Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(309,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.309");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 309.5 | ||
Root | \(-2.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.309 |
Dual form | 770.2.c.e.309.3 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.41421i | − | 0.816497i | −0.912871 | − | 0.408248i | \(-0.866140\pi\) | ||
0.912871 | − | 0.408248i | \(-0.133860\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.63280 | + | 1.52773i | −0.730213 | + | 0.683220i | ||||
\(6\) | 1.41421 | 0.577350 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.52773 | − | 1.63280i | −0.483109 | − | 0.516338i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.41421i | 0.408248i | ||||||||
\(13\) | 1.56282i | 0.433447i | 0.976233 | + | 0.216724i | \(0.0695371\pi\) | ||||
−0.976233 | + | 0.216724i | \(0.930463\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.16053 | + | 2.30913i | 0.557847 | + | 0.596216i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.210157i | − | 0.0509706i | −0.999675 | − | 0.0254853i | \(-0.991887\pi\) | ||
0.999675 | − | 0.0254853i | \(-0.00811310\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 6.24264 | 1.43216 | 0.716080 | − | 0.698018i | \(-0.245935\pi\) | ||||
0.716080 | + | 0.698018i | \(0.245935\pi\) | |||||||
\(20\) | 1.63280 | − | 1.52773i | 0.365106 | − | 0.341610i | ||||
\(21\) | −1.41421 | −0.308607 | ||||||||
\(22\) | − | 1.00000i | − | 0.213201i | ||||||
\(23\) | 8.79073i | 1.83299i | 0.400042 | + | 0.916497i | \(0.368996\pi\) | ||||
−0.400042 | + | 0.916497i | \(0.631004\pi\) | |||||||
\(24\) | −1.41421 | −0.288675 | ||||||||
\(25\) | 0.332104 | − | 4.98896i | 0.0664208 | − | 0.997792i | ||||
\(26\) | −1.56282 | −0.306494 | ||||||||
\(27\) | − | 5.65685i | − | 1.08866i | ||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 9.96230 | 1.84995 | 0.924977 | − | 0.380024i | \(-0.124084\pi\) | ||||
0.924977 | + | 0.380024i | \(0.124084\pi\) | |||||||
\(30\) | −2.30913 | + | 2.16053i | −0.421588 | + | 0.394457i | ||||
\(31\) | 6.93933 | 1.24634 | 0.623170 | − | 0.782086i | \(-0.285844\pi\) | ||||
0.623170 | + | 0.782086i | \(0.285844\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.41421i | 0.246183i | ||||||||
\(34\) | 0.210157 | 0.0360417 | ||||||||
\(35\) | 1.52773 | + | 1.63280i | 0.258233 | + | 0.275994i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 0.358761i | − | 0.0589799i | −0.999565 | − | 0.0294900i | \(-0.990612\pi\) | ||
0.999565 | − | 0.0294900i | \(-0.00938831\pi\) | |||||||
\(38\) | 6.24264i | 1.01269i | ||||||||
\(39\) | 2.21016 | 0.353908 | ||||||||
\(40\) | 1.52773 | + | 1.63280i | 0.241555 | + | 0.258169i | ||||
\(41\) | −4.76687 | −0.744461 | −0.372230 | − | 0.928140i | \(-0.621407\pi\) | ||||
−0.372230 | + | 0.928140i | \(0.621407\pi\) | |||||||
\(42\) | − | 1.41421i | − | 0.218218i | ||||||
\(43\) | 5.44670i | 0.830614i | 0.909681 | + | 0.415307i | \(0.136326\pi\) | ||||
−0.909681 | + | 0.415307i | \(0.863674\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −1.63280 | + | 1.52773i | −0.243404 | + | 0.227740i | ||||
\(46\) | −8.79073 | −1.29612 | ||||||||
\(47\) | 3.65685i | 0.533407i | 0.963779 | + | 0.266704i | \(0.0859344\pi\) | ||||
−0.963779 | + | 0.266704i | \(0.914066\pi\) | |||||||
\(48\) | − | 1.41421i | − | 0.204124i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.98896 | + | 0.332104i | 0.705545 | + | 0.0469666i | ||||
\(51\) | −0.297207 | −0.0416173 | ||||||||
\(52\) | − | 1.56282i | − | 0.216724i | ||||||
\(53\) | − | 2.76687i | − | 0.380059i | −0.981778 | − | 0.190030i | \(-0.939142\pi\) | ||
0.981778 | − | 0.190030i | \(-0.0608584\pi\) | |||||||
\(54\) | 5.65685 | 0.769800 | ||||||||
\(55\) | 1.63280 | − | 1.52773i | 0.220167 | − | 0.205999i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | − | 8.82843i | − | 1.16935i | ||||||
\(58\) | 9.96230i | 1.30811i | ||||||||
\(59\) | 2.11612 | 0.275495 | 0.137748 | − | 0.990467i | \(-0.456014\pi\) | ||||
0.137748 | + | 0.990467i | \(0.456014\pi\) | |||||||
\(60\) | −2.16053 | − | 2.30913i | −0.278923 | − | 0.298108i | ||||
\(61\) | 6.71231 | 0.859423 | 0.429711 | − | 0.902966i | \(-0.358615\pi\) | ||||
0.429711 | + | 0.902966i | \(0.358615\pi\) | |||||||
\(62\) | 6.93933i | 0.881296i | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.38756 | − | 2.55178i | −0.296140 | − | 0.316509i | ||||
\(66\) | −1.41421 | −0.174078 | ||||||||
\(67\) | 11.9779i | 1.46334i | 0.681661 | + | 0.731668i | \(0.261258\pi\) | ||||
−0.681661 | + | 0.731668i | \(0.738742\pi\) | |||||||
\(68\) | 0.210157i | 0.0254853i | ||||||||
\(69\) | 12.4320 | 1.49663 | ||||||||
\(70\) | −1.63280 | + | 1.52773i | −0.195158 | + | 0.182598i | ||||
\(71\) | 10.2751 | 1.21943 | 0.609716 | − | 0.792620i | \(-0.291283\pi\) | ||||
0.609716 | + | 0.792620i | \(0.291283\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | − | 6.02386i | − | 0.705039i | −0.935804 | − | 0.352519i | \(-0.885325\pi\) | ||
0.935804 | − | 0.352519i | \(-0.114675\pi\) | |||||||
\(74\) | 0.358761 | 0.0417051 | ||||||||
\(75\) | −7.05545 | − | 0.469666i | −0.814694 | − | 0.0542324i | ||||
\(76\) | −6.24264 | −0.716080 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 2.21016i | 0.250251i | ||||||||
\(79\) | 9.59530 | 1.07956 | 0.539778 | − | 0.841808i | \(-0.318508\pi\) | ||||
0.539778 | + | 0.841808i | \(0.318508\pi\) | |||||||
\(80\) | −1.63280 | + | 1.52773i | −0.182553 | + | 0.170805i | ||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | − | 4.76687i | − | 0.526413i | ||||||
\(83\) | 1.56282i | 0.171541i | 0.996315 | + | 0.0857707i | \(0.0273353\pi\) | ||||
−0.996315 | + | 0.0857707i | \(0.972665\pi\) | |||||||
\(84\) | 1.41421 | 0.154303 | ||||||||
\(85\) | 0.321063 | + | 0.343146i | 0.0348241 | + | 0.0372194i | ||||
\(86\) | −5.44670 | −0.587332 | ||||||||
\(87\) | − | 14.0888i | − | 1.51048i | ||||||
\(88\) | 1.00000i | 0.106600i | ||||||||
\(89\) | −8.59619 | −0.911194 | −0.455597 | − | 0.890186i | \(-0.650574\pi\) | ||||
−0.455597 | + | 0.890186i | \(0.650574\pi\) | |||||||
\(90\) | −1.52773 | − | 1.63280i | −0.161036 | − | 0.172113i | ||||
\(91\) | 1.56282 | 0.163828 | ||||||||
\(92\) | − | 8.79073i | − | 0.916497i | ||||||
\(93\) | − | 9.81370i | − | 1.01763i | ||||||
\(94\) | −3.65685 | −0.377176 | ||||||||
\(95\) | −10.1930 | + | 9.53705i | −1.04578 | + | 0.978480i | ||||
\(96\) | 1.41421 | 0.144338 | ||||||||
\(97\) | − | 14.1725i | − | 1.43900i | −0.694495 | − | 0.719498i | \(-0.744372\pi\) | ||
0.694495 | − | 0.719498i | \(-0.255628\pi\) | |||||||
\(98\) | − | 1.00000i | − | 0.101015i | ||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −0.332104 | + | 4.98896i | −0.0332104 | + | 0.498896i | ||||
\(101\) | −9.92982 | −0.988054 | −0.494027 | − | 0.869447i | \(-0.664476\pi\) | ||||
−0.494027 | + | 0.869447i | \(0.664476\pi\) | |||||||
\(102\) | − | 0.297207i | − | 0.0294279i | ||||||
\(103\) | − | 10.9393i | − | 1.07788i | −0.842343 | − | 0.538942i | \(-0.818824\pi\) | ||
0.842343 | − | 0.538942i | \(-0.181176\pi\) | |||||||
\(104\) | 1.56282 | 0.153247 | ||||||||
\(105\) | 2.30913 | − | 2.16053i | 0.225348 | − | 0.210846i | ||||
\(106\) | 2.76687 | 0.268743 | ||||||||
\(107\) | 12.8523i | 1.24248i | 0.783622 | + | 0.621239i | \(0.213370\pi\) | ||||
−0.783622 | + | 0.621239i | \(0.786630\pi\) | |||||||
\(108\) | 5.65685i | 0.544331i | ||||||||
\(109\) | −14.4476 | −1.38383 | −0.691914 | − | 0.721980i | \(-0.743232\pi\) | ||||
−0.691914 | + | 0.721980i | \(0.743232\pi\) | |||||||
\(110\) | 1.52773 | + | 1.63280i | 0.145663 | + | 0.155682i | ||||
\(111\) | −0.507364 | −0.0481569 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 5.55760i | 0.522815i | 0.965228 | + | 0.261408i | \(0.0841867\pi\) | ||||
−0.965228 | + | 0.261408i | \(0.915813\pi\) | |||||||
\(114\) | 8.82843 | 0.826858 | ||||||||
\(115\) | −13.4298 | − | 14.3535i | −1.25234 | − | 1.33848i | ||||
\(116\) | −9.96230 | −0.924977 | ||||||||
\(117\) | 1.56282i | 0.144482i | ||||||||
\(118\) | 2.11612i | 0.194805i | ||||||||
