592 | − | 25.3505i | 0.0554102 | − | 0.0497069i | ||||
\(511\) | −126.748 | + | 390.089i | −0.248039 | + | 0.763384i | ||||
\(512\) | 6.99226 | + | 21.5200i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | 209.856 | − | 146.929i | 0.409076 | − | 0.286411i | ||||
\(514\) | −131.837 | + | 405.752i | −0.256492 | + | 0.789401i | ||||
\(515\) | 151.282 | + | 459.354i | 0.293750 | + | 0.891950i | ||||
\(516\) | 19.5717 | + | 44.6579i | 0.0379296 | + | 0.0865464i | ||||
\(517\) | 210.386 | + | 289.572i | 0.406937 | + | 0.560101i | ||||
\(518\) | 809.295 | 1.56235 | ||||||||
\(519\) | 75.0246 | + | 84.3070i | 0.144556 | + | 0.162441i | ||||
\(520\) | 57.9014 | + | 175.813i | 0.111349 | + | 0.338102i | ||||
\(521\) | −91.7046 | + | 126.221i | −0.176016 | + | 0.242266i | −0.887905 | − | 0.460026i | \(-0.847840\pi\) |
0.711889 | + | 0.702292i | \(0.247840\pi\) | |||||||
\(522\) | −35.1088 | + | 76.4432i | −0.0672583 | + | 0.146443i | ||||
\(523\) | −146.477 | − | 47.5934i | −0.280071 | − | 0.0910007i | 0.165613 | − | 0.986191i | \(-0.447040\pi\) |
−0.445685 | + | 0.895190i | \(0.647040\pi\) | |||||||
\(524\) | 472.374i | 0.901477i | ||||||||
\(525\) | 159.389 | − | 757.855i | 0.303598 | − | 1.44353i | ||||
\(526\) | 190.617 | 0.362390 | ||||||||
\(527\) | −22.1856 | + | 68.2803i | −0.0420980 | + | 0.129564i | ||||
\(528\) | 167.575 | + | 98.0570i | 0.317377 | + | 0.185714i | ||||
\(529\) | −571.817 | − | 415.450i | −1.08094 | − | 0.785349i | ||||
\(530\) | 0.890974 | + | 223.377i | 0.00168108 | + | 0.421466i | ||||
\(531\) | −320.456 | − | 295.381i | −0.603495 | − | 0.556272i | ||||
\(532\) | 195.945i | 0.368317i | ||||||||
\(533\) | 487.018 | − | 353.839i | 0.913730 | − | 0.663864i | ||||
\(534\) | −167.568 | − | 382.351i | −0.313798 | − | 0.716013i | ||||
\(535\) | 408.411 | − | 566.871i | 0.763386 | − | 1.05957i | ||||
\(536\) | −308.362 | − | 100.193i | −0.575302 | − | 0.186927i | ||||
\(537\) | 215.190 | + | 491.011i | 0.400725 | + | 0.914360i | ||||
\(538\) | 122.734 | − | 39.8787i | 0.228130 | − | 0.0741240i | ||||
\(539\) | 886.675 | + | 288.098i | 1.64504 | + | 0.534505i | ||||
\(540\) | 257.889 | − | 79.9581i | 0.477572 | − | 0.148071i | ||||
\(541\) | −40.5561 | − | 124.819i | −0.0749651 | − | 0.230719i | 0.906552 | − | 0.422095i | \(-0.138705\pi\) |
−0.981517 | + | 0.191376i | \(0.938705\pi\) | |||||||
\(542\) | 50.7259 | − | 36.8545i | 0.0935903 | − | 0.0679973i | ||||
\(543\) | −23.1251 | − | 233.090i | −0.0425876 | − | 0.429264i | ||||
\(544\) | −8.19018 | + | 5.95051i | −0.0150555 | + | 0.0109384i | ||||
\(545\) | −209.060 | − | 67.0069i | −0.383596 | − | 0.122948i | ||||
\(546\) | −289.590 | + | 494.896i | −0.530385 | + | 0.906404i | ||||
\(547\) | −342.130 | + | 470.902i | −0.625467 | + | 0.860881i | −0.997737 | − | 0.0672433i | \(-0.978580\pi\) |
0.372270 | + | 0.928125i | \(0.378580\pi\) | |||||||
\(548\) | 39.0192 | − | 120.089i | 0.0712029 | − | 0.219140i | ||||
\(549\) | −291.756 | + | 58.4662i | −0.531433 | + | 0.106496i | ||||
\(550\) | 545.433 | + | 172.424i | 0.991696 | + | 0.313498i | ||||
\(551\) | − | 62.7079i | − | 0.113807i | ||||||
\(552\) | 291.407 | + | 63.7191i | 0.527911 | + | 0.115433i | ||||
\(553\) | −591.343 | + | 813.914i | −1.06934 | + | 1.47182i | ||||
\(554\) | 44.3232 | − | 61.0056i | 0.0800058 | − | 0.110119i | ||||
\(555\) | 555.111 | + | 618.804i | 1.00020 | + | 1.11496i | ||||
\(556\) | 131.213 | − | 95.3316i | 0.235994 | − | 0.171460i | ||||
\(557\) | 118.153 | 0.212124 | 0.106062 | − | 0.994359i | \(-0.466176\pi\) | ||||
0.106062 | + | 0.994359i | \(0.466176\pi\) | |||||||
\(558\) | −346.065 | + | 375.443i | −0.620189 | + | 0.672837i | ||||
\(559\) | −32.8683 | − | 101.158i | −0.0587984 | − | 0.180963i | ||||
\(560\) | −63.0330 | + | 196.661i | −0.112559 | + | 0.351181i | ||||
\(561\) | −18.5558 | + | 84.8613i | −0.0330763 | + | 0.151268i | ||||
\(562\) | 419.562 | − | 136.324i | 0.746552 | − | 0.242569i | ||||
\(563\) | −66.4988 | − | 204.662i | −0.118115 | − | 0.363521i | 0.874469 | − | 0.485082i | \(-0.161210\pi\) |
−0.992584 | + | 0.121561i | \(0.961210\pi\) | |||||||
\(564\) | −129.670 | − | 28.3537i | −0.229911 | − | 0.0502724i | ||||
\(565\) | 890.176 | + | 285.315i | 1.57553 | + | 0.504983i | ||||
\(566\) | −174.576 | + | 56.7231i | −0.308438 | + | 0.100217i | ||||
\(567\) | 714.382 | + | 434.978i | 1.25993 | + | 0.767157i | ||||
\(568\) | 288.723i | 0.508314i | ||||||||
\(569\) | −175.537 | − | 241.606i | −0.308501 | − | 0.424615i | 0.626412 | − | 0.779492i | \(-0.284523\pi\) |
−0.934913 | + | 0.354877i | \(0.884523\pi\) | |||||||
\(570\) | −149.823 | + | 134.402i | −0.262848 | + | 0.235793i | ||||
\(571\) | −848.264 | − | 616.300i | −1.48558 | − | 1.07933i | −0.975706 | − | 0.219083i | \(-0.929693\pi\) |
−0.509871 | − | 0.860251i | \(-0.670307\pi\) | |||||||
\(572\) | −342.652 | − | 248.951i | −0.599042 | − | 0.435230i | ||||
\(573\) | 75.3857 | − | 344.761i | 0.131563 | − | 0.601678i | ||||
