Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,4,Mod(769,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("960.769");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(56.6418336055\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.769 |
Dual form | 960.4.f.l.769.1 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.0000 | + | 5.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.0000i | 0.539949i | 0.962867 | + | 0.269975i | \(0.0870153\pi\) | ||||
−0.962867 | + | 0.269975i | \(0.912985\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 46.0000 | 1.26087 | 0.630433 | − | 0.776244i | \(-0.282877\pi\) | ||||
0.630433 | + | 0.776244i | \(0.282877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 34.0000i | − | 0.725377i | −0.931910 | − | 0.362689i | \(-0.881859\pi\) | ||
0.931910 | − | 0.362689i | \(-0.118141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | + | 30.0000i | −0.258199 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 66.0000i | 0.941609i | 0.882238 | + | 0.470804i | \(0.156036\pi\) | ||||
−0.882238 | + | 0.470804i | \(0.843964\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 104.000 | 1.25575 | 0.627875 | − | 0.778314i | \(-0.283925\pi\) | ||||
0.627875 | + | 0.778314i | \(0.283925\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −30.0000 | −0.311740 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 164.000i | − | 1.48680i | −0.668848 | − | 0.743399i | \(-0.733212\pi\) | ||
0.668848 | − | 0.743399i | \(-0.266788\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 75.0000 | + | 100.000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 224.000 | 1.43434 | 0.717168 | − | 0.696900i | \(-0.245438\pi\) | ||||
0.717168 | + | 0.696900i | \(0.245438\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −72.0000 | −0.417148 | −0.208574 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208574 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 138.000i | 0.727961i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −50.0000 | + | 100.000i | −0.241473 | + | 0.482945i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 22.0000i | 0.0977507i | 0.998805 | + | 0.0488754i | \(0.0155637\pi\) | ||||
−0.998805 | + | 0.0488754i | \(0.984436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 102.000 | 0.418797 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 194.000 | 0.738969 | 0.369484 | − | 0.929237i | \(-0.379534\pi\) | ||||
0.369484 | + | 0.929237i | \(0.379534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 108.000i | 0.383020i | 0.981491 | + | 0.191510i | \(0.0613384\pi\) | ||||
−0.981491 | + | 0.191510i | \(0.938662\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −90.0000 | − | 45.0000i | −0.298142 | − | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 480.000i | − | 1.48969i | −0.667240 | − | 0.744843i | \(-0.732525\pi\) | ||
0.667240 | − | 0.744843i | \(-0.267475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 243.000 | 0.708455 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −198.000 | −0.543638 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 286.000i | 0.741229i | 0.928787 | + | 0.370614i | \(0.120853\pi\) | ||||
−0.928787 | + | 0.370614i | \(0.879147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 460.000 | + | 230.000i | 1.12775 | + | 0.563876i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 312.000i | 0.725007i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 426.000 | 0.940008 | 0.470004 | − | 0.882664i | \(-0.344252\pi\) | ||||
0.470004 | + | 0.882664i | \(0.344252\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −698.000 | −1.46508 | −0.732539 | − | 0.680725i | \(-0.761665\pi\) | ||||
−0.732539 | + | 0.680725i | \(0.761665\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 90.0000i | − | 0.179983i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 170.000 | − | 340.000i | 0.324399 | − | 0.648797i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 328.000i | − | 0.598083i | −0.954240 | − | 0.299042i | \(-0.903333\pi\) | ||
0.954240 | − | 0.299042i | \(-0.0966669\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 492.000 | 0.858403 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 188.000 | 0.314246 | 0.157123 | − | 0.987579i | \(-0.449778\pi\) | ||||
0.157123 | + | 0.987579i | \(0.449778\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 740.000i | 1.18644i | 0.805039 | + | 0.593222i | \(0.202144\pi\) | ||||
−0.805039 | + | 0.593222i | \(0.797856\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −300.000 | + | 225.000i | −0.461880 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 460.000i | 0.680803i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1168.00 | −1.66342 | −0.831711 | − | 0.555209i | \(-0.812638\pi\) | ||||
−0.831711 | + | 0.555209i | \(0.812638\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 412.000i | 0.544854i | 0.962176 | + | 0.272427i | \(0.0878263\pi\) | ||||
−0.962176 | + | 0.272427i | \(0.912174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −330.000 | + | 660.000i | −0.421100 | + | 0.842201i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 672.000i | 0.828115i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1206.00 | −1.43636 | −0.718178 | − | 0.695859i | \(-0.755024\pi\) | ||||
