Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(43,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.w (of order \(8\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 43.9 | ||
Character | \(\chi\) | \(=\) | 224.43 |
Dual form | 224.3.w.a.99.9 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.72313 | + | 1.01530i | −0.861564 | + | 0.507649i | ||||
\(3\) | 0.819473 | + | 1.97838i | 0.273158 | + | 0.659461i | 0.999615 | − | 0.0277508i | \(-0.00883447\pi\) |
−0.726457 | + | 0.687212i | \(0.758834\pi\) | |||||||
\(4\) | 1.93834 | − | 3.49898i | 0.484584 | − | 0.874744i | ||||
\(5\) | 1.60646 | − | 3.87835i | 0.321293 | − | 0.775670i | −0.677887 | − | 0.735167i | \(-0.737104\pi\) |
0.999179 | − | 0.0405030i | \(-0.0128960\pi\) | |||||||
\(6\) | −3.42071 | − | 2.57700i | −0.570118 | − | 0.429499i | ||||
\(7\) | −1.87083 | + | 1.87083i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0.212503 | + | 7.99718i | 0.0265629 | + | 0.999647i | ||||
\(9\) | 3.12150 | − | 3.12150i | 0.346833 | − | 0.346833i | ||||
\(10\) | 1.16954 | + | 8.31393i | 0.116954 | + | 0.831393i | ||||
\(11\) | 2.19493 | − | 5.29904i | 0.199539 | − | 0.481731i | −0.792159 | − | 0.610315i | \(-0.791043\pi\) |
0.991699 | + | 0.128584i | \(0.0410431\pi\) | |||||||
\(12\) | 8.51073 | + | 0.967457i | 0.709228 | + | 0.0806214i | ||||
\(13\) | −7.92625 | − | 19.1357i | −0.609712 | − | 1.47197i | −0.863315 | − | 0.504666i | \(-0.831616\pi\) |
0.253603 | − | 0.967308i | \(-0.418384\pi\) | |||||||
\(14\) | 1.32423 | − | 5.12313i | 0.0945877 | − | 0.365938i | ||||
\(15\) | 8.98931 | 0.599287 | ||||||||
\(16\) | −8.48569 | − | 13.5644i | −0.530356 | − | 0.847775i | ||||
\(17\) | − | 8.66263i | − | 0.509566i | −0.966998 | − | 0.254783i | \(-0.917996\pi\) | ||
0.966998 | − | 0.254783i | \(-0.0820041\pi\) | |||||||
\(18\) | −2.20949 | + | 8.54799i | −0.122749 | + | 0.474888i | ||||
\(19\) | 9.92137 | − | 4.10957i | 0.522177 | − | 0.216293i | −0.105996 | − | 0.994367i | \(-0.533803\pi\) |
0.628173 | + | 0.778074i | \(0.283803\pi\) | |||||||
\(20\) | −10.4564 | − | 13.1385i | −0.522819 | − | 0.656927i | ||||
\(21\) | −5.23431 | − | 2.16812i | −0.249253 | − | 0.103244i | ||||
\(22\) | 1.59796 | + | 11.3594i | 0.0726343 | + | 0.516338i | ||||
\(23\) | −1.21606 | − | 1.21606i | −0.0528721 | − | 0.0528721i | 0.680176 | − | 0.733048i | \(-0.261903\pi\) |
−0.733048 | + | 0.680176i | \(0.761903\pi\) | |||||||
\(24\) | −15.6473 | + | 6.97388i | −0.651972 | + | 0.290578i | ||||
\(25\) | 5.21682 | + | 5.21682i | 0.208673 | + | 0.208673i | ||||
\(26\) | 33.0864 | + | 24.9257i | 1.27255 | + | 0.958680i | ||||
\(27\) | 26.5389 | + | 10.9928i | 0.982924 | + | 0.407140i | ||||
\(28\) | 2.91969 | + | 10.1723i | 0.104275 | + | 0.363296i | ||||
\(29\) | 26.8363 | − | 11.1159i | 0.925388 | − | 0.383308i | 0.131461 | − | 0.991321i | \(-0.458033\pi\) |
0.793927 | + | 0.608013i | \(0.208033\pi\) | |||||||
\(30\) | −15.4897 | + | 9.12683i | −0.516324 | + | 0.304228i | ||||
\(31\) | 9.35016i | 0.301618i | 0.988563 | + | 0.150809i | \(0.0481878\pi\) | ||||
−0.988563 | + | 0.150809i | \(0.951812\pi\) | |||||||
\(32\) | 28.3938 | + | 14.7577i | 0.887308 | + | 0.461178i | ||||
\(33\) | 12.2822 | 0.372188 | ||||||||
\(34\) | 8.79515 | + | 14.9268i | 0.258681 | + | 0.439024i | ||||
\(35\) | 4.25030 | + | 10.2611i | 0.121437 | + | 0.293176i | ||||
\(36\) | −4.87153 | − | 16.9726i | −0.135320 | − | 0.471460i | ||||
\(37\) | −10.6588 | + | 25.7325i | −0.288075 | + | 0.695473i | −0.999977 | − | 0.00680503i | \(-0.997834\pi\) |
0.711902 | + | 0.702279i | \(0.247834\pi\) | |||||||
\(38\) | −12.9234 | + | 17.1545i | −0.340088 | + | 0.451433i | ||||
\(39\) | 31.3623 | − | 31.3623i | 0.804162 | − | 0.804162i | ||||
\(40\) | 31.3572 | + | 12.0230i | 0.783930 | + | 0.300575i | ||||
\(41\) | 35.1006 | − | 35.1006i | 0.856111 | − | 0.856111i | −0.134766 | − | 0.990877i | \(-0.543028\pi\) |
0.990877 | + | 0.134766i | \(0.0430283\pi\) | |||||||
\(42\) | 11.2207 | − | 1.57844i | 0.267159 | − | 0.0375818i | ||||
\(43\) | 2.82656 | − | 6.82393i | 0.0657340 | − | 0.158696i | −0.887599 | − | 0.460617i | \(-0.847628\pi\) |
0.953333 | + | 0.301921i | \(0.0976280\pi\) | |||||||
\(44\) | −14.2867 | − | 17.9514i | −0.324698 | − | 0.407985i | ||||
\(45\) | −7.09168 | − | 17.1208i | −0.157593 | − | 0.380463i | ||||
\(46\) | 3.33008 | + | 0.860761i | 0.0723931 | + | 0.0187122i | ||||
\(47\) | −11.2490 | −0.239341 | −0.119670 | − | 0.992814i | \(-0.538184\pi\) | ||||
−0.119670 | + | 0.992814i | \(0.538184\pi\) | |||||||
\(48\) | 19.8818 | − | 27.9036i | 0.414204 | − | 0.581325i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | −14.2859 | − | 3.69261i | −0.285717 | − | 0.0738523i | ||||
\(51\) | 17.1380 | − | 7.09879i | 0.336039 | − | 0.139192i | ||||
\(52\) | −82.3190 | − | 9.35761i | −1.58306 | − | 0.179954i | ||||
\(53\) | −29.0021 | − | 12.0130i | −0.547209 | − | 0.226661i | 0.0919128 | − | 0.995767i | \(-0.470702\pi\) |
−0.639121 | + | 0.769106i | \(0.720702\pi\) | |||||||
\(54\) | −56.8910 | + | 8.00297i | −1.05354 | + | 0.148203i | ||||
\(55\) | −17.0254 | − | 17.0254i | −0.309553 | − | 0.309553i | ||||
\(56\) | −15.3589 | − | 14.5638i | −0.274266 | − | 0.260068i | ||||
\(57\) | 16.2606 | + | 16.2606i | 0.285274 | + | 0.285274i | ||||
\(58\) | −34.9563 | + | 46.4010i | −0.602695 | + | 0.800017i | ||||
\(59\) | 53.3814 | + | 22.1113i | 0.904770 | + | 0.374768i | 0.786052 | − | 0.618160i | \(-0.212122\pi\) |
0.118718 | + | 0.992928i | \(0.462122\pi\) | |||||||
\(60\) | 17.4243 | − | 31.4534i | 0.290405 | − | 0.524223i | ||||
\(61\) | −41.2892 | + | 17.1026i | −0.676872 | + | 0.280370i | −0.694519 | − | 0.719475i | \(-0.744383\pi\) |
0.0176463 | + | 0.999844i | \(0.494383\pi\) | |||||||
\(62\) | −9.49320 | − | 16.1115i | −0.153116 | − | 0.259863i | ||||
\(63\) | 11.6796i | 0.185390i | ||||||||
\(64\) | −63.9097 | + | 3.39885i | −0.998589 | + | 0.0531071i | ||||
\(65\) | −86.9480 | −1.33766 | ||||||||
\(66\) | −21.1638 | + | 12.4701i | −0.320664 | + | 0.188941i | ||||
\(67\) | 7.34359 | + | 17.7290i | 0.109606 | + | 0.264612i | 0.969160 | − | 0.246433i | \(-0.0792585\pi\) |
−0.859554 | + | 0.511045i | \(0.829259\pi\) | |||||||
\(68\) | −30.3103 | − | 16.7911i | −0.445740 | − | 0.246928i | ||||
\(69\) | 1.40930 | − | 3.40235i | 0.0204247 | − | 0.0493095i | ||||
\(70\) | −17.7419 | − | 13.3659i | −0.253456 | − | 0.190942i | ||||
\(71\) | 61.6413 | − | 61.6413i | 0.868188 | − | 0.868188i | −0.124084 | − | 0.992272i | \(-0.539599\pi\) |
0.992272 | + | 0.124084i | \(0.0395992\pi\) | |||||||
\(72\) | 25.6265 | + | 24.2998i | 0.355924 | + | 0.337498i | ||||
\(73\) | −66.1257 | + | 66.1257i | −0.905832 | + | 0.905832i | −0.995933 | − | 0.0901009i | \(-0.971281\pi\) |
0.0901009 | + | 0.995933i | \(0.471281\pi\) | |||||||
\(74\) | −7.75979 | − | 55.1622i | −0.104862 | − | 0.745436i | ||||
\(75\) | −6.04582 | + | 14.5959i | −0.0806109 | + | 0.194612i | ||||
\(76\) | 4.85169 | − | 42.6804i | 0.0638380 | − | 0.561584i | ||||
\(77\) | 5.80725 | + | 14.0199i | 0.0754188 | + | 0.182077i | ||||
\(78\) | −22.1992 | + | 85.8834i | −0.284605 | + | 1.10107i | ||||
\(79\) | −151.433 | −1.91687 | −0.958436 | − | 0.285307i | \(-0.907904\pi\) | ||||
−0.958436 | + | 0.285307i | \(0.907904\pi\) | |||||||
\(80\) | −66.2394 | + | 11.1197i | −0.827993 | + | 0.138997i | ||||
\(81\) | 21.7823i | 0.268917i | ||||||||
\(82\) | −24.8452 | + | 96.1203i | −0.302990 | + | 1.17220i | ||||
\(83\) | 133.888 | − | 55.4584i | 1.61311 | − | 0.668173i | 0.619921 | − | 0.784664i | \(-0.287165\pi\) |
0.993192 | + | 0.116491i | \(0.0371646\pi\) | |||||||
\(84\) | −17.7321 | + | 14.1122i | −0.211096 | + | 0.168002i | ||||
\(85\) | −33.5967 | − | 13.9162i | −0.395255 | − | 0.163720i | ||||
\(86\) | 2.05779 | + | 14.6283i | 0.0239278 | + | 0.170097i | ||||
\(87\) | 43.9832 | + | 43.9832i | 0.505554 | + | 0.505554i | ||||
\(88\) | 42.8438 | + | 16.4272i | 0.486861 | + | 0.186673i | ||||
\(89\) | −59.1122 | − | 59.1122i | −0.664182 | − | 0.664182i | 0.292181 | − | 0.956363i | \(-0.405619\pi\) |
−0.956363 | + | 0.292181i | \(0.905619\pi\) | |||||||
\(90\) | 29.6026 | + | 22.3012i | 0.328918 | + | 0.247791i | ||||
\(91\) | 50.6282 | + | 20.9709i | 0.556354 | + | 0.230449i | ||||
\(92\) | −6.61209 | + | 1.89783i | −0.0718706 | + | 0.0206286i | ||||
\(93\) | −18.4982 | + | 7.66220i | −0.198905 | + | 0.0823893i | ||||
\(94\) | 19.3835 | − | 11.4211i | 0.206207 | − | 0.121501i | ||||
\(95\) | − | 45.0804i | − | 0.474530i | ||||||
\(96\) | −5.92836 | + | 68.2674i | −0.0617538 | + | 0.711119i | ||||
\(97\) | −103.155 | −1.06345 | −0.531724 | − | 0.846917i | \(-0.678456\pi\) | ||||
−0.531724 | + | 0.846917i | \(0.678456\pi\) | |||||||
\(98\) | 7.10709 | + | 12.0619i | 0.0725213 | + | 0.123081i | ||||
\(99\) | −9.68946 | − | 23.3924i | −0.0978733 | − | 0.236287i | ||||
\(100\) | 28.3655 | − | 8.14157i | 0.283655 | − | 0.0814157i | ||||
\(101\) | 12.2300 | − | 29.5258i | 0.121089 | − | 0.292335i | −0.851699 | − | 0.524031i | \(-0.824428\pi\) |
0.972788 | + | 0.231696i | \(0.0744276\pi\) | |||||||
\(102\) | −22.3236 | + | 29.6323i | −0.218858 | + | 0.290513i | ||||
\(103\) | −29.6065 | + | 29.6065i | −0.287442 | + | 0.287442i | −0.836068 | − | 0.548626i | \(-0.815151\pi\) |
0.548626 | + | 0.836068i | \(0.315151\pi\) | |||||||
\(104\) | 151.347 | − | 67.4540i | 1.45526 | − | 0.648597i | ||||
\(105\) | −16.8175 | + | 16.8175i | −0.160166 | + | 0.160166i | ||||
\(106\) | 62.1711 | − | 8.74574i | 0.586520 | − | 0.0825069i | ||||
\(107\) | −55.6693 | + | 134.398i | −0.520274 | + | 1.25605i | 0.417459 | + | 0.908696i | \(0.362921\pi\) |
−0.937733 | + | 0.347357i | \(0.887079\pi\) | |||||||
\(108\) | 89.9050 | − | 71.5514i | 0.832454 | − | 0.662513i | ||||
\(109\) | −54.9789 | − | 132.731i | −0.504393 | − | 1.21771i | −0.947069 | − | 0.321031i | \(-0.895971\pi\) |
0.442675 | − | 0.896682i | \(-0.354029\pi\) | |||||||
\(110\) | 46.6229 | + | 12.0511i | 0.423845 | + | 0.109555i | ||||
\(111\) | −59.6433 | −0.537327 | ||||||||
\(112\) | 41.2520 | + | 9.50140i | 0.368321 | + | 0.0848339i | ||||
\(113\) | 89.0350i | 0.787920i | 0.919128 | + | 0.393960i | \(0.128895\pi\) | ||||
−0.919128 | + | 0.393960i | \(0.871105\pi\) | |||||||