\(574\) | 671.629 | 1.17009 | ||||||||
\(575\) | 878.822 | − | 7.01074i | 1.52839 | − | 0.0121926i | ||||
\(576\) | −70.5965 | + | 14.1471i | −0.122563 | + | 0.0245609i | ||||
\(577\) | 473.444 | + | 153.831i | 0.820526 | + | 0.266605i | 0.689050 | − | 0.724714i | \(-0.258028\pi\) |
0.131477 | + | 0.991319i | \(0.458028\pi\) | |||||||
\(578\) | 326.987 | + | 237.570i | 0.565722 | + | 0.411021i | ||||
\(579\) | −606.841 | − | 355.095i | −1.04808 | − | 0.613290i | ||||
\(580\) | 20.1724 | − | 62.9373i | 0.0347800 | − | 0.108513i | ||||
\(581\) | 190.787 | + | 262.595i | 0.328377 | + | 0.451971i | ||||
\(582\) | −309.674 | + | 30.7230i | −0.532086 | + | 0.0527887i | ||||
\(583\) | −300.431 | − | 413.508i | −0.515320 | − | 0.709277i | ||||
\(584\) | 106.853 | − | 34.7186i | 0.182967 | − | 0.0594496i | ||||
\(585\) | −577.043 | + | 118.032i | −0.986399 | + | 0.201764i | ||||
\(586\) | −221.153 | + | 680.639i | −0.377394 | + | 1.16150i | ||||
\(587\) | −95.9388 | − | 295.269i | −0.163439 | − | 0.503014i | 0.835479 | − | 0.549523i | \(-0.185190\pi\) |
−0.998918 | + | 0.0465089i | \(0.985190\pi\) | |||||||
\(588\) | −316.657 | + | 138.777i | −0.538532 | + | 0.236016i | ||||
\(589\) | 117.623 | − | 362.005i | 0.199699 | − | 0.614609i | ||||
\(590\) | 277.820 | + | 200.160i | 0.470881 | + | 0.339254i | ||||
\(591\) | 637.265 | − | 279.287i | 1.07828 | − | 0.472566i | ||||
\(592\) | −130.301 | − | 179.344i | −0.220103 | − | 0.302946i | ||||
\(593\) | −19.8176 | −0.0334192 | −0.0167096 | − | 0.999860i | \(-0.505319\pi\) | ||||
−0.0167096 | + | 0.999860i | \(0.505319\pi\) | |||||||
\(594\) | −371.823 | + | 493.381i | −0.625965 | + | 0.830607i | ||||
\(595\) | −92.3955 | + | 0.368533i | −0.155287 | + | 0.000619384i | ||||
\(596\) | 86.8392 | − | 119.524i | 0.145703 | − | 0.200544i | ||||
\(597\) | −255.359 | + | 436.397i | −0.427738 | + | 0.730984i | ||||
\(598\) | −618.860 | − | 201.080i | −1.03488 | − | 0.336254i | ||||
\(599\) | − | 523.573i | − | 0.874078i | −0.899443 | − | 0.437039i | \(-0.856027\pi\) | ||
0.899443 | − | 0.437039i | \(-0.143973\pi\) | |||||||
\(600\) | −193.607 | + | 86.6973i | −0.322678 | + | 0.144495i | ||||
\(601\) | −860.125 | −1.43116 | −0.715578 | − | 0.698533i | \(-0.753837\pi\) | ||||
−0.715578 | + | 0.698533i | \(0.753837\pi\) | |||||||
\(602\) | 36.6707 | − | 112.861i | 0.0609148 | − | 0.187476i | ||||
\(603\) | 430.595 | − | 937.543i | 0.714087 | − | 1.55480i | ||||
\(604\) | −97.0576 | − | 70.5165i | −0.160691 | − | 0.116749i | ||||
\(605\) | −668.582 | + | 220.188i | −1.10510 | + | 0.363947i | ||||
\(606\) | 72.9321 | − | 64.9021i | 0.120350 | − | 0.107099i | ||||
\(607\) | − | 827.798i | − | 1.36375i | −0.731468 | − | 0.681876i | \(-0.761164\pi\) | ||
0.731468 | − | 0.681876i | \(-0.238836\pi\) | |||||||
\(608\) | 43.4223 | − | 31.5481i | 0.0714182 | − | 0.0518883i | ||||
\(609\) | 187.515 | − | 82.1800i | 0.307907 | − | 0.134943i | ||||
\(610\) | 222.051 | − | 73.1291i | 0.364018 | − | 0.119884i | ||||
\(611\) | 275.380 | + | 89.4764i | 0.450704 | + | 0.146442i | ||||
\(612\) | −15.7801 | − | 28.0834i | −0.0257844 | − | 0.0458879i | ||||
\(613\) | 259.925 | − | 84.4547i | 0.424021 | − | 0.137773i | −0.0892305 | − | 0.996011i | \(-0.528441\pi\) |
0.513252 | + | 0.858238i | \(0.328441\pi\) | |||||||
\(614\) | −105.007 | − | 34.1187i | −0.171020 | − | 0.0555679i | ||||
\(615\) | 460.683 | + | 513.542i | 0.749078 | + | 0.835027i | ||||
\(616\) | −146.023 | − | 449.412i | −0.237050 | − | 0.729564i | ||||
\(617\) | 402.536 | − | 292.459i | 0.652408 | − | 0.474002i | −0.211682 | − | 0.977339i | \(-0.567894\pi\) |
0.864091 | + | 0.503336i | \(0.167894\pi\) | |||||||
\(618\) | 408.364 | − | 40.5141i | 0.660783 | − | 0.0655568i | ||||
\(619\) | 86.4899 | − | 62.8386i | 0.139725 | − | 0.101516i | −0.515727 | − | 0.856753i | \(-0.672478\pi\) |
0.655452 | + | 0.755237i | \(0.272478\pi\) | |||||||
\(620\) | 234.505 | − | 325.491i | 0.378235 | − | 0.524986i | ||||
\(621\) | −309.056 | + | 897.433i | −0.497674 | + | 1.44514i | ||||
\(622\) | −57.5189 | + | 79.1680i | −0.0924742 | + | 0.127280i | ||||
\(623\) | −313.966 | + | 966.288i | −0.503958 | + | 1.55102i | ||||
\(624\) | 156.297 | − | 15.5063i | 0.250476 | − | 0.0248499i | ||||
\(625\) | −499.710 | + | 375.386i | −0.799537 | + | 0.600617i | ||||
\(626\) | − | 521.508i | − | 0.833080i | ||||||
\(627\) | 98.3781 | − | 449.913i | 0.156903 | − | 0.717565i | ||||
\(628\) | −144.010 | + | 198.212i | −0.229315 | + | 0.315625i | ||||
\(629\) | 58.2973 | − | 80.2393i | 0.0926824 | − | 0.127566i | ||||
\(630\) | −598.248 | − | 271.879i | −0.949600 | − | 0.431554i | ||||
\(631\) | 480.892 | − | 349.389i | 0.762111 | − | 0.553706i | −0.137446 | − | 0.990509i | \(-0.543889\pi\) |
0.899557 | + | 0.436803i | \(0.143889\pi\) | |||||||
\(632\) | 275.577 | 0.436039 | ||||||||
\(633\) | 13.6336 | + | 15.3204i | 0.0215381 | + | 0.0242029i | ||||
\(634\) | −122.012 | − | 375.515i | −0.192448 | − | 0.592295i | ||||
