Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Character | \(\chi\) | \(=\) | 210.163 |
Dual form | 210.3.v.b.67.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | − | 1.36603i | −0.183013 | − | 0.683013i | ||||
\(3\) | −0.448288 | + | 1.67303i | −0.149429 | + | 0.557678i | ||||
\(4\) | −1.73205 | + | 1.00000i | −0.433013 | + | 0.250000i | ||||
\(5\) | −3.58272 | + | 3.48771i | −0.716543 | + | 0.697543i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 3.00056 | − | 6.32429i | 0.428652 | − | 0.903470i | ||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | −2.59808 | − | 1.50000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 6.07567 | + | 3.61749i | 0.607567 | + | 0.361749i | ||||
\(11\) | −1.95694 | − | 3.38951i | −0.177903 | − | 0.308138i | 0.763259 | − | 0.646093i | \(-0.223598\pi\) |
−0.941162 | + | 0.337955i | \(0.890265\pi\) | |||||||
\(12\) | −0.896575 | − | 3.34607i | −0.0747146 | − | 0.278839i | ||||
\(13\) | −8.93314 | − | 8.93314i | −0.687164 | − | 0.687164i | 0.274440 | − | 0.961604i | \(-0.411508\pi\) |
−0.961604 | + | 0.274440i | \(0.911508\pi\) | |||||||
\(14\) | −9.73742 | − | 1.78399i | −0.695530 | − | 0.127428i | ||||
\(15\) | −4.22897 | − | 7.55750i | −0.281931 | − | 0.503833i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.125000 | − | 0.216506i | ||||
\(17\) | −14.3027 | − | 3.83238i | −0.841332 | − | 0.225434i | −0.187681 | − | 0.982230i | \(-0.560097\pi\) |
−0.653651 | + | 0.756796i | \(0.726764\pi\) | |||||||
\(18\) | −1.09808 | + | 4.09808i | −0.0610042 | + | 0.227671i | ||||
\(19\) | −28.0079 | − | 16.1704i | −1.47410 | − | 0.851072i | −0.474526 | − | 0.880242i | \(-0.657380\pi\) |
−0.999574 | + | 0.0291696i | \(0.990714\pi\) | |||||||
\(20\) | 2.71773 | − | 9.62361i | 0.135887 | − | 0.481181i | ||||
\(21\) | 9.23562 | + | 7.85514i | 0.439792 | + | 0.374054i | ||||
\(22\) | −3.91387 | + | 3.91387i | −0.177903 | + | 0.177903i | ||||
\(23\) | 12.3227 | − | 3.30186i | 0.535770 | − | 0.143559i | 0.0192188 | − | 0.999815i | \(-0.493882\pi\) |
0.516552 | + | 0.856256i | \(0.327215\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0.671716 | − | 24.9910i | 0.0268686 | − | 0.999639i | ||||
\(26\) | −8.93314 | + | 15.4726i | −0.343582 | + | 0.595102i | ||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 1.12716 | + | 13.9546i | 0.0402557 | + | 0.498377i | ||||
\(29\) | 26.6068i | 0.917478i | 0.888571 | + | 0.458739i | \(0.151699\pi\) | ||||
−0.888571 | + | 0.458739i | \(0.848301\pi\) | |||||||
\(30\) | −8.77583 | + | 8.54312i | −0.292528 | + | 0.284771i | ||||
\(31\) | −17.0130 | − | 29.4674i | −0.548807 | − | 0.950561i | −0.998357 | − | 0.0573060i | \(-0.981749\pi\) |
0.449550 | − | 0.893255i | \(-0.351584\pi\) | |||||||
\(32\) | −5.46410 | − | 1.46410i | −0.170753 | − | 0.0457532i | ||||
\(33\) | 6.54804 | − | 1.75454i | 0.198425 | − | 0.0531679i | ||||
\(34\) | 20.9405i | 0.615898i | ||||||||
\(35\) | 11.3071 | + | 33.1232i | 0.323061 | + | 0.946378i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 1.67475 | + | 6.25026i | 0.0452636 | + | 0.168926i | 0.984858 | − | 0.173365i | \(-0.0554639\pi\) |
−0.939594 | + | 0.342291i | \(0.888797\pi\) | |||||||
\(38\) | −11.8375 | + | 44.1783i | −0.311514 | + | 1.16259i | ||||
\(39\) | 18.9500 | − | 10.9408i | 0.485898 | − | 0.280534i | ||||
\(40\) | −14.1409 | − | 0.190007i | −0.353521 | − | 0.00475018i | ||||
\(41\) | −26.0073 | −0.634324 | −0.317162 | − | 0.948371i | \(-0.602730\pi\) | ||||
−0.317162 | + | 0.948371i | \(0.602730\pi\) | |||||||
\(42\) | 7.34985 | − | 15.4913i | 0.174996 | − | 0.368840i | ||||
\(43\) | 21.0534 | + | 21.0534i | 0.489614 | + | 0.489614i | 0.908185 | − | 0.418570i | \(-0.137469\pi\) |
−0.418570 | + | 0.908185i | \(0.637469\pi\) | |||||||
\(44\) | 6.77903 | + | 3.91387i | 0.154069 | + | 0.0889516i | ||||
\(45\) | 14.5397 | − | 3.68727i | 0.323105 | − | 0.0819393i | ||||
\(46\) | −9.02086 | − | 15.6246i | −0.196106 | − | 0.339665i | ||||
\(47\) | 10.7473 | + | 40.1094i | 0.228666 | + | 0.853391i | 0.980903 | + | 0.194499i | \(0.0623081\pi\) |
−0.752237 | + | 0.658892i | \(0.771025\pi\) | |||||||
\(48\) | 4.89898 | + | 4.89898i | 0.102062 | + | 0.102062i | ||||
\(49\) | −30.9932 | − | 37.9528i | −0.632515 | − | 0.774548i | ||||
\(50\) | −34.3842 | + | 8.22975i | −0.687683 | + | 0.164595i | ||||
\(51\) | 12.8234 | − | 22.2108i | 0.251439 | − | 0.435506i | ||||
\(52\) | 24.4058 | + | 6.53951i | 0.469342 | + | 0.125760i | ||||
\(53\) | 11.7128 | − | 43.7126i | 0.220995 | − | 0.824766i | −0.762974 | − | 0.646429i | \(-0.776262\pi\) |
0.983969 | − | 0.178337i | \(-0.0570717\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 18.8328 | + | 5.31843i | 0.342414 | + | 0.0966988i | ||||
\(56\) | 18.6497 | − | 6.64745i | 0.333030 | − | 0.118704i | ||||
\(57\) | 39.6092 | − | 39.6092i | 0.694897 | − | 0.694897i | ||||
\(58\) | 36.3456 | − | 9.73878i | 0.626649 | − | 0.167910i | ||||
\(59\) | −20.7971 | + | 12.0072i | −0.352494 | + | 0.203512i | −0.665783 | − | 0.746145i | \(-0.731902\pi\) |
0.313289 | + | 0.949658i | \(0.398569\pi\) | |||||||
\(60\) | 14.8823 | + | 8.86101i | 0.248038 | + | 0.147683i | ||||
\(61\) | 8.39818 | − | 14.5461i | 0.137675 | − | 0.238460i | −0.788941 | − | 0.614469i | \(-0.789370\pi\) |
0.926616 | + | 0.376009i | \(0.122704\pi\) | |||||||
\(62\) | −34.0260 | + | 34.0260i | −0.548807 | + | 0.548807i | ||||
\(63\) | −17.2821 | + | 11.9301i | −0.274319 | + | 0.189367i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 63.1611 | + | 0.848679i | 0.971709 | + | 0.0130566i | ||||
\(66\) | −4.79349 | − | 8.30258i | −0.0726287 | − | 0.125797i | ||||
\(67\) | 57.0249 | + | 15.2798i | 0.851118 | + | 0.228056i | 0.657906 | − | 0.753100i | \(-0.271443\pi\) |
0.193213 | + | 0.981157i | \(0.438109\pi\) | |||||||
\(68\) | 28.6053 | − | 7.66477i | 0.420666 | − | 0.112717i | ||||
\(69\) | 22.0965i | 0.320239i | ||||||||
\(70\) | 41.1085 | − | 27.5698i | 0.587264 | − | 0.393854i | ||||
\(71\) | −132.560 | −1.86705 | −0.933524 | − | 0.358515i | \(-0.883283\pi\) | ||||
−0.933524 | + | 0.358515i | \(0.883283\pi\) | |||||||
\(72\) | −2.19615 | − | 8.19615i | −0.0305021 | − | 0.113835i | ||||
\(73\) | 2.29553 | − | 8.56704i | 0.0314457 | − | 0.117357i | −0.948419 | − | 0.317019i | \(-0.897318\pi\) |
0.979865 | + | 0.199663i | \(0.0639846\pi\) | |||||||
\(74\) | 7.92501 | − | 4.57551i | 0.107095 | − | 0.0618312i | ||||
\(75\) | 41.5096 | + | 12.3269i | 0.553461 | + | 0.164359i | ||||
\(76\) | 64.6815 | 0.851072 | ||||||||
\(77\) | −27.3082 | + | 2.20578i | −0.354651 | + | 0.0286465i | ||||
\(78\) | −21.8816 | − | 21.8816i | −0.280534 | − | 0.280534i | ||||
\(79\) | 90.6550 | + | 52.3397i | 1.14753 | + | 0.662528i | 0.948284 | − | 0.317422i | \(-0.102817\pi\) |
0.199247 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(80\) | 4.91636 | + | 19.3863i | 0.0614545 | + | 0.242329i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 9.51932 | + | 35.5266i | 0.116089 | + | 0.433251i | ||||
\(83\) | 94.1629 | + | 94.1629i | 1.13449 | + | 1.13449i | 0.989421 | + | 0.145072i | \(0.0463413\pi\) |
0.145072 | + | 0.989421i | \(0.453659\pi\) | |||||||
\(84\) | −23.8517 | − | 4.36988i | −0.283949 | − | 0.0520223i | ||||
\(85\) | 64.6086 | − | 36.1532i | 0.760101 | − | 0.425332i | ||||
\(86\) | 21.0534 | − | 36.4656i | 0.244807 | − | 0.424019i | ||||
\(87\) | −44.5141 | − | 11.9275i | −0.511657 | − | 0.137098i | ||||
\(88\) | 2.86515 | − | 10.6929i | 0.0325586 | − | 0.121510i | ||||
\(89\) | −43.2731 | − | 24.9837i | −0.486215 | − | 0.280716i | 0.236788 | − | 0.971561i | \(-0.423905\pi\) |
−0.723003 | + | 0.690845i | \(0.757239\pi\) | |||||||
\(90\) | −10.3588 | − | 18.5120i | −0.115098 | − | 0.205689i | ||||
\(91\) | −83.3002 | + | 29.6913i | −0.915386 | + | 0.326278i | ||||
\(92\) | −18.0417 | + | 18.0417i | −0.196106 | + | 0.196106i | ||||
\(93\) | 56.9266 | − | 15.2534i | 0.612114 | − | 0.164016i | ||||
\(94\) | 50.8567 | − | 29.3621i | 0.541028 | − | 0.312363i | ||||
\(95\) | 156.742 | − | 39.7497i | 1.64992 | − | 0.418418i | ||||
\(96\) | 4.89898 | − | 8.48528i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 118.224 | − | 118.224i | 1.21881 | − | 1.21881i | 0.250755 | − | 0.968050i | \(-0.419321\pi\) |
0.968050 | − | 0.250755i | \(-0.0806790\pi\) | |||||||
\(98\) | −40.5002 | + | 56.2293i | −0.413268 | + | 0.573768i | ||||
\(99\) | 11.7416i | 0.118602i | ||||||||
\(100\) | 23.8275 | + | 43.9574i | 0.238275 | + | 0.439574i | ||||
\(101\) | −55.9197 | − | 96.8557i | −0.553660 | − | 0.958967i | −0.998006 | − | 0.0631124i | \(-0.979897\pi\) |
0.444346 | − | 0.895855i | \(-0.353436\pi\) | |||||||
\(102\) | −35.0342 | − | 9.38738i | −0.343473 | − | 0.0920332i | ||||
\(103\) | −178.865 | + | 47.9268i | −1.73656 | + | 0.465309i | −0.981676 | − | 0.190556i | \(-0.938971\pi\) |
−0.754879 | + | 0.655864i | \(0.772304\pi\) | |||||||
\(104\) | − | 35.7325i | − | 0.343582i | ||||||
\(105\) | −60.4851 | + | 4.06847i | −0.576049 | + | 0.0387473i | ||||
\(106\) | −63.9997 | −0.603771 | ||||||||
\(107\) | 8.28292 | + | 30.9123i | 0.0774105 | + | 0.288900i | 0.993769 | − | 0.111459i | \(-0.0355523\pi\) |
−0.916359 | + | 0.400358i | \(0.868886\pi\) | |||||||
\(108\) | −2.68973 | + | 10.0382i | −0.0249049 | + | 0.0929463i | ||||
\(109\) | −151.129 | + | 87.2544i | −1.38651 | + | 0.800499i | −0.992920 | − | 0.118788i | \(-0.962099\pi\) |
−0.393586 | + | 0.919288i | \(0.628766\pi\) | |||||||
\(110\) | 0.371832 | − | 27.6728i | 0.00338029 | − | 0.251571i | ||||
\(111\) | −11.2077 | −0.100970 | ||||||||
\(112\) | −15.9069 | − | 23.0428i | −0.142025 | − | 0.205740i | ||||
\(113\) | −6.20286 | − | 6.20286i | −0.0548925 | − | 0.0548925i | 0.679128 | − | 0.734020i | \(-0.262358\pi\) |
−0.734020 | + | 0.679128i | \(0.762358\pi\) | |||||||
\(114\) | −68.6051 | − | 39.6092i | −0.601799 | − | 0.347449i | ||||
\(115\) | −32.6329 | + | 54.8078i | −0.283764 | + | 0.476589i | ||||
\(116\) | −26.6068 | − | 46.0844i | −0.229369 | − | 0.397279i | ||||
\(117\) | 9.80926 | + | 36.6087i | 0.0838399 | + | 0.312895i | ||||
\(118\) | 24.0145 | + | 24.0145i | 0.203512 | + | 0.203512i | ||||
\(119\) | −67.1531 | + | 78.9548i | −0.564312 | + | 0.663486i | ||||
\(120\) | 6.65706 | − | 23.5729i | 0.0554755 | − | 0.196441i | ||||
