Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), degree \(4\), not 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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.228765625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(-1.73166 + 0.0369185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.323 |
Dual form | 363.3.h.d.245.2 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.94946 | − | 2.68321i | 0.974732 | − | 1.34160i | 0.0351115 | − | 0.999383i | \(-0.488821\pi\) |
0.939620 | − | 0.342220i | \(-0.111179\pi\) | |||||||
\(3\) | 0.927051 | − | 2.85317i | 0.309017 | − | 0.951057i | ||||
\(4\) | −2.16312 | − | 6.65740i | −0.540780 | − | 1.66435i | ||||
\(5\) | −3.89893 | − | 5.36641i | −0.779785 | − | 1.07328i | −0.995306 | − | 0.0967830i | \(-0.969145\pi\) |
0.215520 | − | 0.976499i | \(-0.430855\pi\) | |||||||
\(6\) | −5.84839 | − | 8.04962i | −0.974732 | − | 1.34160i | ||||
\(7\) | 2.47214 | + | 7.60845i | 0.353162 | + | 1.08692i | 0.957067 | + | 0.289866i | \(0.0936106\pi\) |
−0.603905 | + | 0.797056i | \(0.706389\pi\) | |||||||
\(8\) | −9.46289 | − | 3.07468i | −1.18286 | − | 0.384335i | ||||
\(9\) | −7.28115 | − | 5.29007i | −0.809017 | − | 0.587785i | ||||
\(10\) | −22.0000 | −2.20000 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −21.0000 | −1.75000 | ||||||||
\(13\) | 3.23607 | + | 2.35114i | 0.248928 | + | 0.180857i | 0.705252 | − | 0.708957i | \(-0.250834\pi\) |
−0.456323 | + | 0.889814i | \(0.650834\pi\) | |||||||
\(14\) | 25.2344 | + | 8.19915i | 1.80246 | + | 0.585653i | ||||
\(15\) | −18.9258 | + | 6.14936i | −1.26172 | + | 0.409957i | ||||
\(16\) | −4.04508 | + | 2.93893i | −0.252818 | + | 0.183683i | ||||
\(17\) | −7.79785 | − | 10.7328i | −0.458697 | − | 0.631343i | 0.515541 | − | 0.856865i | \(-0.327591\pi\) |
−0.974238 | + | 0.225523i | \(0.927591\pi\) | |||||||
\(18\) | −28.3887 | + | 9.22404i | −1.57715 | + | 0.512447i | ||||
\(19\) | 1.85410 | − | 5.70634i | 0.0975843 | − | 0.300334i | −0.890334 | − | 0.455307i | \(-0.849529\pi\) |
0.987919 | + | 0.154974i | \(0.0495293\pi\) | |||||||
\(20\) | −27.2925 | + | 37.5649i | −1.36462 | + | 1.87824i | ||||
\(21\) | 24.0000 | 1.14286 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.63325i | − | 0.288402i | −0.989548 | − | 0.144201i | \(-0.953939\pi\) | ||
0.989548 | − | 0.144201i | \(-0.0460612\pi\) | |||||||
\(24\) | −17.5452 | + | 24.1489i | −0.731049 | + | 1.00620i | ||||
\(25\) | −5.87132 | + | 18.0701i | −0.234853 | + | 0.722803i | ||||
\(26\) | 12.6172 | − | 4.09957i | 0.485277 | − | 0.157676i | ||||
\(27\) | −21.8435 | + | 15.8702i | −0.809017 | + | 0.587785i | ||||
\(28\) | 45.3050 | − | 32.9160i | 1.61803 | − | 1.17557i | ||||
\(29\) | 37.8516 | − | 12.2987i | 1.30523 | − | 0.424094i | 0.427830 | − | 0.903859i | \(-0.359278\pi\) |
0.877397 | + | 0.479765i | \(0.159278\pi\) | |||||||
\(30\) | −20.3951 | + | 62.7697i | −0.679837 | + | 2.09232i | ||||
\(31\) | 21.0344 | + | 15.2824i | 0.678530 | + | 0.492981i | 0.872870 | − | 0.487953i | \(-0.162256\pi\) |
−0.194339 | + | 0.980934i | \(0.562256\pi\) | |||||||
\(32\) | − | 23.2164i | − | 0.725512i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −44.0000 | −1.29412 | ||||||||
\(35\) | 31.1914 | − | 42.9313i | 0.891183 | − | 1.22661i | ||||
\(36\) | −19.4681 | + | 59.9166i | −0.540780 | + | 1.66435i | ||||
\(37\) | 9.27051 | + | 28.5317i | 0.250554 | + | 0.771127i | 0.994673 | + | 0.103080i | \(0.0328696\pi\) |
−0.744119 | + | 0.668047i | \(0.767130\pi\) | |||||||
\(38\) | −11.6968 | − | 16.0992i | −0.307810 | − | 0.423664i | ||||
\(39\) | 9.70820 | − | 7.05342i | 0.248928 | − | 0.180857i | ||||
\(40\) | 20.3951 | + | 62.7697i | 0.509878 | + | 1.56924i | ||||
\(41\) | 12.6172 | + | 4.09957i | 0.307736 | + | 0.0999896i | 0.458814 | − | 0.888532i | \(-0.348274\pi\) |
−0.151078 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(42\) | 46.7871 | − | 64.3969i | 1.11398 | − | 1.53326i | ||||
\(43\) | −42.0000 | −0.976744 | −0.488372 | − | 0.872635i | \(-0.662409\pi\) | ||||
−0.488372 | + | 0.872635i | \(0.662409\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 59.6992i | 1.32665i | ||||||||
\(46\) | −17.7984 | − | 12.9313i | −0.386921 | − | 0.281115i | ||||
\(47\) | −82.0117 | − | 26.6472i | −1.74493 | − | 0.566962i | −0.749461 | − | 0.662048i | \(-0.769688\pi\) |
−0.995469 | + | 0.0950856i | \(0.969688\pi\) | |||||||
\(48\) | 4.63525 | + | 14.2658i | 0.0965678 | + | 0.297205i | ||||
\(49\) | −12.1353 | + | 8.81678i | −0.247658 | + | 0.179934i | ||||
\(50\) | 37.0398 | + | 50.9809i | 0.740796 | + | 1.01962i | ||||
\(51\) | −37.8516 | + | 12.2987i | −0.742188 | + | 0.241151i | ||||
\(52\) | 8.65248 | − | 26.6296i | 0.166394 | − | 0.512107i | ||||
\(53\) | 35.0903 | − | 48.2977i | 0.662082 | − | 0.911277i | −0.337466 | − | 0.941338i | \(-0.609570\pi\) |
0.999548 | + | 0.0300602i | \(0.00956989\pi\) | |||||||
\(54\) | 89.5489i | 1.65831i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 79.5990i | − | 1.42141i | ||||||
\(57\) | −14.5623 | − | 10.5801i | −0.255479 | − | 0.185616i | ||||
\(58\) | 40.7902 | − | 125.539i | 0.703280 | − | 2.16447i | ||||
\(59\) | 63.0860 | − | 20.4979i | 1.06925 | − | 0.347421i | 0.279057 | − | 0.960275i | \(-0.409978\pi\) |
0.790197 | + | 0.612853i | \(0.209978\pi\) | |||||||
\(60\) | 81.8775 | + | 112.695i | 1.36462 | + | 1.87824i | ||||
\(61\) | 9.70820 | − | 7.05342i | 0.159151 | − | 0.115630i | −0.505360 | − | 0.862909i | \(-0.668640\pi\) |
0.664510 | + | 0.747279i | \(0.268640\pi\) | |||||||
\(62\) | 82.0117 | − | 26.6472i | 1.32277 | − | 0.429794i | ||||
\(63\) | 22.2492 | − | 68.4761i | 0.353162 | − | 1.08692i | ||||
\(64\) | −78.4746 | − | 57.0152i | −1.22617 | − | 0.890862i | ||||
\(65\) | − | 26.5330i | − | 0.408200i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.0298507 | 0.0149254 | − | 0.999889i | \(-0.495249\pi\) | ||||
0.0149254 | + | 0.999889i | \(0.495249\pi\) | |||||||
\(68\) | −54.5850 | + | 75.1298i | −0.802720 | + | 1.10485i | ||||
\(69\) | −18.9258 | − | 6.14936i | −0.274287 | − | 0.0891212i | ||||
\(70\) | −54.3870 | − | 167.386i | −0.776957 | − | 2.39123i | ||||
\(71\) | −35.0903 | − | 48.2977i | −0.494230 | − | 0.680249i | 0.486931 | − | 0.873440i | \(-0.338116\pi\) |
−0.981161 | + | 0.193191i | \(0.938116\pi\) | |||||||
\(72\) | 52.6355 | + | 72.4466i | 0.731049 | + | 1.00620i | ||||
\(73\) | 22.8673 | + | 70.3782i | 0.313250 | + | 0.964085i | 0.976469 | + | 0.215659i | \(0.0691900\pi\) |
−0.663219 | + | 0.748426i | \(0.730810\pi\) | |||||||
\(74\) | 94.6289 | + | 30.7468i | 1.27877 | + | 0.415497i | ||||
\(75\) | 46.1140 | + | 33.5038i | 0.614853 | + | 0.446717i | ||||
\(76\) | −42.0000 | −0.552632 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 39.7995i | − | 0.510250i | ||||||
\(79\) | −32.3607 | − | 23.5114i | −0.409629 | − | 0.297613i | 0.363823 | − | 0.931468i | \(-0.381471\pi\) |
−0.773452 | + | 0.633855i | \(0.781471\pi\) | |||||||
\(80\) | 31.5430 | + | 10.2489i | 0.394287 | + | 0.128112i | ||||
\(81\) | 25.0304 | + | 77.0356i | 0.309017 | + | 0.951057i | ||||
\(82\) | 35.5967 | − | 25.8626i | 0.434107 | − | 0.315397i | ||||
\(83\) | 23.3936 | + | 32.1985i | 0.281850 | + | 0.387933i | 0.926346 | − | 0.376675i | \(-0.122933\pi\) |
−0.644495 | + | 0.764608i | \(0.722933\pi\) | |||||||
\(84\) | −51.9149 | − | 159.777i | −0.618034 | − | 1.90211i | ||||
\(85\) | −27.1935 | + | 83.6930i | −0.319923 | + | 0.984623i | ||||
\(86\) | −81.8775 | + | 112.695i | −0.952063 | + | 1.31040i | ||||
\(87\) | − | 119.398i | − | 1.37240i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 119.398i | 1.34156i | 0.741658 | + | 0.670778i | \(0.234040\pi\) | ||||
−0.741658 | + | 0.670778i | \(0.765960\pi\) | |||||||
\(90\) | 160.185 | + | 116.381i | 1.77984 | + | 1.29313i | ||||
\(91\) | −9.88854 | + | 30.4338i | −0.108665 | + | 0.334437i | ||||
\(92\) | −44.1602 | + | 14.3485i | −0.480002 | + | 0.155962i | ||||
\(93\) | 63.1033 | − | 45.8472i | 0.678530 | − | 0.492981i | ||||
\(94\) | −231.379 | + | 168.107i | −2.46148 | + | 1.78837i | ||||
\(95\) | −37.8516 | + | 12.2987i | −0.398438 | + | 0.129460i | ||||
\(96\) | −66.2402 | − | 21.5228i | −0.690003 | − | 0.224195i | ||||
\(97\) | −50.1591 | − | 36.4427i | −0.517104 | − | 0.375698i | 0.298408 | − | 0.954438i | \(-0.403544\pi\) |
−0.815512 | + | 0.578741i | \(0.803544\pi\) | |||||||
\(98\) | 49.7494i | 0.507647i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 133.000 | 1.33000 | ||||||||
\(101\) | 62.3828 | − | 85.8626i | 0.617652 | − | 0.850125i | −0.379528 | − | 0.925180i | \(-0.623913\pi\) |
0.997179 | + | 0.0750558i | \(0.0239135\pi\) | |||||||
\(102\) | −40.7902 | + | 125.539i | −0.399904 | + | 1.23078i | ||||
\(103\) | 22.8673 | + | 70.3782i | 0.222012 | + | 0.683283i | 0.998581 | + | 0.0532510i | \(0.0169584\pi\) |
−0.776569 | + | 0.630032i | \(0.783042\pi\) | |||||||
\(104\) | −23.3936 | − | 32.1985i | −0.224938 | − | 0.309601i | ||||
\(105\) | −93.5742 | − | 128.794i | −0.891183 | − | 1.22661i | ||||
\(106\) | −61.1854 | − | 188.309i | −0.577220 | − | 1.77650i | ||||
\(107\) | −37.8516 | − | 12.2987i | −0.353753 | − | 0.114941i | 0.126749 | − | 0.991935i | \(-0.459546\pi\) |
−0.480502 | + | 0.876993i | \(0.659546\pi\) | |||||||
\(108\) | 152.904 | + | 111.091i | 1.41578 | + | 1.02862i | ||||
\(109\) | 200.000 | 1.83486 | 0.917431 | − | 0.397894i | \(-0.130259\pi\) | ||||
0.917431 | + | 0.397894i | \(0.130259\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 90.0000 | 0.810811 | ||||||||
\(112\) | −32.3607 | − | 23.5114i | −0.288935 | − | 0.209923i | ||||
\(113\) | 37.8516 | + | 12.2987i | 0.334970 | + | 0.108838i | 0.471672 | − | 0.881774i | \(-0.343651\pi\) |
−0.136703 | + | 0.990612i | \(0.543651\pi\) | |||||||
\(114\) | −56.7774 | + | 18.4481i | −0.498047 | + | 0.161825i | ||||
