Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.63488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.85100625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-1.34966 + 0.422403i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.3.c.a.31.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99281 | − | 0.169449i | −0.996404 | − | 0.0847243i | ||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 3.94257 | + | 0.675358i | 0.985644 | + | 0.168839i | ||||
\(5\) | −2.23607 | −0.447214 | ||||||||
\(6\) | −0.293494 | + | 3.45165i | −0.0489156 | + | 0.575274i | ||||
\(7\) | − | 12.3959i | − | 1.77084i | −0.464789 | − | 0.885422i | \(-0.653870\pi\) | ||
0.464789 | − | 0.885422i | \(-0.346130\pi\) | |||||||
\(8\) | −7.74236 | − | 2.01392i | −0.967795 | − | 0.251740i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 4.45606 | + | 0.378899i | 0.445606 | + | 0.0378899i | ||||
\(11\) | − | 11.0403i | − | 1.00366i | −0.864965 | − | 0.501832i | \(-0.832659\pi\) | ||
0.864965 | − | 0.501832i | \(-0.167341\pi\) | |||||||
\(12\) | 1.16975 | − | 6.82874i | 0.0974795 | − | 0.569062i | ||||
\(13\) | 2.82009 | 0.216930 | 0.108465 | − | 0.994100i | \(-0.465407\pi\) | ||||
0.108465 | + | 0.994100i | \(0.465407\pi\) | |||||||
\(14\) | −2.10047 | + | 24.7027i | −0.150034 | + | 1.76448i | ||||
\(15\) | 3.87298i | 0.258199i | ||||||||
\(16\) | 15.0878 | + | 5.32529i | 0.942987 | + | 0.332831i | ||||
\(17\) | 6.52606 | 0.383886 | 0.191943 | − | 0.981406i | \(-0.438521\pi\) | ||||
0.191943 | + | 0.981406i | \(0.438521\pi\) | |||||||
\(18\) | 5.97843 | + | 0.508346i | 0.332135 | + | 0.0282414i | ||||
\(19\) | 27.9928i | 1.47330i | 0.676273 | + | 0.736651i | \(0.263594\pi\) | ||||
−0.676273 | + | 0.736651i | \(0.736406\pi\) | |||||||
\(20\) | −8.81586 | − | 1.51015i | −0.440793 | − | 0.0755073i | ||||
\(21\) | −21.4703 | −1.02240 | ||||||||
\(22\) | −1.87077 | + | 22.0012i | −0.0850348 | + | 1.00006i | ||||
\(23\) | 7.90421i | 0.343661i | 0.985126 | + | 0.171831i | \(0.0549682\pi\) | ||||
−0.985126 | + | 0.171831i | \(0.945032\pi\) | |||||||
\(24\) | −3.48822 | + | 13.4102i | −0.145342 | + | 0.558757i | ||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | −5.61989 | − | 0.477860i | −0.216150 | − | 0.0183792i | ||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 8.37167 | − | 48.8718i | 0.298988 | − | 1.74542i | ||||
\(29\) | 50.7169 | 1.74886 | 0.874429 | − | 0.485153i | \(-0.161236\pi\) | ||||
0.874429 | + | 0.485153i | \(0.161236\pi\) | |||||||
\(30\) | 0.656272 | − | 7.71812i | 0.0218757 | − | 0.257271i | ||||
\(31\) | − | 36.3467i | − | 1.17247i | −0.810140 | − | 0.586236i | \(-0.800609\pi\) | ||
0.810140 | − | 0.586236i | \(-0.199391\pi\) | |||||||
\(32\) | −29.1647 | − | 13.1689i | −0.911397 | − | 0.411528i | ||||
\(33\) | −19.1224 | −0.579466 | ||||||||
\(34\) | −13.0052 | − | 1.10583i | −0.382506 | − | 0.0325245i | ||||
\(35\) | 27.7181i | 0.791945i | ||||||||
\(36\) | −11.8277 | − | 2.02607i | −0.328548 | − | 0.0562798i | ||||
\(37\) | −18.9279 | −0.511566 | −0.255783 | − | 0.966734i | \(-0.582333\pi\) | ||||
−0.255783 | + | 0.966734i | \(0.582333\pi\) | |||||||
\(38\) | 4.74333 | − | 55.7842i | 0.124825 | − | 1.46801i | ||||
\(39\) | − | 4.88453i | − | 0.125244i | ||||||
\(40\) | 17.3124 | + | 4.50327i | 0.432811 | + | 0.112582i | ||||
\(41\) | 5.30410 | 0.129368 | 0.0646842 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646842 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(42\) | 42.7863 | + | 3.63812i | 1.01872 | + | 0.0866219i | ||||
\(43\) | 45.5870i | 1.06016i | 0.847947 | + | 0.530081i | \(0.177838\pi\) | ||||
−0.847947 | + | 0.530081i | \(0.822162\pi\) | |||||||
\(44\) | 7.45616 | − | 43.5273i | 0.169458 | − | 0.989256i | ||||
\(45\) | 6.70820 | 0.149071 | ||||||||
\(46\) | 1.33936 | − | 15.7516i | 0.0291165 | − | 0.342426i | ||||
\(47\) | − | 11.7246i | − | 0.249460i | −0.992191 | − | 0.124730i | \(-0.960194\pi\) | ||
0.992191 | − | 0.124730i | \(-0.0398064\pi\) | |||||||
\(48\) | 9.22368 | − | 26.1328i | 0.192160 | − | 0.544434i | ||||
\(49\) | −104.658 | −2.13589 | ||||||||
\(50\) | −9.96404 | − | 0.847243i | −0.199281 | − | 0.0169449i | ||||
\(51\) | − | 11.3035i | − | 0.221637i | ||||||
\(52\) | 11.1184 | + | 1.90457i | 0.213815 | + | 0.0366263i | ||||
\(53\) | 41.1680 | 0.776755 | 0.388378 | − | 0.921500i | \(-0.373036\pi\) | ||||
0.388378 | + | 0.921500i | \(0.373036\pi\) | |||||||
\(54\) | 0.880481 | − | 10.3549i | 0.0163052 | − | 0.191758i | ||||
\(55\) | 24.6869i | 0.448853i | ||||||||
\(56\) | −24.9644 | + | 95.9735i | −0.445793 | + | 1.71381i | ||||
\(57\) | 48.4849 | 0.850612 | ||||||||
\(58\) | −101.069 | − | 8.59391i | −1.74257 | − | 0.148171i | ||||
\(59\) | − | 10.7008i | − | 0.181370i | −0.995880 | − | 0.0906848i | \(-0.971094\pi\) | ||
0.995880 | − | 0.0906848i | \(-0.0289056\pi\) | |||||||
\(60\) | −2.61565 | + | 15.2695i | −0.0435941 | + | 0.254492i | ||||
\(61\) | 56.1297 | 0.920159 | 0.460080 | − | 0.887878i | \(-0.347821\pi\) | ||||
0.460080 | + | 0.887878i | \(0.347821\pi\) | |||||||
\(62\) | −6.15889 | + | 72.4319i | −0.0993370 | + | 1.16826i | ||||
\(63\) | 37.1877i | 0.590281i | ||||||||
\(64\) | 55.8882 | + | 31.1850i | 0.873254 | + | 0.487266i | ||||
\(65\) | −6.30590 | −0.0970139 | ||||||||
\(66\) | 38.1073 | + | 3.24026i | 0.577383 | + | 0.0490949i | ||||
\(67\) | 16.1709i | 0.241357i | 0.992692 | + | 0.120679i | \(0.0385071\pi\) | ||||
−0.992692 | + | 0.120679i | \(0.961493\pi\) | |||||||
\(68\) | 25.7295 | + | 4.40743i | 0.378375 | + | 0.0648151i | ||||
\(69\) | 13.6905 | 0.198413 | ||||||||
\(70\) | 4.69679 | − | 55.2368i | 0.0670970 | − | 0.789098i | ||||
\(71\) | − | 66.1617i | − | 0.931855i | −0.884823 | − | 0.465928i | \(-0.845721\pi\) | ||
0.884823 | − | 0.465928i | \(-0.154279\pi\) | |||||||
\(72\) | 23.2271 | + | 6.04177i | 0.322598 | + | 0.0839134i | ||||
\(73\) | 15.6330 | 0.214150 | 0.107075 | − | 0.994251i | \(-0.465851\pi\) | ||||
0.107075 | + | 0.994251i | \(0.465851\pi\) | |||||||
\(74\) | 37.7198 | + | 3.20731i | 0.509727 | + | 0.0433421i | ||||
\(75\) | − | 8.66025i | − | 0.115470i | ||||||
\(76\) | −18.9051 | + | 110.363i | −0.248752 | + | 1.45215i | ||||
\(77\) | −136.855 | −1.77733 | ||||||||
\(78\) | −0.827677 | + | 9.73394i | −0.0106112 | + | 0.124794i | ||||
\(79\) | − | 123.057i | − | 1.55768i | −0.627223 | − | 0.778840i | \(-0.715809\pi\) | ||
0.627223 | − | 0.778840i | \(-0.284191\pi\) | |||||||
\(80\) | −33.7373 | − | 11.9077i | −0.421716 | − | 0.148847i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −10.5701 | − | 0.898773i | −0.128903 | − | 0.0109606i | ||||
\(83\) | 99.6700i | 1.20084i | 0.799684 | + | 0.600422i | \(0.205001\pi\) | ||||
−0.799684 | + | 0.600422i | \(0.794999\pi\) | |||||||
\(84\) | −84.6484 | − | 14.5002i | −1.00772 | − | 0.172621i | ||||
\(85\) | −14.5927 | −0.171679 | ||||||||
\(86\) | 7.72465 | − | 90.8461i | 0.0898215 | − | 1.05635i | ||||
\(87\) | − | 87.8443i | − | 1.00970i | ||||||
\(88\) | −22.2343 | + | 85.4781i | −0.252663 | + | 0.971342i | ||||
\(89\) | 101.083 | 1.13576 | 0.567881 | − | 0.823110i | \(-0.307763\pi\) | ||||
0.567881 | + | 0.823110i | \(0.307763\pi\) | |||||||
\(90\) | −13.3682 | − | 1.13670i | −0.148535 | − | 0.0126300i | ||||
\(91\) | − | 34.9575i | − | 0.384148i | ||||||
\(92\) | −5.33817 | + | 31.1629i | −0.0580236 | + | 0.338728i | ||||
\(93\) | −62.9543 | −0.676927 | ||||||||
\(94\) | −1.98672 | + | 23.3649i | −0.0211353 | + | 0.248563i | ||||
\(95\) | − | 62.5937i | − | 0.658881i | ||||||
\(96\) | −22.8092 | + | 50.5148i | −0.237596 | + | 0.526195i | ||||
\(97\) | 127.293 | 1.31230 | 0.656151 | − | 0.754630i | \(-0.272183\pi\) | ||||
0.656151 | + | 0.754630i | \(0.272183\pi\) | |||||||
\(98\) | 208.564 | + | 17.7342i | 2.12821 | + | 0.180962i | ||||
\(99\) | 33.1209i | 0.334555i | ||||||||
\(100\) | 19.7129 | + | 3.37679i | 0.197129 | + | 0.0337679i | ||||
\(101\) | −94.3535 | −0.934193 | −0.467096 | − | 0.884206i | \(-0.654700\pi\) | ||||
−0.467096 | + | 0.884206i | \(0.654700\pi\) | |||||||
\(102\) | −1.91536 | + | 22.5257i | −0.0187780 | + | 0.220840i | ||||
\(103\) | 31.8455i | 0.309180i | 0.987979 | + | 0.154590i | \(0.0494056\pi\) | ||||
−0.987979 | + | 0.154590i | \(0.950594\pi\) | |||||||
\(104\) | −21.8341 | − | 5.67943i | −0.209943 | − | 0.0546099i | ||||
\(105\) | 48.0091 | 0.457230 | ||||||||
\(106\) | −82.0400 | − | 6.97587i | −0.773962 | − | 0.0658101i | ||||
\(107\) | − | 33.7912i | − | 0.315805i | −0.987455 | − | 0.157903i | \(-0.949527\pi\) | ||
0.987455 | − | 0.157903i | \(-0.0504732\pi\) | |||||||
\(108\) | −3.50926 | + | 20.4862i | −0.0324932 | + | 0.189687i | ||||
\(109\) | −83.4266 | −0.765382 | −0.382691 | − | 0.923876i | \(-0.625003\pi\) | ||||
−0.382691 | + | 0.923876i | \(0.625003\pi\) | |||||||
\(110\) | 4.18316 | − | 49.1963i | 0.0380287 | − | 0.447239i | ||||
\(111\) | 32.7842i | 0.295353i | ||||||||
\(112\) | 66.0118 | − | 187.027i | 0.589391 | − | 1.66988i | ||||
\(113\) | −111.796 | −0.989342 | −0.494671 | − | 0.869080i | \(-0.664711\pi\) | ||||
−0.494671 | + | 0.869080i | \(0.664711\pi\) | |||||||
\(114\) | −96.6211 | − | 8.21569i | −0.847553 | − | 0.0720675i | ||||
\(115\) | − | 17.6744i | − | 0.153690i | ||||||
