Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(41,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + \cdots + 5760000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.7 | ||
Root | \(-1.39379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.41 |
Dual form | 105.4.b.b.41.10 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.39379i | − | 0.492779i | −0.969171 | − | 0.246389i | \(-0.920756\pi\) | ||
0.969171 | − | 0.246389i | \(-0.0792442\pi\) | |||||||
\(3\) | 5.17944 | − | 0.416449i | 0.996783 | − | 0.0801457i | ||||
\(4\) | 6.05735 | 0.757169 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −0.580442 | − | 7.21904i | −0.0394941 | − | 0.491193i | ||||
\(7\) | −10.8253 | − | 15.0271i | −0.584510 | − | 0.811386i | ||||
\(8\) | − | 19.5930i | − | 0.865895i | ||||||
\(9\) | 26.6531 | − | 4.31394i | 0.987153 | − | 0.159776i | ||||
\(10\) | − | 6.96894i | − | 0.220377i | ||||||
\(11\) | 67.7901i | 1.85813i | 0.369912 | + | 0.929067i | \(0.379388\pi\) | ||||
−0.369912 | + | 0.929067i | \(0.620612\pi\) | |||||||
\(12\) | 31.3737 | − | 2.52258i | 0.754733 | − | 0.0606838i | ||||
\(13\) | − | 2.57864i | − | 0.0550144i | −0.999622 | − | 0.0275072i | \(-0.991243\pi\) | ||
0.999622 | − | 0.0275072i | \(-0.00875692\pi\) | |||||||
\(14\) | −20.9446 | + | 15.0882i | −0.399834 | + | 0.288034i | ||||
\(15\) | 25.8972 | − | 2.08225i | 0.445775 | − | 0.0358422i | ||||
\(16\) | 21.1504 | 0.330474 | ||||||||
\(17\) | −62.5926 | −0.892996 | −0.446498 | − | 0.894785i | \(-0.647329\pi\) | ||||
−0.446498 | + | 0.894785i | \(0.647329\pi\) | |||||||
\(18\) | −6.01273 | − | 37.1488i | −0.0787341 | − | 0.486448i | ||||
\(19\) | − | 134.611i | − | 1.62537i | −0.582705 | − | 0.812684i | \(-0.698006\pi\) | ||
0.582705 | − | 0.812684i | \(-0.301994\pi\) | |||||||
\(20\) | 30.2868 | 0.338616 | ||||||||
\(21\) | −62.3269 | − | 73.3237i | −0.647659 | − | 0.761930i | ||||
\(22\) | 94.4850 | 0.915649 | ||||||||
\(23\) | 58.4546i | 0.529940i | 0.964257 | + | 0.264970i | \(0.0853621\pi\) | ||||
−0.964257 | + | 0.264970i | \(0.914638\pi\) | |||||||
\(24\) | −8.15948 | − | 101.481i | −0.0693978 | − | 0.863110i | ||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −3.59408 | −0.0271099 | ||||||||
\(27\) | 136.252 | − | 33.4435i | 0.971172 | − | 0.238378i | ||||
\(28\) | −65.5726 | − | 91.0244i | −0.442573 | − | 0.614357i | ||||
\(29\) | 91.3578i | 0.584990i | 0.956267 | + | 0.292495i | \(0.0944855\pi\) | ||||
−0.956267 | + | 0.292495i | \(0.905514\pi\) | |||||||
\(30\) | −2.90221 | − | 36.0952i | −0.0176623 | − | 0.219668i | ||||
\(31\) | 182.870i | 1.05950i | 0.848154 | + | 0.529750i | \(0.177714\pi\) | ||||
−0.848154 | + | 0.529750i | \(0.822286\pi\) | |||||||
\(32\) | − | 186.223i | − | 1.02875i | ||||||
\(33\) | 28.2311 | + | 351.114i | 0.148921 | + | 1.85216i | ||||
\(34\) | 87.2408i | 0.440049i | ||||||||
\(35\) | −54.1264 | − | 75.1354i | −0.261401 | − | 0.362863i | ||||
\(36\) | 161.447 | − | 26.1311i | 0.747442 | − | 0.120977i | ||||
\(37\) | −340.482 | −1.51284 | −0.756418 | − | 0.654089i | \(-0.773052\pi\) | ||||
−0.756418 | + | 0.654089i | \(0.773052\pi\) | |||||||
\(38\) | −187.620 | −0.800946 | ||||||||
\(39\) | −1.07387 | − | 13.3559i | −0.00440916 | − | 0.0548374i | ||||
\(40\) | − | 97.9649i | − | 0.387240i | ||||||
\(41\) | 67.1808 | 0.255899 | 0.127950 | − | 0.991781i | \(-0.459160\pi\) | ||||
0.127950 | + | 0.991781i | \(0.459160\pi\) | |||||||
\(42\) | −102.198 | + | 86.8705i | −0.375463 | + | 0.319153i | ||||
\(43\) | −88.7823 | −0.314864 | −0.157432 | − | 0.987530i | \(-0.550322\pi\) | ||||
−0.157432 | + | 0.987530i | \(0.550322\pi\) | |||||||
\(44\) | 410.628i | 1.40692i | ||||||||
\(45\) | 133.266 | − | 21.5697i | 0.441468 | − | 0.0714539i | ||||
\(46\) | 81.4734 | 0.261143 | ||||||||
\(47\) | 157.841 | 0.489860 | 0.244930 | − | 0.969541i | \(-0.421235\pi\) | ||||
0.244930 | + | 0.969541i | \(0.421235\pi\) | |||||||
\(48\) | 109.547 | − | 8.80805i | 0.329411 | − | 0.0264861i | ||||
\(49\) | −108.626 | + | 325.345i | −0.316695 | + | 0.948527i | ||||
\(50\) | − | 34.8447i | − | 0.0985557i | ||||||
\(51\) | −324.194 | + | 26.0666i | −0.890123 | + | 0.0715697i | ||||
\(52\) | − | 15.6198i | − | 0.0416552i | ||||||
\(53\) | 458.943i | 1.18945i | 0.803931 | + | 0.594723i | \(0.202738\pi\) | ||||
−0.803931 | + | 0.594723i | \(0.797262\pi\) | |||||||
\(54\) | −46.6131 | − | 189.906i | −0.117467 | − | 0.478573i | ||||
\(55\) | 338.950i | 0.830983i | ||||||||
\(56\) | −294.425 | + | 212.100i | −0.702576 | + | 0.506125i | ||||
\(57\) | −56.0588 | − | 697.211i | −0.130266 | − | 1.62014i | ||||
\(58\) | 127.333 | 0.288271 | ||||||||
\(59\) | −589.112 | −1.29993 | −0.649965 | − | 0.759964i | \(-0.725216\pi\) | ||||
−0.649965 | + | 0.759964i | \(0.725216\pi\) | |||||||
\(60\) | 156.868 | − | 12.6129i | 0.337527 | − | 0.0271386i | ||||
\(61\) | 431.560i | 0.905829i | 0.891554 | + | 0.452915i | \(0.149616\pi\) | ||||
−0.891554 | + | 0.452915i | \(0.850384\pi\) | |||||||
\(62\) | 254.883 | 0.522099 | ||||||||
\(63\) | −353.354 | − | 353.819i | −0.706641 | − | 0.707572i | ||||
\(64\) | −90.3525 | −0.176470 | ||||||||
\(65\) | − | 12.8932i | − | 0.0246032i | ||||||
\(66\) | 489.379 | − | 39.3482i | 0.912703 | − | 0.0733853i | ||||
\(67\) | 809.483 | 1.47603 | 0.738016 | − | 0.674783i | \(-0.235763\pi\) | ||||
0.738016 | + | 0.674783i | \(0.235763\pi\) | |||||||
\(68\) | −379.145 | −0.676149 | ||||||||
\(69\) | 24.3434 | + | 302.762i | 0.0424724 | + | 0.528236i | ||||
\(70\) | −104.723 | + | 75.4408i | −0.178811 | + | 0.128813i | ||||
\(71\) | − | 80.5430i | − | 0.134629i | −0.997732 | − | 0.0673147i | \(-0.978557\pi\) | ||
0.997732 | − | 0.0673147i | \(-0.0214432\pi\) | |||||||
\(72\) | −84.5230 | − | 522.214i | −0.138349 | − | 0.854772i | ||||
\(73\) | − | 406.079i | − | 0.651068i | −0.945530 | − | 0.325534i | \(-0.894456\pi\) | ||
0.945530 | − | 0.325534i | \(-0.105544\pi\) | |||||||
\(74\) | 474.560i | 0.745493i | ||||||||
\(75\) | 129.486 | − | 10.4112i | 0.199357 | − | 0.0160291i | ||||
\(76\) | − | 815.389i | − | 1.23068i | ||||||
\(77\) | 1018.69 | − | 733.847i | 1.50766 | − | 1.08610i | ||||
\(78\) | −18.6153 | + | 1.49675i | −0.0270227 | + | 0.00217274i | ||||
\(79\) | −657.971 | −0.937058 | −0.468529 | − | 0.883448i | \(-0.655216\pi\) | ||||
−0.468529 | + | 0.883448i | \(0.655216\pi\) | |||||||
\(80\) | 105.752 | 0.147793 | ||||||||
\(81\) | 691.780 | − | 229.960i | 0.948943 | − | 0.315446i | ||||
\(82\) | − | 93.6358i | − | 0.126102i | ||||||
\(83\) | −649.146 | −0.858471 | −0.429235 | − | 0.903193i | \(-0.641217\pi\) | ||||
−0.429235 | + | 0.903193i | \(0.641217\pi\) | |||||||
\(84\) | −377.536 | − | 444.147i | −0.490388 | − | 0.576910i | ||||
\(85\) | −312.963 | −0.399360 | ||||||||
\(86\) | 123.744i | 0.155158i | ||||||||
\(87\) | 38.0459 | + | 473.182i | 0.0468844 | + | 0.583108i | ||||
\(88\) | 1328.21 | 1.60895 | ||||||||
\(89\) | −600.574 | −0.715289 | −0.357644 | − | 0.933858i | \(-0.616420\pi\) | ||||
−0.357644 | + | 0.933858i | \(0.616420\pi\) | |||||||
\(90\) | −30.0636 | − | 185.744i | −0.0352109 | − | 0.217546i | ||||
\(91\) | −38.7495 | + | 27.9145i | −0.0446379 | + | 0.0321565i | ||||
\(92\) | 354.080i | 0.401255i | ||||||||
\(93\) | 76.1562 | + | 947.166i | 0.0849144 | + | 1.05609i | ||||
\(94\) | − | 219.996i | − | 0.241392i | ||||||
\(95\) | − | 673.057i | − | 0.726886i | ||||||
\(96\) | −77.5524 | − | 964.530i | −0.0824496 | − | 1.02544i | ||||
\(97\) | − | 813.824i | − | 0.851869i | −0.904754 | − | 0.425934i | \(-0.859945\pi\) | ||
0.904754 | − | 0.425934i | \(-0.140055\pi\) | |||||||
\(98\) | 453.462 | + | 151.402i | 0.467414 | + | 0.156061i | ||||
\(99\) | 292.443 | + | 1806.82i | 0.296885 | + | 1.83426i | ||||
\(100\) | 151.434 | 0.151434 | ||||||||
\(101\) | 293.929 | 0.289575 | 0.144787 | − | 0.989463i | \(-0.453750\pi\) | ||||
0.144787 | + | 0.989463i | \(0.453750\pi\) | |||||||
\(102\) | 36.3314 | + | 451.858i | 0.0352680 | + | 0.438634i | ||||
\(103\) | − | 658.984i | − | 0.630405i | −0.949025 | − | 0.315202i | \(-0.897928\pi\) | ||
0.949025 | − | 0.315202i | \(-0.102072\pi\) | |||||||
\(104\) | −50.5233 | −0.0476367 | ||||||||
\(105\) | −311.634 | − | 366.618i | −0.289642 | − | 0.340746i | ||||
\(106\) | 639.669 | 0.586133 | ||||||||
\(107\) | − | 514.453i | − | 0.464804i | −0.972620 | − | 0.232402i | \(-0.925341\pi\) | ||
0.972620 | − | 0.232402i | \(-0.0746585\pi\) | |||||||
\(108\) | 825.325 | − | 202.579i | 0.735342 | − | 0.180492i | ||||
\(109\) | 1628.10 | 1.43068 | 0.715340 | − | 0.698777i | \(-0.246272\pi\) | ||||
0.715340 | + | 0.698777i | \(0.246272\pi\) | |||||||
\(110\) | 472.425 | 0.409491 | ||||||||
\(111\) | −1763.51 | + | 141.794i | −1.50797 | + | 0.121247i | ||||
\(112\) | −228.959 | − | 317.828i | −0.193166 | − | 0.268142i | ||||
\(113\) | − | 771.780i | − | 0.642504i | −0.946994 | − | 0.321252i | \(-0.895896\pi\) | ||
