Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.c (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: | \(79.6525785077\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.e.649.2 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 23.0000i | − 1.24188i | −0.783857 | − | 0.620942i | \(-0.786750\pi\) | ||||
0.783857 | − | 0.620942i | \(-0.213250\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.0000 | −0.822304 | −0.411152 | − | 0.911567i | \(-0.634873\pi\) | ||||
−0.411152 | + | 0.911567i | \(0.634873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 34.0000i | − 0.725377i | −0.931910 | − | 0.362689i | \(-0.881859\pi\) | ||||
0.931910 | − | 0.362689i | \(-0.118141\pi\) | |||||||
\(14\) | −46.0000 | −0.878144 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − 42.0000i | − 0.599206i | −0.954064 | − | 0.299603i | \(-0.903146\pi\) | ||||
0.954064 | − | 0.299603i | \(-0.0968542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 139.000 | 1.67836 | 0.839179 | − | 0.543856i | \(-0.183036\pi\) | ||||
0.839179 | + | 0.543856i | \(0.183036\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 60.0000i | 0.581456i | ||||||||
\(23\) | − 192.000i | − 1.74064i | −0.492485 | − | 0.870321i | \(-0.663911\pi\) | ||||
0.492485 | − | 0.870321i | \(-0.336089\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −68.0000 | −0.512919 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 92.0000i | 0.620942i | ||||||||
\(29\) | 234.000 | 1.49837 | 0.749185 | − | 0.662361i | \(-0.230446\pi\) | ||||
0.749185 | + | 0.662361i | \(0.230446\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −55.0000 | −0.318655 | −0.159327 | − | 0.987226i | \(-0.550933\pi\) | ||||
−0.159327 | + | 0.987226i | \(0.550933\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −84.0000 | −0.423702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 191.000i | − 0.848654i | −0.905509 | − | 0.424327i | \(-0.860511\pi\) | ||||
0.905509 | − | 0.424327i | \(-0.139489\pi\) | |||||||
\(38\) | − 278.000i | − 1.18678i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −138.000 | −0.525658 | −0.262829 | − | 0.964842i | \(-0.584656\pi\) | ||||
−0.262829 | + | 0.964842i | \(0.584656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 53.0000i | 0.187963i | 0.995574 | + | 0.0939817i | \(0.0299595\pi\) | ||||
−0.995574 | + | 0.0939817i | \(0.970040\pi\) | |||||||
\(44\) | 120.000 | 0.411152 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −384.000 | −1.23082 | ||||||||
\(47\) | 366.000i | 1.13588i | 0.823068 | + | 0.567942i | \(0.192260\pi\) | ||||
−0.823068 | + | 0.567942i | \(0.807740\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −186.000 | −0.542274 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 136.000i | 0.362689i | ||||||||
\(53\) | 330.000i | 0.855264i | 0.903953 | + | 0.427632i | \(0.140652\pi\) | ||||
−0.903953 | + | 0.427632i | \(0.859348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 184.000 | 0.439072 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 468.000i | − 1.05951i | ||||||||
\(59\) | −396.000 | −0.873810 | −0.436905 | − | 0.899508i | \(-0.643925\pi\) | ||||
−0.436905 | + | 0.899508i | \(0.643925\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.0000 | 0.0482762 | 0.0241381 | − | 0.999709i | \(-0.492316\pi\) | ||||
0.0241381 | + | 0.999709i | \(0.492316\pi\) | |||||||
\(62\) | 110.000i | 0.225323i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 452.000i | − 0.824188i | −0.911141 | − | 0.412094i | \(-0.864798\pi\) | ||||
0.911141 | − | 0.412094i | \(-0.135202\pi\) | |||||||
\(68\) | 168.000i | 0.299603i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −204.000 | −0.340991 | −0.170495 | − | 0.985358i | \(-0.554537\pi\) | ||||
−0.170495 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 691.000i | − 1.10788i | −0.832556 | − | 0.553941i | \(-0.813123\pi\) | ||||
0.832556 | − | 0.553941i | \(-0.186877\pi\) | |||||||
\(74\) | −382.000 | −0.600089 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −556.000 | −0.839179 | ||||||||
\(77\) | 690.000i | 1.02121i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 709.000 | 1.00973 | 0.504865 | − | 0.863198i | \(-0.331542\pi\) | ||||
0.504865 | + | 0.863198i | \(0.331542\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 276.000i | 0.371696i | ||||||||
\(83\) | − 1098.00i | − 1.45206i | −0.687662 | − | 0.726031i | \(-0.741363\pi\) | ||||
0.687662 | − | 0.726031i | \(-0.258637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 106.000 | 0.132910 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 240.000i | − 0.290728i | ||||||||
\(89\) | −816.000 | −0.971863 | −0.485932 | − | 0.873997i | \(-0.661520\pi\) | ||||
−0.485932 | + | 0.873997i | \(0.661520\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −782.000 | −0.900834 | ||||||||
\(92\) | 768.000i | 0.870321i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 732.000 | 0.803192 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 905.000i | − 0.947308i | −0.880711 | − | 0.473654i | \(-0.842935\pi\) | ||||
0.880711 | − | 0.473654i | \(-0.157065\pi\) | |||||||
\(98\) | 372.000i | 0.383446i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1278.00 | 1.25907 | 0.629533 | − | 0.776973i | \(-0.283246\pi\) | ||||
0.629533 | + | 0.776973i | \(0.283246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 605.000i | 0.578761i | 0.957214 | + | 0.289381i | \(0.0934493\pi\) | ||||
−0.957214 | + | 0.289381i | \(0.906551\pi\) | |||||||
\(104\) | 272.000 | 0.256460 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 660.000 | 0.604763 | ||||||||
\(107\) | 1488.00i | 1.34440i | 0.740371 | + | 0.672198i | \(0.234650\pi\) | ||||
−0.740371 | + | 0.672198i | \(0.765350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −593.000 | −0.521093 | −0.260546 | − | 0.965461i | \(-0.583903\pi\) | ||||
−0.260546 | + | 0.965461i | \(0.583903\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 368.000i | − 0.310471i | ||||||||
\(113\) | − 324.000i | − 0.269729i | −0.990864 | − | 0.134864i | \(-0.956940\pi\) | ||||
