Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(1471,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1997017344.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 53x^{4} + 56x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.1 | ||
Root | \(-2.92812i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1471 |
Dual form | 1568.3.d.n.1471.8 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 5.85623i | − 1.95208i | −0.217596 | − | 0.976039i | \(-0.569821\pi\) | ||||
0.217596 | − | 0.976039i | \(-0.430179\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.78167 | 1.15633 | 0.578167 | − | 0.815918i | \(-0.303768\pi\) | ||||
0.578167 | + | 0.815918i | \(0.303768\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.2955 | −2.81061 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.01966i | − 0.274515i | −0.990535 | − | 0.137257i | \(-0.956171\pi\) | ||||
0.990535 | − | 0.137257i | \(-0.0438288\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.78167 | −0.752436 | −0.376218 | − | 0.926531i | \(-0.622776\pi\) | ||||
−0.376218 | + | 0.926531i | \(0.622776\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 33.8588i | − 2.25725i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.6027 | 0.682510 | 0.341255 | − | 0.939971i | \(-0.389148\pi\) | ||||
0.341255 | + | 0.939971i | \(0.389148\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 25.5687i | − 1.34572i | −0.739769 | − | 0.672861i | \(-0.765065\pi\) | ||||
0.739769 | − | 0.672861i | \(-0.234935\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 26.1571i | − 1.13726i | −0.822592 | − | 0.568632i | \(-0.807473\pi\) | ||||
0.822592 | − | 0.568632i | \(-0.192527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.42771 | 0.337109 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 95.4301i | 3.53445i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.56334 | 0.0539083 | 0.0269542 | − | 0.999637i | \(-0.491419\pi\) | ||||
0.0269542 | + | 0.999637i | \(0.491419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 12.0107i | − 0.387443i | −0.981057 | − | 0.193721i | \(-0.937944\pi\) | ||||
0.981057 | − | 0.193721i | \(-0.0620557\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.6839 | −0.535875 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −70.6721 | −1.91006 | −0.955029 | − | 0.296513i | \(-0.904176\pi\) | ||||
−0.955029 | + | 0.296513i | \(0.904176\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 57.2837i | 1.46881i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 49.8775 | 1.21652 | 0.608262 | − | 0.793736i | \(-0.291867\pi\) | ||||
0.608262 | + | 0.793736i | \(0.291867\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 73.2730i | 1.70402i | 0.523522 | + | 0.852012i | \(0.324618\pi\) | ||||
−0.523522 | + | 0.852012i | \(0.675382\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −146.250 | −3.25000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 44.2248i | − 0.940952i | −0.882413 | − | 0.470476i | \(-0.844082\pi\) | ||||
0.882413 | − | 0.470476i | \(-0.155918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 67.9479i | − 1.33231i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −54.2355 | −1.02331 | −0.511655 | − | 0.859191i | \(-0.670968\pi\) | ||||
−0.511655 | + | 0.859191i | \(0.670968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 17.4587i | − 0.317431i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −149.736 | −2.62695 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.4706i | 0.211367i | 0.994400 | + | 0.105683i | \(0.0337030\pi\) | ||||
−0.994400 | + | 0.105683i | \(0.966297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35.6770 | −0.584869 | −0.292435 | − | 0.956285i | \(-0.594465\pi\) | ||||
−0.292435 | + | 0.956285i | \(0.594465\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −56.5544 | −0.870068 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 24.4891i | 0.365509i | 0.983159 | + | 0.182754i | \(0.0585013\pi\) | ||||
−0.983159 | + | 0.182754i | \(0.941499\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −153.182 | −2.22003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 11.0480i | − 0.155606i | −0.996969 | − | 0.0778030i | \(-0.975209\pi\) | ||||
0.996969 | − | 0.0778030i | \(-0.0247905\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −74.3713 | −1.01879 | −0.509393 | − | 0.860534i | \(-0.670130\pi\) | ||||
−0.509393 | + | 0.860534i | \(0.670130\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 49.3547i | − 0.658062i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 22.8912i | 0.289762i | 0.989449 | + | 0.144881i | \(0.0462800\pi\) | ||||
−0.989449 | + | 0.144881i | \(0.953720\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 331.202 | 4.08891 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 48.1934i | − 0.580644i | −0.956929 | − | 0.290322i | \(-0.906238\pi\) | ||||
0.956929 | − | 0.290322i | \(-0.0937623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 67.0828 | 0.789210 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 9.15529i | − 0.105233i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −67.4801 | −0.758204 | −0.379102 | − | 0.925355i | \(-0.623767\pi\) | ||||
−0.379102 | + | 0.925355i | \(0.623767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −70.3376 | −0.756318 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 147.830i | − 1.55610i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.75949 | 0.0799947 | 0.0399974 | − | 0.999200i | \(-0.487265\pi\) | ||||
0.0399974 | + | 0.999200i | \(0.487265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 76.3838i | 0.771554i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 102.524 | 1.01509 | 0.507546 | − | 0.861624i | \(-0.330553\pi\) | ||||
0.507546 | + | 0.861624i | \(0.330553\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.6874i | 0.142596i | 0.997455 | + | 0.0712980i | \(0.0227141\pi\) | ||||
−0.997455 | + | 0.0712980i | \(0.977286\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 70.0212i | 0.654404i | 0.944954 | + | 0.327202i | \(0.106106\pi\) | ||||