\(635\) | 730.643 | − | 535.308i | 1.15062 | − | 0.843005i | ||||
\(636\) | 185.168 | + | 40.4890i | 0.291145 | + | 0.0636619i | ||||
\(637\) | 717.284 | − | 233.060i | 1.12603 | − | 0.365871i | ||||
\(638\) | 46.7314 | + | 143.825i | 0.0732468 | + | 0.225430i | ||||
\(639\) | −912.495 | − | 106.683i | −1.42800 | − | 0.166953i | ||||
\(640\) | 53.7297 | − | 17.6951i | 0.0839527 | − | 0.0276486i | ||||
\(641\) | 215.035 | − | 69.8690i | 0.335468 | − | 0.109000i | −0.136439 | − | 0.990648i | \(-0.543566\pi\) |
0.471907 | + | 0.881648i | \(0.343566\pi\) | |||||||
\(642\) | −394.113 | − | 442.875i | −0.613883 | − | 0.689836i | ||||
\(643\) | − | 136.351i | − | 0.212054i | −0.994363 | − | 0.106027i | \(-0.966187\pi\) | ||
0.994363 | − | 0.106027i | \(-0.0338130\pi\) | |||||||
\(644\) | −426.724 | − | 587.335i | −0.662615 | − | 0.912011i | ||||
\(645\) | 111.449 | − | 49.3742i | 0.172789 | − | 0.0765491i | ||||
\(646\) | 19.4273 | + | 14.1148i | 0.0300733 | + | 0.0218495i | ||||
\(647\) | 821.339 | + | 596.737i | 1.26946 | + | 0.922314i | 0.999181 | − | 0.0404686i | \(-0.0128851\pi\) |
0.270276 | + | 0.962783i | \(0.412885\pi\) | |||||||
\(648\) | −18.6259 | − | 228.344i | −0.0287437 | − | 0.352383i | ||||
\(649\) | −783.496 | −1.20724 | ||||||||
\(650\) | 438.952 | − | 146.505i | 0.675310 | − | 0.225393i | ||||
\(651\) | 1236.65 | − | 122.689i | 1.89961 | − | 0.188462i | ||||
\(652\) | −194.885 | − | 63.3221i | −0.298904 | − | 0.0971198i | ||||
\(653\) | −21.3391 | − | 15.5038i | −0.0326786 | − | 0.0237424i | 0.571326 | − | 0.820723i | \(-0.306429\pi\) |
−0.604005 | + | 0.796981i | \(0.706429\pi\) | |||||||
\(654\) | −94.0804 | + | 160.779i | −0.143854 | + | 0.245839i | ||||
\(655\) | 1180.93 | − | 4.71030i | 1.80294 | − | 0.00719130i | ||||
\(656\) | −108.136 | − | 148.836i | −0.164841 | − | 0.226885i | ||||
\(657\) | 70.2444 | + | 350.532i | 0.106917 | + | 0.533534i | ||||
\(658\) | 189.883 | + | 261.352i | 0.288576 | + | 0.397191i | ||||
\(659\) | 214.919 | − | 69.8315i | 0.326129 | − | 0.105966i | −0.141376 | − | 0.989956i | \(-0.545153\pi\) |
0.467506 | + | 0.883990i | \(0.345153\pi\) | |||||||
\(660\) | 243.470 | − | 419.912i | 0.368893 | − | 0.636230i | ||||
\(661\) | 102.297 | − | 314.838i | 0.154761 | − | 0.476306i | −0.843375 | − | 0.537325i | \(-0.819435\pi\) |
0.998137 | + | 0.0610187i | \(0.0194349\pi\) | |||||||
\(662\) | 174.747 | + | 537.816i | 0.263968 | + | 0.812410i | ||||
\(663\) | 28.2070 | + | 64.3617i | 0.0425445 | + | 0.0970765i | ||||
\(664\) | 27.4747 | − | 84.5585i | 0.0413776 | − | 0.127347i | ||||
\(665\) | 489.857 | − | 1.95387i | 0.736628 | − | 0.00293815i | ||||
\(666\) | 614.954 | − | 345.543i | 0.923354 | − | 0.518833i | ||||
\(667\) | 136.564 | + | 187.964i | 0.204744 | + | 0.281805i | ||||
\(668\) | −535.725 | −0.801983 | ||||||||
\(669\) | −666.792 | + | 593.377i | −0.996700 | + | 0.886961i | ||||
\(670\) | −247.405 | + | 771.898i | −0.369262 | + | 1.15209i | ||||
\(671\) | −314.424 | + | 432.768i | −0.468590 | + | 0.644959i | ||||
\(672\) | 151.244 | + | 88.5009i | 0.225065 | + | 0.131698i | ||||
\(673\) | −848.660 | − | 275.746i | −1.26101 | − | 0.409727i | −0.399156 | − | 0.916883i | \(-0.630697\pi\) |
−0.861854 | + | 0.507156i | \(0.830697\pi\) | |||||||
\(674\) | − | 44.4009i | − | 0.0658767i | ||||||
\(675\) | −202.465 | − | 643.920i | −0.299949 | − | 0.953955i | ||||
\(676\) | −4.62778 | −0.00684583 | ||||||||
\(677\) | −10.5351 | + | 32.4236i | −0.0155614 | + | 0.0478931i | −0.958536 | − | 0.284972i | \(-0.908016\pi\) |
0.942974 | + | 0.332866i | \(0.108016\pi\) | |||||||
\(678\) | 400.594 | − | 684.597i | 0.590847 | − | 1.00973i | ||||
\(679\) | 612.741 | + | 445.182i | 0.902416 | + | 0.655644i | ||||
\(680\) | 14.9578 | + | 20.4159i | 0.0219968 | + | 0.0300235i | ||||
\(681\) | −468.911 | − | 526.927i | −0.688563 | − | 0.773755i | ||||
\(682\) | 917.937i | 1.34595i | ||||||||
\(683\) | −213.330 | + | 154.994i | −0.312343 | + | 0.226931i | −0.732901 | − | 0.680335i | \(-0.761834\pi\) |
0.420558 | + | 0.907266i | \(0.361834\pi\) | |||||||
\(684\) | 83.6619 | + | 148.891i | 0.122313 | + | 0.217677i | ||||
\(685\) | −300.609 | − | 96.3497i | −0.438845 | − | 0.140657i | ||||
\(686\) | 119.744 | + | 38.9072i | 0.174554 | + | 0.0567161i | ||||
\(687\) | −678.702 | + | 297.447i | −0.987921 | + | 0.432964i | ||||
\(688\) | −30.9147 | + | 10.0448i | −0.0449341 | + | 0.0146000i | ||||
\(689\) | −393.242 | − | 127.772i | −0.570743 | − | 0.185446i | ||||
\(690\) | 156.391 | − | 729.146i | 0.226653 | − | 1.05673i | ||||
\(691\) | 218.032 | + | 671.034i | 0.315531 | + | 0.971105i | 0.975535 | + | 0.219843i | \(0.0705546\pi\) |
−0.660004 | + | 0.751262i | \(0.729445\pi\) | |||||||
\(692\) | −60.8680 | + | 44.2232i | −0.0879595 | + | 0.0639064i | ||||
\(693\) | 1474.30 | − | 295.441i | 2.12742 | − | 0.426321i | ||||
\(694\) | −473.213 | + | 343.809i | −0.681863 | + | 0.495402i | ||||
