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 | 67.7 | ||
Character | \(\chi\) | \(=\) | 210.67 |
Dual form | 210.3.v.b.163.7 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||
\(5\) | 0.678362 | + | 4.95377i | 0.135672 | + | 0.990754i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 5.93351 | + | 3.71395i | 0.847645 | + | 0.530564i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.288675 | + | 0.166667i | ||||
\(10\) | −7.01527 | − | 0.886545i | −0.701527 | − | 0.0886545i | ||||
\(11\) | −3.58312 | + | 6.20615i | −0.325738 | + | 0.564195i | −0.981662 | − | 0.190632i | \(-0.938946\pi\) |
0.655923 | + | 0.754828i | \(0.272280\pi\) | |||||||
\(12\) | 0.896575 | − | 3.34607i | 0.0747146 | − | 0.278839i | ||||
\(13\) | 7.28383 | − | 7.28383i | 0.560295 | − | 0.560295i | −0.369097 | − | 0.929391i | \(-0.620333\pi\) |
0.929391 | + | 0.369097i | \(0.120333\pi\) | |||||||
\(14\) | −7.24516 | + | 6.74593i | −0.517512 | + | 0.481852i | ||||
\(15\) | −7.98372 | + | 3.35564i | −0.532248 | + | 0.223709i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | −18.1882 | + | 4.87353i | −1.06990 | + | 0.286678i | −0.750451 | − | 0.660926i | \(-0.770164\pi\) |
−0.319446 | + | 0.947604i | \(0.603497\pi\) | |||||||
\(18\) | −1.09808 | − | 4.09808i | −0.0610042 | − | 0.227671i | ||||
\(19\) | −7.65544 | + | 4.41987i | −0.402918 | + | 0.232625i | −0.687742 | − | 0.725955i | \(-0.741398\pi\) |
0.284824 | + | 0.958580i | \(0.408065\pi\) | |||||||
\(20\) | 3.77881 | − | 9.25854i | 0.188941 | − | 0.462927i | ||||
\(21\) | −3.55363 | + | 11.5919i | −0.169221 | + | 0.551994i | ||||
\(22\) | −7.16624 | − | 7.16624i | −0.325738 | − | 0.325738i | ||||
\(23\) | 0.401994 | + | 0.107714i | 0.0174780 | + | 0.00468322i | 0.267547 | − | 0.963545i | \(-0.413787\pi\) |
−0.250069 | + | 0.968228i | \(0.580453\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | −24.0796 | + | 6.72090i | −0.963186 | + | 0.268836i | ||||
\(26\) | 7.28383 | + | 12.6160i | 0.280147 | + | 0.485229i | ||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | −6.56320 | − | 12.3663i | −0.234400 | − | 0.441652i | ||||
\(29\) | 27.7751i | 0.957761i | 0.877880 | + | 0.478880i | \(0.158957\pi\) | ||||
−0.877880 | + | 0.478880i | \(0.841043\pi\) | |||||||
\(30\) | −1.66164 | − | 12.1342i | −0.0553880 | − | 0.404474i | ||||
\(31\) | 12.5266 | − | 21.6967i | 0.404083 | − | 0.699892i | −0.590131 | − | 0.807307i | \(-0.700924\pi\) |
0.994214 | + | 0.107415i | \(0.0342574\pi\) | |||||||
\(32\) | −5.46410 | + | 1.46410i | −0.170753 | + | 0.0457532i | ||||
\(33\) | −11.9894 | − | 3.21254i | −0.363314 | − | 0.0973497i | ||||
\(34\) | − | 26.6294i | − | 0.783219i | ||||||
\(35\) | −14.3730 | + | 31.9127i | −0.410656 | + | 0.911790i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 13.8182 | − | 51.5702i | 0.373464 | − | 1.39379i | −0.482111 | − | 0.876110i | \(-0.660130\pi\) |
0.855575 | − | 0.517678i | \(-0.173204\pi\) | |||||||
\(38\) | −3.23557 | − | 12.0753i | −0.0851466 | − | 0.317771i | ||||
\(39\) | 15.4513 | + | 8.92083i | 0.396188 | + | 0.228739i | ||||
\(40\) | 11.2643 | + | 8.55081i | 0.281607 | + | 0.213770i | ||||
\(41\) | 46.7769 | 1.14090 | 0.570450 | − | 0.821333i | \(-0.306769\pi\) | ||||
0.570450 | + | 0.821333i | \(0.306769\pi\) | |||||||
\(42\) | −14.5341 | − | 9.09728i | −0.346050 | − | 0.216602i | ||||
\(43\) | −37.3270 | + | 37.3270i | −0.868070 | + | 0.868070i | −0.992259 | − | 0.124189i | \(-0.960367\pi\) |
0.124189 | + | 0.992259i | \(0.460367\pi\) | |||||||
\(44\) | 12.4123 | − | 7.16624i | 0.282098 | − | 0.162869i | ||||
\(45\) | −9.19309 | − | 11.8527i | −0.204291 | − | 0.263394i | ||||
\(46\) | −0.294280 | + | 0.509708i | −0.00639739 | + | 0.0110806i | ||||
\(47\) | 8.32828 | − | 31.0816i | 0.177198 | − | 0.661310i | −0.818969 | − | 0.573837i | \(-0.805454\pi\) |
0.996167 | − | 0.0874729i | \(-0.0278791\pi\) | |||||||
\(48\) | −4.89898 | + | 4.89898i | −0.102062 | + | 0.102062i | ||||
\(49\) | 21.4132 | + | 44.0735i | 0.437004 | + | 0.899460i | ||||
\(50\) | −0.367156 | − | 35.3534i | −0.00734313 | − | 0.707069i | ||||
\(51\) | −16.3071 | − | 28.2448i | −0.319748 | − | 0.553819i | ||||
\(52\) | −19.8998 | + | 5.33213i | −0.382688 | + | 0.102541i | ||||
\(53\) | 18.4455 | + | 68.8397i | 0.348029 | + | 1.29886i | 0.889033 | + | 0.457842i | \(0.151378\pi\) |
−0.541004 | + | 0.841020i | \(0.681956\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | −33.1745 | − | 13.5399i | −0.603172 | − | 0.246181i | ||||
\(56\) | 19.2949 | − | 4.43914i | 0.344552 | − | 0.0792703i | ||||
\(57\) | −10.8264 | − | 10.8264i | −0.189937 | − | 0.189937i | ||||
\(58\) | −37.9414 | − | 10.1664i | −0.654163 | − | 0.175282i | ||||
\(59\) | 35.2552 | + | 20.3546i | 0.597546 | + | 0.344993i | 0.768075 | − | 0.640359i | \(-0.221215\pi\) |
−0.170530 | + | 0.985353i | \(0.554548\pi\) | |||||||
\(60\) | 17.1838 | + | 2.17158i | 0.286397 | + | 0.0361931i | ||||
\(61\) | 3.30356 | + | 5.72193i | 0.0541567 | + | 0.0938021i | 0.891833 | − | 0.452365i | \(-0.149420\pi\) |
−0.837676 | + | 0.546167i | \(0.816086\pi\) | |||||||
\(62\) | 25.0531 | + | 25.0531i | 0.404083 | + | 0.404083i | ||||
\(63\) | −20.9866 | − | 0.748846i | −0.333121 | − | 0.0118864i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 41.0235 | + | 31.1413i | 0.631130 | + | 0.479097i | ||||
\(66\) | 8.77682 | − | 15.2019i | 0.132982 | − | 0.230332i | ||||
\(67\) | 128.699 | − | 34.4848i | 1.92088 | − | 0.514699i | 0.932901 | − | 0.360133i | \(-0.117269\pi\) |
0.987982 | − | 0.154566i | \(-0.0493979\pi\) | |||||||
\(68\) | 36.3765 | + | 9.74705i | 0.534948 | + | 0.143339i | ||||
\(69\) | 0.720836i | 0.0104469i | ||||||||
\(70\) | −38.3326 | − | 31.3147i | −0.547609 | − | 0.447353i | ||||
\(71\) | 129.870 | 1.82915 | 0.914576 | − | 0.404414i | \(-0.132525\pi\) | ||||
0.914576 | + | 0.404414i | \(0.132525\pi\) | |||||||
\(72\) | −2.19615 | + | 8.19615i | −0.0305021 | + | 0.113835i | ||||
\(73\) | 2.10533 | + | 7.85719i | 0.0288401 | + | 0.107633i | 0.978846 | − | 0.204601i | \(-0.0655896\pi\) |
−0.950005 | + | 0.312233i | \(0.898923\pi\) | |||||||
\(74\) | 65.3884 | + | 37.7520i | 0.883626 | + | 0.510162i | ||||
\(75\) | −22.0389 | − | 37.2731i | −0.293852 | − | 0.496975i | ||||
\(76\) | 17.6795 | 0.232625 | ||||||||
\(77\) | −44.3098 | + | 23.5168i | −0.575452 | + | 0.305412i | ||||
\(78\) | −17.8417 | + | 17.8417i | −0.228739 | + | 0.228739i | ||||
\(79\) | 59.9499 | − | 34.6121i | 0.758860 | − | 0.438128i | −0.0700264 | − | 0.997545i | \(-0.522308\pi\) |
0.828886 | + | 0.559417i | \(0.188975\pi\) | |||||||
\(80\) | −15.8036 | + | 12.2575i | −0.197545 | + | 0.153218i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −17.1215 | + | 63.8984i | −0.208799 | + | 0.779249i | ||||
\(83\) | 57.0471 | − | 57.0471i | 0.687314 | − | 0.687314i | −0.274323 | − | 0.961638i | \(-0.588454\pi\) |
0.961638 | + | 0.274323i | \(0.0884538\pi\) | |||||||
\(84\) | 17.7470 | − | 16.5241i | 0.211273 | − | 0.196715i | ||||
\(85\) | −36.4805 | − | 86.7944i | −0.429183 | − | 1.02111i | ||||
\(86\) | −37.3270 | − | 64.6523i | −0.434035 | − | 0.751771i | ||||
\(87\) | −46.4686 | + | 12.4512i | −0.534122 | + | 0.143117i | ||||
\(88\) | 5.24605 | + | 19.5785i | 0.0596143 | + | 0.222483i | ||||
\(89\) | −114.055 | + | 65.8494i | −1.28151 | + | 0.739881i | −0.977125 | − | 0.212667i | \(-0.931785\pi\) |
−0.304387 | + | 0.952548i | \(0.598452\pi\) | |||||||
\(90\) | 19.5560 | − | 8.21960i | 0.217289 | − | 0.0913288i | ||||
\(91\) | 70.2705 | − | 16.1670i | 0.772203 | − | 0.177659i | ||||
\(92\) | −0.588560 | − | 0.588560i | −0.00639739 | − | 0.00639739i | ||||
\(93\) | 41.9147 | + | 11.2310i | 0.450696 | + | 0.120764i | ||||
\(94\) | 39.4099 | + | 22.7533i | 0.419254 | + | 0.242056i | ||||
\(95\) | −27.0882 | − | 34.9250i | −0.285139 | − | 0.367632i | ||||
\(96\) | −4.89898 | − | 8.48528i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −46.0520 | − | 46.0520i | −0.474763 | − | 0.474763i | 0.428689 | − | 0.903452i | \(-0.358976\pi\) |
−0.903452 | + | 0.428689i | \(0.858976\pi\) | |||||||
\(98\) | −68.0433 | + | 13.1189i | −0.694320 | + | 0.133867i | ||||
\(99\) | − | 21.4987i | − | 0.217159i | ||||||
\(100\) | 48.4281 | + | 12.4387i | 0.484281 | + | 0.124387i | ||||
\(101\) | −34.0993 | + | 59.0617i | −0.337617 | + | 0.584769i | −0.983984 | − | 0.178257i | \(-0.942954\pi\) |
0.646367 | + | 0.763027i | \(0.276287\pi\) | |||||||
\(102\) | 44.5519 | − | 11.9377i | 0.436784 | − | 0.117036i | ||||
\(103\) | −134.155 | − | 35.9466i | −1.30247 | − | 0.348996i | −0.460087 | − | 0.887874i | \(-0.652182\pi\) |
−0.842384 | + | 0.538877i | \(0.818849\pi\) | |||||||
\(104\) | − | 29.1353i | − | 0.280147i | ||||||
\(105\) | −59.8341 | − | 9.74038i | −0.569849 | − | 0.0927655i | ||||
\(106\) | −100.788 | −0.950833 | ||||||||
\(107\) | 11.0299 | − | 41.1642i | 0.103083 | − | 0.384712i | −0.895037 | − | 0.445991i | \(-0.852851\pi\) |
0.998121 | + | 0.0612792i | \(0.0195180\pi\) | |||||||
\(108\) | 2.68973 | + | 10.0382i | 0.0249049 | + | 0.0929463i | ||||
\(109\) | 149.701 | + | 86.4300i | 1.37341 | + | 0.792936i | 0.991355 | − | 0.131205i | \(-0.0418847\pi\) |
0.382050 | + | 0.924141i | \(0.375218\pi\) | |||||||
\(110\) | 30.6386 | − | 40.3612i | 0.278533 | − | 0.366920i | ||||
\(111\) | 92.4731 | 0.833091 | ||||||||
\(112\) | −0.998461 | + | 27.9822i | −0.00891483 | + | 0.249841i | ||||
\(113\) | −2.87483 | + | 2.87483i | −0.0254409 | + | 0.0254409i | −0.719713 | − | 0.694272i | \(-0.755727\pi\) |
0.694272 | + | 0.719713i | \(0.255727\pi\) | |||||||
\(114\) | 18.7519 | − | 10.8264i | 0.164491 | − | 0.0949687i | ||||
\(115\) | −0.260893 | + | 2.06445i | −0.00226863 | + | 0.0179518i | ||||
\(116\) | 27.7751 | − | 48.1078i | 0.239440 | − | 0.414723i | ||||
\(117\) | −7.99820 | + | 29.8497i | −0.0683607 | + | 0.255126i | ||||
\(118\) | −40.7092 | + | 40.7092i | −0.344993 | + | 0.344993i | ||||
\(119\) | −126.020 | − | 38.6331i | −1.05899 | − | 0.324648i | ||||
\(120\) | −9.25616 | + | 22.6787i | −0.0771347 | + | 0.188989i | ||||
\(121\) | 34.8225 | + | 60.3143i | 0.287789 | + | 0.498465i | ||||
\(122\) | −9.02549 | + | 2.41837i | −0.0739794 | + | 0.0198227i | ||||