−0.944954 | + | 0.327202i | \(0.893894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −65.9204 | −0.604774 | −0.302387 | − | 0.953185i | \(-0.597783\pi\) | ||||
−0.302387 | + | 0.953185i | \(0.597783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 413.873i | 3.72858i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 83.2184 | 0.736446 | 0.368223 | − | 0.929737i | \(-0.379966\pi\) | ||||
0.368223 | + | 0.929737i | \(0.379966\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 151.232i | − 1.31506i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 247.432 | 2.11480 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 111.882 | 0.924642 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 292.094i | − 2.37475i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −95.8155 | −0.766524 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 102.292i | 0.805452i | 0.915321 | + | 0.402726i | \(0.131937\pi\) | ||||
−0.915321 | + | 0.402726i | \(0.868063\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 429.104 | 3.32639 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 89.1759i | − 0.680732i | −0.940293 | − | 0.340366i | \(-0.889449\pi\) | ||||
0.940293 | − | 0.340366i | \(-0.110551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 551.745i | 4.08700i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.3800 | −0.0830660 | −0.0415330 | − | 0.999137i | \(-0.513224\pi\) | ||||
−0.0415330 | + | 0.999137i | \(0.513224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 121.256i | − 0.872343i | −0.899863 | − | 0.436172i | \(-0.856334\pi\) | ||||
0.899863 | − | 0.436172i | \(-0.143666\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −258.991 | −1.83681 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.5374i | 0.206555i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.03872 | 0.0623360 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −63.5731 | −0.426665 | −0.213333 | − | 0.976980i | \(-0.568432\pi\) | ||||
−0.213333 | + | 0.976980i | \(0.568432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 122.414i | − 0.810689i | −0.914164 | − | 0.405344i | \(-0.867152\pi\) | ||||
0.914164 | − | 0.405344i | \(-0.132848\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −293.495 | −1.91827 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 69.4420i | − 0.448013i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −39.6070 | −0.252274 | −0.126137 | − | 0.992013i | \(-0.540258\pi\) | ||||
−0.126137 | + | 0.992013i | \(0.540258\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 317.616i | 1.99758i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 32.9017i | − 0.201851i | −0.994894 | − | 0.100925i | \(-0.967820\pi\) | ||||
0.994894 | − | 0.100925i | \(-0.0321803\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −102.242 | −0.619650 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 98.0405i | − 0.587069i | −0.955949 | − | 0.293534i | \(-0.905168\pi\) | ||||
0.955949 | − | 0.293534i | \(-0.0948315\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −73.3189 | −0.433840 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 646.772i | 3.78229i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 336.891 | 1.94734 | 0.973672 | − | 0.227951i | \(-0.0732028\pi\) | ||||
0.973672 | + | 0.227951i | \(0.0732028\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 73.0309 | 0.412604 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 51.4537i | − 0.287451i | −0.989618 | − | 0.143725i | \(-0.954092\pi\) | ||||
0.989618 | − | 0.143725i | \(-0.0459082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −281.807 | −1.55695 | −0.778473 | − | 0.627678i | \(-0.784006\pi\) | ||||
−0.778473 | + | 0.627678i | \(0.784006\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 208.933i | 1.14171i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −408.603 | −2.20866 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 35.0362i | − 0.187359i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 165.004i | − 0.863897i | −0.901898 | − | 0.431949i | \(-0.857826\pi\) | ||||
0.901898 | − | 0.431949i | \(-0.142174\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −64.6933 | −0.335199 | −0.167599 | − | 0.985855i | \(-0.553601\pi\) | ||||
−0.167599 | + | 0.985855i | \(0.553601\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 331.196i | 1.69844i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 189.712 | 0.963003 | 0.481501 | − | 0.876445i | \(-0.340092\pi\) | ||||
0.481501 | + | 0.876445i | \(0.340092\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 205.590i | 1.03312i | 0.856252 | + | 0.516559i | \(0.172787\pi\) | ||||
−0.856252 | + | 0.516559i | \(0.827213\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 143.414 | 0.713502 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 288.375 | 1.40671 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 661.655i | 3.19640i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −77.2089 | −0.369421 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 220.725i | 1.04609i | 0.852305 | + | 0.523045i | \(0.175204\pi\) | ||||
−0.852305 | + | 0.523045i | \(0.824796\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −64.6998 | −0.303755 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 423.641i | 1.97042i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 435.536i | 1.98875i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −113.493 | −0.513545 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 163.489i | − 0.733134i | −0.930392 | − | 0.366567i | \(-0.880533\pi\) | ||||
0.930392 | − | 0.366567i | \(-0.119467\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −213.183 | −0.947480 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 221.227i | 0.974569i | 0.873243 | + | 0.487285i | \(0.162013\pi\) | ||||
−0.873243 | + | 0.487285i | \(0.837987\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −233.563 | −1.01993 | −0.509964 | − | 0.860196i | \(-0.670341\pi\) | ||||
−0.509964 | + | 0.860196i | \(0.670341\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.2573 | −0.0568983 | −0.0284491 | − | 0.999595i | \(-0.509057\pi\) | ||||
