Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (of order \(6\), degree \(2\), 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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.8 | ||
Character | \(\chi\) | \(=\) | 169.23 |
Dual form | 169.4.e.h.147.8 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.337850 | + | 0.195058i | −0.119448 | + | 0.0689633i | −0.558534 | − | 0.829482i | \(-0.688636\pi\) |
0.439086 | + | 0.898445i | \(0.355302\pi\) | |||||||
\(3\) | −1.80483 | − | 3.12606i | −0.347340 | − | 0.601611i | 0.638436 | − | 0.769675i | \(-0.279582\pi\) |
−0.985776 | + | 0.168064i | \(0.946249\pi\) | |||||||
\(4\) | −3.92391 | + | 6.79640i | −0.490488 | + | 0.849550i | ||||
\(5\) | − | 7.52136i | − | 0.672731i | −0.941732 | − | 0.336365i | \(-0.890802\pi\) | ||
0.941732 | − | 0.336365i | \(-0.109198\pi\) | |||||||
\(6\) | 1.21953 | + | 0.704093i | 0.0829782 | + | 0.0479075i | ||||
\(7\) | 16.9261 | + | 9.77228i | 0.913923 | + | 0.527654i | 0.881691 | − | 0.471827i | \(-0.156405\pi\) |
0.0322315 | + | 0.999480i | \(0.489739\pi\) | |||||||
\(8\) | − | 6.18247i | − | 0.273229i | ||||||
\(9\) | 6.98515 | − | 12.0986i | 0.258709 | − | 0.448098i | ||||
\(10\) | 1.46710 | + | 2.54109i | 0.0463937 | + | 0.0803563i | ||||
\(11\) | −39.6850 | + | 22.9121i | −1.08777 | + | 0.628024i | −0.932982 | − | 0.359923i | \(-0.882803\pi\) |
−0.154788 | + | 0.987948i | \(0.549469\pi\) | |||||||
\(12\) | 28.3280 | 0.681465 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −7.62463 | −0.145555 | ||||||||
\(15\) | −23.5123 | + | 13.5748i | −0.404722 | + | 0.233667i | ||||
\(16\) | −30.1853 | − | 52.2825i | −0.471645 | − | 0.816914i | ||||
\(17\) | 43.2600 | − | 74.9285i | 0.617182 | − | 1.06899i | −0.372816 | − | 0.927905i | \(-0.621608\pi\) |
0.989998 | − | 0.141085i | \(-0.0450590\pi\) | |||||||
\(18\) | 5.45003i | 0.0713658i | ||||||||
\(19\) | −128.810 | − | 74.3684i | −1.55532 | − | 0.897963i | −0.997694 | − | 0.0678680i | \(-0.978380\pi\) |
−0.557623 | − | 0.830095i | \(-0.688286\pi\) | |||||||
\(20\) | 51.1182 | + | 29.5131i | 0.571519 | + | 0.329966i | ||||
\(21\) | − | 70.5494i | − | 0.733102i | ||||||
\(22\) | 8.93837 | − | 15.4817i | 0.0866212 | − | 0.150032i | ||||
\(23\) | −45.7676 | − | 79.2718i | −0.414922 | − | 0.718665i | 0.580499 | − | 0.814261i | \(-0.302858\pi\) |
−0.995420 | + | 0.0955958i | \(0.969524\pi\) | |||||||
\(24\) | −19.3268 | + | 11.1583i | −0.164378 | + | 0.0949036i | ||||
\(25\) | 68.4292 | 0.547433 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −147.889 | −1.05412 | ||||||||
\(28\) | −132.833 | + | 76.6910i | −0.896536 | + | 0.517616i | ||||
\(29\) | −129.451 | − | 224.215i | −0.828909 | − | 1.43571i | −0.898895 | − | 0.438165i | \(-0.855629\pi\) |
0.0699855 | − | 0.997548i | \(-0.477705\pi\) | |||||||
\(30\) | 5.29574 | − | 9.17249i | 0.0322288 | − | 0.0558220i | ||||
\(31\) | 31.2317i | 0.180948i | 0.995899 | + | 0.0904739i | \(0.0288382\pi\) | ||||
−0.995899 | + | 0.0904739i | \(0.971162\pi\) | |||||||
\(32\) | 63.2296 | + | 36.5056i | 0.349298 | + | 0.201667i | ||||
\(33\) | 143.250 | + | 82.7052i | 0.755653 | + | 0.436276i | ||||
\(34\) | 33.7528i | 0.170252i | ||||||||
\(35\) | 73.5008 | − | 127.307i | 0.354969 | − | 0.614824i | ||||
\(36\) | 54.8181 | + | 94.9478i | 0.253788 | + | 0.439573i | ||||
\(37\) | −128.549 | + | 74.2180i | −0.571173 | + | 0.329767i | −0.757618 | − | 0.652699i | \(-0.773637\pi\) |
0.186445 | + | 0.982465i | \(0.440303\pi\) | |||||||
\(38\) | 58.0245 | 0.247706 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −46.5006 | −0.183810 | ||||||||
\(41\) | 83.0635 | − | 47.9567i | 0.316399 | − | 0.182673i | −0.333388 | − | 0.942790i | \(-0.608192\pi\) |
0.649786 | + | 0.760117i | \(0.274858\pi\) | |||||||
\(42\) | 13.7612 | + | 23.8351i | 0.0505571 | + | 0.0875675i | ||||
\(43\) | −40.4965 | + | 70.1420i | −0.143620 | + | 0.248757i | −0.928857 | − | 0.370438i | \(-0.879208\pi\) |
0.785237 | + | 0.619195i | \(0.212541\pi\) | |||||||
\(44\) | − | 359.620i | − | 1.23215i | ||||||
\(45\) | −90.9982 | − | 52.5378i | −0.301449 | − | 0.174042i | ||||
\(46\) | 30.9251 | + | 17.8546i | 0.0991231 | + | 0.0572287i | ||||
\(47\) | − | 94.3777i | − | 0.292902i | −0.989218 | − | 0.146451i | \(-0.953215\pi\) | ||
0.989218 | − | 0.146451i | \(-0.0467851\pi\) | |||||||
\(48\) | −108.959 | + | 188.722i | −0.327643 | + | 0.567494i | ||||
\(49\) | 19.4949 | + | 33.7662i | 0.0568365 | + | 0.0984436i | ||||
\(50\) | −23.1188 | + | 13.3476i | −0.0653898 | + | 0.0377528i | ||||
\(51\) | −312.308 | −0.857489 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 493.555 | 1.27915 | 0.639575 | − | 0.768729i | \(-0.279110\pi\) | ||||
0.639575 | + | 0.768729i | \(0.279110\pi\) | |||||||
\(54\) | 49.9643 | − | 28.8469i | 0.125913 | − | 0.0726957i | ||||
\(55\) | 172.330 | + | 298.485i | 0.422491 | + | 0.731776i | ||||
\(56\) | 60.4169 | − | 104.645i | 0.144170 | − | 0.249710i | ||||
\(57\) | 536.891i | 1.24759i | ||||||||
\(58\) | 87.4697 | + | 50.5006i | 0.198023 | + | 0.114329i | ||||
\(59\) | −498.558 | − | 287.843i | −1.10011 | − | 0.635152i | −0.163864 | − | 0.986483i | \(-0.552396\pi\) |
−0.936251 | + | 0.351331i | \(0.885729\pi\) | |||||||
\(60\) | − | 213.065i | − | 0.458443i | ||||||
\(61\) | 20.1432 | − | 34.8891i | 0.0422800 | − | 0.0732311i | −0.844111 | − | 0.536168i | \(-0.819871\pi\) |
0.886391 | + | 0.462937i | \(0.153205\pi\) | |||||||
\(62\) | −6.09199 | − | 10.5516i | −0.0124788 | − | 0.0216138i | ||||
\(63\) | 236.462 | − | 136.522i | 0.472880 | − | 0.273018i | ||||
\(64\) | 454.482 | 0.887660 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −64.5291 | −0.120348 | ||||||||
\(67\) | 520.603 | − | 300.570i | 0.949280 | − | 0.548067i | 0.0564231 | − | 0.998407i | \(-0.482030\pi\) |
0.892857 | + | 0.450340i | \(0.148697\pi\) | |||||||
\(68\) | 339.496 | + | 588.025i | 0.605441 | + | 1.04865i | ||||
\(69\) | −165.206 | + | 286.145i | −0.288238 | + | 0.499243i | ||||
\(70\) | 57.3476i | 0.0979193i | ||||||||
\(71\) | 449.294 | + | 259.400i | 0.751006 | + | 0.433593i | 0.826057 | − | 0.563586i | \(-0.190579\pi\) |
−0.0750515 | + | 0.997180i | \(0.523912\pi\) | |||||||
\(72\) | −74.7995 | − | 43.1855i | −0.122433 | − | 0.0706869i | ||||
\(73\) | 1055.21i | 1.69182i | 0.533328 | + | 0.845908i | \(0.320941\pi\) | ||||
−0.533328 | + | 0.845908i | \(0.679059\pi\) | |||||||
\(74\) | 28.9536 | − | 50.1491i | 0.0454836 | − | 0.0787799i | ||||
\(75\) | −123.503 | − | 213.914i | −0.190146 | − | 0.329342i | ||||
\(76\) | 1010.88 | − | 583.629i | 1.52573 | − | 0.880880i | ||||
\(77\) | −895.615 | −1.32552 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −320.840 | −0.456928 | −0.228464 | − | 0.973552i | \(-0.573370\pi\) | ||||
−0.228464 | + | 0.973552i | \(0.573370\pi\) | |||||||
\(80\) | −393.235 | + | 227.034i | −0.549563 | + | 0.317290i | ||||
\(81\) | 78.3164 | + | 135.648i | 0.107430 | + | 0.186074i | ||||
\(82\) | −18.7087 | + | 32.4043i | −0.0251954 | + | 0.0436398i | ||||
\(83\) | − | 32.4841i | − | 0.0429590i | −0.999769 | − | 0.0214795i | \(-0.993162\pi\) | ||
0.999769 | − | 0.0214795i | \(-0.00683766\pi\) | |||||||
\(84\) | 479.482 | + | 276.829i | 0.622807 | + | 0.359578i | ||||
\(85\) | −563.564 | − | 325.374i | −0.719143 | − | 0.415197i | ||||
\(86\) | − | 31.5966i | − | 0.0396180i | ||||||
\(87\) | −467.274 | + | 809.341i | −0.575827 | + | 0.997362i | ||||
\(88\) | 141.654 | + | 245.351i | 0.171595 | + | 0.297211i | ||||
\(89\) | −390.400 | + | 225.398i | −0.464970 | + | 0.268450i | −0.714132 | − | 0.700011i | \(-0.753178\pi\) |
0.249162 | + | 0.968462i | \(0.419845\pi\) | |||||||
\(90\) | 40.9916 | 0.0480099 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 718.350 | 0.814057 | ||||||||
\(93\) | 97.6324 | − | 56.3681i | 0.108860 | − | 0.0628505i | ||||
\(94\) | 18.4091 | + | 31.8855i | 0.0201995 | + | 0.0349865i | ||||
\(95\) | −559.352 | + | 968.826i | −0.604087 | + | 1.04631i | ||||
\(96\) | − | 263.546i | − | 0.280189i | ||||||
\(97\) | −200.695 | − | 115.871i | −0.210077 | − | 0.121288i | 0.391270 | − | 0.920276i | \(-0.372036\pi\) |
−0.601347 | + | 0.798988i | \(0.705369\pi\) | |||||||
\(98\) | −13.1727 | − | 7.60526i | −0.0135780 | − | 0.00783926i | ||||
\(99\) | 640.179i | 0.649903i | ||||||||
\(100\) | −268.510 | + | 465.072i | −0.268510 | + | 0.465072i | ||||
\(101\) | 285.063 | + | 493.743i | 0.280840 | + | 0.486428i | 0.971592 | − | 0.236663i | \(-0.0760538\pi\) |
−0.690752 | + | 0.723092i | \(0.742720\pi\) | |||||||
\(102\) | 105.513 | − | 60.9181i | 0.102425 | − | 0.0591352i | ||||
\(103\) | −969.551 | −0.927502 | −0.463751 | − | 0.885965i | \(-0.653497\pi\) | ||||
−0.463751 | + | 0.885965i | \(0.653497\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −530.627 | −0.493180 | ||||||||
\(106\) | −166.747 | + | 96.2716i | −0.152792 | + | 0.0882144i | ||||
\(107\) | 171.578 | + | 297.182i | 0.155019 | + | 0.268502i | 0.933066 | − | 0.359705i | \(-0.117123\pi\) |
−0.778047 | + | 0.628207i | \(0.783789\pi\) | |||||||
\(108\) | 580.303 | − | 1005.11i | 0.517034 | − | 0.895529i | ||||
\(109\) | − | 83.1640i | − | 0.0730795i | −0.999332 | − | 0.0365398i | \(-0.988366\pi\) | ||
0.999332 | − | 0.0365398i | \(-0.0116336\pi\) | |||||||
\(110\) | −116.444 | − | 67.2287i | −0.100931 | − | 0.0582728i | ||||
\(111\) | 464.021 | + | 267.902i | 0.396783 | + | 0.229083i | ||||
\(112\) | − | 1179.92i | − | 0.995461i | ||||||
\(113\) | 1058.09 | − | 1832.67i | 0.880856 | − | 1.52569i | 0.0304652 | − | 0.999536i | \(-0.490301\pi\) |