\(116\) | 199.955 | + | 34.2520i | 1.72375 | + | 0.295276i | ||||
\(117\) | −8.46026 | −0.0723099 | ||||||||
\(118\) | −1.81324 | + | 21.3247i | −0.0153664 | + | 0.180717i | ||||
\(119\) | − | 80.8964i | − | 0.679802i | ||||||
\(120\) | 7.79989 | − | 29.9860i | 0.0649991 | − | 0.249884i | ||||
\(121\) | −0.888544 | −0.00734334 | ||||||||
\(122\) | −111.856 | − | 9.51110i | −0.916851 | − | 0.0779599i | ||||
\(123\) | − | 9.18697i | − | 0.0746908i | ||||||
\(124\) | 24.5470 | − | 143.299i | 0.197960 | − | 1.15564i | ||||
\(125\) | −11.1803 | −0.0894427 | ||||||||
\(126\) | 6.30141 | − | 74.1080i | 0.0500112 | − | 0.588159i | ||||
\(127\) | − | 16.6855i | − | 0.131382i | −0.997840 | − | 0.0656909i | \(-0.979075\pi\) | ||
0.997840 | − | 0.0656909i | \(-0.0209251\pi\) | |||||||
\(128\) | −106.090 | − | 71.6160i | −0.828831 | − | 0.559500i | ||||
\(129\) | 78.9589 | 0.612085 | ||||||||
\(130\) | 12.5665 | + | 1.06853i | 0.0966651 | + | 0.00821944i | ||||
\(131\) | 196.418i | 1.49937i | 0.661794 | + | 0.749686i | \(0.269796\pi\) | ||||
−0.661794 | + | 0.749686i | \(0.730204\pi\) | |||||||
\(132\) | −75.3914 | − | 12.9144i | −0.571147 | − | 0.0978367i | ||||
\(133\) | 346.995 | 2.60899 | ||||||||
\(134\) | 2.74015 | − | 32.2256i | 0.0204488 | − | 0.240490i | ||||
\(135\) | − | 11.6190i | − | 0.0860663i | ||||||
\(136\) | −50.5271 | − | 13.1430i | −0.371523 | − | 0.0966396i | ||||
\(137\) | −117.127 | −0.854942 | −0.427471 | − | 0.904029i | \(-0.640595\pi\) | ||||
−0.427471 | + | 0.904029i | \(0.640595\pi\) | |||||||
\(138\) | −27.2825 | − | 2.31984i | −0.197700 | − | 0.0168104i | ||||
\(139\) | 187.238i | 1.34704i | 0.739170 | + | 0.673519i | \(0.235218\pi\) | ||||
−0.739170 | + | 0.673519i | \(0.764782\pi\) | |||||||
\(140\) | −18.7196 | + | 109.281i | −0.133712 | + | 0.780576i | ||||
\(141\) | −20.3076 | −0.144026 | ||||||||
\(142\) | −11.2110 | + | 131.848i | −0.0789508 | + | 0.928505i | ||||
\(143\) | − | 31.1346i | − | 0.217725i | ||||||
\(144\) | −45.2634 | − | 15.9759i | −0.314329 | − | 0.110944i | ||||
\(145\) | −113.406 | −0.782113 | ||||||||
\(146\) | −31.1535 | − | 2.64899i | −0.213380 | − | 0.0181437i | ||||
\(147\) | 181.274i | 1.23315i | ||||||||
\(148\) | −74.6248 | − | 12.7831i | −0.504222 | − | 0.0863725i | ||||
\(149\) | −50.2274 | −0.337096 | −0.168548 | − | 0.985693i | \(-0.553908\pi\) | ||||
−0.168548 | + | 0.985693i | \(0.553908\pi\) | |||||||
\(150\) | −1.46747 | + | 17.2582i | −0.00978312 | + | 0.115055i | ||||
\(151\) | 213.160i | 1.41166i | 0.708382 | + | 0.705829i | \(0.249425\pi\) | ||||
−0.708382 | + | 0.705829i | \(0.750575\pi\) | |||||||
\(152\) | 56.3752 | − | 216.730i | 0.370890 | − | 1.42585i | ||||
\(153\) | −19.5782 | −0.127962 | ||||||||
\(154\) | 272.725 | + | 23.1898i | 1.77094 | + | 0.150583i | ||||
\(155\) | 81.2736i | 0.524346i | ||||||||
\(156\) | 3.29880 | − | 19.2576i | 0.0211462 | − | 0.123446i | ||||
\(157\) | 203.918 | 1.29884 | 0.649419 | − | 0.760431i | \(-0.275012\pi\) | ||||
0.649419 | + | 0.760431i | \(0.275012\pi\) | |||||||
\(158\) | −20.8518 | + | 245.228i | −0.131973 | + | 1.55208i | ||||
\(159\) | − | 71.3051i | − | 0.448460i | ||||||
\(160\) | 65.2143 | + | 29.4466i | 0.407589 | + | 0.184041i | ||||
\(161\) | 97.9798 | 0.608570 | ||||||||
\(162\) | −17.9353 | − | 1.52504i | −0.110712 | − | 0.00941381i | ||||
\(163\) | − | 215.898i | − | 1.32452i | −0.749272 | − | 0.662262i | \(-0.769596\pi\) | ||
0.749272 | − | 0.662262i | \(-0.230404\pi\) | |||||||
\(164\) | 20.9118 | + | 3.58216i | 0.127511 | + | 0.0218425i | ||||
\(165\) | 42.7590 | 0.259145 | ||||||||
\(166\) | 16.8889 | − | 198.623i | 0.101741 | − | 1.19653i | ||||
\(167\) | 255.029i | 1.52712i | 0.645737 | + | 0.763560i | \(0.276550\pi\) | ||||
−0.645737 | + | 0.763560i | \(0.723450\pi\) | |||||||
\(168\) | 166.231 | + | 43.2396i | 0.989470 | + | 0.257378i | ||||
\(169\) | −161.047 | −0.952942 | ||||||||
\(170\) | 29.0805 | + | 2.47272i | 0.171062 | + | 0.0145454i | ||||
\(171\) | − | 83.9783i | − | 0.491101i | ||||||
\(172\) | −30.7875 | + | 179.730i | −0.178997 | + | 1.04494i | ||||
\(173\) | −235.426 | −1.36084 | −0.680421 | − | 0.732822i | \(-0.738203\pi\) | ||||
−0.680421 | + | 0.732822i | \(0.738203\pi\) | |||||||
\(174\) | −14.8851 | + | 175.057i | −0.0855465 | + | 1.00607i | ||||
\(175\) | − | 61.9795i | − | 0.354169i | ||||||
\(176\) | 58.7929 | − | 166.574i | 0.334051 | − | 0.946443i | ||||
\(177\) | −18.5343 | −0.104714 | ||||||||
\(178\) | −201.439 | − | 17.1284i | −1.13168 | − | 0.0962267i | ||||
\(179\) | 102.669i | 0.573572i | 0.957995 | + | 0.286786i | \(0.0925869\pi\) | ||||
−0.957995 | + | 0.286786i | \(0.907413\pi\) | |||||||
\(180\) | 26.4476 | + | 4.53044i | 0.146931 | + | 0.0251691i | ||||
\(181\) | −56.8222 | −0.313935 | −0.156967 | − | 0.987604i | \(-0.550172\pi\) | ||||
−0.156967 | + | 0.987604i | \(0.550172\pi\) | |||||||
\(182\) | −5.92350 | + | 69.6636i | −0.0325467 | + | 0.382767i | ||||
\(183\) | − | 97.2195i | − | 0.531254i | ||||||
\(184\) | 15.9185 | − | 61.1972i | 0.0865134 | − | 0.332594i | ||||
\(185\) | 42.3242 | 0.228779 | ||||||||
\(186\) | 125.456 | + | 10.6675i | 0.674493 | + | 0.0573522i | ||||
\(187\) | − | 72.0498i | − | 0.385293i | ||||||
\(188\) | 7.91830 | − | 46.2251i | 0.0421186 | − | 0.245878i | ||||
\(189\) | 64.4110 | 0.340799 | ||||||||
\(190\) | −10.6064 | + | 124.737i | −0.0558232 | + | 0.656512i | ||||
\(191\) | − | 158.493i | − | 0.829808i | −0.909865 | − | 0.414904i | \(-0.863815\pi\) | ||
0.909865 | − | 0.414904i | \(-0.136185\pi\) | |||||||
\(192\) | 54.0140 | − | 96.8013i | 0.281323 | − | 0.504173i | ||||
\(193\) | −156.732 | −0.812084 | −0.406042 | − | 0.913854i | \(-0.633091\pi\) | ||||
−0.406042 | + | 0.913854i | \(0.633091\pi\) | |||||||
\(194\) | −253.671 | − | 21.5697i | −1.30758 | − | 0.111184i | ||||
\(195\) | 10.9221i | 0.0560110i | ||||||||
\(196\) | −412.624 | − | 70.6819i | −2.10522 | − | 0.360622i | ||||
\(197\) | 260.127 | 1.32044 | 0.660221 | − | 0.751072i | \(-0.270463\pi\) | ||||
0.660221 | + | 0.751072i | \(0.270463\pi\) | |||||||
\(198\) | 5.61230 | − | 66.0037i | 0.0283449 | − | 0.333352i | ||||
\(199\) | 14.0326i | 0.0705157i | 0.999378 | + | 0.0352579i | \(0.0112253\pi\) | ||||
−0.999378 | + | 0.0352579i | \(0.988775\pi\) | |||||||
\(200\) | −38.7118 | − | 10.0696i | −0.193559 | − | 0.0503481i | ||||
\(201\) | 28.0089 | 0.139348 | ||||||||
\(202\) | 188.028 | + | 15.9881i | 0.930834 | + | 0.0791489i | ||||
\(203\) | − | 628.682i | − | 3.09696i | ||||||
\(204\) | 7.63389 | − | 44.5648i | 0.0374210 | − | 0.218455i | ||||
\(205\) | −11.8603 | −0.0578553 | ||||||||
\(206\) | 5.39618 | − | 63.4620i | 0.0261950 | − | 0.308068i | ||||
\(207\) | − | 23.7126i | − | 0.114554i | ||||||
\(208\) | 42.5488 | + | 15.0178i | 0.204562 | + | 0.0722009i | ||||
\(209\) | 309.049 | 1.47870 | ||||||||
\(210\) | −95.6730 | − | 8.13508i | −0.455586 | − | 0.0387385i | ||||
\(211\) | − | 74.4941i | − | 0.353052i | −0.984296 | − | 0.176526i | \(-0.943514\pi\) | ||
0.984296 | − | 0.176526i | \(-0.0564860\pi\) | |||||||
\(212\) | 162.308 | + | 27.8031i | 0.765604 | + | 0.131147i | ||||
\(213\) | −114.595 | −0.538007 | ||||||||
\(214\) | −5.72587 | + | 67.3393i | −0.0267564 | + | 0.314670i | ||||
\(215\) | − | 101.936i | − | 0.474119i | ||||||
\(216\) | 10.4646 | − | 40.2305i | 0.0484474 | − | 0.186252i | ||||
\(217\) | −450.550 | −2.07627 | ||||||||
\(218\) | 166.253 | + | 14.1365i | 0.762630 | + | 0.0648465i | ||||
\(219\) | − | 27.0771i | − | 0.123640i | ||||||
\(220\) | −16.6725 | + | 97.3299i | −0.0757840 | + | 0.442409i | ||||
\(221\) | 18.4041 | 0.0832763 | ||||||||
\(222\) | 5.55523 | − | 65.3326i | 0.0250236 | − | 0.294291i | ||||
\(223\) | − | 159.996i | − | 0.717471i | −0.933439 | − | 0.358736i | \(-0.883208\pi\) | ||
0.933439 | − | 0.358736i | \(-0.116792\pi\) | |||||||
\(224\) | −163.240 | + | 361.523i | −0.728752 | + | 1.61394i | ||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 222.787 | + | 18.9436i | 0.985784 | + | 0.0838213i | ||||
\(227\) | − | 175.978i | − | 0.775236i | −0.921820 | − | 0.387618i | \(-0.873298\pi\) | ||
0.921820 | − | 0.387618i | \(-0.126702\pi\) | |||||||
\(228\) | 191.155 | + | 32.7446i | 0.838400 | + | 0.143617i | ||||
\(229\) | −114.170 | −0.498560 | −0.249280 | − | 0.968431i | \(-0.580194\pi\) | ||||
−0.249280 | + | 0.968431i | \(0.580194\pi\) | |||||||
\(230\) | −2.99490 | + | 35.2216i | −0.0130213 | + | 0.153137i | ||||
\(231\) | 237.039i | 1.02614i | ||||||||
\(232\) | −392.668 | − | 102.140i | −1.69254 | − | 0.440258i | ||||
\(233\) | 260.062 | 1.11615 | 0.558073 | − | 0.829792i | \(-0.311541\pi\) | ||||
0.558073 | + | 0.829792i | \(0.311541\pi\) | |||||||
\(234\) | 16.8597 | + | 1.43358i | 0.0720499 | + | 0.00612641i | ||||
\(235\) | 26.2170i | 0.111562i | ||||||||
\(236\) | 7.22687 | − | 42.1887i | 0.0306223 | − | 0.178766i | ||||
\(237\) | −213.140 | −0.899327 | ||||||||
\(238\) | −13.7078 | + | 161.211i | −0.0575958 | + | 0.677358i | ||||
\(239\) | 140.089i | 0.586147i | 0.956090 | + | 0.293073i | \(0.0946780\pi\) | ||||
−0.956090 | + | 0.293073i | \(0.905322\pi\) | |||||||
\(240\) | −20.6248 | + | 58.4347i | −0.0859366 | + | 0.243478i | ||||
\(241\) | 105.920 | 0.439503 | 0.219752 | − | 0.975556i | \(-0.429475\pi\) | ||||