−0.0284491 | + | 0.999595i | \(0.509057\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 255.693i | − 1.08806i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 134.056 | 0.565638 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 353.231i | − 1.47796i | −0.673730 | − | 0.738978i | \(-0.735309\pi\) | ||||
0.673730 | − | 0.738978i | \(-0.264691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −181.261 | −0.752121 | −0.376060 | − | 0.926595i | \(-0.622721\pi\) | ||||
−0.376060 | + | 0.926595i | \(0.622721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1080.72i | − 4.44742i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 250.105i | 1.01257i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −282.232 | −1.13346 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 98.4522i | − 0.392240i | −0.980580 | − | 0.196120i | \(-0.937166\pi\) | ||||
0.980580 | − | 0.196120i | \(-0.0628342\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −78.9856 | −0.312196 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 392.853i | − 1.54060i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 279.527 | 1.08765 | 0.543827 | − | 0.839197i | \(-0.316975\pi\) | ||||
0.543827 | + | 0.839197i | \(0.316975\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −39.5455 | −0.151515 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 45.3085i | − 0.172276i | −0.996283 | − | 0.0861378i | \(-0.972547\pi\) | ||||
0.996283 | − | 0.0861378i | \(-0.0274525\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −313.572 | −1.18329 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 395.179i | 1.48007i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 220.227 | 0.818686 | 0.409343 | − | 0.912380i | \(-0.365758\pi\) | ||||
0.409343 | + | 0.912380i | \(0.365758\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 54.8463i | − 0.202385i | −0.994867 | − | 0.101193i | \(-0.967734\pi\) | ||||
0.994867 | − | 0.101193i | \(-0.0322658\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 25.4489i | − 0.0925413i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 320.078 | 1.15552 | 0.577758 | − | 0.816208i | \(-0.303928\pi\) | ||||
0.577758 | + | 0.816208i | \(0.303928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 303.817i | 1.08895i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 526.445 | 1.87347 | 0.936734 | − | 0.350041i | \(-0.113832\pi\) | ||||
0.936734 | + | 0.350041i | \(0.113832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 331.932i | − 1.17290i | −0.809984 | − | 0.586452i | \(-0.800524\pi\) | ||||
0.809984 | − | 0.586452i | \(-0.199476\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −865.726 | −3.03763 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −154.378 | −0.534180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 45.4414i | − 0.156156i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 240.715 | 0.821554 | 0.410777 | − | 0.911736i | \(-0.365258\pi\) | ||||
0.410777 | + | 0.911736i | \(0.365258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 72.1011i | 0.244410i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 288.167 | 0.970259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 255.860i | 0.855718i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 600.407i | − 1.98154i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −206.273 | −0.676304 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 221.862i | 0.722678i | 0.932435 | + | 0.361339i | \(0.117680\pi\) | ||||
−0.932435 | + | 0.361339i | \(0.882320\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 86.0128 | 0.278359 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 476.048i | − 1.53070i | −0.643614 | − | 0.765350i | \(-0.722566\pi\) | ||||
0.643614 | − | 0.765350i | \(-0.277434\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 495.170 | 1.58201 | 0.791006 | − | 0.611808i | \(-0.209558\pi\) | ||||
0.791006 | + | 0.611808i | \(0.209558\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −493.029 | −1.55530 | −0.777649 | − | 0.628699i | \(-0.783588\pi\) | ||||
−0.777649 | + | 0.628699i | \(0.783588\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 4.72077i | − 0.0147986i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 410.060 | 1.27745 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 296.665i | − 0.918468i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −82.4371 | −0.253653 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 386.045i | 1.18057i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 586.929i | − 1.77320i | −0.462539 | − | 0.886599i | \(-0.653061\pi\) | ||||
0.462539 | − | 0.886599i | \(-0.346939\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1787.69 | 5.36842 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 141.588i | 0.422650i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2636 | 0.0660639 | 0.0330320 | − | 0.999454i | \(-0.489484\pi\) | ||||
0.0330320 | + | 0.999454i | \(0.489484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 487.347i | − 1.43760i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.2683 | −0.106359 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −885.647 | −2.56709 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 264.797i | − 0.763103i | −0.924348 | − | 0.381552i | \(-0.875390\pi\) | ||||
0.924348 | − | 0.381552i | \(-0.124610\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −101.730 | −0.291489 | −0.145745 | − | 0.989322i | \(-0.546558\pi\) | ||||
−0.145745 | + | 0.989322i | \(0.546558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 933.466i | − 2.65945i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −472.399 | −1.33824 | −0.669121 | − | 0.743154i | \(-0.733329\pi\) | ||||
−0.669121 | + | 0.743154i | \(0.733329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 63.8760i | − 0.179933i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 473.453i | 1.31881i | 0.751788 | + | 0.659405i | \(0.229192\pi\) | ||||