\(695\) | −239.635 | − | 327.078i | −0.344799 | − | 0.470617i | ||||
\(696\) | −48.4024 | − | 28.3228i | −0.0695437 | − | 0.0406937i | ||||
\(697\) | 48.3805 | − | 66.5901i | 0.0694125 | − | 0.0955381i | ||||
\(698\) | −148.964 | + | 458.463i | −0.213415 | + | 0.656824i | ||||
\(699\) | 17.5938 | + | 177.338i | 0.0251700 | + | 0.253702i | ||||
\(700\) | 492.278 | + | 155.620i | 0.703254 | + | 0.222315i | ||||
\(701\) | − | 212.674i | − | 0.303386i | −0.988428 | − | 0.151693i | \(-0.951527\pi\) | ||
0.988428 | − | 0.151693i | \(-0.0484726\pi\) | |||||||
\(702\) | −8.74450 | + | 499.699i | −0.0124566 | + | 0.711822i | ||||
\(703\) | −309.077 | + | 425.408i | −0.439655 | + | 0.605133i | ||||
\(704\) | −76.0813 | + | 104.717i | −0.108070 | + | 0.148746i | ||||
\(705\) | −69.5906 | + | 324.455i | −0.0987100 | + | 0.460220i | ||||
\(706\) | 450.253 | − | 327.128i | 0.637753 | − | 0.463355i | ||||
\(707\) | −237.610 | −0.336082 | ||||||||
\(708\) | 217.050 | − | 193.152i | 0.306568 | − | 0.272814i | ||||
\(709\) | 240.527 | + | 740.265i | 0.339248 | + | 1.04410i | 0.964592 | + | 0.263748i | \(0.0849586\pi\) |
−0.625344 | + | 0.780349i | \(0.715041\pi\) | |||||||
\(710\) | 721.801 | − | 2.87901i | 1.01662 | − | 0.00405495i | ||||
\(711\) | −101.825 | + | 870.947i | −0.143214 | + | 1.22496i | ||||
\(712\) | 264.684 | − | 86.0011i | 0.371748 | − | 0.120788i | ||||
\(713\) | 435.799 | + | 1341.25i | 0.611218 | + | 1.88114i | ||||
\(714\) | −16.7474 | + | 76.5912i | −0.0234558 | + | 0.107271i | ||||
\(715\) | −618.956 | + | 859.106i | −0.865673 | + | 1.20155i | ||||
\(716\) | −339.905 | + | 110.442i | −0.474728 | + | 0.154248i | ||||
\(717\) | 695.506 | − | 618.930i | 0.970023 | − | 0.863221i | ||||
\(718\) | − | 504.970i | − | 0.703300i | ||||||
\(719\) | −163.363 | − | 224.850i | −0.227209 | − | 0.312726i | 0.680158 | − | 0.733065i | \(-0.261911\pi\) |
−0.907367 | + | 0.420339i | \(0.861911\pi\) | |||||||
\(720\) | 36.0714 | + | 176.349i | 0.0500992 | + | 0.244929i | ||||
\(721\) | −808.015 | − | 587.057i | −1.12069 | − | 0.814226i | ||||
\(722\) | 310.030 | + | 225.250i | 0.429404 | + | 0.311980i | ||||
\(723\) | 812.307 | + | 177.619i | 1.12352 | + | 0.245670i | ||||
\(724\) | 156.156 | 0.215686 | ||||||||
\(725\) | −157.543 | − | 49.8030i | −0.217301 | − | 0.0686937i | ||||
\(726\) | 58.9676 | + | 594.367i | 0.0812226 | + | 0.818687i | ||||
\(727\) | 397.443 | + | 129.137i | 0.546689 | + | 0.177630i | 0.569323 | − | 0.822114i | \(-0.307205\pi\) |
−0.0226345 | + | 0.999744i | \(0.507205\pi\) | |||||||
\(728\) | −309.259 | − | 224.690i | −0.424806 | − | 0.308640i | ||||
\(729\) | 728.554 | + | 25.5065i | 0.999388 | + | 0.0349884i | ||||
\(730\) | −87.8612 | − | 266.784i | −0.120358 | − | 0.365457i | ||||
\(731\) | −8.54826 | − | 11.7657i | −0.0116939 | − | 0.0160953i | ||||
\(732\) | −19.5844 | − | 197.402i | −0.0267547 | − | 0.269675i | ||||
\(733\) | 250.201 | + | 344.372i | 0.341338 | + | 0.469811i | 0.944832 | − | 0.327557i | \(-0.106225\pi\) |
−0.603494 | + | 0.797368i | \(0.706225\pi\) | |||||||
\(734\) | 814.082 | − | 264.511i | 1.10910 | − | 0.360369i | ||||
\(735\) | 350.098 | + | 790.252i | 0.476324 | + | 1.07517i | ||||
\(736\) | −61.4515 | + | 189.128i | −0.0834939 | + | 0.256968i | ||||
\(737\) | −573.141 | − | 1763.95i | −0.777667 | − | 2.39341i | ||||
\(738\) | 510.346 | − | 286.764i | 0.691526 | − | 0.388569i | ||||
\(739\) | 161.074 | − | 495.736i | 0.217962 | − | 0.670820i | −0.780967 | − | 0.624572i | \(-0.785274\pi\) |
0.998930 | − | 0.0462479i | \(-0.0147264\pi\) | |||||||
\(740\) | −447.057 | + | 327.538i | −0.604130 | + | 0.442619i | ||||
\(741\) | −149.546 | − | 341.229i | −0.201817 | − | 0.460498i | ||||
\(742\) | −271.153 | − | 373.210i | −0.365435 | − | 0.502979i | ||||
\(743\) | −30.5343 | −0.0410960 | −0.0205480 | − | 0.999789i | \(-0.506541\pi\) | ||||
−0.0205480 | + | 0.999789i | \(0.506541\pi\) | |||||||
\(744\) | −226.295 | − | 254.294i | −0.304161 | − | 0.341793i | ||||
\(745\) | −299.673 | − | 215.905i | −0.402246 | − | 0.289805i | ||||
\(746\) | −75.7541 | + | 104.267i | −0.101547 | + | 0.139768i | ||||
\(747\) | 257.091 | + | 118.077i | 0.344165 | + | 0.158068i | ||||
\(748\) | −55.0765 | − | 17.8954i | −0.0736317 | − | 0.0239244i | ||||
\(749\) | 1442.87i | 1.92639i | ||||||||
\(750\) | 218.672 | + | 483.149i | 0.291563 | + | 0.644198i | ||||
\(751\) | 125.127 | 0.166614 | 0.0833068 | − | 0.996524i | \(-0.473452\pi\) | ||||
0.0833068 | + | 0.996524i | \(0.473452\pi\) | |||||||
\(752\) | 27.3446 | − | 84.1581i | 0.0363625 | − | 0.111912i | ||||
\(753\) | −695.366 | − | 406.896i | −0.923461 | − | 0.540366i | ||||
\(754\) | 98.9718 | + | 71.9072i | 0.131262 | + | 0.0953677i | ||||
\(755\) | −175.322 | + | 243.345i | −0.232215 | + | 0.322312i | ||||
\(756\) | −335.588 | + | 445.299i | −0.443899 | + | 0.589019i | ||||
\(757\) | − | 210.053i | − | 0.277481i | −0.990329 | − | 0.138740i | \(-0.955695\pi\) | ||