\(123\) | 20.9695 | + | 78.2592i | 0.170484 | + | 0.636254i | ||||
\(124\) | −43.3933 | + | 25.0531i | −0.349946 | + | 0.202041i | ||||
\(125\) | −49.6285 | − | 114.726i | −0.397028 | − | 0.917806i | ||||
\(126\) | 8.70459 | − | 28.3942i | 0.0690840 | − | 0.225351i | ||||
\(127\) | −17.1629 | − | 17.1629i | −0.135141 | − | 0.135141i | 0.636300 | − | 0.771441i | \(-0.280464\pi\) |
−0.771441 | + | 0.636300i | \(0.780464\pi\) | |||||||
\(128\) | 10.9282 | + | 2.92820i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | −79.1826 | − | 45.7161i | −0.613818 | − | 0.354388i | ||||
\(130\) | −57.5555 | + | 44.6406i | −0.442734 | + | 0.343389i | ||||
\(131\) | −63.5362 | − | 110.048i | −0.485010 | − | 0.840061i | 0.514842 | − | 0.857285i | \(-0.327851\pi\) |
−0.999852 | + | 0.0172239i | \(0.994517\pi\) | |||||||
\(132\) | 17.5536 | + | 17.5536i | 0.132982 | + | 0.132982i | ||||
\(133\) | −61.8389 | − | 2.20653i | −0.464954 | − | 0.0165905i | ||||
\(134\) | 188.429i | 1.40618i | ||||||||
\(135\) | 15.7088 | − | 20.6938i | 0.116362 | − | 0.153287i | ||||
\(136\) | −26.6294 | + | 46.1236i | −0.195805 | + | 0.339144i | ||||
\(137\) | −90.9671 | + | 24.3746i | −0.663994 | + | 0.177917i | −0.575048 | − | 0.818120i | \(-0.695017\pi\) |
−0.0889460 | + | 0.996036i | \(0.528350\pi\) | |||||||
\(138\) | −0.984680 | − | 0.263844i | −0.00713536 | − | 0.00191191i | ||||
\(139\) | − | 91.9640i | − | 0.661612i | −0.943699 | − | 0.330806i | \(-0.892679\pi\) | ||
0.943699 | − | 0.330806i | \(-0.107321\pi\) | |||||||
\(140\) | 56.8074 | − | 40.9014i | 0.405767 | − | 0.292153i | ||||
\(141\) | 55.7340 | 0.395276 | ||||||||
\(142\) | −47.5356 | + | 177.405i | −0.334758 | + | 1.24933i | ||||
\(143\) | 19.1057 | + | 71.3034i | 0.133606 | + | 0.498625i | ||||
\(144\) | −10.3923 | − | 6.00000i | −0.0721688 | − | 0.0416667i | ||||
\(145\) | −137.591 | + | 18.8416i | −0.948905 | + | 0.129942i | ||||
\(146\) | −11.5037 | −0.0787926 | ||||||||
\(147\) | −64.1372 | + | 55.5826i | −0.436307 | + | 0.378113i | ||||
\(148\) | −75.5040 | + | 75.5040i | −0.510162 | + | 0.510162i | ||||
\(149\) | −45.8944 | + | 26.4971i | −0.308016 | + | 0.177833i | −0.646038 | − | 0.763305i | \(-0.723575\pi\) |
0.338022 | + | 0.941138i | \(0.390242\pi\) | |||||||
\(150\) | 58.9829 | − | 16.4628i | 0.393219 | − | 0.109752i | ||||
\(151\) | −12.0722 | + | 20.9097i | −0.0799483 | + | 0.138475i | −0.903227 | − | 0.429162i | \(-0.858809\pi\) |
0.823279 | + | 0.567637i | \(0.192142\pi\) | |||||||
\(152\) | −6.47114 | + | 24.1506i | −0.0425733 | + | 0.158886i | ||||
\(153\) | 39.9442 | − | 39.9442i | 0.261073 | − | 0.261073i | ||||
\(154\) | −15.9060 | − | 69.1361i | −0.103285 | − | 0.448935i | ||||
\(155\) | 115.978 | + | 47.3355i | 0.748244 | + | 0.305391i | ||||
\(156\) | −17.8417 | − | 30.9027i | −0.114370 | − | 0.198094i | ||||
\(157\) | −169.047 | + | 45.2960i | −1.07673 | + | 0.288510i | −0.753257 | − | 0.657727i | \(-0.771518\pi\) |
−0.323476 | + | 0.946236i | \(0.604852\pi\) | |||||||
\(158\) | 25.3378 | + | 94.5620i | 0.160366 | + | 0.598494i | ||||
\(159\) | −106.902 | + | 61.7200i | −0.672340 | + | 0.388176i | ||||
\(160\) | −10.9595 | − | 26.0747i | −0.0684966 | − | 0.162967i | ||||
\(161\) | 1.98519 | + | 2.13211i | 0.0123304 | + | 0.0132429i | ||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 240.830 | + | 64.5303i | 1.47749 | + | 0.395891i | 0.905491 | − | 0.424366i | \(-0.139503\pi\) |
0.571995 | + | 0.820257i | \(0.306170\pi\) | |||||||
\(164\) | −81.0199 | − | 46.7769i | −0.494024 | − | 0.285225i | ||||
\(165\) | 7.78105 | − | 61.5718i | 0.0471579 | − | 0.373162i | ||||
\(166\) | 57.0471 | + | 98.8085i | 0.343657 | + | 0.595232i | ||||
\(167\) | −186.515 | − | 186.515i | −1.11686 | − | 1.11686i | −0.992200 | − | 0.124657i | \(-0.960217\pi\) |
−0.124657 | − | 0.992200i | \(-0.539783\pi\) | |||||||
\(168\) | 16.0765 | + | 30.2910i | 0.0956934 | + | 0.180304i | ||||
\(169\) | 62.8917i | 0.372140i | ||||||||
\(170\) | 131.916 | − | 18.0644i | 0.775977 | − | 0.106261i | ||||
\(171\) | 13.2596 | − | 22.9663i | 0.0775416 | − | 0.134306i | ||||
\(172\) | 101.979 | − | 27.3253i | 0.592903 | − | 0.158868i | ||||
\(173\) | 135.491 | + | 36.3047i | 0.783185 | + | 0.209854i | 0.628189 | − | 0.778061i | \(-0.283797\pi\) |
0.154997 | + | 0.987915i | \(0.450463\pi\) | |||||||
\(174\) | − | 68.0347i | − | 0.391004i | ||||||
\(175\) | −167.838 | − | 49.5520i | −0.959074 | − | 0.283154i | ||||
\(176\) | −28.6650 | −0.162869 | ||||||||
\(177\) | −18.2494 | + | 68.1078i | −0.103104 | + | 0.384790i | ||||
\(178\) | −48.2051 | − | 179.904i | −0.270815 | − | 1.01070i | ||||
\(179\) | −191.781 | − | 110.725i | −1.07140 | − | 0.618573i | −0.142836 | − | 0.989746i | \(-0.545622\pi\) |
−0.928564 | + | 0.371173i | \(0.878956\pi\) | |||||||
\(180\) | 4.07017 | + | 29.7226i | 0.0226121 | + | 0.165126i | ||||
\(181\) | 149.607 | 0.826556 | 0.413278 | − | 0.910605i | \(-0.364384\pi\) | ||||
0.413278 | + | 0.910605i | \(0.364384\pi\) | |||||||
\(182\) | −3.63631 | + | 101.909i | −0.0199797 | + | 0.559938i | ||||
\(183\) | −8.09203 | + | 8.09203i | −0.0442187 | + | 0.0442187i | ||||
\(184\) | 1.01942 | − | 0.588560i | 0.00554030 | − | 0.00319870i | ||||
\(185\) | 264.840 | + | 33.4688i | 1.43157 | + | 0.180913i | ||||
\(186\) | −30.6837 | + | 53.1457i | −0.164966 | + | 0.285730i | ||||
\(187\) | 34.9249 | − | 130.341i | 0.186764 | − | 0.697013i | ||||
\(188\) | −45.5066 | + | 45.5066i | −0.242056 | + | 0.242056i | ||||
\(189\) | −8.15521 | − | 35.4470i | −0.0431493 | − | 0.187550i | ||||
\(190\) | 57.6234 | − | 24.2197i | 0.303281 | − | 0.127472i | ||||
\(191\) | −142.890 | − | 247.493i | −0.748116 | − | 1.29578i | −0.948725 | − | 0.316104i | \(-0.897625\pi\) |
0.200608 | − | 0.979672i | \(-0.435708\pi\) | |||||||
\(192\) | 13.3843 | − | 3.58630i | 0.0697097 | − | 0.0186787i | ||||
\(193\) | −61.1833 | − | 228.339i | −0.317012 | − | 1.18310i | −0.922102 | − | 0.386947i | \(-0.873529\pi\) |
0.605090 | − | 0.796157i | \(-0.293137\pi\) | |||||||
\(194\) | 79.7644 | − | 46.0520i | 0.411157 | − | 0.237382i | ||||
\(195\) | −33.7101 | + | 82.5939i | −0.172873 | + | 0.423558i | ||||
\(196\) | 6.98478 | − | 97.7508i | 0.0356366 | − | 0.498728i | ||||
\(197\) | −72.1108 | − | 72.1108i | −0.366045 | − | 0.366045i | 0.499988 | − | 0.866032i | \(-0.333338\pi\) |
−0.866032 | + | 0.499988i | \(0.833338\pi\) | |||||||
\(198\) | 29.3678 | + | 7.86908i | 0.148322 | + | 0.0397428i | ||||
\(199\) | 248.372 | + | 143.398i | 1.24810 | + | 0.720592i | 0.970731 | − | 0.240171i | \(-0.0772035\pi\) |
0.277371 | + | 0.960763i | \(0.410537\pi\) | |||||||
\(200\) | −34.7175 | + | 61.6011i | −0.173587 | + | 0.308005i | ||||
\(201\) | 115.389 | + | 199.859i | 0.574072 | + | 0.994322i | ||||
\(202\) | −68.1986 | − | 68.1986i | −0.337617 | − | 0.337617i | ||||
\(203\) | −103.155 | + | 164.804i | −0.508153 | + | 0.811841i | ||||
\(204\) | 65.2286i | 0.319748i | ||||||||
\(205\) | 31.7317 | + | 231.722i | 0.154789 | + | 1.13035i | ||||
\(206\) | 98.2080 | − | 170.101i | 0.476738 | − | 0.825734i | ||||
\(207\) | −1.20598 | + | 0.323142i | −0.00582600 | + | 0.00156107i | ||||
\(208\) | 39.7996 | + | 10.6643i | 0.191344 | + | 0.0512705i | ||||
\(209\) | − | 63.3478i | − | 0.303099i | ||||||
\(210\) | 35.2064 | − | 78.1697i | 0.167650 | − | 0.372237i | ||||
\(211\) | 293.048 | 1.38885 | 0.694427 | − | 0.719563i | \(-0.255658\pi\) | ||||
0.694427 | + | 0.719563i | \(0.255658\pi\) | |||||||
\(212\) | 36.8911 | − | 137.679i | 0.174015 | − | 0.649431i | ||||
\(213\) | 58.2190 | + | 217.276i | 0.273329 | + | 1.02008i | ||||
\(214\) | 52.1941 | + | 30.1343i | 0.243897 | + | 0.140814i | ||||
\(215\) | −210.231 | − | 159.588i | −0.977817 | − | 0.742271i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 154.907 | − | 82.2144i | 0.713856 | − | 0.378868i | ||||
\(218\) | −172.860 | + | 172.860i | −0.792936 | + | 0.792936i | ||||
\(219\) | −12.2015 | + | 7.04456i | −0.0557148 | + | 0.0321670i | ||||
\(220\) | 43.9199 | + | 56.6263i | 0.199636 | + | 0.257392i | ||||
\(221\) | −96.9822 | + | 167.978i | −0.438833 | + | 0.760082i | ||||
\(222\) | −33.8475 | + | 126.321i | −0.152466 | + | 0.569012i | ||||
\(223\) | 166.941 | − | 166.941i | 0.748615 | − | 0.748615i | −0.225604 | − | 0.974219i | \(-0.572436\pi\) |
0.974219 | + | 0.225604i | \(0.0724356\pi\) | |||||||
\(224\) | −37.8589 | − | 11.6061i | −0.169013 | − | 0.0518130i | ||||
\(225\) | 52.4794 | − | 53.5809i | 0.233242 | − | 0.238137i | ||||
\(226\) | −2.87483 | − | 4.97934i | −0.0127205 | − | 0.0220325i | ||||
\(227\) | 294.427 | − | 78.8916i | 1.29704 | − | 0.347540i | 0.456708 | − | 0.889617i | \(-0.349028\pi\) |
0.840329 | + | 0.542076i | \(0.182362\pi\) | |||||||
\(228\) | 7.92550 | + | 29.5784i | 0.0347610 | + | 0.129730i | ||||
\(229\) | −194.928 | + | 112.542i | −0.851213 | + | 0.491448i | −0.861060 | − | 0.508503i | \(-0.830199\pi\) |
0.00984691 | + | 0.999952i | \(0.496866\pi\) | |||||||
\(230\) | −2.72460 | − | 1.11203i | −0.0118461 | − | 0.00483491i | ||||
\(231\) | −59.2078 | − | 63.5895i | −0.256311 | − | 0.275279i | ||||
\(232\) | 55.5501 | + | 55.5501i | 0.239440 | + | 0.239440i | ||||
\(233\) | 97.8963 | + | 26.2312i | 0.420156 | + | 0.112580i | 0.462702 | − | 0.886514i | \(-0.346880\pi\) |
−0.0425458 | + | 0.999095i | \(0.513547\pi\) | |||||||
\(234\) | −37.8479 | − | 21.8515i | −0.161743 | − | 0.0933824i | ||||
\(235\) | 159.621 | + | 20.1718i | 0.679236 | + | 0.0858375i | ||||
\(236\) | −40.7092 | − | 70.5104i | −0.172497 | − | 0.298773i | ||||
\(237\) | 84.7820 | + | 84.7820i | 0.357730 | + | 0.357730i | ||||
\(238\) | 98.9003 | − | 158.006i | 0.415548 | − | 0.663892i | ||||
\(239\) | 191.422i | 0.800927i | 0.916313 | + | 0.400464i | \(0.131151\pi\) | ||||
−0.916313 | + | 0.400464i | \(0.868849\pi\) | |||||||
\(240\) | −27.5917 | − | 20.9451i | −0.114965 | − | 0.0872714i | ||||
\(241\) | −134.250 | + | 232.528i | −0.557054 | + | 0.964846i | 0.440687 | + | 0.897661i | \(0.354735\pi\) |
−0.997741 | + | 0.0671848i | \(0.978598\pi\) | |||||||
\(242\) | −95.1368 | + | 25.4918i | −0.393127 | + | 0.105338i | ||||
\(243\) | 15.0573 | + | 4.03459i | 0.0619642 | + | 0.0166032i | ||||
\(244\) | − | 13.2142i | − | 0.0541567i | ||||||