−0.751788 | + | 0.659405i | \(0.770808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −292.758 | −0.810965 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 655.205i | − 1.80497i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −429.991 | −1.17806 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 467.459i | − 1.27373i | −0.770975 | − | 0.636866i | \(-0.780231\pi\) | ||||
0.770975 | − | 0.636866i | \(-0.219769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1261.67 | −3.41917 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 534.491 | 1.43295 | 0.716475 | − | 0.697613i | \(-0.245754\pi\) | ||||
0.716475 | + | 0.697613i | \(0.245754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 561.118i | 1.49631i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.2921 | −0.0405626 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 204.355i | − 0.539196i | −0.962973 | − | 0.269598i | \(-0.913109\pi\) | ||||
0.962973 | − | 0.269598i | \(-0.0868908\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 599.048 | 1.57231 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 622.590i | − 1.62556i | −0.582570 | − | 0.812781i | \(-0.697953\pi\) | ||||
0.582570 | − | 0.812781i | \(-0.302047\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1853.48i | − 4.78934i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −510.568 | −1.31251 | −0.656257 | − | 0.754537i | \(-0.727861\pi\) | ||||
−0.656257 | + | 0.754537i | \(0.727861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 303.492i | − 0.776194i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −522.235 | −1.32884 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 132.349i | 0.335062i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 591.459 | 1.48982 | 0.744910 | − | 0.667165i | \(-0.232492\pi\) | ||||
0.744910 | + | 0.667165i | \(0.232492\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.0538 | 0.0724534 | 0.0362267 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362267 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 117.485i | 0.291526i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1914.90 | 4.72815 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 213.406i | 0.524339i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −120.749 | −0.295230 | −0.147615 | − | 0.989045i | \(-0.547160\pi\) | ||||
−0.147615 | + | 0.989045i | \(0.547160\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 66.6442i | 0.162151i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 278.638i | − 0.671418i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −710.102 | −1.70288 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 379.985i | − 0.906885i | −0.891286 | − | 0.453443i | \(-0.850196\pi\) | ||||
0.891286 | − | 0.453443i | \(-0.149804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −536.480 | −1.27430 | −0.637149 | − | 0.770740i | \(-0.719887\pi\) | ||||
−0.637149 | + | 0.770740i | \(0.719887\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1118.69i | 2.64465i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 97.7840 | 0.230080 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 172.978 | 0.403211 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 384.935i | − 0.893120i | −0.894754 | − | 0.446560i | \(-0.852649\pi\) | ||||
0.894754 | − | 0.446560i | \(-0.147351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 667.115 | 1.54068 | 0.770340 | − | 0.637633i | \(-0.220086\pi\) | ||||
0.770340 | + | 0.637633i | \(0.220086\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 52.9329i | − 0.121685i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −668.802 | −1.53044 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 521.733i | 1.18846i | 0.804296 | + | 0.594229i | \(0.202543\pi\) | ||||
−0.804296 | + | 0.594229i | \(0.797457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 204.156i | 0.460848i | 0.973090 | + | 0.230424i | \(0.0740114\pi\) | ||||
−0.973090 | + | 0.230424i | \(0.925989\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −390.148 | −0.876737 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 372.299i | 0.832884i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 513.424 | 1.14348 | 0.571742 | − | 0.820434i | \(-0.306268\pi\) | ||||
0.571742 | + | 0.820434i | \(0.306268\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 150.613i | − 0.333954i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −716.885 | −1.58253 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −134.029 | −0.293281 | −0.146641 | − | 0.989190i | \(-0.546846\pi\) | ||||
−0.146641 | + | 0.989190i | \(0.546846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1107.24i | 2.41230i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.06740 | −0.0174998 | −0.00874990 | − | 0.999962i | \(-0.502785\pi\) | ||||
−0.00874990 | + | 0.999962i | \(0.502785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 837.707i | 1.80930i | 0.426152 | + | 0.904652i | \(0.359869\pi\) | ||||
−0.426152 | + | 0.904652i | \(0.640131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −406.669 | −0.874556 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 495.780i | 1.06163i | 0.847489 | + | 0.530814i | \(0.178114\pi\) | ||||
−0.847489 | + | 0.530814i | \(0.821886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 231.948i | 0.492458i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 221.260 | 0.467780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 215.486i | − 0.453654i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1371.91 | 2.87613 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 225.993i | − 0.471802i | −0.971777 | − | 0.235901i | \(-0.924196\pi\) | ||||
0.971777 | − | 0.235901i | \(-0.0758042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 691.292 | 1.43720 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.8628 | 0.0925006 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 728.173i | − 1.49522i | −0.664137 | − | 0.747611i | \(-0.731201\pi\) | ||||
0.664137 | − | 0.747611i | \(-0.268799\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −192.680 | −0.394028 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 724.908i | 1.47639i | 0.674587 | + | 0.738196i | \(0.264322\pi\) | ||||