\(115\) | −35.5967 | + | 25.8626i | −0.309537 | + | 0.224892i | ||||
\(116\) | −163.755 | − | 225.389i | −1.41168 | − | 1.94301i | ||||
\(117\) | −11.1246 | − | 34.2380i | −0.0950822 | − | 0.292633i | ||||
\(118\) | 67.9837 | − | 209.232i | 0.576133 | − | 1.77316i | ||||
\(119\) | 62.3828 | − | 85.8626i | 0.524225 | − | 0.721534i | ||||
\(120\) | 198.000 | 1.65000 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 39.7995i | − | 0.326225i | ||||||
\(123\) | 23.3936 | − | 32.1985i | 0.190192 | − | 0.261776i | ||||
\(124\) | 56.2411 | − | 173.092i | 0.453557 | − | 1.39591i | ||||
\(125\) | −37.8516 | + | 12.2987i | −0.302813 | + | 0.0983898i | ||||
\(126\) | −140.361 | − | 193.191i | −1.11398 | − | 1.53326i | ||||
\(127\) | 152.095 | − | 110.504i | 1.19760 | − | 0.870107i | 0.203553 | − | 0.979064i | \(-0.434751\pi\) |
0.994047 | + | 0.108957i | \(0.0347509\pi\) | |||||||
\(128\) | −217.647 | + | 70.7176i | −1.70036 | + | 0.552482i | ||||
\(129\) | −38.9361 | + | 119.833i | −0.301831 | + | 0.928939i | ||||
\(130\) | −71.1935 | − | 51.7251i | −0.547642 | − | 0.397885i | ||||
\(131\) | 39.7995i | 0.303813i | 0.988395 | + | 0.151906i | \(0.0485413\pi\) | ||||
−0.988395 | + | 0.151906i | \(0.951459\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 48.0000 | 0.360902 | ||||||||
\(134\) | 3.89893 | − | 5.36641i | 0.0290965 | − | 0.0400478i | ||||
\(135\) | 170.332 | + | 55.3442i | 1.26172 | + | 0.409957i | ||||
\(136\) | 40.7902 | + | 125.539i | 0.299928 | + | 0.923084i | ||||
\(137\) | 62.3828 | + | 85.8626i | 0.455349 | + | 0.626734i | 0.973536 | − | 0.228533i | \(-0.0733929\pi\) |
−0.518187 | + | 0.855267i | \(0.673393\pi\) | |||||||
\(138\) | −53.3951 | + | 38.7938i | −0.386921 | + | 0.281115i | ||||
\(139\) | 22.8673 | + | 70.3782i | 0.164513 | + | 0.506318i | 0.999000 | − | 0.0447092i | \(-0.0142361\pi\) |
−0.834487 | + | 0.551027i | \(0.814236\pi\) | |||||||
\(140\) | −353.281 | − | 114.788i | −2.52344 | − | 0.819915i | ||||
\(141\) | −152.058 | + | 209.290i | −1.07843 | + | 1.48433i | ||||
\(142\) | −198.000 | −1.39437 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 45.0000 | 0.312500 | ||||||||
\(145\) | −213.580 | − | 155.175i | −1.47297 | − | 1.07017i | ||||
\(146\) | 233.418 | + | 75.8421i | 1.59875 | + | 0.519467i | ||||
\(147\) | 13.9058 | + | 42.7975i | 0.0945970 | + | 0.291140i | ||||
\(148\) | 169.894 | − | 123.435i | 1.14793 | − | 0.834020i | ||||
\(149\) | 54.5850 | + | 75.1298i | 0.366342 | + | 0.504227i | 0.951902 | − | 0.306402i | \(-0.0991253\pi\) |
−0.585560 | + | 0.810629i | \(0.699125\pi\) | |||||||
\(150\) | 179.795 | − | 58.4189i | 1.19863 | − | 0.389460i | ||||
\(151\) | 49.4427 | − | 152.169i | 0.327435 | − | 1.00774i | −0.642894 | − | 0.765955i | \(-0.722266\pi\) |
0.970329 | − | 0.241787i | \(-0.0777335\pi\) | |||||||
\(152\) | −35.0903 | + | 48.2977i | −0.230857 | + | 0.317748i | ||||
\(153\) | 119.398i | 0.780382i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 172.464i | − | 1.11267i | ||||||
\(156\) | −67.9574 | − | 49.3740i | −0.435625 | − | 0.316500i | ||||
\(157\) | 56.2411 | − | 173.092i | 0.358224 | − | 1.10250i | −0.595893 | − | 0.803064i | \(-0.703202\pi\) |
0.954117 | − | 0.299435i | \(-0.0967982\pi\) | |||||||
\(158\) | −126.172 | + | 40.9957i | −0.798556 | + | 0.259467i | ||||
\(159\) | −105.271 | − | 144.893i | −0.662082 | − | 0.911277i | ||||
\(160\) | −124.589 | + | 90.5189i | −0.778679 | + | 0.565743i | ||||
\(161\) | 50.4688 | − | 16.3983i | 0.313471 | − | 0.101853i | ||||
\(162\) | 255.498 | + | 83.0164i | 1.57715 | + | 0.512447i | ||||
\(163\) | 234.615 | + | 170.458i | 1.43936 | + | 1.04575i | 0.988177 | + | 0.153319i | \(0.0489963\pi\) |
0.451179 | + | 0.892434i | \(0.351004\pi\) | |||||||
\(164\) | − | 92.8655i | − | 0.566253i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 132.000 | 0.795181 | ||||||||
\(167\) | −140.361 | + | 193.191i | −0.840487 | + | 1.15683i | 0.145392 | + | 0.989374i | \(0.453556\pi\) |
−0.985879 | + | 0.167457i | \(0.946444\pi\) | |||||||
\(168\) | −227.109 | − | 73.7923i | −1.35184 | − | 0.439240i | ||||
\(169\) | −47.2796 | − | 145.512i | −0.279761 | − | 0.861016i | ||||
\(170\) | 171.553 | + | 236.122i | 1.00913 | + | 1.38895i | ||||
\(171\) | −43.6869 | + | 31.7404i | −0.255479 | + | 0.185616i | ||||
\(172\) | 90.8510 | + | 279.611i | 0.528203 | + | 1.62564i | ||||
\(173\) | 189.258 | + | 61.4936i | 1.09398 | + | 0.355454i | 0.799782 | − | 0.600291i | \(-0.204949\pi\) |
0.294195 | + | 0.955746i | \(0.404949\pi\) | |||||||
\(174\) | −320.371 | − | 232.763i | −1.84121 | − | 1.33772i | ||||
\(175\) | −152.000 | −0.868571 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 198.997i | − | 1.12428i | ||||||
\(178\) | 320.371 | + | 232.763i | 1.79984 | + | 1.30766i | ||||
\(179\) | −189.258 | − | 61.4936i | −1.05731 | − | 0.343540i | −0.271775 | − | 0.962361i | \(-0.587611\pi\) |
−0.785532 | + | 0.618821i | \(0.787611\pi\) | |||||||
\(180\) | 397.441 | − | 129.137i | 2.20801 | − | 0.717425i | ||||
\(181\) | −8.09017 | + | 5.87785i | −0.0446971 | + | 0.0324743i | −0.609909 | − | 0.792471i | \(-0.708794\pi\) |
0.565212 | + | 0.824945i | \(0.308794\pi\) | |||||||
\(182\) | 62.3828 | + | 85.8626i | 0.342763 | + | 0.471772i | ||||
\(183\) | −11.1246 | − | 34.2380i | −0.0607902 | − | 0.187093i | ||||
\(184\) | −20.3951 | + | 62.7697i | −0.110843 | + | 0.341140i | ||||
\(185\) | 116.968 | − | 160.992i | 0.632258 | − | 0.870229i | ||||
\(186\) | − | 258.697i | − | 1.39084i | ||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 603.626i | 3.21078i | ||||||||
\(189\) | −174.748 | − | 126.962i | −0.924591 | − | 0.671755i | ||||
\(190\) | −40.7902 | + | 125.539i | −0.214685 | + | 0.660734i | ||||
\(191\) | −107.246 | + | 34.8464i | −0.561498 | + | 0.182442i | −0.575995 | − | 0.817453i | \(-0.695385\pi\) |
0.0144971 | + | 0.999895i | \(0.495385\pi\) | |||||||
\(192\) | −235.424 | + | 171.046i | −1.22617 | + | 0.890862i | ||||
\(193\) | 241.087 | − | 175.160i | 1.24916 | − | 0.907565i | 0.250983 | − | 0.967991i | \(-0.419246\pi\) |
0.998173 | + | 0.0604267i | \(0.0192461\pi\) | |||||||
\(194\) | −195.566 | + | 63.5434i | −1.00807 | + | 0.327543i | ||||
\(195\) | −75.7031 | − | 24.5974i | −0.388221 | − | 0.126141i | ||||
\(196\) | 84.9468 | + | 61.7175i | 0.433402 | + | 0.314885i | ||||
\(197\) | 132.665i | 0.673426i | 0.941607 | + | 0.336713i | \(0.109315\pi\) | ||||
−0.941607 | + | 0.336713i | \(0.890685\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −42.0000 | −0.211055 | −0.105528 | − | 0.994416i | \(-0.533653\pi\) | ||||
−0.105528 | + | 0.994416i | \(0.533653\pi\) | |||||||
\(200\) | 111.119 | − | 152.943i | 0.555597 | − | 0.764714i | ||||
\(201\) | 1.85410 | − | 5.70634i | 0.00922439 | − | 0.0283897i | ||||
\(202\) | −108.774 | − | 334.772i | −0.538485 | − | 1.65729i | ||||
\(203\) | 187.148 | + | 257.588i | 0.921914 | + | 1.26891i | ||||
\(204\) | 163.755 | + | 225.389i | 0.802720 | + | 1.10485i | ||||
\(205\) | −27.1935 | − | 83.6930i | −0.132651 | − | 0.408258i | ||||
\(206\) | 233.418 | + | 75.8421i | 1.13310 | + | 0.368166i | ||||
\(207\) | −35.0903 | + | 48.2977i | −0.169519 | + | 0.233322i | ||||
\(208\) | −20.0000 | −0.0961538 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −528.000 | −2.51429 | ||||||||
\(211\) | 199.018 | + | 144.595i | 0.943214 | + | 0.685285i | 0.949192 | − | 0.314697i | \(-0.101903\pi\) |
−0.00597807 | + | 0.999982i | \(0.501903\pi\) | |||||||
\(212\) | −397.441 | − | 129.137i | −1.87472 | − | 0.609135i | ||||
\(213\) | −170.332 | + | 55.3442i | −0.799681 | + | 0.259832i | ||||
\(214\) | −106.790 | + | 77.5877i | −0.499020 | + | 0.362559i | ||||
\(215\) | 163.755 | + | 225.389i | 0.761651 | + | 1.04832i | ||||
\(216\) | 255.498 | − | 83.0164i | 1.18286 | − | 0.384335i | ||||
\(217\) | −64.2755 | + | 197.820i | −0.296201 | + | 0.911612i | ||||
\(218\) | 389.893 | − | 536.641i | 1.78850 | − | 2.46166i | ||||
\(219\) | 222.000 | 1.01370 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 53.0660i | − | 0.240118i | ||||||
\(222\) | 175.452 | − | 241.489i | 0.790323 | − | 1.08779i | ||||
\(223\) | −93.3231 | + | 287.219i | −0.418489 | + | 1.28798i | 0.490603 | + | 0.871383i | \(0.336777\pi\) |
−0.909092 | + | 0.416595i | \(0.863223\pi\) | |||||||
\(224\) | 176.641 | − | 57.3940i | 0.788574 | − | 0.256223i | ||||
\(225\) | 138.342 | − | 100.511i | 0.614853 | − | 0.446717i | ||||
\(226\) | 106.790 | − | 77.5877i | 0.472523 | − | 0.343308i | ||||
\(227\) | 189.258 | − | 61.4936i | 0.833735 | − | 0.270897i | 0.139117 | − | 0.990276i | \(-0.455574\pi\) |
0.694618 | + | 0.719379i | \(0.255574\pi\) | |||||||
\(228\) | −38.9361 | + | 119.833i | −0.170773 | + | 0.525584i | ||||
\(229\) | −121.353 | − | 88.1678i | −0.529924 | − | 0.385012i | 0.290405 | − | 0.956904i | \(-0.406210\pi\) |
−0.820329 | + | 0.571892i | \(0.806210\pi\) | |||||||
\(230\) | 145.931i | 0.634485i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −396.000 | −1.70690 | ||||||||
\(233\) | −257.329 | + | 354.183i | −1.10442 | + | 1.52010i | −0.275021 | + | 0.961438i | \(0.588685\pi\) |
−0.829396 | + | 0.558661i | \(0.811315\pi\) | |||||||
\(234\) | −113.555 | − | 36.8962i | −0.485277 | − | 0.157676i | ||||
\(235\) | 176.758 | + | 544.004i | 0.752161 | + | 2.31491i | ||||
\(236\) | −272.925 | − | 375.649i | −1.15646 | − | 1.59173i | ||||
\(237\) | −97.0820 | + | 70.5342i | −0.409629 | + | 0.297613i | ||||
\(238\) | −108.774 | − | 334.772i | −0.457034 | − | 1.40660i | ||||
\(239\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(240\) | 58.4839 | − | 80.4962i | 0.243683 | − | 0.335401i | ||||
\(241\) | −130.000 | −0.539419 | −0.269710 | − | 0.962942i | \(-0.586928\pi\) | ||||
−0.269710 | + | 0.962942i | \(0.586928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 1.00000 | ||||||||