0.219752 | + | 0.975556i | \(0.429475\pi\) | |||||||
\(242\) | 1.77070 | + | 0.150563i | 0.00731693 | + | 0.000622159i | ||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 221.296 | + | 37.9076i | 0.906949 | + | 0.155359i | ||||
\(245\) | 234.023 | 0.955197 | ||||||||
\(246\) | −1.55672 | + | 18.3079i | −0.00632813 | + | 0.0744223i | ||||
\(247\) | 78.9419i | 0.319603i | ||||||||
\(248\) | −73.1993 | + | 281.409i | −0.295159 | + | 1.13471i | ||||
\(249\) | 172.633 | 0.693307 | ||||||||
\(250\) | 22.2803 | + | 1.89449i | 0.0891211 | + | 0.00757797i | ||||
\(251\) | 167.879i | 0.668839i | 0.942424 | + | 0.334420i | \(0.108540\pi\) | ||||
−0.942424 | + | 0.334420i | \(0.891460\pi\) | |||||||
\(252\) | −25.1150 | + | 146.615i | −0.0996627 | + | 0.581807i | ||||
\(253\) | 87.2650 | 0.344921 | ||||||||
\(254\) | −2.82733 | + | 33.2510i | −0.0111312 | + | 0.130909i | ||||
\(255\) | 25.2753i | 0.0991190i | ||||||||
\(256\) | 199.282 | + | 160.694i | 0.778447 | + | 0.627710i | ||||
\(257\) | 198.849 | 0.773732 | 0.386866 | − | 0.922136i | \(-0.373558\pi\) | ||||
0.386866 | + | 0.922136i | \(0.373558\pi\) | |||||||
\(258\) | −157.350 | − | 13.3795i | −0.609884 | − | 0.0518585i | ||||
\(259\) | 234.629i | 0.905903i | ||||||||
\(260\) | −24.8615 | − | 4.25874i | −0.0956211 | − | 0.0163798i | ||||
\(261\) | −152.151 | −0.582953 | ||||||||
\(262\) | 33.2827 | − | 391.423i | 0.127033 | − | 1.49398i | ||||
\(263\) | 480.528i | 1.82710i | 0.406722 | + | 0.913552i | \(0.366672\pi\) | ||||
−0.406722 | + | 0.913552i | \(0.633328\pi\) | |||||||
\(264\) | 148.052 | + | 38.5110i | 0.560804 | + | 0.145875i | ||||
\(265\) | −92.0545 | −0.347376 | ||||||||
\(266\) | −691.496 | − | 58.7979i | −2.59961 | − | 0.221045i | ||||
\(267\) | − | 175.081i | − | 0.655733i | ||||||
\(268\) | −10.9212 | + | 63.7552i | −0.0407506 | + | 0.237892i | ||||
\(269\) | −291.496 | −1.08363 | −0.541815 | − | 0.840498i | \(-0.682263\pi\) | ||||
−0.541815 | + | 0.840498i | \(0.682263\pi\) | |||||||
\(270\) | −1.96882 | + | 23.1543i | −0.00729191 | + | 0.0857568i | ||||
\(271\) | 174.063i | 0.642299i | 0.947029 | + | 0.321150i | \(0.104069\pi\) | ||||
−0.947029 | + | 0.321150i | \(0.895931\pi\) | |||||||
\(272\) | 98.4638 | + | 34.7532i | 0.361999 | + | 0.127769i | ||||
\(273\) | −60.5482 | −0.221788 | ||||||||
\(274\) | 233.412 | + | 19.8470i | 0.851868 | + | 0.0724344i | ||||
\(275\) | − | 55.2016i | − | 0.200733i | ||||||
\(276\) | 53.9758 | + | 9.24598i | 0.195564 | + | 0.0334999i | ||||
\(277\) | −50.5203 | −0.182384 | −0.0911918 | − | 0.995833i | \(-0.529068\pi\) | ||||
−0.0911918 | + | 0.995833i | \(0.529068\pi\) | |||||||
\(278\) | 31.7273 | − | 373.130i | 0.114127 | − | 1.34219i | ||||
\(279\) | 109.040i | 0.390824i | ||||||||
\(280\) | 55.8221 | − | 214.603i | 0.199365 | − | 0.766441i | ||||
\(281\) | −66.0514 | −0.235058 | −0.117529 | − | 0.993069i | \(-0.537497\pi\) | ||||
−0.117529 | + | 0.993069i | \(0.537497\pi\) | |||||||
\(282\) | 40.4692 | + | 3.44110i | 0.143508 | + | 0.0122025i | ||||
\(283\) | − | 116.934i | − | 0.413196i | −0.978426 | − | 0.206598i | \(-0.933761\pi\) | ||
0.978426 | − | 0.206598i | \(-0.0662392\pi\) | |||||||
\(284\) | 44.6828 | − | 260.848i | 0.157334 | − | 0.918477i | ||||
\(285\) | −108.415 | −0.380405 | ||||||||
\(286\) | −5.27572 | + | 62.0454i | −0.0184466 | + | 0.216942i | ||||
\(287\) | − | 65.7491i | − | 0.229091i | ||||||
\(288\) | 87.4941 | + | 39.5067i | 0.303799 | + | 0.137176i | ||||
\(289\) | −246.411 | −0.852631 | ||||||||
\(290\) | 225.997 | + | 19.2166i | 0.779301 | + | 0.0662640i | ||||
\(291\) | − | 220.478i | − | 0.757658i | ||||||
\(292\) | 61.6341 | + | 10.5578i | 0.211076 | + | 0.0361570i | ||||
\(293\) | −68.3732 | −0.233356 | −0.116678 | − | 0.993170i | \(-0.537224\pi\) | ||||
−0.116678 | + | 0.993170i | \(0.537224\pi\) | |||||||
\(294\) | 30.7166 | − | 361.244i | 0.104478 | − | 1.22872i | ||||
\(295\) | 23.9277i | 0.0811110i | ||||||||
\(296\) | 146.547 | + | 38.1194i | 0.495091 | + | 0.128782i | ||||
\(297\) | 57.3672 | 0.193155 | ||||||||
\(298\) | 100.094 | + | 8.51096i | 0.335884 | + | 0.0285603i | ||||
\(299\) | 22.2905i | 0.0745503i | ||||||||
\(300\) | 5.84877 | − | 34.1437i | 0.0194959 | − | 0.113812i | ||||
\(301\) | 565.092 | 1.87738 | ||||||||
\(302\) | 36.1197 | − | 424.788i | 0.119602 | − | 1.40658i | ||||
\(303\) | 163.425i | 0.539356i | ||||||||
\(304\) | −149.070 | + | 422.349i | −0.490361 | + | 1.38930i | ||||
\(305\) | −125.510 | −0.411508 | ||||||||
\(306\) | 39.0156 | + | 3.31750i | 0.127502 | + | 0.0108415i | ||||
\(307\) | 369.497i | 1.20357i | 0.798657 | + | 0.601786i | \(0.205544\pi\) | ||||
−0.798657 | + | 0.601786i | \(0.794456\pi\) | |||||||
\(308\) | −539.560 | − | 92.4258i | −1.75182 | − | 0.300084i | ||||
\(309\) | 55.1580 | 0.178505 | ||||||||
\(310\) | 13.7717 | − | 161.963i | 0.0444248 | − | 0.522460i | ||||
\(311\) | 303.446i | 0.975712i | 0.872924 | + | 0.487856i | \(0.162221\pi\) | ||||
−0.872924 | + | 0.487856i | \(0.837779\pi\) | |||||||
\(312\) | −9.83707 | + | 37.8178i | −0.0315291 | + | 0.121211i | ||||
\(313\) | 297.693 | 0.951097 | 0.475549 | − | 0.879689i | \(-0.342250\pi\) | ||||
0.475549 | + | 0.879689i | \(0.342250\pi\) | |||||||
\(314\) | −406.369 | − | 34.5536i | −1.29417 | − | 0.110043i | ||||
\(315\) | − | 83.1542i | − | 0.263982i | ||||||
\(316\) | 83.1072 | − | 485.160i | 0.262998 | − | 1.53532i | ||||
\(317\) | 264.678 | 0.834948 | 0.417474 | − | 0.908689i | \(-0.362916\pi\) | ||||
0.417474 | + | 0.908689i | \(0.362916\pi\) | |||||||
\(318\) | −12.0826 | + | 142.097i | −0.0379955 | + | 0.446847i | ||||
\(319\) | − | 559.931i | − | 1.75527i | ||||||
\(320\) | −124.970 | − | 69.7318i | −0.390531 | − | 0.217912i | ||||
\(321\) | −58.5280 | −0.182330 | ||||||||
\(322\) | −195.255 | − | 16.6026i | −0.606382 | − | 0.0515607i | ||||
\(323\) | 182.682i | 0.565580i | ||||||||
\(324\) | 35.4832 | + | 6.07822i | 0.109516 | + | 0.0187599i | ||||
\(325\) | 14.1004 | 0.0433859 | ||||||||
\(326\) | −36.5835 | + | 430.243i | −0.112219 | + | 1.31976i | ||||
\(327\) | 144.499i | 0.441893i | ||||||||
\(328\) | −41.0663 | − | 10.6820i | −0.125202 | − | 0.0325672i | ||||
\(329\) | −145.337 | −0.441754 | ||||||||
\(330\) | −85.2104 | − | 7.24545i | −0.258213 | − | 0.0219559i | ||||
\(331\) | − | 473.426i | − | 1.43029i | −0.698976 | − | 0.715145i | \(-0.746361\pi\) | ||
0.698976 | − | 0.715145i | \(-0.253639\pi\) | |||||||
\(332\) | −67.3129 | + | 392.956i | −0.202750 | + | 1.18360i | ||||
\(333\) | 56.7838 | 0.170522 | ||||||||
\(334\) | 43.2143 | − | 508.224i | 0.129384 | − | 1.52163i | ||||
\(335\) | − | 36.1593i | − | 0.107938i | ||||||
\(336\) | −323.940 | − | 114.336i | −0.964107 | − | 0.340285i | ||||
\(337\) | 29.7588 | 0.0883051 | 0.0441526 | − | 0.999025i | \(-0.485941\pi\) | ||||
0.0441526 | + | 0.999025i | \(0.485941\pi\) | |||||||
\(338\) | 320.936 | + | 27.2892i | 0.949515 | + | 0.0807373i | ||||
\(339\) | 193.636i | 0.571197i | ||||||||
\(340\) | −57.5329 | − | 9.85530i | −0.169214 | − | 0.0289862i | ||||
\(341\) | −401.278 | −1.17677 | ||||||||
\(342\) | −14.2300 | + | 167.353i | −0.0416082 | + | 0.489335i | ||||
\(343\) | 689.937i | 2.01148i | ||||||||
\(344\) | 91.8086 | − | 352.951i | 0.266885 | − | 1.02602i | ||||
\(345\) | −30.6129 | −0.0887330 | ||||||||
\(346\) | 469.158 | + | 39.8925i | 1.35595 | + | 0.115296i | ||||
\(347\) | − | 306.190i | − | 0.882391i | −0.897411 | − | 0.441195i | \(-0.854555\pi\) | ||
0.897411 | − | 0.441195i | \(-0.145445\pi\) | |||||||
\(348\) | 59.3263 | − | 346.333i | 0.170478 | − | 0.995208i | ||||
\(349\) | 649.149 | 1.86002 | 0.930012 | − | 0.367528i | \(-0.119796\pi\) | ||||
0.930012 | + | 0.367528i | \(0.119796\pi\) | |||||||
\(350\) | −10.5023 | + | 123.513i | −0.0300067 | + | 0.352895i | ||||
\(351\) | 14.6536i | 0.0417481i | ||||||||
\(352\) | −145.389 | + | 321.988i | −0.413036 | + | 0.914737i | ||||
\(353\) | −275.547 | −0.780587 | −0.390293 | − | 0.920691i | \(-0.627626\pi\) | ||||
−0.390293 | + | 0.920691i | \(0.627626\pi\) | |||||||
\(354\) | 36.9354 | + | 3.14062i | 0.104337 | + | 0.00887181i | ||||
\(355\) | 147.942i | 0.416738i | ||||||||
\(356\) | 398.527 | + | 68.2671i | 1.11946 | + | 0.191761i | ||||
\(357\) | −140.117 | −0.392484 | ||||||||
\(358\) | 17.3972 | − | 204.600i | 0.0485955 | − | 0.571510i | ||||
\(359\) | − | 507.672i | − | 1.41413i | −0.707149 | − | 0.707065i | \(-0.750019\pi\) | ||
0.707149 | − | 0.707065i | \(-0.249981\pi\) | |||||||
\(360\) | −51.9373 | − | 13.5098i | −0.144270 | − | 0.0375272i | ||||
\(361\) | −422.594 | −1.17062 | ||||||||
\(362\) | 113.236 | + | 9.62845i | 0.312806 | + | 0.0265979i | ||||
\(363\) | 1.53900i | 0.00423968i | ||||||||
\(364\) | 23.6088 | − | 137.823i | 0.0648594 | − | 0.378633i | ||||
\(365\) | −34.9564 | −0.0957709 | ||||||||
\(366\) | −16.4737 | + | 193.740i | −0.0450102 | + | 0.529344i | ||||
\(367\) | 62.7671i | 0.171028i | 0.996337 | + | 0.0855138i | \(0.0272532\pi\) | ||||
−0.996337 | + | 0.0855138i | \(0.972747\pi\) | |||||||
\(368\) | −42.0923 | + | 119.257i | −0.114381 | + | 0.324068i | ||||
\(369\) | −15.9123 | −0.0431228 | ||||||||
\(370\) | −84.3440 | − | 7.17177i | −0.227957 | − | 0.0193832i | ||||
\(371\) | − | 510.315i | − | 1.37551i | ||||||