−0.674587 | + | 0.738196i | \(0.735678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.1389 | 0.0367930 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 441.626i | 0.892174i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 691.520i | − 1.38581i | −0.721028 | − | 0.692906i | \(-0.756330\pi\) | ||||
0.721028 | − | 0.692906i | \(-0.243670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −574.148 | −1.14600 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 518.951i | − 1.03171i | −0.856675 | − | 0.515856i | \(-0.827474\pi\) | ||||
0.856675 | − | 0.515856i | \(-0.172526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 592.762 | 1.17379 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 429.373i | 0.846889i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −823.772 | −1.61841 | −0.809206 | − | 0.587525i | \(-0.800102\pi\) | ||||
−0.809206 | + | 0.587525i | \(0.800102\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2440.02 | 4.75638 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 84.9177i | 0.164889i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −133.544 | −0.258305 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 1972.91i | − 3.80137i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 533.963 | 1.02488 | 0.512440 | − | 0.858723i | \(-0.328742\pi\) | ||||
0.512440 | + | 0.858723i | \(0.328742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 709.660i | − 1.35690i | −0.734646 | − | 0.678451i | \(-0.762652\pi\) | ||||
0.734646 | − | 0.678451i | \(-0.237348\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 139.356i | − 0.264433i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −155.192 | −0.293369 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 315.450i | − 0.594069i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −487.885 | −0.915356 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 404.839i | 0.756709i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −301.325 | −0.561126 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −666.282 | −1.23157 | −0.615787 | − | 0.787913i | \(-0.711162\pi\) | ||||
−0.615787 | + | 0.787913i | \(0.711162\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1650.33i | 3.03928i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −381.130 | −0.699321 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 65.3904i | − 0.119544i | −0.998212 | − | 0.0597718i | \(-0.980963\pi\) | ||||
0.998212 | − | 0.0597718i | \(-0.0190373\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 902.467 | 1.64384 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 39.9726i | − 0.0725456i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2392.87i | 4.31149i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −671.474 | −1.20552 | −0.602759 | − | 0.797923i | \(-0.705932\pi\) | ||||
−0.602759 | + | 0.797923i | \(0.705932\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 716.733i | − 1.28217i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −205.180 | −0.365740 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 629.362i | − 1.11787i | −0.829211 | − | 0.558936i | \(-0.811210\pi\) | ||||
0.829211 | − | 0.558936i | \(-0.188790\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 481.142 | 0.851578 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −49.5333 | −0.0870533 | −0.0435267 | − | 0.999052i | \(-0.513859\pi\) | ||||
−0.0435267 | + | 0.999052i | \(0.513859\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 988.807i | − 1.73171i | −0.500294 | − | 0.865856i | \(-0.666775\pi\) | ||||
0.500294 | − | 0.865856i | \(-0.333225\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −966.304 | −1.68639 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 220.444i | − 0.383381i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 63.1355 | 0.109420 | 0.0547101 | − | 0.998502i | \(-0.482577\pi\) | ||||
0.0547101 | + | 0.998502i | \(0.482577\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 378.859i | 0.654334i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 163.773i | 0.280914i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1430.57 | 2.44542 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 9.88169i | − 0.0168342i | −0.999965 | − | 0.00841711i | \(-0.997321\pi\) | ||||
0.999965 | − | 0.00841711i | \(-0.00267928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −307.098 | −0.521390 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 1111.00i | − 1.87986i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 147.865 | 0.249351 | 0.124676 | − | 0.992198i | \(-0.460211\pi\) | ||||
0.124676 | + | 0.992198i | \(0.460211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1203.99 | 2.01673 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 464.007i | 0.774636i | 0.921946 | + | 0.387318i | \(0.126599\pi\) | ||||
−0.921946 | + | 0.387318i | \(0.873401\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −215.359 | −0.358334 | −0.179167 | − | 0.983819i | \(-0.557340\pi\) | ||||
−0.179167 | + | 0.983819i | \(0.557340\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 619.463i | − 1.02730i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 646.863 | 1.06919 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 310.053i | − 0.510796i | −0.966836 | − | 0.255398i | \(-0.917794\pi\) | ||||
0.966836 | − | 0.255398i | \(-0.0822065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 432.592i | 0.708007i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −791.288 | −1.29084 | −0.645422 | − | 0.763826i | \(-0.723319\pi\) | ||||
−0.645422 | + | 0.763826i | \(0.723319\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 1688.79i | − 2.74600i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1139.17 | 1.84631 | 0.923153 | − | 0.384433i | \(-0.125603\pi\) | ||||
0.923153 | + | 0.384433i | \(0.125603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 419.673i | 0.677985i | 0.940789 | + | 0.338992i | \(0.110086\pi\) | ||||