\(244\) | −67.9574 | − | 49.3740i | −0.278514 | − | 0.202352i | ||||
\(245\) | 94.6289 | + | 30.7468i | 0.386241 | + | 0.125497i | ||||
\(246\) | −40.7902 | − | 125.539i | −0.165814 | − | 0.510323i | ||||
\(247\) | 19.4164 | − | 14.1068i | 0.0786089 | − | 0.0571127i | ||||
\(248\) | −152.058 | − | 209.290i | −0.613138 | − | 0.843912i | ||||
\(249\) | 113.555 | − | 36.8962i | 0.456043 | − | 0.148177i | ||||
\(250\) | −40.7902 | + | 125.539i | −0.163161 | + | 0.502158i | ||||
\(251\) | −171.553 | + | 236.122i | −0.683477 | + | 0.940726i | −0.999969 | − | 0.00786966i | \(-0.997495\pi\) |
0.316492 | + | 0.948595i | \(0.397495\pi\) | |||||||
\(252\) | −504.000 | −2.00000 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 623.525i | − | 2.45482i | ||||||
\(255\) | 213.580 | + | 155.175i | 0.837571 | + | 0.608531i | ||||
\(256\) | −114.645 | + | 352.842i | −0.447833 | + | 1.37829i | ||||
\(257\) | 466.836 | − | 151.684i | 1.81648 | − | 0.590211i | 0.816567 | − | 0.577251i | \(-0.195875\pi\) |
0.999916 | − | 0.0129598i | \(-0.00412536\pi\) | |||||||
\(258\) | 245.632 | + | 338.084i | 0.952063 | + | 1.31040i | ||||
\(259\) | −194.164 | + | 141.068i | −0.749668 | + | 0.544666i | ||||
\(260\) | −176.641 | + | 57.3940i | −0.679387 | + | 0.220746i | ||||
\(261\) | −340.664 | − | 110.688i | −1.30523 | − | 0.424094i | ||||
\(262\) | 106.790 | + | 77.5877i | 0.407596 | + | 0.296136i | ||||
\(263\) | 225.530i | 0.857530i | 0.903416 | + | 0.428765i | \(0.141051\pi\) | ||||
−0.903416 | + | 0.428765i | \(0.858949\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −396.000 | −1.49434 | ||||||||
\(266\) | 93.5742 | − | 128.794i | 0.351783 | − | 0.484188i | ||||
\(267\) | 340.664 | + | 110.688i | 1.27590 | + | 0.414564i | ||||
\(268\) | −4.32624 | − | 13.3148i | −0.0161427 | − | 0.0496821i | ||||
\(269\) | 42.8882 | + | 59.0305i | 0.159436 | + | 0.219444i | 0.881260 | − | 0.472632i | \(-0.156696\pi\) |
−0.721824 | + | 0.692077i | \(0.756696\pi\) | |||||||
\(270\) | 480.556 | − | 349.144i | 1.77984 | − | 1.29313i | ||||
\(271\) | 138.440 | + | 426.073i | 0.510847 | + | 1.57223i | 0.790713 | + | 0.612187i | \(0.209710\pi\) |
−0.279866 | + | 0.960039i | \(0.590290\pi\) | |||||||
\(272\) | 63.0860 | + | 20.4979i | 0.231934 | + | 0.0753598i | ||||
\(273\) | 77.6656 | + | 56.4274i | 0.284489 | + | 0.206694i | ||||
\(274\) | 352.000 | 1.28467 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 139.298i | 0.504704i | ||||||||
\(277\) | −210.344 | − | 152.824i | −0.759366 | − | 0.551712i | 0.139350 | − | 0.990243i | \(-0.455499\pi\) |
−0.898716 | + | 0.438531i | \(0.855499\pi\) | |||||||
\(278\) | 233.418 | + | 75.8421i | 0.839633 | + | 0.272813i | ||||
\(279\) | −72.3100 | − | 222.547i | −0.259176 | − | 0.797660i | ||||
\(280\) | −427.161 | + | 310.351i | −1.52557 | + | 1.10840i | ||||
\(281\) | 116.968 | + | 160.992i | 0.416255 | + | 0.572927i | 0.964730 | − | 0.263241i | \(-0.0847913\pi\) |
−0.548475 | + | 0.836167i | \(0.684791\pi\) | |||||||
\(282\) | 265.137 | + | 816.006i | 0.940201 | + | 2.89364i | ||||
\(283\) | 15.4508 | − | 47.5528i | 0.0545966 | − | 0.168031i | −0.920040 | − | 0.391824i | \(-0.871844\pi\) |
0.974637 | + | 0.223793i | \(0.0718441\pi\) | |||||||
\(284\) | −245.632 | + | 338.084i | −0.864903 | + | 1.19044i | ||||
\(285\) | 119.398i | 0.418942i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 106.132i | 0.369798i | ||||||||
\(288\) | −122.816 | + | 169.042i | −0.426445 | + | 0.586951i | ||||
\(289\) | 34.9189 | − | 107.469i | 0.120827 | − | 0.371866i | ||||
\(290\) | −832.735 | + | 270.572i | −2.87150 | + | 0.933006i | ||||
\(291\) | −150.477 | + | 109.328i | −0.517104 | + | 0.375698i | ||||
\(292\) | 419.071 | − | 304.473i | 1.43517 | − | 1.04271i | ||||
\(293\) | −454.219 | + | 147.585i | −1.55024 | + | 0.503702i | −0.954178 | − | 0.299240i | \(-0.903267\pi\) |
−0.596057 | + | 0.802942i | \(0.703267\pi\) | |||||||
\(294\) | 141.943 | + | 46.1202i | 0.482801 | + | 0.156871i | ||||
\(295\) | −355.967 | − | 258.626i | −1.20667 | − | 0.876697i | ||||
\(296\) | − | 298.496i | − | 1.00843i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 308.000 | 1.03356 | ||||||||
\(299\) | 15.5957 | − | 21.4656i | 0.0521595 | − | 0.0717915i | ||||
\(300\) | 123.298 | − | 379.472i | 0.410993 | − | 1.26491i | ||||
\(301\) | −103.830 | − | 319.555i | −0.344949 | − | 1.06164i | ||||
\(302\) | −311.914 | − | 429.313i | −1.03283 | − | 1.42157i | ||||
\(303\) | −187.148 | − | 257.588i | −0.617652 | − | 0.850125i | ||||
\(304\) | 9.27051 | + | 28.5317i | 0.0304951 | + | 0.0938543i | ||||
\(305\) | −75.7031 | − | 24.5974i | −0.248207 | − | 0.0806474i | ||||
\(306\) | 320.371 | + | 232.763i | 1.04696 | + | 0.760663i | ||||
\(307\) | −86.0000 | −0.280130 | −0.140065 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140065 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 222.000 | 0.718447 | ||||||||
\(310\) | −462.758 | − | 336.213i | −1.49277 | − | 1.08456i | ||||
\(311\) | −18.9258 | − | 6.14936i | −0.0608546 | − | 0.0197729i | 0.278431 | − | 0.960456i | \(-0.410185\pi\) |
−0.339286 | + | 0.940683i | \(0.610185\pi\) | |||||||
\(312\) | −113.555 | + | 36.8962i | −0.363957 | + | 0.118257i | ||||
\(313\) | −79.2837 | + | 57.6030i | −0.253302 | + | 0.184035i | −0.707189 | − | 0.707024i | \(-0.750037\pi\) |
0.453887 | + | 0.891059i | \(0.350037\pi\) | |||||||
\(314\) | −354.802 | − | 488.343i | −1.12994 | − | 1.55523i | ||||
\(315\) | −454.219 | + | 147.585i | −1.44196 | + | 0.468523i | ||||
\(316\) | −86.5248 | + | 266.296i | −0.273813 | + | 0.842708i | ||||
\(317\) | −183.250 | + | 252.221i | −0.578074 | + | 0.795651i | −0.993483 | − | 0.113984i | \(-0.963639\pi\) |
0.415408 | + | 0.909635i | \(0.363639\pi\) | |||||||
\(318\) | −594.000 | −1.86792 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 643.425i | 2.01070i | ||||||||
\(321\) | −70.1807 | + | 96.5954i | −0.218631 | + | 0.300920i | ||||
\(322\) | 54.3870 | − | 167.386i | 0.168904 | − | 0.519832i | ||||
\(323\) | −75.7031 | + | 24.5974i | −0.234375 | + | 0.0761531i | ||||
\(324\) | 458.713 | − | 333.274i | 1.41578 | − | 1.02862i | ||||
\(325\) | −61.4853 | + | 44.6717i | −0.189186 | + | 0.137451i | ||||
\(326\) | 914.746 | − | 297.219i | 2.80597 | − | 0.911715i | ||||
\(327\) | 185.410 | − | 570.634i | 0.567004 | − | 1.74506i | ||||
\(328\) | −106.790 | − | 77.5877i | −0.325580 | − | 0.236548i | ||||
\(329\) | − | 689.858i | − | 2.09683i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −218.000 | −0.658610 | −0.329305 | − | 0.944224i | \(-0.606814\pi\) | ||||
−0.329305 | + | 0.944224i | \(0.606814\pi\) | |||||||
\(332\) | 163.755 | − | 225.389i | 0.493238 | − | 0.678883i | ||||
\(333\) | 83.4346 | − | 256.785i | 0.250554 | − | 0.771127i | ||||
\(334\) | 244.741 | + | 753.237i | 0.732759 | + | 2.25520i | ||||
\(335\) | −7.79785 | − | 10.7328i | −0.0232772 | − | 0.0320383i | ||||
\(336\) | −97.0820 | + | 70.5342i | −0.288935 | + | 0.209923i | ||||
\(337\) | −85.9067 | − | 264.394i | −0.254916 | − | 0.784551i | −0.993846 | − | 0.110769i | \(-0.964669\pi\) |
0.738930 | − | 0.673782i | \(-0.235331\pi\) | |||||||
\(338\) | −482.608 | − | 156.809i | −1.42783 | − | 0.463931i | ||||
\(339\) | 70.1807 | − | 96.5954i | 0.207023 | − | 0.284942i | ||||
\(340\) | 616.000 | 1.81176 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 179.098i | 0.523678i | ||||||||
\(343\) | 220.053 | + | 159.878i | 0.641553 | + | 0.466115i | ||||
\(344\) | 397.441 | + | 129.137i | 1.15535 | + | 0.375397i | ||||
\(345\) | 40.7902 | + | 125.539i | 0.118233 | + | 0.363882i | ||||
\(346\) | 533.951 | − | 387.938i | 1.54321 | − | 1.12121i | ||||
\(347\) | −194.946 | − | 268.321i | −0.561805 | − | 0.773258i | 0.429750 | − | 0.902948i | \(-0.358602\pi\) |
−0.991555 | + | 0.129690i | \(0.958602\pi\) | |||||||
\(348\) | −794.883 | + | 258.273i | −2.28415 | + | 0.742164i | ||||
\(349\) | −100.122 | + | 308.142i | −0.286881 | + | 0.882929i | 0.698947 | + | 0.715173i | \(0.253652\pi\) |
−0.985829 | + | 0.167756i | \(0.946348\pi\) | |||||||
\(350\) | −296.318 | + | 407.847i | −0.846624 | + | 1.16528i | ||||
\(351\) | −108.000 | −0.307692 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 397.995i | − | 1.12746i | −0.825958 | − | 0.563732i | \(-0.809365\pi\) | ||
0.825958 | − | 0.563732i | \(-0.190635\pi\) | |||||||
\(354\) | −533.951 | − | 387.938i | −1.50834 | − | 1.09587i | ||||
\(355\) | −122.371 | + | 376.618i | −0.344706 | + | 1.06090i | ||||
\(356\) | 794.883 | − | 258.273i | 2.23282 | − | 0.725486i | ||||
\(357\) | −187.148 | − | 257.588i | −0.524225 | − | 0.721534i | ||||
\(358\) | −533.951 | + | 387.938i | −1.49148 | + | 1.08363i | ||||
\(359\) | 290.195 | − | 94.2902i | 0.808344 | − | 0.262647i | 0.124448 | − | 0.992226i | \(-0.460284\pi\) |
0.683896 | + | 0.729579i | \(0.260284\pi\) | |||||||
\(360\) | 183.556 | − | 564.928i | 0.509878 | − | 1.56924i | ||||
\(361\) | 262.931 | + | 191.030i | 0.728339 | + | 0.529170i | ||||
\(362\) | 33.1662i | 0.0916195i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 224.000 | 0.615385 | ||||||||
\(365\) | 288.521 | − | 397.114i | 0.790467 | − | 1.08798i | ||||
\(366\) | −113.555 | − | 36.8962i | −0.310259 | − | 0.100809i | ||||
\(367\) | −85.9067 | − | 264.394i | −0.234078 | − | 0.720419i | −0.997242 | − | 0.0742141i | \(-0.976355\pi\) |
0.763164 | − | 0.646205i | \(-0.223645\pi\) | |||||||
\(368\) | 19.4946 | + | 26.8321i | 0.0529745 | + | 0.0729132i | ||||
\(369\) | −70.1807 | − | 96.5954i | −0.190192 | − | 0.261776i | ||||
\(370\) | −203.951 | − | 627.697i | −0.551220 | − | 1.69648i | ||||
\(371\) | 454.219 | + | 147.585i | 1.22431 | + | 0.397802i | ||||
\(372\) | −441.723 | − | 320.931i | −1.18743 | − | 0.862717i | ||||