0.990329 | − | 0.138740i | \(-0.0443053\pi\) | |||||||
\(758\) | −356.145 | + | 258.754i | −0.469848 | + | 0.341364i | ||||
\(759\) | 684.927 | + | 1562.84i | 0.902408 | + | 2.05908i | ||||
\(760\) | −79.3026 | − | 108.240i | −0.104346 | − | 0.142421i | ||||
\(761\) | −207.729 | − | 67.4953i | −0.272969 | − | 0.0886929i | 0.169334 | − | 0.985559i | \(-0.445838\pi\) |
−0.442303 | + | 0.896866i | \(0.645838\pi\) | |||||||
\(762\) | −308.501 | − | 703.925i | −0.404857 | − | 0.923786i | ||||
\(763\) | 431.186 | − | 140.101i | 0.565119 | − | 0.183618i | ||||
\(764\) | 223.756 | + | 72.7029i | 0.292875 | + | 0.0951608i | ||||
\(765\) | −70.0506 | + | 39.7299i | −0.0915694 | + | 0.0519345i | ||||
\(766\) | 7.01565 | + | 21.5920i | 0.00915881 | + | 0.0281879i | ||||
\(767\) | −512.768 | + | 372.548i | −0.668538 | + | 0.485721i | ||||
\(768\) | −4.73885 | − | 47.7655i | −0.00617038 | − | 0.0621947i | ||||
\(769\) | 954.296 | − | 693.337i | 1.24096 | − | 0.901608i | 0.243296 | − | 0.969952i | \(-0.421771\pi\) |
0.997662 | + | 0.0683437i | \(0.0217714\pi\) | |||||||
\(770\) | −1122.06 | + | 369.535i | −1.45723 | + | 0.479916i | ||||
\(771\) | 457.077 | − | 781.123i | 0.592836 | − | 1.01313i | ||||
\(772\) | 275.514 | − | 379.213i | 0.356884 | − | 0.491208i | ||||
\(773\) | 158.479 | − | 487.748i | 0.205018 | − | 0.630980i | −0.794695 | − | 0.607009i | \(-0.792369\pi\) |
0.999713 | − | 0.0239709i | \(-0.00763091\pi\) | |||||||
\(774\) | −20.3231 | − | 101.416i | −0.0262573 | − | 0.131028i | ||||
\(775\) | −816.060 | − | 583.013i | −1.05298 | − | 0.752275i | ||||
\(776\) | − | 207.463i | − | 0.267349i | ||||||
\(777\) | −1677.15 | − | 366.726i | −2.15849 | − | 0.471977i | ||||
\(778\) | 447.278 | − | 615.626i | 0.574908 | − | 0.791293i | ||||
\(779\) | −256.501 | + | 353.044i | −0.329270 | + | 0.453201i | ||||
\(780\) | −40.3241 | − | 390.585i | −0.0516975 | − | 0.500750i | ||||
\(781\) | −1336.17 | + | 970.787i | −1.71085 | + | 1.24300i | ||||
\(782\) | −88.9715 | −0.113774 | ||||||||
\(783\) | 107.398 | − | 142.508i | 0.137162 | − | 0.182003i | ||||
\(784\) | −71.2247 | − | 219.207i | −0.0908479 | − | 0.279601i | ||||
\(785\) | 496.963 | + | 358.045i | 0.633074 | + | 0.456108i | ||||
\(786\) | 214.053 | − | 978.927i | 0.272332 | − | 1.24545i | ||||
\(787\) | 64.9505 | − | 21.1037i | 0.0825292 | − | 0.0268154i | −0.267461 | − | 0.963569i | \(-0.586185\pi\) |
0.349991 | + | 0.936753i | \(0.386185\pi\) | |||||||
\(788\) | 143.338 | + | 441.150i | 0.181901 | + | 0.559835i | ||||
\(789\) | −395.027 | − | 86.3768i | −0.500668 | − | 0.109476i | ||||
\(790\) | −2.74793 | − | 688.936i | −0.00347839 | − | 0.872071i | ||||
\(791\) | −1835.99 | + | 596.549i | −2.32110 | + | 0.754171i | ||||
\(792\) | −302.841 | − | 279.144i | −0.382375 | − | 0.352455i | ||||
\(793\) | 432.737i | 0.545696i | ||||||||
\(794\) | −37.9786 | − | 52.2730i | −0.0478320 | − | 0.0658351i | ||||
\(795\) | 99.3752 | − | 463.321i | 0.125000 | − | 0.582794i | ||||
\(796\) | −272.703 | − | 198.130i | −0.342592 | − | 0.248908i | ||||
\(797\) | −117.868 | − | 85.6363i | −0.147890 | − | 0.107448i | 0.511380 | − | 0.859355i | \(-0.329135\pi\) |
−0.659270 | + | 0.751906i | \(0.729135\pi\) | |||||||
\(798\) | 88.7907 | − | 406.067i | 0.111267 | − | 0.508856i | ||||
\(799\) | 39.5905 | 0.0495500 | ||||||||
\(800\) | −44.7731 | − | 134.147i | −0.0559664 | − | 0.167684i | ||||
\(801\) | 174.002 | + | 868.300i | 0.217231 | + | 1.08402i | ||||
\(802\) | 205.027 | + | 66.6174i | 0.255645 | + | 0.0830641i | ||||
\(803\) | 519.950 | + | 377.766i | 0.647509 | + | 0.470443i | ||||
\(804\) | 593.635 | + | 347.367i | 0.738351 | + | 0.432049i | ||||
\(805\) | −1464.07 | + | 1072.66i | −1.81872 | + | 1.33249i | ||||
\(806\) | 436.474 | + | 600.755i | 0.541531 | + | 0.745354i | ||||
\(807\) | −272.419 | + | 27.0269i | −0.337570 | + | 0.0334906i | ||||
\(808\) | 38.2565 | + | 52.6556i | 0.0473472 | + | 0.0651678i | ||||
\(809\) | 401.858 | − | 130.571i | 0.496734 | − | 0.161399i | −0.0499268 | − | 0.998753i | \(-0.515899\pi\) |
0.546661 | + | 0.837354i | \(0.315899\pi\) | |||||||
\(810\) | −570.670 | + | 48.8414i | −0.704531 | + | 0.0602981i | ||||
\(811\) | 262.414 | − | 807.627i | 0.323569 | − | 0.995842i | −0.648514 | − | 0.761203i | \(-0.724609\pi\) |
0.972083 | − | 0.234639i | \(-0.0753908\pi\) | |||||||
\(812\) | 42.1773 | + | 129.808i | 0.0519424 | + | 0.159862i | ||||
\(813\) | −121.823 | + | 53.3897i | −0.149843 | + | 0.0656700i | ||||
\(814\) | 391.864 | − | 1206.03i | 0.481405 | − | 1.48161i | ||||
\(815\) | −156.361 | + | 487.841i | −0.191854 | + | 0.598578i | ||||
\(816\) | 19.6694 | − | 8.62027i | 0.0241047 | − | 0.0105641i | ||||
\(817\) | 45.3207 | + | 62.3786i | 0.0554721 | + | 0.0763508i | ||||
\(818\) | −588.324 | −0.719223 | ||||||||
\(819\) | 824.393 | − | 894.376i | 1.00658 | − | 1.09203i | ||||
\(820\) | −371.009 | + | 271.822i | −0.452451 | + | 0.331490i | ||||