\(372\) | −248.202 | − | 42.5166i | −0.667209 | − | 0.114292i | ||||
\(373\) | −272.776 | −0.731302 | −0.365651 | − | 0.930752i | \(-0.619154\pi\) | ||||
−0.365651 | + | 0.930752i | \(0.619154\pi\) | |||||||
\(374\) | −12.2087 | + | 143.581i | −0.0326437 | + | 0.383908i | ||||
\(375\) | 19.3649i | 0.0516398i | ||||||||
\(376\) | −23.6124 | + | 90.7761i | −0.0627990 | + | 0.241426i | ||||
\(377\) | 143.026 | 0.379379 | ||||||||
\(378\) | −128.359 | − | 10.9144i | −0.339574 | − | 0.0288740i | ||||
\(379\) | − | 376.828i | − | 0.994270i | −0.867673 | − | 0.497135i | \(-0.834385\pi\) | ||
0.867673 | − | 0.497135i | \(-0.165615\pi\) | |||||||
\(380\) | 42.2731 | − | 246.780i | 0.111245 | − | 0.649422i | ||||
\(381\) | −28.9001 | −0.0758533 | ||||||||
\(382\) | −26.8565 | + | 315.847i | −0.0703049 | + | 0.826825i | ||||
\(383\) | 412.206i | 1.07625i | 0.842864 | + | 0.538127i | \(0.180868\pi\) | ||||
−0.842864 | + | 0.538127i | \(0.819132\pi\) | |||||||
\(384\) | −124.042 | + | 183.754i | −0.323027 | + | 0.478526i | ||||
\(385\) | 306.016 | 0.794848 | ||||||||
\(386\) | 312.337 | + | 26.5581i | 0.809164 | + | 0.0688032i | ||||
\(387\) | − | 136.761i | − | 0.353387i | ||||||
\(388\) | 501.863 | + | 85.9685i | 1.29346 | + | 0.221568i | ||||
\(389\) | −161.289 | −0.414623 | −0.207312 | − | 0.978275i | \(-0.566471\pi\) | ||||
−0.207312 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(390\) | 1.85074 | − | 21.7657i | 0.00474549 | − | 0.0558096i | ||||
\(391\) | 51.5834i | 0.131927i | ||||||||
\(392\) | 810.303 | + | 210.774i | 2.06710 | + | 0.537689i | ||||
\(393\) | 340.206 | 0.865663 | ||||||||
\(394\) | −518.383 | − | 44.0782i | −1.31569 | − | 0.111874i | ||||
\(395\) | 275.163i | 0.696615i | ||||||||
\(396\) | −22.3685 | + | 130.582i | −0.0564861 | + | 0.329752i | ||||
\(397\) | −186.505 | −0.469785 | −0.234893 | − | 0.972021i | \(-0.575474\pi\) | ||||
−0.234893 | + | 0.972021i | \(0.575474\pi\) | |||||||
\(398\) | 2.37781 | − | 27.9643i | 0.00597440 | − | 0.0702622i | ||||
\(399\) | − | 601.014i | − | 1.50630i | ||||||
\(400\) | 75.4389 | + | 26.6265i | 0.188597 | + | 0.0665662i | ||||
\(401\) | 239.061 | 0.596162 | 0.298081 | − | 0.954541i | \(-0.403653\pi\) | ||||
0.298081 | + | 0.954541i | \(0.403653\pi\) | |||||||
\(402\) | −55.8164 | − | 4.74607i | −0.138847 | − | 0.0118061i | ||||
\(403\) | − | 102.501i | − | 0.254344i | ||||||
\(404\) | −371.996 | − | 63.7223i | −0.920781 | − | 0.157729i | ||||
\(405\) | −20.1246 | −0.0496904 | ||||||||
\(406\) | −106.529 | + | 1252.84i | −0.262387 | + | 3.08582i | ||||
\(407\) | 208.970i | 0.513441i | ||||||||
\(408\) | −22.7643 | + | 87.5155i | −0.0557949 | + | 0.214499i | ||||
\(409\) | 47.8016 | 0.116874 | 0.0584372 | − | 0.998291i | \(-0.481388\pi\) | ||||
0.0584372 | + | 0.998291i | \(0.481388\pi\) | |||||||
\(410\) | 23.6354 | + | 2.00972i | 0.0576473 | + | 0.00490175i | ||||
\(411\) | 202.870i | 0.493601i | ||||||||
\(412\) | −21.5071 | + | 125.553i | −0.0522017 | + | 0.304741i | ||||
\(413\) | −132.646 | −0.321177 | ||||||||
\(414\) | −4.01807 | + | 47.2547i | −0.00970549 | + | 0.114142i | ||||
\(415\) | − | 222.869i | − | 0.537033i | ||||||
\(416\) | −82.2470 | − | 37.1374i | −0.197709 | − | 0.0892726i | ||||
\(417\) | 324.306 | 0.777713 | ||||||||
\(418\) | −615.875 | − | 52.3679i | −1.47339 | − | 0.125282i | ||||
\(419\) | 239.009i | 0.570428i | 0.958464 | + | 0.285214i | \(0.0920647\pi\) | ||||
−0.958464 | + | 0.285214i | \(0.907935\pi\) | |||||||
\(420\) | 189.280 | + | 32.4233i | 0.450666 | + | 0.0771984i | ||||
\(421\) | −257.592 | −0.611857 | −0.305929 | − | 0.952054i | \(-0.598967\pi\) | ||||
−0.305929 | + | 0.952054i | \(0.598967\pi\) | |||||||
\(422\) | −12.6229 | + | 148.452i | −0.0299121 | + | 0.351783i | ||||
\(423\) | 35.1738i | 0.0831532i | ||||||||
\(424\) | −318.738 | − | 82.9092i | −0.751740 | − | 0.195541i | ||||
\(425\) | 32.6303 | 0.0767772 | ||||||||
\(426\) | 228.367 | + | 19.4181i | 0.536073 | + | 0.0455823i | ||||
\(427\) | − | 695.779i | − | 1.62946i | ||||||
\(428\) | 22.8211 | − | 133.224i | 0.0533204 | − | 0.311271i | ||||
\(429\) | −53.9268 | −0.125703 | ||||||||
\(430\) | −17.2728 | + | 203.138i | −0.0401694 | + | 0.472414i | ||||
\(431\) | − | 343.164i | − | 0.796205i | −0.917341 | − | 0.398103i | \(-0.869669\pi\) | ||
0.917341 | − | 0.398103i | \(-0.130331\pi\) | |||||||
\(432\) | −27.6710 | + | 78.3984i | −0.0640533 | + | 0.181478i | ||||
\(433\) | −234.760 | −0.542171 | −0.271085 | − | 0.962555i | \(-0.587383\pi\) | ||||
−0.271085 | + | 0.962555i | \(0.587383\pi\) | |||||||
\(434\) | 897.859 | + | 76.3450i | 2.06880 | + | 0.175910i | ||||
\(435\) | 196.426i | 0.451553i | ||||||||
\(436\) | −328.916 | − | 56.3428i | −0.754394 | − | 0.129227i | ||||
\(437\) | −221.261 | −0.506317 | ||||||||
\(438\) | −4.58818 | + | 53.9595i | −0.0104753 | + | 0.123195i | ||||
\(439\) | 374.473i | 0.853013i | 0.904484 | + | 0.426507i | \(0.140256\pi\) | ||||
−0.904484 | + | 0.426507i | \(0.859744\pi\) | |||||||
\(440\) | 49.7175 | − | 191.135i | 0.112994 | − | 0.434397i | ||||
\(441\) | 313.975 | 0.711962 | ||||||||
\(442\) | −36.6758 | − | 3.11854i | −0.0829768 | − | 0.00705553i | ||||
\(443\) | − | 108.557i | − | 0.245050i | −0.992465 | − | 0.122525i | \(-0.960901\pi\) | ||
0.992465 | − | 0.122525i | \(-0.0390992\pi\) | |||||||
\(444\) | −22.1410 | + | 129.254i | −0.0498672 | + | 0.291113i | ||||
\(445\) | −226.028 | −0.507929 | ||||||||
\(446\) | −27.1111 | + | 318.842i | −0.0607873 | + | 0.714891i | ||||
\(447\) | 86.9963i | 0.194623i | ||||||||
\(448\) | 386.566 | − | 692.785i | 0.862872 | − | 1.54640i | ||||
\(449\) | −431.511 | −0.961050 | −0.480525 | − | 0.876981i | \(-0.659554\pi\) | ||||
−0.480525 | + | 0.876981i | \(0.659554\pi\) | |||||||
\(450\) | 29.8921 | + | 2.54173i | 0.0664270 | + | 0.00564829i | ||||
\(451\) | − | 58.5589i | − | 0.129842i | ||||||
\(452\) | −440.762 | − | 75.5020i | −0.975138 | − | 0.167040i | ||||
\(453\) | 369.205 | 0.815021 | ||||||||
\(454\) | −29.8193 | + | 350.692i | −0.0656813 | + | 0.772448i | ||||
\(455\) | 78.1674i | 0.171796i | ||||||||
\(456\) | −375.387 | − | 97.6448i | −0.823218 | − | 0.214133i | ||||
\(457\) | 219.747 | 0.480847 | 0.240424 | − | 0.970668i | \(-0.422714\pi\) | ||||
0.240424 | + | 0.970668i | \(0.422714\pi\) | |||||||
\(458\) | 227.520 | + | 19.3460i | 0.496768 | + | 0.0422402i | ||||
\(459\) | 33.9104i | 0.0738789i | ||||||||
\(460\) | 11.9365 | − | 69.6825i | 0.0259489 | − | 0.151484i | ||||
\(461\) | 223.434 | 0.484673 | 0.242337 | − | 0.970192i | \(-0.422086\pi\) | ||||
0.242337 | + | 0.970192i | \(0.422086\pi\) | |||||||
\(462\) | 40.1660 | − | 472.374i | 0.0869394 | − | 1.02245i | ||||
\(463\) | 740.855i | 1.60012i | 0.599921 | + | 0.800059i | \(0.295198\pi\) | ||||
−0.599921 | + | 0.800059i | \(0.704802\pi\) | |||||||
\(464\) | 765.206 | + | 270.082i | 1.64915 | + | 0.582074i | ||||
\(465\) | 140.770 | 0.302731 | ||||||||
\(466\) | −518.254 | − | 44.0672i | −1.11213 | − | 0.0945648i | ||||
\(467\) | 249.381i | 0.534007i | 0.963696 | + | 0.267004i | \(0.0860336\pi\) | ||||
−0.963696 | + | 0.267004i | \(0.913966\pi\) | |||||||
\(468\) | −33.3552 | − | 5.71370i | −0.0712718 | − | 0.0122088i | ||||
\(469\) | 200.454 | 0.427406 | ||||||||
\(470\) | 4.44244 | − | 52.2455i | 0.00945199 | − | 0.111161i | ||||
\(471\) | − | 353.196i | − | 0.749885i | ||||||
\(472\) | −21.5506 | + | 82.8495i | −0.0456580 | + | 0.175529i | ||||
\(473\) | 503.294 | 1.06405 | ||||||||
\(474\) | 424.748 | + | 36.1164i | 0.896093 | + | 0.0761948i | ||||
\(475\) | 139.964i | 0.294661i | ||||||||
\(476\) | 54.6340 | − | 318.940i | 0.114777 | − | 0.670043i | ||||
\(477\) | −123.504 | −0.258918 | ||||||||
\(478\) | 23.7379 | − | 279.171i | 0.0496609 | − | 0.584039i | ||||
\(479\) | − | 210.915i | − | 0.440324i | −0.975463 | − | 0.220162i | \(-0.929341\pi\) | ||
0.975463 | − | 0.220162i | \(-0.0706587\pi\) | |||||||
\(480\) | 51.0029 | − | 112.954i | 0.106256 | − | 0.235322i | ||||
\(481\) | −53.3784 | −0.110974 | ||||||||
\(482\) | −211.079 | − | 17.9480i | −0.437923 | − | 0.0372366i | ||||
\(483\) | − | 169.706i | − | 0.351358i | ||||||
\(484\) | −3.50315 | − | 0.600085i | −0.00723791 | − | 0.00123984i | ||||
\(485\) | −284.636 | −0.586879 | ||||||||
\(486\) | −2.64144 | + | 31.0648i | −0.00543507 | + | 0.0639194i | ||||
\(487\) | − | 710.541i | − | 1.45902i | −0.683972 | − | 0.729508i | \(-0.739749\pi\) | ||
0.683972 | − | 0.729508i | \(-0.260251\pi\) | |||||||
\(488\) | −434.576 | − | 113.041i | −0.890525 | − | 0.231641i | ||||
\(489\) | −373.946 | −0.764715 | ||||||||
\(490\) | −466.364 | − | 39.6549i | −0.951763 | − | 0.0809285i | ||||
\(491\) | − | 697.876i | − | 1.42134i | −0.703528 | − | 0.710668i | \(-0.748393\pi\) | ||
0.703528 | − | 0.710668i | \(-0.251607\pi\) | |||||||
\(492\) | 6.20449 | − | 36.2203i | 0.0126108 | − | 0.0736185i | ||||
\(493\) | 330.982 | 0.671363 | ||||||||
\(494\) | 13.3766 | − | 157.316i | 0.0270781 | − | 0.318454i | ||||
\(495\) | − | 74.0607i | − | 0.149618i | ||||||
\(496\) | 193.557 | − | 548.390i | 0.390235 | − | 1.10563i | ||||
\(497\) | −820.135 | −1.65017 | ||||||||
\(498\) | −344.025 | − | 29.2525i | −0.690814 | − | 0.0587400i | ||||
\(499\) | 875.602i | 1.75471i | 0.479838 | + | 0.877357i | \(0.340695\pi\) | ||||