−0.940789 | + | 0.338992i | \(0.889914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2496.17 | 4.01960 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −764.666 | −1.22347 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 452.153i | 0.721138i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −819.985 | −1.30363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 506.397i | 0.802530i | 0.915962 | + | 0.401265i | \(0.131429\pi\) | ||||
−0.915962 | + | 0.401265i | \(0.868571\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1292.62 | 2.04205 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 591.421i | 0.931372i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 279.465i | 0.437347i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −501.692 | −0.782671 | −0.391335 | − | 0.920248i | \(-0.627987\pi\) | ||||
−0.391335 | + | 0.920248i | \(0.627987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 691.217i | 1.07499i | 0.843268 | + | 0.537493i | \(0.180629\pi\) | ||||
−0.843268 | + | 0.537493i | \(0.819371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2480.94 | 3.84642 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 711.553i | − 1.09977i | −0.835239 | − | 0.549886i | \(-0.814671\pi\) | ||||
0.835239 | − | 0.549886i | \(-0.185329\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.6571 | 0.0580233 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 455.205 | 0.697099 | 0.348549 | − | 0.937290i | \(-0.386674\pi\) | ||||
0.348549 | + | 0.937290i | \(0.386674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 515.586i | − 0.787154i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1881.26 | 2.86341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 156.616i | − 0.237656i | −0.992915 | − | 0.118828i | \(-0.962086\pi\) | ||||
0.992915 | − | 0.118828i | \(-0.0379138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −241.002 | −0.364602 | −0.182301 | − | 0.983243i | \(-0.558354\pi\) | ||||
−0.182301 | + | 0.983243i | \(0.558354\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 664.644i | 1.00248i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 40.8924i | − 0.0613080i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −957.429 | −1.43114 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 107.733i | 0.160555i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 623.074 | 0.925816 | 0.462908 | − | 0.886406i | \(-0.346806\pi\) | ||||
0.462908 | + | 0.886406i | \(0.346806\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 804.258i | 1.19149i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −343.461 | −0.507328 | −0.253664 | − | 0.967292i | \(-0.581636\pi\) | ||||
−0.253664 | + | 0.967292i | \(0.581636\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1295.56 | 1.90243 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 909.578i | − 1.33174i | −0.746068 | − | 0.665870i | \(-0.768061\pi\) | ||||
0.746068 | − | 0.665870i | \(-0.231939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −65.7957 | −0.0960521 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1367.80i | 1.99098i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 530.514 | 0.769976 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 325.753i | − 0.471423i | −0.971823 | − | 0.235711i | \(-0.924258\pi\) | ||||
0.971823 | − | 0.235711i | \(-0.0757420\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 701.061i | − 1.00872i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 578.712 | 0.830290 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 77.6379i | 0.111070i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −414.315 | −0.591034 | −0.295517 | − | 0.955338i | \(-0.595492\pi\) | ||||
−0.295517 | + | 0.955338i | \(0.595492\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1806.99i | 2.57040i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1497.40 | −2.12397 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1146.48 | 1.61703 | 0.808517 | − | 0.588472i | \(-0.200270\pi\) | ||||
0.808517 | + | 0.588472i | \(0.200270\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 579.044i | − 0.814408i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −314.165 | −0.440624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 170.775i | 0.238847i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2068.60 | −2.88508 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 387.316i | 0.538687i | 0.963044 | + | 0.269344i | \(0.0868067\pi\) | ||||
−0.963044 | + | 0.269344i | \(0.913193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1061.51i | 1.46820i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.1754 | 0.0181730 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 620.563i | 0.853594i | 0.904347 | + | 0.426797i | \(0.140358\pi\) | ||||
−0.904347 | + | 0.426797i | \(0.859642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3348.15 | −4.59280 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 850.163i | 1.16301i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −96.8796 | −0.132169 | −0.0660843 | − | 0.997814i | \(-0.521051\pi\) | ||||
−0.0660843 | + | 0.997814i | \(0.521051\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 73.9488 | 0.100338 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 782.913i | − 1.05942i | −0.848178 | − | 0.529711i | \(-0.822300\pi\) | ||||
0.848178 | − | 0.529711i | \(-0.177700\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1464.67 | 1.97661 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.0641i | 0.0646892i | 0.999477 | + | 0.0323446i | \(0.0102974\pi\) | ||||
−0.999477 | + | 0.0323446i | \(0.989703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −367.559 | −0.493368 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1219.08i | 1.63196i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 284.489i | − 0.378814i | −0.981899 | − | 0.189407i | \(-0.939343\pi\) | ||||
0.981899 | − | 0.189407i | \(-0.0606565\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −576.559 | −0.765683 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 707.757i | − 0.937427i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −797.514 | −1.05352 | −0.526759 | − | 0.850014i | \(-0.676593\pi\) | ||||