\(245\) | −203.804 | + | 135.974i | −0.831854 | + | 0.554995i | ||||
\(246\) | −114.579 | −0.465770 | ||||||||
\(247\) | −23.5673 | + | 87.9545i | −0.0954144 | + | 0.356091i | ||||
\(248\) | −18.3402 | − | 68.4465i | −0.0739523 | − | 0.275994i | ||||
\(249\) | 121.015 | + | 69.8681i | 0.486005 | + | 0.280595i | ||||
\(250\) | 174.884 | − | 25.8012i | 0.699535 | − | 0.103205i | ||||
\(251\) | −314.645 | −1.25357 | −0.626784 | − | 0.779193i | \(-0.715629\pi\) | ||||
−0.626784 | + | 0.779193i | \(0.715629\pi\) | |||||||
\(252\) | 35.6011 | + | 22.2837i | 0.141274 | + | 0.0884273i | ||||
\(253\) | −2.10888 | + | 2.10888i | −0.00833550 | + | 0.00833550i | ||||
\(254\) | 29.7271 | − | 17.1629i | 0.117036 | − | 0.0675706i | ||||
\(255\) | 128.856 | − | 99.9420i | 0.505318 | − | 0.391929i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 96.6597 | − | 360.739i | 0.376108 | − | 1.40365i | −0.475612 | − | 0.879655i | \(-0.657773\pi\) |
0.851720 | − | 0.523998i | \(-0.175560\pi\) | |||||||
\(258\) | 91.4321 | − | 91.4321i | 0.354388 | − | 0.354388i | ||||
\(259\) | 273.519 | − | 254.672i | 1.05606 | − | 0.983291i | ||||
\(260\) | −39.9134 | − | 94.9618i | −0.153513 | − | 0.365238i | ||||
\(261\) | −41.6626 | − | 72.1617i | −0.159627 | − | 0.276482i | ||||
\(262\) | 173.584 | − | 46.5118i | 0.662535 | − | 0.177526i | ||||
\(263\) | 6.68028 | + | 24.9311i | 0.0254003 | + | 0.0947952i | 0.977462 | − | 0.211110i | \(-0.0677077\pi\) |
−0.952062 | + | 0.305905i | \(0.901041\pi\) | |||||||
\(264\) | −30.4038 | + | 17.5536i | −0.115166 | + | 0.0664911i | ||||
\(265\) | −328.503 | + | 138.073i | −1.23963 | + | 0.521031i | ||||
\(266\) | 25.6488 | − | 83.6658i | 0.0964240 | − | 0.314533i | ||||
\(267\) | −161.297 | − | 161.297i | −0.604110 | − | 0.604110i | ||||
\(268\) | −257.398 | − | 68.9697i | −0.960442 | − | 0.257350i | ||||
\(269\) | 189.173 | + | 109.219i | 0.703246 | + | 0.406020i | 0.808555 | − | 0.588420i | \(-0.200250\pi\) |
−0.105309 | + | 0.994440i | \(0.533583\pi\) | |||||||
\(270\) | 22.5184 | + | 29.0331i | 0.0834014 | + | 0.107530i | ||||
\(271\) | 14.9730 | + | 25.9340i | 0.0552510 | + | 0.0956975i | 0.892328 | − | 0.451387i | \(-0.149071\pi\) |
−0.837077 | + | 0.547085i | \(0.815737\pi\) | |||||||
\(272\) | −53.2589 | − | 53.2589i | −0.195805 | − | 0.195805i | ||||
\(273\) | 58.5492 | + | 110.317i | 0.214466 | + | 0.404093i | ||||
\(274\) | − | 133.185i | − | 0.486077i | ||||||
\(275\) | 44.5694 | − | 173.524i | 0.162071 | − | 0.630995i | ||||
\(276\) | 0.720836 | − | 1.24852i | 0.00261172 | − | 0.00452364i | ||||
\(277\) | 514.112 | − | 137.756i | 1.85600 | − | 0.497314i | 0.856188 | − | 0.516665i | \(-0.172827\pi\) |
0.999813 | + | 0.0193511i | \(0.00616002\pi\) | |||||||
\(278\) | 125.625 | + | 33.6612i | 0.451889 | + | 0.121083i | ||||
\(279\) | 75.1594i | 0.269389i | ||||||||
\(280\) | 35.0794 | + | 92.5712i | 0.125284 | + | 0.330612i | ||||
\(281\) | 69.2961 | 0.246605 | 0.123303 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123303 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(282\) | −20.4000 | + | 76.1340i | −0.0723406 | + | 0.269979i | ||||
\(283\) | −90.7385 | − | 338.641i | −0.320631 | − | 1.19661i | −0.918632 | − | 0.395115i | \(-0.870705\pi\) |
0.598001 | − | 0.801495i | \(-0.295962\pi\) | |||||||
\(284\) | −224.941 | − | 129.870i | −0.792046 | − | 0.457288i | ||||
\(285\) | 46.2874 | − | 60.9759i | 0.162412 | − | 0.213950i | ||||
\(286\) | −104.395 | −0.365019 | ||||||||
\(287\) | 277.551 | + | 173.727i | 0.967078 | + | 0.605320i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 56.7798 | − | 32.7818i | 0.196470 | − | 0.113432i | ||||
\(290\) | 24.6239 | − | 194.850i | 0.0849098 | − | 0.671895i | ||||
\(291\) | 56.4020 | − | 97.6911i | 0.193821 | − | 0.335708i | ||||
\(292\) | 4.21066 | − | 15.7144i | 0.0144201 | − | 0.0538164i | ||||
\(293\) | 371.421 | − | 371.421i | 1.26765 | − | 1.26765i | 0.320351 | − | 0.947299i | \(-0.396199\pi\) |
0.947299 | − | 0.320351i | \(-0.103801\pi\) | |||||||
\(294\) | −52.4514 | − | 107.958i | −0.178406 | − | 0.367203i | ||||
\(295\) | −76.9162 | + | 188.454i | −0.260733 | + | 0.638827i | ||||
\(296\) | −75.5040 | − | 130.777i | −0.255081 | − | 0.441813i | ||||
\(297\) | 35.9681 | − | 9.63762i | 0.121105 | − | 0.0324499i | ||||
\(298\) | −19.3972 | − | 72.3915i | −0.0650914 | − | 0.242924i | ||||
\(299\) | 3.71263 | − | 2.14349i | 0.0124168 | − | 0.00716885i | ||||
\(300\) | 0.899346 | + | 86.5979i | 0.00299782 | + | 0.288660i | ||||
\(301\) | −360.111 | + | 82.8498i | −1.19638 | + | 0.275249i | ||||
\(302\) | −24.1444 | − | 24.1444i | −0.0799483 | − | 0.0799483i | ||||
\(303\) | −114.098 | − | 30.5726i | −0.376563 | − | 0.100900i | ||||
\(304\) | −30.6218 | − | 17.6795i | −0.100730 | − | 0.0581562i | ||||
\(305\) | −26.1041 | + | 20.2466i | −0.0855872 | + | 0.0663823i | ||||
\(306\) | 39.9442 | + | 69.1853i | 0.130536 | + | 0.226096i | ||||
\(307\) | −76.4698 | − | 76.4698i | −0.249087 | − | 0.249087i | 0.571509 | − | 0.820596i | \(-0.306358\pi\) |
−0.820596 | + | 0.571509i | \(0.806358\pi\) | |||||||
\(308\) | 100.264 | + | 3.57761i | 0.325531 | + | 0.0116156i | ||||
\(309\) | − | 240.559i | − | 0.778509i | ||||||
\(310\) | −107.112 | + | 141.103i | −0.345524 | + | 0.455170i | ||||
\(311\) | −104.711 | + | 181.364i | −0.336690 | + | 0.583164i | −0.983808 | − | 0.179226i | \(-0.942641\pi\) |
0.647118 | + | 0.762390i | \(0.275974\pi\) | |||||||
\(312\) | 48.7443 | − | 13.0610i | 0.156232 | − | 0.0418622i | ||||
\(313\) | −284.971 | − | 76.3577i | −0.910450 | − | 0.243954i | −0.226952 | − | 0.973906i | \(-0.572876\pi\) |
−0.683499 | + | 0.729952i | \(0.739543\pi\) | |||||||
\(314\) | − | 247.502i | − | 0.788223i | ||||||
\(315\) | −10.5269 | − | 104.471i | −0.0334189 | − | 0.331654i | ||||
\(316\) | −138.448 | −0.438128 | ||||||||
\(317\) | −161.418 | + | 602.418i | −0.509204 | + | 1.90037i | −0.0809415 | + | 0.996719i | \(0.525793\pi\) |
−0.428262 | + | 0.903655i | \(0.640874\pi\) | |||||||
\(318\) | −45.1822 | − | 168.622i | −0.142082 | − | 0.530258i | ||||
\(319\) | −172.376 | − | 99.5215i | −0.540364 | − | 0.311979i | ||||
\(320\) | 39.6301 | − | 5.42690i | 0.123844 | − | 0.0169591i | ||||
\(321\) | 73.8135 | 0.229949 | ||||||||
\(322\) | −3.63914 | + | 1.93142i | −0.0113017 | + | 0.00599820i | ||||
\(323\) | 117.699 | − | 117.699i | 0.364392 | − | 0.364392i | ||||
\(324\) | −15.5885 | + | 9.00000i | −0.0481125 | + | 0.0277778i | ||||
\(325\) | −126.438 | + | 224.346i | −0.389041 | + | 0.690295i | ||||
\(326\) | −176.300 | + | 305.361i | −0.540797 | + | 0.936689i | ||||
\(327\) | −77.4911 | + | 289.201i | −0.236976 | + | 0.884405i | ||||
\(328\) | 93.5538 | − | 93.5538i | 0.285225 | − | 0.285225i | ||||
\(329\) | 164.851 | − | 153.492i | 0.501068 | − | 0.466542i | ||||
\(330\) | 81.2606 | + | 33.1659i | 0.246244 | + | 0.100503i | ||||
\(331\) | 79.4501 | + | 137.612i | 0.240031 | + | 0.415745i | 0.960723 | − | 0.277510i | \(-0.0895092\pi\) |
−0.720692 | + | 0.693255i | \(0.756176\pi\) | |||||||
\(332\) | −155.856 | + | 41.7614i | −0.469445 | + | 0.125787i | ||||
\(333\) | 41.4546 | + | 154.711i | 0.124488 | + | 0.464596i | ||||
\(334\) | 323.054 | − | 186.515i | 0.967226 | − | 0.558428i | ||||
\(335\) | 258.135 | + | 614.153i | 0.770551 | + | 1.83329i | ||||
\(336\) | −47.2627 | + | 10.8736i | −0.140663 | + | 0.0323620i | ||||
\(337\) | −39.4387 | − | 39.4387i | −0.117029 | − | 0.117029i | 0.646167 | − | 0.763196i | \(-0.276371\pi\) |
−0.763196 | + | 0.646167i | \(0.776371\pi\) | |||||||
\(338\) | −85.9116 | − | 23.0199i | −0.254176 | − | 0.0681064i | ||||
\(339\) | −6.09843 | − | 3.52093i | −0.0179895 | − | 0.0103862i | ||||
\(340\) | −23.6082 | + | 186.813i | −0.0694359 | + | 0.549449i | ||||
\(341\) | 89.7685 | + | 155.484i | 0.263251 | + | 0.455963i | ||||
\(342\) | 26.5192 | + | 26.5192i | 0.0775416 | + | 0.0775416i | ||||
\(343\) | −36.6312 | + | 341.038i | −0.106797 | + | 0.994281i | ||||
\(344\) | 149.308i | 0.434035i | ||||||||
\(345\) | −3.57085 | + | 0.488988i | −0.0103503 | + | 0.00141736i | ||||
\(346\) | −99.1863 | + | 171.796i | −0.286666 | + | 0.496520i | ||||
\(347\) | −282.917 | + | 75.8074i | −0.815323 | + | 0.218465i | −0.642301 | − | 0.766453i | \(-0.722020\pi\) |
−0.173023 | + | 0.984918i | \(0.555353\pi\) | |||||||
\(348\) | 92.9372 | + | 24.9024i | 0.267061 | + | 0.0715587i | ||||
\(349\) | 475.392i | 1.36216i | 0.732211 | + | 0.681078i | \(0.238489\pi\) | ||||
−0.732211 | + | 0.681078i | \(0.761511\pi\) | |||||||
\(350\) | 129.122 | − | 211.134i | 0.368921 | − | 0.603239i | ||||
\(351\) | −53.5250 | −0.152493 | ||||||||
\(352\) | 10.4921 | − | 39.1571i | 0.0298071 | − | 0.111242i | ||||
\(353\) | −149.006 | − | 556.098i | −0.422114 | − | 1.57535i | −0.770147 | − | 0.637867i | \(-0.779817\pi\) |
0.348033 | − | 0.937482i | \(-0.386850\pi\) | |||||||
\(354\) | −86.3573 | − | 49.8584i | −0.243947 | − | 0.140843i | ||||
\(355\) | 88.0988 | + | 643.345i | 0.248166 | + | 1.81224i | ||||
\(356\) | 263.398 | 0.739881 | ||||||||
\(357\) | 8.14102 | − | 228.155i | 0.0228040 | − | 0.639089i | ||||
\(358\) | 221.449 | − | 221.449i | 0.618573 | − | 0.618573i | ||||
\(359\) | 38.5401 | − | 22.2511i | 0.107354 | − | 0.0619808i | −0.445362 | − | 0.895351i | \(-0.646925\pi\) |
0.552716 | + | 0.833370i | \(0.313592\pi\) | |||||||
\(360\) | −42.0916 | − | 5.31927i | −0.116921 | − | 0.0147758i | ||||
\(361\) | −141.429 | + | 244.963i | −0.391771 | + | 0.678568i | ||||
\(362\) | −54.7598 | + | 204.366i | −0.151270 | + | 0.564548i | ||||
\(363\) | −85.2973 | + | 85.2973i | −0.234979 | + | 0.234979i | ||||
\(364\) | −137.879 | − | 42.2685i | −0.378788 | − | 0.116122i | ||||
\(365\) | −37.4945 | + | 15.7593i | −0.102725 | + | 0.0431762i | ||||
\(366\) | −8.09203 | − | 14.0158i | −0.0221094 | − | 0.0382945i | ||||
\(367\) | −359.065 | + | 96.2112i | −0.978379 | + | 0.262156i | −0.712362 | − | 0.701812i | \(-0.752375\pi\) |
−0.266017 | + | 0.963968i | \(0.585708\pi\) | |||||||
\(368\) | 0.430856 | + | 1.60798i | 0.00117080 | + | 0.00436950i | ||||
\(369\) | −121.530 | + | 70.1653i | −0.329349 | + | 0.190150i | ||||
\(370\) | −142.658 | + | 349.528i | −0.385561 | + | 0.944671i | ||||