\(373\) | 68.0000 | 0.182306 | 0.0911528 | − | 0.995837i | \(-0.470945\pi\) | ||||
0.0911528 | + | 0.995837i | \(0.470945\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 119.398i | 0.318396i | ||||||||
\(376\) | 694.137 | + | 504.320i | 1.84611 | + | 1.34128i | ||||
\(377\) | 151.406 | + | 49.1949i | 0.401608 | + | 0.130490i | ||||
\(378\) | −681.328 | + | 221.377i | −1.80246 | + | 0.585653i | ||||
\(379\) | −542.041 | + | 393.816i | −1.43019 | + | 1.03909i | −0.440207 | + | 0.897896i | \(0.645095\pi\) |
−0.989982 | + | 0.141196i | \(0.954905\pi\) | |||||||
\(380\) | 163.755 | + | 225.389i | 0.430934 | + | 0.593130i | ||||
\(381\) | −174.286 | − | 536.396i | −0.457442 | − | 1.40786i | ||||
\(382\) | −115.572 | + | 355.695i | −0.302545 | + | 0.931139i | ||||
\(383\) | 19.4946 | − | 26.8321i | 0.0508998 | − | 0.0700576i | −0.782808 | − | 0.622263i | \(-0.786214\pi\) |
0.833708 | + | 0.552205i | \(0.186214\pi\) | |||||||
\(384\) | 686.541i | 1.78787i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 988.354i | − | 2.56050i | ||||||
\(387\) | 305.808 | + | 222.183i | 0.790203 | + | 0.574116i | ||||
\(388\) | −134.113 | + | 412.759i | −0.345653 | + | 1.06381i | ||||
\(389\) | −397.441 | + | 129.137i | −1.02170 | + | 0.331971i | −0.771504 | − | 0.636224i | \(-0.780495\pi\) |
−0.250197 | + | 0.968195i | \(0.580495\pi\) | |||||||
\(390\) | −213.580 | + | 155.175i | −0.547642 | + | 0.397885i | ||||
\(391\) | −71.1935 | + | 51.7251i | −0.182081 | + | 0.132289i | ||||
\(392\) | 141.943 | − | 46.1202i | 0.362100 | − | 0.117654i | ||||
\(393\) | 113.555 | + | 36.8962i | 0.288943 | + | 0.0938834i | ||||
\(394\) | 355.967 | + | 258.626i | 0.903471 | + | 0.656410i | ||||
\(395\) | 265.330i | 0.671721i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −86.0000 | −0.216625 | −0.108312 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108312 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(398\) | −81.8775 | + | 112.695i | −0.205722 | + | 0.283152i | ||||
\(399\) | 44.4984 | − | 136.952i | 0.111525 | − | 0.343238i | ||||
\(400\) | −29.3566 | − | 90.3504i | −0.0733915 | − | 0.225876i | ||||
\(401\) | −148.159 | − | 203.924i | −0.369474 | − | 0.508538i | 0.583284 | − | 0.812269i | \(-0.301768\pi\) |
−0.952758 | + | 0.303731i | \(0.901768\pi\) | |||||||
\(402\) | −11.6968 | − | 16.0992i | −0.0290965 | − | 0.0400478i | ||||
\(403\) | 32.1378 | + | 98.9099i | 0.0797463 | + | 0.245434i | ||||
\(404\) | −706.563 | − | 229.576i | −1.74892 | − | 0.568258i | ||||
\(405\) | 315.813 | − | 434.679i | 0.779785 | − | 1.07328i | ||||
\(406\) | 1056.00 | 2.60099 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 396.000 | 0.970588 | ||||||||
\(409\) | 412.599 | + | 299.770i | 1.00880 | + | 0.732935i | 0.963957 | − | 0.266059i | \(-0.0857216\pi\) |
0.0448419 | + | 0.998994i | \(0.485722\pi\) | |||||||
\(410\) | −277.578 | − | 90.1906i | −0.677020 | − | 0.219977i | ||||
\(411\) | 302.813 | − | 98.3898i | 0.736770 | − | 0.239391i | ||||
\(412\) | 419.071 | − | 304.473i | 1.01716 | − | 0.739012i | ||||
\(413\) | 311.914 | + | 429.313i | 0.755240 | + | 1.03950i | ||||
\(414\) | 61.1854 | + | 188.309i | 0.147791 | + | 0.454853i | ||||
\(415\) | 81.5805 | − | 251.079i | 0.196579 | − | 0.605009i | ||||
\(416\) | 54.5850 | − | 75.1298i | 0.131214 | − | 0.180600i | ||||
\(417\) | 222.000 | 0.532374 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 530.660i | 1.26649i | 0.773951 | + | 0.633246i | \(0.218278\pi\) | ||||
−0.773951 | + | 0.633246i | \(0.781722\pi\) | |||||||
\(420\) | −655.020 | + | 901.557i | −1.55957 | + | 2.14656i | ||||
\(421\) | −52.5329 | + | 161.680i | −0.124781 | + | 0.384037i | −0.993861 | − | 0.110635i | \(-0.964712\pi\) |
0.869080 | + | 0.494672i | \(0.164712\pi\) | |||||||
\(422\) | 775.957 | − | 252.124i | 1.83876 | − | 0.597450i | ||||
\(423\) | 456.174 | + | 627.870i | 1.07843 | + | 1.48433i | ||||
\(424\) | −480.556 | + | 349.144i | −1.13339 | + | 0.823454i | ||||
\(425\) | 239.727 | − | 77.8919i | 0.564063 | − | 0.183275i | ||||
\(426\) | −183.556 | + | 564.928i | −0.430883 | + | 1.32612i | ||||
\(427\) | 77.6656 | + | 56.4274i | 0.181887 | + | 0.132148i | ||||
\(428\) | 278.596i | 0.650926i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 924.000 | 2.14884 | ||||||||
\(431\) | 163.755 | − | 225.389i | 0.379942 | − | 0.522945i | −0.575627 | − | 0.817712i | \(-0.695242\pi\) |
0.955569 | + | 0.294767i | \(0.0952421\pi\) | |||||||
\(432\) | 41.7173 | − | 128.393i | 0.0965678 | − | 0.297205i | ||||
\(433\) | −167.487 | − | 515.473i | −0.386806 | − | 1.19047i | −0.935161 | − | 0.354222i | \(-0.884746\pi\) |
0.548355 | − | 0.836246i | \(-0.315254\pi\) | |||||||
\(434\) | 405.488 | + | 558.107i | 0.934305 | + | 1.28596i | ||||
\(435\) | −640.741 | + | 465.526i | −1.47297 | + | 1.07017i | ||||
\(436\) | −432.624 | − | 1331.48i | −0.992256 | − | 3.05385i | ||||
\(437\) | −37.8516 | − | 12.2987i | −0.0866169 | − | 0.0281435i | ||||
\(438\) | 432.781 | − | 595.672i | 0.988084 | − | 1.35998i | ||||
\(439\) | −328.000 | −0.747153 | −0.373576 | − | 0.927599i | \(-0.621869\pi\) | ||||
−0.373576 | + | 0.927599i | \(0.621869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 135.000 | 0.306122 | ||||||||
\(442\) | −142.387 | − | 103.450i | −0.322143 | − | 0.234050i | ||||
\(443\) | −126.172 | − | 40.9957i | −0.284812 | − | 0.0925412i | 0.163127 | − | 0.986605i | \(-0.447842\pi\) |
−0.447939 | + | 0.894064i | \(0.647842\pi\) | |||||||
\(444\) | −194.681 | − | 599.166i | −0.438470 | − | 1.34947i | ||||
\(445\) | 640.741 | − | 465.526i | 1.43987 | − | 1.04613i | ||||
\(446\) | 588.738 | + | 810.328i | 1.32004 | + | 1.81688i | ||||
\(447\) | 264.961 | − | 86.0910i | 0.592754 | − | 0.192597i | ||||
\(448\) | 239.797 | − | 738.020i | 0.535262 | − | 1.64737i | ||||
\(449\) | 265.127 | − | 364.916i | 0.590483 | − | 0.812730i | −0.404312 | − | 0.914621i | \(-0.632489\pi\) |
0.994796 | + | 0.101890i | \(0.0324891\pi\) | |||||||
\(450\) | − | 567.143i | − | 1.26032i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 278.596i | − | 0.616364i | ||||||
\(453\) | −388.328 | − | 282.137i | −0.857237 | − | 0.622819i | ||||
\(454\) | 203.951 | − | 627.697i | 0.449232 | − | 1.38259i | ||||
\(455\) | 201.875 | − | 65.5932i | 0.443681 | − | 0.144161i | ||||
\(456\) | 105.271 | + | 144.893i | 0.230857 | + | 0.317748i | ||||
\(457\) | 276.684 | − | 201.023i | 0.605435 | − | 0.439874i | −0.242369 | − | 0.970184i | \(-0.577924\pi\) |
0.847804 | + | 0.530310i | \(0.177924\pi\) | |||||||
\(458\) | −473.145 | + | 153.734i | −1.03307 | + | 0.335664i | ||||
\(459\) | 340.664 | + | 110.688i | 0.742188 | + | 0.241151i | ||||
\(460\) | 249.177 | + | 181.038i | 0.541690 | + | 0.393561i | ||||
\(461\) | − | 79.5990i | − | 0.172666i | −0.996266 | − | 0.0863330i | \(-0.972485\pi\) | ||
0.996266 | − | 0.0863330i | \(-0.0275149\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −86.0000 | −0.185745 | −0.0928726 | − | 0.995678i | \(-0.529605\pi\) | ||||
−0.0928726 | + | 0.995678i | \(0.529605\pi\) | |||||||
\(464\) | −116.968 | + | 160.992i | −0.252086 | + | 0.346966i | ||||
\(465\) | −492.070 | − | 159.883i | −1.05822 | − | 0.343835i | ||||
\(466\) | 448.693 | + | 1380.93i | 0.962860 | + | 2.96338i | ||||
\(467\) | −350.903 | − | 482.977i | −0.751399 | − | 1.03421i | −0.997881 | − | 0.0650647i | \(-0.979275\pi\) |
0.246482 | − | 0.969147i | \(-0.420725\pi\) | |||||||
\(468\) | −203.872 | + | 148.122i | −0.435625 | + | 0.316500i | ||||
\(469\) | 4.94427 | + | 15.2169i | 0.0105422 | + | 0.0324454i | ||||
\(470\) | 1804.26 | + | 586.239i | 3.83885 | + | 1.24732i | ||||
\(471\) | −441.723 | − | 320.931i | −0.937841 | − | 0.681382i | ||||
\(472\) | −660.000 | −1.39831 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 397.995i | 0.839652i | ||||||||
\(475\) | 92.2279 | + | 67.0075i | 0.194164 | + | 0.141068i | ||||
\(476\) | −706.563 | − | 229.576i | −1.48438 | − | 0.482303i | ||||
\(477\) | −510.996 | + | 166.033i | −1.07127 | + | 0.348077i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −132.563 | − | 182.458i | −0.276751 | − | 0.380914i | 0.647904 | − | 0.761722i | \(-0.275646\pi\) |
−0.924654 | + | 0.380808i | \(0.875646\pi\) | |||||||
\(480\) | 142.766 | + | 439.388i | 0.297429 | + | 0.915392i | ||||
\(481\) | −37.0820 | + | 114.127i | −0.0770936 | + | 0.237270i | ||||
\(482\) | −253.430 | + | 348.817i | −0.525789 | + | 0.723686i | ||||
\(483\) | − | 159.198i | − | 0.329602i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 411.261i | 0.847962i | ||||||||
\(486\) | 473.720 | − | 652.019i | 0.974732 | − | 1.34160i | ||||
\(487\) | 137.822 | − | 424.171i | 0.283001 | − | 0.870988i | −0.703989 | − | 0.710210i | \(-0.748600\pi\) |
0.986991 | − | 0.160778i | \(-0.0514002\pi\) | |||||||
\(488\) | −113.555 | + | 36.8962i | −0.232694 | + | 0.0756069i | ||||
\(489\) | 703.845 | − | 511.373i | 1.43936 | − | 1.04575i | ||||
\(490\) | 266.976 | − | 193.969i | 0.544848 | − | 0.395855i | ||||
\(491\) | 668.711 | − | 217.277i | 1.36194 | − | 0.442520i | 0.465248 | − | 0.885181i | \(-0.345965\pi\) |
0.896689 | + | 0.442660i | \(0.145965\pi\) | |||||||
\(492\) | −264.961 | − | 86.0910i | −0.538539 | − | 0.174982i | ||||
\(493\) | −427.161 | − | 310.351i | −0.866452 | − | 0.629514i | ||||
\(494\) | − | 79.5990i | − | 0.161132i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −130.000 | −0.262097 | ||||||||
\(497\) | 280.723 | − | 386.382i | 0.564834 | − | 0.777428i | ||||
\(498\) | 122.371 | − | 376.618i | 0.245724 | − | 0.756262i | ||||
\(499\) | −17.9230 | − | 55.1613i | −0.0359178 | − | 0.110544i | 0.931490 | − | 0.363767i | \(-0.118509\pi\) |
−0.967408 | + | 0.253223i | \(0.918509\pi\) | |||||||
\(500\) | 163.755 | + | 225.389i | 0.327510 | + | 0.450779i | ||||
