Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(38.2332376837\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 433.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.433 |
Dual form | 648.4.i.c.217.1 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.0000 | − | 31.1769i | −0.971909 | − | 1.68340i | −0.689781 | − | 0.724018i | \(-0.742293\pi\) |
−0.282128 | − | 0.959377i | \(-0.591040\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 32.0000 | + | 55.4256i | 0.877124 | + | 1.51922i | 0.854483 | + | 0.519480i | \(0.173874\pi\) |
0.0226410 | + | 0.999744i | \(0.492793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.5000 | − | 56.2917i | 0.693375 | − | 1.20096i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −59.0000 | −0.841741 | −0.420871 | − | 0.907121i | \(-0.638275\pi\) | ||||
−0.420871 | + | 0.907121i | \(0.638275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.0000 | −0.338086 | −0.169043 | − | 0.985609i | \(-0.554068\pi\) | ||||
−0.169043 | + | 0.985609i | \(0.554068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 80.0000 | − | 138.564i | 0.725268 | − | 1.25620i | −0.233596 | − | 0.972334i | \(-0.575049\pi\) |
0.958864 | − | 0.283867i | \(-0.0916173\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 50.0000 | + | 86.6025i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28.5000 | − | 49.3634i | −0.182494 | − | 0.316088i | 0.760235 | − | 0.649648i | \(-0.225084\pi\) |
−0.942729 | + | 0.333559i | \(0.891750\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −82.0000 | + | 142.028i | −0.475085 | + | 0.822871i | −0.999593 | − | 0.0285343i | \(-0.990916\pi\) |
0.524508 | + | 0.851406i | \(0.324249\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 180.000 | 0.869302 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −321.000 | −1.42627 | −0.713136 | − | 0.701026i | \(-0.752726\pi\) | ||||
−0.713136 | + | 0.701026i | \(0.752726\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −123.000 | + | 213.042i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | + | 6.92820i | 0.0141859 | + | 0.0245707i | 0.873031 | − | 0.487664i | \(-0.162151\pi\) |
−0.858845 | + | 0.512235i | \(0.828818\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 42.0000 | + | 72.7461i | 0.130347 | + | 0.225768i | 0.923811 | − | 0.382850i | \(-0.125057\pi\) |
−0.793463 | + | 0.608618i | \(0.791724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −476.500 | + | 825.322i | −1.38921 | + | 2.40619i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −478.000 | −1.23884 | −0.619418 | − | 0.785061i | \(-0.712632\pi\) | ||||
−0.619418 | + | 0.785061i | \(0.712632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −320.000 | −0.784523 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −16.0000 | + | 27.7128i | −0.0353055 | + | 0.0611509i | −0.883138 | − | 0.469113i | \(-0.844574\pi\) |
0.847833 | + | 0.530264i | \(0.177907\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −207.500 | − | 359.401i | −0.435535 | − | 0.754369i | 0.561804 | − | 0.827270i | \(-0.310108\pi\) |
−0.997339 | + | 0.0729012i | \(0.976774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 162.500 | + | 281.458i | 0.310087 | + | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 110.000 | − | 190.526i | 0.200577 | − | 0.347409i | −0.748138 | − | 0.663544i | \(-0.769052\pi\) |
0.948714 | + | 0.316134i | \(0.102385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −884.000 | −1.47763 | −0.738813 | − | 0.673910i | \(-0.764614\pi\) | ||||
−0.738813 | + | 0.673910i | \(0.764614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −77.0000 | −0.123454 | −0.0617272 | − | 0.998093i | \(-0.519661\pi\) | ||||
−0.0617272 | + | 0.998093i | \(0.519661\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1152.00 | − | 1995.32i | 1.70497 | − | 2.95309i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 40.0000 | + | 69.2820i | 0.0569665 | + | 0.0986688i | 0.893102 | − | 0.449854i | \(-0.148524\pi\) |
−0.836136 | + | 0.548522i | \(0.815191\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 634.000 | + | 1098.12i | 0.838440 | + | 1.45222i | 0.891198 | + | 0.453614i | \(0.149865\pi\) |
−0.0527581 | + | 0.998607i | \(0.516801\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 147.500 | − | 255.477i | 0.188219 | − | 0.326005i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −123.000 | −0.146494 | −0.0732470 | − | 0.997314i | \(-0.523336\pi\) | ||||
−0.0732470 | + | 0.997314i | \(0.523336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2340.00 | −2.69559 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 70.0000 | − | 121.244i | 0.0755984 | − | 0.130940i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −673.000 | − | 1165.67i | −0.704462 | − | 1.22016i | −0.966885 | − | 0.255211i | \(-0.917855\pi\) |
0.262424 | − | 0.964953i | \(-0.415478\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −417.000 | − | 722.265i | −0.410822 | − | 0.711565i | 0.584158 | − | 0.811640i | \(-0.301425\pi\) |
−0.994980 | + | 0.100075i | \(0.968092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −530.000 | + | 917.987i | −0.507014 | + | 0.878174i | 0.492953 | + | 0.870056i | \(0.335917\pi\) |
−0.999967 | + | 0.00811820i | \(0.997416\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −300.000 | −0.271048 | −0.135524 | − | 0.990774i | \(-0.543272\pi\) | ||||
−0.135524 | + | 0.990774i | \(0.543272\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −557.000 | −0.489458 | −0.244729 | − | 0.969592i | \(-0.578699\pi\) | ||||
−0.244729 | + | 0.969592i | \(0.578699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −808.500 | + | 1400.36i | −0.673073 | + | 1.16580i | 0.303955 | + | 0.952686i | \(0.401693\pi\) |