0.850391 | − | 0.526152i | \(-0.176366\pi\) | |||||||
\(114\) | −104.725 | − | 181.388i | −0.0860383 | − | 0.149023i | ||||
\(115\) | −596.231 | + | 344.234i | −0.483468 | + | 0.279131i | ||||
\(116\) | 2031.81 | 1.62628 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 224.584 | 0.175209 | ||||||||
\(119\) | 1464.44 | − | 845.498i | 1.12811 | − | 0.651316i | ||||
\(120\) | 83.9259 | + | 145.364i | 0.0638446 | + | 0.110582i | ||||
\(121\) | 384.431 | − | 665.855i | 0.288829 | − | 0.500266i | ||||
\(122\) | 15.7164i | 0.0116631i | ||||||||
\(123\) | −299.832 | − | 173.108i | −0.219796 | − | 0.126899i | ||||
\(124\) | −212.263 | − | 122.550i | −0.153724 | − | 0.0887528i | ||||
\(125\) | − | 1454.85i | − | 1.04101i | ||||||
\(126\) | −53.2592 | + | 92.2476i | −0.0376564 | + | 0.0652228i | ||||
\(127\) | −588.346 | − | 1019.04i | −0.411081 | − | 0.712012i | 0.583928 | − | 0.811806i | \(-0.301515\pi\) |
−0.995008 | + | 0.0997933i | \(0.968182\pi\) | |||||||
\(128\) | −659.384 | + | 380.695i | −0.455327 | + | 0.262883i | ||||
\(129\) | 292.358 | 0.199540 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 775.336 | 0.517110 | 0.258555 | − | 0.965996i | \(-0.416754\pi\) | ||||
0.258555 | + | 0.965996i | \(0.416754\pi\) | |||||||
\(132\) | −1124.20 | + | 649.055i | −0.741278 | + | 0.427977i | ||||
\(133\) | −1453.50 | − | 2517.53i | −0.947626 | − | 1.64134i | ||||
\(134\) | −117.257 | + | 203.095i | −0.0755931 | + | 0.130931i | ||||
\(135\) | 1112.33i | 0.709140i | ||||||||
\(136\) | −463.243 | − | 267.454i | −0.292079 | − | 0.168632i | ||||
\(137\) | 2201.98 | + | 1271.31i | 1.37319 | + | 0.792814i | 0.991329 | − | 0.131404i | \(-0.0419485\pi\) |
0.381865 | + | 0.924218i | \(0.375282\pi\) | |||||||
\(138\) | − | 128.899i | − | 0.0795114i | ||||||
\(139\) | 143.158 | − | 247.958i | 0.0873564 | − | 0.151306i | −0.819036 | − | 0.573741i | \(-0.805491\pi\) |
0.906393 | + | 0.422436i | \(0.138825\pi\) | |||||||
\(140\) | 576.821 | + | 999.082i | 0.348216 | + | 0.603128i | ||||
\(141\) | −295.031 | + | 170.336i | −0.176213 | + | 0.101737i | ||||
\(142\) | −202.392 | −0.119608 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −843.395 | −0.488076 | ||||||||
\(145\) | −1686.40 | + | 973.644i | −0.965848 | + | 0.557633i | ||||
\(146\) | −205.826 | − | 356.501i | −0.116673 | − | 0.202084i | ||||
\(147\) | 70.3701 | − | 121.885i | 0.0394832 | − | 0.0683869i | ||||
\(148\) | − | 1164.90i | − | 0.646987i | ||||||
\(149\) | −2038.73 | − | 1177.06i | −1.12094 | − | 0.647173i | −0.179297 | − | 0.983795i | \(-0.557382\pi\) |
−0.941640 | + | 0.336622i | \(0.890716\pi\) | |||||||
\(150\) | 83.4511 | + | 48.1805i | 0.0454250 | + | 0.0262261i | ||||
\(151\) | 165.158i | 0.0890089i | 0.999009 | + | 0.0445045i | \(0.0141709\pi\) | ||||
−0.999009 | + | 0.0445045i | \(0.985829\pi\) | |||||||
\(152\) | −459.781 | + | 796.364i | −0.245350 | + | 0.424958i | ||||
\(153\) | −604.355 | − | 1046.77i | −0.319341 | − | 0.553115i | ||||
\(154\) | 302.583 | − | 174.697i | 0.158330 | − | 0.0914120i | ||||
\(155\) | 234.905 | 0.121729 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3095.72 | −1.57367 | −0.786833 | − | 0.617166i | \(-0.788281\pi\) | ||||
−0.786833 | + | 0.617166i | \(0.788281\pi\) | |||||||
\(158\) | 108.396 | − | 62.5823i | 0.0545791 | − | 0.0315113i | ||||
\(159\) | −890.784 | − | 1542.88i | −0.444301 | − | 0.769551i | ||||
\(160\) | 274.572 | − | 475.573i | 0.135668 | − | 0.234983i | ||||
\(161\) | − | 1789.01i | − | 0.875740i | ||||||
\(162\) | −52.9183 | − | 30.5524i | −0.0256646 | − | 0.0148174i | ||||
\(163\) | −259.210 | − | 149.655i | −0.124558 | − | 0.0719134i | 0.436427 | − | 0.899740i | \(-0.356244\pi\) |
−0.560984 | + | 0.827826i | \(0.689577\pi\) | |||||||
\(164\) | 752.711i | 0.358395i | ||||||||
\(165\) | 622.055 | − | 1077.43i | 0.293497 | − | 0.508351i | ||||
\(166\) | 6.33628 | + | 10.9748i | 0.00296259 | + | 0.00513136i | ||||
\(167\) | −2602.55 | + | 1502.59i | −1.20594 | + | 0.696249i | −0.961869 | − | 0.273509i | \(-0.911816\pi\) |
−0.244069 | + | 0.969758i | \(0.578482\pi\) | |||||||
\(168\) | −436.170 | −0.200305 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 253.867 | 0.114533 | ||||||||
\(171\) | −1799.51 | + | 1038.95i | −0.804750 | + | 0.464622i | ||||
\(172\) | −317.809 | − | 550.461i | −0.140888 | − | 0.244025i | ||||
\(173\) | 227.926 | − | 394.780i | 0.100167 | − | 0.173495i | −0.811586 | − | 0.584233i | \(-0.801396\pi\) |
0.911753 | + | 0.410738i | \(0.134729\pi\) | |||||||
\(174\) | − | 364.581i | − | 0.158844i | ||||||
\(175\) | 1158.24 | + | 668.709i | 0.500312 | + | 0.288855i | ||||
\(176\) | 2395.81 | + | 1383.22i | 1.02608 | + | 0.592409i | ||||
\(177\) | 2078.03i | 0.882455i | ||||||||
\(178\) | 87.9310 | − | 152.301i | 0.0370265 | − | 0.0641317i | ||||
\(179\) | 682.097 | + | 1181.43i | 0.284818 | + | 0.493318i | 0.972565 | − | 0.232632i | \(-0.0747337\pi\) |
−0.687747 | + | 0.725950i | \(0.741400\pi\) | |||||||
\(180\) | 714.136 | − | 412.307i | 0.295714 | − | 0.170731i | ||||
\(181\) | 2026.11 | 0.832041 | 0.416021 | − | 0.909355i | \(-0.363424\pi\) | ||||
0.416021 | + | 0.909355i | \(0.363424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −145.421 | −0.0587422 | ||||||||
\(184\) | −490.096 | + | 282.957i | −0.196360 | + | 0.113369i | ||||
\(185\) | 558.220 | + | 966.866i | 0.221844 | + | 0.384246i | ||||
\(186\) | −21.9901 | + | 38.0879i | −0.00866876 | + | 0.0150147i | ||||
\(187\) | 3964.71i | 1.55042i | ||||||||
\(188\) | 641.429 | + | 370.329i | 0.248835 | + | 0.143665i | ||||
\(189\) | −2503.18 | − | 1445.21i | −0.963386 | − | 0.556211i | ||||
\(190\) | − | 436.423i | − | 0.166639i | ||||||
\(191\) | −1080.53 | + | 1871.54i | −0.409343 | + | 0.709003i | −0.994816 | − | 0.101689i | \(-0.967575\pi\) |
0.585473 | + | 0.810692i | \(0.300909\pi\) | |||||||
\(192\) | −820.265 | − | 1420.74i | −0.308320 | − | 0.534026i | ||||
\(193\) | 1046.05 | − | 603.938i | 0.390137 | − | 0.225246i | −0.292083 | − | 0.956393i | \(-0.594348\pi\) |
0.682219 | + | 0.731147i | \(0.261015\pi\) | |||||||
\(194\) | 90.4063 | 0.0334577 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −305.985 | −0.111510 | ||||||||
\(197\) | 4266.70 | − | 2463.38i | 1.54309 | − | 0.890906i | 0.544454 | − | 0.838791i | \(-0.316737\pi\) |
0.998641 | − | 0.0521154i | \(-0.0165964\pi\) | |||||||
\(198\) | −124.872 | − | 216.284i | −0.0448194 | − | 0.0776295i | ||||
\(199\) | 504.727 | − | 874.212i | 0.179795 | − | 0.311413i | −0.762016 | − | 0.647559i | \(-0.775790\pi\) |
0.941810 | + | 0.336145i | \(0.109123\pi\) | |||||||
\(200\) | − | 423.061i | − | 0.149575i | ||||||
\(201\) | −1879.20 | − | 1084.96i | −0.659447 | − | 0.380732i | ||||
\(202\) | −192.617 | − | 111.207i | −0.0670914 | − | 0.0387352i | ||||
\(203\) | − | 5060.11i | − | 1.74951i | ||||||
\(204\) | 1225.47 | − | 2122.57i | 0.420588 | − | 0.728480i | ||||
\(205\) | −360.700 | − | 624.751i | −0.122890 | − | 0.212851i | ||||
\(206\) | 327.563 | − | 189.118i | 0.110788 | − | 0.0639636i | ||||
\(207\) | −1278.77 | −0.429376 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6815.76 | 2.25577 | ||||||||
\(210\) | 179.272 | − | 103.503i | 0.0589093 | − | 0.0340113i | ||||
\(211\) | 2455.66 | + | 4253.33i | 0.801206 | + | 1.38773i | 0.918823 | + | 0.394671i | \(0.129141\pi\) |
−0.117616 | + | 0.993059i | \(0.537525\pi\) | |||||||
\(212\) | −1936.66 | + | 3354.40i | −0.627408 | + | 1.08670i | ||||
\(213\) | − | 1872.70i | − | 0.602418i | ||||||
\(214\) | −115.935 | − | 66.9353i | −0.0370335 | − | 0.0213813i | ||||
\(215\) | 527.563 | + | 304.589i | 0.167347 | + | 0.0966176i | ||||
\(216\) | 914.321i | 0.288017i | ||||||||
\(217\) | −305.205 | + | 528.631i | −0.0954778 | + | 0.165372i | ||||
\(218\) | 16.2218 | + | 28.0969i | 0.00503980 | + | 0.00872920i | ||||
\(219\) | 3298.64 | − | 1904.47i | 1.01782 | − | 0.587636i | ||||
\(220\) | −2704.83 | −0.828908 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −209.026 | −0.0631932 | ||||||||
\(223\) | −1181.76 | + | 682.289i | −0.354872 | + | 0.204885i | −0.666829 | − | 0.745211i | \(-0.732349\pi\) |
0.311957 | + | 0.950096i | \(0.399016\pi\) | |||||||
\(224\) | 713.487 | + | 1235.80i | 0.212821 | + | 0.368616i | ||||
\(225\) | 477.988 | − | 827.899i | 0.141626 | − | 0.245303i | ||||
\(226\) | 825.554i | 0.242987i | ||||||||
\(227\) | 3611.22 | + | 2084.94i | 1.05588 | + | 0.609614i | 0.924290 | − | 0.381690i | \(-0.124658\pi\) |
0.131592 | + | 0.991304i | \(0.457991\pi\) | |||||||
\(228\) | −3648.93 | − | 2106.71i | −1.05989 | − | 0.611931i | ||||
\(229\) | 3506.89i | 1.01197i | 0.862541 | + | 0.505987i | \(0.168872\pi\) | ||||
−0.862541 | + | 0.505987i | \(0.831128\pi\) | |||||||
\(230\) | 134.291 | − | 232.599i | 0.0384995 | − | 0.0666831i | ||||
\(231\) | 1616.44 | + | 2799.75i | 0.460406 | + | 0.797446i | ||||
\(232\) | −1386.20 | + | 800.325i | −0.392279 | + | 0.226482i | ||||
\(233\) | 570.253 | 0.160337 | 0.0801684 | − | 0.996781i | \(-0.474454\pi\) | ||||
0.0801684 | + | 0.996781i | \(0.474454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −709.848 | −0.197044 | ||||||||
\(236\) | 3912.59 | − | 2258.94i | 1.07919 | − | 0.623069i | ||||
\(237\) | 579.063 | + | 1002.97i | 0.158710 | + | 0.274893i | ||||
\(238\) | −329.842 | + | 571.302i | −0.0898338 | + | 0.155597i | ||||
\(239\) | − | 231.056i | − | 0.0625347i | −0.999511 | − | 0.0312674i | \(-0.990046\pi\) | ||