\(121\) | 52.8408 | − | 91.5230i | 0.436701 | − | 0.756388i | ||||
\(122\) | −22.9443 | − | 6.14790i | −0.188068 | − | 0.0503926i | ||||
\(123\) | 11.6587 | − | 43.5110i | 0.0947865 | − | 0.353748i | ||||
\(124\) | 58.9348 | + | 34.0260i | 0.475281 | + | 0.274403i | ||||
\(125\) | 84.7548 | + | 91.8783i | 0.678038 | + | 0.735027i | ||||
\(126\) | 22.6226 | + | 19.2411i | 0.179544 | + | 0.152707i | ||||
\(127\) | 38.4037 | − | 38.4037i | 0.302392 | − | 0.302392i | −0.539557 | − | 0.841949i | \(-0.681408\pi\) |
0.841949 | + | 0.539557i | \(0.181408\pi\) | |||||||
\(128\) | 10.9282 | − | 2.92820i | 0.0853766 | − | 0.0228766i | ||||
\(129\) | −44.6610 | + | 25.7851i | −0.346210 | + | 0.199884i | ||||
\(130\) | −21.9593 | − | 86.5903i | −0.168917 | − | 0.666079i | ||||
\(131\) | −73.5861 | + | 127.455i | −0.561726 | + | 0.972938i | 0.435620 | + | 0.900131i | \(0.356529\pi\) |
−0.997346 | + | 0.0728073i | \(0.976804\pi\) | |||||||
\(132\) | −9.58699 | + | 9.58699i | −0.0726287 | + | 0.0726287i | ||||
\(133\) | −186.306 | + | 128.610i | −1.40079 | + | 0.966991i | ||||
\(134\) | − | 83.4903i | − | 0.623062i | ||||||
\(135\) | −0.349065 | + | 25.9784i | −0.00258567 | + | 0.192433i | ||||
\(136\) | −20.9405 | − | 36.2701i | −0.153975 | − | 0.266692i | ||||
\(137\) | 1.13179 | + | 0.303261i | 0.00826122 | + | 0.00221359i | 0.262947 | − | 0.964810i | \(-0.415305\pi\) |
−0.254686 | + | 0.967024i | \(0.581972\pi\) | |||||||
\(138\) | 30.1844 | − | 8.08788i | 0.218727 | − | 0.0586078i | ||||
\(139\) | 234.615i | 1.68788i | 0.536439 | + | 0.843939i | \(0.319769\pi\) | ||||
−0.536439 | + | 0.843939i | \(0.680231\pi\) | |||||||
\(140\) | −52.7078 | − | 46.0640i | −0.376484 | − | 0.329028i | ||||
\(141\) | −71.9222 | −0.510086 | ||||||||
\(142\) | 48.5205 | + | 181.081i | 0.341694 | + | 1.27522i | ||||
\(143\) | −12.7974 | + | 47.7605i | −0.0894923 | + | 0.333990i | ||||
\(144\) | −10.3923 | + | 6.00000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | −92.7971 | − | 95.3248i | −0.639980 | − | 0.657412i | ||||
\(146\) | −12.5430 | −0.0859111 | ||||||||
\(147\) | 77.3902 | − | 34.8389i | 0.526464 | − | 0.236999i | ||||
\(148\) | −9.15101 | − | 9.15101i | −0.0618312 | − | 0.0618312i | ||||
\(149\) | −224.139 | − | 129.407i | −1.50429 | − | 0.868501i | −0.999988 | − | 0.00497290i | \(-0.998417\pi\) |
−0.504300 | − | 0.863528i | \(-0.668250\pi\) | |||||||
\(150\) | 1.64536 | − | 61.2151i | 0.0109691 | − | 0.408101i | ||||
\(151\) | −72.8305 | − | 126.146i | −0.482321 | − | 0.835405i | 0.517473 | − | 0.855700i | \(-0.326873\pi\) |
−0.999794 | + | 0.0202948i | \(0.993540\pi\) | |||||||
\(152\) | −23.6751 | − | 88.3565i | −0.155757 | − | 0.581293i | ||||
\(153\) | 31.4108 | + | 31.4108i | 0.205299 | + | 0.205299i | ||||
\(154\) | 13.0086 | + | 36.4963i | 0.0844717 | + | 0.236989i | ||||
\(155\) | 163.727 | + | 46.2368i | 1.05630 | + | 0.298302i | ||||
\(156\) | −21.8816 | + | 37.9001i | −0.140267 | + | 0.242949i | ||||
\(157\) | 9.55304 | + | 2.55973i | 0.0608474 | + | 0.0163040i | 0.289114 | − | 0.957295i | \(-0.406639\pi\) |
−0.228267 | + | 0.973599i | \(0.573306\pi\) | |||||||
\(158\) | 38.3153 | − | 142.995i | 0.242502 | − | 0.905029i | ||||
\(159\) | 67.8819 | + | 39.1917i | 0.426930 | + | 0.246488i | ||||
\(160\) | 24.6827 | − | 13.8118i | 0.154267 | − | 0.0863235i | ||||
\(161\) | 16.0932 | − | 87.8399i | 0.0999575 | − | 0.545589i | ||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −221.655 | + | 59.3922i | −1.35985 | + | 0.364369i | −0.863760 | − | 0.503904i | \(-0.831896\pi\) |
−0.496086 | + | 0.868274i | \(0.665230\pi\) | |||||||
\(164\) | 45.0459 | − | 26.0073i | 0.274670 | − | 0.158581i | ||||
\(165\) | −17.3404 | + | 29.1237i | −0.105093 | + | 0.176507i | ||||
\(166\) | 94.1629 | − | 163.095i | 0.567246 | − | 0.982500i | ||||
\(167\) | 181.703 | − | 181.703i | 1.08804 | − | 1.08804i | 0.0923104 | − | 0.995730i | \(-0.470575\pi\) |
0.995730 | − | 0.0923104i | \(-0.0294252\pi\) | |||||||
\(168\) | 2.76097 | + | 34.1815i | 0.0164343 | + | 0.203461i | ||||
\(169\) | − | 9.39820i | − | 0.0556106i | ||||||
\(170\) | −73.0346 | − | 75.0240i | −0.429615 | − | 0.441318i | ||||
\(171\) | 48.5111 | + | 84.0237i | 0.283691 | + | 0.491367i | ||||
\(172\) | −57.5190 | − | 15.4122i | −0.334413 | − | 0.0896057i | ||||
\(173\) | −250.733 | + | 67.1837i | −1.44932 | + | 0.388345i | −0.895788 | − | 0.444481i | \(-0.853388\pi\) |
−0.553535 | + | 0.832826i | \(0.686721\pi\) | |||||||
\(174\) | 65.1732i | 0.374559i | ||||||||
\(175\) | −156.035 | − | 79.2351i | −0.891626 | − | 0.452772i | ||||
\(176\) | −15.6555 | −0.0889516 | ||||||||
\(177\) | −10.7654 | − | 40.1770i | −0.0608214 | − | 0.226988i | ||||
\(178\) | −18.2894 | + | 68.2568i | −0.102749 | + | 0.383465i | ||||
\(179\) | 267.294 | − | 154.322i | 1.49326 | − | 0.862135i | 0.493292 | − | 0.869864i | \(-0.335794\pi\) |
0.999970 | + | 0.00772900i | \(0.00246024\pi\) | |||||||
\(180\) | −21.4963 | + | 20.9263i | −0.119424 | + | 0.116257i | ||||
\(181\) | 172.566 | 0.953406 | 0.476703 | − | 0.879064i | \(-0.341832\pi\) | ||||
0.476703 | + | 0.879064i | \(0.341832\pi\) | |||||||
\(182\) | 71.0490 | + | 102.922i | 0.390379 | + | 0.565507i | ||||
\(183\) | 20.5713 | + | 20.5713i | 0.112411 | + | 0.112411i | ||||
\(184\) | 31.2492 | + | 18.0417i | 0.169832 | + | 0.0980528i | ||||
\(185\) | −27.7993 | − | 16.5518i | −0.150266 | − | 0.0894695i | ||||
\(186\) | −41.6732 | − | 72.1801i | −0.224049 | − | 0.388065i | ||||
\(187\) | 14.9995 | + | 55.9787i | 0.0802110 | + | 0.299352i | ||||
\(188\) | −58.7242 | − | 58.7242i | −0.312363 | − | 0.312363i | ||||
\(189\) | −12.2121 | − | 34.2617i | −0.0646145 | − | 0.181279i | ||||
\(190\) | −111.671 | − | 199.564i | −0.587740 | − | 1.05034i | ||||
\(191\) | 67.6472 | − | 117.168i | 0.354174 | − | 0.613447i | −0.632802 | − | 0.774313i | \(-0.718095\pi\) |
0.986976 | + | 0.160866i | \(0.0514288\pi\) | |||||||
\(192\) | −13.3843 | − | 3.58630i | −0.0697097 | − | 0.0186787i | ||||
\(193\) | 5.69944 | − | 21.2706i | 0.0295308 | − | 0.110210i | −0.949587 | − | 0.313503i | \(-0.898498\pi\) |
0.979118 | + | 0.203292i | \(0.0651642\pi\) | |||||||
\(194\) | −204.770 | − | 118.224i | −1.05552 | − | 0.609403i | ||||
\(195\) | −29.7342 | + | 105.290i | −0.152483 | + | 0.539949i | ||||
\(196\) | 91.6347 | + | 34.7430i | 0.467524 | + | 0.177260i | ||||
\(197\) | 61.7521 | − | 61.7521i | 0.313462 | − | 0.313462i | −0.532787 | − | 0.846249i | \(-0.678855\pi\) |
0.846249 | + | 0.532787i | \(0.178855\pi\) | |||||||
\(198\) | 16.0393 | − | 4.29773i | 0.0810068 | − | 0.0217057i | ||||
\(199\) | 287.540 | − | 166.011i | 1.44492 | − | 0.834227i | 0.446751 | − | 0.894658i | \(-0.352581\pi\) |
0.998172 | + | 0.0604310i | \(0.0192475\pi\) | |||||||
\(200\) | 51.3254 | − | 48.6385i | 0.256627 | − | 0.243193i | ||||
\(201\) | −51.1272 | + | 88.5548i | −0.254364 | + | 0.440571i | ||||
\(202\) | −111.839 | + | 111.839i | −0.553660 | + | 0.553660i | ||||
\(203\) | 168.269 | + | 79.8355i | 0.828913 | + | 0.393278i | ||||
\(204\) | 51.2936i | 0.251439i | ||||||||
\(205\) | 93.1767 | − | 90.7059i | 0.454520 | − | 0.442468i | ||||
\(206\) | 130.938 | + | 226.792i | 0.635623 | + | 1.10093i | ||||
\(207\) | −36.9682 | − | 9.90559i | −0.178590 | − | 0.0478531i | ||||
\(208\) | −48.8116 | + | 13.0790i | −0.234671 | + | 0.0628799i | ||||
\(209\) | 126.578i | 0.605634i | ||||||||
\(210\) | 27.6967 | + | 81.1350i | 0.131889 | + | 0.386357i | ||||
\(211\) | −4.76592 | −0.0225873 | −0.0112936 | − | 0.999936i | \(-0.503595\pi\) | ||||
−0.0112936 | + | 0.999936i | \(0.503595\pi\) | |||||||
\(212\) | 23.4255 | + | 87.4252i | 0.110498 | + | 0.412383i | ||||
\(213\) | 59.4252 | − | 221.778i | 0.278992 | − | 1.04121i | ||||
\(214\) | 39.1952 | − | 22.6294i | 0.183155 | − | 0.105745i | ||||
\(215\) | −148.857 | − | 2.00015i | −0.692357 | − | 0.00930302i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −237.409 | + | 19.1764i | −1.09405 | + | 0.0883705i | ||||
\(218\) | 174.509 | + | 174.509i | 0.800499 | + | 0.800499i | ||||
\(219\) | 13.3039 | + | 7.68100i | 0.0607483 | + | 0.0350731i | ||||
\(220\) | −37.9378 | + | 9.62100i | −0.172444 | + | 0.0437318i | ||||
\(221\) | 93.5323 | + | 162.003i | 0.423223 | + | 0.733044i | ||||
\(222\) | 4.10229 | + | 15.3099i | 0.0184788 | + | 0.0689637i | ||||
\(223\) | −96.4999 | − | 96.4999i | −0.432735 | − | 0.432735i | 0.456823 | − | 0.889558i | \(-0.348987\pi\) |
−0.889558 | + | 0.456823i | \(0.848987\pi\) | |||||||
\(224\) | −25.6548 | + | 30.1634i | −0.114530 | + | 0.134658i | ||||
\(225\) | −39.2316 | + | 63.9209i | −0.174363 | + | 0.284093i | ||||
\(226\) | −6.20286 | + | 10.7437i | −0.0274463 | + | 0.0475383i | ||||
\(227\) | 59.5258 | + | 15.9499i | 0.262228 | + | 0.0702639i | 0.387538 | − | 0.921854i | \(-0.373326\pi\) |
−0.125309 | + | 0.992118i | \(0.539992\pi\) | |||||||
\(228\) | −28.9959 | + | 108.214i | −0.127175 | + | 0.474624i | ||||
\(229\) | 390.888 | + | 225.680i | 1.70694 | + | 0.985500i | 0.938305 | + | 0.345808i | \(0.112395\pi\) |
0.768631 | + | 0.639693i | \(0.220938\pi\) | |||||||
\(230\) | 86.8132 | + | 24.5163i | 0.377449 | + | 0.106593i | ||||
\(231\) | 8.55157 | − | 46.6763i | 0.0370198 | − | 0.202062i | ||||
\(232\) | −53.2137 | + | 53.2137i | −0.229369 | + | 0.229369i | ||||
\(233\) | 247.666 | − | 66.3620i | 1.06295 | − | 0.284816i | 0.315354 | − | 0.948974i | \(-0.397877\pi\) |
0.747592 | + | 0.664158i | \(0.231210\pi\) | |||||||
\(234\) | 46.4179 | − | 26.7994i | 0.198367 | − | 0.114527i | ||||
\(235\) | −178.395 | − | 106.217i | −0.759126 | − | 0.451988i | ||||
\(236\) | 24.0145 | − | 41.5943i | 0.101756 | − | 0.176247i | ||||
\(237\) | −128.205 | + | 128.205i | −0.540951 | + | 0.540951i | ||||
\(238\) | 132.434 | + | 62.8334i | 0.556445 | + | 0.264006i | ||||
\(239\) | − | 7.06316i | − | 0.0295529i | −0.999891 | − | 0.0147765i | \(-0.995296\pi\) | ||
0.999891 | − | 0.0147765i | \(-0.00470367\pi\) | |||||||
\(240\) | −34.6379 | − | 0.465420i | −0.144325 | − | 0.00193925i | ||||
\(241\) | −45.2255 | − | 78.3328i | −0.187658 | − | 0.325033i | 0.756811 | − | 0.653634i | \(-0.226756\pi\) |
−0.944469 | + | 0.328601i | \(0.893423\pi\) | |||||||