−0.977028 | + | 0.213111i | \(0.931641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 400.000 | + | 692.820i | 0.324349 | + | 0.561790i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1062.00 | + | 1839.44i | 0.818096 | + | 1.41698i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1382.50 | + | 2394.56i | −1.03869 | + | 1.79907i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1125.00 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1136.00 | −0.793730 | −0.396865 | − | 0.917877i | \(-0.629902\pi\) | ||||
−0.396865 | + | 0.917877i | \(0.629902\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 58.0000 | − | 100.459i | 0.0386831 | − | 0.0670011i | −0.846036 | − | 0.533126i | \(-0.821017\pi\) |
0.884719 | + | 0.466125i | \(0.154350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 504.000 | + | 872.954i | 0.328589 | + | 0.569133i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 307.500 | + | 532.606i | 0.191763 | + | 0.332143i | 0.945834 | − | 0.324649i | \(-0.105246\pi\) |
−0.754072 | + | 0.656792i | \(0.771913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −726.000 | + | 1257.47i | −0.443011 | + | 0.767317i | −0.997911 | − | 0.0645994i | \(-0.979423\pi\) |
0.554900 | + | 0.831917i | \(0.312756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4160.00 | 2.43270 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 285.000 | 0.163227 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 419.500 | − | 726.595i | 0.230650 | − | 0.399497i | −0.727350 | − | 0.686267i | \(-0.759248\pi\) |
0.957999 | + | 0.286770i | \(0.0925816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1028.00 | + | 1780.55i | 0.554023 | + | 0.959596i | 0.997979 | + | 0.0635472i | \(0.0202413\pi\) |
−0.443956 | + | 0.896049i | \(0.646425\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −410.000 | − | 710.141i | −0.212464 | − | 0.367999i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −549.500 | + | 951.762i | −0.279330 | + | 0.483814i | −0.971219 | − | 0.238190i | \(-0.923446\pi\) |
0.691888 | + | 0.722005i | \(0.256779\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5760.00 | −2.81958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −72.0000 | −0.0345980 | −0.0172990 | − | 0.999850i | \(-0.505507\pi\) | ||||
−0.0172990 | + | 0.999850i | \(0.505507\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1062.00 | − | 1839.44i | 0.492096 | − | 0.852335i | −0.507863 | − | 0.861438i | \(-0.669564\pi\) |
0.999959 | + | 0.00910286i | \(0.00289757\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1014.00 | − | 1756.30i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2002.50 | − | 3468.43i | −0.880042 | − | 1.52428i | −0.851293 | − | 0.524691i | \(-0.824181\pi\) |
−0.0287490 | − | 0.999587i | \(-0.509152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1800.00 | − | 3117.69i | 0.777527 | − | 1.34672i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1428.00 | 0.596278 | 0.298139 | − | 0.954522i | \(-0.403634\pi\) | ||||
0.298139 | + | 0.954522i | \(0.403634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2226.00 | −0.914129 | −0.457064 | − | 0.889434i | \(-0.651099\pi\) | ||||
−0.457064 | + | 0.889434i | \(0.651099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 802.500 | − | 1389.97i | 0.318924 | − | 0.552393i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1888.00 | − | 3270.11i | −0.738311 | − | 1.27879i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1878.00 | + | 3252.79i | 0.711452 | + | 1.23227i | 0.964312 | + | 0.264768i | \(0.0852954\pi\) |
−0.252860 | + | 0.967503i | \(0.581371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1818.50 | − | 3149.73i | 0.678231 | − | 1.17473i | −0.297283 | − | 0.954789i | \(-0.596080\pi\) |
0.975513 | − | 0.219940i | \(-0.0705863\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −795.000 | −0.287520 | −0.143760 | − | 0.989613i | \(-0.545919\pi\) | ||||
−0.143760 | + | 0.989613i | \(0.545919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2500.00 | 0.890554 | 0.445277 | − | 0.895393i | \(-0.353105\pi\) | ||||
0.445277 | + | 0.895393i | \(0.353105\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1026.00 | + | 1777.08i | −0.354734 | + | 0.614418i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −615.000 | − | 1065.21i | −0.209529 | − | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −896.000 | − | 1551.92i | −0.296544 | − | 0.513629i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1972.00 | − | 3415.60i | 0.643403 | − | 1.11441i | −0.341265 | − | 0.939967i | \(-0.610855\pi\) |
0.984668 | − | 0.174440i | \(-0.0558114\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −40.0000 | −0.0126883 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5904.00 | 1.84696 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1917.50 | + | 3321.21i | −0.583643 | + | 1.01090i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 340.000 | + | 588.897i | 0.102099 | + | 0.176841i | 0.912549 | − | 0.408967i | \(-0.134111\pi\) |
−0.810450 | + | 0.585807i | \(0.800777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1962.00 | + | 3398.28i | 0.573667 | + | 0.993621i | 0.996185 | + | 0.0872664i | \(0.0278132\pi\) |
−0.422518 | + | 0.906355i | \(0.638854\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2307.50 | + | 3996.71i | −0.665869 | + | 1.15332i | 0.313181 | + | 0.949694i | \(0.398606\pi\) |
−0.979049 | + | 0.203625i | \(0.934728\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4493.00 | 1.26329 | 0.631644 | − | 0.775258i | \(-0.282380\pi\) | ||||
0.631644 | + | 0.775258i | \(0.282380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −420.000 | −0.116586 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1562.00 | + | 2705.46i | −0.422751 | + | 0.732225i | −0.996207 | − | 0.0870103i | \(-0.972269\pi\) |