0.999511 | − | 0.0312674i | \(-0.00995433\pi\) | |||||||
\(240\) | 1419.45 | + | 819.519i | 0.381771 | + | 0.220416i | ||||
\(241\) | −2674.72 | − | 1544.25i | −0.714911 | − | 0.412754i | 0.0979656 | − | 0.995190i | \(-0.468766\pi\) |
−0.812877 | + | 0.582436i | \(0.802100\pi\) | |||||||
\(242\) | 299.945i | 0.0796744i | ||||||||
\(243\) | −1713.81 | + | 2968.40i | −0.452431 | + | 0.783634i | ||||
\(244\) | 158.080 | + | 273.803i | 0.0414756 | + | 0.0718379i | ||||
\(245\) | 253.968 | − | 146.628i | 0.0662261 | − | 0.0382356i | ||||
\(246\) | 135.064 | 0.0350056 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 193.089 | 0.0494403 | ||||||||
\(249\) | −101.547 | + | 58.6285i | −0.0258446 | + | 0.0149214i | ||||
\(250\) | 283.780 | + | 491.521i | 0.0717912 | + | 0.124346i | ||||
\(251\) | −1222.82 | + | 2117.98i | −0.307504 | + | 0.532613i | −0.977816 | − | 0.209467i | \(-0.932827\pi\) |
0.670311 | + | 0.742080i | \(0.266161\pi\) | |||||||
\(252\) | 2142.79i | 0.535648i | ||||||||
\(253\) | 3632.57 | + | 2097.27i | 0.902679 | + | 0.521162i | ||||
\(254\) | 397.545 | + | 229.523i | 0.0982054 | + | 0.0566989i | ||||
\(255\) | 2348.98i | 0.576859i | ||||||||
\(256\) | −1669.41 | + | 2891.51i | −0.407572 | + | 0.705935i | ||||
\(257\) | 1637.00 | + | 2835.36i | 0.397327 | + | 0.688191i | 0.993395 | − | 0.114743i | \(-0.0366045\pi\) |
−0.596068 | + | 0.802934i | \(0.703271\pi\) | |||||||
\(258\) | −98.7731 | + | 57.0266i | −0.0238347 | + | 0.0137609i | ||||
\(259\) | −2901.12 | −0.696010 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3616.93 | −0.857786 | ||||||||
\(262\) | −261.947 | + | 151.235i | −0.0617678 | + | 0.0356616i | ||||
\(263\) | 2315.64 | + | 4010.80i | 0.542921 | + | 0.940367i | 0.998735 | + | 0.0502918i | \(0.0160151\pi\) |
−0.455813 | + | 0.890075i | \(0.650652\pi\) | |||||||
\(264\) | 511.323 | − | 885.637i | 0.119204 | − | 0.206467i | ||||
\(265\) | − | 3712.20i | − | 0.860524i | ||||||
\(266\) | 982.128 | + | 567.032i | 0.226384 | + | 0.130703i | ||||
\(267\) | 1409.21 | + | 813.610i | 0.323006 | + | 0.186487i | ||||
\(268\) | 4717.64i | 1.07528i | ||||||||
\(269\) | 1419.26 | − | 2458.23i | 0.321686 | − | 0.557177i | −0.659150 | − | 0.752012i | \(-0.729084\pi\) |
0.980836 | + | 0.194835i | \(0.0624170\pi\) | |||||||
\(270\) | −216.968 | − | 375.800i | −0.0489046 | − | 0.0847053i | ||||
\(271\) | 6107.48 | − | 3526.16i | 1.36902 | − | 0.790401i | 0.378213 | − | 0.925719i | \(-0.376539\pi\) |
0.990802 | + | 0.135317i | \(0.0432054\pi\) | |||||||
\(272\) | −5223.26 | −1.16436 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −991.917 | −0.218700 | ||||||||
\(275\) | −2715.61 | + | 1567.86i | −0.595481 | + | 0.343801i | ||||
\(276\) | −1296.50 | − | 2245.61i | −0.282755 | − | 0.489746i | ||||
\(277\) | −969.154 | + | 1678.62i | −0.210220 | + | 0.364111i | −0.951783 | − | 0.306772i | \(-0.900751\pi\) |
0.741564 | + | 0.670883i | \(0.234085\pi\) | |||||||
\(278\) | 111.697i | 0.0240975i | ||||||||
\(279\) | 377.861 | + | 218.158i | 0.0810823 | + | 0.0468129i | ||||
\(280\) | −787.073 | − | 454.417i | −0.167988 | − | 0.0969879i | ||||
\(281\) | − | 3290.74i | − | 0.698609i | −0.937009 | − | 0.349305i | \(-0.886418\pi\) | ||
0.937009 | − | 0.349305i | \(-0.113582\pi\) | |||||||
\(282\) | 66.4507 | − | 115.096i | 0.0140322 | − | 0.0243045i | ||||
\(283\) | −3959.04 | − | 6857.26i | −0.831592 | − | 1.44036i | −0.896776 | − | 0.442486i | \(-0.854097\pi\) |
0.0651839 | − | 0.997873i | \(-0.479237\pi\) | |||||||
\(284\) | −3525.98 | + | 2035.72i | −0.736719 | + | 0.425345i | ||||
\(285\) | 4038.15 | 0.839296 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1874.59 | 0.385552 | ||||||||
\(288\) | 883.337 | − | 509.995i | 0.180733 | − | 0.104346i | ||||
\(289\) | −1286.35 | − | 2228.03i | −0.261827 | − | 0.453497i | ||||
\(290\) | 379.833 | − | 657.891i | 0.0769124 | − | 0.133216i | ||||
\(291\) | 836.514i | 0.168513i | ||||||||
\(292\) | −7171.61 | − | 4140.53i | −1.43728 | − | 0.829816i | ||||
\(293\) | −4915.07 | − | 2837.71i | −0.980004 | − | 0.565806i | −0.0777327 | − | 0.996974i | \(-0.524768\pi\) |
−0.902271 | + | 0.431169i | \(0.858101\pi\) | |||||||
\(294\) | 54.9049i | 0.0108916i | ||||||||
\(295\) | −2164.97 | + | 3749.84i | −0.427286 | + | 0.740081i | ||||
\(296\) | 458.851 | + | 794.753i | 0.0901019 | + | 0.156061i | ||||
\(297\) | 5868.98 | − | 3388.46i | 1.14664 | − | 0.662014i | ||||
\(298\) | 918.381 | 0.178525 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1938.46 | 0.373057 | ||||||||
\(301\) | −1370.89 | + | 791.487i | −0.262515 | + | 0.151563i | ||||
\(302\) | −32.2153 | − | 55.7985i | −0.00613835 | − | 0.0106319i | ||||
\(303\) | 1028.98 | − | 1782.25i | 0.195094 | − | 0.337913i | ||||
\(304\) | 8979.33i | 1.69408i | ||||||||
\(305\) | −262.414 | − | 151.505i | −0.0492648 | − | 0.0284430i | ||||
\(306\) | 408.362 | + | 235.768i | 0.0762893 | + | 0.0440456i | ||||
\(307\) | − | 4338.86i | − | 0.806618i | −0.915064 | − | 0.403309i | \(-0.867860\pi\) | ||
0.915064 | − | 0.403309i | \(-0.132140\pi\) | |||||||
\(308\) | 3514.31 | − | 6086.96i | 0.650150 | − | 1.12609i | ||||
\(309\) | 1749.88 | + | 3030.88i | 0.322159 | + | 0.557996i | ||||
\(310\) | −79.3626 | + | 45.8200i | −0.0145403 | + | 0.00839485i | ||||
\(311\) | 5234.75 | 0.954454 | 0.477227 | − | 0.878780i | \(-0.341642\pi\) | ||||
0.477227 | + | 0.878780i | \(0.341642\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2167.86 | 0.391484 | 0.195742 | − | 0.980655i | \(-0.437288\pi\) | ||||
0.195742 | + | 0.980655i | \(0.437288\pi\) | |||||||
\(314\) | 1045.89 | − | 603.844i | 0.187971 | − | 0.108525i | ||||
\(315\) | −1026.83 | − | 1778.52i | −0.183667 | − | 0.318121i | ||||
\(316\) | 1258.95 | − | 2180.56i | 0.224118 | − | 0.388184i | ||||
\(317\) | − | 4863.71i | − | 0.861744i | −0.902413 | − | 0.430872i | \(-0.858206\pi\) | ||
0.902413 | − | 0.430872i | \(-0.141794\pi\) | |||||||
\(318\) | 601.902 | + | 347.509i | 0.106142 | + | 0.0612809i | ||||
\(319\) | 10274.5 | + | 5931.98i | 1.80332 | + | 1.04115i | ||||
\(320\) | − | 3418.32i | − | 0.597156i | ||||||
\(321\) | 619.340 | − | 1072.73i | 0.107689 | − | 0.186523i | ||||
\(322\) | 348.961 | + | 604.418i | 0.0603939 | + | 0.104605i | ||||
\(323\) | −11144.6 | + | 6434.36i | −1.91983 | + | 1.10841i | ||||
\(324\) | −1229.22 | −0.210772 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 116.765 | 0.0198375 | ||||||||
\(327\) | −259.976 | + | 150.097i | −0.0439655 | + | 0.0253835i | ||||
\(328\) | −296.491 | − | 513.538i | −0.0499116 | − | 0.0864494i | ||||
\(329\) | 922.285 | − | 1597.44i | 0.154551 | − | 0.267690i | ||||
\(330\) | 485.347i | 0.0809620i | ||||||||
\(331\) | −2325.51 | − | 1342.63i | −0.386167 | − | 0.222954i | 0.294331 | − | 0.955704i | \(-0.404903\pi\) |
−0.680498 | + | 0.732750i | \(0.738237\pi\) | |||||||
\(332\) | 220.775 | + | 127.465i | 0.0364958 | + | 0.0210709i | ||||
\(333\) | 2073.70i | 0.341255i | ||||||||
\(334\) | 586.182 | − | 1015.30i | 0.0960312 | − | 0.166331i | ||||
\(335\) | −2260.70 | − | 3915.64i | −0.368702 | − | 0.638610i | ||||
\(336\) | −3688.50 | + | 2129.55i | −0.598881 | + | 0.345764i | ||||
\(337\) | 6518.36 | 1.05364 | 0.526821 | − | 0.849976i | \(-0.323384\pi\) | ||||
0.526821 | + | 0.849976i | \(0.323384\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7638.71 | −1.22383 | ||||||||
\(340\) | 4422.74 | − | 2553.47i | 0.705462 | − | 0.407299i | ||||
\(341\) | −715.585 | − | 1239.43i | −0.113640 | − | 0.196830i | ||||
\(342\) | 405.310 | − | 702.017i | 0.0640838 | − | 0.110996i | ||||
\(343\) | − | 5941.75i | − | 0.935347i | ||||||
\(344\) | 433.651 | + | 250.369i | 0.0679677 | + | 0.0392412i | ||||
\(345\) | 2152.20 | + | 1242.57i | 0.335856 | + | 0.193907i | ||||
\(346\) | 177.835i | 0.0276314i | ||||||||
\(347\) | −37.8982 | + | 65.6415i | −0.00586305 | + | 0.0101551i | −0.868942 | − | 0.494914i | \(-0.835200\pi\) |
0.863079 | + | 0.505069i | \(0.168533\pi\) | |||||||
\(348\) | −3667.07 | − | 6351.56i | −0.564873 | − | 0.978389i | ||||
\(349\) | −3188.78 | + | 1841.04i | −0.489088 | + | 0.282375i | −0.724196 | − | 0.689594i | \(-0.757789\pi\) |
0.235108 | + | 0.971969i | \(0.424456\pi\) | |||||||
\(350\) | −521.747 | −0.0796816 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3345.69 | −0.506607 | ||||||||
\(353\) | −8687.58 | + | 5015.77i | −1.30990 | + | 0.756268i | −0.982078 | − | 0.188473i | \(-0.939646\pi\) |
−0.327817 | + | 0.944741i | \(0.606313\pi\) | |||||||
\(354\) | −405.336 | − | 702.063i | −0.0608570 | − | 0.105407i | ||||
\(355\) | 1951.04 | − | 3379.30i | 0.291692 | − | 0.505225i | ||||
\(356\) | − | 3537.75i | − | 0.526687i | ||||||
\(357\) | −5286.16 | − | 3051.97i | −0.783678 | − | 0.452457i | ||||
\(358\) | −460.893 | − | 266.097i | −0.0680417 | − | 0.0392839i | ||||
\(359\) | − | 6869.76i | − | 1.00995i | −0.863134 | − | 0.504975i | \(-0.831502\pi\) | ||
0.863134 | − | 0.504975i | \(-0.168498\pi\) | |||||||
\(360\) | −324.814 | + | 562.594i | −0.0475533 | + | 0.0823647i | ||||
\(361\) | 7631.83 | + | 13218.7i | 1.11267 | + | 1.92721i | ||||
\(362\) | −684.520 | + | 395.208i | −0.0993856 | + | 0.0573803i | ||||
\(363\) | −2775.34 | −0.401288 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7936.59 | 1.13814 | ||||||||
\(366\) | 49.1304 | − | 28.3654i | 0.00701663 | − | 0.00405105i | ||||
\(367\) | −4441.64 | − | 7693.15i | −0.631749 | − | 1.09422i | −0.987194 | − | 0.159524i | \(-0.949004\pi\) |