0.946994 | − | 0.321252i | \(-0.104104\pi\) | |||||||
\(114\) | −971.765 | + | 78.1341i | −0.798370 | + | 0.0641924i | ||||
\(115\) | 292.273i | 0.236997i | ||||||||
\(116\) | 553.386i | 0.442937i | ||||||||
\(117\) | −11.1241 | − | 68.7289i | −0.00878996 | − | 0.0543076i | ||||
\(118\) | 821.098i | 0.640578i | ||||||||
\(119\) | 677.582 | + | 940.584i | 0.521965 | + | 0.724564i | ||||
\(120\) | −40.7974 | − | 507.403i | −0.0310356 | − | 0.385995i | ||||
\(121\) | −3264.49 | −2.45266 | ||||||||
\(122\) | 601.503 | 0.446373 | ||||||||
\(123\) | 347.959 | − | 27.9774i | 0.255076 | − | 0.0205092i | ||||
\(124\) | 1107.71i | 0.802221i | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −493.149 | + | 492.501i | −0.348676 | + | 0.348218i | ||||
\(127\) | 1500.54 | 1.04844 | 0.524218 | − | 0.851584i | \(-0.324358\pi\) | ||||
0.524218 | + | 0.851584i | \(0.324358\pi\) | |||||||
\(128\) | − | 1363.85i | − | 0.941786i | ||||||
\(129\) | −459.842 | + | 36.9733i | −0.313852 | + | 0.0252350i | ||||
\(130\) | −17.9704 | −0.0121239 | ||||||||
\(131\) | 1840.55 | 1.22756 | 0.613778 | − | 0.789479i | \(-0.289649\pi\) | ||||
0.613778 | + | 0.789479i | \(0.289649\pi\) | |||||||
\(132\) | 171.006 | + | 2126.82i | 0.112759 | + | 1.40240i | ||||
\(133\) | −2022.82 | + | 1457.21i | −1.31880 | + | 0.950044i | ||||
\(134\) | − | 1128.25i | − | 0.727357i | ||||||
\(135\) | 681.259 | − | 167.217i | 0.434322 | − | 0.106606i | ||||
\(136\) | 1226.37i | 0.773241i | ||||||||
\(137\) | − | 1789.29i | − | 1.11583i | −0.829897 | − | 0.557916i | \(-0.811601\pi\) | ||
0.829897 | − | 0.557916i | \(-0.188399\pi\) | |||||||
\(138\) | 421.986 | − | 33.9295i | 0.260303 | − | 0.0209295i | ||||
\(139\) | − | 2246.13i | − | 1.37061i | −0.728258 | − | 0.685303i | \(-0.759670\pi\) | ||
0.728258 | − | 0.685303i | \(-0.240330\pi\) | |||||||
\(140\) | −327.863 | − | 455.122i | −0.197925 | − | 0.274749i | ||||
\(141\) | 817.525 | − | 65.7325i | 0.488284 | − | 0.0392601i | ||||
\(142\) | −112.260 | −0.0663425 | ||||||||
\(143\) | 174.806 | 0.102224 | ||||||||
\(144\) | 563.723 | − | 91.2415i | 0.326229 | − | 0.0528018i | ||||
\(145\) | 456.789i | 0.261616i | ||||||||
\(146\) | −565.989 | −0.320833 | ||||||||
\(147\) | −427.134 | + | 1730.34i | −0.239656 | + | 0.970858i | ||||
\(148\) | −2062.42 | −1.14547 | ||||||||
\(149\) | − | 293.931i | − | 0.161609i | −0.996730 | − | 0.0808046i | \(-0.974251\pi\) | ||
0.996730 | − | 0.0808046i | \(-0.0257490\pi\) | |||||||
\(150\) | −14.5111 | − | 180.476i | −0.00789882 | − | 0.0982387i | ||||
\(151\) | −951.272 | −0.512672 | −0.256336 | − | 0.966588i | \(-0.582515\pi\) | ||||
−0.256336 | + | 0.966588i | \(0.582515\pi\) | |||||||
\(152\) | −2637.44 | −1.40740 | ||||||||
\(153\) | −1668.29 | + | 270.021i | −0.881524 | + | 0.142679i | ||||
\(154\) | −1022.83 | − | 1419.83i | −0.535206 | − | 0.742945i | ||||
\(155\) | 914.352i | 0.473823i | ||||||||
\(156\) | −6.50483 | − | 80.9015i | −0.00333848 | − | 0.0415212i | ||||
\(157\) | 1703.52i | 0.865960i | 0.901404 | + | 0.432980i | \(0.142538\pi\) | ||||
−0.901404 | + | 0.432980i | \(0.857462\pi\) | |||||||
\(158\) | 917.073i | 0.461762i | ||||||||
\(159\) | 191.126 | + | 2377.06i | 0.0953289 | + | 1.18562i | ||||
\(160\) | − | 931.115i | − | 0.460069i | ||||||
\(161\) | 878.402 | − | 632.788i | 0.429986 | − | 0.309756i | ||||
\(162\) | −320.516 | − | 964.195i | −0.155445 | − | 0.467619i | ||||
\(163\) | 1738.35 | 0.835325 | 0.417663 | − | 0.908602i | \(-0.362849\pi\) | ||||
0.417663 | + | 0.908602i | \(0.362849\pi\) | |||||||
\(164\) | 406.938 | 0.193759 | ||||||||
\(165\) | 141.156 | + | 1755.57i | 0.0665997 | + | 0.828310i | ||||
\(166\) | 904.773i | 0.423036i | ||||||||
\(167\) | 1674.27 | 0.775802 | 0.387901 | − | 0.921701i | \(-0.373200\pi\) | ||||
0.387901 | + | 0.921701i | \(0.373200\pi\) | |||||||
\(168\) | −1436.63 | + | 1221.17i | −0.659752 | + | 0.560805i | ||||
\(169\) | 2190.35 | 0.996973 | ||||||||
\(170\) | 436.204i | 0.196796i | ||||||||
\(171\) | −580.706 | − | 3587.82i | −0.259694 | − | 1.60449i | ||||
\(172\) | −537.786 | −0.238406 | ||||||||
\(173\) | −1741.35 | −0.765275 | −0.382638 | − | 0.923899i | \(-0.624984\pi\) | ||||
−0.382638 | + | 0.923899i | \(0.624984\pi\) | |||||||
\(174\) | 659.516 | − | 53.0279i | 0.287343 | − | 0.0231036i | ||||
\(175\) | −270.632 | − | 375.677i | −0.116902 | − | 0.162277i | ||||
\(176\) | 1433.78i | 0.614066i | ||||||||
\(177\) | −3051.27 | + | 245.335i | −1.29575 | + | 0.104184i | ||||
\(178\) | 837.073i | 0.352479i | ||||||||
\(179\) | − | 1666.76i | − | 0.695976i | −0.937499 | − | 0.347988i | \(-0.886865\pi\) | ||
0.937499 | − | 0.347988i | \(-0.113135\pi\) | |||||||
\(180\) | 807.237 | − | 130.655i | 0.334266 | − | 0.0541027i | ||||
\(181\) | 4189.97i | 1.72065i | 0.509746 | + | 0.860325i | \(0.329740\pi\) | ||||
−0.509746 | + | 0.860325i | \(0.670260\pi\) | |||||||
\(182\) | 38.9070 | + | 54.0086i | 0.0158460 | + | 0.0219966i | ||||
\(183\) | 179.723 | + | 2235.24i | 0.0725983 | + | 0.902915i | ||||
\(184\) | 1145.30 | 0.458873 | ||||||||
\(185\) | −1702.41 | −0.676561 | ||||||||
\(186\) | 1320.15 | − | 106.146i | 0.520420 | − | 0.0418440i | ||||
\(187\) | − | 4243.15i | − | 1.65931i | ||||||
\(188\) | 956.096 | 0.370907 | ||||||||
\(189\) | −1977.52 | − | 1685.43i | −0.761077 | − | 0.648662i | ||||
\(190\) | −938.099 | −0.358194 | ||||||||
\(191\) | − | 3858.58i | − | 1.46176i | −0.682504 | − | 0.730882i | \(-0.739109\pi\) | ||
0.682504 | − | 0.730882i | \(-0.260891\pi\) | |||||||
\(192\) | −467.975 | + | 37.6272i | −0.175902 | + | 0.0141433i | ||||
\(193\) | 1129.53 | 0.421272 | 0.210636 | − | 0.977565i | \(-0.432447\pi\) | ||||
0.210636 | + | 0.977565i | \(0.432447\pi\) | |||||||
\(194\) | −1134.30 | −0.419783 | ||||||||
\(195\) | −5.36937 | − | 66.7796i | −0.00197184 | − | 0.0245240i | ||||
\(196\) | −657.989 | + | 1970.73i | −0.239792 | + | 0.718196i | ||||
\(197\) | 3793.36i | 1.37191i | 0.727646 | + | 0.685953i | \(0.240615\pi\) | ||||
−0.727646 | + | 0.685953i | \(0.759385\pi\) | |||||||
\(198\) | 2518.32 | − | 407.603i | 0.903886 | − | 0.146298i | ||||
\(199\) | − | 2716.52i | − | 0.967684i | −0.875155 | − | 0.483842i | \(-0.839241\pi\) | ||
0.875155 | − | 0.483842i | \(-0.160759\pi\) | |||||||
\(200\) | − | 489.824i | − | 0.173179i | ||||||
\(201\) | 4192.67 | − | 337.109i | 1.47128 | − | 0.118298i | ||||
\(202\) | − | 409.675i | − | 0.142696i | ||||||
\(203\) | 1372.84 | − | 988.974i | 0.474653 | − | 0.341933i | ||||
\(204\) | −1963.76 | + | 157.895i | −0.673974 | + | 0.0541904i | ||||
\(205\) | 335.904 | 0.114442 | ||||||||
\(206\) | −918.485 | −0.310650 | ||||||||
\(207\) | 252.170 | + | 1558.00i | 0.0846716 | + | 0.523132i | ||||
\(208\) | − | 54.5392i | − | 0.0181808i | ||||||
\(209\) | 9125.32 | 3.02015 | ||||||||
\(210\) | −510.988 | + | 434.353i | −0.167912 | + | 0.142729i | ||||
\(211\) | 2986.43 | 0.974379 | 0.487190 | − | 0.873296i | \(-0.338022\pi\) | ||||
0.487190 | + | 0.873296i | \(0.338022\pi\) | |||||||
\(212\) | 2779.98i | 0.900611i | ||||||||
\(213\) | −33.5421 | − | 417.167i | −0.0107900 | − | 0.134196i | ||||
\(214\) | −717.038 | −0.229046 | ||||||||
\(215\) | −443.911 | −0.140812 | ||||||||
\(216\) | −655.257 | − | 2669.58i | −0.206410 | − | 0.840934i | ||||
\(217\) | 2748.01 | − | 1979.62i | 0.859664 | − | 0.619289i | ||||
\(218\) | − | 2269.23i | − | 0.705009i | ||||||
\(219\) | −169.111 | − | 2103.26i | −0.0521803 | − | 0.648974i | ||||
\(220\) | 2053.14i | 0.629195i | ||||||||
\(221\) | 161.404i | 0.0491276i | ||||||||
\(222\) | 197.630 | + | 2457.95i | 0.0597481 | + | 0.743095i | ||||
\(223\) | − | 5668.92i | − | 1.70233i | −0.524900 | − | 0.851164i | \(-0.675897\pi\) | ||
0.524900 | − | 0.851164i | \(-0.324103\pi\) | |||||||
\(224\) | −2798.39 | + | 2015.92i | −0.834710 | + | 0.601313i | ||||
\(225\) | 666.329 | − | 107.849i | 0.197431 | − | 0.0319551i | ||||
\(226\) | −1075.70 | −0.316612 | ||||||||
\(227\) | −1778.27 | −0.519946 | −0.259973 | − | 0.965616i | \(-0.583714\pi\) | ||||
−0.259973 | + | 0.965616i | \(0.583714\pi\) | |||||||
\(228\) | −339.568 | − | 4223.26i | −0.0986335 | − | 1.22672i | ||||
\(229\) | − | 1353.76i | − | 0.390650i | −0.980739 | − | 0.195325i | \(-0.937424\pi\) | ||
0.980739 | − | 0.195325i | \(-0.0625762\pi\) | |||||||
\(230\) | 407.367 | 0.116787 | ||||||||
\(231\) | 4970.61 | − | 4225.14i | 1.41577 | − | 1.20344i | ||||
\(232\) | 1789.97 | 0.506540 | ||||||||
\(233\) | 2216.62i | 0.623242i | 0.950206 | + | 0.311621i | \(0.100872\pi\) | ||||
−0.950206 | + | 0.311621i | \(0.899128\pi\) | |||||||
\(234\) | −95.7936 | + | 15.5047i | −0.0267616 | + | 0.00433151i | ||||
\(235\) | 789.203 | 0.219072 | ||||||||
\(236\) | −3568.46 | −0.984267 | ||||||||
\(237\) | −3407.92 | + | 274.012i | −0.934044 | + | 0.0751011i | ||||
\(238\) | 1310.97 | − | 944.406i | 0.357050 | − | 0.257213i | ||||