−0.479838 | + | 0.877357i | \(0.659305\pi\) | |||||||
\(500\) | −44.0793 | − | 7.55073i | −0.0881586 | − | 0.0151015i | ||||
\(501\) | 441.723 | 0.881683 | ||||||||
\(502\) | 28.4468 | − | 334.550i | 0.0566670 | − | 0.666434i | ||||
\(503\) | − | 142.849i | − | 0.283995i | −0.989867 | − | 0.141997i | \(-0.954648\pi\) | ||
0.989867 | − | 0.141997i | \(-0.0453524\pi\) | |||||||
\(504\) | 74.8932 | − | 287.921i | 0.148598 | − | 0.571271i | ||||
\(505\) | 210.981 | 0.417784 | ||||||||
\(506\) | −173.902 | − | 14.7869i | −0.343681 | − | 0.0292232i | ||||
\(507\) | 278.942i | 0.550181i | ||||||||
\(508\) | 11.2687 | − | 65.7837i | 0.0221824 | − | 0.129496i | ||||
\(509\) | −147.662 | −0.290102 | −0.145051 | − | 0.989424i | \(-0.546335\pi\) | ||||
−0.145051 | + | 0.989424i | \(0.546335\pi\) | |||||||
\(510\) | 4.28287 | − | 50.3689i | 0.00839779 | − | 0.0987626i | ||||
\(511\) | − | 193.785i | − | 0.379227i | ||||||
\(512\) | −369.903 | − | 354.000i | −0.722466 | − | 0.691407i | ||||
\(513\) | −145.455 | −0.283537 | ||||||||
\(514\) | −396.268 | − | 33.6947i | −0.770950 | − | 0.0655539i | ||||
\(515\) | − | 71.2087i | − | 0.138269i | ||||||
\(516\) | 311.301 | + | 53.3255i | 0.603297 | + | 0.103344i | ||||
\(517\) | −129.443 | −0.250374 | ||||||||
\(518\) | 39.7576 | − | 467.571i | 0.0767520 | − | 0.902646i | ||||
\(519\) | 407.769i | 0.785682i | ||||||||
\(520\) | 48.8226 | + | 12.6996i | 0.0938895 | + | 0.0244223i | ||||
\(521\) | −348.592 | −0.669082 | −0.334541 | − | 0.942381i | \(-0.608581\pi\) | ||||
−0.334541 | + | 0.942381i | \(0.608581\pi\) | |||||||
\(522\) | 303.207 | + | 25.7817i | 0.580857 | + | 0.0493903i | ||||
\(523\) | − | 370.317i | − | 0.708063i | −0.935233 | − | 0.354032i | \(-0.884811\pi\) | ||
0.935233 | − | 0.354032i | \(-0.115189\pi\) | |||||||
\(524\) | −132.652 | + | 774.392i | −0.253153 | + | 1.47785i | ||||
\(525\) | −107.352 | −0.204479 | ||||||||
\(526\) | 81.4249 | − | 957.601i | 0.154800 | − | 1.82053i | ||||
\(527\) | − | 237.201i | − | 0.450096i | ||||||
\(528\) | −288.514 | − | 101.832i | −0.546429 | − | 0.192864i | ||||
\(529\) | 466.523 | 0.881897 | ||||||||
\(530\) | 183.447 | + | 15.5985i | 0.346127 | + | 0.0294312i | ||||
\(531\) | 32.1024i | 0.0604565i | ||||||||
\(532\) | 1368.06 | + | 234.346i | 2.57153 | + | 0.440500i | ||||
\(533\) | 14.9580 | 0.0280638 | ||||||||
\(534\) | −29.6672 | + | 348.902i | −0.0555565 | + | 0.653375i | ||||
\(535\) | 75.5593i | 0.141232i | ||||||||
\(536\) | 32.5670 | − | 125.201i | 0.0607594 | − | 0.233584i | ||||
\(537\) | 177.829 | 0.331152 | ||||||||
\(538\) | 580.897 | + | 49.3937i | 1.07973 | + | 0.0918098i | ||||
\(539\) | 1155.46i | 2.14371i | ||||||||
\(540\) | 7.84695 | − | 45.8086i | 0.0145314 | − | 0.0848307i | ||||
\(541\) | −279.719 | −0.517041 | −0.258520 | − | 0.966006i | \(-0.583235\pi\) | ||||
−0.258520 | + | 0.966006i | \(0.583235\pi\) | |||||||
\(542\) | 29.4947 | − | 346.874i | 0.0544183 | − | 0.639990i | ||||
\(543\) | 98.4190i | 0.181250i | ||||||||
\(544\) | −190.331 | − | 85.9411i | −0.349873 | − | 0.157980i | ||||
\(545\) | 186.548 | 0.342289 | ||||||||
\(546\) | 120.661 | + | 10.2598i | 0.220991 | + | 0.0187909i | ||||
\(547\) | 387.716i | 0.708804i | 0.935093 | + | 0.354402i | \(0.115315\pi\) | ||||
−0.935093 | + | 0.354402i | \(0.884685\pi\) | |||||||
\(548\) | −461.782 | − | 79.1026i | −0.842668 | − | 0.144348i | ||||
\(549\) | −168.389 | −0.306720 | ||||||||
\(550\) | −9.35383 | + | 110.006i | −0.0170070 | + | 0.200011i | ||||
\(551\) | 1419.71i | 2.57660i | ||||||||
\(552\) | −105.997 | − | 27.5716i | −0.192023 | − | 0.0499485i | ||||
\(553\) | −1525.40 | −2.75841 | ||||||||
\(554\) | 100.677 | + | 8.56059i | 0.181728 | + | 0.0154523i | ||||
\(555\) | − | 73.3076i | − | 0.132086i | ||||||
\(556\) | −126.453 | + | 738.201i | −0.227433 | + | 1.32770i | ||||
\(557\) | 43.5564 | 0.0781983 | 0.0390991 | − | 0.999235i | \(-0.487551\pi\) | ||||
0.0390991 | + | 0.999235i | \(0.487551\pi\) | |||||||
\(558\) | 18.4767 | − | 217.296i | 0.0331123 | − | 0.389419i | ||||
\(559\) | 128.559i | 0.229981i | ||||||||
\(560\) | −147.607 | + | 418.204i | −0.263584 | + | 0.746794i | ||||
\(561\) | −124.794 | −0.222449 | ||||||||
\(562\) | 131.628 | + | 11.1923i | 0.234213 | + | 0.0199152i | ||||
\(563\) | 361.646i | 0.642355i | 0.947019 | + | 0.321178i | \(0.104079\pi\) | ||||
−0.947019 | + | 0.321178i | \(0.895921\pi\) | |||||||
\(564\) | −80.0642 | − | 13.7149i | −0.141958 | − | 0.0243172i | ||||
\(565\) | 249.983 | 0.442447 | ||||||||
\(566\) | −19.8144 | + | 233.028i | −0.0350078 | + | 0.411710i | ||||
\(567\) | − | 111.563i | − | 0.196760i | ||||||
\(568\) | −133.245 | + | 512.248i | −0.234586 | + | 0.901845i | ||||
\(569\) | 888.559 | 1.56161 | 0.780807 | − | 0.624772i | \(-0.214808\pi\) | ||||
0.780807 | + | 0.624772i | \(0.214808\pi\) | |||||||
\(570\) | 216.051 | + | 18.3709i | 0.379037 | + | 0.0322296i | ||||
\(571\) | 447.745i | 0.784142i | 0.919935 | + | 0.392071i | \(0.128241\pi\) | ||||
−0.919935 | + | 0.392071i | \(0.871759\pi\) | |||||||
\(572\) | 21.0270 | − | 122.751i | 0.0367605 | − | 0.214599i | ||||
\(573\) | −274.519 | −0.479090 | ||||||||
\(574\) | −11.1411 | + | 131.025i | −0.0194096 | + | 0.228267i | ||||
\(575\) | 39.5211i | 0.0687323i | ||||||||
\(576\) | −167.665 | − | 93.5551i | −0.291085 | − | 0.162422i | ||||
\(577\) | 1069.90 | 1.85425 | 0.927124 | − | 0.374756i | \(-0.122273\pi\) | ||||
0.927124 | + | 0.374756i | \(0.122273\pi\) | |||||||
\(578\) | 491.049 | + | 41.7539i | 0.849566 | + | 0.0722386i | ||||
\(579\) | 271.468i | 0.468857i | ||||||||
\(580\) | −447.113 | − | 76.5899i | −0.770885 | − | 0.132052i | ||||
\(581\) | 1235.50 | 2.12651 | ||||||||
\(582\) | −37.3598 | + | 439.371i | −0.0641921 | + | 0.754934i | ||||
\(583\) | − | 454.508i | − | 0.779602i | ||||||
\(584\) | −121.036 | − | 31.4836i | −0.207253 | − | 0.0539102i | ||||
\(585\) | 18.9177 | 0.0323380 | ||||||||
\(586\) | 136.255 | + | 11.5857i | 0.232517 | + | 0.0197709i | ||||
\(587\) | 129.637i | 0.220847i | 0.993885 | + | 0.110424i | \(0.0352208\pi\) | ||||
−0.993885 | + | 0.110424i | \(0.964779\pi\) | |||||||
\(588\) | −122.425 | + | 714.685i | −0.208205 | + | 1.21545i | ||||
\(589\) | 1017.44 | 1.72741 | ||||||||
\(590\) | 4.05452 | − | 47.6834i | 0.00687207 | − | 0.0808193i | ||||
\(591\) | − | 450.553i | − | 0.762357i | ||||||
\(592\) | −285.581 | − | 100.797i | −0.482400 | − | 0.170265i | ||||
\(593\) | 892.757 | 1.50549 | 0.752746 | − | 0.658311i | \(-0.228729\pi\) | ||||
0.752746 | + | 0.658311i | \(0.228729\pi\) | |||||||
\(594\) | −114.322 | − | 9.72079i | −0.192461 | − | 0.0163650i | ||||
\(595\) | 180.890i | 0.304017i | ||||||||
\(596\) | −198.025 | − | 33.9214i | −0.332257 | − | 0.0569151i | ||||
\(597\) | 24.3052 | 0.0407123 | ||||||||
\(598\) | 3.77710 | − | 44.4208i | 0.00631623 | − | 0.0742823i | ||||
\(599\) | − | 1030.62i | − | 1.72057i | −0.509816 | − | 0.860284i | \(-0.670286\pi\) | ||
0.509816 | − | 0.860284i | \(-0.329714\pi\) | |||||||
\(600\) | −17.4411 | + | 67.0508i | −0.0290685 | + | 0.111751i | ||||
\(601\) | −815.961 | −1.35767 | −0.678836 | − | 0.734289i | \(-0.737515\pi\) | ||||
−0.678836 | + | 0.734289i | \(0.737515\pi\) | |||||||
\(602\) | −1126.12 | − | 95.7540i | −1.87063 | − | 0.159060i | ||||
\(603\) | − | 48.5128i | − | 0.0804525i | ||||||
\(604\) | −143.959 | + | 840.401i | −0.238343 | + | 1.39139i | ||||
\(605\) | 1.98684 | 0.00328404 | ||||||||
\(606\) | 27.6921 | − | 325.675i | 0.0456966 | − | 0.537417i | ||||
\(607\) | 842.678i | 1.38827i | 0.719847 | + | 0.694133i | \(0.244212\pi\) | ||||
−0.719847 | + | 0.694133i | \(0.755788\pi\) | |||||||
\(608\) | 368.634 | − | 816.400i | 0.606305 | − | 1.34276i | ||||
\(609\) | −1088.91 | −1.78803 | ||||||||
\(610\) | 250.117 | + | 21.2675i | 0.410028 | + | 0.0348647i | ||||
\(611\) | − | 33.0644i | − | 0.0541152i | ||||||
\(612\) | −77.1885 | − | 13.2223i | −0.126125 | − | 0.0216050i | ||||
\(613\) | −731.088 | −1.19264 | −0.596320 | − | 0.802747i | \(-0.703371\pi\) | ||||
−0.596320 | + | 0.802747i | \(0.703371\pi\) | |||||||
\(614\) | 62.6107 | − | 736.336i | 0.101972 | − | 1.19924i | ||||
\(615\) | 20.5427i | 0.0334028i | ||||||||
\(616\) | 1059.58 | + | 275.615i | 1.72009 | + | 0.447426i | ||||
\(617\) | −919.609 | −1.49045 | −0.745226 | − | 0.666812i | \(-0.767658\pi\) | ||||
−0.745226 | + | 0.666812i | \(0.767658\pi\) | |||||||
\(618\) | −109.919 | − | 9.34645i | −0.177863 | − | 0.0151237i | ||||
\(619\) | − | 688.974i | − | 1.11304i | −0.830833 | − | 0.556522i | \(-0.812135\pi\) | ||
0.830833 | − | 0.556522i | \(-0.187865\pi\) | |||||||
\(620\) | −54.8887 | + | 320.427i | −0.0885302 | + | 0.516818i | ||||
\(621\) | −41.0715 | −0.0661377 | ||||||||
\(622\) | 51.4186 | − | 604.711i | 0.0826665 | − | 0.972203i | ||||
\(623\) | − | 1253.01i | − | 2.01126i | ||||||
\(624\) | 26.0116 | − | 73.6968i | 0.0416852 | − | 0.118104i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | −593.246 | − | 50.4438i | −0.947678 | − | 0.0805811i | ||||
\(627\) | − | 535.288i | − | 0.853729i | ||||||
\(628\) | 803.960 | + | 137.717i | 1.28019 | + | 0.219295i | ||||
\(629\) | −123.525 | −0.196383 | ||||||||
\(630\) | −14.0904 | + | 165.711i | −0.0223657 | + | 0.263033i | ||||