\(114\) | −44.5284 | − | 11.5097i | −0.390600 | − | 0.100962i | ||||
\(115\) | −6.66985 | + | 2.76274i | −0.0579987 | + | 0.0240238i | ||||
\(116\) | 13.1233 | − | 115.446i | 0.113132 | − | 0.995224i | ||||
\(117\) | −84.4737 | − | 34.9902i | −0.721998 | − | 0.299061i | ||||
\(118\) | −114.433 | + | 16.0975i | −0.969768 | + | 0.136419i | ||||
\(119\) | 16.2063 | + | 16.2063i | 0.136187 | + | 0.136187i | ||||
\(120\) | 1.91026 | + | 71.8891i | 0.0159188 | + | 0.599076i | ||||
\(121\) | 62.2978 | + | 62.2978i | 0.514858 | + | 0.514858i | ||||
\(122\) | 53.7824 | − | 71.3908i | 0.440839 | − | 0.585170i | ||||
\(123\) | 98.2063 | + | 40.6784i | 0.798425 | + | 0.330719i | ||||
\(124\) | 32.7160 | + | 18.1238i | 0.263839 | + | 0.146159i | ||||
\(125\) | 125.572 | − | 52.0136i | 1.00458 | − | 0.416109i | ||||
\(126\) | −11.8583 | − | 20.1254i | −0.0941132 | − | 0.159725i | ||||
\(127\) | − | 35.6942i | − | 0.281057i | −0.990077 | − | 0.140528i | \(-0.955120\pi\) | ||
0.990077 | − | 0.140528i | \(-0.0448801\pi\) | |||||||
\(128\) | 106.674 | − | 70.7441i | 0.833388 | − | 0.552688i | ||||
\(129\) | 15.8166 | 0.122610 | ||||||||
\(130\) | 149.823 | − | 88.2782i | 1.15248 | − | 0.679063i | ||||
\(131\) | 13.3566 | + | 32.2457i | 0.101959 | + | 0.246150i | 0.966624 | − | 0.256197i | \(-0.0824697\pi\) |
−0.864666 | + | 0.502348i | \(0.832470\pi\) | |||||||
\(132\) | 23.8071 | − | 42.9752i | 0.180357 | − | 0.325570i | ||||
\(133\) | −10.8729 | + | 26.2495i | −0.0817510 | + | 0.197364i | ||||
\(134\) | −30.6542 | − | 23.0934i | −0.228763 | − | 0.172339i | ||||
\(135\) | 85.2677 | − | 85.2677i | 0.631613 | − | 0.631613i | ||||
\(136\) | 69.2766 | − | 1.84084i | 0.509387 | − | 0.0135356i | ||||
\(137\) | −171.296 | + | 171.296i | −1.25033 | + | 1.25033i | −0.294763 | + | 0.955571i | \(0.595241\pi\) |
−0.955571 | + | 0.294763i | \(0.904759\pi\) | |||||||
\(138\) | 1.02600 | + | 7.29355i | 0.00743478 | + | 0.0528518i | ||||
\(139\) | 0.0590034 | − | 0.142447i | 0.000424485 | − | 0.00102480i | −0.923667 | − | 0.383196i | \(-0.874823\pi\) |
0.924092 | + | 0.382171i | \(0.124823\pi\) | |||||||
\(140\) | 44.1420 | + | 5.01784i | 0.315300 | + | 0.0358417i | ||||
\(141\) | −9.21825 | − | 22.2548i | −0.0653777 | − | 0.157836i | ||||
\(142\) | −43.6315 | + | 168.800i | −0.307264 | + | 1.18873i | ||||
\(143\) | −118.798 | −0.830757 | ||||||||
\(144\) | −68.8293 | − | 15.8532i | −0.477981 | − | 0.110092i | ||||
\(145\) | − | 121.938i | − | 0.840950i | ||||||
\(146\) | 46.8057 | − | 181.080i | 0.320587 | − | 1.24028i | ||||
\(147\) | 13.8487 | − | 5.73631i | 0.0942087 | − | 0.0390225i | ||||
\(148\) | 69.3772 | + | 87.1731i | 0.468765 | + | 0.589007i | ||||
\(149\) | 259.331 | + | 107.419i | 1.74048 | + | 0.720930i | 0.998737 | + | 0.0502455i | \(0.0160004\pi\) |
0.741743 | + | 0.670685i | \(0.234000\pi\) | |||||||
\(150\) | −4.40148 | − | 31.2889i | −0.0293432 | − | 0.208593i | ||||
\(151\) | 64.4337 | + | 64.4337i | 0.426713 | + | 0.426713i | 0.887507 | − | 0.460794i | \(-0.152435\pi\) |
−0.460794 | + | 0.887507i | \(0.652435\pi\) | |||||||
\(152\) | 34.9733 | + | 78.4697i | 0.230087 | + | 0.516248i | ||||
\(153\) | −27.0404 | − | 27.0404i | −0.176734 | − | 0.176734i | ||||
\(154\) | −24.2411 | − | 18.2621i | −0.157409 | − | 0.118585i | ||||
\(155\) | 36.2632 | + | 15.0207i | 0.233956 | + | 0.0969077i | ||||
\(156\) | −48.9453 | − | 170.527i | −0.313752 | − | 1.09312i | ||||
\(157\) | 98.2618 | − | 40.7014i | 0.625872 | − | 0.259244i | −0.0471263 | − | 0.998889i | \(-0.515006\pi\) |
0.672998 | + | 0.739644i | \(0.265006\pi\) | |||||||
\(158\) | 260.938 | − | 153.750i | 1.65151 | − | 0.973099i | ||||
\(159\) | − | 67.2215i | − | 0.422777i | ||||||
\(160\) | 102.849 | − | 86.4135i | 0.642807 | − | 0.540085i | ||||
\(161\) | 4.55007 | 0.0282613 | ||||||||
\(162\) | −22.1155 | − | 37.5337i | −0.136516 | − | 0.231690i | ||||
\(163\) | 120.921 | + | 291.929i | 0.741846 | + | 1.79098i | 0.598201 | + | 0.801346i | \(0.295882\pi\) |
0.143645 | + | 0.989629i | \(0.454118\pi\) | |||||||
\(164\) | −54.7793 | − | 190.853i | −0.334020 | − | 1.16374i | ||||
\(165\) | 19.7309 | − | 47.6347i | 0.119581 | − | 0.288695i | ||||
\(166\) | −174.400 | + | 231.499i | −1.05060 | + | 1.39457i | ||||
\(167\) | 110.675 | − | 110.675i | 0.662726 | − | 0.662726i | −0.293295 | − | 0.956022i | \(-0.594752\pi\) |
0.956022 | + | 0.293295i | \(0.0947520\pi\) | |||||||
\(168\) | 16.2265 | − | 42.3204i | 0.0965866 | − | 0.251907i | ||||
\(169\) | −183.847 | + | 183.847i | −1.08785 | + | 1.08785i | ||||
\(170\) | 72.0205 | − | 10.1313i | 0.423650 | − | 0.0595957i | ||||
\(171\) | 18.1415 | − | 43.7975i | 0.106091 | − | 0.256126i | ||||
\(172\) | −18.3979 | − | 23.1172i | −0.106965 | − | 0.134402i | ||||
\(173\) | −82.6562 | − | 199.550i | −0.477781 | − | 1.15347i | −0.960647 | − | 0.277772i | \(-0.910404\pi\) |
0.482866 | − | 0.875694i | \(-0.339596\pi\) | |||||||
\(174\) | −120.445 | − | 31.1326i | −0.692211 | − | 0.178923i | ||||
\(175\) | −19.5195 | −0.111540 | ||||||||
\(176\) | −90.5038 | + | 15.1930i | −0.514226 | + | 0.0863241i | ||||
\(177\) | 123.729i | 0.699031i | ||||||||
\(178\) | 161.874 | + | 41.8413i | 0.909407 | + | 0.235064i | ||||
\(179\) | −121.524 | + | 50.3370i | −0.678906 | + | 0.281212i | −0.695369 | − | 0.718652i | \(-0.744759\pi\) |
0.0164635 | + | 0.999864i | \(0.494759\pi\) | |||||||
\(180\) | −73.6515 | − | 8.37232i | −0.409175 | − | 0.0465129i | ||||
\(181\) | 228.110 | + | 94.4865i | 1.26028 | + | 0.522025i | 0.909995 | − | 0.414619i | \(-0.136085\pi\) |
0.350284 | + | 0.936644i | \(0.386085\pi\) | |||||||
\(182\) | −108.531 | + | 15.2672i | −0.596322 | + | 0.0838859i | ||||
\(183\) | −67.6708 | − | 67.6708i | −0.369786 | − | 0.369786i | ||||
\(184\) | 9.46661 | − | 9.98345i | 0.0514490 | − | 0.0542579i | ||||
\(185\) | 82.6767 | + | 82.6767i | 0.446901 | + | 0.446901i | ||||
\(186\) | 24.0953 | − | 31.9841i | 0.129545 | − | 0.171958i | ||||
\(187\) | −45.9036 | − | 19.0139i | −0.245474 | − | 0.101679i | ||||
\(188\) | −21.8044 | + | 39.3600i | −0.115981 | + | 0.209362i | ||||
\(189\) | −70.2155 | + | 29.0842i | −0.371510 | + | 0.153885i | ||||
\(190\) | 45.7701 | + | 77.6793i | 0.240895 | + | 0.408838i | ||||
\(191\) | 203.563i | 1.06577i | 0.846186 | + | 0.532887i | \(0.178893\pi\) | ||||
−0.846186 | + | 0.532887i | \(0.821107\pi\) | |||||||
\(192\) | −59.0965 | − | 123.653i | −0.307794 | − | 0.644024i | ||||
\(193\) | 123.408 | 0.639419 | 0.319710 | − | 0.947516i | \(-0.396415\pi\) | ||||
0.319710 | + | 0.947516i | \(0.396415\pi\) | |||||||
\(194\) | 177.748 | − | 104.733i | 0.916229 | − | 0.539859i | ||||
\(195\) | −71.2516 | − | 172.016i | −0.365393 | − | 0.882136i | ||||
\(196\) | −24.4928 | − | 13.5684i | −0.124963 | − | 0.0692264i | ||||
\(197\) | −87.1234 | + | 210.335i | −0.442251 | + | 1.06769i | 0.532906 | + | 0.846174i | \(0.321100\pi\) |
−0.975157 | + | 0.221514i | \(0.928900\pi\) | |||||||
\(198\) | 40.4465 | + | 30.4704i | 0.204275 | + | 0.153891i | ||||
\(199\) | −252.119 | + | 252.119i | −1.26693 | + | 1.26693i | −0.319266 | + | 0.947665i | \(0.603436\pi\) |
−0.947665 | + | 0.319266i | \(0.896564\pi\) | |||||||
\(200\) | −40.6112 | + | 42.8284i | −0.203056 | + | 0.214142i | ||||
\(201\) | −29.0569 | + | 29.0569i | −0.144562 | + | 0.144562i | ||||
\(202\) | 8.90367 | + | 63.2938i | 0.0440776 | + | 0.313336i | ||||
\(203\) | −29.4100 | + | 71.0021i | −0.144877 | + | 0.349764i | ||||
\(204\) | 8.38072 | − | 73.7253i | 0.0410819 | − | 0.361399i | ||||
\(205\) | −79.7444 | − | 192.520i | −0.388997 | − | 0.939122i | ||||
\(206\) | 20.9563 | − | 81.0752i | 0.101730 | − | 0.393569i | ||||
\(207\) | −7.59185 | −0.0366756 | ||||||||
\(208\) | −192.304 | + | 269.894i | −0.924539 | + | 1.29757i | ||||
\(209\) | − | 61.5940i | − | 0.294708i | ||||||
\(210\) | 11.9039 | − | 46.0534i | 0.0566852 | − | 0.219302i | ||||
\(211\) | 48.5772 | − | 20.1213i | 0.230224 | − | 0.0953618i | −0.264590 | − | 0.964361i | \(-0.585236\pi\) |
0.494813 | + | 0.868999i | \(0.335236\pi\) | |||||||
\(212\) | −98.2492 | + | 78.1922i | −0.463440 | + | 0.368831i | ||||
\(213\) | 172.464 | + | 71.4368i | 0.809688 | + | 0.335384i | ||||
\(214\) | −40.5284 | − | 288.105i | −0.189385 | − | 1.34629i | ||||
\(215\) | −21.9248 | − | 21.9248i | −0.101976 | − | 0.101976i | ||||
\(216\) | −82.2717 | + | 214.573i | −0.380887 | + | 0.993392i | ||||
\(217\) | −17.4925 | − | 17.4925i | −0.0806108 | − | 0.0806108i | ||||
\(218\) | 229.497 | + | 172.892i | 1.05274 | + | 0.793083i | ||||
\(219\) | −185.010 | − | 76.6337i | −0.844796 | − | 0.349926i | ||||
\(220\) | −92.5727 | + | 26.5706i | −0.420785 | + | 0.120775i | ||||
\(221\) | −165.765 | + | 68.6622i | −0.750069 | + | 0.310689i | ||||
\(222\) | 102.773 | − | 60.5558i | 0.462942 | − | 0.272774i | ||||
\(223\) | 47.2993i | 0.212104i | 0.994361 | + | 0.106052i | \(0.0338211\pi\) | ||||
−0.994361 | + | 0.106052i | \(0.966179\pi\) | |||||||
\(224\) | −80.7291 | + | 25.5109i | −0.360398 | + | 0.113888i | ||||
\(225\) | 32.5686 | 0.144749 | ||||||||
\(226\) | −90.3971 | − | 153.419i | −0.399987 | − | 0.678844i | ||||
\(227\) | −102.193 | − | 246.717i | −0.450191 | − | 1.08686i | −0.972249 | − | 0.233948i | \(-0.924836\pi\) |
0.522058 | − | 0.852910i | \(-0.325164\pi\) | |||||||
\(228\) | 88.4140 | − | 25.3769i | 0.387781 | − | 0.111302i | ||||
\(229\) | 146.075 | − | 352.657i | 0.637884 | − | 1.53999i | −0.191610 | − | 0.981471i | \(-0.561371\pi\) |
0.829494 | − | 0.558516i | \(-0.188629\pi\) | |||||||
\(230\) | 8.68799 | − | 11.5324i | 0.0377739 | − | 0.0501411i | ||||
\(231\) | −22.9779 | + | 22.9779i | −0.0994715 | + | 0.0994715i | ||||
\(232\) | 94.5990 | + | 212.252i | 0.407754 | + | 0.914880i | ||||
\(233\) | −76.5866 | + | 76.5866i | −0.328698 | + | 0.328698i | −0.852091 | − | 0.523393i | \(-0.824666\pi\) |
0.523393 | + | 0.852091i | \(0.324666\pi\) | |||||||
\(234\) | 181.085 | − | 25.4735i | 0.773865 | − | 0.108861i | ||||
\(235\) | −18.0711 | + | 43.6275i | −0.0768984 | + | 0.185649i | ||||
\(236\) | 180.838 | − | 143.921i | 0.766264 | − | 0.609836i | ||||
\(237\) | −124.095 | − | 299.592i | −0.523608 | − | 1.26410i | ||||
\(238\) | −44.3797 | − | 11.4713i | −0.186469 | − | 0.0481987i | ||||