\(239\) | − | 4546.46i | − | 1.23048i | −0.788338 | − | 0.615242i | \(-0.789058\pi\) | ||
0.788338 | − | 0.615242i | \(-0.210942\pi\) | |||||||
\(240\) | 547.735 | − | 44.0402i | 0.147317 | − | 0.0118449i | ||||
\(241\) | 35.5837i | 0.00951099i | 0.999989 | + | 0.00475549i | \(0.00151373\pi\) | ||||
−0.999989 | + | 0.00475549i | \(0.998486\pi\) | |||||||
\(242\) | 4550.01i | 1.20862i | ||||||||
\(243\) | 3487.26 | − | 1479.16i | 0.920609 | − | 0.390485i | ||||
\(244\) | 2614.11i | 0.685866i | ||||||||
\(245\) | −543.132 | + | 1626.72i | −0.141630 | + | 0.424194i | ||||
\(246\) | −38.9945 | − | 484.981i | −0.0101065 | − | 0.125696i | ||||
\(247\) | −347.115 | −0.0894186 | ||||||||
\(248\) | 3582.98 | 0.917416 | ||||||||
\(249\) | −3362.21 | + | 270.336i | −0.855709 | + | 0.0688027i | ||||
\(250\) | − | 174.224i | − | 0.0440755i | ||||||
\(251\) | −555.734 | −0.139752 | −0.0698758 | − | 0.997556i | \(-0.522260\pi\) | ||||
−0.0698758 | + | 0.997556i | \(0.522260\pi\) | |||||||
\(252\) | −2140.39 | − | 2143.21i | −0.535047 | − | 0.535752i | ||||
\(253\) | −3962.64 | −0.984700 | ||||||||
\(254\) | − | 2091.43i | − | 0.516647i | ||||||
\(255\) | −1620.97 | + | 130.333i | −0.398075 | + | 0.0320070i | ||||
\(256\) | −2623.74 | −0.640562 | ||||||||
\(257\) | −5009.10 | −1.21580 | −0.607898 | − | 0.794016i | \(-0.707987\pi\) | ||||
−0.607898 | + | 0.794016i | \(0.707987\pi\) | |||||||
\(258\) | 51.5330 | + | 640.923i | 0.0124353 | + | 0.154659i | ||||
\(259\) | 3685.82 | + | 5116.45i | 0.884268 | + | 1.22749i | ||||
\(260\) | − | 78.0988i | − | 0.0186288i | ||||||
\(261\) | 394.112 | + | 2434.97i | 0.0934672 | + | 0.577475i | ||||
\(262\) | − | 2565.34i | − | 0.604913i | ||||||
\(263\) | 334.413i | 0.0784061i | 0.999231 | + | 0.0392031i | \(0.0124819\pi\) | ||||
−0.999231 | + | 0.0392031i | \(0.987518\pi\) | |||||||
\(264\) | 6879.38 | − | 553.132i | 1.60377 | − | 0.128950i | ||||
\(265\) | 2294.71i | 0.531936i | ||||||||
\(266\) | 2031.04 | + | 2819.38i | 0.468162 | + | 0.649877i | ||||
\(267\) | −3110.64 | + | 250.108i | −0.712988 | + | 0.0573273i | ||||
\(268\) | 4903.33 | 1.11761 | ||||||||
\(269\) | −5366.63 | −1.21639 | −0.608195 | − | 0.793787i | \(-0.708106\pi\) | ||||
−0.608195 | + | 0.793787i | \(0.708106\pi\) | |||||||
\(270\) | −233.066 | − | 949.530i | −0.0525331 | − | 0.214024i | ||||
\(271\) | 2497.86i | 0.559905i | 0.960014 | + | 0.279953i | \(0.0903188\pi\) | ||||
−0.960014 | + | 0.279953i | \(0.909681\pi\) | |||||||
\(272\) | −1323.86 | −0.295112 | ||||||||
\(273\) | −189.076 | + | 160.719i | −0.0419171 | + | 0.0356306i | ||||
\(274\) | −2493.89 | −0.549858 | ||||||||
\(275\) | 1694.75i | 0.371627i | ||||||||
\(276\) | 147.456 | + | 1833.94i | 0.0321588 | + | 0.399964i | ||||
\(277\) | −2734.48 | −0.593136 | −0.296568 | − | 0.955012i | \(-0.595842\pi\) | ||||
−0.296568 | + | 0.955012i | \(0.595842\pi\) | |||||||
\(278\) | −3130.63 | −0.675405 | ||||||||
\(279\) | 788.893 | + | 4874.07i | 0.169282 | + | 1.04589i | ||||
\(280\) | −1472.13 | + | 1060.50i | −0.314201 | + | 0.226346i | ||||
\(281\) | − | 561.914i | − | 0.119292i | −0.998220 | − | 0.0596459i | \(-0.981003\pi\) | ||
0.998220 | − | 0.0596459i | \(-0.0189972\pi\) | |||||||
\(282\) | −91.6173 | − | 1139.46i | −0.0193466 | − | 0.240616i | ||||
\(283\) | 312.314i | 0.0656012i | 0.999462 | + | 0.0328006i | \(0.0104426\pi\) | ||||
−0.999462 | + | 0.0328006i | \(0.989557\pi\) | |||||||
\(284\) | − | 487.877i | − | 0.101937i | ||||||
\(285\) | −280.294 | − | 3486.06i | −0.0582568 | − | 0.724548i | ||||
\(286\) | − | 243.643i | − | 0.0503738i | ||||||
\(287\) | −727.251 | − | 1009.53i | −0.149576 | − | 0.207633i | ||||
\(288\) | −803.355 | − | 4963.43i | −0.164369 | − | 1.01553i | ||||
\(289\) | −995.171 | −0.202559 | ||||||||
\(290\) | 636.667 | 0.128919 | ||||||||
\(291\) | −338.916 | − | 4215.15i | −0.0682736 | − | 0.849128i | ||||
\(292\) | − | 2459.77i | − | 0.492969i | ||||||
\(293\) | −5189.02 | −1.03463 | −0.517313 | − | 0.855796i | \(-0.673068\pi\) | ||||
−0.517313 | + | 0.855796i | \(0.673068\pi\) | |||||||
\(294\) | 2411.73 | + | 595.335i | 0.478418 | + | 0.118097i | ||||
\(295\) | −2945.56 | −0.581346 | ||||||||
\(296\) | 6671.06i | 1.30996i | ||||||||
\(297\) | 2267.14 | + | 9236.51i | 0.442938 | + | 1.80457i | ||||
\(298\) | −409.678 | −0.0796375 | ||||||||
\(299\) | 150.734 | 0.0291543 | ||||||||
\(300\) | 784.342 | − | 63.0645i | 0.150947 | − | 0.0121368i | ||||
\(301\) | 961.093 | + | 1334.14i | 0.184042 | + | 0.255477i | ||||
\(302\) | 1325.87i | 0.252634i | ||||||||
\(303\) | 1522.39 | − | 122.406i | 0.288643 | − | 0.0232082i | ||||
\(304\) | − | 2847.08i | − | 0.537142i | ||||||
\(305\) | 2157.80i | 0.405099i | ||||||||
\(306\) | 376.352 | + | 2325.24i | 0.0703092 | + | 0.434396i | ||||
\(307\) | 324.556i | 0.0603367i | 0.999545 | + | 0.0301684i | \(0.00960434\pi\) | ||||
−0.999545 | + | 0.0301684i | \(0.990396\pi\) | |||||||
\(308\) | 6170.55 | − | 4445.17i | 1.14156 | − | 0.822360i | ||||
\(309\) | −274.433 | − | 3413.17i | −0.0505242 | − | 0.628377i | ||||
\(310\) | 1274.41 | 0.233490 | ||||||||
\(311\) | 6882.09 | 1.25481 | 0.627407 | − | 0.778691i | \(-0.284116\pi\) | ||||
0.627407 | + | 0.778691i | \(0.284116\pi\) | |||||||
\(312\) | −261.682 | + | 21.0404i | −0.0474835 | + | 0.00381788i | ||||
\(313\) | 10414.6i | 1.88072i | 0.340181 | + | 0.940360i | \(0.389512\pi\) | ||||
−0.340181 | + | 0.940360i | \(0.610488\pi\) | |||||||
\(314\) | 2374.35 | 0.426727 | ||||||||
\(315\) | −1766.77 | − | 1769.10i | −0.316020 | − | 0.316436i | ||||
\(316\) | −3985.57 | −0.709511 | ||||||||
\(317\) | 2351.44i | 0.416625i | 0.978062 | + | 0.208312i | \(0.0667971\pi\) | ||||
−0.978062 | + | 0.208312i | \(0.933203\pi\) | |||||||
\(318\) | 3313.12 | − | 266.390i | 0.584248 | − | 0.0469760i | ||||
\(319\) | −6193.15 | −1.08699 | ||||||||
\(320\) | −451.763 | −0.0789197 | ||||||||
\(321\) | −214.243 | − | 2664.58i | −0.0372520 | − | 0.463309i | ||||
\(322\) | −881.972 | − | 1224.31i | −0.152641 | − | 0.211888i | ||||
\(323\) | 8425.68i | 1.45145i | ||||||||
\(324\) | 4190.35 | − | 1392.95i | 0.718511 | − | 0.238846i | ||||
\(325\) | − | 64.4661i | − | 0.0110029i | ||||||
\(326\) | − | 2422.89i | − | 0.411631i | ||||||
\(327\) | 8432.66 | − | 678.023i | 1.42608 | − | 0.114663i | ||||
\(328\) | − | 1316.27i | − | 0.221582i | ||||||
\(329\) | −1708.67 | − | 2371.88i | −0.286328 | − | 0.397465i | ||||
\(330\) | 2446.90 | − | 196.741i | 0.408173 | − | 0.0328189i | ||||
\(331\) | 116.712 | 0.0193809 | 0.00969047 | − | 0.999953i | \(-0.496915\pi\) | ||||
0.00969047 | + | 0.999953i | \(0.496915\pi\) | |||||||
\(332\) | −3932.11 | −0.650008 | ||||||||
\(333\) | −9074.92 | + | 1468.82i | −1.49340 | + | 0.241714i | ||||
\(334\) | − | 2333.58i | − | 0.382298i | ||||||
\(335\) | 4047.42 | 0.660101 | ||||||||
\(336\) | −1318.24 | − | 1550.82i | −0.214035 | − | 0.251798i | ||||
\(337\) | −482.498 | −0.0779921 | −0.0389961 | − | 0.999239i | \(-0.512416\pi\) | ||||
−0.0389961 | + | 0.999239i | \(0.512416\pi\) | |||||||
\(338\) | − | 3052.89i | − | 0.491287i | ||||||
\(339\) | −321.407 | − | 3997.39i | −0.0514939 | − | 0.640437i | ||||
\(340\) | −1895.73 | −0.302383 | ||||||||
\(341\) | −12396.8 | −1.96869 | ||||||||
\(342\) | −5000.66 | + | 809.382i | −0.790657 | + | 0.127972i | ||||
\(343\) | 6064.90 | − | 1889.61i | 0.954734 | − | 0.297462i | ||||
\(344\) | 1739.51i | 0.272640i | ||||||||
\(345\) | 121.717 | + | 1513.81i | 0.0189942 | + | 0.236234i | ||||
\(346\) | 2427.08i | 0.377111i | ||||||||
\(347\) | − | 1524.90i | − | 0.235911i | −0.993019 | − | 0.117955i | \(-0.962366\pi\) | ||
0.993019 | − | 0.117955i | \(-0.0376340\pi\) | |||||||
\(348\) | 230.457 | + | 2866.23i | 0.0354994 | + | 0.441512i | ||||
\(349\) | − | 2797.89i | − | 0.429133i | −0.976709 | − | 0.214567i | \(-0.931166\pi\) | ||
0.976709 | − | 0.214567i | \(-0.0688339\pi\) | |||||||
\(350\) | −523.614 | + | 377.204i | −0.0799668 | + | 0.0576069i | ||||
\(351\) | −86.2388 | − | 351.345i | −0.0131142 | − | 0.0534285i | ||||
\(352\) | 12624.1 | 1.91155 | ||||||||
\(353\) | 6871.80 | 1.03612 | 0.518058 | − | 0.855346i | \(-0.326655\pi\) | ||||
0.518058 | + | 0.855346i | \(0.326655\pi\) | |||||||
\(354\) | 341.945 | + | 4252.82i | 0.0513395 | + | 0.638517i | ||||
\(355\) | − | 402.715i | − | 0.0602081i | ||||||
\(356\) | −3637.89 | −0.541595 | ||||||||
\(357\) | 3901.20 | + | 4589.52i | 0.578357 | + | 0.680400i | ||||
\(358\) | −2323.11 | −0.342962 | ||||||||
\(359\) | 9204.67i | 1.35321i | 0.736344 | + | 0.676607i | \(0.236550\pi\) | ||||
−0.736344 | + | 0.676607i | \(0.763450\pi\) | |||||||
\(360\) | −422.615 | − | 2611.07i | −0.0618716 | − | 0.382265i | ||||
\(361\) | −11261.2 | −1.64182 | ||||||||
\(362\) | 5839.93 | 0.847900 | ||||||||
\(363\) | −16908.2 | + | 1359.50i | −2.44477 | + | 0.196570i | ||||