\(242\) | −144.364 | − | 38.6822i | −0.596544 | − | 0.159844i | ||||
\(243\) | −15.0573 | + | 4.03459i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | 33.5927i | 0.137675i | ||||||||
\(245\) | 243.409 | + | 27.8788i | 0.993505 | + | 0.113791i | ||||
\(246\) | −63.7046 | −0.258962 | ||||||||
\(247\) | 105.746 | + | 394.650i | 0.428123 | + | 1.59778i | ||||
\(248\) | 24.9088 | − | 92.9608i | 0.100439 | − | 0.374842i | ||||
\(249\) | −199.750 | + | 115.326i | −0.802208 | + | 0.463155i | ||||
\(250\) | 94.4857 | − | 149.407i | 0.377943 | − | 0.597628i | ||||
\(251\) | 79.0027 | 0.314752 | 0.157376 | − | 0.987539i | \(-0.449697\pi\) | ||||
0.157376 | + | 0.987539i | \(0.449697\pi\) | |||||||
\(252\) | 18.0034 | − | 37.9457i | 0.0714420 | − | 0.150578i | ||||
\(253\) | −35.3065 | − | 35.3065i | −0.139551 | − | 0.139551i | ||||
\(254\) | −66.5172 | − | 38.4037i | −0.261879 | − | 0.151196i | ||||
\(255\) | 31.5222 | + | 124.299i | 0.123617 | + | 0.487448i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −74.5277 | − | 278.141i | −0.289991 | − | 1.08226i | −0.945115 | − | 0.326739i | \(-0.894050\pi\) |
0.655124 | − | 0.755522i | \(-0.272617\pi\) | |||||||
\(258\) | 51.5701 | + | 51.5701i | 0.199884 | + | 0.199884i | ||||
\(259\) | 44.5536 | + | 8.16268i | 0.172022 | + | 0.0315161i | ||||
\(260\) | −110.247 | + | 61.6911i | −0.424027 | + | 0.237274i | ||||
\(261\) | 39.9103 | − | 69.1266i | 0.152913 | − | 0.264853i | ||||
\(262\) | 201.041 | + | 53.8688i | 0.767332 | + | 0.205606i | ||||
\(263\) | 69.0735 | − | 257.786i | 0.262637 | − | 0.980174i | −0.701044 | − | 0.713118i | \(-0.747282\pi\) |
0.963681 | − | 0.267056i | \(-0.0860509\pi\) | |||||||
\(264\) | 16.6052 | + | 9.58699i | 0.0628983 | + | 0.0363144i | ||||
\(265\) | 110.494 | + | 197.461i | 0.416957 | + | 0.745134i | ||||
\(266\) | 243.877 | + | 207.424i | 0.916830 | + | 0.779788i | ||||
\(267\) | 61.1974 | − | 61.1974i | 0.229204 | − | 0.229204i | ||||
\(268\) | −114.050 | + | 30.5596i | −0.425559 | + | 0.114028i | ||||
\(269\) | 127.690 | − | 73.7221i | 0.474686 | − | 0.274060i | −0.243514 | − | 0.969898i | \(-0.578300\pi\) |
0.718199 | + | 0.695838i | \(0.244967\pi\) | |||||||
\(270\) | 35.6149 | − | 9.03193i | 0.131907 | − | 0.0334516i | ||||
\(271\) | −248.993 | + | 431.268i | −0.918793 | + | 1.59140i | −0.117542 | + | 0.993068i | \(0.537501\pi\) |
−0.801251 | + | 0.598328i | \(0.795832\pi\) | |||||||
\(272\) | −41.8811 | + | 41.8811i | −0.153975 | + | 0.153975i | ||||
\(273\) | −12.3321 | − | 152.674i | −0.0451724 | − | 0.559246i | ||||
\(274\) | − | 1.65705i | − | 0.00604763i | ||||||
\(275\) | −86.0217 | + | 46.6289i | −0.312806 | + | 0.169560i | ||||
\(276\) | −22.0965 | − | 38.2723i | −0.0800598 | − | 0.138668i | ||||
\(277\) | −251.215 | − | 67.3127i | −0.906912 | − | 0.243006i | −0.224930 | − | 0.974375i | \(-0.572215\pi\) |
−0.681982 | + | 0.731369i | \(0.738882\pi\) | |||||||
\(278\) | 320.490 | − | 85.8751i | 1.15284 | − | 0.308903i | ||||
\(279\) | 102.078i | 0.365871i | ||||||||
\(280\) | −43.6322 | + | 88.8607i | −0.155829 | + | 0.317360i | ||||
\(281\) | −170.124 | −0.605422 | −0.302711 | − | 0.953082i | \(-0.597892\pi\) | ||||
−0.302711 | + | 0.953082i | \(0.597892\pi\) | |||||||
\(282\) | 26.3253 | + | 98.2475i | 0.0933523 | + | 0.348396i | ||||
\(283\) | 87.9512 | − | 328.238i | 0.310782 | − | 1.15985i | −0.617072 | − | 0.786907i | \(-0.711681\pi\) |
0.927853 | − | 0.372946i | \(-0.121652\pi\) | |||||||
\(284\) | 229.601 | − | 132.560i | 0.808456 | − | 0.466762i | ||||
\(285\) | −3.76301 | + | 280.054i | −0.0132035 | + | 0.982645i | ||||
\(286\) | 69.9263 | 0.244498 | ||||||||
\(287\) | −78.0365 | + | 164.478i | −0.271904 | + | 0.573092i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | −60.4027 | − | 34.8735i | −0.209006 | − | 0.120670i | ||||
\(290\) | −96.2500 | + | 161.654i | −0.331897 | + | 0.557429i | ||||
\(291\) | 144.794 | + | 250.791i | 0.497575 | + | 0.861826i | ||||
\(292\) | 4.59106 | + | 17.1341i | 0.0157228 | + | 0.0586784i | ||||
\(293\) | −373.925 | − | 373.925i | −1.27619 | − | 1.27619i | −0.942780 | − | 0.333415i | \(-0.891799\pi\) |
−0.333415 | − | 0.942780i | \(-0.608201\pi\) | |||||||
\(294\) | −75.9176 | − | 92.9651i | −0.258223 | − | 0.316208i | ||||
\(295\) | 32.6324 | − | 115.553i | 0.110618 | − | 0.391705i | ||||
\(296\) | −9.15101 | + | 15.8500i | −0.0309156 | + | 0.0535474i | ||||
\(297\) | −19.6441 | − | 5.26362i | −0.0661418 | − | 0.0177226i | ||||
\(298\) | −94.7323 | + | 353.546i | −0.317893 | + | 1.18639i | ||||
\(299\) | −139.577 | − | 80.5845i | −0.466811 | − | 0.269514i | ||||
\(300\) | −84.2237 | + | 20.1587i | −0.280746 | + | 0.0671956i | ||||
\(301\) | 196.320 | − | 69.9758i | 0.652226 | − | 0.232478i | ||||
\(302\) | −145.661 | + | 145.661i | −0.482321 | + | 0.482321i | ||||
\(303\) | 187.111 | − | 50.1362i | 0.617528 | − | 0.165466i | ||||
\(304\) | −112.032 | + | 64.6815i | −0.368525 | + | 0.212768i | ||||
\(305\) | 20.6442 | + | 81.4049i | 0.0676861 | + | 0.266901i | ||||
\(306\) | 31.4108 | − | 54.4051i | 0.102650 | − | 0.177794i | ||||
\(307\) | −7.39324 | + | 7.39324i | −0.0240822 | + | 0.0240822i | −0.719045 | − | 0.694963i | \(-0.755421\pi\) |
0.694963 | + | 0.719045i | \(0.255421\pi\) | |||||||
\(308\) | 45.0933 | − | 31.1287i | 0.146407 | − | 0.101067i | ||||
\(309\) | − | 320.732i | − | 1.03797i | ||||||
\(310\) | 3.23259 | − | 240.579i | 0.0104277 | − | 0.776060i | ||||
\(311\) | −146.398 | − | 253.569i | −0.470733 | − | 0.815334i | 0.528707 | − | 0.848805i | \(-0.322677\pi\) |
−0.999440 | + | 0.0334709i | \(0.989344\pi\) | |||||||
\(312\) | 59.7817 | + | 16.0185i | 0.191608 | + | 0.0513412i | ||||
\(313\) | 332.842 | − | 89.1847i | 1.06339 | − | 0.284935i | 0.315617 | − | 0.948887i | \(-0.397788\pi\) |
0.747776 | + | 0.663951i | \(0.231122\pi\) | |||||||
\(314\) | − | 13.9866i | − | 0.0445434i | ||||||
\(315\) | 20.3081 | − | 103.017i | 0.0644700 | − | 0.327039i | ||||
\(316\) | −209.359 | −0.662528 | ||||||||
\(317\) | −33.0285 | − | 123.264i | −0.104191 | − | 0.388845i | 0.894061 | − | 0.447944i | \(-0.147844\pi\) |
−0.998252 | + | 0.0590994i | \(0.981177\pi\) | |||||||
\(318\) | 28.6903 | − | 107.074i | 0.0902210 | − | 0.336709i | ||||
\(319\) | 90.1842 | − | 52.0679i | 0.282709 | − | 0.163222i | ||||
\(320\) | −27.9017 | − | 28.6617i | −0.0871928 | − | 0.0895679i | ||||
\(321\) | −55.4304 | −0.172680 | ||||||||
\(322\) | −125.882 | + | 10.1680i | −0.390938 | + | 0.0315775i | ||||
\(323\) | 338.616 | + | 338.616i | 1.04835 | + | 1.04835i | ||||
\(324\) | −15.5885 | − | 9.00000i | −0.0481125 | − | 0.0277778i | ||||
\(325\) | −229.248 | + | 217.247i | −0.705379 | + | 0.668453i | ||||
\(326\) | 162.263 | + | 281.047i | 0.497738 | + | 0.862107i | ||||
\(327\) | −78.2302 | − | 291.959i | −0.239236 | − | 0.892841i | ||||
\(328\) | −52.0146 | − | 52.0146i | −0.158581 | − | 0.158581i | ||||
\(329\) | 285.911 | + | 52.3819i | 0.869031 | + | 0.159215i | ||||
\(330\) | 46.1307 | + | 13.0274i | 0.139790 | + | 0.0394771i | ||||
\(331\) | 115.234 | − | 199.591i | 0.348139 | − | 0.602994i | −0.637780 | − | 0.770218i | \(-0.720147\pi\) |
0.985919 | + | 0.167225i | \(0.0534805\pi\) | |||||||
\(332\) | −257.258 | − | 68.9320i | −0.774873 | − | 0.207627i | ||||
\(333\) | 5.02425 | − | 18.7508i | 0.0150879 | − | 0.0563086i | ||||
\(334\) | −314.718 | − | 181.703i | −0.942271 | − | 0.544020i | ||||
\(335\) | −257.596 | + | 144.143i | −0.768942 | + | 0.430279i | ||||
\(336\) | 45.6823 | − | 16.2829i | 0.135959 | − | 0.0484609i | ||||
\(337\) | 261.018 | − | 261.018i | 0.774533 | − | 0.774533i | −0.204363 | − | 0.978895i | \(-0.565512\pi\) |
0.978895 | + | 0.204363i | \(0.0655122\pi\) | |||||||
\(338\) | −12.8382 | + | 3.43998i | −0.0379828 | + | 0.0101775i | ||||
\(339\) | 13.1582 | − | 7.59692i | 0.0388149 | − | 0.0224098i | ||||
\(340\) | −75.7522 | + | 127.228i | −0.222801 | + | 0.374199i | ||||
\(341\) | −66.5867 | + | 115.332i | −0.195269 | + | 0.338216i | ||||
\(342\) | 97.0222 | − | 97.0222i | 0.283691 | − | 0.283691i | ||||
\(343\) | −333.022 | + | 82.1303i | −0.970909 | + | 0.239447i | ||||
\(344\) | 84.2137i | 0.244807i | ||||||||
\(345\) | −77.0662 | − | 79.1655i | −0.223380 | − | 0.229465i | ||||
\(346\) | 183.549 | + | 317.917i | 0.530489 | + | 0.918834i | ||||
\(347\) | 100.891 | + | 27.0336i | 0.290751 | + | 0.0779066i | 0.401247 | − | 0.915970i | \(-0.368577\pi\) |
−0.110495 | + | 0.993877i | \(0.535244\pi\) | |||||||
\(348\) | 89.0283 | − | 23.8550i | 0.255828 | − | 0.0685490i | ||||
\(349\) | − | 425.240i | − | 1.21845i | −0.792996 | − | 0.609227i | \(-0.791480\pi\) | ||
0.792996 | − | 0.609227i | \(-0.208520\pi\) | |||||||
\(350\) | −51.1246 | + | 242.149i | −0.146070 | + | 0.691855i | ||||
\(351\) | −65.6449 | −0.187022 | ||||||||
\(352\) | 5.73031 | + | 21.3858i | 0.0162793 | + | 0.0607551i | ||||
\(353\) | 15.7714 | − | 58.8597i | 0.0446782 | − | 0.166741i | −0.939982 | − | 0.341224i | \(-0.889159\pi\) |
0.984660 | + | 0.174483i | \(0.0558253\pi\) | |||||||
\(354\) | −50.9423 | + | 29.4116i | −0.143905 | + | 0.0830836i | ||||
\(355\) | 474.926 | − | 462.333i | 1.33782 | − | 1.30235i | ||||
\(356\) | 99.9350 | 0.280716 | ||||||||
\(357\) | −101.990 | − | 147.744i | −0.285686 | − | 0.413848i | ||||
\(358\) | −308.644 | − | 308.644i | −0.862135 | − | 0.862135i | ||||
\(359\) | −527.860 | − | 304.760i | −1.47036 | − | 0.848914i | −0.470916 | − | 0.882178i | \(-0.656076\pi\) |
−0.999447 | + | 0.0332639i | \(0.989410\pi\) | |||||||
\(360\) | 36.4540 | + | 21.7049i | 0.101261 | + | 0.0602915i | ||||
\(361\) | 342.462 | + | 593.161i | 0.948647 | + | 1.64311i | ||||
\(362\) | −63.1637 | − | 235.730i | −0.174485 | − | 0.651188i | ||||
\(363\) | 129.433 | + | 129.433i | 0.356565 | + | 0.356565i | ||||
\(364\) | 114.589 | − | 134.727i | 0.314804 | − | 0.370129i | ||||
\(365\) | 21.6551 | + | 38.6994i | 0.0593292 | + | 0.106026i | ||||
\(366\) | 20.5713 | − | 35.6305i | 0.0562056 | − | 0.0973510i | ||||
\(367\) | −81.0326 | − | 21.7126i | −0.220797 | − | 0.0591625i | 0.146724 | − | 0.989177i | \(-0.453127\pi\) |
−0.367522 | + | 0.930015i | \(0.619794\pi\) | |||||||
\(368\) | 13.2075 | − | 49.2909i | 0.0358898 | − | 0.133943i | ||||
\(369\) | 67.5689 | + | 39.0109i | 0.183114 | + | 0.105721i | ||||