\(239\) | −423.059 | −1.77012 | −0.885061 | − | 0.465475i | \(-0.845884\pi\) | ||||
−0.885061 | + | 0.465475i | \(0.845884\pi\) | |||||||
\(240\) | −76.2805 | − | 121.935i | −0.317836 | − | 0.508061i | ||||
\(241\) | − | 248.004i | − | 1.02906i | −0.857472 | − | 0.514530i | \(-0.827966\pi\) | ||
0.857472 | − | 0.514530i | \(-0.172034\pi\) | |||||||
\(242\) | −170.598 | − | 44.0962i | −0.704950 | − | 0.182216i | ||||
\(243\) | 195.757 | − | 81.0851i | 0.805583 | − | 0.333684i | ||||
\(244\) | −20.1910 | + | 177.621i | −0.0827500 | + | 0.727953i | ||||
\(245\) | −27.1484 | − | 11.2452i | −0.110810 | − | 0.0458990i | ||||
\(246\) | −210.523 | + | 29.6147i | −0.855783 | + | 0.120385i | ||||
\(247\) | −157.279 | − | 157.279i | −0.636755 | − | 0.636755i | ||||
\(248\) | −74.7749 | + | 1.98694i | −0.301512 | + | 0.00801185i | ||||
\(249\) | 219.436 | + | 219.436i | 0.881268 | + | 0.881268i | ||||
\(250\) | −163.567 | + | 217.119i | −0.654269 | + | 0.868476i | ||||
\(251\) | 3.93106 | + | 1.62830i | 0.0156616 | + | 0.00648725i | 0.390500 | − | 0.920603i | \(-0.372302\pi\) |
−0.374839 | + | 0.927090i | \(0.622302\pi\) | |||||||
\(252\) | 40.8666 | + | 22.6390i | 0.162169 | + | 0.0898372i | ||||
\(253\) | −9.11311 | + | 3.77477i | −0.0360202 | + | 0.0149200i | ||||
\(254\) | 36.2402 | + | 61.5056i | 0.142678 | + | 0.242148i | ||||
\(255\) | − | 77.8711i | − | 0.305377i | ||||||
\(256\) | −111.986 | + | 230.207i | −0.437446 | + | 0.899245i | ||||
\(257\) | 328.650 | 1.27879 | 0.639397 | − | 0.768877i | \(-0.279184\pi\) | ||||
0.639397 | + | 0.768877i | \(0.279184\pi\) | |||||||
\(258\) | −27.2541 | + | 16.0586i | −0.105636 | + | 0.0622426i | ||||
\(259\) | −28.2004 | − | 68.0818i | −0.108882 | − | 0.262864i | ||||
\(260\) | −168.535 | + | 304.229i | −0.648210 | + | 1.17011i | ||||
\(261\) | 49.0709 | − | 118.468i | 0.188011 | − | 0.453899i | ||||
\(262\) | −55.7542 | − | 42.0025i | −0.212802 | − | 0.160315i | ||||
\(263\) | −54.3548 | + | 54.3548i | −0.206672 | + | 0.206672i | −0.802851 | − | 0.596179i | \(-0.796685\pi\) |
0.596179 | + | 0.802851i | \(0.296685\pi\) | |||||||
\(264\) | 2.61001 | + | 98.2231i | 0.00988641 | + | 0.372057i | ||||
\(265\) | −93.1815 | + | 93.1815i | −0.351628 | + | 0.351628i | ||||
\(266\) | −7.91568 | − | 56.2704i | −0.0297582 | − | 0.211543i | ||||
\(267\) | 68.5057 | − | 165.387i | 0.256576 | − | 0.619428i | ||||
\(268\) | 76.2678 | + | 8.66973i | 0.284581 | + | 0.0323497i | ||||
\(269\) | 81.3377 | + | 196.366i | 0.302370 | + | 0.729987i | 0.999910 | + | 0.0134403i | \(0.00427829\pi\) |
−0.697539 | + | 0.716547i | \(0.745722\pi\) | |||||||
\(270\) | −60.3550 | + | 233.499i | −0.223537 | + | 0.864813i | ||||
\(271\) | −55.9797 | −0.206567 | −0.103284 | − | 0.994652i | \(-0.532935\pi\) | ||||
−0.103284 | + | 0.994652i | \(0.532935\pi\) | |||||||
\(272\) | −117.503 | + | 73.5084i | −0.431998 | + | 0.270251i | ||||
\(273\) | 117.347i | 0.429843i | ||||||||
\(274\) | 121.248 | − | 469.080i | 0.442511 | − | 1.71197i | ||||
\(275\) | 39.0947 | − | 16.1935i | 0.142162 | − | 0.0588856i | ||||
\(276\) | −9.17306 | − | 11.5260i | −0.0332357 | − | 0.0417610i | ||||
\(277\) | 234.982 | + | 97.3327i | 0.848310 | + | 0.351382i | 0.764125 | − | 0.645068i | \(-0.223171\pi\) |
0.0841856 | + | 0.996450i | \(0.473171\pi\) | |||||||
\(278\) | 0.0429556 | + | 0.305360i | 0.000154517 | + | 0.00109842i | ||||
\(279\) | 29.1865 | + | 29.1865i | 0.104611 | + | 0.104611i | ||||
\(280\) | −81.1570 | + | 36.1710i | −0.289846 | + | 0.129182i | ||||
\(281\) | −77.2032 | − | 77.2032i | −0.274744 | − | 0.274744i | 0.556262 | − | 0.831007i | \(-0.312235\pi\) |
−0.831007 | + | 0.556262i | \(0.812235\pi\) | |||||||
\(282\) | 38.4795 | + | 28.9886i | 0.136452 | + | 0.102797i | ||||
\(283\) | 134.816 | + | 55.8427i | 0.476382 | + | 0.197324i | 0.607937 | − | 0.793985i | \(-0.291997\pi\) |
−0.131555 | + | 0.991309i | \(0.541997\pi\) | |||||||
\(284\) | −96.1999 | − | 335.163i | −0.338732 | − | 1.18015i | ||||
\(285\) | 89.1863 | − | 36.9422i | 0.312934 | − | 0.129622i | ||||
\(286\) | 204.705 | − | 120.616i | 0.715750 | − | 0.421733i | ||||
\(287\) | 131.334i | 0.457611i | ||||||||
\(288\) | 134.697 | − | 42.5653i | 0.467699 | − | 0.147796i | ||||
\(289\) | 213.959 | 0.740342 | ||||||||
\(290\) | 123.803 | + | 210.114i | 0.426908 | + | 0.724532i | ||||
\(291\) | −84.5324 | − | 204.079i | −0.290489 | − | 0.701303i | ||||
\(292\) | 103.198 | + | 359.546i | 0.353419 | + | 1.23132i | ||||
\(293\) | 4.70697 | − | 11.3636i | 0.0160647 | − | 0.0387837i | −0.915644 | − | 0.401991i | \(-0.868318\pi\) |
0.931708 | + | 0.363207i | \(0.118318\pi\) | |||||||
\(294\) | −18.0390 | + | 23.9449i | −0.0613571 | + | 0.0814454i | ||||
\(295\) | 171.511 | − | 171.511i | 0.581392 | − | 0.581392i | ||||
\(296\) | −208.053 | − | 79.7717i | −0.702880 | − | 0.269499i | ||||
\(297\) | 116.502 | − | 116.502i | 0.392264 | − | 0.392264i | ||||
\(298\) | −555.923 | + | 78.2029i | −1.86551 | + | 0.262426i | ||||
\(299\) | −13.6313 | + | 32.9089i | −0.0455896 | + | 0.110063i | ||||
\(300\) | 39.3519 | + | 49.4460i | 0.131173 | + | 0.164820i | ||||
\(301\) | 7.47838 | + | 18.0544i | 0.0248451 | + | 0.0599814i | ||||
\(302\) | −176.447 | − | 45.6080i | −0.584261 | − | 0.151020i | ||||
\(303\) | 68.4355 | 0.225860 | ||||||||
\(304\) | −139.933 | − | 99.7049i | −0.460308 | − | 0.327977i | ||||
\(305\) | 187.609i | 0.615110i | ||||||||
\(306\) | 74.0481 | + | 19.1400i | 0.241987 | + | 0.0625489i | ||||
\(307\) | −0.506747 | + | 0.209902i | −0.00165064 | + | 0.000683718i | −0.383509 | − | 0.923537i | \(-0.625284\pi\) |
0.381858 | + | 0.924221i | \(0.375284\pi\) | |||||||
\(308\) | 60.3119 | + | 6.85595i | 0.195818 | + | 0.0222596i | ||||
\(309\) | −82.8347 | − | 34.3112i | −0.268073 | − | 0.111040i | ||||
\(310\) | −77.7366 | + | 10.9354i | −0.250763 | + | 0.0352754i | ||||
\(311\) | 120.370 | + | 120.370i | 0.387040 | + | 0.387040i | 0.873630 | − | 0.486590i | \(-0.161759\pi\) |
−0.486590 | + | 0.873630i | \(0.661759\pi\) | |||||||
\(312\) | 257.475 | + | 244.145i | 0.825239 | + | 0.782518i | ||||
\(313\) | 188.546 | + | 188.546i | 0.602383 | + | 0.602383i | 0.940944 | − | 0.338562i | \(-0.109940\pi\) |
−0.338562 | + | 0.940944i | \(0.609940\pi\) | |||||||
\(314\) | −127.994 | + | 169.899i | −0.407623 | + | 0.541079i | ||||
\(315\) | 45.2975 | + | 18.7628i | 0.143801 | + | 0.0595645i | ||||
\(316\) | −293.528 | + | 529.860i | −0.928886 | + | 1.67677i | ||||
\(317\) | −79.6039 | + | 32.9730i | −0.251116 | + | 0.104016i | −0.504691 | − | 0.863300i | \(-0.668394\pi\) |
0.253575 | + | 0.967316i | \(0.418394\pi\) | |||||||
\(318\) | 68.2499 | + | 115.831i | 0.214622 | + | 0.364249i | ||||
\(319\) | − | 166.605i | − | 0.522273i | ||||||
\(320\) | −89.4867 | + | 253.324i | −0.279646 | + | 0.791638i | ||||
\(321\) | −311.509 | −0.970434 | ||||||||
\(322\) | −7.84035 | + | 4.61968i | −0.0243489 | + | 0.0143468i | ||||
\(323\) | −35.5996 | − | 85.9451i | −0.110216 | − | 0.266084i | ||||
\(324\) | 76.2158 | + | 42.2215i | 0.235234 | + | 0.130313i | ||||
\(325\) | 58.4774 | − | 141.177i | 0.179931 | − | 0.434391i | ||||
\(326\) | −504.757 | − | 380.260i | −1.54834 | − | 1.16644i | ||||
\(327\) | 217.539 | − | 217.539i | 0.665255 | − | 0.665255i | ||||
\(328\) | 288.164 | + | 273.246i | 0.878550 | + | 0.833068i | ||||
\(329\) | 21.0450 | − | 21.0450i | 0.0639664 | − | 0.0639664i | ||||
\(330\) | 14.3645 | + | 102.113i | 0.0435288 | + | 0.309435i | ||||
\(331\) | −213.255 | + | 514.844i | −0.644276 | + | 1.55542i | 0.176580 | + | 0.984286i | \(0.443497\pi\) |
−0.820856 | + | 0.571135i | \(0.806503\pi\) | |||||||
\(332\) | 65.4733 | − | 575.969i | 0.197209 | − | 1.73485i | ||||
\(333\) | 47.0527 | + | 113.595i | 0.141299 | + | 0.341127i | ||||
\(334\) | −78.3392 | + | 303.076i | −0.234549 | + | 0.907414i | ||||
\(335\) | 80.5565 | 0.240467 | ||||||||
\(336\) | 15.0075 | + | 89.3983i | 0.0446651 | + | 0.266066i | ||||
\(337\) | − | 618.277i | − | 1.83465i | −0.398140 | − | 0.917325i | \(-0.630344\pi\) | ||
0.398140 | − | 0.917325i | \(-0.369656\pi\) | |||||||
\(338\) | 130.132 | − | 503.452i | 0.385007 | − | 1.48950i | ||||
\(339\) | −176.145 | + | 72.9618i | −0.519603 | + | 0.215226i | ||||
\(340\) | −113.814 | + | 90.5797i | −0.334748 | + | 0.266411i | ||||
\(341\) | 49.5469 | + | 20.5230i | 0.145299 | + | 0.0601847i | ||||
\(342\) | 13.2074 | + | 93.8878i | 0.0386181 | + | 0.274526i | ||||
\(343\) | 13.0958 | + | 13.0958i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 55.1728 | + | 21.1544i | 0.160386 | + | 0.0614954i | ||||
\(345\) | −10.9315 | − | 10.9315i | −0.0316856 | − | 0.0316856i | ||||
\(346\) | 345.030 | + | 259.929i | 0.997195 | + | 0.751239i | ||||
\(347\) | 101.100 | + | 41.8772i | 0.291356 | + | 0.120683i | 0.523574 | − | 0.851980i | \(-0.324598\pi\) |
−0.232218 | + | 0.972664i | \(0.574598\pi\) | |||||||
\(348\) | 239.150 | − | 68.6419i | 0.687214 | − | 0.197247i | ||||
\(349\) | 120.493 | − | 49.9099i | 0.345252 | − | 0.143008i | −0.203318 | − | 0.979113i | \(-0.565172\pi\) |
0.548570 | + | 0.836105i | \(0.315172\pi\) | |||||||
\(350\) | 33.6347 | − | 19.8182i | 0.0960990 | − | 0.0566233i | ||||
\(351\) | − | 594.972i | − | 1.69508i | ||||||
\(352\) | 140.524 | − | 118.068i | 0.399216 | − | 0.335420i | ||||
\(353\) | 595.396 | 1.68667 | 0.843337 | − | 0.537384i | \(-0.180588\pi\) | ||||
0.843337 | + | 0.537384i | \(0.180588\pi\) | |||||||
\(354\) | −125.621 | − | 213.200i | −0.354863 | − | 0.602260i | ||||
\(355\) | −140.042 | − | 338.091i | −0.394484 | − | 0.952369i | ||||
\(356\) | −321.412 | + | 92.2528i | −0.902842 | + | 0.259137i | ||||
\(357\) | −18.7816 | + | 45.3429i | −0.0526096 | + | 0.127011i | ||||
\(358\) | 158.295 | − | 210.120i | 0.442164 | − | 0.586928i | ||||
\(359\) | 0.0485624 | − | 0.0485624i | 0.000135271 | − | 0.000135271i | −0.707039 | − | 0.707174i | \(-0.749970\pi\) |
0.707174 | + | 0.707039i | \(0.249970\pi\) | |||||||
\(360\) | 135.411 | − | 60.3517i | 0.376143 | − | 0.167643i | ||||
\(361\) | −173.721 | + | 173.721i | −0.481220 | + | 0.481220i | ||||
\(362\) | −488.995 | + | 68.7880i | −1.35082 | + | 0.190022i | ||||
\(363\) | −72.1976 | + | 174.300i | −0.198891 | + | 0.480166i | ||||
\(364\) | 171.511 | − | 136.498i | 0.471185 | − | 0.374995i | ||||