−0.718178 | + | 0.695859i | \(0.755024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 340.000 | 0.391667 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 216.000i | − | 0.240840i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1040.00 | + | 520.000i | 1.12318 | + | 0.561588i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1384.00i | − | 1.44870i | −0.689432 | − | 0.724350i | \(-0.742140\pi\) | ||
0.689432 | − | 0.724350i | \(-0.257860\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −414.000 | −0.420289 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1128.00 | 1.11129 | 0.555645 | − | 0.831420i | \(-0.312472\pi\) | ||||
0.555645 | + | 0.831420i | \(0.312472\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 758.000i | 0.725126i | 0.931959 | + | 0.362563i | \(0.118098\pi\) | ||||
−0.931959 | + | 0.362563i | \(0.881902\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −300.000 | − | 150.000i | −0.278829 | − | 0.139414i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1324.00i | − | 1.19622i | −0.801413 | − | 0.598112i | \(-0.795918\pi\) | ||
0.801413 | − | 0.598112i | \(-0.204082\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1602.00 | 1.40774 | 0.703871 | − | 0.710328i | \(-0.251454\pi\) | ||||
0.703871 | + | 0.710328i | \(0.251454\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −66.0000 | −0.0564364 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2074.00i | 1.72660i | 0.504693 | + | 0.863299i | \(0.331606\pi\) | ||||
−0.504693 | + | 0.863299i | \(0.668394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 820.000 | − | 1640.00i | 0.664916 | − | 1.32983i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 306.000i | 0.241792i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −660.000 | −0.508421 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 785.000 | 0.589782 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 582.000i | 0.426644i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 250.000 | + | 1375.00i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 534.000i | − | 0.373109i | −0.982445 | − | 0.186554i | \(-0.940268\pi\) | ||
0.982445 | − | 0.186554i | \(-0.0597321\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −324.000 | −0.221137 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1806.00 | −1.20451 | −0.602256 | − | 0.798303i | \(-0.705731\pi\) | ||||
−0.602256 | + | 0.798303i | \(0.705731\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1040.00i | 0.678041i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | − | 270.000i | 0.0860663 | − | 0.172133i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1822.00i | 1.13623i | 0.822948 | + | 0.568117i | \(0.192328\pi\) | ||||
−0.822948 | + | 0.568117i | \(0.807672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 532.000 | 0.324631 | 0.162315 | − | 0.986739i | \(-0.448104\pi\) | ||||
0.162315 | + | 0.986739i | \(0.448104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1440.00 | 0.860070 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1564.00i | − | 0.914603i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2240.00 | + | 1120.00i | 1.28291 | + | 0.641455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 729.000i | 0.409027i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1284.00 | −0.705969 | −0.352984 | − | 0.935629i | \(-0.614833\pi\) | ||||
−0.352984 | + | 0.935629i | \(0.614833\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 184.000 | 0.0991636 | 0.0495818 | − | 0.998770i | \(-0.484211\pi\) | ||||
0.0495818 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 594.000i | − | 0.313870i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −720.000 | − | 360.000i | −0.373108 | − | 0.186554i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3746.00i | 1.90423i | 0.305748 | + | 0.952113i | \(0.401094\pi\) | ||||
−0.305748 | + | 0.952113i | \(0.598906\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −858.000 | −0.427949 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1640.00 | 0.802796 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1504.00i | 0.722714i | 0.932428 | + | 0.361357i | \(0.117686\pi\) | ||||
−0.932428 | + | 0.361357i | \(0.882314\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −690.000 | + | 1380.00i | −0.325554 | + | 0.651108i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3012.00i | 1.39566i | 0.716262 | + | 0.697831i | \(0.245851\pi\) | ||||
−0.716262 | + | 0.697831i | \(0.754149\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1041.00 | 0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −936.000 | −0.418583 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 438.000i | − | 0.192489i | −0.995358 | − | 0.0962443i | \(-0.969317\pi\) | ||
0.995358 | − | 0.0962443i | \(-0.0306830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1000.00 | + | 750.000i | −0.431959 | + | 0.323970i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1278.00i | 0.542714i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1462.00 | −0.610475 | −0.305237 | − | 0.952276i | \(-0.598736\pi\) | ||||
−0.305237 | + | 0.952276i | \(0.598736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −586.000 | −0.240647 | −0.120323 | − | 0.992735i | \(-0.538393\pi\) | ||||
−0.120323 | + | 0.992735i | \(0.538393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2094.00i | − | 0.845863i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −110.000 | + | 220.000i | −0.0437155 | + | 0.0874309i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3036.00i | 1.18724i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 270.000 | 0.103913 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 60.0000 | 0.0227301 | 0.0113650 | − | 0.999935i | \(-0.496382\pi\) | ||||