\(370\) | −12.4350 | + | 44.0329i | −0.0336081 | + | 0.119008i | ||||
\(371\) | −241.306 | − | 205.237i | −0.650421 | − | 0.553200i | ||||
\(372\) | −83.3464 | + | 83.3464i | −0.224049 | + | 0.224049i | ||||
\(373\) | 136.229 | − | 36.5025i | 0.365226 | − | 0.0978620i | −0.0715386 | − | 0.997438i | \(-0.522791\pi\) |
0.436765 | + | 0.899576i | \(0.356124\pi\) | |||||||
\(374\) | 70.9782 | − | 40.9793i | 0.189781 | − | 0.109570i | ||||
\(375\) | −191.710 | + | 100.610i | −0.511227 | + | 0.268292i | ||||
\(376\) | −58.7242 | + | 101.713i | −0.156181 | + | 0.270514i | ||||
\(377\) | 237.683 | − | 237.683i | 0.630458 | − | 0.630458i | ||||
\(378\) | −42.3324 | + | 29.2228i | −0.111990 | + | 0.0773089i | ||||
\(379\) | 123.783i | 0.326603i | 0.986576 | + | 0.163302i | \(0.0522144\pi\) | ||||
−0.986576 | + | 0.163302i | \(0.947786\pi\) | |||||||
\(380\) | −231.735 | + | 225.590i | −0.609830 | + | 0.593659i | ||||
\(381\) | 47.0348 | + | 81.4666i | 0.123451 | + | 0.213823i | ||||
\(382\) | −184.816 | − | 49.5212i | −0.483810 | − | 0.129637i | ||||
\(383\) | −305.182 | + | 81.7732i | −0.796819 | + | 0.213507i | −0.634187 | − | 0.773180i | \(-0.718665\pi\) |
−0.162632 | + | 0.986687i | \(0.551998\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 90.1443 | − | 103.146i | 0.234141 | − | 0.267911i | ||||
\(386\) | −31.1423 | −0.0806796 | ||||||||
\(387\) | −23.1183 | − | 86.2785i | −0.0597371 | − | 0.222942i | ||||
\(388\) | −86.5461 | + | 322.994i | −0.223057 | + | 0.832460i | ||||
\(389\) | −300.792 | + | 173.662i | −0.773243 | + | 0.446432i | −0.834030 | − | 0.551718i | \(-0.813972\pi\) |
0.0607870 | + | 0.998151i | \(0.480639\pi\) | |||||||
\(390\) | 154.712 | + | 2.07883i | 0.396699 | + | 0.00533034i | ||||
\(391\) | −188.902 | −0.483124 | ||||||||
\(392\) | 13.9192 | − | 137.892i | 0.0355082 | − | 0.351766i | ||||
\(393\) | −180.248 | − | 180.248i | −0.458647 | − | 0.458647i | ||||
\(394\) | −106.958 | − | 61.7521i | −0.271466 | − | 0.156731i | ||||
\(395\) | −507.337 | + | 128.660i | −1.28440 | + | 0.325722i | ||||
\(396\) | −11.7416 | − | 20.3371i | −0.0296505 | − | 0.0513563i | ||||
\(397\) | 97.9772 | + | 365.656i | 0.246794 | + | 0.921047i | 0.972473 | + | 0.233014i | \(0.0748589\pi\) |
−0.725679 | + | 0.688033i | \(0.758474\pi\) | |||||||
\(398\) | −332.022 | − | 332.022i | −0.834227 | − | 0.834227i | ||||
\(399\) | −131.650 | − | 369.349i | −0.329950 | − | 0.925688i | ||||
\(400\) | −85.2278 | − | 52.3088i | −0.213070 | − | 0.130772i | ||||
\(401\) | −85.2179 | + | 147.602i | −0.212513 | + | 0.368084i | −0.952500 | − | 0.304537i | \(-0.901498\pi\) |
0.739987 | + | 0.672621i | \(0.234832\pi\) | |||||||
\(402\) | 139.682 | + | 37.4277i | 0.347468 | + | 0.0931037i | ||||
\(403\) | −111.257 | + | 415.216i | −0.276071 | + | 1.03031i | ||||
\(404\) | 193.711 | + | 111.839i | 0.479484 | + | 0.276830i | ||||
\(405\) | −43.3063 | − | 12.2298i | −0.106929 | − | 0.0301970i | ||||
\(406\) | 47.4665 | − | 259.082i | 0.116913 | − | 0.638133i | ||||
\(407\) | 17.9079 | − | 17.9079i | 0.0439999 | − | 0.0439999i | ||||
\(408\) | 70.0684 | − | 18.7748i | 0.171736 | − | 0.0460166i | ||||
\(409\) | 230.144 | − | 132.873i | 0.562698 | − | 0.324874i | −0.191530 | − | 0.981487i | \(-0.561345\pi\) |
0.754228 | + | 0.656613i | \(0.228011\pi\) | |||||||
\(410\) | −158.012 | − | 94.0811i | −0.385394 | − | 0.229466i | ||||
\(411\) | −1.01473 | + | 1.75757i | −0.00246894 | + | 0.00427632i | ||||
\(412\) | 261.877 | − | 261.877i | 0.635623 | − | 0.635623i | ||||
\(413\) | 13.5341 | + | 167.555i | 0.0327702 | + | 0.405703i | ||||
\(414\) | 54.1251i | 0.130737i | ||||||||
\(415\) | −665.772 | − | 8.94581i | −1.60427 | − | 0.0215562i | ||||
\(416\) | 35.7325 | + | 61.8906i | 0.0858955 | + | 0.148775i | ||||
\(417\) | −392.519 | − | 105.175i | −0.941292 | − | 0.252218i | ||||
\(418\) | 172.908 | − | 46.3306i | 0.413656 | − | 0.110839i | ||||
\(419\) | 173.250i | 0.413485i | 0.978395 | + | 0.206742i | \(0.0662862\pi\) | ||||
−0.978395 | + | 0.206742i | \(0.933714\pi\) | |||||||
\(420\) | 100.695 | − | 67.5319i | 0.239750 | − | 0.160790i | ||||
\(421\) | 541.087 | 1.28524 | 0.642621 | − | 0.766184i | \(-0.277847\pi\) | ||||
0.642621 | + | 0.766184i | \(0.277847\pi\) | |||||||
\(422\) | 1.74445 | + | 6.51036i | 0.00413376 | + | 0.0154274i | ||||
\(423\) | 32.2418 | − | 120.328i | 0.0762218 | − | 0.284464i | ||||
\(424\) | 110.851 | − | 63.9997i | 0.261440 | − | 0.150943i | ||||
\(425\) | −105.382 | + | 354.863i | −0.247958 | + | 0.834972i | ||||
\(426\) | −324.705 | −0.762219 | ||||||||
\(427\) | −66.7943 | − | 96.7590i | −0.156427 | − | 0.226602i | ||||
\(428\) | −45.2587 | − | 45.2587i | −0.105745 | − | 0.105745i | ||||
\(429\) | −74.1680 | − | 42.8209i | −0.172886 | − | 0.0998157i | ||||
\(430\) | 51.7531 | + | 204.074i | 0.120356 | + | 0.474591i | ||||
\(431\) | 272.438 | + | 471.876i | 0.632106 | + | 1.09484i | 0.987120 | + | 0.159979i | \(0.0511428\pi\) |
−0.355014 | + | 0.934861i | \(0.615524\pi\) | |||||||
\(432\) | −5.37945 | − | 20.0764i | −0.0124524 | − | 0.0464731i | ||||
\(433\) | −440.714 | − | 440.714i | −1.01782 | − | 1.01782i | −0.999838 | − | 0.0179771i | \(-0.994277\pi\) |
−0.0179771 | − | 0.999838i | \(-0.505723\pi\) | |||||||
\(434\) | 113.093 | + | 317.288i | 0.260583 | + | 0.731077i | ||||
\(435\) | 201.081 | − | 112.520i | 0.462256 | − | 0.258666i | ||||
\(436\) | 174.509 | − | 302.258i | 0.400250 | − | 0.693253i | ||||
\(437\) | −398.526 | − | 106.785i | −0.911959 | − | 0.244359i | ||||
\(438\) | 5.62288 | − | 20.9849i | 0.0128376 | − | 0.0479107i | ||||
\(439\) | 411.747 | + | 237.722i | 0.937920 | + | 0.541508i | 0.889308 | − | 0.457310i | \(-0.151187\pi\) |
0.0486121 | + | 0.998818i | \(0.484520\pi\) | |||||||
\(440\) | 27.0287 | + | 48.3025i | 0.0614289 | + | 0.109778i | ||||
\(441\) | 23.5935 | + | 145.094i | 0.0535001 | + | 0.329012i | ||||
\(442\) | 187.065 | − | 187.065i | 0.423223 | − | 0.423223i | ||||
\(443\) | 454.552 | − | 121.797i | 1.02608 | − | 0.274937i | 0.293745 | − | 0.955884i | \(-0.405098\pi\) |
0.732332 | + | 0.680947i | \(0.238432\pi\) | |||||||
\(444\) | 19.4122 | − | 11.2077i | 0.0437212 | − | 0.0252425i | ||||
\(445\) | 242.171 | − | 61.4145i | 0.544205 | − | 0.138010i | ||||
\(446\) | −96.4999 | + | 167.143i | −0.216367 | + | 0.374759i | ||||
\(447\) | 316.980 | − | 316.980i | 0.709128 | − | 0.709128i | ||||
\(448\) | 50.5943 | + | 24.0045i | 0.112934 | + | 0.0535815i | ||||
\(449\) | 728.737i | 1.62302i | 0.584337 | + | 0.811511i | \(0.301355\pi\) | ||||
−0.584337 | + | 0.811511i | \(0.698645\pi\) | |||||||
\(450\) | 101.677 | + | 30.1947i | 0.225950 | + | 0.0670994i | ||||
\(451\) | 50.8946 | + | 88.1520i | 0.112848 | + | 0.195459i | ||||
\(452\) | 16.9465 | + | 4.54081i | 0.0374923 | + | 0.0100460i | ||||
\(453\) | 243.696 | − | 65.2980i | 0.537959 | − | 0.144146i | ||||
\(454\) | − | 87.1519i | − | 0.191965i | ||||||
\(455\) | 194.886 | − | 396.903i | 0.428321 | − | 0.872313i | ||||
\(456\) | 158.437 | 0.347449 | ||||||||
\(457\) | 161.152 | + | 601.427i | 0.352630 | + | 1.31603i | 0.883441 | + | 0.468543i | \(0.155221\pi\) |
−0.530811 | + | 0.847490i | \(0.678113\pi\) | |||||||
\(458\) | 165.209 | − | 616.568i | 0.360718 | − | 1.34622i | ||||
\(459\) | −66.6324 | + | 38.4702i | −0.145169 | + | 0.0838131i | ||||
\(460\) | 1.71403 | − | 127.563i | 0.00372614 | − | 0.277310i | ||||
\(461\) | −796.674 | −1.72814 | −0.864071 | − | 0.503370i | \(-0.832093\pi\) | ||||
−0.864071 | + | 0.503370i | \(0.832093\pi\) | |||||||
\(462\) | −66.8911 | + | 5.40304i | −0.144786 | + | 0.0116949i | ||||
\(463\) | 215.541 | + | 215.541i | 0.465531 | + | 0.465531i | 0.900463 | − | 0.434932i | \(-0.143228\pi\) |
−0.434932 | + | 0.900463i | \(0.643228\pi\) | |||||||
\(464\) | 92.1688 | + | 53.2137i | 0.198640 | + | 0.114685i | ||||
\(465\) | −150.752 | + | 253.193i | −0.324199 | + | 0.544500i | ||||
\(466\) | −181.304 | − | 314.028i | −0.389065 | − | 0.673881i | ||||
\(467\) | −74.0339 | − | 276.298i | −0.158531 | − | 0.591645i | −0.998777 | − | 0.0494401i | \(-0.984256\pi\) |
0.840246 | − | 0.542205i | \(-0.182410\pi\) | |||||||
\(468\) | −53.5988 | − | 53.5988i | −0.114527 | − | 0.114527i | ||||
\(469\) | 267.741 | − | 314.794i | 0.570876 | − | 0.671203i | ||||
\(470\) | −79.7984 | + | 282.570i | −0.169784 | + | 0.601212i | ||||
\(471\) | −8.56502 | + | 14.8351i | −0.0181848 | + | 0.0314969i | ||||
\(472\) | −65.6087 | − | 17.5798i | −0.139001 | − | 0.0372453i | ||||
\(473\) | 30.1606 | − | 112.561i | 0.0637646 | − | 0.237973i | ||||
\(474\) | 222.058 | + | 128.205i | 0.468478 | + | 0.270476i | ||||
\(475\) | −422.927 | + | 689.083i | −0.890372 | + | 1.45070i | ||||
\(476\) | 37.3578 | − | 203.907i | 0.0784828 | − | 0.428376i | ||||
\(477\) | −95.9996 | + | 95.9996i | −0.201257 | + | 0.201257i | ||||
\(478\) | −9.64845 | + | 2.58529i | −0.0201850 | + | 0.00540857i | ||||
\(479\) | −581.667 | + | 335.826i | −1.21434 | + | 0.701098i | −0.963701 | − | 0.266984i | \(-0.913973\pi\) |
−0.250636 | + | 0.968081i | \(0.580640\pi\) | |||||||
\(480\) | 12.0426 | + | 47.4866i | 0.0250887 | + | 0.0989304i | ||||
\(481\) | 40.8736 | − | 70.7952i | 0.0849763 | − | 0.147183i | ||||
\(482\) | −90.4510 | + | 90.4510i | −0.187658 | + | 0.187658i | ||||
\(483\) | 139.745 | + | 66.3019i | 0.289326 | + | 0.137271i | ||||
\(484\) | 211.363i | 0.436701i | ||||||||
\(485\) | −11.2317 | + | 835.896i | −0.0231582 | + | 1.72350i | ||||
\(486\) | 11.0227 | + | 19.0919i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −98.7957 | − | 26.4722i | −0.202866 | − | 0.0543578i | 0.155955 | − | 0.987764i | \(-0.450154\pi\) |
−0.358821 | + | 0.933406i | \(0.616821\pi\) | |||||||
\(488\) | 45.8885 | − | 12.2958i | 0.0940339 | − | 0.0251963i | ||||
\(489\) | − | 397.460i | − | 0.812802i | ||||||
\(490\) | −51.0107 | − | 342.707i | −0.104103 | − | 0.699402i | ||||
\(491\) | 260.790 | 0.531140 | 0.265570 | − | 0.964092i | \(-0.414440\pi\) | ||||
0.265570 | + | 0.964092i | \(0.414440\pi\) | |||||||
\(492\) | 23.3175 | + | 87.0220i | 0.0473933 | + | 0.176874i | ||||
\(493\) | 101.968 | − | 380.548i | 0.206831 | − | 0.771904i | ||||
\(494\) | 500.397 | − | 288.904i | 1.01295 | − | 0.584826i | ||||