0.573457 | + | 0.819236i | \(0.305602\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 154.500 | + | 267.602i | 0.0412955 | + | 0.0715259i | 0.885934 | − | 0.463811i | \(-0.153518\pi\) |
−0.844639 | + | 0.535336i | \(0.820185\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2382.50 | − | 4126.61i | −0.621275 | − | 1.07608i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −910.000 | + | 1576.17i | −0.234421 | + | 0.406029i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1352.00 | −0.339990 | −0.169995 | − | 0.985445i | \(-0.554375\pi\) | ||||
−0.169995 | + | 0.985445i | \(0.554375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10240.0 | 2.54460 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1847.50 | − | 3199.96i | 0.448420 | − | 0.776686i | −0.549864 | − | 0.835254i | \(-0.685320\pi\) |
0.998283 | + | 0.0585686i | \(0.0186536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5778.00 | + | 10007.8i | 1.38621 | + | 2.40098i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −490.000 | − | 848.705i | −0.114885 | − | 0.198986i | 0.802849 | − | 0.596183i | \(-0.203317\pi\) |
−0.917734 | + | 0.397196i | \(0.869983\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1195.00 | − | 2069.80i | 0.277012 | − | 0.479799i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5293.00 | 1.19970 | 0.599851 | − | 0.800112i | \(-0.295226\pi\) | ||||
0.599851 | + | 0.800112i | \(0.295226\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4912.00 | −1.10104 | −0.550522 | − | 0.834821i | \(-0.685571\pi\) | ||||
−0.550522 | + | 0.834821i | \(0.685571\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3200.00 | + | 5542.56i | −0.701699 | + | 1.21538i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 697.000 | + | 1207.24i | 0.151187 | + | 0.261863i | 0.931664 | − | 0.363321i | \(-0.118357\pi\) |
−0.780477 | + | 0.625184i | \(0.785024\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3582.50 | − | 6205.07i | −0.760548 | − | 1.31731i | −0.942568 | − | 0.334013i | \(-0.891597\pi\) |
0.182020 | − | 0.983295i | \(-0.441736\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4670.00 | − | 8088.68i | 0.980928 | − | 1.69902i | 0.322134 | − | 0.946694i | \(-0.395600\pi\) |
0.658794 | − | 0.752324i | \(-0.271067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8856.00 | 1.82144 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1432.00 | −0.291472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3436.50 | + | 5952.19i | −0.685196 | + | 1.18679i | 0.288179 | + | 0.957577i | \(0.406950\pi\) |
−0.973375 | + | 0.229218i | \(0.926383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −80.0000 | − | 138.564i | −0.0157891 | − | 0.0273475i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5200.00 | − | 9006.66i | −1.00577 | − | 1.74204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 144.000 | − | 249.415i | 0.0275748 | − | 0.0477610i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2075.00 | 0.389555 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 204.000 | 0.0379247 | 0.0189624 | − | 0.999820i | \(-0.493964\pi\) | ||||
0.0189624 | + | 0.999820i | \(0.493964\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2028.00 | − | 3512.60i | 0.369766 | − | 0.640454i | −0.619762 | − | 0.784789i | \(-0.712771\pi\) |
0.989529 | + | 0.144335i | \(0.0461044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −547.500 | − | 948.298i | −0.0988707 | − | 0.171249i | 0.812347 | − | 0.583175i | \(-0.198190\pi\) |
−0.911217 | + | 0.411926i | \(0.864856\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5209.50 | + | 9023.12i | 0.923012 | + | 1.59870i | 0.794728 | + | 0.606965i | \(0.207613\pi\) |
0.128283 | + | 0.991738i | \(0.459053\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1824.00 | − | 3159.26i | 0.320139 | − | 0.554497i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1652.00 | 0.284581 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6500.00 | 1.10940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1512.00 | − | 2618.86i | 0.253372 | − | 0.438852i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1798.00 | − | 3114.23i | −0.298571 | − | 0.517140i | 0.677238 | − | 0.735764i | \(-0.263177\pi\) |
−0.975809 | + | 0.218624i | \(0.929843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 550.000 | + | 952.628i | 0.0897006 | + | 0.155366i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1455.00 | − | 2520.13i | 0.235190 | − | 0.407360i | −0.724138 | − | 0.689655i | \(-0.757762\pi\) |
0.959328 | + | 0.282295i | \(0.0910956\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10496.0 | −1.66683 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21960.0 | 3.45693 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2538.00 | + | 4395.94i | −0.392643 | + | 0.680077i | −0.992797 | − | 0.119807i | \(-0.961772\pi\) |
0.600155 | + | 0.799884i | \(0.295106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4059.00 | − | 7030.39i | −0.622560 | − | 1.07830i | −0.989007 | − | 0.147866i | \(-0.952760\pi\) |
0.366448 | − | 0.930439i | \(-0.380574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4631.00 | − | 8021.13i | −0.698253 | − | 1.20941i | −0.969072 | − | 0.246779i | \(-0.920628\pi\) |
0.270819 | − | 0.962630i | \(-0.412706\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2210.00 | − | 3827.83i | 0.330407 | − | 0.572282i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1248.00 | −0.183473 | −0.0917367 | − | 0.995783i | \(-0.529242\pi\) | ||||
−0.0917367 | + | 0.995783i | \(0.529242\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 192.500 | − | 333.420i | 0.0276052 | − | 0.0478137i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4940.00 | − | 8556.33i | −0.702632 | − | 1.21699i | −0.967539 | − | 0.252720i | \(-0.918675\pi\) |