\(631\) | − | 418.968i | − | 0.663975i | −0.943284 | − | 0.331987i | \(-0.892281\pi\) | ||
0.943284 | − | 0.331987i | \(-0.107719\pi\) | |||||||
\(632\) | −247.827 | + | 952.749i | −0.392131 | + | 1.50751i | ||||
\(633\) | −129.027 | −0.203835 | ||||||||
\(634\) | −527.454 | − | 44.8494i | −0.831946 | − | 0.0707404i | ||||
\(635\) | 37.3099i | 0.0587557i | ||||||||
\(636\) | 48.1565 | − | 281.126i | 0.0757177 | − | 0.442022i | ||||
\(637\) | −295.146 | −0.463337 | ||||||||
\(638\) | −94.8795 | + | 1115.83i | −0.148714 | + | 1.74896i | ||||
\(639\) | 198.485i | 0.310618i | ||||||||
\(640\) | 237.225 | + | 160.138i | 0.370664 | + | 0.250216i | ||||
\(641\) | −47.2426 | −0.0737014 | −0.0368507 | − | 0.999321i | \(-0.511733\pi\) | ||||
−0.0368507 | + | 0.999321i | \(0.511733\pi\) | |||||||
\(642\) | 116.635 | + | 9.91749i | 0.181675 | + | 0.0154478i | ||||
\(643\) | − | 710.880i | − | 1.10557i | −0.833325 | − | 0.552784i | \(-0.813565\pi\) | ||
0.833325 | − | 0.552784i | \(-0.186435\pi\) | |||||||
\(644\) | 386.293 | + | 66.1714i | 0.599834 | + | 0.102751i | ||||
\(645\) | −176.558 | −0.273733 | ||||||||
\(646\) | 30.9553 | − | 364.051i | 0.0479184 | − | 0.563547i | ||||
\(647\) | − | 468.195i | − | 0.723641i | −0.932248 | − | 0.361820i | \(-0.882155\pi\) | ||
0.932248 | − | 0.361820i | \(-0.117845\pi\) | |||||||
\(648\) | −69.6812 | − | 18.1253i | −0.107533 | − | 0.0279711i | ||||
\(649\) | −118.140 | −0.182034 | ||||||||
\(650\) | −28.0995 | − | 2.38930i | −0.0432299 | − | 0.00367584i | ||||
\(651\) | 780.375i | 1.19873i | ||||||||
\(652\) | 145.808 | − | 851.192i | 0.223632 | − | 1.30551i | ||||
\(653\) | 551.066 | 0.843900 | 0.421950 | − | 0.906619i | \(-0.361346\pi\) | ||||
0.421950 | + | 0.906619i | \(0.361346\pi\) | |||||||
\(654\) | 24.4852 | − | 287.959i | 0.0374391 | − | 0.440304i | ||||
\(655\) | − | 439.203i | − | 0.670540i | ||||||
\(656\) | 80.0271 | + | 28.2459i | 0.121993 | + | 0.0430578i | ||||
\(657\) | −46.8989 | −0.0713834 | ||||||||
\(658\) | 289.629 | + | 24.6272i | 0.440165 | + | 0.0374273i | ||||
\(659\) | 158.259i | 0.240151i | 0.992765 | + | 0.120075i | \(0.0383136\pi\) | ||||
−0.992765 | + | 0.120075i | \(0.961686\pi\) | |||||||
\(660\) | 168.580 | + | 28.8776i | 0.255425 | + | 0.0437539i | ||||
\(661\) | 92.4953 | 0.139932 | 0.0699662 | − | 0.997549i | \(-0.477711\pi\) | ||||
0.0699662 | + | 0.997549i | \(0.477711\pi\) | |||||||
\(662\) | −80.2214 | + | 943.447i | −0.121180 | + | 1.42515i | ||||
\(663\) | − | 31.8768i | − | 0.0480796i | ||||||
\(664\) | 200.728 | − | 771.681i | 0.302301 | − | 1.16217i | ||||
\(665\) | −775.905 | −1.16678 | ||||||||
\(666\) | −113.159 | − | 9.62194i | −0.169909 | − | 0.0144474i | ||||
\(667\) | 400.877i | 0.601015i | ||||||||
\(668\) | −172.236 | + | 1005.47i | −0.257838 | + | 1.50520i | ||||
\(669\) | −277.121 | −0.414232 | ||||||||
\(670\) | −6.12715 | + | 72.0587i | −0.00914500 | + | 0.107550i | ||||
\(671\) | − | 619.690i | − | 0.923532i | ||||||
\(672\) | 626.176 | + | 282.741i | 0.931810 | + | 0.420745i | ||||
\(673\) | 956.062 | 1.42060 | 0.710299 | − | 0.703900i | \(-0.248560\pi\) | ||||
0.710299 | + | 0.703900i | \(0.248560\pi\) | |||||||
\(674\) | −59.3037 | − | 5.04259i | −0.0879876 | − | 0.00748159i | ||||
\(675\) | 25.9808i | 0.0384900i | ||||||||
\(676\) | −634.940 | − | 108.764i | −0.939261 | − | 0.160894i | ||||
\(677\) | 1116.67 | 1.64944 | 0.824719 | − | 0.565543i | \(-0.191333\pi\) | ||||
0.824719 | + | 0.565543i | \(0.191333\pi\) | |||||||
\(678\) | 32.8113 | − | 385.879i | 0.0483942 | − | 0.569143i | ||||
\(679\) | − | 1577.92i | − | 2.32388i | ||||||
\(680\) | 112.982 | + | 29.3886i | 0.166150 | + | 0.0432185i | ||||
\(681\) | −304.804 | −0.447583 | ||||||||
\(682\) | 799.671 | + | 67.9961i | 1.17254 | + | 0.0997010i | ||||
\(683\) | − | 826.776i | − | 1.21051i | −0.796033 | − | 0.605254i | \(-0.793072\pi\) | ||
0.796033 | − | 0.605254i | \(-0.206928\pi\) | |||||||
\(684\) | 56.7153 | − | 331.090i | 0.0829172 | − | 0.484050i | ||||
\(685\) | 261.904 | 0.382342 | ||||||||
\(686\) | 116.909 | − | 1374.91i | 0.170421 | − | 2.00424i | ||||
\(687\) | 197.749i | 0.287844i | ||||||||
\(688\) | −242.764 | + | 687.806i | −0.352855 | + | 0.999718i | ||||
\(689\) | 116.097 | 0.168501 | ||||||||
\(690\) | 61.0056 | + | 5.18731i | 0.0884139 | + | 0.00751784i | ||||
\(691\) | 965.432i | 1.39715i | 0.715536 | + | 0.698576i | \(0.246182\pi\) | ||||
−0.715536 | + | 0.698576i | \(0.753818\pi\) | |||||||
\(692\) | −928.183 | − | 158.996i | −1.34130 | − | 0.229764i | ||||
\(693\) | 410.564 | 0.592444 | ||||||||
\(694\) | −51.8834 | + | 610.177i | −0.0747600 | + | 0.879218i | ||||
\(695\) | − | 418.677i | − | 0.602414i | ||||||
\(696\) | −176.912 | + | 680.122i | −0.254183 | + | 0.977186i | ||||
\(697\) | 34.6149 | 0.0496627 | ||||||||
\(698\) | −1293.63 | − | 109.997i | −1.85334 | − | 0.157589i | ||||
\(699\) | − | 450.441i | − | 0.644408i | ||||||
\(700\) | 41.8583 | − | 244.359i | 0.0597976 | − | 0.349084i | ||||
\(701\) | −1109.94 | −1.58337 | −0.791686 | − | 0.610928i | \(-0.790797\pi\) | ||||
−0.791686 | + | 0.610928i | \(0.790797\pi\) | |||||||
\(702\) | 2.48303 | − | 29.2018i | 0.00353708 | − | 0.0415980i | ||||
\(703\) | − | 529.845i | − | 0.753691i | ||||||
\(704\) | 344.292 | − | 617.024i | 0.489052 | − | 0.876454i | ||||
\(705\) | 45.4092 | 0.0644102 | ||||||||
\(706\) | 549.113 | + | 46.6911i | 0.777780 | + | 0.0661347i | ||||
\(707\) | 1169.60i | 1.65431i | ||||||||
\(708\) | −73.0730 | − | 12.5173i | −0.103210 | − | 0.0176798i | ||||
\(709\) | −964.244 | −1.36001 | −0.680003 | − | 0.733210i | \(-0.738021\pi\) | ||||
−0.680003 | + | 0.733210i | \(0.738021\pi\) | |||||||
\(710\) | 25.0686 | − | 294.820i | 0.0353079 | − | 0.415240i | ||||
\(711\) | 369.170i | 0.519226i | ||||||||
\(712\) | −782.620 | − | 203.573i | −1.09919 | − | 0.285917i | ||||
\(713\) | 287.292 | 0.402934 | ||||||||
\(714\) | 279.226 | + | 23.7426i | 0.391073 | + | 0.0332529i | ||||
\(715\) | 69.6191i | 0.0973694i | ||||||||
\(716\) | −69.3385 | + | 404.782i | −0.0968415 | + | 0.565338i | ||||
\(717\) | 242.641 | 0.338412 | ||||||||
\(718\) | −86.0244 | + | 1011.69i | −0.119811 | + | 1.40904i | ||||
\(719\) | 190.820i | 0.265396i | 0.991157 | + | 0.132698i | \(0.0423641\pi\) | ||||
−0.991157 | + | 0.132698i | \(0.957636\pi\) | |||||||
\(720\) | 101.212 | + | 35.7232i | 0.140572 | + | 0.0496155i | ||||
\(721\) | 394.754 | 0.547509 | ||||||||
\(722\) | 842.149 | + | 71.6080i | 1.16641 | + | 0.0991801i | ||||
\(723\) | − | 183.459i | − | 0.253747i | ||||||
\(724\) | −224.026 | − | 38.3753i | −0.309428 | − | 0.0530046i | ||||
\(725\) | 253.585 | 0.349772 | ||||||||
\(726\) | 0.260782 | − | 3.06694i | 0.000359204 | − | 0.00422443i | ||||
\(727\) | 202.134i | 0.278039i | 0.990290 | + | 0.139019i | \(0.0443951\pi\) | ||||
−0.990290 | + | 0.139019i | \(0.955605\pi\) | |||||||
\(728\) | −70.4017 | + | 270.654i | −0.0967056 | + | 0.371777i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 69.6614 | + | 5.92331i | 0.0954265 | + | 0.00811412i | ||||
\(731\) | 297.503i | 0.406981i | ||||||||
\(732\) | 65.6579 | − | 383.295i | 0.0896966 | − | 0.523627i | ||||
\(733\) | −962.435 | −1.31301 | −0.656504 | − | 0.754322i | \(-0.727966\pi\) | ||||
−0.656504 | + | 0.754322i | \(0.727966\pi\) | |||||||
\(734\) | 10.6358 | − | 125.083i | 0.0144902 | − | 0.170413i | ||||
\(735\) | − | 405.340i | − | 0.551483i | ||||||
\(736\) | 104.090 | − | 230.524i | 0.141426 | − | 0.313212i | ||||
\(737\) | 178.532 | 0.242242 | ||||||||
\(738\) | 31.7102 | + | 2.69632i | 0.0429677 | + | 0.00365355i | ||||
\(739\) | 932.112i | 1.26132i | 0.776061 | + | 0.630658i | \(0.217215\pi\) | ||||
−0.776061 | + | 0.630658i | \(0.782785\pi\) | |||||||
\(740\) | 166.866 | + | 28.5839i | 0.225495 | + | 0.0386269i | ||||
\(741\) | 136.731 | 0.184523 | ||||||||
\(742\) | −86.4722 | + | 1016.96i | −0.116539 | + | 1.37057i | ||||
\(743\) | 1153.70i | 1.55276i | 0.630266 | + | 0.776379i | \(0.282946\pi\) | ||||
−0.630266 | + | 0.776379i | \(0.717054\pi\) | |||||||
\(744\) | 487.414 | + | 126.785i | 0.655127 | + | 0.170410i | ||||
\(745\) | 112.312 | 0.150754 | ||||||||
\(746\) | 543.590 | + | 46.2215i | 0.728672 | + | 0.0619591i | ||||
\(747\) | − | 299.010i | − | 0.400281i | ||||||
\(748\) | 48.6594 | − | 284.062i | 0.0650526 | − | 0.379762i | ||||
\(749\) | −418.872 | −0.559242 | ||||||||
\(750\) | 3.28136 | − | 38.5906i | 0.00437515 | − | 0.0514541i | ||||
\(751\) | 204.359i | 0.272116i | 0.990701 | + | 0.136058i | \(0.0434434\pi\) | ||||
−0.990701 | + | 0.136058i | \(0.956557\pi\) | |||||||
\(752\) | 62.4369 | − | 176.898i | 0.0830279 | − | 0.235237i | ||||
\(753\) | 290.774 | 0.386155 | ||||||||
\(754\) | −285.023 | − | 24.2356i | −0.378015 | − | 0.0321427i | ||||
\(755\) | − | 476.641i | − | 0.631313i | ||||||
\(756\) | 253.945 | + | 43.5005i | 0.335906 | + | 0.0575403i | ||||
\(757\) | −216.739 | −0.286314 | −0.143157 | − | 0.989700i | \(-0.545725\pi\) | ||||
−0.143157 | + | 0.989700i | \(0.545725\pi\) | |||||||
\(758\) | −63.8530 | + | 750.947i | −0.0842388 | + | 0.990695i | ||||
\(759\) | − | 151.147i | − | 0.199140i | ||||||
\(760\) | −126.059 | + | 484.623i | −0.165867 | + | 0.637662i | ||||