0.0113650 | + | 0.999935i | \(0.496382\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4676.00i | 1.74397i | 0.489534 | + | 0.871984i | \(0.337167\pi\) | ||||
−0.489534 | + | 0.871984i | \(0.662833\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1020.00 | + | 510.000i | 0.374583 | + | 0.187292i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2286.00i | − | 0.826755i | −0.910560 | − | 0.413378i | \(-0.864349\pi\) | ||
0.910560 | − | 0.413378i | \(-0.135651\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3536.00 | 1.25960 | 0.629800 | − | 0.776757i | \(-0.283137\pi\) | ||||
0.629800 | + | 0.776757i | \(0.283137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 984.000 | 0.345304 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2240.00i | 0.774469i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1940.00 | + | 970.000i | 0.660954 | + | 0.330477i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1476.00i | 0.495599i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4784.00 | 1.58333 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3500.00 | 1.14194 | 0.570971 | − | 0.820970i | \(-0.306567\pi\) | ||||
0.570971 | + | 0.820970i | \(0.306567\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 564.000i | 0.181430i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −540.000 | + | 1080.00i | −0.171292 | + | 0.342583i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 720.000i | − | 0.225239i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2220.00 | −0.684994 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2244.00 | 0.683022 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5874.00i | − | 1.76391i | −0.471333 | − | 0.881955i | \(-0.656227\pi\) | ||
0.471333 | − | 0.881955i | \(-0.343773\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −675.000 | − | 900.000i | −0.200000 | − | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 124.000i | 0.0362563i | 0.999836 | + | 0.0181281i | \(0.00577068\pi\) | ||||
−0.999836 | + | 0.0181281i | \(0.994229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1362.00 | −0.393028 | −0.196514 | − | 0.980501i | \(-0.562962\pi\) | ||||
−0.196514 | + | 0.980501i | \(0.562962\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1380.00 | −0.393062 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3870.00i | 1.08812i | 0.839046 | + | 0.544060i | \(0.183114\pi\) | ||||
−0.839046 | + | 0.544060i | \(0.816886\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2400.00 | − | 4800.00i | 0.666207 | − | 1.33241i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3504.00i | − | 0.960377i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6116.00 | −1.65528 | −0.827638 | − | 0.561262i | \(-0.810316\pi\) | ||||
−0.827638 | + | 0.561262i | \(0.810316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5962.00 | −1.59355 | −0.796776 | − | 0.604274i | \(-0.793463\pi\) | ||||
−0.796776 | + | 0.604274i | \(0.793463\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2430.00 | + | 1215.00i | 0.633661 | + | 0.316831i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3536.00i | − | 0.910892i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1236.00 | −0.314572 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1490.00 | 0.374693 | 0.187347 | − | 0.982294i | \(-0.440011\pi\) | ||||
0.187347 | + | 0.982294i | \(0.440011\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7544.00i | − | 1.87465i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1980.00 | − | 990.000i | −0.486245 | − | 0.243122i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5394.00i | − | 1.30922i | −0.755969 | − | 0.654608i | \(-0.772834\pi\) | ||
0.755969 | − | 0.654608i | \(-0.227166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −220.000 | −0.0527804 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2016.00 | −0.478112 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 636.000i | 0.149116i | 0.997217 | + | 0.0745579i | \(0.0237546\pi\) | ||||
−0.997217 | + | 0.0745579i | \(0.976245\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1430.00 | + | 2860.00i | −0.331488 | + | 0.662975i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3618.00i | − | 0.829281i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3360.00 | −0.761572 | −0.380786 | − | 0.924663i | \(-0.624347\pi\) | ||||
−0.380786 | + | 0.924663i | \(0.624347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5768.00 | 1.29292 | 0.646459 | − | 0.762948i | \(-0.276249\pi\) | ||||
0.646459 | + | 0.762948i | \(0.276249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1020.00i | 0.226129i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3450.00 | + | 4600.00i | 0.756519 | + | 1.00869i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1398.00i | 0.303241i | 0.988439 | + | 0.151620i | \(0.0484491\pi\) | ||||
−0.988439 | + | 0.151620i | \(0.951551\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 648.000 | 0.139049 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4194.00 | −0.890367 | −0.445183 | − | 0.895439i | \(-0.646862\pi\) | ||||
−0.445183 | + | 0.895439i | \(0.646862\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8256.00i | − | 1.73416i | −0.498166 | − | 0.867082i | \(-0.665993\pi\) | ||