\(365\) | 150.230 | + | 362.687i | 0.411589 | + | 0.993663i | ||||
\(366\) | 185.312 | + | 47.8994i | 0.506316 | + | 0.130873i | ||||
\(367\) | −611.483 | −1.66617 | −0.833083 | − | 0.553148i | \(-0.813427\pi\) | ||||
−0.833083 | + | 0.553148i | \(0.813427\pi\) | |||||||
\(368\) | −6.17601 | + | 26.8142i | −0.0167826 | + | 0.0728647i | ||||
\(369\) | − | 219.133i | − | 0.593856i | ||||||
\(370\) | −226.404 | − | 58.5210i | −0.611903 | − | 0.158165i | ||||
\(371\) | 76.7322 | − | 31.7835i | 0.206825 | − | 0.0856699i | ||||
\(372\) | −9.04587 | + | 79.5767i | −0.0243169 | + | 0.213916i | ||||
\(373\) | 385.354 | + | 159.619i | 1.03312 | + | 0.427932i | 0.833838 | − | 0.552010i | \(-0.186139\pi\) |
0.199282 | + | 0.979942i | \(0.436139\pi\) | |||||||
\(374\) | 98.4026 | − | 13.8425i | 0.263108 | − | 0.0370120i | ||||
\(375\) | 205.806 | + | 205.806i | 0.548815 | + | 0.548815i | ||||
\(376\) | −2.39045 | − | 89.9603i | −0.00635758 | − | 0.239256i | ||||
\(377\) | −425.422 | − | 425.422i | −1.12844 | − | 1.12844i | ||||
\(378\) | 91.4611 | − | 121.405i | 0.241960 | − | 0.321178i | ||||
\(379\) | 529.081 | + | 219.152i | 1.39599 | + | 0.578239i | 0.948708 | − | 0.316153i | \(-0.102391\pi\) |
0.447284 | + | 0.894392i | \(0.352391\pi\) | |||||||
\(380\) | −157.735 | − | 87.3810i | −0.415093 | − | 0.229950i | ||||
\(381\) | 70.6168 | − | 29.2504i | 0.185346 | − | 0.0767728i | ||||
\(382\) | −206.677 | − | 350.765i | −0.541039 | − | 0.918232i | ||||
\(383\) | 22.9825i | 0.0600065i | 0.999550 | + | 0.0300032i | \(0.00955176\pi\) | ||||
−0.999550 | + | 0.0300032i | \(0.990448\pi\) | |||||||
\(384\) | 227.375 | + | 153.069i | 0.592123 | + | 0.398616i | ||||
\(385\) | 63.7033 | 0.165463 | ||||||||
\(386\) | −212.648 | + | 125.296i | −0.550900 | + | 0.324601i | ||||
\(387\) | −12.4778 | − | 30.1240i | −0.0322423 | − | 0.0778398i | ||||
\(388\) | −199.948 | + | 360.935i | −0.515331 | + | 0.930246i | ||||
\(389\) | −221.493 | + | 534.732i | −0.569392 | + | 1.37463i | 0.332677 | + | 0.943041i | \(0.392048\pi\) |
−0.902069 | + | 0.431593i | \(0.857952\pi\) | |||||||
\(390\) | 297.424 | + | 224.065i | 0.762625 | + | 0.574525i | ||||
\(391\) | −10.5343 | + | 10.5343i | −0.0269418 | + | 0.0269418i | ||||
\(392\) | 55.9802 | − | 1.48752i | 0.142807 | − | 0.00379470i | ||||
\(393\) | −52.8490 | + | 52.8490i | −0.134476 | + | 0.134476i | ||||
\(394\) | −63.4276 | − | 450.890i | −0.160984 | − | 1.14439i | ||||
\(395\) | −243.272 | + | 587.309i | −0.615877 | + | 1.48686i | ||||
\(396\) | −100.631 | − | 11.4392i | −0.254119 | − | 0.0288869i | ||||
\(397\) | −100.290 | − | 242.122i | −0.252621 | − | 0.609880i | 0.745793 | − | 0.666177i | \(-0.232071\pi\) |
−0.998414 | + | 0.0562971i | \(0.982071\pi\) | |||||||
\(398\) | 178.457 | − | 690.410i | 0.448385 | − | 1.73470i | ||||
\(399\) | −60.8416 | −0.152485 | ||||||||
\(400\) | 26.4947 | − | 115.031i | 0.0662367 | − | 0.287578i | ||||
\(401\) | − | 313.535i | − | 0.781883i | −0.920416 | − | 0.390941i | \(-0.872150\pi\) | ||
0.920416 | − | 0.390941i | \(-0.127850\pi\) | |||||||
\(402\) | 20.5673 | − | 79.5701i | 0.0511625 | − | 0.197936i | ||||
\(403\) | 178.922 | − | 74.1117i | 0.443974 | − | 0.183900i | ||||
\(404\) | −79.6043 | − | 100.023i | −0.197040 | − | 0.247583i | ||||
\(405\) | 84.4794 | + | 34.9925i | 0.208591 | + | 0.0864012i | ||||
\(406\) | −21.4111 | − | 152.206i | −0.0527366 | − | 0.374891i | ||||
\(407\) | 112.962 | + | 112.962i | 0.277549 | + | 0.277549i | ||||
\(408\) | 60.4122 | + | 135.547i | 0.148069 | + | 0.332223i | ||||
\(409\) | 73.0580 | + | 73.0580i | 0.178626 | + | 0.178626i | 0.790757 | − | 0.612131i | \(-0.209687\pi\) |
−0.612131 | + | 0.790757i | \(0.709687\pi\) | |||||||
\(410\) | 332.875 | + | 250.772i | 0.811890 | + | 0.611639i | ||||
\(411\) | −479.260 | − | 198.516i | −1.16608 | − | 0.483008i | ||||
\(412\) | 46.2051 | + | 160.980i | 0.112148 | + | 0.390728i | ||||
\(413\) | −141.234 | + | 58.5011i | −0.341971 | + | 0.141649i | ||||
\(414\) | 13.0817 | − | 7.70799i | 0.0315984 | − | 0.0186183i | ||||
\(415\) | − | 608.358i | − | 1.46592i | ||||||
\(416\) | 57.3414 | − | 660.308i | 0.137840 | − | 1.58728i | ||||
\(417\) | 0.330166 | 0.000791765 | ||||||||
\(418\) | 62.5363 | + | 106.134i | 0.149608 | + | 0.253910i | ||||
\(419\) | −198.670 | − | 479.631i | −0.474152 | − | 1.14470i | −0.962311 | − | 0.271950i | \(-0.912332\pi\) |
0.488159 | − | 0.872754i | \(-0.337668\pi\) | |||||||
\(420\) | 26.2460 | + | 91.4418i | 0.0624905 | + | 0.217719i | ||||
\(421\) | 61.5597 | − | 148.618i | 0.146223 | − | 0.353013i | −0.833751 | − | 0.552141i | \(-0.813811\pi\) |
0.979973 | + | 0.199128i | \(0.0638111\pi\) | |||||||
\(422\) | −63.2755 | + | 83.9920i | −0.149942 | + | 0.199033i | ||||
\(423\) | −35.1137 | + | 35.1137i | −0.0830112 | + | 0.0830112i | ||||
\(424\) | 89.9074 | − | 234.487i | 0.212046 | − | 0.553036i | ||||
\(425\) | 45.1913 | − | 45.1913i | 0.106333 | − | 0.106333i | ||||
\(426\) | −369.706 | + | 52.0074i | −0.867855 | + | 0.122083i | ||||
\(427\) | 45.2491 | − | 109.241i | 0.105970 | − | 0.255834i | ||||
\(428\) | 362.348 | + | 455.294i | 0.846608 | + | 1.06377i | ||||
\(429\) | −97.3520 | − | 235.028i | −0.226928 | − | 0.547852i | ||||
\(430\) | 60.0394 | + | 15.5190i | 0.139627 | + | 0.0360907i | ||||
\(431\) | 607.699 | 1.40998 | 0.704988 | − | 0.709220i | \(-0.250953\pi\) | ||||
0.704988 | + | 0.709220i | \(0.250953\pi\) | |||||||
\(432\) | −76.0907 | − | 453.266i | −0.176136 | − | 1.04923i | ||||
\(433\) | 464.600i | 1.07298i | 0.843907 | + | 0.536489i | \(0.180250\pi\) | ||||
−0.843907 | + | 0.536489i | \(0.819750\pi\) | |||||||
\(434\) | 47.9020 | + | 12.3817i | 0.110373 | + | 0.0285293i | ||||
\(435\) | 241.240 | − | 99.9247i | 0.554574 | − | 0.229712i | ||||
\(436\) | −570.990 | − | 64.9072i | −1.30961 | − | 0.148870i | ||||
\(437\) | −17.0624 | − | 7.06749i | −0.0390445 | − | 0.0161727i | ||||
\(438\) | 396.602 | − | 55.7909i | 0.905485 | − | 0.127376i | ||||
\(439\) | −458.960 | − | 458.960i | −1.04547 | − | 1.04547i | −0.998916 | − | 0.0465501i | \(-0.985177\pi\) |
−0.0465501 | − | 0.998916i | \(-0.514823\pi\) | |||||||
\(440\) | 132.537 | − | 139.773i | 0.301222 | − | 0.317667i | ||||
\(441\) | −21.8505 | − | 21.8505i | −0.0495476 | − | 0.0495476i | ||||
\(442\) | 215.922 | − | 286.615i | 0.488511 | − | 0.648450i | ||||
\(443\) | 679.713 | + | 281.546i | 1.53434 | + | 0.635544i | 0.980401 | − | 0.197013i | \(-0.0631241\pi\) |
0.553939 | + | 0.832557i | \(0.313124\pi\) | |||||||
\(444\) | −115.609 | + | 208.691i | −0.260381 | + | 0.470024i | ||||
\(445\) | −324.219 | + | 134.296i | −0.728583 | + | 0.301789i | ||||
\(446\) | −48.0229 | − | 81.5027i | −0.107675 | − | 0.182741i | ||||
\(447\) | 601.084i | 1.34471i | ||||||||
\(448\) | 113.205 | − | 125.923i | 0.252691 | − | 0.281078i | ||||
\(449\) | 227.489 | 0.506657 | 0.253328 | − | 0.967380i | \(-0.418475\pi\) | ||||
0.253328 | + | 0.967380i | \(0.418475\pi\) | |||||||
\(450\) | −56.1198 | + | 33.0668i | −0.124711 | + | 0.0734818i | ||||
\(451\) | −108.956 | − | 263.043i | −0.241587 | − | 0.583243i | ||||
\(452\) | 311.531 | + | 172.580i | 0.689229 | + | 0.381814i | ||||
\(453\) | −74.6728 | + | 180.276i | −0.164841 | + | 0.397961i | ||||
\(454\) | 426.583 | + | 321.368i | 0.939611 | + | 0.707858i | ||||
\(455\) | 162.665 | − | 162.665i | 0.357505 | − | 0.357505i | ||||
\(456\) | −126.583 | + | 133.494i | −0.277595 | + | 0.292751i | ||||
\(457\) | 180.745 | − | 180.745i | 0.395504 | − | 0.395504i | −0.481140 | − | 0.876644i | \(-0.659777\pi\) |
0.876644 | + | 0.481140i | \(0.159777\pi\) | |||||||
\(458\) | 106.346 | + | 755.983i | 0.232196 | + | 1.65062i | ||||
\(459\) | 95.2265 | − | 229.897i | 0.207465 | − | 0.500865i | ||||
\(460\) | −3.26165 | + | 28.6928i | −0.00709054 | + | 0.0623756i | ||||
\(461\) | 156.103 | + | 376.865i | 0.338618 | + | 0.817495i | 0.997849 | + | 0.0655552i | \(0.0208818\pi\) |
−0.659231 | + | 0.751940i | \(0.729118\pi\) | |||||||
\(462\) | 16.2644 | − | 62.9234i | 0.0352044 | − | 0.136198i | ||||
\(463\) | 112.633 | 0.243267 | 0.121634 | − | 0.992575i | \(-0.461187\pi\) | ||||
0.121634 | + | 0.992575i | \(0.461187\pi\) | |||||||
\(464\) | −378.505 | − | 269.691i | −0.815744 | − | 0.581231i | ||||
\(465\) | 84.0515i | 0.180756i | ||||||||
\(466\) | 54.2102 | − | 209.727i | 0.116331 | − | 0.450058i | ||||
\(467\) | −26.6319 | + | 11.0313i | −0.0570276 | + | 0.0236216i | −0.411015 | − | 0.911629i | \(-0.634826\pi\) |
0.353987 | + | 0.935250i | \(0.384826\pi\) | |||||||
\(468\) | −286.168 | + | 227.749i | −0.611471 | + | 0.486643i | ||||
\(469\) | −46.9065 | − | 19.4293i | −0.100014 | − | 0.0414271i | ||||
\(470\) | −13.1561 | − | 93.5234i | −0.0279918 | − | 0.198986i | ||||
\(471\) | 161.046 | + | 161.046i | 0.341923 | + | 0.341923i | ||||
\(472\) | −165.484 | + | 431.600i | −0.350603 | + | 0.914406i | ||||
\(473\) | −29.9561 | − | 29.9561i | −0.0633322 | − | 0.0633322i | ||||
\(474\) | 518.007 | + | 390.242i | 1.09284 | + | 0.823295i | ||||
\(475\) | 73.1968 | + | 30.3191i | 0.154099 | + | 0.0638297i | ||||
\(476\) | 88.1187 | − | 25.2922i | 0.185123 | − | 0.0531348i | ||||
\(477\) | −128.029 | + | 53.0312i | −0.268404 | + | 0.111176i | ||||
\(478\) | 728.985 | − | 429.531i | 1.52507 | − | 0.898601i | ||||
\(479\) | 708.778i | 1.47970i | 0.672770 | + | 0.739852i | \(0.265104\pi\) | ||||
−0.672770 | + | 0.739852i | \(0.734896\pi\) | |||||||
\(480\) | 255.241 | + | 132.661i | 0.531752 | + | 0.276378i | ||||
\(481\) | 576.893 | 1.19936 | ||||||||
\(482\) | 251.798 | + | 427.342i | 0.522402 | + | 0.886601i | ||||
\(483\) | 3.72866 | + | 9.00178i | 0.00771980 | + | 0.0186372i | ||||
\(484\) | 338.733 | − | 97.2245i | 0.699862 | − | 0.200877i | ||||
\(485\) | −165.714 | + | 400.069i | −0.341678 | + | 0.824885i | ||||
\(486\) | −254.988 | + | 338.472i | −0.524667 | + | 0.696444i | ||||
\(487\) | −246.756 | + | 246.756i | −0.506686 | + | 0.506686i | −0.913508 | − | 0.406822i | \(-0.866637\pi\) |
0.406822 | + | 0.913508i | \(0.366637\pi\) | |||||||
\(488\) | −145.546 | − | 326.563i | −0.298251 | − | 0.669186i | ||||
\(489\) | −478.456 | + | 478.456i | −0.978437 | + | 0.978437i | ||||
\(490\) | 58.1975 | − | 8.18676i | 0.118770 | − | 0.0167077i | ||||