−0.526759 | + | 0.850014i | \(0.676593\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 462.558i | 0.609431i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1004.15 | −1.31951 | −0.659756 | − | 0.751480i | \(-0.729340\pi\) | ||||
−0.659756 | + | 0.751480i | \(0.729340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1696.89 | −2.21816 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 121.984i | − 0.159040i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 959.769 | 1.24807 | 0.624037 | − | 0.781395i | \(-0.285491\pi\) | ||||
0.624037 | + | 0.781395i | \(0.285491\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1636.98i | − 2.12319i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 94.4740 | 0.122217 | 0.0611086 | − | 0.998131i | \(-0.480536\pi\) | ||||
0.0611086 | + | 0.998131i | \(0.480536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 101.223i | − 0.130610i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1275.30i | − 1.63710i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.3613 | −0.0427162 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 149.190i | 0.190536i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −228.994 | −0.291713 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 108.864i | 0.138328i | 0.997605 | + | 0.0691642i | \(0.0220332\pi\) | ||||
−0.997605 | + | 0.0691642i | \(0.977967\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −265.337 | −0.336295 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 348.981 | 0.440077 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1836.35i | 2.30987i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −887.200 | −1.11317 | −0.556587 | − | 0.830789i | \(-0.687889\pi\) | ||||
−0.556587 | + | 0.830789i | \(0.687889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 513.125i | − 0.642209i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1706.94 | 2.13101 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 224.576i | 0.279672i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1289.70i | − 1.59814i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 485.529 | 0.600160 | 0.300080 | − | 0.953914i | \(-0.402987\pi\) | ||||
0.300080 | + | 0.953914i | \(0.402987\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1118.90i | − 1.37966i | −0.723972 | − | 0.689830i | \(-0.757685\pi\) | ||||
0.723972 | − | 0.689830i | \(-0.242315\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −321.193 | −0.395071 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 190.227i | − 0.233407i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1873.50 | 2.29314 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −486.539 | −0.592617 | −0.296308 | − | 0.955092i | \(-0.595756\pi\) | ||||
−0.296308 | + | 0.955092i | \(0.595756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1049.45i | − 1.27515i | −0.770389 | − | 0.637575i | \(-0.779938\pi\) | ||||
0.770389 | − | 0.637575i | \(-0.220062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −149.035 | −0.180648 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1472.00i | 1.77993i | 0.456031 | + | 0.889964i | \(0.349271\pi\) | ||||
−0.456031 | + | 0.889964i | \(0.650729\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1049.47 | −1.26595 | −0.632973 | − | 0.774174i | \(-0.718166\pi\) | ||||
−0.632973 | + | 0.774174i | \(0.718166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1874.45i | − 2.25566i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 566.838i | − 0.678848i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1146.18 | 1.36940 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1456.31i | 1.73576i | 0.496771 | + | 0.867882i | \(0.334519\pi\) | ||||
−0.496771 | + | 0.867882i | \(0.665481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −838.556 | −0.997094 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 3082.98i | − 3.65716i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −423.906 | −0.501664 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1943.87 | −2.28960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1848.58i | 2.17224i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −121.003 | −0.141855 | −0.0709277 | − | 0.997481i | \(-0.522596\pi\) | ||||
−0.0709277 | + | 0.997481i | \(0.522596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3739.42i | 4.37360i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1405.84 | −1.64041 | −0.820207 | − | 0.572066i | \(-0.806142\pi\) | ||||
−0.820207 | + | 0.572066i | \(0.806142\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 991.383i | − 1.15411i | −0.816704 | − | 0.577057i | \(-0.804201\pi\) | ||||
0.816704 | − | 0.577057i | \(-0.195799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 284.139i | 0.329245i | 0.986357 | + | 0.164623i | \(0.0526406\pi\) | ||||
−0.986357 | + | 0.164623i | \(0.947359\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1947.79 | 2.25178 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 904.074i | 1.04276i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 69.1238 | 0.0795440 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 239.544i | − 0.275022i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −196.280 | −0.224834 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −255.174 | −0.290963 | −0.145481 | − | 0.989361i | \(-0.546473\pi\) | ||||
−0.145481 | + | 0.989361i | \(0.546473\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1409.68i | − 1.60374i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 421.803 | 0.478778 | 0.239389 | − | 0.970924i | \(-0.423053\pi\) | ||||
0.239389 | + | 0.970924i | \(0.423053\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1069.35i | − 1.21105i | −0.795827 | − | 0.605524i | \(-0.792964\pi\) | ||||
0.795827 | − | 0.605524i | \(-0.207036\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 422.241 | 0.477108 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 619.581i | 0.698513i | 0.937027 | + | 0.349256i | \(0.113566\pi\) | ||||