\(364\) | −234.719 | + | 169.088i | −0.0337984 | + | 0.0243479i | ||||
\(365\) | − | 2030.40i | − | 0.291167i | ||||||
\(366\) | 3115.45 | − | 250.495i | 0.444937 | − | 0.0357749i | ||||
\(367\) | 3102.52i | 0.441281i | 0.975355 | + | 0.220641i | \(0.0708148\pi\) | ||||
−0.975355 | + | 0.220641i | \(0.929185\pi\) | |||||||
\(368\) | 1236.34i | 0.175132i | ||||||||
\(369\) | 1790.58 | − | 289.814i | 0.252612 | − | 0.0408865i | ||||
\(370\) | 2372.80i | 0.333395i | ||||||||
\(371\) | 6896.57 | − | 4968.18i | 0.965100 | − | 0.695243i | ||||
\(372\) | 461.305 | + | 5737.32i | 0.0642945 | + | 0.799640i | ||||
\(373\) | −6036.54 | −0.837963 | −0.418981 | − | 0.907995i | \(-0.637613\pi\) | ||||
−0.418981 | + | 0.907995i | \(0.637613\pi\) | |||||||
\(374\) | −5914.06 | −0.817670 | ||||||||
\(375\) | 647.430 | − | 52.0561i | 0.0891550 | − | 0.00716845i | ||||
\(376\) | − | 3092.57i | − | 0.424167i | ||||||
\(377\) | 235.579 | 0.0321829 | ||||||||
\(378\) | −2349.13 | + | 2756.25i | −0.319647 | + | 0.375042i | ||||
\(379\) | 8484.08 | 1.14986 | 0.574931 | − | 0.818202i | \(-0.305029\pi\) | ||||
0.574931 | + | 0.818202i | \(0.305029\pi\) | |||||||
\(380\) | − | 4076.95i | − | 0.550376i | ||||||
\(381\) | 7771.95 | − | 624.898i | 1.04506 | − | 0.0840276i | ||||
\(382\) | −5378.04 | −0.720326 | ||||||||
\(383\) | −6784.15 | −0.905101 | −0.452551 | − | 0.891739i | \(-0.649486\pi\) | ||||
−0.452551 | + | 0.891739i | \(0.649486\pi\) | |||||||
\(384\) | −567.975 | − | 7063.98i | −0.0754800 | − | 0.938756i | ||||
\(385\) | 5093.43 | − | 3669.23i | 0.674248 | − | 0.485718i | ||||
\(386\) | − | 1574.33i | − | 0.207594i | ||||||
\(387\) | −2366.33 | + | 383.002i | −0.310819 | + | 0.0503077i | ||||
\(388\) | − | 4929.62i | − | 0.645009i | ||||||
\(389\) | − | 2023.40i | − | 0.263729i | −0.991268 | − | 0.131865i | \(-0.957904\pi\) | ||
0.991268 | − | 0.131865i | \(-0.0420964\pi\) | |||||||
\(390\) | −93.0766 | + | 7.48376i | −0.0120849 | + | 0.000971680i | ||||
\(391\) | − | 3658.82i | − | 0.473234i | ||||||
\(392\) | 6374.48 | + | 2128.32i | 0.821326 | + | 0.274225i | ||||
\(393\) | 9533.03 | − | 766.497i | 1.22361 | − | 0.0983833i | ||||
\(394\) | 5287.14 | 0.676046 | ||||||||
\(395\) | −3289.86 | −0.419065 | ||||||||
\(396\) | 1771.43 | + | 10944.5i | 0.224792 | + | 1.38885i | ||||
\(397\) | 792.398i | 0.100175i | 0.998745 | + | 0.0500873i | \(0.0159500\pi\) | ||||
−0.998745 | + | 0.0500873i | \(0.984050\pi\) | |||||||
\(398\) | −3786.26 | −0.476854 | ||||||||
\(399\) | −9870.20 | + | 8389.91i | −1.23842 | + | 1.05268i | ||||
\(400\) | 528.759 | 0.0660949 | ||||||||
\(401\) | − | 13954.2i | − | 1.73776i | −0.495024 | − | 0.868880i | \(-0.664841\pi\) | ||
0.495024 | − | 0.868880i | \(-0.335159\pi\) | |||||||
\(402\) | −469.858 | − | 5843.69i | −0.0582945 | − | 0.725017i | ||||
\(403\) | 471.558 | 0.0582877 | ||||||||
\(404\) | 1780.43 | 0.219257 | ||||||||
\(405\) | 3458.90 | − | 1149.80i | 0.424380 | − | 0.141072i | ||||
\(406\) | −1378.42 | − | 1913.45i | −0.168497 | − | 0.233899i | ||||
\(407\) | − | 23081.3i | − | 2.81105i | ||||||
\(408\) | 510.723 | + | 6351.93i | 0.0619719 | + | 0.770754i | ||||
\(409\) | − | 2366.91i | − | 0.286152i | −0.989712 | − | 0.143076i | \(-0.954301\pi\) | ||
0.989712 | − | 0.143076i | \(-0.0456993\pi\) | |||||||
\(410\) | − | 468.179i | − | 0.0563944i | ||||||
\(411\) | −745.146 | − | 9267.49i | −0.0894291 | − | 1.11224i | ||||
\(412\) | − | 3991.70i | − | 0.477323i | ||||||
\(413\) | 6377.31 | + | 8852.63i | 0.759822 | + | 1.05474i | ||||
\(414\) | 2171.52 | − | 351.472i | 0.257788 | − | 0.0417244i | ||||
\(415\) | −3245.73 | −0.383920 | ||||||||
\(416\) | −480.203 | −0.0565958 | ||||||||
\(417\) | −935.399 | − | 11633.7i | −0.109848 | − | 1.36620i | ||||
\(418\) | − | 12718.8i | − | 1.48827i | ||||||
\(419\) | 15398.7 | 1.79541 | 0.897703 | − | 0.440600i | \(-0.145234\pi\) | ||||
0.897703 | + | 0.440600i | \(0.145234\pi\) | |||||||
\(420\) | −1887.68 | − | 2220.74i | −0.219308 | − | 0.258002i | ||||
\(421\) | 4342.52 | 0.502711 | 0.251356 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251356 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(422\) | − | 4162.45i | − | 0.480153i | ||||||
\(423\) | 4206.95 | − | 680.915i | 0.483567 | − | 0.0782677i | ||||
\(424\) | 8992.05 | 1.02994 | ||||||||
\(425\) | −1564.81 | −0.178599 | ||||||||
\(426\) | −581.443 | + | 46.7505i | −0.0661291 | + | 0.00531707i | ||||
\(427\) | 6485.08 | − | 4671.76i | 0.734977 | − | 0.529467i | ||||
\(428\) | − | 3116.22i | − | 0.351935i | ||||||
\(429\) | 905.399 | − | 72.7980i | 0.101895 | − | 0.00819282i | ||||
\(430\) | 618.719i | 0.0693890i | ||||||||
\(431\) | 3165.86i | 0.353814i | 0.984228 | + | 0.176907i | \(0.0566092\pi\) | ||||
−0.984228 | + | 0.176907i | \(0.943391\pi\) | |||||||
\(432\) | 2881.77 | − | 707.342i | 0.320948 | − | 0.0787778i | ||||
\(433\) | 11822.9i | 1.31217i | 0.754685 | + | 0.656087i | \(0.227790\pi\) | ||||
−0.754685 | + | 0.656087i | \(0.772210\pi\) | |||||||
\(434\) | −2759.18 | − | 3830.14i | −0.305172 | − | 0.423624i | ||||
\(435\) | 190.229 | + | 2365.91i | 0.0209674 | + | 0.260774i | ||||
\(436\) | 9862.00 | 1.08327 | ||||||||
\(437\) | 7868.66 | 0.861348 | ||||||||
\(438\) | −2931.50 | + | 235.705i | −0.319800 | + | 0.0257133i | ||||
\(439\) | 11914.9i | 1.29537i | 0.761909 | + | 0.647684i | \(0.224262\pi\) | ||||
−0.761909 | + | 0.647684i | \(0.775738\pi\) | |||||||
\(440\) | 6641.05 | 0.719544 | ||||||||
\(441\) | −1491.72 | + | 9140.07i | −0.161075 | + | 0.986942i | ||||
\(442\) | 224.963 | 0.0242090 | ||||||||
\(443\) | 8026.37i | 0.860823i | 0.902633 | + | 0.430411i | \(0.141632\pi\) | ||||
−0.902633 | + | 0.430411i | \(0.858368\pi\) | |||||||
\(444\) | −10682.2 | + | 858.893i | −1.14179 | + | 0.0918047i | ||||
\(445\) | −3002.87 | −0.319887 | ||||||||
\(446\) | −7901.28 | −0.838871 | ||||||||
\(447\) | −122.407 | − | 1522.40i | −0.0129523 | − | 0.161089i | ||||
\(448\) | 978.092 | + | 1357.74i | 0.103148 | + | 0.143185i | ||||
\(449\) | 15264.8i | 1.60443i | 0.597036 | + | 0.802214i | \(0.296345\pi\) | ||||
−0.597036 | + | 0.802214i | \(0.703655\pi\) | |||||||
\(450\) | −150.318 | − | 928.721i | −0.0157468 | − | 0.0972896i | ||||
\(451\) | 4554.19i | 0.475495i | ||||||||
\(452\) | − | 4674.95i | − | 0.486484i | ||||||
\(453\) | −4927.06 | + | 396.157i | −0.511023 | + | 0.0410884i | ||||
\(454\) | 2478.53i | 0.256218i | ||||||||
\(455\) | −193.747 | + | 139.573i | −0.0199627 | + | 0.0143808i | ||||
\(456\) | −13660.4 | + | 1098.36i | −1.40287 | + | 0.112797i | ||||
\(457\) | −1121.90 | −0.114836 | −0.0574180 | − | 0.998350i | \(-0.518287\pi\) | ||||
−0.0574180 | + | 0.998350i | \(0.518287\pi\) | |||||||
\(458\) | −1886.85 | −0.192504 | ||||||||
\(459\) | −8528.35 | + | 2093.31i | −0.867253 | + | 0.212870i | ||||
\(460\) | 1770.40i | 0.179446i | ||||||||
\(461\) | 7671.75 | 0.775074 | 0.387537 | − | 0.921854i | \(-0.373326\pi\) | ||||
0.387537 | + | 0.921854i | \(0.373326\pi\) | |||||||
\(462\) | −5888.96 | − | 6927.99i | −0.593028 | − | 0.697660i | ||||
\(463\) | 3491.25 | 0.350436 | 0.175218 | − | 0.984530i | \(-0.443937\pi\) | ||||
0.175218 | + | 0.984530i | \(0.443937\pi\) | |||||||
\(464\) | 1932.25i | 0.193324i | ||||||||
\(465\) | 380.781 | + | 4735.83i | 0.0379749 | + | 0.472299i | ||||
\(466\) | 3089.50 | 0.307121 | ||||||||
\(467\) | 4518.50 | 0.447733 | 0.223866 | − | 0.974620i | \(-0.428132\pi\) | ||||
0.223866 | + | 0.974620i | \(0.428132\pi\) | |||||||
\(468\) | −67.3827 | − | 416.315i | −0.00665549 | − | 0.0411201i | ||||
\(469\) | −8762.89 | − | 12164.2i | −0.862756 | − | 1.19763i | ||||
\(470\) | − | 1099.98i | − | 0.107954i | ||||||
\(471\) | 709.430 | + | 8823.28i | 0.0694030 | + | 0.863174i | ||||
\(472\) | 11542.5i | 1.12560i | ||||||||
\(473\) | − | 6018.56i | − | 0.585060i | ||||||
\(474\) | 381.914 | + | 4749.92i | 0.0370082 | + | 0.460277i | ||||
\(475\) | − | 3365.29i | − | 0.325073i | ||||||
\(476\) | 4104.36 | + | 5697.45i | 0.395216 | + | 0.548618i | ||||
\(477\) | 1979.85 | + | 12232.3i | 0.190044 | + | 1.17416i | ||||
\(478\) | −6336.80 | −0.606357 | ||||||||
\(479\) | −18591.3 | −1.77340 | −0.886698 | − | 0.462348i | \(-0.847007\pi\) | ||||
−0.886698 | + | 0.462348i | \(0.847007\pi\) | |||||||
\(480\) | −387.762 | − | 4822.65i | −0.0368726 | − | 0.458589i | ||||
\(481\) | 877.982i | 0.0832277i | ||||||||
\(482\) | 49.5962 | 0.00468681 | ||||||||
\(483\) | 4286.11 | − | 3643.29i | 0.403778 | − | 0.343221i | ||||
\(484\) | −19774.2 | −1.85708 | ||||||||
\(485\) | − | 4069.12i | − | 0.380967i | ||||||
\(486\) | −2061.63 | − | 4860.51i | −0.192423 | − | 0.453657i | ||||
\(487\) | 62.4942 | 0.00581495 | 0.00290748 | − | 0.999996i | \(-0.499075\pi\) | ||||
0.00290748 | + | 0.999996i | \(0.499075\pi\) | |||||||
\(488\) | 8455.54 | 0.784353 | ||||||||
\(489\) | 9003.67 | − | 723.934i | 0.832638 | − | 0.0669477i | ||||