\(491\) | −22.4270 | + | 54.1436i | −0.0456762 | + | 0.110272i | −0.945071 | − | 0.326865i | \(-0.894008\pi\) |
0.899395 | + | 0.437137i | \(0.144008\pi\) | |||||||
\(492\) | 332.690 | − | 264.773i | 0.676199 | − | 0.538157i | ||||
\(493\) | −96.2933 | − | 232.473i | −0.195321 | − | 0.471547i | ||||
\(494\) | 430.696 | + | 111.326i | 0.871854 | + | 0.225357i | ||||
\(495\) | −106.290 | −0.214727 | ||||||||
\(496\) | 126.829 | − | 79.3426i | 0.255704 | − | 0.159965i | ||||
\(497\) | 230.641i | 0.464066i | ||||||||
\(498\) | −600.909 | − | 155.323i | −1.20664 | − | 0.311894i | ||||
\(499\) | −790.484 | + | 327.429i | −1.58414 | + | 0.656171i | −0.989062 | − | 0.147500i | \(-0.952877\pi\) |
−0.595074 | + | 0.803671i | \(0.702877\pi\) | |||||||
\(500\) | 61.4064 | − | 540.193i | 0.122813 | − | 1.08039i | ||||
\(501\) | 309.654 | + | 128.263i | 0.618071 | + | 0.256013i | ||||
\(502\) | −8.42694 | + | 1.18543i | −0.0167867 | + | 0.00236142i | ||||
\(503\) | 212.220 | + | 212.220i | 0.421908 | + | 0.421908i | 0.885860 | − | 0.463952i | \(-0.153569\pi\) |
−0.463952 | + | 0.885860i | \(0.653569\pi\) | |||||||
\(504\) | −93.4036 | + | 2.48195i | −0.185325 | + | 0.00492450i | ||||
\(505\) | −94.8643 | − | 94.8643i | −0.187850 | − | 0.187850i | ||||
\(506\) | 11.8705 | − | 15.7569i | 0.0234595 | − | 0.0311402i | ||||
\(507\) | −514.378 | − | 213.062i | −1.01455 | − | 0.420241i | ||||
\(508\) | −124.893 | − | 69.1874i | −0.245853 | − | 0.136196i | ||||
\(509\) | −605.640 | + | 250.864i | −1.18986 | + | 0.492857i | −0.887710 | − | 0.460403i | \(-0.847705\pi\) |
−0.302152 | + | 0.953260i | \(0.597705\pi\) | |||||||
\(510\) | 79.0624 | + | 134.182i | 0.155024 | + | 0.263101i | ||||
\(511\) | − | 247.420i | − | 0.484187i | ||||||
\(512\) | −40.7622 | − | 510.375i | −0.0796138 | − | 0.996826i | ||||
\(513\) | 308.478 | 0.601322 | ||||||||
\(514\) | −566.306 | + | 333.678i | −1.10176 | + | 0.649179i | ||||
\(515\) | 67.2625 | + | 162.386i | 0.130607 | + | 0.315313i | ||||
\(516\) | 30.6580 | − | 55.3420i | 0.0594147 | − | 0.107252i | ||||
\(517\) | −24.6908 | + | 59.6089i | −0.0477579 | + | 0.115298i | ||||
\(518\) | 117.716 | + | 88.6819i | 0.227252 | + | 0.171201i | ||||
\(519\) | 327.051 | − | 327.051i | 0.630156 | − | 0.630156i | ||||
\(520\) | −18.4767 | − | 695.339i | −0.0355322 | − | 1.33719i | ||||
\(521\) | 267.635 | − | 267.635i | 0.513695 | − | 0.513695i | −0.401962 | − | 0.915657i | \(-0.631671\pi\) |
0.915657 | + | 0.401962i | \(0.131671\pi\) | |||||||
\(522\) | 35.7246 | + | 253.957i | 0.0684380 | + | 0.486507i | ||||
\(523\) | −233.003 | + | 562.519i | −0.445512 | + | 1.07556i | 0.528473 | + | 0.848950i | \(0.322765\pi\) |
−0.973985 | + | 0.226612i | \(0.927235\pi\) | |||||||
\(524\) | 138.717 | + | 15.7686i | 0.264726 | + | 0.0300927i | ||||
\(525\) | −15.9957 | − | 38.6171i | −0.0304681 | − | 0.0735564i | ||||
\(526\) | 38.4739 | − | 148.847i | 0.0731444 | − | 0.282979i | ||||
\(527\) | 80.9969 | 0.153694 | ||||||||
\(528\) | −104.223 | − | 166.601i | −0.197392 | − | 0.315532i | ||||
\(529\) | − | 526.042i | − | 0.994409i | ||||||
\(530\) | 65.9566 | − | 255.171i | 0.124446 | − | 0.481454i | ||||
\(531\) | 235.651 | − | 97.6097i | 0.443786 | − | 0.183822i | ||||
\(532\) | 70.7710 | + | 88.9244i | 0.133028 | + | 0.167151i | ||||
\(533\) | −949.889 | − | 393.457i | −1.78216 | − | 0.738193i | ||||
\(534\) | 49.8735 | + | 354.537i | 0.0933961 | + | 0.663928i | ||||
\(535\) | 431.810 | + | 431.810i | 0.807121 | + | 0.807121i | ||||
\(536\) | −140.221 | + | 62.4955i | −0.261607 | + | 0.116596i | ||||
\(537\) | −199.172 | − | 199.172i | −0.370897 | − | 0.370897i | ||||
\(538\) | −339.526 | − | 255.782i | −0.631089 | − | 0.475432i | ||||
\(539\) | −37.0933 | − | 15.3645i | −0.0688187 | − | 0.0285056i | ||||
\(540\) | −133.072 | − | 463.628i | −0.246430 | − | 0.858570i | ||||
\(541\) | −122.630 | + | 50.7952i | −0.226674 | + | 0.0938913i | −0.493130 | − | 0.869956i | \(-0.664147\pi\) |
0.266456 | + | 0.963847i | \(0.414147\pi\) | |||||||
\(542\) | 96.4602 | − | 56.8361i | 0.177971 | − | 0.104864i | ||||
\(543\) | 528.719i | 0.973700i | ||||||||
\(544\) | 127.840 | − | 245.965i | 0.235001 | − | 0.452142i | ||||
\(545\) | −603.098 | −1.10660 | ||||||||
\(546\) | −119.142 | − | 202.204i | −0.218209 | − | 0.370337i | ||||
\(547\) | −89.7367 | − | 216.643i | −0.164052 | − | 0.396058i | 0.820381 | − | 0.571818i | \(-0.193762\pi\) |
−0.984433 | + | 0.175760i | \(0.943762\pi\) | |||||||
\(548\) | 267.331 | + | 931.388i | 0.487830 | + | 1.69961i | ||||
\(549\) | −75.4986 | + | 182.270i | −0.137520 | + | 0.332003i | ||||
\(550\) | −50.9238 | + | 67.5963i | −0.0925888 | + | 0.122902i | ||||
\(551\) | 220.571 | − | 220.571i | 0.400310 | − | 0.400310i | ||||
\(552\) | 27.5087 | + | 10.5474i | 0.0498346 | + | 0.0191076i | ||||
\(553\) | 283.305 | − | 283.305i | 0.512306 | − | 0.512306i | ||||
\(554\) | −503.726 | + | 70.8601i | −0.909252 | + | 0.127906i | ||||
\(555\) | −95.8149 | + | 231.318i | −0.172639 | + | 0.416789i | ||||
\(556\) | −0.384050 | − | 0.482562i | −0.000690737 | − | 0.000867917i | ||||
\(557\) | −225.718 | − | 544.931i | −0.405238 | − | 0.978332i | −0.986373 | − | 0.164524i | \(-0.947391\pi\) |
0.581135 | − | 0.813807i | \(-0.302609\pi\) | |||||||
\(558\) | −79.9251 | − | 20.6591i | −0.143235 | − | 0.0370234i | ||||
\(559\) | −152.984 | −0.273675 | ||||||||
\(560\) | 103.120 | − | 144.726i | 0.184142 | − | 0.258439i | ||||
\(561\) | − | 106.396i | − | 0.189655i | ||||||
\(562\) | 211.415 | + | 54.6467i | 0.376184 | + | 0.0972361i | ||||
\(563\) | −724.075 | + | 299.922i | −1.28610 | + | 0.532721i | −0.917821 | − | 0.396994i | \(-0.870053\pi\) |
−0.368280 | + | 0.929715i | \(0.620053\pi\) | |||||||
\(564\) | −95.7373 | − | 10.8829i | −0.169747 | − | 0.0192960i | ||||
\(565\) | 345.309 | + | 143.032i | 0.611166 | + | 0.253153i | ||||
\(566\) | −289.002 | + | 40.6546i | −0.510605 | + | 0.0718278i | ||||
\(567\) | −40.7510 | − | 40.7510i | −0.0718712 | − | 0.0718712i | ||||
\(568\) | 506.056 | + | 479.858i | 0.890943 | + | 0.844820i | ||||
\(569\) | −474.755 | − | 474.755i | −0.834367 | − | 0.834367i | 0.153744 | − | 0.988111i | \(-0.450867\pi\) |
−0.988111 | + | 0.153744i | \(0.950867\pi\) | |||||||
\(570\) | −116.172 | + | 154.207i | −0.203811 | + | 0.270538i | ||||
\(571\) | −480.443 | − | 199.006i | −0.841406 | − | 0.348522i | −0.0799979 | − | 0.996795i | \(-0.525491\pi\) |
−0.761408 | + | 0.648273i | \(0.775491\pi\) | |||||||
\(572\) | −230.271 | + | 415.673i | −0.402572 | + | 0.726700i | ||||
\(573\) | −402.725 | + | 166.814i | −0.702836 | + | 0.291124i | ||||
\(574\) | −133.343 | − | 226.306i | −0.232306 | − | 0.394261i | ||||
\(575\) | − | 12.6879i | − | 0.0220659i | ||||||
\(576\) | −188.884 | + | 210.103i | −0.327924 | + | 0.364763i | ||||
\(577\) | −226.938 | −0.393306 | −0.196653 | − | 0.980473i | \(-0.563007\pi\) | ||||
−0.196653 | + | 0.980473i | \(0.563007\pi\) | |||||||
\(578\) | −368.678 | + | 217.232i | −0.637852 | + | 0.375834i | ||||
\(579\) | 101.129 | + | 244.148i | 0.174662 | + | 0.421672i | ||||
\(580\) | −426.657 | − | 236.357i | −0.735616 | − | 0.407511i | ||||
\(581\) | −146.729 | + | 354.235i | −0.252546 | + | 0.609699i | ||||
\(582\) | 352.861 | + | 265.829i | 0.606291 | + | 0.456751i | ||||
\(583\) | −127.315 | + | 127.315i | −0.218379 | + | 0.218379i | ||||
\(584\) | −542.871 | − | 514.767i | −0.929574 | − | 0.881451i | ||||
\(585\) | −271.408 | + | 271.408i | −0.463945 | + | 0.463945i | ||||
\(586\) | 3.42676 | + | 24.3599i | 0.00584772 | + | 0.0415699i | ||||
\(587\) | 15.0818 | − | 36.4106i | 0.0256930 | − | 0.0620283i | −0.910512 | − | 0.413482i | \(-0.864312\pi\) |
0.936205 | + | 0.351454i | \(0.114312\pi\) | |||||||
\(588\) | 6.77220 | − | 59.5751i | 0.0115173 | − | 0.101318i | ||||
\(589\) | 38.4251 | + | 92.7664i | 0.0652378 | + | 0.157498i | ||||
\(590\) | −121.400 | + | 469.670i | −0.205763 | + | 0.796050i | ||||
\(591\) | −487.518 | −0.824903 | ||||||||
\(592\) | 439.493 | − | 73.7785i | 0.742387 | − | 0.124626i | ||||
\(593\) | − | 653.847i | − | 1.10261i | −0.834304 | − | 0.551304i | \(-0.814130\pi\) | ||
0.834304 | − | 0.551304i | \(-0.185870\pi\) | |||||||
\(594\) | −82.4639 | + | 319.033i | −0.138828 | + | 0.537093i | ||||
\(595\) | 88.8885 | − | 36.8188i | 0.149392 | − | 0.0618803i | ||||
\(596\) | 878.527 | − | 699.181i | 1.47404 | − | 1.17312i | ||||
\(597\) | −705.394 | − | 292.184i | −1.18156 | − | 0.489420i | ||||
\(598\) | −9.92385 | − | 70.5460i | −0.0165951 | − | 0.117970i | ||||
\(599\) | 639.281 | + | 639.281i | 1.06725 | + | 1.06725i | 0.997570 | + | 0.0696767i | \(0.0221968\pi\) |
0.0696767 | + | 0.997570i | \(0.477803\pi\) | |||||||
\(600\) | −118.011 | − | 45.2478i | −0.196685 | − | 0.0754130i | ||||
\(601\) | 0.494897 | + | 0.494897i | 0.000823457 | + | 0.000823457i | 0.707518 | − | 0.706695i | \(-0.249815\pi\) |
−0.706695 | + | 0.707518i | \(0.749815\pi\) | |||||||
\(602\) | −31.2168 | − | 23.5173i | −0.0518552 | − | 0.0390652i | ||||
\(603\) | 78.2641 | + | 32.4180i | 0.129791 | + | 0.0537613i | ||||
\(604\) | 350.346 | − | 100.558i | 0.580043 | − | 0.166486i | ||||
\(605\) | 341.692 | − | 141.533i | 0.564780 | − | 0.233940i | ||||
\(606\) | −117.923 | + | 69.4825i | −0.194593 | + | 0.114658i | ||||
\(607\) | 973.678i | 1.60408i | 0.597269 | + | 0.802041i | \(0.296252\pi\) | ||||
−0.597269 | + | 0.802041i | \(0.703748\pi\) | |||||||
\(608\) | 342.354 | + | 29.7301i | 0.563082 | + | 0.0488982i | ||||
\(609\) | −164.570 | −0.270230 | ||||||||
\(610\) | −190.479 | − | 323.274i | −0.312260 | − | 0.529957i | ||||
\(611\) | 89.1624 | + | 215.257i | 0.145929 | + | 0.352303i | ||||
\(612\) | −147.027 | + | 42.2003i | −0.240240 | + | 0.0689547i | ||||
\(613\) | 28.1023 | − | 67.8448i | 0.0458438 | − | 0.110677i | −0.899299 | − | 0.437335i | \(-0.855923\pi\) |
0.945143 | + | 0.326658i | \(0.105923\pi\) | |||||||
\(614\) | 0.660077 | − | 0.876187i | 0.00107504 | − | 0.00142701i | ||||
\(615\) | 315.530 | − | 315.530i | 0.513057 | − | 0.513057i | ||||
\(616\) | −110.886 | + | 49.4209i | −0.180010 | + | 0.0802287i | ||||
\(617\) | −257.190 | + | 257.190i | −0.416840 | + | 0.416840i | −0.884113 | − | 0.467273i | \(-0.845237\pi\) |