\(821\) | 320.493 | − | 441.121i | 0.390369 | − | 0.537297i | −0.567925 | − | 0.823080i | \(-0.692254\pi\) |
0.958294 | + | 0.285783i | \(0.0922537\pi\) | |||||||
\(822\) | −135.279 | + | 231.185i | −0.164573 | + | 0.281247i | ||||
\(823\) | 854.455 | + | 277.629i | 1.03822 | + | 0.337338i | 0.778035 | − | 0.628221i | \(-0.216217\pi\) |
0.260185 | + | 0.965559i | \(0.416217\pi\) | |||||||
\(824\) | 273.579i | 0.332014i | ||||||||
\(825\) | −1052.20 | − | 604.482i | −1.27539 | − | 0.732706i | ||||
\(826\) | −707.141 | −0.856103 | ||||||||
\(827\) | −350.989 | + | 1080.23i | −0.424412 | + | 1.30621i | 0.479143 | + | 0.877737i | \(0.340947\pi\) |
−0.903556 | + | 0.428470i | \(0.859053\pi\) | |||||||
\(828\) | −575.025 | − | 264.097i | −0.694474 | − | 0.318958i | ||||
\(829\) | −584.813 | − | 424.891i | −0.705444 | − | 0.512535i | 0.176257 | − | 0.984344i | \(-0.443601\pi\) |
−0.881701 | + | 0.471809i | \(0.843601\pi\) | |||||||
\(830\) | −211.669 | − | 67.8431i | −0.255022 | − | 0.0817387i | ||||
\(831\) | −119.498 | + | 106.341i | −0.143800 | + | 0.127967i | ||||
\(832\) | 104.710i | 0.125853i | ||||||||
\(833\) | 83.4271 | − | 60.6133i | 0.100153 | − | 0.0727651i | ||||
\(834\) | −315.118 | + | 138.103i | −0.377840 | + | 0.165591i | ||||
\(835\) | 5.34200 | + | 1339.30i | 0.00639761 | + | 1.60395i | ||||
\(836\) | 292.002 | + | 94.8771i | 0.349284 | + | 0.113489i | ||||
\(837\) | 887.300 | − | 621.235i | 1.06010 | − | 0.742216i | ||||
\(838\) | −182.984 | + | 59.4552i | −0.218358 | + | 0.0709490i | ||||
\(839\) | −1198.87 | − | 389.535i | −1.42892 | − | 0.464285i | −0.510498 | − | 0.859879i | \(-0.670539\pi\) |
−0.918426 | + | 0.395594i | \(0.870539\pi\) | |||||||
\(840\) | 219.742 | − | 378.989i | 0.261598 | − | 0.451178i | ||||
\(841\) | 246.385 | + | 758.296i | 0.292967 | + | 0.901660i | ||||
\(842\) | 306.664 | − | 222.805i | 0.364209 | − | 0.264614i | ||||
\(843\) | −931.256 | + | 92.3907i | −1.10469 | + | 0.109597i | ||||
\(844\) | −11.0611 | + | 8.03632i | −0.0131055 | + | 0.00952171i | ||||
\(845\) | 0.0461461 | + | 11.5694i | 5.46108e−5 | + | 0.0136915i | ||||
\(846\) | 255.874 | + | 117.518i | 0.302452 | + | 0.138910i | ||||
\(847\) | 854.452 | − | 1176.05i | 1.00880 | − | 1.38849i | ||||
\(848\) | −39.0481 | + | 120.178i | −0.0460473 | + | 0.141719i | ||||
\(849\) | 387.487 | − | 38.4429i | 0.456404 | − | 0.0452802i | ||||
\(850\) | 50.8903 | − | 37.5979i | 0.0598710 | − | 0.0442328i | ||||
\(851\) | − | 1948.25i | − | 2.28936i | ||||||
\(852\) | 130.832 | − | 598.336i | 0.153559 | − | 0.702273i | ||||
\(853\) | −234.337 | + | 322.537i | −0.274721 | + | 0.378120i | −0.923976 | − | 0.382450i | \(-0.875081\pi\) |
0.649256 | + | 0.760570i | \(0.275081\pi\) | |||||||
\(854\) | −283.782 | + | 390.592i | −0.332297 | + | 0.457368i | ||||
\(855\) | 371.390 | − | 210.638i | 0.434375 | − | 0.246360i | ||||
\(856\) | 319.747 | − | 232.310i | 0.373536 | − | 0.271390i | ||||
\(857\) | −1540.49 | −1.79754 | −0.898768 | − | 0.438425i | \(-0.855537\pi\) | ||||
−0.898768 | + | 0.438425i | \(0.855537\pi\) | |||||||
\(858\) | 597.287 | + | 671.186i | 0.696139 | + | 0.782268i | ||||
\(859\) | −336.512 | − | 1035.68i | −0.391749 | − | 1.20568i | −0.931465 | − | 0.363831i | \(-0.881469\pi\) |
0.539716 | − | 0.841847i | \(-0.318531\pi\) | |||||||
\(860\) | 25.4200 | + | 77.1859i | 0.0295582 | + | 0.0897510i | ||||
\(861\) | −1391.86 | − | 304.344i | −1.61656 | − | 0.353477i | ||||
\(862\) | 404.670 | − | 131.485i | 0.469455 | − | 0.152535i | ||||
\(863\) | −521.721 | − | 1605.69i | −0.604543 | − | 1.86059i | −0.499902 | − | 0.866082i | \(-0.666631\pi\) |
−0.104641 | − | 0.994510i | \(-0.533369\pi\) | |||||||
\(864\) | 152.712 | + | 2.67238i | 0.176750 | + | 0.00309304i | ||||
\(865\) | 111.164 | + | 151.728i | 0.128513 | + | 0.175408i | ||||
\(866\) | −315.042 | + | 102.363i | −0.363790 | + | 0.118202i | ||||
\(867\) | −569.981 | − | 640.502i | −0.657418 | − | 0.738756i | ||||
\(868\) | 828.480i | 0.954470i | ||||||||
\(869\) | 926.586 | + | 1275.34i | 1.06627 | + | 1.46759i | ||||
\(870\) | −70.3239 | + | 121.287i | −0.0808320 | + | 0.139411i | ||||
\(871\) | −1213.85 | − | 881.911i | −1.39362 | − | 1.01253i | ||||
\(872\) | −100.470 | − | 72.9959i | −0.115218 | − | 0.0837109i | ||||
\(873\) | 655.677 | + | 76.6574i | 0.751062 | + | 0.0878091i | ||||
\(874\) | 471.704 | 0.539707 | ||||||||
\(875\) | 384.139 | − | 1232.24i | 0.439016 | − | 1.40827i | ||||
\(876\) | −237.169 | + | 23.5298i | −0.270741 | + | 0.0268605i | ||||
\(877\) | −965.679 | − | 313.768i | −1.10112 | − | 0.357774i | −0.298584 | − | 0.954383i | \(-0.596514\pi\) |
−0.802532 | + | 0.596609i | \(0.796514\pi\) | |||||||
\(878\) | 6.22612 | + | 4.52354i | 0.00709125 | + | 0.00515210i | ||||
\(879\) | 766.735 | − | 1310.31i | 0.872281 | − | 1.49069i | ||||
\(880\) | 262.549 | + | 189.158i | 0.298351 | + | 0.214952i | ||||
\(881\) | 605.502 | + | 833.402i | 0.687290 | + | 0.945973i | 0.999992 | − | 0.00387781i | \(-0.00123435\pi\) |