\(490\) | 2267.31 | + | 757.011i | 0.209034 | + | 0.0697924i | ||||
\(491\) | 11712.0i | 1.07649i | 0.842789 | + | 0.538244i | \(0.180912\pi\) | ||||
−0.842789 | + | 0.538244i | \(0.819088\pi\) | |||||||
\(492\) | 2107.71 | − | 169.469i | 0.193136 | − | 0.0155290i | ||||
\(493\) | − | 5718.32i | − | 0.522394i | ||||||
\(494\) | 483.805i | 0.0440636i | ||||||||
\(495\) | 1462.21 | + | 9034.09i | 0.132771 | + | 0.820307i | ||||
\(496\) | 3867.78i | 0.350138i | ||||||||
\(497\) | −1210.33 | + | 871.901i | −0.109236 | + | 0.0786923i | ||||
\(498\) | 376.792 | + | 4686.21i | 0.0339045 | + | 0.421675i | ||||
\(499\) | −10826.2 | −0.971237 | −0.485618 | − | 0.874171i | \(-0.661405\pi\) | ||||
−0.485618 | + | 0.874171i | \(0.661405\pi\) | |||||||
\(500\) | 757.169 | 0.0677233 | ||||||||
\(501\) | 8671.77 | − | 697.248i | 0.773306 | − | 0.0621771i | ||||
\(502\) | 774.576i | 0.0688666i | ||||||||
\(503\) | −11386.8 | −1.00937 | −0.504684 | − | 0.863304i | \(-0.668391\pi\) | ||||
−0.504684 | + | 0.863304i | \(0.668391\pi\) | |||||||
\(504\) | −6932.37 | + | 6923.25i | −0.612683 | + | 0.611877i | ||||
\(505\) | 1469.65 | 0.129502 | ||||||||
\(506\) | 5523.08i | 0.485239i | ||||||||
\(507\) | 11344.8 | − | 912.170i | 0.993766 | − | 0.0799031i | ||||
\(508\) | 9089.29 | 0.793843 | ||||||||
\(509\) | −755.673 | −0.0658047 | −0.0329024 | − | 0.999459i | \(-0.510475\pi\) | ||||
−0.0329024 | + | 0.999459i | \(0.510475\pi\) | |||||||
\(510\) | 181.657 | + | 2259.29i | 0.0157723 | + | 0.196163i | ||||
\(511\) | −6102.19 | + | 4395.92i | −0.528268 | + | 0.380556i | ||||
\(512\) | − | 7253.87i | − | 0.626131i | ||||||
\(513\) | −4501.87 | − | 18341.0i | −0.387452 | − | 1.57851i | ||||
\(514\) | 6981.63i | 0.599118i | ||||||||
\(515\) | − | 3294.92i | − | 0.281925i | ||||||
\(516\) | −2785.43 | + | 223.960i | −0.237639 | + | 0.0191072i | ||||
\(517\) | 10700.0i | 0.910225i | ||||||||
\(518\) | 7131.26 | − | 5137.25i | 0.604883 | − | 0.435749i | ||||
\(519\) | −9019.23 | + | 725.185i | −0.762813 | + | 0.0613335i | ||||
\(520\) | −252.616 | −0.0213038 | ||||||||
\(521\) | −14676.3 | −1.23413 | −0.617064 | − | 0.786913i | \(-0.711678\pi\) | ||||
−0.617064 | + | 0.786913i | \(0.711678\pi\) | |||||||
\(522\) | 3393.84 | − | 549.309i | 0.284567 | − | 0.0460587i | ||||
\(523\) | − | 10547.2i | − | 0.881832i | −0.897548 | − | 0.440916i | \(-0.854654\pi\) | ||
0.897548 | − | 0.440916i | \(-0.145346\pi\) | |||||||
\(524\) | 11148.9 | 0.929468 | ||||||||
\(525\) | −1558.17 | − | 1833.09i | −0.129532 | − | 0.152386i | ||||
\(526\) | 466.101 | 0.0386369 | ||||||||
\(527\) | − | 11446.3i | − | 0.946129i | ||||||
\(528\) | 597.098 | + | 7426.20i | 0.0492147 | + | 0.612090i | ||||
\(529\) | 8750.06 | 0.719163 | ||||||||
\(530\) | 3198.34 | 0.262127 | ||||||||
\(531\) | −15701.7 | + | 2541.40i | −1.28323 | + | 0.207697i | ||||
\(532\) | −12252.9 | + | 8826.82i | −0.998555 | + | 0.719344i | ||||
\(533\) | − | 173.235i | − | 0.0140781i | ||||||
\(534\) | 348.598 | + | 4335.57i | 0.0282497 | + | 0.351345i | ||||
\(535\) | − | 2572.26i | − | 0.207867i | ||||||
\(536\) | − | 15860.2i | − | 1.27809i | ||||||
\(537\) | −694.121 | − | 8632.89i | −0.0557794 | − | 0.693737i | ||||
\(538\) | 7479.95i | 0.599411i | ||||||||
\(539\) | −22055.2 | − | 7363.79i | −1.76249 | − | 0.588462i | ||||
\(540\) | 4126.62 | − | 1012.89i | 0.328855 | − | 0.0807186i | ||||
\(541\) | 7767.39 | 0.617276 | 0.308638 | − | 0.951180i | \(-0.400127\pi\) | ||||
0.308638 | + | 0.951180i | \(0.400127\pi\) | |||||||
\(542\) | 3481.49 | 0.275909 | ||||||||
\(543\) | 1744.91 | + | 21701.7i | 0.137903 | + | 1.71512i | ||||
\(544\) | 11656.2i | 0.918666i | ||||||||
\(545\) | 8140.52 | 0.639820 | ||||||||
\(546\) | 224.008 | + | 263.531i | 0.0175580 | + | 0.0206559i | ||||
\(547\) | −10163.9 | −0.794473 | −0.397237 | − | 0.917716i | \(-0.630031\pi\) | ||||
−0.397237 | + | 0.917716i | \(0.630031\pi\) | |||||||
\(548\) | − | 10838.3i | − | 0.844874i | ||||||
\(549\) | 1861.72 | + | 11502.4i | 0.144729 | + | 0.894192i | ||||
\(550\) | 2362.13 | 0.183130 | ||||||||
\(551\) | 12297.8 | 0.950824 | ||||||||
\(552\) | 5932.01 | − | 476.959i | 0.457397 | − | 0.0367767i | ||||
\(553\) | 7122.73 | + | 9887.39i | 0.547720 | + | 0.760316i | ||||
\(554\) | 3811.28i | 0.292285i | ||||||||
\(555\) | −8817.53 | + | 708.968i | −0.674384 | + | 0.0542234i | ||||
\(556\) | − | 13605.6i | − | 1.03778i | ||||||
\(557\) | 16917.4i | 1.28692i | 0.765480 | + | 0.643460i | \(0.222502\pi\) | ||||
−0.765480 | + | 0.643460i | \(0.777498\pi\) | |||||||
\(558\) | 6793.43 | − | 1099.55i | 0.515392 | − | 0.0834188i | ||||
\(559\) | 228.938i | 0.0173221i | ||||||||
\(560\) | −1144.79 | − | 1589.14i | −0.0863863 | − | 0.119917i | ||||
\(561\) | −1767.06 | − | 21977.1i | −0.132986 | − | 1.65397i | ||||
\(562\) | −783.190 | −0.0587845 | ||||||||
\(563\) | 13413.1 | 1.00408 | 0.502038 | − | 0.864846i | \(-0.332584\pi\) | ||||
0.502038 | + | 0.864846i | \(0.332584\pi\) | |||||||
\(564\) | 4952.04 | − | 398.165i | 0.369713 | − | 0.0297266i | ||||
\(565\) | − | 3858.90i | − | 0.287337i | ||||||
\(566\) | 435.300 | 0.0323269 | ||||||||
\(567\) | −10944.3 | − | 7906.05i | −0.810616 | − | 0.585578i | ||||
\(568\) | −1578.08 | −0.116575 | ||||||||
\(569\) | − | 8625.40i | − | 0.635493i | −0.948176 | − | 0.317747i | \(-0.897074\pi\) | ||
0.948176 | − | 0.317747i | \(-0.102926\pi\) | |||||||
\(570\) | −4858.83 | + | 390.671i | −0.357042 | + | 0.0287077i | ||||
\(571\) | 17682.5 | 1.29596 | 0.647978 | − | 0.761659i | \(-0.275615\pi\) | ||||
0.647978 | + | 0.761659i | \(0.275615\pi\) | |||||||
\(572\) | 1058.86 | 0.0774009 | ||||||||
\(573\) | −1606.90 | − | 19985.3i | −0.117154 | − | 1.45706i | ||||
\(574\) | −1407.07 | + | 1013.63i | −0.102317 | + | 0.0737078i | ||||
\(575\) | 1461.37i | 0.105988i | ||||||||
\(576\) | −2408.18 | + | 389.776i | −0.174203 | + | 0.0281956i | ||||
\(577\) | − | 22409.4i | − | 1.61684i | −0.588606 | − | 0.808420i | \(-0.700323\pi\) | ||
0.588606 | − | 0.808420i | \(-0.299677\pi\) | |||||||
\(578\) | 1387.06i | 0.0998166i | ||||||||
\(579\) | 5850.33 | − | 470.392i | 0.419916 | − | 0.0337631i | ||||
\(580\) | 2766.93i | 0.198087i | ||||||||
\(581\) | 7027.19 | + | 9754.78i | 0.501785 | + | 0.696551i | ||||
\(582\) | −5875.02 | + | 472.377i | −0.418432 | + | 0.0336438i | ||||
\(583\) | −31111.7 | −2.21015 | ||||||||
\(584\) | −7956.30 | −0.563757 | ||||||||
\(585\) | −55.6206 | − | 343.645i | −0.00393099 | − | 0.0242871i | ||||
\(586\) | 7232.39i | 0.509842i | ||||||||
\(587\) | −273.325 | −0.0192186 | −0.00960930 | − | 0.999954i | \(-0.503059\pi\) | ||||
−0.00960930 | + | 0.999954i | \(0.503059\pi\) | |||||||
\(588\) | −2587.30 | + | 10481.3i | −0.181460 | + | 0.735104i | ||||
\(589\) | 24616.5 | 1.72208 | ||||||||
\(590\) | 4105.49i | 0.286475i | ||||||||
\(591\) | 1579.74 | + | 19647.5i | 0.109952 | + | 1.36749i | ||||
\(592\) | −7201.32 | −0.499954 | ||||||||
\(593\) | −21856.6 | −1.51356 | −0.756780 | − | 0.653669i | \(-0.773229\pi\) | ||||
−0.756780 | + | 0.653669i | \(0.773229\pi\) | |||||||
\(594\) | 12873.7 | − | 3159.91i | 0.889253 | − | 0.218270i | ||||
\(595\) | 3387.91 | + | 4702.92i | 0.233430 | + | 0.324035i | ||||
\(596\) | − | 1780.44i | − | 0.122365i | ||||||
\(597\) | −1131.29 | − | 14070.1i | −0.0775557 | − | 0.964571i | ||||
\(598\) | − | 210.091i | − | 0.0143666i | ||||||
\(599\) | 11295.6i | 0.770493i | 0.922814 | + | 0.385246i | \(0.125884\pi\) | ||||
−0.922814 | + | 0.385246i | \(0.874116\pi\) | |||||||
\(600\) | −203.987 | − | 2537.02i | −0.0138796 | − | 0.172622i | ||||
\(601\) | − | 4883.39i | − | 0.331443i | −0.986173 | − | 0.165722i | \(-0.947005\pi\) | ||
0.986173 | − | 0.165722i | \(-0.0529953\pi\) | |||||||
\(602\) | 1859.51 | − | 1339.56i | 0.125893 | − | 0.0906917i | ||||
\(603\) | 21575.3 | − | 3492.07i | 1.45707 | − | 0.235834i | ||||
\(604\) | −5762.19 | −0.388179 | ||||||||
\(605\) | −16322.5 | −1.09686 | ||||||||
\(606\) | −170.609 | − | 2121.89i | −0.0114365 | − | 0.142237i | ||||
\(607\) | 11389.4i | 0.761583i | 0.924661 | + | 0.380792i | \(0.124348\pi\) | ||||
−0.924661 | + | 0.380792i | \(0.875652\pi\) | |||||||
\(608\) | −25067.7 | −1.67209 | ||||||||
\(609\) | 6698.69 | − | 5694.05i | 0.445722 | − | 0.378874i | ||||
\(610\) | 3007.52 | 0.199624 | ||||||||
\(611\) | − | 407.014i | − | 0.0269493i | ||||||
\(612\) | −10105.4 | + | 1635.61i | −0.667463 | + | 0.108032i | ||||
\(613\) | −683.834 | −0.0450567 | −0.0225284 | − | 0.999746i | \(-0.507172\pi\) | ||||
−0.0225284 | + | 0.999746i | \(0.507172\pi\) | |||||||
\(614\) | 452.362 | 0.0297326 | ||||||||
\(615\) | 1739.79 | − | 139.887i | 0.114074 | − | 0.00917200i | ||||
\(616\) | −14378.2 | − | 19959.1i | −0.940448 | − | 1.30548i | ||||
\(617\) | 7945.11i | 0.518409i | 0.965822 | + | 0.259204i | \(0.0834603\pi\) | ||||