\(119\) | −0.210157 | −0.0192651 | ||||||||
\(120\) | 2.30913 | − | 2.16053i | 0.210794 | − | 0.197229i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.71231i | 0.607704i | ||||||||
\(123\) | 6.74138i | 0.607850i | ||||||||
\(124\) | −6.93933 | −0.623170 | ||||||||
\(125\) | 7.07950 | + | 8.65336i | 0.633210 | + | 0.773980i | ||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 1.07232i | 0.0951531i | 0.998868 | + | 0.0475766i | \(0.0151498\pi\) | ||||
−0.998868 | + | 0.0475766i | \(0.984850\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 7.70279 | 0.678193 | ||||||||
\(130\) | 2.55178 | − | 2.38756i | 0.223806 | − | 0.209403i | ||||
\(131\) | −21.8700 | −1.91079 | −0.955397 | − | 0.295324i | \(-0.904572\pi\) | ||||
−0.955397 | + | 0.295324i | \(0.904572\pi\) | |||||||
\(132\) | − | 1.41421i | − | 0.123091i | ||||||
\(133\) | − | 6.24264i | − | 0.541306i | ||||||
\(134\) | −11.9779 | −1.03473 | ||||||||
\(135\) | 8.64213 | + | 9.23654i | 0.743796 | + | 0.794955i | ||||
\(136\) | −0.210157 | −0.0180208 | ||||||||
\(137\) | − | 8.22181i | − | 0.702437i | −0.936294 | − | 0.351218i | \(-0.885767\pi\) | ||
0.936294 | − | 0.351218i | \(-0.114233\pi\) | |||||||
\(138\) | 12.4320i | 1.05828i | ||||||||
\(139\) | −9.71319 | −0.823862 | −0.411931 | − | 0.911215i | \(-0.635146\pi\) | ||||
−0.411931 | + | 0.911215i | \(0.635146\pi\) | |||||||
\(140\) | −1.52773 | − | 1.63280i | −0.129116 | − | 0.137997i | ||||
\(141\) | 5.17157 | 0.435525 | ||||||||
\(142\) | 10.2751i | 0.862269i | ||||||||
\(143\) | − | 1.56282i | − | 0.130689i | ||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −16.2665 | + | 15.2197i | −1.35086 | + | 1.26392i | ||||
\(146\) | 6.02386 | 0.498538 | ||||||||
\(147\) | 1.41421i | 0.116642i | ||||||||
\(148\) | 0.358761i | 0.0294900i | ||||||||
\(149\) | 5.02297 | 0.411498 | 0.205749 | − | 0.978605i | \(-0.434037\pi\) | ||||
0.205749 | + | 0.978605i | \(0.434037\pi\) | |||||||
\(150\) | 0.469666 | − | 7.05545i | 0.0383481 | − | 0.576075i | ||||
\(151\) | 2.56892 | 0.209056 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(152\) | − | 6.24264i | − | 0.506345i | ||||||
\(153\) | − | 0.210157i | − | 0.0169902i | ||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | −11.3306 | + | 10.6014i | −0.910094 | + | 0.851525i | ||||
\(156\) | −2.21016 | −0.176954 | ||||||||
\(157\) | − | 16.8692i | − | 1.34630i | −0.739504 | − | 0.673152i | \(-0.764940\pi\) | ||
0.739504 | − | 0.673152i | \(-0.235060\pi\) | |||||||
\(158\) | 9.59530i | 0.763361i | ||||||||
\(159\) | −3.91295 | −0.310317 | ||||||||
\(160\) | −1.52773 | − | 1.63280i | −0.120777 | − | 0.129085i | ||||
\(161\) | 8.79073 | 0.692807 | ||||||||
\(162\) | − | 5.00000i | − | 0.392837i | ||||||
\(163\) | − | 12.5723i | − | 0.984741i | −0.870386 | − | 0.492370i | \(-0.836131\pi\) | ||
0.870386 | − | 0.492370i | \(-0.163869\pi\) | |||||||
\(164\) | 4.76687 | 0.372230 | ||||||||
\(165\) | −2.16053 | − | 2.30913i | −0.168197 | − | 0.179766i | ||||
\(166\) | −1.56282 | −0.121298 | ||||||||
\(167\) | − | 13.0962i | − | 1.01341i | −0.862119 | − | 0.506706i | \(-0.830863\pi\) | ||
0.862119 | − | 0.506706i | \(-0.169137\pi\) | |||||||
\(168\) | 1.41421i | 0.109109i | ||||||||
\(169\) | 10.5576 | 0.812123 | ||||||||
\(170\) | −0.343146 | + | 0.321063i | −0.0263181 | + | 0.0246244i | ||||
\(171\) | 6.24264 | 0.477387 | ||||||||
\(172\) | − | 5.44670i | − | 0.415307i | ||||||
\(173\) | 0.461038i | 0.0350521i | 0.999846 | + | 0.0175260i | \(0.00557900\pi\) | ||||
−0.999846 | + | 0.0175260i | \(0.994421\pi\) | |||||||
\(174\) | 14.0888 | 1.06807 | ||||||||
\(175\) | −4.98896 | − | 0.332104i | −0.377130 | − | 0.0251047i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | − | 2.99265i | − | 0.224941i | ||||||
\(178\) | − | 8.59619i | − | 0.644311i | ||||||
\(179\) | 4.69544 | 0.350954 | 0.175477 | − | 0.984484i | \(-0.443853\pi\) | ||||
0.175477 | + | 0.984484i | \(0.443853\pi\) | |||||||
\(180\) | 1.63280 | − | 1.52773i | 0.121702 | − | 0.113870i | ||||
\(181\) | −15.4537 | −1.14866 | −0.574332 | − | 0.818623i | \(-0.694738\pi\) | ||||
−0.574332 | + | 0.818623i | \(0.694738\pi\) | |||||||
\(182\) | 1.56282i | 0.115844i | ||||||||
\(183\) | − | 9.49264i | − | 0.701716i | ||||||
\(184\) | 8.79073 | 0.648061 | ||||||||
\(185\) | 0.548088 | + | 0.585786i | 0.0402963 | + | 0.0430679i | ||||
\(186\) | 9.81370 | 0.719575 | ||||||||
\(187\) | 0.210157i | 0.0153682i | ||||||||
\(188\) | − | 3.65685i | − | 0.266704i | ||||||
\(189\) | −5.65685 | −0.411476 | ||||||||
\(190\) | −9.53705 | − | 10.1930i | −0.691890 | − | 0.739479i | ||||
\(191\) | −14.6954 | −1.06332 | −0.531662 | − | 0.846956i | \(-0.678432\pi\) | ||||
−0.531662 | + | 0.846956i | \(0.678432\pi\) | |||||||
\(192\) | 1.41421i | 0.102062i | ||||||||
\(193\) | 18.2751i | 1.31547i | 0.753248 | + | 0.657736i | \(0.228486\pi\) | ||||
−0.753248 | + | 0.657736i | \(0.771514\pi\) | |||||||
\(194\) | 14.1725 | 1.01752 | ||||||||
\(195\) | −3.60876 | + | 3.37652i | −0.258428 | + | 0.241797i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 19.8787i | 1.41630i | 0.706064 | + | 0.708148i | \(0.250469\pi\) | ||||
−0.706064 | + | 0.708148i | \(0.749531\pi\) | |||||||
\(198\) | − | 1.00000i | − | 0.0710669i | ||||||
\(199\) | 22.7941 | 1.61583 | 0.807917 | − | 0.589296i | \(-0.200595\pi\) | ||||
0.807917 | + | 0.589296i | \(0.200595\pi\) | |||||||
\(200\) | −4.98896 | − | 0.332104i | −0.352773 | − | 0.0234833i | ||||
\(201\) | 16.9393 | 1.19481 | ||||||||
\(202\) | − | 9.92982i | − | 0.698660i | ||||||
\(203\) | − | 9.96230i | − | 0.699217i | ||||||
\(204\) | 0.297207 | 0.0208087 | ||||||||
\(205\) | 7.78337 | − | 7.28248i | 0.543614 | − | 0.508630i | ||||
\(206\) | 10.9393 | 0.762179 | ||||||||
\(207\) | 8.79073i | 0.610998i | ||||||||
\(208\) | 1.56282i | 0.108362i | ||||||||
\(209\) | −6.24264 | −0.431812 | ||||||||
\(210\) | 2.16053 | + | 2.30913i | 0.149091 | + | 0.159345i | ||||
\(211\) | −13.8449 | −0.953124 | −0.476562 | − | 0.879141i | \(-0.658117\pi\) | ||||
−0.476562 | + | 0.879141i | \(0.658117\pi\) | |||||||
\(212\) | 2.76687i | 0.190030i | ||||||||
\(213\) | − | 14.5312i | − | 0.995663i | ||||||
\(214\) | −12.8523 | −0.878564 | ||||||||
\(215\) | −8.32106 | − | 8.89339i | −0.567492 | − | 0.606524i | ||||
\(216\) | −5.65685 | −0.384900 | ||||||||
\(217\) | − | 6.93933i | − | 0.471073i | ||||||
\(218\) | − | 14.4476i | − | 0.978514i | ||||||
\(219\) | −8.51902 | −0.575662 | ||||||||
\(220\) | −1.63280 | + | 1.52773i | −0.110084 | + | 0.102999i | ||||
\(221\) | 0.328437 | 0.0220931 | ||||||||
\(222\) | − | 0.507364i | − | 0.0340521i | ||||||
\(223\) | − | 11.1274i | − | 0.745146i | −0.928003 | − | 0.372573i | \(-0.878476\pi\) | ||
0.928003 | − | 0.372573i | \(-0.121524\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0.332104 | − | 4.98896i | 0.0221403 | − | 0.332597i | ||||
\(226\) | −5.55760 | −0.369686 | ||||||||
\(227\) | 17.0021i | 1.12847i | 0.825614 | + | 0.564236i | \(0.190829\pi\) | ||||
−0.825614 | + | 0.564236i | \(0.809171\pi\) | |||||||
\(228\) | 8.82843i | 0.584677i | ||||||||
\(229\) | −14.7895 | −0.977316 | −0.488658 | − | 0.872475i | \(-0.662513\pi\) | ||||
−0.488658 | + | 0.872475i | \(0.662513\pi\) | |||||||
\(230\) | 14.3535 | − | 13.4298i | 0.946445 | − | 0.885537i | ||||
\(231\) | 1.41421 | 0.0930484 | ||||||||
\(232\) | − | 9.96230i | − | 0.654057i | ||||||
\(233\) | − | 22.0888i | − | 1.44709i | −0.690279 | − | 0.723543i | \(-0.742512\pi\) | ||
0.690279 | − | 0.723543i | \(-0.257488\pi\) | |||||||
\(234\) | −1.56282 | −0.102165 | ||||||||
\(235\) | −5.58667 | − | 5.97093i | −0.364434 | − | 0.389501i | ||||
\(236\) | −2.11612 | −0.137748 | ||||||||
\(237\) | − | 13.5698i | − | 0.881454i | ||||||
\(238\) | − | 0.210157i | − | 0.0136225i | ||||||
\(239\) | 12.3489 | 0.798783 | 0.399391 | − | 0.916781i | \(-0.369221\pi\) | ||||
0.399391 | + | 0.916781i | \(0.369221\pi\) | |||||||
\(240\) | 2.16053 | + | 2.30913i | 0.139462 | + | 0.149054i | ||||
\(241\) | 11.0659 | 0.712814 | 0.356407 | − | 0.934331i | \(-0.384002\pi\) | ||||