\(501\) | 421.084 | + | 579.572i | 0.840487 | + | 1.15683i | ||||
\(502\) | 299.128 | + | 920.623i | 0.595873 | + | 1.83391i | ||||
\(503\) | −479.453 | − | 155.784i | −0.953187 | − | 0.309709i | −0.209177 | − | 0.977878i | \(-0.567079\pi\) |
−0.744010 | + | 0.668168i | \(0.767079\pi\) | |||||||
\(504\) | −421.084 | + | 579.572i | −0.835484 | + | 1.14995i | ||||
\(505\) | −704.000 | −1.39406 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −459.000 | −0.905325 | ||||||||
\(508\) | −1064.67 | − | 773.525i | −2.09580 | − | 1.52269i | ||||
\(509\) | −700.254 | − | 227.526i | −1.37574 | − | 0.447007i | −0.474477 | − | 0.880268i | \(-0.657363\pi\) |
−0.901268 | + | 0.433262i | \(0.857363\pi\) | |||||||
\(510\) | 832.735 | − | 270.572i | 1.63281 | − | 0.530533i | ||||
\(511\) | −478.938 | + | 347.969i | −0.937256 | + | 0.680957i | ||||
\(512\) | 185.199 | + | 254.905i | 0.361717 | + | 0.497860i | ||||
\(513\) | 50.0608 | + | 154.071i | 0.0975843 | + | 0.300334i | ||||
\(514\) | 503.080 | − | 1548.32i | 0.978754 | − | 3.01230i | ||||
\(515\) | 288.521 | − | 397.114i | 0.560234 | − | 0.771096i | ||||
\(516\) | 882.000 | 1.70930 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 795.990i | 1.53666i | ||||||||
\(519\) | 350.903 | − | 482.977i | 0.676114 | − | 0.930592i | ||||
\(520\) | −81.5805 | + | 251.079i | −0.156886 | + | 0.482844i | ||||
\(521\) | 264.961 | − | 86.0910i | 0.508562 | − | 0.165242i | −0.0434860 | − | 0.999054i | \(-0.513846\pi\) |
0.552048 | + | 0.833812i | \(0.313846\pi\) | |||||||
\(522\) | −961.112 | + | 698.289i | −1.84121 | + | 1.33772i | ||||
\(523\) | −114.880 | + | 83.4655i | −0.219657 | + | 0.159590i | −0.692172 | − | 0.721733i | \(-0.743346\pi\) |
0.472515 | + | 0.881322i | \(0.343346\pi\) | |||||||
\(524\) | 264.961 | − | 86.0910i | 0.505651 | − | 0.164296i | ||||
\(525\) | −140.912 | + | 433.682i | −0.268403 | + | 0.826061i | ||||
\(526\) | 605.145 | + | 439.663i | 1.15047 | + | 0.835862i | ||||
\(527\) | − | 344.929i | − | 0.654514i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 485.000 | 0.916824 | ||||||||
\(530\) | −771.987 | + | 1062.55i | −1.45658 | + | 2.00481i | ||||
\(531\) | −567.774 | − | 184.481i | −1.06925 | − | 0.347421i | ||||
\(532\) | −103.830 | − | 319.555i | −0.195169 | − | 0.600667i | ||||
\(533\) | 31.1914 | + | 42.9313i | 0.0585205 | + | 0.0805465i | ||||
\(534\) | 961.112 | − | 698.289i | 1.79984 | − | 1.30766i | ||||
\(535\) | 81.5805 | + | 251.079i | 0.152487 | + | 0.469306i | ||||
\(536\) | −18.9258 | − | 6.14936i | −0.0353093 | − | 0.0114727i | ||||
\(537\) | −350.903 | + | 482.977i | −0.653451 | + | 0.899399i | ||||
\(538\) | 242.000 | 0.449814 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 1253.68i | − | 2.32164i | ||||||
\(541\) | 323.607 | + | 235.114i | 0.598164 | + | 0.434592i | 0.845227 | − | 0.534408i | \(-0.179465\pi\) |
−0.247063 | + | 0.969000i | \(0.579465\pi\) | |||||||
\(542\) | 1413.13 | + | 459.152i | 2.60724 | + | 0.847144i | ||||
\(543\) | 9.27051 | + | 28.5317i | 0.0170728 | + | 0.0525446i | ||||
\(544\) | −249.177 | + | 181.038i | −0.458046 | + | 0.332790i | ||||
\(545\) | −779.785 | − | 1073.28i | −1.43080 | − | 1.96933i | ||||
\(546\) | 302.813 | − | 98.3898i | 0.554602 | − | 0.180201i | ||||
\(547\) | −52.5329 | + | 161.680i | −0.0960382 | + | 0.295575i | −0.987523 | − | 0.157476i | \(-0.949664\pi\) |
0.891485 | + | 0.453051i | \(0.149664\pi\) | |||||||
\(548\) | 436.680 | − | 601.038i | 0.796861 | − | 1.09678i | ||||
\(549\) | −108.000 | −0.196721 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 238.797i | − | 0.433388i | ||||||
\(552\) | 160.185 | + | 116.381i | 0.290191 | + | 0.210836i | ||||
\(553\) | 98.8854 | − | 304.338i | 0.178816 | − | 0.550340i | ||||
\(554\) | −820.117 | + | 266.472i | −1.48036 | + | 0.480997i | ||||
\(555\) | −350.903 | − | 482.977i | −0.632258 | − | 0.870229i | ||||
\(556\) | 419.071 | − | 304.473i | 0.753724 | − | 0.547613i | ||||
\(557\) | −807.500 | + | 262.373i | −1.44973 | + | 0.471046i | −0.924916 | − | 0.380170i | \(-0.875865\pi\) |
−0.524815 | + | 0.851217i | \(0.675865\pi\) | |||||||
\(558\) | −738.106 | − | 239.825i | −1.32277 | − | 0.429794i | ||||
\(559\) | −135.915 | − | 98.7479i | −0.243139 | − | 0.176651i | ||||
\(560\) | 265.330i | 0.473804i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 660.000 | 1.17438 | ||||||||
\(563\) | −413.286 | + | 568.840i | −0.734078 | + | 1.01037i | 0.264859 | + | 0.964287i | \(0.414675\pi\) |
−0.998938 | + | 0.0460852i | \(0.985325\pi\) | |||||||
\(564\) | 1722.25 | + | 559.592i | 3.05363 | + | 0.992184i | ||||
\(565\) | −81.5805 | − | 251.079i | −0.144390 | − | 0.444387i | ||||
\(566\) | −97.4732 | − | 134.160i | −0.172214 | − | 0.237032i | ||||
\(567\) | −524.243 | + | 380.885i | −0.924591 | + | 0.671755i | ||||
\(568\) | 183.556 | + | 564.928i | 0.323162 | + | 0.994591i | ||||
\(569\) | −113.555 | − | 36.8962i | −0.199569 | − | 0.0648439i | 0.207527 | − | 0.978229i | \(-0.433459\pi\) |
−0.407096 | + | 0.913385i | \(0.633459\pi\) | |||||||
\(570\) | 320.371 | + | 232.763i | 0.562054 | + | 0.408356i | ||||
\(571\) | 706.000 | 1.23643 | 0.618214 | − | 0.786010i | \(-0.287857\pi\) | ||||
0.618214 | + | 0.786010i | \(0.287857\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 338.296i | 0.590394i | ||||||||
\(574\) | 284.774 | + | 206.900i | 0.496122 | + | 0.360454i | ||||
\(575\) | 119.863 | + | 38.9460i | 0.208458 | + | 0.0677321i | ||||
\(576\) | 269.772 | + | 830.272i | 0.468354 | + | 1.44145i | ||||
\(577\) | 597.055 | − | 433.786i | 1.03476 | − | 0.751795i | 0.0655014 | − | 0.997852i | \(-0.479135\pi\) |
0.969255 | + | 0.246058i | \(0.0791353\pi\) | |||||||
\(578\) | −220.289 | − | 303.202i | −0.381123 | − | 0.524571i | ||||
\(579\) | −276.261 | − | 850.245i | −0.477135 | − | 1.46847i | ||||
\(580\) | −571.063 | + | 1757.55i | −0.984592 | + | 3.03026i | ||||
\(581\) | −187.148 | + | 257.588i | −0.322114 | + | 0.443352i | ||||
\(582\) | 616.892i | 1.05995i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 736.291i | − | 1.26077i | ||||||
\(585\) | −140.361 | + | 193.191i | −0.239934 | + | 0.330241i | ||||
\(586\) | −489.483 | + | 1506.47i | −0.835295 | + | 2.57077i | ||||
\(587\) | −895.821 | + | 291.070i | −1.52610 | + | 0.495860i | −0.947501 | − | 0.319753i | \(-0.896400\pi\) |
−0.578599 | + | 0.815612i | \(0.696400\pi\) | |||||||
\(588\) | 254.840 | − | 185.152i | 0.433402 | − | 0.314885i | ||||
\(589\) | 126.207 | − | 91.6945i | 0.214273 | − | 0.155678i | ||||
\(590\) | −1387.89 | + | 450.953i | −2.35236 | + | 0.764327i | ||||
\(591\) | 378.516 | + | 122.987i | 0.640467 | + | 0.208100i | ||||
\(592\) | −121.353 | − | 88.1678i | −0.204987 | − | 0.148932i | ||||
\(593\) | 543.926i | 0.917245i | 0.888631 | + | 0.458623i | \(0.151657\pi\) | ||||
−0.888631 | + | 0.458623i | \(0.848343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −704.000 | −1.18319 | ||||||||
\(596\) | 382.095 | − | 525.908i | 0.641099 | − | 0.882397i | ||||
\(597\) | −38.9361 | + | 119.833i | −0.0652197 | + | 0.200725i | ||||
\(598\) | −27.1935 | − | 83.6930i | −0.0454741 | − | 0.139955i | ||||
\(599\) | −27.2925 | − | 37.5649i | −0.0455634 | − | 0.0627127i | 0.785627 | − | 0.618700i | \(-0.212340\pi\) |
−0.831191 | + | 0.555987i | \(0.812340\pi\) | |||||||
\(600\) | −333.358 | − | 458.828i | −0.555597 | − | 0.764714i | ||||
\(601\) | −167.487 | − | 515.473i | −0.278681 | − | 0.857692i | −0.988222 | − | 0.153027i | \(-0.951098\pi\) |
0.709541 | − | 0.704664i | \(-0.248902\pi\) | |||||||
\(602\) | −1059.84 | − | 344.364i | −1.76054 | − | 0.572034i | ||||
\(603\) | −14.5623 | − | 10.5801i | −0.0241498 | − | 0.0175458i | ||||
\(604\) | −1120.00 | −1.85430 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1056.00 | −1.74257 | ||||||||
\(607\) | −566.312 | − | 411.450i | −0.932969 | − | 0.677841i | 0.0137493 | − | 0.999905i | \(-0.495623\pi\) |
−0.946718 | + | 0.322064i | \(0.895623\pi\) | |||||||
\(608\) | −132.480 | − | 43.0455i | −0.217896 | − | 0.0707986i | ||||
\(609\) | 908.438 | − | 295.169i | 1.49169 | − | 0.484679i | ||||
\(610\) | −213.580 | + | 155.175i | −0.350132 | + | 0.254386i | ||||
\(611\) | −202.744 | − | 279.053i | −0.331824 | − | 0.456716i | ||||
\(612\) | 794.883 | − | 258.273i | 1.29883 | − | 0.422015i | ||||
\(613\) | −236.089 | + | 726.607i | −0.385137 | + | 1.18533i | 0.551244 | + | 0.834344i | \(0.314153\pi\) |
−0.936381 | + | 0.350986i | \(0.885847\pi\) | |||||||
\(614\) | −167.654 | + | 230.756i | −0.273052 | + | 0.375824i | ||||
\(615\) | −264.000 | −0.429268 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 39.7995i | − | 0.0645049i | −0.999480 | − | 0.0322524i | \(-0.989732\pi\) | ||
0.999480 | − | 0.0322524i | \(-0.0102680\pi\) | |||||||
\(618\) | 432.781 | − | 595.672i | 0.700293 | − | 0.963870i | ||||
\(619\) | −229.291 | + | 705.684i | −0.370421 | + | 1.14004i | 0.576095 | + | 0.817383i | \(0.304576\pi\) |
−0.946516 | + | 0.322656i | \(0.895424\pi\) | |||||||
\(620\) | −1148.16 | + | 373.061i | −1.85188 | + | 0.601712i | ||||
\(621\) | 105.271 | + | 144.893i | 0.169519 | + | 0.233322i | ||||
\(622\) | −53.3951 | + | 38.7938i | −0.0858442 | + | 0.0623695i | ||||
\(623\) | −908.438 | + | 295.169i | −1.45817 | + | 0.473787i | ||||
\(624\) | −18.5410 | + | 57.0634i | −0.0297132 | + | 0.0914477i | ||||
\(625\) | 597.864 | + | 434.373i | 0.956582 | + | 0.694997i | ||||
\(626\) | 325.029i | 0.519216i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1274.00 | −2.02866 | ||||||||
\(629\) | 233.936 | − | 321.985i | 0.371917 | − | 0.511899i | ||||
\(630\) | −489.483 | + | 1506.47i | −0.776957 | + | 2.39123i | ||||
\(631\) | −126.697 | − | 389.933i | −0.200788 | − | 0.617961i | −0.999860 | − | 0.0167260i | \(-0.994676\pi\) |
0.799073 | − | 0.601235i | \(-0.205324\pi\) | |||||||