\(371\) | −146.220 | + | 476.967i | −0.394124 | + | 1.28563i | ||||
\(372\) | −61.3674 | − | 61.3674i | −0.164966 | − | 0.164966i | ||||
\(373\) | −613.473 | − | 164.380i | −1.64470 | − | 0.440696i | −0.686577 | − | 0.727057i | \(-0.740888\pi\) |
−0.958122 | + | 0.286361i | \(0.907554\pi\) | |||||||
\(374\) | 165.266 | + | 95.4165i | 0.441889 | + | 0.255124i | ||||
\(375\) | 169.692 | − | 134.460i | 0.452512 | − | 0.358561i | ||||
\(376\) | −45.5066 | − | 78.8197i | −0.121028 | − | 0.209627i | ||||
\(377\) | 202.309 | + | 202.309i | 0.536628 | + | 0.536628i | ||||
\(378\) | 51.4066 | + | 1.83429i | 0.135996 | + | 0.00485262i | ||||
\(379\) | − | 203.740i | − | 0.537573i | −0.963200 | − | 0.268787i | \(-0.913377\pi\) | ||
0.963200 | − | 0.268787i | \(-0.0866226\pi\) | |||||||
\(380\) | 11.9931 | + | 87.5801i | 0.0315608 | + | 0.230474i | ||||
\(381\) | 21.0202 | − | 36.4081i | 0.0551711 | − | 0.0955592i | ||||
\(382\) | 390.383 | − | 104.603i | 1.02195 | − | 0.273830i | ||||
\(383\) | −134.722 | − | 36.0986i | −0.351754 | − | 0.0942522i | 0.0786154 | − | 0.996905i | \(-0.474950\pi\) |
−0.430370 | + | 0.902653i | \(0.641617\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −146.555 | − | 203.548i | −0.380661 | − | 0.528695i | ||||
\(386\) | 334.312 | 0.866093 | ||||||||
\(387\) | 40.9879 | − | 152.969i | 0.105912 | − | 0.395269i | ||||
\(388\) | 33.7124 | + | 125.816i | 0.0868877 | + | 0.324269i | ||||
\(389\) | −477.792 | − | 275.853i | −1.22826 | − | 0.709134i | −0.261592 | − | 0.965179i | \(-0.584247\pi\) |
−0.966665 | + | 0.256044i | \(0.917581\pi\) | |||||||
\(390\) | −100.487 | − | 76.2804i | −0.257658 | − | 0.195591i | ||||
\(391\) | −7.83651 | −0.0200422 | ||||||||
\(392\) | 130.973 | + | 45.3207i | 0.334116 | + | 0.115614i | ||||
\(393\) | 155.631 | − | 155.631i | 0.396009 | − | 0.396009i | ||||
\(394\) | 124.900 | − | 72.1108i | 0.317004 | − | 0.183022i | ||||
\(395\) | 212.128 | + | 273.498i | 0.537033 | + | 0.692401i | ||||
\(396\) | −21.4987 | + | 37.2369i | −0.0542897 | + | 0.0940326i | ||||
\(397\) | 116.583 | − | 435.093i | 0.293660 | − | 1.09595i | −0.648617 | − | 0.761115i | \(-0.724652\pi\) |
0.942276 | − | 0.334837i | \(-0.108681\pi\) | |||||||
\(398\) | −286.796 | + | 286.796i | −0.720592 | + | 0.720592i | ||||
\(399\) | −24.0300 | − | 104.448i | −0.0602256 | − | 0.261773i | ||||
\(400\) | −71.4412 | − | 69.9726i | −0.178603 | − | 0.174931i | ||||
\(401\) | −228.287 | − | 395.405i | −0.569295 | − | 0.986048i | −0.996636 | − | 0.0819577i | \(-0.973883\pi\) |
0.427340 | − | 0.904091i | \(-0.359451\pi\) | |||||||
\(402\) | −315.247 | + | 84.4703i | −0.784197 | + | 0.210125i | ||||
\(403\) | −66.7933 | − | 249.276i | −0.165740 | − | 0.618551i | ||||
\(404\) | 118.123 | − | 68.1986i | 0.292385 | − | 0.168808i | ||||
\(405\) | 41.6634 | + | 17.0046i | 0.102873 | + | 0.0419868i | ||||
\(406\) | −187.369 | − | 201.235i | −0.461499 | − | 0.495652i | ||||
\(407\) | 270.540 | + | 270.540i | 0.664717 | + | 0.664717i | ||||
\(408\) | −89.1039 | − | 23.8753i | −0.218392 | − | 0.0585179i | ||||
\(409\) | −502.237 | − | 289.967i | −1.22796 | − | 0.708965i | −0.261361 | − | 0.965241i | \(-0.584171\pi\) |
−0.966604 | + | 0.256276i | \(0.917504\pi\) | |||||||
\(410\) | −328.153 | − | 41.4698i | −0.800372 | − | 0.101146i | ||||
\(411\) | −81.5589 | − | 141.264i | −0.198440 | − | 0.343708i | ||||
\(412\) | 196.416 | + | 196.416i | 0.476738 | + | 0.476738i | ||||
\(413\) | 133.591 | + | 251.710i | 0.323466 | + | 0.609468i | ||||
\(414\) | − | 1.76568i | − | 0.00426493i | ||||||
\(415\) | 321.297 | + | 243.900i | 0.774209 | + | 0.587710i | ||||
\(416\) | −29.1353 | + | 50.4638i | −0.0700368 | + | 0.121307i | ||||
\(417\) | 153.859 | − | 41.2263i | 0.368966 | − | 0.0988641i | ||||
\(418\) | 86.5347 | + | 23.1869i | 0.207021 | + | 0.0554710i | ||||
\(419\) | − | 466.412i | − | 1.11315i | −0.830796 | − | 0.556577i | \(-0.812114\pi\) | ||
0.830796 | − | 0.556577i | \(-0.187886\pi\) | |||||||
\(420\) | 93.8954 | + | 76.7050i | 0.223560 | + | 0.182631i | ||||
\(421\) | −8.56578 | −0.0203463 | −0.0101731 | − | 0.999948i | \(-0.503238\pi\) | ||||
−0.0101731 | + | 0.999948i | \(0.503238\pi\) | |||||||
\(422\) | −107.263 | + | 400.311i | −0.254178 | + | 0.948605i | ||||
\(423\) | 24.9849 | + | 93.2447i | 0.0590658 | + | 0.220437i | ||||
\(424\) | 174.570 | + | 100.788i | 0.411723 | + | 0.237708i | ||||
\(425\) | 405.212 | − | 239.594i | 0.953440 | − | 0.563751i | ||||
\(426\) | −318.115 | −0.746748 | ||||||||
\(427\) | −1.64924 | + | 46.2204i | −0.00386238 | + | 0.108244i | ||||
\(428\) | −60.2685 | + | 60.2685i | −0.140814 | + | 0.140814i | ||||
\(429\) | −110.728 | + | 63.9289i | −0.258107 | + | 0.149018i | ||||
\(430\) | 294.951 | − | 228.767i | 0.685933 | − | 0.532016i | ||||
\(431\) | −70.0856 | + | 121.392i | −0.162612 | + | 0.281652i | −0.935805 | − | 0.352519i | \(-0.885325\pi\) |
0.773193 | + | 0.634171i | \(0.218658\pi\) | |||||||
\(432\) | 5.37945 | − | 20.0764i | 0.0124524 | − | 0.0464731i | ||||
\(433\) | 20.7110 | − | 20.7110i | 0.0478314 | − | 0.0478314i | −0.682787 | − | 0.730618i | \(-0.739232\pi\) |
0.730618 | + | 0.682787i | \(0.239232\pi\) | |||||||
\(434\) | 55.6071 | + | 241.699i | 0.128127 | + | 0.556911i | ||||
\(435\) | −93.2030 | − | 221.748i | −0.214260 | − | 0.509766i | ||||
\(436\) | −172.860 | − | 299.402i | −0.396468 | − | 0.686703i | ||||
\(437\) | −3.55352 | + | 0.952164i | −0.00813164 | + | 0.00217887i | ||||
\(438\) | −5.15698 | − | 19.2461i | −0.0117739 | − | 0.0439409i | ||||
\(439\) | −262.272 | + | 151.423i | −0.597430 | + | 0.344926i | −0.768030 | − | 0.640414i | \(-0.778763\pi\) |
0.170600 | + | 0.985340i | \(0.445429\pi\) | |||||||
\(440\) | −93.4288 | + | 39.2691i | −0.212338 | + | 0.0892479i | ||||
\(441\) | −121.743 | − | 82.3866i | −0.276062 | − | 0.186818i | ||||
\(442\) | −193.964 | − | 193.964i | −0.438833 | − | 0.438833i | ||||
\(443\) | 557.570 | + | 149.400i | 1.25862 | + | 0.337247i | 0.825661 | − | 0.564166i | \(-0.190802\pi\) |
0.432961 | + | 0.901413i | \(0.357469\pi\) | |||||||
\(444\) | −160.168 | − | 92.4731i | −0.360739 | − | 0.208273i | ||||
\(445\) | −403.573 | − | 520.330i | −0.906906 | − | 1.16928i | ||||
\(446\) | 166.941 | + | 289.151i | 0.374307 | + | 0.648320i | ||||
\(447\) | −64.9044 | − | 64.9044i | −0.145200 | − | 0.145200i | ||||
\(448\) | 29.7116 | − | 47.4681i | 0.0663205 | − | 0.105956i | ||||
\(449\) | − | 31.4156i | − | 0.0699679i | −0.999388 | − | 0.0349840i | \(-0.988862\pi\) | ||
0.999388 | − | 0.0349840i | \(-0.0111380\pi\) | |||||||
\(450\) | 53.9840 | + | 91.3002i | 0.119965 | + | 0.202889i | ||||
\(451\) | −167.607 | + | 290.304i | −0.371635 | + | 0.643690i | ||||
\(452\) | 7.85417 | − | 2.10452i | 0.0173765 | − | 0.00465601i | ||||
\(453\) | −40.3943 | − | 10.8236i | −0.0891707 | − | 0.0238932i | ||||
\(454\) | 431.072i | 0.949497i | ||||||||
\(455\) | 127.756 | + | 337.137i | 0.280783 | + | 0.740960i | ||||
\(456\) | −43.3057 | −0.0949687 | ||||||||
\(457\) | −73.5073 | + | 274.333i | −0.160848 | + | 0.600291i | 0.837686 | + | 0.546152i | \(0.183908\pi\) |
−0.998533 | + | 0.0541389i | \(0.982759\pi\) | |||||||
\(458\) | −82.3862 | − | 307.469i | −0.179882 | − | 0.671331i | ||||
\(459\) | 84.7344 | + | 48.9214i | 0.184606 | + | 0.106583i | ||||
\(460\) | 2.51633 | − | 3.31485i | 0.00547029 | − | 0.00720619i | ||||
\(461\) | −8.38183 | −0.0181818 | −0.00909092 | − | 0.999959i | \(-0.502894\pi\) | ||||
−0.00909092 | + | 0.999959i | \(0.502894\pi\) | |||||||
\(462\) | 108.536 | − | 57.6040i | 0.234927 | − | 0.124684i | ||||
\(463\) | −59.5826 | + | 59.5826i | −0.128688 | + | 0.128688i | −0.768517 | − | 0.639829i | \(-0.779005\pi\) |
0.639829 | + | 0.768517i | \(0.279005\pi\) | |||||||
\(464\) | −96.2157 | + | 55.5501i | −0.207361 | + | 0.119720i | ||||
\(465\) | −27.2025 | + | 215.255i | −0.0585000 | + | 0.462913i | ||||
\(466\) | −71.6651 | + | 124.128i | −0.153788 | + | 0.266368i | ||||
\(467\) | 126.941 | − | 473.750i | 0.271822 | − | 1.01445i | −0.686119 | − | 0.727489i | \(-0.740687\pi\) |
0.957941 | − | 0.286964i | \(-0.0926461\pi\) | |||||||
\(468\) | 43.7030 | − | 43.7030i | 0.0933824 | − | 0.0933824i | ||||
\(469\) | 891.713 | + | 273.366i | 1.90131 | + | 0.582869i | ||||
\(470\) | −85.9804 | + | 210.662i | −0.182937 | + | 0.448218i | ||||
\(471\) | −151.563 | − | 262.516i | −0.321791 | − | 0.557358i | ||||
\(472\) | 111.220 | − | 29.8012i | 0.235635 | − | 0.0631381i | ||||
\(473\) | −97.9098 | − | 365.404i | −0.206997 | − | 0.772525i | ||||
\(474\) | −146.847 | + | 84.7820i | −0.309803 | + | 0.178865i | ||||
\(475\) | 154.635 | − | 157.880i | 0.325547 | − | 0.332380i | ||||
\(476\) | 179.640 | + | 192.935i | 0.377396 | + | 0.405325i | ||||
\(477\) | −151.182 | − | 151.182i | −0.316944 | − | 0.316944i | ||||
\(478\) | −261.487 | − | 70.0652i | −0.547044 | − | 0.146580i | ||||
\(479\) | −395.262 | − | 228.205i | −0.825183 | − | 0.476419i | 0.0270178 | − | 0.999635i | \(-0.491399\pi\) |
−0.852200 | + | 0.523216i | \(0.824732\pi\) | |||||||
\(480\) | 38.7108 | − | 30.0245i | 0.0806476 | − | 0.0625511i | ||||
\(481\) | −274.979 | − | 476.278i | −0.571682 | − | 0.990182i | ||||
\(482\) | −268.500 | − | 268.500i | −0.557054 | − | 0.557054i | ||||
\(483\) | −2.67715 | + | 4.27709i | −0.00554275 | + | 0.00885526i | ||||
\(484\) | − | 139.290i | − | 0.287789i | ||||||
\(485\) | 196.891 | − | 259.371i | 0.405961 | − | 0.534786i | ||||
\(486\) | −11.0227 | + | 19.0919i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 0.712445 | − | 0.190899i | 0.00146293 | − | 0.000391990i | −0.258088 | − | 0.966122i | \(-0.583092\pi\) |
0.259550 | + | 0.965730i | \(0.416426\pi\) | |||||||
\(488\) | 18.0510 | + | 4.83674i | 0.0369897 | + | 0.00991136i | ||||
\(489\) | 431.845i | 0.883119i | ||||||||
\(490\) | −111.146 | − | 328.171i | −0.226829 | − | 0.669738i | ||||
\(491\) | 335.358 | 0.683010 | 0.341505 | − | 0.939880i | \(-0.389063\pi\) | ||||
0.341505 | + | 0.939880i | \(0.389063\pi\) | |||||||
\(492\) | 41.9390 | − | 156.518i | 0.0852419 | − | 0.318127i | ||||
\(493\) | −135.363 | − | 505.180i | −0.274569 | − | 1.02471i | ||||
\(494\) | −111.522 | − | 64.3872i | −0.225753 | − | 0.130338i | ||||