0.467273 | + | 0.884113i | \(0.345237\pi\) | |||||||
\(618\) | 177.571 | − | 24.9793i | 0.287332 | − | 0.0404195i | ||||
\(619\) | 104.274 | − | 251.741i | 0.168456 | − | 0.406689i | −0.816996 | − | 0.576644i | \(-0.804362\pi\) |
0.985452 | + | 0.169955i | \(0.0543621\pi\) | |||||||
\(620\) | 122.847 | − | 97.7688i | 0.198141 | − | 0.157692i | ||||
\(621\) | −18.9050 | − | 45.6408i | −0.0304429 | − | 0.0734956i | ||||
\(622\) | −329.623 | − | 85.2011i | −0.529941 | − | 0.136979i | ||||
\(623\) | 221.178 | 0.355020 | ||||||||
\(624\) | −691.542 | − | 159.280i | −1.10824 | − | 0.255257i | ||||
\(625\) | − | 386.127i | − | 0.617804i | ||||||
\(626\) | −516.319 | − | 133.458i | −0.824790 | − | 0.213192i | ||||
\(627\) | 121.856 | − | 50.4746i | 0.194348 | − | 0.0805017i | ||||
\(628\) | 48.0514 | − | 422.709i | 0.0765150 | − | 0.673104i | ||||
\(629\) | 222.911 | + | 92.3329i | 0.354390 | + | 0.146793i | ||||
\(630\) | −97.1032 | + | 13.6597i | −0.154132 | + | 0.0216821i | ||||
\(631\) | 550.270 | + | 550.270i | 0.872061 | + | 0.872061i | 0.992697 | − | 0.120636i | \(-0.0384934\pi\) |
−0.120636 | + | 0.992697i | \(0.538493\pi\) | |||||||
\(632\) | −32.1800 | − | 1211.04i | −0.0509177 | − | 1.91620i | ||||
\(633\) | 79.6154 | + | 79.6154i | 0.125775 | + | 0.125775i | ||||
\(634\) | 103.690 | − | 137.638i | 0.163549 | − | 0.217095i | ||||
\(635\) | −138.434 | − | 57.3414i | −0.218007 | − | 0.0903015i | ||||
\(636\) | −235.207 | − | 130.298i | −0.369822 | − | 0.204871i | ||||
\(637\) | −133.950 | + | 55.4838i | −0.210282 | + | 0.0871017i | ||||
\(638\) | 169.154 | + | 287.082i | 0.265132 | + | 0.449972i | ||||
\(639\) | − | 384.827i | − | 0.602233i | ||||||
\(640\) | −103.003 | − | 527.366i | −0.160942 | − | 0.824009i | ||||
\(641\) | −1000.57 | −1.56096 | −0.780480 | − | 0.625181i | \(-0.785025\pi\) | ||||
−0.780480 | + | 0.625181i | \(0.785025\pi\) | |||||||
\(642\) | 536.770 | − | 316.275i | 0.836091 | − | 0.492640i | ||||
\(643\) | −312.476 | − | 754.383i | −0.485965 | − | 1.17322i | −0.956733 | − | 0.290967i | \(-0.906023\pi\) |
0.470768 | − | 0.882257i | \(-0.343977\pi\) | |||||||
\(644\) | 8.81958 | − | 15.9206i | 0.0136950 | − | 0.0247214i | ||||
\(645\) | 25.4089 | − | 61.3424i | 0.0393936 | − | 0.0951045i | ||||
\(646\) | 148.603 | + | 111.950i | 0.230035 | + | 0.173297i | ||||
\(647\) | −51.8944 | + | 51.8944i | −0.0802077 | + | 0.0802077i | −0.746072 | − | 0.665865i | \(-0.768063\pi\) |
0.665865 | + | 0.746072i | \(0.268063\pi\) | |||||||
\(648\) | −174.197 | + | 4.62881i | −0.268823 | + | 0.00714323i | ||||
\(649\) | 234.338 | − | 234.338i | 0.361075 | − | 0.361075i | ||||
\(650\) | 42.5727 | + | 302.638i | 0.0654965 | + | 0.465597i | ||||
\(651\) | 20.2723 | − | 48.9416i | 0.0311402 | − | 0.0751791i | ||||
\(652\) | 1255.84 | + | 142.757i | 1.92613 | + | 0.218953i | ||||
\(653\) | 440.155 | + | 1062.63i | 0.674051 | + | 1.62730i | 0.774660 | + | 0.632378i | \(0.217921\pi\) |
−0.100609 | + | 0.994926i | \(0.532079\pi\) | |||||||
\(654\) | −153.980 | + | 595.713i | −0.235444 | + | 0.910876i | ||||
\(655\) | 146.517 | 0.223690 | ||||||||
\(656\) | −773.971 | − | 178.266i | −1.17983 | − | 0.271746i | ||||
\(657\) | 412.823i | 0.628345i | ||||||||
\(658\) | −14.8962 | + | 57.6301i | −0.0226387 | + | 0.0875837i | ||||
\(659\) | −246.623 | + | 102.155i | −0.374239 | + | 0.155015i | −0.561872 | − | 0.827224i | \(-0.689918\pi\) |
0.187633 | + | 0.982239i | \(0.439918\pi\) | |||||||
\(660\) | −128.428 | − | 161.370i | −0.194587 | − | 0.244500i | ||||
\(661\) | −234.890 | − | 97.2947i | −0.355356 | − | 0.147193i | 0.197862 | − | 0.980230i | \(-0.436600\pi\) |
−0.553218 | + | 0.833037i | \(0.686600\pi\) | |||||||
\(662\) | −155.254 | − | 1103.66i | −0.234523 | − | 1.66716i | ||||
\(663\) | −271.680 | − | 271.680i | −0.409774 | − | 0.409774i | ||||
\(664\) | 471.962 | + | 1058.94i | 0.710786 | + | 1.59479i | ||||
\(665\) | 84.3377 | + | 84.3377i | 0.126824 | + | 0.126824i | ||||
\(666\) | −196.411 | − | 147.967i | −0.294911 | − | 0.222172i | ||||
\(667\) | −46.1521 | − | 19.1168i | −0.0691935 | − | 0.0286609i | ||||
\(668\) | −172.724 | − | 601.777i | −0.258569 | − | 0.900863i | ||||
\(669\) | −93.5761 | + | 38.7605i | −0.139875 | + | 0.0579379i | ||||
\(670\) | −138.809 | + | 81.7889i | −0.207178 | + | 0.122073i | ||||
\(671\) | 256.332i | 0.382015i | ||||||||
\(672\) | −116.626 | − | 138.808i | −0.173550 | − | 0.206559i | ||||
\(673\) | 178.759 | 0.265615 | 0.132807 | − | 0.991142i | \(-0.457601\pi\) | ||||
0.132807 | + | 0.991142i | \(0.457601\pi\) | |||||||
\(674\) | 627.736 | + | 1065.37i | 0.931358 | + | 1.58067i | ||||
\(675\) | 81.1014 | + | 195.796i | 0.120150 | + | 0.290068i | ||||
\(676\) | 286.919 | + | 999.636i | 0.424437 | + | 1.47875i | ||||
\(677\) | −247.393 | + | 597.261i | −0.365426 | + | 0.882217i | 0.629061 | + | 0.777356i | \(0.283440\pi\) |
−0.994487 | + | 0.104861i | \(0.966560\pi\) | |||||||
\(678\) | 229.443 | − | 304.563i | 0.338411 | − | 0.449207i | ||||
\(679\) | 192.984 | − | 192.984i | 0.284219 | − | 0.284219i | ||||
\(680\) | 104.151 | − | 271.636i | 0.153163 | − | 0.399464i | ||||
\(681\) | 404.355 | − | 404.355i | 0.593767 | − | 0.593767i | ||||
\(682\) | −106.213 | + | 14.9411i | −0.155737 | + | 0.0219078i | ||||
\(683\) | 493.311 | − | 1190.96i | 0.722271 | − | 1.74372i | 0.0554925 | − | 0.998459i | \(-0.482327\pi\) |
0.666778 | − | 0.745256i | \(-0.267673\pi\) | |||||||
\(684\) | −118.082 | − | 148.371i | −0.172635 | − | 0.216917i | ||||
\(685\) | 389.164 | + | 939.524i | 0.568122 | + | 1.37157i | ||||
\(686\) | −35.8619 | − | 9.26959i | −0.0522768 | − | 0.0135125i | ||||
\(687\) | 817.396 | 1.18980 | ||||||||
\(688\) | −116.548 | + | 19.5651i | −0.169401 | + | 0.0284376i | ||||
\(689\) | 650.192i | 0.943675i | ||||||||
\(690\) | 29.9352 | + | 7.73765i | 0.0433843 | + | 0.0112140i | ||||
\(691\) | 1190.00 | − | 492.914i | 1.72214 | − | 0.713334i | 0.722380 | − | 0.691496i | \(-0.243048\pi\) |
0.999762 | − | 0.0218384i | \(-0.00695192\pi\) | |||||||
\(692\) | −858.435 | − | 97.5825i | −1.24051 | − | 0.141015i | ||||
\(693\) | 61.8905 | + | 25.6359i | 0.0893081 | + | 0.0369926i | ||||
\(694\) | −216.727 | + | 30.4874i | −0.312286 | + | 0.0439300i | ||||
\(695\) | −0.457671 | − | 0.457671i | −0.000658520 | − | 0.000658520i | ||||
\(696\) | −342.395 | + | 361.088i | −0.491946 | + | 0.518804i | ||||
\(697\) | −304.063 | − | 304.063i | −0.436245 | − | 0.436245i | ||||
\(698\) | −156.952 | + | 208.338i | −0.224859 | + | 0.298478i | ||||
\(699\) | −214.278 | − | 88.7570i | −0.306550 | − | 0.126977i | ||||
\(700\) | −37.8355 | + | 68.2984i | −0.0540507 | + | 0.0975692i | ||||
\(701\) | −281.010 | + | 116.398i | −0.400871 | + | 0.166046i | −0.574004 | − | 0.818852i | \(-0.694611\pi\) |
0.173134 | + | 0.984898i | \(0.444611\pi\) | |||||||
\(702\) | 604.074 | + | 1025.21i | 0.860505 | + | 1.46042i | ||||
\(703\) | 299.105i | 0.425469i | ||||||||
\(704\) | −122.267 | + | 346.120i | −0.173675 | + | 0.491648i | ||||
\(705\) | −101.121 | −0.143434 | ||||||||
\(706\) | −1025.94 | + | 604.505i | −1.45318 | + | 0.856239i | ||||
\(707\) | 32.3575 | + | 78.1179i | 0.0457673 | + | 0.110492i | ||||
\(708\) | 432.924 | + | 239.828i | 0.611474 | + | 0.338740i | ||||
\(709\) | 219.418 | − | 529.722i | 0.309476 | − | 0.747140i | −0.690247 | − | 0.723574i | \(-0.742498\pi\) |
0.999722 | − | 0.0235660i | \(-0.00750198\pi\) | |||||||
\(710\) | 584.574 | + | 440.390i | 0.823343 | + | 0.620267i | ||||
\(711\) | −472.698 | + | 472.698i | −0.664835 | + | 0.664835i | ||||
\(712\) | 460.169 | − | 485.292i | 0.646305 | − | 0.681590i | ||||
\(713\) | 11.3703 | − | 11.3703i | 0.0159472 | − | 0.0159472i | ||||
\(714\) | −13.6734 | − | 97.2005i | −0.0191504 | − | 0.136135i | ||||
\(715\) | −190.845 | + | 460.741i | −0.266916 | + | 0.644393i | ||||
\(716\) | −59.4270 | + | 522.780i | −0.0829986 | + | 0.730140i | ||||
\(717\) | −346.686 | − | 836.973i | −0.483522 | − | 1.16733i | ||||
\(718\) | −0.0343739 | + | 0.132984i | −4.78745e−5 | + | 0.000185215i | ||||
\(719\) | 528.842 | 0.735525 | 0.367762 | − | 0.929920i | \(-0.380124\pi\) | ||||
0.367762 | + | 0.929920i | \(0.380124\pi\) | |||||||
\(720\) | −172.056 | + | 241.477i | −0.238967 | + | 0.335384i | ||||
\(721\) | − | 110.777i | − | 0.153644i | ||||||
\(722\) | 122.964 | − | 475.721i | 0.170311 | − | 0.658893i | ||||
\(723\) | 490.646 | − | 203.232i | 0.678625 | − | 0.281096i | ||||
\(724\) | 772.761 | − | 615.007i | 1.06735 | − | 0.849457i | ||||
\(725\) | 197.990 | + | 82.0100i | 0.273089 | + | 0.113117i | ||||
\(726\) | −52.5613 | − | 373.644i | −0.0723984 | − | 0.514661i | ||||
\(727\) | 689.078 | + | 689.078i | 0.947838 | + | 0.947838i | 0.998705 | − | 0.0508675i | \(-0.0161986\pi\) |
−0.0508675 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(728\) | −156.949 | + | 409.339i | −0.215590 | + | 0.562279i | ||||
\(729\) | 459.457 | + | 459.457i | 0.630256 | + | 0.630256i | ||||
\(730\) | −627.101 | − | 472.428i | −0.859043 | − | 0.647162i | ||||
\(731\) | −59.1131 | − | 24.4855i | −0.0808661 | − | 0.0334958i | ||||
\(732\) | −367.948 | + | 105.610i | −0.502661 | + | 0.144276i | ||||
\(733\) | −269.119 | + | 111.473i | −0.367148 | + | 0.152078i | −0.558627 | − | 0.829419i | \(-0.688672\pi\) |
0.191479 | + | 0.981497i | \(0.438672\pi\) | |||||||
\(734\) | 1053.66 | − | 620.838i | 1.43551 | − | 0.845828i | ||||
\(735\) | − | 62.9252i | − | 0.0856125i | ||||||
\(736\) | −16.5824 | − | 52.4748i | −0.0225304 | − | 0.0712972i | ||||
\(737\) | 110.065 | 0.149342 | ||||||||
\(738\) | 222.485 | + | 377.594i | 0.301470 | + | 0.511644i | ||||
\(739\) | −68.3919 | − | 165.113i | −0.0925466 | − | 0.223427i | 0.870827 | − | 0.491589i | \(-0.163584\pi\) |
−0.963374 | + | 0.268162i | \(0.913584\pi\) | |||||||
\(740\) | 449.540 | − | 129.029i | 0.607486 | − | 0.174363i | ||||
\(741\) | 182.272 | − | 440.043i | 0.245981 | − | 0.593850i | ||||
\(742\) | −99.9497 | + | 132.673i | −0.134703 | + | 0.178805i | ||||
\(743\) | 698.165 | − | 698.165i | 0.939657 | − | 0.939657i | −0.0586236 | − | 0.998280i | \(-0.518671\pi\) |
0.998280 | + | 0.0586236i | \(0.0186712\pi\) | |||||||
\(744\) | −65.2069 | − | 146.305i | −0.0876437 | − | 0.196647i | ||||