\(632\) | 233.936 | + | 321.985i | 0.370151 | + | 0.509469i | ||||
\(633\) | 597.055 | − | 433.786i | 0.943214 | − | 0.685285i | ||||
\(634\) | 319.524 | + | 983.392i | 0.503980 | + | 1.55109i | ||||
\(635\) | −1186.02 | − | 385.360i | −1.86774 | − | 0.606866i | ||||
\(636\) | −736.897 | + | 1014.25i | −1.15864 | + | 1.59474i | ||||
\(637\) | −60.0000 | −0.0941915 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 537.293i | 0.840834i | ||||||||
\(640\) | 1228.09 | + | 892.258i | 1.91889 | + | 1.39415i | ||||
\(641\) | 719.180 | + | 233.676i | 1.12197 | + | 0.364549i | 0.810517 | − | 0.585715i | \(-0.199186\pi\) |
0.311448 | + | 0.950263i | \(0.399186\pi\) | |||||||
\(642\) | 122.371 | + | 376.618i | 0.190609 | + | 0.586633i | ||||
\(643\) | −720.025 | + | 523.129i | −1.11979 | + | 0.813575i | −0.984177 | − | 0.177187i | \(-0.943300\pi\) |
−0.135613 | + | 0.990762i | \(0.543300\pi\) | |||||||
\(644\) | −218.340 | − | 300.519i | −0.339037 | − | 0.466644i | ||||
\(645\) | 794.883 | − | 258.273i | 1.23238 | − | 0.400423i | ||||
\(646\) | −81.5805 | + | 251.079i | −0.126286 | + | 0.388667i | ||||
\(647\) | −284.622 | + | 391.748i | −0.439910 | + | 0.605484i | −0.970192 | − | 0.242337i | \(-0.922086\pi\) |
0.530282 | + | 0.847821i | \(0.322086\pi\) | |||||||
\(648\) | − | 805.940i | − | 1.24373i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 252.063i | 0.387790i | ||||||||
\(651\) | 504.827 | + | 366.778i | 0.775463 | + | 0.563407i | ||||
\(652\) | 627.304 | − | 1930.64i | 0.962123 | − | 2.96111i | ||||
\(653\) | 372.207 | − | 120.937i | 0.569996 | − | 0.185203i | −0.00981822 | − | 0.999952i | \(-0.503125\pi\) |
0.579814 | + | 0.814749i | \(0.303125\pi\) | |||||||
\(654\) | −1169.68 | − | 1609.92i | −1.78850 | − | 2.46166i | ||||
\(655\) | 213.580 | − | 155.175i | 0.326077 | − | 0.236909i | ||||
\(656\) | −63.0860 | + | 20.4979i | −0.0961676 | + | 0.0312468i | ||||
\(657\) | 205.805 | − | 633.404i | 0.313250 | − | 0.964085i | ||||
\(658\) | −1851.03 | − | 1344.85i | −2.81312 | − | 2.04385i | ||||
\(659\) | − | 384.728i | − | 0.583806i | −0.956448 | − | 0.291903i | \(-0.905711\pi\) | ||
0.956448 | − | 0.291903i | \(-0.0942885\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −746.000 | −1.12859 | −0.564297 | − | 0.825572i | \(-0.690853\pi\) | ||||
−0.564297 | + | 0.825572i | \(0.690853\pi\) | |||||||
\(662\) | −424.983 | + | 584.939i | −0.641968 | + | 0.883593i | ||||
\(663\) | −151.406 | − | 49.1949i | −0.228365 | − | 0.0742004i | ||||
\(664\) | −122.371 | − | 376.618i | −0.184293 | − | 0.567196i | ||||
\(665\) | −187.148 | − | 257.588i | −0.281426 | − | 0.387350i | ||||
\(666\) | −526.355 | − | 724.466i | −0.790323 | − | 1.08779i | ||||
\(667\) | −81.5805 | − | 251.079i | −0.122310 | − | 0.376430i | ||||
\(668\) | 1589.77 | + | 516.546i | 2.37989 | + | 0.773273i | ||||
\(669\) | 732.969 | + | 532.533i | 1.09562 | + | 0.796014i | ||||
\(670\) | −44.0000 | −0.0656716 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 557.193i | − | 0.829156i | ||||||
\(673\) | −512.917 | − | 372.656i | −0.762135 | − | 0.553723i | 0.137430 | − | 0.990512i | \(-0.456116\pi\) |
−0.899564 | + | 0.436788i | \(0.856116\pi\) | |||||||
\(674\) | −876.895 | − | 284.920i | −1.30103 | − | 0.422731i | ||||
\(675\) | −158.526 | − | 487.892i | −0.234853 | − | 0.722803i | ||||
\(676\) | −866.457 | + | 629.518i | −1.28174 | + | 0.931240i | ||||
\(677\) | −467.871 | − | 643.969i | −0.691095 | − | 0.951210i | −1.00000 | 0.000117512i | \(-0.999963\pi\) | |
0.308905 | − | 0.951093i | \(-0.400037\pi\) | |||||||
\(678\) | −122.371 | − | 376.618i | −0.180488 | − | 0.555484i | ||||
\(679\) | 153.272 | − | 471.724i | 0.225733 | − | 0.694733i | ||||
\(680\) | 514.658 | − | 708.366i | 0.756850 | − | 1.04172i | ||||
\(681\) | − | 596.992i | − | 0.876641i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 451.061i | 0.660411i | 0.943909 | + | 0.330206i | \(0.107118\pi\) | ||||
−0.943909 | + | 0.330206i | \(0.892882\pi\) | |||||||
\(684\) | 305.808 | + | 222.183i | 0.447088 | + | 0.324829i | ||||
\(685\) | 217.548 | − | 669.544i | 0.317588 | − | 0.977436i | ||||
\(686\) | 857.969 | − | 278.771i | 1.25068 | − | 0.406372i | ||||
\(687\) | −364.058 | + | 264.503i | −0.529924 | + | 0.385012i | ||||
\(688\) | 169.894 | − | 123.435i | 0.246938 | − | 0.179411i | ||||
\(689\) | 227.109 | − | 73.7923i | 0.329622 | − | 0.107101i | ||||
\(690\) | 416.367 | + | 135.286i | 0.603431 | + | 0.196067i | ||||
\(691\) | −370.530 | − | 269.206i | −0.536223 | − | 0.389588i | 0.286458 | − | 0.958093i | \(-0.407522\pi\) |
−0.822680 | + | 0.568504i | \(0.807522\pi\) | |||||||
\(692\) | − | 1392.98i | − | 2.01298i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1100.00 | −1.58501 | ||||||||
\(695\) | 288.521 | − | 397.114i | 0.415137 | − | 0.571388i | ||||
\(696\) | −367.112 | + | 1129.86i | −0.527460 | + | 1.62336i | ||||
\(697\) | −54.3870 | − | 167.386i | −0.0780301 | − | 0.240152i | ||||
\(698\) | 631.626 | + | 869.359i | 0.904908 | + | 1.24550i | ||||
\(699\) | 771.987 | + | 1062.55i | 1.10442 | + | 1.52010i | ||||
\(700\) | 328.794 | + | 1011.92i | 0.469706 | + | 1.44561i | ||||
\(701\) | 479.453 | + | 155.784i | 0.683956 | + | 0.222231i | 0.630327 | − | 0.776330i | \(-0.282921\pi\) |
0.0536295 | + | 0.998561i | \(0.482921\pi\) | |||||||
\(702\) | −210.542 | + | 289.786i | −0.299917 | + | 0.412801i | ||||
\(703\) | 180.000 | 0.256046 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1716.00 | 2.43404 | ||||||||
\(706\) | −1067.90 | − | 775.877i | −1.51261 | − | 1.09898i | ||||
\(707\) | 807.500 | + | 262.373i | 1.14215 | + | 0.371107i | ||||
\(708\) | −1324.80 | + | 430.455i | −1.87119 | + | 0.607988i | ||||
\(709\) | 454.668 | − | 330.335i | 0.641280 | − | 0.465917i | −0.219010 | − | 0.975723i | \(-0.570283\pi\) |
0.860290 | + | 0.509805i | \(0.170283\pi\) | |||||||
\(710\) | 771.987 | + | 1062.55i | 1.08731 | + | 1.49655i | ||||
\(711\) | 111.246 | + | 342.380i | 0.156464 | + | 0.481548i | ||||
\(712\) | 367.112 | − | 1129.86i | 0.515607 | − | 1.58688i | ||||
\(713\) | 101.372 | − | 139.527i | 0.142177 | − | 0.195690i | ||||
\(714\) | −1056.00 | −1.47899 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1392.98i | 1.94551i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 312.725 | − | 962.469i | 0.435550 | − | 1.34049i | ||||
\(719\) | 321.738 | − | 104.539i | 0.447480 | − | 0.145395i | −0.0766039 | − | 0.997062i | \(-0.524408\pi\) |
0.524084 | + | 0.851666i | \(0.324408\pi\) | |||||||
\(720\) | −175.452 | − | 241.489i | −0.243683 | − | 0.335401i | ||||
\(721\) | −478.938 | + | 347.969i | −0.664269 | + | 0.482620i | ||||
\(722\) | 1025.15 | − | 333.090i | 1.41987 | − | 0.461344i | ||||
\(723\) | −120.517 | + | 370.912i | −0.166690 | + | 0.513018i | ||||
\(724\) | 56.6312 | + | 41.1450i | 0.0782199 | + | 0.0568301i | ||||
\(725\) | 756.190i | 1.04302i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0000 | −0.0577717 | −0.0288858 | − | 0.999583i | \(-0.509196\pi\) | ||||
−0.0288858 | + | 0.999583i | \(0.509196\pi\) | |||||||
\(728\) | 187.148 | − | 257.588i | 0.257072 | − | 0.353829i | ||||
\(729\) | 225.273 | − | 693.320i | 0.309017 | − | 0.951057i | ||||
\(730\) | −503.080 | − | 1548.32i | −0.689150 | − | 2.12099i | ||||
\(731\) | 327.510 | + | 450.779i | 0.448030 | + | 0.616660i | ||||
\(732\) | −203.872 | + | 148.122i | −0.278514 | + | 0.202352i | ||||
\(733\) | 192.827 | + | 593.459i | 0.263065 | + | 0.809631i | 0.992133 | + | 0.125189i | \(0.0399538\pi\) |
−0.729068 | + | 0.684441i | \(0.760046\pi\) | |||||||
\(734\) | −876.895 | − | 284.920i | −1.19468 | − | 0.388175i | ||||
\(735\) | 175.452 | − | 241.489i | 0.238710 | − | 0.328556i | ||||
\(736\) | −154.000 | −0.209239 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −396.000 | −0.536585 | ||||||||
\(739\) | 554.986 | + | 403.221i | 0.750995 | + | 0.545630i | 0.896135 | − | 0.443781i | \(-0.146363\pi\) |
−0.145140 | + | 0.989411i | \(0.546363\pi\) | |||||||
\(740\) | −1324.80 | − | 430.455i | −1.79028 | − | 0.581696i | ||||
\(741\) | −22.2492 | − | 68.4761i | −0.0300259 | − | 0.0924103i | ||||
\(742\) | 1281.48 | − | 931.052i | 1.72707 | − | 1.25479i | ||||
\(743\) | 506.860 | + | 697.634i | 0.682181 | + | 0.938941i | 0.999957 | − | 0.00922416i | \(-0.00293618\pi\) |
−0.317777 | + | 0.948166i | \(0.602936\pi\) | |||||||
\(744\) | −738.106 | + | 239.825i | −0.992077 | + | 0.322346i | ||||
\(745\) | 190.354 | − | 585.851i | 0.255509 | − | 0.786377i | ||||
\(746\) | 132.563 | − | 182.458i | 0.177699 | − | 0.244582i | ||||
\(747\) | − | 358.195i | − | 0.479512i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 318.396i | − | 0.425095i | ||||||
\(750\) | 320.371 | + | 232.763i | 0.427161 | + | 0.310351i | ||||
\(751\) | 29.0476 | − | 89.3993i | 0.0386786 | − | 0.119040i | −0.929853 | − | 0.367931i | \(-0.880066\pi\) |
0.968531 | + | 0.248891i | \(0.0800661\pi\) | |||||||
\(752\) | 410.059 | − | 133.236i | 0.545291 | − | 0.177176i | ||||
\(753\) | 514.658 | + | 708.366i | 0.683477 | + | 0.940726i | ||||
\(754\) | 427.161 | − | 310.351i | 0.566526 | − | 0.411606i | ||||
\(755\) | −1009.38 | + | 327.966i | −1.33692 | + | 0.434392i | ||||
\(756\) | −467.234 | + | 1438.00i | −0.618034 | + | 1.90211i | ||||
\(757\) | −904.481 | − | 657.144i | −1.19482 | − | 0.868090i | −0.201057 | − | 0.979579i | \(-0.564438\pi\) |
−0.993766 | + | 0.111490i | \(0.964438\pi\) | |||||||
\(758\) | 2222.14i | 2.93158i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 396.000 | 0.521053 | ||||||||
\(761\) | −678.413 | + | 933.756i | −0.891476 | + | 1.22701i | 0.0816322 | + | 0.996663i | \(0.473987\pi\) |
−0.973108 | + | 0.230349i | \(0.926013\pi\) | |||||||
\(762\) | −1779.02 | − | 578.040i | −2.33468 | − | 0.758583i | ||||