0.498166 | − | 0.867082i | \(-0.334007\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1560.00 | + | 3120.00i | −0.324233 | + | 0.648466i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1940.00i | 0.399006i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 557.000 | 0.113373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4152.00 | 0.836407 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5534.00i | 1.10341i | 0.834039 | + | 0.551706i | \(0.186023\pi\) | ||||
−0.834039 | + | 0.551706i | \(0.813977\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4260.00 | + | 2130.00i | 0.840769 | + | 0.420384i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1242.00i | − | 0.242654i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5576.00 | −1.07849 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1080.00 | −0.206811 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3384.00i | 0.641603i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6980.00 | − | 3490.00i | −1.31041 | − | 0.655203i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 484.000i | 0.0899783i | 0.998987 | + | 0.0449892i | \(0.0143253\pi\) | ||||
−0.998987 | + | 0.0449892i | \(0.985675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2274.00 | −0.418652 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2724.00 | −0.496668 | −0.248334 | − | 0.968674i | \(-0.579883\pi\) | ||||
−0.248334 | + | 0.968674i | \(0.579883\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5308.00i | − | 0.958549i | −0.877665 | − | 0.479275i | \(-0.840900\pi\) | ||
0.877665 | − | 0.479275i | \(-0.159100\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 450.000 | − | 900.000i | 0.0804909 | − | 0.160982i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4218.00i | − | 0.747339i | −0.927562 | − | 0.373670i | \(-0.878099\pi\) | ||
0.927562 | − | 0.373670i | \(-0.121901\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10304.0 | 1.80851 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3972.00 | 0.690640 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6864.00i | 1.18242i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3400.00 | − | 2550.00i | 0.580302 | − | 0.435226i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4806.00i | 0.812760i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4800.00 | 0.804354 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4640.00 | 0.770506 | 0.385253 | − | 0.922811i | \(-0.374114\pi\) | ||||
0.385253 | + | 0.922811i | \(0.374114\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 198.000i | − | 0.0325836i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1640.00 | − | 3280.00i | 0.267471 | − | 0.534942i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8156.00i | − | 1.31835i | −0.751987 | − | 0.659177i | \(-0.770905\pi\) | ||
0.751987 | − | 0.659177i | \(-0.229095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6222.00 | −0.996851 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3312.00 | −0.525967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5860.00i | 0.922479i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4920.00 | + | 2460.00i | 0.767779 | + | 0.383890i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4124.00i | − | 0.638006i | −0.947754 | − | 0.319003i | \(-0.896652\pi\) | ||
0.947754 | − | 0.319003i | \(-0.103348\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3650.00 | 0.559828 | 0.279914 | − | 0.960025i | \(-0.409694\pi\) | ||||
0.279914 | + | 0.960025i | \(0.409694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −918.000 | −0.139599 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6834.00i | − | 1.03042i | −0.857065 | − | 0.515208i | \(-0.827715\pi\) | ||
0.857065 | − | 0.515208i | \(-0.172285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1880.00 | + | 940.000i | 0.281071 | + | 0.140535i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1980.00i | − | 0.293537i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3904.00 | −0.573942 | −0.286971 | − | 0.957939i | \(-0.592648\pi\) | ||||
−0.286971 | + | 0.957939i | \(0.592648\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3957.00 | 0.576906 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2355.00i | 0.340511i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3700.00 | + | 7400.00i | −0.530594 | + | 1.06119i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13174.0i | − | 1.87378i | −0.349624 | − | 0.936890i | \(-0.613691\pi\) | ||
0.349624 | − | 0.936890i | \(-0.386309\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1746.00 | −0.246323 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2860.00 | −0.400226 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1090.00i | − | 0.151308i | −0.997134 | − | 0.0756542i | \(-0.975895\pi\) | ||
0.997134 | − | 0.0756542i | \(-0.0241045\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4125.00 | + | 750.000i | −0.568038 | + | 0.103280i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7616.00i | − | 1.04043i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9220.00 | −1.24960 | −0.624802 | − | 0.780784i | \(-0.714820\pi\) | ||||
−0.624802 | + | 0.780784i | \(0.714820\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1602.00 | 0.215415 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3960.00i | 0.528320i | 0.964479 | + | 0.264160i | \(0.0850947\pi\) | ||||