0.990864 | − | 0.134864i | \(-0.0430599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −936.000 | −0.749185 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 792.000i | 0.617877i | ||||||||
\(119\) | −966.000 | −0.744143 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −431.000 | −0.323817 | ||||||||
\(122\) | − 46.0000i | − 0.0341364i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 220.000 | 0.159327 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1928.00i | − 1.34711i | −0.739139 | − | 0.673553i | \(-0.764768\pi\) | ||||
0.739139 | − | 0.673553i | \(-0.235232\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2742.00 | −1.82878 | −0.914388 | − | 0.404839i | \(-0.867328\pi\) | ||||
−0.914388 | + | 0.404839i | \(0.867328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3197.00i | − 2.08432i | ||||||||
\(134\) | −904.000 | −0.582789 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 336.000 | 0.211851 | ||||||||
\(137\) | 1326.00i | 0.826918i | 0.910523 | + | 0.413459i | \(0.135680\pi\) | ||||
−0.910523 | + | 0.413459i | \(0.864320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −893.000 | −0.544916 | −0.272458 | − | 0.962168i | \(-0.587837\pi\) | ||||
−0.272458 | + | 0.962168i | \(0.587837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 408.000i | 0.241117i | ||||||||
\(143\) | 1020.00i | 0.596480i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1382.00 | −0.783391 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 764.000i | 0.424327i | ||||||||
\(149\) | −2502.00 | −1.37565 | −0.687825 | − | 0.725877i | \(-0.741434\pi\) | ||||
−0.687825 | + | 0.725877i | \(0.741434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2767.00 | −1.49123 | −0.745613 | − | 0.666379i | \(-0.767843\pi\) | ||||
−0.745613 | + | 0.666379i | \(0.767843\pi\) | |||||||
\(152\) | 1112.00i | 0.593389i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1380.00 | 0.722101 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2701.00i | 1.37301i | 0.727123 | + | 0.686507i | \(0.240857\pi\) | ||||
−0.727123 | + | 0.686507i | \(0.759143\pi\) | |||||||
\(158\) | − 1418.00i | − 0.713987i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4416.00 | −2.16167 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1748.00i | 0.839963i | 0.907533 | + | 0.419981i | \(0.137963\pi\) | ||||
−0.907533 | + | 0.419981i | \(0.862037\pi\) | |||||||
\(164\) | 552.000 | 0.262829 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2196.00 | −1.02676 | ||||||||
\(167\) | − 534.000i | − 0.247438i | −0.992317 | − | 0.123719i | \(-0.960518\pi\) | ||||
0.992317 | − | 0.123719i | \(-0.0394822\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1041.00 | 0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 212.000i | − 0.0939817i | ||||||||
\(173\) | 192.000i | 0.0843786i | 0.999110 | + | 0.0421893i | \(0.0134333\pi\) | ||||
−0.999110 | + | 0.0421893i | \(0.986567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −480.000 | −0.205576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1632.00i | 0.687211i | ||||||||
\(179\) | 1140.00 | 0.476020 | 0.238010 | − | 0.971263i | \(-0.423505\pi\) | ||||
0.238010 | + | 0.971263i | \(0.423505\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 398.000 | 0.163443 | 0.0817213 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817213 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(182\) | 1564.00i | 0.636986i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1536.00 | 0.615410 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1260.00i | 0.492729i | ||||||||
\(188\) | − 1464.00i | − 0.567942i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3474.00 | −1.31607 | −0.658036 | − | 0.752986i | \(-0.728613\pi\) | ||||
−0.658036 | + | 0.752986i | \(0.728613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 2713.00i | − 1.01184i | −0.862579 | − | 0.505922i | \(-0.831152\pi\) | ||||
0.862579 | − | 0.505922i | \(-0.168848\pi\) | |||||||
\(194\) | −1810.00 | −0.669848 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 744.000 | 0.271137 | ||||||||
\(197\) | 4734.00i | 1.71210i | 0.516894 | + | 0.856050i | \(0.327088\pi\) | ||||
−0.516894 | + | 0.856050i | \(0.672912\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5132.00 | −1.82813 | −0.914065 | − | 0.405568i | \(-0.867074\pi\) | ||||
−0.914065 | + | 0.405568i | \(0.867074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 2556.00i | − 0.890295i | ||||||||
\(203\) | − 5382.00i | − 1.86080i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1210.00 | 0.409246 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 544.000i | − 0.181344i | ||||||||
\(209\) | −4170.00 | −1.38012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5240.00 | 1.70965 | 0.854826 | − | 0.518915i | \(-0.173664\pi\) | ||||
0.854826 | + | 0.518915i | \(0.173664\pi\) | |||||||
\(212\) | − 1320.00i | − 0.427632i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2976.00 | 0.950632 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1265.00i | 0.395732i | ||||||||
\(218\) | 1186.00i | 0.368468i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1428.00 | −0.434650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4519.00i | − 1.35702i | −0.734593 | − | 0.678508i | \(-0.762627\pi\) | ||||
0.734593 | − | 0.678508i | \(-0.237373\pi\) | |||||||
\(224\) | −736.000 | −0.219536 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −648.000 | −0.190727 | ||||||||
\(227\) | 5064.00i | 1.48066i | 0.672244 | + | 0.740329i | \(0.265330\pi\) | ||||
−0.672244 | + | 0.740329i | \(0.734670\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2573.00 | −0.742483 | −0.371242 | − | 0.928536i | \(-0.621068\pi\) | ||||
−0.371242 | + | 0.928536i | \(0.621068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1872.00i | 0.529754i | ||||||||
\(233\) | − 4098.00i | − 1.15223i | −0.817370 | − | 0.576114i | \(-0.804569\pi\) | ||||
0.817370 | − | 0.576114i | \(-0.195431\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1584.00 | 0.436905 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1932.00i | 0.526189i | ||||||||
\(239\) | −306.000 | −0.0828180 | −0.0414090 | − | 0.999142i | \(-0.513185\pi\) | ||||