\(763\) | 494.427 | + | 1521.69i | 0.648004 | + | 1.99435i | ||||
\(764\) | 463.972 | + | 638.603i | 0.607293 | + | 0.835868i | ||||
\(765\) | 640.741 | − | 465.526i | 0.837571 | − | 0.608531i | ||||
\(766\) | −33.9919 | − | 104.616i | −0.0443758 | − | 0.136575i | ||||
\(767\) | 252.344 | + | 81.9915i | 0.329001 | + | 0.106899i | ||||
\(768\) | 900.436 | + | 654.205i | 1.17244 | + | 0.851829i | ||||
\(769\) | −1274.00 | −1.65670 | −0.828349 | − | 0.560213i | \(-0.810719\pi\) | ||||
−0.828349 | + | 0.560213i | \(0.810719\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1472.58i | − | 1.90996i | ||||||
\(772\) | −1687.61 | − | 1226.12i | −2.18602 | − | 1.58824i | ||||
\(773\) | 889.512 | + | 289.020i | 1.15073 | + | 0.373894i | 0.821417 | − | 0.570328i | \(-0.193184\pi\) |
0.329310 | + | 0.944222i | \(0.393184\pi\) | |||||||
\(774\) | 1192.32 | − | 387.410i | 1.54047 | − | 0.500529i | ||||
\(775\) | −399.654 | + | 290.366i | −0.515683 | + | 0.374666i | ||||
\(776\) | 362.600 | + | 499.076i | 0.467268 | + | 0.643140i | ||||
\(777\) | 222.492 | + | 684.761i | 0.286348 | + | 0.881288i | ||||
\(778\) | −428.298 | + | 1318.16i | −0.550511 | + | 1.69430i | ||||
\(779\) | 46.7871 | − | 64.3969i | 0.0600605 | − | 0.0826662i | ||||
\(780\) | 557.193i | 0.714350i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 291.863i | 0.373226i | ||||||||
\(783\) | −631.626 | + | 869.359i | −0.806674 | + | 1.11029i | ||||
\(784\) | 23.1763 | − | 71.3292i | 0.0295616 | − | 0.0909812i | ||||
\(785\) | −1148.16 | + | 373.061i | −1.46263 | + | 0.475237i | ||||
\(786\) | 320.371 | − | 232.763i | 0.407596 | − | 0.296136i | ||||
\(787\) | 241.087 | − | 175.160i | 0.306337 | − | 0.222567i | −0.423986 | − | 0.905669i | \(-0.639370\pi\) |
0.730323 | + | 0.683102i | \(0.239370\pi\) | |||||||
\(788\) | 883.203 | − | 286.970i | 1.12082 | − | 0.364175i | ||||
\(789\) | 643.477 | + | 209.078i | 0.815560 | + | 0.264991i | ||||
\(790\) | 711.935 | + | 517.251i | 0.901183 | + | 0.654748i | ||||
\(791\) | 318.396i | 0.402523i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 0.0605296 | ||||||||
\(794\) | −167.654 | + | 230.756i | −0.211151 | + | 0.290624i | ||||
\(795\) | −367.112 | + | 1129.86i | −0.461776 | + | 1.42120i | ||||
\(796\) | 90.8510 | + | 279.611i | 0.114134 | + | 0.351270i | ||||
\(797\) | 308.015 | + | 423.947i | 0.386468 | + | 0.531928i | 0.957284 | − | 0.289151i | \(-0.0933728\pi\) |
−0.570815 | + | 0.821078i | \(0.693373\pi\) | |||||||
\(798\) | −280.723 | − | 386.382i | −0.351783 | − | 0.484188i | ||||
\(799\) | 353.515 | + | 1088.01i | 0.442447 | + | 1.36171i | ||||
\(800\) | 419.522 | + | 136.311i | 0.524402 | + | 0.170389i | ||||
\(801\) | 631.626 | − | 869.359i | 0.788547 | − | 1.08534i | ||||
\(802\) | −836.000 | −1.04239 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −42.0000 | −0.0522388 | ||||||||
\(805\) | −284.774 | − | 206.900i | −0.353756 | − | 0.257019i | ||||
\(806\) | 328.047 | + | 106.589i | 0.407006 | + | 0.132244i | ||||
\(807\) | 208.184 | − | 67.6430i | 0.257972 | − | 0.0838203i | ||||
\(808\) | −854.322 | + | 620.701i | −1.05733 | + | 0.768195i | ||||
\(809\) | 538.052 | + | 740.565i | 0.665083 | + | 0.915408i | 0.999636 | − | 0.0269690i | \(-0.00858555\pi\) |
−0.334554 | + | 0.942377i | \(0.608586\pi\) | |||||||
\(810\) | −550.668 | − | 1694.78i | −0.679837 | − | 2.09232i | ||||
\(811\) | 56.2411 | − | 173.092i | 0.0693478 | − | 0.213431i | −0.910377 | − | 0.413781i | \(-0.864208\pi\) |
0.979724 | + | 0.200350i | \(0.0642080\pi\) | |||||||
\(812\) | 1310.04 | − | 1803.11i | 1.61335 | − | 2.22058i | ||||
\(813\) | 1344.00 | 1.65314 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1923.64i | − | 2.36030i | ||||||
\(816\) | 116.968 | − | 160.992i | 0.143343 | − | 0.197295i | ||||
\(817\) | −77.8723 | + | 239.666i | −0.0953149 | + | 0.293349i | ||||
\(818\) | 1608.69 | − | 522.696i | 1.96662 | − | 0.638992i | ||||
\(819\) | 232.997 | − | 169.282i | 0.284489 | − | 0.206694i | ||||
\(820\) | −498.354 | + | 362.076i | −0.607749 | + | 0.441556i | ||||
\(821\) | 782.266 | − | 254.174i | 0.952821 | − | 0.309590i | 0.208959 | − | 0.977924i | \(-0.432992\pi\) |
0.743861 | + | 0.668334i | \(0.232992\pi\) | |||||||
\(822\) | 326.322 | − | 1004.32i | 0.396985 | − | 1.22180i | ||||
\(823\) | 199.018 | + | 144.595i | 0.241820 | + | 0.175693i | 0.702094 | − | 0.712084i | \(-0.252249\pi\) |
−0.460274 | + | 0.887777i | \(0.652249\pi\) | |||||||
\(824\) | − | 736.291i | − | 0.893557i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1760.00 | 2.13075 | ||||||||
\(827\) | 319.712 | − | 440.046i | 0.386592 | − | 0.532099i | −0.570724 | − | 0.821142i | \(-0.693337\pi\) |
0.957316 | + | 0.289043i | \(0.0933372\pi\) | |||||||
\(828\) | 397.441 | + | 129.137i | 0.480002 | + | 0.155962i | ||||
\(829\) | 77.2542 | + | 237.764i | 0.0931897 | + | 0.286808i | 0.986778 | − | 0.162080i | \(-0.0518202\pi\) |
−0.893588 | + | 0.448888i | \(0.851820\pi\) | |||||||
\(830\) | −514.658 | − | 708.366i | −0.620070 | − | 0.853453i | ||||
\(831\) | −631.033 | + | 458.472i | −0.759366 | + | 0.551712i | ||||
\(832\) | −119.899 | − | 369.010i | −0.144109 | − | 0.443522i | ||||
\(833\) | 189.258 | + | 61.4936i | 0.227200 | + | 0.0738219i | ||||
\(834\) | 432.781 | − | 595.672i | 0.518922 | − | 0.714235i | ||||
\(835\) | 1584.00 | 1.89701 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −702.000 | −0.838710 | ||||||||
\(838\) | 1423.87 | + | 1034.50i | 1.69913 | + | 1.23449i | ||||
\(839\) | −447.910 | − | 145.535i | −0.533862 | − | 0.173462i | 0.0296650 | − | 0.999560i | \(-0.490556\pi\) |
−0.563527 | + | 0.826098i | \(0.690556\pi\) | |||||||
\(840\) | 489.483 | + | 1506.47i | 0.582718 | + | 1.79342i | ||||
\(841\) | 601.100 | − | 436.724i | 0.714744 | − | 0.519292i | ||||
\(842\) | 331.409 | + | 456.145i | 0.393597 | + | 0.541740i | ||||
\(843\) | 567.774 | − | 184.481i | 0.673516 | − | 0.218838i | ||||
\(844\) | 532.127 | − | 1637.72i | 0.630483 | − | 1.94043i | ||||
\(845\) | −596.536 | + | 821.061i | −0.705959 | + | 0.971670i | ||||
\(846\) | 2574.00 | 3.04255 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 298.496i | 0.352000i | ||||||||
\(849\) | −121.353 | − | 88.1678i | −0.142936 | − | 0.103849i | ||||
\(850\) | 258.338 | − | 795.083i | 0.303927 | − | 0.935392i | ||||
\(851\) | 189.258 | − | 61.4936i | 0.222395 | − | 0.0722604i | ||||
\(852\) | 736.897 | + | 1014.25i | 0.864903 | + | 1.19044i | ||||
\(853\) | 45.3050 | − | 32.9160i | 0.0531125 | − | 0.0385885i | −0.560912 | − | 0.827875i | \(-0.689549\pi\) |
0.614025 | + | 0.789287i | \(0.289549\pi\) | |||||||
\(854\) | 302.813 | − | 98.3898i | 0.354581 | − | 0.115211i | ||||
\(855\) | 340.664 | + | 110.688i | 0.398438 | + | 0.129460i | ||||
\(856\) | 320.371 | + | 232.763i | 0.374265 | + | 0.271919i | ||||
\(857\) | − | 252.063i | − | 0.294123i | −0.989127 | − | 0.147062i | \(-0.953018\pi\) | ||
0.989127 | − | 0.147062i | \(-0.0469815\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1278.00 | 1.48778 | 0.743888 | − | 0.668304i | \(-0.232979\pi\) | ||||
0.743888 | + | 0.668304i | \(0.232979\pi\) | |||||||
\(860\) | 1146.28 | − | 1577.73i | 1.33289 | − | 1.83456i | ||||
\(861\) | 302.813 | + | 98.3898i | 0.351699 | + | 0.114274i | ||||
\(862\) | −285.532 | − | 878.776i | −0.331243 | − | 1.01946i | ||||
\(863\) | −666.716 | − | 917.656i | −0.772557 | − | 1.06333i | −0.996065 | − | 0.0886309i | \(-0.971751\pi\) |
0.223508 | − | 0.974702i | \(-0.428249\pi\) | |||||||
\(864\) | 368.449 | + | 507.126i | 0.426445 | + | 0.586951i | ||||
\(865\) | −407.902 | − | 1255.39i | −0.471564 | − | 1.45132i | ||||
\(866\) | −1709.63 | − | 555.492i | −1.97417 | − | 0.641446i | ||||
\(867\) | −274.257 | − | 199.259i | −0.316328 | − | 0.229826i | ||||
\(868\) | 1456.00 | 1.67742 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2626.77i | 3.01927i | ||||||||
\(871\) | 6.47214 | + | 4.70228i | 0.00743070 | + | 0.00539872i | ||||
\(872\) | −1892.58 | − | 614.936i | −2.17039 | − | 0.705202i | ||||
\(873\) | 172.431 | + | 530.690i | 0.197516 | + | 0.607892i | ||||
\(874\) | −106.790 | + | 77.5877i | −0.122186 | + | 0.0887731i | ||||
\(875\) | −187.148 | − | 257.588i | −0.213884 | − | 0.294386i | ||||
\(876\) | −480.212 | − | 1477.94i | −0.548188 | − | 1.68715i | ||||
\(877\) | −140.912 | + | 433.682i | −0.160675 | + | 0.494506i | −0.998692 | − | 0.0511384i | \(-0.983715\pi\) |
0.838017 | + | 0.545644i | \(0.183715\pi\) | |||||||
\(878\) | −639.424 | + | 880.092i | −0.728273 | + | 1.00238i | ||||
\(879\) | 1432.78i | 1.63001i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 610.259i | 0.692689i | 0.938107 | + | 0.346344i | \(0.112577\pi\) | ||||
−0.938107 | + | 0.346344i | \(0.887423\pi\) | |||||||
\(882\) | 263.178 | − | 362.233i | 0.298387 | − | 0.410695i | ||||
\(883\) | −338.065 | + | 1040.46i | −0.382859 | + | 1.17832i | 0.555162 | + | 0.831742i | \(0.312656\pi\) |
−0.938021 | + | 0.346577i | \(0.887344\pi\) | |||||||
\(884\) | −353.281 | + | 114.788i | −0.399640 | + | 0.129851i | ||||
\(885\) | −1067.90 | + | 775.877i | −1.20667 | + | 0.876697i | ||||
\(886\) | −355.967 | + | 258.626i | −0.401769 | + | 0.291902i | ||||
\(887\) | −138.789 | + | 45.0953i | −0.156470 | + | 0.0508403i | −0.386205 | − | 0.922413i | \(-0.626214\pi\) |
0.229735 | + | 0.973253i | \(0.426214\pi\) | |||||||
\(888\) | −851.660 | − | 276.721i | −0.959077 | − | 0.311623i | ||||
\(889\) | 1216.76 | + | 884.029i | 1.36869 | + | 0.994408i | ||||
\(890\) | − | 2626.77i | − | 2.95142i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2114.00 | 2.36996 | ||||||||
\(893\) | −304.116 | + | 418.580i | −0.340556 | + | 0.468735i | ||||
\(894\) | 285.532 | − | 878.776i | 0.319387 | − | 0.982971i | ||||
\(895\) | 407.902 | + | 1255.39i | 0.455757 | + | 1.40268i | ||||