0.264907 | − | 0.964274i | \(-0.414659\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8604.00 | + | 14902.6i | 1.20404 | + | 2.08545i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4889.00 | − | 8468.00i | 0.678667 | − | 1.17549i | −0.296715 | − | 0.954966i | \(-0.595891\pi\) |
0.975382 | − | 0.220520i | \(-0.0707754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3705.00 | −0.506146 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3260.00 | 0.441834 | 0.220917 | − | 0.975293i | \(-0.429095\pi\) | ||||
0.220917 | + | 0.975293i | \(0.429095\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 810.000 | − | 1402.96i | 0.108065 | − | 0.187175i | −0.806921 | − | 0.590659i | \(-0.798868\pi\) |
0.914986 | + | 0.403484i | \(0.132201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5760.00 | + | 9976.61i | 0.762485 | + | 1.32066i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3455.00 | + | 5984.24i | 0.450323 | + | 0.779981i | 0.998406 | − | 0.0564423i | \(-0.0179757\pi\) |
−0.548083 | + | 0.836424i | \(0.684642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4720.00 | + | 8175.28i | −0.610488 | + | 1.05740i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −400.000 | −0.0509524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1705.00 | −0.215545 | −0.107773 | − | 0.994176i | \(-0.534372\pi\) | ||||
−0.107773 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2002.50 | + | 3468.43i | −0.249377 | + | 0.431933i | −0.963353 | − | 0.268237i | \(-0.913559\pi\) |
0.713976 | + | 0.700170i | \(0.246892\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5330.00 | + | 9231.83i | 0.658824 | + | 1.14112i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10272.0 | − | 17791.6i | −1.25102 | − | 2.16683i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2692.50 | − | 4663.55i | 0.325515 | − | 0.563808i | −0.656102 | − | 0.754673i | \(-0.727796\pi\) |
0.981616 | + | 0.190864i | \(0.0611291\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1152.00 | 0.137255 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6340.00 | −0.749924 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2820.00 | − | 4884.38i | 0.328797 | − | 0.569493i | −0.653476 | − | 0.756947i | \(-0.726690\pi\) |
0.982273 | + | 0.187454i | \(0.0600234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2165.50 | − | 3750.76i | −0.250689 | − | 0.434206i | 0.713027 | − | 0.701137i | \(-0.247324\pi\) |
−0.963716 | + | 0.266931i | \(0.913990\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2950.00 | − | 5109.55i | −0.336697 | − | 0.583175i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7470.00 | + | 12938.4i | −0.846601 | + | 1.46636i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11596.0 | 1.29596 | 0.647981 | − | 0.761656i | \(-0.275614\pi\) | ||||
0.647981 | + | 0.761656i | \(0.275614\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2765.00 | −0.306876 | −0.153438 | − | 0.988158i | \(-0.549035\pi\) | ||||
−0.153438 | + | 0.988158i | \(0.549035\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2240.00 | + | 3879.79i | −0.245203 | + | 0.424704i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3966.00 | − | 6869.31i | −0.431177 | − | 0.746821i | 0.565798 | − | 0.824544i | \(-0.308568\pi\) |
−0.996975 | + | 0.0777231i | \(0.975235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6134.00 | − | 10624.4i | −0.657867 | − | 1.13946i | −0.981167 | − | 0.193163i | \(-0.938126\pi\) |
0.323300 | − | 0.946297i | \(-0.395208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 307.500 | − | 532.606i | 0.0327571 | − | 0.0567369i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10478.0 | 1.10131 | 0.550654 | − | 0.834734i | \(-0.314378\pi\) | ||||
0.550654 | + | 0.834734i | \(0.314378\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15744.0 | −1.64380 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5850.00 | − | 10132.5i | 0.602752 | − | 1.04400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8064.50 | + | 13968.1i | 0.825474 | + | 1.42976i | 0.901557 | + | 0.432661i | \(0.142425\pi\) |
−0.0760834 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −517.000 | − | 895.470i | −0.0522323 | − | 0.0904690i | 0.838727 | − | 0.544552i | \(-0.183300\pi\) |
−0.890959 | + | 0.454083i | \(0.849967\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4540.00 | + | 7863.51i | −0.455706 | + | 0.789305i | −0.998728 | − | 0.0504127i | \(-0.983946\pi\) |
0.543023 | + | 0.839718i | \(0.317280\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18504.0 | −1.83354 | −0.916770 | − | 0.399416i | \(-0.869213\pi\) | ||||
−0.916770 | + | 0.399416i | \(0.869213\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7920.00 | −0.779769 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −256.000 | + | 443.405i | −0.0248856 | + | 0.0431031i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1400.00 | − | 2424.87i | −0.135235 | − | 0.234233i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8506.00 | + | 14732.8i | 0.811376 | + | 1.40534i | 0.911901 | + | 0.410410i | \(0.134614\pi\) |
−0.100525 | + | 0.994935i | \(0.532052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10432.5 | + | 18069.6i | −0.988942 | + | 1.71290i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6730.00 | 0.630090 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6140.00 | −0.571314 | −0.285657 | − | 0.958332i | \(-0.592212\pi\) | ||||
−0.285657 | + | 0.958332i | \(0.592212\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5472.00 | + | 9477.78i | −0.502949 | + | 0.871133i | 0.497045 | + | 0.867725i | \(0.334418\pi\) |