−0.0414090 | + | 0.999142i | \(0.513185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6482.00 | 1.73254 | 0.866270 | − | 0.499575i | \(-0.166511\pi\) | ||||
0.866270 | + | 0.499575i | \(0.166511\pi\) | |||||||
\(242\) | 862.000i | 0.228973i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −92.0000 | −0.0241381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4726.00i | − 1.21744i | ||||||||
\(248\) | − 440.000i | − 0.112661i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5850.00 | 1.47111 | 0.735555 | − | 0.677465i | \(-0.236921\pi\) | ||||
0.735555 | + | 0.677465i | \(0.236921\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5760.00i | 1.43134i | ||||||||
\(254\) | −3856.00 | −0.952547 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5598.00i | 1.35873i | 0.733800 | + | 0.679365i | \(0.237745\pi\) | ||||
−0.733800 | + | 0.679365i | \(0.762255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4393.00 | −1.05393 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5484.00i | 1.29314i | ||||||||
\(263\) | 8286.00i | 1.94272i | 0.237603 | + | 0.971362i | \(0.423638\pi\) | ||||
−0.237603 | + | 0.971362i | \(0.576362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6394.00 | −1.47384 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1808.00i | 0.412094i | ||||||||
\(269\) | −504.000 | −0.114236 | −0.0571179 | − | 0.998367i | \(-0.518191\pi\) | ||||
−0.0571179 | + | 0.998367i | \(0.518191\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4489.00 | −1.00623 | −0.503113 | − | 0.864221i | \(-0.667812\pi\) | ||||
−0.503113 | + | 0.864221i | \(0.667812\pi\) | |||||||
\(272\) | − 672.000i | − 0.149801i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2652.00 | 0.584720 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2213.00i | − 0.480023i | −0.970770 | − | 0.240011i | \(-0.922849\pi\) | ||||
0.970770 | − | 0.240011i | \(-0.0771512\pi\) | |||||||
\(278\) | 1786.00i | 0.385314i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2718.00 | 0.577019 | 0.288509 | − | 0.957477i | \(-0.406840\pi\) | ||||
0.288509 | + | 0.957477i | \(0.406840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5615.00i | 1.17942i | 0.807613 | + | 0.589712i | \(0.200759\pi\) | ||||
−0.807613 | + | 0.589712i | \(0.799241\pi\) | |||||||
\(284\) | 816.000 | 0.170495 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2040.00 | 0.421775 | ||||||||
\(287\) | 3174.00i | 0.652806i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3149.00 | 0.640953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2764.00i | 0.553941i | ||||||||
\(293\) | − 1488.00i | − 0.296689i | −0.988936 | − | 0.148345i | \(-0.952606\pi\) | ||||
0.988936 | − | 0.148345i | \(-0.0473945\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1528.00 | 0.300045 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5004.00i | 0.972731i | ||||||||
\(299\) | −6528.00 | −1.26262 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1219.00 | 0.233429 | ||||||||
\(302\) | 5534.00i | 1.05446i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2224.00 | 0.419589 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7487.00i | − 1.39188i | −0.718102 | − | 0.695938i | \(-0.754989\pi\) | ||||
0.718102 | − | 0.695938i | \(-0.245011\pi\) | |||||||
\(308\) | − 2760.00i | − 0.510603i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8118.00 | −1.48016 | −0.740080 | − | 0.672519i | \(-0.765212\pi\) | ||||
−0.740080 | + | 0.672519i | \(0.765212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5002.00i | − 0.903290i | −0.892198 | − | 0.451645i | \(-0.850837\pi\) | ||||
0.892198 | − | 0.451645i | \(-0.149163\pi\) | |||||||
\(314\) | 5402.00 | 0.970868 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2836.00 | −0.504865 | ||||||||
\(317\) | 5082.00i | 0.900421i | 0.892922 | + | 0.450211i | \(0.148651\pi\) | ||||
−0.892922 | + | 0.450211i | \(0.851349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7020.00 | −1.23211 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8832.00i | 1.52853i | ||||||||
\(323\) | − 5838.00i | − 1.00568i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3496.00 | 0.593943 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 1104.00i | − 0.185848i | ||||||||
\(329\) | 8418.00 | 1.41064 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7625.00 | 1.26619 | 0.633094 | − | 0.774075i | \(-0.281785\pi\) | ||||
0.633094 | + | 0.774075i | \(0.281785\pi\) | |||||||
\(332\) | 4392.00i | 0.726031i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1068.00 | −0.174965 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3778.00i | 0.610685i | 0.952243 | + | 0.305342i | \(0.0987709\pi\) | ||||
−0.952243 | + | 0.305342i | \(0.901229\pi\) | |||||||
\(338\) | − 2082.00i | − 0.335047i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1650.00 | 0.262031 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3611.00i | − 0.568442i | ||||||||
\(344\) | −424.000 | −0.0664551 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 384.000 | 0.0596646 | ||||||||
\(347\) | − 8268.00i | − 1.27911i | −0.768747 | − | 0.639553i | \(-0.779120\pi\) | ||||
0.768747 | − | 0.639553i | \(-0.220880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1379.00 | −0.211508 | −0.105754 | − | 0.994392i | \(-0.533726\pi\) | ||||
−0.105754 | + | 0.994392i | \(0.533726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 960.000i | 0.145364i | ||||||||
\(353\) | − 3072.00i | − 0.463190i | −0.972812 | − | 0.231595i | \(-0.925606\pi\) | ||||
0.972812 | − | 0.231595i | \(-0.0743944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3264.00 | 0.485932 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 2280.00i | − 0.336597i | ||||||||
\(359\) | −7446.00 | −1.09467 | −0.547333 | − | 0.836915i | \(-0.684357\pi\) | ||||
−0.547333 | + | 0.836915i | \(0.684357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12462.0 | 1.81688 | ||||||||
\(362\) | − 796.000i | − 0.115571i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3128.00 | 0.450417 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6496.00i | 0.923947i | 0.886894 | + | 0.461973i | \(0.152858\pi\) | ||||