−0.937027 | + | 0.349256i | \(0.886434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1000.12i | − 1.12247i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1130.77 | −1.26626 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 297.488i | − 0.332389i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1498.37 | 1.67043 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 18.7769i | − 0.0208864i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −629.276 | −0.698420 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1629.32 | −1.80035 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 302.666i | 0.333700i | 0.985982 | + | 0.166850i | \(0.0533595\pi\) | ||||
−0.985982 | + | 0.166850i | \(0.946640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2593.40 | −2.85303 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1004.97i | − 1.10315i | −0.834127 | − | 0.551573i | \(-0.814028\pi\) | ||||
0.834127 | − | 0.551573i | \(-0.185972\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −145.528 | −0.159395 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1207.98i | 1.32020i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 73.2026i | − 0.0796546i | −0.999207 | − | 0.0398273i | \(-0.987319\pi\) | ||||
0.999207 | − | 0.0398273i | \(-0.0126808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1299.28 | 1.41072 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 108.068i | 0.117084i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −595.605 | −0.643897 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 371.525i | − 0.400782i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −225.883 | −0.243146 | −0.121573 | − | 0.992582i | \(-0.538794\pi\) | ||||
−0.121573 | + | 0.992582i | \(0.538794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2787.85 | −2.98805 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 202.568i | − 0.216650i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1168.51 | 1.24708 | 0.623540 | − | 0.781792i | \(-0.285694\pi\) | ||||
0.623540 | + | 0.781792i | \(0.285694\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 2899.83i | − 3.08821i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 119.216 | 0.126690 | 0.0633452 | − | 0.997992i | \(-0.479823\pi\) | ||||
0.0633452 | + | 0.997992i | \(0.479823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1304.65i | − 1.38351i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 875.062i | 0.924036i | 0.886871 | + | 0.462018i | \(0.152874\pi\) | ||||
−0.886871 | + | 0.462018i | \(0.847126\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 727.476 | 0.766571 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2887.30i | 3.03606i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −468.167 | −0.491256 | −0.245628 | − | 0.969364i | \(-0.578994\pi\) | ||||
−0.245628 | + | 0.969364i | \(0.578994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 954.001i | − 0.998954i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27.6459 | −0.0288881 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 816.743 | 0.849888 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1771.22i | − 1.83927i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −374.036 | −0.387602 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1139.67i | − 1.17856i | −0.807930 | − | 0.589279i | \(-0.799412\pi\) | ||||
0.807930 | − | 0.589279i | \(-0.200588\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1737.34 | −1.79292 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 237.061i | 0.244141i | 0.992521 | + | 0.122071i | \(0.0389534\pi\) | ||||
−0.992521 | + | 0.122071i | \(0.961047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 482.771i | 0.495150i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 422.059 | 0.431994 | 0.215997 | − | 0.976394i | \(-0.430700\pi\) | ||||
0.215997 | + | 0.976394i | \(0.430700\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 203.767i | 0.208138i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1667.49 | 1.69978 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1614.06i | − 1.64197i | −0.570946 | − | 0.820987i | \(-0.693424\pi\) | ||||
0.570946 | − | 0.820987i | \(-0.306576\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1096.85 | 1.11355 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1916.61 | 1.93792 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 226.772i | − 0.228832i | −0.993433 | − | 0.114416i | \(-0.963500\pi\) | ||||
0.993433 | − | 0.114416i | \(-0.0364996\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3437.19 | −3.46142 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1188.66i | 1.19463i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1555.56 | 1.56024 | 0.780120 | − | 0.625629i | \(-0.215158\pi\) | ||||
0.780120 | + | 0.625629i | \(0.215158\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 6744.25i | − 6.75100i |
(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 | 1568.3.d.n.1471.1 | 8 | ||
4.3 | odd | 2 | inner | 1568.3.d.n.1471.8 | 8 | ||
7.6 | odd | 2 | 224.3.d.b.127.8 | yes | 8 | ||
21.20 | even | 2 | 2016.3.m.c.127.7 | 8 | |||
28.27 | even | 2 | 224.3.d.b.127.1 | ✓ | 8 | ||
56.13 | odd | 2 | 448.3.d.e.127.1 | 8 | |||
56.27 | even | 2 | 448.3.d.e.127.8 | 8 | |||
84.83 | odd | 2 | 2016.3.m.c.127.8 | 8 | |||
112.13 | odd | 4 | 1792.3.g.d.127.2 | 8 | |||
112.27 | even | 4 | 1792.3.g.d.127.1 | 8 | |||
112.69 | odd | 4 | 1792.3.g.f.127.7 | 8 | |||
112.83 | even | 4 | 1792.3.g.f.127.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.d.b.127.1 | ✓ | 8 | 28.27 | even | 2 | ||
224.3.d.b.127.8 | yes | 8 | 7.6 | odd | 2 | ||
448.3.d.e.127.1 | 8 | 56.13 | odd | 2 | |||
448.3.d.e.127.8 | 8 | 56.27 | even | 2 | |||
1568.3.d.n.1471.1 | 8 | 1.1 | even | 1 | trivial | ||
1568.3.d.n.1471.8 | 8 | 4.3 | odd | 2 | inner | ||
1792.3.g.d.127.1 | 8 | 112.27 | even | 4 | |||
1792.3.g.d.127.2 | 8 | 112.13 | odd | 4 | |||
1792.3.g.f.127.7 | 8 | 112.69 | odd | 4 | |||
1792.3.g.f.127.8 | 8 | 112.83 | even | 4 | |||
2016.3.m.c.127.7 | 8 | 21.20 | even | 2 | |||
2016.3.m.c.127.8 | 8 | 84.83 | odd | 2 |