−0.312703 | + | 0.949851i | \(0.601234\pi\) | |||||||
\(882\) | 719.112 | − | 144.106i | 0.815320 | − | 0.163385i | ||||
\(883\) | 190.011 | + | 261.528i | 0.215188 | + | 0.296181i | 0.902942 | − | 0.429763i | \(-0.141403\pi\) |
−0.687753 | + | 0.725944i | \(0.741403\pi\) | |||||||
\(884\) | −44.5547 | + | 14.4767i | −0.0504012 | + | 0.0163764i | ||||
\(885\) | −485.041 | − | 540.694i | −0.548069 | − | 0.610954i | ||||
\(886\) | −346.306 | + | 1065.82i | −0.390865 | + | 1.20296i | ||||
\(887\) | 460.598 | + | 1417.58i | 0.519276 | + | 1.59817i | 0.775364 | + | 0.631515i | \(0.217567\pi\) |
−0.256087 | + | 0.966654i | \(0.582433\pi\) | |||||||
\(888\) | 188.762 | + | 430.709i | 0.212569 | + | 0.485033i | ||||
\(889\) | −578.026 | + | 1778.98i | −0.650197 | + | 2.00110i | ||||
\(890\) | −217.640 | − | 660.848i | −0.244540 | − | 0.742526i | ||||
\(891\) | 994.123 | − | 853.972i | 1.11574 | − | 0.958442i | ||||
\(892\) | −349.766 | − | 481.411i | −0.392114 | − | 0.539699i | ||||
\(893\) | −209.899 | −0.235049 | ||||||||
\(894\) | −234.123 | + | 208.346i | −0.261883 | + | 0.233049i | ||||
\(895\) | 279.492 | + | 848.654i | 0.312281 | + | 0.948217i | ||||
\(896\) | −68.6669 | + | 94.5118i | −0.0766371 | + | 0.105482i | ||||
\(897\) | 1191.38 | + | 697.141i | 1.32818 | + | 0.777192i | ||||
\(898\) | 96.2186 | + | 31.2633i | 0.107148 | + | 0.0348144i | ||||
\(899\) | − | 265.137i | − | 0.294925i | ||||||
\(900\) | 440.508 | − | 91.9363i | 0.489454 | − | 0.102151i | ||||
\(901\) | −56.5351 | −0.0627470 | ||||||||
\(902\) | 325.206 | − | 1000.88i | 0.360538 | − | 1.10962i | ||||
\(903\) | −127.137 | + | 217.271i | −0.140794 | + | 0.240610i | ||||
\(904\) | 427.802 | + | 310.817i | 0.473233 | + | 0.343824i | ||||
\(905\) | −1.55712 | − | 390.388i | −0.00172058 | − | 0.431368i | ||||
\(906\) | 169.184 | + | 190.116i | 0.186737 | + | 0.209841i | ||||
\(907\) | − | 1512.95i | − | 1.66808i | −0.551701 | − | 0.834042i | \(-0.686021\pi\) | ||
0.551701 | − | 0.834042i | \(-0.313979\pi\) | |||||||
\(908\) | 380.431 | − | 276.399i | 0.418977 | − | 0.304405i | ||||
\(909\) | −180.551 | + | 101.452i | −0.198626 | + | 0.111608i | ||||
\(910\) | −558.636 | + | 775.382i | −0.613886 | + | 0.852068i | ||||
\(911\) | −425.630 | − | 138.295i | −0.467211 | − | 0.151806i | 0.0659443 | − | 0.997823i | \(-0.478994\pi\) |
−0.533156 | + | 0.846017i | \(0.678994\pi\) | |||||||
\(912\) | −104.282 | + | 45.7025i | −0.114344 | + | 0.0501124i | ||||
\(913\) | 483.706 | − | 157.166i | 0.529799 | − | 0.172142i | ||||
\(914\) | 306.012 | + | 99.4292i | 0.334805 | + | 0.108785i | ||||
\(915\) | −493.306 | + | 50.9291i | −0.539133 | + | 0.0556602i | ||||
\(916\) | −152.659 | − | 469.835i | −0.166658 | − | 0.512920i | ||||
\(917\) | −1973.05 | + | 1433.50i | −2.15163 | + | 1.56325i | ||||
\(918\) | 19.9761 | + | 65.3494i | 0.0217605 | + | 0.0711867i | ||||
\(919\) | 869.814 | − | 631.957i | 0.946478 | − | 0.687657i | −0.00349305 | − | 0.999994i | \(-0.501112\pi\) |
0.949971 | + | 0.312337i | \(0.101112\pi\) | |||||||
\(920\) | 473.429 | + | 151.742i | 0.514597 | + | 0.164936i | ||||
\(921\) | 202.150 | + | 118.289i | 0.219490 | + | 0.128435i | ||||
\(922\) | 742.252 | − | 1021.62i | 0.805046 | − | 1.10805i | ||||
\(923\) | −412.871 | + | 1270.69i | −0.447314 | + | 1.37669i | ||||
\(924\) | 98.9637 | + | 997.510i | 0.107104 | + | 1.07956i | ||||
\(925\) | 823.296 | + | 1114.37i | 0.890050 | + | 1.20472i | ||||
\(926\) | 635.368i | 0.686142i | ||||||||
\(927\) | −864.634 | − | 101.087i | −0.932723 | − | 0.109048i | ||||
\(928\) | 21.9754 | − | 30.2465i | 0.0236804 | − | 0.0325932i | ||||
\(929\) | −227.333 | + | 312.897i | −0.244708 | + | 0.336811i | −0.913649 | − | 0.406504i | \(-0.866748\pi\) |
0.668941 | + | 0.743315i | \(0.266748\pi\) | |||||||
\(930\) | −633.473 | + | 568.270i | −0.681154 | + | 0.611043i | ||||
\(931\) | −442.309 | + | 321.356i | −0.475090 | + | 0.345173i | ||||
\(932\) | −118.806 | −0.127474 | ||||||||
\(933\) | 155.074 | − | 138.000i | 0.166210 | − | 0.147910i | ||||
\(934\) | 38.6115 | + | 118.834i | 0.0413399 | + | 0.127231i | ||||
\(935\) | −44.1891 | + | 137.869i | −0.0472610 | + | 0.147453i | ||||
\(936\) | −330.930 | − | 38.6901i | −0.353557 | − | 0.0413356i | ||||
\(937\) | 9.02374 | − | 2.93199i | 0.00963046 | − | 0.00312913i | −0.304198 | − | 0.952609i | \(-0.598388\pi\) |
0.313828 | + | 0.949480i | \(0.398388\pi\) | |||||||
\(938\) | −517.286 | − | 1592.04i | −0.551477 | − | 1.69727i | ||||
\(939\) | −236.317 | + | 1080.75i | −0.251669 | + | 1.15096i | ||||
\(940\) | −210.666 | − | 67.5218i | −0.224113 | − | 0.0718317i | ||||
\(941\) | 1752.51 | − | 569.426i | 1.86239 | − | 0.605129i | 0.868377 | − | 0.495905i | \(-0.165163\pi\) |
0.994017 | − | 0.109224i | \(-0.0348365\pi\) | |||||||
\(942\) | 388.258 | − | 345.510i | 0.412163 | − | 0.366783i | ||||
\(943\) | − | 1616.84i | − | 1.71457i | ||||||