−0.886894 | + | 0.461973i | \(0.847142\pi\) | |||||||
\(368\) | − 3072.00i | − 0.435161i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7590.00 | 1.06214 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1633.00i | − 0.226685i | −0.993556 | − | 0.113343i | \(-0.963844\pi\) | ||||
0.993556 | − | 0.113343i | \(-0.0361557\pi\) | |||||||
\(374\) | 2520.00 | 0.348412 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2928.00 | −0.401596 | ||||||||
\(377\) | − 7956.00i | − 1.08688i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6788.00 | −0.919990 | −0.459995 | − | 0.887922i | \(-0.652149\pi\) | ||||
−0.459995 | + | 0.887922i | \(0.652149\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6948.00i | 0.930604i | ||||||||
\(383\) | − 6582.00i | − 0.878132i | −0.898455 | − | 0.439066i | \(-0.855309\pi\) | ||||
0.898455 | − | 0.439066i | \(-0.144691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5426.00 | −0.715482 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3620.00i | 0.473654i | ||||||||
\(389\) | 2850.00 | 0.371467 | 0.185734 | − | 0.982600i | \(-0.440534\pi\) | ||||
0.185734 | + | 0.982600i | \(0.440534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8064.00 | −1.04300 | ||||||||
\(392\) | − 1488.00i | − 0.191723i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9468.00 | 1.21064 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7451.00i | − 0.941952i | −0.882146 | − | 0.470976i | \(-0.843902\pi\) | ||||
0.882146 | − | 0.470976i | \(-0.156098\pi\) | |||||||
\(398\) | 10264.0i | 1.29268i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14124.0 | −1.75890 | −0.879450 | − | 0.475991i | \(-0.842089\pi\) | ||||
−0.879450 | + | 0.475991i | \(0.842089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1870.00i | 0.231145i | ||||||||
\(404\) | −5112.00 | −0.629533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10764.0 | −1.31578 | ||||||||
\(407\) | 5730.00i | 0.697851i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6374.00 | −0.770597 | −0.385298 | − | 0.922792i | \(-0.625901\pi\) | ||||
−0.385298 | + | 0.922792i | \(0.625901\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 2420.00i | − 0.289381i | ||||||||
\(413\) | 9108.00i | 1.08517i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1088.00 | −0.128230 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8340.00i | 0.975892i | ||||||||
\(419\) | 3948.00 | 0.460316 | 0.230158 | − | 0.973153i | \(-0.426076\pi\) | ||||
0.230158 | + | 0.973153i | \(0.426076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12629.0 | 1.46199 | 0.730997 | − | 0.682380i | \(-0.239055\pi\) | ||||
0.730997 | + | 0.682380i | \(0.239055\pi\) | |||||||
\(422\) | − 10480.0i | − 1.20891i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2640.00 | −0.302381 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 529.000i | − 0.0599534i | ||||||||
\(428\) | − 5952.00i | − 0.672198i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4842.00 | −0.541139 | −0.270570 | − | 0.962700i | \(-0.587212\pi\) | ||||
−0.270570 | + | 0.962700i | \(0.587212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3851.00i | 0.427407i | 0.976899 | + | 0.213704i | \(0.0685526\pi\) | ||||
−0.976899 | + | 0.213704i | \(0.931447\pi\) | |||||||
\(434\) | 2530.00 | 0.279825 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2372.00 | 0.260546 | ||||||||
\(437\) | − 26688.0i | − 2.92142i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7435.00 | 0.808322 | 0.404161 | − | 0.914688i | \(-0.367564\pi\) | ||||
0.404161 | + | 0.914688i | \(0.367564\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2856.00i | 0.307344i | ||||||||
\(443\) | 5760.00i | 0.617756i | 0.951102 | + | 0.308878i | \(0.0999535\pi\) | ||||
−0.951102 | + | 0.308878i | \(0.900047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9038.00 | −0.959555 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1472.00i | 0.155235i | ||||||||
\(449\) | −2190.00 | −0.230184 | −0.115092 | − | 0.993355i | \(-0.536716\pi\) | ||||
−0.115092 | + | 0.993355i | \(0.536716\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4140.00 | 0.432251 | ||||||||
\(452\) | 1296.00i | 0.134864i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10128.0 | 1.04698 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 7202.00i | − 0.737189i | −0.929590 | − | 0.368594i | \(-0.879839\pi\) | ||||
0.929590 | − | 0.368594i | \(-0.120161\pi\) | |||||||
\(458\) | 5146.00i | 0.525015i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13476.0 | 1.36147 | 0.680737 | − | 0.732528i | \(-0.261659\pi\) | ||||
0.680737 | + | 0.732528i | \(0.261659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 10843.0i | − 1.08837i | −0.838964 | − | 0.544187i | \(-0.816838\pi\) | ||||
0.838964 | − | 0.544187i | \(-0.183162\pi\) | |||||||
\(464\) | 3744.00 | 0.374592 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8196.00 | −0.814748 | ||||||||
\(467\) | 6108.00i | 0.605235i | 0.953112 | + | 0.302617i | \(0.0978604\pi\) | ||||
−0.953112 | + | 0.302617i | \(0.902140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10396.0 | −1.02355 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 3168.00i | − 0.308939i | ||||||||
\(473\) | − 1590.00i | − 0.154563i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3864.00 | 0.372072 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 612.000i | 0.0585611i | ||||||||
\(479\) | 9852.00 | 0.939769 | 0.469885 | − | 0.882728i | \(-0.344296\pi\) | ||||
0.469885 | + | 0.882728i | \(0.344296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6494.00 | −0.615594 | ||||||||
\(482\) | − 12964.0i | − 1.22509i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1724.00 | 0.161908 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 7796.00i | − 0.725401i | −0.931906 | − | 0.362701i | \(-0.881855\pi\) | ||||
0.931906 | − | 0.362701i | \(-0.118145\pi\) | |||||||
\(488\) | 184.000i | 0.0170682i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2454.00 | −0.225555 | −0.112777 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112777 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 9828.00i | − 0.897831i | ||||||||