0.356407 | + | 0.934331i | \(0.384002\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | − | 9.89949i | − | 0.635053i | ||||||
\(244\) | −6.71231 | −0.429711 | ||||||||
\(245\) | 1.63280 | − | 1.52773i | 0.104316 | − | 0.0976029i | ||||
\(246\) | −6.74138 | −0.429815 | ||||||||
\(247\) | 9.75611i | 0.620766i | ||||||||
\(248\) | − | 6.93933i | − | 0.440648i | ||||||
\(249\) | 2.21016 | 0.140063 | ||||||||
\(250\) | −8.65336 | + | 7.07950i | −0.547287 | + | 0.447747i | ||||
\(251\) | 21.9488 | 1.38540 | 0.692699 | − | 0.721226i | \(-0.256421\pi\) | ||||
0.692699 | + | 0.721226i | \(0.256421\pi\) | |||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | − | 8.79073i | − | 0.552668i | ||||||
\(254\) | −1.07232 | −0.0672834 | ||||||||
\(255\) | 0.485281 | − | 0.454051i | 0.0303895 | − | 0.0284338i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 3.93845i | − | 0.245674i | −0.992427 | − | 0.122837i | \(-0.960801\pi\) | ||
0.992427 | − | 0.122837i | \(-0.0391992\pi\) | |||||||
\(258\) | 7.70279i | 0.479555i | ||||||||
\(259\) | −0.358761 | −0.0222923 | ||||||||
\(260\) | 2.38756 | + | 2.55178i | 0.148070 | + | 0.158254i | ||||
\(261\) | 9.96230 | 0.616651 | ||||||||
\(262\) | − | 21.8700i | − | 1.35114i | ||||||
\(263\) | 1.77996i | 0.109757i | 0.998493 | + | 0.0548786i | \(0.0174772\pi\) | ||||
−0.998493 | + | 0.0548786i | \(0.982523\pi\) | |||||||
\(264\) | 1.41421 | 0.0870388 | ||||||||
\(265\) | 4.22703 | + | 4.51776i | 0.259664 | + | 0.277524i | ||||
\(266\) | 6.24264 | 0.382761 | ||||||||
\(267\) | 12.1568i | 0.743987i | ||||||||
\(268\) | − | 11.9779i | − | 0.731668i | ||||||
\(269\) | 19.0555 | 1.16183 | 0.580916 | − | 0.813964i | \(-0.302695\pi\) | ||||
0.580916 | + | 0.813964i | \(0.302695\pi\) | |||||||
\(270\) | −9.23654 | + | 8.64213i | −0.562118 | + | 0.525943i | ||||
\(271\) | −12.5190 | −0.760476 | −0.380238 | − | 0.924889i | \(-0.624158\pi\) | ||||
−0.380238 | + | 0.924889i | \(0.624158\pi\) | |||||||
\(272\) | − | 0.210157i | − | 0.0127427i | ||||||
\(273\) | − | 2.21016i | − | 0.133765i | ||||||
\(274\) | 8.22181 | 0.496698 | ||||||||
\(275\) | −0.332104 | + | 4.98896i | −0.0200266 | + | 0.300846i | ||||
\(276\) | −12.4320 | −0.748317 | ||||||||
\(277\) | − | 2.75126i | − | 0.165307i | −0.996578 | − | 0.0826535i | \(-0.973661\pi\) | ||
0.996578 | − | 0.0826535i | \(-0.0263395\pi\) | |||||||
\(278\) | − | 9.71319i | − | 0.582559i | ||||||
\(279\) | 6.93933 | 0.415447 | ||||||||
\(280\) | 1.63280 | − | 1.52773i | 0.0975788 | − | 0.0912991i | ||||
\(281\) | 9.75050 | 0.581666 | 0.290833 | − | 0.956774i | \(-0.406068\pi\) | ||||
0.290833 | + | 0.956774i | \(0.406068\pi\) | |||||||
\(282\) | 5.17157i | 0.307963i | ||||||||
\(283\) | 26.1608i | 1.55510i | 0.628823 | + | 0.777548i | \(0.283537\pi\) | ||||
−0.628823 | + | 0.777548i | \(0.716463\pi\) | |||||||
\(284\) | −10.2751 | −0.609716 | ||||||||
\(285\) | 13.4874 | + | 14.4151i | 0.798926 | + | 0.853877i | ||||
\(286\) | 1.56282 | 0.0924113 | ||||||||
\(287\) | 4.76687i | 0.281380i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 16.9558 | 0.997402 | ||||||||
\(290\) | −15.2197 | − | 16.2665i | −0.893730 | − | 0.955202i | ||||
\(291\) | −20.0429 | −1.17493 | ||||||||
\(292\) | 6.02386i | 0.352519i | ||||||||
\(293\) | 0.814065i | 0.0475582i | 0.999717 | + | 0.0237791i | \(0.00756984\pi\) | ||||
−0.999717 | + | 0.0237791i | \(0.992430\pi\) | |||||||
\(294\) | −1.41421 | −0.0824786 | ||||||||
\(295\) | −3.45521 | + | 3.23285i | −0.201170 | + | 0.188224i | ||||
\(296\) | −0.358761 | −0.0208525 | ||||||||
\(297\) | 5.65685i | 0.328244i | ||||||||
\(298\) | 5.02297i | 0.290973i | ||||||||
\(299\) | −13.7383 | −0.794507 | ||||||||
\(300\) | 7.05545 | + | 0.469666i | 0.407347 | + | 0.0271162i | ||||
\(301\) | 5.44670 | 0.313942 | ||||||||
\(302\) | 2.56892i | 0.147825i | ||||||||
\(303\) | 14.0429i | 0.806743i | ||||||||
\(304\) | 6.24264 | 0.358040 | ||||||||
\(305\) | −10.9599 | + | 10.2546i | −0.627561 | + | 0.587175i | ||||
\(306\) | 0.210157 | 0.0120139 | ||||||||
\(307\) | 24.8593i | 1.41879i | 0.704809 | + | 0.709397i | \(0.251033\pi\) | ||||
−0.704809 | + | 0.709397i | \(0.748967\pi\) | |||||||
\(308\) | − | 1.00000i | − | 0.0569803i | ||||||
\(309\) | −15.4706 | −0.880089 | ||||||||
\(310\) | −10.6014 | − | 11.3306i | −0.602119 | − | 0.643534i | ||||
\(311\) | −13.6447 | −0.773717 | −0.386859 | − | 0.922139i | \(-0.626440\pi\) | ||||
−0.386859 | + | 0.922139i | \(0.626440\pi\) | |||||||
\(312\) | − | 2.21016i | − | 0.125126i | ||||||
\(313\) | − | 22.3943i | − | 1.26580i | −0.774234 | − | 0.632899i | \(-0.781865\pi\) | ||
0.774234 | − | 0.632899i | \(-0.218135\pi\) | |||||||
\(314\) | 16.8692 | 0.951981 | ||||||||
\(315\) | 1.52773 | + | 1.63280i | 0.0860776 | + | 0.0919981i | ||||
\(316\) | −9.59530 | −0.539778 | ||||||||
\(317\) | 19.3753i | 1.08822i | 0.839013 | + | 0.544112i | \(0.183133\pi\) | ||||
−0.839013 | + | 0.544112i | \(0.816867\pi\) | |||||||
\(318\) | − | 3.91295i | − | 0.219427i | ||||||
\(319\) | −9.96230 | −0.557782 | ||||||||
\(320\) | 1.63280 | − | 1.52773i | 0.0912766 | − | 0.0854025i | ||||
\(321\) | 18.1759 | 1.01448 | ||||||||
\(322\) | 8.79073i | 0.489888i | ||||||||
\(323\) | − | 1.31194i | − | 0.0729981i | ||||||
\(324\) | 5.00000 | 0.277778 | ||||||||
\(325\) | 7.79683 | + | 0.519018i | 0.432490 | + | 0.0287899i | ||||
\(326\) | 12.5723 | 0.696317 | ||||||||
\(327\) | 20.4320i | 1.12989i | ||||||||
\(328\) | 4.76687i | 0.263207i | ||||||||
\(329\) | 3.65685 | 0.201609 | ||||||||
\(330\) | 2.30913 | − | 2.16053i | 0.127114 | − | 0.118933i | ||||
\(331\) | −33.1391 | −1.82149 | −0.910744 | − | 0.412972i | \(-0.864491\pi\) | ||||
−0.910744 | + | 0.412972i | \(0.864491\pi\) | |||||||
\(332\) | − | 1.56282i | − | 0.0857707i | ||||||
\(333\) | − | 0.358761i | − | 0.0196600i | ||||||
\(334\) | 13.0962 | 0.716591 | ||||||||
\(335\) | −18.2990 | − | 19.5576i | −0.999780 | − | 1.06855i | ||||
\(336\) | −1.41421 | −0.0771517 | ||||||||
\(337\) | − | 9.62740i | − | 0.524438i | −0.965008 | − | 0.262219i | \(-0.915546\pi\) | ||
0.965008 | − | 0.262219i | \(-0.0844542\pi\) | |||||||
\(338\) | 10.5576i | 0.574258i | ||||||||
\(339\) | 7.85964 | 0.426877 | ||||||||
\(340\) | −0.321063 | − | 0.343146i | −0.0174121 | − | 0.0186097i | ||||
\(341\) | −6.93933 | −0.375786 | ||||||||
\(342\) | 6.24264i | 0.337563i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 5.44670 | 0.293666 | ||||||||
\(345\) | −20.2990 | + | 18.9926i | −1.09286 | + | 1.02253i | ||||
\(346\) | −0.461038 | −0.0247856 | ||||||||
\(347\) | 29.9147i | 1.60591i | 0.596042 | + | 0.802953i | \(0.296739\pi\) | ||||
−0.596042 | + | 0.802953i | \(0.703261\pi\) | |||||||
\(348\) | 14.0888i | 0.755240i | ||||||||
\(349\) | 8.89861 | 0.476332 | 0.238166 | − | 0.971225i | \(-0.423454\pi\) | ||||
0.238166 | + | 0.971225i | \(0.423454\pi\) | |||||||
\(350\) | 0.332104 | − | 4.98896i | 0.0177517 | − | 0.266671i | ||||
\(351\) | 8.84063 | 0.471878 | ||||||||
\(352\) | − | 1.00000i | − | 0.0533002i | ||||||
\(353\) | − | 13.6265i | − | 0.725267i | −0.931932 | − | 0.362634i | \(-0.881878\pi\) | ||
0.931932 | − | 0.362634i | \(-0.118122\pi\) | |||||||
\(354\) | 2.99265 | 0.159057 | ||||||||
\(355\) | −16.7773 | + | 15.6976i | −0.890445 | + | 0.833141i | ||||
\(356\) | 8.59619 | 0.455597 | ||||||||
\(357\) | 0.297207i | 0.0157299i | ||||||||
\(358\) | 4.69544i | 0.248162i | ||||||||
\(359\) | 23.2110 | 1.22503 | 0.612516 | − | 0.790458i | \(-0.290157\pi\) | ||||
0.612516 | + | 0.790458i | \(0.290157\pi\) | |||||||
\(360\) | 1.52773 | + | 1.63280i | 0.0805182 | + | 0.0860564i | ||||
\(361\) | 19.9706 | 1.05108 | ||||||||
\(362\) | − | 15.4537i | − | 0.812228i | ||||||
\(363\) | − | 1.41421i | − | 0.0742270i | ||||||
\(364\) | −1.56282 | −0.0819139 | ||||||||
\(365\) | 9.20280 | + | 9.83578i | 0.481697 | + | 0.514828i | ||||
\(366\) | 9.49264 | 0.496188 | ||||||||
\(367\) | 9.84316i | 0.513809i | 0.966437 | + | 0.256904i | \(0.0827025\pi\) | ||||
−0.966437 | + | 0.256904i | \(0.917297\pi\) | |||||||