−0.965822 | + | 0.259204i | \(0.916540\pi\) | |||||||
\(618\) | −4757.24 | + | 382.502i | −0.309651 | + | 0.0248972i | ||||
\(619\) | − | 18920.0i | − | 1.22853i | −0.789100 | − | 0.614264i | \(-0.789453\pi\) | ||
0.789100 | − | 0.614264i | \(-0.210547\pi\) | |||||||
\(620\) | 5538.56i | 0.358764i | ||||||||
\(621\) | 1954.93 | + | 7964.54i | 0.126326 | + | 0.514664i | ||||
\(622\) | − | 9592.17i | − | 0.618346i | ||||||
\(623\) | 6501.38 | + | 9024.87i | 0.418094 | + | 0.580376i | ||||
\(624\) | −22.7128 | − | 282.483i | −0.00145712 | − | 0.0181224i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 14515.7 | 0.926779 | ||||||||
\(627\) | 47264.0 | − | 3800.23i | 3.01044 | − | 0.242052i | ||||
\(628\) | 10318.8i | 0.655678i | ||||||||
\(629\) | 21311.7 | 1.35096 | ||||||||
\(630\) | −2465.75 | + | 2462.50i | −0.155933 | + | 0.155728i | ||||
\(631\) | −1816.54 | −0.114604 | −0.0573022 | − | 0.998357i | \(-0.518250\pi\) | ||||
−0.0573022 | + | 0.998357i | \(0.518250\pi\) | |||||||
\(632\) | 12891.6i | 0.811394i | ||||||||
\(633\) | 15468.0 | − | 1243.69i | 0.971245 | − | 0.0780923i | ||||
\(634\) | 3277.41 | 0.205304 | ||||||||
\(635\) | 7502.69 | 0.468875 | ||||||||
\(636\) | 1157.72 | + | 14398.7i | 0.0721801 | + | 0.897714i | ||||
\(637\) | 838.948 | + | 280.109i | 0.0521826 | + | 0.0174228i | ||||
\(638\) | 8631.94i | 0.535646i | ||||||||
\(639\) | −347.458 | − | 2146.72i | −0.0215105 | − | 0.132900i | ||||
\(640\) | − | 6819.26i | − | 0.421179i | ||||||
\(641\) | 15359.9i | 0.946457i | 0.880940 | + | 0.473229i | \(0.156912\pi\) | ||||
−0.880940 | + | 0.473229i | \(0.843088\pi\) | |||||||
\(642\) | −3713.86 | + | 298.610i | −0.228309 | + | 0.0183570i | ||||
\(643\) | − | 11392.9i | − | 0.698745i | −0.936984 | − | 0.349373i | \(-0.886395\pi\) | ||
0.936984 | − | 0.349373i | \(-0.113605\pi\) | |||||||
\(644\) | 5320.79 | − | 3833.02i | 0.325572 | − | 0.234537i | ||||
\(645\) | −2299.21 | + | 184.866i | −0.140359 | + | 0.0112854i | ||||
\(646\) | 11743.6 | 0.715242 | ||||||||
\(647\) | 4600.01 | 0.279513 | 0.139757 | − | 0.990186i | \(-0.455368\pi\) | ||||
0.139757 | + | 0.990186i | \(0.455368\pi\) | |||||||
\(648\) | −4505.61 | − | 13554.0i | −0.273143 | − | 0.821686i | ||||
\(649\) | − | 39935.9i | − | 2.41544i | ||||||
\(650\) | −89.8521 | −0.00542198 | ||||||||
\(651\) | 13408.7 | − | 11397.7i | 0.807265 | − | 0.686195i | ||||
\(652\) | 10529.8 | 0.632483 | ||||||||
\(653\) | 19253.3i | 1.15381i | 0.816810 | + | 0.576907i | \(0.195741\pi\) | ||||
−0.816810 | + | 0.576907i | \(0.804259\pi\) | |||||||
\(654\) | −945.020 | − | 11753.4i | −0.0565034 | − | 0.702741i | ||||
\(655\) | 9202.76 | 0.548980 | ||||||||
\(656\) | 1420.90 | 0.0845682 | ||||||||
\(657\) | −1751.80 | − | 10823.3i | −0.104025 | − | 0.642704i | ||||
\(658\) | −3305.90 | + | 2381.52i | −0.195862 | + | 0.141096i | ||||
\(659\) | − | 1117.61i | − | 0.0660635i | −0.999454 | − | 0.0330317i | \(-0.989484\pi\) | ||
0.999454 | − | 0.0330317i | \(-0.0105162\pi\) | |||||||
\(660\) | 855.029 | + | 10634.1i | 0.0504272 | + | 0.627171i | ||||
\(661\) | − | 15114.5i | − | 0.889390i | −0.895682 | − | 0.444695i | \(-0.853312\pi\) | ||
0.895682 | − | 0.444695i | \(-0.146688\pi\) | |||||||
\(662\) | − | 162.672i | − | 0.00955051i | ||||||
\(663\) | 67.2165 | + | 835.981i | 0.00393736 | + | 0.0489696i | ||||
\(664\) | 12718.7i | 0.743346i | ||||||||
\(665\) | −10114.1 | + | 7286.04i | −0.589786 | + | 0.424873i | ||||
\(666\) | 2047.23 | + | 12648.5i | 0.119112 | + | 0.735916i | ||||
\(667\) | −5340.28 | −0.310010 | ||||||||
\(668\) | 10141.6 | 0.587413 | ||||||||
\(669\) | −2360.82 | − | 29361.8i | −0.136434 | − | 1.69685i | ||||
\(670\) | − | 5641.24i | − | 0.325284i | ||||||
\(671\) | −29255.5 | −1.68315 | ||||||||
\(672\) | −13654.5 | + | 11606.7i | −0.783833 | + | 0.666277i | ||||
\(673\) | 20340.5 | 1.16503 | 0.582516 | − | 0.812819i | \(-0.302068\pi\) | ||||
0.582516 | + | 0.812819i | \(0.302068\pi\) | |||||||
\(674\) | 672.500i | 0.0384329i | ||||||||
\(675\) | 3406.29 | − | 836.087i | 0.194234 | − | 0.0476756i | ||||
\(676\) | 13267.7 | 0.754878 | ||||||||
\(677\) | −28057.2 | −1.59280 | −0.796399 | − | 0.604772i | \(-0.793264\pi\) | ||||
−0.796399 | + | 0.604772i | \(0.793264\pi\) | |||||||
\(678\) | −5571.51 | + | 447.974i | −0.315594 | + | 0.0253751i | ||||
\(679\) | −12229.4 | + | 8809.87i | −0.691194 | + | 0.497926i | ||||
\(680\) | 6131.87i | 0.345804i | ||||||||
\(681\) | −9210.42 | + | 740.557i | −0.518273 | + | 0.0416714i | ||||
\(682\) | 17278.5i | 0.970130i | ||||||||
\(683\) | − | 19325.6i | − | 1.08268i | −0.840802 | − | 0.541342i | \(-0.817916\pi\) | ||
0.840802 | − | 0.541342i | \(-0.182084\pi\) | |||||||
\(684\) | −3517.54 | − | 21732.7i | −0.196632 | − | 1.21487i | ||||
\(685\) | − | 8946.43i | − | 0.499015i | ||||||
\(686\) | −2633.72 | − | 8453.18i | −0.146583 | − | 0.470472i | ||||
\(687\) | −563.772 | − | 7011.71i | −0.0313089 | − | 0.389393i | ||||
\(688\) | −1877.78 | −0.104055 | ||||||||
\(689\) | 1183.45 | 0.0654366 | ||||||||
\(690\) | 2109.93 | − | 169.648i | 0.116411 | − | 0.00935996i | ||||
\(691\) | − | 13253.9i | − | 0.729669i | −0.931072 | − | 0.364835i | \(-0.881126\pi\) | ||
0.931072 | − | 0.364835i | \(-0.118874\pi\) | |||||||
\(692\) | −10548.0 | −0.579443 | ||||||||
\(693\) | 23985.4 | − | 23953.9i | 1.31476 | − | 1.31303i | ||||
\(694\) | −2125.39 | −0.116252 | ||||||||
\(695\) | − | 11230.7i | − | 0.612954i | ||||||
\(696\) | 9271.04 | − | 745.432i | 0.504911 | − | 0.0405970i | ||||
\(697\) | −4205.02 | −0.228517 | ||||||||
\(698\) | −3899.66 | −0.211468 | ||||||||
\(699\) | 923.109 | + | 11480.8i | 0.0499502 | + | 0.621238i | ||||
\(700\) | −1639.31 | − | 2275.61i | −0.0885147 | − | 0.122871i | ||||
\(701\) | − | 3313.99i | − | 0.178556i | −0.996007 | − | 0.0892779i | \(-0.971544\pi\) | ||
0.996007 | − | 0.0892779i | \(-0.0284559\pi\) | |||||||
\(702\) | −489.700 | + | 120.199i | −0.0263284 | + | 0.00646240i | ||||
\(703\) | 45832.8i | 2.45891i | ||||||||
\(704\) | − | 6125.00i | − | 0.327905i | ||||||
\(705\) | 4087.62 | − | 328.663i | 0.218367 | − | 0.0175577i | ||||
\(706\) | − | 9577.83i | − | 0.510576i | ||||||
\(707\) | −3181.87 | − | 4416.90i | −0.169259 | − | 0.234957i | ||||
\(708\) | −18482.6 | + | 1486.08i | −0.981100 | + | 0.0788847i | ||||
\(709\) | 1427.42 | 0.0756104 | 0.0378052 | − | 0.999285i | \(-0.487963\pi\) | ||||
0.0378052 | + | 0.999285i | \(0.487963\pi\) | |||||||
\(710\) | −561.299 | −0.0296693 | ||||||||
\(711\) | −17537.0 | + | 2838.45i | −0.925020 | + | 0.149719i | ||||
\(712\) | 11767.0i | 0.619365i | ||||||||
\(713\) | −10689.6 | −0.561472 | ||||||||
\(714\) | 6396.81 | − | 5437.45i | 0.335287 | − | 0.285002i | ||||
\(715\) | 874.032 | 0.0457160 | ||||||||
\(716\) | − | 10096.2i | − | 0.526971i | ||||||
\(717\) | −1893.37 | − | 23548.1i | −0.0986180 | − | 1.22653i | ||||
\(718\) | 12829.4 | 0.666835 | ||||||||
\(719\) | 25522.1 | 1.32380 | 0.661902 | − | 0.749591i | \(-0.269750\pi\) | ||||
0.661902 | + | 0.749591i | \(0.269750\pi\) | |||||||
\(720\) | 2818.62 | − | 456.207i | 0.145894 | − | 0.0236137i | ||||
\(721\) | −9902.61 | + | 7133.69i | −0.511502 | + | 0.368478i | ||||
\(722\) | 15695.8i | 0.809054i | ||||||||
\(723\) | 14.8188 | + | 184.304i | 0.000762265 | + | 0.00948039i | ||||
\(724\) | 25380.1i | 1.30282i | ||||||||
\(725\) | 2283.94i | 0.116998i | ||||||||
\(726\) | 1894.85 | + | 23566.5i | 0.0968656 | + | 1.20473i | ||||
\(727\) | 28266.9i | 1.44204i | 0.692916 | + | 0.721018i | \(0.256326\pi\) | ||||
−0.692916 | + | 0.721018i | \(0.743674\pi\) | |||||||
\(728\) | 546.929 | + | 759.218i | 0.0278442 | + | 0.0386518i | ||||
\(729\) | 17446.1 | − | 9113.46i | 0.886352 | − | 0.463012i | ||||
\(730\) | −2829.94 | −0.143481 | ||||||||
\(731\) | 5557.11 | 0.281173 | ||||||||
\(732\) | 1088.64 | + | 13539.6i | 0.0549692 | + | 0.683659i | ||||
\(733\) | 24004.4i | 1.20958i | 0.796385 | + | 0.604790i | \(0.206743\pi\) | ||||
−0.796385 | + | 0.604790i | \(0.793257\pi\) | |||||||
\(734\) | 4324.26 | 0.217454 | ||||||||
\(735\) | −2135.67 | + | 8651.70i | −0.107177 | + | 0.434181i | ||||
\(736\) | 10885.6 | 0.545174 | ||||||||
\(737\) | 54874.9i | 2.74266i | ||||||||
\(738\) | −403.939 | − | 2495.69i | −0.0201480 | − | 0.124482i | ||||
\(739\) | 12241.0 | 0.609324 | 0.304662 | − | 0.952460i | \(-0.401456\pi\) | ||||
0.304662 | + | 0.952460i | \(0.401456\pi\) | |||||||
\(740\) | −10312.1 | −0.512271 | ||||||||
\(741\) | −1797.86 | + | 144.556i | −0.0891309 | + | 0.00716651i | ||||
\(742\) | −6924.60 | − | 9612.36i | −0.342601 | − | 0.475580i | ||||
\(743\) | − | 33949.2i | − | 1.67628i | −0.545455 | − | 0.838140i | \(-0.683643\pi\) | ||
0.545455 | − | 0.838140i | \(-0.316357\pi\) | |||||||
\(744\) | 18557.8 | − | 1492.13i | 0.914465 | − | 0.0735270i | ||||
\(745\) | − | 1469.65i | − | 0.0722738i | ||||||
\(746\) | 8413.66i | 0.412930i | ||||||||