\(494\) | −9452.00 | −0.860862 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −880.000 | −0.0796636 | ||||||||
\(497\) | 4692.00i | 0.423471i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2953.00 | 0.264919 | 0.132459 | − | 0.991188i | \(-0.457713\pi\) | ||||
0.132459 | + | 0.991188i | \(0.457713\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 11700.0i | − 1.04023i | ||||||||
\(503\) | 11322.0i | 1.00362i | 0.864977 | + | 0.501812i | \(0.167333\pi\) | ||||
−0.864977 | + | 0.501812i | \(0.832667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11520.0 | 1.01211 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7712.00i | 0.673553i | ||||||||
\(509\) | 9696.00 | 0.844337 | 0.422169 | − | 0.906517i | \(-0.361269\pi\) | ||||
0.422169 | + | 0.906517i | \(0.361269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15893.0 | −1.37586 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11196.0 | 0.960767 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 10980.0i | − 0.934042i | ||||||||
\(518\) | 8786.00i | 0.745241i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12192.0 | 1.02522 | 0.512612 | − | 0.858621i | \(-0.328678\pi\) | ||||
0.512612 | + | 0.858621i | \(0.328678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8491.00i | − 0.709915i | −0.934882 | − | 0.354957i | \(-0.884495\pi\) | ||||
0.934882 | − | 0.354957i | \(-0.115505\pi\) | |||||||
\(524\) | 10968.0 | 0.914388 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16572.0 | 1.37371 | ||||||||
\(527\) | 2310.00i | 0.190940i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24697.0 | −2.02983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12788.0i | 1.04216i | ||||||||
\(533\) | 4692.00i | 0.381300i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3616.00 | 0.291394 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1008.00i | 0.0807769i | ||||||||
\(539\) | 5580.00 | 0.445914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9355.00 | −0.743443 | −0.371722 | − | 0.928344i | \(-0.621232\pi\) | ||||
−0.371722 | + | 0.928344i | \(0.621232\pi\) | |||||||
\(542\) | 8978.00i | 0.711509i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1344.00 | −0.105926 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 295.000i | 0.0230590i | 0.999934 | + | 0.0115295i | \(0.00367004\pi\) | ||||
−0.999934 | + | 0.0115295i | \(0.996330\pi\) | |||||||
\(548\) | − 5304.00i | − 0.413459i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32526.0 | 2.51480 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 16307.0i | − 1.25397i | ||||||||
\(554\) | −4426.00 | −0.339427 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3572.00 | 0.272458 | ||||||||
\(557\) | − 16914.0i | − 1.28666i | −0.765589 | − | 0.643330i | \(-0.777552\pi\) | ||||
0.765589 | − | 0.643330i | \(-0.222448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1802.00 | 0.136344 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 5436.00i | − 0.408014i | ||||||||
\(563\) | 12108.0i | 0.906379i | 0.891414 | + | 0.453189i | \(0.149714\pi\) | ||||
−0.891414 | + | 0.453189i | \(0.850286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11230.0 | 0.833979 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 1632.00i | − 0.120558i | ||||||||
\(569\) | −6960.00 | −0.512792 | −0.256396 | − | 0.966572i | \(-0.582535\pi\) | ||||
−0.256396 | + | 0.966572i | \(0.582535\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10687.0 | −0.783252 | −0.391626 | − | 0.920124i | \(-0.628087\pi\) | ||||
−0.391626 | + | 0.920124i | \(0.628087\pi\) | |||||||
\(572\) | − 4080.00i | − 0.298240i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6348.00 | 0.461603 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8329.00i | 0.600937i | 0.953792 | + | 0.300469i | \(0.0971431\pi\) | ||||
−0.953792 | + | 0.300469i | \(0.902857\pi\) | |||||||
\(578\) | − 6298.00i | − 0.453222i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25254.0 | −1.80329 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9900.00i | − 0.703287i | ||||||||
\(584\) | 5528.00 | 0.391696 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2976.00 | −0.209791 | ||||||||
\(587\) | − 25302.0i | − 1.77909i | −0.456848 | − | 0.889545i | \(-0.651022\pi\) | ||||
0.456848 | − | 0.889545i | \(-0.348978\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7645.00 | −0.534816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 3056.00i | − 0.212164i | ||||||||
\(593\) | 22248.0i | 1.54067i | 0.637641 | + | 0.770334i | \(0.279910\pi\) | ||||
−0.637641 | + | 0.770334i | \(0.720090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10008.0 | 0.687825 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13056.0i | 0.892809i | ||||||||
\(599\) | 24252.0 | 1.65427 | 0.827137 | − | 0.562001i | \(-0.189968\pi\) | ||||
0.827137 | + | 0.562001i | \(0.189968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9829.00 | −0.667110 | −0.333555 | − | 0.942731i | \(-0.608248\pi\) | ||||
−0.333555 | + | 0.942731i | \(0.608248\pi\) | |||||||
\(602\) | − 2438.00i | − 0.165059i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11068.0 | 0.745613 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14155.0i | 0.946514i | 0.880925 | + | 0.473257i | \(0.156922\pi\) | ||||
−0.880925 | + | 0.473257i | \(0.843078\pi\) | |||||||
\(608\) | − 4448.00i | − 0.296694i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12444.0 | 0.823945 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23051.0i | 1.51879i | 0.650627 | + | 0.759397i | \(0.274506\pi\) | ||||
−0.650627 | + | 0.759397i | \(0.725494\pi\) | |||||||
\(614\) | −14974.0 | −0.984204 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5520.00 | −0.361051 | ||||||||
\(617\) | − 8352.00i | − 0.544958i | −0.962162 | − | 0.272479i | \(-0.912157\pi\) | ||||
0.962162 | − | 0.272479i | \(-0.0878435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24331.0 | 1.57988 | 0.789940 | − | 0.613184i | \(-0.210112\pi\) | ||||
0.789940 | + | 0.613184i | \(0.210112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16236.0i | 1.04663i | ||||||||