\(495\) | 106.500 | − | 14.5839i | 0.215151 | − | 0.0294625i | ||||
\(496\) | 100.213 | 0.202041 | ||||||||
\(497\) | 770.584 | + | 482.329i | 1.55047 | + | 0.970482i | ||||
\(498\) | −139.736 | + | 139.736i | −0.280595 | + | 0.280595i | ||||
\(499\) | 530.603 | − | 306.344i | 1.06333 | − | 0.613915i | 0.136980 | − | 0.990574i | \(-0.456260\pi\) |
0.926352 | + | 0.376658i | \(0.122927\pi\) | |||||||
\(500\) | −28.7667 | + | 248.339i | −0.0575334 | + | 0.496679i | ||||
\(501\) | 228.433 | − | 395.658i | 0.455955 | − | 0.789737i | ||||
\(502\) | 115.168 | − | 429.814i | 0.229419 | − | 0.856202i | ||||
\(503\) | −377.103 | + | 377.103i | −0.749707 | + | 0.749707i | −0.974424 | − | 0.224717i | \(-0.927854\pi\) |
0.224717 | + | 0.974424i | \(0.427854\pi\) | |||||||
\(504\) | −43.4710 | + | 40.4756i | −0.0862519 | + | 0.0803087i | ||||
\(505\) | −315.710 | − | 128.855i | −0.625168 | − | 0.255158i | ||||
\(506\) | −2.10888 | − | 3.65269i | −0.00416775 | − | 0.00721876i | ||||
\(507\) | −105.220 | + | 28.1936i | −0.207534 | + | 0.0556086i | ||||
\(508\) | 12.5641 | + | 46.8900i | 0.0247325 | + | 0.0923031i | ||||
\(509\) | 683.042 | − | 394.355i | 1.34193 | − | 0.774764i | 0.354840 | − | 0.934927i | \(-0.384535\pi\) |
0.987091 | + | 0.160163i | \(0.0512021\pi\) | |||||||
\(510\) | 89.3587 | + | 212.602i | 0.175213 | + | 0.416866i | ||||
\(511\) | −16.6892 | + | 54.4398i | −0.0326599 | + | 0.106536i | ||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 44.3675 | + | 11.8882i | 0.0864864 | + | 0.0231740i | ||||
\(514\) | 457.398 | + | 264.079i | 0.889880 | + | 0.513773i | ||||
\(515\) | 87.0658 | − | 688.955i | 0.169060 | − | 1.33778i | ||||
\(516\) | 91.4321 | + | 158.365i | 0.177194 | + | 0.306909i | ||||
\(517\) | 163.056 | + | 163.056i | 0.315388 | + | 0.315388i | ||||
\(518\) | 247.774 | + | 466.851i | 0.478328 | + | 0.901257i | ||||
\(519\) | 242.956i | 0.468123i | ||||||||
\(520\) | 144.330 | − | 19.7643i | 0.277557 | − | 0.0380083i | ||||
\(521\) | −5.25649 | + | 9.10450i | −0.0100892 | + | 0.0174750i | −0.871026 | − | 0.491237i | \(-0.836545\pi\) |
0.860937 | + | 0.508712i | \(0.169878\pi\) | |||||||
\(522\) | 113.824 | − | 30.4991i | 0.218054 | − | 0.0584275i | ||||
\(523\) | 672.226 | + | 180.122i | 1.28533 | + | 0.344402i | 0.835884 | − | 0.548906i | \(-0.184956\pi\) |
0.449444 | + | 0.893309i | \(0.351622\pi\) | |||||||
\(524\) | 254.145i | 0.485010i | ||||||||
\(525\) | 7.66236 | − | 303.012i | 0.0145950 | − | 0.577166i | ||||
\(526\) | −36.5017 | −0.0693949 | ||||||||
\(527\) | −122.097 | + | 455.673i | −0.231683 | + | 0.864654i | ||||
\(528\) | −12.8502 | − | 47.9574i | −0.0243374 | − | 0.0908285i | ||||
\(529\) | −457.977 | − | 264.413i | −0.865742 | − | 0.499836i | ||||
\(530\) | −68.3710 | − | 499.282i | −0.129002 | − | 0.942041i | ||||
\(531\) | −122.128 | −0.229995 | ||||||||
\(532\) | 104.902 | + | 65.6607i | 0.197183 | + | 0.123422i | ||||
\(533\) | 340.715 | − | 340.715i | 0.639240 | − | 0.639240i | ||||
\(534\) | 279.375 | − | 161.297i | 0.523175 | − | 0.302055i | ||||
\(535\) | 211.400 | + | 26.7154i | 0.395140 | + | 0.0499353i | ||||
\(536\) | 188.429 | − | 326.368i | 0.351546 | − | 0.608896i | ||||
\(537\) | 99.2729 | − | 370.492i | 0.184866 | − | 0.689928i | ||||
\(538\) | −218.439 | + | 218.439i | −0.406020 | + | 0.406020i | ||||
\(539\) | −350.253 | − | 25.0273i | −0.649820 | − | 0.0464329i | ||||
\(540\) | −47.9023 | + | 20.1338i | −0.0887079 | + | 0.0372848i | ||||
\(541\) | −370.192 | − | 641.191i | −0.684273 | − | 1.18520i | −0.973665 | − | 0.227985i | \(-0.926786\pi\) |
0.289392 | − | 0.957211i | \(-0.406547\pi\) | |||||||
\(542\) | −40.9070 | + | 10.9610i | −0.0754742 | + | 0.0202233i | ||||
\(543\) | 67.0668 | + | 250.297i | 0.123512 | + | 0.460951i | ||||
\(544\) | 92.2471 | − | 53.2589i | 0.169572 | − | 0.0979024i | ||||
\(545\) | −326.603 | + | 800.216i | −0.599271 | + | 1.46829i | ||||
\(546\) | −172.127 | + | 39.6008i | −0.315251 | + | 0.0725289i | ||||
\(547\) | −452.053 | − | 452.053i | −0.826421 | − | 0.826421i | 0.160598 | − | 0.987020i | \(-0.448658\pi\) |
−0.987020 | + | 0.160598i | \(0.948658\pi\) | |||||||
\(548\) | 181.934 | + | 48.7491i | 0.331997 | + | 0.0889583i | ||||
\(549\) | −17.1658 | − | 9.91067i | −0.0312674 | − | 0.0180522i | ||||
\(550\) | 220.724 | + | 124.397i | 0.401317 | + | 0.226176i | ||||
\(551\) | −122.762 | − | 212.630i | −0.222799 | − | 0.385899i | ||||
\(552\) | 1.44167 | + | 1.44167i | 0.00261172 | + | 0.00261172i | ||||
\(553\) | 484.261 | + | 17.2794i | 0.875698 | + | 0.0312467i | ||||
\(554\) | 752.712i | 1.35869i | ||||||||
\(555\) | 62.7303 | + | 458.090i | 0.113028 | + | 0.825388i | ||||
\(556\) | −91.9640 | + | 159.286i | −0.165403 | + | 0.286486i | ||||
\(557\) | −433.341 | + | 116.113i | −0.777991 | + | 0.208462i | −0.625899 | − | 0.779904i | \(-0.715268\pi\) |
−0.152092 | + | 0.988366i | \(0.548601\pi\) | |||||||
\(558\) | −102.670 | − | 27.5103i | −0.183996 | − | 0.0493015i | ||||
\(559\) | 543.767i | 0.972750i | ||||||||
\(560\) | −139.295 | + | 14.0359i | −0.248740 | + | 0.0250641i | ||||
\(561\) | 233.722 | 0.416616 | ||||||||
\(562\) | −25.3641 | + | 94.6602i | −0.0451319 | + | 0.168435i | ||||
\(563\) | 126.933 | + | 473.720i | 0.225458 | + | 0.841422i | 0.982220 | + | 0.187731i | \(0.0601134\pi\) |
−0.756762 | + | 0.653690i | \(0.773220\pi\) | |||||||
\(564\) | −96.5341 | − | 55.7340i | −0.171160 | − | 0.0988191i | ||||
\(565\) | −16.1914 | − | 12.2910i | −0.0286573 | − | 0.0217541i | ||||
\(566\) | 495.805 | 0.875980 | ||||||||
\(567\) | 55.6482 | − | 29.5344i | 0.0981449 | − | 0.0520889i | ||||
\(568\) | 259.740 | − | 259.740i | 0.457288 | − | 0.457288i | ||||
\(569\) | 489.271 | − | 282.480i | 0.859878 | − | 0.496451i | −0.00409346 | − | 0.999992i | \(-0.501303\pi\) |
0.863971 | + | 0.503541i | \(0.167970\pi\) | |||||||
\(570\) | 66.3522 | + | 85.5485i | 0.116407 | + | 0.150085i | ||||
\(571\) | −54.3972 | + | 94.2188i | −0.0952666 | + | 0.165007i | −0.909720 | − | 0.415223i | \(-0.863704\pi\) |
0.814453 | + | 0.580229i | \(0.197037\pi\) | |||||||
\(572\) | 38.2114 | − | 142.607i | 0.0668031 | − | 0.249313i | ||||
\(573\) | 350.008 | − | 350.008i | 0.610834 | − | 0.610834i | ||||
\(574\) | −338.906 | + | 315.554i | −0.590429 | + | 0.549745i | ||||
\(575\) | −10.4038 | + | 0.108047i | −0.0180936 | + | 0.000187907i | ||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 353.163 | − | 94.6298i | 0.612068 | − | 0.164003i | 0.0605486 | − | 0.998165i | \(-0.480715\pi\) |
0.551519 | + | 0.834162i | \(0.314048\pi\) | |||||||
\(578\) | 23.9980 | + | 89.5616i | 0.0415190 | + | 0.154951i | ||||
\(579\) | 354.591 | − | 204.723i | 0.612420 | − | 0.353581i | ||||
\(580\) | 257.157 | + | 104.957i | 0.443373 | + | 0.180960i | ||||
\(581\) | 550.360 | − | 126.620i | 0.947263 | − | 0.217934i | ||||
\(582\) | 112.804 | + | 112.804i | 0.193821 | + | 0.193821i | ||||
\(583\) | −493.322 | − | 132.185i | −0.846178 | − | 0.226733i | ||||
\(584\) | 19.9250 | + | 11.5037i | 0.0341182 | + | 0.0196982i | ||||
\(585\) | −153.294 | − | 19.3723i | −0.262041 | − | 0.0331151i | ||||
\(586\) | 371.421 | + | 643.321i | 0.633825 | + | 1.09782i | ||||
\(587\) | −488.112 | − | 488.112i | −0.831537 | − | 0.831537i | 0.156190 | − | 0.987727i | \(-0.450079\pi\) |
−0.987727 | + | 0.156190i | \(0.950079\pi\) | |||||||
\(588\) | 166.671 | − | 32.1347i | 0.283455 | − | 0.0546509i | ||||
\(589\) | 221.463i | 0.375999i | ||||||||
\(590\) | −229.280 | − | 174.048i | −0.388609 | − | 0.294997i | ||||
\(591\) | 88.3173 | − | 152.970i | 0.149437 | − | 0.258833i | ||||
\(592\) | 206.281 | − | 55.2727i | 0.348447 | − | 0.0933661i | ||||
\(593\) | 204.070 | + | 54.6805i | 0.344132 | + | 0.0922099i | 0.426745 | − | 0.904372i | \(-0.359660\pi\) |
−0.0826135 | + | 0.996582i | \(0.526327\pi\) | |||||||
\(594\) | 52.6609i | 0.0886547i | ||||||||
\(595\) | 105.892 | − | 650.482i | 0.177969 | − | 1.09325i | ||||
\(596\) | 105.988 | 0.177833 | ||||||||
\(597\) | −128.567 | + | 479.818i | −0.215355 | + | 0.803716i | ||||
\(598\) | 1.56914 | + | 5.85611i | 0.00262398 | + | 0.00979283i | ||||
\(599\) | −245.514 | − | 141.748i | −0.409874 | − | 0.236641i | 0.280862 | − | 0.959748i | \(-0.409380\pi\) |
−0.690735 | + | 0.723108i | \(0.742713\pi\) | |||||||
\(600\) | −118.624 | − | 30.4685i | −0.197707 | − | 0.0507808i | ||||
\(601\) | 685.441 | 1.14050 | 0.570251 | − | 0.821471i | \(-0.306846\pi\) | ||||
0.570251 | + | 0.821471i | \(0.306846\pi\) | |||||||
\(602\) | 18.6348 | − | 522.246i | 0.0309548 | − | 0.867518i | ||||
\(603\) | −282.643 | + | 282.643i | −0.468728 | + | 0.468728i | ||||
\(604\) | 41.8193 | − | 24.1444i | 0.0692373 | − | 0.0399741i | ||||
\(605\) | −275.161 | + | 213.417i | −0.454811 | + | 0.352756i | ||||
\(606\) | 83.5259 | − | 144.671i | 0.137831 | − | 0.238731i | ||||
\(607\) | −267.402 | + | 997.957i | −0.440530 | + | 1.64408i | 0.286945 | + | 0.957947i | \(0.407360\pi\) |
−0.727475 | + | 0.686134i | \(0.759306\pi\) | |||||||
\(608\) | 35.3590 | − | 35.3590i | 0.0581562 | − | 0.0581562i | ||||
\(609\) | −321.965 | − | 98.7024i | −0.528679 | − | 0.162073i | ||||
\(610\) | −18.1026 | − | 43.0696i | −0.0296764 | − | 0.0706060i | ||||
\(611\) | −165.731 | − | 287.055i | −0.271246 | − | 0.469811i | ||||
\(612\) | −109.129 | + | 29.2412i | −0.178316 | + | 0.0477797i | ||||
\(613\) | 161.961 | + | 604.447i | 0.264211 | + | 0.986048i | 0.962732 | + | 0.270458i | \(0.0871751\pi\) |
−0.698521 | + | 0.715589i | \(0.746158\pi\) | |||||||
\(614\) | 132.450 | − | 76.4698i | 0.215716 | − | 0.124544i | ||||
\(615\) | −373.453 | + | 156.966i | −0.607241 | + | 0.255230i | ||||
\(616\) | −41.5861 | + | 135.653i | −0.0675099 | + | 0.220216i | ||||
\(617\) | 230.449 | + | 230.449i | 0.373498 | + | 0.373498i | 0.868750 | − | 0.495251i | \(-0.164924\pi\) |
−0.495251 | + | 0.868750i | \(0.664924\pi\) | |||||||
\(618\) | 328.610 | + | 88.0508i | 0.531732 | + | 0.142477i | ||||
\(619\) | −459.874 | − | 265.509i | −0.742931 | − | 0.428931i | 0.0802030 | − | 0.996779i | \(-0.474443\pi\) |
−0.823134 | + | 0.567847i | \(0.807776\pi\) | |||||||
\(620\) | −153.544 | − | 197.965i | −0.247651 | − | 0.319299i | ||||