\(761\) | 1324.78 | 1.74085 | 0.870424 | − | 0.492303i | \(-0.163845\pi\) | ||||
0.870424 | + | 0.492303i | \(0.163845\pi\) | |||||||
\(762\) | 57.5924 | + | 4.89708i | 0.0755805 | + | 0.00642662i | ||||
\(763\) | 1034.15i | 1.35537i | ||||||||
\(764\) | 107.040 | − | 624.872i | 0.140104 | − | 0.817895i | ||||
\(765\) | 43.7782 | 0.0572264 | ||||||||
\(766\) | 69.8477 | − | 821.447i | 0.0911849 | − | 1.07238i | ||||
\(767\) | − | 30.1772i | − | 0.0393444i | ||||||
\(768\) | 278.330 | − | 345.167i | 0.362409 | − | 0.449437i | ||||
\(769\) | 444.088 | 0.577488 | 0.288744 | − | 0.957406i | \(-0.406762\pi\) | ||||
0.288744 | + | 0.957406i | \(0.406762\pi\) | |||||||
\(770\) | −609.832 | − | 51.8541i | −0.791990 | − | 0.0673429i | ||||
\(771\) | − | 344.417i | − | 0.446714i | ||||||
\(772\) | −617.928 | − | 105.850i | −0.800425 | − | 0.137112i | ||||
\(773\) | −751.987 | −0.972817 | −0.486408 | − | 0.873732i | \(-0.661693\pi\) | ||||
−0.486408 | + | 0.873732i | \(0.661693\pi\) | |||||||
\(774\) | −23.1739 | + | 272.538i | −0.0299405 | + | 0.352117i | ||||
\(775\) | − | 181.733i | − | 0.234495i | ||||||
\(776\) | −985.550 | − | 256.359i | −1.27004 | − | 0.330359i | ||||
\(777\) | 406.389 | 0.523023 | ||||||||
\(778\) | 321.417 | + | 27.3301i | 0.413133 | + | 0.0351287i | ||||
\(779\) | 148.476i | 0.190599i | ||||||||
\(780\) | −7.37635 | + | 43.0614i | −0.00945686 | + | 0.0552069i | ||||
\(781\) | −730.446 | −0.935271 | ||||||||
\(782\) | 8.74073 | − | 102.796i | 0.0111774 | − | 0.131452i | ||||
\(783\) | 263.533i | 0.336568i | ||||||||
\(784\) | −1579.06 | − | 557.337i | −2.01411 | − | 0.710889i | ||||
\(785\) | −455.974 | −0.580858 | ||||||||
\(786\) | −677.965 | − | 57.6474i | −0.862550 | − | 0.0733427i | ||||
\(787\) | − | 442.296i | − | 0.562002i | −0.959707 | − | 0.281001i | \(-0.909334\pi\) | ||
0.959707 | − | 0.281001i | \(-0.0906665\pi\) | |||||||
\(788\) | 1025.57 | + | 175.679i | 1.30148 | + | 0.222943i | ||||
\(789\) | 832.299 | 1.05488 | ||||||||
\(790\) | 46.6260 | − | 548.347i | 0.0590203 | − | 0.694111i | ||||
\(791\) | 1385.81i | 1.75197i | ||||||||
\(792\) | 66.7030 | − | 256.434i | 0.0842210 | − | 0.323781i | ||||
\(793\) | 158.291 | 0.199610 | ||||||||
\(794\) | 371.668 | + | 31.6030i | 0.468096 | + | 0.0398022i | ||||
\(795\) | 159.443i | 0.200557i | ||||||||
\(796\) | −9.47704 | + | 55.3247i | −0.0119058 | + | 0.0695034i | ||||
\(797\) | −56.2072 | −0.0705235 | −0.0352618 | − | 0.999378i | \(-0.511226\pi\) | ||||
−0.0352618 | + | 0.999378i | \(0.511226\pi\) | |||||||
\(798\) | −101.841 | + | 1197.71i | −0.127620 | + | 1.50088i | ||||
\(799\) | − | 76.5155i | − | 0.0957641i | ||||||
\(800\) | −145.824 | − | 65.8445i | −0.182279 | − | 0.0823056i | ||||
\(801\) | −303.249 | −0.378588 | ||||||||
\(802\) | −476.403 | − | 40.5086i | −0.594019 | − | 0.0505094i | ||||
\(803\) | − | 172.593i | − | 0.214935i | ||||||
\(804\) | 110.427 | + | 18.9160i | 0.137347 | + | 0.0235274i | ||||
\(805\) | −219.090 | −0.272161 | ||||||||
\(806\) | −17.3686 | + | 204.264i | −0.0215491 | + | 0.253430i | ||||
\(807\) | 504.887i | 0.625634i | ||||||||
\(808\) | 730.518 | + | 190.021i | 0.904107 | + | 0.235174i | ||||
\(809\) | 1522.16 | 1.88153 | 0.940765 | − | 0.339060i | \(-0.110109\pi\) | ||||
0.940765 | + | 0.339060i | \(0.110109\pi\) | |||||||
\(810\) | 40.1045 | + | 3.41009i | 0.0495117 | + | 0.00420999i | ||||
\(811\) | 930.734i | 1.14764i | 0.818982 | + | 0.573819i | \(0.194539\pi\) | ||||
−0.818982 | + | 0.573819i | \(0.805461\pi\) | |||||||
\(812\) | 424.585 | − | 2478.63i | 0.522888 | − | 3.05249i | ||||
\(813\) | 301.486 | 0.370832 | ||||||||
\(814\) | 35.4098 | − | 416.438i | 0.0435009 | − | 0.511595i | ||||
\(815\) | 482.762i | 0.592346i | ||||||||
\(816\) | 60.1943 | − | 170.544i | 0.0737676 | − | 0.209000i | ||||
\(817\) | −1276.10 | −1.56194 | ||||||||
\(818\) | −95.2595 | − | 8.09992i | −0.116454 | − | 0.00990210i | ||||
\(819\) | 104.873i | 0.128049i | ||||||||
\(820\) | −46.7602 | − | 8.00996i | −0.0570247 | − | 0.00976825i | ||||
\(821\) | 349.814 | 0.426083 | 0.213041 | − | 0.977043i | \(-0.431663\pi\) | ||||
0.213041 | + | 0.977043i | \(0.431663\pi\) | |||||||
\(822\) | 34.3761 | − | 404.281i | 0.0418200 | − | 0.491826i | ||||
\(823\) | 61.2187i | 0.0743849i | 0.999308 | + | 0.0371924i | \(0.0118414\pi\) | ||||
−0.999308 | + | 0.0371924i | \(0.988159\pi\) | |||||||
\(824\) | 64.1344 | − | 246.559i | 0.0778330 | − | 0.299222i | ||||
\(825\) | −95.6119 | −0.115893 | ||||||||
\(826\) | 264.338 | + | 22.4767i | 0.320022 | + | 0.0272115i | ||||
\(827\) | 46.2063i | 0.0558721i | 0.999610 | + | 0.0279361i | \(0.00889348\pi\) | ||||
−0.999610 | + | 0.0279361i | \(0.991107\pi\) | |||||||
\(828\) | 16.0145 | − | 93.4888i | 0.0193412 | − | 0.112909i | ||||
\(829\) | 223.832 | 0.270002 | 0.135001 | − | 0.990845i | \(-0.456896\pi\) | ||||
0.135001 | + | 0.990845i | \(0.456896\pi\) | |||||||
\(830\) | −37.7648 | + | 444.135i | −0.0454998 | + | 0.535102i | ||||
\(831\) | 87.5037i | 0.105299i | ||||||||
\(832\) | 157.610 | + | 87.9444i | 0.189435 | + | 0.105702i | ||||
\(833\) | −683.007 | −0.819937 | ||||||||
\(834\) | −646.280 | − | 54.9532i | −0.774916 | − | 0.0658912i | ||||
\(835\) | − | 570.262i | − | 0.682949i | ||||||
\(836\) | 1218.45 | + | 208.718i | 1.45747 | + | 0.249663i | ||||
\(837\) | 188.863 | 0.225642 | ||||||||
\(838\) | 40.4998 | − | 476.300i | 0.0483291 | − | 0.568377i | ||||
\(839\) | − | 361.794i | − | 0.431220i | −0.976480 | − | 0.215610i | \(-0.930826\pi\) | ||
0.976480 | − | 0.215610i | \(-0.0691740\pi\) | |||||||
\(840\) | −371.704 | − | 96.6867i | −0.442505 | − | 0.115103i | ||||
\(841\) | 1731.20 | 2.05851 | ||||||||
\(842\) | 513.332 | + | 43.6486i | 0.609657 | + | 0.0518392i | ||||
\(843\) | 114.404i | 0.135711i | ||||||||
\(844\) | 50.3101 | − | 293.698i | 0.0596092 | − | 0.347984i | ||||
\(845\) | 360.112 | 0.426168 | ||||||||
\(846\) | 5.96015 | − | 70.0947i | 0.00704510 | − | 0.0828542i | ||||
\(847\) | 11.0143i | 0.0130039i | ||||||||
\(848\) | 621.134 | + | 219.232i | 0.732470 | + | 0.258528i | ||||
\(849\) | −202.536 | −0.238559 | ||||||||
\(850\) | −65.0260 | − | 5.52916i | −0.0765012 | − | 0.00650490i | ||||
\(851\) | − | 149.610i | − | 0.175805i | ||||||
\(852\) | −451.801 | − | 77.3929i | −0.530283 | − | 0.0908368i | ||||
\(853\) | −844.503 | −0.990039 | −0.495019 | − | 0.868882i | \(-0.664839\pi\) | ||||
−0.495019 | + | 0.868882i | \(0.664839\pi\) | |||||||
\(854\) | −117.899 | + | 1386.55i | −0.138055 | + | 1.62360i | ||||
\(855\) | 187.781i | 0.219627i | ||||||||
\(856\) | −68.0528 | + | 261.623i | −0.0795009 | + | 0.305635i | ||||
\(857\) | −1389.51 | −1.62137 | −0.810685 | − | 0.585482i | \(-0.800905\pi\) | ||||
−0.810685 | + | 0.585482i | \(0.800905\pi\) | |||||||
\(858\) | 107.466 | + | 9.13782i | 0.125251 | + | 0.0106501i | ||||
\(859\) | 1205.45i | 1.40332i | 0.712512 | + | 0.701660i | \(0.247558\pi\) | ||||
−0.712512 | + | 0.701660i | \(0.752442\pi\) | |||||||
\(860\) | 68.8429 | − | 401.888i | 0.0800499 | − | 0.467312i | ||||
\(861\) | −113.881 | −0.132266 | ||||||||
\(862\) | −58.1487 | + | 683.861i | −0.0674579 | + | 0.793342i | ||||
\(863\) | 258.868i | 0.299963i | 0.988689 | + | 0.149981i | \(0.0479214\pi\) | ||||
−0.988689 | + | 0.149981i | \(0.952079\pi\) | |||||||
\(864\) | 68.4276 | − | 151.544i | 0.0791986 | − | 0.175398i | ||||
\(865\) | 526.428 | 0.608587 | ||||||||
\(866\) | 467.832 | + | 39.7798i | 0.540222 | + | 0.0459351i | ||||
\(867\) | 426.796i | 0.492267i | ||||||||
\(868\) | −1776.33 | − | 304.282i | −2.04646 | − | 0.350555i | ||||
\(869\) | −1358.58 | −1.56339 | ||||||||
\(870\) | 33.2841 | − | 391.439i | 0.0382576 | − | 0.449930i | ||||
\(871\) | 45.6035i | 0.0523576i | ||||||||
\(872\) | 645.919 | + | 168.015i | 0.740732 | + | 0.192677i | ||||
\(873\) | −381.880 | −0.437434 | ||||||||
\(874\) | 440.930 | + | 37.4923i | 0.504497 | + | 0.0428974i | ||||
\(875\) | 138.590i | 0.158389i | ||||||||
\(876\) | 18.2867 | − | 106.753i | 0.0208752 | − | 0.121865i | ||||
\(877\) | −156.268 | −0.178185 | −0.0890926 | − | 0.996023i | \(-0.528397\pi\) | ||||
−0.0890926 | + | 0.996023i | \(0.528397\pi\) | |||||||
\(878\) | 63.4539 | − | 746.253i | 0.0722710 | − | 0.849946i | ||||
\(879\) | 118.426i | 0.134728i | ||||||||
\(880\) | −131.465 | + | 372.471i | −0.149392 | + | 0.423262i | ||||
\(881\) | −1343.58 | −1.52507 | −0.762533 | − | 0.646950i | \(-0.776044\pi\) | ||||
−0.762533 | + | 0.646950i | \(0.776044\pi\) | |||||||
\(882\) | −625.693 | − | 53.2027i | −0.709402 | − | 0.0603205i | ||||
\(883\) | 149.478i | 0.169284i | 0.996411 | + | 0.0846420i | \(0.0269747\pi\) | ||||
−0.996411 | + | 0.0846420i | \(0.973025\pi\) | |||||||
\(884\) | 72.5594 | + | 12.4293i | 0.0820807 | + | 0.0140603i | ||||
\(885\) | 41.4440 | 0.0468294 | ||||||||
\(886\) | −18.3949 | + | 216.334i | −0.0207617 | + | 0.244169i | ||||
\(887\) | − | 1532.07i | − | 1.72725i | −0.504134 | − | 0.863626i | \(-0.668188\pi\) | ||
0.504134 | − | 0.863626i | \(-0.331812\pi\) | |||||||
\(888\) | 66.0247 | − | 253.827i | 0.0743522 | − | 0.285841i | ||||
\(889\) | −206.832 | −0.232656 | ||||||||
\(890\) | 450.431 | + | 38.3002i | 0.506102 | + | 0.0430339i | ||||
\(891\) | − | 99.3628i | − | 0.111518i | ||||||