\(623\) | 18768.0i | 1.20694i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10004.0 | −0.638722 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 10804.0i | − 0.686507i | ||||||||
\(629\) | −8022.00 | −0.508518 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2216.00 | 0.139806 | 0.0699030 | − | 0.997554i | \(-0.477731\pi\) | ||||
0.0699030 | + | 0.997554i | \(0.477731\pi\) | |||||||
\(632\) | 5672.00i | 0.356994i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10164.0 | 0.636694 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6324.00i | 0.393353i | ||||||||
\(638\) | 14040.0i | 0.871237i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28500.0 | 1.75613 | 0.878067 | − | 0.478537i | \(-0.158833\pi\) | ||||
0.878067 | + | 0.478537i | \(0.158833\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 25252.0i | − 1.54874i | −0.632731 | − | 0.774371i | \(-0.718066\pi\) | ||||
0.632731 | − | 0.774371i | \(-0.281934\pi\) | |||||||
\(644\) | 17664.0 | 1.08084 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11676.0 | −0.711124 | ||||||||
\(647\) | − 28920.0i | − 1.75728i | −0.477481 | − | 0.878642i | \(-0.658450\pi\) | ||||
0.477481 | − | 0.878642i | \(-0.341550\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11880.0 | 0.718537 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 6992.00i | − 0.419981i | ||||||||
\(653\) | − 32268.0i | − 1.93376i | −0.255234 | − | 0.966879i | \(-0.582152\pi\) | ||||
0.255234 | − | 0.966879i | \(-0.417848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2208.00 | −0.131415 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 16836.0i | − 0.997471i | ||||||||
\(659\) | −10050.0 | −0.594070 | −0.297035 | − | 0.954867i | \(-0.595998\pi\) | ||||
−0.297035 | + | 0.954867i | \(0.595998\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4561.00 | −0.268385 | −0.134192 | − | 0.990955i | \(-0.542844\pi\) | ||||
−0.134192 | + | 0.990955i | \(0.542844\pi\) | |||||||
\(662\) | − 15250.0i | − 0.895329i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8784.00 | 0.513381 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 44928.0i | − 2.60812i | ||||||||
\(668\) | 2136.00i | 0.123719i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −690.000 | −0.0396977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21359.0i | 1.22337i | 0.791101 | + | 0.611686i | \(0.209508\pi\) | ||||
−0.791101 | + | 0.611686i | \(0.790492\pi\) | |||||||
\(674\) | 7556.00 | 0.431819 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4164.00 | −0.236914 | ||||||||
\(677\) | 15042.0i | 0.853931i | 0.904268 | + | 0.426965i | \(0.140417\pi\) | ||||
−0.904268 | + | 0.426965i | \(0.859583\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20815.0 | −1.17645 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 3300.00i | − 0.185284i | ||||||||
\(683\) | − 27462.0i | − 1.53851i | −0.638940 | − | 0.769256i | \(-0.720627\pi\) | ||||
0.638940 | − | 0.769256i | \(-0.279373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7222.00 | −0.401949 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 848.000i | 0.0469908i | ||||||||
\(689\) | 11220.0 | 0.620389 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6212.00 | 0.341991 | 0.170995 | − | 0.985272i | \(-0.445302\pi\) | ||||
0.170995 | + | 0.985272i | \(0.445302\pi\) | |||||||
\(692\) | − 768.000i | − 0.0421893i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16536.0 | −0.904464 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5796.00i | 0.314977i | ||||||||
\(698\) | 2758.00i | 0.149559i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13224.0 | 0.712502 | 0.356251 | − | 0.934390i | \(-0.384055\pi\) | ||||
0.356251 | + | 0.934390i | \(0.384055\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 26549.0i | − 1.42434i | ||||||||
\(704\) | 1920.00 | 0.102788 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6144.00 | −0.327525 | ||||||||
\(707\) | − 29394.0i | − 1.56361i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34709.0 | −1.83854 | −0.919269 | − | 0.393629i | \(-0.871219\pi\) | ||||
−0.919269 | + | 0.393629i | \(0.871219\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 6528.00i | − 0.343606i | ||||||||
\(713\) | 10560.0i | 0.554664i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4560.00 | −0.238010 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14892.0i | 0.774045i | ||||||||
\(719\) | 32070.0 | 1.66343 | 0.831717 | − | 0.555200i | \(-0.187358\pi\) | ||||
0.831717 | + | 0.555200i | \(0.187358\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13915.0 | 0.718754 | ||||||||
\(722\) | − 24924.0i | − 1.28473i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1592.00 | −0.0817213 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 125.000i | − 0.00637688i | −0.999995 | − | 0.00318844i | \(-0.998985\pi\) | ||||
0.999995 | − | 0.00318844i | \(-0.00101491\pi\) | |||||||
\(728\) | − 6256.00i | − 0.318493i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2226.00 | 0.112629 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32222.0i | 1.62367i | 0.583890 | + | 0.811833i | \(0.301530\pi\) | ||||
−0.583890 | + | 0.811833i | \(0.698470\pi\) | |||||||
\(734\) | 12992.0 | 0.653329 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6144.00 | −0.307705 | ||||||||
\(737\) | 13560.0i | 0.677733i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19240.0 | 0.957720 | 0.478860 | − | 0.877891i | \(-0.341050\pi\) | ||||
0.478860 | + | 0.877891i | \(0.341050\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 15180.0i | − 0.751045i | ||||||||
\(743\) | − 30252.0i | − 1.49373i | −0.664978 | − | 0.746863i | \(-0.731559\pi\) | ||||
0.664978 | − | 0.746863i | \(-0.268441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3266.00 | −0.160291 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 5040.00i | − 0.246365i | ||||||||
\(749\) | 34224.0 | 1.66958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12517.0 | −0.608192 | −0.304096 | − | 0.952641i | \(-0.598354\pi\) | ||||
−0.304096 | + | 0.952641i | \(0.598354\pi\) | |||||||