−0.999994 | + | 0.00340843i | \(0.998915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1681.50 | + | 2912.44i | 0.153612 | + | 0.266065i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15912.0 | + | 27560.4i | 1.43612 | + | 2.48743i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2604.00 | − | 4510.26i | 0.233609 | − | 0.404623i | −0.725258 | − | 0.688477i | \(-0.758280\pi\) |
0.958868 | + | 0.283854i | \(0.0916130\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1440.00 | −0.127647 | −0.0638235 | − | 0.997961i | \(-0.520329\pi\) | ||||
−0.0638235 | + | 0.997961i | \(0.520329\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4170.00 | 0.367451 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1155.00 | − | 2000.52i | 0.100579 | − | 0.174207i | −0.811345 | − | 0.584568i | \(-0.801264\pi\) |
0.911923 | + | 0.410361i | \(0.134597\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1386.00 | + | 2400.62i | 0.119986 | + | 0.207822i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2650.00 | − | 4589.93i | −0.226744 | − | 0.392731i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2688.00 | + | 4655.75i | −0.228662 | + | 0.396054i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9910.00 | 0.833330 | 0.416665 | − | 0.909060i | \(-0.363199\pi\) | ||||
0.416665 | + | 0.909060i | \(0.363199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6640.00 | 0.555157 | 0.277578 | − | 0.960703i | \(-0.410468\pi\) | ||||
0.277578 | + | 0.960703i | \(0.410468\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4838.00 | − | 8379.66i | 0.399899 | − | 0.692645i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6716.50 | − | 11633.3i | −0.552026 | − | 0.956137i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7995.00 | + | 13847.7i | 0.649722 | + | 1.12535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 750.000 | − | 1299.04i | 0.0606081 | − | 0.104976i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −60992.0 | −4.87405 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15969.0 | −1.26906 | −0.634530 | − | 0.772899i | \(-0.718806\pi\) | ||||
−0.634530 | + | 0.772899i | \(0.718806\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1392.50 | − | 2411.88i | 0.109446 | − | 0.189566i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −250.000 | − | 433.013i | −0.0195416 | − | 0.0338470i | 0.856089 | − | 0.516828i | \(-0.172887\pi\) |
−0.875631 | + | 0.482981i | \(0.839554\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 798.000 | + | 1382.18i | 0.0616986 | + | 0.106865i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1440.00 | − | 2494.15i | 0.110732 | − | 0.191794i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3845.00 | 0.292492 | 0.146246 | − | 0.989248i | \(-0.453281\pi\) | ||||
0.146246 | + | 0.989248i | \(0.453281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 520.000 | 0.0393446 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1594.00 | + | 2760.89i | −0.119323 | + | 0.206674i | −0.919500 | − | 0.393091i | \(-0.871406\pi\) |
0.800176 | + | 0.599765i | \(0.204739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4042.50 | − | 7001.82i | −0.301008 | − | 0.521360i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8631.50 | + | 14950.2i | 0.635943 | + | 1.10148i | 0.986315 | + | 0.164874i | \(0.0527218\pi\) |
−0.350372 | + | 0.936611i | \(0.613945\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2328.00 | − | 4032.21i | 0.170620 | − | 0.295522i | −0.768017 | − | 0.640429i | \(-0.778756\pi\) |
0.938637 | + | 0.344908i | \(0.112090\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16000.0 | 1.16043 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23209.0 | −1.67453 | −0.837265 | − | 0.546798i | \(-0.815847\pi\) | ||||
−0.837265 | + | 0.546798i | \(0.815847\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22824.0 | − | 39532.3i | 1.62977 | − | 2.82285i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15296.0 | − | 26493.4i | −1.08661 | − | 1.88207i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8812.00 | − | 15262.8i | −0.619608 | − | 1.07319i | −0.989557 | − | 0.144141i | \(-0.953958\pi\) |
0.369949 | − | 0.929052i | \(-0.379375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2296.00 | − | 3976.79i | 0.160620 | − | 0.278202i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17695.0 | −1.22537 | −0.612687 | − | 0.790326i | \(-0.709911\pi\) | ||||
−0.612687 | + | 0.790326i | \(0.709911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10620.0 | −0.731727 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1374.00 | − | 2379.84i | 0.0937231 | − | 0.162333i | −0.815352 | − | 0.578966i | \(-0.803457\pi\) |
0.909075 | + | 0.416633i | \(0.136790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9789.50 | − | 16955.9i | −0.664429 | − | 1.15083i | −0.979440 | − | 0.201737i | \(-0.935341\pi\) |
0.315010 | − | 0.949088i | \(-0.397992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6912.50 | − | 11972.8i | −0.464518 | − | 0.804568i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8902.00 | + | 15418.7i | −0.595257 | + | 1.03102i | 0.398253 | + | 0.917275i | \(0.369616\pi\) |
−0.993511 | + | 0.113740i | \(0.963717\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5460.00 | 0.361519 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22690.0 | −1.49501 | −0.747504 | − | 0.664257i | \(-0.768748\pi\) | ||||
−0.747504 | + | 0.664257i | \(0.768748\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 877.500 | − | 1519.87i | 0.0572558 | − | 0.0991699i | −0.835977 | − | 0.548765i | \(-0.815098\pi\) |
0.893233 | + | 0.449595i | \(0.148432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3460.00 | + | 5992.90i | 0.224667 | + | 0.389135i | 0.956220 | − | 0.292650i | \(-0.0945371\pi\) |