−0.964479 | + | 0.264160i | \(0.914905\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2300.00 | + | 4600.00i | −0.304465 | + | 0.608929i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 972.000i | − | 0.127673i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1788.00 | −0.233047 | −0.116523 | − | 0.993188i | \(-0.537175\pi\) | ||||
−0.116523 | + | 0.993188i | \(0.537175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10824.0 | 1.39998 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5418.00i | − | 0.695425i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11680.0 | − | 5840.00i | −1.48781 | − | 0.743905i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9642.00i | − | 1.21894i | −0.792810 | − | 0.609469i | \(-0.791383\pi\) | ||
0.792810 | − | 0.609469i | \(-0.208617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3120.00 | −0.391467 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −410.000 | −0.0510584 | −0.0255292 | − | 0.999674i | \(-0.508127\pi\) | ||||
−0.0255292 | + | 0.999674i | \(0.508127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2448.00i | 0.302589i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 810.000 | + | 405.000i | 0.0993808 | + | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1012.00i | 0.123251i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13766.0 | −1.66427 | −0.832133 | − | 0.554576i | \(-0.812880\pi\) | ||||
−0.832133 | + | 0.554576i | \(0.812880\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5466.00 | −0.656005 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4260.00i | 0.507557i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2060.00 | + | 4120.00i | −0.243666 | + | 0.487332i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1596.00i | 0.187426i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16998.0 | 1.98188 | 0.990939 | − | 0.134315i | \(-0.0428833\pi\) | ||||
0.990939 | + | 0.134315i | \(0.0428833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2450.00 | 0.283624 | 0.141812 | − | 0.989894i | \(-0.454707\pi\) | ||||
0.141812 | + | 0.989894i | \(0.454707\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4320.00i | 0.496562i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6600.00 | + | 4950.00i | −0.753287 | + | 0.564965i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6980.00i | − | 0.791068i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4692.00 | 0.528046 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9248.00 | −1.03355 | −0.516776 | − | 0.856121i | \(-0.672868\pi\) | ||||
−0.516776 | + | 0.856121i | \(0.672868\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5028.00i | 0.558038i | 0.960286 | + | 0.279019i | \(0.0900092\pi\) | ||||
−0.960286 | + | 0.279019i | \(0.909991\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3360.00 | + | 6720.00i | −0.370344 | + | 0.740688i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 17056.0i | − | 1.86705i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3120.00 | −0.339202 | −0.169601 | − | 0.985513i | \(-0.554248\pi\) | ||||
−0.169601 | + | 0.985513i | \(0.554248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2187.00 | −0.236152 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 8220.00i | − | 0.881589i | −0.897608 | − | 0.440795i | \(-0.854697\pi\) | ||
0.897608 | − | 0.440795i | \(-0.145303\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12060.0 | − | 6030.00i | −1.28472 | − | 0.642358i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 3852.00i | − | 0.407591i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5826.00 | 0.612352 | 0.306176 | − | 0.951975i | \(-0.400950\pi\) | ||||
0.306176 | + | 0.951975i | \(0.400950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8924.00 | 0.931740 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 552.000i | 0.0572521i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3400.00 | + | 1700.00i | 0.350317 | + | 0.175159i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16896.0i | − | 1.72946i | −0.502240 | − | 0.864728i | \(-0.667491\pi\) | ||
0.502240 | − | 0.864728i | \(-0.332509\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1782.00 | 0.181213 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 996.000 | 0.100625 | 0.0503127 | − | 0.998734i | \(-0.483978\pi\) | ||||
0.0503127 | + | 0.998734i | \(0.483978\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10046.0i | − | 1.00837i | −0.863594 | − | 0.504187i | \(-0.831792\pi\) | ||
0.863594 | − | 0.504187i | \(-0.168208\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1080.00 | − | 2160.00i | 0.107707 | − | 0.215414i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8388.00i | 0.831157i | 0.909557 | + | 0.415579i | \(0.136421\pi\) | ||||
−0.909557 | + | 0.415579i | \(0.863579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3280.00 | 0.322935 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11238.0 | −1.09940 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4968.00i | 0.482936i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7800.00 | + | 10400.0i | 0.753450 | + | 1.00460i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2574.00i | − | 0.247076i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11396.0 | −1.08705 | −0.543525 | − | 0.839393i | \(-0.682911\pi\) | ||||
−0.543525 | + | 0.839393i | \(0.682911\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 748.000 | 0.0709062 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4920.00i | 0.463494i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6920.00 | − | 13840.0i | 0.647878 | − | 1.29576i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6454.00i | 0.600531i | 0.953856 | + | 0.300266i | \(0.0970753\pi\) | ||||