\(621\) | −1.08125 | − | 1.87279i | −0.00174115 | − | 0.00301576i | ||||
\(622\) | −209.421 | − | 209.421i | −0.336690 | − | 0.336690i | ||||
\(623\) | −921.305 | − | 32.8740i | −1.47882 | − | 0.0527673i | ||||
\(624\) | 71.3667i | 0.114370i | ||||||||
\(625\) | 534.659 | − | 323.674i | 0.855454 | − | 0.517878i | ||||
\(626\) | 208.613 | − | 361.329i | 0.333248 | − | 0.577202i | ||||
\(627\) | 105.983 | − | 28.3980i | 0.169032 | − | 0.0452919i | ||||
\(628\) | 338.094 | + | 90.5920i | 0.538366 | + | 0.144255i | ||||
\(629\) | 1005.31i | 1.59827i | ||||||||
\(630\) | 146.563 | + | 23.8590i | 0.232640 | + | 0.0378714i | ||||
\(631\) | 545.090 | 0.863852 | 0.431926 | − | 0.901909i | \(-0.357834\pi\) | ||||
0.431926 | + | 0.901909i | \(0.357834\pi\) | |||||||
\(632\) | 50.6756 | − | 189.124i | 0.0801830 | − | 0.299247i | ||||
\(633\) | 131.370 | + | 490.279i | 0.207535 | + | 0.774533i | ||||
\(634\) | −763.836 | − | 441.001i | −1.20479 | − | 0.695585i | ||||
\(635\) | 73.3785 | − | 96.6638i | 0.115557 | − | 0.152226i | ||||
\(636\) | 246.880 | 0.388176 | ||||||||
\(637\) | 476.994 | + | 165.054i | 0.748813 | + | 0.259111i | ||||
\(638\) | 199.043 | − | 199.043i | 0.311979 | − | 0.311979i | ||||
\(639\) | −337.412 | + | 194.805i | −0.528031 | + | 0.304859i | ||||
\(640\) | −7.09236 | + | 56.1222i | −0.0110818 | + | 0.0876909i | ||||
\(641\) | −377.578 | + | 653.985i | −0.589046 | + | 1.02026i | 0.405312 | + | 0.914179i | \(0.367163\pi\) |
−0.994358 | + | 0.106079i | \(0.966170\pi\) | |||||||
\(642\) | −27.0176 | + | 100.831i | −0.0420835 | + | 0.157058i | ||||
\(643\) | −222.457 | + | 222.457i | −0.345967 | + | 0.345967i | −0.858605 | − | 0.512638i | \(-0.828668\pi\) |
0.512638 | + | 0.858605i | \(0.328668\pi\) | |||||||
\(644\) | −1.30635 | − | 5.67811i | −0.00202849 | − | 0.00881694i | ||||
\(645\) | 172.752 | − | 423.264i | 0.267833 | − | 0.656223i | ||||
\(646\) | 117.699 | + | 203.860i | 0.182196 | + | 0.315573i | ||||
\(647\) | −387.467 | + | 103.822i | −0.598867 | + | 0.160466i | −0.545503 | − | 0.838109i | \(-0.683661\pi\) |
−0.0533647 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(648\) | −6.58846 | − | 24.5885i | −0.0101674 | − | 0.0379452i | ||||
\(649\) | −252.647 | + | 145.866i | −0.389287 | + | 0.224755i | ||||
\(650\) | −260.183 | − | 254.834i | −0.400281 | − | 0.392052i | ||||
\(651\) | 206.990 | + | 222.308i | 0.317957 | + | 0.341488i | ||||
\(652\) | −352.600 | − | 352.600i | −0.540797 | − | 0.540797i | ||||
\(653\) | −870.447 | − | 233.236i | −1.33300 | − | 0.357175i | −0.479165 | − | 0.877725i | \(-0.659061\pi\) |
−0.853832 | + | 0.520549i | \(0.825727\pi\) | |||||||
\(654\) | −366.692 | − | 211.709i | −0.560691 | − | 0.323715i | ||||
\(655\) | 502.052 | − | 389.396i | 0.766491 | − | 0.594498i | ||||
\(656\) | 93.5538 | + | 162.040i | 0.142612 | + | 0.247012i | ||||
\(657\) | −17.2556 | − | 17.2556i | −0.0262642 | − | 0.0262642i | ||||
\(658\) | 149.334 | + | 281.373i | 0.226952 | + | 0.427619i | ||||
\(659\) | − | 996.771i | − | 1.51255i | −0.654253 | − | 0.756275i | \(-0.727017\pi\) | ||
0.654253 | − | 0.756275i | \(-0.272983\pi\) | |||||||
\(660\) | −75.0489 | + | 98.8644i | −0.113711 | + | 0.149795i | ||||
\(661\) | 582.202 | − | 1008.40i | 0.880789 | − | 1.52557i | 0.0303238 | − | 0.999540i | \(-0.490346\pi\) |
0.850465 | − | 0.526031i | \(-0.176321\pi\) | |||||||
\(662\) | −217.062 | + | 58.1615i | −0.327888 | + | 0.0878573i | ||||
\(663\) | −324.509 | − | 86.9518i | −0.489455 | − | 0.131149i | ||||
\(664\) | − | 228.188i | − | 0.343657i | ||||||
\(665\) | −31.0185 | − | 307.832i | −0.0466443 | − | 0.462906i | ||||
\(666\) | −226.512 | −0.340108 | ||||||||
\(667\) | −2.99176 | + | 11.1654i | −0.00448540 | + | 0.0167397i | ||||
\(668\) | 136.539 | + | 509.569i | 0.204399 | + | 0.762827i | ||||
\(669\) | 354.136 | + | 204.460i | 0.529351 | + | 0.305621i | ||||
\(670\) | −933.432 | + | 127.823i | −1.39318 | + | 0.190780i | ||||
\(671\) | −47.3482 | −0.0705636 | ||||||||
\(672\) | 2.44572 | − | 68.5421i | 0.00363946 | − | 0.101997i | ||||
\(673\) | −419.133 | + | 419.133i | −0.622783 | + | 0.622783i | −0.946242 | − | 0.323459i | \(-0.895154\pi\) |
0.323459 | + | 0.946242i | \(0.395154\pi\) | |||||||
\(674\) | 68.3098 | − | 39.4387i | 0.101350 | − | 0.0585144i | ||||
\(675\) | 113.168 | + | 63.7801i | 0.167657 | + | 0.0944891i | ||||
\(676\) | 62.8917 | − | 108.932i | 0.0930350 | − | 0.161141i | ||||
\(677\) | 188.771 | − | 704.503i | 0.278834 | − | 1.04062i | −0.674393 | − | 0.738372i | \(-0.735595\pi\) |
0.953228 | − | 0.302252i | \(-0.0977385\pi\) | |||||||
\(678\) | 7.04185 | − | 7.04185i | 0.0103862 | − | 0.0103862i | ||||
\(679\) | −102.216 | − | 444.285i | −0.150538 | − | 0.654323i | ||||
\(680\) | −246.550 | − | 100.628i | −0.362573 | − | 0.147982i | ||||
\(681\) | 263.976 | + | 457.221i | 0.387631 | + | 0.671396i | ||||
\(682\) | −245.252 | + | 65.7151i | −0.359607 | + | 0.0963564i | ||||
\(683\) | 276.981 | + | 1033.71i | 0.405535 | + | 1.51348i | 0.803066 | + | 0.595890i | \(0.203200\pi\) |
−0.397531 | + | 0.917589i | \(0.630133\pi\) | |||||||
\(684\) | −45.9327 | + | 26.5192i | −0.0671530 | + | 0.0387708i | ||||
\(685\) | −182.455 | − | 434.095i | −0.266357 | − | 0.633716i | ||||
\(686\) | −452.459 | − | 174.868i | −0.659561 | − | 0.254909i | ||||
\(687\) | −275.670 | − | 275.670i | −0.401266 | − | 0.401266i | ||||
\(688\) | −203.959 | − | 54.6505i | −0.296451 | − | 0.0794339i | ||||
\(689\) | 635.771 | + | 367.062i | 0.922744 | + | 0.532747i | ||||
\(690\) | 0.639054 | − | 5.05686i | 0.000926165 | − | 0.00732878i | ||||
\(691\) | 490.628 | + | 849.792i | 0.710026 | + | 1.22980i | 0.964847 | + | 0.262812i | \(0.0846500\pi\) |
−0.254821 | + | 0.966988i | \(0.582017\pi\) | |||||||
\(692\) | −198.373 | − | 198.373i | −0.286666 | − | 0.286666i | ||||
\(693\) | 79.8452 | − | 127.563i | 0.115217 | − | 0.184074i | ||||
\(694\) | − | 414.220i | − | 0.596858i | ||||||
\(695\) | 455.568 | − | 62.3849i | 0.655494 | − | 0.0897625i | ||||
\(696\) | −68.0347 | + | 117.840i | −0.0977511 | + | 0.169310i | ||||
\(697\) | −850.790 | + | 227.968i | −1.22064 | + | 0.327071i | ||||
\(698\) | −649.398 | − | 174.006i | −0.930370 | − | 0.249292i | ||||
\(699\) | 175.543i | 0.251134i | ||||||||
\(700\) | 241.152 | + | 253.665i | 0.344503 | + | 0.362378i | ||||
\(701\) | −940.348 | −1.34144 | −0.670719 | − | 0.741711i | \(-0.734014\pi\) | ||||
−0.670719 | + | 0.741711i | \(0.734014\pi\) | |||||||
\(702\) | 19.5915 | − | 73.1165i | 0.0279081 | − | 0.104155i | ||||
\(703\) | 122.149 | + | 455.867i | 0.173754 | + | 0.648460i | ||||
\(704\) | 49.6492 | + | 28.6650i | 0.0705244 | + | 0.0407173i | ||||
\(705\) | 37.8078 | + | 276.093i | 0.0536281 | + | 0.391621i | ||||
\(706\) | 814.184 | 1.15324 | ||||||||
\(707\) | −421.681 | + | 223.801i | −0.596437 | + | 0.316550i | ||||
\(708\) | 99.7168 | − | 99.7168i | 0.140843 | − | 0.140843i | ||||
\(709\) | −364.698 | + | 210.559i | −0.514384 | + | 0.296980i | −0.734634 | − | 0.678464i | \(-0.762646\pi\) |
0.220250 | + | 0.975443i | \(0.429313\pi\) | |||||||
\(710\) | −911.072 | − | 115.135i | −1.28320 | − | 0.162163i | ||||
\(711\) | −103.836 | + | 179.850i | −0.146043 | + | 0.252953i | ||||
\(712\) | −96.4102 | + | 359.808i | −0.135408 | + | 0.505348i | ||||
\(713\) | 7.37264 | − | 7.37264i | 0.0103403 | − | 0.0103403i | ||||
\(714\) | 308.685 | + | 94.6313i | 0.432332 | + | 0.132537i | ||||
\(715\) | −340.260 | + | 143.015i | −0.475888 | + | 0.200020i | ||||
\(716\) | 221.449 | + | 383.561i | 0.309286 | + | 0.535700i | ||||
\(717\) | −320.255 | + | 85.8120i | −0.446659 | + | 0.119682i | ||||
\(718\) | 16.2889 | + | 60.7912i | 0.0226865 | + | 0.0846674i | ||||
\(719\) | −331.576 | + | 191.436i | −0.461163 | + | 0.266253i | −0.712533 | − | 0.701638i | \(-0.752452\pi\) |
0.251370 | + | 0.967891i | \(0.419119\pi\) | |||||||
\(720\) | 22.6729 | − | 55.5512i | 0.0314901 | − | 0.0771545i | ||||
\(721\) | −662.504 | − | 711.533i | −0.918869 | − | 0.986869i | ||||
\(722\) | −282.859 | − | 282.859i | −0.391771 | − | 0.391771i | ||||
\(723\) | −449.209 | − | 120.365i | −0.621313 | − | 0.166480i | ||||
\(724\) | −259.126 | − | 149.607i | −0.357909 | − | 0.206639i | ||||
\(725\) | −186.673 | − | 668.814i | −0.257481 | − | 0.922502i | ||||
\(726\) | −85.2973 | − | 147.739i | −0.117489 | − | 0.203498i | ||||
\(727\) | −666.033 | − | 666.033i | −0.916139 | − | 0.916139i | 0.0806067 | − | 0.996746i | \(-0.474314\pi\) |
−0.996746 | + | 0.0806067i | \(0.974314\pi\) | |||||||
\(728\) | 108.207 | − | 172.875i | 0.148636 | − | 0.237465i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −7.80369 | − | 56.9868i | −0.0106900 | − | 0.0780641i | ||||
\(731\) | 496.999 | − | 860.827i | 0.679889 | − | 1.17760i | ||||
\(732\) | 22.1078 | − | 5.92378i | 0.0302020 | − | 0.00809259i | ||||
\(733\) | −30.7894 | − | 8.24999i | −0.0420046 | − | 0.0112551i | 0.237756 | − | 0.971325i | \(-0.423588\pi\) |
−0.279760 | + | 0.960070i | \(0.590255\pi\) | |||||||
\(734\) | − | 525.708i | − | 0.716223i | ||||||
\(735\) | −318.852 | − | 280.016i | −0.433812 | − | 0.380974i | ||||
\(736\) | −2.35424 | −0.00319870 | ||||||||
\(737\) | −247.127 | + | 922.290i | −0.335314 | + | 1.25141i | ||||
\(738\) | −51.3646 | − | 191.695i | −0.0695997 | − | 0.259750i | ||||
\(739\) | 770.669 | + | 444.946i | 1.04285 | + | 0.602092i | 0.920640 | − | 0.390412i | \(-0.127667\pi\) |
0.122214 | + | 0.992504i | \(0.461001\pi\) | |||||||
\(740\) | −425.248 | − | 322.810i | −0.574660 | − | 0.436230i | ||||
\(741\) | −157.716 | −0.212842 | ||||||||
\(742\) | −598.029 | − | 374.322i | −0.805969 | − | 0.504478i | ||||
\(743\) | −380.855 | + | 380.855i | −0.512591 | + | 0.512591i | −0.915319 | − | 0.402729i | \(-0.868062\pi\) |
0.402729 | + | 0.915319i | \(0.368062\pi\) | |||||||
\(744\) | 106.291 | − | 61.3674i | 0.142865 | − | 0.0824831i | ||||
\(745\) | −162.394 | − | 209.375i | −0.217978 | − | 0.281041i | ||||
\(746\) | 449.093 | − | 777.852i | 0.602002 | − | 1.04270i | ||||
\(747\) | −62.6421 | + | 233.783i | −0.0838582 | + | 0.312963i | ||||
\(748\) | −190.833 | + | 190.833i | −0.255124 | + | 0.255124i | ||||
\(749\) | 218.328 | − | 203.284i | 0.291492 | − | 0.271407i | ||||