−0.731552 | + | 0.681785i | \(0.761204\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2214.00 | + | 3834.76i | 0.142379 | + | 0.246607i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3437.50 | + | 5953.92i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18939.0 | 1.20055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10744.0 | 0.677832 | 0.338916 | − | 0.940817i | \(-0.389940\pi\) | ||||
0.338916 | + | 0.940817i | \(0.389940\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2840.00 | − | 4919.02i | 0.177483 | − | 0.307410i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30972.5 | + | 53645.9i | 1.92649 | + | 3.33678i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4965.50 | + | 8600.50i | 0.305968 | + | 0.529952i | 0.977476 | − | 0.211045i | \(-0.0676866\pi\) |
−0.671508 | + | 0.740997i | \(0.734353\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2034.00 | + | 3522.99i | −0.124748 | + | 0.216070i | −0.921635 | − | 0.388059i | \(-0.873146\pi\) |
0.796886 | + | 0.604129i | \(0.206479\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17540.0 | −1.06579 | −0.532897 | − | 0.846180i | \(-0.678897\pi\) | ||||
−0.532897 | + | 0.846180i | \(0.678897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2048.00 | −0.123869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15045.0 | + | 26058.7i | −0.901618 | + | 1.56165i | −0.0762235 | + | 0.997091i | \(0.524286\pi\) |
−0.825394 | + | 0.564557i | \(0.809047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 290.000 | + | 502.295i | 0.0172996 | + | 0.0299638i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4410.00 | − | 7638.34i | −0.260682 | − | 0.451514i | 0.705742 | − | 0.708469i | \(-0.250614\pi\) |
−0.966423 | + | 0.256955i | \(0.917281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6659.50 | + | 11534.6i | −0.391868 | + | 0.678735i | −0.992696 | − | 0.120643i | \(-0.961504\pi\) |
0.600828 | + | 0.799378i | \(0.294838\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5040.00 | −0.293899 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9120.00 | −0.529427 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13280.0 | − | 23001.6i | 0.764037 | − | 1.32335i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7017.50 | − | 12154.7i | −0.401939 | − | 0.696178i | 0.592021 | − | 0.805922i | \(-0.298330\pi\) |
−0.993960 | + | 0.109744i | \(0.964997\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4705.00 | − | 8149.30i | −0.267102 | − | 0.462634i | 0.701010 | − | 0.713151i | \(-0.252733\pi\) |
−0.968112 | + | 0.250517i | \(0.919399\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24228.0 | + | 41964.1i | −1.36935 | + | 2.37178i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1060.00 | −0.0593847 | −0.0296924 | − | 0.999559i | \(-0.509453\pi\) | ||||
−0.0296924 | + | 0.999559i | \(0.509453\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3075.00 | −0.171518 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15535.0 | + | 26907.4i | −0.858979 | + | 1.48779i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4270.00 | − | 7395.86i | −0.235077 | − | 0.407166i | 0.724218 | − | 0.689571i | \(-0.242201\pi\) |
−0.959295 | + | 0.282405i | \(0.908868\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3630.00 | − | 6287.34i | −0.198121 | − | 0.343155i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7257.00 | − | 12569.5i | 0.394374 | − | 0.683075i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17259.0 | −0.929905 | −0.464953 | − | 0.885336i | \(-0.653929\pi\) | ||||
−0.464953 | + | 0.885336i | \(0.653929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8988.00 | 0.482203 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15012.0 | + | 26001.5i | −0.798563 | + | 1.38315i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12072.5 | + | 20910.2i | 0.639481 | + | 1.10761i | 0.985547 | + | 0.169404i | \(0.0541842\pi\) |
−0.346065 | + | 0.938210i | \(0.612482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13120.0 | + | 22724.5i | 0.689127 | + | 1.19360i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10400.0 | + | 18013.3i | −0.543969 | + | 0.942182i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17792.0 | 0.922851 | 0.461425 | − | 0.887179i | \(-0.347338\pi\) | ||||
0.461425 | + | 0.887179i | \(0.347338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38160.0 | 1.97109 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2850.00 | − | 4936.34i | 0.145995 | − | 0.252871i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5310.00 | − | 9197.19i | −0.270890 | − | 0.469195i | 0.698200 | − | 0.715903i | \(-0.253985\pi\) |
−0.969090 | + | 0.246708i | \(0.920651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −236.000 | − | 408.764i | −0.0119409 | − | 0.0206822i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4325.00 | − | 7491.12i | 0.217937 | − | 0.377477i | −0.736240 | − | 0.676720i | \(-0.763401\pi\) |
0.954177 | + | 0.299243i | \(0.0967341\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14080.0 | 0.703722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4652.00 | 0.231565 | 0.115783 | − | 0.993275i | \(-0.463062\pi\) | ||||
0.115783 | + | 0.993275i | \(0.463062\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16934.0 | − | 29330.5i | 0.836135 | − | 1.44823i | −0.0569682 | − | 0.998376i | \(-0.518143\pi\) |
0.893103 | − | 0.449852i | \(-0.148523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2097.50 | + | 3632.98i | 0.103150 | + | 0.178660i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5400.00 | + | 9353.07i | 0.263434 | + | 0.456280i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6426.00 | − | 11130.2i | 0.312234 | − | 0.540806i | −0.666611 | − | 0.745406i | \(-0.732256\pi\) |