\(495\) | −40.9514 | − | 42.0669i | −0.0827301 | − | 0.0849836i | ||||
\(496\) | −136.104 | −0.274403 | ||||||||
\(497\) | −397.756 | + | 838.350i | −0.800314 | + | 1.68682i | ||||
\(498\) | 230.651 | + | 230.651i | 0.463155 | + | 0.463155i | ||||
\(499\) | 82.9389 | + | 47.8848i | 0.166210 | + | 0.0959615i | 0.580798 | − | 0.814048i | \(-0.302741\pi\) |
−0.414587 | + | 0.910009i | \(0.636074\pi\) | |||||||
\(500\) | −238.678 | − | 74.3832i | −0.477356 | − | 0.148766i | ||||
\(501\) | 222.540 | + | 385.450i | 0.444191 | + | 0.769361i | ||||
\(502\) | −28.9170 | − | 107.920i | −0.0576036 | − | 0.214979i | ||||
\(503\) | −172.595 | − | 172.595i | −0.343132 | − | 0.343132i | 0.514412 | − | 0.857543i | \(-0.328010\pi\) |
−0.857543 | + | 0.514412i | \(0.828010\pi\) | |||||||
\(504\) | −58.4245 | − | 10.7040i | −0.115922 | − | 0.0212380i | ||||
\(505\) | 538.149 | + | 151.975i | 1.06564 | + | 0.300940i | ||||
\(506\) | −35.3065 | + | 61.1526i | −0.0697757 | + | 0.120855i | ||||
\(507\) | 15.7235 | + | 4.21310i | 0.0310128 | + | 0.00830985i | ||||
\(508\) | −28.1135 | + | 104.921i | −0.0553415 | + | 0.206537i | ||||
\(509\) | 165.245 | + | 95.4042i | 0.324646 | + | 0.187435i | 0.653462 | − | 0.756960i | \(-0.273316\pi\) |
−0.328815 | + | 0.944394i | \(0.606649\pi\) | |||||||
\(510\) | 158.258 | − | 88.5569i | 0.310310 | − | 0.173641i | ||||
\(511\) | −47.2926 | − | 40.2236i | −0.0925491 | − | 0.0787154i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −162.321 | + | 43.4939i | −0.316416 | + | 0.0847834i | ||||
\(514\) | −352.669 | + | 203.613i | −0.686126 | + | 0.396135i | ||||
\(515\) | 473.668 | − | 795.539i | 0.919744 | − | 1.54473i | ||||
\(516\) | 51.5701 | − | 89.3221i | 0.0999421 | − | 0.173105i | ||||
\(517\) | 114.920 | − | 114.920i | 0.222282 | − | 0.222282i | ||||
\(518\) | −5.15733 | − | 63.8491i | −0.00995624 | − | 0.123261i | ||||
\(519\) | − | 449.602i | − | 0.866285i | ||||||
\(520\) | 124.625 | + | 128.020i | 0.239663 | + | 0.246191i | ||||
\(521\) | 321.064 | + | 556.100i | 0.616246 | + | 1.06737i | 0.990164 | + | 0.139908i | \(0.0446808\pi\) |
−0.373918 | + | 0.927462i | \(0.621986\pi\) | |||||||
\(522\) | −109.037 | − | 29.2163i | −0.208883 | − | 0.0559700i | ||||
\(523\) | −112.482 | + | 30.1396i | −0.215072 | + | 0.0576283i | −0.364746 | − | 0.931107i | \(-0.618844\pi\) |
0.149674 | + | 0.988735i | \(0.452177\pi\) | |||||||
\(524\) | − | 294.344i | − | 0.561726i | ||||||
\(525\) | 202.511 | − | 225.531i | 0.385736 | − | 0.429583i | ||||
\(526\) | −377.424 | −0.717537 | ||||||||
\(527\) | 130.401 | + | 486.662i | 0.247440 | + | 0.923458i | ||||
\(528\) | 7.01816 | − | 26.1921i | 0.0132920 | − | 0.0496063i | ||||
\(529\) | −317.180 | + | 183.124i | −0.599585 | + | 0.346170i | ||||
\(530\) | 229.293 | − | 223.213i | 0.432628 | − | 0.421156i | ||||
\(531\) | 72.0434 | 0.135675 | ||||||||
\(532\) | 194.081 | − | 409.064i | 0.364814 | − | 0.768918i | ||||
\(533\) | 232.327 | + | 232.327i | 0.435885 | + | 0.435885i | ||||
\(534\) | −105.997 | − | 61.1974i | −0.198496 | − | 0.114602i | ||||
\(535\) | −137.488 | − | 81.8615i | −0.256988 | − | 0.153012i | ||||
\(536\) | 83.4903 | + | 144.609i | 0.155765 | + | 0.269794i | ||||
\(537\) | 138.361 | + | 516.372i | 0.257656 | + | 0.961587i | ||||
\(538\) | −147.444 | − | 147.444i | −0.274060 | − | 0.274060i | ||||
\(539\) | −67.9899 | + | 179.323i | −0.126141 | + | 0.332696i | ||||
\(540\) | −25.3738 | − | 45.3450i | −0.0469886 | − | 0.0839722i | ||||
\(541\) | 211.339 | − | 366.049i | 0.390645 | − | 0.676616i | −0.601890 | − | 0.798579i | \(-0.705585\pi\) |
0.992535 | + | 0.121963i | \(0.0389188\pi\) | |||||||
\(542\) | 680.261 | + | 182.275i | 1.25509 | + | 0.336302i | ||||
\(543\) | −77.3594 | + | 288.709i | −0.142467 | + | 0.531693i | ||||
\(544\) | 72.5401 | + | 41.8811i | 0.133346 | + | 0.0769873i | ||||
\(545\) | 237.134 | − | 839.703i | 0.435109 | − | 1.54074i | ||||
\(546\) | −204.043 | + | 72.7285i | −0.373705 | + | 0.133202i | ||||
\(547\) | −57.9153 | + | 57.9153i | −0.105878 | + | 0.105878i | −0.758061 | − | 0.652183i | \(-0.773853\pi\) |
0.652183 | + | 0.758061i | \(0.273853\pi\) | |||||||
\(548\) | −2.26357 | + | 0.606523i | −0.00413061 | + | 0.00110679i | ||||
\(549\) | −43.6382 | + | 25.1946i | −0.0794868 | + | 0.0458917i | ||||
\(550\) | 95.1825 | + | 100.440i | 0.173059 | + | 0.182619i | ||||
\(551\) | 430.243 | − | 745.202i | 0.780840 | − | 1.35245i | ||||
\(552\) | −44.1930 | + | 44.1930i | −0.0800598 | + | 0.0800598i | ||||
\(553\) | 603.027 | − | 416.280i | 1.09046 | − | 0.752766i | ||||
\(554\) | 367.804i | 0.663906i | ||||||||
\(555\) | 40.1539 | − | 39.0891i | 0.0723493 | − | 0.0704308i | ||||
\(556\) | −234.615 | − | 406.365i | −0.421970 | − | 0.730873i | ||||
\(557\) | 25.9058 | + | 6.94144i | 0.0465095 | + | 0.0124622i | 0.281999 | − | 0.959415i | \(-0.409003\pi\) |
−0.235489 | + | 0.971877i | \(0.575669\pi\) | |||||||
\(558\) | 139.441 | − | 37.3632i | 0.249895 | − | 0.0669591i | ||||
\(559\) | − | 376.146i | − | 0.672891i | ||||||
\(560\) | 137.357 | + | 27.0774i | 0.245280 | + | 0.0483525i | ||||
\(561\) | −100.378 | −0.178928 | ||||||||
\(562\) | 62.2696 | + | 232.393i | 0.110800 | + | 0.413511i | ||||
\(563\) | −268.804 | + | 1003.19i | −0.477449 | + | 1.78186i | 0.134443 | + | 0.990921i | \(0.457075\pi\) |
−0.611892 | + | 0.790942i | \(0.709591\pi\) | |||||||
\(564\) | 124.573 | − | 71.9222i | 0.220874 | − | 0.127522i | ||||
\(565\) | 43.8569 | + | 0.589293i | 0.0776228 | + | 0.00104300i | ||||
\(566\) | −480.574 | −0.849071 | ||||||||
\(567\) | 62.7955 | − | 5.07222i | 0.110750 | − | 0.00894572i | ||||
\(568\) | −265.121 | − | 265.121i | −0.466762 | − | 0.466762i | ||||
\(569\) | −35.1341 | − | 20.2847i | −0.0617471 | − | 0.0356497i | 0.468809 | − | 0.883300i | \(-0.344683\pi\) |
−0.530556 | + | 0.847650i | \(0.678017\pi\) | |||||||
\(570\) | 383.938 | − | 97.3664i | 0.673575 | − | 0.170818i | ||||
\(571\) | −104.960 | − | 181.797i | −0.183819 | − | 0.318383i | 0.759359 | − | 0.650672i | \(-0.225513\pi\) |
−0.943178 | + | 0.332289i | \(0.892179\pi\) | |||||||
\(572\) | −25.5948 | − | 95.5211i | −0.0447462 | − | 0.166995i | ||||
\(573\) | 165.701 | + | 165.701i | 0.289182 | + | 0.289182i | ||||
\(574\) | 253.244 | + | 46.3969i | 0.441191 | + | 0.0808308i | ||||
\(575\) | −74.2394 | − | 310.175i | −0.129112 | − | 0.539434i | ||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −35.7155 | − | 9.56994i | −0.0618986 | − | 0.0165857i | 0.227737 | − | 0.973723i | \(-0.426867\pi\) |
−0.289635 | + | 0.957137i | \(0.593534\pi\) | |||||||
\(578\) | −25.5292 | + | 95.2762i | −0.0441681 | + | 0.164838i | ||||
\(579\) | 33.0314 | + | 19.0707i | 0.0570491 | + | 0.0329373i | ||||
\(580\) | 256.054 | + | 72.3103i | 0.441472 | + | 0.124673i | ||||
\(581\) | 878.055 | − | 312.972i | 1.51128 | − | 0.538678i | ||||
\(582\) | 289.589 | − | 289.589i | 0.497575 | − | 0.497575i | ||||
\(583\) | −171.086 | + | 45.8422i | −0.293457 | + | 0.0786316i | ||||
\(584\) | 21.7252 | − | 12.5430i | 0.0372006 | − | 0.0214778i | ||||
\(585\) | −162.824 | − | 96.9466i | −0.278332 | − | 0.165721i | ||||
\(586\) | −373.925 | + | 647.657i | −0.638097 | + | 1.10522i | ||||
\(587\) | 452.761 | − | 452.761i | 0.771314 | − | 0.771314i | −0.207022 | − | 0.978336i | \(-0.566377\pi\) |
0.978336 | + | 0.207022i | \(0.0663773\pi\) | |||||||
\(588\) | −99.2049 | + | 137.733i | −0.168716 | + | 0.234240i | ||||
\(589\) | 1100.43i | 1.86830i | ||||||||
\(590\) | −169.792 | − | 2.28146i | −0.287784 | − | 0.00386688i | ||||
\(591\) | 75.6305 | + | 130.996i | 0.127970 | + | 0.221651i | ||||
\(592\) | 25.0010 | + | 6.69901i | 0.0422315 | + | 0.0113159i | ||||
\(593\) | −3.93666 | + | 1.05483i | −0.00663855 | + | 0.00177880i | −0.262137 | − | 0.965031i | \(-0.584427\pi\) |
0.255498 | + | 0.966810i | \(0.417760\pi\) | |||||||
\(594\) | 28.7610i | 0.0484191i | ||||||||
\(595\) | −34.7811 | − | 517.083i | −0.0584556 | − | 0.869048i | ||||
\(596\) | 517.627 | 0.868501 | ||||||||
\(597\) | 148.842 | + | 555.484i | 0.249316 | + | 0.930459i | ||||
\(598\) | −58.9920 | + | 220.161i | −0.0986488 | + | 0.368162i | ||||
\(599\) | 499.784 | − | 288.550i | 0.834364 | − | 0.481720i | −0.0209807 | − | 0.999780i | \(-0.506679\pi\) |
0.855344 | + | 0.518060i | \(0.173346\pi\) | |||||||
\(600\) | 58.3653 | + | 107.673i | 0.0972755 | + | 0.179455i | ||||
\(601\) | 16.8472 | 0.0280319 | 0.0140160 | − | 0.999902i | \(-0.495538\pi\) | ||||
0.0140160 | + | 0.999902i | \(0.495538\pi\) | |||||||
\(602\) | −167.447 | − | 242.565i | −0.278151 | − | 0.402932i | ||||
\(603\) | −125.235 | − | 125.235i | −0.207687 | − | 0.207687i | ||||
\(604\) | 252.292 | + | 145.661i | 0.417702 | + | 0.241161i | ||||
\(605\) | 129.892 | + | 512.194i | 0.214698 | + | 0.846602i | ||||
\(606\) | −136.975 | − | 237.247i | −0.226031 | − | 0.391497i | ||||
\(607\) | −107.298 | − | 400.443i | −0.176768 | − | 0.659709i | −0.996244 | − | 0.0865941i | \(-0.972402\pi\) |
0.819475 | − | 0.573115i | \(-0.194265\pi\) | |||||||
\(608\) | 129.363 | + | 129.363i | 0.212768 | + | 0.212768i | ||||
\(609\) | −209.001 | + | 245.731i | −0.343186 | + | 0.403499i | ||||
\(610\) | 103.645 | − | 57.9968i | 0.169910 | − | 0.0950768i | ||||
\(611\) | 262.296 | − | 454.310i | 0.429289 | − | 0.743551i | ||||
\(612\) | −85.8159 | − | 22.9943i | −0.140222 | − | 0.0375724i | ||||
\(613\) | −256.791 | + | 958.356i | −0.418908 | + | 1.56339i | 0.357968 | + | 0.933734i | \(0.383470\pi\) |
−0.776876 | + | 0.629653i | \(0.783197\pi\) | |||||||
\(614\) | 12.8055 | + | 7.39324i | 0.0208558 | + | 0.0120411i | ||||
\(615\) | 109.984 | + | 196.550i | 0.178836 | + | 0.319594i | ||||
\(616\) | −59.0279 | − | 50.2048i | −0.0958245 | − | 0.0815012i | ||||
\(617\) | −435.763 | + | 435.763i | −0.706261 | + | 0.706261i | −0.965747 | − | 0.259486i | \(-0.916447\pi\) |
0.259486 | + | 0.965747i | \(0.416447\pi\) | |||||||
\(618\) | −438.128 | + | 117.396i | −0.708946 | + | 0.189961i | ||||
\(619\) | 339.430 | − | 195.970i | 0.548352 | − | 0.316591i | −0.200105 | − | 0.979774i | \(-0.564128\pi\) |
0.748457 | + | 0.663183i | \(0.230795\pi\) | |||||||
\(620\) | −329.820 | + | 83.6421i | −0.531967 | + | 0.134907i | ||||