\(892\) | 108.055 | − | 630.796i | 0.121137 | − | 0.707171i | ||||
\(893\) | 328.204 | 0.367529 | ||||||||
\(894\) | 14.7414 | − | 173.367i | 0.0164893 | − | 0.193923i | ||||
\(895\) | − | 229.576i | − | 0.256509i | ||||||
\(896\) | −887.745 | + | 1315.09i | −0.990786 | + | 1.46773i | ||||
\(897\) | 38.6084 | 0.0430417 | ||||||||
\(898\) | 859.919 | + | 73.1190i | 0.957594 | + | 0.0814243i | ||||
\(899\) | − | 1843.39i | − | 2.05049i | ||||||
\(900\) | −59.1386 | − | 10.1304i | −0.0657096 | − | 0.0112560i | ||||
\(901\) | 268.665 | 0.298186 | ||||||||
\(902\) | −9.92273 | + | 116.697i | −0.0110008 | + | 0.129376i | ||||
\(903\) | − | 978.767i | − | 1.08391i | ||||||
\(904\) | 865.562 | + | 225.148i | 0.957480 | + | 0.249057i | ||||
\(905\) | 127.058 | 0.140396 | ||||||||
\(906\) | −735.754 | − | 62.5612i | −0.812091 | − | 0.0690521i | ||||
\(907\) | − | 1245.02i | − | 1.37268i | −0.727280 | − | 0.686341i | \(-0.759216\pi\) | ||
0.727280 | − | 0.686341i | \(-0.240784\pi\) | |||||||
\(908\) | 118.848 | − | 693.808i | 0.130890 | − | 0.764106i | ||||
\(909\) | 283.060 | 0.311398 | ||||||||
\(910\) | 13.2454 | − | 155.773i | 0.0145553 | − | 0.171179i | ||||
\(911\) | − | 173.681i | − | 0.190649i | −0.995446 | − | 0.0953245i | \(-0.969611\pi\) | ||
0.995446 | − | 0.0953245i | \(-0.0303889\pi\) | |||||||
\(912\) | 731.529 | + | 258.196i | 0.802115 | + | 0.283110i | ||||
\(913\) | 1100.39 | 1.20524 | ||||||||
\(914\) | −437.914 | − | 37.2359i | −0.479118 | − | 0.0407395i | ||||
\(915\) | 217.389i | 0.237584i | ||||||||
\(916\) | −450.125 | − | 77.1058i | −0.491403 | − | 0.0841766i | ||||
\(917\) | 2434.78 | 2.65515 | ||||||||
\(918\) | 5.74607 | − | 67.5770i | 0.00625934 | − | 0.0736133i | ||||
\(919\) | 874.426i | 0.951498i | 0.879581 | + | 0.475749i | \(0.157823\pi\) | ||||
−0.879581 | + | 0.475749i | \(0.842177\pi\) | |||||||
\(920\) | −35.5948 | + | 136.841i | −0.0386900 | + | 0.148740i | ||||
\(921\) | 639.987 | 0.694882 | ||||||||
\(922\) | −445.262 | − | 37.8607i | −0.482931 | − | 0.0410636i | ||||
\(923\) | − | 186.582i | − | 0.202147i | ||||||
\(924\) | −160.086 | + | 934.545i | −0.173254 | + | 1.01141i | ||||
\(925\) | −94.6397 | −0.102313 | ||||||||
\(926\) | 125.537 | − | 1476.38i | 0.135569 | − | 1.59436i | ||||
\(927\) | − | 95.5365i | − | 0.103060i | ||||||
\(928\) | −1479.14 | − | 667.886i | −1.59390 | − | 0.719705i | ||||
\(929\) | −1564.05 | −1.68358 | −0.841792 | − | 0.539803i | \(-0.818499\pi\) | ||||
−0.841792 | + | 0.539803i | \(0.818499\pi\) | |||||||
\(930\) | −280.528 | − | 23.8533i | −0.301643 | − | 0.0256487i | ||||
\(931\) | − | 2929.68i | − | 3.14681i | ||||||
\(932\) | 1025.31 | + | 175.635i | 1.10012 | + | 0.188450i | ||||
\(933\) | 525.584 | 0.563327 | ||||||||
\(934\) | 42.2573 | − | 496.970i | 0.0452434 | − | 0.532087i | ||||
\(935\) | 161.108i | 0.172308i | ||||||||
\(936\) | 65.5023 | + | 17.0383i | 0.0699811 | + | 0.0182033i | ||||
\(937\) | 958.621 | 1.02308 | 0.511538 | − | 0.859261i | \(-0.329076\pi\) | ||||
0.511538 | + | 0.859261i | \(0.329076\pi\) | |||||||
\(938\) | −399.466 | − | 33.9666i | −0.425869 | − | 0.0362117i | ||||
\(939\) | − | 515.620i | − | 0.549116i | ||||||
\(940\) | −17.7059 | + | 103.362i | −0.0188360 | + | 0.109960i | ||||
\(941\) | −752.357 | −0.799529 | −0.399765 | − | 0.916618i | \(-0.630908\pi\) | ||||
−0.399765 | + | 0.916618i | \(0.630908\pi\) | |||||||
\(942\) | −59.8485 | + | 703.852i | −0.0635335 | + | 0.747188i | ||||
\(943\) | 41.9247i | 0.0444589i | ||||||||
\(944\) | 56.9849 | − | 161.451i | 0.0603654 | − | 0.171029i | ||||
\(945\) | −144.027 | −0.152410 | ||||||||
\(946\) | −1002.97 | − | 85.2825i | −1.06022 | − | 0.0901507i | ||||
\(947\) | 1013.16i | 1.06986i | 0.844895 | + | 0.534932i | \(0.179663\pi\) | ||||
−0.844895 | + | 0.534932i | \(0.820337\pi\) | |||||||
\(948\) | −840.322 | − | 143.946i | −0.886415 | − | 0.151842i | ||||
\(949\) | 44.0863 | 0.0464555 | ||||||||
\(950\) | 23.7167 | − | 278.921i | 0.0249649 | − | 0.293601i | ||||
\(951\) | − | 458.436i | − | 0.482057i | ||||||
\(952\) | −162.919 | + | 626.329i | −0.171134 | + | 0.657909i | ||||
\(953\) | −21.5482 | −0.0226109 | −0.0113054 | − | 0.999936i | \(-0.503599\pi\) | ||||
−0.0113054 | + | 0.999936i | \(0.503599\pi\) | |||||||
\(954\) | 246.120 | + | 20.9276i | 0.257987 | + | 0.0219367i | ||||
\(955\) | 354.402i | 0.371102i | ||||||||
\(956\) | −94.6102 | + | 552.312i | −0.0989646 | + | 0.577732i | ||||
\(957\) | −969.828 | −1.01340 | ||||||||
\(958\) | −35.7393 | + | 420.314i | −0.0373062 | + | 0.438741i | ||||
\(959\) | 1451.90i | 1.51397i | ||||||||
\(960\) | −120.779 | + | 216.454i | −0.125812 | + | 0.225473i | ||||
\(961\) | −360.079 | −0.374692 | ||||||||
\(962\) | 106.373 | + | 9.04490i | 0.110575 | + | 0.00940218i | ||||
\(963\) | 101.373i | 0.105268i | ||||||||
\(964\) | 417.599 | + | 71.5340i | 0.433193 | + | 0.0742054i | ||||
\(965\) | 350.464 | 0.363175 | ||||||||
\(966\) | −28.7565 | + | 338.192i | −0.0297686 | + | 0.350095i | ||||
\(967\) | 303.965i | 0.314338i | 0.987572 | + | 0.157169i | \(0.0502367\pi\) | ||||
−0.987572 | + | 0.157169i | \(0.949763\pi\) | |||||||
\(968\) | 6.87942 | + | 1.78946i | 0.00710684 | + | 0.00184861i | ||||
\(969\) | 316.415 | 0.326538 | ||||||||
\(970\) | 567.226 | + | 48.2313i | 0.584769 | + | 0.0497230i | ||||
\(971\) | − | 356.162i | − | 0.366799i | −0.983038 | − | 0.183399i | \(-0.941290\pi\) | ||
0.983038 | − | 0.183399i | \(-0.0587101\pi\) | |||||||
\(972\) | 10.5278 | − | 61.4587i | 0.0108311 | − | 0.0632291i | ||||
\(973\) | 2320.99 | 2.38539 | ||||||||
\(974\) | −120.400 | + | 1415.97i | −0.123614 | + | 1.45377i | ||||
\(975\) | − | 24.4227i | − | 0.0250489i | ||||||
\(976\) | 846.873 | + | 298.907i | 0.867698 | + | 0.306257i | ||||
\(977\) | −1845.09 | −1.88852 | −0.944262 | − | 0.329194i | \(-0.893223\pi\) | ||||
−0.944262 | + | 0.329194i | \(0.893223\pi\) | |||||||
\(978\) | 745.202 | + | 63.3646i | 0.761965 | + | 0.0647899i | ||||
\(979\) | − | 1115.99i | − | 1.13993i | ||||||
\(980\) | 922.654 | + | 158.049i | 0.941484 | + | 0.161275i | ||||
\(981\) | 250.280 | 0.255127 | ||||||||
\(982\) | −118.254 | + | 1390.73i | −0.120422 | + | 1.41623i | ||||
\(983\) | − | 289.444i | − | 0.294449i | −0.989103 | − | 0.147225i | \(-0.952966\pi\) | ||
0.989103 | − | 0.147225i | \(-0.0470340\pi\) | |||||||
\(984\) | −18.5019 | + | 71.1288i | −0.0188027 | + | 0.0722854i | ||||
\(985\) | −581.662 | −0.590519 | ||||||||
\(986\) | −659.583 | − | 56.0844i | −0.668949 | − | 0.0568807i | ||||
\(987\) | 251.731i | 0.255047i | ||||||||
\(988\) | −53.3140 | + | 311.234i | −0.0539616 | + | 0.315015i | ||||
\(989\) | −360.329 | −0.364337 | ||||||||
\(990\) | −12.5495 | + | 147.589i | −0.0126762 | + | 0.149080i | ||||
\(991\) | − | 441.980i | − | 0.445994i | −0.974819 | − | 0.222997i | \(-0.928416\pi\) | ||
0.974819 | − | 0.222997i | \(-0.0715840\pi\) | |||||||
\(992\) | −478.645 | + | 1060.04i | −0.482505 | + | 1.06859i | ||||
\(993\) | −819.998 | −0.825778 | ||||||||
\(994\) | 1634.37 | + | 138.971i | 1.64424 | + | 0.139810i | ||||
\(995\) | − | 31.3779i | − | 0.0315356i | ||||||
\(996\) | 680.620 | + | 116.589i | 0.683354 | + | 0.117058i | ||||
\(997\) | −1045.42 | −1.04856 | −0.524282 | − | 0.851545i | \(-0.675666\pi\) | ||||
−0.524282 | + | 0.851545i | \(0.675666\pi\) | |||||||
\(998\) | 148.370 | − | 1744.91i | 0.148667 | − | 1.74841i | ||||
\(999\) | − | 98.3525i | − | 0.0984509i |
(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 | 60.3.c.a.31.1 | ✓ | 8 | |
3.2 | odd | 2 | 180.3.c.b.91.8 | 8 | |||
4.3 | odd | 2 | inner | 60.3.c.a.31.2 | yes | 8 | |
5.2 | odd | 4 | 300.3.f.b.199.9 | 16 | |||
5.3 | odd | 4 | 300.3.f.b.199.8 | 16 | |||
5.4 | even | 2 | 300.3.c.d.151.8 | 8 | |||
8.3 | odd | 2 | 960.3.e.c.511.4 | 8 | |||
8.5 | even | 2 | 960.3.e.c.511.7 | 8 | |||
12.11 | even | 2 | 180.3.c.b.91.7 | 8 | |||
15.2 | even | 4 | 900.3.f.f.199.8 | 16 | |||
15.8 | even | 4 | 900.3.f.f.199.9 | 16 | |||
15.14 | odd | 2 | 900.3.c.u.451.1 | 8 | |||
20.3 | even | 4 | 300.3.f.b.199.10 | 16 | |||
20.7 | even | 4 | 300.3.f.b.199.7 | 16 | |||
20.19 | odd | 2 | 300.3.c.d.151.7 | 8 | |||
24.5 | odd | 2 | 2880.3.e.j.2431.1 | 8 | |||
24.11 | even | 2 | 2880.3.e.j.2431.4 | 8 | |||
60.23 | odd | 4 | 900.3.f.f.199.7 | 16 | |||
60.47 | odd | 4 | 900.3.f.f.199.10 | 16 | |||
60.59 | even | 2 | 900.3.c.u.451.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
60.3.c.a.31.2 | yes | 8 | 4.3 | odd | 2 | inner | |
180.3.c.b.91.7 | 8 | 12.11 | even | 2 | |||
180.3.c.b.91.8 | 8 | 3.2 | odd | 2 | |||
300.3.c.d.151.7 | 8 | 20.19 | odd | 2 | |||
300.3.c.d.151.8 | 8 | 5.4 | even | 2 | |||
300.3.f.b.199.7 | 16 | 20.7 | even | 4 | |||
300.3.f.b.199.8 | 16 | 5.3 | odd | 4 | |||
300.3.f.b.199.9 | 16 | 5.2 | odd | 4 | |||
300.3.f.b.199.10 | 16 | 20.3 | even | 4 | |||
900.3.c.u.451.1 | 8 | 15.14 | odd | 2 | |||
900.3.c.u.451.2 | 8 | 60.59 | even | 2 | |||
900.3.f.f.199.7 | 16 | 60.23 | odd | 4 | |||
900.3.f.f.199.8 | 16 | 15.2 | even | 4 | |||
900.3.f.f.199.9 | 16 | 15.8 | even | 4 | |||
900.3.f.f.199.10 | 16 | 60.47 | odd | 4 | |||
960.3.e.c.511.4 | 8 | 8.3 | odd | 2 | |||
960.3.e.c.511.7 | 8 | 8.5 | even | 2 | |||
2880.3.e.j.2431.1 | 8 | 24.5 | odd | 2 | |||
2880.3.e.j.2431.4 | 8 | 24.11 | even | 2 |