\(368\) | 8.79073i | 0.458248i | ||||||||
\(369\) | −4.76687 | −0.248154 | ||||||||
\(370\) | −0.585786 | + | 0.548088i | −0.0304536 | + | 0.0284938i | ||||
\(371\) | −2.76687 | −0.143649 | ||||||||
\(372\) | 9.81370i | 0.508817i | ||||||||
\(373\) | 4.71929i | 0.244356i | 0.992508 | + | 0.122178i | \(0.0389878\pi\) | ||||
−0.992508 | + | 0.122178i | \(0.961012\pi\) | |||||||
\(374\) | −0.210157 | −0.0108670 | ||||||||
\(375\) | 12.2377 | − | 10.0119i | 0.631952 | − | 0.517014i | ||||
\(376\) | 3.65685 | 0.188588 | ||||||||
\(377\) | 15.5693i | 0.801857i | ||||||||
\(378\) | − | 5.65685i | − | 0.290957i | ||||||
\(379\) | −21.6906 | −1.11417 | −0.557085 | − | 0.830455i | \(-0.688080\pi\) | ||||
−0.557085 | + | 0.830455i | \(0.688080\pi\) | |||||||
\(380\) | 10.1930 | − | 9.53705i | 0.522891 | − | 0.489240i | ||||
\(381\) | 1.51649 | 0.0776922 | ||||||||
\(382\) | − | 14.6954i | − | 0.751884i | ||||||
\(383\) | 20.1759i | 1.03094i | 0.856908 | + | 0.515469i | \(0.172382\pi\) | ||||
−0.856908 | + | 0.515469i | \(0.827618\pi\) | |||||||
\(384\) | −1.41421 | −0.0721688 | ||||||||
\(385\) | −1.52773 | − | 1.63280i | −0.0778601 | − | 0.0832154i | ||||
\(386\) | −18.2751 | −0.930179 | ||||||||
\(387\) | 5.44670i | 0.276871i | ||||||||
\(388\) | 14.1725i | 0.719498i | ||||||||
\(389\) | 15.3769 | 0.779640 | 0.389820 | − | 0.920891i | \(-0.372537\pi\) | ||||
0.389820 | + | 0.920891i | \(0.372537\pi\) | |||||||
\(390\) | −3.37652 | − | 3.60876i | −0.170977 | − | 0.182736i | ||||
\(391\) | 1.84744 | 0.0934288 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | 30.9289i | 1.56016i | ||||||||
\(394\) | −19.8787 | −1.00147 | ||||||||
\(395\) | −15.6673 | + | 14.6590i | −0.788305 | + | 0.737574i | ||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 1.42983i | 0.0717610i | 0.999356 | + | 0.0358805i | \(0.0114236\pi\) | ||||
−0.999356 | + | 0.0358805i | \(0.988576\pi\) | |||||||
\(398\) | 22.7941i | 1.14257i | ||||||||
\(399\) | −8.82843 | −0.441974 | ||||||||
\(400\) | 0.332104 | − | 4.98896i | 0.0166052 | − | 0.249448i | ||||
\(401\) | −32.3761 | −1.61679 | −0.808394 | − | 0.588642i | \(-0.799663\pi\) | ||||
−0.808394 | + | 0.588642i | \(0.799663\pi\) | |||||||
\(402\) | 16.9393i | 0.844857i | ||||||||
\(403\) | 10.8449i | 0.540223i | ||||||||
\(404\) | 9.92982 | 0.494027 | ||||||||
\(405\) | 8.16402 | − | 7.63863i | 0.405674 | − | 0.379567i | ||||
\(406\) | 9.96230 | 0.494421 | ||||||||
\(407\) | 0.358761i | 0.0177831i | ||||||||
\(408\) | 0.297207i | 0.0147139i | ||||||||
\(409\) | 19.1100 | 0.944930 | 0.472465 | − | 0.881350i | \(-0.343364\pi\) | ||||
0.472465 | + | 0.881350i | \(0.343364\pi\) | |||||||
\(410\) | 7.28248 | + | 7.78337i | 0.359656 | + | 0.384393i | ||||
\(411\) | −11.6274 | −0.573537 | ||||||||
\(412\) | 10.9393i | 0.538942i | ||||||||
\(413\) | − | 2.11612i | − | 0.104127i | ||||||
\(414\) | −8.79073 | −0.432041 | ||||||||
\(415\) | −2.38756 | − | 2.55178i | −0.117201 | − | 0.125262i | ||||
\(416\) | −1.56282 | −0.0766234 | ||||||||
\(417\) | 13.7365i | 0.672681i | ||||||||
\(418\) | − | 6.24264i | − | 0.305338i | ||||||
\(419\) | 34.7453 | 1.69742 | 0.848710 | − | 0.528859i | \(-0.177380\pi\) | ||||
0.848710 | + | 0.528859i | \(0.177380\pi\) | |||||||
\(420\) | −2.30913 | + | 2.16053i | −0.112674 | + | 0.105423i | ||||
\(421\) | 22.3787 | 1.09067 | 0.545334 | − | 0.838219i | \(-0.316403\pi\) | ||||
0.545334 | + | 0.838219i | \(0.316403\pi\) | |||||||
\(422\) | − | 13.8449i | − | 0.673961i | ||||||
\(423\) | 3.65685i | 0.177802i | ||||||||
\(424\) | −2.76687 | −0.134371 | ||||||||
\(425\) | −1.04847 | − | 0.0697941i | −0.0508581 | − | 0.00338551i | ||||
\(426\) | 14.5312 | 0.704040 | ||||||||
\(427\) | − | 6.71231i | − | 0.324831i | ||||||
\(428\) | − | 12.8523i | − | 0.621239i | ||||||
\(429\) | −2.21016 | −0.106707 | ||||||||
\(430\) | 8.89339 | − | 8.32106i | 0.428878 | − | 0.401277i | ||||
\(431\) | −12.6971 | −0.611597 | −0.305798 | − | 0.952096i | \(-0.598923\pi\) | ||||
−0.305798 | + | 0.952096i | \(0.598923\pi\) | |||||||
\(432\) | − | 5.65685i | − | 0.272166i | ||||||
\(433\) | 15.0131i | 0.721483i | 0.932666 | + | 0.360741i | \(0.117476\pi\) | ||||
−0.932666 | + | 0.360741i | \(0.882524\pi\) | |||||||
\(434\) | 6.93933 | 0.333099 | ||||||||
\(435\) | 21.5239 | + | 23.0043i | 1.03199 | + | 1.10297i | ||||
\(436\) | 14.4476 | 0.691914 | ||||||||
\(437\) | 54.8774i | 2.62514i | ||||||||
\(438\) | − | 8.51902i | − | 0.407054i | ||||||
\(439\) | −4.29721 | −0.205095 | −0.102547 | − | 0.994728i | \(-0.532699\pi\) | ||||
−0.102547 | + | 0.994728i | \(0.532699\pi\) | |||||||
\(440\) | −1.52773 | − | 1.63280i | −0.0728315 | − | 0.0778409i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0.328437i | 0.0156222i | ||||||||
\(443\) | − | 41.8228i | − | 1.98706i | −0.113555 | − | 0.993532i | \(-0.536224\pi\) | ||
0.113555 | − | 0.993532i | \(-0.463776\pi\) | |||||||
\(444\) | 0.507364 | 0.0240784 | ||||||||
\(445\) | 14.0359 | − | 13.1326i | 0.665365 | − | 0.622546i | ||||
\(446\) | 11.1274 | 0.526898 | ||||||||
\(447\) | − | 7.10355i | − | 0.335986i | ||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | −15.4804 | −0.730567 | −0.365283 | − | 0.930896i | \(-0.619028\pi\) | ||||
−0.365283 | + | 0.930896i | \(0.619028\pi\) | |||||||
\(450\) | 4.98896 | + | 0.332104i | 0.235182 | + | 0.0156555i | ||||
\(451\) | 4.76687 | 0.224463 | ||||||||
\(452\) | − | 5.55760i | − | 0.261408i | ||||||
\(453\) | − | 3.63300i | − | 0.170693i | ||||||
\(454\) | −17.0021 | −0.797950 | ||||||||
\(455\) | −2.55178 | + | 2.38756i | −0.119629 | + | 0.111930i | ||||
\(456\) | −8.82843 | −0.413429 | ||||||||
\(457\) | − | 34.5980i | − | 1.61842i | −0.587517 | − | 0.809212i | \(-0.699894\pi\) | ||
0.587517 | − | 0.809212i | \(-0.300106\pi\) | |||||||
\(458\) | − | 14.7895i | − | 0.691067i | ||||||
\(459\) | −1.18883 | −0.0554898 | ||||||||
\(460\) | 13.4298 | + | 14.3535i | 0.626169 | + | 0.669238i | ||||
\(461\) | −30.8250 | −1.43566 | −0.717831 | − | 0.696217i | \(-0.754865\pi\) | ||||
−0.717831 | + | 0.696217i | \(0.754865\pi\) | |||||||
\(462\) | 1.41421i | 0.0657952i | ||||||||
\(463\) | − | 41.3648i | − | 1.92239i | −0.275875 | − | 0.961193i | \(-0.588968\pi\) | ||
0.275875 | − | 0.961193i | \(-0.411032\pi\) | |||||||
\(464\) | 9.96230 | 0.462488 | ||||||||
\(465\) | 14.9926 | + | 16.0239i | 0.695267 | + | 0.743089i | ||||
\(466\) | 22.0888 | 1.02324 | ||||||||
\(467\) | − | 8.74440i | − | 0.404643i | −0.979319 | − | 0.202321i | \(-0.935151\pi\) | ||
0.979319 | − | 0.202321i | \(-0.0648485\pi\) | |||||||
\(468\) | − | 1.56282i | − | 0.0722412i | ||||||
\(469\) | 11.9779 | 0.553089 | ||||||||
\(470\) | 5.97093 | − | 5.58667i | 0.275418 | − | 0.257694i | ||||
\(471\) | −23.8566 | −1.09925 | ||||||||
\(472\) | − | 2.11612i | − | 0.0974023i | ||||||
\(473\) | − | 5.44670i | − | 0.250439i | ||||||
\(474\) | 13.5698 | 0.623282 | ||||||||
\(475\) | 2.07321 | − | 31.1443i | 0.0951253 | − | 1.42900i | ||||
\(476\) | 0.210157 | 0.00963254 | ||||||||
\(477\) | − | 2.76687i | − | 0.126686i | ||||||
\(478\) | 12.3489i | 0.564825i | ||||||||
\(479\) | 4.87437 | 0.222715 | 0.111358 | − | 0.993780i | \(-0.464480\pi\) | ||||
0.111358 | + | 0.993780i | \(0.464480\pi\) | |||||||
\(480\) | −2.30913 | + | 2.16053i | −0.105397 | + | 0.0986143i | ||||
\(481\) | 0.560678 | 0.0255647 | ||||||||
\(482\) | 11.0659i | 0.504036i | ||||||||
\(483\) | − | 12.4320i | − | 0.565674i | ||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 21.6516 | + | 23.1409i | 0.983150 | + | 1.05077i | ||||
\(486\) | 9.89949 | 0.449050 | ||||||||
\(487\) | 16.3704i | 0.741814i | 0.928670 | + | 0.370907i | \(0.120953\pi\) | ||||
−0.928670 | + | 0.370907i | \(0.879047\pi\) | |||||||
\(488\) | − | 6.71231i | − | 0.303852i | ||||||
\(489\) | −17.7800 | −0.804038 | ||||||||
\(490\) | 1.52773 | + | 1.63280i | 0.0690156 | + | 0.0737626i | ||||
\(491\) | 9.39088 | 0.423804 | 0.211902 | − | 0.977291i | \(-0.432034\pi\) | ||||
0.211902 | + | 0.977291i | \(0.432034\pi\) | |||||||
\(492\) | − | 6.74138i | − | 0.303925i | ||||||