\(750\) | 121.565 | + | 281.020i | 0.162086 | + | 0.374693i | ||||
\(751\) | −62.9757 | − | 109.077i | −0.0838558 | − | 0.145242i | 0.821047 | − | 0.570860i | \(-0.193390\pi\) |
−0.904903 | + | 0.425618i | \(0.860057\pi\) | |||||||
\(752\) | 124.326 | − | 33.3131i | 0.165328 | − | 0.0442994i | ||||
\(753\) | −141.052 | − | 526.412i | −0.187320 | − | 0.699086i | ||||
\(754\) | −350.409 | + | 202.309i | −0.464734 | + | 0.268314i | ||||
\(755\) | −111.771 | − | 45.6185i | −0.148041 | − | 0.0604219i | ||||
\(756\) | −21.3218 | + | 69.5513i | −0.0282034 | + | 0.0919991i | ||||
\(757\) | 896.465 | + | 896.465i | 1.18423 | + | 1.18423i | 0.978637 | + | 0.205597i | \(0.0659135\pi\) |
0.205597 | + | 0.978637i | \(0.434087\pi\) | |||||||
\(758\) | 278.314 | + | 74.5741i | 0.367169 | + | 0.0983827i | ||||
\(759\) | −4.47362 | − | 2.58284i | −0.00589409 | − | 0.00340296i | ||||
\(760\) | −124.026 | − | 15.6737i | −0.163193 | − | 0.0206232i | ||||
\(761\) | 292.491 | + | 506.610i | 0.384351 | + | 0.665716i | 0.991679 | − | 0.128736i | \(-0.0410918\pi\) |
−0.607328 | + | 0.794451i | \(0.707759\pi\) | |||||||
\(762\) | 42.0404 | + | 42.0404i | 0.0551711 | + | 0.0551711i | ||||
\(763\) | 567.258 | + | 1068.82i | 0.743457 | + | 1.40081i | ||||
\(764\) | 571.561i | 0.748116i | ||||||||
\(765\) | 224.971 | + | 170.778i | 0.294079 | + | 0.223239i | ||||
\(766\) | 98.6232 | − | 170.820i | 0.128751 | − | 0.223003i | ||||
\(767\) | 405.052 | − | 108.533i | 0.528099 | − | 0.141504i | ||||
\(768\) | −26.7685 | − | 7.17260i | −0.0348548 | − | 0.00933933i | ||||
\(769\) | 885.685i | 1.15174i | 0.817543 | + | 0.575868i | \(0.195336\pi\) | ||||
−0.817543 | + | 0.575868i | \(0.804664\pi\) | |||||||
\(770\) | 331.694 | − | 125.694i | 0.430772 | − | 0.163239i | ||||
\(771\) | 646.859 | 0.838987 | ||||||||
\(772\) | −122.367 | + | 456.678i | −0.158506 | + | 0.591552i | ||||
\(773\) | −225.605 | − | 841.968i | −0.291856 | − | 1.08922i | −0.943682 | − | 0.330853i | \(-0.892664\pi\) |
0.651826 | − | 0.758368i | \(-0.274003\pi\) | |||||||
\(774\) | 193.957 | + | 111.981i | 0.250590 | + | 0.144678i | ||||
\(775\) | −155.814 | + | 606.638i | −0.201051 | + | 0.782758i | ||||
\(776\) | −184.208 | −0.237382 | ||||||||
\(777\) | 548.691 | + | 343.440i | 0.706165 | + | 0.442008i | ||||
\(778\) | 551.707 | − | 551.707i | 0.709134 | − | 0.709134i | ||||
\(779\) | −358.098 | + | 206.748i | −0.459689 | + | 0.265402i | ||||
\(780\) | 140.982 | − | 109.347i | 0.180746 | − | 0.140188i | ||||
\(781\) | −465.339 | + | 805.991i | −0.595825 | + | 1.03200i | ||||
\(782\) | 2.86836 | − | 10.7049i | 0.00366798 | − | 0.0136891i | ||||
\(783\) | 102.052 | − | 102.052i | 0.130335 | − | 0.130335i | ||||
\(784\) | −109.849 | + | 162.325i | −0.140113 | + | 0.207047i | ||||
\(785\) | −339.061 | − | 806.693i | −0.431925 | − | 1.02763i | ||||
\(786\) | 155.631 | + | 269.561i | 0.198004 | + | 0.342954i | ||||
\(787\) | −532.157 | + | 142.591i | −0.676184 | + | 0.181183i | −0.580539 | − | 0.814233i | \(-0.697158\pi\) |
−0.0956451 | + | 0.995416i | \(0.530491\pi\) | |||||||
\(788\) | 52.7888 | + | 197.010i | 0.0669908 | + | 0.250013i | ||||
\(789\) | −38.7159 | + | 22.3526i | −0.0490696 | + | 0.0283303i | ||||
\(790\) | −451.250 | + | 189.665i | −0.571203 | + | 0.240082i | ||||
\(791\) | −27.7348 | + | 6.38087i | −0.0350629 | + | 0.00806684i | ||||
\(792\) | −42.9975 | − | 42.9975i | −0.0542897 | − | 0.0542897i | ||||
\(793\) | 65.7401 | + | 17.6150i | 0.0829005 | + | 0.0222131i | ||||
\(794\) | 551.676 | + | 318.510i | 0.694806 | + | 0.401146i | ||||
\(795\) | −378.265 | − | 487.700i | −0.475805 | − | 0.613459i | ||||
\(796\) | −286.796 | − | 496.745i | −0.360296 | − | 0.624051i | ||||
\(797\) | −522.605 | − | 522.605i | −0.655716 | − | 0.655716i | 0.298648 | − | 0.954363i | \(-0.403464\pi\) |
−0.954363 | + | 0.298648i | \(0.903464\pi\) | |||||||
\(798\) | 151.474 | + | 5.40488i | 0.189817 | + | 0.00677304i | ||||
\(799\) | 605.908i | 0.758332i | ||||||||
\(800\) | 121.734 | − | 71.9787i | 0.152167 | − | 0.0899734i | ||||
\(801\) | 197.548 | − | 342.164i | 0.246627 | − | 0.427171i | ||||
\(802\) | 623.693 | − | 167.118i | 0.777672 | − | 0.208377i | ||||
\(803\) | −56.3065 | − | 15.0873i | −0.0701202 | − | 0.0187887i | ||||
\(804\) | − | 461.554i | − | 0.574072i | ||||||
\(805\) | −9.21528 | + | 11.2805i | −0.0114476 | + | 0.0140131i | ||||
\(806\) | 364.966 | 0.452811 | ||||||||
\(807\) | −97.9233 | + | 365.455i | −0.121342 | + | 0.452856i | ||||
\(808\) | 49.9248 | + | 186.322i | 0.0617882 | + | 0.230597i | ||||
\(809\) | 717.903 | + | 414.482i | 0.887396 | + | 0.512338i | 0.873090 | − | 0.487559i | \(-0.162113\pi\) |
0.0143061 | + | 0.999898i | \(0.495446\pi\) | |||||||
\(810\) | −38.4787 | + | 50.6892i | −0.0475045 | + | 0.0625792i | ||||
\(811\) | 1182.48 | 1.45805 | 0.729024 | − | 0.684489i | \(-0.239974\pi\) | ||||
0.729024 | + | 0.684489i | \(0.239974\pi\) | |||||||
\(812\) | 343.474 | − | 182.293i | 0.422997 | − | 0.224499i | ||||
\(813\) | −36.6762 | + | 36.6762i | −0.0451122 | + | 0.0451122i | ||||
\(814\) | −468.589 | + | 270.540i | −0.575662 | + | 0.332359i | ||||
\(815\) | −156.298 | + | 1236.79i | −0.191777 | + | 1.51754i | ||||
\(816\) | 65.2286 | − | 112.979i | 0.0799369 | − | 0.138455i | ||||
\(817\) | 120.774 | − | 450.736i | 0.147826 | − | 0.551696i | ||||
\(818\) | 579.934 | − | 579.934i | 0.708965 | − | 0.708965i | ||||
\(819\) | −158.318 | + | 147.409i | −0.193306 | + | 0.179986i | ||||
\(820\) | 176.761 | − | 433.086i | 0.215562 | − | 0.528153i | ||||
\(821\) | −386.788 | − | 669.937i | −0.471119 | − | 0.816002i | 0.528335 | − | 0.849036i | \(-0.322816\pi\) |
−0.999454 | + | 0.0330341i | \(0.989483\pi\) | |||||||
\(822\) | 222.823 | − | 59.7053i | 0.271074 | − | 0.0726341i | ||||
\(823\) | 179.453 | + | 669.726i | 0.218047 | + | 0.813762i | 0.985072 | + | 0.172145i | \(0.0550696\pi\) |
−0.767025 | + | 0.641617i | \(0.778264\pi\) | |||||||
\(824\) | −340.202 | + | 196.416i | −0.412867 | + | 0.238369i | ||||
\(825\) | 310.291 | − | 3.22247i | 0.376110 | − | 0.00390602i | ||||
\(826\) | −392.740 | + | 90.3568i | −0.475473 | + | 0.109391i | ||||
\(827\) | 578.176 | + | 578.176i | 0.699124 | + | 0.699124i | 0.964222 | − | 0.265097i | \(-0.0854041\pi\) |
−0.265097 | + | 0.964222i | \(0.585404\pi\) | |||||||
\(828\) | 2.41196 | + | 0.646284i | 0.00291300 | + | 0.000780536i | ||||
\(829\) | 291.249 | + | 168.153i | 0.351326 | + | 0.202838i | 0.665269 | − | 0.746604i | \(-0.268317\pi\) |
−0.313943 | + | 0.949442i | \(0.601650\pi\) | |||||||
\(830\) | −450.776 | + | 349.626i | −0.543103 | + | 0.421236i | ||||
\(831\) | 460.940 | + | 798.372i | 0.554681 | + | 0.960737i | ||||
\(832\) | −58.2706 | − | 58.2706i | −0.0700368 | − | 0.0700368i | ||||
\(833\) | −604.262 | − | 697.262i | −0.725405 | − | 0.837050i | ||||
\(834\) | 225.265i | 0.270102i | ||||||||
\(835\) | 797.428 | − | 1050.48i | 0.955003 | − | 1.25806i | ||||
\(836\) | −63.3478 | + | 109.722i | −0.0757748 | + | 0.131246i | ||||
\(837\) | −125.744 | + | 33.6931i | −0.150232 | + | 0.0402545i | ||||
\(838\) | 637.131 | + | 170.719i | 0.760299 | + | 0.203722i | ||||
\(839\) | − | 815.549i | − | 0.972049i | −0.873945 | − | 0.486024i | \(-0.838447\pi\) | ||
0.873945 | − | 0.486024i | \(-0.161553\pi\) | |||||||
\(840\) | −139.149 | + | 100.188i | −0.165654 | + | 0.119271i | ||||
\(841\) | 69.5456 | 0.0826939 | ||||||||
\(842\) | 3.13529 | − | 11.7011i | 0.00372362 | − | 0.0138968i | ||||
\(843\) | 31.0646 | + | 115.935i | 0.0368500 | + | 0.137526i | ||||
\(844\) | −507.575 | − | 293.048i | −0.601392 | − | 0.347214i | ||||
\(845\) | −311.551 | + | 42.6633i | −0.368699 | + | 0.0504892i | ||||
\(846\) | −136.520 | −0.161371 | ||||||||
\(847\) | −17.3844 | + | 487.205i | −0.0205247 | + | 0.575212i | ||||
\(848\) | −201.577 | + | 201.577i | −0.237708 | + | 0.237708i | ||||
\(849\) | 525.880 | − | 303.617i | 0.619411 | − | 0.357617i | ||||
\(850\) | 178.974 | + | 641.228i | 0.210557 | + | 0.754386i | ||||
\(851\) | 11.1097 | − | 19.2425i | 0.0130548 | − | 0.0226116i | ||||
\(852\) | 116.438 | − | 434.553i | 0.136664 | − | 0.510038i | ||||
\(853\) | 321.111 | − | 321.111i | 0.376449 | − | 0.376449i | −0.493371 | − | 0.869819i | \(-0.664235\pi\) |
0.869819 | + | 0.493371i | \(0.164235\pi\) | |||||||
\(854\) | −62.5346 | − | 19.1707i | −0.0732255 | − | 0.0224482i | ||||
\(855\) | 122.765 | + | 50.1056i | 0.143584 | + | 0.0586030i | ||||
\(856\) | −60.2685 | − | 104.388i | −0.0704071 | − | 0.121949i | ||||
\(857\) | 795.967 | − | 213.279i | 0.928782 | − | 0.248867i | 0.237447 | − | 0.971400i | \(-0.423689\pi\) |
0.691335 | + | 0.722534i | \(0.257023\pi\) | |||||||
\(858\) | −46.7992 | − | 174.657i | −0.0545445 | − | 0.203563i | ||||
\(859\) | 82.8602 | − | 47.8393i | 0.0964612 | − | 0.0556919i | −0.450993 | − | 0.892527i | \(-0.648930\pi\) |
0.547455 | + | 0.836835i | \(0.315597\pi\) | |||||||
\(860\) | 204.542 | + | 486.645i | 0.237840 | + | 0.565867i | ||||
\(861\) | −166.228 | + | 542.232i | −0.193064 | + | 0.629770i | ||||
\(862\) | −140.171 | − | 140.171i | −0.162612 | − | 0.162612i | ||||
\(863\) | −1163.66 | − | 311.803i | −1.34839 | − | 0.361301i | −0.488852 | − | 0.872367i | \(-0.662584\pi\) |
−0.859542 | + | 0.511065i | \(0.829251\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −87.9332 | + | 695.819i | −0.101657 | + | 0.804415i | ||||
\(866\) | 20.7110 | + | 35.8725i | 0.0239157 | + | 0.0414232i | ||||
\(867\) | 80.2987 | + | 80.2987i | 0.0926168 | + | 0.0926168i | ||||
\(868\) | −350.521 | − | 12.5073i | −0.403826 | − | 0.0144093i | ||||
\(869\) | 496.078i | 0.570860i | ||||||||
\(870\) | 337.028 | − | 46.1522i | 0.387389 | − | 0.0530485i | ||||
\(871\) | 686.241 | − | 1188.60i | 0.787877 | − | 1.36464i | ||||
\(872\) | 472.263 | − | 126.542i | 0.541585 | − | 0.145117i | ||||
\(873\) | 188.725 | + | 50.5686i | 0.216179 | + | 0.0579251i | ||||
\(874\) | − | 5.20272i | − | 0.00595277i | ||||||
\(875\) | 131.614 | − | 865.045i | 0.150416 | − | 0.988623i | ||||
\(876\) | 28.1783 | 0.0321670 | ||||||||
\(877\) | −81.8983 | + | 305.649i | −0.0933846 | + | 0.348516i | −0.996770 | − | 0.0803144i | \(-0.974408\pi\) |
0.903385 | + | 0.428830i | \(0.141074\pi\) | |||||||