0.978846 | + | 0.204600i | \(0.0655892\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10280.0 | −0.495533 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9730.00 | −0.467164 | −0.233582 | − | 0.972337i | \(-0.575045\pi\) | ||||
−0.233582 | + | 0.972337i | \(0.575045\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16680.5 | + | 28891.5i | −0.794570 | + | 1.37624i | 0.128542 | + | 0.991704i | \(0.458970\pi\) |
−0.923112 | + | 0.384531i | \(0.874363\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10026.0 | + | 17365.5i | 0.475708 | + | 0.823951i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1040.00 | + | 1801.33i | 0.0489599 | + | 0.0848010i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13278.5 | − | 22999.0i | 0.622672 | − | 1.07850i | −0.366314 | − | 0.930491i | \(-0.619380\pi\) |
0.988986 | − | 0.148009i | \(-0.0472863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18333.0 | 0.853030 | 0.426515 | − | 0.904480i | \(-0.359741\pi\) | ||||
0.426515 | + | 0.904480i | \(0.359741\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16400.0 | −0.760136 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3444.00 | − | 5965.18i | 0.158401 | − | 0.274358i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28288.0 | − | 48996.3i | −1.29606 | − | 2.24484i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2747.50 | − | 4758.81i | −0.124920 | − | 0.216368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18688.0 | − | 32368.6i | 0.846449 | − | 1.46609i | −0.0379081 | − | 0.999281i | \(-0.512069\pi\) |
0.884357 | − | 0.466811i | \(-0.154597\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 58212.0 | 2.61666 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26975.0 | −1.20796 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8037.50 | − | 13921.4i | 0.357218 | − | 0.618720i | −0.630277 | − | 0.776370i | \(-0.717059\pi\) |
0.987495 | + | 0.157651i | \(0.0503919\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2478.00 | − | 4292.02i | −0.109719 | − | 0.190039i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2464.00 | − | 4267.77i | −0.108285 | − | 0.187555i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14400.0 | − | 24941.5i | 0.630476 | − | 1.09202i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32183.0 | −1.39863 | −0.699316 | − | 0.714812i | \(-0.746512\pi\) | ||||
−0.699316 | + | 0.714812i | \(0.746512\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1424.00 | −0.0616565 | −0.0308282 | − | 0.999525i | \(-0.509814\pi\) | ||||
−0.0308282 | + | 0.999525i | \(0.509814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 180.000 | − | 311.769i | 0.00773635 | − | 0.0133998i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −112.000 | − | 193.990i | −0.00479606 | − | 0.00830703i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13480.5 | − | 23348.9i | −0.573048 | − | 0.992549i | −0.996251 | − | 0.0865136i | \(-0.972427\pi\) |
0.423202 | − | 0.906035i | \(-0.360906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10550.0 | − | 18273.1i | 0.446841 | − | 0.773951i | −0.551338 | − | 0.834282i | \(-0.685882\pi\) |
0.998178 | + | 0.0603314i | \(0.0192157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35120.0 | −1.47671 | −0.738357 | − | 0.674410i | \(-0.764398\pi\) | ||||
−0.738357 | + | 0.674410i | \(0.764398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21238.0 | 0.889778 | 0.444889 | − | 0.895586i | \(-0.353243\pi\) | ||||
0.444889 | + | 0.895586i | \(0.353243\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28113.5 | − | 48694.0i | 1.16936 | − | 2.02539i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5310.00 | + | 9197.19i | 0.220072 | + | 0.381176i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13044.0 | − | 22592.9i | −0.536745 | − | 0.929669i | −0.999077 | − | 0.0429623i | \(-0.986320\pi\) |
0.462332 | − | 0.886707i | \(-0.347013\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10570.0 | − | 18307.8i | 0.433392 | − | 0.750657i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10140.0 | 0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 99540.0 | 4.03806 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25680.0 | + | 44479.1i | −1.03443 | + | 1.79168i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5561.00 | + | 9631.93i | 0.223218 | + | 0.386625i | 0.955783 | − | 0.294072i | \(-0.0950105\pi\) |
−0.732565 | + | 0.680697i | \(0.761677\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1492.50 | − | 2585.09i | −0.0594899 | − | 0.103039i | 0.834747 | − | 0.550634i | \(-0.185614\pi\) |
−0.894237 | + | 0.447595i | \(0.852281\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24774.0 | − | 42909.8i | 0.984026 | − | 1.70438i | 0.337837 | − | 0.941205i | \(-0.390305\pi\) |
0.646189 | − | 0.763178i | \(-0.276362\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21688.0 | −0.855467 | −0.427734 | − | 0.903905i | \(-0.640688\pi\) | ||||
−0.427734 | + | 0.903905i | \(0.640688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20025.0 | 0.787133 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2560.00 | + | 4434.05i | −0.0999333 | + | 0.173090i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7150.00 | − | 12384.2i | −0.278150 | − | 0.481770i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20250.0 | + | 35074.0i | 0.782371 | + | 1.35511i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5467.50 | + | 9469.99i | −0.210518 | + | 0.364628i | −0.951877 | − | 0.306481i | \(-0.900848\pi\) |
0.741359 | + | 0.671109i | \(0.234182\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40126.0 | 1.53448 | 0.767241 | − | 0.641358i | \(-0.221629\pi\) | ||||
0.767241 | + | 0.641358i | \(0.221629\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42748.0 | −1.62920 | −0.814601 | − | 0.580022i | \(-0.803044\pi\) | ||||