\(493\) | − | 2.09365i | − | 0.0942932i | ||||||
\(494\) | −9.75611 | −0.438948 | ||||||||
\(495\) | 1.63280 | − | 1.52773i | 0.0733891 | − | 0.0686662i | ||||
\(496\) | 6.93933 | 0.311585 | ||||||||
\(497\) | − | 10.2751i | − | 0.460902i | ||||||
\(498\) | 2.21016i | 0.0990395i | ||||||||
\(499\) | −35.6703 | −1.59682 | −0.798411 | − | 0.602113i | \(-0.794325\pi\) | ||||
−0.798411 | + | 0.602113i | \(0.794325\pi\) | |||||||
\(500\) | −7.07950 | − | 8.65336i | −0.316605 | − | 0.386990i | ||||
\(501\) | −18.5208 | −0.827448 | ||||||||
\(502\) | 21.9488i | 0.979625i | ||||||||
\(503\) | − | 0.313688i | − | 0.0139867i | −0.999976 | − | 0.00699333i | \(-0.997774\pi\) | ||
0.999976 | − | 0.00699333i | \(-0.00222606\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 16.2135 | − | 15.1700i | 0.721489 | − | 0.675058i | ||||
\(506\) | 8.79073 | 0.390796 | ||||||||
\(507\) | − | 14.9307i | − | 0.663096i | ||||||
\(508\) | − | 1.07232i | − | 0.0475766i | ||||||
\(509\) | −0.0922646 | −0.00408956 | −0.00204478 | − | 0.999998i | \(-0.500651\pi\) | ||||
−0.00204478 | + | 0.999998i | \(0.500651\pi\) | |||||||
\(510\) | 0.454051 | + | 0.485281i | 0.0201057 | + | 0.0214886i | ||||
\(511\) | −6.02386 | −0.266480 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 35.3137i | − | 1.55914i | ||||||
\(514\) | 3.93845 | 0.173717 | ||||||||
\(515\) | 16.7123 | + | 17.8618i | 0.736432 | + | 0.787085i | ||||
\(516\) | −7.70279 | −0.339097 | ||||||||
\(517\) | − | 3.65685i | − | 0.160828i | ||||||
\(518\) | − | 0.358761i | − | 0.0157630i | ||||||
\(519\) | 0.652007 | 0.0286199 | ||||||||
\(520\) | −2.55178 | + | 2.38756i | −0.111903 | + | 0.104701i | ||||
\(521\) | −12.2850 | −0.538216 | −0.269108 | − | 0.963110i | \(-0.586729\pi\) | ||||
−0.269108 | + | 0.963110i | \(0.586729\pi\) | |||||||
\(522\) | 9.96230i | 0.436038i | ||||||||
\(523\) | 2.46841i | 0.107936i | 0.998543 | + | 0.0539681i | \(0.0171869\pi\) | ||||
−0.998543 | + | 0.0539681i | \(0.982813\pi\) | |||||||
\(524\) | 21.8700 | 0.955397 | ||||||||
\(525\) | −0.469666 | + | 7.05545i | −0.0204979 | + | 0.307925i | ||||
\(526\) | −1.77996 | −0.0776100 | ||||||||
\(527\) | − | 1.45835i | − | 0.0635268i | ||||||
\(528\) | 1.41421i | 0.0615457i | ||||||||
\(529\) | −54.2769 | −2.35987 | ||||||||
\(530\) | −4.51776 | + | 4.22703i | −0.196239 | + | 0.183610i | ||||
\(531\) | 2.11612 | 0.0918318 | ||||||||
\(532\) | 6.24264i | 0.270653i | ||||||||
\(533\) | − | 7.44975i | − | 0.322685i | ||||||
\(534\) | −12.1568 | −0.526078 | ||||||||
\(535\) | −19.6348 | − | 20.9853i | −0.848885 | − | 0.907272i | ||||
\(536\) | 11.9779 | 0.517367 | ||||||||
\(537\) | − | 6.64035i | − | 0.286552i | ||||||
\(538\) | 19.0555i | 0.821539i | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −8.64213 | − | 9.23654i | −0.371898 | − | 0.397477i | ||||
\(541\) | −38.8991 | −1.67240 | −0.836202 | − | 0.548421i | \(-0.815229\pi\) | ||||
−0.836202 | + | 0.548421i | \(0.815229\pi\) | |||||||
\(542\) | − | 12.5190i | − | 0.537738i | ||||||
\(543\) | 21.8548i | 0.937880i | ||||||||
\(544\) | 0.210157 | 0.00901042 | ||||||||
\(545\) | 23.5901 | − | 22.0720i | 1.01049 | − | 0.945459i | ||||
\(546\) | 2.21016 | 0.0945860 | ||||||||
\(547\) | − | 34.2548i | − | 1.46463i | −0.680966 | − | 0.732315i | \(-0.738440\pi\) | ||
0.680966 | − | 0.732315i | \(-0.261560\pi\) | |||||||
\(548\) | 8.22181i | 0.351218i | ||||||||
\(549\) | 6.71231 | 0.286474 | ||||||||
\(550\) | −4.98896 | − | 0.332104i | −0.212730 | − | 0.0141610i | ||||
\(551\) | 62.1911 | 2.64943 | ||||||||
\(552\) | − | 12.4320i | − | 0.529140i | ||||||
\(553\) | − | 9.59530i | − | 0.408034i | ||||||
\(554\) | 2.75126 | 0.116890 | ||||||||
\(555\) | 0.828427 | − | 0.775114i | 0.0351648 | − | 0.0329018i | ||||
\(556\) | 9.71319 | 0.411931 | ||||||||
\(557\) | 29.2383i | 1.23887i | 0.785049 | + | 0.619434i | \(0.212638\pi\) | ||||
−0.785049 | + | 0.619434i | \(0.787362\pi\) | |||||||
\(558\) | 6.93933i | 0.293765i | ||||||||
\(559\) | −8.51219 | −0.360027 | ||||||||
\(560\) | 1.52773 | + | 1.63280i | 0.0645582 | + | 0.0689986i | ||||
\(561\) | 0.297207 | 0.0125481 | ||||||||
\(562\) | 9.75050i | 0.411300i | ||||||||
\(563\) | 26.8783i | 1.13279i | 0.824136 | + | 0.566393i | \(0.191661\pi\) | ||||
−0.824136 | + | 0.566393i | \(0.808339\pi\) | |||||||
\(564\) | −5.17157 | −0.217763 | ||||||||
\(565\) | −8.49050 | − | 9.07448i | −0.357198 | − | 0.381766i | ||||
\(566\) | −26.1608 | −1.09962 | ||||||||
\(567\) | 5.00000i | 0.209980i | ||||||||
\(568\) | − | 10.2751i | − | 0.431135i | ||||||
\(569\) | −6.92945 | −0.290498 | −0.145249 | − | 0.989395i | \(-0.546398\pi\) | ||||
−0.145249 | + | 0.989395i | \(0.546398\pi\) | |||||||
\(570\) | −14.4151 | + | 13.4874i | −0.603782 | + | 0.564926i | ||||
\(571\) | 29.3155 | 1.22681 | 0.613407 | − | 0.789767i | \(-0.289798\pi\) | ||||
0.613407 | + | 0.789767i | \(0.289798\pi\) | |||||||
\(572\) | 1.56282i | 0.0653447i | ||||||||
\(573\) | 20.7825i | 0.868201i | ||||||||
\(574\) | −4.76687 | −0.198965 | ||||||||
\(575\) | 43.8566 | + | 2.91944i | 1.82895 | + | 0.121749i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − | 4.09278i | − | 0.170385i | −0.996365 | − | 0.0851924i | \(-0.972850\pi\) | ||
0.996365 | − | 0.0851924i | \(-0.0271505\pi\) | |||||||
\(578\) | 16.9558i | 0.705270i | ||||||||
\(579\) | 25.8449 | 1.07408 | ||||||||
\(580\) | 16.2665 | − | 15.2197i | 0.675429 | − | 0.631962i | ||||
\(581\) | 1.56282 | 0.0648366 | ||||||||
\(582\) | − | 20.0429i | − | 0.830804i | ||||||
\(583\) | 2.76687i | 0.114592i | ||||||||
\(584\) | −6.02386 | −0.249269 | ||||||||
\(585\) | −2.38756 | − | 2.55178i | −0.0987133 | − | 0.105503i | ||||
\(586\) | −0.814065 | −0.0336287 | ||||||||
\(587\) | − | 42.7157i | − | 1.76307i | −0.472122 | − | 0.881533i | \(-0.656512\pi\) | ||
0.472122 | − | 0.881533i | \(-0.343488\pi\) | |||||||
\(588\) | − | 1.41421i | − | 0.0583212i | ||||||
\(589\) | 43.3198 | 1.78496 | ||||||||
\(590\) | −3.23285 | − | 3.45521i | −0.133094 | − | 0.142249i | ||||
\(591\) | 28.1127 | 1.15640 | ||||||||
\(592\) | − | 0.358761i | − | 0.0147450i | ||||||
\(593\) | − | 1.86952i | − | 0.0767719i | −0.999263 | − | 0.0383860i | \(-0.987778\pi\) | ||
0.999263 | − | 0.0383860i | \(-0.0122216\pi\) | |||||||
\(594\) | −5.65685 | −0.232104 | ||||||||
\(595\) | 0.343146 | − | 0.321063i | 0.0140676 | − | 0.0131623i | ||||
\(596\) | −5.02297 | −0.205749 | ||||||||
\(597\) | − | 32.2358i | − | 1.31932i | ||||||
\(598\) | − | 13.7383i | − | 0.561801i | ||||||
\(599\) | 13.5264 | 0.552673 | 0.276336 | − | 0.961061i | \(-0.410880\pi\) | ||||
0.276336 | + | 0.961061i | \(0.410880\pi\) | |||||||
\(600\) | −0.469666 | + | 7.05545i | −0.0191740 | + | 0.288038i | ||||
\(601\) | −11.9714 | −0.488326 | −0.244163 | − | 0.969734i | \(-0.578513\pi\) | ||||
−0.244163 | + | 0.969734i | \(0.578513\pi\) | |||||||
\(602\) | 5.44670i | 0.221991i | ||||||||
\(603\) | 11.9779i | 0.487778i | ||||||||
\(604\) | −2.56892 | −0.104528 | ||||||||
\(605\) | −1.63280 | + | 1.52773i | −0.0663830 | + | 0.0621109i | ||||
\(606\) | −14.0429 | −0.570453 | ||||||||
\(607\) | − | 8.99265i | − | 0.365000i | −0.983206 | − | 0.182500i | \(-0.941581\pi\) | ||
0.983206 | − | 0.182500i | \(-0.0584190\pi\) | |||||||
\(608\) | 6.24264i | 0.253173i | ||||||||
\(609\) | −14.0888 | −0.570908 | ||||||||
\(610\) | −10.2546 | − | 10.9599i | −0.415195 | − | 0.443753i | ||||
\(611\) | −5.71499 | −0.231204 | ||||||||
\(612\) | 0.210157i | 0.00849510i | ||||||||
\(613\) | − | 8.56245i | − | 0.345834i | −0.984936 | − | 0.172917i | \(-0.944681\pi\) | ||
0.984936 | − | 0.172917i | \(-0.0553193\pi\) | |||||||
\(614\) | −24.8593 | −1.00324 | ||||||||
\(615\) | −10.2990 | − | 11.0074i | −0.415295 | − | 0.443859i | ||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | − | 3.97614i | − | 0.160074i | −0.996792 | − | 0.0800368i | \(-0.974496\pi\) | ||
0.996792 | − | 0.0800368i | \(-0.0255038\pi\) | |||||||
\(618\) | − | 15.4706i | − | 0.622317i | ||||||
\(619\) | −39.0450 | −1.56935 | −0.784676 | − | 0.619906i | \(-0.787171\pi\) | ||||