0.355445 | − | 0.934697i | \(-0.384329\pi\) | |||||||
\(368\) | −2763.02 | + | 4785.68i | −0.391392 | + | 0.677910i | ||||
\(369\) | − | 1339.94i | − | 0.189037i | ||||||
\(370\) | −377.189 | − | 217.770i | −0.0529977 | − | 0.0305982i | ||||
\(371\) | 8353.95 | + | 4823.15i | 1.16904 | + | 0.674948i | ||||
\(372\) | 884.732i | 0.123310i | ||||||||
\(373\) | 2727.25 | − | 4723.73i | 0.378583 | − | 0.655725i | −0.612273 | − | 0.790646i | \(-0.709745\pi\) |
0.990856 | + | 0.134921i | \(0.0430780\pi\) | |||||||
\(374\) | −773.348 | − | 1339.48i | −0.106922 | − | 0.185195i | ||||
\(375\) | −4547.95 | + | 2625.76i | −0.626281 | + | 0.361584i | ||||
\(376\) | −583.487 | −0.0800294 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1127.60 | 0.153433 | ||||||||
\(379\) | −5752.27 | + | 3321.07i | −0.779615 | + | 0.450111i | −0.836294 | − | 0.548281i | \(-0.815282\pi\) |
0.0566786 | + | 0.998392i | \(0.481949\pi\) | |||||||
\(380\) | −4389.69 | − | 7603.16i | −0.592595 | − | 1.02640i | ||||
\(381\) | −2123.73 | + | 3678.41i | −0.285570 | + | 0.494621i | ||||
\(382\) | − | 843.064i | − | 0.112919i | ||||||
\(383\) | 1093.21 | + | 631.167i | 0.145850 | + | 0.0842066i | 0.571149 | − | 0.820846i | \(-0.306498\pi\) |
−0.425299 | + | 0.905053i | \(0.639831\pi\) | |||||||
\(384\) | 2380.16 | + | 1374.18i | 0.316307 | + | 0.182620i | ||||
\(385\) | 6736.24i | 0.891716i | ||||||||
\(386\) | −235.605 | + | 408.081i | −0.0310674 | + | 0.0538102i | ||||
\(387\) | 565.748 | + | 979.905i | 0.0743116 | + | 0.128712i | ||||
\(388\) | 1575.02 | − | 909.336i | 0.206081 | − | 0.118981i | ||||
\(389\) | 2793.42 | 0.364093 | 0.182046 | − | 0.983290i | \(-0.441728\pi\) | ||||
0.182046 | + | 0.983290i | \(0.441728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7919.62 | −1.02433 | ||||||||
\(392\) | 208.758 | − | 120.527i | 0.0268977 | − | 0.0155294i | ||||
\(393\) | −1399.35 | − | 2423.75i | −0.179613 | − | 0.311099i | ||||
\(394\) | −961.002 | + | 1664.50i | −0.122880 | + | 0.212834i | ||||
\(395\) | 2413.15i | 0.307390i | ||||||||
\(396\) | −4350.91 | − | 2512.00i | −0.552125 | − | 0.318770i | ||||
\(397\) | −5931.33 | − | 3424.45i | −0.749836 | − | 0.432918i | 0.0757988 | − | 0.997123i | \(-0.475849\pi\) |
−0.825635 | + | 0.564205i | \(0.809183\pi\) | |||||||
\(398\) | 393.803i | 0.0495969i | ||||||||
\(399\) | −5246.65 | + | 9087.46i | −0.658298 | + | 1.14021i | ||||
\(400\) | −2065.55 | − | 3577.65i | −0.258194 | − | 0.447206i | ||||
\(401\) | 9547.50 | − | 5512.25i | 1.18898 | − | 0.686456i | 0.230903 | − | 0.972977i | \(-0.425832\pi\) |
0.958074 | + | 0.286521i | \(0.0924988\pi\) | |||||||
\(402\) | 846.518 | 0.105026 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4474.24 | −0.550994 | ||||||||
\(405\) | 1020.26 | − | 589.046i | 0.125178 | − | 0.0722714i | ||||
\(406\) | 987.013 | + | 1709.56i | 0.120652 | + | 0.208975i | ||||
\(407\) | 3400.99 | − | 5890.68i | 0.414203 | − | 0.717421i | ||||
\(408\) | 1930.84i | 0.234291i | ||||||||
\(409\) | 3057.55 | + | 1765.28i | 0.369648 | + | 0.213417i | 0.673305 | − | 0.739365i | \(-0.264874\pi\) |
−0.303656 | + | 0.952782i | \(0.598207\pi\) | |||||||
\(410\) | 243.725 | + | 140.715i | 0.0293578 | + | 0.0169497i | ||||
\(411\) | − | 9178.03i | − | 1.10151i | ||||||
\(412\) | 3804.43 | − | 6589.46i | 0.454929 | − | 0.787960i | ||||
\(413\) | −5625.76 | − | 9744.11i | −0.670280 | − | 1.16096i | ||||
\(414\) | 432.033 | − | 249.434i | 0.0512881 | − | 0.0296112i | ||||
\(415\) | −244.325 | −0.0288998 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1033.51 | −0.121370 | ||||||||
\(418\) | −2302.70 | + | 1329.47i | −0.269447 | + | 0.155565i | ||||
\(419\) | 2089.61 | + | 3619.31i | 0.243637 | + | 0.421992i | 0.961748 | − | 0.273937i | \(-0.0883260\pi\) |
−0.718110 | + | 0.695929i | \(0.754993\pi\) | |||||||
\(420\) | 2082.13 | − | 3606.36i | 0.241899 | − | 0.418981i | ||||
\(421\) | 6209.31i | 0.718820i | 0.933180 | + | 0.359410i | \(0.117022\pi\) | ||||
−0.933180 | + | 0.359410i | \(0.882978\pi\) | |||||||
\(422\) | −1659.29 | − | 957.990i | −0.191405 | − | 0.110508i | ||||
\(423\) | −1141.84 | − | 659.242i | −0.131249 | − | 0.0757765i | ||||
\(424\) | − | 3051.39i | − | 0.349501i | ||||||
\(425\) | 2960.24 | − | 5127.29i | 0.337866 | − | 0.585201i | ||||
\(426\) | 365.284 | + | 632.690i | 0.0415447 | + | 0.0719576i | ||||
\(427\) | 681.893 | − | 393.691i | 0.0772812 | − | 0.0446183i | ||||
\(428\) | −2693.03 | −0.304141 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −237.650 | −0.0266523 | ||||||||
\(431\) | 10288.6 | − | 5940.11i | 1.14985 | − | 0.663864i | 0.200996 | − | 0.979592i | \(-0.435582\pi\) |
0.948850 | + | 0.315729i | \(0.102249\pi\) | |||||||
\(432\) | 4464.08 | + | 7732.01i | 0.497172 | + | 0.861126i | ||||
\(433\) | 4362.86 | − | 7556.69i | 0.484216 | − | 0.838686i | −0.515620 | − | 0.856818i | \(-0.672438\pi\) |
0.999836 | + | 0.0181311i | \(0.00577161\pi\) | |||||||
\(434\) | − | 238.130i | − | 0.0263378i | ||||||
\(435\) | 6087.35 | + | 3514.53i | 0.670956 | + | 0.387377i | ||||
\(436\) | 565.216 | + | 326.328i | 0.0620847 | + | 0.0358446i | ||||
\(437\) | 13614.7i | 1.49034i | ||||||||
\(438\) | −742.964 | + | 1286.85i | −0.0810507 | + | 0.140384i | ||||
\(439\) | −600.187 | − | 1039.55i | −0.0652514 | − | 0.113019i | 0.831554 | − | 0.555444i | \(-0.187452\pi\) |
−0.896805 | + | 0.442425i | \(0.854118\pi\) | |||||||
\(440\) | 1845.37 | − | 1065.43i | 0.199943 | − | 0.115437i | ||||
\(441\) | 544.699 | 0.0588165 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2258.86 | 0.242261 | 0.121130 | − | 0.992637i | \(-0.461348\pi\) | ||||
0.121130 | + | 0.992637i | \(0.461348\pi\) | |||||||
\(444\) | −3641.55 | + | 2102.45i | −0.389235 | + | 0.224725i | ||||
\(445\) | 1695.30 | + | 2936.34i | 0.180595 | + | 0.312800i | ||||
\(446\) | 266.171 | − | 461.022i | 0.0282591 | − | 0.0489463i | ||||
\(447\) | 8497.62i | 0.899158i | ||||||||
\(448\) | 7692.60 | + | 4441.33i | 0.811253 | + | 0.468377i | ||||
\(449\) | −12698.0 | − | 7331.22i | −1.33465 | − | 0.770561i | −0.348642 | − | 0.937256i | \(-0.613357\pi\) |
−0.986008 | + | 0.166695i | \(0.946690\pi\) | |||||||
\(450\) | 372.941i | 0.0390680i | ||||||||
\(451\) | −2197.58 | + | 3806.32i | −0.229446 | + | 0.397412i | ||||
\(452\) | 8303.69 | + | 14382.4i | 0.864099 | + | 1.49666i | ||||
\(453\) | 516.294 | − | 298.082i | 0.0535488 | − | 0.0309164i | ||||
\(454\) | −1626.73 | −0.168164 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3319.31 | 0.340879 | ||||||||
\(457\) | 8084.29 | − | 4667.47i | 0.827500 | − | 0.477757i | −0.0254962 | − | 0.999675i | \(-0.508117\pi\) |
0.852996 | + | 0.521918i | \(0.174783\pi\) | |||||||
\(458\) | −684.046 | − | 1184.80i | −0.0697891 | − | 0.120878i | ||||
\(459\) | −6397.68 | + | 11081.1i | −0.650585 | + | 1.12685i | ||||
\(460\) | − | 5402.97i | − | 0.547641i | ||||||
\(461\) | −9298.39 | − | 5368.43i | −0.939413 | − | 0.542370i | −0.0496365 | − | 0.998767i | \(-0.515806\pi\) |
−0.889776 | + | 0.456397i | \(0.849140\pi\) | |||||||
\(462\) | −1092.23 | − | 630.597i | −0.109989 | − | 0.0635022i | ||||
\(463\) | − | 10650.0i | − | 1.06900i | −0.845168 | − | 0.534501i | \(-0.820499\pi\) | ||
0.845168 | − | 0.534501i | \(-0.179501\pi\) | |||||||
\(464\) | −7815.01 | + | 13536.0i | −0.781902 | + | 1.35429i | ||||
\(465\) | −423.965 | − | 734.328i | −0.0422815 | − | 0.0732337i | ||||
\(466\) | −192.660 | + | 111.232i | −0.0191519 | + | 0.0110574i | ||||
\(467\) | 2638.11 | 0.261407 | 0.130703 | − | 0.991422i | \(-0.458276\pi\) | ||||
0.130703 | + | 0.991422i | \(0.458276\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11749.0 | 1.15676 | ||||||||
\(470\) | 239.822 | − | 138.461i | 0.0235365 | − | 0.0135888i | ||||
\(471\) | 5587.26 | + | 9677.43i | 0.546598 | + | 0.946735i | ||||
\(472\) | −1779.58 | + | 3082.32i | −0.173542 | + | 0.300584i | ||||
\(473\) | − | 3711.45i | − | 0.360787i | ||||||
\(474\) | −391.273 | − | 225.901i | −0.0379151 | − | 0.0218903i | ||||
\(475\) | −8814.35 | − | 5088.97i | −0.851432 | − | 0.491575i | ||||
\(476\) | 13270.6i | 1.27785i | ||||||||
\(477\) | 3447.55 | − | 5971.34i | 0.330928 | − | 0.573184i | ||||
\(478\) | 45.0693 | + | 78.0623i | 0.00431260 | + | 0.00746964i | ||||
\(479\) | 2793.20 | − | 1612.66i | 0.266440 | − | 0.153829i | −0.360829 | − | 0.932632i | \(-0.617506\pi\) |
0.627269 | + | 0.778803i | \(0.284173\pi\) | |||||||
\(480\) | −1982.23 | −0.188491 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1204.87 | 0.113860 | ||||||||
\(483\) | −5592.57 | + | 3228.87i | −0.526855 | + | 0.304180i | ||||
\(484\) | 3016.94 | + | 5225.50i | 0.283334 | + | 0.490749i | ||||
\(485\) | −871.510 | + | 1509.50i | −0.0815943 | + | 0.141325i | ||||
\(486\) | − | 1337.17i | − | 0.124805i | ||||||
\(487\) | 1295.91 | + | 748.196i | 0.120582 | + | 0.0696181i | 0.559078 | − | 0.829115i | \(-0.311155\pi\) |
−0.438496 | + | 0.898733i | \(0.644489\pi\) | |||||||
\(488\) | −215.701 | − | 124.535i | −0.0200089 | − | 0.0115521i | ||||
\(489\) | 1080.41i | 0.0999137i | ||||||||
\(490\) | −57.2019 | + | 99.0766i | −0.00527371 | + | 0.00913434i | ||||
\(491\) | −259.204 | − | 448.955i | −0.0238243 | − | 0.0412648i | 0.853867 | − | 0.520491i | \(-0.174251\pi\) |
−0.877692 | + | 0.479226i | \(0.840918\pi\) | |||||||
\(492\) | 2353.02 | − | 1358.52i | 0.215615 | − | 0.124485i | ||||
\(493\) | −22400.1 | −2.04635 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4815.01 | 0.437210 | ||||||||