\(745\) | 833.213 | − | 833.213i | 1.11841 | − | 1.11841i | ||||
\(746\) | −826.074 | + | 116.206i | −1.10734 | + | 0.155772i | ||||
\(747\) | 244.819 | − | 591.046i | 0.327736 | − | 0.791226i | ||||
\(748\) | −155.506 | + | 123.760i | −0.207896 | + | 0.165455i | ||||
\(749\) | −147.287 | − | 355.583i | −0.196645 | − | 0.474743i | ||||
\(750\) | −563.584 | − | 145.675i | −0.751445 | − | 0.194234i | ||||
\(751\) | −478.635 | −0.637330 | −0.318665 | − | 0.947867i | \(-0.603235\pi\) | ||||
−0.318665 | + | 0.947867i | \(0.603235\pi\) | |||||||
\(752\) | 95.4556 | + | 152.586i | 0.126936 | + | 0.202907i | ||||
\(753\) | 9.11150i | 0.0121003i | ||||||||
\(754\) | 1164.99 | + | 301.126i | 1.54508 | + | 0.399371i | ||||
\(755\) | 353.407 | − | 146.386i | 0.468088 | − | 0.193888i | ||||
\(756\) | −34.3363 | + | 302.057i | −0.0454184 | + | 0.399547i | ||||
\(757\) | −534.494 | − | 221.395i | −0.706069 | − | 0.292463i | 0.000607955 | − | 1.00000i | \(-0.499806\pi\) |
−0.706677 | + | 0.707537i | \(0.749806\pi\) | |||||||
\(758\) | −1134.18 | + | 159.547i | −1.49628 | + | 0.210485i | ||||
\(759\) | −14.9359 | − | 14.9359i | −0.0196784 | − | 0.0196784i | ||||
\(760\) | 360.516 | − | 9.57973i | 0.474363 | − | 0.0126049i | ||||
\(761\) | 276.510 | + | 276.510i | 0.363351 | + | 0.363351i | 0.865045 | − | 0.501694i | \(-0.167290\pi\) |
−0.501694 | + | 0.865045i | \(0.667290\pi\) | |||||||
\(762\) | −91.9838 | + | 122.099i | −0.120714 | + | 0.160235i | ||||
\(763\) | 351.173 | + | 145.460i | 0.460252 | + | 0.190643i | ||||
\(764\) | 712.262 | + | 394.574i | 0.932280 | + | 0.516458i | ||||
\(765\) | −148.311 | + | 61.4326i | −0.193871 | + | 0.0803040i | ||||
\(766\) | −23.3341 | − | 39.6018i | −0.0304623 | − | 0.0516994i | ||||
\(767\) | − | 1196.75i | − | 1.56030i | ||||||
\(768\) | −547.207 | − | 32.9031i | −0.712509 | − | 0.0428426i | ||||
\(769\) | 536.842 | 0.698104 | 0.349052 | − | 0.937103i | \(-0.386504\pi\) | ||||
0.349052 | + | 0.937103i | \(0.386504\pi\) | |||||||
\(770\) | −109.769 | + | 64.6779i | −0.142557 | + | 0.0839973i | ||||
\(771\) | 269.320 | + | 650.196i | 0.349312 | + | 0.843315i | ||||
\(772\) | 239.206 | − | 431.801i | 0.309853 | − | 0.559328i | ||||
\(773\) | 112.375 | − | 271.297i | 0.145375 | − | 0.350966i | −0.834373 | − | 0.551200i | \(-0.814170\pi\) |
0.979748 | + | 0.200234i | \(0.0641702\pi\) | |||||||
\(774\) | 52.0856 | + | 39.2388i | 0.0672941 | + | 0.0506961i | ||||
\(775\) | −48.7781 | + | 48.7781i | −0.0629394 | + | 0.0629394i | ||||
\(776\) | −21.9207 | − | 824.945i | −0.0282483 | − | 1.06307i | ||||
\(777\) | 111.582 | − | 111.582i | 0.143607 | − | 0.143607i | ||||
\(778\) | −161.252 | − | 1146.29i | −0.207264 | − | 1.47339i | ||||
\(779\) | 203.998 | − | 492.494i | 0.261871 | − | 0.632213i | ||||
\(780\) | −739.991 | − | 84.1184i | −0.948707 | − | 0.107844i | ||||
\(781\) | −191.341 | − | 461.939i | −0.244995 | − | 0.591471i | ||||
\(782\) | 7.45645 | − | 28.8473i | 0.00953511 | − | 0.0368891i | ||||
\(783\) | 834.401 | 1.06565 | ||||||||
\(784\) | −94.9508 | + | 59.3998i | −0.121111 | + | 0.0757651i | ||||
\(785\) | − | 446.479i | − | 0.568763i | ||||||
\(786\) | 37.4080 | − | 144.723i | 0.0475929 | − | 0.184126i | ||||
\(787\) | −940.723 | + | 389.660i | −1.19533 | + | 0.495121i | −0.889487 | − | 0.456961i | \(-0.848938\pi\) |
−0.305842 | + | 0.952082i | \(0.598938\pi\) | |||||||
\(788\) | 567.081 | + | 712.542i | 0.719646 | + | 0.904242i | ||||
\(789\) | −152.077 | − | 62.9924i | −0.192747 | − | 0.0798382i | ||||
\(790\) | −177.106 | − | 1259.00i | −0.224185 | − | 1.59367i | ||||
\(791\) | −166.569 | − | 166.569i | −0.210581 | − | 0.210581i | ||||
\(792\) | 185.014 | − | 82.4593i | 0.233604 | − | 0.104115i | ||||
\(793\) | 654.538 | + | 654.538i | 0.825394 | + | 0.825394i | ||||
\(794\) | 418.640 | + | 315.383i | 0.527254 | + | 0.397208i | ||||
\(795\) | −260.709 | − | 107.989i | −0.327935 | − | 0.135835i | ||||
\(796\) | 393.467 | + | 1370.85i | 0.494306 | + | 1.72218i | ||||
\(797\) | 1216.03 | − | 503.696i | 1.52576 | − | 0.631991i | 0.547025 | − | 0.837117i | \(-0.315760\pi\) |
0.978736 | + | 0.205126i | \(0.0657604\pi\) | |||||||
\(798\) | 104.838 | − | 61.7723i | 0.131376 | − | 0.0774089i | ||||
\(799\) | 97.4459i | 0.121960i | ||||||||
\(800\) | 71.1373 | + | 225.114i | 0.0889217 | + | 0.281392i | ||||
\(801\) | −369.037 | −0.460721 | ||||||||
\(802\) | 318.332 | + | 540.261i | 0.396922 | + | 0.673642i | ||||
\(803\) | 205.261 | + | 495.544i | 0.255618 | + | 0.617116i | ||||
\(804\) | 45.3473 | + | 157.991i | 0.0564022 | + | 0.196507i | ||||
\(805\) | 7.30953 | − | 17.6468i | 0.00908016 | − | 0.0219214i | ||||
\(806\) | −233.059 | + | 309.363i | −0.289155 | + | 0.383825i | ||||
\(807\) | −321.834 | + | 321.834i | −0.398803 | + | 0.398803i | ||||
\(808\) | 238.722 | + | 91.5311i | 0.295448 | + | 0.113281i | ||||
\(809\) | −389.937 | + | 389.937i | −0.481999 | + | 0.481999i | −0.905769 | − | 0.423771i | \(-0.860706\pi\) |
0.423771 | + | 0.905769i | \(0.360706\pi\) | |||||||
\(810\) | −181.097 | + | 25.4752i | −0.223576 | + | 0.0314509i | ||||
\(811\) | 331.461 | − | 800.219i | 0.408707 | − | 0.986706i | −0.576771 | − | 0.816906i | \(-0.695688\pi\) |
0.985478 | − | 0.169800i | \(-0.0543123\pi\) | |||||||
\(812\) | 191.428 | + | 240.531i | 0.235749 | + | 0.296220i | ||||
\(813\) | −45.8738 | − | 110.749i | −0.0564254 | − | 0.136223i | ||||
\(814\) | −309.339 | − | 79.9581i | −0.380023 | − | 0.0982286i | ||||
\(815\) | 1326.46 | 1.62755 | ||||||||
\(816\) | −241.719 | − | 172.229i | −0.296224 | − | 0.211064i | ||||
\(817\) | − | 79.3186i | − | 0.0970852i | ||||||
\(818\) | −200.064 | − | 51.7126i | −0.244577 | − | 0.0632183i | ||||
\(819\) | 223.497 | − | 92.5753i | 0.272890 | − | 0.113035i | ||||
\(820\) | −828.195 | − | 94.1449i | −1.00999 | − | 0.114811i | ||||
\(821\) | 887.051 | + | 367.428i | 1.08045 | + | 0.447538i | 0.850668 | − | 0.525704i | \(-0.176198\pi\) |
0.229784 | + | 0.973242i | \(0.426198\pi\) | |||||||
\(822\) | 1027.38 | − | 144.524i | 1.24985 | − | 0.175820i | ||||
\(823\) | −653.916 | − | 653.916i | −0.794551 | − | 0.794551i | 0.187679 | − | 0.982230i | \(-0.439904\pi\) |
−0.982230 | + | 0.187679i | \(0.939904\pi\) | |||||||
\(824\) | −243.060 | − | 230.477i | −0.294975 | − | 0.279705i | ||||
\(825\) | 64.0741 | + | 64.0741i | 0.0776655 | + | 0.0776655i | ||||
\(826\) | 183.968 | − | 244.199i | 0.222722 | − | 0.295641i | ||||
\(827\) | −183.358 | − | 75.9494i | −0.221715 | − | 0.0918373i | 0.269061 | − | 0.963123i | \(-0.413287\pi\) |
−0.490776 | + | 0.871286i | \(0.663287\pi\) | |||||||
\(828\) | −14.7156 | + | 26.5637i | −0.0177724 | + | 0.0320818i | ||||
\(829\) | 1332.63 | − | 551.992i | 1.60751 | − | 0.665852i | 0.615057 | − | 0.788482i | \(-0.289133\pi\) |
0.992452 | + | 0.122630i | \(0.0391328\pi\) | |||||||
\(830\) | 617.664 | + | 1048.28i | 0.744174 | + | 1.26299i | ||||
\(831\) | 544.646i | 0.655410i | ||||||||
\(832\) | 571.604 | + | 1196.01i | 0.687024 | + | 1.43752i | ||||
\(833\) | −60.6384 | −0.0727952 | ||||||||
\(834\) | −0.568918 | + | 0.335217i | −0.000682156 | + | 0.000401939i | ||||
\(835\) | −251.441 | − | 607.033i | −0.301127 | − | 0.726986i | ||||
\(836\) | −215.516 | − | 119.390i | −0.257794 | − | 0.142811i | ||||
\(837\) | −102.784 | + | 248.143i | −0.122801 | + | 0.296468i | ||||
\(838\) | 829.302 | + | 624.757i | 0.989620 | + | 0.745533i | ||||
\(839\) | 88.7195 | − | 88.7195i | 0.105744 | − | 0.105744i | −0.652255 | − | 0.757999i | \(-0.726177\pi\) |
0.757999 | + | 0.652255i | \(0.226177\pi\) | |||||||
\(840\) | −138.066 | − | 130.918i | −0.164364 | − | 0.155855i | ||||
\(841\) | 1.94397 | − | 1.94397i | 0.00231149 | − | 0.00231149i | ||||
\(842\) | 44.8167 | + | 318.590i | 0.0532265 | + | 0.378373i | ||||
\(843\) | 89.4716 | − | 216.003i | 0.106135 | − | 0.256232i | ||||
\(844\) | 23.7549 | − | 208.972i | 0.0281456 | − | 0.247598i | ||||
\(845\) | 417.680 | + | 1008.37i | 0.494295 | + | 1.19333i | ||||
\(846\) | 24.8545 | − | 96.1564i | 0.0293789 | − | 0.113660i | ||||
\(847\) | −233.097 | −0.275203 | ||||||||
\(848\) | 83.1528 | + | 495.335i | 0.0980575 | + | 0.584121i | ||||
\(849\) | 312.479i | 0.368056i | ||||||||
\(850\) | −31.9877 | + | 123.753i | −0.0376326 | + | 0.145592i | ||||
\(851\) | 44.2539 | − | 18.3306i | 0.0520022 | − | 0.0215400i | ||||
\(852\) | 584.248 | − | 464.978i | 0.685737 | − | 0.545748i | ||||
\(853\) | −684.841 | − | 283.671i | −0.802862 | − | 0.332556i | −0.0567599 | − | 0.998388i | \(-0.518077\pi\) |
−0.746102 | + | 0.665831i | \(0.768077\pi\) | |||||||
\(854\) | 32.9422 | + | 234.178i | 0.0385741 | + | 0.274213i | ||||
\(855\) | −140.718 | − | 140.718i | −0.164583 | − | 0.164583i | ||||
\(856\) | −1086.63 | − | 416.637i | −1.26943 | − | 0.486726i | ||||
\(857\) | −610.017 | − | 610.017i | −0.711806 | − | 0.711806i | 0.255107 | − | 0.966913i | \(-0.417889\pi\) |
−0.966913 | + | 0.255107i | \(0.917889\pi\) | |||||||
\(858\) | 406.374 | + | 306.143i | 0.473629 | + | 0.356810i | ||||
\(859\) | −643.826 | − | 266.681i | −0.749506 | − | 0.310455i | −0.0249659 | − | 0.999688i | \(-0.507948\pi\) |
−0.724540 | + | 0.689233i | \(0.757948\pi\) | |||||||
\(860\) | −119.212 | + | 34.2167i | −0.138619 | + | 0.0397869i | ||||
\(861\) | −259.829 | + | 107.625i | −0.301776 | + | 0.125000i | ||||
\(862\) | −1047.14 | + | 616.996i | −1.21478 | + | 0.715773i | ||||
\(863\) | − | 1602.59i | − | 1.85700i | −0.371329 | − | 0.928501i | \(-0.621098\pi\) | ||
0.371329 | − | 0.928501i | \(-0.378902\pi\) | |||||||
\(864\) | 591.315 | + | 703.781i | 0.684392 | + | 0.814562i | ||||
\(865\) | −906.707 | −1.04822 | ||||||||
\(866\) | −471.707 | − | 800.565i | −0.544697 | − | 0.924440i | ||||
\(867\) | 175.334 | + | 423.293i | 0.202230 | + | 0.488227i | ||||
\(868\) | −95.1125 | + | 27.2996i | −0.109577 | + | 0.0314511i | ||||
\(869\) | −332.385 | + | 802.449i | −0.382492 | + | 0.923416i | ||||
\(870\) | −314.233 | + | 417.113i | −0.361187 | + | 0.479440i | ||||
\(871\) | 281.049 | − | 281.049i | 0.322674 | − | 0.322674i | ||||
\(872\) | 1049.79 | − | 467.881i | 1.20389 | − | 0.536561i | ||||
\(873\) | −321.997 | + | 321.997i | −0.368839 | + | 0.368839i | ||||
\(874\) | 36.5764 | − | 5.14527i | 0.0418494 | − | 0.00588704i | ||||