\(878\) | −110.849 | − | 413.694i | −0.126252 | − | 0.471178i | ||||
\(879\) | 787.904 | + | 454.897i | 0.896364 | + | 0.517516i | ||||
\(880\) | −19.4452 | − | 142.000i | −0.0220969 | − | 0.161363i | ||||
\(881\) | −905.723 | −1.02806 | −0.514031 | − | 0.857771i | \(-0.671849\pi\) | ||||
−0.514031 | + | 0.857771i | \(0.671849\pi\) | |||||||
\(882\) | 157.103 | − | 136.149i | 0.178122 | − | 0.154364i | ||||
\(883\) | −960.055 | + | 960.055i | −1.08726 | + | 1.08726i | −0.0914558 | + | 0.995809i | \(0.529152\pi\) |
−0.995809 | + | 0.0914558i | \(0.970848\pi\) | |||||||
\(884\) | 335.956 | − | 193.964i | 0.380041 | − | 0.219417i | ||||
\(885\) | −349.770 | − | 44.2017i | −0.395220 | − | 0.0499454i | ||||
\(886\) | −408.169 | + | 706.970i | −0.460688 | + | 0.797934i | ||||
\(887\) | 46.1805 | − | 172.348i | 0.0520637 | − | 0.194304i | −0.934996 | − | 0.354659i | \(-0.884597\pi\) |
0.987060 | + | 0.160354i | \(0.0512637\pi\) | |||||||
\(888\) | 184.946 | − | 184.946i | 0.208273 | − | 0.208273i | ||||
\(889\) | −38.0943 | − | 165.579i | −0.0428507 | − | 0.186253i | ||||
\(890\) | 858.502 | − | 360.837i | 0.964609 | − | 0.405435i | ||||
\(891\) | 32.2481 | + | 55.8553i | 0.0361931 | + | 0.0626884i | ||||
\(892\) | −456.092 | + | 122.209i | −0.511314 | + | 0.137006i | ||||
\(893\) | 73.6199 | + | 274.753i | 0.0824411 | + | 0.307674i | ||||
\(894\) | 112.418 | − | 64.9044i | 0.125747 | − | 0.0726000i | ||||
\(895\) | 418.407 | − | 1025.15i | 0.467494 | − | 1.14542i | ||||
\(896\) | 53.9675 | + | 57.9613i | 0.0602315 | + | 0.0646890i | ||||
\(897\) | 5.25045 | + | 5.25045i | 0.00585334 | + | 0.00585334i | ||||
\(898\) | 42.9145 | + | 11.4989i | 0.0477890 | + | 0.0128050i | ||||
\(899\) | 602.626 | + | 347.926i | 0.670329 | + | 0.387015i | ||||
\(900\) | −144.478 | + | 40.3254i | −0.160531 | + | 0.0448060i | ||||
\(901\) | −670.984 | − | 1162.18i | −0.744710 | − | 1.28988i | ||||
\(902\) | −335.215 | − | 335.215i | −0.371635 | − | 0.371635i | ||||
\(903\) | −300.044 | − | 565.337i | −0.332274 | − | 0.626065i | ||||
\(904\) | 11.4993i | 0.0127205i | ||||||||
\(905\) | 101.487 | + | 741.116i | 0.112141 | + | 0.818913i | ||||
\(906\) | 29.5707 | − | 51.2180i | 0.0326388 | − | 0.0565320i | ||||
\(907\) | 969.850 | − | 259.870i | 1.06929 | − | 0.286517i | 0.319091 | − | 0.947724i | \(-0.396622\pi\) |
0.750203 | + | 0.661207i | \(0.229956\pi\) | |||||||
\(908\) | −588.855 | − | 157.783i | −0.648519 | − | 0.173770i | ||||
\(909\) | − | 204.596i | − | 0.225078i | ||||||
\(910\) | −507.299 | + | 51.1176i | −0.557472 | + | 0.0561732i | ||||
\(911\) | 145.014 | 0.159181 | 0.0795905 | − | 0.996828i | \(-0.474639\pi\) | ||||
0.0795905 | + | 0.996828i | \(0.474639\pi\) | |||||||
\(912\) | 15.8510 | − | 59.1567i | 0.0173805 | − | 0.0648648i | ||||
\(913\) | 149.636 | + | 558.450i | 0.163895 | + | 0.611664i | ||||
\(914\) | −347.840 | − | 200.826i | −0.380569 | − | 0.219722i | ||||
\(915\) | −45.5754 | − | 34.5967i | −0.0498091 | − | 0.0378106i | ||||
\(916\) | 450.166 | 0.491448 | ||||||||
\(917\) | 31.7192 | − | 888.942i | 0.0345902 | − | 0.969402i | ||||
\(918\) | −97.8428 | + | 97.8428i | −0.106583 | + | 0.106583i | ||||
\(919\) | 881.023 | − | 508.659i | 0.958676 | − | 0.553492i | 0.0629106 | − | 0.998019i | \(-0.479962\pi\) |
0.895765 | + | 0.444527i | \(0.146628\pi\) | |||||||
\(920\) | 3.60712 | + | 4.65069i | 0.00392079 | + | 0.00505510i | ||||
\(921\) | 93.6560 | − | 162.217i | 0.101689 | − | 0.176131i | ||||
\(922\) | 3.06796 | − | 11.4498i | 0.00332751 | − | 0.0124184i | ||||
\(923\) | 945.949 | − | 945.949i | 1.02486 | − | 1.02486i | ||||
\(924\) | 38.9615 | + | 169.348i | 0.0421661 | + | 0.183277i | ||||
\(925\) | 13.8609 | + | 1334.66i | 0.0149847 | + | 1.44288i | ||||
\(926\) | −59.5826 | − | 103.200i | −0.0643440 | − | 0.111447i | ||||
\(927\) | 402.464 | − | 107.840i | 0.434157 | − | 0.116332i | ||||
\(928\) | −40.6655 | − | 151.766i | −0.0438206 | − | 0.163541i | ||||
\(929\) | −181.351 | + | 104.703i | −0.195210 | + | 0.112705i | −0.594419 | − | 0.804155i | \(-0.702618\pi\) |
0.399209 | + | 0.916860i | \(0.369285\pi\) | |||||||
\(930\) | −284.086 | − | 115.948i | −0.305469 | − | 0.124675i | ||||
\(931\) | −358.727 | − | 242.759i | −0.385313 | − | 0.260751i | ||||
\(932\) | −143.330 | − | 143.330i | −0.153788 | − | 0.153788i | ||||
\(933\) | −350.368 | − | 93.8809i | −0.375529 | − | 0.100623i | ||||
\(934\) | 600.690 | + | 346.809i | 0.643137 | + | 0.371316i | ||||
\(935\) | 669.373 | + | 84.5911i | 0.715907 | + | 0.0904717i | ||||
\(936\) | 43.7030 | + | 75.6958i | 0.0466912 | + | 0.0808716i | ||||
\(937\) | −727.770 | − | 727.770i | −0.776702 | − | 0.776702i | 0.202566 | − | 0.979269i | \(-0.435072\pi\) |
−0.979269 | + | 0.202566i | \(0.935072\pi\) | |||||||
\(938\) | −699.814 | + | 1118.04i | −0.746071 | + | 1.19194i | ||||
\(939\) | − | 510.996i | − | 0.544192i | ||||||
\(940\) | −256.299 | − | 194.559i | −0.272659 | − | 0.206978i | ||||
\(941\) | −373.861 | + | 647.547i | −0.397302 | + | 0.688147i | −0.993392 | − | 0.114770i | \(-0.963387\pi\) |
0.596090 | + | 0.802918i | \(0.296720\pi\) | |||||||
\(942\) | 414.079 | − | 110.952i | 0.439574 | − | 0.117784i | ||||
\(943\) | 18.8040 | + | 5.03852i | 0.0199406 | + | 0.00534308i | ||||
\(944\) | 162.837i | 0.172497i | ||||||||
\(945\) | 170.064 | − | 64.4450i | 0.179962 | − | 0.0681957i | ||||
\(946\) | 534.989 | 0.565527 | ||||||||
\(947\) | 50.2461 | − | 187.521i | 0.0530581 | − | 0.198016i | −0.934309 | − | 0.356464i | \(-0.883982\pi\) |
0.987367 | + | 0.158448i | \(0.0506490\pi\) | |||||||
\(948\) | −62.0647 | − | 231.629i | −0.0654691 | − | 0.244334i | ||||
\(949\) | 72.5653 | + | 41.8956i | 0.0764650 | + | 0.0441471i | ||||
\(950\) | 159.068 | + | 269.023i | 0.167440 | + | 0.283183i | ||||
\(951\) | −1080.23 | −1.13589 | ||||||||
\(952\) | −329.307 | + | 174.774i | −0.345910 | + | 0.183587i | ||||
\(953\) | 292.564 | − | 292.564i | 0.306993 | − | 0.306993i | −0.536749 | − | 0.843742i | \(-0.680348\pi\) |
0.843742 | + | 0.536749i | \(0.180348\pi\) | |||||||
\(954\) | 261.856 | − | 151.182i | 0.274482 | − | 0.158472i | ||||
\(955\) | 1129.09 | − | 875.735i | 1.18230 | − | 0.917000i | ||||
\(956\) | 191.422 | − | 331.552i | 0.200232 | − | 0.346812i | ||||
\(957\) | 89.2285 | − | 333.005i | 0.0932377 | − | 0.347968i | ||||
\(958\) | 456.410 | − | 456.410i | 0.476419 | − | 0.476419i | ||||
\(959\) | −630.281 | − | 193.220i | −0.657227 | − | 0.201481i | ||||
\(960\) | 26.8451 | + | 63.8697i | 0.0279636 | + | 0.0665310i | ||||
\(961\) | 166.670 | + | 288.681i | 0.173434 | + | 0.300396i | ||||
\(962\) | 751.257 | − | 201.299i | 0.780932 | − | 0.209250i | ||||
\(963\) | 33.0897 | + | 123.492i | 0.0343611 | + | 0.128237i | ||||
\(964\) | 465.056 | − | 268.500i | 0.482423 | − | 0.278527i | ||||
\(965\) | 1089.64 | − | 457.985i | 1.12916 | − | 0.474595i | ||||
\(966\) | −4.86271 | − | 5.22257i | −0.00503386 | − | 0.00540639i | ||||
\(967\) | 648.542 | + | 648.542i | 0.670674 | + | 0.670674i | 0.957871 | − | 0.287197i | \(-0.0927236\pi\) |
−0.287197 | + | 0.957871i | \(0.592724\pi\) | |||||||
\(968\) | 190.274 | + | 50.9836i | 0.196564 | + | 0.0526691i | ||||
\(969\) | 249.677 | + | 144.151i | 0.257664 | + | 0.148763i | ||||
\(970\) | 282.240 | + | 363.895i | 0.290969 | + | 0.375149i | ||||
\(971\) | 35.0337 | + | 60.6802i | 0.0360800 | + | 0.0624924i | 0.883502 | − | 0.468428i | \(-0.155180\pi\) |
−0.847422 | + | 0.530921i | \(0.821846\pi\) | |||||||
\(972\) | −22.0454 | − | 22.0454i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 341.550 | − | 545.670i | 0.351027 | − | 0.560812i | ||||
\(974\) | 1.04309i | 0.00107094i | ||||||||
\(975\) | −432.019 | − | 110.964i | −0.443096 | − | 0.113809i | ||||
\(976\) | −13.2142 | + | 22.8877i | −0.0135392 | + | 0.0234505i | ||||
\(977\) | 200.723 | − | 53.7837i | 0.205449 | − | 0.0550498i | −0.154627 | − | 0.987973i | \(-0.549418\pi\) |
0.360076 | + | 0.932923i | \(0.382751\pi\) | |||||||
\(978\) | −589.911 | − | 158.066i | −0.603181 | − | 0.161622i | ||||
\(979\) | − | 943.786i | − | 0.964031i | ||||||
\(980\) | 488.973 | − | 31.7094i | 0.498952 | − | 0.0323566i | ||||
\(981\) | −518.580 | −0.528624 | ||||||||
\(982\) | −122.750 | + | 458.107i | −0.125000 | + | 0.466504i | ||||
\(983\) | −243.942 | − | 910.404i | −0.248161 | − | 0.926149i | −0.971768 | − | 0.235937i | \(-0.924184\pi\) |
0.723607 | − | 0.690212i | \(-0.242483\pi\) | |||||||
\(984\) | 198.457 | + | 114.579i | 0.201684 | + | 0.116443i | ||||
\(985\) | 308.303 | − | 406.137i | 0.312998 | − | 0.412322i | ||||
\(986\) | 739.635 | 0.750137 | ||||||||
\(987\) | 330.698 | + | 206.993i | 0.335054 | + | 0.209719i | ||||
\(988\) | 128.774 | − | 128.774i | 0.130338 | − | 0.130338i | ||||
\(989\) | −19.0259 | + | 10.9846i | −0.0192375 | + | 0.0111068i | ||||
\(990\) | −19.0596 | + | 150.819i | −0.0192521 | + | 0.152343i | ||||
\(991\) | 333.587 | − | 577.790i | 0.336617 | − | 0.583038i | −0.647177 | − | 0.762340i | \(-0.724051\pi\) |
0.983794 | + | 0.179302i | \(0.0573839\pi\) | |||||||
\(992\) | −36.6803 | + | 136.893i | −0.0369762 | + | 0.137997i | ||||
\(993\) | −194.612 | + | 194.612i | −0.195984 | + | 0.195984i | ||||
\(994\) | −940.928 | + | 876.093i | −0.946607 | + | 0.881381i | ||||
\(995\) | −541.873 | + | 1327.65i | −0.544596 | + | 1.33433i | ||||
\(996\) | −139.736 | − | 242.030i | −0.140297 | − | 0.243002i | ||||
\(997\) | −272.014 | + | 72.8859i | −0.272832 | + | 0.0731052i | −0.392641 | − | 0.919692i | \(-0.628439\pi\) |
0.119809 | + | 0.992797i | \(0.461772\pi\) | |||||||
\(998\) | 224.259 | + | 836.947i | 0.224709 | + | 0.838624i | ||||
\(999\) | −240.252 | + | 138.710i | −0.240493 | + | 0.138849i |
(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.67.7 | yes | 32 | |
5.3 | odd | 4 | inner | 210.3.v.b.193.4 | yes | 32 | |
7.2 | even | 3 | inner | 210.3.v.b.37.4 | ✓ | 32 | |
35.23 | odd | 12 | inner | 210.3.v.b.163.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.b.37.4 | ✓ | 32 | 7.2 | even | 3 | inner | |
210.3.v.b.67.7 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.v.b.163.7 | yes | 32 | 35.23 | odd | 12 | inner | |
210.3.v.b.193.4 | yes | 32 | 5.3 | odd | 4 | inner |