\(896\) | −1076.10 | − | 1481.13i | −1.20101 | − | 1.65305i | ||||
\(897\) | −46.7871 | − | 64.3969i | −0.0521595 | − | 0.0717915i | ||||
\(898\) | −462.289 | − | 1422.78i | −0.514799 | − | 1.58439i | ||||
\(899\) | 984.141 | + | 319.767i | 1.09471 | + | 0.355692i | ||||
\(900\) | −968.393 | − | 703.579i | −1.07599 | − | 0.781754i | ||||
\(901\) | −792.000 | −0.879023 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1008.00 | −1.11628 | ||||||||
\(904\) | −320.371 | − | 232.763i | −0.354392 | − | 0.257481i | ||||
\(905\) | 63.0860 | + | 20.4979i | 0.0697082 | + | 0.0226496i | ||||
\(906\) | −1514.06 | + | 491.949i | −1.67115 | + | 0.542990i | ||||
\(907\) | −150.477 | + | 109.328i | −0.165906 | + | 0.120538i | −0.667640 | − | 0.744484i | \(-0.732696\pi\) |
0.501734 | + | 0.865022i | \(0.332696\pi\) | |||||||
\(908\) | −818.775 | − | 1126.95i | −0.901734 | − | 1.24113i | ||||
\(909\) | −908.438 | + | 295.169i | −0.999381 | + | 0.324719i | ||||
\(910\) | 217.548 | − | 669.544i | 0.239064 | − | 0.735762i | ||||
\(911\) | −502.961 | + | 692.267i | −0.552098 | + | 0.759898i | −0.990295 | − | 0.138981i | \(-0.955617\pi\) |
0.438197 | + | 0.898879i | \(0.355617\pi\) | |||||||
\(912\) | 90.0000 | 0.0986842 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 1134.29i | − | 1.24101i | ||||||
\(915\) | −140.361 | + | 193.191i | −0.153400 | + | 0.211138i | ||||
\(916\) | −324.468 | + | 998.609i | −0.354223 | + | 1.09018i | ||||
\(917\) | −302.813 | + | 98.3898i | −0.330221 | + | 0.107295i | ||||
\(918\) | 961.112 | − | 698.289i | 1.04696 | − | 0.760663i | ||||
\(919\) | −346.259 | + | 251.572i | −0.376778 | + | 0.273745i | −0.760016 | − | 0.649904i | \(-0.774809\pi\) |
0.383238 | + | 0.923650i | \(0.374809\pi\) | |||||||
\(920\) | 416.367 | − | 135.286i | 0.452573 | − | 0.147050i | ||||
\(921\) | −79.7264 | + | 245.373i | −0.0865650 | + | 0.266420i | ||||
\(922\) | −213.580 | − | 155.175i | −0.231649 | − | 0.168303i | ||||
\(923\) | − | 238.797i | − | 0.258718i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −570.000 | −0.616216 | ||||||||
\(926\) | −167.654 | + | 230.756i | −0.181052 | + | 0.249196i | ||||
\(927\) | 205.805 | − | 633.404i | 0.222012 | − | 0.683283i | ||||
\(928\) | −285.532 | − | 878.776i | −0.307685 | − | 0.946957i | ||||
\(929\) | 374.297 | + | 515.176i | 0.402903 | + | 0.554548i | 0.961470 | − | 0.274911i | \(-0.0886485\pi\) |
−0.558567 | + | 0.829460i | \(0.688648\pi\) | |||||||
\(930\) | −1388.27 | + | 1008.64i | −1.49277 | + | 1.08456i | ||||
\(931\) | 27.8115 | + | 85.5951i | 0.0298727 | + | 0.0919389i | ||||
\(932\) | 2914.57 | + | 947.002i | 3.12722 | + | 1.01610i | ||||
\(933\) | −35.0903 | + | 48.2977i | −0.0376102 | + | 0.0517660i | ||||
\(934\) | −1980.00 | −2.11991 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 358.195i | 0.382687i | ||||||||
\(937\) | 234.615 | + | 170.458i | 0.250389 | + | 0.181919i | 0.705899 | − | 0.708312i | \(-0.250543\pi\) |
−0.455510 | + | 0.890231i | \(0.650543\pi\) | |||||||
\(938\) | 50.4688 | + | 16.3983i | 0.0538047 | + | 0.0174822i | ||||
\(939\) | 90.8510 | + | 279.611i | 0.0967529 | + | 0.297775i | ||||
\(940\) | 3239.30 | − | 2353.49i | 3.44607 | − | 2.50372i | ||||
\(941\) | −514.658 | − | 708.366i | −0.546927 | − | 0.752780i | 0.442664 | − | 0.896687i | \(-0.354033\pi\) |
−0.989591 | + | 0.143907i | \(0.954033\pi\) | |||||||
\(942\) | −1722.25 | + | 559.592i | −1.82829 | + | 0.594047i | ||||
\(943\) | 27.1935 | − | 83.6930i | 0.0288372 | − | 0.0887518i | ||||
\(944\) | −194.946 | + | 268.321i | −0.206511 | + | 0.284238i | ||||
\(945\) | 1432.78i | 1.51617i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 79.5990i | 0.0840538i | 0.999116 | + | 0.0420269i | \(0.0133815\pi\) | ||||
−0.999116 | + | 0.0420269i | \(0.986618\pi\) | |||||||
\(948\) | 679.574 | + | 493.740i | 0.716851 | + | 0.520822i | ||||
\(949\) | −91.4690 | + | 281.513i | −0.0963846 | + | 0.296641i | ||||
\(950\) | 359.590 | − | 116.838i | 0.378516 | − | 0.122987i | ||||
\(951\) | 549.749 | + | 756.664i | 0.578074 | + | 0.795651i | ||||
\(952\) | −854.322 | + | 620.701i | −0.897397 | + | 0.651997i | ||||
\(953\) | 744.414 | − | 241.875i | 0.781127 | − | 0.253804i | 0.108806 | − | 0.994063i | \(-0.465297\pi\) |
0.672321 | + | 0.740259i | \(0.265297\pi\) | |||||||
\(954\) | −550.668 | + | 1694.78i | −0.577220 | + | 1.77650i | ||||
\(955\) | 605.145 | + | 439.663i | 0.633659 | + | 0.460380i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −748.000 | −0.780793 | ||||||||
\(959\) | −499.063 | + | 686.901i | −0.520399 | + | 0.716268i | ||||
\(960\) | 1835.80 | + | 596.488i | 1.91229 | + | 0.621342i | ||||
\(961\) | −88.0698 | − | 271.051i | −0.0916440 | − | 0.282051i | ||||
\(962\) | 233.936 | + | 321.985i | 0.243176 | + | 0.334703i | ||||
\(963\) | 210.542 | + | 289.786i | 0.218631 | + | 0.300920i | ||||
\(964\) | 281.205 | + | 865.461i | 0.291707 | + | 0.897782i | ||||
\(965\) | −1879.96 | − | 610.836i | −1.94815 | − | 0.632991i | ||||
\(966\) | −427.161 | − | 310.351i | −0.442196 | − | 0.321274i | ||||
\(967\) | −460.000 | −0.475698 | −0.237849 | − | 0.971302i | \(-0.576442\pi\) | ||||
−0.237849 | + | 0.971302i | \(0.576442\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 238.797i | 0.246437i | ||||||||
\(970\) | 1103.50 | + | 801.739i | 1.13763 | + | 0.826535i | ||||
\(971\) | 1110.31 | + | 360.762i | 1.14347 | + | 0.371537i | 0.818681 | − | 0.574248i | \(-0.194706\pi\) |
0.324792 | + | 0.945785i | \(0.394706\pi\) | |||||||
\(972\) | −525.638 | − | 1617.75i | −0.540780 | − | 1.66435i | ||||
\(973\) | −478.938 | + | 347.969i | −0.492228 | + | 0.357625i | ||||
\(974\) | −869.461 | − | 1196.71i | −0.892670 | − | 1.22865i | ||||
\(975\) | 70.4559 | + | 216.841i | 0.0722624 | + | 0.222401i | ||||
\(976\) | −18.5410 | + | 57.0634i | −0.0189969 | + | 0.0584666i | ||||
\(977\) | −771.987 | + | 1062.55i | −0.790161 | + | 1.08756i | 0.203927 | + | 0.978986i | \(0.434630\pi\) |
−0.994088 | + | 0.108577i | \(0.965370\pi\) | |||||||
\(978\) | − | 2885.46i | − | 2.95037i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 696.491i | − | 0.710705i | ||||||
\(981\) | −1456.23 | − | 1058.01i | −1.48443 | − | 1.07851i | ||||
\(982\) | 720.628 | − | 2217.86i | 0.733837 | − | 2.25852i | ||||
\(983\) | 397.441 | − | 129.137i | 0.404315 | − | 0.131370i | −0.0997979 | − | 0.995008i | \(-0.531820\pi\) |
0.504113 | + | 0.863638i | \(0.331820\pi\) | |||||||
\(984\) | −320.371 | + | 232.763i | −0.325580 | + | 0.236548i | ||||
\(985\) | 711.935 | − | 517.251i | 0.722777 | − | 0.525128i | ||||
\(986\) | −1665.47 | + | 541.144i | −1.68912 | + | 0.548827i | ||||
\(987\) | −1968.28 | − | 639.533i | −1.99421 | − | 0.647957i | ||||
\(988\) | −135.915 | − | 98.7479i | −0.137566 | − | 0.0999473i | ||||
\(989\) | 278.596i | 0.281695i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 838.000 | 0.845610 | 0.422805 | − | 0.906221i | \(-0.361045\pi\) | ||||
0.422805 | + | 0.906221i | \(0.361045\pi\) | |||||||
\(992\) | 354.802 | − | 488.343i | 0.357664 | − | 0.492282i | ||||
\(993\) | −202.097 | + | 621.991i | −0.203522 | + | 0.626376i | ||||
\(994\) | −489.483 | − | 1506.47i | −0.492438 | − | 1.51557i | ||||
\(995\) | 163.755 | + | 225.389i | 0.164578 | + | 0.226522i | ||||
\(996\) | −491.265 | − | 676.168i | −0.493238 | − | 0.678883i | ||||
\(997\) | 16.0689 | + | 49.4549i | 0.0161172 | + | 0.0496038i | 0.958792 | − | 0.284110i | \(-0.0916981\pi\) |
−0.942674 | + | 0.333714i | \(0.891698\pi\) | |||||||
\(998\) | −182.949 | − | 59.4438i | −0.183316 | − | 0.0595629i | ||||
\(999\) | −655.304 | − | 476.106i | −0.655960 | − | 0.476583i |
(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 | 363.3.h.d.323.2 | 8 | ||
3.2 | odd | 2 | inner | 363.3.h.d.323.1 | 8 | ||
11.2 | odd | 10 | 363.3.h.e.269.2 | 8 | |||
11.3 | even | 5 | inner | 363.3.h.d.245.1 | 8 | ||
11.4 | even | 5 | inner | 363.3.h.d.251.2 | 8 | ||
11.5 | even | 5 | 363.3.b.d.122.2 | 2 | |||
11.6 | odd | 10 | 33.3.b.a.23.1 | ✓ | 2 | ||
11.7 | odd | 10 | 363.3.h.e.251.1 | 8 | |||
11.8 | odd | 10 | 363.3.h.e.245.2 | 8 | |||
11.9 | even | 5 | inner | 363.3.h.d.269.1 | 8 | ||
11.10 | odd | 2 | 363.3.h.e.323.1 | 8 | |||
33.2 | even | 10 | 363.3.h.e.269.1 | 8 | |||
33.5 | odd | 10 | 363.3.b.d.122.1 | 2 | |||
33.8 | even | 10 | 363.3.h.e.245.1 | 8 | |||
33.14 | odd | 10 | inner | 363.3.h.d.245.2 | 8 | ||
33.17 | even | 10 | 33.3.b.a.23.2 | yes | 2 | ||
33.20 | odd | 10 | inner | 363.3.h.d.269.2 | 8 | ||
33.26 | odd | 10 | inner | 363.3.h.d.251.1 | 8 | ||
33.29 | even | 10 | 363.3.h.e.251.2 | 8 | |||
33.32 | even | 2 | 363.3.h.e.323.2 | 8 | |||
44.39 | even | 10 | 528.3.i.a.353.2 | 2 | |||
132.83 | odd | 10 | 528.3.i.a.353.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.b.a.23.1 | ✓ | 2 | 11.6 | odd | 10 | ||
33.3.b.a.23.2 | yes | 2 | 33.17 | even | 10 | ||
363.3.b.d.122.1 | 2 | 33.5 | odd | 10 | |||
363.3.b.d.122.2 | 2 | 11.5 | even | 5 | |||
363.3.h.d.245.1 | 8 | 11.3 | even | 5 | inner | ||
363.3.h.d.245.2 | 8 | 33.14 | odd | 10 | inner | ||
363.3.h.d.251.1 | 8 | 33.26 | odd | 10 | inner | ||
363.3.h.d.251.2 | 8 | 11.4 | even | 5 | inner | ||
363.3.h.d.269.1 | 8 | 11.9 | even | 5 | inner | ||
363.3.h.d.269.2 | 8 | 33.20 | odd | 10 | inner | ||
363.3.h.d.323.1 | 8 | 3.2 | odd | 2 | inner | ||
363.3.h.d.323.2 | 8 | 1.1 | even | 1 | trivial | ||
363.3.h.e.245.1 | 8 | 33.8 | even | 10 | |||
363.3.h.e.245.2 | 8 | 11.8 | odd | 10 | |||
363.3.h.e.251.1 | 8 | 11.7 | odd | 10 | |||
363.3.h.e.251.2 | 8 | 33.29 | even | 10 | |||
363.3.h.e.269.1 | 8 | 33.2 | even | 10 | |||
363.3.h.e.269.2 | 8 | 11.2 | odd | 10 | |||
363.3.h.e.323.1 | 8 | 11.10 | odd | 2 | |||
363.3.h.e.323.2 | 8 | 33.32 | even | 2 | |||
528.3.i.a.353.1 | 2 | 132.83 | odd | 10 | |||
528.3.i.a.353.2 | 2 | 44.39 | even | 10 |