\(621\) | 33.1447 | − | 57.4084i | 0.0533732 | − | 0.0924451i | ||||
\(622\) | −292.796 | + | 292.796i | −0.470733 | + | 0.470733i | ||||
\(623\) | −287.848 | + | 198.706i | −0.462035 | + | 0.318951i | ||||
\(624\) | − | 87.5265i | − | 0.140267i | ||||||
\(625\) | −624.098 | − | 33.5737i | −0.998556 | − | 0.0537179i | ||||
\(626\) | −243.657 | − | 422.027i | −0.389229 | − | 0.674164i | ||||
\(627\) | −211.768 | − | 56.7431i | −0.337748 | − | 0.0904994i | ||||
\(628\) | −19.1061 | + | 5.11946i | −0.0304237 | + | 0.00815201i | ||||
\(629\) | − | 95.8136i | − | 0.152327i | ||||||
\(630\) | −148.158 | + | 9.96567i | −0.235171 | + | 0.0158185i | ||||
\(631\) | −786.782 | −1.24688 | −0.623441 | − | 0.781870i | \(-0.714266\pi\) | ||||
−0.623441 | + | 0.781870i | \(0.714266\pi\) | |||||||
\(632\) | 76.6306 | + | 285.989i | 0.121251 | + | 0.452515i | ||||
\(633\) | 2.13650 | − | 7.97353i | 0.00337520 | − | 0.0125964i | ||||
\(634\) | −156.292 | + | 90.2354i | −0.246518 | + | 0.142327i | ||||
\(635\) | −3.64849 | + | 271.531i | −0.00574565 | + | 0.427608i | ||||
\(636\) | −156.767 | −0.246488 | ||||||||
\(637\) | −62.1711 | + | 615.905i | −0.0975998 | + | 0.966883i | ||||
\(638\) | −104.136 | − | 104.136i | −0.163222 | − | 0.163222i | ||||
\(639\) | 344.402 | + | 198.841i | 0.538970 | + | 0.311175i | ||||
\(640\) | −28.9399 | + | 48.6054i | −0.0452186 | + | 0.0759459i | ||||
\(641\) | −350.141 | − | 606.461i | −0.546241 | − | 0.946118i | −0.998528 | − | 0.0542449i | \(-0.982725\pi\) |
0.452286 | − | 0.891873i | \(-0.350609\pi\) | |||||||
\(642\) | 20.2889 | + | 75.7193i | 0.0316027 | + | 0.117943i | ||||
\(643\) | 175.844 | + | 175.844i | 0.273474 | + | 0.273474i | 0.830497 | − | 0.557023i | \(-0.188056\pi\) |
−0.557023 | + | 0.830497i | \(0.688056\pi\) | |||||||
\(644\) | 59.9657 | + | 168.236i | 0.0931144 | + | 0.261236i | ||||
\(645\) | 70.0770 | − | 248.146i | 0.108646 | − | 0.384722i | ||||
\(646\) | 338.616 | − | 586.500i | 0.524174 | − | 0.907895i | ||||
\(647\) | 1197.59 | + | 320.893i | 1.85099 | + | 0.495971i | 0.999592 | − | 0.0285523i | \(-0.00908973\pi\) |
0.851396 | + | 0.524523i | \(0.175756\pi\) | |||||||
\(648\) | −6.58846 | + | 24.5885i | −0.0101674 | + | 0.0379452i | ||||
\(649\) | 81.3973 | + | 46.9947i | 0.125420 | + | 0.0724110i | ||||
\(650\) | 380.676 | + | 233.641i | 0.585655 | + | 0.359448i | ||||
\(651\) | 74.3448 | − | 405.789i | 0.114201 | − | 0.623332i | ||||
\(652\) | 324.525 | − | 324.525i | 0.497738 | − | 0.497738i | ||||
\(653\) | 49.1787 | − | 13.1774i | 0.0753119 | − | 0.0201798i | −0.220966 | − | 0.975281i | \(-0.570921\pi\) |
0.296278 | + | 0.955102i | \(0.404254\pi\) | |||||||
\(654\) | −370.189 | + | 213.729i | −0.566039 | + | 0.326802i | ||||
\(655\) | −180.888 | − | 713.282i | −0.276165 | − | 1.08898i | ||||
\(656\) | −52.0146 | + | 90.0919i | −0.0792905 | + | 0.137335i | ||||
\(657\) | −18.8145 | + | 18.8145i | −0.0286370 | + | 0.0286370i | ||||
\(658\) | −33.0958 | − | 409.735i | −0.0502976 | − | 0.622698i | ||||
\(659\) | − | 741.347i | − | 1.12496i | −0.826812 | − | 0.562479i | \(-0.809848\pi\) | ||
0.826812 | − | 0.562479i | \(-0.190152\pi\) | |||||||
\(660\) | 0.910798 | − | 67.7841i | 0.00138000 | − | 0.102703i | ||||
\(661\) | −337.951 | − | 585.348i | −0.511272 | − | 0.885549i | −0.999915 | − | 0.0130653i | \(-0.995841\pi\) |
0.488642 | − | 0.872484i | \(-0.337492\pi\) | |||||||
\(662\) | −314.825 | − | 84.3571i | −0.475566 | − | 0.127428i | ||||
\(663\) | −312.965 | + | 83.8588i | −0.472044 | + | 0.126484i | ||||
\(664\) | 376.652i | 0.567246i | ||||||||
\(665\) | 218.926 | − | 1110.55i | 0.329212 | − | 1.67000i | ||||
\(666\) | −27.4530 | −0.0412208 | ||||||||
\(667\) | 87.8522 | + | 327.869i | 0.131712 | + | 0.491557i | ||||
\(668\) | −133.016 | + | 496.421i | −0.199125 | + | 0.743146i | ||||
\(669\) | 204.707 | − | 118.188i | 0.305990 | − | 0.176663i | ||||
\(670\) | 291.190 | + | 299.122i | 0.434612 | + | 0.446451i | ||||
\(671\) | −65.7388 | −0.0979714 | ||||||||
\(672\) | −38.9637 | − | 56.4432i | −0.0579817 | − | 0.0839928i | ||||
\(673\) | 212.014 | + | 212.014i | 0.315029 | + | 0.315029i | 0.846854 | − | 0.531825i | \(-0.178494\pi\) |
−0.531825 | + | 0.846854i | \(0.678494\pi\) | |||||||
\(674\) | −452.096 | − | 261.018i | −0.670765 | − | 0.387266i | ||||
\(675\) | −89.3547 | − | 94.2907i | −0.132377 | − | 0.139690i | ||||
\(676\) | 9.39820 | + | 16.2782i | 0.0139027 | + | 0.0240801i | ||||
\(677\) | −218.391 | − | 815.048i | −0.322587 | − | 1.20391i | −0.916715 | − | 0.399541i | \(-0.869170\pi\) |
0.594128 | − | 0.804370i | \(-0.297497\pi\) | |||||||
\(678\) | −15.1938 | − | 15.1938i | −0.0224098 | − | 0.0224098i | ||||
\(679\) | −392.945 | − | 1102.42i | −0.578711 | − | 1.62360i | ||||
\(680\) | 201.524 | + | 56.9108i | 0.296358 | + | 0.0836924i | ||||
\(681\) | −53.3694 | + | 92.4385i | −0.0783692 | + | 0.135739i | ||||
\(682\) | 181.918 | + | 48.7449i | 0.266742 | + | 0.0714734i | ||||
\(683\) | −243.853 | + | 910.072i | −0.357032 | + | 1.33246i | 0.520875 | + | 0.853633i | \(0.325606\pi\) |
−0.877908 | + | 0.478830i | \(0.841061\pi\) | |||||||
\(684\) | −168.047 | − | 97.0222i | −0.245683 | − | 0.141845i | ||||
\(685\) | −5.11256 | + | 2.86085i | −0.00746359 | + | 0.00417642i | ||||
\(686\) | 234.087 | + | 424.855i | 0.341234 | + | 0.619322i | ||||
\(687\) | −552.800 | + | 552.800i | −0.804658 | + | 0.804658i | ||||
\(688\) | 115.038 | − | 30.8243i | 0.167206 | − | 0.0448028i | ||||
\(689\) | −495.122 | + | 285.859i | −0.718610 | + | 0.414890i | ||||
\(690\) | −79.9339 | + | 134.251i | −0.115846 | + | 0.194567i | ||||
\(691\) | 241.773 | − | 418.764i | 0.349889 | − | 0.606026i | −0.636340 | − | 0.771408i | \(-0.719553\pi\) |
0.986229 | + | 0.165383i | \(0.0528860\pi\) | |||||||
\(692\) | 367.098 | − | 367.098i | 0.530489 | − | 0.530489i | ||||
\(693\) | 74.2574 | + | 35.2315i | 0.107153 | + | 0.0508390i | ||||
\(694\) | − | 147.714i | − | 0.212845i | ||||||
\(695\) | −818.270 | − | 840.559i | −1.17737 | − | 1.20944i | ||||
\(696\) | −65.1732 | − | 112.883i | −0.0936397 | − | 0.162189i | ||||
\(697\) | 371.973 | + | 99.6699i | 0.533677 | + | 0.142998i | ||||
\(698\) | −580.889 | + | 155.649i | −0.832220 | + | 0.222993i | ||||
\(699\) | 444.103i | 0.635341i | ||||||||
\(700\) | 349.495 | − | 18.7954i | 0.499279 | − | 0.0268505i | ||||
\(701\) | −1192.55 | −1.70122 | −0.850609 | − | 0.525799i | \(-0.823767\pi\) | ||||
−0.850609 | + | 0.525799i | \(0.823767\pi\) | |||||||
\(702\) | 24.0277 | + | 89.6726i | 0.0342275 | + | 0.127739i | ||||
\(703\) | 54.1627 | − | 202.138i | 0.0770451 | − | 0.287536i | ||||
\(704\) | 27.1161 | − | 15.6555i | 0.0385172 | − | 0.0222379i | ||||
\(705\) | 257.677 | − | 250.844i | 0.365499 | − | 0.355807i | ||||
\(706\) | −86.1765 | −0.122063 | ||||||||
\(707\) | −780.334 | + | 63.0305i | −1.10373 | + | 0.0891520i | ||||
\(708\) | 58.8232 | + | 58.8232i | 0.0830836 | + | 0.0830836i | ||||
\(709\) | −1102.14 | − | 636.323i | −1.55450 | − | 0.897494i | −0.997766 | − | 0.0668057i | \(-0.978719\pi\) |
−0.556738 | − | 0.830688i | \(-0.687947\pi\) | |||||||
\(710\) | −805.393 | − | 479.536i | −1.13436 | − | 0.675403i | ||||
\(711\) | −157.019 | − | 271.965i | −0.220843 | − | 0.382510i | ||||
\(712\) | −36.5787 | − | 136.514i | −0.0513746 | − | 0.191733i | ||||
\(713\) | −306.944 | − | 306.944i | −0.430496 | − | 0.430496i | ||||
\(714\) | −164.491 | + | 193.399i | −0.230379 | + | 0.270867i | ||||
\(715\) | −120.726 | − | 215.746i | −0.168847 | − | 0.301743i | ||||
\(716\) | −308.644 | + | 534.588i | −0.431068 | + | 0.746631i | ||||
\(717\) | 11.8169 | + | 3.16633i | 0.0164810 | + | 0.00441608i | ||||
\(718\) | −223.100 | + | 832.620i | −0.310724 | + | 1.15964i | ||||
\(719\) | −492.720 | − | 284.472i | −0.685285 | − | 0.395650i | 0.116558 | − | 0.993184i | \(-0.462814\pi\) |
−0.801843 | + | 0.597534i | \(0.796147\pi\) | |||||||
\(720\) | 16.3064 | − | 57.7417i | 0.0226478 | − | 0.0801968i | ||||
\(721\) | −233.593 | + | 1275.00i | −0.323985 | + | 1.76838i | ||||
\(722\) | 684.923 | − | 684.923i | 0.948647 | − | 0.948647i | ||||
\(723\) | 151.327 | − | 40.5481i | 0.209305 | − | 0.0560831i | ||||
\(724\) | −298.894 | + | 172.566i | −0.412837 | + | 0.238351i | ||||
\(725\) | 664.931 | + | 17.8722i | 0.917146 | + | 0.0246514i | ||||
\(726\) | 129.433 | − | 224.185i | 0.178282 | − | 0.308794i | ||||
\(727\) | −467.794 | + | 467.794i | −0.643459 | + | 0.643459i | −0.951404 | − | 0.307945i | \(-0.900359\pi\) |
0.307945 | + | 0.951404i | \(0.400359\pi\) | |||||||
\(728\) | −225.983 | − | 107.218i | −0.310416 | − | 0.147277i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 44.9381 | − | 43.7465i | 0.0615590 | − | 0.0599267i | ||||
\(731\) | −220.435 | − | 381.805i | −0.301553 | − | 0.522304i | ||||
\(732\) | −56.2017 | − | 15.0592i | −0.0767783 | − | 0.0205727i | ||||
\(733\) | 615.162 | − | 164.832i | 0.839239 | − | 0.224873i | 0.186499 | − | 0.982455i | \(-0.440286\pi\) |
0.652740 | + | 0.757582i | \(0.273619\pi\) | |||||||
\(734\) | 118.640i | 0.161635i | ||||||||
\(735\) | −155.759 | + | 394.733i | −0.211917 | + | 0.537052i | ||||
\(736\) | −72.1669 | −0.0980528 | ||||||||
\(737\) | −59.8031 | − | 223.188i | −0.0811440 | − | 0.302833i | ||||
\(738\) | 28.5580 | − | 106.580i | 0.0386964 | − | 0.144417i | ||||
\(739\) | −306.153 | + | 176.758i | −0.414280 | + | 0.239185i | −0.692627 | − | 0.721296i | \(-0.743547\pi\) |
0.278347 | + | 0.960481i | \(0.410213\pi\) | |||||||
\(740\) | 64.7016 | + | 0.869378i | 0.0874346 | + | 0.00117484i | ||||
\(741\) | −707.668 | −0.955017 | ||||||||
\(742\) | −192.035 | + | 404.753i | −0.258807 | + | 0.545489i | ||||
\(743\) | −278.067 | − | 278.067i | −0.374250 | − | 0.374250i | 0.494773 | − | 0.869022i | \(-0.335251\pi\) |
−0.869022 | + | 0.494773i | \(0.835251\pi\) | |||||||
\(744\) | 144.360 | + | 83.3464i | 0.194032 | + | 0.112025i | ||||
\(745\) | 1254.36 | − | 318.105i | 1.68370 | − | 0.426986i | ||||
\(746\) | −99.7268 | − | 172.732i | −0.133682 | − | 0.231544i | ||||
\(747\) | −103.398 | − | 385.887i | −0.138418 | − | 0.516582i | ||||
\(748\) | −81.9586 | − | 81.9586i | −0.109570 | − | 0.109570i | ||||
\(749\) | 220.352 | + | 40.3707i | 0.294194 | + | 0.0538994i | ||||