\(944\) | 113.853 | + | 156.706i | 0.120607 | + | 0.166002i | ||||
\(945\) | 1116.58 | + | 834.522i | 1.18157 | + | 0.883092i | ||||
\(946\) | −150.432 | − | 109.295i | −0.159019 | − | 0.115534i | ||||
\(947\) | 1412.88 | + | 1026.52i | 1.49195 | + | 1.08397i | 0.973453 | + | 0.228888i | \(0.0735088\pi\) |
0.518498 | + | 0.855079i | \(0.326491\pi\) | |||||||
\(948\) | −571.093 | − | 124.875i | −0.602419 | − | 0.131725i | ||||
\(949\) | 519.913 | 0.547853 | ||||||||
\(950\) | −269.808 | + | 199.334i | −0.284008 | + | 0.209826i | ||||
\(951\) | 82.6912 | + | 833.490i | 0.0869518 | + | 0.876436i | ||||
\(952\) | −49.7091 | − | 16.1515i | −0.0522154 | − | 0.0169658i | ||||
\(953\) | 1327.86 | + | 964.749i | 1.39335 | + | 1.01233i | 0.995488 | + | 0.0948824i | \(0.0302475\pi\) |
0.397861 | + | 0.917446i | \(0.369752\pi\) | |||||||
\(954\) | −365.388 | − | 167.815i | −0.383006 | − | 0.175907i | ||||
\(955\) | 179.525 | − | 560.112i | 0.187984 | − | 0.586504i | ||||
\(956\) | 364.828 | + | 502.142i | 0.381619 | + | 0.525253i | ||||
\(957\) | −31.6712 | − | 319.232i | −0.0330943 | − | 0.333576i | ||||
\(958\) | −642.485 | − | 884.304i | −0.670652 | − | 0.923073i | ||||
\(959\) | 620.006 | − | 201.452i | 0.646513 | − | 0.210065i | ||||
\(960\) | −119.366 | + | 12.3233i | −0.124339 | + | 0.0128368i | ||||
\(961\) | 200.359 | − | 616.640i | 0.208490 | − | 0.641665i | ||||
\(962\) | −317.002 | − | 975.632i | −0.329524 | − | 1.01417i | ||||
\(963\) | 616.058 | + | 1096.38i | 0.639728 | + | 1.13851i | ||||
\(964\) | −171.298 | + | 527.202i | −0.177695 | + | 0.546890i | ||||
\(965\) | −950.771 | − | 684.998i | −0.985255 | − | 0.709843i | ||||
\(966\) | 618.178 | + | 1410.53i | 0.639936 | + | 1.46018i | ||||
\(967\) | 639.828 | + | 880.648i | 0.661663 | + | 0.910701i | 0.999535 | − | 0.0304908i | \(-0.00970703\pi\) |
−0.337872 | + | 0.941192i | \(0.609707\pi\) | |||||||
\(968\) | −398.190 | −0.411353 | ||||||||
\(969\) | −33.8644 | − | 38.0542i | −0.0349477 | − | 0.0392716i | ||||
\(970\) | −518.653 | + | 2.06873i | −0.534694 | + | 0.00213271i | ||||
\(971\) | 68.8826 | − | 94.8088i | 0.0709399 | − | 0.0976404i | −0.772073 | − | 0.635534i | \(-0.780780\pi\) |
0.843013 | + | 0.537894i | \(0.180780\pi\) | |||||||
\(972\) | −64.8728 | + | 481.651i | −0.0667415 | + | 0.495526i | ||||
\(973\) | 796.376 | + | 258.758i | 0.818474 | + | 0.265938i | ||||
\(974\) | 194.924i | 0.200128i | ||||||||
\(975\) | −976.052 | + | 104.704i | −1.00108 | + | 0.107389i | ||||
\(976\) | 132.248 | 0.135500 | ||||||||
\(977\) | 305.409 | − | 939.952i | 0.312599 | − | 0.962080i | −0.664133 | − | 0.747615i | \(-0.731199\pi\) |
0.976732 | − | 0.214466i | \(-0.0688010\pi\) | |||||||
\(978\) | 375.178 | + | 219.537i | 0.383618 | + | 0.224475i | ||||
\(979\) | 1287.96 | + | 935.761i | 1.31559 | + | 0.955833i | ||||
\(980\) | −547.303 | + | 180.246i | −0.558473 | + | 0.183925i | ||||
\(981\) | 267.824 | − | 290.560i | 0.273011 | − | 0.296187i | ||||
\(982\) | 560.040i | 0.570305i | ||||||||
\(983\) | 1381.07 | − | 1003.41i | 1.40495 | − | 1.02076i | 0.410922 | − | 0.911670i | \(-0.365207\pi\) |
0.994032 | − | 0.109088i | \(-0.0347932\pi\) | |||||||
\(984\) | 156.652 | + | 357.443i | 0.159199 | + | 0.363255i | ||||
\(985\) | 1101.44 | − | 362.742i | 1.11821 | − | 0.368266i | ||||
\(986\) | 15.9083 | + | 5.16893i | 0.0161342 | + | 0.00524232i | ||||
\(987\) | −275.076 | − | 627.659i | −0.278699 | − | 0.635926i | ||||
\(988\) | 236.218 | − | 76.7518i | 0.239087 | − | 0.0776840i | ||||
\(989\) | −271.694 | − | 88.2786i | −0.274716 | − | 0.0892605i | ||||
\(990\) | −694.836 | + | 759.880i | −0.701854 | + | 0.767556i | ||||
\(991\) | −361.325 | − | 1112.05i | −0.364607 | − | 1.12214i | −0.950227 | − | 0.311559i | \(-0.899149\pi\) |
0.585620 | − | 0.810586i | \(-0.300851\pi\) | |||||||
\(992\) | 183.595 | − | 133.390i | 0.185076 | − | 0.134465i | ||||
\(993\) | −118.431 | − | 1193.73i | −0.119266 | − | 1.20215i | ||||
\(994\) | −1205.96 | + | 876.179i | −1.21324 | + | 0.881468i | ||||
\(995\) | −492.603 | + | 683.728i | −0.495078 | + | 0.687164i | ||||
\(996\) | −95.2545 | + | 162.785i | −0.0956370 | + | 0.163439i | ||||
\(997\) | −847.026 | + | 1165.83i | −0.849574 | + | 1.16934i | 0.134382 | + | 0.990930i | \(0.457095\pi\) |
−0.983956 | + | 0.178409i | \(0.942905\pi\) | |||||||
\(998\) | −158.151 | + | 486.740i | −0.158468 | + | 0.487715i | ||||
\(999\) | −1430.98 | + | 437.426i | −1.43242 | + | 0.437864i |
(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 | 150.3.i.a.29.14 | yes | 80 | |
3.2 | odd | 2 | inner | 150.3.i.a.29.4 | ✓ | 80 | |
25.19 | even | 10 | inner | 150.3.i.a.119.4 | yes | 80 | |
75.44 | odd | 10 | inner | 150.3.i.a.119.14 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.3.i.a.29.4 | ✓ | 80 | 3.2 | odd | 2 | inner | |
150.3.i.a.29.14 | yes | 80 | 1.1 | even | 1 | trivial | |
150.3.i.a.119.4 | yes | 80 | 25.19 | even | 10 | inner | |
150.3.i.a.119.14 | yes | 80 | 75.44 | odd | 10 | inner |