\(747\) | −17301.8 | + | 2800.38i | −0.847442 | + | 0.137163i | ||||
\(748\) | − | 25702.3i | − | 1.25638i | ||||||
\(749\) | −7730.73 | + | 5569.10i | −0.377136 | + | 0.271683i | ||||
\(750\) | −72.5553 | − | 902.380i | −0.00353246 | − | 0.0439337i | ||||
\(751\) | −14152.1 | −0.687640 | −0.343820 | − | 0.939036i | \(-0.611721\pi\) | ||||
−0.343820 | + | 0.939036i | \(0.611721\pi\) | |||||||
\(752\) | 3338.38 | 0.161886 | ||||||||
\(753\) | −2878.39 | + | 231.435i | −0.139302 | + | 0.0112005i | ||||
\(754\) | − | 328.348i | − | 0.0158590i | ||||||
\(755\) | −4756.36 | −0.229274 | ||||||||
\(756\) | −11978.5 | − | 10209.2i | −0.576264 | − | 0.491147i | ||||
\(757\) | −17424.1 | −0.836579 | −0.418290 | − | 0.908314i | \(-0.637370\pi\) | ||||
−0.418290 | + | 0.908314i | \(0.637370\pi\) | |||||||
\(758\) | − | 11825.0i | − | 0.566628i | ||||||
\(759\) | −20524.3 | + | 1650.24i | −0.981533 | + | 0.0789195i | ||||
\(760\) | −13187.2 | −0.629408 | ||||||||
\(761\) | 10979.4 | 0.522999 | 0.261500 | − | 0.965204i | \(-0.415783\pi\) | ||||
0.261500 | + | 0.965204i | \(0.415783\pi\) | |||||||
\(762\) | −870.976 | − | 10832.4i | −0.0414070 | − | 0.514985i | ||||
\(763\) | −17624.7 | − | 24465.7i | −0.836247 | − | 1.16083i | ||||
\(764\) | − | 23372.8i | − | 1.10680i | ||||||
\(765\) | −8341.44 | + | 1350.10i | −0.394229 | + | 0.0638080i | ||||
\(766\) | 9455.67i | 0.446015i | ||||||||
\(767\) | 1519.11i | 0.0715148i | ||||||||
\(768\) | −13589.5 | + | 1092.65i | −0.638501 | + | 0.0513382i | ||||
\(769\) | 20853.1i | 0.977868i | 0.872321 | + | 0.488934i | \(0.162614\pi\) | ||||
−0.872321 | + | 0.488934i | \(0.837386\pi\) | |||||||
\(770\) | −5114.14 | − | 7099.17i | −0.239352 | − | 0.332255i | ||||
\(771\) | −25944.3 | + | 2086.04i | −1.21188 | + | 0.0974407i | ||||
\(772\) | 6841.97 | 0.318974 | ||||||||
\(773\) | 7220.83 | 0.335983 | 0.167992 | − | 0.985788i | \(-0.446272\pi\) | ||||
0.167992 | + | 0.985788i | \(0.446272\pi\) | |||||||
\(774\) | 533.823 | + | 3298.16i | 0.0247906 | + | 0.153165i | ||||
\(775\) | 4571.76i | 0.211900i | ||||||||
\(776\) | −15945.2 | −0.737629 | ||||||||
\(777\) | 21221.2 | + | 24965.4i | 0.979802 | + | 1.15268i | ||||
\(778\) | −2820.20 | −0.129960 | ||||||||
\(779\) | − | 9043.30i | − | 0.415930i | ||||||
\(780\) | −32.5242 | − | 404.508i | −0.00149302 | − | 0.0185688i | ||||
\(781\) | 5460.01 | 0.250160 | ||||||||
\(782\) | −5099.63 | −0.233200 | ||||||||
\(783\) | 3055.32 | + | 12447.7i | 0.139449 | + | 0.568126i | ||||
\(784\) | −2297.49 | + | 6881.16i | −0.104660 | + | 0.313464i | ||||
\(785\) | 8517.60i | 0.387269i | ||||||||
\(786\) | −1068.33 | − | 13287.0i | −0.0484812 | − | 0.602967i | ||||
\(787\) | − | 6781.22i | − | 0.307147i | −0.988137 | − | 0.153573i | \(-0.950922\pi\) | ||
0.988137 | − | 0.153573i | \(-0.0490781\pi\) | |||||||
\(788\) | 22977.7i | 1.03877i | ||||||||
\(789\) | 139.266 | + | 1732.07i | 0.00628391 | + | 0.0781539i | ||||
\(790\) | 4585.37i | 0.206506i | ||||||||
\(791\) | −11597.6 | + | 8354.74i | −0.521319 | + | 0.375550i | ||||
\(792\) | 35400.9 | − | 5729.82i | 1.58828 | − | 0.257071i | ||||
\(793\) | 1112.84 | 0.0498336 | ||||||||
\(794\) | 1104.44 | 0.0493639 | ||||||||
\(795\) | 955.631 | + | 11885.3i | 0.0426324 | + | 0.530225i | ||||
\(796\) | − | 16454.9i | − | 0.732701i | ||||||
\(797\) | −13204.8 | −0.586873 | −0.293436 | − | 0.955979i | \(-0.594799\pi\) | ||||
−0.293436 | + | 0.955979i | \(0.594799\pi\) | |||||||
\(798\) | 11693.8 | + | 13757.0i | 0.518740 | + | 0.610265i | ||||
\(799\) | −9879.64 | −0.437443 | ||||||||
\(800\) | − | 4655.57i | − | 0.205749i | ||||||
\(801\) | −16007.2 | + | 2590.84i | −0.706100 | + | 0.114286i | ||||
\(802\) | −19449.3 | −0.856331 | ||||||||
\(803\) | 27528.1 | 1.20977 | ||||||||
\(804\) | 25396.5 | − | 2041.99i | 1.11401 | − | 0.0895713i | ||||
\(805\) | 4392.01 | − | 3163.94i | 0.192296 | − | 0.138527i | ||||
\(806\) | − | 657.252i | − | 0.0287230i | ||||||
\(807\) | −27796.1 | + | 2234.93i | −1.21248 | + | 0.0974885i | ||||
\(808\) | − | 5758.95i | − | 0.250741i | ||||||
\(809\) | 14180.1i | 0.616248i | 0.951346 | + | 0.308124i | \(0.0997012\pi\) | ||||
−0.951346 | + | 0.308124i | \(0.900299\pi\) | |||||||
\(810\) | −1602.58 | − | 4820.97i | −0.0695172 | − | 0.209126i | ||||
\(811\) | − | 4883.94i | − | 0.211465i | −0.994395 | − | 0.105733i | \(-0.966281\pi\) | ||
0.994395 | − | 0.105733i | \(-0.0337188\pi\) | |||||||
\(812\) | 8315.78 | − | 5990.57i | 0.359393 | − | 0.258901i | ||||
\(813\) | 1040.23 | + | 12937.5i | 0.0448740 | + | 0.558104i | ||||
\(814\) | −32170.5 | −1.38523 | ||||||||
\(815\) | 8691.75 | 0.373569 | ||||||||
\(816\) | −6856.82 | + | 551.318i | −0.294163 | + | 0.0236520i | ||||
\(817\) | 11951.1i | 0.511770i | ||||||||
\(818\) | −3298.97 | −0.141009 | ||||||||
\(819\) | −912.374 | + | 911.173i | −0.0389266 | + | 0.0388754i | ||||
\(820\) | 2034.69 | 0.0866517 | ||||||||
\(821\) | 5023.86i | 0.213561i | 0.994283 | + | 0.106781i | \(0.0340543\pi\) | ||||
−0.994283 | + | 0.106781i | \(0.965946\pi\) | |||||||
\(822\) | −12916.9 | + | 1038.58i | −0.548089 | + | 0.0440688i | ||||
\(823\) | 8525.75 | 0.361104 | 0.180552 | − | 0.983565i | \(-0.442212\pi\) | ||||
0.180552 | + | 0.983565i | \(0.442212\pi\) | |||||||
\(824\) | −12911.5 | −0.545864 | ||||||||
\(825\) | 705.778 | + | 8777.86i | 0.0297843 | + | 0.370431i | ||||
\(826\) | 12338.7 | − | 8888.62i | 0.519756 | − | 0.374424i | ||||
\(827\) | 12413.7i | 0.521965i | 0.965344 | + | 0.260983i | \(0.0840465\pi\) | ||||
−0.965344 | + | 0.260983i | \(0.915953\pi\) | |||||||
\(828\) | 1527.48 | + | 9437.35i | 0.0641107 | + | 0.396100i | ||||
\(829\) | 33996.1i | 1.42429i | 0.702034 | + | 0.712144i | \(0.252275\pi\) | ||||
−0.702034 | + | 0.712144i | \(0.747725\pi\) | |||||||
\(830\) | 4523.86i | 0.189187i | ||||||||
\(831\) | −14163.1 | + | 1138.77i | −0.591228 | + | 0.0475373i | ||||
\(832\) | 232.987i | 0.00970838i | ||||||||
\(833\) | 6799.21 | − | 20364.2i | 0.282807 | − | 0.847031i | ||||
\(834\) | −16214.9 | + | 1303.75i | −0.673233 | + | 0.0541308i | ||||
\(835\) | 8371.35 | 0.346949 | ||||||||
\(836\) | 55275.3 | 2.28676 | ||||||||
\(837\) | 6115.82 | + | 24916.4i | 0.252561 | + | 1.02896i | ||||
\(838\) | − | 21462.5i | − | 0.884738i | ||||||
\(839\) | 31623.9 | 1.30129 | 0.650643 | − | 0.759384i | \(-0.274500\pi\) | ||||
0.650643 | + | 0.759384i | \(0.274500\pi\) | |||||||
\(840\) | −7183.14 | + | 6105.85i | −0.295050 | + | 0.250800i | ||||
\(841\) | 16042.8 | 0.657786 | ||||||||
\(842\) | − | 6052.55i | − | 0.247725i | ||||||
\(843\) | −234.009 | − | 2910.40i | −0.00956072 | − | 0.118908i | ||||
\(844\) | 18089.8 | 0.737770 | ||||||||
\(845\) | 10951.8 | 0.445860 | ||||||||
\(846\) | −949.052 | − | 5863.59i | −0.0385686 | − | 0.238291i | ||||
\(847\) | 35339.1 | + | 49055.8i | 1.43361 | + | 1.99006i | ||||
\(848\) | 9706.80i | 0.393081i | ||||||||
\(849\) | 130.063 | + | 1617.61i | 0.00525765 | + | 0.0653902i | ||||
\(850\) | 2181.02i | 0.0880098i | ||||||||
\(851\) | − | 19902.8i | − | 0.801713i | ||||||
\(852\) | −203.176 | − | 2526.93i | −0.00816983 | − | 0.101609i | ||||
\(853\) | − | 8122.18i | − | 0.326024i | −0.986624 | − | 0.163012i | \(-0.947879\pi\) | ||
0.986624 | − | 0.163012i | \(-0.0521209\pi\) | |||||||
\(854\) | −6511.44 | − | 9038.84i | −0.260910 | − | 0.362181i | ||||
\(855\) | −2903.53 | − | 17939.1i | −0.116139 | − | 0.717548i | ||||
\(856\) | −10079.7 | −0.402472 | ||||||||
\(857\) | −32466.5 | −1.29409 | −0.647045 | − | 0.762451i | \(-0.723996\pi\) | ||||
−0.647045 | + | 0.762451i | \(0.723996\pi\) | |||||||
\(858\) | −101.465 | − | 1261.93i | −0.00403725 | − | 0.0502118i | ||||
\(859\) | 36463.5i | 1.44833i | 0.689625 | + | 0.724166i | \(0.257775\pi\) | ||||
−0.689625 | + | 0.724166i | \(0.742225\pi\) | |||||||
\(860\) | −2688.93 | −0.106618 | ||||||||
\(861\) | −4187.17 | − | 4925.94i | −0.165736 | − | 0.194977i | ||||
\(862\) | 4412.53 | 0.174352 | ||||||||
\(863\) | − | 27677.6i | − | 1.09172i | −0.837876 | − | 0.545860i | \(-0.816203\pi\) | ||
0.837876 | − | 0.545860i | \(-0.183797\pi\) | |||||||
\(864\) | −6227.94 | − | 25373.2i | −0.245230 | − | 0.999090i | ||||
\(865\) | −8706.76 | −0.342241 | ||||||||
\(866\) | 16478.6 | 0.646612 | ||||||||
\(867\) | −5154.43 | + | 414.438i | −0.201907 | + | 0.0162342i | ||||
\(868\) | 16645.7 | − | 11991.3i | 0.650911 | − | 0.468906i | ||||
\(869\) | − | 44603.9i | − | 1.74118i | ||||||
\(870\) | 3297.58 | − | 265.140i | 0.128504 | − | 0.0103323i | ||||
\(871\) | − | 2087.37i | − | 0.0812030i | ||||||
\(872\) | − | 31899.4i | − | 1.23882i | ||||||
\(873\) | −3510.79 | − | 21691.0i | −0.136108 | − | 0.840925i | ||||
\(874\) | − | 10967.2i | − | 0.424454i | ||||||
\(875\) | −1353.16 | − | 1878.39i | −0.0522802 | − | 0.0725726i | ||||
\(876\) | −1024.37 | − | 12740.2i | −0.0395093 | − | 0.491383i | ||||