\(752\) | 5856.00i | 0.283971i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15912.0 | −0.768542 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 2201.00i | − 0.105676i | −0.998603 | − | 0.0528380i | \(-0.983173\pi\) | ||||
0.998603 | − | 0.0528380i | \(-0.0168267\pi\) | |||||||
\(758\) | 13576.0i | 0.650531i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8742.00 | −0.416422 | −0.208211 | − | 0.978084i | \(-0.566764\pi\) | ||||
−0.208211 | + | 0.978084i | \(0.566764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13639.0i | 0.647136i | ||||||||
\(764\) | 13896.0 | 0.658036 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13164.0 | −0.620933 | ||||||||
\(767\) | 13464.0i | 0.633842i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28618.0 | 1.34199 | 0.670996 | − | 0.741461i | \(-0.265867\pi\) | ||||
0.670996 | + | 0.741461i | \(0.265867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10852.0i | 0.505922i | ||||||||
\(773\) | − 6594.00i | − 0.306817i | −0.988163 | − | 0.153409i | \(-0.950975\pi\) | ||||
0.988163 | − | 0.153409i | \(-0.0490251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7240.00 | 0.334924 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 5700.00i | − 0.262667i | ||||||||
\(779\) | −19182.0 | −0.882242 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6120.00 | 0.280398 | ||||||||
\(782\) | 16128.0i | 0.737514i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2976.00 | −0.135569 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 15881.0i | − 0.719309i | −0.933085 | − | 0.359655i | \(-0.882894\pi\) | ||||
0.933085 | − | 0.359655i | \(-0.117106\pi\) | |||||||
\(788\) | − 18936.0i | − 0.856050i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7452.00 | −0.334972 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 782.000i | − 0.0350185i | ||||||||
\(794\) | −14902.0 | −0.666061 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20528.0 | 0.914065 | ||||||||
\(797\) | − 26052.0i | − 1.15785i | −0.815380 | − | 0.578927i | \(-0.803472\pi\) | ||||
0.815380 | − | 0.578927i | \(-0.196528\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15372.0 | 0.680629 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28248.0i | 1.24373i | ||||||||
\(803\) | 20730.0i | 0.911016i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3740.00 | 0.163444 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10224.0i | 0.445147i | ||||||||
\(809\) | 12648.0 | 0.549666 | 0.274833 | − | 0.961492i | \(-0.411377\pi\) | ||||
0.274833 | + | 0.961492i | \(0.411377\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27179.0 | 1.17680 | 0.588399 | − | 0.808570i | \(-0.299758\pi\) | ||||
0.588399 | + | 0.808570i | \(0.299758\pi\) | |||||||
\(812\) | 21528.0i | 0.930400i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11460.0 | 0.493456 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7367.00i | 0.315470i | ||||||||
\(818\) | 12748.0i | 0.544894i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11874.0 | −0.504757 | −0.252378 | − | 0.967629i | \(-0.581213\pi\) | ||||
−0.252378 | + | 0.967629i | \(0.581213\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 18448.0i | − 0.781357i | −0.920527 | − | 0.390679i | \(-0.872240\pi\) | ||||
0.920527 | − | 0.390679i | \(-0.127760\pi\) | |||||||
\(824\) | −4840.00 | −0.204623 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18216.0 | 0.767331 | ||||||||
\(827\) | − 3234.00i | − 0.135982i | −0.997686 | − | 0.0679911i | \(-0.978341\pi\) | ||||
0.997686 | − | 0.0679911i | \(-0.0216589\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32155.0 | 1.34715 | 0.673576 | − | 0.739118i | \(-0.264757\pi\) | ||||
0.673576 | + | 0.739118i | \(0.264757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2176.00i | 0.0906721i | ||||||||
\(833\) | 7812.00i | 0.324934i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16680.0 | 0.690060 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 7896.00i | − 0.325493i | ||||||||
\(839\) | −21996.0 | −0.905109 | −0.452554 | − | 0.891737i | \(-0.649487\pi\) | ||||
−0.452554 | + | 0.891737i | \(0.649487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30367.0 | 1.24511 | ||||||||
\(842\) | − 25258.0i | − 1.03379i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20960.0 | −0.854826 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9913.00i | 0.402143i | ||||||||
\(848\) | 5280.00i | 0.213816i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36672.0 | −1.47720 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3278.00i | 0.131579i | 0.997834 | + | 0.0657893i | \(0.0209565\pi\) | ||||
−0.997834 | + | 0.0657893i | \(0.979043\pi\) | |||||||
\(854\) | −1058.00 | −0.0423935 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11904.0 | −0.475316 | ||||||||
\(857\) | − 21228.0i | − 0.846131i | −0.906099 | − | 0.423066i | \(-0.860954\pi\) | ||||
0.906099 | − | 0.423066i | \(-0.139046\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5767.00 | 0.229066 | 0.114533 | − | 0.993419i | \(-0.463463\pi\) | ||||
0.114533 | + | 0.993419i | \(0.463463\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9684.00i | 0.382643i | ||||||||
\(863\) | 5322.00i | 0.209922i | 0.994476 | + | 0.104961i | \(0.0334718\pi\) | ||||
−0.994476 | + | 0.104961i | \(0.966528\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7702.00 | 0.302222 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 5060.00i | − 0.197866i | ||||||||
\(869\) | −21270.0 | −0.830305 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15368.0 | −0.597847 | ||||||||
\(872\) | − 4744.00i | − 0.184234i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −53376.0 | −2.06576 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42097.0i | 1.62088i | 0.585819 | + | 0.810442i | \(0.300773\pi\) | ||||
−0.585819 | + | 0.810442i | \(0.699227\pi\) | |||||||
\(878\) | − 14870.0i | − 0.571570i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17658.0 | 0.675270 | 0.337635 | − | 0.941277i | \(-0.390373\pi\) | ||||
0.337635 | + | 0.941277i | \(0.390373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 22297.0i | − 0.849778i | −0.905246 | − | 0.424889i | \(-0.860313\pi\) | ||||