\(750\) | 207.606 | + | 225.055i | 0.276808 | + | 0.300073i | ||||
\(751\) | 375.703 | − | 650.737i | 0.500271 | − | 0.866494i | −0.499729 | − | 0.866182i | \(-0.666567\pi\) |
1.00000 | 0.000312486i | \(-9.94674e-5\pi\) | ||||||||
\(752\) | 160.438 | + | 42.9891i | 0.213348 | + | 0.0571664i | ||||
\(753\) | −35.4159 | + | 132.174i | −0.0470331 | + | 0.175530i | ||||
\(754\) | −411.678 | − | 237.683i | −0.545992 | − | 0.315229i | ||||
\(755\) | 700.893 | + | 197.934i | 0.928335 | + | 0.262164i | ||||
\(756\) | 55.4137 | + | 47.1308i | 0.0732986 | + | 0.0623424i | ||||
\(757\) | −554.603 | + | 554.603i | −0.732632 | + | 0.732632i | −0.971140 | − | 0.238508i | \(-0.923342\pi\) |
0.238508 | + | 0.971140i | \(0.423342\pi\) | |||||||
\(758\) | 169.090 | − | 45.3076i | 0.223074 | − | 0.0597726i | ||||
\(759\) | 74.8964 | − | 43.2414i | 0.0986777 | − | 0.0569716i | ||||
\(760\) | 392.983 | + | 233.985i | 0.517083 | + | 0.307874i | ||||
\(761\) | 127.641 | − | 221.080i | 0.167728 | − | 0.290513i | −0.769893 | − | 0.638173i | \(-0.779690\pi\) |
0.937621 | + | 0.347660i | \(0.113024\pi\) | |||||||
\(762\) | 94.0696 | − | 94.0696i | 0.123451 | − | 0.123451i | ||||
\(763\) | 98.3498 | + | 1217.60i | 0.128899 | + | 1.59580i | ||||
\(764\) | 270.589i | 0.354174i | ||||||||
\(765\) | −222.088 | − | 2.98414i | −0.290311 | − | 0.00390083i | ||||
\(766\) | 223.409 | + | 386.955i | 0.291656 | + | 0.505163i | ||||
\(767\) | 293.046 | + | 78.5214i | 0.382067 | + | 0.102375i | ||||
\(768\) | 26.7685 | − | 7.17260i | 0.0348548 | − | 0.00933933i | ||||
\(769\) | 274.062i | 0.356387i | 0.983995 | + | 0.178194i | \(0.0570253\pi\) | ||||
−0.983995 | + | 0.178194i | \(0.942975\pi\) | |||||||
\(770\) | −173.895 | − | 85.3854i | −0.225837 | − | 0.110890i | ||||
\(771\) | 498.749 | 0.646886 | ||||||||
\(772\) | 11.3989 | + | 42.5412i | 0.0147654 | + | 0.0551052i | ||||
\(773\) | 46.3214 | − | 172.874i | 0.0599242 | − | 0.223640i | −0.929469 | − | 0.368899i | \(-0.879735\pi\) |
0.989394 | + | 0.145259i | \(0.0464015\pi\) | |||||||
\(774\) | −109.397 | + | 63.1603i | −0.141340 | + | 0.0816024i | ||||
\(775\) | −747.847 | + | 405.378i | −0.964964 | + | 0.523068i | ||||
\(776\) | 472.897 | 0.609403 | ||||||||
\(777\) | −33.6293 | + | 70.8804i | −0.0432809 | + | 0.0912232i | ||||
\(778\) | 347.324 | + | 347.324i | 0.446432 | + | 0.446432i | ||||
\(779\) | 728.409 | + | 420.547i | 0.935057 | + | 0.539855i | ||||
\(780\) | −53.7890 | − | 212.102i | −0.0689602 | − | 0.271926i | ||||
\(781\) | 259.412 | + | 449.315i | 0.332154 | + | 0.575308i | ||||
\(782\) | 69.1428 | + | 258.044i | 0.0884179 | + | 0.329980i | ||||
\(783\) | 97.7598 | + | 97.7598i | 0.124853 | + | 0.124853i | ||||
\(784\) | −193.459 | + | 31.4580i | −0.246759 | + | 0.0401251i | ||||
\(785\) | −43.1535 | + | 24.1475i | −0.0549725 | + | 0.0307611i | ||||
\(786\) | −180.248 | + | 312.199i | −0.229324 | + | 0.397200i | ||||
\(787\) | −308.617 | − | 82.6936i | −0.392143 | − | 0.105074i | 0.0573592 | − | 0.998354i | \(-0.481732\pi\) |
−0.449502 | + | 0.893279i | \(0.648399\pi\) | |||||||
\(788\) | −45.2057 | + | 168.710i | −0.0573676 | + | 0.214099i | ||||
\(789\) | 400.319 | + | 231.124i | 0.507375 | + | 0.292933i | ||||
\(790\) | 361.451 | + | 645.942i | 0.457533 | + | 0.817648i | ||||
\(791\) | −57.8407 | + | 20.6166i | −0.0731235 | + | 0.0260640i | ||||
\(792\) | −23.4832 | + | 23.4832i | −0.0296505 | + | 0.0296505i | ||||
\(793\) | −204.964 | + | 54.9200i | −0.258467 | + | 0.0692560i | ||||
\(794\) | 463.633 | − | 267.679i | 0.583920 | − | 0.337127i | ||||
\(795\) | −379.891 | + | 96.3401i | −0.477850 | + | 0.121183i | ||||
\(796\) | −332.022 | + | 575.080i | −0.417114 | + | 0.722462i | ||||
\(797\) | 360.903 | − | 360.903i | 0.452827 | − | 0.452827i | −0.443464 | − | 0.896292i | \(-0.646251\pi\) |
0.896292 | + | 0.443464i | \(0.146251\pi\) | |||||||
\(798\) | −456.354 | + | 315.028i | −0.571872 | + | 0.394773i | ||||
\(799\) | − | 614.858i | − | 0.769535i | ||||||
\(800\) | −40.2596 | + | 135.570i | −0.0503246 | + | 0.169462i | ||||
\(801\) | 74.9512 | + | 129.819i | 0.0935721 | + | 0.162072i | ||||
\(802\) | 232.820 | + | 62.3838i | 0.290299 | + | 0.0777853i | ||||
\(803\) | −33.5303 | + | 8.98442i | −0.0417563 | + | 0.0111886i | ||||
\(804\) | − | 204.509i | − | 0.254364i | ||||||
\(805\) | 248.703 | + | 370.834i | 0.308948 | + | 0.460663i | ||||
\(806\) | 607.918 | 0.754241 | ||||||||
\(807\) | 66.0974 | + | 246.679i | 0.0819051 | + | 0.305674i | ||||
\(808\) | 81.8721 | − | 305.551i | 0.101327 | − | 0.378157i | ||||
\(809\) | −720.956 | + | 416.244i | −0.891169 | + | 0.514517i | −0.874325 | − | 0.485342i | \(-0.838695\pi\) |
−0.0168442 | + | 0.999858i | \(0.505362\pi\) | |||||||
\(810\) | −0.855032 | + | 63.6339i | −0.00105559 | + | 0.0785603i | ||||
\(811\) | −375.130 | −0.462553 | −0.231276 | − | 0.972888i | \(-0.574290\pi\) | ||||
−0.231276 | + | 0.972888i | \(0.574290\pi\) | |||||||
\(812\) | −371.287 | + | 29.9902i | −0.457250 | + | 0.0369337i | ||||
\(813\) | −609.905 | − | 609.905i | −0.750191 | − | 0.750191i | ||||
\(814\) | −31.0175 | − | 17.9079i | −0.0381050 | − | 0.0219999i | ||||
\(815\) | 586.983 | − | 985.854i | 0.720225 | − | 1.20964i | ||||
\(816\) | −51.2936 | − | 88.8432i | −0.0628598 | − | 0.108876i | ||||
\(817\) | −249.221 | − | 930.104i | −0.305043 | − | 1.13844i | ||||
\(818\) | −265.747 | − | 265.747i | −0.324874 | − | 0.324874i | ||||
\(819\) | 260.957 | + | 47.8100i | 0.318629 | + | 0.0583761i | ||||
\(820\) | −70.6809 | + | 250.284i | −0.0861962 | + | 0.305224i | ||||
\(821\) | 701.328 | − | 1214.74i | 0.854236 | − | 1.47958i | −0.0231161 | − | 0.999733i | \(-0.507359\pi\) |
0.877352 | − | 0.479847i | \(-0.159308\pi\) | |||||||
\(822\) | 2.77230 | + | 0.742836i | 0.00337263 | + | 0.000903693i | ||||
\(823\) | 223.496 | − | 834.098i | 0.271562 | − | 1.01348i | −0.686548 | − | 0.727085i | \(-0.740875\pi\) |
0.958110 | − | 0.286400i | \(-0.0924585\pi\) | |||||||
\(824\) | −453.584 | − | 261.877i | −0.550466 | − | 0.317812i | ||||
\(825\) | −39.4493 | − | 164.820i | −0.0478173 | − | 0.199782i | ||||
\(826\) | 223.931 | − | 79.8174i | 0.271103 | − | 0.0966313i | ||||
\(827\) | 785.335 | − | 785.335i | 0.949619 | − | 0.949619i | −0.0491718 | − | 0.998790i | \(-0.515658\pi\) |
0.998790 | + | 0.0491718i | \(0.0156582\pi\) | |||||||
\(828\) | 73.9363 | − | 19.8112i | 0.0892951 | − | 0.0239265i | ||||
\(829\) | −1243.93 | + | 718.182i | −1.50052 | + | 0.866324i | −0.500517 | + | 0.865727i | \(0.666857\pi\) |
−1.00000 | 0.000596877i | \(0.999810\pi\) | ||||||||
\(830\) | 231.469 | + | 912.736i | 0.278879 | + | 1.09968i | ||||
\(831\) | 225.233 | − | 390.115i | 0.271038 | − | 0.469452i | ||||
\(832\) | 71.4651 | − | 71.4651i | 0.0858955 | − | 0.0858955i | ||||
\(833\) | 297.836 | + | 661.604i | 0.357546 | + | 0.794243i | ||||
\(834\) | 574.687i | 0.689073i | ||||||||
\(835\) | −17.2624 | + | 1284.72i | −0.0206735 | + | 1.53858i | ||||
\(836\) | −126.578 | − | 219.239i | −0.151409 | − | 0.262247i | ||||
\(837\) | −170.780 | − | 45.7603i | −0.204038 | − | 0.0546719i | ||||
\(838\) | 236.664 | − | 63.4140i | 0.282415 | − | 0.0756730i | ||||
\(839\) | 702.434i | 0.837228i | 0.908164 | + | 0.418614i | \(0.137484\pi\) | ||||
−0.908164 | + | 0.418614i | \(0.862516\pi\) | |||||||
\(840\) | −129.107 | − | 112.833i | −0.153699 | − | 0.134325i | ||||
\(841\) | 133.076 | 0.158235 | ||||||||
\(842\) | −198.051 | − | 739.138i | −0.235216 | − | 0.877836i | ||||
\(843\) | 76.2644 | − | 284.623i | 0.0904678 | − | 0.337631i | ||||
\(844\) | 8.25481 | − | 4.76592i | 0.00978058 | − | 0.00564682i | ||||
\(845\) | 32.7782 | + | 33.6711i | 0.0387908 | + | 0.0398474i | ||||
\(846\) | −176.173 | −0.208242 | ||||||||
\(847\) | −420.265 | − | 608.801i | −0.496181 | − | 0.718773i | ||||
\(848\) | −127.999 | − | 127.999i | −0.150943 | − | 0.150943i | ||||
\(849\) | 509.726 | + | 294.290i | 0.600384 | + | 0.346632i | ||||
\(850\) | 523.324 | + | 14.0661i | 0.615676 | + | 0.0165483i | ||||
\(851\) | 41.2750 | + | 71.4904i | 0.0485018 | + | 0.0840075i | ||||
\(852\) | 118.850 | + | 443.556i | 0.139496 | + | 0.520605i | ||||
\(853\) | −230.504 | − | 230.504i | −0.270227 | − | 0.270227i | 0.558964 | − | 0.829192i | \(-0.311199\pi\) |
−0.829192 | + | 0.558964i | \(0.811199\pi\) | |||||||
\(854\) | −107.727 | + | 126.659i | −0.126144 | + | 0.148313i | ||||
\(855\) | −466.852 | − | 131.840i | −0.546026 | − | 0.154199i | ||||
\(856\) | −45.2587 | + | 78.3904i | −0.0528723 | + | 0.0915775i | ||||
\(857\) | 1059.53 | + | 283.900i | 1.23632 | + | 0.331272i | 0.817038 | − | 0.576583i | \(-0.195614\pi\) |
0.419284 | + | 0.907855i | \(0.362281\pi\) | |||||||
\(858\) | −31.3471 | + | 116.989i | −0.0365351 | + | 0.136351i | ||||
\(859\) | 629.320 | + | 363.338i | 0.732619 | + | 0.422978i | 0.819380 | − | 0.573251i | \(-0.194318\pi\) |
−0.0867605 | + | 0.996229i | \(0.527651\pi\) | |||||||
\(860\) | 259.828 | − | 145.392i | 0.302125 | − | 0.169061i | ||||
\(861\) | −240.193 | − | 204.291i | −0.278970 | − | 0.237272i | ||||
\(862\) | 544.876 | − | 544.876i | 0.632106 | − | 0.632106i | ||||
\(863\) | 718.251 | − | 192.455i | 0.832272 | − | 0.223007i | 0.182567 | − | 0.983193i | \(-0.441559\pi\) |
0.649705 | + | 0.760187i | \(0.274893\pi\) | |||||||
\(864\) | −25.4558 | + | 14.6969i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 663.987 | − | 1115.18i | 0.767616 | − | 1.28923i | ||||
\(866\) | −440.714 | + | 763.339i | −0.508908 | + | 0.881454i | ||||
\(867\) | 85.4223 | − | 85.4223i | 0.0985263 | − | 0.0985263i | ||||
\(868\) | 392.028 | − | 270.623i | 0.451645 | − | 0.311778i | ||||
\(869\) | − | 409.702i | − | 0.471463i | ||||||
\(870\) | −227.305 | − | 233.497i | −0.261271 | − | 0.268387i | ||||
\(871\) | −372.915 | − | 645.908i | −0.428146 | − | 0.741570i | ||||
\(872\) | −476.767 | − | 127.749i | −0.546751 | − | 0.146502i | ||||
\(873\) | −484.492 | + | 129.819i | −0.554973 | + | 0.148705i | ||||
\(874\) | 583.482i | 0.667600i | ||||||||
\(875\) | 835.377 | − | 260.327i | 0.954717 | − | 0.297517i | ||||
\(876\) | −30.7240 | −0.0350731 | ||||||||
\(877\) | −322.376 | − | 1203.12i | −0.367589 | − | 1.37186i | −0.863877 | − | 0.503703i | \(-0.831971\pi\) |