\(877\) | 21309.8 | 0.820504 | 0.410252 | − | 0.911972i | \(-0.365441\pi\) | ||||
0.410252 | + | 0.911972i | \(0.365441\pi\) | |||||||
\(878\) | 16606.8 | 0.638330 | ||||||||
\(879\) | −26876.2 | + | 2160.96i | −1.03130 | + | 0.0829208i | ||||
\(880\) | 7168.92i | 0.274618i | ||||||||
\(881\) | 7499.34 | 0.286787 | 0.143393 | − | 0.989666i | \(-0.454199\pi\) | ||||
0.143393 | + | 0.989666i | \(0.454199\pi\) | |||||||
\(882\) | 12739.3 | + | 2079.14i | 0.486344 | + | 0.0793743i | ||||
\(883\) | −21250.7 | −0.809902 | −0.404951 | − | 0.914338i | \(-0.632711\pi\) | ||||
−0.404951 | + | 0.914338i | \(0.632711\pi\) | |||||||
\(884\) | 977.680i | 0.0371979i | ||||||||
\(885\) | −15256.3 | + | 1226.68i | −0.579476 | + | 0.0465924i | ||||
\(886\) | 11187.1 | 0.424195 | ||||||||
\(887\) | 24278.0 | 0.919024 | 0.459512 | − | 0.888171i | \(-0.348024\pi\) | ||||
0.459512 | + | 0.888171i | \(0.348024\pi\) | |||||||
\(888\) | 2778.16 | + | 34552.3i | 0.104987 | + | 1.30574i | ||||
\(889\) | −16243.8 | − | 22548.7i | −0.612821 | − | 0.850686i | ||||
\(890\) | 4185.37i | 0.157633i | ||||||||
\(891\) | 15589.0 | + | 46895.8i | 0.586141 | + | 1.76326i | ||||
\(892\) | − | 34338.7i | − | 1.28895i | ||||||
\(893\) | − | 21247.1i | − | 0.796202i | ||||||
\(894\) | −2121.90 | + | 170.610i | −0.0793813 | + | 0.00638260i | ||||
\(895\) | − | 8333.81i | − | 0.311250i | ||||||
\(896\) | −20494.7 | + | 14764.1i | −0.764152 | + | 0.550484i | ||||
\(897\) | 780.715 | − | 62.7729i | 0.0290606 | − | 0.00233659i | ||||
\(898\) | 21275.8 | 0.790628 | ||||||||
\(899\) | −16706.6 | −0.619797 | ||||||||
\(900\) | 4036.19 | − | 653.277i | 0.149488 | − | 0.0241954i | ||||
\(901\) | − | 28726.4i | − | 1.06217i | ||||||
\(902\) | 6347.57 | 0.234314 | ||||||||
\(903\) | 5533.52 | + | 6509.84i | 0.203925 | + | 0.239905i | ||||
\(904\) | −15121.5 | −0.556342 | ||||||||
\(905\) | 20949.8i | 0.769498i | ||||||||
\(906\) | 552.158 | + | 6867.27i | 0.0202475 | + | 0.251821i | ||||
\(907\) | −38164.2 | −1.39716 | −0.698579 | − | 0.715533i | \(-0.746184\pi\) | ||||
−0.698579 | + | 0.715533i | \(0.746184\pi\) | |||||||
\(908\) | −10771.6 | −0.393687 | ||||||||
\(909\) | 7834.13 | − | 1267.99i | 0.285855 | − | 0.0462670i | ||||
\(910\) | 194.535 | + | 270.043i | 0.00708656 | + | 0.00983718i | ||||
\(911\) | 27030.1i | 0.983038i | 0.870867 | + | 0.491519i | \(0.163558\pi\) | ||||
−0.870867 | + | 0.491519i | \(0.836442\pi\) | |||||||
\(912\) | −1185.66 | − | 14746.3i | −0.0430496 | − | 0.535414i | ||||
\(913\) | − | 44005.7i | − | 1.59515i | ||||||
\(914\) | 1563.69i | 0.0565888i | ||||||||
\(915\) | 898.613 | + | 11176.2i | 0.0324669 | + | 0.403796i | ||||
\(916\) | − | 8200.19i | − | 0.295788i | ||||||
\(917\) | −19924.5 | − | 27658.1i | −0.717519 | − | 0.996022i | ||||
\(918\) | 2917.64 | + | 11886.7i | 0.104898 | + | 0.427364i | ||||
\(919\) | 14738.9 | 0.529045 | 0.264523 | − | 0.964380i | \(-0.414786\pi\) | ||||
0.264523 | + | 0.964380i | \(0.414786\pi\) | |||||||
\(920\) | 5726.50 | 0.205214 | ||||||||
\(921\) | 135.161 | + | 1681.02i | 0.00483573 | + | 0.0601426i | ||||
\(922\) | − | 10692.8i | − | 0.381940i | ||||||
\(923\) | −207.692 | −0.00740656 | ||||||||
\(924\) | 30108.8 | − | 25593.2i | 1.07198 | − | 0.911206i | ||||
\(925\) | −8512.06 | −0.302567 | ||||||||
\(926\) | − | 4866.06i | − | 0.172688i | ||||||
\(927\) | −2842.82 | − | 17564.0i | −0.100723 | − | 0.622306i | ||||
\(928\) | 17012.9 | 0.601806 | ||||||||
\(929\) | 28651.5 | 1.01187 | 0.505933 | − | 0.862573i | \(-0.331148\pi\) | ||||
0.505933 | + | 0.862573i | \(0.331148\pi\) | |||||||
\(930\) | 6600.75 | − | 530.729i | 0.232739 | − | 0.0187132i | ||||
\(931\) | 43795.1 | + | 14622.4i | 1.54171 | + | 0.514746i | ||||
\(932\) | 13426.8i | 0.471900i | ||||||||
\(933\) | 35645.3 | − | 2866.04i | 1.25078 | − | 0.100568i | ||||
\(934\) | − | 6297.83i | − | 0.220633i | ||||||
\(935\) | − | 21215.8i | − | 0.742064i | ||||||
\(936\) | −1346.60 | + | 217.955i | −0.0470247 | + | 0.00761119i | ||||
\(937\) | − | 40156.3i | − | 1.40005i | −0.714117 | − | 0.700026i | \(-0.753172\pi\) | ||
0.714117 | − | 0.700026i | \(-0.246828\pi\) | |||||||
\(938\) | −16954.3 | + | 12213.6i | −0.590167 | + | 0.425148i | ||||
\(939\) | 4337.13 | + | 53941.5i | 0.150732 | + | 1.87467i | ||||
\(940\) | 4780.48 | 0.165874 | ||||||||
\(941\) | −16366.2 | −0.566973 | −0.283487 | − | 0.958976i | \(-0.591491\pi\) | ||||
−0.283487 | + | 0.958976i | \(0.591491\pi\) | |||||||
\(942\) | 12297.8 | − | 988.795i | 0.425354 | − | 0.0342003i | ||||
\(943\) | 3927.03i | 0.135611i | ||||||||
\(944\) | −12459.9 | −0.429593 | ||||||||
\(945\) | −9887.61 | − | 8427.15i | −0.340364 | − | 0.290090i | ||||
\(946\) | −8388.59 | −0.288305 | ||||||||
\(947\) | − | 33729.1i | − | 1.15739i | −0.815544 | − | 0.578695i | \(-0.803562\pi\) | ||
0.815544 | − | 0.578695i | \(-0.196438\pi\) | |||||||
\(948\) | −20643.0 | + | 1659.79i | −0.707229 | + | 0.0568643i | ||||
\(949\) | −1047.13 | −0.0358181 | ||||||||
\(950\) | −4690.50 | −0.160189 | ||||||||
\(951\) | 979.255 | + | 12179.1i | 0.0333907 | + | 0.415285i | ||||
\(952\) | 18428.8 | − | 13275.9i | 0.627397 | − | 0.451967i | ||||
\(953\) | 4151.70i | 0.141120i | 0.997508 | + | 0.0705598i | \(0.0224785\pi\) | ||||
−0.997508 | + | 0.0705598i | \(0.977521\pi\) | |||||||
\(954\) | 17049.2 | − | 2759.50i | 0.578603 | − | 0.0936499i | ||||
\(955\) | − | 19292.9i | − | 0.653721i | ||||||
\(956\) | − | 27539.5i | − | 0.931685i | ||||||
\(957\) | −32077.0 | + | 2579.13i | −1.08349 | + | 0.0871176i | ||||
\(958\) | 25912.3i | 0.873892i | ||||||||
\(959\) | −26887.7 | + | 19369.5i | −0.905371 | + | 0.652215i | ||||
\(960\) | −2339.88 | + | 188.136i | −0.0786658 | + | 0.00632507i | ||||
\(961\) | −3650.61 | −0.122541 | ||||||||
\(962\) | 1223.72 | 0.0410129 | ||||||||
\(963\) | −2219.32 | − | 13711.8i | −0.0742644 | − | 0.458833i | ||||
\(964\) | 215.543i | 0.00720143i | ||||||||
\(965\) | 5647.65 | 0.188398 | ||||||||
\(966\) | −5077.98 | − | 5973.92i | −0.169132 | − | 0.198973i | ||||
\(967\) | −50915.8 | −1.69322 | −0.846609 | − | 0.532216i | \(-0.821360\pi\) | ||||
−0.846609 | + | 0.532216i | \(0.821360\pi\) | |||||||
\(968\) | 63961.1i | 2.12375i | ||||||||
\(969\) | 3508.87 | + | 43640.3i | 0.116327 | + | 1.44678i | ||||
\(970\) | −5671.49 | −0.187733 | ||||||||
\(971\) | 22112.0 | 0.730801 | 0.365400 | − | 0.930850i | \(-0.380932\pi\) | ||||
0.365400 | + | 0.930850i | \(0.380932\pi\) | |||||||
\(972\) | 21123.6 | − | 8959.77i | 0.697057 | − | 0.295663i | ||||
\(973\) | −33752.8 | + | 24315.0i | −1.11209 | + | 0.801134i | ||||
\(974\) | − | 87.1037i | − | 0.00286548i | ||||||
\(975\) | −26.8468 | − | 333.898i | −0.000881833 | − | 0.0109675i | ||||
\(976\) | 9127.64i | 0.299353i | ||||||||
\(977\) | 14762.3i | 0.483407i | 0.970350 | + | 0.241704i | \(0.0777061\pi\) | ||||
−0.970350 | + | 0.241704i | \(0.922294\pi\) | |||||||
\(978\) | −1009.01 | − | 12549.2i | −0.0329904 | − | 0.410306i | ||||
\(979\) | − | 40712.9i | − | 1.32910i | ||||||
\(980\) | −3289.94 | + | 9853.65i | −0.107238 | + | 0.321187i | ||||
\(981\) | 43394.1 | − | 7023.55i | 1.41230 | − | 0.228588i | ||||
\(982\) | 16324.1 | 0.530471 | ||||||||
\(983\) | −21515.6 | −0.698110 | −0.349055 | − | 0.937102i | \(-0.613497\pi\) | ||||
−0.349055 | + | 0.937102i | \(0.613497\pi\) | |||||||
\(984\) | −548.160 | − | 6817.54i | −0.0177588 | − | 0.220869i | ||||
\(985\) | 18966.8i | 0.613535i | ||||||||
\(986\) | −7970.13 | −0.257424 | ||||||||
\(987\) | −9837.71 | − | 11573.4i | −0.317262 | − | 0.373239i | ||||
\(988\) | −2102.60 | −0.0677050 | ||||||||
\(989\) | − | 5189.73i | − | 0.166859i | ||||||
\(990\) | 12591.6 | − | 2038.02i | 0.404230 | − | 0.0654266i | ||||
\(991\) | −25694.9 | −0.823639 | −0.411820 | − | 0.911265i | \(-0.635107\pi\) | ||||
−0.411820 | + | 0.911265i | \(0.635107\pi\) | |||||||
\(992\) | 34054.7 | 1.08996 | ||||||||
\(993\) | 604.504 | − | 48.6047i | 0.0193186 | − | 0.00155330i | ||||
\(994\) | 1215.25 | + | 1686.94i | 0.0387779 | + | 0.0538294i | ||||
\(995\) | − | 13582.6i | − | 0.432761i | ||||||
\(996\) | −20366.1 | + | 1637.52i | −0.647917 | + | 0.0520953i | ||||
\(997\) | 37820.6i | 1.20140i | 0.799476 | + | 0.600698i | \(0.205110\pi\) | ||||
−0.799476 | + | 0.600698i | \(0.794890\pi\) | |||||||
\(998\) | 15089.4i | 0.478605i | ||||||||
\(999\) | −46391.3 | + | 11386.9i | −1.46922 | + | 0.360627i |
(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 | 105.4.b.b.41.7 | yes | 16 | |
3.2 | odd | 2 | 105.4.b.a.41.10 | yes | 16 | ||
7.6 | odd | 2 | 105.4.b.a.41.7 | ✓ | 16 | ||
21.20 | even | 2 | inner | 105.4.b.b.41.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.b.a.41.7 | ✓ | 16 | 7.6 | odd | 2 | ||
105.4.b.a.41.10 | yes | 16 | 3.2 | odd | 2 | ||
105.4.b.b.41.7 | yes | 16 | 1.1 | even | 1 | trivial | |
105.4.b.b.41.10 | yes | 16 | 21.20 | even | 2 | inner |