−0.784676 | + | 0.619906i | \(0.787171\pi\) | |||||||
\(620\) | 11.3306 | − | 10.6014i | 0.455047 | − | 0.425763i | ||||
\(621\) | 49.7279 | 1.99551 | ||||||||
\(622\) | − | 13.6447i | − | 0.547101i | ||||||
\(623\) | 8.59619i | 0.344399i | ||||||||
\(624\) | 2.21016 | 0.0884771 | ||||||||
\(625\) | −24.7794 | − | 3.31371i | −0.991177 | − | 0.132548i | ||||
\(626\) | 22.3943 | 0.895055 | ||||||||
\(627\) | 8.82843i | 0.352573i | ||||||||
\(628\) | 16.8692i | 0.673152i | ||||||||
\(629\) | −0.0753962 | −0.00300624 | ||||||||
\(630\) | −1.63280 | + | 1.52773i | −0.0650525 | + | 0.0608661i | ||||
\(631\) | −28.2769 | −1.12569 | −0.562843 | − | 0.826564i | \(-0.690292\pi\) | ||||
−0.562843 | + | 0.826564i | \(0.690292\pi\) | |||||||
\(632\) | − | 9.59530i | − | 0.381681i | ||||||
\(633\) | 19.5797i | 0.778223i | ||||||||
\(634\) | −19.3753 | −0.769490 | ||||||||
\(635\) | −1.63821 | − | 1.75089i | −0.0650105 | − | 0.0694820i | ||||
\(636\) | 3.91295 | 0.155159 | ||||||||
\(637\) | − | 1.56282i | − | 0.0619211i | ||||||
\(638\) | − | 9.96230i | − | 0.394411i | ||||||
\(639\) | 10.2751 | 0.406478 | ||||||||
\(640\) | 1.52773 | + | 1.63280i | 0.0603887 | + | 0.0645423i | ||||
\(641\) | −6.78909 | −0.268153 | −0.134076 | − | 0.990971i | \(-0.542807\pi\) | ||||
−0.134076 | + | 0.990971i | \(0.542807\pi\) | |||||||
\(642\) | 18.1759i | 0.717344i | ||||||||
\(643\) | 12.7861i | 0.504233i | 0.967697 | + | 0.252117i | \(0.0811266\pi\) | ||||
−0.967697 | + | 0.252117i | \(0.918873\pi\) | |||||||
\(644\) | −8.79073 | −0.346403 | ||||||||
\(645\) | −12.5772 | + | 11.7678i | −0.495225 | + | 0.463355i | ||||
\(646\) | 1.31194 | 0.0516174 | ||||||||
\(647\) | − | 34.0312i | − | 1.33791i | −0.743305 | − | 0.668953i | \(-0.766743\pi\) | ||
0.743305 | − | 0.668953i | \(-0.233257\pi\) | |||||||
\(648\) | 5.00000i | 0.196419i | ||||||||
\(649\) | −2.11612 | −0.0830650 | ||||||||
\(650\) | −0.519018 | + | 7.79683i | −0.0203576 | + | 0.305817i | ||||
\(651\) | −9.81370 | −0.384629 | ||||||||
\(652\) | 12.5723i | 0.492370i | ||||||||
\(653\) | − | 6.01812i | − | 0.235507i | −0.993043 | − | 0.117754i | \(-0.962431\pi\) | ||
0.993043 | − | 0.117754i | \(-0.0375693\pi\) | |||||||
\(654\) | −20.4320 | −0.798953 | ||||||||
\(655\) | 35.7095 | − | 33.4114i | 1.39529 | − | 1.30549i | ||||
\(656\) | −4.76687 | −0.186115 | ||||||||
\(657\) | − | 6.02386i | − | 0.235013i | ||||||
\(658\) | 3.65685i | 0.142559i | ||||||||
\(659\) | −16.9498 | −0.660269 | −0.330134 | − | 0.943934i | \(-0.607094\pi\) | ||||
−0.330134 | + | 0.943934i | \(0.607094\pi\) | |||||||
\(660\) | 2.16053 | + | 2.30913i | 0.0840986 | + | 0.0898830i | ||||
\(661\) | 40.0714 | 1.55860 | 0.779299 | − | 0.626653i | \(-0.215576\pi\) | ||||
0.779299 | + | 0.626653i | \(0.215576\pi\) | |||||||
\(662\) | − | 33.1391i | − | 1.28799i | ||||||
\(663\) | − | 0.464480i | − | 0.0180389i | ||||||
\(664\) | 1.56282 | 0.0606491 | ||||||||
\(665\) | 9.53705 | + | 10.1930i | 0.369831 | + | 0.395268i | ||||
\(666\) | 0.358761 | 0.0139017 | ||||||||
\(667\) | 87.5759i | 3.39095i | ||||||||
\(668\) | 13.0962i | 0.506706i | ||||||||
\(669\) | −15.7365 | −0.608409 | ||||||||
\(670\) | 19.5576 | − | 18.2990i | 0.755576 | − | 0.706951i | ||||
\(671\) | −6.71231 | −0.259126 | ||||||||
\(672\) | − | 1.41421i | − | 0.0545545i | ||||||
\(673\) | − | 24.4797i | − | 0.943622i | −0.881700 | − | 0.471811i | \(-0.843600\pi\) | ||
0.881700 | − | 0.471811i | \(-0.156400\pi\) | |||||||
\(674\) | 9.62740 | 0.370833 | ||||||||
\(675\) | −28.2218 | − | 1.87867i | −1.08626 | − | 0.0723099i | ||||
\(676\) | −10.5576 | −0.406062 | ||||||||
\(677\) | − | 33.0788i | − | 1.27132i | −0.771969 | − | 0.635660i | \(-0.780728\pi\) | ||
0.771969 | − | 0.635660i | \(-0.219272\pi\) | |||||||
\(678\) | 7.85964i | 0.301848i | ||||||||
\(679\) | −14.1725 | −0.543889 | ||||||||
\(680\) | 0.343146 | − | 0.321063i | 0.0131590 | − | 0.0123122i | ||||
\(681\) | 24.0447 | 0.921393 | ||||||||
\(682\) | − | 6.93933i | − | 0.265721i | ||||||
\(683\) | − | 33.6175i | − | 1.28634i | −0.765724 | − | 0.643169i | \(-0.777619\pi\) | ||
0.765724 | − | 0.643169i | \(-0.222381\pi\) | |||||||
\(684\) | −6.24264 | −0.238693 | ||||||||
\(685\) | 12.5607 | + | 13.4246i | 0.479919 | + | 0.512928i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 20.9155i | 0.797975i | ||||||||
\(688\) | 5.44670i | 0.207653i | ||||||||
\(689\) | 4.32412 | 0.164736 | ||||||||
\(690\) | −18.9926 | − | 20.2990i | −0.723038 | − | 0.772769i | ||||
\(691\) | 16.7877 | 0.638634 | 0.319317 | − | 0.947648i | \(-0.396546\pi\) | ||||
0.319317 | + | 0.947648i | \(0.396546\pi\) | |||||||
\(692\) | − | 0.461038i | − | 0.0175260i | ||||||
\(693\) | 1.00000i | 0.0379869i | ||||||||
\(694\) | −29.9147 | −1.13555 | ||||||||
\(695\) | 15.8598 | − | 14.8391i | 0.601595 | − | 0.562879i | ||||
\(696\) | −14.0888 | −0.534035 | ||||||||
\(697\) | 1.00179i | 0.0379456i | ||||||||
\(698\) | 8.89861i | 0.336817i | ||||||||
\(699\) | −31.2383 | −1.18154 | ||||||||
\(700\) | 4.98896 | + | 0.332104i | 0.188565 | + | 0.0125524i | ||||
\(701\) | −4.99606 | −0.188699 | −0.0943493 | − | 0.995539i | \(-0.530077\pi\) | ||||
−0.0943493 | + | 0.995539i | \(0.530077\pi\) | |||||||
\(702\) | 8.84063i | 0.333668i | ||||||||
\(703\) | − | 2.23961i | − | 0.0844687i | ||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −8.44417 | + | 7.90075i | −0.318026 | + | 0.297559i | ||||
\(706\) | 13.6265 | 0.512841 | ||||||||
\(707\) | 9.92982i | 0.373449i | ||||||||
\(708\) | 2.99265i | 0.112471i | ||||||||
\(709\) | 13.3310 | 0.500655 | 0.250327 | − | 0.968161i | \(-0.419462\pi\) | ||||
0.250327 | + | 0.968161i | \(0.419462\pi\) | |||||||
\(710\) | −15.6976 | − | 16.7773i | −0.589120 | − | 0.629640i | ||||
\(711\) | 9.59530 | 0.359852 | ||||||||
\(712\) | 8.59619i | 0.322156i | ||||||||
\(713\) | 61.0018i | 2.28454i | ||||||||
\(714\) | −0.297207 | −0.0111227 | ||||||||
\(715\) | 2.38756 | + | 2.55178i | 0.0892896 | + | 0.0954310i | ||||
\(716\) | −4.69544 | −0.175477 | ||||||||
\(717\) | − | 17.4640i | − | 0.652203i | ||||||
\(718\) | 23.2110i | 0.866228i | ||||||||
\(719\) | 6.39823 | 0.238614 | 0.119307 | − | 0.992857i | \(-0.461933\pi\) | ||||
0.119307 | + | 0.992857i | \(0.461933\pi\) | |||||||
\(720\) | −1.63280 | + | 1.52773i | −0.0608510 | + | 0.0569350i | ||||
\(721\) | −10.9393 | −0.407402 | ||||||||
\(722\) | 19.9706i | 0.743227i | ||||||||
\(723\) | − | 15.6495i | − | 0.582010i | ||||||
\(724\) | 15.4537 | 0.574332 | ||||||||
\(725\) | 3.30852 | − | 49.7015i | 0.122875 | − | 1.84587i | ||||
\(726\) | 1.41421 | 0.0524864 | ||||||||
\(727\) | − | 2.00000i | − | 0.0741759i | −0.999312 | − | 0.0370879i | \(-0.988192\pi\) | ||
0.999312 | − | 0.0370879i | \(-0.0118082\pi\) | |||||||
\(728\) | − | 1.56282i | − | 0.0579219i | ||||||
\(729\) | −29.0000 | −1.07407 | ||||||||
\(730\) | −9.83578 | + | 9.20280i | −0.364039 | + | 0.340611i | ||||
\(731\) | 1.14466 | 0.0423369 | ||||||||
\(732\) | 9.49264i | 0.350858i | ||||||||
\(733\) | − | 22.4463i | − | 0.829074i | −0.910032 | − | 0.414537i | \(-0.863944\pi\) | ||
0.910032 | − | 0.414537i | \(-0.136056\pi\) | |||||||
\(734\) | −9.84316 | −0.363318 | ||||||||
\(735\) | −2.16053 | − | 2.30913i | −0.0796924 | − | 0.0851737i | ||||
\(736\) | −8.79073 | −0.324031 | ||||||||
\(737\) | − | 11.9779i | − | 0.441212i | ||||||
\(738\) | − | 4.76687i | − | 0.175471i | ||||||
\(739\) | 37.6127 | 1.38361 | 0.691803 | − | 0.722087i | \(-0.256817\pi\) | ||||
0.691803 | + | 0.722087i | \(0.256817\pi\) | |||||||
\(740\) | −0.548088 | − | 0.585786i | −0.0201481 | − | 0.0215339i | ||||
\(741\) | 13.7972 | 0.506853 | ||||||||
\(742\) | − | 2.76687i | − | 0.101575i | ||||||
\(743\) | − | 23.4779i | − | 0.861322i | −0.902514 | − | 0.430661i | \(-0.858281\pi\) | ||
0.902514 | − | 0.430661i | \(-0.141719\pi\) | |||||||
\(744\) | −9.81370 | −0.359788 | ||||||||
\(745\) | −8.20153 | + | 7.67372i | −0.300481 | + | 0.281143i | ||||
\(746\) | −4.71929 | −0.172786 | ||||||||
\(747\) | 1.56282i | 0.0571805i | ||||||||