\(875\) | −137.615 | + | 332.232i | −0.157274 | + | 0.379694i | ||||
\(876\) | −626.752 | + | 498.805i | −0.715470 | + | 0.569412i | ||||
\(877\) | −498.165 | − | 1202.68i | −0.568033 | − | 1.37135i | −0.903211 | − | 0.429198i | \(-0.858796\pi\) |
0.335178 | − | 0.942155i | \(-0.391204\pi\) | |||||||
\(878\) | 1256.83 | + | 324.865i | 1.43147 | + | 0.370006i | ||||
\(879\) | 26.3388 | 0.0299645 | ||||||||
\(880\) | −86.4673 | + | 375.412i | −0.0982583 | + | 0.426605i | ||||
\(881\) | − | 69.1364i | − | 0.0784749i | −0.999230 | − | 0.0392374i | \(-0.987507\pi\) | ||
0.999230 | − | 0.0392374i | \(-0.0124929\pi\) | |||||||
\(882\) | 59.8359 | + | 15.4664i | 0.0678412 | + | 0.0175356i | ||||
\(883\) | −626.468 | + | 259.492i | −0.709477 | + | 0.293875i | −0.708088 | − | 0.706124i | \(-0.750442\pi\) |
−0.00138876 | + | 0.999999i | \(0.500442\pi\) | |||||||
\(884\) | −81.0615 | + | 713.099i | −0.0916985 | + | 0.806673i | ||||
\(885\) | 479.862 | + | 198.766i | 0.542217 | + | 0.224594i | ||||
\(886\) | −1457.08 | + | 204.971i | −1.64457 | + | 0.231344i | ||||
\(887\) | −308.592 | − | 308.592i | −0.347906 | − | 0.347906i | 0.511423 | − | 0.859329i | \(-0.329118\pi\) |
−0.859329 | + | 0.511423i | \(0.829118\pi\) | |||||||
\(888\) | −12.6744 | − | 476.978i | −0.0142730 | − | 0.537138i | ||||
\(889\) | 66.7777 | + | 66.7777i | 0.0751155 | + | 0.0751155i | ||||
\(890\) | 422.321 | − | 560.588i | 0.474518 | − | 0.629875i | ||||
\(891\) | 115.425 | + | 47.8107i | 0.129546 | + | 0.0536596i | ||||
\(892\) | 165.499 | + | 91.6820i | 0.185537 | + | 0.102782i | ||||
\(893\) | −111.606 | + | 46.2285i | −0.124978 | + | 0.0517677i | ||||
\(894\) | −610.279 | − | 1035.74i | −0.682639 | − | 1.15855i | ||||
\(895\) | 552.178i | 0.616958i | ||||||||
\(896\) | −67.2182 | + | 331.918i | −0.0750203 | + | 0.370444i | ||||
\(897\) | −76.2768 | −0.0850355 | ||||||||
\(898\) | −391.992 | + | 230.969i | −0.436517 | + | 0.257204i | ||||
\(899\) | 103.936 | + | 250.923i | 0.115613 | + | 0.279114i | ||||
\(900\) | 63.1289 | − | 113.957i | 0.0701432 | − | 0.126619i | ||||
\(901\) | −104.065 | + | 251.234i | −0.115499 | + | 0.278839i | ||||
\(902\) | 454.812 | + | 342.633i | 0.504226 | + | 0.379860i | ||||
\(903\) | −29.5902 | + | 29.5902i | −0.0327688 | + | 0.0327688i | ||||
\(904\) | −712.029 | + | 18.9202i | −0.787642 | + | 0.0209295i | ||||
\(905\) | 732.903 | − | 732.903i | 0.809837 | − | 0.809837i | ||||
\(906\) | −54.3633 | − | 386.454i | −0.0600036 | − | 0.426550i | ||||
\(907\) | 382.590 | − | 923.655i | 0.421819 | − | 1.01836i | −0.559991 | − | 0.828499i | \(-0.689195\pi\) |
0.981810 | − | 0.189864i | \(-0.0608046\pi\) | |||||||
\(908\) | −1061.34 | − | 120.648i | −1.16888 | − | 0.132872i | ||||
\(909\) | −53.9889 | − | 130.341i | −0.0593937 | − | 0.143389i | ||||
\(910\) | −115.139 | + | 445.446i | −0.126526 | + | 0.489501i | ||||
\(911\) | −167.149 | −0.183479 | −0.0917394 | − | 0.995783i | \(-0.529243\pi\) | ||||
−0.0917394 | + | 0.995783i | \(0.529243\pi\) | |||||||
\(912\) | 82.5828 | − | 358.548i | 0.0905513 | − | 0.393144i | ||||
\(913\) | − | 831.207i | − | 0.910413i | ||||||
\(914\) | −127.937 | + | 494.957i | −0.139975 | + | 0.541529i | ||||
\(915\) | −371.162 | + | 153.740i | −0.405641 | + | 0.168022i | ||||
\(916\) | −950.796 | − | 1194.68i | −1.03799 | − | 1.30424i | ||||
\(917\) | −85.3141 | − | 35.3383i | −0.0930361 | − | 0.0385368i | ||||
\(918\) | 69.3267 | + | 492.825i | 0.0755193 | + | 0.536847i | ||||
\(919\) | −1152.11 | − | 1152.11i | −1.25365 | − | 1.25365i | −0.954071 | − | 0.299582i | \(-0.903153\pi\) |
−0.299582 | − | 0.954071i | \(-0.596847\pi\) | |||||||
\(920\) | −23.5115 | − | 52.7529i | −0.0255560 | − | 0.0573401i | ||||
\(921\) | −0.830531 | − | 0.830531i | −0.000901771 | − | 0.000901771i | ||||
\(922\) | −651.616 | − | 490.896i | −0.706742 | − | 0.532425i | ||||
\(923\) | −1668.13 | − | 690.963i | −1.80729 | − | 0.748606i | ||||
\(924\) | 35.8603 | + | 124.938i | 0.0388098 | + | 0.135215i | ||||
\(925\) | −189.847 | + | 78.6370i | −0.205240 | + | 0.0850130i | ||||
\(926\) | −194.081 | + | 114.356i | −0.209590 | + | 0.123494i | ||||
\(927\) | 184.833i | 0.199389i | ||||||||
\(928\) | 926.030 | + | 80.4167i | 0.997878 | + | 0.0866560i | ||||
\(929\) | −64.6601 | −0.0696018 | −0.0348009 | − | 0.999394i | \(-0.511080\pi\) | ||||
−0.0348009 | + | 0.999394i | \(0.511080\pi\) | |||||||
\(930\) | −85.3373 | − | 144.831i | −0.0917606 | − | 0.155733i | ||||
\(931\) | −28.7670 | − | 69.4496i | −0.0308990 | − | 0.0745968i | ||||
\(932\) | 119.524 | + | 416.426i | 0.128245 | + | 0.446809i | ||||
\(933\) | −139.497 | + | 336.777i | −0.149515 | + | 0.360961i | ||||
\(934\) | 34.6901 | − | 46.0477i | 0.0371414 | − | 0.0493016i | ||||
\(935\) | −147.485 | + | 147.485i | −0.157738 | + | 0.157738i | ||||
\(936\) | 261.872 | − | 682.987i | 0.279777 | − | 0.729687i | ||||
\(937\) | −840.477 | + | 840.477i | −0.896987 | + | 0.896987i | −0.995169 | − | 0.0981812i | \(-0.968698\pi\) |
0.0981812 | + | 0.995169i | \(0.468698\pi\) | |||||||
\(938\) | 100.553 | − | 14.1449i | 0.107199 | − | 0.0150799i | ||||
\(939\) | −218.508 | + | 527.524i | −0.232702 | + | 0.561793i | ||||
\(940\) | 117.624 | + | 147.795i | 0.125132 | + | 0.157229i | ||||
\(941\) | 232.141 | + | 560.437i | 0.246696 | + | 0.595576i | 0.997920 | − | 0.0644714i | \(-0.0205361\pi\) |
−0.751224 | + | 0.660048i | \(0.770536\pi\) | |||||||
\(942\) | −441.012 | − | 113.993i | −0.468166 | − | 0.121012i | ||||
\(943\) | −85.3686 | −0.0905288 | ||||||||
\(944\) | −153.052 | − | 911.717i | −0.162131 | − | 0.965802i | ||||
\(945\) | 319.043i | 0.337611i | ||||||||
\(946\) | 82.0327 | + | 21.2038i | 0.0867153 | + | 0.0224142i | ||||
\(947\) | −1514.65 | + | 627.390i | −1.59942 | + | 0.662503i | −0.991334 | − | 0.131366i | \(-0.958064\pi\) |
−0.608089 | + | 0.793868i | \(0.708064\pi\) | |||||||
\(948\) | −1288.81 | − | 146.505i | −1.35950 | − | 0.154541i | ||||
\(949\) | 1789.49 | + | 741.231i | 1.88566 | + | 0.781065i | ||||
\(950\) | −156.910 | + | 22.0729i | −0.165169 | + | 0.0232346i | ||||
\(951\) | −130.467 | − | 130.467i | −0.137189 | − | 0.137189i | ||||
\(952\) | −126.161 | + | 133.048i | −0.132522 | + | 0.139757i | ||||
\(953\) | 90.7722 | + | 90.7722i | 0.0952489 | + | 0.0952489i | 0.753126 | − | 0.657877i | \(-0.228545\pi\) |
−0.657877 | + | 0.753126i | \(0.728545\pi\) | |||||||
\(954\) | 166.767 | − | 221.367i | 0.174808 | − | 0.232041i | ||||
\(955\) | 789.487 | + | 327.016i | 0.826688 | + | 0.342426i | ||||
\(956\) | −820.032 | + | 1480.27i | −0.857774 | + | 1.54840i | ||||
\(957\) | 329.609 | − | 136.528i | 0.344419 | − | 0.142663i | ||||
\(958\) | −719.621 | − | 1221.32i | −0.751170 | − | 1.27486i | ||||
\(959\) | − | 640.930i | − | 0.668331i | ||||||
\(960\) | −574.504 | + | 30.5533i | −0.598442 | + | 0.0318264i | ||||
\(961\) | 873.575 | 0.909027 | ||||||||
\(962\) | −994.060 | + | 585.719i | −1.03333 | + | 0.608855i | ||||
\(963\) | 245.750 | + | 593.294i | 0.255192 | + | 0.616089i | ||||
\(964\) | −867.759 | − | 480.715i | −0.900165 | − | 0.498667i | ||||
\(965\) | 198.250 | − | 478.619i | 0.205441 | − | 0.495978i | ||||
\(966\) | −15.5645 | − | 11.7255i | −0.0161123 | − | 0.0121382i | ||||
\(967\) | −1133.06 | + | 1133.06i | −1.17173 | + | 1.17173i | −0.189929 | + | 0.981798i | \(0.560826\pi\) |
−0.981798 | + | 0.189929i | \(0.939174\pi\) | |||||||
\(968\) | −484.968 | + | 511.445i | −0.501000 | + | 0.528353i | ||||
\(969\) | 140.859 | − | 140.859i | 0.145366 | − | 0.145366i | ||||
\(970\) | −120.643 | − | 857.619i | −0.124374 | − | 0.884144i | ||||
\(971\) | −298.980 | + | 721.802i | −0.307910 | + | 0.743359i | 0.691863 | + | 0.722029i | \(0.256790\pi\) |
−0.999772 | + | 0.0213306i | \(0.993210\pi\) | |||||||
\(972\) | 95.7278 | − | 842.119i | 0.0984854 | − | 0.866378i | ||||
\(973\) | 0.156108 | + | 0.376879i | 0.000160440 | + | 0.000387337i | ||||
\(974\) | 174.661 | − | 675.723i | 0.179324 | − | 0.693761i | ||||
\(975\) | 327.223 | 0.335613 | ||||||||
\(976\) | 582.354 | + | 414.937i | 0.596674 | + | 0.425140i | ||||
\(977\) | − | 794.155i | − | 0.812851i | −0.913684 | − | 0.406426i | \(-0.866775\pi\) | ||
0.913684 | − | 0.406426i | \(-0.133225\pi\) | |||||||
\(978\) | 338.665 | − | 1310.22i | 0.346283 | − | 1.33969i | ||||
\(979\) | −442.985 | + | 183.490i | −0.452487 | + | 0.187426i | ||||
\(980\) | −91.9697 | + | 73.1947i | −0.0938467 | + | 0.0746884i | ||||
\(981\) | −585.935 | − | 242.702i | −0.597284 | − | 0.247403i | ||||
\(982\) | −16.3273 | − | 116.067i | −0.0166266 | − | 0.118194i | ||||
\(983\) | −69.2305 | − | 69.2305i | −0.0704278 | − | 0.0704278i | 0.671016 | − | 0.741443i | \(-0.265858\pi\) |
−0.741443 | + | 0.671016i | \(0.765858\pi\) | |||||||
\(984\) | −304.443 | + | 794.018i | −0.309393 | + | 0.806928i | ||||
\(985\) | 675.790 | + | 675.790i | 0.686081 | + | 0.686081i | ||||
\(986\) | 401.955 | + | 302.813i | 0.407662 | + | 0.307113i | ||||
\(987\) | 58.8808 | + | 24.3892i | 0.0596563 | + | 0.0247104i | ||||
\(988\) | −855.173 | + | 245.455i | −0.865560 | + | 0.248436i | ||||
\(989\) | −11.7356 | + | 4.86103i | −0.0118661 | + | 0.00491509i | ||||
\(990\) | 183.151 | − | 107.916i | 0.185001 | − | 0.109006i | ||||
\(991\) | 458.563i | 0.462728i | 0.972867 | + | 0.231364i | \(0.0743188\pi\) | ||||
−0.972867 | + | 0.231364i | \(0.925681\pi\) | |||||||
\(992\) | −137.987 | + | 265.487i | −0.139100 | + | 0.267628i | ||||
\(993\) | −1193.32 | −1.20173 | ||||||||
\(994\) | −234.169 | − | 397.423i | −0.235583 | − | 0.399822i | ||||
\(995\) | 572.786 | + | 1382.83i | 0.575664 | + | 1.38978i | ||||
\(996\) | 1193.14 | − | 342.460i | 1.19793 | − | 0.343836i | ||||
\(997\) | 461.101 | − | 1113.20i | 0.462489 | − | 1.11655i | −0.504883 | − | 0.863188i | \(-0.668464\pi\) |
0.967372 | − | 0.253359i | \(-0.0815355\pi\) | |||||||
\(998\) | 1029.67 | − | 1366.78i | 1.03173 | − | 1.36952i | ||||
\(999\) | −565.744 | + | 565.744i | −0.566311 | + | 0.566311i |
(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 | 224.3.w.a.43.9 | ✓ | 192 | |
32.3 | odd | 8 | inner | 224.3.w.a.99.9 | yes | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.w.a.43.9 | ✓ | 192 | 1.1 | even | 1 | trivial | |
224.3.w.a.99.9 | yes | 192 | 32.3 | odd | 8 | inner |