0.905246 | − | 0.424889i | \(-0.139687\pi\) | |||||||
\(884\) | 5712.00 | 0.217325 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11520.0 | 0.436819 | ||||||||
\(887\) | − 10542.0i | − 0.399059i | −0.979892 | − | 0.199530i | \(-0.936059\pi\) | ||||
0.979892 | − | 0.199530i | \(-0.0639414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44344.0 | −1.67295 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18076.0i | 0.678508i | ||||||||
\(893\) | 50874.0i | 1.90642i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2944.00 | 0.109768 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4380.00i | 0.162764i | ||||||||
\(899\) | −12870.0 | −0.477462 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13860.0 | 0.512479 | ||||||||
\(902\) | − 8280.00i | − 0.305647i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2592.00 | 0.0953635 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 47639.0i | − 1.74402i | −0.489487 | − | 0.872010i | \(-0.662816\pi\) | ||||
0.489487 | − | 0.872010i | \(-0.337184\pi\) | |||||||
\(908\) | − 20256.0i | − 0.740329i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10326.0 | 0.375539 | 0.187769 | − | 0.982213i | \(-0.439874\pi\) | ||||
0.187769 | + | 0.982213i | \(0.439874\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32940.0i | 1.19404i | ||||||||
\(914\) | −14404.0 | −0.521271 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10292.0 | 0.371242 | ||||||||
\(917\) | 63066.0i | 2.27113i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5147.00 | −0.184748 | −0.0923742 | − | 0.995724i | \(-0.529446\pi\) | ||||
−0.0923742 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 26952.0i | − 0.962708i | ||||||||
\(923\) | 6936.00i | 0.247347i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21686.0 | −0.769596 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 7488.00i | − 0.264877i | ||||||||
\(929\) | −47064.0 | −1.66213 | −0.831066 | − | 0.556175i | \(-0.812269\pi\) | ||||
−0.831066 | + | 0.556175i | \(0.812269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25854.0 | −0.910130 | ||||||||
\(932\) | 16392.0i | 0.576114i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12216.0 | 0.427965 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15385.0i | 0.536399i | 0.963363 | + | 0.268200i | \(0.0864287\pi\) | ||||
−0.963363 | + | 0.268200i | \(0.913571\pi\) | |||||||
\(938\) | 20792.0i | 0.723756i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34914.0 | 1.20953 | 0.604763 | − | 0.796406i | \(-0.293268\pi\) | ||||
0.604763 | + | 0.796406i | \(0.293268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26496.0i | 0.914982i | ||||||||
\(944\) | −6336.00 | −0.218453 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3180.00 | −0.109293 | ||||||||
\(947\) | 37434.0i | 1.28452i | 0.766486 | + | 0.642261i | \(0.222003\pi\) | ||||
−0.766486 | + | 0.642261i | \(0.777997\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23494.0 | −0.803633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 7728.00i | − 0.263094i | ||||||||
\(953\) | − 8778.00i | − 0.298371i | −0.988809 | − | 0.149185i | \(-0.952335\pi\) | ||||
0.988809 | − | 0.149185i | \(-0.0476651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1224.00 | 0.0414090 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 19704.0i | − 0.664517i | ||||||||
\(959\) | 30498.0 | 1.02694 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26766.0 | −0.898459 | ||||||||
\(962\) | 12988.0i | 0.435291i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25928.0 | −0.866270 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54061.0i | 1.79781i | 0.438141 | + | 0.898906i | \(0.355637\pi\) | ||||
−0.438141 | + | 0.898906i | \(0.644363\pi\) | |||||||
\(968\) | − 3448.00i | − 0.114486i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3084.00 | 0.101926 | 0.0509631 | − | 0.998701i | \(-0.483771\pi\) | ||||
0.0509631 | + | 0.998701i | \(0.483771\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20539.0i | 0.676722i | ||||||||
\(974\) | −15592.0 | −0.512936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 368.000 | 0.0120691 | ||||||||
\(977\) | 12048.0i | 0.394524i | 0.980351 | + | 0.197262i | \(0.0632049\pi\) | ||||
−0.980351 | + | 0.197262i | \(0.936795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24480.0 | 0.799167 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4908.00i | 0.159491i | ||||||||
\(983\) | − 33618.0i | − 1.09079i | −0.838179 | − | 0.545396i | \(-0.816379\pi\) | ||||
0.838179 | − | 0.545396i | \(-0.183621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −19656.0 | −0.634863 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18904.0i | 0.608721i | ||||||||
\(989\) | 10176.0 | 0.327177 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25043.0 | 0.802742 | 0.401371 | − | 0.915916i | \(-0.368534\pi\) | ||||
0.401371 | + | 0.915916i | \(0.368534\pi\) | |||||||
\(992\) | 1760.00i | 0.0563307i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9384.00 | 0.299439 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17710.0i | 0.562569i | 0.959624 | + | 0.281285i | \(0.0907605\pi\) | ||||
−0.959624 | + | 0.281285i | \(0.909240\pi\) | |||||||
\(998\) | − 5906.00i | − 0.187326i | ||||||||
\(999\) | 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 | 1350.4.c.e.649.1 | 2 | ||
3.2 | odd | 2 | 1350.4.c.p.649.2 | 2 | |||
5.2 | odd | 4 | 1350.4.a.ba.1.1 | yes | 1 | ||
5.3 | odd | 4 | 1350.4.a.b.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 1350.4.c.e.649.2 | 2 | ||
15.2 | even | 4 | 1350.4.a.m.1.1 | yes | 1 | ||
15.8 | even | 4 | 1350.4.a.p.1.1 | yes | 1 | ||
15.14 | odd | 2 | 1350.4.c.p.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.4.a.b.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
1350.4.a.m.1.1 | yes | 1 | 15.2 | even | 4 | ||
1350.4.a.p.1.1 | yes | 1 | 15.8 | even | 4 | ||
1350.4.a.ba.1.1 | yes | 1 | 5.2 | odd | 4 | ||
1350.4.c.e.649.1 | 2 | 1.1 | even | 1 | trivial | ||
1350.4.c.e.649.2 | 2 | 5.4 | even | 2 | inner | ||
1350.4.c.p.649.1 | 2 | 15.14 | odd | 2 | |||
1350.4.c.p.649.2 | 2 | 3.2 | odd | 2 |