\(496\) | 1632.87 | − | 942.739i | 0.147819 | − | 0.0853432i | ||||
\(497\) | 5069.86 | + | 8781.26i | 0.457574 | + | 0.792542i | ||||
\(498\) | 22.8719 | − | 39.6152i | 0.00205806 | − | 0.00356466i | ||||
\(499\) | − | 2405.01i | − | 0.215757i | −0.994164 | − | 0.107879i | \(-0.965594\pi\) | ||
0.994164 | − | 0.107879i | \(-0.0344058\pi\) | |||||||
\(500\) | 9887.75 | + | 5708.69i | 0.884387 | + | 0.510601i | ||||
\(501\) | 9394.36 | + | 5423.83i | 0.837742 | + | 0.483671i | ||||
\(502\) | − | 954.080i | − | 0.0848260i | ||||||
\(503\) | −1206.88 | + | 2090.38i | −0.106983 | + | 0.185299i | −0.914546 | − | 0.404481i | \(-0.867452\pi\) |
0.807564 | + | 0.589780i | \(0.200786\pi\) | |||||||
\(504\) | −844.041 | − | 1461.92i | −0.0745964 | − | 0.129205i | ||||
\(505\) | 3713.62 | − | 2144.06i | 0.327235 | − | 0.188929i | ||||
\(506\) | −1636.35 | −0.143764 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9234.45 | 0.806520 | ||||||||
\(509\) | 13577.8 | − | 7839.15i | 1.18237 | − | 0.682641i | 0.225807 | − | 0.974172i | \(-0.427498\pi\) |
0.956561 | + | 0.291531i | \(0.0941647\pi\) | |||||||
\(510\) | −458.187 | − | 793.604i | −0.0397821 | − | 0.0689046i | ||||
\(511\) | −10311.8 | + | 17860.5i | −0.892693 | + | 1.54619i | ||||
\(512\) | − | 7393.65i | − | 0.638196i | ||||||
\(513\) | 19049.6 | + | 10998.3i | 1.63949 | + | 0.946562i | ||||
\(514\) | −1106.12 | − | 638.618i | −0.0949198 | − | 0.0548020i | ||||
\(515\) | 7292.34i | 0.623959i | ||||||||
\(516\) | −1147.18 | + | 1986.98i | −0.0978721 | + | 0.169519i | ||||
\(517\) | 2162.39 | + | 3745.37i | 0.183950 | + | 0.318610i | ||||
\(518\) | 980.142 | − | 565.885i | 0.0831370 | − | 0.0479992i | ||||
\(519\) | −1645.48 | −0.139168 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11691.5 | −0.983135 | −0.491568 | − | 0.870839i | \(-0.663576\pi\) | ||||
−0.491568 | + | 0.870839i | \(0.663576\pi\) | |||||||
\(522\) | 1221.98 | − | 705.509i | 0.102461 | − | 0.0591557i | ||||
\(523\) | 1939.48 | + | 3359.27i | 0.162156 | + | 0.280862i | 0.935642 | − | 0.352952i | \(-0.114822\pi\) |
−0.773486 | + | 0.633814i | \(0.781489\pi\) | |||||||
\(524\) | −3042.35 | + | 5269.50i | −0.253637 | + | 0.439311i | ||||
\(525\) | − | 4827.63i | − | 0.401324i | ||||||
\(526\) | −1564.67 | − | 903.365i | −0.129702 | − | 0.0748833i | ||||
\(527\) | 2340.15 | + | 1351.08i | 0.193431 | + | 0.111678i | ||||
\(528\) | − | 9985.92i | − | 0.823071i | ||||||
\(529\) | 1894.16 | − | 3280.78i | 0.155680 | − | 0.269646i | ||||
\(530\) | 724.093 | + | 1254.17i | 0.0593445 | + | 0.102788i | ||||
\(531\) | −6965.01 | + | 4021.25i | −0.569220 | + | 0.328639i | ||||
\(532\) | 22813.6 | 1.85920 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −634.804 | −0.0514431 | ||||||||
\(535\) | 2235.21 | − | 1290.50i | 0.180629 | − | 0.104286i | ||||
\(536\) | −1858.27 | − | 3218.61i | −0.149748 | − | 0.259371i | ||||
\(537\) | 2462.14 | − | 4264.56i | 0.197857 | − | 0.342699i | ||||
\(538\) | 1107.35i | 0.0887382i | ||||||||
\(539\) | −1547.31 | − | 893.340i | −0.123650 | − | 0.0713894i | ||||
\(540\) | −7559.83 | − | 4364.67i | −0.602450 | − | 0.347825i | ||||
\(541\) | 16353.0i | 1.29958i | 0.760115 | + | 0.649788i | \(0.225142\pi\) | ||||
−0.760115 | + | 0.649788i | \(0.774858\pi\) | |||||||
\(542\) | −1375.61 | + | 2382.62i | −0.109017 | + | 0.188824i | ||||
\(543\) | −3656.79 | − | 6333.75i | −0.289002 | − | 0.500565i | ||||
\(544\) | 5470.63 | − | 3158.47i | 0.431160 | − | 0.248930i | ||||
\(545\) | −625.506 | −0.0491628 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2748.67 | 0.214853 | 0.107426 | − | 0.994213i | \(-0.465739\pi\) | ||||
0.107426 | + | 0.994213i | \(0.465739\pi\) | |||||||
\(548\) | −17280.7 | + | 9977.02i | −1.34707 | + | 0.777732i | ||||
\(549\) | −281.407 | − | 487.411i | −0.0218764 | − | 0.0378911i | ||||
\(550\) | 611.645 | − | 1059.40i | 0.0474193 | − | 0.0821327i | ||||
\(551\) | 38508.1i | 2.97732i | ||||||||
\(552\) | 1769.08 | + | 1021.38i | 0.136408 | + | 0.0787551i | ||||
\(553\) | −5430.57 | − | 3135.34i | −0.417597 | − | 0.241100i | ||||
\(554\) | − | 756.163i | − | 0.0579897i | ||||||
\(555\) | 2014.99 | − | 3490.07i | 0.154111 | − | 0.266928i | ||||
\(556\) | 1123.48 | + | 1945.93i | 0.0856946 | + | 0.148427i | ||||
\(557\) | 14519.4 | − | 8382.81i | 1.10450 | − | 0.637686i | 0.167104 | − | 0.985939i | \(-0.446558\pi\) |
0.937400 | + | 0.348254i | \(0.113225\pi\) | |||||||
\(558\) | −170.214 | −0.0129135 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −8874.58 | −0.669677 | ||||||||
\(561\) | 12394.0 | − | 7155.65i | 0.932750 | − | 0.538524i | ||||
\(562\) | 641.884 | + | 1111.78i | 0.0481784 | + | 0.0834474i | ||||
\(563\) | 9246.21 | − | 16014.9i | 0.692151 | − | 1.19884i | −0.278980 | − | 0.960297i | \(-0.589996\pi\) |
0.971132 | − | 0.238545i | \(-0.0766703\pi\) | |||||||
\(564\) | − | 2673.53i | − | 0.199603i | ||||||
\(565\) | −13784.1 | − | 7958.27i | −1.02638 | − | 0.592579i | ||||
\(566\) | 2675.12 | + | 1544.48i | 0.198664 | + | 0.114699i | ||||
\(567\) | 3061.32i | 0.226743i | ||||||||
\(568\) | 1603.73 | − | 2777.75i | 0.118470 | − | 0.205197i | ||||
\(569\) | 781.639 | + | 1353.84i | 0.0575888 | + | 0.0997467i | 0.893383 | − | 0.449297i | \(-0.148325\pi\) |
−0.835794 | + | 0.549044i | \(0.814992\pi\) | |||||||
\(570\) | −1364.29 | + | 787.672i | −0.100252 | + | 0.0578806i | ||||
\(571\) | −9165.98 | −0.671776 | −0.335888 | − | 0.941902i | \(-0.609036\pi\) | ||||
−0.335888 | + | 0.941902i | \(0.609036\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7800.72 | 0.568726 | ||||||||
\(574\) | −633.329 | + | 365.652i | −0.0460534 | + | 0.0265889i | ||||
\(575\) | −3131.84 | − | 5424.50i | −0.227142 | − | 0.393421i | ||||
\(576\) | 3174.62 | − | 5498.61i | 0.229646 | − | 0.397758i | ||||
\(577\) | − | 18762.5i | − | 1.35372i | −0.736114 | − | 0.676858i | \(-0.763341\pi\) | ||
0.736114 | − | 0.676858i | \(-0.236659\pi\) | |||||||
\(578\) | 869.189 | + | 501.826i | 0.0625493 | + | 0.0361128i | ||||
\(579\) | −3775.90 | − | 2180.02i | −0.271021 | − | 0.156474i | ||||
\(580\) | − | 15281.9i | − | 1.09405i | ||||||
\(581\) | 317.444 | − | 549.829i | 0.0226675 | − | 0.0392612i | ||||
\(582\) | −163.168 | − | 282.616i | −0.0116212 | − | 0.0201285i | ||||
\(583\) | −19586.7 | + | 11308.4i | −1.39142 | + | 0.803337i | ||||
\(584\) | 6523.79 | 0.462254 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2214.07 | 0.156079 | ||||||||
\(587\) | −10952.0 | + | 6323.14i | −0.770080 | + | 0.444606i | −0.832903 | − | 0.553419i | \(-0.813323\pi\) |
0.0628229 | + | 0.998025i | \(0.479990\pi\) | |||||||
\(588\) | 552.252 | + | 956.528i | 0.0387321 | + | 0.0670859i | ||||
\(589\) | 2322.65 | − | 4022.96i | 0.162484 | − | 0.281431i | ||||
\(590\) | − | 1689.18i | − | 0.117868i | ||||||
\(591\) | −15401.4 | − | 8891.98i | −1.07196 | − | 0.618896i | ||||
\(592\) | 7760.60 | + | 4480.59i | 0.538782 | + | 0.311066i | ||||
\(593\) | − | 9662.74i | − | 0.669142i | −0.942371 | − | 0.334571i | \(-0.891409\pi\) | ||
0.942371 | − | 0.334571i | \(-0.108591\pi\) | |||||||
\(594\) | −1321.89 | + | 2289.58i | −0.0913093 | + | 0.158152i | ||||
\(595\) | −6359.29 | − | 11014.6i | −0.438161 | − | 0.758916i | ||||
\(596\) | 15999.6 | − | 9237.37i | 1.09961 | − | 0.634862i | ||||
\(597\) | −3643.79 | −0.249800 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26968.7 | −1.83959 | −0.919794 | − | 0.392402i | \(-0.871644\pi\) | ||||
−0.919794 | + | 0.392402i | \(0.871644\pi\) | |||||||
\(600\) | −1322.52 | + | 763.556i | −0.0899859 | + | 0.0519534i | ||||
\(601\) | −5640.06 | − | 9768.87i | −0.382800 | − | 0.663029i | 0.608661 | − | 0.793430i | \(-0.291707\pi\) |
−0.991461 | + | 0.130401i | \(0.958373\pi\) | |||||||
\(602\) | 308.771 | − | 534.807i | 0.0209046 | − | 0.0362078i | ||||
\(603\) | − | 8398.11i | − | 0.567160i | ||||||
\(604\) | −1122.48 | − | 648.063i | −0.0756175 | − | 0.0436578i | ||||
\(605\) | −5008.13 | − | 2891.45i | −0.336545 | − | 0.194304i | ||||
\(606\) | 802.843i | 0.0538173i | ||||||||
\(607\) | −6026.30 | + | 10437.9i | −0.402965 | + | 0.697957i | −0.994082 | − | 0.108629i | \(-0.965354\pi\) |
0.591117 | + | 0.806586i | \(0.298687\pi\) | |||||||
\(608\) | −5429.73 | − | 9404.58i | −0.362179 | − | 0.627312i | ||||
\(609\) | −15818.2 | + | 9132.66i | −1.05252 | + | 0.607675i | ||||
\(610\) | 118.208 | 0.00784610 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 9485.73 | 0.626532 | ||||||||
\(613\) | −9751.17 | + | 5629.84i | −0.642489 | + | 0.370941i | −0.785573 | − | 0.618769i | \(-0.787632\pi\) |
0.143083 | + | 0.989711i | \(0.454298\pi\) | |||||||
\(614\) | 846.327 | + | 1465.88i | 0.0556270 | + | 0.0963488i | ||||
\(615\) | −1302.01 | + | 2255.14i | −0.0853691 | + | 0.147864i | ||||
\(616\) | 5537.12i | 0.362170i | ||||||||
\(617\) | −20835.0 | − | 12029.1i | −1.35946 | − | 0.784882i | −0.369906 | − | 0.929069i | \(-0.620610\pi\) |
−0.989550 | + | 0.144187i | \(0.953943\pi\) | |||||||
\(618\) | −1182.39 | − | 682.655i | −0.0769625 | − | 0.0444343i | ||||
\(619\) | − | 2793.41i | − | 0.181384i | −0.995879 | − | 0.0906919i | \(-0.971092\pi\) | ||
0.995879 | − | 0.0906919i | \(-0.0289079\pi\) | |||||||
\(620\) | −921.745 | + | 1596.51i | −0.0597067 | + | 0.103415i | ||||
\(621\) | 6768.53 | + | 11723.4i | 0.437378 | + | 0.757561i | ||||
\(622\) | −1768.56 | + | 1021.08i | −0.114008 | + | 0.0658223i | ||||
\(623\) | −8810.59 | −0.566595 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2388.81 | −0.152884 | ||||||||