−0.953856 | + | 0.300266i | \(0.902925\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4512.00 | −0.417259 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18638.0 | −1.71308 | −0.856539 | − | 0.516083i | \(-0.827390\pi\) | ||||
−0.856539 | + | 0.516083i | \(0.827390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14784.0i | 1.35058i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4140.00 | − | 2070.00i | −0.375917 | − | 0.187959i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1880.00i | 0.169677i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17768.0 | 1.59400 | 0.796999 | − | 0.603981i | \(-0.206420\pi\) | ||||
0.796999 | + | 0.603981i | \(0.206420\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9036.00 | −0.805786 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7952.00i | 0.704895i | 0.935832 | + | 0.352447i | \(0.114650\pi\) | ||||
−0.935832 | + | 0.352447i | \(0.885350\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11280.0 | + | 5640.00i | 0.993967 | + | 0.496984i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3123.00i | 0.273565i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12896.0 | −1.12300 | −0.561498 | − | 0.827478i | \(-0.689775\pi\) | ||||
−0.561498 | + | 0.827478i | \(0.689775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7400.00 | −0.640620 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2808.00i | − | 0.241669i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3790.00 | + | 7580.00i | −0.324286 | + | 0.648572i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 22080.0i | − | 1.87829i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1314.00 | 0.111133 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2714.00 | −0.228220 | −0.114110 | − | 0.993468i | \(-0.536402\pi\) | ||||
−0.114110 | + | 0.993468i | \(0.536402\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 13792.0i | − | 1.15312i | −0.817055 | − | 0.576560i | \(-0.804395\pi\) | ||
0.817055 | − | 0.576560i | \(-0.195605\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2250.00 | − | 3000.00i | −0.187044 | − | 0.249392i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4752.00i | − | 0.392790i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14729.0 | −1.21057 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3834.00 | −0.313336 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6596.00i | − | 0.536031i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6620.00 | − | 13240.0i | 0.534967 | − | 1.06993i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 4386.00i | − | 0.352458i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11178.0 | 0.893266 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6802.00 | −0.540556 | −0.270278 | − | 0.962782i | \(-0.587116\pi\) | ||||
−0.270278 | + | 0.962782i | \(0.587116\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1758.00i | − | 0.138937i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16020.0 | + | 8010.00i | 1.25912 | + | 0.629561i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18188.0i | 1.42169i | 0.703350 | + | 0.710843i | \(0.251687\pi\) | ||||
−0.703350 | + | 0.710843i | \(0.748313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6282.00 | 0.488359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23296.0 | 1.80117 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 11680.0i | − | 0.898163i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −660.000 | − | 330.000i | −0.0504783 | − | 0.0252391i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 21462.0i | − | 1.63263i | −0.577608 | − | 0.816314i | \(-0.696014\pi\) | ||
0.577608 | − | 0.816314i | \(-0.303986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3672.00 | 0.277834 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9108.00 | −0.685455 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 17244.0i | − | 1.29085i | −0.763824 | − | 0.645424i | \(-0.776681\pi\) | ||
0.763824 | − | 0.645424i | \(-0.223319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10370.0 | + | 20740.0i | −0.772158 | + | 1.54432i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 810.000i | 0.0599944i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8790.00 | −0.647620 | −0.323810 | − | 0.946122i | \(-0.604964\pi\) | ||||
−0.323810 | + | 0.946122i | \(0.604964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5984.00 | 0.438568 | 0.219284 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219284 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 180.000i | 0.0131232i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16400.0 | − | 12300.0i | 1.18944 | − | 0.892079i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9344.00i | − | 0.674170i | −0.941474 | − | 0.337085i | \(-0.890559\pi\) | ||
0.941474 | − | 0.337085i | \(-0.109441\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14028.0 | −1.00688 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4120.00 | −0.294193 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13156.0i | 0.934590i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1530.00 | + | 3060.00i | −0.108133 | + | 0.216266i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6932.00i | 0.487418i | 0.969848 | + | 0.243709i | \(0.0783642\pi\) | ||||