0.496288 | − | 0.868158i | \(-0.334696\pi\) | |||||||
\(878\) | 174.025 | − | 649.469i | 0.198206 | − | 0.739714i | ||||
\(879\) | 793.215 | − | 457.963i | 0.902406 | − | 0.521004i | ||||
\(880\) | 56.0892 | − | 54.6018i | 0.0637377 | − | 0.0620476i | ||||
\(881\) | 308.518 | 0.350191 | 0.175095 | − | 0.984551i | \(-0.443977\pi\) | ||||
0.175095 | + | 0.984551i | \(0.443977\pi\) | |||||||
\(882\) | 189.567 | − | 85.3376i | 0.214928 | − | 0.0967546i | ||||
\(883\) | −113.247 | − | 113.247i | −0.128252 | − | 0.128252i | 0.640067 | − | 0.768319i | \(-0.278907\pi\) |
−0.768319 | + | 0.640067i | \(0.778907\pi\) | |||||||
\(884\) | −324.005 | − | 187.065i | −0.366522 | − | 0.211612i | ||||
\(885\) | 178.695 | + | 106.396i | 0.201915 | + | 0.120222i | ||||
\(886\) | −332.755 | − | 576.349i | −0.375570 | − | 0.650507i | ||||
\(887\) | 262.503 | + | 979.674i | 0.295945 | + | 1.10448i | 0.940464 | + | 0.339892i | \(0.110391\pi\) |
−0.644520 | + | 0.764588i | \(0.722943\pi\) | |||||||
\(888\) | −22.4153 | − | 22.4153i | −0.0252425 | − | 0.0252425i | ||||
\(889\) | −127.643 | − | 358.109i | −0.143581 | − | 0.402822i | ||||
\(890\) | −172.535 | − | 308.333i | −0.193859 | − | 0.346442i | ||||
\(891\) | 17.6124 | − | 30.5056i | 0.0197670 | − | 0.0342375i | ||||
\(892\) | 263.643 | + | 70.6428i | 0.295563 | + | 0.0791960i | ||||
\(893\) | 347.575 | − | 1297.17i | 0.389222 | − | 1.45260i | ||||
\(894\) | −549.026 | − | 316.980i | −0.614123 | − | 0.354564i | ||||
\(895\) | −419.407 | + | 1485.14i | −0.468611 | + | 1.65937i | ||||
\(896\) | 14.2720 | − | 77.8994i | 0.0159285 | − | 0.0869413i | ||||
\(897\) | 197.391 | − | 197.391i | 0.220057 | − | 0.220057i | ||||
\(898\) | 995.473 | − | 266.736i | 1.10854 | − | 0.297034i | ||||
\(899\) | 784.035 | − | 452.663i | 0.872119 | − | 0.503518i | ||||
\(900\) | 4.03029 | − | 149.946i | 0.00447810 | − | 0.166606i | ||||
\(901\) | −335.047 | + | 580.318i | −0.371861 | + | 0.644083i | ||||
\(902\) | 101.789 | − | 101.789i | 0.112848 | − | 0.112848i | ||||
\(903\) | 29.0639 | + | 359.819i | 0.0321860 | + | 0.398471i | ||||
\(904\) | − | 24.8114i | − | 0.0274463i | ||||||
\(905\) | −618.257 | + | 601.862i | −0.683157 | + | 0.665041i | ||||
\(906\) | −178.398 | − | 308.994i | −0.196907 | − | 0.341053i | ||||
\(907\) | 531.590 | + | 142.439i | 0.586097 | + | 0.157044i | 0.539669 | − | 0.841877i | \(-0.318549\pi\) |
0.0464285 | + | 0.998922i | \(0.485216\pi\) | |||||||
\(908\) | −119.052 | + | 31.8998i | −0.131114 | + | 0.0351319i | ||||
\(909\) | 335.518i | 0.369107i | ||||||||
\(910\) | −613.512 | − | 120.943i | −0.674189 | − | 0.132904i | ||||
\(911\) | −1091.64 | −1.19829 | −0.599144 | − | 0.800641i | \(-0.704492\pi\) | ||||
−0.599144 | + | 0.800641i | \(0.704492\pi\) | |||||||
\(912\) | −57.9918 | − | 216.428i | −0.0635875 | − | 0.237312i | ||||
\(913\) | 134.896 | − | 503.437i | 0.147750 | − | 0.551410i | ||||
\(914\) | 762.579 | − | 440.275i | 0.834331 | − | 0.481701i | ||||
\(915\) | −145.448 | − | 1.95434i | −0.158959 | − | 0.00213589i | ||||
\(916\) | −902.718 | −0.985500 | ||||||||
\(917\) | 585.262 | + | 847.816i | 0.638235 | + | 0.924554i | ||||
\(918\) | 76.9404 | + | 76.9404i | 0.0838131 | + | 0.0838131i | ||||
\(919\) | −448.935 | − | 259.193i | −0.488503 | − | 0.282038i | 0.235450 | − | 0.971886i | \(-0.424344\pi\) |
−0.723953 | + | 0.689849i | \(0.757677\pi\) | |||||||
\(920\) | −174.881 | + | 44.3498i | −0.190088 | + | 0.0482063i | ||||
\(921\) | −9.05484 | − | 15.6834i | −0.00983153 | − | 0.0170287i | ||||
\(922\) | 291.603 | + | 1088.28i | 0.316272 | + | 1.18034i | ||||
\(923\) | 1184.18 | + | 1184.18i | 1.28297 | + | 1.28297i | ||||
\(924\) | 31.8645 | + | 89.3972i | 0.0344854 | + | 0.0967503i | ||||
\(925\) | 157.325 | − | 37.6553i | 0.170081 | − | 0.0407084i | ||||
\(926\) | 215.541 | − | 373.327i | 0.232765 | − | 0.403161i | ||||
\(927\) | 536.596 | + | 143.780i | 0.578852 | + | 0.155103i | ||||
\(928\) | 38.9551 | − | 145.383i | 0.0419775 | − | 0.156662i | ||||
\(929\) | 191.262 | + | 110.425i | 0.205879 | + | 0.118864i | 0.599395 | − | 0.800453i | \(-0.295408\pi\) |
−0.393516 | + | 0.919318i | \(0.628741\pi\) | |||||||
\(930\) | 401.047 | + | 113.257i | 0.431233 | + | 0.121781i | ||||
\(931\) | 254.344 | + | 1564.15i | 0.273195 | + | 1.68008i | ||||
\(932\) | −362.609 | + | 362.609i | −0.389065 | + | 0.389065i | ||||
\(933\) | 489.857 | − | 131.257i | 0.525035 | − | 0.140683i | ||||
\(934\) | −350.332 | + | 202.264i | −0.375088 | + | 0.216557i | ||||
\(935\) | −248.977 | − | 148.242i | −0.266285 | − | 0.158548i | ||||
\(936\) | −53.5988 | + | 92.8359i | −0.0572637 | + | 0.0991836i | ||||
\(937\) | 999.171 | − | 999.171i | 1.06635 | − | 1.06635i | 0.0687153 | − | 0.997636i | \(-0.478110\pi\) |
0.997636 | − | 0.0687153i | \(-0.0218900\pi\) | |||||||
\(938\) | −528.017 | − | 250.518i | −0.562918 | − | 0.267077i | ||||
\(939\) | 596.836i | 0.635608i | ||||||||
\(940\) | 415.205 | + | 5.57901i | 0.441708 | + | 0.00593512i | ||||
\(941\) | −252.279 | − | 436.960i | −0.268097 | − | 0.464357i | 0.700274 | − | 0.713875i | \(-0.253061\pi\) |
−0.968370 | + | 0.249517i | \(0.919728\pi\) | |||||||
\(942\) | 23.4001 | + | 6.27003i | 0.0248409 | + | 0.00665609i | ||||
\(943\) | −320.480 | + | 85.8725i | −0.339852 | + | 0.0910631i | ||||
\(944\) | 96.0578i | 0.101756i | ||||||||
\(945\) | 163.248 | + | 80.1575i | 0.172749 | + | 0.0848227i | ||||
\(946\) | −164.801 | −0.174208 | ||||||||
\(947\) | 252.109 | + | 940.882i | 0.266218 | + | 0.993540i | 0.961501 | + | 0.274803i | \(0.0886127\pi\) |
−0.695282 | + | 0.718737i | \(0.744721\pi\) | |||||||
\(948\) | 93.8529 | − | 350.264i | 0.0990010 | − | 0.369477i | ||||
\(949\) | −97.0369 | + | 56.0243i | −0.102252 | + | 0.0590350i | ||||
\(950\) | 1096.11 | + | 325.507i | 1.15380 | + | 0.342639i | ||||
\(951\) | 221.031 | 0.232419 | ||||||||
\(952\) | −292.216 | + | 23.6034i | −0.306949 | + | 0.0247934i | ||||
\(953\) | −166.543 | − | 166.543i | −0.174757 | − | 0.174757i | 0.614309 | − | 0.789066i | \(-0.289435\pi\) |
−0.789066 | + | 0.614309i | \(0.789435\pi\) | |||||||
\(954\) | 166.276 | + | 95.9996i | 0.174294 | + | 0.100628i | ||||
\(955\) | 166.289 | + | 655.715i | 0.174125 | + | 0.686613i | ||||
\(956\) | 7.06316 | + | 12.2337i | 0.00738824 | + | 0.0127968i | ||||
\(957\) | 46.6828 | + | 174.223i | 0.0487804 | + | 0.182051i | ||||
\(958\) | 671.652 | + | 671.652i | 0.701098 | + | 0.701098i | ||||
\(959\) | 5.31391 | − | 6.24779i | 0.00554110 | − | 0.00651490i | ||||
\(960\) | 60.4600 | − | 33.8318i | 0.0629792 | − | 0.0352414i | ||||
\(961\) | −98.3850 | + | 170.408i | −0.102378 | + | 0.177323i | ||||
\(962\) | −111.669 | − | 29.9216i | −0.116080 | − | 0.0311035i | ||||
\(963\) | 24.8488 | − | 92.7368i | 0.0258035 | − | 0.0962999i | ||||
\(964\) | 156.666 | + | 90.4510i | 0.162516 | + | 0.0938288i | ||||
\(965\) | 53.7662 | + | 96.0845i | 0.0557163 | + | 0.0995694i | ||||
\(966\) | 39.4200 | − | 215.163i | 0.0408075 | − | 0.222736i | ||||
\(967\) | −75.7515 | + | 75.7515i | −0.0783366 | + | 0.0783366i | −0.745189 | − | 0.666853i | \(-0.767641\pi\) |
0.666853 | + | 0.745189i | \(0.267641\pi\) | |||||||
\(968\) | 288.728 | − | 77.3643i | 0.298272 | − | 0.0799218i | ||||
\(969\) | −718.313 | + | 414.718i | −0.741293 | + | 0.427986i | ||||
\(970\) | 1145.97 | − | 290.616i | 1.18141 | − | 0.299604i | ||||
\(971\) | 222.519 | − | 385.415i | 0.229165 | − | 0.396926i | −0.728396 | − | 0.685157i | \(-0.759734\pi\) |
0.957561 | + | 0.288231i | \(0.0930670\pi\) | |||||||
\(972\) | 22.0454 | − | 22.0454i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | 1483.77 | + | 703.977i | 1.52495 | + | 0.723512i | ||||
\(974\) | 144.647i | 0.148508i | ||||||||
\(975\) | −260.692 | − | 480.929i | −0.267377 | − | 0.493261i | ||||
\(976\) | −33.5927 | − | 58.1843i | −0.0344188 | − | 0.0596151i | ||||
\(977\) | −1758.30 | − | 471.135i | −1.79969 | − | 0.482226i | −0.805763 | − | 0.592238i | \(-0.798245\pi\) |
−0.993930 | + | 0.110012i | \(0.964911\pi\) | |||||||
\(978\) | −542.941 | + | 145.481i | −0.555154 | + | 0.148753i | ||||
\(979\) | 195.566i | 0.199761i | ||||||||
\(980\) | −449.475 | + | 195.121i | −0.458648 | + | 0.199103i | ||||
\(981\) | 523.527 | 0.533666 | ||||||||
\(982\) | −95.4557 | − | 356.246i | −0.0972054 | − | 0.362775i | ||||
\(983\) | −191.894 | + | 716.158i | −0.195213 | + | 0.728543i | 0.796999 | + | 0.603980i | \(0.206420\pi\) |
−0.992212 | + | 0.124563i | \(0.960247\pi\) | |||||||
\(984\) | 110.340 | − | 63.7046i | 0.112134 | − | 0.0647404i | ||||
\(985\) | −5.86666 | + | 436.614i | −0.00595600 | + | 0.443263i | ||||
\(986\) | −557.162 | −0.565073 | ||||||||
\(987\) | −215.807 | + | 454.857i | −0.218650 | + | 0.460848i | ||||
\(988\) | −577.808 | − | 577.808i | −0.584826 | − | 0.584826i | ||||
\(989\) | 328.951 | + | 189.920i | 0.332610 | + | 0.192032i | ||||
\(990\) | −42.4752 | + | 71.3382i | −0.0429042 | + | 0.0720588i | ||||
\(991\) | −135.511 | − | 234.713i | −0.136742 | − | 0.236844i | 0.789520 | − | 0.613725i | \(-0.210330\pi\) |
−0.926262 | + | 0.376881i | \(0.876996\pi\) | |||||||
\(992\) | 49.8176 | + | 185.922i | 0.0502193 | + | 0.187421i | ||||
\(993\) | 282.264 | + | 282.264i | 0.284254 | + | 0.284254i | ||||
\(994\) | 1290.80 | + | 236.487i | 1.29859 | + | 0.237915i | ||||
\(995\) | −451.174 | + | 1597.63i | −0.453441 | + | 1.60566i | ||||
\(996\) | 230.651 | − | 399.499i | 0.231577 | − | 0.401104i | ||||
\(997\) | −388.246 | − | 104.030i | −0.389415 | − | 0.104343i | 0.0587989 | − | 0.998270i | \(-0.481273\pi\) |
−0.448214 | + | 0.893927i | \(0.647940\pi\) | |||||||
\(998\) | 35.0541 | − | 130.824i | 0.0351244 | − | 0.131086i | ||||
\(999\) | 29.1183 | + | 16.8115i | 0.0291475 | + | 0.0168283i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 210.3.v.b.163.2 | yes | 32 | |
5.2 | odd | 4 | inner | 210.3.v.b.37.6 | ✓ | 32 | |
7.4 | even | 3 | inner | 210.3.v.b.193.6 | yes | 32 | |
35.32 | odd | 12 | inner | 210.3.v.b.67.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.b.37.6 | ✓ | 32 | 5.2 | odd | 4 | inner | |
210.3.v.b.67.2 | yes | 32 | 35.32 | odd | 12 | inner | |
210.3.v.b.163.2 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.v.b.193.6 | yes | 32 | 7.4 | even | 3 | inner |