\(626\) | −732.410 | + | 422.857i | −0.0467619 | + | 0.0269980i | ||||
\(627\) | −12301.3 | − | 21306.5i | −0.783520 | − | 1.35710i | ||||
\(628\) | 12147.3 | − | 21039.8i | 0.771864 | − | 1.33691i | ||||
\(629\) | 12842.7i | 0.814104i | ||||||||
\(630\) | 693.827 | + | 400.581i | 0.0438774 | + | 0.0253326i | ||||
\(631\) | 21520.7 | + | 12425.0i | 1.35773 | + | 0.783883i | 0.989317 | − | 0.145780i | \(-0.0465693\pi\) |
0.368409 | + | 0.929664i | \(0.379903\pi\) | |||||||
\(632\) | 1983.59i | 0.124846i | ||||||||
\(633\) | 8864.11 | − | 15353.1i | 0.556583 | − | 0.964030i | ||||
\(634\) | 948.703 | + | 1643.20i | 0.0594287 | + | 0.102934i | ||||
\(635\) | −7664.60 | + | 4425.16i | −0.478993 | + | 0.276547i | ||||
\(636\) | 13981.4 | 0.871696 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4628.31 | −0.287205 | ||||||||
\(639\) | 6276.77 | − | 3623.90i | 0.388584 | − | 0.224349i | ||||
\(640\) | 2863.35 | + | 4959.46i | 0.176850 | + | 0.306312i | ||||
\(641\) | −3897.35 | + | 6750.41i | −0.240150 | + | 0.415952i | −0.960757 | − | 0.277392i | \(-0.910530\pi\) |
0.720607 | + | 0.693344i | \(0.243863\pi\) | |||||||
\(642\) | 483.228i | 0.0297064i | ||||||||
\(643\) | 23997.5 | + | 13854.9i | 1.47180 | + | 0.849744i | 0.999498 | − | 0.0316924i | \(-0.0100897\pi\) |
0.472302 | + | 0.881437i | \(0.343423\pi\) | |||||||
\(644\) | 12158.9 | + | 7019.92i | 0.743985 | + | 0.429540i | ||||
\(645\) | − | 2198.93i | − | 0.134237i | ||||||
\(646\) | 2510.14 | − | 4347.69i | 0.152880 | − | 0.264795i | ||||
\(647\) | 5575.47 | + | 9656.99i | 0.338786 | + | 0.586794i | 0.984205 | − | 0.177035i | \(-0.0566505\pi\) |
−0.645419 | + | 0.763829i | \(0.723317\pi\) | |||||||
\(648\) | 838.640 | − | 484.189i | 0.0508409 | − | 0.0293530i | ||||
\(649\) | 26380.4 | 1.59556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2203.38 | 0.132653 | ||||||||
\(652\) | 2034.23 | − | 1174.46i | 0.122188 | − | 0.0705453i | ||||
\(653\) | −14568.7 | − | 25233.8i | −0.873077 | − | 1.51221i | −0.858797 | − | 0.512315i | \(-0.828788\pi\) |
−0.0142794 | − | 0.999898i | \(-0.504545\pi\) | |||||||
\(654\) | 58.5552 | − | 101.421i | 0.00350106 | − | 0.00606401i | ||||
\(655\) | − | 5831.58i | − | 0.347876i | ||||||
\(656\) | −5014.59 | − | 2895.18i | −0.298456 | − | 0.172314i | ||||
\(657\) | 12766.6 | + | 7370.78i | 0.758099 | + | 0.437689i | ||||
\(658\) | 719.595i | 0.0426333i | ||||||||
\(659\) | 2650.06 | − | 4590.04i | 0.156649 | − | 0.271324i | −0.777009 | − | 0.629489i | \(-0.783264\pi\) |
0.933658 | + | 0.358165i | \(0.116598\pi\) | |||||||
\(660\) | 4881.77 | + | 8455.48i | 0.287913 | + | 0.498680i | ||||
\(661\) | −23739.9 | + | 13706.3i | −1.39694 | + | 0.806523i | −0.994071 | − | 0.108735i | \(-0.965320\pi\) |
−0.402868 | + | 0.915258i | \(0.631987\pi\) | |||||||
\(662\) | 1047.56 | 0.0615025 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −200.832 | −0.0117377 | ||||||||
\(665\) | −18935.3 | + | 10932.3i | −1.10418 | + | 0.637497i | ||||
\(666\) | −404.490 | − | 700.598i | −0.0235341 | − | 0.0407622i | ||||
\(667\) | −11849.3 | + | 20523.5i | −0.687865 | + | 1.19142i | ||||
\(668\) | − | 23584.0i | − | 1.36601i | ||||||
\(669\) | 4265.76 | + | 2462.84i | 0.246523 | + | 0.142330i | ||||
\(670\) | 1527.55 | + | 881.933i | 0.0880813 | + | 0.0508538i | ||||
\(671\) | 1846.10i | 0.106211i | ||||||||
\(672\) | 2575.45 | − | 4460.81i | 0.147842 | − | 0.256071i | ||||
\(673\) | −10641.0 | − | 18430.8i | −0.609482 | − | 1.05565i | −0.991326 | − | 0.131427i | \(-0.958044\pi\) |
0.381844 | − | 0.924227i | \(-0.375289\pi\) | |||||||
\(674\) | −2202.22 | + | 1271.46i | −0.125855 | + | 0.0726626i | ||||
\(675\) | −10119.9 | −0.577061 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13544.2 | −0.768904 | −0.384452 | − | 0.923145i | \(-0.625610\pi\) | ||||
−0.384452 | + | 0.923145i | \(0.625610\pi\) | |||||||
\(678\) | 2580.74 | − | 1489.99i | 0.146184 | − | 0.0843992i | ||||
\(679\) | −2264.65 | − | 3922.49i | −0.127996 | − | 0.221696i | ||||
\(680\) | −2011.62 | + | 3484.22i | −0.113444 | + | 0.196491i | ||||
\(681\) | − | 15051.9i | − | 0.846974i | ||||||
\(682\) | 483.521 | + | 279.161i | 0.0271480 | + | 0.0156739i | ||||
\(683\) | −8963.48 | − | 5175.06i | −0.502164 | − | 0.289924i | 0.227443 | − | 0.973791i | \(-0.426963\pi\) |
−0.729607 | + | 0.683867i | \(0.760297\pi\) | |||||||
\(684\) | − | 16307.0i | − | 0.911567i | ||||||
\(685\) | 9562.00 | − | 16561.9i | 0.533350 | − | 0.923790i | ||||
\(686\) | 1158.98 | + | 2007.42i | 0.0645046 | + | 0.111725i | ||||
\(687\) | 10962.8 | − | 6329.36i | 0.608815 | − | 0.351499i | ||||
\(688\) | 4889.60 | 0.270951 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −969.492 | −0.0534898 | ||||||||
\(691\) | 22269.7 | − | 12857.4i | 1.22602 | − | 0.707843i | 0.259825 | − | 0.965656i | \(-0.416335\pi\) |
0.966195 | + | 0.257813i | \(0.0830019\pi\) | |||||||
\(692\) | 1788.72 | + | 3098.16i | 0.0982617 | + | 0.170194i | ||||
\(693\) | −6256.00 | + | 10835.7i | −0.342923 | + | 0.593961i | ||||
\(694\) | − | 29.5693i | − | 0.00161734i | ||||||
\(695\) | −1864.98 | − | 1076.75i | −0.101788 | − | 0.0587674i | ||||
\(696\) | 5003.73 | + | 2888.91i | 0.272509 | + | 0.157333i | ||||
\(697\) | − | 8298.43i | − | 0.450969i | ||||||
\(698\) | 718.219 | − | 1243.99i | 0.0389470 | − | 0.0674582i | ||||
\(699\) | −1029.21 | − | 1782.65i | −0.0556915 | − | 0.0964605i | ||||
\(700\) | −9089.63 | + | 5247.90i | −0.490794 | + | 0.283360i | ||||
\(701\) | −7431.30 | −0.400394 | −0.200197 | − | 0.979756i | \(-0.564158\pi\) | ||||
−0.200197 | + | 0.979756i | \(0.564158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22077.9 | 1.18447 | ||||||||
\(704\) | −18036.1 | + | 10413.2i | −0.965570 | + | 0.557472i | ||||
\(705\) | 1281.16 | + | 2219.03i | 0.0684414 | + | 0.118544i | ||||
\(706\) | 1956.73 | − | 3389.16i | 0.104310 | − | 0.180669i | ||||
\(707\) | 11142.8i | 0.592744i | ||||||||
\(708\) | −14123.2 | − | 8154.01i | −0.749690 | − | 0.432834i | ||||
\(709\) | 17309.1 | + | 9993.40i | 0.916863 | + | 0.529351i | 0.882633 | − | 0.470063i | \(-0.155769\pi\) |
0.0342303 | + | 0.999414i | \(0.489102\pi\) | |||||||
\(710\) | 1522.26i | 0.0804641i | ||||||||
\(711\) | −2241.12 | + | 3881.73i | −0.118212 | + | 0.204748i | ||||
\(712\) | 1393.51 | + | 2413.64i | 0.0733485 | + | 0.127043i | ||||
\(713\) | 2475.79 | − | 1429.40i | 0.130041 | − | 0.0750792i | ||||
\(714\) | 2381.24 | 0.124812 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10705.9 | −0.558798 | ||||||||
\(717\) | −722.297 | + | 417.018i | −0.0376216 | + | 0.0217208i | ||||
\(718\) | 1340.00 | + | 2320.95i | 0.0696495 | + | 0.120636i | ||||
\(719\) | 18050.9 | − | 31265.1i | 0.936281 | − | 1.62169i | 0.163948 | − | 0.986469i | \(-0.447577\pi\) |
0.772333 | − | 0.635218i | \(-0.219090\pi\) | |||||||
\(720\) | 6343.48i | 0.328344i | ||||||||
\(721\) | −16410.7 | − | 9474.73i | −0.847665 | − | 0.489400i | ||||
\(722\) | −5156.82 | − | 2977.29i | −0.265813 | − | 0.153467i | ||||
\(723\) | 11148.4i | 0.573465i | ||||||||
\(724\) | −7950.26 | + | 13770.2i | −0.408106 | + | 0.706861i | ||||
\(725\) | −8858.19 | − | 15342.8i | −0.453772 | − | 0.785957i | ||||
\(726\) | 937.648 | − | 541.351i | 0.0479330 | − | 0.0276741i | ||||
\(727\) | 1751.90 | 0.0893735 | 0.0446868 | − | 0.999001i | \(-0.485771\pi\) | ||||
0.0446868 | + | 0.999001i | \(0.485771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16601.6 | 0.843451 | ||||||||
\(730\) | −2681.37 | + | 1548.09i | −0.135948 | + | 0.0784897i | ||||
\(731\) | 3503.76 | + | 6068.69i | 0.177279 | + | 0.307057i | ||||
\(732\) | 570.618 | − | 988.339i | 0.0288123 | − | 0.0499044i | ||||
\(733\) | 20031.3i | 1.00938i | 0.863302 | + | 0.504688i | \(0.168393\pi\) | ||||
−0.863302 | + | 0.504688i | \(0.831607\pi\) | |||||||
\(734\) | 3001.22 | + | 1732.75i | 0.150922 | + | 0.0871350i | ||||
\(735\) | −916.738 | − | 529.279i | −0.0460060 | − | 0.0265616i | ||||
\(736\) | − | 6683.10i | − | 0.334704i | ||||||
\(737\) | −13773.4 | + | 23856.2i | −0.688399 | + | 1.19234i | ||||
\(738\) | 261.366 | + | 452.698i | 0.0130366 | + | 0.0225800i | ||||
\(739\) | 16136.6 | − | 9316.47i | 0.803240 | − | 0.463751i | −0.0413627 | − | 0.999144i | \(-0.513170\pi\) |
0.844603 | + | 0.535393i | \(0.179837\pi\) | |||||||
\(740\) | −8761.62 | −0.435248 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3763.17 | −0.186187 | ||||||||
\(743\) | −4250.19 | + | 2453.85i | −0.209858 | + | 0.121161i | −0.601245 | − | 0.799065i | \(-0.705329\pi\) |
0.391388 | + | 0.920226i | \(0.371995\pi\) | |||||||
\(744\) | −348.494 | − | 603.610i | −0.0171726 | − | 0.0297438i | ||||
\(745\) | −8853.12 | + | 15334.1i | −0.435373 | + | 0.754089i | ||||
\(746\) | 2127.88i | 0.104433i | ||||||||
\(747\) | −393.014 | − | 226.906i | −0.0192498 | − | 0.0111139i | ||||
\(748\) | −26945.8 | − | 15557.2i | −1.31716 | − | 0.760463i | ||||
\(749\) | 6706.84i | 0.327186i | ||||||||
\(750\) | 1024.35 | − | 1774.23i | 0.0498720 | − | 0.0863808i | ||||
\(751\) | 15578.4 | + | 26982.7i | 0.756945 | + | 1.31107i | 0.944402 | + | 0.328794i | \(0.106642\pi\) |
−0.187457 | + | 0.982273i | \(0.560024\pi\) | |||||||
\(752\) | −4934.30 | + | 2848.82i | −0.239276 | + | 0.138146i | ||||
\(753\) | 8827.93 | 0.427235 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1242.21 | 0.0598790 | ||||||||
\(756\) | 19644.5 | − | 11341.8i | 0.945058 | − | 0.545630i | ||||