−0.969848 | + | 0.243709i | \(0.921636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7488.00 | −0.523833 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6858.00 | 0.477327 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9382.00i | − | 0.649701i | −0.945765 | − | 0.324850i | \(-0.894686\pi\) | ||
0.945765 | − | 0.324850i | \(-0.105314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6600.00 | − | 3300.00i | −0.454746 | − | 0.227373i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10608.0i | 0.727230i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4096.00 | −0.279396 | −0.139698 | − | 0.990194i | \(-0.544613\pi\) | ||||
−0.139698 | + | 0.990194i | \(0.544613\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22962.0 | 1.55847 | 0.779234 | − | 0.626733i | \(-0.215608\pi\) | ||||
0.779234 | + | 0.626733i | \(0.215608\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2952.00i | 0.199361i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7850.00 | + | 3925.00i | 0.527517 | + | 0.263759i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3490.00i | − | 0.233369i | −0.993169 | − | 0.116684i | \(-0.962773\pi\) | ||
0.993169 | − | 0.116684i | \(-0.0372266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6720.00 | −0.447140 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16320.0 | −1.08058 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6386.00i | 0.420764i | 0.977619 | + | 0.210382i | \(0.0674707\pi\) | ||||
−0.977619 | + | 0.210382i | \(0.932529\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2910.00 | + | 5820.00i | −0.190801 | + | 0.381602i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19534.0i | − | 1.27457i | −0.770629 | − | 0.637285i | \(-0.780058\pi\) | ||
0.770629 | − | 0.637285i | \(-0.219942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8764.00 | 0.569071 | 0.284535 | − | 0.958666i | \(-0.408161\pi\) | ||||
0.284535 | + | 0.958666i | \(0.408161\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4428.00 | −0.286134 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 12060.0i | − | 0.775560i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4375.00 | + | 15000.0i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14352.0i | 0.914137i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1452.00 | −0.0920430 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7856.00 | 0.495630 | 0.247815 | − | 0.968807i | \(-0.420288\pi\) | ||||
0.247815 | + | 0.968807i | \(0.420288\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10500.0i | 0.659301i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2670.00 | − | 5340.00i | 0.166859 | − | 0.333719i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 8262.00i | − | 0.513897i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1692.00 | −0.104749 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22974.0 | −1.41563 | −0.707815 | − | 0.706398i | \(-0.750319\pi\) | ||||
−0.707815 | + | 0.706398i | \(0.750319\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6216.00i | − | 0.381237i | −0.981664 | − | 0.190618i | \(-0.938951\pi\) | ||
0.981664 | − | 0.190618i | \(-0.0610493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3240.00 | − | 1620.00i | −0.197791 | − | 0.0988953i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13384.0i | 0.813260i | 0.913593 | + | 0.406630i | \(0.133296\pi\) | ||||
−0.913593 | + | 0.406630i | \(0.866704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19596.0 | 1.18522 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2160.00 | 0.130042 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12882.0i | 0.771993i | 0.922500 | + | 0.385997i | \(0.126142\pi\) | ||||
−0.922500 | + | 0.385997i | \(0.873858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18060.0 | − | 9030.00i | −1.07735 | − | 0.538674i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6660.00i | − | 0.395482i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2082.00 | −0.123070 | −0.0615351 | − | 0.998105i | \(-0.519600\pi\) | ||||
−0.0615351 | + | 0.998105i | \(0.519600\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9430.00 | 0.554893 | 0.277447 | − | 0.960741i | \(-0.410512\pi\) | ||||
0.277447 | + | 0.960741i | \(0.410512\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6732.00i | 0.394343i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5200.00 | + | 10400.0i | −0.303229 | + | 0.606458i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 36736.0i | − | 2.13257i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17622.0 | 1.01839 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32108.0 | −1.84727 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3268.00i | − | 0.187180i | −0.995611 | − | 0.0935900i | \(-0.970166\pi\) | ||
0.995611 | − | 0.0935900i | \(-0.0298343\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2700.00 | − | 2025.00i | 0.153960 | − | 0.115470i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15606.0i | 0.885949i | 0.896534 | + | 0.442974i | \(0.146077\pi\) | ||||
−0.896534 | + | 0.442974i | \(0.853923\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13840.0 | 0.782225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −372.000 | −0.0209326 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 428.000i | 0.0239780i | 0.999928 | + | 0.0119890i | \(0.00381631\pi\) | ||||