−0.814601 | + | 0.580022i | \(0.803044\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13748.0 | + | 23812.2i | −0.520420 | + | 0.901394i | 0.479298 | + | 0.877652i | \(0.340891\pi\) |
−0.999718 | + | 0.0237419i | \(0.992442\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20448.0 | + | 35417.0i | 0.771433 | + | 1.33616i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1176.00 | − | 2036.89i | −0.0440687 | − | 0.0763292i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3570.00 | + | 6183.42i | −0.133332 | + | 0.230937i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9348.00 | 0.346800 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28202.0 | 1.04278 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5565.00 | − | 9638.86i | 0.204405 | − | 0.354040i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10840.0 | + | 18775.4i | 0.396843 | + | 0.687352i | 0.993334 | − | 0.115268i | \(-0.0367725\pi\) |
−0.596492 | + | 0.802619i | \(0.703439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3412.00 | − | 5909.76i | −0.124088 | − | 0.214928i | 0.797288 | − | 0.603599i | \(-0.206267\pi\) |
−0.921376 | + | 0.388672i | \(0.872934\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40576.0 | + | 70279.7i | −1.47083 | + | 2.54756i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4176.00 | −0.150386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26512.0 | 0.951632 | 0.475816 | − | 0.879545i | \(-0.342153\pi\) | ||||
0.475816 | + | 0.879545i | \(0.342153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28730.0 | + | 49761.8i | −1.02455 | + | 1.77457i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16050.0 | − | 27799.4i | −0.570509 | − | 0.988150i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11298.5 | − | 19569.6i | −0.399022 | − | 0.691127i | 0.594583 | − | 0.804034i | \(-0.297317\pi\) |
−0.993606 | + | 0.112907i | \(0.963984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13342.0 | − | 23109.0i | 0.469674 | − | 0.813499i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18880.0 | 0.660366 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38115.0 | 1.32888 | 0.664441 | − | 0.747341i | \(-0.268670\pi\) | ||||
0.664441 | + | 0.747341i | \(0.268670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21742.5 | + | 37659.1i | −0.753226 | + | 1.30462i | 0.193026 | + | 0.981194i | \(0.438170\pi\) |
−0.946252 | + | 0.323431i | \(0.895164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19680.0 | + | 34086.8i | 0.679607 | + | 1.17711i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22710.0 | − | 39334.9i | −0.779278 | − | 1.34975i | −0.932359 | − | 0.361535i | \(-0.882253\pi\) |
0.153081 | − | 0.988214i | \(-0.451080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2502.50 | + | 4334.46i | −0.0856002 | + | 0.148264i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32505.0 | 1.10487 | 0.552435 | − | 0.833556i | \(-0.313699\pi\) | ||||
0.552435 | + | 0.833556i | \(0.313699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18780.0 | −0.636342 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11070.0 | − | 19173.8i | 0.372752 | − | 0.645625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1447.50 | + | 2507.14i | 0.0485885 | + | 0.0841578i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9092.50 | + | 15748.7i | 0.303314 | + | 0.525355i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7138.00 | + | 12363.4i | −0.237376 | + | 0.411147i | −0.959961 | − | 0.280135i | \(-0.909621\pi\) |
0.722585 | + | 0.691283i | \(0.242954\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35844.0 | 1.18464 | 0.592322 | − | 0.805702i | \(-0.298211\pi\) | ||||
0.592322 | + | 0.805702i | \(0.298211\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52272.0 | 1.72226 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12135.0 | + | 21018.4i | −0.397373 | + | 0.688270i | −0.993401 | − | 0.114694i | \(-0.963411\pi\) |
0.596028 | + | 0.802963i | \(0.296745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3936.00 | − | 6817.35i | −0.128493 | − | 0.222557i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9576.00 | + | 16586.1i | 0.310709 | + | 0.538164i | 0.978516 | − | 0.206171i | \(-0.0661002\pi\) |
−0.667807 | + | 0.744334i | \(0.732767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1987.50 | − | 3442.45i | 0.0642914 | − | 0.111356i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1280.00 | 0.0411543 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9164.00 | −0.293748 | −0.146874 | − | 0.989155i | \(-0.546921\pi\) | ||||
−0.146874 | + | 0.989155i | \(0.546921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6250.00 | + | 10825.3i | −0.199134 | + | 0.344910i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18129.5 | − | 31401.2i | −0.575895 | − | 0.997479i | −0.995944 | − | 0.0899775i | \(-0.971320\pi\) |
0.420049 | − | 0.907501i | \(-0.362013\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 648.4.i.c.433.1 | 2 | ||
3.2 | odd | 2 | 648.4.i.j.433.1 | 2 | |||
9.2 | odd | 6 | 648.4.i.j.217.1 | 2 | |||
9.4 | even | 3 | 648.4.a.b.1.1 | yes | 1 | ||
9.5 | odd | 6 | 648.4.a.a.1.1 | ✓ | 1 | ||
9.7 | even | 3 | inner | 648.4.i.c.217.1 | 2 | ||
36.23 | even | 6 | 1296.4.a.c.1.1 | 1 | |||
36.31 | odd | 6 | 1296.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.a.1.1 | ✓ | 1 | 9.5 | odd | 6 | ||
648.4.a.b.1.1 | yes | 1 | 9.4 | even | 3 | ||
648.4.i.c.217.1 | 2 | 9.7 | even | 3 | inner | ||
648.4.i.c.433.1 | 2 | 1.1 | even | 1 | trivial | ||
648.4.i.j.217.1 | 2 | 9.2 | odd | 6 | |||
648.4.i.j.433.1 | 2 | 3.2 | odd | 2 | |||
1296.4.a.c.1.1 | 1 | 36.23 | even | 6 | |||
1296.4.a.f.1.1 | 1 | 36.31 | odd | 6 |