\(757\) | 5523.49 | + | 9566.97i | 0.265198 | + | 0.459336i | 0.967615 | − | 0.252429i | \(-0.0812294\pi\) |
−0.702418 | + | 0.711765i | \(0.747896\pi\) | |||||||
\(758\) | 1295.60 | − | 2244.05i | 0.0620823 | − | 0.107530i | ||||
\(759\) | − | 15140.9i | − | 0.724082i | ||||||
\(760\) | 5989.74 | + | 3458.18i | 0.285882 | + | 0.165054i | ||||
\(761\) | −23907.6 | − | 13803.0i | −1.13883 | − | 0.657503i | −0.192688 | − | 0.981260i | \(-0.561721\pi\) |
−0.946140 | + | 0.323757i | \(0.895054\pi\) | |||||||
\(762\) | − | 1657.00i | − | 0.0787753i | ||||||
\(763\) | 812.702 | − | 1407.64i | 0.0385607 | − | 0.0667890i | ||||
\(764\) | −8479.81 | − | 14687.5i | −0.401556 | − | 0.695515i | ||||
\(765\) | −7873.16 | + | 4545.57i | −0.372098 | + | 0.214831i | ||||
\(766\) | −492.456 | −0.0232287 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 12052.1 | 0.566264 | ||||||||
\(769\) | 3199.72 | − | 1847.36i | 0.150045 | − | 0.0866287i | −0.423098 | − | 0.906084i | \(-0.639057\pi\) |
0.573143 | + | 0.819455i | \(0.305724\pi\) | |||||||
\(770\) | −1313.96 | − | 2275.84i | −0.0614957 | − | 0.106514i | ||||
\(771\) | 5909.02 | − | 10234.7i | 0.276016 | − | 0.478073i | ||||
\(772\) | 9479.18i | 0.441921i | ||||||||
\(773\) | 17154.2 | + | 9904.01i | 0.798183 | + | 0.460831i | 0.842835 | − | 0.538172i | \(-0.180885\pi\) |
−0.0446525 | + | 0.999003i | \(0.514218\pi\) | |||||||
\(774\) | −382.276 | − | 220.707i | −0.0177527 | − | 0.0102496i | ||||
\(775\) | 2137.16i | 0.0990569i | ||||||||
\(776\) | −716.371 | + | 1240.79i | −0.0331395 | + | 0.0573992i | ||||
\(777\) | 5236.04 | + | 9069.08i | 0.241753 | + | 0.418728i | ||||
\(778\) | −943.757 | + | 544.878i | −0.0434901 | + | 0.0251090i | ||||
\(779\) | −14265.9 | −0.656133 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23773.6 | −1.08923 | ||||||||
\(782\) | 2675.64 | − | 1544.78i | 0.122354 | − | 0.0706411i | ||||
\(783\) | 19144.3 | + | 33159.0i | 0.873771 | + | 1.51342i | ||||
\(784\) | 1176.92 | − | 2038.48i | 0.0536133 | − | 0.0928610i | ||||
\(785\) | 23284.0i | 1.05865i | ||||||||
\(786\) | 945.542 | + | 545.909i | 0.0429089 | + | 0.0247735i | ||||
\(787\) | 3565.24 | + | 2058.39i | 0.161483 | + | 0.0932322i | 0.578564 | − | 0.815637i | \(-0.303613\pi\) |
−0.417081 | + | 0.908869i | \(0.636947\pi\) | |||||||
\(788\) | 38664.3i | 1.74792i | ||||||||
\(789\) | 8358.68 | − | 14477.7i | 0.377157 | − | 0.653255i | ||||
\(790\) | −470.704 | − | 815.284i | −0.0211986 | − | 0.0367171i | ||||
\(791\) | 35818.6 | − | 20679.9i | 1.61007 | − | 0.929574i | ||||
\(792\) | 3957.89 | 0.177572 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2671.86 | 0.119422 | ||||||||
\(795\) | −11604.6 | + | 6699.91i | −0.517701 | + | 0.298895i | ||||
\(796\) | 3961.00 | + | 6860.65i | 0.176374 | + | 0.305489i | ||||
\(797\) | 12679.6 | − | 21961.8i | 0.563533 | − | 0.976068i | −0.433652 | − | 0.901081i | \(-0.642775\pi\) |
0.997185 | − | 0.0749871i | \(-0.0238916\pi\) | |||||||
\(798\) | − | 4093.59i | − | 0.181594i | ||||||
\(799\) | −7071.58 | − | 4082.78i | −0.313109 | − | 0.180774i | ||||
\(800\) | 4326.75 | + | 2498.05i | 0.191217 | + | 0.110399i | ||||
\(801\) | 6297.74i | 0.277802i | ||||||||
\(802\) | −2150.41 | + | 3724.63i | −0.0946805 | + | 0.163991i | ||||
\(803\) | −24177.0 | − | 41875.9i | −1.06250 | − | 1.84031i | ||||
\(804\) | 14747.6 | − | 8514.55i | 0.646902 | − | 0.373489i | ||||
\(805\) | −13455.8 | −0.589137 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10246.1 | −0.446939 | ||||||||
\(808\) | 3052.55 | − | 1762.39i | 0.132906 | − | 0.0767336i | ||||
\(809\) | 2779.37 | + | 4814.00i | 0.120788 | + | 0.209211i | 0.920079 | − | 0.391734i | \(-0.128125\pi\) |
−0.799291 | + | 0.600944i | \(0.794791\pi\) | |||||||
\(810\) | −229.796 | + | 398.018i | −0.00996815 | + | 0.0172653i | ||||
\(811\) | − | 15021.4i | − | 0.650399i | −0.945646 | − | 0.325199i | \(-0.894569\pi\) | ||
0.945646 | − | 0.325199i | \(-0.105431\pi\) | |||||||
\(812\) | 34390.5 | + | 19855.4i | 1.48629 | + | 0.858113i | ||||
\(813\) | −22046.0 | − | 12728.3i | −0.951029 | − | 0.549077i | ||||
\(814\) | 2653.55i | 0.114259i | ||||||||
\(815\) | −1125.61 | + | 1949.61i | −0.0483784 | + | 0.0837938i | ||||
\(816\) | 9427.12 | + | 16328.3i | 0.404431 | + | 0.700494i | ||||
\(817\) | 10432.7 | − | 6023.32i | 0.446749 | − | 0.257931i | ||||
\(818\) | −1377.32 | −0.0588717 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5661.41 | 0.241104 | ||||||||
\(821\) | 13771.2 | − | 7950.78i | 0.585404 | − | 0.337983i | −0.177874 | − | 0.984053i | \(-0.556922\pi\) |
0.763278 | + | 0.646070i | \(0.223589\pi\) | |||||||
\(822\) | 1790.24 | + | 3100.80i | 0.0759635 | + | 0.131573i | ||||
\(823\) | −20139.6 | + | 34882.9i | −0.853006 | + | 1.47745i | 0.0254768 | + | 0.999675i | \(0.491890\pi\) |
−0.878483 | + | 0.477774i | \(0.841444\pi\) | |||||||
\(824\) | 5994.23i | 0.253421i | ||||||||
\(825\) | 9802.45 | + | 5659.45i | 0.413670 | + | 0.238832i | ||||
\(826\) | 3801.32 | + | 2194.70i | 0.160127 | + | 0.0924494i | ||||
\(827\) | − | 5251.09i | − | 0.220796i | −0.993887 | − | 0.110398i | \(-0.964787\pi\) | ||
0.993887 | − | 0.110398i | \(-0.0352125\pi\) | |||||||
\(828\) | 5017.78 | − | 8691.06i | 0.210604 | − | 0.364777i | ||||
\(829\) | 16982.2 | + | 29414.0i | 0.711479 | + | 1.23232i | 0.964302 | + | 0.264805i | \(0.0853075\pi\) |
−0.252823 | + | 0.967512i | \(0.581359\pi\) | |||||||
\(830\) | 82.5451 | − | 47.6574i | 0.00345203 | − | 0.00199303i | ||||
\(831\) | 6996.65 | 0.292071 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3373.40 | 0.140314 | ||||||||
\(834\) | 349.171 | − | 201.594i | 0.0144974 | − | 0.00837005i | ||||
\(835\) | 11301.5 | + | 19574.7i | 0.468388 | + | 0.811272i | ||||
\(836\) | −26744.4 | + | 46322.6i | −1.10643 | + | 1.91639i | ||||
\(837\) | − | 4618.83i | − | 0.190741i | ||||||
\(838\) | −1411.95 | − | 815.188i | −0.0582039 | − | 0.0336041i | ||||
\(839\) | −13410.4 | − | 7742.49i | −0.551821 | − | 0.318594i | 0.198035 | − | 0.980195i | \(-0.436544\pi\) |
−0.749856 | + | 0.661601i | \(0.769877\pi\) | |||||||
\(840\) | 3280.59i | 0.134751i | ||||||||
\(841\) | −21320.4 | + | 36928.0i | −0.874181 | + | 1.51413i | ||||
\(842\) | −1211.17 | − | 2097.81i | −0.0495722 | − | 0.0858615i | ||||
\(843\) | −10287.1 | + | 5939.24i | −0.420291 | + | 0.242655i | ||||
\(844\) | −38543.1 | −1.57193 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 514.361 | 0.0209032 | ||||||||
\(847\) | 13013.8 | − | 7513.54i | 0.527935 | − | 0.304803i | ||||
\(848\) | −14898.1 | − | 25804.3i | −0.603305 | − | 1.04496i | ||||
\(849\) | −14290.8 | + | 24752.4i | −0.577691 | + | 1.00059i | ||||
\(850\) | 2309.67i | 0.0932014i | ||||||||
\(851\) | 11766.8 | + | 6793.56i | 0.473984 | + | 0.273655i | ||||
\(852\) | 12727.6 | + | 7348.28i | 0.511784 | + | 0.295479i | ||||
\(853\) | − | 20057.8i | − | 0.805118i | −0.915394 | − | 0.402559i | \(-0.868121\pi\) | ||
0.915394 | − | 0.402559i | \(-0.131879\pi\) | |||||||
\(854\) | −153.585 | + | 266.017i | −0.00615406 | + | 0.0106591i | ||||
\(855\) | 7814.31 | + | 13534.8i | 0.312566 | + | 0.541380i | ||||
\(856\) | 1837.32 | − | 1060.78i | 0.0733625 | − | 0.0423559i | ||||
\(857\) | 8066.23 | 0.321514 | 0.160757 | − | 0.986994i | \(-0.448606\pi\) | ||||
0.160757 | + | 0.986994i | \(0.448606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39719.0 | 1.57764 | 0.788821 | − | 0.614623i | \(-0.210692\pi\) | ||||
0.788821 | + | 0.614623i | \(0.210692\pi\) | |||||||
\(860\) | −4140.22 | + | 2390.36i | −0.164163 | + | 0.0947796i | ||||
\(861\) | −3383.32 | − | 5860.08i | −0.133918 | − | 0.231952i | ||||
\(862\) | −2317.33 | + | 4013.73i | −0.0915644 | + | 0.158594i | ||||
\(863\) | − | 24473.8i | − | 0.965351i | −0.875799 | − | 0.482676i | \(-0.839665\pi\) | ||
0.875799 | − | 0.482676i | \(-0.160335\pi\) | |||||||
\(864\) | −9350.98 | − | 5398.79i | −0.368202 | − | 0.212582i | ||||
\(865\) | −2969.28 | − | 1714.32i | −0.116715 | − | 0.0673856i | ||||
\(866\) | 3404.03i | 0.133572i | ||||||||
\(867\) | −4643.31 | + | 8042.45i | −0.181886 | + | 0.315036i | ||||
\(868\) | −2395.19 | − | 4148.60i | −0.0936614 | − | 0.162226i | ||||
\(869\) | 12732.5 | − | 7351.13i | 0.497033 | − | 0.286962i | ||||
\(870\) | −2742.15 | −0.106859 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −514.159 | −0.0199675 | ||||||||
\(873\) | −2803.77 | + | 1618.76i | −0.108698 | + | 0.0627567i | ||||
\(874\) | −2655.64 | − | 4599.71i | −0.102779 | − | 0.178018i | ||||
\(875\) | 14217.2 | − | 24624.9i | 0.549290 | − | 0.951399i | ||||
\(876\) | 29891.9i | 1.15291i | ||||||||
\(877\) | 21933.5 | + | 12663.3i | 0.844515 | + | 0.487581i | 0.858797 | − | 0.512317i | \(-0.171213\pi\) |
−0.0142811 | + | 0.999898i | \(0.504546\pi\) | |||||||
\(878\) | 405.546 | + | 234.142i | 0.0155883 | + | 0.00899990i | ||||
\(879\) | 20486.4i | 0.786109i | ||||||||
\(880\) | 10403.7 | − | 18019.7i | 0.398532 | − | 0.690278i | ||||
\(881\) | 663.719 | + | 1149.59i | 0.0253817 | + | 0.0439624i | 0.878437 | − | 0.477858i | \(-0.158587\pi\) |
−0.853056 | + | 0.521820i | \(0.825253\pi\) | |||||||
\(882\) | −184.027 | + | 106.248i | −0.00702551 | + | 0.00405618i | ||||
\(883\) | 2112.05 | 0.0804941 | 0.0402470 | − | 0.999190i | \(-0.487186\pi\) | ||||
0.0402470 | + | 0.999190i | \(0.487186\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15629.6 | 0.593655 | ||||||||
\(886\) | −763.154 | + | 440.607i | −0.0289375 | + | 0.0167071i | ||||