−0.999928 | + | 0.0119890i | \(0.996184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9110.00 | + | 18220.0i | −0.508139 | + | 1.01628i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4086.00i | − | 0.226915i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9724.00 | 0.537670 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6384.00 | 0.351460 | 0.175730 | − | 0.984438i | \(-0.443771\pi\) | ||||
0.175730 | + | 0.984438i | \(0.443771\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 4140.00i | − | 0.226934i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5320.00 | + | 2660.00i | 0.290358 | + | 0.145179i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12804.0i | 0.695819i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11610.0 | −0.628227 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12224.0 | 0.658622 | 0.329311 | − | 0.944221i | \(-0.393184\pi\) | ||||
0.329311 | + | 0.944221i | \(0.393184\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2288.00i | 0.122750i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14400.0 | + | 7200.00i | 0.769270 | + | 0.384635i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11280.0i | 0.600040i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19510.0 | 1.03345 | 0.516723 | − | 0.856153i | \(-0.327152\pi\) | ||||
0.516723 | + | 0.856153i | \(0.327152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10512.0 | 0.554474 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11808.0i | 0.620215i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7820.00 | − | 15640.0i | 0.409023 | − | 0.818046i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 18348.0i | − | 0.955674i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3368.00 | 0.174694 | 0.0873472 | − | 0.996178i | \(-0.472161\pi\) | ||||
0.0873472 | + | 0.996178i | \(0.472161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7580.00 | −0.391531 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 17886.0i | − | 0.920038i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16800.0 | + | 22400.0i | 0.860602 | + | 1.14747i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22134.0i | 1.12917i | 0.825376 | + | 0.564584i | \(0.190963\pi\) | ||||
−0.825376 | + | 0.564584i | \(0.809037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7128.00 | −0.360655 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32298.0i | 1.62750i | 0.581219 | + | 0.813748i | \(0.302576\pi\) | ||||
−0.581219 | + | 0.813748i | \(0.697424\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3645.00 | + | 7290.00i | −0.182922 | + | 0.365844i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 15088.0i | − | 0.754103i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25104.0 | 1.24962 | 0.624808 | − | 0.780779i | \(-0.285177\pi\) | ||||
0.624808 | + | 0.780779i | \(0.285177\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10608.0 | 0.525904 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27696.0i | 1.36752i | 0.729707 | + | 0.683760i | \(0.239657\pi\) | ||||
−0.729707 | + | 0.683760i | \(0.760343\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12840.0 | − | 6420.00i | −0.631438 | − | 0.315719i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3708.00i | − | 0.181618i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13240.0 | 0.645900 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2176.00 | −0.105730 | −0.0528651 | − | 0.998602i | \(-0.516835\pi\) | ||||
−0.0528651 | + | 0.998602i | \(0.516835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4470.00i | 0.216329i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1840.00 | + | 920.000i | 0.0886946 | + | 0.0443473i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25514.0i | − | 1.22500i | −0.790472 | − | 0.612498i | \(-0.790165\pi\) | ||
0.790472 | − | 0.612498i | \(-0.209835\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22632.0 | 1.08233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18238.0 | 0.868761 | 0.434380 | − | 0.900730i | \(-0.356967\pi\) | ||||
0.434380 | + | 0.900730i | \(0.356967\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16020.0i | 0.760109i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2970.00 | − | 5940.00i | 0.140367 | − | 0.280734i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 14484.0i | − | 0.681860i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14462.0 | 0.678170 | 0.339085 | − | 0.940756i | \(-0.389882\pi\) | ||||
0.339085 | + | 0.940756i | \(0.389882\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16182.0 | 0.755876 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34034.0i | 1.58359i | 0.610785 | + | 0.791797i | \(0.290854\pi\) | ||||
−0.610785 | + | 0.791797i | \(0.709146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5400.00 | − | 7200.00i | −0.250289 | − | 0.333718i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 660.000i | − | 0.0304728i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20176.0 | 0.927959 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8648.00 | 0.396222 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6048.00i | − | 0.276038i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18730.0 | + | 37460.0i | −0.851595 | + | 1.70319i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 22064.0i | − | 0.999360i | −0.866210 | − | 0.499680i | \(-0.833451\pi\) | ||
0.866210 | − | 0.499680i | \(-0.166549\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1908.00 | −0.0860920 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20740.0 |