\(748\) | − | 0.210157i | − | 0.00768411i | ||||||
\(749\) | 12.8523 | 0.469612 | ||||||||
\(750\) | 10.0119 | + | 12.2377i | 0.365584 | + | 0.446858i | ||||
\(751\) | 10.9540 | 0.399719 | 0.199859 | − | 0.979825i | \(-0.435951\pi\) | ||||
0.199859 | + | 0.979825i | \(0.435951\pi\) | |||||||
\(752\) | 3.65685i | 0.133352i | ||||||||
\(753\) | − | 31.0404i | − | 1.13117i | ||||||
\(754\) | −15.5693 | −0.566999 | ||||||||
\(755\) | −4.19454 | + | 3.92460i | −0.152655 | + | 0.142831i | ||||
\(756\) | 5.65685 | 0.205738 | ||||||||
\(757\) | − | 4.62223i | − | 0.167998i | −0.996466 | − | 0.0839989i | \(-0.973231\pi\) | ||
0.996466 | − | 0.0839989i | \(-0.0267692\pi\) | |||||||
\(758\) | − | 21.6906i | − | 0.787838i | ||||||
\(759\) | −12.4320 | −0.451252 | ||||||||
\(760\) | 9.53705 | + | 10.1930i | 0.345945 | + | 0.369740i | ||||
\(761\) | −42.6932 | −1.54763 | −0.773815 | − | 0.633412i | \(-0.781654\pi\) | ||||
−0.773815 | + | 0.633412i | \(0.781654\pi\) | |||||||
\(762\) | 1.51649i | 0.0549367i | ||||||||
\(763\) | 14.4476i | 0.523038i | ||||||||
\(764\) | 14.6954 | 0.531662 | ||||||||
\(765\) | 0.321063 | + | 0.343146i | 0.0116080 | + | 0.0124065i | ||||
\(766\) | −20.1759 | −0.728984 | ||||||||
\(767\) | 3.30711i | 0.119413i | ||||||||
\(768\) | − | 1.41421i | − | 0.0510310i | ||||||
\(769\) | −48.9133 | −1.76386 | −0.881929 | − | 0.471382i | \(-0.843755\pi\) | ||||
−0.881929 | + | 0.471382i | \(0.843755\pi\) | |||||||
\(770\) | 1.63280 | − | 1.52773i | 0.0588422 | − | 0.0550554i | ||||
\(771\) | −5.56980 | −0.200592 | ||||||||
\(772\) | − | 18.2751i | − | 0.657736i | ||||||
\(773\) | 48.4801i | 1.74371i | 0.489767 | + | 0.871853i | \(0.337082\pi\) | ||||
−0.489767 | + | 0.871853i | \(0.662918\pi\) | |||||||
\(774\) | −5.44670 | −0.195777 | ||||||||
\(775\) | 2.30458 | − | 34.6200i | 0.0827830 | − | 1.24359i | ||||
\(776\) | −14.1725 | −0.508762 | ||||||||
\(777\) | 0.507364i | 0.0182016i | ||||||||
\(778\) | 15.3769i | 0.551289i | ||||||||
\(779\) | −29.7579 | −1.06619 | ||||||||
\(780\) | 3.60876 | − | 3.37652i | 0.129214 | − | 0.120899i | ||||
\(781\) | −10.2751 | −0.367673 | ||||||||
\(782\) | 1.84744i | 0.0660641i | ||||||||
\(783\) | − | 56.3553i | − | 2.01397i | ||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 25.7714 | + | 27.5440i | 0.919822 | + | 0.983089i | ||||
\(786\) | −30.9289 | −1.10320 | ||||||||
\(787\) | 10.5021i | 0.374361i | 0.982326 | + | 0.187181i | \(0.0599350\pi\) | ||||
−0.982326 | + | 0.187181i | \(0.940065\pi\) | |||||||
\(788\) | − | 19.8787i | − | 0.708148i | ||||||
\(789\) | 2.51725 | 0.0896163 | ||||||||
\(790\) | −14.6590 | − | 15.6673i | −0.521544 | − | 0.557416i | ||||
\(791\) | 5.55760 | 0.197606 | ||||||||
\(792\) | 1.00000i | 0.0355335i | ||||||||
\(793\) | 10.4901i | 0.372515i | ||||||||
\(794\) | −1.42983 | −0.0507427 | ||||||||
\(795\) | 6.38908 | − | 5.97792i | 0.226597 | − | 0.212015i | ||||
\(796\) | −22.7941 | −0.807917 | ||||||||
\(797\) | − | 37.1872i | − | 1.31724i | −0.752477 | − | 0.658618i | \(-0.771141\pi\) | ||
0.752477 | − | 0.658618i | \(-0.228859\pi\) | |||||||
\(798\) | − | 8.82843i | − | 0.312523i | ||||||
\(799\) | 0.768514 | 0.0271881 | ||||||||
\(800\) | 4.98896 | + | 0.332104i | 0.176386 | + | 0.0117417i | ||||
\(801\) | −8.59619 | −0.303731 | ||||||||
\(802\) | − | 32.3761i | − | 1.14324i | ||||||
\(803\) | 6.02386i | 0.212577i | ||||||||
\(804\) | −16.9393 | −0.597404 | ||||||||
\(805\) | −14.3535 | + | 13.4298i | −0.505896 | + | 0.473339i | ||||
\(806\) | −10.8449 | −0.381996 | ||||||||
\(807\) | − | 26.9485i | − | 0.948631i | ||||||
\(808\) | 9.92982i | 0.349330i | ||||||||
\(809\) | −43.5403 | −1.53080 | −0.765399 | − | 0.643557i | \(-0.777458\pi\) | ||||
−0.765399 | + | 0.643557i | \(0.777458\pi\) | |||||||
\(810\) | 7.63863 | + | 8.16402i | 0.268394 | + | 0.286855i | ||||
\(811\) | −47.0147 | −1.65091 | −0.825455 | − | 0.564468i | \(-0.809081\pi\) | ||||
−0.825455 | + | 0.564468i | \(0.809081\pi\) | |||||||
\(812\) | 9.96230i | 0.349608i | ||||||||
\(813\) | 17.7046i | 0.620926i | ||||||||
\(814\) | −0.358761 | −0.0125746 | ||||||||
\(815\) | 19.2071 | + | 20.5282i | 0.672795 | + | 0.719070i | ||||
\(816\) | −0.297207 | −0.0104043 | ||||||||
\(817\) | 34.0018i | 1.18957i | ||||||||
\(818\) | 19.1100i | 0.668166i | ||||||||
\(819\) | 1.56282 | 0.0546093 | ||||||||
\(820\) | −7.78337 | + | 7.28248i | −0.271807 | + | 0.254315i | ||||
\(821\) | −42.5126 | −1.48370 | −0.741849 | − | 0.670567i | \(-0.766051\pi\) | ||||
−0.741849 | + | 0.670567i | \(0.766051\pi\) | |||||||
\(822\) | − | 11.6274i | − | 0.405552i | ||||||
\(823\) | 23.9262i | 0.834016i | 0.908903 | + | 0.417008i | \(0.136921\pi\) | ||||
−0.908903 | + | 0.417008i | \(0.863079\pi\) | |||||||
\(824\) | −10.9393 | −0.381090 | ||||||||
\(825\) | 7.05545 | + | 0.469666i | 0.245639 | + | 0.0163517i | ||||
\(826\) | 2.11612 | 0.0736292 | ||||||||
\(827\) | 12.5944i | 0.437951i | 0.975730 | + | 0.218975i | \(0.0702714\pi\) | ||||
−0.975730 | + | 0.218975i | \(0.929729\pi\) | |||||||
\(828\) | − | 8.79073i | − | 0.305499i | ||||||
\(829\) | −11.6836 | −0.405788 | −0.202894 | − | 0.979201i | \(-0.565035\pi\) | ||||
−0.202894 | + | 0.979201i | \(0.565035\pi\) | |||||||
\(830\) | 2.55178 | − | 2.38756i | 0.0885734 | − | 0.0828733i | ||||
\(831\) | −3.89087 | −0.134973 | ||||||||
\(832\) | − | 1.56282i | − | 0.0541809i | ||||||
\(833\) | 0.210157i | 0.00728152i | ||||||||
\(834\) | −13.7365 | −0.475657 | ||||||||
\(835\) | 20.0074 | + | 21.3835i | 0.692384 | + | 0.740007i | ||||
\(836\) | 6.24264 | 0.215906 | ||||||||
\(837\) | − | 39.2548i | − | 1.35684i | ||||||
\(838\) | 34.7453i | 1.20026i | ||||||||
\(839\) | −40.3302 | −1.39235 | −0.696177 | − | 0.717870i | \(-0.745117\pi\) | ||||
−0.696177 | + | 0.717870i | \(0.745117\pi\) | |||||||
\(840\) | −2.16053 | − | 2.30913i | −0.0745454 | − | 0.0796727i | ||||
\(841\) | 70.2475 | 2.42233 | ||||||||
\(842\) | 22.3787i | 0.771219i | ||||||||
\(843\) | − | 13.7893i | − | 0.474929i | ||||||
\(844\) | 13.8449 | 0.476562 | ||||||||
\(845\) | −17.2385 | + | 16.1291i | −0.593023 | + | 0.554859i | ||||
\(846\) | −3.65685 | −0.125725 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | − | 2.76687i | − | 0.0950148i | ||||||
\(849\) | 36.9969 | 1.26973 | ||||||||
\(850\) | 0.0697941 | − | 1.04847i | 0.00239392 | − | 0.0359621i | ||||
\(851\) | 3.15377 | 0.108110 | ||||||||
\(852\) | 14.5312i | 0.497831i | ||||||||
\(853\) | 30.2920i | 1.03718i | 0.855024 | + | 0.518589i | \(0.173543\pi\) | ||||
−0.855024 | + | 0.518589i | \(0.826457\pi\) | |||||||
\(854\) | 6.71231 | 0.229690 | ||||||||
\(855\) | −10.1930 | + | 9.53705i | −0.348594 | + | 0.326160i | ||||
\(856\) | 12.8523 | 0.439282 | ||||||||
\(857\) | − | 34.0134i | − | 1.16188i | −0.813948 | − | 0.580938i | \(-0.802686\pi\) | ||
0.813948 | − | 0.580938i | \(-0.197314\pi\) | |||||||
\(858\) | − | 2.21016i | − | 0.0754535i | ||||||
\(859\) | 19.3250 | 0.659360 | 0.329680 | − | 0.944093i | \(-0.393059\pi\) | ||||
0.329680 | + | 0.944093i | \(0.393059\pi\) | |||||||
\(860\) | 8.32106 | + | 8.89339i | 0.283746 | + | 0.303262i | ||||
\(861\) | 6.74138 | 0.229746 | ||||||||
\(862\) | − | 12.6971i | − | 0.432464i | ||||||
\(863\) | − | 23.2331i | − | 0.790865i | −0.918495 | − | 0.395432i | \(-0.870595\pi\) | ||
0.918495 | − | 0.395432i | \(-0.129405\pi\) | |||||||
\(864\) | 5.65685 | 0.192450 | ||||||||
\(865\) | −0.704340 | − | 0.752786i | −0.0239483 | − | 0.0255955i | ||||
\(866\) | −15.0131 | −0.510165 | ||||||||
\(867\) | − | 23.9792i | − | 0.814375i | ||||||
\(868\) | 6.93933i | 0.235536i | ||||||||
\(869\) | −9.59530 | −0.325498 | ||||||||
\(870\) | −23.0043 | + | 21.5239i | −0.779919 | + | 0.729727i | ||||
\(871\) | −18.7193 | −0.634279 | ||||||||
\(872\) | 14.4476i | 0.489257i | ||||||||
\(873\) | − | 14.1725i | − | 0.479665i | ||||||
\(874\) | −54.8774 | −1.85625 | ||||||||
\(875\) | 8.65336 | − | 7.07950i | 0.292537 | − | 0.239331i | ||||
\(876\) | 8.51902 | 0.287831 | ||||||||
\(877\) | − | 2.37260i | − | 0.0801171i | −0.999197 | − | 0.0400586i | \(-0.987246\pi\) | ||