\(887\) | 20467.7 | + | 35451.1i | 0.774790 | + | 1.34197i | 0.934913 | + | 0.354878i | \(0.115478\pi\) |
−0.160123 | + | 0.987097i | \(0.551189\pi\) | |||||||
\(888\) | 1656.30 | − | 2868.80i | 0.0625921 | − | 0.108413i | ||||
\(889\) | − | 22997.9i | − | 0.867632i | ||||||
\(890\) | −1145.51 | − | 661.361i | −0.0431434 | − | 0.0249088i | ||||
\(891\) | −6215.97 | − | 3588.79i | −0.233718 | − | 0.134937i | ||||
\(892\) | − | 10708.9i | − | 0.401975i | ||||||
\(893\) | −7018.72 | + | 12156.8i | −0.263015 | + | 0.455555i | ||||
\(894\) | −1657.53 | − | 2870.92i | −0.0620089 | − | 0.107403i | ||||
\(895\) | 8885.94 | − | 5130.30i | 0.331871 | − | 0.191606i | ||||
\(896\) | −14881.0 | −0.554845 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5720.04 | 0.212562 | ||||||||
\(899\) | 7002.62 | − | 4042.96i | 0.259789 | − | 0.149989i | ||||
\(900\) | 3751.16 | + | 6497.20i | 0.138932 | + | 0.240637i | ||||
\(901\) | 21351.2 | − | 36981.3i | 0.789468 | − | 1.36740i | ||||
\(902\) | − | 1714.62i | − | 0.0632934i | ||||||
\(903\) | 4948.48 | + | 2857.00i | 0.182364 | + | 0.105288i | ||||
\(904\) | −11330.4 | − | 6541.61i | −0.416862 | − | 0.240676i | ||||
\(905\) | − | 15239.1i | − | 0.559740i | ||||||
\(906\) | −116.286 | + | 201.414i | −0.00426419 | + | 0.00738580i | ||||
\(907\) | 76.9840 | + | 133.340i | 0.00281831 | + | 0.00488146i | 0.867431 | − | 0.497557i | \(-0.165770\pi\) |
−0.864613 | + | 0.502439i | \(0.832436\pi\) | |||||||
\(908\) | −28340.2 | + | 16362.2i | −1.03580 | + | 0.598017i | ||||
\(909\) | 7964.82 | 0.290623 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −733.607 | −0.0266800 | −0.0133400 | − | 0.999911i | \(-0.504246\pi\) | ||||
−0.0133400 | + | 0.999911i | \(0.504246\pi\) | |||||||
\(912\) | 28070.0 | − | 16206.2i | 1.01918 | − | 0.588422i | ||||
\(913\) | 744.280 | + | 1289.13i | 0.0269793 | + | 0.0467295i | ||||
\(914\) | −1820.85 | + | 3153.81i | −0.0658954 | + | 0.114134i | ||||
\(915\) | 1093.76i | 0.0395177i | ||||||||
\(916\) | −23834.3 | − | 13760.7i | −0.859723 | − | 0.496361i | ||||
\(917\) | 13123.4 | + | 7576.80i | 0.472599 | + | 0.272855i | ||||
\(918\) | − | 4991.67i | − | 0.179466i | ||||||
\(919\) | 25553.2 | − | 44259.4i | 0.917216 | − | 1.58867i | 0.113592 | − | 0.993527i | \(-0.463764\pi\) |
0.803624 | − | 0.595138i | \(-0.202902\pi\) | |||||||
\(920\) | 2128.22 | + | 3686.18i | 0.0762667 | + | 0.132098i | ||||
\(921\) | −13563.5 | + | 7830.92i | −0.485270 | + | 0.280171i | ||||
\(922\) | 4188.61 | 0.149615 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −25371.0 | −0.903294 | ||||||||
\(925\) | −8796.53 | + | 5078.68i | −0.312679 | + | 0.180525i | ||||
\(926\) | 2077.37 | + | 3598.10i | 0.0737219 | + | 0.127690i | ||||
\(927\) | −6772.46 | + | 11730.2i | −0.239953 | + | 0.415611i | ||||
\(928\) | − | 18902.7i | − | 0.668655i | ||||||
\(929\) | −26539.5 | − | 15322.6i | −0.937280 | − | 0.541139i | −0.0481735 | − | 0.998839i | \(-0.515340\pi\) |
−0.889107 | + | 0.457700i | \(0.848673\pi\) | |||||||
\(930\) | 286.473 | + | 165.395i | 0.0101009 | + | 0.00583174i | ||||
\(931\) | − | 5799.22i | − | 0.204148i | ||||||
\(932\) | −2237.62 | + | 3875.67i | −0.0786433 | + | 0.136214i | ||||
\(933\) | −9447.85 | − | 16364.2i | −0.331520 | − | 0.574210i | ||||
\(934\) | −891.284 | + | 514.583i | −0.0312245 | + | 0.0180275i | ||||
\(935\) | 29820.0 | 1.04302 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24422.2 | −0.851482 | −0.425741 | − | 0.904845i | \(-0.639987\pi\) | ||||
−0.425741 | + | 0.904845i | \(0.639987\pi\) | |||||||
\(938\) | −3969.41 | + | 2291.74i | −0.138172 | + | 0.0797739i | ||||
\(939\) | −3912.62 | − | 6776.86i | −0.135978 | − | 0.235521i | ||||
\(940\) | 2785.38 | − | 4824.41i | 0.0966479 | − | 0.167399i | ||||
\(941\) | 16475.9i | 0.570774i | 0.958412 | + | 0.285387i | \(0.0921221\pi\) | ||||
−0.958412 | + | 0.285387i | \(0.907878\pi\) | |||||||
\(942\) | −3775.31 | − | 2179.68i | −0.130580 | − | 0.0753904i | ||||
\(943\) | −7603.23 | − | 4389.73i | −0.262561 | − | 0.151590i | ||||
\(944\) | 34754.5i | 1.19827i | ||||||||
\(945\) | −10870.0 | + | 18827.4i | −0.374180 | + | 0.648099i | ||||
\(946\) | 723.946 | + | 1253.91i | 0.0248811 | + | 0.0430953i | ||||
\(947\) | −8765.97 | + | 5061.03i | −0.300798 | + | 0.173666i | −0.642801 | − | 0.766033i | \(-0.722228\pi\) |
0.342003 | + | 0.939699i | \(0.388895\pi\) | |||||||
\(948\) | −9088.76 | −0.311381 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3970.57 | 0.135602 | ||||||||
\(951\) | −15204.3 | + | 8778.18i | −0.518435 | + | 0.299319i | ||||
\(952\) | −5227.27 | − | 9053.89i | −0.177959 | − | 0.308233i | ||||
\(953\) | 19048.6 | − | 32993.1i | 0.647475 | − | 1.12146i | −0.336248 | − | 0.941773i | \(-0.609158\pi\) |
0.983724 | − | 0.179687i | \(-0.0575085\pi\) | |||||||
\(954\) | 2689.89i | 0.0912875i | ||||||||
\(955\) | 14076.5 | + | 8127.07i | 0.476968 | + | 0.275378i | ||||
\(956\) | 1570.35 | + | 906.643i | 0.0531264 | + | 0.0306725i | ||||
\(957\) | − | 42824.9i | − | 1.44653i | ||||||
\(958\) | −629.121 | + | 1089.67i | −0.0212171 | + | 0.0367491i | ||||
\(959\) | 24847.2 | + | 43036.7i | 0.836662 | + | 1.44914i | ||||
\(960\) | −10685.9 | + | 6169.50i | −0.359256 | + | 0.207417i | ||||
\(961\) | 28815.6 | 0.967258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4794.00 | 0.160420 | ||||||||
\(964\) | 20990.7 | − | 12119.0i | 0.701311 | − | 0.404902i | ||||
\(965\) | −4542.43 | − | 7867.73i | −0.151530 | − | 0.262457i | ||||
\(966\) | 1259.63 | − | 2181.75i | 0.0419545 | − | 0.0726673i | ||||
\(967\) | 44515.5i | 1.48037i | 0.672401 | + | 0.740187i | \(0.265263\pi\) | ||||
−0.672401 | + | 0.740187i | \(0.734737\pi\) | |||||||
\(968\) | −4116.63 | − | 2376.74i | −0.136687 | − | 0.0789165i | ||||
\(969\) | 40228.4 | + | 23225.9i | 1.33367 | + | 0.769993i | ||||
\(970\) | − | 679.978i | − | 0.0225080i | ||||||
\(971\) | 12722.2 | − | 22035.4i | 0.420467 | − | 0.728270i | −0.575518 | − | 0.817789i | \(-0.695200\pi\) |
0.995985 | + | 0.0895186i | \(0.0285329\pi\) | |||||||
\(972\) | −13449.6 | − | 23295.5i | −0.443824 | − | 0.768726i | ||||
\(973\) | 4846.22 | − | 2797.97i | 0.159674 | − | 0.0921878i | ||||
\(974\) | −583.765 | −0.0192044 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2432.12 | −0.0797646 | ||||||||
\(977\) | −34180.2 | + | 19734.0i | −1.11927 | + | 0.646208i | −0.941213 | − | 0.337813i | \(-0.890313\pi\) |
−0.178052 | + | 0.984021i | \(0.556980\pi\) | |||||||
\(978\) | −210.742 | − | 365.016i | −0.00689038 | − | 0.0119345i | ||||
\(979\) | 10328.7 | − | 17889.8i | 0.337187 | − | 0.584025i | ||||
\(980\) | 2301.42i | 0.0750165i | ||||||||
\(981\) | −1006.17 | − | 580.913i | −0.0327467 | − | 0.0189063i | ||||
\(982\) | 175.144 | + | 101.119i | 0.00569152 | + | 0.00328600i | ||||
\(983\) | − | 14970.4i | − | 0.485740i | −0.970059 | − | 0.242870i | \(-0.921911\pi\) | ||
0.970059 | − | 0.242870i | \(-0.0780888\pi\) | |||||||
\(984\) | −1070.24 | + | 1853.70i | −0.0346726 | + | 0.0600547i | ||||
\(985\) | −18528.0 | − | 32091.4i | −0.599340 | − | 1.03809i | ||||
\(986\) | 7567.88 | − | 4369.31i | 0.244432 | − | 0.141123i | ||||
\(987\) | −6658.28 | −0.214727 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7413.71 | 0.238364 | ||||||||
\(990\) | −1626.75 | + | 939.205i | −0.0522238 | + | 0.0301514i | ||||
\(991\) | −29211.2 | − | 50595.3i | −0.936352 | − | 1.62181i | −0.772206 | − | 0.635373i | \(-0.780846\pi\) |
−0.164146 | − | 0.986436i | \(-0.552487\pi\) | |||||||
\(992\) | −1140.13 | + | 1974.77i | −0.0364912 | + | 0.0632047i | ||||
\(993\) | 9692.91i | 0.309763i | ||||||||
\(994\) | −3425.70 | − | 1977.83i | −0.109313 | − | 0.0631116i | ||||
\(995\) | −6575.26 | − | 3796.23i | −0.209497 | − | 0.120953i | ||||
\(996\) | − | 920.210i | − | 0.0292751i | ||||||
\(997\) | −10065.8 | + | 17434.5i | −0.319746 | + | 0.553817i | −0.980435 | − | 0.196843i | \(-0.936931\pi\) |
0.660689 | + | 0.750660i | \(0.270264\pi\) | |||||||
\(998\) | 469.115 | + | 812.531i | 0.0148793 | + | 0.0257718i | ||||
\(999\) | 19011.1 | − | 10976.0i | 0.602086 | − | 0.347614i |
(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 | 169.4.e.h.23.8 | 36 | ||
13.2 | odd | 12 | 169.4.a.l.1.4 | yes | 9 | ||
13.3 | even | 3 | 169.4.b.g.168.8 | 18 | |||
13.4 | even | 6 | inner | 169.4.e.h.147.8 | 36 | ||
13.5 | odd | 4 | 169.4.c.k.146.6 | 18 | |||
13.6 | odd | 12 | 169.4.c.k.22.6 | 18 | |||
13.7 | odd | 12 | 169.4.c.l.22.4 | 18 | |||
13.8 | odd | 4 | 169.4.c.l.146.4 | 18 | |||
13.9 | even | 3 | inner | 169.4.e.h.147.11 | 36 | ||
13.10 | even | 6 | 169.4.b.g.168.11 | 18 | |||
13.11 | odd | 12 | 169.4.a.k.1.6 | ✓ | 9 | ||
13.12 | even | 2 | inner | 169.4.e.h.23.11 | 36 | ||
39.2 | even | 12 | 1521.4.a.bg.1.6 | 9 | |||
39.11 | even | 12 | 1521.4.a.bh.1.4 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.4.a.k.1.6 | ✓ | 9 | 13.11 | odd | 12 | ||
169.4.a.l.1.4 | yes | 9 | 13.2 | odd | 12 | ||
169.4.b.g.168.8 | 18 | 13.3 | even | 3 | |||
169.4.b.g.168.11 | 18 | 13.10 | even | 6 | |||
169.4.c.k.22.6 | 18 | 13.6 | odd | 12 | |||
169.4.c.k.146.6 | 18 | 13.5 | odd | 4 | |||
169.4.c.l.22.4 | 18 | 13.7 | odd | 12 | |||
169.4.c.l.146.4 | 18 | 13.8 | odd | 4 | |||
169.4.e.h.23.8 | 36 | 1.1 | even | 1 | trivial | ||
169.4.e.h.23.11 | 36 | 13.12 | even | 2 | inner | ||
169.4.e.h.147.8 | 36 | 13.4 | even | 6 | inner | ||
169.4.e.h.147.11 | 36 | 13.9 | even | 3 | inner | ||
1521.4.a.bg.1.6 | 9 | 39.2 | even | 12 | |||
1521.4.a.bh.1.4 | 9 | 39.11 | even | 12 |