0.999197 | − | 0.0400586i | \(-0.0127544\pi\) | |||||||
\(878\) | − | 4.29721i | − | 0.145024i | ||||||
\(879\) | 1.15126 | 0.0388311 | ||||||||
\(880\) | 1.63280 | − | 1.52773i | 0.0550418 | − | 0.0514996i | ||||
\(881\) | 10.6665 | 0.359364 | 0.179682 | − | 0.983725i | \(-0.442493\pi\) | ||||
0.179682 | + | 0.983725i | \(0.442493\pi\) | |||||||
\(882\) | − | 1.00000i | − | 0.0336718i | ||||||
\(883\) | − | 33.1018i | − | 1.11396i | −0.830525 | − | 0.556982i | \(-0.811959\pi\) | ||
0.830525 | − | 0.556982i | \(-0.188041\pi\) | |||||||
\(884\) | −0.328437 | −0.0110465 | ||||||||
\(885\) | 4.57194 | + | 4.88641i | 0.153684 | + | 0.164255i | ||||
\(886\) | 41.8228 | 1.40507 | ||||||||
\(887\) | 18.4246i | 0.618637i | 0.950958 | + | 0.309319i | \(0.100101\pi\) | ||||
−0.950958 | + | 0.309319i | \(0.899899\pi\) | |||||||
\(888\) | 0.507364i | 0.0170260i | ||||||||
\(889\) | 1.07232 | 0.0359645 | ||||||||
\(890\) | 13.1326 | + | 14.0359i | 0.440206 | + | 0.470484i | ||||
\(891\) | 5.00000 | 0.167506 | ||||||||
\(892\) | 11.1274i | 0.372573i | ||||||||
\(893\) | 22.8284i | 0.763924i | ||||||||
\(894\) | 7.10355 | 0.237578 | ||||||||
\(895\) | −7.66674 | + | 7.17335i | −0.256271 | + | 0.239778i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 19.4289i | 0.648712i | ||||||||
\(898\) | − | 15.4804i | − | 0.516589i | ||||||
\(899\) | 69.1317 | 2.30567 | ||||||||
\(900\) | −0.332104 | + | 4.98896i | −0.0110701 | + | 0.166299i | ||||
\(901\) | −0.581478 | −0.0193719 | ||||||||
\(902\) | 4.76687i | 0.158720i | ||||||||
\(903\) | − | 7.70279i | − | 0.256333i | ||||||
\(904\) | 5.55760 | 0.184843 | ||||||||
\(905\) | 25.2329 | − | 23.6090i | 0.838768 | − | 0.784790i | ||||
\(906\) | 3.63300 | 0.120698 | ||||||||
\(907\) | − | 2.13048i | − | 0.0707415i | −0.999374 | − | 0.0353707i | \(-0.988739\pi\) | ||
0.999374 | − | 0.0353707i | \(-0.0112612\pi\) | |||||||
\(908\) | − | 17.0021i | − | 0.564236i | ||||||
\(909\) | −9.92982 | −0.329351 | ||||||||
\(910\) | −2.38756 | − | 2.55178i | −0.0791467 | − | 0.0845905i | ||||
\(911\) | −18.0330 | −0.597460 | −0.298730 | − | 0.954338i | \(-0.596563\pi\) | ||||
−0.298730 | + | 0.954338i | \(0.596563\pi\) | |||||||
\(912\) | − | 8.82843i | − | 0.292338i | ||||||
\(913\) | − | 1.56282i | − | 0.0517217i | ||||||
\(914\) | 34.5980 | 1.14440 | ||||||||
\(915\) | 14.5021 | + | 15.4996i | 0.479426 | + | 0.512402i | ||||
\(916\) | 14.7895 | 0.488658 | ||||||||
\(917\) | 21.8700i | 0.722212i | ||||||||
\(918\) | − | 1.18883i | − | 0.0392372i | ||||||
\(919\) | 31.1326 | 1.02697 | 0.513485 | − | 0.858099i | \(-0.328354\pi\) | ||||
0.513485 | + | 0.858099i | \(0.328354\pi\) | |||||||
\(920\) | −14.3535 | + | 13.4298i | −0.473222 | + | 0.442768i | ||||
\(921\) | 35.1563 | 1.15844 | ||||||||
\(922\) | − | 30.8250i | − | 1.01517i | ||||||
\(923\) | 16.0581i | 0.528560i | ||||||||
\(924\) | −1.41421 | −0.0465242 | ||||||||
\(925\) | −1.78984 | − | 0.119146i | −0.0588497 | − | 0.00391750i | ||||
\(926\) | 41.3648 | 1.35933 | ||||||||
\(927\) | − | 10.9393i | − | 0.359295i | ||||||
\(928\) | 9.96230i | 0.327029i | ||||||||
\(929\) | −40.0911 | −1.31535 | −0.657674 | − | 0.753303i | \(-0.728459\pi\) | ||||
−0.657674 | + | 0.753303i | \(0.728459\pi\) | |||||||
\(930\) | −16.0239 | + | 14.9926i | −0.525443 | + | 0.491628i | ||||
\(931\) | −6.24264 | −0.204594 | ||||||||
\(932\) | 22.0888i | 0.723543i | ||||||||
\(933\) | 19.2965i | 0.631737i | ||||||||
\(934\) | 8.74440 | 0.286126 | ||||||||
\(935\) | −0.321063 | − | 0.343146i | −0.0104999 | − | 0.0112221i | ||||
\(936\) | 1.56282 | 0.0510823 | ||||||||
\(937\) | − | 2.48834i | − | 0.0812904i | −0.999174 | − | 0.0406452i | \(-0.987059\pi\) | ||
0.999174 | − | 0.0406452i | \(-0.0129413\pi\) | |||||||
\(938\) | 11.9779i | 0.391093i | ||||||||
\(939\) | −31.6703 | −1.03352 | ||||||||
\(940\) | 5.58667 | + | 5.97093i | 0.182217 | + | 0.194750i | ||||
\(941\) | −23.3300 | −0.760537 | −0.380269 | − | 0.924876i | \(-0.624168\pi\) | ||||
−0.380269 | + | 0.924876i | \(0.624168\pi\) | |||||||
\(942\) | − | 23.8566i | − | 0.777289i | ||||||
\(943\) | − | 41.9043i | − | 1.36459i | ||||||
\(944\) | 2.11612 | 0.0688738 | ||||||||
\(945\) | 9.23654 | − | 8.64213i | 0.300465 | − | 0.281128i | ||||
\(946\) | 5.44670 | 0.177087 | ||||||||
\(947\) | 25.6556i | 0.833694i | 0.908977 | + | 0.416847i | \(0.136865\pi\) | ||||
−0.908977 | + | 0.416847i | \(0.863135\pi\) | |||||||
\(948\) | 13.5698i | 0.440727i | ||||||||
\(949\) | 9.41418 | 0.305597 | ||||||||
\(950\) | 31.1443 | + | 2.07321i | 1.01045 | + | 0.0672637i | ||||
\(951\) | 27.4008 | 0.888530 | ||||||||
\(952\) | 0.210157i | 0.00681123i | ||||||||
\(953\) | − | 9.07970i | − | 0.294120i | −0.989128 | − | 0.147060i | \(-0.953019\pi\) | ||
0.989128 | − | 0.147060i | \(-0.0469811\pi\) | |||||||
\(954\) | 2.76687 | 0.0895808 | ||||||||
\(955\) | 23.9948 | − | 22.4506i | 0.776453 | − | 0.726485i | ||||
\(956\) | −12.3489 | −0.399391 | ||||||||
\(957\) | 14.0888i | 0.455427i | ||||||||
\(958\) | 4.87437i | 0.157484i | ||||||||
\(959\) | −8.22181 | −0.265496 | ||||||||
\(960\) | −2.16053 | − | 2.30913i | −0.0697308 | − | 0.0745270i | ||||
\(961\) | 17.1543 | 0.553366 | ||||||||
\(962\) | 0.560678i | 0.0180770i | ||||||||
\(963\) | 12.8523i | 0.414159i | ||||||||
\(964\) | −11.0659 | −0.356407 | ||||||||
\(965\) | −27.9194 | − | 29.8397i | −0.898757 | − | 0.960574i | ||||
\(966\) | 12.4320 | 0.399992 | ||||||||
\(967\) | 52.3419i | 1.68320i | 0.540101 | + | 0.841600i | \(0.318386\pi\) | ||||
−0.540101 | + | 0.841600i | \(0.681614\pi\) | |||||||
\(968\) | − | 1.00000i | − | 0.0321412i | ||||||
\(969\) | −1.85536 | −0.0596027 | ||||||||
\(970\) | −23.1409 | + | 21.6516i | −0.743008 | + | 0.695192i | ||||
\(971\) | 23.2600 | 0.746449 | 0.373225 | − | 0.927741i | \(-0.378252\pi\) | ||||
0.373225 | + | 0.927741i | \(0.378252\pi\) | |||||||
\(972\) | 9.89949i | 0.317526i | ||||||||
\(973\) | 9.71319i | 0.311391i | ||||||||
\(974\) | −16.3704 | −0.524542 | ||||||||
\(975\) | 0.734003 | − | 11.0264i | 0.0235069 | − | 0.353127i | ||||
\(976\) | 6.71231 | 0.214856 | ||||||||
\(977\) | − | 48.4436i | − | 1.54985i | −0.632054 | − | 0.774924i | \(-0.717788\pi\) | ||
0.632054 | − | 0.774924i | \(-0.282212\pi\) | |||||||
\(978\) | − | 17.7800i | − | 0.568540i | ||||||
\(979\) | 8.59619 | 0.274735 | ||||||||
\(980\) | −1.63280 | + | 1.52773i | −0.0521580 | + | 0.0488014i | ||||
\(981\) | −14.4476 | −0.461276 | ||||||||
\(982\) | 9.39088i | 0.299675i | ||||||||
\(983\) | − | 2.25304i | − | 0.0718609i | −0.999354 | − | 0.0359304i | \(-0.988561\pi\) | ||
0.999354 | − | 0.0359304i | \(-0.0114395\pi\) | |||||||
\(984\) | 6.74138 | 0.214907 | ||||||||
\(985\) | −30.3692 | − | 32.4580i | −0.967642 | − | 1.03420i | ||||
\(986\) | 2.09365 | 0.0666754 | ||||||||
\(987\) | − | 5.17157i | − | 0.164613i | ||||||
\(988\) | − | 9.75611i | − | 0.310383i | ||||||
\(989\) | −47.8804 | −1.52251 | ||||||||
\(990\) | 1.52773 | + | 1.63280i | 0.0485543 | + | 0.0518939i | ||||
\(991\) | 27.8254 | 0.883901 | 0.441951 | − | 0.897039i | \(-0.354287\pi\) | ||||
0.441951 | + | 0.897039i | \(0.354287\pi\) | |||||||
\(992\) | 6.93933i | 0.220324i | ||||||||
\(993\) | 46.8657i | 1.48724i | ||||||||
\(994\) | 10.2751 | 0.325907 | ||||||||
\(995\) | −37.2184 | + | 34.8232i | −1.17990 | + | 1.10397i | ||||
\(996\) | −2.21016 | −0.0700315 | ||||||||
\(997\) | − | 39.9966i | − | 1.26670i | −0.773864 | − | 0.633352i | \(-0.781679\pi\) | ||
0.773864 | − | 0.633352i | \(-0.218321\pi\) | |||||||
\(998\) | − | 35.6703i | − | 1.12912i | ||||||
\(999\) | −2.02946 | −0.0642092 |
(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 | 770.2.c.e.309.5 | yes | 8 | |
5.2 | odd | 4 | 3850.2.a.bx.1.1 | 4 | |||
5.3 | odd | 4 | 3850.2.a.by.1.4 | 4 | |||
5.4 | even | 2 | inner | 770.2.c.e.309.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.c.e.309.3 | ✓ | 8 | 5.4 | even | 2 | inner | |
770.2.c.e.309.5 | yes | 8 | 1.1 | even | 1 | trivial | |
3850.2.a.bx.1.1 | 4 | 5.2 | odd | 4 | |||
3850.2.a.by.1.4 | 4 | 5.3 | odd | 4 |